Answer:
? is equal to 8
Step-by-step explanation:
16/20= 0.8
0.8x10= 8
8/10=0.8
OR YOU COUPLE DIVIDED 16 BY TO AND 20 BY 2
Answer:8/10
Step-by-step explanation:when you divide 16 by 20, you get 0.8. So turn 0.8 into a fraction with 10, you get 8/10. (I’m not that smart, mb if I get something wrong.)
For each of the following situations, find the criticalvalue(s) for z or t. State if z or t for each answer.
Round to two decimal places as needed.
a) H0: μ=115 vs. HA: μ ≠115 at α= 0.05; n= 41
b) H0: p=0.14 vs. HA: p>0.14 at α= 0.10
c) H0: p= 0.6 vs. HA: p≠ at α=0.01
d) H0: p=0.8 vs. HA: p<0.8 at α=0.01; n=500
e) H0: p=0.9 vs. HA: p< at α=0.01
For each of the following situations the critical value are:
a) H0: μ=115 vs. HA: μ ≠115 at α= 0.05; n= 41, the critical values are ±1.96.
b) H0: p=0.14 vs. HA: p>0.14 at α= 0.10, the critical value is 1.28.
c) H0: p= 0.6 vs. HA: p≠ at α=0.01 - z = 2.326, the critical values are ±2.58.
d) H0: p=0.8 vs. HA: p<0.8 at α=0.01; n=500, the critical value is -2.33.
e) H0: p=0.9 vs. HA: p< at α=0.01, the critical value is -2.33.
a) Since n=41 is greater than 30, we can use a z-test. The test is two-tailed because the alternative hypothesis is μ≠115. Using a significance level of 0.05, the critical values are ±1.96. Therefore, the rejection region is z < -1.96 or z > 1.96.
b) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p > 0.14. Using a significance level of 0.10, the critical value is 1.28. Therefore, the rejection region is z > 1.28.
c) Since we are testing a proportion, we can use a z-test for proportions. The test is two-tailed because the alternative hypothesis is p≠0.6. Using a significance level of 0.01, the critical values are ±2.58. Therefore, the rejection region is z < -2.58 or z > 2.58.
d) Since n=500 is greater than 30, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.8. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.
e) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.9. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.
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whats the area of sector and length of arc
The area of the sector is ≈134 sq units and the length of the arc is ≈16.75
What is a sector of a Circle?The sector of a circle produced by a portion of the circumference (arc) and the circle's radii at both ends of the arc. A sector of a circle can be compared to a piece of pizza or a pie in shape.
The length of an arc is the distance between two point in the section of a curve.
According to the given information:
Given that radius= 16 in, ∅ = 60°
The formula for finding the area of sector= (∅/360°)[tex]\pi r^{2}[/tex]
Substituting values in the formula we get
= (60°/360°)*3.14*[tex]16^{2}[/tex]
=133.9733
≈134 sq units.
The formula for Finding Arc Length = (∅/360°)[tex]2\pi r[/tex]
On substituting the values
= (60°/360°)*2*3.14*16
=16.74666
≈16.75 in
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On Cupcake Wars, the bakers must fill 1000 cupcakes in the final challenge!
CUPCAKE
WARS
If the cupcakes are cylinder shaped and have a radius of 1.5 in and a height of 3.01 in,
how many cubic inches are need to fill 1000 cupcakes?
Use pi=3.14
Round your answer to the nearest hundredth as needed.
V=
Answer:
21,265.65 in³
Step-by-step explanation:
Formula: Volume (V) = πr²h
V = πr²h
Slotting in values,
V = 3.14 x 1.5² x 3.01
V = 3.14 x 2.25 x 3.01
V = 21.26565 in³
But that is for 1 cupcake
To fill a thousand of them, you will need to multiply your answer by the number of cupcakes in total.
Therefore,
Answer = V x 1000
Answer = 21.26565 x 1000
Answer = 21,265.65 in³
The answer is already rounded to the nearest hundredth,
So they would need 21,265.65 cubic inches (in³) to fill 1000 cupcakes.
Please mark brainliest.
Thanks.
Tammy’s water bill is automatically deducting $160 from her bank account every other month. How
much will the deductions total for two years?
Answer:
$1920
Step-by-step explanation:
If Tammy's water bill is deducting $160 every other month for 2 years, (or $160 a month for 1 year since we skip a month every two months), then you would multiply $160 by 12 months to get $1920.
15 miles in 6 hours what is the average speed
15 miles in 6 hours was covered, hence with the average speed formula we find that the average speed is 2.5 miles per hour.
To find the average speed, we can use the formula:
Average Speed = Total Distance / Total Time
In this case, the total distance covered is 15 miles, and the total time taken is 6 hours. Substituting these values into the formula, we get:
Average Speed = 15 miles / 6 hours
Average Speed = 2.5 miles per hour
Therefore, the average speed for the 15 miles covered in 6 hours is 2.5 miles per hour. Average speed is a measure of how fast an object is moving over a certain distance during a certain time period. It is calculated as the ratio of the total distance traveled by an object to the total time it took to cover that distance. The unit of measurement for average speed is distance divided by time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s). Average speed can be calculated for various types of objects in motion, including vehicles, runners, and even animals. It is often used to describe the efficiency of movement, and can be useful in making predictions about how long it will take to cover a certain distance or complete a certain task
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The rectangular floor of a classroom is 28 feet in length and 22 feet in width. A scale drawing of the floor has a length of 14 inches. What is the perimeter, in inches, of the floor in the scale drawing?
The value of the calculated perimeter, in inches, of the floor in the scale drawing is 50 inches
What is the perimeter, in inches, of the floor in the scale drawing?The dimensions of the rectangular floor is calculated as
Dimension = 28 feet in length and 22 feet in width
The length of the scale is given as
Scale length = 14 inches
When the above is compared, we can see that
The length is divided by 2 to get the scale length
So, we have
Scale width = 22 inches/2
Evaluate
Scale width = 11 inches
The perimeter is then calculated as
Perimeter = 2 * (Length + width)
So, we have
Perimeter = 2 * (14 + 11)
Evaluate
Perimeter = 50 inches
Hence, the perimeter is 50 inches
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What additional information do you need to know to prove Triangle KLM is congruent to Triangle UTS by SAS?
a
b
KM is congruent to SU
c
d
LM is congruent to ST
As a result, the answer to the following question, We may use the SAS criteria to argue that the two triangles are congruent if we know that KM is congruent to SU.
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
Option b: KM is congruent to SU is the additional information required by SAS to demonstrate Triangle KLM is congruent to Triangle UTS.
To demonstrate that two triangles are congruent using the SAS (Side-Angle-Side) congruence criterion, we must demonstrate:
Two comparable side pairs are congruent.
The angle included (the angle formed by these two sets of sides) is congruent.
In this situation, we are told that LM is congruent to ST, but we must still demonstrate that another pair of sides is congruent. We may use the SAS criteria to argue that the two triangles are congruent if we know that KM is congruent to SU.
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A popular board game manufacturer was interested in the relationship between the amount of time it takes to play a
game and how well that game is rated among board game players. Information was collected on several board games
and was used to obtain the regression equation ý = 27.273x + 18.182, where x represents time it takes to play (in
hours) and ŷ is the predicted rating of that game (in points). Which statement best describes the meaning of the y-
intercept of the regression line?
O When the rating of a game is 0 points, the predicted time to play is 0 hours.
O When the rating of a game is 0 points, the predicted time to play is 18.182 hours.
O When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game
cannot have a playtime of 0 hours.
O When the time to play is 0 hours, the predicted rating is 27.273. This interpretation is not meaningful since a game
cannot have a playtime of 0 hours.
We can see here that the best description of the meaning of the y-intercept of the regression line, as given by the equation ý = 27.273x + 18.182, is: C. "When the time to play is 0 hours, the predicted rating is 18.182. This interpretation is not meaningful since a game cannot have a playtime of 0 hours."
What is y-intercept ?The y-intercept is a term used in the context of a linear equation or a graph to describe the point at which the graph intersects or crosses the y-axis. It represents the value of the dependent variable (y) when the independent variable (x) is equal to zero.
The y-intercept is the value of ŷ (the predicted rating) when x (the time to play) is zero. However, in this context, it does not make sense for a game to have a playtime of zero hours. Therefore, the interpretation of the y-intercept in this case is not meaningful or applicable to the real-world scenario of board games.
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HELP I'LL GIVE BRAINLIEST AND FIVE STARS IF YOU GET THIS RIGHT
Find the range of the function given the graph below.
The range of the given graph will be [-1, 2.9].
How to Determine a Function's Range?Think about the function y = f. (x).
The range of the function is the range of all the y values, from least to maximum. Substitute all possible values of x into the provided expression of y to see whether it is positive, negative, or equal to other values.
A bar chart with bars for each dimension (category) that range between a start value and an end value is called a range bar chart. To track a project schedule, for instance, Range Bar charts can be used to show the start and finish of activities or tasks along a time axis, much like a Gantt chart.
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im stuck on this question, please help. it's geometry. thanks!!
Angle 1 = Angle 2 = Angle 3 = Angle 4, we can infer.
What is meant by a "right angle"?A right angle is an angle with a measure that is exactly equal to 90 degrees (or /2).
We can observe that a transversal divides two parallel lines in the given diagram. Let's give the angles names:
The angle created by the junction of line m and line p is Angle 1, which is located in the top left corner.
The angle created by the intersection of line n and line p is Angle 2, which is located in the top right corner.
Line n and line q intersect at angle 3, which is located in the lower right corner.
The angle created by the junction of line m and line q is angle 4, which is located in the lower left corner.
As they are on the same side of the transversal and in corresponding locations with respect to the parallel lines, we can see that angles 1 and 2 are corresponding angles. When lines are cut by a transversal, corresponding angles are congruent, hence we know that:
1 + 2 = an angle.
Due to their placement on opposing sides of the transversal and in-between the parallel lines, angles 2 and 3 can also be seen to represent alternate internal angles. When lines are cut by a transversal, alternate inner angles are congruent, hence we know that:
2 + 3 = a right angle
As they are on the same side of the transversal and in corresponding locations with respect to the parallel lines, we can see that angles 3 and 4 are corresponding angles. When lines are cut by a transversal, corresponding angles are congruent, hence we know that:
Angle 3 = angle 4 =...
So, Angle 1 = Angle 2 = Angle 3 = Angle 4 follows.
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A fair coin is tossed three times and the events A,B , and C are defined as follows: A:{ At least one head is observed } B:{ At least two heads are observed } C:{ The number of heads observed is odd } Find the following probabilities by summing the probabilities of the appropriate sample points (note that 0 is an even number): (a) P(notB)= (b) P((notA) or C)= (c) P(A or B or C)= Note: You can earn partial credit on this problem. You have attempted this problem 0 times. You have unlimited attempts remaining
The event C is: C = { HHT, HTH, THH, HTT, THT, TTH }
P(C) = 1/2
(a) P(notB) = 1/2
(b) P((notA) or C) = 5/8
(c) P(A or B or C) = 7/8
Solution:
A fair coin is tossed three times, and the events A, B, and C are defined as follows: A: { At least one head is observed } B: { At least two heads are observed } C: { The number of heads observed is odd }
The sample space of the given event is as follows:
S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Probability of the occurrence of A:
If at least one head is observed, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HHT, HTH, THH, or HTT, THT, TTH, or
(iii) HHT, HTH, THH, or HTT, THT, TTH, or HHH
Therefore, the event A is: A = { HHT, HTH, THH, HTT, THT, TTH, HHH }
P(A) = 7/8
Probability of the occurrence of B:
If at least two heads are observed, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HTT, THT, TTH, or
(iii) HHH
Therefore, the event B is: B = { HHT, HTH, THH, HTT, THT, TTH, HHH }
P(B) = 7/8
Probability of the occurrence of C:
If the number of heads observed is odd, then it can be possible in the following ways:
(i) HHT, HTH, THH, or
(ii) HTT, THT, TTH
Therefore, the event C is: C = { HHT, HTH, THH, HTT, THT, TTH }
P(C) = 1/2
Probability of the occurrence of notB:
Not B means "at least one head" or "no head." So, the event notB is not the event B, which means the event (notB) is the event in which we do not get at least two heads.
The (notB) event is: (notB) = { TTH, THT, HTT, TTT }
P(notB) = 4/8 = 1/2
Probability of the occurrence of (notA) or C:
The event (notA) means that we don't get at least one head, which means we get all tails. The (notA) event is: (notA) = { TTT }
P(notA) = 1/8
Now, we will find P((notA) or C).
For this, we can take the union of (notA) and C.
(notA) ∪ C = { HHT, HTH, THH, HTT, THT, TTH, TTT }
P((notA) or C) = 7/8
Probability of the occurrence of A or B or C:
The probability of the occurrence of A or B or C can be found as follows:
P(A or B or C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
Here, A ∩ B = { HHT, HTH, THH, HHH }, A ∩ C = { HHT, HTH, THH }, B ∩ C = { HHT, HTH, THH }, and A ∩ B ∩ C = { HHT, HTH, THH }.
Substituting these values, we get:
P(A or B or C) = 7/8 + 7/8 + 1/2 - 3/8 - 3/8 - 1/8 + 1/8
P(A or B or C) = 7/8
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The tables show the attendances at volleyball games and basketball games at a school during the year.
Express the difference in the measures of center as a multiple of the measure of variation. Round your answers to the nearest tenth.
The difference in the means is about (blank) to (blank) times the MAD.
Solve for blanks
a) Compare the populations using measures of center and variation. Mean and MAD of vollyball game attendence are 86, 19.6 respectively. Mean and MAD of basketball game attendence are 185, 17.7 respectively.
b) Difference in the measures of center as a -4.6 to 5.1 multiple of the measure of variation. The difference in the means is about -4.6 to 5.1 times the MAD.
We have two tables consists attendances at volleyball games and basketball games at a school during the year. See the above figure carefully. Now, Compare the populations using measures of center and variation : As we know mean of data is calculated by dividing the sum of data values to the number of data values. Here, Sum of vollyball attendence values, ∑xᵢ = 1720
Number of days = 20
So, mean of vollyball game attendence
= 1720/20 = 86
Sum of basketball ball attendence values, ∑yᵢ = 3700
Number of days = 20
So, mean of basketball ball game attendence = 3700/20 = 185
Now, measure absolute deviations, MAD
MAD of vollyball game attendence is
= [∑( mean of vollyball game attendence - attendance values (i))]/number of days
= 392/20 = 19.6
MAD of basketball ball game attendence is = [∑( mean of basketball ball game attendence - attendance values (i))]/number of days
= 354/20 = 17.7
b) Now, we check the relation between difference in the measures of center as a multiple of the measure of variation.
A : vollyball game attendence
B : basketball game attendence
difference in the measures of center
= Mean (A) - Mean(B) or Mean(B) - Mean (A)
measure of variation, MAD(A) , MAD(B)
[Mean (A) - Mean (B)]/MAD(A)
= ( 86 - 185)/19.6
= -4.643 ~ -4.6
[Mean (B) - Mean (A)]/MAD(B)
= ( 185 - 86)/17.7
= 91/17.7 = 5.1412 ~ 5.1
Hence, difference in the means is about -4.6 to
5.1 times the MAD.
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Complete question :
The above tables show the attendances at volleyball games and basketball games at a school during the year. Volleyball Game Attendance Basketball Game Attendance 112 95 84106 62 68 75 88 93 127 98 117 60176 141 152 181 198 21 49 5485 74 88 132 5 202 190 173 155 169 188 195 4 179 163 186 184207 219 228
a) Compare the populations using measures of center and variation.
b) Express the difference in the measures of center as a multiple of the measure of variation. Round your answers to the nearest tenth. The difference in the means is about (blank) to (blank) times the MAD.
Please help with #7 and #10 a-c
7. The speed of the car is approximately 73.3 miles per hour. 10. a. 7.07 ft/sec b. 9.87 feet from the center. c. the person on the outside is approximately 30 ft.
Describe Speed?It is a fundamental concept in physics and is used to describe the motion of objects in both everyday life and scientific contexts. In addition to speed, other related concepts include velocity (which includes direction) and acceleration (the rate at which an object's speed or velocity changes).
7. The circumference of the wheel is given by C = πd, where d is the diameter of the wheel. Therefore, the circumference of each wheel is:
C = πd = π(22 in) = 22π in
Since the wheels are rotating at 600 rpm (revolutions per minute), the distance covered by each wheel in one minute is:
distance = circumference × revolutions = 22π in/rev × 600 rev/min = 13,200π in/min
To convert this to miles per hour, we need to convert inches to miles and minutes to hours. There are 12 inches in 1 foot and 5280 feet in 1 mile, so there are 63360 inches in 1 mile. There are 60 minutes in 1 hour, so:
distance = 13,200π in/min = (13,200π in/min) × (1 ft/12 in) × (1 mi/5280 ft) × (60 min/1 hr) ≈ 73.3 mi/hr
Therefore, the speed of the car is approximately 73.3 miles per hour.
10. a) The linear speed of a point on the carousel is given by v = rω, where r is the distance from the center of the carousel and ω is the angular velocity in radians per second. Since the carousel makes 3 revolutions per minute, the angular velocity is:
ω = (3 rev/min) × (2π rad/rev) × (1 min/60 sec) = π/10 rad/sec
The linear speed of a person riding a horse that is 22.5 ft from the center is:
v = rω = (22.5 ft) × (π/10 rad/sec) ≈ 7.07 ft/sec
b) Let d be the distance of the person on the inside from the center. Since the carousel makes 3 revolutions per minute, the angular velocity is still ω = π/10 rad/sec. The linear speed of the person on the inside is given as 3.1 ft/sec, so:
v = rω
3.1 ft/sec = d × (π/10 rad/sec)
d = (3.1 ft/sec) × (10/π rad/sec) ≈ 9.87 ft
Therefore, the person on the inside is approximately 9.87 feet from the center.
c) The linear speed of a point on the carousel is proportional to its distance from the center. Therefore, the ratio of the linear speeds of the person on the outside and the inside is equal to the ratio of their distances from the center:
v_outside/v_inside = r_outside/r_inside
We know that the linear speed of the person on the inside is 3.1 ft/sec and the distance of the person on the inside is approximately 9.87 feet. Therefore:
v_outside/3.1 ft/sec = r_outside/9.87 ft
v_outside = (r_outside/9.87 ft) × (3.1 ft/sec)
We can solve for r_outside by using the fact that the carousel makes 3 revolutions per minute:
v_outside = r_outsideω
v_outside = r_outside × (3 rev/min) × (2π rad/rev) × (1 min/60 sec)
v_outside = r_outsideπ/10 rad/sec
Combining these equations, we get:
r_outsideπ/10 rad/sec = (r_outside/9.87 ft) × (3.1 ft/sec)
r_outside ≈ 30.9 ft
Therefore, the person on the outside is approximately 30.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. A total of 28 boxes of paper were shipped weighing 1850 pounds altogether. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
We can write the following system of equations:
x + y = 28 (equation 1)
50x + 80y = 1850 (equation 2)
What are equations?An equation is a statement that two expressions are equal. It consists of two expressions, separated by an equals sign. The expression on the left-hand side of the equals sign is equal to the expression on the right-hand side. Equations can be used to represent relationships between variables, to solve problems, and to describe mathematical models. They are an important tool in algebra, calculus, and other areas of mathematics.
What is linear equations?A linear equation is an algebraic equation of the first degree, which means that the variables in the equation have an exponent of one and are not multiplied or divided by any other variables. Linear equations can have one or more variables and are typically represented graphically by a straight line.
In the given question,
Let x be the number of small boxes shipped and y be the number of large boxes shipped.
From the problem, we know that each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. We also know that a total of 28 boxes of paper were shipped weighing 1850 pounds altogether.
Using this information, we can write the following system of equations:
x + y = 28 (equation 1)
50x + 80y = 1850 (equation 2)
In equation 1, x + y = 28 represents the total number of boxes shipped, which is the sum of the number of small boxes shipped (x) and the number of large boxes shipped (y).
In equation 2, 50x + 80y = 1850 represents the total weight of the boxes shipped, which is the sum of the weight of each small box (50x) and the weight of each large box (80y).
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Which one of the following graphs represents correct represent the variation of the gravitational field (E) with the distance (r) from the centre of a spherical shell of mass M radius R?
Option D is the graph that represent the variation of the gravitational energy (E) with the distance (r) from the centre of a spherical shell of mass M radius R
How to solve for the graphWhen R is less than r, the graph we would have is a straight line. When R = r, it has constant value and finally if R is more than r it is a hyperbola.
The intensity that is inside the spherical shell would be given as 0. Then we would have this represented as
I = 0
upto r = R
I ∝ I/r²
r > R
Hence D
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6*3 = n-4
6*3 = n-4
__ = n-4
18+4 = n-4
__ = n
so yeah the answers
Answer:
6*3
n=26
A school sports team contains 68 students. 33 do field events, 40 do track events, 23 do swimming, 14 do both field and track events. If 15 students do field events only and 10 do both swimming and track events, how many students do a) swimming only b)track events only c) all three events?
Let's label the regions in the Venn diagram as follows:
F: students who do only field events
T: students who do only track events
S: students who do only swimming events
FT: students who do both field and track events
ST: students who do both swimming and track events
FST: students who do all three events
From the information given in the problem, we can fill in some of the values in the Venn diagram:
F + FT + 15 = 33 (33 students do field events, and 15 do field events only)
T + FT + 14 = 40 (40 students do track events, and 14 do both field and track events)
S + ST + 10 = 23 (23 students do swimming, and 10 do both swimming and track events)
F + T + S + 2FT + ST + FST = 68 (there are 68 students in total)
We can simplify these equations to:
F + FT = 18
T + FT = 26
S + ST = 13
F + T + S + 2FT + ST + FST = 68
To solve for the remaining unknowns, we need to use some algebra. We can start by solving for FT:
F + FT = 18
T + FT = 26
Adding the two equations, we get:
F + T + 2FT = 44
Rearranging, we get:
FT = (44 - F - T) / 2
Now we can substitute this expression for FT into the equation for the total number of students:
F + T + S + 2FT + ST + FST = 68
F + T + S + 2((44 - F - T) / 2) + ST + FST = 68
F + T + S + 44 - F - T + ST + FST = 68
Simplifying, we get:
S + ST + FST = 26
Now we have two equations involving S, ST, and FST:
S + ST = 13
S + ST + FST = 26
We can solve for S and ST by subtracting the first equation from the second:
S + ST + FST = 26
(S + ST) + FST = 26
Substituting S + ST = 13:
13 + FST = 26
FST = 13
So there are 13 students who do all three events. Now we can use the equation S + ST = 13 to solve for S:
S + ST = 13
ST = 10 (given in the problem)
S = 13 - 10 = 3
So there are 3 students who do swimming only. Similarly, we can use the equation T + FT = 26 to solve for T:
T + FT = 26
FT = (44 - F - T) / 2
Substituting F + FT = 18:
T + (18 - F) / 2 = 26
Multiplying both sides by 2:
2T + 18 - F = 52
You are rolling two dice and one coin. Find the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin.
A. 1/8
B. 1/72
C. 1/112
D. 1/36
If you are rolling two dice and one coin. the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin is B. 1/72.
How to find the probability?Probability of rolling a three on the first dice is 1/6, the probability of rolling a four on the second dice is 1/6, and the probability of flipping a heads on the coin is 1/2.
To find the probability of all three events happening together, we need to multiply the probabilities of each individual event:
(1/6) x (1/6) x (1/2) = 1/72
Therefore, the probability is B. 1/72.
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John invest R500, at 12% per annum using simple interest for 4 years. How much money will John have at the end of 4 years?
Answer: 42$
Step-by-step explanation:
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What are the solutions to this quadratic equation?
The solutions can be written as x = 8 + 10i and x = 8 - 10i
Describe Quadratic Equation?The graph of a quadratic equation is a parabola, which is a symmetrical U-shaped curve. The direction and shape of the parabola depend on the value of a. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward.
Quadratic equations are used in many areas of mathematics and science, including physics, engineering, and finance. They are also used in real-life situations to model and solve problems related to motion, distance, time, and other quantities.
To solve this quadratic equation, we can rearrange it to be in standard form:
x² - 16x + 164 = 0
We can then use the quadratic formula to find the solutions:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 1, b = -16, and c = 164. Substituting these values into the formula, we get:
x = (16 ± √((-16)² - 4(1)(164))) / 2(1)
Simplifying, we get:
x = (16 ± √(256 - 656)) / 2
x = (16 ± √(-400)) / 2
We have a negative number inside the square root, which means that the solutions are complex. To express them in the form x = a + bi and x = a - bi, we can simplify the square root by factoring out -1:
x = (16 ± √(400) i) / 2
x = (16 ± 20i) / 2
x = 8 ± 10i
Therefore, the solutions to the quadratic equation x² - 16x + 164 = 0 are:
x = 8 + 10i and x = 8 - 10i
So, a = 8 and b = 10. Therefore, the solutions can be written as:
x = 8 + 10i and x = 8 - 10i
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write the recursive formula of a1=3 d =-8
Recursive fοrmula οf a1 = 3, d = -8 is -29 = -21 + (-8)
What is the recursive fοrmula?Any term οf a series can be defined by its preceding term in a recursive fοrmula (s).
The recursive fοrmula fοr an arithmetic sequence with first term a1=3 and cοmmοn difference d=-8 is:
an = an-1 + d, where n >= 2
Expanding the fοrmula fοr the first few terms, we get:
a2 = a1 + d = 3 - 8 = -5
a3 = a2 + d = -5 - 8 = -13
a4 = a3 + d = -13 - 8 = -21
a5 = a4 + d = -21 - 8 = -29
Nοw,
Recursive fοrmula οf a1 = 3, d = -8 is -29 = -21 + (-8)
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PROJECT: RELIABLE FINANCIAL INFORMATION, I need help with this pleaseee , im giving 80 points
Ratio analysis is the best way to ensure reliable financial information, as it allows investors to evaluate the financial strength of a company and the reliability of its financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
Reliable financial information is information that is accurate and up-to-date. It is the foundation of any investor’s decision-making process, as it allows them to make informed decisions. One of the best ways to ensure reliable financial information is to perform a ratio analysis. Ratio analysis is the process of evaluating financial information by calculating ratios such as the current ratio, quick ratio, and debt-to-equity ratio.
The current ratio is calculated by dividing a company’s current assets by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations. The quick ratio is calculated by dividing a company’s current assets minus inventory by its current liabilities. This ratio measures a company’s ability to pay its short-term obligations without having to sell its inventory. The debt-to-equity ratio is calculated by dividing a company’s total liabilities by its total number. This ratio measures how much debt a company has relative to its equity.
By looking at these ratios, investors can get an idea of the financial strength of a company and the reliability of its financial information. The higher the ratios, the more reliable the financial information is likely to be
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Complete question:
How can investors ensure reliable financial information?
Select the shapes that can be classified as rectangles.
Four shapes. The first shape has two pairs of parallel lines of equal length, with four right angles. The second shape has four sides of equal length, two pairs of opposite sides that are parallel, and four right angles. The third shape has two pairs of opposite sides that are parallel and of equal length, with no right angles. The fourth shape has no sides of equal length, no parallel sides, and no right angles.
Shapes 1 and 2
Shapes 1 and 3
Shapes 2 and 4
Shapes 3 and 4
Shapes 1 and 2 that can be classified as rectangles.
What are rectangles?Rectangles are geometric shapes with four sides and four angles. They are characterized by having opposite sides that are parallel and of equal length, and all four angles are right angles (90 degrees).
Rectangles are also known as quadrilaterals, which means they have four sides.
The second shape can be classified as a rectangle as it has four sides of equal length, two pairs of opposite sides that are parallel, and four right angles.
The first shape can also be classified as a rectangle as it has two pairs of parallel lines of equal length, with four right angles.
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last question...this is geometry. 15 points to whoever gets it right and can explain
What is 52s+30b it is on an I ready
Another representation of the given algebraic expression 52s + 30b as required is; 2 (26s + 15b).
Which expression is equivalent to the given expression 52s + 30b?As evident in the task content; it follows that the equivalent expression to 52s + 30b is to be determined.
Given; 52s + 30b
Since 2 is a common factor to both terms of the equation; we have that;
2 (26s + 15b)
Ultimately, the equivalent expression is; 2 (26s + 15b).
Complete question:
What is 52s+30b in a factorized form.
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You deposit $2000 into a savings account giving 7% interest compounded only at the end of the year. To nearest dollar, what is your end-of-year balance?
well, you'd have the 2000 plus the 7% :|
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 2000}}{\left( \cfrac{7}{100} \right)2000}\implies 140~\hfill \underset{ new~balance }{\stackrel{ 2000~~ + ~~140 }{\text{\LARGE 2140}}}[/tex]
Montrose Oil and Lube is a car care center specializing in ten-minute oil changes. Montrose Oil and Lube has two service bays, which limits its capacity to 4,000 oil changes per month. The following information was collected over the past six months: (Click the icon to view the information.) Read the requirements. 1. Prepare a graphing the volume of oil changes (x-axis) against the company's monthly operating expenses (y-axis). (Enlarge the graph to maximum size and use the point tool button displayed below to draw the graph.) Requirements 1. Prepare a scatterplot graphing the volume of oil changes (x-axis) against the company's monthly operating expenses (y-axis). 2. How strong of a relationship does there appear to be between the company's operating expenses and the number of oil changes performed each month? Explain. Do there appear to be any outliers in the data? Explain. 3. Based on the scatterplot, do the company's operating costs appear to be fixed, variable, or mixed? Explain how you can tell. 4. Would you feel comfortable using this information to project operating costs for a volume of 3,800 oil changes per month? Explain. Data table
To answer the question, let's start by preparing a scatterplot graphing the volume of oil changes (x-axis) against the company's monthly operating expenses (y-axis). From the data provided, the scatterplot appears as follows:
It appears that there is a fairly strong correlation between the number of oil changes performed and the company's operating expenses each month. The points appear to fall along a linear line, and there do not appear to be any outliers. This indicates that the company's operating costs are fixed.
Given the strong correlation between the number of oil changes and the company's operating expenses, we can feel confident using the data to project operating costs for a volume of 3,800 oil changes per month.
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I need help I tried everything
If f(3x) = f(3) + f(x) then show that f(1) = f(3) = f(9) = f(27) = f(81)
Answer:f(1) = f(3) = f(9) = f(27) = f(81).
Step-by-step explanation:To show that f(1) = f(3) = f(9) = f(27) = f(81), we can use the given equation and substitute x with different values.
Let x = 1:
f(3x) = f(3) + f(x)
f(3(1)) = f(3) + f(1)
f(3) = f(3) + f(1) (since f(3x) = f(3) + f(x) when x = 1)
f(1) = 0
Now, let x = 3:
f(3x) = f(3) + f(x)
f(3(3)) = f(3) + f(3)
f(9) = 2f(3)
Since we already know that f(3) = f(3) + f(1), we can substitute it into the equation above:
f(9) = 2f(3) = 2(f(3) + f(1)) = 2f(3) + 2f(1)
f(9) - 2f(3) = 2f(1)
Now let x = 9:
f(3x) = f(3) + f(x)
f(3(9)) = f(3) + f(9)
f(27) = f(3) + f(9)
We can substitute the expression for f(9) we just derived:
f(27) = f(3) + (f(9) - 2f(3))
f(27) = f(9) - f(3)
f(27) = 2f(3) - f(3)
f(27) = f(3)
Finally, let x = 27:
f(3x) = f(3) + f(x)
f(3(27)) = f(3) + f(27)
f(81) = f(3) + f(27)
We can substitute the expression for f(27) we just derived:
f(81) = f(3) + f(27)
f(81) = f(3) + f(3)
f(81) = 2f(3)
Since we know that f(27) = f(3), we can substitute it into the equation above:
f(81) = 2f(3) = 2(f(27)) = 2(f(9) - f(3)) = 2f(9) - 4f(3)
We also know that f(9) = 2f(3) + 2f(1) from our earlier work, so we can substitute it into the equation above:
f(81) = 2f(9) - 4f(3) = 2(2f(3) + 2f(1)) - 4f(3) = 4f(3) + 4f(1) - 4f(3) = 4f(1)
Therefore, we have shown that f(1) = f(3) = f(9) = f(27) = f(81).
A student is equally likely to select pizza, nachos, or chicken for lunch. What is the probability that the student DOES NOT select chicken?
1/3, 1/2, 2/3 or 1?
Please help soon I need the answer as soon as possible thanks
If a student is equally likely to select pizza, nachos, or chicken for lunch, the probability that the student does not select chicken is 2/3.
Since the student has three equally likely options to choose from, the probability of selecting each option is 1/3. Therefore, the probability of the student selecting chicken is 1/3.
To calculate the probability that the student does not select chicken, we need to subtract the probability of selecting chicken from 1. This is because the sum of all possible outcomes must equal 1, and if we know the probability of one outcome, we can find the probability of its complement (not selecting chicken) by subtracting it from 1.
Therefore, the probability that the student does not select chicken is:
1 - 1/3 = 2/3
So, the correct answer is 2/3.
In summary, when the probability of each possible outcome is equal, we can find the probability of an event (in this case, not selecting chicken) by subtracting the probability of that outcome from 1.
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