The fraction when five friends divide three bags of apples equally between them is 3/5.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Therefore, the fraction when five friends divide three bags of apples equally between them will be:
= Number of apple / Number of friends
= 3/5
The fraction is 3/5.
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It costs a craftsperson 110 to bring 150 picture frames to market and the picture frames sell for 2. The difference between the cost and the income from sales is the craftsperson’s profit?
If a circular flower bed has a diameter of 18ft.
What is the area of the flower bed?
What is the circumference of the flower bed?
Answer:
Area = 81 pi
circumstance = 18 pi
Step-by-step explanation:
radius = 9
The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 8000.(a) Find a function n(t) = n0ert that models the population after t hours.(b) Find the population after 1.5 hours.(c) After how many hours will the number of bacteria reach 15,000?(d) Sketch the graph of the population function.
(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, the population is 22646.
(c) t=1.7 will it take for there to be 15,000 bacteria
(d) The population function's graph is in the picture.
Given that,
One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.
We have to find
(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, locate the population.
(c) How long will it take for there to be 15,000 bacteria?
(d) Draw the population function's graph.
We know that,
(a) The initial size of the culture is 1000 bacteria.
So,
n₀=500
The size of the culture after one hour (for t =1) is 4000 so we extract the equation:
n(1) = 8000
1000er¹=8000
e to the power of r =8
[taking logarithms both side]
r ln e = ln 8
r=2.080
[ln e = 1]
So, we got
n₀=1000 and r=2.08
The function will be,
n(t)=1000[tex]e^{2.08t}[/tex]
(b) for t = 1.5
n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]
22646
(c) 15000=1000[tex]e^{2.08t}[/tex]
15=[tex]e^{2.08t}[/tex]
Taking log on both sides
ln15= 2.08(t)lne
t=3.68/2.08
t=1.7
(d) Since we have have the exponential equation therefore our graph should be curve not straight line.
Also at t=1, population of bacteria is 4000
Hence the correct graph will be in picture.
Therefore,
(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.
(a) After 1.5 hours, the population is 22646.
(c) t=1.7 will it take for there to be 15,000 bacteria
(d) The population function's graph is in the picture.
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Adam has 5 blue pencils. How many red pencils would he need to have so that the ratio of blue pencils to red pencils is 1:2?.
The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
Explain the term ratio of the number?A ratio in mathematics demonstrates how several times one number is present in another. An set of points of numbers an as well as b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Let the number of number of red pencils be 'x'.
Total blue pencils = 5.
Ratio = blue pencils/red pencils
5/x = 1/2
x = 5 x 2
x = 10
Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 170 engines and the mean pressure was 6.7 lbs/square inch. assume the standard deviation is known to be 1. if the valve was designed to produce a mean pressure of 6.6 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
What is the Null hypothesis?In inferential statistics, the null hypothesis states that two possibilities are equal.
The observed difference is thought to be the sole product of chance, which is the underlying premise.
Statistical tests can be used to calculate the likelihood that the null hypothesis is true.
So,
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
As the population standard deviation is given when n > 30
So, we'll run the Z test.
Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]
Replace the values:
[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]
For the p-value, see the z table.
Consequently, p = 0.9927.
The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146
α = 0.1
p value< α
Thus, we disregard the null hypothesis.
Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.
Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
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Find the angel between the two vectors (4,1) and (-8,3)
The angle between the two vectors (4,1) and (-8,3) will be 145.4°.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is possible to calculate the angle () between two vectors using the formula
[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
Calculate dot product:
=a · b
= ax · bx + ay · by
= 4 · (-8) + 1 · 3
= - 32 + 3
= -29
=|a|
= √ax² + ay²
= √4² + 1²
= √16 + 1
= √17
=|b|
=√ bx² + by²
= √(-8)² + 3²
= √64 + 9
= √73
[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
α = 145.40771131249005°
Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.
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Which should equal 92° to prove that r ∥ s? w x y z
w should be equal to 92° to prove that r || s.
To prove whether the two lines are parallel we should know whether
the pairs of corresponding angles are congruent if a transversal cuts two parallel lines (Corresponding Angles Theorem)the pairs of alternate interior angles are congruent if a transversal cuts two parallel lines (Alternate Interior Angles Theorem)the pairs of alternate exterior angles are congruent if a transversal cuts two parallel lines (Alternate Exterior Angles Theorem)the pairs of consecutive interior angles are supplementary if a transversal cuts two parallel lines (Consecutive Interior Angles Theorem)So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.
From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.
The answer is w. Therefore, option a is correct.
The complete question is -
Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?
a)w
b)x
c)y
d)z
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Let A be a complex (or real) n x n matrix, and let x in C^n be an eigenvector corresponding to an eigenvalue (lambda) in C Show that for each nonzero complex scalar (nu) , the vector (nu) x is an eigenvector of A
The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).
Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.
Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)
As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).
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The sum of two numbers is 31. The second number is 4 more than the first number.
Answer:
13.5, 17.5
Step-by-step explanation:
You have two numbers whose sum is 31 and whose difference is 4. The second number is larger.
SetupLet x represent the larger number. Then the smaller is x-4, and their sum is ...
x +(x -4) = 31
SolutionSimplifying the expression gives ...
2x -4 = 31
2x = 35 . . . . . add 4
x = 17.5 . . . . . divide by 2
x -4 = 13.5
The two numbers are 13.5 and 17.5.
__
Additional comment
As we have seen here, the larger number is half the total of the 'sum' and 'difference'. (31+4)/2 = 17.5. This is the generic solution to any "sum and difference" problem.
there are 3 seniors and 15 juniors in mrs. gillis’s math class. three students are chosen at random from the class. a. what is the probability that the group consists of a senior and two juniors? b. if the group consists of a senior and two juniors, what is the probability that stephanie, a senior, and jan, a junior, are chosen?
The answer of a) Probability = 0.386 and of b) Probability = 0.017
Explain probability.
Estimating the likelihood that experiments will succeed or fail is one use of probability theory. The likelihood of flipping a coin and getting heads or tails, for example, or the likelihood of making a research error, can all be calculated using probabilities. In order to fully appreciate this area of mathematics, it is crucial to comprehend the formula for computing probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together.
no of seniors = 3
no of juniors = 15
a) probability that a group consist of a senior and two juniors =
[tex]\frac{^{3}C_{1} * ^{15}C_{2}}{^{18}C_{3}} \\= \frac{3*105}{316}=0.386\\[/tex]
b) if the name of a student given then there is only one way to select it
For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by ([tex]^{14}C_{1}=14[/tex]) different ways.
probability = [tex]\frac{1*1*^{14}C_{1} }{^{18}C_{3} }=\frac{14}{316}=0.017[/tex]
Hence the answer of a) is 0.386 and of b) is 0.017
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find the equation parallel to y=-2x-18 through (-3,2)
Answer:
y= -2x-4
Step-by-step explanation:
parallel==> a line has the same slope ===> (m = -2)
y= -2x+b
and a line pass through the (-3,2) ===> x=-3, y=2
2= -2(-3)+b
2=6+b (subtract 6 from both sides )
-4=b
y= -2x-4
nine people sit down for dinner where there are three choices of meals. three people order the beef meal, three order the chicken meal, and three order the fish meal. the waiter serves the nine meals in random order. find the number of ways in which the waiter could serve the meal types to the n
There are a total of 216 ways in which the waiter could serve the meal types.
Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.
Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.
If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.
If the two B people both get F's, the situation is identical to the above and three possibilities arise.
If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.
In total, we see there are 24 possibilities, so the answer is 9*24 = 216
Thus, there are a total of 216 ways in which the waiter could serve the meal types.
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Your question was incomplete. Check for missing part below-
Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.
Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 100x2 + 49y2 = 1
The area bounded by the sin (100x² + 49y²) dA is calculated by using integration is 2π (1 - cos 1).
An area bounded by the curve: When the two curves intersect then they bound the region is known as the area bounded by the curve.
Evaluate the integral by making an appropriate change of variables.
The equation of the ellipse is 100x² + 49y² = 1
Let cos t = 10x and sin t = 7y. Then we have
or x = 1/10 cost , y = 1/7 sint.
Then
=> 100 (1/10cost)^2 + 49 (1/7 sint)^2 = 1
=> cos^2 t + sin^2t = 1 which suggests a change of variable will be:
[tex]\left \{ {{x(r,t) = r/10cost} \atop {y(r,t)=r/7sint}} \right.[/tex]
where 0≤r≤1 and 0≤t≤2[tex]\pi[/tex]. Then we also have,
100x² + 49y² = r²
So,
=> ∫∫ sin (100x^2 + 49y^2)dA
R
=> [tex]\\[/tex]2 ∫2[tex]\pi[/tex] ∫[tex]1[/tex] sinr^2 dr dt
0 0
=> 4[tex]\pi[/tex] ∫[tex]1[/tex] rsinr^2 dr
0
Now r² is replaced by r, then we get
=> 2[tex]\pi[/tex] ∫[tex]2[/tex] sinr^2 d(r^2)
0
=> - 2[tex]\pi[/tex] cos r^2 [tex]\left \{ {{r^2=1} \atop {r^2=0}} \right.[/tex]
=> -2[tex]\pi[/tex] (cos1-cos0)
=> -2[tex]\pi[/tex] (-1 + cos1)
=> 2[tex]\pi[/tex](1-cos1)
Evaluating the integral by making an appropriate change of variables 2 sin(100x^2 + 49y^2) dA.
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please help me solve this problem I will give 20 points
Answer:
94
Step-by-step explanation:
if 3 pairs of mittens equal 30 then 1 pair of mitten is 10
And 1 mitten is 5
2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11
X+11+10=24
x+21=24
x=3
One hat is 3
We can write the last problem like this
2(3)+11x(11-3)
6+11x8
6+88
94
Hopes this helps and I hope this is right with these riddles I’m sure I missed something
Answer:
Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10
And 1 mitten is 5
2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11
X+11+10=24
x+21=24
x=3
One hat is 3
We can write the last problem like this
2(3)+11x(11-3)
6+11x8
6+88
94
Hopes this helps and I hope this is right with these riddles I’m sure I missed something
write in slop form of the equation and each line given the slope and y intercept. slope = 1/2. y intercept = 2
Answer:Y=1/2x+2
Step-by-step explanation:
Slope intercept form is y=mx+b
m=slope
b= y intercept
y=1/2x+2
Two interior angles of a triangle are 54 and 112. What is the measure of the third angle?
Answer: 14 degrees.
Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.
In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:
180 degrees = 54 degrees + 112 degrees + x
180 degrees = 166 degrees + x
x = 180 degrees - 166 degrees
x = 14 degrees
Therefore, the measure of the third angle of the triangle is 14 degrees.
a box contains 3 donuts cake, 4 jelly cake and 5 chocolate cake. if a person selects one cake at random, find the probability that it is either a donut or a chocolate cake
Answer:
50%
Step-by-step explanation:
It is a half chance, you could be lucky
how many students say yes to liking pizza
Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1 A 125-page document is being printed by five printers. Each page will be printed exactly once. (a) Suppose that there are no restrictions on how many pages a printer can print. How many ways are there for the 125 pages to be assigned to the five printers? One possible combination: printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer
The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.
As per the question,
A 125-page document is being printed by four printers.
Each page will be printed exactly once.
There are no restrictions on how many pages a printer can print.
One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.
Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.
⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways
⇒ Number of possible ways 125 pages can be assigned to the four printers
= 5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )
= ways.
Therefore, In ways we can assign 125 pages to four printers with no restrictions.
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Help me please please please please System of equations and inequalities aglebera 1
HELP
For the diagram below, calculate the value of x. Show your work
Answer: x = 6
Step-by-step explanation:
2x + 7 = 9x - 35
-7x + 7 = -35
-7x = -42
x=6
What is the polar form of negative 9 minus 9 i startroot 3 endroot ?
Using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
So, we have -9 - 9√3i:
This quantity has a modulus.
|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18
And argument θ to the effect:
tan(θ) = (-9√3) / (-9) = √3
We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:
θ = arctan(√3) - π = π/3 - π = -2π/3
The polar form is then:
18 (cos(-2π/3) + i sin(-2π/3))
And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))
Therefore, using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?
a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Answer:
18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Step-by-step explanation:
D
Mt.Mckinley is 20,321 ft in elevation. Mt.McKinley is 8,707 ft lower than Mt. Everest. What is the elevation of Mt.Everest?
I need to explain the variable
write an equation
and solve it
Answer:
29,028 ft.
Step-by-step:
Consider the following:
Mt. Everest - x
Equation:
We are given that Mt. McKinley is 20,321 ft in elevation, and that it is 8,707 ft. lower than Mt. Everest.
When writing this numerically:
20,321 = x - 8,707
Solve for x:
20,321 = x
+8,707 + 8,707
-------------------------
x = 29,028
Mt. Everest is 29,028 ft. in elevation.
35 Points!!!! 7 2/5= 2/3x −4 1/2
Enter your answer as a mixed number in simplest form in the box.
Solving for x in the equation 7 2/5 = 2/3x −4 1/2 gives 17 17/20
How to determine the value of xIn the given equation, we find the value of x by applying the following operations
7 2/5 = 2/3x −4 1/2
7 2/5 = 2x/3 −4 1/2
collecting like terms
7 2/5 + 4 1/2 =
2x/3 = 119/10
multiplying by 3
2x = 119/10 * 3
2x = 357/10
dividing by 2
x = 357 / 10 * 1/2
x = 357/20
x = 17 17/20
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Given the image below, complete find the missing parts of the proof to find the value of x.
(2x +43)°
(2x – 3) °
.
°
Statements
1. Line 1 is parallel to line mi
and
2. (2x +43) + (2x - 3) = 180
3. 4x + 40 = 180
4. 4x = 140
| 5. x = 35
Reasons
1. Given
2. ?
3. Simplifing Equation
4. Subtraction POE
5. ?
Answer:
just telling you but we need to see the image which we cannot but I'm not entirely sure but I think it's 2 although I cannot see the image and the other one is 4 I thinke
Sara has 7,241 beads. She wants to make them into necklaces to sell at a charity fundraiser. She wants to use 13 beads on each necklace. How many necklaces is she able to make?
Answer:
557
Step-by-step explanation:
7,241 divided by 13 = 557
if 11600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
The compound interest after 5 years is $7,081.916.
Compound interest:
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Here we have to find the interest earned after 5 years.
Data given:
Principle (P) = $11600
rate(r) = 10%
time(t) = 5 years.
Formula to find compound interest:
CI = P( 1 + r/100[tex])^{t}[/tex] - P
Now put the values in the formula.
CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600
= 18681.916 - 11600
= 7081.916
Therefore the compound interest is $7081.916.
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1.15 x240 not the answer the work I want.
Answer:
Step-by-step explanation:
true or false: when two variables are highly correlated, a change in the value of one will cause a change in the value of another.
The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.
What are variables?Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.
Independent, dependent, and controlled variables are typically present in an experiment.
The variable that is altered by the scientist is the independent variable.
A false correlation between two variables indicates that their correlation coefficient is almost zero.
When two variables have a strong correlation, altering the value of one will not affect the other.
Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.
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A paper cup is in the shape of an inverted right circular cone with both height and diameter of 6 inches. It is being filled with water at a rate of 2 cubic inches per minute. How fast is the water level rising when it is 2 inches deep.
Pls give answer in inches per minute
Using the implicit differentiation, it is found that the water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.
What is the volume of a cone?The volume of the cone of radius r and height h is given as follows:
V = π r² h / 3
Applying implicit differentiation to find the rate of change of the volume as function of time is given as follows:
[tex]\frac{dV}{dt}[/tex] = 2 π [tex]\frac{rh}{3}[/tex][tex]\frac{dr}{dt}[/tex] + [tex]\frac{π r² }{3}[/tex] [tex]\frac{dh}{dt}[/tex]
As the radius is constant, hence:
.[tex]\frac{dr}{dt}[/tex] = 0
Considering that the radius is half of the diameter, the other parameters are:
r = 3 and [tex]\frac{dV}{dt}[/tex] = 2
Hence:
2 = [tex]\frac{π * 3^{2} }{3}[/tex] [tex]\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}[/tex] = 6 / 9 π
dh/dt = 0.21.
The water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.
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