Answer: I believe the answer is Yolanda.
Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.
The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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please help fast i don’t feel like typing
Answer:
he should have subtracted 17 from both sides of the equation
Step-by-step explanation:
x+ 17 = 22
subtract 17 from both sides
X + 17 = 22
-17 -17
x = 5
please answer all 3 and show work
The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ
Sky's family should take the offer of $5000 for the boatThe rule of the function is f(x) = 8 * 0.6ˣCalculating the equations of the functionsDamari's investment
Given that
Initial value, a = 30000
B(3) = 32306.72
The function is calculated as
B(x) = a * bˣ
Using B(3), we have
30000 * b³ = 32306.72
So, we have
b³ = 1.077
Take the cube root of both sides
b = 1.03
So, we have
B(x) = 30000 * 1.03ˣ
So, the function is B(x) = 30000 * 1.03ˣ
The boat of Sky's family
Here, we have
Initial value = 6000
Rate of depreciation = 6%
So, the function is
f(x) = 6000 * (1 - 6%)ˣ
So, we have
f(x) = 6000 * (0.94)ˣ
In 2024, we have
x = 2024 - 2021
x = 3
So, we have
f(3) = 6000 * (0.94)³
Evaluate
f(3) = 4983.50
This value is less than the offered value of $5000
This means that Sky's family should take the offer
The rule of the function
Here, we have the graph
From the graph, we have
Initial value, a = 8
Rate, b = 4.8/8
So, we have
Rate, b = 0.6
So, the function is
f(x) = 8 * 0.6ˣ
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The length and breadth of a rectangular flower bed are 16m and 9 m, respectively. How many plants can be planted in it, if each plant requires a space of 1.2m x 1m?
The calculated number of plants the flower bed can contain is 120
Calculating hw many plants can be planted in itFrom the question, we have the following parameters that can be used in our computation:
Dimensions = 16 m by 9 m
So, the area of the flower bed is
Area = 16 * 9
Evaluate
Area = 144
Also, we have
Each plant requires a space of 1.2m x 1m?
This means that
Plant area = 1.2 * 1
Plant area = 1.2
So, we have
Plants = 144/1.2
Evaluate
Plants = 120
Hence, the number of plants is 120
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Answer:
Step-by-step explanation:
To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.
The area of the flower bed is calculated by multiplying its length and breadth.
So, the area of the flower bed is 16m x 9m = 144 sq.m.
Each plant requires a space of 1.2m x 1m = 1.2 sq.m.
Therefore, the number of plants that can be planted in the flower bed is:
144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.
So, you can plant 120 plants in the rectangular flower bed.
A ball pit contains 190 balls.
50 are orange, 100 are purple and 40 are yellow.
What is the ratio of yellow to purple balls in its simplest form?
Step-by-step explanation:
40 :100 yellow to purple, divide both sides by 20
2:5
Answer:
the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.
Step-by-step explanation:
Hope it helps.
The nth term of an arithmetic sequence is given by un=15-3n.
a. [1 mark] State the value of the first term, u1.
b. [2 marks] Given that the nth term of this sequence is -33, find the value of n.
c. [2 marks] Find the common difference, d.
a. The first term of the arithmetic sequence is 12.
b. The value of n for which the nth term is -33 is 16.
c. The common difference of the arithmetic sequence is -3.
a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:
u1 = 15 - 3(1) = 12
b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:
un = 15 - 3n = -33
Adding 3n to both sides, we get:
15 = -33 + 3n
Adding 33 to both sides, we get:
48 = 3n
Dividing both sides by 3, we get:
n = 16
c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:
u2 = 15 - 3(2) = 9
u1 = 15 - 3(1) = 12
d = u2 - u1 = 9 - 12 = -3
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Pretest: Unit 5
Question 6 of 25
If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
OA. (0.6, 0.69)
B. (0.65, 0.7)
O C. (0.5, 0.89)
OD. (0.5, 0.8)
SUBMIT
The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.
Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:
SE = sqrt[(p * (1 - p)) / n]
Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:
SE = sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.
With a sample proportion of 0.65, the margin of error can be estimated as:
ME = 1.96 * sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.
Using this margin of error, we can construct the following range of possible values for the population parameter:
0.65 ± 0.05
This range can be expressed as (0.6, 0.7), which corresponds to option A.
Therefore, the correct answer is option A) (0.6, 0.69).
If ARSU-AVST, then the triangles are
similar by:
Answer:
AA sim post
Step-by-step explanation:
They DO have equal (similar) angles.....but they do not have equal sides
Erik has been collecting comic books for the past few years. The number of total comic books in his collection each year is as follows. • 30 comic books the first year • 60 comic books the second year • 90 comic books the third year • 120 comic books the fourth year Write a function that represents the number of comic book as a function of the number of years, t.
The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.
How to Write a Linear Function?We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.
To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:
First year: (1, 30)
Fourth year: (4, 120)
The slope, m, of the line can be calculated using the formula:
m = change in y / change in x = (120 - 30) / (4 - 1)
m = 90 / 3
m = 30
The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:
30 = 30(1) + b
b = 0
Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:
y = 30x
or
f(t) = 30t [where t represents the number of years.]
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XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.
The values of the constants m and c include the following:
m = -1.3
c = 7.1
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;
2 = -7m + c ...equation 1.
-11 = 3m + c ...equation 2.
By solving the system of equations simultaneously, we have:
2 = -7m - 3m - 11
11 + 2 = -10m
13 = -10m
m = -1.3
c = 7m + 2
c = 7(-1.3) + 2
c = -7.1
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A ladder is leaning against a building, forming a 70° angle with the ground: The base of the ladder is 8.2 ft from the base of the
building.
What is the length of the ladder?
Round your answer to the nearest tenth of a foot.
22.5 ft
24.0 ft
28.0 ft
28.7 ft
The length of the ladder that is leaning on the building would be = 24ft. That is option B.
How to determine the length of the ladder?To determine the length of the ladder, the sine rule needs to be obeyed. That is
= a/sinA = b/sinB
Where;
a = 8.2 ft
A = 180-( 70+90
= 180- 160
= 20°
b = X
B = 90°
That is;
8.2/sin20° = b/sin90°
Make b the subject of formula;
b = 8.2×1/0.342020
= 23.9
= 24 ft
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Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarity:
In the given triangle ABC, angle A is 90° and segment AD is perpendicular to segment BC.
The figure shows triangle ABC with right angle at A and segment AD. Point D is on side BC.
Which of these could be a step to prove that BC2 = AB2 + AC2?
possible answers -
By the cross product property, AB2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by BD.
By the cross product property, AC2 = BC multiplied by AD.
By the cross product property, AB2 = BC multiplied by AD.
The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:
Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.
By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).
Using the proportionality of similar triangles, we can write the following ratio:
[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]
Cross-multiplying, we get:
[tex]$AB^2 = BC \cdot AD$[/tex]
Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:
[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]
Cross-multiplying, we have:
[tex]$AC^2 = BC \cdot AD$[/tex]
Now, we can substitute the derived expressions into the original equation:
[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]
It was made possible by cross-product property.
Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:
By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].
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Let's say you (a 16-year old) open a savings account with an interest rate of 6% per year and you
aren't adding any additional funds in the future. If you make $80,000 within the year you turn 60, what
is the total amount in your account at 60 years old?
The total amount in the account when turning 60 years is A = $ 11,13,706.08
Given data ,
A savings account with an interest rate of 6% per year and you aren't adding any additional funds in the future
Now , you make $80,000 within the year you turn 60
So , the number of years = 60 - 16 = 44 years
And , from the compound interest , we get
A = P ( 1 + r/n )ⁿᵇ
On simplifying , we get
Where A is the final amount, P is the initial amount (which is 0 in this case), r is the annual interest rate (6% or 0.06), n is the number of times the interest is compounded per year (let's assume it is compounded monthly, so n=12), t is the time in years (44 years from age 16 to age 60).
A = 80,000 ( 1 + 0.06/12 )¹²ˣ⁴⁴
A = $ 11,13,706.08
Hence , the amount in account is A = $ 11,13,706.08
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Help pls anyone I’m rlly bad at these
144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.
145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.
How to determine the value of X when two triangles are congruent?
For question 144.)
Two triangles are congruent means that the angles are equal to each other. That is;
2.3x +25 = 5.8x + 11
Bring like terms together;
5.8x-2.3x = 25-11
3.5x = 14
X = 14/3.5
= 4.
For question 145.)
When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.
The two given angles are congruent;
That is;
13x -15 = 22x + 9
Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9
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Sobre una embarcación de 160 kg que está en reposo con su proa apuntando a la orilla, comienza a caminar una persona de 70 kg desde la proa hacia la popa, a 0.80 m/s respecto a la embarcación. ¿Cuáles son las velocidades de la embarcación y de la persona respecto a la orilla? Desprecia la resistencia del agua al movimiento.
The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.
How to calculate the velocityWe can use the conservation of momentum equation:
(mboat + mperson) * vboat = mperson * vperson
(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)
230 kg * vboat = 56 kg * (0.80 m/s + vperson)
vboat = (56/230) * (0.80 m/s + vperson)
vperson = 0.80 m/s + vboat
vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)
(174/115) * vperson = (504/115) * m/s
Dividing both sides by (174/115), we get:
vperson = 2.896 m/s
vboat = (56/230) * (0.80 m/s + vperson)
Substituting the value of vperson, we get:
vboat = 1.337 m/s
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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.
The figure below is a net for a cube. 3.9 ft What is the surface area of the cube, in square feet?
Answer:91.26ft squared
Brenda types 15 words per minute. How long will it take her to type 750 words?
It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.
To solve this problem, we can use the formula:
time = amount of work / rate
In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:
time = 750 / 15 = 50 minutes
This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.
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please help me thank you so much
Answer:
1)
7+9-15 = add 7 and 9, then subtract 15
2)
15-(7+9) = The sum of 7 and 9 subtracted from 15
3)
15-(7+9) = subtract 7 from 15, then add 9
Step-by-step explanation:
Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient
In ΔJKL,
�
�
‾
JL
is extended through point L to point M,
m
∠
�
�
�
=
(
3
�
−
16
)
∘
m∠JKL=(3x−16)
∘
,
m
∠
�
�
�
=
(
2
�
+
15
)
∘
m∠LJK=(2x+15)
∘
, and
m
∠
�
�
�
=
(
8
�
−
19
)
∘
m∠KLM=(8x−19)
∘
. Find
m
∠
�
�
�
.
m∠LJK.
The angle measure of LJK is 27 degrees
How to determine the angleFollowing the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees
Also, we need to know that the sum of angles on a straight line is 180, then, we have;
<JLK = 180 - <LKM = 180 - (8x - 19)
Then, substitute the value, we have that;
<JKL + < JLK + < KJL = 180
Then,
3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180
expand the bracket, we have;
3x - 16 - 8x - 19 + 2x + 15 = 0
add the like terms
-3x + 18 = 0
collect the terms
-3x = -18
x = 6
Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees
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On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles. The same map shows that the movie theater is 20 inches from the school.
What is the actual distance from the movie theater to the school, rounded to the nearest mile?
A: 15
B:27
C:30
D:60
The actual distance from the movie theater to the school is given as follows:
A. 15 miles.
How to calculate the actual distance?The actual distance from the movie theater to the school is obtained applying the proportions in the context of the problem.
On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles, hence the scale factor is of:
2 inches = 1.5 miles
1 inch = 0.75 miles.
The same map shows that the movie theater is 20 inches from the school, hence the actual distance is given as follows:
20 x 0.75 = 15 miles.
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Find the value for the side marked below. Round your answer to the nearest tenth 210 37 degrees
Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.
How to Find the Value of the Marked Side Using the Cosine Ratio?The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:
cos ∅ = length of hypotenuse/length of adjacent side.
From the image attached below, we have the following:
Reference angle (∅) = 37°
length of hypotenuse = 210
length of adjacent side = y
Plug in the values:
cos 37 = y/210
210 * cos 37 = y
y = 167.7
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Which point would be a solution to the system of linear inequalities shown below?
Answer:
(-2, 10)
Step-by-step explanation:
You want the point that would be a solution to the inequalities ...
y ≥ 5/2x +2y ≥ -4x -7GraphIt can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection is the solution space.
The attachment shows the point (-2, 10) is a solution.
Try the answersFrom the shape and location of the solution space, we can eliminate the choices ...
(-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant
(10, -3) — no part of the 4th quadrant is in the solution space
General formIt can work nicely to rewrite the inequalities as a comparison to zero.
5x -2y +4 ≤ 0 . . . . . the first inequality in general form
point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution
point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution
4x +y +7 ≥ 0 . . . . . . the second inequality in general form
point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution
point (4, 9): don't need to test (already known not a solution)
Point (-2, 10) is a solution.
__
Additional comment
We chose the use of "general form" inequalities for evaluating answer choices because ...
the arithmetic is mainly with positive integers (no fractions)the comparison to zero does not require a lot of mental effort<95141404393>
I have not gone to school in a month for family reasons and I have to submit 39 math assignments before Friday HELP
Diego is correct as the number of groups result to 6/5 or 1 1/5.
We have to find the number of groups of 5/6 in 1.
So, we need to perform the division as
= 1/ (5/6)
= 1 x 6/5
= 6/5
= 1 1/5
Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.
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Which factor of 24 can help you solve 24 divided by 4?
Answer:
im an expert
Step-by-step explanation:
For positive acute angles A and B, it is known that SinA= 11/61 and tan B=4/3. Find the value of Cos(A-B) in simplest form.
For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.
We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).
First, we need to find the value of cosA and sinB:
Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:
cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61
Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:
hypotenuse = √(4² + 3²) = 5
sinB = opposite/hypotenuse = 4/5
Now we can substitute these values into the formula:
cos(A-B) = cosA cosB + sinA sinB
= (60/61)(3/5) + (11/61)(4/5)
= 180/305 + 44/305
= 224/305
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Troys toy box is 4 ft x 3ft x 5 ft. What is the Volume of his toy box?
Answer:
60 ft^2
Step-by-step explanation:
To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.
4 x 3 x 5 = 15x 4 = 60
Answer:
60 ft³
Step-by-step explanation:
V = 4 ft × 3 ft × 5 ft
V = 12 ft² × 5 ft
V = 60 ft³
#CMIIWWhat is the ratio for 3 rectangles and 4 ovals in its simplest form?
The ratios for the rectangles and the ovals is 4 : 3
Calculating the ratios for the rectangles and the ovalsFrom the question, we have the following parameters that can be used in our computation:
Rectangle = 4
Oval = 3
The ratio can be represented as
Ratio = Rectangle : Oval
When the given values are substituted in the above equation, we have the following equation
Rectangle : Oval = 4 : 3
The above ratio cannot be further simplified
This means that the ratio expression would remain as 4 : 3
Hence, the solution is 4 : 3
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60% of the books in a library are for adults, 5% are for young people and the rest are for children. If there are 280 books for children, how many books are there altogether?
Answer:
800 books
problem solving steps：
adults:60%
young people:5%
children=100%-60%-5%
=35%
35%=280 books
1%=280÷35
=8
100%=800
so,there are 800 books
Katrina wants to make a cover for her laptop to fit into her bag in order to protect it. She measured the top of her laptop and found it was 57,000 mm2. “No one sells covers using square millimeters,” her friend noted. Describe the area of the top of Katrina’s laptop using square centimeters.
Answer:
To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).
So, the area of the top of Katrina's laptop in square centimeters would be:
57,000 mm² ÷ 100 = 570 cm²
Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
A coordinate plane with points at negative 4 comma 4, negative 2 comma 0, 0 comma negative 3, 3 comma 1, and 5 comma negative 2.
What is the domain of the relation?
{−4, −3, −2, 0, 1, 3, 4, 5}
{−4, −2, 0, 3, 5}
{−3, −2, 0, 1, 4}
{0, 3, 4, 5}
The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.
How to determine domain relation?The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.
Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.
Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.
Hence, the correct option is {−4, −2, 0, 3, 5}.
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