The pie chart for the data is given below.
To create a pie chart from the given data, we first need to determine the percentage of each score in relation to the total frequency. Here's the calculation:
Score Frequency Percentage
60 2 (2/24) x 100 = 8.33%
63 2 (2/24) x 100 = 8.33%
65 1 (1/24) x 100 = 4.17%
67 1 (1/24) x 100 = 4.17%
71 1 (1/24) x 100 = 4.17%
72 1 (1/24) x 100 = 4.17%
73 2 (2/24) x 100 = 8.33%
74 2 (2/24) x 100 = 8.33%
75 2 (2/24) x 100 = 8.33%
76 1 (1/24) x 100 = 4.17%
78 1 (1/24) x 100 = 4.17%
79 2 (2/24) x 100 = 8.33%
80 1 (1/24) x 100 = 4.17%
81 2 (2/24) x 100 = 8.33%
82 1 (1/24) x 100 = 4.17%
84 1 (1/24) x 100 = 4.17%
85 1 (1/24) x 100 = 4.17%
87 1 (1/24) x 100 = 4.17%
88 1 (1/24) x 100 = 4.17%
89 1 (1/24) x 100 = 4.17%
90 1 (1/24) x 100 = 4.17%
92 1 (1/24) x 100 = 4.17%
94 1 (1/24) x 100 = 4.17%
Now, we can use this information to create a pie chart. The chart will have 24 segments, each representing one score. The size of each segment will correspond to the percentage calculated above.
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PLEASE HELP ME ANSWER THIS QUESTION I NEED IT PLEASE.
Find ∫ x^5 √(2 - x^3) dx
Answer:
[tex]\displaystyle \frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]
Step-by-step explanation:
[tex]\displaystyle \int x^5\sqrt{2-x^3}\,dx\\\\=\int x^5(2-x^3)^{\frac{1}{2}}\,dx\\\\=\int x^3x^2(2-x^3)^{\frac{1}{2}}\,dx[/tex] <-- Breaking up [tex]x^5[/tex] into [tex]x^3x^2[/tex] helps us later
Let [tex]u=2-x^3[/tex] and [tex]du=-3x^2\,dx[/tex] so that [tex]2-u=x^3[/tex] and [tex]\displaystyle -\frac{1}{3}du=x^2dx[/tex]:
[tex]\displaystyle -\frac{1}{3} \int (2-u)u^{\frac{1}{2}}\,du\\\\=-\frac{1}{3} \int 2u^{\frac{1}{2}}-u^{\frac{3}{2}}\,du\\\\=-\frac{1}{3}\biggr(\frac{4}{3}u^{\frac{3}{2}}-\frac{2}{5}u^{\frac{5}{2}}\biggr)+C\\\\=-\frac{1}{3}\biggr(\frac{4}{3}(2-x^3)^{\frac{3}{2}}-\frac{2}{5}(2-x^3)^{\frac{5}{2}}\biggr)+C\\\\=-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+\frac{2}{15}(2-x^3)^{\frac{5}{2}}+C\\\\=\frac{2}{15}(2-x^3)^{\frac{5}{2}}-\frac{4}{9}(2-x^3)^{\frac{3}{2}}+C[/tex]
HELP IMAGE ATTACHED ANSWER FAST!! 6) Match the equations to the lines below:
Answer:
Step-by-step explanation:
In order from top to bottom:
3
2
1
4
Find the volume of a pyramid with a square base, where the side length of the base is
14.4
m
14.4 m and the height of the pyramid is
15.3
m
15.3 m. Round your answer to the nearest tenth of a cubic meter.
The volume of a pyramid with a square base is 3172.608 cubic meter.
Given that, the side length of the base is 14.4 m and the height of the pyramid is 15.3 m.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, volume = 14.4²×15.3
= 3172.608 cubic meter
Therefore, the volume of a pyramid with a square base is 3172.608 cubic meter.
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Multiply
4 8/9 • 1 1/3
Answer:
Step-by-step explanation:
[tex]4\frac{8}{9} . 1\frac{1}{3}\\= \frac{44}{9}.\frac{4}{3} \\= \frac{176}{27}[/tex]
What types of angles are angle 4 and angle 6 ?
Answer:
same side interior
Step-by-step explanation:
they are on the SAME SIDE as the transversal (diagonal line) which means that they can't be alternate. also, they are inside (interior) of the two horizantal parallel lines. this means that they must be same side interior
Consider the equation below. (If an answer does not exist, enter DNE.)
f(x) = x3 − 3x2 − 9x + 3
The interval on which f(x) is increasing is (-∞, -1) and (3, ∞).
To find the interval on which the function f(x) = x³ - x² - 9x + 3 is increasing, we need to determine where the derivative of the function is positive.
First, let's find the derivative of f(x):
f'(x) = 3x² - 6x - 9
3x² - 6x - 9 = 0
3(x - 3)(x + 1) = 0
x - 3 = 0 or x + 1 = 0
x = 3 or x = -1
These are the critical points of the function.
Let's test a value from each interval:
For x < -1, let's use x = -2:
f'(-2) = 3(-2)² - 6(-2) - 9 = 12 + 12 - 9 = 15 > 0
For -1 < x < 3, let's use x = 0:
f'(0) = 3(0)² - 6(0) - 9 = -9 < 0
For x > 3, let's use x = 4:
f'(4) = 3(4)² - 6(4) - 9 = 12 - 24 - 9 = -21 < 0
From these test values, we can see that f(x) is increasing on the interval (-∞, -1) and (3, ∞).
Therefore, the interval on which f(x) is increasing is (-∞, -1) and (3, ∞).
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A home decor store donated a percent of every sale to hospitals. The total sales were $8,400 so the store donated $672. What percent of $8,400 was donated to hospitals?
Answer:
8% of sales donated-----------------------
What percent of $8400 is $672?
672/8400 * 100% = 0.08 * 100% = 8%Answer:
8%
Step-by-step explanation:
To find the percentage that was donated to hospitals, we can set up the following equation:
[tex]\sf \dfrac{total\: donation}{ total \:sales} * 100 = percentage \:donated[/tex]
In this case, the total donation was $672 and the total sales were $8,400.
Substituting these values into the equation, we get:
[tex]\sf \dfrac{672}{8400} * 100 = percentage \:donated[/tex]
Simplifying this expression:
(0.08) * 100 = percentage donated
8% = percentage donated
Therefore, the home decor store donated 8% of $8,400 to hospitals.
PLEASE SOLVE. I MARK YOU BRaINALIST
The force of gravity on the rocket is 30 N/kg, the mass of the rocket stays constant while its weight varies
What is force of gravity?The force of gravity is the force exerted on an object by the earth or a planet.
Given that the force of gravity on an object when it is launched is 30 N/kg. This is three times larger than Earth's gravity. To determine what happens to the mass and weight of the object when gravity is 30 N/kg, we proceed as follows.
We know that weight, W = mg where
m = mass of object and g = gravitySince gravity g = 30 N/kg, we have that
W = mg
= m × 30 N/kg
= 30m
Now, we know that mass is an intrinsic property and weight is an extrinsic property. This means that the mass of the object is constant but its weight can change based on the object's position and depends on the amount of mass.
So, since the force of gravity on the rocket is 30 N/kg, the mass of the rocket stays constant while its weight varies
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21. (1 point) Let y 00 −64y = 0. Find all values of r such that y = kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. r = help (numbers) Answer(s) submitted:
The values of r for which y = e^(rx) satisfies the differential equation y″ - 64y = 0 are r = 8 and r = -8.
How to calculate the valueFirst, differentiate y twice:
y' = [tex]re^{rx}[/tex]
y'' = r²[tex]e^{rx}[/tex]
y'' - 64y = r²[tex]e^{rx}[/tex] - 64[tex]e^{rx}[/tex] = 0
[tex]e^{rx}[/tex] * ([tex]r^{2}[/tex] - 64) = 0
[tex]r^{2}[/tex] - 64 = 0:
Solving this quadratic equation gives:
[tex]r^{2}[/tex] = 64
r = ±8
Therefore, the values of r that satisfy the differential equation are r = 8 and r = -8.
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Let y″−64y=0.
Find all values of r such that y=kerx satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.
3 2 points Find the height of a cone with a diameter of 12 m whose volume is 188 m³. Use 3.14 for 77 and round your answer to the nearest meter. Please record your work/justification on your paper or document
5m
6 m
2m
12 m
4 m
5m is the height of a cone with a diameter of 12 m whose volume is 188 m³.
To find the height of a cone, we can use the formula for the volume of a cone and solve for the height.
The formula for the volume of a cone is:
V = (1/3)× π × r² × h
Given that the diameter of the cone is 12 m, the radius (r) is half of the diameter, which is 6 m.
We are also given that the volume of the cone is 188 m³.
Using the formula, we can rearrange it to solve for the height (h):
h = (3V) / (πr²)
Plugging in the values:
h = (3 × 188) / (3.14 × 6²)
h = 564 / (3.14 × 36)
h = 564 / 113.04
h =4.9916
h=5
Therefore, the height of a cone with a diameter of 12 m whose volume is 188 m³ is 5 m.
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In a group of 150 kids 6 have green eyes 52% have brown eyes 16% have gray eyes and the rest have blue eyes what percentage of the kids have blue eyes.
Answer:
[tex]\boxed{\boxed{\sf{\:\:\: \green{Percentage = 28\%}\:\:\: }}}[/tex][tex]\\[/tex]
Step-by-step explanation:
We know that the total number of kids is 150. We can find the number of kids with green, brown, and gray eyes using the given percentages:
[tex]\sf\dashrightarrow Green\: eyes = 6\: kids[/tex]
[tex]\sf\dashrightarrow Brown\: eyes = 0.52 \times 150 = 78\: kids[/tex]
[tex]\sf\dashrightarrow Gray\: eyes = 0.16 \times 150 = 24\: kids[/tex]
[tex]\\[/tex]
To find the number of kids with blue eyes, we can subtract the number of kids with green, brown, and gray eyes from the total number of kids:
[tex]\sf\dashrightarrow Blue\: eyes = 150 - 6 - 78 - 24[/tex]
[tex]\sf\dashrightarrow Blue\: eyes = 42\: kids[/tex]
[tex]\\[/tex]
Finally, we can calculate the percentage of kids with blue eyes by dividing the number of kids with blue eyes by the total number of kids and multiplying by 100:
[tex]\sf\implies Percentage = \dfrac{42}{150} \times 100[/tex]
[tex]\sf\implies Percentage = \dfrac{4,200}{150}[/tex]
[tex]\sf\implies Percentage = \green{28\%}[/tex]
[tex]\\[/tex]
[tex]\\[/tex]
Therefore, 28% of the kids have blue eyes.
PLEASE HELP QUICK!! WILL MARK BRAILIEST!!
Question the formula (equation) for finding the VOLUME of a rectangular prism is?
A= 1/2 bh
A= lw
V= lwh
V= x + 3
Answer:
V = lwh
Step-by-step explanation:
The volume of a rectangular prism or a rectangle stretched is the basic rectangle area formula ( wh ) multiplied by the new factor, the length ( l ). This makes the formula V = lwh
Hope this helped
Find the equation of the line.
Use exact numbers
Answer:
y = [tex]\frac{2}{3}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line
a farmer sells 7.2kilograms of pears and apples at a farmers market . 3/5 of this wirght is pears, and the rest is apples . how many kilograms of apples did she sell at the farmers market
The farmer sold 3.6 kilograms of apples at the farmers market.
To find the weight of apples the farmer sold at the farmers market, we need to subtract the weight of pears from the total weight.
We have,
3/5 of the weight is pears, the weight of pears
= (3/5) x 7.2 kilograms.
= 3.6 Kg
Since the remaining weight is apples, we can calculate the weight of apples by subtracting the weight of pears from the total weight:
Weight of apples = Total weight - Weight of pears
= 7.2 - 3.6
= 3.6 kilograms
Therefore, the farmer sold 3.6 kilograms of apples at the farmers market.
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15. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
The surface area of the larger solid is approximately 172 mm sq. approx
Given
The volume of the smaller solid = 540 mm cube
The volume of the larger solid = 857.5 mm cube
The surface area of the smaller solid = 108 mm sq.
Required to find the surface area of the larger solid =?
Let the surface area of the larger solid be x.
(surface area of smaller solid) / (volume of smaller solid) = (surface area of larger solid) / (volume of larger solid)
Putting the values in the above formula we get the value of x.
108 mm^2 / 540 mm^3 = x / 857.5 mm^3
x = 171.5 mm sq
Thus, the surface area of the larger solid is approximately 172 mm sq
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Consider polygon ABCD, shown below.
B
C
E
A
G
F
D
Select all the ways that describe rigid transformations that take AEFD to CFEB.
The option that describes the rigid transformation that take AEFD to CFEB are:
Rotate AEFD 180 degrees counterclockwise around point GRotate AEFD 180 degrees clockwise around point G.What does it mean to rotate shape 180°?To rotate a form 180°, turn it about its center point such that it faces the opposite way. This is accomplished by tracing the form on a sheet of paper and then folding it in half so that the two sides of the shape line up. The form is now rotated 180 degrees.
A rigid transformation (also known as a Euclidean transformation or Euclidean isometry) in mathematics is a geometric transformation of a Euclidean space that retains the Euclidean distance between each pair of points.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
The population of a city after t years is given by P(t)=36,442e0.042t,
where t=0
corresponds to the current year.
How many years from the current year will it take for the population of the city to reach 75,000
?
Round to the nearest hundredth of a year.
Answer:
[tex]36442 {e}^{.042t} = 75000[/tex]
[tex]t = 17.18 \: years[/tex]
HELP PLS
The equation for the area of a trapezoid is A equals one-half times h times the quantity of b subscript 1 plus b subscript 2 end quantity.. If A = 28, b1 = 6, and b2 = 8, what is the height of the trapezoid?
h = 2
h = 4
h = 6
h = 7
Answer:
h = 4 units
Step-by-step explanation:
Given equation:
[tex]\text{A}_{\text{trapezoid} } = \dfrac{1}{2}(h)(b_{1} + b_2)[/tex]
Given numerical values:
A = 28b₁ = 6b₂ = 8Plug in all values into the equation and simplify it to find the height:
[tex]\implies \text{28} = \dfrac{1}{2}(h)(6 + 8)[/tex]
[tex]\implies\text{28} = (h)(3 + 4) = 7h[/tex]
[tex]\implies h = \dfrac{28}{7} = 4[/tex]
Therefore, the measure of the height is 4 units.
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Is the following a statistical question?
How expensive are homes in your neighborhood?
yes
No
Answer:
YES
Step-by-step explanation:
A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.
9. Jack recorded the number of different colored marbles he has in a pouch. The results are provided in the table below. Color blue 5 brown 4 green. 3 orange 5 red 4 yellow 4 Part B. Jack has another jar of 275 marbles that have the same distribution as the table above. Based on the information in the table, determine the number of yellow marbles
Based on the information provided in the table, Jack has 4h yellow marbles.
To determine the number of yellow marbles in the jar of 275 marbles, we can use the information from the table to find the proportion of yellow marbles in the first pouch.
According to the table, there are 4 yellow marbles out of a total of 25 marbles in the first pouch.
Therefore, the proportion of yellow marbles in the first pouch is 4/25.
To find the number of yellow marbles in the jar of 275 marbles, we can multiply this proportion by the total number of marbles in the jar.
Number of yellow marbles = (4/25) x 275 = 44
Therefore, there are 44 yellow marbles in the jar of 275 marbles.
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What is one over two to the fifth power?
Answer:0.03125
Step-by-step explanation:
GOO*OOGLE
Step-by-step explanation:
(1/2)^5 = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The stemplot shows the snowfall, in inches, in US cities during December.
Use this graphic to answer the question.
Use the drop-down menus to complete the statements about the snowfall amounts shown in the stemplot.
This distribution of snowfall amounts is
. There appears to be one outlier in snowfall amount at
inches.
This distribution of snowfall amounts is skewed to the right
When are data skewed to the rightData is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.
In a positively skewed distribution majority of the data is concentrated towards the lower values.
Considering the stemplot the majority of the data is in the lower values
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Answer:
to the second part
18.7 inches
Will mark brilliant
14. What information below would be enough to prove ADEF = ARPQ?
E
The information which would be enough to prove the triangles to be congruent are either DE = RP or ∠F = ∠Q.
Given two triangles,
ΔDEF and ΔRPQ.
If ΔDEF is congruent to ΔRPQ, then the corresponding vertices of D, E and F are R, P and Q respectively.
Already we have from the figure,
∠D = ∠R
DF = RQ
Now, it is enough to prove either DE = RP or ∠F = ∠Q.
When DE = RP, by SAS congruence theorem, corresponding two sides and the included angle of each triangle are equal and thus triangles are congruent.
When ∠F = ∠Q, by ASA congruence theorem, corresponding two angles and the included side of each triangle are equal and thus triangles are congruent.
Hence the information required are either DE = RP or ∠F = ∠Q.
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Please help due !!!! Please asap !
Answer:
hello
the answer to (a) is:
y = kx ----> y = (1/8)x
and the answer to (b) is:
if x = 7
y = (1/8) × 7 = 7/8 or 0.875
Find a dimensionless product relating the torque, (ML²T-²) produced by an automobile engine, the engine's rotation rate, (T-¹), the volume V of air displaced by the engine, and the air density p.
The dimensionless product relating the torque, rotation rate, volume, and air density is:
Pi = (torque) * (rotation rate)² * (volume)^(1/3)
To find a dimensionless product relating the torque (ML²T⁻²) produced by an automobile engine, the engine's rotation rate (T⁻¹), the volume V of air displaced by the engine, and the air density p, we can make use of the Buckingham Pi theorem.
The Buckingham Pi theorem states that in a physical problem involving n variables with k fundamental dimensions, there will be n - k dimensionless quantities that can be formed as products of powers of the original variables.
In this case, we have 4 variables with 3 fundamental dimensions: torque (M L² T⁻²), rotation rate (T⁻¹), volume (L³), and air density (M L⁻³). Therefore, we expect to have 4 - 3 = 1 dimensionless product.
Let's define the dimensionless product (Pi) as:
Pi = (torque)ᵃ * (rotation rate)ᵇ * (volume)ᶜ * (air density)ᵈ
To determine the powers (a, b, c, d), we equate the dimensions on both sides of the equation:
M L² T⁻² = (M)ᵃ * (T⁻¹)ᵇ * (L³)ᶜ * (M L⁻³)ᵈ
Equating the dimensions of mass (M):
1 = a + d
Equating the dimensions of length (L):
2 = 3c - 3d
Equating the dimensions of time (T):
-2 = -b
Solving these equations, we find:
a = 1
b = 2
c = 1/3
d = 0
This dimensionless product captures the relationship between these variables, independent of their specific units and scaling factors.
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Here are the first five terms of a number sequence. 23 20 17 14 11 (a) Write down the 8th term of this sequence. *********
The 8th term of the sequence is 2.
To find the 8th term of the given number sequence, we can observe that the sequence is decreasing by 3 with each term.
Starting from the first term, which is 23, we subtract 3 repeatedly to get the subsequent terms:
23 - 3 = 20
20 - 3 = 17
17 - 3 = 14
14 - 3 = 11
We can see that each term is obtained by subtracting 3 from the previous term.
To find the 8th term, we continue this pattern:
11 - 3 = 8
8 - 3 = 5
5 - 3 = 2
Therefore, the 8th term of the sequence is 2.
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If u⃗ =⟨3,9⟩ and w⃗ =⟨−3,1⟩, find 13u⃗ −2w⃗ .
The resultant vector of the operation 13u - 2w is given as follows:
13u - 2w = <45, 115>.
How to obtain the resultant vector?The vectors in the context of this problem are defined as follows:
u = <3,9>.w = <-3,1>.When we multiply a vector by a constant, each component of the vector is multiplied by the constant, hence:
13u = <39, 117>.2w = <-6, 2>.Then when the two vectors are subtracted, the equivalent components of each vector are subtracted, hence:
13u - 2w = <39, 117> - <-6, 2>
13u - 2w = <45, 115>.
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The volume of a right cone is 2325
�
π units
3
3
. If its radius measures 15 units, find its height.
The height of the cone in this problem is given as follows:
h = 16.4 units.
How to obtain the volume?The volume of a cone of radius r and height h is given by the equation presented as follows:
V = πr²h/3.
The parameters for this problem are given as follows:
V = 2325 π, r = 15.
Hence the height is obtained as follows:
2325 = π x 15² x h/3
h = 2325 x 5/(15² x π)
h = 16.4 units.
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Ms. Chung drives the same distance to go to work every Monday through Friday. On Saturday she drove g the distance she drives to work. The distance she drove on Saturday was 0.9 miles. Part A: In the first box, enter an equation to represent the distance, d, that Ms. Chung drives to work. Part B: In the second box, enter the distance Ms. Chung drives to work.
A) The algebraic expression will be 12d + 7 = 91
B) He drives 7 miles per day to work.
For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.
The distance she drove on Saturday was; 0.9 miles.
The number of miles she drives per day:
84 miles/12
= 7 miles per day
Let the number of miles she travels be day = d
12d + 7 = 91 miles
12d + 7 = 91
12d = 91 - 7
12d = 84
d = 84/12
d = 7 miles per day
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