Answer:
Step-by-step explanation:
A circle has an area of 45 square meters. What is the area of a sector with an arc measure of 70 degree?
______m^2
The area of a sector is 8.75 [tex]m^{2}[/tex].
What is a sector?A sector is a part of a given circle which is bounded by two radii and an arc. The area of a sector can be determined by;
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
where r is the radius, and θ is the central angle.
Given a circle whose area is 45 sq. m.; then;
area of a circle = π[tex]r^{2}[/tex]
45 = π[tex]r^{2}[/tex]
r = [tex]\sqrt{\frac{45}{\pi } }[/tex]
Then,
area of a sector = (θ/ 360)π[tex]r^{2}[/tex]
= ([tex]\frac{70}{360}[/tex])*π*[tex][\sqrt{\frac{45}{\pi } }] ^{2}[/tex]
= [tex]\frac{7}{36}[/tex]*π*45/π
= [tex]\frac{7}{36}[/tex]*45
= 8.75 sq. m.
The area of the sector is 8.75 [tex]m^{2}[/tex].
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A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
The volume of this rectangular prism is equal to: B. 8 in³.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.Since this rectangular prism is filled with 16 cubes and each cube is a 1/2 inch cube, the dimensions of the rectangular prism is given by;
Dimensions = 16 × (1/2)³ = 2inches.
By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 2 × 2 × 2
Volume of rectangular prism = 8 cubic inches.
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Complete Question:
A rectangular prism is filled with 16 cubes. Each cube is a 1/2 inch cube. What is the volume of the rectangular prism?
A. 2 in³
B. 8 in³
C. 16 in³
D. 32 in³
Find the sum of x+9 and 7x^- 2x+1.
The sum of given two expressions x+9 and 7x²-2x+1 results in the expression 7x² - x + 10.
To find the sum of two expressions, we simply add their like terms.
The given expressions are x+9 and 7x²-2x+1.
The first expression has two terms - x and 9.
The second expression has three terms - 7x², -2x, and 1.
We cannot add the terms of the two expressions directly since they are not like terms. However, we can simplify the expressions and then add the like terms.
First, we can simplify the second expression by combining the like terms -2x and 1.
7x² - 2x + 1 = 7x² - (2x - 1)
Now, we can add the like terms from both expressions.
(x + 9) + (7x² - 2x + 1) = x + 7x² - (2x - 1) + 9
= 7x² - x + 10
Note that we could also have added the two expressions without simplifying the second expression first. We would get the same result.
(x + 9) + (7x² - 2x + 1) = x + 7x² - 2x + 9 + 1
= 7x² - x + 10
In either case, the final answer is 7x² - x + 10.
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Help is appreciated!
Answer:
Snacks: $75
Alcohol: $200
Dairy: $300
Average delivery charge per week: $63.89 (rounded to two decimal places)
Step-by-step explanation:
To find the average delivery charge the store pays each week, first calculate the total delivery cost for each category and then find the total cost for all deliveries. Finally, divide the total cost by the total number of deliveries.
Snacks:
3 deliveries * $25 per delivery = $75
Alcohol:
2 deliveries * $100 per delivery = $200
Dairy:
4 deliveries * $75 per delivery = $300
Total cost for all deliveries:
$75 (Snacks) + $200 (Alcohol) + $300 (Dairy) = $575
Total number of deliveries:
3 (Snacks) + 2 (Alcohol) + 4 (Dairy) = 9
Average delivery charge per week:
$575 (total cost) / 9 (total number of deliveries) = $63.89 (rounded to two decimal places)
Determine the equation of the circle graphed below.
The equation of the circle graphed is (x + 4)^2 + (y + 5)^2 = 16
Determining the equation of the circle graphedFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (-4, -5)
Radius, r = 4 units
The equation of the circle graphed is represented as
(x - a)^2 + (y - b)^2 = r^2
So, we have
(x + 4)^2 + (y + 5)^2 = 4^2
Evaluate
(x + 4)^2 + (y + 5)^2 = 16
Hence, the equation is (x + 4)^2 + (y + 5)^2 = 16
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Please help me I am stuck at this thanks so much
Answer:
34.83/.9 = 38.7 g mass (after one hour)
38.7/.9 = 43 g (starting mass)
The starting mass of the ice cube was 43 grams.
complete the following table , what’s C, AC, BC
Answer:
C = 45
AC = 1
BC = 2
Step-by-step explanation:
C: 180 - (90 + 45) = 45
AC: Because the angles are the same, it is equal to the other leg, 1 cm
BC: a^2 + b^2 = c^2, so 1 + 1 = 2
Someone help please! I’m taking a test and just need some assistance
Answer: Given b=2√14 and c=9,
a = 5
Step-by-step explanation:
Identify parallelograms, rectangles and squares
Answer:
figure A = square ( All sides are equal)
figure B = Rectangle (Two sides are equal)
Figure C = parallelogram (is a four-sided polygon (a quadrilateral) in which opposite sides are parallel and equal in length)
The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist entirely of boys?
0.2
0.04
0.33
0.02
The required experimental probability that a team will consist entirely of boys is 0.04. Option B is correct.
To find the experimental probability that a team will consist entirely of boys, we need to count the number of trials in which all three coin tosses resulted in tails (which represents a team consisting entirely of boys), and divide by the total number of trials (which is 50).
From the data, we can see that there are only 2 trials where all three coin tosses resulted in tails, so the experimental probability of a team consisting entirely of boys is:
2/50 = 0.04
Therefore, the experimental probability that a team will consist entirely of boys is 0.04.
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The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
For which distribution is the mode the best measure of center?
A. Skewed
B. Normal
C. Biomodal
Answer:
The mode is the best measure of center for a distribution that is bimodal, meaning that it has two peaks. In such a distribution, the mean and median may not be representative of the center of the data, but the mode is a good measure of center because it reflects the most common value(s) in the data.
For skewed distributions, the mode may not be a good measure of center because the peak of the distribution is not necessarily at the center of the data. In a normal distribution, the mean, median, and mode are all equal and are good measures of center.
For many years, businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent survey showed that 52% of employers are likely to require higher employee contributions for health care coverage this year relative to last year. Suppose the survey was based on a sample of 900 companies likely to require higher employee contributions for health care coverage this year relative to last year.
1. At 95% confidence, compute the margin of error for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answer to four decimal places.)
2. Compute a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage. (Round your answers to four decimal places.)
The margin of error for the proportion of companies likely to require higher employee contributions for health care coverage is 0.0344. The 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage is ( 0.4823, 0.5577.).
To compute the margin of error for the proportion, we use the formula:
Margin of error = z*√((P(1-P))/n)
where z is the z-score for the desired confidence level (95% confidence corresponds to a z-score of 1.96), P is the sample proportion, and n is the sample size. From the information given, we have
P = 0.52 (sample proportion)
n = 900 (sample size)
z = 1.96 (for 95% confidence level)
Substituting these values into the formula, we get
Margin of error = 1.96√((0.52(1-0.52))/900) ≈ 0.0344
Therefore, the margin of error is approximately 0.0344, or 3.44%.
To compute the confidence interval, we use the formula:
Confidence interval = P ± z*(√((P(1-P))/n))
where P, z, and n are the same as in part 1. Substituting these values into the formula, we get
Confidence interval = 0.52 ± 1.96*(√((0.52*(1-0.52))/900)) ≈ (0.4823, 0.5577)
Therefore, we can say with 95% confidence that the true proportion of companies likely to require higher employee contributions for health care coverage this year relative to last year is between 0.4823 and 0.5577.
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1/3 divided by 2/9 simplified?
Answer:3/2
Step-by-step explanation:
1/3 ÷ 2/9=
1/3 ×9/2=3/2
Answer:
3/2 u can also do 1 1/2 their equivalent fractions
Step-by-step explanation:
sorry about the handwriting :) not the best
Write an equation for a parabola with vertex (1,8) and directrix y = 3.
i Got u Bro!
Ov=zo « = 192 +8 5 Or = 1/2 (x + 2)² – 8 20 Ov=« 2)2-4 DELL.
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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Select the correct answer.
What are the zeros of g(x) = x³ + 6x² - 9x-54?
A. 1, 2,27
B.3, -3, -6
C.-6, 3, 6
D. 2, -1, 18
Answer:
The answer is C
Step-by-step explanation:
The zeros of g(x) = x³ + 6x² - 9x-54 are -6, 3, 6. Therefore, the correct answer is C.
Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 24, 32, and 40 and a second triangle labeled D prime with side lengths of 6, 8, and 10 Determine the scale factor used. Scale factor of one half Scale factor of 4 Scale factor of 2 Scale factor of one fourth
The scale factor used is 1/4.
We have,
Length of sides of triangle D 24, 32, and 40.
Length of sides of triangle D' 6, 8, and 10.
So, scale factor
= length of corresponding side in D' / length of corresponding side in D
= 6/24
= 1/4
Thus, the scale factor used is 1/4.
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a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.
Represent a⃗ +b⃗ by using the head to tail method.
Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.
To use the Vector tool, select the initial point and then the terminal point.
The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,
a + b = < 3, -5 >
The graph of the vector sum is given below.
The addition of vectors suggests the addition of the corresponding components of the involving vectors.
Given the vectors are:
a = < 4, - 3 >
b = < - 1, - 2 >
So doing vector addition we get,
a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>
Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.
Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,
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Answer: Look at the image below
Step-by-step explanation: I took the test.
Step 1: Select Vector
Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)
Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)
Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)
Your answer should now look like mine, now go get that A.
Simplify each of the following exponential expressions. a. 7⁴= ? b. (–10)⁴= ? c. 5¹ = ? d. 0⁴= ? e. –6²= ? f. –3⁰= ?
The exponential expressions when simplified are 2401, 10000, 5, 0, 36 and 1
Simplifying each of the exponential expressionsFrom the question, we have the following parameters that can be used in our computation:
The exponential expressions a to f
The general rule is that
a^b = a * a * a..... in b places
Using the above as a guide, we have the following:
a. 7⁴ = 7 * 7 * 7 * 7 = 2401
b. (–10)⁴ = (–10) * (–10) * (–10) * (–10) = 10000
c. 5¹ = 5
d. 0⁴ = 0 * 0 * 0 * 0
e. –6² = -6 * -6 = 36
f. –3⁰ = 1
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a. Find x. The figure is not drawn to scale. b. Is the triangle equilateral, isosceles, or scalene? Explain.
*
0 points
Captionless Image
Answer: Based on the given figure above, we can conclude that the triangle is an isosceles triangle. By definition, an isosceles triangle is a triangle that has at least two equal sides. Since this is an isosceles triangle, 8x-10 =6x. Now we can solve for x. So,
8x-10 =6x
8x-6x = 10
2x =10
x= 5.
Therefore, the value of x in the figure is 5. Hope this is the answer that you are looking for.
Please im begging someone please help me this is so hard. If you help me ill give you 60 points. PLEASE ILL GIVE BRAINLIEST
Answer: B, C, D
Step-by-step explanation:
Looking at the parabola, this is a width vs area graph.
A) Incorrect. the greatest possible area is not 10. Area goes higher
B) True. The highest possible area, highest point for area is 100
C) True. The area is 0 when width is 0
D)True. The area is also 0 when the width is 20
Point A is at 0 radians with coordinates (1,0) on the unit circle. Point B is the result of point A rotating 7 pie/6 radians counterclockwise
around the unit circle. Name two other positive angles of rotation that take A to B.
Answer:
19π/6 radians and 31π/6 radians
Step-by-step explanation:
To rotate point A counterclockwise by 7π/6 radians, we can add this angle to the angle of point A, which is 0 radians, to get the angle of point B:
The angle of point B = angle of point A + 7π/6 radians
= 0 radians + 7π/6 radians
= 7π/6 radians
Angle of point B in degrees = (7π/6) * (180/π) degrees
= 210 degrees
To find two other positive angles of rotation that take A to B, we can add any multiple of 2π radians to the angle of point B. This is because adding 2π radians is equivalent to a full rotation around the unit circle, which brings us back to the same point. Therefore, we have:
angle of rotation 1 = angle of point B + 2π radians
= 7π/6 radians + 2π radians
= 19π/6 radians
angle of rotation 1 in degrees = (19π/6) * (180/π) degrees
= 285 degrees
angle of rotation 2 = angle of point B + 4π radians
= 7π/6 radians + 4π radians
= 31π/6 radians
angle of rotation 2 in degrees = (31π/6) * (180/π) degrees
= 465 degrees
So the two other positive angles of rotation that take A to B are (19π/6 radians and 31π/6 radians) or 285 degrees and 465 degrees respectively.
Note:
To convert the angles from radians to degrees, we can use the conversion factor:
1 radian = 180/π degrees
Mathematics
Find the rate
What percent of 200 is 50?
What percent of 50 is 40?
What percent of 10 is 6?
200 is what percent of 200?
What percent of 800 is 200?
Show your solution, HELP PLS ASAP!!!
I'LL GIVE 20 POINTS!!
Answer:
Step-by-step explanation:
25%
80%
60%
100%
25%
Question 3 of 5
What is the median of the data set?
7, 9, 11, 14, 18, 20, 30, 35
Answer:
16
Step-by-step explanation:
To find the median, we find the middle of the data set.
7, 9, 11, 14, 18, 20, 30, 35
There are 8 values
7, 9, 11, 14, 18, 20, 30, 35
The median is between the 4th and 5th numbers
We need to find the mean of the middle two numbers
(14+18)/2 =32/2= 16
Answer:
16
Step-by-step explanation:
Median means the middle term in a data set.Remember that, you have to arrange the data points from smallest to largest to find the median of a data set.The formula to find the median of a data set is:[tex]\sf (\frac{n+1}{2}\:)^ t^h \:data[/tex]
Here,
n ⇒ number of terms
Let us find it now.
7, 9, 11, 14, 18, 20, 30, 35
[tex]\sf Median=\sf (\frac{n+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf (\frac{8+1}{2}\:)^ t^h \:data\\\\\sf Median=\sf 4.5^ t^h \:data[/tex]
In this case, add 4th and 5th data and divide it by 2.
[tex]\sf Median = \frac{14+18}{2}\\\\ \sf Median = \frac{32}{2}\\\\\sf Median = 16[/tex]
CAN SOMEONE HELP WITH THIS QUESTION?
The number of cars that pass through the intersection between 6 am and 10 am is 4800.
To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].
Integrating r(t) with respect to t, we get:
∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C
where C is the constant of integration.
Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:
(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars
In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.
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marcus deposits $500 in an account that pays 6.8% simple annual interest. if he keeps the money in the account for 5 years how much interest will he earn
Marcus will earn $170 in interest after keeping his $500 in the account for 5 years.
To calculate the interest Marcus will earn, we can use the formula:
I = P * r * t
where I is the interest earned, P is the principal amount deposited, r is the annual interest rate as a decimal, and t is the time period in years.
In this case, Marcus deposited $500 and the annual interest rate is 6.8%, which is 0.068 as a decimal. He kept the money in the account for 5 years.
So we can plug in these values into the formula:
I = 500 * 0.068 * 5
I = $170
This is simple interest, which means that the interest is only earned on the original principal amount and not on any accumulated interest.
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What is the domain of the function shown on the graph?
Answer:
A
Step-by-step explanation:
the domain is the values of x covered by the graph
on the left the graph → - ∞
on the right the graph tends to + ∞
there are no excluded values of x on the domain , so
domain is - ∞ < x < ∞
Find the length of each segment.
Answer:
1. 30; 2. 6.25.
Step-by-step explanation:
1. CE:CF=FD:DG; ⇒ 32/24=40/DG; ⇒ DG=30;
2. PQ:QM=RN:RM; ⇒ 5/8=RN/10; ⇒ RN=6.25.
The table below shows different possibilities for the number of games a team would
need to win to maintain a certain percentage of wins.
A 18 20
B 30 20
POSSIBLE BASEBALL
GAMES WON
C 18 30
D 50 30
Number of
Games Won
6
24
36
42
Which ratio of the number of games won to the number of games played could also be
included in this table?
Number of
Games Played
10
40
60
70
The ratio that could also be included in this table is (c) 18 : 30
Calculating the ratio that could also be included in this table?From the question, we have the following parameters that can be used in our computation:
Games won Games played
6 10
24 40
36 60
42 70
From the above, we have the ratio of the number of games won to the number of games played to be
Ratio = 6 : 10
Simplify
Ratio = 3 : 5
From the options, we have
(c) 18 : 30
Simplify
Ratio = 3 : 5
Hence, the ratio that could also be included in this table is (c) 18 : 30
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