The required sample size for the confidence interval and given margin of error is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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Kevin got the following scores on his math tests this semester.
85, 94, 98, 88, 85, 92, 97, 81
What is his mean score so far?
ANSWERED
What score will Kevin need to get on his next test to raise his mean score to exactly 91?
Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
To find out what score Kevin will need to get on his next test to raise his mean score to exactly 91, we can use the formula for the mean:
mean = (sum of all scores) / (number of scores)
We know the current mean score is:
mean = (85 + 94 + 98 + 88 + 85 + 92 + 97 + 81) / 8
= 89.5
To raise the mean to 91, we can set up the equation:
(85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x) / 9 = 91
where x is the score Kevin needs to get on his next test.
Multiplying both sides of the equation by 9, we get:
85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x = 819
Simplifying, we get:
710 + x = 819
Subtracting 710 from both sides, we get:
x = 109
Therefore, Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.
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A firm has an unlevered cost of capital of 10 percent, a cost of debt of 9 percent, and a tax rate of 34 percent. If it desires a cost of equity of 14 percent, what must its target debt/equity ratio be
The required target debt/equity ratio is 0.5 or 1:2.
To calculate the target debt/equity ratio,
Use the following formula,
⇒ Target D/E Ratio = (Target Equity / Target Debt)
First, we need to calculate the weights of equity and debt in the firm's capital structure.
We can use the following formula,
Weight of Equity = Equity / (Equity + Debt)
Weight of Debt = Debt / (Equity + Debt)
Since the firm is unlevered,
its capital structure consists only of equity.
Therefore,
The weight of equity is 1 and the weight of debt is 0.
Now we can use the weighted average cost of capital (WACC) formula to find the firm's current cost of equity.
The WACC formula is as follows,
WACC = (Weight of Equity Cost of Equity)
+ (Weight of Debt Cost of Debt x (1 - Tax Rate))
Substituting the given values, we get:
⇒ 10% = (1 Cost of Equity) + (0 9% x (1 - 34%))
Solving for Cost of Equity, we get:
Cost of Equity = 10% - (0 9% (1 - 34%))
Cost of Equity = 10%
Since the firm desires a cost of equity of 14%,
we can set up an equation to solve for the target debt/equity ratio:
⇒ 14% = (1 / (1 + Target D/E Ratio)) 10% + ((Target D/E Ratio) / (1 + Target D/E Ratio)) 9% x (1 - 34%)
Simplifying the equation, we get:
⇒ 14% = 10% / (1 + Target D/E Ratio) + 0.0594 x Target D/E Ratio
Multiplying both sides by (1 + Target D/E Ratio), we get:
⇒ 0.14 + 0.14 Target D/E Ratio = 0.1 + 0.0594 Target D/E Ratio
Subtracting 0.0594 x Target D/E Ratio from both sides, we get:
⇒ 0.08 x Target D/E Ratio = 0.04
Dividing both sides by 0.08, we get:
⇒ Target D/E Ratio = 0.5
Therefore, the firm's target debt/equity ratio is 0.5 or 1:2.
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(PLEASE SHOW WORK EXPLAIN YOUR ANSWER!!!!)
After a party,Brad had leftover pizza. Brad had  1/2 of a cheese pizza . 3/4 of sausage pizza and 2/6 of a pepperoni pizza? How much leftover pizza did Brad have?
Part A: How much leftover pizza did Brad have?
Part B: Steve had 2/3 of a pizza how much more does bread have the Steven?
Part A:
To find out how much leftover pizza Brad had, we need to add up the fractions of each type of pizza:
1/2 cheese pizza + 3/4 sausage pizza + 2/6 pepperoni pizza
We can simplify the fractions by finding a common denominator:
1/2 = 3/6
3/4 = 4.5/6
2/6 = 2/6
Now, we can add the fractions:
3/6 + 4.5/6 + 2/6 = 9.5/6
This means Brad had 9.5/6 of a pizza leftover.
Part B:
Steve had 2/3 of a pizza. To compare this to Brad's leftover pizza, we need to convert Brad's leftover pizza to a fraction with the same denominator as 2/3:
9.5/6 = 9/6 + 0.5/6 = 3/2 + 1/12 = 19/12
Now we can compare:
19/12 - 2/3 = 38/12 - 8/12 = 30/12 = 2.5
This means Brad has 2.5 more pizzas than Steve.
The graph show the probability distribution of a
random variable.
What is the value of P(2 < X <5)?
O 0.30
O 0.35
O 0.40
O 0.45
0.3
0.25
0.2
0.15
0.1
0.05
1
Probability Distribution
2
3 4
S.
9.
N
B
The solution is : the value of P(2≤X≤5) is 0.50.
Here, we have,
given that,
The graph show the probability distribution of a random variable.
we know that,
The probability distribution of a random variable X is P(X = xi) = pi for x = xi and P(X = xi) = 0 for x ≠ xi. The range of probability distribution for all possible values of a random variable is from 0 to 1, i.e., 0 ≤ p(x) ≤ 1.
so, we have,
P(2≤X≤5)
=P(x=2)+ P(x=3)+ P(x=4)+ P(x=5)
= 0.2+ 0.1 +0.05+0.15
= 0.50
Hence, The solution is : the value of P(2≤X≤5) is 0.50.
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A ring was purchased in 2012 for $900the value of the ring increases by 7% each year, find the value of the ring in 2030. Round to the nearest cent
The value of the ring in 2030 would be; 2,034
Given that the Purchase price of the Diamond ring= $900
Value of ring increase by 7% each year.
First find a number of the year between 2012 and 2040,
Time period= 2030 - 2012
∴ Time period of value appreciation is 18 years.
Now, finding the value of a diamond ring increased after 28 years.
The value of ring increased after 18 years= 900 x 0.07 x 18
∴ Increased value of diamond ring after 18years= $1,134
Next, Value of diamond ring after 18 years= 1,134 + 900
Hence, value of a diamond ring in 2030 is $2,034
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Find the value of 20x when x = 10.
(a) 200
(c) 2
(b) 30
(d) 5
Last year, the Ross family spent $3,336 for electricity. They are opting to use balanced billing for next year. What will their monthly payment be?
Using balanced billing, the monthly payment is $278
What will be their monthly payment?Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.
Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:
Monthly payment = Total cost / Number of months
Monthly payment = $3,336 / 12
Monthly payment = $278
Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.
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A rectangular prism.
What are the shapes of the cross sections formed by a plane slicing the rectangular pyramid?
A plane intersects the pyramid parallel to its base. The cross section is a
._____
A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a
_________
A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle
A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:
Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.
Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.
It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.
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The arc length of a 330° sector is 33π. Find the area of the sector
The area of the sector is 297π units squared.
How to find the area of a sector?The arc length of a 330° sector is 33π. Therefore, let's find the area of the sector.
Let's find the radius of the circle.
length of arc = ∅/ 360 × 2πr
where
∅= central angler = radiusTherefore,
33π = 330 / 360 × 2π × r
cross multiply
660πr = 11880π
divide both sides by 660π
r = 11880π / 660π
r = 18 units
Therefore,
area of the sector = 330 / 360 × π × 18²
area of the sector = 106920 / 360 π
area of the sector = 297π units²
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Maurice ran 110 meters in 20.9 seconds. Yolanda ran 110 meters in 20.0 seconds. Who had the fastest time, Maurice or Yolanda?
A.Yolanda
B.Maurice
apex
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.
What are the measure of angels 1 to 8
Let's just compare the angles to start - - - these are two parallel lines cut by another line (transversal), so there are a lot of equal angles.
Angles 1 and 5 are the same
Angles 2 and the 65 degree angles are the same.
Angles 4 and 8 are the same.
And 3 and 7 are the same.
There are even more similar angles:
1 and 3 are the same. 2 and 4 are the same.
5 and 7 are the same, and 8 and the 65 degree angle are the same.
So without any math, Angles 2, 4 and 8 are all 65 degrees.
So Angle 65 + Angle 5 = 180. Therefore Angle 5 = 115.
Therefore angle 7 is 115. (You could also say that 65+ Angle 7 = 180.)
Since angle 7 is 115, so is angle 3 and angle 1.
So in conclusion
Angle 1: 115
Angle 2: 65
Angle 3: 115
Angle 4: 65
Angle 5: 115
Angle 7: 115
Angle 8: 65
What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]
[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]
[tex]\sf V = \dfrac{433.44 }{3}[/tex]
[tex]\sf V = 144.48 \ cubic \ feet[/tex].
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
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Which of the following is a difference of perfect squares?
A). x^2+4
B). 9x^2-100
C). x^2-18
D). 4x^2+36
SECTION B - Skills Analysis Question 8 Use the diagram to determine the sum of the series 1 + 3 + 5 + 7 + ... + (2n-1) in terms of n. Show your reasoning and explanation fully. n : [4]
Answer:
weel you have to start by addition of tose numbers and after you're done with the addition if the numbers you do 2n-1 which is equal to n so you use this formula to solve it hope this helps
Ravi has two and one-fourth meters of rope. He gives ninety-three centimeters of the rope to his brother. How many centimeters of rope does Ravi have left?
If he gives ninety-three centimeters of the rope to his brother, Ravi has 132 centimeters of rope left.
Two and one-fourth meters of rope can be written as 2.25 meters. Since 1 meter is equal to 100 centimeters, we can convert 2.25 meters to centimeters by multiplying it by 100, giving us 225 centimeters.
If Ravi gives 93 centimeters of the rope to his brother, we can subtract it from the original length to find how much rope he has left.
225 cm - 93 cm = 132 cm
In general, to convert between meters and centimeters, you can multiply the number of meters by 100 to get the length in centimeters. To convert between centimeters and meters, you can divide the number of centimeters by 100 to get the length in meters.
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HELP PLEASE DUE IN 10 MIN
The correct statement regarding the measure of variability used to represent the data is given as follows:
The IQR of 10 is the most accurate to use, as the data is skewed.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.
The charity received 18 donations, hence the quartiles are given as follows:
First quartile: 0.25 x 18 = 4.5th element = median of 10 and 15 = 12.5.Third quartile: 0.75 x 18 = 13.5th element = median of 20 and 25 = 22.5.Hence the IQR is given as follows:
IQR = 22.5 - 12.5
IQR = 10.
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graphing stuff needs done soon
The value of x in each equation is:
a) x = -1
b) x = 3
c) x = 3
d) x = 9
e) x = -45
We have,
Substitute y = 2 in each equation.
a)
y = 6x + 8
2 = 6x + 8
2 - 8 = 6x
-6 = 6x
x = -1
b)
y = 2/3 x
2 = 2/3 x
x = 3
c)
y = -x + 5
2 = -x + 5
2 - 5 = -x
-3 = -x
x = 3
d)
y = 3/4 x - 2(1/2)
2 = 3/2 x - 5/2
2 + 5/2 = 3/2 x
9/2 = 3/2 x
x = 9
e)
y = 1.5 x + 11
2 = 1/5x + 11
2 - 11 = 1/5 x
-9 = 1/5 x
x = -45
Thus,
The value of x in each equation is:
a) x = -1
b) x = 3
c) x = 3
d) x = 9
e) x = -45
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There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people didn't use any facilities?
8 people didn't use any of the gym pool or track facilities.
The number of people use any facilities need to subtract the total number of people who used at least one facility from the total number of people in the sport centre.
The total number of people who used at least one facility by adding the number of people who used each facility and subtracting the number of people who used two facilities and three facilities:
Total = Gym + Pool + Track - (Gym and Pool) - (Pool and Track) - (Gym and Track) + (Gym and Pool and Track)
Total = 77 + 62 + 65 - 27 - 23 - 31 + 4
Total = 127
The number of people who didn't use any facilities is:
135 - 127 = 8
8 people didn't use any of the gym, pool or track facilities.
The number of individuals who did not utilise any facilities must be subtracted from the total number of individuals who utilised at least one facility.
The total number of individuals who utilised at least one facility is calculated by adding the individuals who utilised each facility and deducting the individuals who utilised two and three facilities:
Total = Fitness Centre + Pool + Track - Fitness Centre and Pool - Fitness Centre and Track - Fitness Centre and Pool and Track
Total = 77 + 62 + 65 - 27 - 23 - 31 + 4
Total = 134-127
= 8
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When Mrs Munyai wanted to swim in her new pool, the temperature of the wate 19 °C and she said she would only swim if the temperature of the water was 25 °C temperature must increase by 6 °C. Calculate what the temperature change would be in °F. You may use the following formula: (°F-32) ÷ 1,8 = °C +
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
The formula to convert the temperature from Celcius to Fahrenheit is:
[tex]\textdegree F = (\textdegree C * 1.8) + 32[/tex]
We need to calculate the temperature change of [tex]6 \textdegree C[/tex] in Fahrenheit:
[tex]\Delta \textdegree C = 6\\\Delta \textdegree F = \Delta \textdegree C * 1.8 = 10.8[/tex]
The temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
We can calculate the Fahrenheit temperature of the water and the desired temperature in Fahrenheit:
[tex]^{\circ}C = 19\\^{\circ}F = (19 * 1.8) + 32 = 66.2[/tex]
[tex]^{\circ}C = 25\\^{\circ}F = (25 * 1.8) + 32 = 77[/tex]
The current temperature of the pool is [tex]66.2 ^{\circ} F[/tex] and the desired temperature is [tex]77 ^{\circ} F[/tex].
Therefore the temperature needs to be increased by:
[tex]\Delta ^{\circ}F = 77 - 66.2 = 10.8 ^{\circ}F[/tex]
which is the same temperature change we calculated earlier in Fahrenheit.
Therefore, the temperature needs to be increased by [tex]10.8 ^{\circ}F[/tex] for Mrs. Munyai to swim in the pool.
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What the surface area
Step-by-step explanation:
the surface area is the sum of all areas of the individual outside faces/sides.
so, what do we see here, what outside sides do we have here ?
of course, we have to assume that this is a regular object (left and right sides are the same).
2 right-angled triangles (left and right).
1 rectangle in the back.
1 rectangle at the bottom.
1 times rectangle in the front.
the area of a right-angled triangle is
leg1 × leg2 / 2
in our case that is
6 × 2.5 /2 = 3 × 2.5 = 7.5 mm²
we have 2 of these triangles :
2×7.5 = 15 mm²
the area of the rectangle in the back is
8 × 6 = 48 mm²
the area of the rectangle at the bottom is
8 × 2.5 = 20 mm²
the area of the rectangle in the front is
8 × 6.5 = 52 mm²
the surface of the object is the sum of all that :
15 + 48 + 20 + 52 = 135 mm²
Leigh designs and conducts a computer simulation with 30 trials and uses the data from the stimulation to create the relative frequency bar graph shown. The graph shows the relative frequency of the number of spins needed for a spinner divided into 6 equal sections labeled A through F on each letter at least once
The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%
How to explain the probabilityExperimental probability is a type of probability that is based on actual observations or experiments.
In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.
In this case, experimental probability = number of times the event occurred / total number of trials
Experimental probability = 0.1 + 0.35 + 0.3 / 1
= 0.75 / 1
= 75%
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If 3² + 4² = c², then c equals
Answer:
The answer is 5
Step-by-step explanation:
c²=3²+4²
c²=9+16
c²=25
[tex] \sqrt{ {c}^{2} } = \sqrt{25} [/tex]
c=5
The value of c is :
↬ c = 5, c = -5
Solution:
First off, we should square the numbers:
[tex]\sf{3^2+4^2=c^2}[/tex]
[tex]\sf{9+16=c^2}[/tex]
[tex]\sf{25=c^2}[/tex]
Now I square-root each side :
[tex]\sf{5=c}[/tex]
[tex]\sf{-5=c}[/tex]
This means that :
[tex]\sf{c=5,\:c=-5}[/tex]
How did this happen? We should know that once we take the square root of a number, we end up with two solutions that are opposites of each other. This phenomenon is explained below.
When we square 5, we get 25. When we square -5, we also get 25.
So then, when taking the square root of 25, we get both 5 and -5. And now, we know why.
Hence, c = 5 and c = -5.50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
Polygon D is similar to polygon ABCD.
I’ll give brainliest pls help me my future is in risk rn.
Both containers hold the same amount of water.
Given are two solid figures, we need to compare which of them holds more water,
The container one has a base dimension of 3 ft × 180 in with height 90 in. and the second container has base dimension of 3 ft × 180 in with height 90 in.
To compare which container holds more water, we can calculate the volume of each container.
For consistency, let's convert all measurements to a single unit.
1 foot is equal to 12 inches, so the base dimensions of both containers can be expressed as
3 ft × (180 in + 3 ft × 12 in/ft) = 3 ft × 216 in
= 648 in × 648 in.
The volume of a container is calculated by multiplying the base area by the height.
Therefore, the volume of each container can be determined as follows:
Container 1:
Volume = Base area × Height
Volume = (648 in × 648 in) × 90 in
Container 2:
Volume = Base area × Height
Volume = (648 in × 648 in) × 90 in
Since the base dimensions and the height are identical for both containers, their volumes will also be the same.
Therefore, both containers hold the same amount of water.
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Rachel has discovered the perfect recipe for icing that she wants to put on top of her cinnamon buns. The recipe calls for 5 tablespoons (tbsp) of sugar for every 2 teaspoons (tsp) of milk. Rachel already made her cinnamon buns and is ready to put on the icing. She has 7 teaspoons of milk for her next batch. How many tablespoons of sugar does she need?
Answer:
Step-by-step explanation:
Rachel already has 7 teaspoons of milk.
so 7 x 5 = 35
So Racheal will need 35 teaspoons of surger.
What is 50% of half of 10?
Answer:
2.5
Step-by-step explanation:
half of 10 is 10/2 = 5
so 50% of 5 is 2.5
need help with edualastic question answer a b c or d
the amount of cubic feet(Volume) the tent can hold is 165 ft³.
What is volume?Volume is the space occupied by an object.
To caculate the amount of cubic feet(Volume), the tent can hold, we use the formula below.
Formula:
V = bhL/2..................... Equation 1Where:
V = Volume of the tenthb = Base of the triangleh = Height of the triangleL = Height of the tentFrom the question,
Given:
b = 5 fth = 6 ftL = 11 ftSubstitute these values into equation 1
V = 5×6×11/2V = 165 ft³Hence, the right option is (A) 165 ft³.
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f(x) = (x − a) (x − b)
f(x) = (x − a) (x −b) (x-c)
Describe the relationship between these equations and
their graphs.
The relationship between graph of functions is described below.
Since we can see that,
Both equations are quadratic functions, meaning that their graphs are parabolic.
The first equation,
f(x) = (x - a)(x - b),
It represents a parabola that opens upwards or downwards depending on the values of a and b.
If a < b,
the parabola opens upwards,
and if a > b, it opens downwards.
To graph f(x),
we can first find its x-intercepts by setting f(x) = 0,
⇒ 0 = (x - a)(x - b)(x - c)
This gives us three x-intercepts,
⇒ x = a, x = b, and x = c.
The value of c is important because it determines the direction in which the parabola opens.
If c is greater than both a and b,
the parabola opens upwards, and if c is less than both a and b,
the parabola opens downwards.
If c is between a and b, the parabola has a minimum or maximum point.
Now, we can find the y-intercept by setting x = 0,
⇒ f(0) = (0 - a)(0 - b)(0 - c) = -abc
This tells us that the y-intercept is -abc.
To graph the parabola, we can plot the x-intercepts and the y-intercept, and then use the shape of the parabola to connect the points.
If the parabola opens upwards, it will have a minimum point at the vertex, and if it opens downwards, it will have a maximum point.
The second equation, f(x) = (x - a)(x - b)(x - c),
represents a cubic function,
meaning that its graph is a curve with either a local minimum or maximum.
To graph f(x), we can use the same process as above to find the x-intercepts and y-intercept, and then use the shape of the curve to connect the points.
After plotting can see, the cubic function has two local minima and one local maximum.
It also has a point of inflection at x = (a + b + c)/3.
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Sam is training for a 5
km run. While training he runs for 6
minutes, then rests for 2
minutes, runs for 6
minutes, rests for 2
minutes, etc., until he finishes the 5
km. It takes him 26
minutes in total (with the rest periods) to finish the 5
km rum. If Sam runs at a constant speed (when he is not resting), what is this speed in kilometers per hour? (Recall there are 60
minutes in 1
hour.)
Answer:
15 km/h
Step-by-step explanation:
How many intervals of running and resting are needed to run and rest for 26 minutes?
Running is in parentheses, resting is not.
Each time he runs (6 minutes) and rests (2 minutes), he takes 8 minutes.
Three times this cycle is 24 minutes. He needs 2 more minutes of running to have a total of 26 minutes.
(6) + 2 + (6) + 2 + (6) + 2 + (2)
Add all the numbers in parentheses which are the times of running.
6 + 6 + 6 + 2 = 20
He ran for 20 minutes and rested for 6 minutes.
He ran 5 km in 20 minutes (of running).
speed = distance/time
speed = [5 km / (20 minutes)] × (60 minutes)/(1 hour)
speed = 15 km/h
Answer: 15 km/h
There are approximately as many boys between 167 and 169 as there are between 169 and 170. True False
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
In statistics, understanding and interpreting data is an essential skill. One way to interpret data is by analyzing the distribution of values within a certain range.
To determine whether the statement is true or false, we need to analyze the distribution of boy's heights between the two ranges. Assuming the heights of boys are normally distributed, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of boys within each range.
The empirical rule states that in a normal distribution:
68% of the values fall within one standard deviation of the mean
95% of the values fall within two standard deviations of the mean
99.7% of the values fall within three standard deviations of the mean
We can use this rule to estimate the percentage of boys within each range as follows:
Between 167 and 169: This range is one standard deviation below the mean. Therefore, approximately 68% of boys' heights fall within this range.
Between 169 and 170: This range is between one and two standard deviations below the mean. Therefore, approximately 27% of boys' heights fall within this range.
Based on this analysis, we can see that there are not approximately as many boys between 167 and 169 as there are between 169 and 170. In fact, there are significantly more boys between 167 and 169 than there are between 169 and 170.
The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.
To know more about Normal Distribution here
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