How do the expressions y=7x3+2 and y=11x3+2 differ?
Answer: A
Step-by-step explanation:
16. The population of the United States in July of 2000 was 282.2 million people. A year later in July of 2001
the population was 284.8 million.
Find an exponential model, in the form of P(t)= a(b)', that models the population of the United States in
millions of people. The variable t represents the number of years since July of 2000. Round your value of b
to the nearest thousandth.
Step-by-step explanation:
284.8 = 282.2 ( b)^1 1 is the number of years....looking for 'b'
284.8 / 282.2 = b = ~ 1.009
P(t) = 282.2 ( 1.009)^t where P(t) is in millions and :
The variable t represents the number of years since July of 2000. Round your value of b to the nearest thousandth.
The height, h, in feet of a ball suspended from a spring as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction pi Over 2 EndFraction (t + 2)) + 5. Which of the following is the graph of this equation?
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (2, 8), and then decreases to (6, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 8). It decreases to (4, 2), and then increases to (8, 8).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It increases to (1, 8), and then decreases to (3, 2).
On a coordinate plane, a curve crosses the y-axis at (0, 5). It decreases to (2, 1), and then increases to (3, 8).
The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2). The graph of the equation, shown below.
What is the term graph means?The term "graph" can refer to a visual representation of data or information, typically in the form of a diagram or chart. Graphs can be used to show relationships or patterns between different sets of data.
For the given equation,
[tex]h=3Sin [\frac{\pi }{2} (t+2)] +5[/tex]
Follow the steps for drawing the graph,
Choose a range of values for t that we want to graph. Since the period of the oscillation is 2 seconds, we can choose a range of t values that spans one or more full periods of the oscillation.Substitute each t value into the equation to find the corresponding h value. For example, when t = 0,[tex]h = 3 Sin [\frac{\pi }{2} (0 + 2)] + 5 = 3 Sin [\pi] + 5 = 5[/tex]
This means that when the ball is at the midpoint of its oscillation (i.e., at time t = 0), its height is 5 feet above the equilibrium position.
Plot the (t, h) pairs as points on a graph, with t values on the x-axis and h values on the y-axis.Connect the plotted points with a smooth curve to create the graph of the equation.The coordinate plane of curve crosses the y-axis at (0, 5), it increases to (2, 8), and then decreases to (6, 2).Using these steps, we can create the graph of the equation, which looks like the below diagram.
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Verify the following identities
Answer:
See below for proof.
Step-by-step explanation:
Use the following trigonometric identities to verify the given identities:
[tex]\boxed{\cot(x)=\dfrac{\cos(x)}{\sin(x)}}[/tex]
[tex]\boxed{\sec(x)=\dfrac{1}{\cos(x)} \implies \cos(x)=\dfrac{1}{\sec(x)}}[/tex]
[tex]\boxed{\tan(x)=\dfrac{\sin(x)}{\cos(x)}}[/tex]
[tex]\boxed{\sin^2(x)+\cos^2(x)=1 \implies \cos^2(x)=1-\sin^2(x)}[/tex]
Question a)[tex]\begin{aligned}\dfrac{1}{\sin(x)\cot(x)}&=\dfrac{1}{\sin(x) \cdot\frac{\cos(x)}{\sin(x)}}\\\\&=\dfrac{1}{\frac{\sin(x)\cos(x)}{\sin(x)}}\\\\&=\dfrac{\sin(x)}{\sin(x)\cos(x)}\\\\&=\dfrac{1}{\cos(x)}\end{aligned}[/tex]
Question b)[tex]\begin{aligned}\sec(x)-\tan(x)\sin(x)&=\dfrac{1}{\cos(x)}-\dfrac{\sin(x)}{\cos(x)} \cdot \sin(x)\\\\&=\dfrac{1}{\cos(x)}-\dfrac{\sin^2(x)}{\cos(x)}\\\\&=\dfrac{1-\sin^2(x)}{\cos(x)}\\\\&=\dfrac{\cos^2(x)}{\cos(x)}\\\\&=\cos(x)\\\\&=\dfrac{1}{\sec(x)}\end{aligned}[/tex]
HELP!!!! I NEED AN ANSWER QUICK!!! WILL MARK BRAINLIEST!!!!
the surface area of the cylinder is 420 in^2. what is its base area ? use 3.14 for pie and round the answer to the nearest hundredth.
The surface area of the cylinder is 420 in^2. The base area of the cylinder is 67.02 in².
Given that the surface area of the cylinder is 420 in², we have to find its base area.
To find the base area of the cylinder, we have to use the formula for the surface area of the cylinder.
The formula is:
Surface area of the cylinder = 2πr(r + h)
Here, π = 3.14,
r is the radius of the base of the cylinder, and h is the height of the cylinder.
Since the base is a circle, the area of the base is given by the formula:
A = πr²We can calculate the radius of the cylinder using the given surface area.
420 = 2πr(r + h)420
= 2 × 3.14 × r(r + h)420
= 6.28 r² + 6.28 rh
Now we need to assume some value of h. For example, if we take h = 7, then we have:
420 = 6.28 r² + 6.28 r (7)
420 = 6.28 r² + 43.96 or
6.28 r² + 43.96 r - 420 = 0
Now we can solve this quadratic equation to find the value of r. Using the quadratic formula:
r = [-b ± sqrt(b² - 4ac)] / 2a
Putting a = 6.28, b = 43.96, and c = -420, we get:
r = [-43.96 ± sqrt(43.96² + 4(6.28)(420))] / 2(6.28)
r = [-43.96 ± sqrt(3291.84)] / 12.56r = (-43.96 + 57.40) / 12.56 or
r = (-43.96 - 57.40) / 12.56r = 1.10 or r = -1.82
We can discard the negative value of r, so we have:r = 1.10
Now we can calculate the base area of the cylinder using the formula for the area of a circle.A = πr²A = 3.14 × (1.10)²A = 3.14 × 1.21A = 3.80 (rounded to the nearest hundredth)
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Find value of x in simplest form
The value of x in its simplest form is x = 67√2 = 94.75.
What is sine function?The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilise the sine function. The ratio between the side perpendicular to the angle and the hypotenuse is known as the sine of an angle in a right-angled triangle.
The relation between the opposite side and the hypotenuse is given by the sine function.
Thus,
sin (45) = opposite side / hypotenuse = 67 / x
1 / √2 = 67/x
x = 67√2 = 94.75
Hence, the value of x in its simplest form is x = 67√2 = 94.75.
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An African elephant weighs 5,500 pounds. How many ounces is that?
An African elephant weighs 88,000 ounces. To convert pounds to ounces, we need to know the conversion factor between the two units.
There are 16 ounces in one pound, which means we can convert pounds to ounces by multiplying the weight in pounds by 16. A pound is equal to 28 grams. A one-quarter ounce contains seven grams. A half-ounce has 14 grams in it. One-eighth of an ounce has 3.5 grams.
In this case, the African elephant weighs 5,500 pounds. To find out how many ounces that is, we can multiply 5,500 by 16:
5,500 pounds x 16 ounces/pound = 88,000 ouncesTherefore, the African elephant weighs 88,000 ounces.
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Ratna wants to pave stone in his triangular yard of sides 50m, 50m and 60m. If the area of each stone is 120cm², find the total number of stones required for it. Also, calculate the total cost at the rate of Rs. 5 per stone
The total number of stones required to pave the yard would be 100,000√3 stones and the cost would be Rs. 500000√3 at the rate of Rs. 5 per stone.
Rate calculationTo find the number of stones required, we need to find the area of the triangular yard and then divide it by the area of each stone.
First, let's find the area of the triangular yard using Heron's formula:
s = (50 + 50 + 60) / 2 = 80
Area = √(s(s-50)(s-50)(s-60)) = √(803030*20) = 1200√3 m²
Now, we need to convert the area to cm² and divide by the area of each stone:
Area in cm² = (1200√3) * 10000 = 12000000√3 cm²
Number of stones required = (Area in cm²) / (Area of each stone) = (12000000√3) / 120 = 100000√3 stones
Finally, to calculate the total cost at the rate of Rs. 5 per stone, we simply multiply the number of stones by the rate per stone:
Total cost = (100000√3) * Rs. 5 = Rs. 500000√3
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The no. 1 basketball team made 72% of its free throws over the past 5 seasons and shot 450 free throws in total. The
no. 2 team made 64% of its free throws over the past 5 seasons and shot 550 free throws in total. You randomly select
40 free throws from each team and record whether they made the shot. Let o, -, be the difference in the sample
proportions of successful free throws where o, is the proportion of free throw shots made by the no. 1 team and is
the proportion of free throw shots made by the no. 2 team.
Determine the mean of the sampling distribution of Ô, - Ôz. Enter your answer as a decimal rounded to the
hundredths place.
The mean difference of the sampling distribution of the difference in the proportion of free throw shots made between
the no. 1 and no. 2 teams is
The mean of the sampling distribution of Ô1 - Ô2 is 0.08, which indicates that on average, the no. 1 team makes 8% more free throws than the no. 2 team.
The mean of the sampling distribution of the difference in sample proportions of successful free throws, Ô1 - Ô2, can be calculated as:
mean(Ô1 - Ô2) = Ô1 - Ô2
Since the samples are random and independent, the mean of the sampling distribution is simply the difference between the population proportions:
mean(Ô1 - Ô2) = Ô1 - Ô2 = 0.72 - 0.64 = 0.08
Therefore, the mean of the sampling distribution of Ô1 - Ô2 is 0.08, which indicates that on average, the no. 1 team makes 8% more free throws than the no. 2 team.
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For a particular population, the largest distance (gap) between
a score and the mean is 11 points. The smallest distance between a
score and the mean is 4 points. Therefore, the standard deviation
___
The largest deviation and mean are 11 and the smallest deviation and mean are 4, respectively. Although we cannot give an exact answer, the standard deviation will always fall between 4 and 11. It will be the average of these values.
The standard deviation reveals how far data deviates from the mean. While a high standard deviation indicates that the data are more dispersed, a low standard deviation indicates that the data are clustered around the mean.
Standard deviation is important because it makes measurements easier to understand when the data is distributed.
standardstandard deviation of the data will be higher the more evenly distributed the data is.
The largest deviation and mean are 11 and the smallest deviation and mean are 4, respectively. Although we cannot give an exact answer, the standard deviation will always fall between 4 and 11. It will be the average of these values.
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fencing a garden a homeowner has 100 ft of fencing to enclose a rectangular garden. if the garden is to be 5 ft longer than it is wide, find its dimensions.
The dimensions of the rectangular garden is 25 feet by 50 feet
To find the dimensions of a rectangular garden that is 5 feet longer than it is wide, when the homeowner has 100 feet of fencing to enclose it, you can use the equation for the perimeter of a rectangle (P = 2l + 2w). Since the perimeter of the rectangle is given (100 feet), you can solve for l and w, the length and width of the rectangle.
P = 2l + 2w
100 = 2l + 2w
50 = l + w l = 50 - w
2(50 - w) + 2w = 100
100 - w = 2w , w = 25 l = 50 - 25, l = 25
Therefore, the dimensions of the rectangular garden that is 5 feet longer than it is wide, when the homeowner has 100 feet of fencing to enclose it, is 25 feet by 50 feet.
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URGENT ‼️ rephrased my exponential growth word problem now i need help on how to set up my equation
The Population of salmonella doubles in size every 25 hours.
There are about 10 grams of salmonella enterica bacteria in
"one cell, determine how many
cells have increased after 75 hours.
The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.
What is exponential growth?Exponential growth is a pattern of growth that is rapid and often exponential. It occurs when the rate of change in a variable is proportional to the variable's current value. This means that a small change in the variable can result in a large increase or decrease in its value over a short period of time.
The population of salmonella enterica bacteria doubles every 25 hours. This means that each hour, the population of the bacteria increases by a factor of two. To calculate the number of bacteria after 75 hours, we need to apply the concept of exponential growth. Exponential growth is a process by which the value of a variable increases exponentially, or multiplicatively, over time.
Assuming that the population of salmonella enterica was initially 10 grams, the population after 75 hours can be calculated using the equation:
Population = 10 * 2⁽⁷⁵÷²⁵⁾
The population after 75 hours is thus 10 * 2³ = 80 grams. This means that the population of salmonella enterica has increased from 10 grams to 80 grams after 75 hours.
Since each cell of salmonella enterica has a mass of 10 grams, the population after 75 hours can also be calculated in terms of cells. The population of salmonella enterica after 75 hours is 80 grams, which is equivalent to 8 cells. That is, the population of salmonella enterica has increased from 1 cell to 8 cells after 75 hours.
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Histograms Suppose we have a table called data with two numerical columns, "x" and·y. Consider the following scatter plot, which was generated by calling data.scatter('x', 'y') 2.0 1.5 1.0atos- 0.0 Histogram A: E 25 D 20 E 15 10 0 1 2 3 1 4 Histogram B: 40 C 30 20 a 10 0.0 0.5 1.0 1.5 .02.5 3.0 Question 1. One of these two lines of code generated Histogram A, and the other generated Histogram B . data.hist('x) data.hist'y) Which line generated Histogram A? Which generated Histogram B? Explain. Write your answer here. Question 2. Suppose we run this line of code new_data -Table().with_columns( data.column(x)5, y, data.column(y') We then run new_data.hist(x). What does the new histogram look like?
The shape of the histogram will remain the same but will stretch horizontally.
1. Histograms Suppose that the line of code data.hist('x') generated Histogram A and the line of code data.hist('y') generated Histogram B. This is because Histogram A shows the distribution of the x values and Histogram B shows the distribution of the y values.
The x-axis of Histogram A corresponds to the x values and the y-axis corresponds to the frequency of those values. Similarly, the x-axis of Histogram B corresponds to the y values and the y-axis corresponds to the frequency of those values.
2. The new histogram generated by running new_data.hist('x') will look similar to Histogram A, but the x values will be multiplied by 5. This means that the x-axis will have larger values and the bars will be shifted to the right. The y-axis, which corresponds to the frequency of the x values, will remain the same.
The overall shape of the histogram will also remain the same, but it will be stretched horizontally.
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what is the distance between the two points (−8,−3) and (−1,4) in simplest radical form
Answer:
the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.
Step-by-step explanation:
We can use the distance formula to find the distance between the two points:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given coordinates:
d = sqrt((-1 - (-8))^2 + (4 - (-3))^2)
d = sqrt(7^2 + 7^2)
d = sqrt(2 x 7^2)
d = 7sqrt(2)
Therefore, the distance between the two points (-8,-3) and (-1,4) is 7sqrt(2) units.
PLEASE HELP MEEEE I NEEED HEELPPPPP
Answer:
I think its (C) - 2/3
What value of y makes the equation true? y+2.91=11
A) 8.1
B) 8.09
C) 9.1
D) 13.91
Answer:
Step-by-step explanation:
If Y+2.91=11, simply subtract 2.91 from 11. 11-2.91 is 8.09. Y is 8.09.
Answer:
B) 8.09
Equation:
y + 2.91 = 11
To solve for the value of y, we need to isolate y on one side of the equation by performing the same operation on both sides.
Start by subtracting 2.91 from both sides:
y + 2.91 - 2.91 = 11 - 2.91
Finally, all we need to do is simplify:
y = 8.09
Therefore, the value of y that makes the equation true is 8.09.
Shirley's water bottle is half full. She pours
it into another bottle that is one-third full,
and it fills that bottle. If the second bottle
holds 2 quarts, how much did the first
bottle hold?
Answer:
Shirley's water bottle holds 4 quarts when it is half full.
Step-by-Step-Explanation
If the second bottle is one-third full and holds 2 quarts, then it means that it can hold a total of 2 / (1/3) = 6 quarts when completely full.
Let's call the amount of water in Shirley's bottle "x" quarts. We know that when she pours it into the second bottle, it becomes completely full with 6 quarts. So we can set up the equation:
x + 2 = 6
Solving for x, we get:
x = 6 - 2
x = 4
can someone help?? Need the answer ASAP !!
The slope and the y-intercept of the line that is perpendicular to y = 5x - 2 and passes through the origin are given as follows:
Slope of -1/5.Intercept of zero.How to obtain the slope and the intercept of the perpendicular line?The line for this problem is given as follows:
y = 5x - 2.
Meaning that the slope and the intercept are given as follows:
Slope of 5.Intercept of -2.When two lines are perpendicular, the multiplication of their slopes is of -1, hence the slope of the line perpendicular to y = 5x - 2 is given as follows:
5m = -1
m = -1/5.
The line also passes through the origin, meaning that when x = 0, y = 0, hence the intercept is of zero.
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Write an equation of the line below.
Answer: y=3/2x+4
Step-by-step explanation: The equation for the line below is [tex]y=\frac{3}{2}x +4[/tex]
This equation is correct because the formula is y=mx+b. m is the slope and you can see the slope is [tex]\frac{3}{2}[/tex] and x is to represent that the number is the slope. The b, or +4 represents where the line crosses over the x-axis.
The equation is [tex]y=\frac{3}{2}x +4[/tex]
Let me know if you have any other questions about this problem.
-Your Brainly Helper!
gcf of 17,22, and 46
Answer:
1
Step-by-step explanation:
17 is a prime number, so only 1 and 17 are its factors. 17 is not a factor of either 22 or 46, but 1 is.
It is 7 feet long, 3 1/4 feet deep, And has a volume of 159 1/4 what is the width
The width of the rectangular prism is 7 feet, given the length is 7 feet, the depth is 3 1/4 feet, and the volume is 159 1/4 cubic feet.
We can use the volume of a rectangular prism formula, which is length x width x height. We are given the length (7 feet), the depth (3 1/4 feet), and the volume (159 1/4 cubic feet). Let's substitute these values into the formula and solve for the width:
7 feet x width x 3 1/4 feet = 159 1/4 cubic feet
Multiplying 7 feet and 3 1/4 feet, we get:
22 3/4 square feet x width = 159 1/4 cubic feet
Dividing both sides by 22 3/4 square feet, we get:
width = (159 1/4 cubic feet) / (22 3/4 square feet)
Simplifying the fraction, we get:
width = (637/4) / (91/4)
As multiplying by a fraction's reciprocal is equivalent to dividing by it, we get:
width = (637/4) x (4/91)
The factor of 4 in the numerator and denominator cancels out, so we get:
width = 637/91
Simplifying the fraction, we get:
width = 7
Therefore, the width of the rectangular prism is 7 feet.
Given the length, depth, and volume of a rectangular prism, we can use the formula for the volume to solve for the width. In this case, we substitute the given values and solve for the unknown width by simplifying the algebraic expression. The resulting width is 7 feet.
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Need help with this project
The function that represents the graph below is given as follows:
c. y = 4x³.
How to obtain the function which defines the graph?Before defining the function which defines the graph, we must obtain the domain and the range of the function, as follows:
Domain -> set of input values assumed by the function -> x values -> all real values in the graph.Range -> set of output values assumed by the function -> y values -> all real values in the graph.As the function has a range of all real values, we know that it is a cube function and not a square function, removing options a and b.
The function is positive and negative as follows:
Positive: positive values of x.Negative: negative values of x.Hence the function has a positive leading coefficient, meaning that option c is the correct option.
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Break-Even Sales
Anheuser-Busch InBev SA/NV (BUD) reported the following operating information for a recent year (in millions):
The anticipated break-even number of barrels for the following year is 254.40 million per barrel.
a) To compute the break-even number of barrels for the current year, we need to first calculate the total fixed costs and the total variable costs for the year.
Total Fixed Costs = Selling, general, and administrative expenses - Variable Selling, general, and administrative expenses + Operating Income before special items
Total Fixed Costs = 14,439 - (0.5 * 14,439) + 13,275
Total Fixed Costs = $20,494.5 million
Total Variable Costs = Cost of goods sold - Variable Cost of goods sold
Total Variable Costs = 17,803 - (0.75 * 17,803)
Total Variable Costs = $4,450.75 million
Now, we can calculate the contribution margin per barrel as follows:
Contribution Margin per Barrel = (Sales - Variable Costs) / Number of Barrels
Contribution Margin per Barrel = ($45,517 - $4,451) / 500
Contribution Margin per Barrel = $82.132 million / barrel
To find the break-even number of barrels, we can use the following formula:
Break-even Number of Barrels = Total Fixed Costs / Contribution Margin per Barrel
Break-even Number of Barrels = $20,494.5 million / $82.132 million per barrel
Break-even Number of Barrels = 249.53 million barrels
Therefore, the break-even number of barrels for the current year is 249.53 million.
To compute the anticipated break-even number of barrels for the following year, we need to consider the increase in fixed costs due to the new distribution and general office facilities. Assuming all other costs and per-barrel amounts remain constant, the new total fixed costs would be:
New Total Fixed Costs = Total Fixed Costs + Increase in Fixed Costs
New Total Fixed Costs = $20,494.5 million + $400 million
New Total Fixed Costs = $20,894.5 million
Using the same contribution margin per barrel as in the current year, we can calculate the anticipated break-even number of barrels for the following year:
b) Anticipated Break-even Number of Barrels = New Total Fixed Costs / Contribution Margin per Barrel
Anticipated Break-even Number of Barrels = $20,894.5 million / $82.132 million per barrel
Anticipated Break-even Number of Barrels = 254.40 million barrels
Therefore, the anticipated break-even number of barrels for the following year is 254.40 million.
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The correct question would be:
Break-Even Sales Anheuser-Busch InBev SA/NV (BUD) reported the following operating information for a recent year (in millions): $45,517 Sales Cost of goods sold Selling, general, and administrative expenses $17,803 14,439 (32,242) Operating income $13,275 *Before special items In addition, assume that Anheuser-Busch InBev sold 500 million barrels of beer during the year. Assume that variable costs were 75% of the cost of goods sold and 50% of selling, general, and administrative expenses. Assume that the remaining costs are faced. For the following year, assume that Anheuser-Busch InBev expects pricing variable costs per barrel and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $400 million
a. Compute the break-even number of barrels for the current year. In computing variable and fixed costs and per-barrel amounts, round to two decimal places. Round the break-even number of barrels to one decimal place. million barrels
b. Compute the anticipated break-even number of barbels for the following year Round to one decimal place in millions of barrels million barrels.
WHAT IS THE ANSWER?
HELP ME PLeese
Answer:
Step-by-step explanation:
An account with an initial balance of $1250 earns interest that is compounded quarterly. If no other deposits or withdrawals are made, the
account will have a balance of $1406.08 after 9 months. Find the annual interest rate.
Answer:
If no other deposits or withdrawals are made, the account will have a balance of $1406.08 after 9 months. Find the annual interest rate. Expert Answer.
1 answer
·
Top answer:
Given that P=1,250A=1,406.08n=9 month
Step-by-step explanation:
There are 70 students traveling to a soccer tournament. All of the vans can take 9 students each. How many vans are needed to take all of the students to the tournament?
Answer:
They need 8 vans.
Step-by-step explanation:
8 × 9 is 72. If you have 8 vans that carry 9 students each, you will have room for 72 students. Then you have enough room for 70 students.
If you only have 7 vans you can only transport 7 × 9, or 63 students. That is not enough. They need 8 vans.
Answer this question.
According to the question the fraction of the bigger square that is shaded is 50%.
What is fraction?Fraction is a numerical representation of a part of a whole or a ratio between two numbers. It is written in the form of a/b where a is the numerator and b is the denominator. A fraction can refer to a part of a whole number, a part of a set, or a part of a unit. Fractions are commonly used in mathematics, cooking, science, and many other areas.
This is because the ratio of the area of the smaller square to the area of the bigger square to the area of the triangle is 1:3:2. Therefore, the ratio of the area of the shaded parts of the squares to the area of the shaded triangle is 25%: 25%:50%. Since the area of the bigger square is three times that of the smaller square, then 50% of the bigger square must be shaded to maintain the given ratio.
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4. A researcher is studying life expectancy in different parts of the world. Using birth and death
records, she randomly selects a sample of 20 people from Town A and a sample of 20 people
from Town B and records their lifespans in years.
Mean Lifespan in Years Standard Deviation
Town A
Town B
78.5
74.4
11.2
12.3
The researcher wants to test the claim that there is a significant difference in lifespan for people
in the two towns. What is the P-value and conclusion at a significance level of 0.10?
(1 point)
OP-value = 0.277; fail to reject the null hypothesis that the means of the populations are equal
OP-value = 0.076228; fail to reject the null hypothesis that the means of the populations are equal
OP-value = 0.277; reject the null hypothesis that the means of the populations are equal
OP-value = 0.076228; reject the null hypothesis that the means of the populations are equal
The required p-value of 0.277 is greater than the significance level of 0.10, we again fail to reject the null hypothesis.
How to find the P-value?To test the claim of a significant difference in lifespan for people in Town A and Town B, we can use a two-sample t-test. The null hypothesis is that there is no significant difference in the mean lifespan between the two towns, while the alternative hypothesis is that there is a significant difference.
Let [tex]$\mu_A and \mu_B$[/tex] be the true mean lifespans of the populations in Town A and Town B, respectively. Then the null and alternative hypotheses can be written as:
[tex]$H_0: \mu_A = \mu_B$[/tex]
[tex]$H_1: \mu_A \neq \mu_B$[/tex]
We can use the t-test statistic to test this hypothesis, which is calculated as:
[tex]$t = \frac{\bar{x}_A - \bar{x}_B}{\sqrt{\frac{s_A^2}{n_A} + \frac{s_B^2}{n_B}}}$[/tex]
where [tex]$\bar{x}_A$[/tex]and [tex]$\bar{x}_B$[/tex] are the sample means, [tex]$s_A$[/tex] and [tex]$s_B$[/tex] are the sample standard deviations, and[tex]$n_A$[/tex] and [tex]$n_B$[/tex] are the sample sizes.
Substituting the given values, we get:
[tex]$t = \frac{78.5 - 74.4}{\sqrt{\frac{11.2^2}{20} + \frac{12.3^2}{20}}} = 1.102$[/tex]
Using a two-tailed t-test with 38 degrees of freedom (20 + 20 - 2), and a significance level of 0.10, the critical value of t is:
[tex]$t_{\alpha/2,38} = \pm 1.686$[/tex]
Since the calculated t-value of 1.102 is less than the critical value of 1.686, we fail to reject the null hypothesis.
To find the p-value, we can use a t-distribution table or a calculator to find the probability of getting a t-value of 1.102 or more extreme (in either direction) if the null hypothesis is true. This is a two-tailed test, so we need to multiply the resulting probability by 2:
p-value = P(|t| > 1.102) = 2P(t > 1.102) = 2(1 - P(t < 1.102)) =0.277
Since the p-value of 0.277 is greater than the significance level of 0.10, we again fail to reject the null hypothesis.
Therefore, at a significance level of 0.10, we do not have sufficient evidence to conclude that there is a significant difference in lifespan for people in Town A and Town B.
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What is the correct way to name the following image?
The correct way to name the image is Southwest Vector BA, indicating the direction of the vector from B to A.
How do we name the vector diagram?
Vector BA : This notation indicates that the vector starts at point B and ends at point A, and it is read as "vector B-A" or "B-A vector". The order of the letters reflects the direction of the arrow, from B to A.
Arrow SW or SW arrow: This notation indicates the direction of the vector, which is towards the southwest, and it is read as "arrow southwest" or "southwest arrow". The order of the letters reflects the direction of the vector, from the northwest to the southeast.
Southwest Vector BA : This notation combines both the direction and the points of the arrow, and it is read as "southwest vector B-A" or "B-A southwest vector". The order of the words reflects the direction of the vector, from the northwest to the southeast, and the order of the letters reflects the starting and ending points of the arrow.
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