The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is: 39,600
How to find number of ways to arrange 8 letters a, b, c, d, e, f, g, h?(a) The number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is given by:
number of arrangements with a in first position + number of arrangements with b in last position - number of arrangements with both a in first position and b in last position
= (7!) + (7!) - (6!)
Number of ways with a in first position = 7! (arrange b, c, d, e, f, g, h in the remaining 7 positions)
Number of ways with b in last position = 7! (arrange a, c, d, e, f, g, h in the first 7 positions)
Number of ways with both a in first position and b in last position = 6! (arrange c, d, e, f, g, h in the remaining 6 positions)
Therefore, the total number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a is in the first position or b is in the last position is:
7! + 7! - 6! = 10,080
(b) To find the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b, we can use complementary counting.
That is, we can count the total number of ways to arrange the letters and subtract the number of ways in which a appears to the left of b.
Total number of ways to arrange 8 letters = 8! = 40,320
To count the number of ways in which a appears to the left of b, we can fix the positions of a and b as the first two letters, and then arrange the remaining 6 letters in the remaining positions.
There are 6! ways to do this.
Therefore, the number of ways to arrange 8 letters a, b, c, d, e, f, g, h such that a appears somewhere to the right of b is:
8! - 6! = 40,320 - 720 = 39,600
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Help me— My brain goes brrr in this question word problem thing ; - ;
A table tennis ball has a radius of 0. 04m. Estimate how many table tennis balls you could fit into the coin building! [search up what it is—]
( Width: 20m | height: 110m )
- How did you calculate your estimate?
- Explain how accurate you think your prediction is?
( Show Work. )
Number of balls ≈ [tex]1.03 * 10^9[/tex]
To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.
Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.
The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:
V = (4/3)πr³
where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:
V = (4/3) x 3.14 x 0.04³
[tex]V =2.14 * 10^{-5} m^3[/tex]
Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.
Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:
V = l x w x h
where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 20 x 10 x 110
V = 22000 m³
Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:
Number of balls ≈ [tex]V_building / V_ball[/tex]
Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]
Number of balls ≈ [tex]1.03 * 10^9[/tex]
So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.
As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.
For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.
Additionally, we rounded some of our values and used approximations for pi.
Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.
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A florist sells flower bouquets. the table shows the prices for various amounts and kinds of bouquets.
total price
bouquets
2
flower
daisies
tulips
roses
$23.90
$60.80
2
1
2
a
the expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is
$18.45 more than a bouquet of tulips.
b
the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is
$18.45 more than a bouquet of daisies.
с
the expression 23.90 - 60.80 represents that a bouquet of tulips is $36.90 more than a
bouquet of daisies.
d
the expression 60.80 - 23.90 represents that a bouquet of daises is $36.90 more than a
bouquet of tulips.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
The given table shows the prices for various amounts and kinds of bouquets sold by a florist. The prices depend on the number and type of flowers in the bouquet. The table shows prices for bouquets of 2 flowers with daisies, tulips, and roses.
The expression (23.90 - 2) - (60.80 – 2) represents that a bouquet of daisies is $18.45 more expensive than a bouquet of tulips. This is because the cost of a 2-flower bouquet of daisies is $23.90 and the cost of a 2-flower bouquet of tulips is $60.80, so the difference between them is $36.90.
However, we subtract 2 from each price to get the price of the actual flowers in the bouquet, which are the same for both daisies and tulips. Therefore, we get the difference of $18.45.
Similarly, the expression (60.80 - 2) - (23.90 + 2) represents that a bouquet of tulips is $18.45 more expensive than a bouquet of daisies. Here, we subtract the price of a 2-flower bouquet of daisies plus the cost of 2 flowers from the price of a 2-flower bouquet of tulips.
Again, the actual cost of flowers in both bouquets is the same, so we get the difference of $18.45.
The expressions 23.90 - 60.80 and 60.80 - 23.90 represent the price difference between bouquets of daisies and tulips, respectively. The former expression gives a negative result of $36.90, which means that a bouquet of tulips is $36.90 more expensive than a bouquet of daisies.
The latter expression gives a positive result of $36.90, which means that a bouquet of daisies is $36.90 more expensive than a bouquet of tulips.
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Consider the function f(x) = 1 – 5x², -3 ≤ x ≤ 2. The absolute maximum value is and this occurs at x equals The absolute minimum value is and this occurs at x equals
The absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.
To find the absolute maximum and minimum values of the function f(x) = 1 - 5x² on the interval [-3, 2], we first find the critical points of f(x) and then evaluate f(x) at the critical points and endpoints of the interval.
The derivative of f(x) is:
f'(x) = -10x
Setting f'(x) = 0, we get:
-10x = 0
which has only one critical point at x = 0.
Now, we evaluate f(x) at the critical point and endpoints of the interval:
f(-3) = 1 - 5(-3)² = -44
f(0) = 1 - 5(0)² = 1
f(2) = 1 - 5(2)² = -49
Therefore, the absolute maximum value of f(x) on the interval [-3, 2] is 1, which occurs at x = 0. The absolute minimum value of f(x) on the interval [-3, 2] is -49, which occurs at x = 2.
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Find the value of c step by step
PLEASE HELP
Answer:
c = 12
Step-by-step explanation:
[tex] {5}^{2} + {c}^{2} = {13}^{2} [/tex]
[tex]25 + {c}^{2} = 169[/tex]
[tex] {c}^{2} = 144[/tex]
[tex]c = 12[/tex]
Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 4 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
6:14
2 to 3
2 over 4
1 to 10
the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3. Thus, option B is correct.
What is the ratio?To write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans, we need to find the common factor between the number of pairs of blue jeans each person donated.
Hallie donated 4 pairs of blue jeans, and Mattie donated 6 pairs of blue jeans.
The common factor between 4 and 6 is 2. We can divide both 4 and 6 by 2 to get:
Hallie donated 2 pairs of blue jeans.
Mattie donated 3 pairs of blue jeans.
Now we can write the ratio of Hallie's donation to Mattie's donation as:
2:3
Therefore, the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3.
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Help Pythagorean Theorem quickly please
Answer:
[tex]h = \sqrt{ {21}^{2} - {19}^{2} } = \sqrt{441 - 361} = \sqrt{80} = 4 \sqrt{5} [/tex]
h = 4√5 feet = 8.9 feet
1. The following circles are not drawn to scale. Find the area of each circle. (Use as an approximation for TT. )
21 cm
Lesson 17 Problem Set
81 ft
45
2
cm
The area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²
Finding the area of each circleFrom the question, we have the following parameters that can be used in our computation:
Radii = 21 cm, 81 ft, 45/2 cm
The area of a circle is calculated as
Area = πr²
substitute the known values in the above equation, so, we have the following representation
Area = 3.14 * 21² = 1384.74
Area = 3.14 * 81² = 20601.54
Area = 3.14 * (45/2)² = 1589.625
Hence, the area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²
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Express the quantity "14 revolutions per second" in radians per second. Write your answers in terms of pi
14 revolutions per second can be expressed as 28π radians per second.
A radian is an angle whose corresponding arc in a circle is equal to the radius of the circle. A revolution is a full rotation, or a complete, 360-degree turn.
1 revolution per second is expressed as 2π radians per second.
To calculate the number of radians in 14 revolutions per second, we have to multiply 2π by 14.
14 revolutions per second = 14 * 2π
= 28π radians per second
Thus, the answer to the given question comes out to be 28 π radians per second
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Please help with this
a) The table is completed as follows:
x = -5, y = -3.x = 0, y = 2.x = 3, y = 5.b) The graph is given by the image presented at the end of the answer.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The function for this problem is given as follows:
y= x + 2.
Hence the numeric values of the function are given as follows:
x = -5, y = -5 + 2 = -3.x = 0, y = 0 + 2 = 2.x = 3, y = 3 + 2 = 5.Then the graph is constructed connecting two of these points and tracing a line through them.
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A piece of equipment costs $75,000 new but depreciates 12% per year in each succeeding year . Find its value after 8 years
The equipment's value after 8 years, given its original value was $75,000 and it depreciates by 12% each year, is approximately $27,506.62.
To find the value of the equipment after 8 years, we need to calculate its value at the end of each year, taking into account the 12% depreciation per year.
At the end of year 1, the equipment will be worth 88% of its original value
Value at end of year 1 = 0.88 x $75,000 = $66,000
At the end of year 2, the equipment will be worth 88% of its value at the end of year 1
Value at end of year 2 = 0.88 x $66,000 = $58,080
We can continue this process for each year
Value at end of year 3 = 0.88 x $58,080 = $51,206.40
Value at end of year 4 = 0.88 x $51,206.40 = $45,065.91
Value at end of year 5 = 0.88 x $45,065.91 = $39,654.02
Value at end of year 6 = 0.88 x $39,654.02 = $34,991.23
Value at end of year 7 = 0.88 x $34,991.23 = $31,191.80
Value at end of year 8 = 0.88 x $31,191.80 = $27,506.62
Therefore, the value of the equipment after 8 years is $27,506.62.
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HELP
I need all the help to figure this annoying thing out
Answer:
x = 30 , y = 54
Step-by-step explanation:
the figure is a trapezium
each lower base angle is supplementary to the upper base angle on the same side, then
4x + y + 6 = 180 ( subtract 6 from both sides )
4x + y = 174 ( subtract 4x from both sides )
y = 174 - 4x → (1)
and
2x + 12 + 2y = 180 → (2)
substitute y = 174 - 4x into (2)
2x + 12 + 2(174 - 4x) = 180
2x + 12 + 348 - 8x = 180
- 6x + 360 = 180 ( subtract 360 from both sides )
- 6x = - 180 ( divide both sides by - 6 )
x = 30
substitute x = 30 into (1)
y = 174 - 4(30) = 174 - 120 = 54
thus x = 30 and y = 54
The equation for line c can be written as y=–67x–1. line d is parallel to line c and passes through (10,–9). what is the equation of line d?write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
Answer:
y = -6/7x - 3/7 or 7y = -6x - 3
Step-by-step explanation:
I'm guessing you mean line c: y = -6/7x - 1
Parallel lines have same slope => line d will have slope = -6/7
y = mx + b
-9 = -6/7(10) + b
-9 = -60/7 + b
b = 60/7 - 9 = 60/7 - 63/7 = -3/7
y = -6/7x - 3/7
or 7y = -6x - 3
The equation, with a restriction on x, is the terminal side of an angle theta in standard position. 5x + y = 0, x ≥ 0 Give the exact values of the six trigonometric functions of theta. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sin theta = (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using radicals as needed. Rationalize all denominators.) B. The function is undefined.
Sin theta = -5/sqrt(26) Is the correct option , To find the six trigonometric functions of theta, we need to first find the values of x and y on the terminal side of theta. From the given equation, 5x + y = 0 and x ≥ 0, we can solve for y in terms of x:
y = -5x
Since x ≥ 0, we know that (x, y) lies in the fourth quadrant. We can now use the Pythagorean theorem to find the length of the hypotenuse:
r =[tex]sqrt(x^2 + y^2) = sqrt(x^2 + (-5x)^2) = sqrt(26x^2)[/tex]
Now we can find the six trigonometric functions:
sin(theta) = y/r = [tex]-5x/sqrt(26x^2) = -5/sqrt(26)[/tex]
cos(theta) = x/r =[tex]x/sqrt(26x^2) = 1/sqrt(26)[/tex]
tan(theta) = y/x = -5x/x = -5
csc(theta) = r/y = [tex]sqrt(26x^2)/(-5x) = -sqrt(26)/5[/tex]
sec(theta) = r/x = sqrt(26x^2)/x = sqrt(26)/1 = sqrt(26)
cot(theta) = 1/tan(theta) = -1/5
Therefore, the exact values of the six trigonometric functions of theta are:
sin(theta) = -5/sqrt(26)
cos(theta) = 1/sqrt(26)
tan(theta) = -5
csc(theta) = -sqrt(26)/5
sec(theta) = sqrt(26)
cot(theta) = -1/5
Answer: A. sin theta = -5/sqrt(26)
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Chad buys pineapples, watermelons, and a bag of grapes for a fruit salad. He spends a total of $29.68 on the fruit salad. Pineapples
cost $2.15 each, and watermelons cost $3.75 each. The bag of grapes costs $4.48.
Create an equation to model this situation, where p represents the number of pineapples Chad can purchase and w represents the
number of watermelons he can purchase.
An equation that models the situation, where p represents the number of pineapples Chad can purchase and w represents the number of watermelons he can purchase will be; 2.15p + 3.75w = 25.20.
Let's use the given information to create an equation to model this situation. We know that Chad spends a total of $29.68 on the fruit salad, so we can start with;
2.15p + 3.75w + 4.48 = 29.68
This equation represents the total cost of the fruit salad, which includes the cost of the pineapples (2.15p), the cost of the watermelons (3.75w), and the cost of the bag of grapes (4.48).
To make this equation more specific to the problem of finding the number of pineapples and watermelons Chad can purchase, we need to use the variables p and w to represent those quantities. We can set up a second equation based on the information given about the total number of fruits;
p + w + 1 = T
Here, T represents the total number of fruits in the salad, and we add 1 to account for the bag of grapes.
Now we can use substitution to eliminate the variable T. Solving for T in terms of p and w;
T = p + w + 1
Substitute this expression for T into first equation;
2.15p + 3.75w + 4.48 = 29.68
Simplify;
2.15p + 3.75w = 25.20
Therefore, the model of this situation is; 2.15p + 3.75w = 25.20
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1. Order: Kefzol 1. 125 g IV q6h
A Kefzol labeled 225 mg per 4mL
How many L?
To determine the number of liters needed for an order of Kefzol 1.125 g IV q6h, we first need to convert the grams to milligrams.
1.125 g = 1,125 mg
Next, we need to calculate the total volume of Kefzol needed for each dose.
225 mg is equal to 4 mL, so:
1,125 mg ÷ 225 mg/mL = 5 mL
Therefore, each dose of Kefzol requires 5 mL.
To determine the number of liters needed for the entire order, we need to know how many doses will be given per day.
Assuming a standard dosing schedule of q6h, this means the patient will receive 4 doses per day.
So, the total volume of Kefzol needed per day is:
4 doses/day x 5 mL/dose = 20 mL/day
To convert this to liters, we divide by 1000:
20 mL/day ÷ 1000 = 0.02 L/day
Therefore, for an order of Kefzol 1.125 g IV q6h, we will need approximately 0.02 liters per day.
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HELP ASAP ! Given the rectangle in this example, and a scale factor of 3.5, what are the side lengths of the new rectangle?
Answer:
Length: 22 inches × 3.5 = 77 inches
Width: 10 inches × 3.5 = 35 inches
The salaries of professional baseball players are heavily skewed right with a mean of $3. 2 million and a standard
deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. Which of the
following best describes the sampling distribution of all possible samples of size 40?
skewed right with a mean of 3. 2 million and a standard deviation of 2 million
skewed right with a mean of 3. 2 million and a standard deviation of 0. 32 million
approximately Normal with a mean of 3. 2 million and a standard deviation of 2 million
approximately Normal with a mean of 3. 2 million and a standard deviation of 0. 32 million
The best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.
The sampling distribution of the mean of a sample is approximately normal if the sample size is sufficiently large, regardless of the distribution of the population from which the sample is drawn.
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean, which is $3.2$ million. The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size, which is [tex]$2/\sqrt{40} \approx 0.3162$[/tex] million.
Therefore, the best answer is approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million.
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What is the volume of this shape? help me please i really need help
The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.
A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.
Volume of cube = length × breadth × height
length = 5 unit
breadth = 5 unit
height = 5 unit
Volume = 5 × 5 × 5
= 125 unit³
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the function g(x) = x2 is transformed to obtain function h: h(x) = g(x) + 1. Which statement describes how the graph of h is different from the graph of g? A. The graph of h is the graph of g horizontally shifted right 1 unit. B. The graph of h is the graph of g vertically shifted up 1 unit. C. The graph of h is the graph of g vertically shifted down 1 unit. D. The graph of h is the graph of g horizontally shifted left 1 unit.
The statement that describes how the graph of h is different from the graph of g is: B. The graph of h is the graph of g vertically shifted up 1 unit.
Which statement describes how the graph of h is different from the graph of g?The function h(x) = g(x) + 1 is obtained by adding a constant (1) to the output of the function g(x) = x^2. This means that the graph of h(x) will be the same as the graph of g(x), except that every point on the graph of h(x) will be shifted vertically upward by 1 unit.
Therefore, the correct statement is: B. The graph of h is the graph of g vertically shifted up 1 unit.
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52.03×9.81
I’ve been having troubles with decimals and I need some help with this. Thanks.
answer please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9/7
explain:
(36-27) 7
9/7
i need help quickk please
The true statements about the rectangular prism are Prism B has a greater volume than Prism C, Prism B has the greatest volume, and Prism A has the least volume.
What is the volume of each of the prisms?To understand, the differences between the prisms and therefore to verify the statements about them, let's calculate the volume of each by using the formula length x width x height.
Prism A: 2 x 2 x 3= 12 cubic units
Prism B: 2 x 3 x 4 = 24 cubic units
Prism C: 3 x 2 x 3 = 18cubic units
Based on this, the statements A, D, and E are correct.
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Find the function, f, that satisfies the following conditions f"(x)=-sin x/2, f'(π) = 0, f(π/3)=-3
The function f(x) = -4*sin(x/2) - 1 is the solution that meets the specified conditions.
To find the function, f, that satisfies the given conditions f"(x) = -sin(x/2), f'(π) = 0, and f(π/3) = -3, we need to integrate the given second derivative twice and apply the boundary conditions. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x).
1. Integrate f"(x) = -sin(x/2) with respect to x to find f'(x):
f'(x) = ∫(-sin(x/2)) dx = -2*cos(x/2) + C1, where C1 is the integration constant
2. Apply the boundary condition f'(π) = 0:
0 = -2*cos(π/2) + C1
C1 = 0, since cos(π/2) = 0.
3. Now, f'(x) = -2*cos(x/2).
4. Integrate f'(x) = -2*cos(x/2) with respect to x to find f(x):
f(x) = ∫(-2*cos(x/2)) dx = -4*sin(x/2) + C2, where C2 is the integration constant.
5. Apply the boundary condition f(π/3) = -3:
-3 = -4*sin(π/6) + C2
-3 = -4*(1/2) + C2
C2 = -1.
So, the function f(x) that satisfies the given conditions is f(x) = -4*sin(x/2) - 1.
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if a researcher finds a small difference in average test scores between a large sample (over 700) of experimental participants and a large sample (same size) of control participants, it is very likely that the difference is
The null and alternative hypotheses are H₀: μ₁ - μ₂ = 0 and H₁: μ₁- μ₂ ≠ 0 and the test statistic value is equal to 0.45.
The null hypothesis (H₀) states,
That there is no significant difference between the population means of the experimental group and the control group.
The alternative hypothesis (H₁) states that there is a significant difference between the two means.
State the hypotheses as,
H₀: μ₁ - μ₂ = 0 (there is no difference in means)
H₁: μ₁- μ₂ ≠ 0 (there is a difference in means)
where μ₁ is the population mean of the experimental group
And μ₂ is the population mean of the control group.
The test statistic,
Use the t-test formula,
t = (x - μ) / (s / sqrt(n))
where x is the sample mean = 102
μ is the hypothesized population mean = 100
s is the sample standard deviation =88
n is the sample size= 10
Plugging in the values, we get,
t = (102 - 100) / (88 / sqrt(10))
= 0.45
Therefore, the null and the alternative hypotheses states that H₀: μ₁ - μ₂ = 0 there is no difference in means and H₁: μ₁- μ₂ ≠ 0 there is a difference in means and the test statistic for a sample mean of 102 is 0.45.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a researcher finds a small difference in average test scores between a large sample of 700 experimental participants with a standard deviation of 88, a mean of 100, and with a sample size of 10.
a. State the null and the alternative hypotheses.
b. Compute the test statistic for sample mean 102.
from a circular sheet of a radius 5cm, a circle of radius 3cm is removed. find the area of the remaining sheet
Check the picture below.
[tex]\textit{area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{outer}{radius}\\ r=\stackrel{inner}{radius}\\[-0.5em] \hrulefill\\ R=5\\ r=3 \end{cases}\implies A=\pi (5^2-3^2)\implies A\approx 50.27~cm^2[/tex]
The ages of a and b are in the ratio 8:3.6 years later their ages are ok the ratio 9:4.Find their present ages
Answer:
The present ages of A and B will be 48 and 18 years.
Step-by-step explanation:
Let the coefficient be x.
A's age = 8x
B's age = 3x
Six years hence,
Ages will be 8x+6 and 3x+6.
Now, As per the question,
(8x+6) /(3x+6) = 9/4
32x+24 = 27x+54
5x = 30
x = 6.
You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0. 32 to make each donut. Each box costs $0. 18 per square foot of cardboard. There are 144 square inches in 1 square foot.
The total cost for one dozen donuts include the cost to make the donuts and the cost of the box. Create an expression to model the cost for one dozen donuts where t represents the total surface area of the box
create an expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet.
help please :(
The cost for one donut is $0.32, so the cost for one dozen donuts is:
12 donuts x $0.32/donut = $3.84
The cost for the cardboard box is $0.18 per square foot of cardboard, and there are 144 square inches in 1 square foot, so the cost per square inch of cardboard is:
$0.18 / 144 sq in = $0.00125/sq in
If t represents the total surface area of the box in square inches, then the cost of the box is:
t x $0.00125/sq in
To convert square inches to square feet, we divide by 144:
t/144 square feet x $0.18/square foot = t x $0.00125/sq in
Thus, the expression to model the total cost for one dozen donuts where t represents the total surface area of the box in square feet is:
$3.84 + (t/144) x $0.18
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There is a 40% chance that weather causes one or more days of school to be canceled each year. Use the table of simulated values to find the experimental probability that weather will cause school to be canceled in at least three of the next four school years. Use the digits 1 through 4 as years with a cancellation
The experimental probability of weather causing school to be canceled in at least three of the next four school years is (3+1)/24, which simplifies to 1/6 or approximately 0.1667.
What is the experimental probability of weather?To find the experimental probability of weather causing school to be canceled in at least three of the next four school years, we need to count the number of times there were three or more cancellations in each set of four years and divide that by the total number of sets of four years.
According to the table of simulated values, there are 24 sets of four years. Out of these, there were three or more cancellations in three sets of four years, and there were four cancellations in one set of four years. Therefore, the experimental probability of weather causing school to be canceled in at least three of the next four school years is 20%.
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An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a comfield and the number of
bushels of com produced. This is the regression line of the data, where y is measured in bushes and is measured in pounds of nitrogen
0. 43
What is the meaning of the intercept of the regression line?
O A When no nitrogen is added to the field, 28. 7 bushels of corn are produced
When 28. 7 pounds of nitrogen is added to the held, no bushels of corn are produced
When 0. 43 pounds of nitrogen is added to the field. 28. 7 bushels of corn are produced
B. When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced
The meaning of the intercept of the regression line is option B- When 38. 7 pounds of nitrogen is added to the field, 0. 43 bushels of com are produced
We are given the equation of the experiment that tells a relationship.
y = 0.43x + 28.5
The linear regression line is an algebraic model to show the relationship between the two models by putting the value of one variable to get the value of the other.
A linear regression line can be represented as,
y = Ax + B
Here y is the dependent variable and x is the explanatory variable. A is the slope of the line and
B is the intercept here. In the given equation there are two variables given.
Variable x representsthe amount of nitrogen added, and the variable y represents the number of bushels of corn produced.
As putting the value of x, y increases with the value of number 0.43. Therefore, as we are increasing the value of the nitrogen by one unit, the number of bushels of corn produced is increasing by 0.43 units. Hence, for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
Therefore option B is the correct option.
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The complete question is "An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of
bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of
nitrogen.
y = 0.43x + 28.5
What is the meaning of the slope of the regression line?
O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels."
Help translations and reflections
Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)
Explain about the reflection along the y-axis:A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).Given coordinates of points A, B and C
A(6, 10), B(2, -8), C(-4 , -7)
After reflection (x, y) ---> (-x, y).
Thus, Coordinates of image of points A', B' and C' are-
A'(-6, 10), B'(-2, -8), C'(4 , -7)
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