Rowan thinks of a number. His number is a factor of both 18 and 30. His number is odd. What is the largest possible number he could be thinking of?​

For the function transformation form of f(x), [tex]g(x) = a f(\frac{1}{b} x - h) + k [/tex], we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.

A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,

We have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, [tex]g(x) = a f(\frac{1}{b} x - h) + k [/tex], now see the graph carefully.

Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.

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Complete question:

The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k

replacing which variable with what number will result in the transformation displayed in the graph?

a) b is replacing by 1/2

b) k is replacing by -1/2

c) h is replacing by -2

d) a is replacing by 2

We are 95% certain that the average hourly earnings for waitresses in Iowa City

Based on the given data, the sample mean hourly earnings of waiters in Weston, West Virginia is x = 17.1 dollars. The standard deviation of the hourly earnings is given as $4.50. We can use this information to estimate the mean hourly earnings for all waitresses in Iowa City with 95% confidence.

To do this, we use the formula for the confidence interval:

CI = x ± t*(s/√n)

where CI is the confidence interval, x is the sample mean, t is the t-value from the t-distribution with (n-1) degrees of freedom and a confidence level of 95%, s is the sample standard deviation, and n is the sample size.

Using the given data, we have:

x = 17.1
s = $4.50
n = 10

To find the t-value, we look up the value in a t-table with (10-1) = 9 degrees of freedom and a confidence level of 95%. The t-value is 2.262.

Plugging in the values, we get:

CI = 17.1 ± 2.262*($4.50/√10)
CI = 17.1 ± $3.76
CI = ($13.34, $20.86)

Interpretation:

We can interpret this confidence interval as follows: if we were to take many random samples of 10 waiters in Weston, West Virginia, and calculate a confidence interval for each sample, we would expect that 95% of these intervals would contain the true mean hourly earnings for all waitresses in Iowa City. Based on this particular sample of 10 waiters, we are 95% confident that the true mean hourly earnings for all waitresses in Iowa City lies between $13.34 and $20.86.
To estimate the mean hourly earnings with 95% confidence for all waitresses in Iowa City, we will use the sample data from Weston, West Virginia, and assume that the standard deviation is the same in both locations.

Given the mean (x) of the sample is 17.1, and the sample size (n) is 10, with a standard deviation (σ) of $4.50, we can calculate the margin of error for the 95% confidence interval using the formula:

Margin of Error = (Z * σ) / square root n

For a 95% confidence interval, the Z-score is 1.96.

Margin of Error = (1.96 * 4.50) / square root 10 = 2.775

Now, we can calculate the confidence interval:

Lower Bound = x - Margin of Error = 17.1 - 2.775 = 14.325
Upper Bound = x + Margin of Error = 17.1 + 2.775 = 19.875

We can conclude with 95% confidence that the mean hourly earnings for all waitresses in Iowa City fall within the range of $14.325 to $19.875. This means that we are 95% certain that the average hourly earnings for waitresses in Iowa City, including tips, is between these values.

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The areas and legths are:

L = 120 - 2w

when width = 10

L = 120 - 2 x 10

120 - 20

Length = 100

Area = L x W

= 10 x 100

= 1000

When width is 30

L = 120 - 2 x 30

L = 60

Area = 30 x 60

= 1800

When width = 40

L = 120 - 2 x 40

L = 120 - 80

L = 40

Area = 40 x 40

= 1600

Hence the area and length are

1. Length = 100

Area = 1000

2. Length = 60

Area = 1800

3. Length = 40

Area = 1600

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Answer:

v-at/m

Step-by-step explanation:

v=mu+at

change of subject of the formula

mu=v-at

u=v-at/m

We are given the expression for the velocity of a moving vehicle, [tex]v=mu+at[/tex] and asked to rewrite the expression in terms of "u."

To complete this, we simply need to use our knowledge of algebra.

[tex]\Longrightarrow v=mu+at[/tex]

[tex]\Longrightarrow v-at=mu\\[/tex] - Subtracted "at" from both sides of the equation

[tex]\Longrightarrow \frac{v-at}{m} =u\\[/tex] - Divided both sides by "m"

[tex]\Longrightarrow \boxed{u=\frac{v-at}{m} \\} \therefore Sol.[/tex]

Answer:

if you mean graph here's the answer

Root (2 , 0)

Domain x

Range y€ { - infinite , 0 }

Maximum (2 , 0)

Vertical intercept (0 , -12)

Step-by-step explanation:

if anything otherwise I don't know, sorry

Answer:

The answer is "d"

-3(4x-2)-2x

-12x+6-2x

-12x-2x+6

-14x+6

Hence, the answer is D.

Answer:

The would-be option number D

Step-by-step explanation:

Distribute - 3 through the parentheses

[tex]-12x+6-2x \\-14+6[/tex]

The quantity of tomatoes in ounces Amanda picks each day as required to be determined on the task content is; 1.5 ounces.

It follows from the task content that Amanda grows tomatoes in pots on the rooftop of her building in which case, after 2 days, she picked a total amount of 3 pounds of tomatoes.

Since the same amount of tomatoes is picked each day;

The unit rate which represents the ounces of tomatoes she picked each day is; 3/2 = 1.5 ounces per day.

Ultimately, the number of ounces of tomatoes she picks each day is; 1.5 ounces.

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The standard enthalpy of reaction for the given chemical reaction is -188.42 kJ/mol.

To calculate the standard enthalpy of reaction for the given chemical reaction, we need to use the standard enthalpies of formation for the reactants and products.

First, we need to write the balanced chemical equation for the reaction:

2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g)

However, we need to account for the stoichiometry of the reaction by multiplying each standard enthalpy of formation by the corresponding stoichiometric coefficient in the balanced equation.

ΔH°f(NaOH) = -470.11 kJ/mol x 2 = -940.22 kJ/mol

ΔH°f(H₂O) = -285.8 kJ/mol x 2 = -571.6 kJ/mol

The standard enthalpy of formation for Na(s) and H₂(g) are both zero, as they are in their standard states.

Now, we can use the standard enthalpies of formation to calculate the standard enthalpy of reaction using Hess's law. Hess's law states that the enthalpy change for a reaction is the same regardless of the route taken from reactants to products, provided that the initial and final conditions are the same.

ΔH°rxn = ΣΔH°f(products) - ΣΔH°f(reactants)

ΔH°rxn = [2ΔH°f(NaOH) + ΔH°f(H₂)] - [2ΔH°f(H₂O) + 0]

ΔH°rxn = [2(-940.22 kJ/mol) + 0 kJ/mol] - [2(-571.6 kJ/mol) + 0 kJ/mol]

ΔH°rxn = -188.42 kJ/mol

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The value of x in the arc length is 12.

We have,

Arc length = 2 x inscribed angle.

And,

∠M = 1/2 x 124 = 62

And,

The sum of the angles in a triangle = 180

69 + 62 + ∠L = 180

∠L = 180 - 131

∠L = 49

∠L = 1/2 x (7x + 14)

49 = 1/2 x (7x) + 1/2 x 14

49 = (7/2)x + 7

49 - 7 = (7/2)x

42 = (7/2)x

x = 6 x 2

x = 12

Thus,

The value of x in the arc length is 12.

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Answer:

length= 19cm

width= 9.1cm

Step-by-step explanation:

Answer:

[tex]\frac{11}{3}[/tex]

Step-by-step explanation:

2[tex]\frac{1}{5}[/tex] ÷ [tex]\frac{3}{5}[/tex]

2 1/5 = 11/5

[tex]\frac{11}{5}[/tex] ÷ [tex]\frac{3}{5}[/tex] = [tex]\frac{11}{5}[/tex] · [tex]\frac{5}{3}[/tex] = [tex]\frac{55}{15}[/tex] = [tex]\frac{11}{3}[/tex]

So, the answer is  [tex]\frac{11}{3}[/tex]

The smoking during pregnancy is related with the "pre-mature" births of the child, and the 95% confidence interval to estimate length of pregnancy for smoker women is (258.49, 263.51) days.

The "Confidence-Interval" is defined as a range of values which is likely to contain the "true-value" of a population parameter based on a sample of data. It is a measure of the precision of the estimate.

Yes, the smoking during pregnancy has been associated with premature births in previous research.

To find the 95% confidence interval to estimate the length of pregnancy for women who smoke, we can use the formula:

⇒ Confidence Interval = x' ± [tex]z_{c}[/tex] × (σ/√n),

where, x' is = sample mean = 261 days, [tex]z_{c}[/tex] is = critical z-value = 1.96,

⇒ σ is = population standard deviation = 15 days, and

⇒ n is = sample size = 137,

Substituting the values in Confidence Interval Formula,

We get,

⇒ Confidence Interval = 261 ± 1.96 × (15/√137),

⇒ Confidence Interval = 261 ± 2.51,

⇒ Confidence Interval = (258.49, 263.51),

Therefore, the 95% confidence interval to estimate the length of pregnancy for women who smoke is (258.49, 263.51) days.

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To find the length of the loop of the given curve, we need to use the formula for arc length: L = ∫√(dx/dt)² + (dy/dt)² dt.

where dx/dt and dy/dt are the derivatives of x and y with respect to t.
In this case, we have:

dx/dt = 12 - 12t²
dy/dt = 24t

Therefore,
(dx/dt)² + (dy/dt)² = (12 - 12t²)² + (24t)² = 144t⁴ - 96t² + 144
and √(dx/dt)² + (dy/dt)² = √(144t⁴ - 96t² + 144)
The loop of the curve occurs when y = 0, which implies 12t² = 0, i.e., t = 0.

So, we need to integrate from t = 0 to t = 2: L = ∫₀² √(144t⁴ - 96t² + 144) dt
This integral can be quite difficult to solve analytically, so we can use numerical methods to approximate the value of L. Using a numerical integration tool, we get: L ≈ 33.14

Therefore, the length of the loop of the given curve is approximately 33.14 units.

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Answer:

List 3 is the correct sample space.

According to the given conditions, there were 8 sandwich meals and 13 pizza meals ordered.

Solving equations involves finding the values of the variables that make the equation true. This is often done by manipulating the equation using algebraic operations and rules until the variable being solved for is isolated on one side of the equation.

Let's represent the number of sandwich meals ordered by 'x' and the number of pizza meals ordered by 'y'.

From the problem statement, we know that:

x + y = 21 (since there were 21 students who ate lunch)

4.99x + 5.95y = 117.27 (since the total cost of all the meals was $117.27)

We can use the first equation to solve for one variable in terms of the other. Solving for 'x', we get:

x = 21 - y

Substituting this into the second equation, we get:

4.99(21-y) + 5.95y = 117.27

104.79 - 4.99y + 5.95y = 117.27

0.96y = 12.48

y = 13

So, 13 pizza meals were ordered. Substituting this back into the first equation, we get:

x + 13 = 21

x = 8

8 sandwich meals were ordered.

Therefore, according to the given conditions there were 8 sandwich meals and 13 pizza meals ordered.

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Answer:12

Step-by-step explanation:

12

the answer is 8 ddddddddddddddddddddddddddd

42.7

Step-by-step explanation:

V=1/3base area×height

1/3(4×4)×8

5.333×8

42.7

The merchant has two choices: either sell each pen for 15p (by charging 45p for a pack of three), or sell each pen for 10p (by pricing £1 for a box of ten).

Make the set of three pens cost 50p instead of 45p, making each pen 16.67p. The second choice is to make the pack of 10 pens, which is now priced at £1.20, only cost £1, making each pen 10p. Only one pricing needs to be altered in both scenarios.

The cost of a pack of three pens would be 50p, and each pen would cost 16.67p, if the shopkeeper chooses the first course of action. The cost of the second option would be £1 for a pack of ten pens and 10p for each pen. The shopkeeper can potentially enhance sales by making it simpler for customers to make purchasing decisions by asking the same amount for each pen.

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The Matrix represents combined points scored per quarter for the first 4 games

A + B =  [ 6  3  2  3

              28 32 7 13

              17  37 18 17

              23 0 44 24]

We have two Matrix as

A = [ 6  0  13  3

       21  18 0  7

       14  28 6  0

       0   0  35  7 ]

and, B = [ 0  3  9  0

                7  14  7  6

                3  9  12  17

                23 0 9   7 ]

As, Only when the given matrices are in the same order may matrices be added. By order, we mean that the matrices have the same amount of rows and columns.

So, the Matrix represents combined points scored per quarter for the first 4 games

A + B =  [ 6  3  2  3

              28 32 7 13

              17  37 18 17

              23 0 44 24]

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A concave hexagon with 2 pairs of congruent sides is a shape that has six sides and two pairs of sides that are of equal length, but the shape curves inward at one or more angles, creating a concave indentation.

A hexagon is a six-sided polygon, and when two pairs of its sides are congruent,

it means that four of its sides have the same length, if the shape curves inward at one or more angles,

it creates a concave hexagon, which means that the indentation on the shape is facing inward, rather than outward, a concave hexagon with 2 pairs of congruent sides is a six-sided polygon with four sides of equal length, but with a curvature that creates an inward indentation.

Hence, a concave hexagon with 2 pairs of congruent sides is a six-sided figure with an indentation and two sets of sides with equal lengths.

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Here the concept Pythagoras theorem is used here to prove that the square of hypotenuse is the sum of square of the base and altitude. It is an important topic in Maths which explains the relation between the sides of a right-angled triangle.

Pythagoras theorem states that ''In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides. The sides of this triangle have been named perpendicular base and hypotenuse.

Here Hypotenuse is the longest side as it is opposite to the angle 90°. The formula of Pythagoras theorem is:

Hypotenuse² = Perpendicular² + Base²

In triangle STU, Pythagoras theorem is applied.

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'A study that compares standardized test scores before and after a course is taken' is  most likely to be dependent samples.

The most likely dependent samples are those in which the measurements are taken from the same individual or group of individuals in different conditions. Based on this, the answer is:

'a study that compares standardized test scores before and after a course is taken'

In this case, the same individuals are being measured twice (before and after taking the course), and their scores are being compared. The scores are dependent because they are being measured from the same individuals in both conditions.

The other options are less likely to involve dependent samples:

a) In comparing wait times at two different emergency rooms, the measurements are independent because they are taken from different individuals at different locations.

b) In comparing salaries earned by men and women in the same job position, the measurements are independent because they are taken from different individuals.

c) In comparing weight gain for puppies who eat two different brands of food, the measurements are independent because they are taken from different individuals (puppies) who are being exposed to different conditions (different brands of food).

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The area of the pentagon is given by A = 688.19 mm²

Given data ,

Let the area of the pentagon be represented as A

Now , the value of A is

Let the side length of the pentagon be a

where A = ( 1/4 )√5 ( 5 + 2√5 ) a²

On simplifying , we get

A = ( 1/4 ) √5 ( 5 + 2√5 )( 20 )²

On further simplification , we get

A = 688.19096 mm²

Hence , the area is A = 688.19 mm²

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The total cost of a car including sales tax and other things is $20334.5.

Given that, Diego just bought a used car from his cousin for $18,500.

Registration cost=$75, Emission Test=$42 and weather-protection for paint = $330.

Sales tax =7.5%

Here, sales tax = 7.5% of 18500

7.5/100 ×18500

= 0.075×18500

= $1387.5

Total cost of a car = 18,500+75+42+330+1387.5

= $20334.5

Therefore, the total cost of a car including sales tax and other things is $20334.5.

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Step-by-step explanation:

FV = PV ( 1 + i)^n     FV = future value      PV = present value ( 150)

                                  i = decimal interest per period (.067)

                                  n = periods = 5

FV = 150 ( 1 + .067)^5   = $ 207.45

The average of the points A, B and C with weights 1, 1 and 1

respectively is: (-5/3, -2)

A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.

Thus:

Weighted average = [(w₁ × x₁) + (w₂ × x₂) + (w₃ × x₃)]/(w₁ + w₂ + w₃)

Where:

w_i is the weight of the ith point

x_i is the coordinate of the ith point.

Thus:

x-coordinate = [(1 × -4) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

x-coordinate = -5/3

y-coordinate = [(1 × -5) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

y-coordinate = -2

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Step-by-step explanation:

29.3125  lb  -  3.75 lb = 25.5625   pounds heavier

Answer: 25.5625 pounds, rounded 25.6

Step-by-step explanation:

29.3125 - 3.75 = 25.5625