An artist uses 60 pounds of clay to make 80 bowls. The ratio of pounds of clay she uses to the number of bowls she makes is a proportional relationship. Select all the true statements.

Answer:

y+2=1/2(x+3)

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

Answer:

6x = 360

rate = x = 60 mph (Faster car rate)

Slower car rate = distance/time = 294/6 = 46 mph

Step-by-step explanation

brainly pls

Answer:

6√7 m/s

Step-by-step explanation:

Given,

u = 12

a = - 3

s = 18

v^2 = u^2 - 2as

= 12^2 - 2 ( - 3 ) ( 18 )

= 144 + 108

v^2 = 252

v = √252

v = 6√7 m/s

Step-by-step explanation:

hope it helps you...:)....

We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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The total return over the year is 15.46%. The dividend yield is 7.21%, and the capital gain rate is 15.46%.

The price of a stock is equal to the current dividend plus the present value of all future dividends plus the price in one year. As a result, the share price of SPCC after a year will be:$112 = $7 + $105 + PV$PV = $0

Using the formula of the total return of an asset, which is equal to its capital gain plus dividend yield, we have;Total Return = Capital Gain + Dividend YieldCapital Gain = (Ending Price - Initial Price) / Initial PriceCapital Gain = ($112 - $97) / $97 = 0.1546 or 15.46%Dividend Yield = Annual Dividend per Share / Initial PriceDividend Yield = $7 / $97 = 0.0721 or 7.21%

Therefore, the total return over the year is 15.46%. The dividend yield is 7.21%, and the capital gain rate is 15.46%.

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When we vary two inputs or decision variables and want to see how the changes in these quantities change a single output.

When we vary two inputs or decision variables and want to see how the changes in these quantities change a single output, the table we use is called the Two-way Table.A two-way table is a table that shows the frequency distribution of categorical data in two different ways. It has two rows and two columns with one categorical variable defining the row and the other defining the column.To display the distribution of one variable along one dimension and the distribution of the other variable along the other dimension, we use a two-way frequency table. It's the same as a contingency table, but it includes frequency counts for each mix of the two variables.A two-way table is used in statistics to show the distribution of data when two different variables are taken into account. It is created to make comparisons between data in a tabular format to highlight correlations or relationships between the variables. Hence, the correct answer is the option d. Two-way Table.

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Answer:

7.81cm/ c

Step-by-step explanation:

Answer:

$2.85

Step-by-step explanation:

8.55/3

Answer:

$2.85 per foot

Step-by-step explanation:

all u gotta do is 8.55/3

Given:

The current volume of the lake is 198,000 gallons.

Its volume grew by 3000 gallons every week

To find: An equation modeling the number of gallons in the lake after some weeks.

Explanation:

As we know,

If the growth or decay involves increasing or decreasing by a fixed number, then we must use a linear function.

Here, the increasing rate is 3000.

The current volume is 198,000 gallons.

Thus, the linear function that represents this situation is,

Where w represents the number of weeks and V represents the volume.

Final answer:

The equation is,

An augmented matrix is invertible if the linear system has a unique solution.

The augmented matrix is known as a rectangular matrix.

The properties of an augmented matrix includes:

Note that the inverse of a matrix must be unique

And If A is invertible, then its inverse is unique.

If the linear system is unique, then the augmented matrix is invertible.

Thus, an augmented matrix is invertible if the linear system has a unique solution.

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Answer:

S = R θ      where θ is in radians

If θ  = 2 pi then S = 2 pi R       the circumference of the circle

θ = S / R = 9.7 / 9 = 1.08 rad

Since 1 rad = 360 / (2 pi) = 57.3 deg

the angle included = 1.08 rad * 57.3 deg/rad = 61.9 deg

The correct statement about the parent function f(x) = x² and the function g(x) = 1/4x² is: the function g(x) = 1/4x² is a vertically compressed version of the parent function f(x) = x².

A function is a mathematical concept that describes the relationship between a set of inputs (called the domain) and a set of outputs (called the range). It assigns each input value to exactly one output value.

The function g(x) = 1/4x² is a vertically compressed version of the parent function f(x) = x².

The function g(x) = 1/4x² has a coefficient of 1/4 in front of the x² term, which means that the graph of g(x) is vertically compressed compared to the graph of the parent function f(x) = x². The compression factor of 1/4 indicates that the values of g(x) will be one-fourth the height of the corresponding values of f(x).

In other words, for any given value of x, the y-coordinate of g(x) will be one-fourth the value of the corresponding point on the graph of f(x).

Therefore, the correct statement is that the function g(x) = 1/4x² is a vertically compressed version of the parent function f(x) = x².

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Answer:

There were 24 chocolates in the box to begin with.

Step-by-step explanation:

Let's use working backwards to solve this problem.

We know that there are 12 chocolates left in the box. Let's call the number of chocolates that were in the box to begin with "x".

After eating 1/4 of what was left, Forest had 3/4 of the chocolates left. So, we can set up an equation:

3/4 (x - 1/3x) = 12

We can simplify this equation by multiplying both sides by 4/3:

x - 1/3x = 16

Multiplying both sides by 3:

2x = 48

x = 24

Therefore, there were 24 chocolates in the box to begin with.

so we can look at this as two triangles, one on the upper part, it has a base of 5+5 and a height of 5, and another triangle on the lower part, it has a base of 5+5 and a height of 12, let's get their area and sum them up.

\(\stackrel{ \textit{upper part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{5})}~~ + ~~\stackrel{ \textit{lower part} }{\cfrac{1}{2}(\underset{b}{5+5})(\underset{h}{12})}\implies25+60\implies \text{\LARGE 85}\)

Respuesta:

88,8 cm²

Explicación:

Consideremos un hexágono regular. Su apotema, la distancia más corta entre el centro del hexágono y uno de sus lados, es 3,7 cm y sus lados miden 8 cm.

Primero debemos calcular su perímetro, que es igual a la suma de sus 6 lados.

Perímetro = 8 cm + 8 cm + 8 cm + 8 cm + 8 cm + 8 cm = 48 cm

Luego, podemos calcular el área del hexágono usando la siguiente fórmula:

Area = Perímetro × Apotema / 2

Area = 48 cm × 3,7 cm / 2 = 88,8 cm²

Answer:

551.06feet

Step-by-step explanation:

Given the equation

y=-16x^2+174x+78

At maximum height, dy/dx = 0

dy/dx = -32x + 174

0 = -32x+174

32x = 174

x = 174/32

x = 5.4375

GEt the maximum height

y=-16x^2+174x+78

y=-16(5.4375)^2+174(5.4375)+78

y = -473.0625 + 946.125 + 78

y = 551.0625

Hence the maximum height is 551.06feet to the nearest hundredth

Answer: The way you would write this in standerd form would be like this one  point fourty four times one hundered six. Let me know if this correct or not.

Step-by-step explanation:

Answer:

13 and 32

Step-by-step explanation:

let one number be x

Then the other number is x + 19 , then

x + x + 19 = 45

2x + 19 = 45 ( subtract 19 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13

The 2 numbers are 13 and 13 + 19 = 32

The derivative of the given expression using the chain rule is -e^(-t/τ) cos(ωt)/τ.

To find the derivative of the given expression using the chain rule, we need to apply the chain rule formula, which states that if y = f(u) and u = g(x), then:

dy/dx = dy/du * du/dx

In this case, we have:

y = e^(-t/τ) * sin(ωt)

u = -t/τ

f(u) = e^u

g(x) = -t/τ

Using the chain rule formula, we can find:

dy/dx = dy/du * du/dx

dy/du = d/dx(e^u) = e^u * du/dx

du/dx = -1/τ

Substituting these values, we get:

dy/dx = e^(-t/τ) * cos(ωt) * (-1/τ)

dy/dx = -e^(-t/τ) * cos(ωt)/τ

Therefore, the value obtained is -e^(-t/τ) * cos(ωt)/τ.

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Answer:

Step-by-step explanation:

The point at which the line intersects the given plane x = 1 − t, y = 5 t, z = 2t; x − y +4z = 2

(x, y, z) =(1/2 ,5/2, 1)

The point at which the line intersects the given plane x = 1 − t, y = 5 t, z = 2t; x − y -4z = 2

(x, y, z) = (15/14,-5/14, -1/7)

The points on the line are x = 1 − t, y = 5 t, z = 2t

a) When Equation of Plane is x- y+ 4z = 2

The point of intersection of a line and a plane is the point where the meet each other and passes after.

Thus, we can rewrite the equation of plane with the values of x, y, z as x = 1 − t, y = 5 t, z = 2t, we get,

(1-t) - 5t +4(2t) = 2

⇒ 1 - 6t + 8t = 2

⇒2t = 1

⇒ t = 1/2 (= 0.5)

Putting t= 1/2 in x = 1 − t, y = 5 t, z = 2t, we get

x= 1- 1/2 = 1/2

y= 5(1/2) = 5/2  , and

z= 2(1/2) = 1

At x=1/2 , y= 5/2 and z=1 the given line intersects the plane  x- y+ 4z = 2.

b) When Equation of Plane is x- y- 4z = 2

The point of intersection of a line and a plane is the point where the meet each other and passes after.

Thus, we can rewrite the equation of plane with the values of x, y, z as x = 1 − t, y = 5 t, z = 2t, we get,

(1-t) - 5t -4(2t) = 2

⇒ 1 - 6t - 8t = 2

⇒-14t = 1

⇒ t =- 1/14

Putting t= -1/14 in x = 1 − t, y = 5 t, z = 2t, we get

x= 1-(- 1/14) = 15/14

y= 5(-1/14) = -5/14 , and

z= 2(-1/14) = -1/7

At x=15/14, y=-5/14 and z= -1/7 the given line intersects the plane (x-y-4z = 2).

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Answer:

29/150

Step-by-step explanation:

Probability is the number of times a certain value is obtained out of the total number of attempts.

If Carol got 6 29 times out of 150, then the probability of getting a 6 = 29/150.

This can be written as a percent or decimal too = 0.193 = 19.3%

Hope this helps.

Good Luck

Answer:

m∠U = 54.5°

Step-by-step explanation:

ΔUVW is an isosceles triangle.  The angles opposite UV and VW are congruent.

That means m∠U = m∠W

Since the measures of the angles of a triangle have a sum of 180, then

m∠U + m∠W + m∠V = 180

m∠U + m∠U + 71 = 180

2 m∠U = 109

m∠U = 54.5°

Answer:

I believe it's 15

Step-by-step explanation:

15^2 is 225

Answer:

6 and 102 = 62

119 and 23 = 38

96 and 51 = 33

28 and 87 = 65

Step-by-step explanation:

just did mine :D

For mileages more than 173 miles, Company A charges less than Company B.

This can be represented as an inequality: $104 < 0.6m + 65$, where $m$ is the number of miles driven. Solving this inequality for $m$, we get $m > 173$ miles drivenThe question is asking about the mileages where Company A charges less than Company B. Company A charges a flat fee of $104 with unlimited mileage, while Company B charges an initial fee of $65 and an additional $0.60 for every mile driven. To determine the mileage where Company A charges less than Company B, we need to set up an inequality to compare the prices of the two companies. The inequality can be represented as $104 < 0.6m + 65$, where $m$ is the number of miles driven. Solving for $m$, we get $m > 173$ miles driven. Therefore, for mileages more than 173 miles, Company A charges less than Company B.

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Answer:

The answer is a = -13 - 1/4b

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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