A foundry has been commissioned to make souvenir coins. The coins are to be made from an alloy that is 40% silver. The foundry has on hand two alloys, one with 50% silver content and one with a 25% silver content. How many kilograms of each alloy should be used to make 40 kilograms of the 40% silver alloy?

50% alloy kg

25% alloy kg

The picture for reduction and enlargement is attached

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying. while that of decrease is reduction.

The drawing of the the reduction is a square of side 8 units. The scale factor given is 1/2 hence we have the dimensions are as follows

preimage: 8 units x 8 units

image: 4 units x 4 units

The drawing of the the enlargement is a circle of radius 2 units. The scale factor given is 2, hence we have the dimensions are as follows

preimage: radius = 2 units

image: radius = 4 units

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The formula for the inverse function h⁻¹(P) is:

The population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is approximately 17.5 days.

To find the inverse function h⁻¹(P), we need to solve the equation P = h(t) for t in terms of P.

Starting with P = h(t) = [tex]100/1+4e^-^0^.^0^5^t[/tex]

we can first multiply both sides by [tex]1+4e^-^0^.^0^5^t[/tex] to get:

[tex]P(1+4e^-^0^.^0^5^t) = 100[/tex]

t = -20ln(4/(P-100)+1)

Therefore, the formula for the inverse function h⁻¹(P) is:

h⁻¹(P) = -20ln(4/(P-100)+1)

(b) To find h⁻¹(90)

we substitute P = 90 into the formula for h^-1(P):

h⁻¹(90) = -20ln(4/(90-100)+1)

= 17.5

This means that if the population of insects in the lab experiment is 90, then the number of days it takes for the population to reach that size is  17.5 days.

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The product of two given vectors is 48.

Given that, |v|=8, |w|=12 and the angle between v and w is 60 degrees.

We know that, |a|·|b|=|a|×|b|×cosθ.

Here, |v|·|w|=8×12×cos60°

= 96× 1/2

= 48

Therefore, the product of two given vectors is 48.

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For an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment will be; 1.86 units.

To Determine the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we need to find the slope of the line, which is the coefficient of x in the equation.

We are given that the equation of the line of best fit, y = −0.76x8.76

The slope is 1.86, that means that for every one unit increase in x (which in this case is one hour worked), y (in this case is the amount of money spent on entertainment) is predicted to increase by 1.86 units.

This is the change in the dependent variable (y) for a unit increase in the independent variable (x),

Based on the linear relationship described by the equation of the line fit.

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The reasonable estimate would be 25

We have to solve this using the rule of 3

9 out of 30 members said that they run more than 5 days a week.

We will form the equations

when 9 ran = 30 menbers

when n ran = 84 members

we will then cross multiply

84 x 9 = 30 x n

n = 25.2

When we round this, the reasonable estimate would be 25

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Complete question

Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.

There are 84 Freemont Run Club members.

Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?

Step-by-step explanation:

Exponetial (compounding ) growth

  New Price = original price ( 1 + .10)^n      n is months  .10 is 10% per month

                     = $  110 ( 1.10)^3 = $ 146 . 41   three months later

Using the sine ratio, the value of p in the right triangle, in simplest form is: p = 4.

To find the value of p, we have to determine what formula to use. We would apply the sine ratio, which is:

sin ∅ = opposite side / hypotenuse.

From the right triangle in the diagram, we have:

sin 30 = p / 8

p = sin 30 * 8

Note: sin 30 = 1/2

Therefore, we have:

p = 1/2 * 8

p = 4

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The momentum change of the rock caused by its fall will be 35.49 x [tex]10{-24[/tex] m/sec and the magnitude of the earth velocity will be 212.94 kgm/s

We have,

Mass of the rock = 18 kg

Distance traveled = 7 m

Mass of earth = 6 x [tex]10^{24[/tex] Kg

Using second equation of motion

S= ut  + 1/2 at²

If the body freely falls initial velocity will be zero.

u = initial velocity = 0

Then, S = 1/2 at²

7 = 1/2 x 10 x t²

14/ 10= t²

t= 1.183 sec

Now, Change in the momentum of the rock will be,

ΔP= FΔT

ΔP = (mg ) ΔT

ΔP= (18) x  10 x 1.183

ΔP=212.94 kg-m/s²

Now,  Earth will also have same momentum change

ΔP(earth)= ΔP(rock)

6 x [tex]10^{24[/tex] Kg x Δv = 212.94

Δv = 35.49 x [tex]10{-24[/tex] m /sec

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If your objective is to save $300,000 over 25 years, you would need to put away around $3077.41 every six months.

To solve this problem, we can use the formula for the future value of an annuity:

[tex]FV = P *\frac{((1 + r/n)^{(n*t)} - 1)}{(r/n)}[/tex]

where FV is the future value, P is the periodic payment, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Since the interest is compounded annually, we have n = 1 and r = 0.05. To find the periodic payment P, we can rearrange the formula:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Plugging in the given values, we have:

[tex]P = 300000 * (0.05/2) / ((1 + 0.05/2)^{(2*25)} - 1)[/tex]

P ≈ $3077.41

Therefore, you would need to invest approximately $3077.41 every six months to reach a savings goal of $300,000 at the end of 25 years.

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The length the one-inch pipe should be cut to make a flute with a lowest desired note of 523.25 Hz, based on the acoustic length formula is 12.9 inches

The acoustic length is the length obtained from the sum of  the bore length and the corrections at the foot and the sound hole.

The frequency of the lowest note = 523.25 Hz

Whereby the frequency of the lowest note = The fundamental frequency

The acoustic length formula for finding the length of the pipe, L, can be presented as follows;

L = (v/(2·f)) × √(1 + 4·A²/v²)

Where;

L = The length of the pipe

f = The frequency = 523.25 Hz

A = The cross-sectional area of the pipe = π × 1.315²/4 ≈ 1.36 in²

v = The speed of sound ≈ 343 m/s ≈ 13503.9 in/s

L = (v/(2·f)) × √(1 + 4·A²/v²)

L = (13503.9/(2×523.25)) × √(1 + 4×1.26²/13503.9²) ≈ 12.9

The length of the pipe is about 12.9 inches

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The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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The probability of landing on a white square is 4/5.

We have toss board of measurement 5 x 5.

Total squares in board = 25

White square = 20

Black square= 5

So, the probability of landing on a white square

= 20 / 25

= 4/5

Thus, the required probability is 4/5.

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Answer:

There are 36 possible outcomes when two dice are rolled (6 outcomes for the first die and 6 outcomes for the second die). To find the probability that the sum of the two numbers on the dice will be greater than 9, we need to count the number of outcomes where the sum is greater than 9.

The possible outcomes where the sum is greater than 9 are (4,6), (5,5), (5,6), and (6,5), for a total of 4 outcomes. Therefore, the probability of getting a sum greater than 9 is 4/36 or 1/9.

Answer: C) 1/12.

The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]

We have,

To write an exponential model given two points (6,85) and (7,92), we can use the general exponential function form:

y = a[tex]b^x[/tex]

where y is the dependent variable, x is the independent variable, a is the initial value (when x = 0), and b is the base of the exponential function.

To find the values of a and b, we can use the two given points as follows:

When x = 6, y = 85:

85 = a b^6

When x = 7, y = 92:

92 = a b^7

We now have a system of two equations with two unknowns (a and b).

We can solve for a by dividing the second equation by the first equation:

92/85 = (ab^7) / (ab^6)

1.0824 = b

Substitute this value of b into one of the equations to solve for a:

85 = a (1.0824)^6

a = 41.62

Therefore,

The exponential function that models the relationship between the two points is [tex]y = 41.62 (1.0824)^x.[/tex]

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The machine's purchasing cost is $309,210.

The acquisition cost of the machine is the total cost incurred by the firm to purchase and put the machine into service.

To determine the acquisition cost of the machine, we need to add up all the costs listed in the question.

Invoice price = $299,000

Applicable sales tax = $2,100

Freight paid = $1,160

Cost of insurance coverage = $1,025

Installation costs = $1,900

Testing and adjusting costs = $1,375

Repair of damages caused by the firm's employees = $1,450

Prepaid maintenance contract = $1,200

Total acquisition cost = Invoice price + Sales tax + Freight paid + Cost of insurance coverage + Installation costs + Testing and adjusting costs + Repair of damages caused by the firm's employees + Prepaid maintenance contract

Total acquisition cost = $299,000 + $2,100 + $1,160 + $1,025 + $1,900 + $1,375 + $1,450 + $1,200

Total acquisition cost = $309,210

Therefore, the acquisition cost of the machine is $309,210.

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The y-intercept of the line is 2.

In the equation y = 9x + 2, x and y are variables that represent the coordinates of any point on the line.

To find the Y-intercept, we need to find the value of y when x equals 0.

When x equals 0, the equation becomes:

y = 9(0) + 2

Any number multiplied by 0 is 0, so the first term drops out and we are left with:

y = 0 + 2

Which simplifies to:

y = 2

Therefore, when x equals 0, y equals 2. This means that the point (0, 2) is on the line. In other words, the line intersects the y-axis at y = 2, which is the Y-intercept of the line.

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The amount of soil to fill the garden box is V = 1,134 inches³

Given data ,

Let the volume of the first rectangular box be V₁

Let the volume of the second rectangular box be V₂

where Volume of Rectangle = Length x Width x Height

So , V₁ = 21 x 7 x 2

V₁ = 294 inches³

And , V₂ = 12 x 10 x ( 7 )

V₂ = 120 x 7

V₂ = 840 inches³

And , the total soil in the garden box = V₁ + V₂

Amount of soil in garden box = 1,134 inches³

Hence , the volume is V = 1,134 inches³

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The probability that the sum would be an even number, can be found to be 1 / 2 .

There are six sides on each die so the total number of outcomes is:

= 6 x 6

= 36 outcomes

We will get an even number if we get two odd numbers, and two even numbers. We will not get even, with an even number and an odd number.

The number of two odd number outcomes is:

= 3 x 3

= 9 outcomes

The two even outcomes:

= 3 x 3

= 9 outcomes

The probability that the sum is even is:

= ( 9 + 9 ) / 36 total outcomes

= 18 / 36

= 1 / 2

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The student can choose four questions from a question paper that contains six questions as follow:

a. 10 ways.

b. 5 ways.

c. 15 ways.

Combination is a way of selecting items from a collection where the order of selection does not matter.

a. If Question No. 1 is compulsory, then the student can choose three more questions from the remaining five. That is:

5C3 (i.e. 5 combination 3) ways =  10 ways.

b. If Question No. 2 should not be chosen, then the student can choose four questions from the remaining five. That is:

5C4 ways =  5 ways.

c. If there is no restriction on any of the questions, the student can choose any four questions from the remaining six. That is:

6C4 ways = 15 ways

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Answer: The cost of a large pizza with 2 toppings depends on the pizza place. Let's say the cost is $15 per pizza, and each additional topping costs $2.

Let t be the number of toppings Anna has on her pizza. Then, the total cost of her pizza can be expressed as:

Total cost = $15 + $2t

Since Anna has 2 toppings on her pizza, we can substitute t = 2:

Total cost = $15 + $2(2)

Total cost = $15 + $4

Total cost = $19

Therefore, the total cost of Anna's pizza with 2 toppings is $19.

Note that the volume (V) of the resulting solid which is revolved around it's axis is given as V = 37.699 cubic  units.

If we used the distance formula, to computer the distance between the coordinates, we'd arrive at the following side lenghts:


3,  4, and 5.

Since we are   looking at a right  triangle, it is correct to infr that the hypotenuse is the longer side, which is 5.

We can assume the height to be four  units and the radius to be 3 units.

Thus, using the formula fo rthe volume of a cone:

V = (1/3) * π * r² * h

Inputting values, we have

V = (1/3) * 3.14159 * 3² * 4
V = 1.0472 * 9 * 4
V = 37.6992

If we approximate to the nearest thousandth, we have:

V = 37.699 cubic units

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Jada is directing a comparative analysis to identify whether mold thrives faster in tap water or bottled water.

To upgrade her design and procure data that would be more viable for addressing the question of interest, Jada might reflect on the following:

Randomized Controlled Trial (RCT): Preferably of just contrasting the rate of growth of mold in tap water versus bottled water in a glass, Jada could arbitrarily allote separate glasses to either tap water or bottled water categories.

Replicates and Sample Size: Jada may utilize several copies for each type of water to escalate the probabilistic force of her study.

Control Group: Jada should integrate a control group in her study, where no water is integrated into the glass.

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The best reason why 2/5 is the exact quotient for 1/4 divided by 5/8 is: ²/₅ * ⁵/₈ = ¹/₄

To divide fractions, firstly, you need to turn the 2nd fraction upside down. For example, 3/8 divided by 3/4 would be 3/8 divided by 4/3. After you have flipped the second fraction, you multiply them - 3*4 = 12. 8*3 = 24 so the answer would be 12/24. Which then could be cancelled down to 1/2.

Now, from the given question, we can say that:

1/4 ÷ 5/8

Now, from the earlier step in dividing fractions, the next step is to turn the 2nd fraction upside down and multiply by the first to get:

¹/₄ * ⁸/₅ = ²/₅

Rearranging, we have:

²/₅ * ⁵/₈ = ¹/₄

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Complete question is:

Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/8

The four math sentences that have an answer of 2.4 are 1.2 + 1.2, 1.2 * 2, 3.6 - 1.2 and  4.8/2

From the question, we have the following parameters that can be used in our computation:

An answer of 2.4

Using a different operation in each sentence., we have the following math sentences

1.2 + 1.2

1.2 * 2

3.6 - 1.2

4.8/2

The solution to each of the above sentences is 2.4

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The account's total value is $498,174.72.

The total interest paid is $174,174.72.

We can utilize the calculation for the future value of a compound interest annuity to resolve this issue:

FV = P*(((1 + r/n)(n*t))-1) / (r/n).

where

When we enter the values, we obtain:

FV = 600 * (((1 + 0.12/4)^(4*60)) - 1) / (0.12/4) = 498,174.72

After the 60th deposit, the account's total value is $498,174.72.

We can deduct the total amount deposited from the account's total value to calculate the cumulative interest:

Added interest is calculated as follows: FV - (P * t * n) = 498,174.72 - (600 * 60 * 4) = 174,174.72

Therefore, the total interest paid is $174,174.72.

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Only afford a home with a market value of about $375,000, and she would require a down payment of $75,000 to do so.

First, we have to ascertain how much Kelly can comfortably afford to pay for her mortgage each month. Her income, expenses, and other financial commitments will determine this. Her monthly mortgage payment should not be more than 28% of her total monthly income, on average.

The loan is interest rate is the next thing we need to think about. Kelly will have a constant monthly payment for the duration of the loan thanks to a 30-year fixed rate loan at the current market rate of 4.25%.

With a 20% down payment and a loan with a 4.25% interest rate, we could be calculate the maximum purchase price to be roughly $375,000 using a mortgage calculator.

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The y-intercept for the function g(x) is 4.

The y-intercept of a function is a point where the line crosses the y-axis. The linear function can be given as below.

f(x) = mx+n

Where m is the slope of the line and n is a real number and y-intercept of the line.

The given function is f(x)=-4x—2.

The function is vertically translated 6 units up to g(x).

The y-intercept of the function f(x) is -2. Then the y-intercept for the function g(x) can be given as below.

y-intercept g(x) = -2+6

y-intercept g(x) = 4

Hence,  the y-intercept for the function g(x) is 4.

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slope = -5, y intercept = 2

The graph is below.

======================================

Work Shown:

20x+4y = 8

4y = 8-20x

4y = -20x + 8

y = (-20x+8)/4

y = -20x/4 + 8/4

y = -5x + 2 is the final answer

slope = -5, y intercept = 2

Two points on this line are (0,2) and (1, -3)

The graph is below. I used GeoGebra to make it, but Desmos is another good choice.

The equation r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8 to rectangular form is (x - 1)² + y² = 9

From the question, we have the following parameters that can be used in our computation:

r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8

The above equation is in its polar form, where

r² = x² + y²

cos(θ) = x/r

sin(θ) = y/r

Rearrange the terms in r²cos²(θ) - 2rcos(θ) + r²sin²(θ) = 8

So, we have

r²cos²(θ)  + r²sin²(θ) - 2rcos(θ) = 8

Factorize

r²(cos²(θ)  + sin²(θ)) - 2rcos(θ) = 8

In trigonometry

cos²(θ)  + sin²(θ) = 1

So, we have

r² - 2rcos(θ) = 8

Recall that

r² = x² + y²

cos(θ) = x/r

So, we have

x² + y² - 2r * x/r = 8

Evaluate

x² + y² - 2x = 8

Rearrange

x²  - 2x + y² = 8

Express as perfect squares

(x - 1)² + y² = 8 + 1

So, we have

(x - 1)² + y² = 9

Hence, the equation to rectangular form is (x - 1)² + y² = 9

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