Use substitution!!!

Pt. a
truck a costs $20,345. You can expect to pay an average of $1230 per year for repairs. truck b costs about 16,000. It will cost an average of $1425 for repairs per year. After how many years are the total costs for cars the same?
(I can solve it, can you just turn the words into an equation for me?)

Pt. B
You have 56 coins that are all nickles and dimes. The value of the coins is $2.05. Find the number of nickels and dimes.
(Can you also just make an equation out of this for me?)

Tom is installing 6 windows each day and Suzanne is installing 6 windows each day as well.

To find the number of days it takes for each homebuilder to install the windows, we need to solve for x in each equation.

Tom's equation: 42 = 7x + 2

Subtracting 2 from both sides:

40 = 7x

Dividing both sides by 7:

x = 5.71 ≈ 6

So it will take Tom approximately 6 days to install the windows on his home.

Suzanne's equation: 37 = 6x + 5

Subtracting 5 from both sides:

32 = 6x

Dividing both sides by 6:

x = 5.33 ≈ 6.

So it will take Suzanne approximately 6 days to install the windows on her home.

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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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The area of the shaded region is 559 ft².

In order to find the area of the shaded region, we will subtract the area of the square from the area of the rectangle. That is:

area of the shaded region = area of rectangle - area of square

area of the shaded region = (32 * 20) - (9 * 9)

area of the shaded region = 640 - 81

area of the shaded region = 559 ft²

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Complete Question

See attached image

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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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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Answer:

yes

Step-by-step explanation:

log4(64)=3－0,4*4*4=64

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.

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

Statement " There will be 5 dots above 7" is true. Therefore, option D is the correct answer.

A line plot is an effective way to visualize and compare data in a table. In this case, the line plot would show the total number of people on each team, with dots representing the values.

The greatest value in the table is 11, but this would not be represented with a dot in the line plot. There will be 11 dots in total, representing the 11 teams listed in the table.

There will be 4 more dots above 7 than above 8, since there are 4 teams with 7 people on each team and only 3 teams with 8 people on each team.

Finally, there will be 5 dots above 7, since there are 5 teams with 7 or more people on each team.

Therefore, option D is the correct answer.

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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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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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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 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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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?

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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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.

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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Answer:

Step-by-step explanation: However, say that the car loses 50% of its value every year. This means that if you originally bought a car for 2,000 dollars in 2015, in 2016 it would be world 2,000/2=1,000, 1,000/2=500 the year after that, and so on. We can try to put this into a linear function, but it's hard to put it into one equation because we're not subtracting or adding to the cost of the car by a specific amount each year. If we had our equation as y=-0.5*x+2000, this wouldn't work because it's adding to the original amount, not multiplying. However, if we used an exponential equation such as y=b(m^a), with y representing the end cost, b representing the starting cost, m representing the amount multiplied per year, and a representing the number of years. This works because we start with a value, and multiply it by an amount each year. Since 50%=0.5, we plug that into m to get y=2,000(0.5^a). Therefore, this works well here. If the minivan were to depreciate by 3,000 every year, starting at $29,248, this means that we first have to find out what we multiply by 29,248 by the first year to subtract 3,000. As, after one year, the value is 29,248-3,000=26,248, we have 26,248=29,248(m^1). Therefore, we can divide 29,248 by both sides to get around 0.9 as our answer form. Thus, our equation is y=29,248(0.9^a). This type of equation would not work if we subtracted an amount every year because we're not multiplying by the same amount then. For example, if a toy was valued at 3$ and gained a value of one dollar every year, we could multiply the toy by 4/3 the first year to get 4, but the next year we wouldn't get 5.

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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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 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 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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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 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 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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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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The smallest approximate sample size required to obtain the desired margin of error is b. 180 Chihuahuas

The sample size is defined as the number of observations used for determining the estimations of a given population. It should be noted that the size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.

The sample size will be:

= (2.576 × 26 / 5)²

= 180

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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 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