the formula for the cost of buying a car=
cost=12×monthly pavement +deposit

the cost of another car is 8000 pounds
find the monthly pavement when deposit is 2600 pounds

Answer:

7) A    8) C

Step-by-step explanation:

number 7 tells us that y=x+1

so we just basically plug it in

2x+3(x+1)=4  Answer: A

to eliminate x's in number 8, we have to multiply one of the equations by -1

let's multiply the second one

4x+3y=6

4x ·-1-y·1=2·-1

4x+3y=6

-4x+y=-2

x's eliminate

4y=4, meaning that the answer is C

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3

From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.

The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24

The probability that the next piece of track Carly picks will be straight is calculated as follows:

Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T

Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.

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Answer: 1/3

Step-by-step explanation: i did this question and got it right

Answer:

A) 4\(x^{4}\)-4\(x^{3}\)-16\(x^{2}\)+16x

B)4\(x^{4}\)-4\(x^{3}\)-16\(x^{2}\)+16x

Step-by-step explanation:

look at picture

The other two angle measures of a right triangle with side lengths 5, 12, and 13 can be found using trigonometric ratios. Let's label the sides of the triangle as follows:

- The side opposite the angle we are looking for is 5.
- The side adjacent to the angle we are looking for is 12.
- The hypotenuse is 13.

To find the first angle, we will use the inverse tangent function (tan^(-1)). The formula is:
Angle = tan^(-1)(opposite/adjacent)

Plugging in the values, we get:
Angle = tan^(-1)(5/12)

Using a calculator, we find this angle to be approximately 22.6 degrees (rounded to the nearest degree).

To find the second angle, we will use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, the second angle can be found by subtracting the right angle (90 degrees) and the first angle from 180 degrees.
Second angle = 180 - 90 - 22.6

Calculating this, we find the second angle to be approximately 67.4 degrees (rounded to the nearest degree).

Therefore, the other two angle measures of the right triangle are approximately 23 degrees and 67 degrees.

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Answer:

2y + 3 = 6

Step-by-step explanation:

2y + 3 = 6 Subtract 3 from both sides

2y = 3 Divide 2 from both sides

y = 3/2

The sum of t+4/t+5 and 9/t-1 with a common denominator is (t²+12t+41)/[(t+5)(t-1)].

To find a common denominator for the given expressions t+4/t+5 and 9/t-1, we need to determine the least common multiple (LCM) of the denominators (t+5) and (t-1):

The prime factorization of t+5 is (t+5).

The prime factorization of t-1 is (t-1).

Therefore, the LCM is (t+5)(t-1).

To convert t+4/t+5 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t-1):

t+4/t+5 = (t+4)(t-1)/[(t+5)(t-1)] = (t²+3t-4)/[(t+5)(t-1)]

To convert 9/t-1 into an equivalent fraction with the denominator (t+5)(t-1), we multiply both the numerator and denominator by (t+5):

9/t-1 = 9(t+5)/[(t+5)(t-1)] = (9t+45)/[(t+5)(t-1)]

Now both fractions have the same denominator, so we can add them:

(t²+3t-4)/[(t+5)(t-1)] + (9t+45)/[(t+5)(t-1)] = (t²+3t-4+9t+45)/[(t+5)(t-1)]

Simplifying the numerator gives:

t²+12t+41

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Answer:

It would take 5 turns

Step-by-step explanation:

One acre is equal to 43,560 square feet. To convert acres to square feet, you can multiply the number of acres by 43,560.

For example, if you want to convert 6 acres to square feet, you can multiply 6 by 43,560:

6 acres x 43,560 square feet/acre = 261,360square feet

So, 6 acres is equal to 261,360square feet.

Acres and feet are area and length measurement units, respectively. There is no direct conversion between acres and feet because they measure different things. However, you can convert acres to square feet using a conversion factor.

Please keep in mind that this conversion only applies to area measurements. If you need to convert linear measurements from acres to feet, you'll need more information about the area's shape and dimensions.

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Yes, it is possible to find a whole number less than 100 that when divided by 10 has a remainder of 4 and when divided by 47 has a remainder of 17.

To find this number, follow these steps:
Write down the two congruences based on the given information:
  a) x ≡ 4 (mod 10)
  b) x ≡ 17 (mod 47)
Now, solve the congruences to find the smallest positive integer solution for x. In this case, you can use trial and error to find the smallest positive integer that satisfies both congruences. Start by testing the first congruence:
  a) x = 10n + 4, where n is an integer.
Substitute this expression into the second congruence and solve for n:
  b) 10n + 4 ≡ 17 (mod 47)
  c) 10n ≡ 13 (mod 47)
Find the smallest positive integer for n that satisfies this congruence.

In this case, n = 5 is the smallest positive integer,

since 10(5) ≡ 13 (mod 47).
Substitute the value of n back into the expression for x:
  x = 10(5) + 4 = 54
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Answer:

0.8

Step-by-step explanation:

Answer:

-4/5

Step-by-step explanation:

\(\frac{1}{10}+-\frac{9}{10}=-\frac{8}{10}=-\frac{4}{5}\)

Answer: Original Price: $5

Step-by-step explanation:

x+0.2x=6

1.2x=6

x=5

Original Price: $5

Answer:1.20$

Step-by-step explanation:

so with some problems like this what you can do is multiply the numbers you’re given especially with percentages this makes it really easy to solve all you need to do is multiply the 6$ and the 20% by making the 20% into a decimal and for this problem the 20% would be 0.2. and after you’ve done that you multiply the 6$ with 0.2 and you should get your answer

Answer:

x > 0

Step-by-step explanation:

Restriction on x from the numerator.

The radicand cannot be negative.

4x² ≥ 0

x ≥ 0

From the numerator, we get that x must be greater than or equal to zero.

Restriction on x from the denominator.

Since here we have a square root in the denominator, and division by zero is undefined, the radicand must be greater than zero.

3x > 0

x > 0

From the denominator, the restriction includes zero also, in addition to not allowing negative values of x.

Answer: x > 0

Answer:

1:8

Step-by-step explanation:

since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.

16=1/2(2)h

32=2h

16=h

the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8

Answer: -1.3

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

Length × width × height

Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

The algebraic expression that represents the number of eggs that he gives to his cousin is e-1/3e-7 (option B)

An algebraic expression is an expression in mathematics that is made up of  constant algebraic numbers, variables, and the algebraic operations.

The number of eggs that would be given to the cousin is what is left after he gives his friends the eggs.

Number of eggs the farmer has = e

Number of eggs he gave to the first friend 1/3 x e = 1/3e

Number of eggs he gave the second friend = 7

Number of eggs left = e - 1/3e - 7

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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There is multiple names it has, like for example “Zero” and in British English it is “nought” which is often used as an archaic word for nothing, I hope this help’s.

Answer:

\( \sqrt{9 } = 3 \)

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

x-y=-3

Step-by-step explanation:

The average speeds are 78 km/h and 84 km/h respectively

An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.

The equation for speed is:

Speed = distance / time

a) James drove for 1.5 hours at an average speed of x km/h and then 2.5 hours at an average speed of y km/h.

For distance 1:

x = distance 1 / 1.5

distance 1 = 1.5x

For distance 2:

y = distance 2 / 2.5

distance 2 = 2.5y

Total distance = distance 1 + distance 2

1.5x + 2.5y = 327

multiply through by 2:

3x + 5y = 654    (1)

b) Ryan drove for 4 hours at an average speed of x km/h and then 6 hours at an average speed of y km/h. He drove a total distance of 816 km

For distance 1:

x = distance 1 / 4

distance 1 = 4x

For distance 2:

y = distance 2 / 6

distance 2 = 6y

Total distance = distance 1 + distance 2

4x + 6y = 816     (2)

c) Solving equations 1 and 2 simultaneously:

x = 78; y = 84

The value of x and y are 78 and 84 respectively

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Answer:

350.85

Step-by-step explanation:

90.6*2 = 181.2

27*2 = 54 (diameter)

54*pi = 169.646003294

169.646003294 + 181.2 = 350.846003294

350.846003294 = 350.85

Answer:

g*2+4

Step-by-step explanation:

When comparing the means between two independent samples, the alternative hypothesis should be stated as: "There is a significant difference between the means of the two independent samples."

In this context, the alternative hypothesis (often denoted as H1 or Ha) proposes that there is a meaningful or notable difference between the means of the two groups being compared, suggesting that the observed difference is not due to chance or sampling error.

The alternative hypothesis is tested against the null hypothesis (H 0), which states that there is no significant difference between the means of the two independent samples. In other words, the null hypothesis suggests that any observed difference is simply due to random chance or sampling variability.

When conducting a hypothesis test, researchers use statistical tests, such as the t-test or ANOVA, to determine the likelihood of the observed difference between the means occurring by chance alone. If the probability of obtaining the observed difference under the null hypothesis is sufficiently low (typically less than 0.05), the null hypothesis is rejected in favor of the alternative hypothesis, indicating that there is a significant difference between the means of the two independent samples.

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