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Remark

There are two formulas for doing this. I'll use the one that does not involve the slope. I think it will be easier for you to understand.

Step One

Decide which point is (x1,y1)

Since point P is 2/5 the way up from point A, we will call (x1,y1) point A

Step Two

Write the givens.

Point(A) = (-2,-3)

Point(B) = (3,2)

Step Three

Write the formula

x1 + ratio*(x2 - x1), y1 + ratio(y2 - y1)

Sub and solve.

-2 + 2/5 *(3 - - 2) , -3 + 2/5*(2 - -3)

-2 + 2/5(5) , - 3 + 2

-2 + 2 , - 1

P = (0 , - 1) <<<<<< Answer

If this turns out to be incorrect please notify me.

Answer:  The required solutions are

[tex](x,y)=(3,2),~(-3,2),~(3,-2),~(-3, -2).[/tex]

Step-by-step explanation:  We are given to solve the following system of equations:

[tex]4x^2+9y^2=72~~~~~~~~~~~~~~~~~~~~(i)\\\\x^2-y^2=5~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Let us consider that

[tex]x^2=a,~~~~~y^2=b.[/tex]

So, equations (i) and (ii) becomes

[tex]4a+9b=72~~~~~~~~~~~~~~~~(iii)\\\\a-b=5~~~~~~~~~~~~~~~~~~~~(iv)[/tex]

Multiplying equation (iv) by 4 and then subtracting from equation (iii), we get

[tex](4a+9b)-(4a-4b)=72-4\times 5\\\\\Rightarrow 4a+9b-4a+4b=72-20\\\\\Rightarrow 13b=52\\\\\Rightarrow b=4.[/tex]

From equation (iv), we get

[tex]a-b=5\\\\\Rightarrow a-4=5\\\\\Rightarrow a=9.[/tex]

Therefore,

[tex]a=9~~~~~\Rightarrow x^2=9~~~~~\Rightarrow x=\pm3,\\\\b=4~~~~~\Rightarrow y^2=4~~~~~\Rightarrow y=\pm2.[/tex]

Thus, the required solutions are

[tex](x,y)=(3,2),~(-3,2),~(3, -2),~(-3, -2).[/tex]

Just plug in -3 for x and solve

y= -10

From the computation, the rate per revolution will be 360°.

From the information given, it was stated that the wheel rotates through 1,800 degrees in 5 revolutions.

Therefore, the rate per revolution will be:

= 1800/5

= 360°

Therefore, the rate per revolution is 360°.

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The missing number of chicken nuggets will be 5.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

The following data points represent the number of chicken nuggets on each family member's plate.

1, 3, 0, 6, x

If the mean of the data set is 3 chicken nuggets. Then the missing number of chicken nuggets is calculated as,

3 = (1 + 3 + 0 + 6 + x) / 5

15 = 10 + x

x = 5

The missing number of chicken nuggets will be 5.

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The answer is 15.

15 students earned an 83% or better on the last math test.

60% of 25 students means 60% * 25 = 15 students earned an 83% or better on Ms. Smith's last math test. Therefore, the answer is 15.

The smallest possible length of one of the two congruent sides is 5.7 cm and this can be determined by using the Pythagorean theorem for an acute triangle.

Given :

The longest side of an acute isosceles triangle is 8 centimeters.

The following steps can be used in order to determine the smallest possible length of one of the two congruent sides:

Step 1 - The Pythagorean theorem for an acute triangle can be used in order to determine the smallest possible length of one of the two congruent sides.

Step 2 - Let the length of the smaller sides be 'a' and let the length of the larger side be 'b'.

Step 3 - According to the Pythagorean theorem for an acute triangle:

[tex]\rm H^2 < B^2+P^2[/tex]

where H is the hypotenuse, B is the base, and P is the perpendicular.

Step 4 - Substitute the values of the known terms in the above expression.

[tex]a^2+a^2>b^2[/tex]

[tex]2a^2>b^2[/tex]

Step 5 - Substitute the value of x in the above expression.

[tex]2a^2>8^2[/tex]

a > [tex]\sqrt{32}[/tex]

a > 5.6

Therefore, the correct option is D).

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f(x+3) = 6x+20

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

f(x) = 6x+2

f(x+3) = 6(x+3) + 2

         = 6x + 18 + 2

         = 6x + 20

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To find the length of PC when PA=14 and PD=10, apply the cosine rule formula in trigonometry.

The length of PC can be calculated using trigonometry and the given information.

The statement is false as the Student's t-distribution is actually more peaked and has thicker tails with smaller sample sizes, and it becomes similar to the standard normal distribution as the sample size, and consequently the degrees of freedom, increase.

The statement that every Student's t-distribution with n < N, where n is the sample size and N is the population size, will be less peaked and have thinner tails is false. In reality, the t-distribution is more peaked and has thicker tails when the sample size is smaller, which happens due to the reduced degrees of freedom (df).

The shape of the Student's t-distribution is determined by the degrees of freedom, which is n - 1 for a sample size n. As n approaches the population size N, the t-distribution approaches the standard normal distribution. This is further supported by the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample means tends to be normal. Therefore:

The statement in the question is false; the t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.

The Student's t-distribution is a probability distribution that is used when the sample size is small and the population standard deviation is unknown. It is similar to the standard normal distribution, but has thicker tails and less probability in the center. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution. Therefore, the statement in the question is false. The t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.

Answer:

4.4%

Step-by-step explanation:

Answer:

answer C

Step-by-step explanation:

Answer:

The equation we can use is 0.1(175-n)+0.05 n=13.30

Step-by-step explanation:

Number of Dimes= d

Number of Nickels= n

n+d=175, so d=175-n

The value of the dime is $0.10 and the value of each nickel is $0.05 and the whole  collection is worth $13.30, so

0.1 d+0.05 n=13.30

Replacing

0.1(175-n)+0.05 n=13.30 this is the equation we have to use to get the number of nickels.

Final answer:

The tax on the television is $35.25.

Explanation:

To find the amount of tax, we first need to determine the original cost of the television. Since the total cost, including tax, is $270.25, we can set up the equation:

$270.25 = x + 0.15x

Where x is the original cost of the television. Combining like terms, we get:

$270.25 = 1.15x

To solve for x, divide both sides of the equation by 1.15:

x = $270.25 ÷ 1.15

Using a calculator, we find that x is approximately $235.00. Therefore, the tax on the television is:

$270.25 - $235.00 = $35.25

Answer:

[tex](x+3)(x-15)[/tex] is the required factorized form of the given expression.

Step-by-step explanation:

The given equation is:

[tex]x^2-12x-45[/tex], we have to factorized this equation,

Upon solving the above equation, we get

⇒[tex]x^2-15x+3x-45[/tex]

⇒[tex]x(x-15)+3(x-15)[/tex]

⇒[tex](x+3)(x-15)[/tex]

which is the required factorized form of the given expression.

By investing $300 at a 7.5% per year simple interest rate, the accrued interest over 11 years is $247.50. Adding this to the initial investment, the total in the account at the beginning of the 11th year will be $547.50.

To determine how much you will have in an account at the beginning of the 11th year with simple interest, you can use the formula for simple interest:

Simple Interest (I) = P × r × t

Where:

Let's calculate the simple interest first:

So, the interest earned over 11 years is $247.50. Now, add this to the principal amount to get the total amount in the account at the beginning of the 11th year:

Total Amount = Principal + Interest

Total Amount = 300 + 247.50

Total Amount = 547.50

We are given the following data:

Year       Estimated Population

0                               100       

1                               79       

2                               62       

3                               49    

4                               39       

Just by looking at the data we can see that the relationship of year and estimated population is not linear. The decrease in the population does not follow a linear path, that is:

79 – 100 is not equal to 62 – 79

-21 is not equal to -17

Therefore, the relationship must be exponential. Let us find the common ratio by dividing the population in year 1 and year 0:

common ratio, r = 79 / 100 = 0.79

This means that the population decreases by 21% every year.

So the model for this data can be written as:

yn = y0 * r^n

Where,

yn = is the population after n years

y0 = initial population

r = growth rate = decreasing

n = number of years