25x^2+20x+4=0 solve by factoring pls show work (50points)

To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.

To calculate the confidence interval, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))

First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.

Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.

Next, we calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380

Finally, we can calculate the lower and upper bounds of the confidence interval:

Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62

Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38

Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.

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The simplified form of each of the given expressions as required is as follows;

a. -2 + 5 = 3

b. (−4) • (6) = -24

c. 4 − (−3) = 4 + 3 = 7

d. 10 + (−2) − 7 = 10 - 2 - 7 = 1.

e. −5 − 3(2 − 6) = -5 -3(-4) = -5 + 12 = 7.

f. (3 − 3)(102 − 11) = (0) (91) = 0.

It follows from the task content that the given arithmetic operations are to be simplified.

The PEMDAS guidelines which prescribe the order of mathematical operations is used for the computation.

where;

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

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Answer:

\(x = 10\)

Step-by-step explanation:

If we have our proportion set up like this:

\(\frac{5}{n} = \frac{16}{32}\)

Then using the cross products property, we can find the value of n.

The property states that the two numbers that are diagonal to each other DIVIDED by the number diagonal to the variable will equal the variable.

So:

\(32\cdot5 = 160\\160\div16 = 10\)

Hope this helped!

Answer:

there is no expression to answer this based off of

Step-by-step explanation:

we can't answer an incomplete question sorry try again and maybe then

In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Answer:

it's four

8×4=32

Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

I think it's 1456

Step-by-step explanation:

first, you have to calculate what in the parenthesis

(4*10)=40

(5.2*10-3) =(5.2*7)

5.2*7=36.4

so after you multiply 40*36.4

which equals 1456

Answer:

answer on the picture. Let me know if I am right!

To find the partial derivatives of the function f(x,t) = t^8 * e^(-x) with respect to x and t.

We simply differentiate the function with respect to each variable while treating the other as a constant:

∂f/∂x = -t^8 * e^(-x)

∂f/∂t = 8t^7 * e^(-x)

Therefore, the first partial derivative of f(x,t) with respect to x is -t^8 * e^(-x), and the first partial derivative of f(x,t) with respect to t is 8t^7 * e^(-x).

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Step-by-step explanation:

a/2-3=8

a-6 =8

2

a-6=16

a=16+6

a=22

hope it helps.

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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Answer:

(8x-5y)(8x+5y)

Step-by-step explanation:

Using the square principal because the square root of 64x2 is 8x and the square root of 25y2 is 5y and +- because +times- is only minus and the equation is minus.

Answer:

He walked 15 feet

Step-by-step explanation:

its kinda hard to explain for me, but thats the answer :)

Rational addition

1/7+3/7+2/7

\( \\ \frac{1}{7} + \frac{3}{7} + \frac{2}{7} \)

\( \\ = \frac{1 + 3 + 2}{7} \)

\( \\ = \frac{6}{7} \: or \: 0.85\)

Therefore, by adding 1/7+3/7+2/7 we got 6/7 or 0.85

Answer:

1) y=2x-4

2) y=1/4x+2

The value of x, which is  the sample mean and represents the average weight gain after quitting smoking, is 20. Therefore, the correct option is B.

Given that the random sample of 100 smokers reveals an average weight gain of 20 pounds after quitting smoking and a standard deviation of 6 pounds, the value of x is determined as follows.

1. Random sample of 100 smokers (n = 100)

2. Average weight gain after quitting smoking is 20 pounds (mean, x' = 20)

3. Standard deviation is 6 pounds (σ = 6)

Option A (6) is incorrect because it does not relate to the given information.

Option C (100) is also incorrect because it refers to the sample size, which is not relevant to finding the value of x.

Option D (6/√100 = 0.6) is incorrect because it calculates the standard error of the mean, which is not what the question is asking for.

Therefore, the correct answer is option B: 20, which is the sample mean and represents the average weight gain after quitting smoking.

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Answer:

60

Step-by-step explanation:

the total cupcakes are:

(57/95) . 100 = 60

The students are expected to make $85 in week 8 if the trend continues.

To determine the earnings for week 8, we need to analyze the given data and look for a pattern or trend. Since the table shows the earnings for the first 6 weeks, we can use this information to make a prediction for week 8.

Week | Earnings

-----|---------

1    | $50

2    | $55

3    | $60

4    | $65

5    | $70

6    | $75

From the given data, we can observe that the earnings increase by $5 each week. This indicates a constant weekly increment in earnings. To predict the earnings for week 8, we can apply the same pattern and add $5 to the earnings of week 6.

Earnings for week 6: $75

Increment: $5

Earnings for week 8 = Earnings for week 6 + (Increment * Number of additional weeks)

Number of additional weeks = 8 - 6 = 2

Earnings for week 8 = $75 + ($5 * 2) = $75 + $10 = $85

According to the pattern observed in the given data, the students are expected to make $85 in week 8 if the trend continues.

However, it's important to note that this prediction assumes the pattern remains consistent throughout the 6-month period. In reality, there might be variations or changes in the earning pattern due to various factors.

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Answer:

4.25 + 2.50x < 25

Step-by-step explanation:

Note:

< →  Less than

> → Greater than

Manny can't spend more than $25 and you pay an initial fee of 4.25 for the shoes and 2.50 for each game so the inequality would be

[D] $4.25 + 2.50x < 25.

~Lenvy~

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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The probability at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

To determine the probability that at least 7 of the puppies will be male, we will have to use the binomial probability formula.

P(X ≥ k) = 1 - P(X < k)

where X is the number of male puppies, P is the probability of a puppy being male and k is the minimum number of male puppies required.

We can solve this problem by finding the probability that 0, 1, 2, 3, 4, 5, or 6 of the puppies are male, and then subtracting that probability from 1. We use the binomial distribution formula to find each of these individual probabilities.

P(X=k) = nCk * pk * (1-p)n-k

where n is the total number of puppies, p is the probability of a puppy being male (0.5), k is the number of male puppies, and nCk is the number of ways to choose k puppies out of n puppies. We'll use a calculator to compute each probability:

P(X < 7) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6)

P(X = 0) = 11C0 * 0.5⁰ * (1-0.5)¹¹ = 0.00048828125

P(X = 1) = 11C1 * 0.5¹ * (1-0.5)¹⁰ = 0.00537109375

P(X = 2) = 11C2 * 0.5² * (1-0.5)⁹ = 0.03295898438

P(X = 3) = 11C3 * 0.5³ * (1-0.5)⁸ = 0.1171875

P(X = 4) = 11C4 * 0.5⁴ * (1-0.5)⁷ = 0.24609375

P(X = 5) = 11C5 * 0.5⁵ * (1-0.5)⁶ = 0.35595703125

P(X = 6) = 11C6 * 0.5⁶ * (1-0.5)⁵ = 0.32421875

P(X < 7) = 0.00048828125 + 0.00537109375 + 0.03295898438 + 0.1171875 + 0.24609375 + 0.35595703125 + 0.32421875 = 1 - P(X < 7) = 1 - 1.08184814453 = -0.08184814453 ≈ 0.0805

Therefore, the probability that at least 7 of the puppies will be male is approximately 0.0805 or 8.05%.

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A firm's variable costs are costs that increase as quantity produced increases. These costs are often illustrated by the increasingly steeper slope of the total cost curve.

As production increases, variable costs such as raw materials, labor, and energy expenses increase in proportion to the level of output. This is due to factors like the need for additional resources or increased utilization of existing resources.

On the other hand, a firm's fixed costs are costs that are incurred even if there is no output. These costs do not change in the short run as production increases. Examples of fixed costs include rent, depreciation of equipment, and insurance. Regardless of the level of production, fixed costs remain constant, representing the expenses that the firm must cover to maintain its operations and infrastructure.

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As HF=GH

It's an isosceles traingle

Since the sides, HF and HG are congruent ∠G and ∠F will be also congruent I.e.

\(∠G = ∠F\)

So, If ∠G = 47°, ∠F is also equal to 47°...~

Answer:

50%

Step-by-step explanation:

Para resolver este problema vamos a definir 4 variables:

V= número de varones bailando.

M= número de mujeres bailando.

V' = número de varones que no están bailando.

M' = número de mujeres que no están bailando.

Sabemos que hay 40 personas en la fiesta, por lo que podemos construir la siguiente ecuación:

V+M+V'+M'=40

Vamos a suponer que cada mujer que está bailando, está bailando varón respectivamente. (El problema no da más información, entonces podemos suponer esto.)

Entonces si hay 5 mujeres bailando, entonces también hay 5 hombres bailando, por lo que nuestra ecuación se reescribe de la siguiente manera:

5+5+V'+M'=40

y simplificamos:

10+V'+M'=40

V'+M'=40-10

V'+M'=30

Ahora bien, el problem nos dice que el número de varones que no bailan es el doble del número de mujeres que no bailan en un determinado momento. Entonces con esta información podemos construir la siguiente ecuación:

V'=2M'

Y podemos despejar el número de mujeres que no bailan, lo que nos da:

\(M'=\frac{V'}{2}\)

Entonces podemos sustituir esto dentro de nuestra ecuación para obtener:

\(\frac{V'}{2}+V'=30\)

y podemos entonces despejar V'

\(\frac{3V'}{2}=30\)

\(V'=\frac{2(30)}{3}\)

V'=20

Entonces hay 20 varones que no están bailando, por lo que la probabilidad de que el varón que se escoge al azar no esté bailando está dada por la siguiente fórmula:

\(P=\frac{V'}{total}\)

\(P=\frac{20}{40}=\frac{1}{2}\)

P=50%

Answer:

30 dollars

Step-by-step explanation:

if the mom and son have 30 and 36, the highest value you can get from both would be 30

Answer:

The greatest donation they can make is 30 dollars

Step-by-step explanation:

Money Word Problem

Let us analyze the given problem.

What is asked?

The greatest donation that Anthony and Jennifer can make.

What are the given?

Anthony's money - 30 dollars

Jennifer's money - 36 dollars

Finding the greatest donation that they can make, means finding their greatest common factor. Then, find out how many of their common factor they can get from their money.

How to find the greatest common factor?

There are three steps to find the GCF of two numbers:

1. Find all the factors of each number.

2. Find the common factors.

3. Choose the greatest factor or number.

Solution:

30 = 1, 3, 5, 6, 10, 30

36 = 1, 2, 3, 4, 6, 9, 12, 36

The greatest common factor is 6.

Now we need to know how many sixes we can get from their money.

30 = 6+6+6+6+6

36 = 6+6+6+6+6+6

Therefore, we can get 5 sixes from their money.

5 × 6 = 30

Final Answer:

The greatest donation that they can make is 30 dollars.