What is the axis of symmetry of h(x) = 5x2 + 40x + 64?

x = −16
x = −4
x = 4
x = 16

Answer:

The answer for question 2 is, 3/8. The answer for question 3 is, 2/1.

Step-by-step explanation:

Question 2.

Since all the numerators are the same, the fraction with the smallest denominator is the largest. This means 3/8 is the answer.

Question 3.

Since all the denominators are one or the same, the smallest numerator is the answer. This means 2/1 is the answer.

The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

We know that the phone numbers of a small town either begin with 373 or 377. We are required to find out the number of phone numbers that are available. To solve this question, we need to count the number of phone numbers that are available for each prefix.

The prefix 373 can have numbers ranging from 3730000 to 3739999. Similarly, the prefix 377 can have numbers ranging from 3770000 to 3779999.

Therefore, the total number of phone numbers that are available is the sum of the phone numbers available for each prefix.

Total number of phone numbers = Number of phone numbers available for prefix 373 + Number of phone numbers available for prefix 377

Total number of phone numbers = 10000 + 10000

Total number of phone numbers = 20000

Therefore, The correct option is A. 20,000, as there are a total of 20,000 phone numbers available for the small town.

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Answer:

The question doesn’t show

Step-by-step explanation:

How

The solution for the given problem is (a) P(X ≥ 20,000) = 0.4493, P(X ≤ 30,000) = 0.7769, P(20,000 ≤ X ≤ 30,000) = 0.3276. (b) P(X > 75,000) = 0.0821, P(X > 100,000) = 0.0183.

Solution: a) To find the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000). Now, Mean time until failure is 25,000 hours which is given and is represented by µ. Hence, µ = 25,000 hrs. The parameter used for the Exponential distribution is λ.λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004. Therefore, the probability that a randomly selected fan will last at least 20,000 hours. P(X ≥ 20,000) =  e -λt = e -0.00004 × 20,000 ≈ 0.4493The probability that a randomly selected fan will last at least 20,000 hours is 0.4493.

To find the probability that a randomly selected fan will last at most 30,000 hours. P(X ≤ 30,000) = 1 - e -λt = 1 - e -0.00004 × 30,000 ≈ 0.7769. The probability that a randomly selected fan will last at most 30,000 hours is 0.7769.

To find the probability that a randomly selected fan will last between 20,000 and 30,000 hours. P(20,000 ≤ X ≤ 30,000) = P(X ≤ 30,000) - P(X ≤ 20,000)P(20,000 ≤ X ≤ 30,000) = (1 - e -λt) - (1 - e -λt)P(20,000 ≤ X ≤ 30,000) = e -0.00004 × 20,000 - e -0.00004 × 30,000 ≈ 0.3276. The probability that a randomly selected fan will last between 20,000 and 30,000 hours is 0.3276.

b) To find the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

z = (X - µ) / σZ = (X - µ) / σ = (X - 25,000) / (25,000)λ = 1 / µλ = 1 / 25,000 hrs. λ = 0.00004

The formula for z is z = (X - µ) / σ => X = z σ + µ

The standard deviation of the Exponential distribution is σ = 1 / λσ = 1 / 0.00004 = 25,000 hrs

Z = (X - µ) / σ = (X - 25,000) / (25,000)Z > 2z > 2 => (X - 25,000) / (25,000) > 2 => X > 75,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations.

P(X > 75,000) = e -λt = e -0.00004 × 75,000 ≈ 0.0821

The probability that the lifetime of a fan exceeds the mean value by more than 2 standard deviations is 0.0821

To find the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations.

Z > 3z > 3 => (X - 25,000) / (25,000) > 3 => X > 100,000 hrs.

Now, the probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations P(X > 100,000) = e -λt = e -0.00004 × 100,000 ≈ 0.0183

The probability that the lifetime of a fan exceeds the mean value by more than 3 standard deviations is 0.0183.

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Answer:

y - 7 = 1/2(x + 4)

Step-by-step explanation:

Point-Slope Form: y - y₁ = m(x - x₁)

Step 1: Define

Slope m = 1/2

Point (-4, 7)

Step 2: Substitute

y - 7 = 1/2(x + 4)

Answer:

Step-by-step explanation:

Answer:

x>1/2

Step-by-step explanation:

2x+1−8x<8x−2−8x

−6x+1<−2

−6x+1−1<−2−1

−6x /−6 <

−3 /−6

x>1/2

The expression given involves various terms and operations. To simplify it completely, each term needs to be evaluated and simplified. The given expression includes square roots, fractions, and exponentiation.

a. To simplify 16a, we need more information about the variable 'a' to provide a specific answer.
b. The expression 18² can be simplified as 324, since 18 squared equals 324.
c. For 26/(6 - √2), we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is 6 + √2. Simplifying this will result in (26(6 + √2))/(36 - 2) = (156 + 26√2)/34 = (78 + 13√2)/17.
d. SA²²¹ is an unknown term, so it cannot be simplified further without additional information.
e. The expression 5 - √(101) is already in its simplest form, since the square root cannot be simplified further.
f. The expression 12(2/2)(KE83) can be simplified as 12 * 1 * KE83 = 12KE83, assuming KE83 represents a known quantity.
In summary, the given expression involves various terms, some of which can be simplified, while others require additional information or are already in their simplest form.

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Answer:

y = 0.6028x+103.34929

*y=mx+b*

To generate a list of product names and unit prices ranked by unit price into three categories (1, 2, 3) based on price, you can use a SQL query with the RANK() function.

The highest-priced products will be marked with a 1, the second-highest-priced products with a 2, and so on.

In SQL, you can use the RANK() function along with the ORDER BY clause to rank the products based on their unit prices. The RANK() function assigns a rank to each row in the result set based on the specified ordering criteria. Here's an example SQL query to achieve this:

In this query, products is the name of the table containing the product information. We select the product_name and unit_price columns from the table. The RANK() OVER (ORDER BY unit_price DESC) part ranks the rows based on the unit_price column in descending order, with the highest prices receiving a rank of 1.

The result of this query will include the product names, unit prices, and the assigned price ranks. You can then filter the results based on the price ranks to categorize the products into three categories (1, 2, 3) based on their price rankings.

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The answer is 1/30.

There are 6! = 720 ways to seat 6 people in a row. There are 3! = 6 ways to arrange the 3 couples, and 2! = 2 ways to seat each couple (husband first or wife first). This gives us 6 * 2! * 2! = 24 ways to seat the couples so that each woman is to the left of her husband. So, the probability is 24/720 = 1/30.

Here is a more detailed explanation:

We can think of the problem as a 3-step process:

1. The 3 couples are arranged in some order.

2. Within each couple, the husband and wife are seated in some order.

3. The 6 people are seated in a row, taking into account the order of the couples and the order of the husband and wife within each couple.

There are 3! = 6 ways to arrange the 3 couples. For each way of arranging the couples, there are 2! = 2 ways to seat each couple (husband first or wife first). This gives us 6 * 2! * 2! = 24 ways to seat the couples so that each woman is to the left of her husband.

Finally, there are 6! = 720 ways to seat 6 people in a row. So, the probability that each woman is to the left of her husband is 24/720 = 1/30.

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Answer:

5n - 3

Step-by-step explanation:

3 less then 5 time a number (n)

first of all we know were subtracting

-3

and were multiplying 5 and a number

5n

in my mind the one thing that makes sense is

5n - 3

but the problem can be switched

-3 + 5n

[tex]\boxed{5n-3}[/tex]

Answer: To interpret this expression, we first identify that "3 less than 5" means that we are subtracting 3 from 5. Our equation looks like this:

5 - 3

Now, we add the variable. We would put n in front of 5, because the problem says "5 times a number n." It now looks like:

5n - 3

Your answer would be option A.

Answer:

19 square units

Step-by-step explanation:

There are a LOT of different ways to solve this problem, most of which involve breaking up the shape into smaller shapes.  For me, it’s easier to draw a rectangle around the figure, find that area, and then subtract the four areas not in the figure.

Rectangle: would be from -3 to 3 (6) and -2 to 4 (6).  6x6=36

The four missing triangles:

AB = 1/2(3)(2)=3

BC = 1/2(2)(4)=4

CD = 1/2(2)(4)=4

DA = 1/2(4)(3)=6

6+4+4+3=17

36-17=19

Answer:

A line is a simple geometric shape that extends in both the directions, but a line segment has two defined endpoints. Both the figures are also different from a ray, as a ray has only one endpoint and extend infinitely in one direction.

Step-by-step explanation:

Answer:

Area of the floor not covered = 240ft²

Step-by-step explanation:

Find the diagram attached

The area of the floor not covered = area of the office floor - area of the rug covered

Area of the office floor = 7in×5in = 35in²

Area of the rug = 5in×4in = 20in²

Area of the floor not covered = 35in²-20in² = 15in²

Since 1in = 4ft

1in² = 16ft²

Given the area of the floor not covered to be 15in²

In square feet will be 16×15 = 240ft²

Answer:

6

Step-by-step explanation:

I used a calculator hope its correct

Answer:

b = -6.5

Step-by-step explanation:

92 - 16b = 12

now you want to get the number(s) and variables on different sides

92 - 16b - 92 = -16b

12 + 92 = 104

-16b = 104

now divide each side by -16

-16b / -16 = b

104 / -16 = -6.5

b = -6.5

Answer:

4x-15+6x-35=180

Step-by-step explanation:

4x−15+6x−35=180

Step 1: Simplify both sides of the equation.

4x−15+6x−35=180

4x+−15+6x+−35=180

(4x+6x)+(−15+−35)=180(Combine Like Terms)

10x+−50=180

10x−50=180

Step 2: Add 50 to both sides.

10x−50+50=180+50

10x=230

Step 3: Divide both sides by 10.

10x/10=230/10

Answer:10x

Step-by-step explanation: 6x+4x=10x

Answer:

3

Step-by-step explanation:

15:5

9:HE

15/5 = 9/HE

15HE = 45

HE = 3

Answer:

4 3/5

Step-by-step explanation:

Answer:

4 3/5

Step-by-step explanation:

How many 5s are in 23?

4 whole 5s and 3 left over.

23/5 = 4 3/5

Answer:

D.

Hope this helps

Answer:  43.75 of 225 will be the price. so 98.4375 after being rounded it is 98.4

Step-by-step explanation:

a) The magnitude of the earthquake is approximately 3.0.

b) The intensity of the earthquake is approximately 1258.925.

(a) To find the magnitude of an earthquake based on the intensity, we can use the following equation:

Magnitude = log10(Intensity) + 1.5

Given that the intensity is 30.25, we can calculate the magnitude as follows:

Magnitude = log10(30.25) + 1.5 ≈ 1.48 + 1.5 ≈ 2.98

Rounding to one decimal place, the magnitude of the earthquake is approximately 3.0.

(b) To find the intensity of an earthquake based on the magnitude, we can use the following equation:

Intensity = 10^(Magnitude - 1.5)

Given that the magnitude is 4.6, we can calculate the intensity as follows:

Intensity = 10^(4.6 - 1.5) ≈ 10^3.1 ≈ 1258.925

Therefore, the intensity of the earthquake is approximately 1258.925.

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Answer:

m = -4

b = -12

Step-by-step explanation:

First, identify the slope-intercept form:

y = mx + b

y = -4x - 12

Whereas m = slope and b = y-intercept.

Slope is the steepness of the line.

The y-intercept is where the line intersects the y axis.

Answer:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{1}{2}[/tex]

Step-by-step explanation:

We have the equation:

[tex]2y^2+2=x^2[/tex]

And we want to find d²y/dx² at the point (-2, -1).

So, let's take the derivative of both sides with respect to x:

[tex]\frac{d}{dx}[2y^2+2]=\frac{d}{dx}[x^2][/tex]

On the left, let's implicitly differentiate:

[tex]4y\frac{dy}{dx}=\frac{d}{dx}[x^2][/tex]

Differentiate normally on the left:

[tex]4y\frac{dy}{dx}=2x[/tex]

Solve for the first derivative. Divide both sides by 4y:

[tex]\frac{dy}{dx}=\frac{x}{2y}[/tex]

Now, let's take the derivative of both sides again:

[tex]\frac{d}{dx}[\frac{dy}{dx}]=\frac{d}{dx}[\frac{x}{2y}][/tex]

We will need to use the quotient rule:

[tex]\frac{d}{dx}[f/g]=\frac{f'g-fg'}{g^2}[/tex]

So:

[tex]\frac{d^2y}{dx^2}=\frac{\frac{d}{dx}[(x)](2y)-x\frac{d}{dx}[(2y)]}{(2y)^2}[/tex]

Differentiate:

[tex]\frac{d^2y}{dx^2}=\frac{(1)(2y)-x(2\frac{dy}{dx})}{4y^2}[/tex]

Simplify:

[tex]\frac{d^2y}{dx^2}=\frac{2y-2x\frac{dy}{dx}}{4y^2}[/tex]

Substitute x/2y for dy/dx. This yields:

[tex]\frac{d^2y}{dx^2}=\frac{2y-2x\frac{x}{2y}}{4y^2}[/tex]

Simplify:

[tex]\frac{d^2y}{dx^2}=\frac{2y-\frac{2x^2}{2y}}{4y^2}[/tex]

Simplify. Multiply both the numerator and denominator by 2y. So:

[tex]\frac{d^2y}{dx^2}=\frac{4y^2-2x^2}{8y^3}[/tex]

Reduce. Therefore, our second derivative is:

[tex]\frac{d^2y}{dx^2}=\frac{2y^2-x^2}{4y^3}[/tex]

We want to find the second derivative at the point (-2, -1).

So, let's substitute -2 for x and -1 for y. This yields:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2(-1)^2-(-2)^2}{4(-1)^3}[/tex]

Evaluate:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2(1)-(4)}{4(-1)}[/tex]

Multiply:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{2-4}{-4}[/tex]

Subtract:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{-2}{-4}[/tex]

Reduce. So, our answer is:

[tex]\frac{d^2y}{dx^2}_{(-2, -1)}=\frac{1}{2}[/tex]

And we're done!

Answer:

32

Step-by-step explanation:

Answer:

a(n-3)+8=bn

Step 1: Add -bn to both sides.

an−3a+8+−bn=bn+−bn

an−bn−3a+8=0

Step 2: Add 3a to both sides.

an−bn−3a+8+3a=0+3a

an−bn+8=3a

Step 3: Add -8 to both sides.

an−bn+8+−8=3a+−8

an−bn=3a−8

Step 4: Factor out variable n.

n(a−b)=3a−8

Step 5: Divide both sides by a-b.

n(a−b)

a−b

=3a−8/a−b

n=3a−8/a−b

Answer:

n=3a−8/a-b

The value of the test statistic is χ2 = 17.71 (rounded to two Decimal places).Therefore, the value of test statistic is 17.71 (rounded to two decimal places).

Hypothesis testing is a way of making statistical decisions using experimental data. In hypothesis testing, we have a null hypothesis H0 and an alternative hypothesis Ha.

A hypothesis test is performed on the data, and a conclusion is drawn about the null hypothesis. We reject the null hypothesis if the p-value is less than the level of significance. The level of significance, denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true.In this problem, the null hypothesis is that there is no significant difference between the spreadsheet skill level and campus location.

The alternative hypothesis is that there is a significant difference between the two. The level of significance is α = 0.05.

Step 1: Calculate the expected values We start by calculating the expected values for each cell under the assumption that there is no association between the two variables. We use the formula: Expected value = (row total x column total) / grand total

The grand total is the total number of observations. In this case, it is 130.

The expected value of the "good" and "north" cell = (37 x 50) / 130 = 14.23Expected value of the "not good" and "north" cell = (13 x 50) / 130 = 5.00Expected value of the "good" and "south" cell = (21 x 80) / 130 = 12.92Expected value of the "not good" and "south" cell = (59 x 80) / 130 = 36.15

Step 2: Calculate the chi-square statistic use the formula:χ2 = ∑ (observed value - expected value)2 / expected valueThe degrees of freedom is (r - 1) x (c - 1) = (2 - 1) x (2 - 1) = 1χ2 = [(37 - 14.23)2 / 14.23] + [(13 - 5.00)2 / 5.00] + [(21 - 12.92)2 / 12.92] + [(59 - 36.15)2 / 36.15]χ2 = 17.71

Step 3: Find the p-valueWe use the chi-square distribution table with 1 degree of freedom and α = 0.05. The critical value is 3.84.

The p-value is the area to the right of the chi-square statistic. p-value = P(χ2 > 17.71) ≈ 0.00003Step 4: Make a decision since the p-value is less than the level of significance, we reject the null hypothesis. There is significant evidence of association between student skill level and campus location.

The value of the test statistic is χ2 = 17.71 (rounded to two decimal places).Therefore, the value of test statistic is 17.71 (rounded to two decimal places).

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Answer:

224

Step-by-step explanation:

56 x 4 = 224 (aka 100%)

Sorry I can't explain more, but I hope this helps!

Answer:

224

Step-by-step explanation: