What is the vertex of the graph of the function f(x) = x2 + 6x + 9?
0 A. (-3,0)
B. (0, -3)
C. (0, 3)
O D. (3, 0)

Answer:

b

Step-by-step explanation:

i did it rn

Answer:

B: 57.12

Step-by-step explanation:

2.8 times 1.2 times 17 is 57:12

The required probability is obtained as:

(a) P(X^2 < 1) = 0.8413.

(b) P(X^2 + Y^2 < 1) = 0.7854.

(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:

P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))

Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:

P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))

Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.

(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.

We can use polar coordinates to express X and Y as:

X = Rcosθ

Y = Rsinθ

where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).

Therefore, we can find P(X^2 + Y^2 < 1) as:

P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))

Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:

P(R^2 < 1) = 0.7854

Therefore, P(X^2 + Y^2 < 1) = 0.7854.

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Answer:

The answer is -285

Step-by-step explanation:

The surface area of the triangular prism is  936 cm².

In geometry, a triangular prism is a three-sided prism.

Therefore, the surface area of the triangular prism can be calculated as follows:

surface area of triangular prism = bh + L(x + y + z)

where

Therefore,

surface area of triangular prism = 24 × 18 + 7(18 + 30 + 24)

surface area of triangular prism = 432 + 7(72)

surface area of triangular prism = 432 + 504

surface area of triangular prism = 936 cm²

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Answer: i) \(p=\dfrac{d-3}{2}\)

ii) He has to attend 5 practices to run 13 miles.

Step-by-step explanation:

Given: The distance (d) in miles that Cecil runs depends on the number of track practices (p) he attends.

\(d=2p+3\)

i) To solve for p . first subtract 3 from both sides , we get

\(d-3=2p\)

Divide both sides by 2

\(\dfrac{d-3}{2}=p\)

So. \(p=\dfrac{d-3}{2}\)

ii) Put d= 13 , we get

\(p=\dfrac{13-3}{2}=\dfrac{10}{2}=5\)

i.e. he has to attend 5 practices to run 13 miles.

The probability that a randomly selected adult has an IQ greater than a certain value can be found using the normal distribution. Assuming adults' IQ scores are normally distributed with a mean of 99.7 and a standard deviation of 21.4, we can calculate the probability.

To find the probability of an IQ score being greater than a specific value, we need to standardize the score using the z-score formula: z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation.

Let's say we want to find the probability of an IQ score greater than X. We calculate the z-score as z = (X - 99.7) / 21.4. Using a standard normal distribution table or a statistical calculator, we can find the area under the curve corresponding to this z-score. This area represents the probability that an IQ score is less than X.

To find the probability that an IQ score is greater than X, we subtract the previously calculated probability from 1: P(X > X) = 1 - P(X < X).

By using the z-score formula and subtracting the probability from 1, we can determine the probability that a randomly selected adult has an IQ greater than a certain value.

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The figure H''B''G''P'' created following the transformations applied to HBGP such that HBGP is larger than  H''B''G''P'', inverted and on the other side of the y-axis indicates;

The completed table is presented as follows;

\(\begin{array}{|c|c|c|c|c|\pi \pi }\text{Preimage} &\text{Side Length} & \text{Image} &\text{Side Length}&\text{Ratio of Preimage to Image Lengths } \\GB & 5 &G''P'' &2.5&2:1 \\PH &3 & P''H'' &1.5&2:1 \\HB & 5 & H''B'' &2.5&2:1 \\BG &3 & B''G'' & 1.5& 2:1 \\\end{vmatrix}\)

A geometric transformation involves making changes to a geometric figure.

The coordinates if the vertices of the quadrilateral HBGP are;

H(-1, -2), B(-6, -2), G(-6, 1), and P(-1, 1)

The approximate coordinates of the vertices of the quadrilateral H''B''G''P'' are;

H''(0.5, 1), B''(3, 1), G''(3, -0.5), P''(0.5, -0.5)

The length of the side GP in quadrilateral HBGP = -1 - (-6_) = -1 + 6 = 5

Length of the side PH in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

Length of the side HB in quadrilateral HBGP = -1 - (-6) = -1 + 6 = 5

Length of the side BG in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

The possible transformations applied to HBGP to create H''B''G''P'' includes;

A dilation, a rotation of 180° and a translation

The length of the side G''P'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side P''H'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

The length of the side H''B'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side B''G'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

Ratio of the side length of GP to the side length of G''P'' = 5:2.5 = 2:1

Ratio of the side length of PH to the side length of P''H'' = 3:1.5 = 2:1

Ratio of the side length of HB to the side length of H''B'' = 5:2.5 = 2:1

Ratio of the side length of BG to the side length of B''G'' = 3:1.5 = 2:1

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Answer:

hello again !

this isn't classified as a polynomial because polynomials do not contain variables raised to a negative number, such as this, which is raised to -3.

Answer:

D, X^2 -18 + 81 = -45 + 81

Step-by-step explanation:

it is complating squer method that used for solving x in a quadratic equetion . in this step you will add

(y/2)^2 if y is the cofitient of x .

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Answer:

50%

Step-by-step explanation:

Given that :

Let Probability of rain today = P(rain today) = 50% = 0.5

The complement of an event A denoted as A' means the opposite of event A is obtained by subtracting event a from 1.

P(rain today) = 0.5

The complement of P(rain today) ; means the probability that it will NOT rain today;

Hence, P(raintoday') = 1 - 0.5 = 0.5 = 50%

There is no solution for x.

2 cosx+3 cos.x=- 1 The trigonometric identity:cos(a + b) = cos a cos b - sin a sin bHere, a = x and b = π Therefore, cos (x + π) = cos x cos π - sin x sin π= -cos x

Therefore,2 cos x + 3 cos (x + π) = 2 cos x - 3 cos x= -cos x Therefore, -cos x = -1 x = π This solution satisfies the given inequality, so the solution is x = π.2. log, (x+5)-log, (x-1)=2Let's use the quotient rule of logarithms:

a) log a - log b = log (a/b)b) log a + log b = log (ab) Applying the quotient rule of logarithms, we get log((x + 5)/(x - 1)) = 2Then, (x + 5)/(x - 1) = 10^2= 100x + 5 = 100x - 1005 = -100x Simplifying, we getx = -5/100= -1/20This value of x does not satisfy the given interval, so the solution is rejected.

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Using the circumference formula, we can conclude that the circumference of the given circle is 8π inches.

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

Sao, we know that area of the circle is:

16π

Area formula:
πr²

Now, calculate the radius:

πr² = 16π

r² = 16

r = 4

Now, the circumference formula:

2πr

Now, insert values as follows:

2πr

2π(4)

8π

Therefore, using the circumference formula, we can conclude that the circumference of the given circle is 8π inches.

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Answer:

18 treats

Step-by-step explanation:

If she gives  2/5  of 30  = 12

so 3/5 of 30 is 18  (also 30-12 =18)

Numbers can either be equal or unequal.

There are several ways to compare decimals.

Some of which are:

By division

Divide the given numbers

\(n = \frac{6.75}{6.732}\)

\(n = 1.00026738\)

Notice  that the quotient of the numbers is greater than 1.

This means that the number at the numerator is greater than the other number.

If the quotient is smaller than 1, then the number at the denominator is greater than the other number.

By subtraction

Subtraction the given numbers

\(n = 6.75 - 6.732\)

\(n = 0.018\)

Notice  that the difference of the numbers is greater than 0.

This means that the number at the first number is greater than the other number.

If the difference is less than 0, then the first number at the less than the other number.

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To calculate the 90% confidence interval for the given random sample of 5 observations, we need to find the sample mean and sample standard deviation.

The sample mean (X bar) can be calculated by summing up all the observations and dividing by the sample size (n):

X (bar) = (15 + 10 + 16 + 19 + 14) / 5 = 14.8

Next, we need to calculate the sample standard deviation (s). The formula for the sample standard deviation is as follows:

s = sqrt(Σ(xi - x(bar))² / (n - 1))

Using the formula, we calculate the sample standard deviation:

s = sqrt(((15 - 14.8)² + (10 - 14.8)² + (16 - 14.8)² + (19 - 14.8)² + (14 - 14.8)²) / (5 - 1))

 = sqrt((0.16 + 18.24 + 0.16 + 17.64 + 0.16) / 4)

 = sqrt(36.4 / 4)

 = sqrt(9.1)

 ≈ 3.02

Now, we can calculate the margin of error (E) using the formula:

E = t * (s / sqrt(n))

Since the sample size is small (n = 5) and the confidence level is 90%, we need to use the t-distribution. The degrees of freedom (df) for a sample size of 5 and 90% confidence level is 4. From the t-distribution table, the corresponding t-value is approximately 2.776. Plugging in the values:

E = 2.776 * (3.02 / sqrt(5))

 ≈ 3.26

Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample mean:

Confidence interval = (x(bar) - E, x(bar) + E)

                  = (14.8 - 3.26, 14.8 + 3.26)

                  ≈ (11.54, 18.06)

Therefore, the 90% confidence interval for the given random sample is approximately (11.54, 18.06).

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Answer:

1. - A; 2. - A.

Step-by-step explanation:

'1' = '1' = 8 / √2 = 4√2.

Answer:

y = x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (6, 3) and (x₂, y₂ ) = (4, 1)

m = \(\frac{1-3}{4-6}\) = \(\frac{-2}{-2}\) = 1 , then

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 1 )

1 = 4 + c ⇒ c = 1 - 4 = - 3

y = x - 3 ← equation of line

The equation that represents the total cost of k kites and 2 spools of kite string is c = 5k + 6.

Let's define:

k as the number of kites.

c as the total cost of k kites and 2 spools of kite string.

According to the problem statement, each kite costs \($5\) including tax, and each spool of kite string costs. \($3\) including tax.

The cost of k kites and 2 spools of kite string can be expressed as:

c = (5k + 2 × 3) dollars

We add 2 × 3 to account for the cost of the two spools of kite string. Simplifying the expression, we get:

c = 5k + 6

The equation that represents the total cost of k kites and 2 spools of kite string is c = 5k + 6.

Let's say that k is the quantity of kites.

k kites and 2 spools of kite string cost c in total.

The issue statement states that each kite costs

The cost of each spool of kite string, with tax adding taxes.

The formula for the price of k kites and 2 spools of kite string is: c = (5k + 23) dollars.

To account for the cost of the two kite string spools, we add 2 3.

When we condense the phrase, we get:

c = 5k + 6

C = 5k + 6 reflects the overall cost of k kites and 2 spools of kite string.

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Answer:

Step-by-step explanation:

The equation of the line is y = 4x + 9

Given,

The points; (x₁, y₁) = (1, 5)

The line is parallel to, y = 4x - 2

Here,

The line given is in the Slope Intercept Form

y = mx + b

y = 4x - 2

Parallel Lines have the same slope

So,

Slope, m = 4

Then,

y = 4x + b

Since it passes through point p(1, 5) we can use these coordinates to solve for b

5 = -4 + b

Solve for b

9 = b

Therefore, the equation of the line;

y = 4x + 9

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Four types of discontinuity of a function are as follow:

Jump discontinuity , infinite discontinuity, endpoint discontinuity, and Mixed discontinuity.

As given in the question,

Four types of discontinuity are given by :

1. Jump discontinuity :

In this type of discontinuity both side of limit that left hand side and right hand side limit exist but both represents the different value .

2. Infinite discontinuity :

In this case both the side of limit exist but are reaches to infinity.

3. Endpoint discontinuity:

In this case only one side either left or right side of limit exist.

4. Mixed discontinuity:

In this case at least one side of limit either right or left does not exist.

Therefore, the four types of discontinuity are :

Jump discontinuity , infinite discontinuity, endpoint discontinuity, and Mixed discontinuity.

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Answer:

Step-by-step explanation:

25g + 35 = 260

25g = 225

g = 9 games

Answer:

option e

Step-by-step explanation:

It should be arranged in table form

Row ------> Classes

Column  -----> Courses

                     Sophomores           Juniors          Seniors

Biology                 110                        60                 20

Chemistry              50                        140               85

Physics                    17                         70                107

Answer:

Step-by-step explanation:

let the plane intersects the join of points in the ratio k:1

let (x,y,z) be the point of intersection.

\(x=\frac{3k+2}{k+1} \\y=\frac{5k+4}{k+1} \\z=\frac{-4k+16}{k+1} \\\because ~(x,y,z)~lies~on~the~plane.\\2(\frac{3k+2}{k+1} )-3(\frac{5k+4}{k+1} )+\frac{-4k+16}{k+1} +6=0\\multiply~by~k+1\\2(3k+2)-3(5k+4)+(-4k+16)+6(k+1)=0\\6k+4-15k-12-4k+16+6k+6=0\\-7k+14=0\\k=2\\x=\frac{3*2+2}{2+1} =\frac{8}{3} \\y=\frac{5*2+4}{2+1}= \frac{14}{3} \\z=\frac{-4*2+16}{2+1} =\frac{8}{3}\)

point of intersection is (8/3,14/3,8/3)

and ratio of division is 2:1

Answer:

Slope is 1/4

Step-by-step explanation:

Slope=Rise/Run=(y2-y1)/(x2-x1)=(9-6)/(5-(-7))=3/12=1/4

Answer:

Step-by-step explanation:

The formula for calculating the perimeter of the square patio is expressed as;

P = 4L

L is the length of each side of the square patio

Given

L = 8.5 feet

Required

Perimeter in feet of Rocio's patio

Substitute the given parameter into the formula;

Perimeter = 4 * 8.5

Perimeter = 34ft²

Option B is correct.

Answer:

Step-by-step explanation:

72.25 the answer

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The standard error of the mean for this random sample of 100 customers is 0.1.

The correct option is C.

The standard error of the mean is a measure that indicates the precision or variability of the sample mean in relation to the population mean. It represents the average amount of sampling error we can expect when estimating the population means based on a sample.

To calculate the standard error of the mean, we divide the standard deviation of the population by the square root of the sample size. In this case, the standard deviation is 1 minute and the sample size is 100.

Dividing 1 by the square root of 100, we get 1/10 or 0.1. This means that the standard error of the mean for this sample is 0.1.

A smaller standard error of the mean indicates that the sample mean is a more accurate estimate of the population mean. In this case, a standard error of 0.1 suggests that the average length of time it took customers to check out may vary around the sample mean by approximately 0.1 minutes.

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