te the function.
f(x) = -22 + x + 13
Find f(9)

Answer:

$6.90 is the cost of 9 tennis balls

Answer:

11 ft

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is

A = L * W.  

Represent the length, L, by 2W + 1 ("1 more than twice the width").  Then the area formula (above) becomes:

A = 55 ft^2 = (2W + 1)(W), which, when simplified, results in:

2W^2 + W - 55 = 0, whose coefficients are {2, 1, -55}.  Let's use the quadratic formula to solve this for W:

The discriminant, b^2 - 4ac, is 1^2 - 4(2)(-55), or 441.  The square root of 441 is 21.  Thus, the quadratic formula gives us:

        -1 ± 21

W = ------------- = (1/4)(-1 + 21), or W = 5 and W = -22/4 = -11/2

            2(2)

A measure of length can't be negative, so we reject W = -11/2 in favor of W = 5.

Then, according to the formula for L that we found earlier, L  = 2W + 1, or

L = 2(5) + 1, or L = 11.

Check:  Does L * W result in an area of 55 ft²?  Yes

The length dimension of the rectangle is 11 ft

Answer:

It's gonna be C and good luck!

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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A sample is a subset of the population. When conducting a survey, it is often impractical to gather data from every member of a population, and therefore, a sample is used. The goal of a sample is to gather data that is representative of the population. In the case of the instructional designer, they would need to identify the population of learners they are interested in (e.g. learners enrolled in their course) and take a sample of those learners to estimate the proportion who use Firefox as their primary browser.

There are various sampling procedures that can be used, but the most common is simple random sampling. In simple random sampling, each member of the population has an equal chance of being selected for the sample. The instructional designer could use a random number generator or a table of random numbers to select their sample of learners. Once they have their sample, they can count the number of learners who use Firefox as their primary browser and use this proportion to estimate the proportion in the population.

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Answer:

14 Plants per row

Step-by-step explanation:

Divide 42 by 3

42/3 = 17

Answer:

14

Stage 1: Divide.

42 divided by 3 is 14.

Stage 2:

Solution = 14.

Hope it helps!

Answer:

= 65

Step-by-step explanation:

= 2×(-5)² - 5×(-5) - 10

= 2×25 + 25 - 10

= 50 + 15

= 65

Answer:

65

Step-by-step explanation:

The person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).

Distance is the length of one point to the next.

Time refers to the hours or minutes consumed in making a displacement.

Speed shows the rate of the change in displacement resulting from the interaction of distance with time.

Speed measures the ratio of distance to time.

Thus, the person can run 5.33 miles (distance) in 16 minutes (time) if they run 20 per hour (speed).

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The probability that both numbers will be even will be ( 1 / 4 ). The correct option is C.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that two 12-sided dice are rolled and need to calculate the probability of getting an even number.

Number of favorable outcomes = 6 x 6 = 36

Number of sample = 12 x 12 = 144

The probability of getting an even number will be calculated as:-

Probability = Number of favorable outcomes / Number of sample

Probability = 36 / 144

Probability  = 1 / 4

Therefore, the probability that both numbers will be even will be ( 1 / 4 ). The correct option is C.

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In order to find constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9, the following steps should be used. Let f(x) = axe^(bx)F'(x) = a(e^bx) + baxe^(bx)

We have to find the constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9. So, let's begin by first finding the derivative of the function, which is f'(x) = a(e^bx) + baxe^(bx). Next, we need to plug in x = 1/9 in the function f(x) and solve it. That is, f(1/9) = 1.

We can obtain the value of a from here.1 = a(e^-1)Therefore, a = e.Now, let's find the value of b. We know that the function has a local maximum at x = 1/9. Therefore, the derivative of the function must be equal to zero at x = 1/9. So, f'(1/9) = 0.

We can solve this equation for b.0 = a(e^b/9) + bae^(b/9)/9 Dividing the above equation by a(e^-1), we get:1 = e^(b/9) - 9b/9e^(b/9)Simplifying the above equation, we get:b = -9 Thus, the values of constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9 are a = e and b = -9.

The constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9 are a = e and b = -9. The solution is done.

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Answer:

B. -1/3

Step-by-step explanation:

Choose 2 points. From the lower points count up until it is in line with the other point. Then count left until you reach the second point.

Rise/Run

Rise=1

Run=-3

\(-\frac{1}{3}\)

Hope this helps!

Answer: -1/3 is the answer

Step-by-step explanation:

The equation of the line, with slope equal to 0 and passing through the point located at (4 , -2), is y = -2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 0 and (x1 , y1) = (4 , -2)

(y - -2) = 0(x - 4)

(y + 2) = 0

y = -2

In slope-intercept form, the equation of the line is:

(y + 2) = 0

y = -2

In standard form, the equation of the line is:

y = -2

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Answer:

11.41= 6x=2.11

x=1.35

Step-by-step explanation:

The option that follows is c .

The between-group estimate for calculating the degrees of freedom in ANOVA is calculated using the formula k - 1, where k represents the number of groups or treatments being compared.

This estimate represents the variability between the group means and is used in the F-ratio calculation to determine if the differences between the groups are significant.

When conducting ANOVA, the between-group estimate is an important factor in determining the degrees of freedom. This estimate represents the variability between the group means and is used to calculate the F-ratio, which determines if the differences between the groups are significant. The between-group estimate is calculated using the formula k - 1, where k represents the number of groups being compared. This formula is used because the estimate is based on the number of independent sources of variation between the groups. By accurately calculating the degrees of freedom, researchers can determine if the differences between the groups are statistically significant.

The between-group estimate for calculating the degrees of freedom in ANOVA is crucial for determining the statistical significance of differences between groups. It is calculated using the formula k - 1, where k represents the number of groups being compared. This estimate represents the variability between the group means and is used in the F-ratio calculation. Accurately calculating the degrees of freedom is essential in conducting valid ANOVA analyses.

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Answer:

parallelogram

Answer:

3200

Step-by-step explanation:

growth = current population + rate * time

            = 2000 * .04 * 15

            = 1200

original population + growth = total

2000 + 1200 = 3200

1) The probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) The probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) The probability that a sitcom will have more than 10 minutes of commercials (or other non-programming interruptions) is 0.250.

To solve this problem, we can use the probability density function of a uniform distribution

f(x) = 1/(b-a) for a <= x <= b

= 0 otherwise

where a and b are the endpoints of the interval.

Given that the programming time for sitcoms follows a uniform distribution from 18 to 26 minutes, we have

a = 18

b = 26

Therefore, the probability density function for the programming time is

f(x) = 1/8 for 18 <= x <= 26

= 0 otherwise

1) P(X >= 25) = ∫(25 to 26) f(x) dx

= ∫(25 to 26) 1/8 dx

= [x/8] from 25 to 26

= (26/8) - (25/8)

= 1/8

Therefore, the probability that a sitcom will have 25 or more minutes of programming is 0.125.

2) P(21 <= X <= 25) = ∫(21 to 25) f(x) dx

= ∫(21 to 25) 1/8 dx

= [x/8] from 21 to 25

= (25/8) - (21/8)

= 1

Therefore, the probability that a sitcom will have between 21 and 25 minutes of programming is 1.000.

3) Since the total running time of a sitcom is 30 minutes and the programming time is uniformly distributed between 18 and 26 minutes, the time for commercials and interruptions is:

T = 30 - X

where X is the programming time.

Therefore, the probability of having more than 10 minutes of commercials and interruptions is

P(T > 10) = P(30 - X > 10)

= P(X < 20)

Using the cumulative distribution function (CDF) of the uniform distribution, we get

F(x) = (x - a)/(b - a) for a <= x <= b

= 0 for x < a

= 1 for x >= b

Therefore

P(X < 20) = F(20)

= (20 - 18)/(26 - 18)

= 2/8

= 0.250

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Let the unkown be x. the given proportion would be

20/3 = x/6

By crossmultiplying, it becomes

x * 3 = 20 * 6

3x = 120

x = 120/3

x = 40

The correct option is C

Answer:

Use a model to find the sum of two fractions with the same denominator

Add fractions with a common denominator without a model

Add fractions with a common denominator that contain a variable h

Step-by-step explanation:

h

Convenience sampling is not a type of statistical sampling.

What is statistical sampling?

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study.

If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

Main body:

Simple random sample:

Each individual and group of individuals have the same chance of being selected for the sample. To obtain a basic random sample, one needs technology, random number generators, or some other type of chance mechanism.

stratified Random sample :

The population is first divided into sections. There are some people from each group in the overall sample. Each group's participants are chosen at random.

Cluster sampling:

Grouping the population first, a cluster random sample is taken. Every member of some of the groups makes up the overall sample. The selection of the groups is random.

Hence Convenience sampling is not a type of statistical sampling.

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Answer:

\({ \rm{ \frac{ {4}^{a + 2} + {4}^{a} }{17 \times {4}^{a} } }} \\ \\ = { \rm{ \frac{( {4}^{a} \times {4}^{2} ) + {4}^{a} }{17 \times {4}^{a} } }} \\ \\ = { \rm{ \frac{ {4}^{a} }{ {4}^{a} } ( \frac{ {4}^{2} + 1}{17}) }} \\ \\ = { \rm{ \frac{ {4}^{2} + 1 }{17} }} \\ \\ = { \rm{ \frac{16 + 1}{17} }} \\ \\ { \rm{ = \frac{17}{17} }} \\ \\ = 1\)

hence proved

The first four terms of the sequence are 2, 3, 5, and 8.

The position of a number in a sequence is indicated by a word in the sequence. For instance, the number two is the third term in the Fibonacci sequence 1, 1, 2, 5, 8,... The first "one" in the series is the first word. In mathematics, the letter n can be used to denote a sequence's terms.

Using the given formula, we can find the terms of the sequence as follows:

a(1) = 2 (given)

a(2) = 3 (given)

a(3) = a(2) + a(1) = 3 + 2 = 5

a(4) = a(3) + a(2) = 5 + 3 = 8

Therefore, the first four terms of the sequence are 2, 3, 5, and 8.

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Answer:

Step-by-step explanation:

4:12= 1:3

Answer:

cow = 4

pig = 5

chicken = 9

horse = 3

horse + chicken - pig =7

Answer:

32 and 4

Step-by-step explanation:

128=2^7

(8xa)xb=128

axb=2^4=16

(8x4)x4=128

The image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

The coordinate point is given as:

P = (-3, 2)

The translation is given as

T<2,1>

The translation can be represented as:

(x, y) = (x + 2, y + 1)

So, we have the following equation

P' = (-3 + 2, 2 + 1)

Evaluate the sum

P' = (-1, 3)

Hence, the image of the point P(-3, 2) under the translation T<2,1> is (-1, 3)

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Answer:Jenny has 15 favorite toys

Step-by-step explanation:

Jenny has 3 times as many new toys as she has favorite toys means that the ratio of new toys to favorite toys can be written as 3:1

Total Ratio=3+1=4

Since the total number of toys is given as 60

Amount of Favorite toys = ratio of favorite toys / Total ratio x Total number of toys

Amount of Favorite toys = 1/4 x 60=15

Therefore Jenny has 15 favorite toys.

Answer:

see below

Step-by-step explanation:

\( \huge14 {x}^{ 5 } = 2 {x}^{3} . \boxed{7 {x}^{2} }\)

Answer:

Which Number Is x, You Didnt Specify

Answer:

$15.00 - $12.95 = $2.05

Step-by-step explanation:

Jared has $2.05 left