Select the corrert answer. Which number line represents the sorution to |x-5|<3 ?

Cafeteria A has 7 packs of granola bars and 12 loose granola bars. Cafeteria B has 3 packs of granola bars and 84 loose granola bars. If the cafeterias have the same number of granola bars, each package has 18 granola bars.

A linear equation is an algebraic equation of the form y=mx+b. regarding best a consistent and a primary-order (linear) term, where m is the slope and b is the y-intercept. every now and then, the above is known as a "linear equation of two variables," wherein y and x are the variables.

We can find the number of granola bars in each pack using the liner equation.

First, form the equation

Let "\(x\)" be the total number of granola bars that each pack of granola has.

Let "\(y\)" be the total amount of granola bars that each cafeteria has.

Cafeteria A: \(7x + 12 = y\)

Cafeteria B: \(3x + 84 = y\)

Then, since both the equations are solved \(y\), we may take the argument at the left side of the equal sign from both equations and equal them.  \(7x + 12 = 3x + 84\)

Find the value of \(x\)

\(7x + 12 = 3x + 84\)

\(7x-3x = 84 - 12\) ( Subtract \(3x\) and \(12\) from both sides. )

\(4x = 72\) ( Simplify by solving the subtraction. )

\(\frac{4x}{4}=\frac{72}{4}\) ( Divide both sides by 4. )

\(x=18\)

Now, substitute the value of \(x\) by \(x\) on any of the equations.

\(y=7(18)+12\)

\(y=138\)

If a system of linear equations was created, where 2 equations gave the number of granola bars that each cafeteria has, then the \(x\) value obtained when the system was solved, indicates the number of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

Learn more about linear equations here brainly.com/question/2030026

#SPJ9

Answer:

The missing value is -9

Step-by-step explanation:

Given

\(-7 = _ -(-2)\)

Required

Determine the missing value

Represent _ with a variable

\(-7 = x -(-2)\)

Open the bracket

\(-7 = x -1*-2\)

\(-7 = x + 2\)

Subtract 2 from both sides

\(-7 - 2 = x + 2 - 2\)

\(-9 = x\)

Reorder

\(x = -9\)

Hence, the missing value is -9

Answer:

The answer is 4=−2+6

Step-by-step explanation:

I checked on khan

Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

For more such question on distance . visit :

https://brainly.com/question/30395212

#SPJ8

Answer:

A=-1, B=2

Step-by-step explanation:

2a + 3b=4 equation 1

a-b=-3 equation 2

a=-3+b isolate a in equation 2

2(-3+b) + 3b=4. Substitute value of a in equation 2 (-3+b) into a value of  equ 1

-6+2b+3b=4

5b=10

b=2

solve for a:

a-b=-3

a-(2)=-3

a-2=-3

a=-1

Answer:

1.5m/sec is the answer

Step-by-step explanation:

54×1000m/60×60sec

54000m/3600sec

1.5m/sec

Answer:

15 m/s

Step-by-step explanation:

54 ÷ 3.6 = 15 m/s

The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

To know more about matrices here: brainly.com/question/29102682

#SPJ11

Answer:

No

Step-by-step explanation:

x + (-8x - 3) = 7

x -8x - 3 = 7

-7x = 10

x = -10/7

y = -8(-10/7) - 3

y = 80/7 - 3

y = 59/7

The solution to the system of equations is x = 3 and y = -8.  the two expressions for y and solve for x.

To solve the system of equations using the equal values method, we'll equate the two expressions for y and solve for x.

Given the equations:

y = 5x - 23   ...(Equation 1)

y = 2 1/2 - 3 1/2x   ...(Equation 2)

First, let's simplify Equation 2 by converting the mixed fractions into improper fractions:

y = 2 + 1/2 - 3 - 1/2x

y = 5/2 - 7/2x

Now, we'll equate the two expressions for y:

5x - 23 = 5/2 - 7/2x

To solve for x, we'll eliminate the fractions by multiplying the entire equation by 2:

2(5x - 23) = 2(5/2 - 7/2x)

10x - 46 = 5 - 7x

Next, we'll simplify the equation by combining like terms:

10x + 7x = 5 + 46

17x = 51

To isolate x, we'll divide both sides of the equation by 17:

x = 51/17

x = 3

Now that we have the value of x, we can substitute it back into either Equation 1 or Equation 2 to find the corresponding value of y. Let's use Equation 1:

y = 5(3) - 23

y = 15 - 23

y = -8

Therefore, the solution to the system of equations is x = 3 and y = -8.

Learn more about system of equations here

https://brainly.com/question/13729904

#SPJ11

the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

Learn more about volume here:

https://brainly.com/question/13338592

#SPJ11

Answer:

CD = 7

Step-by-step explanation:

Given that the triangles are congruent, then corresponding sides are congruent, that is

CD = AB , substitute values

3y + 1 = 15 - 4y ( add 4y to both sides )

7y + 1 = 15 ( subtract 1 from both sides )

7y = 14 ( divide both sides by 7 )

y = 2

Thus

CD = 3y + 1 = 3(2) + 1 = 6 + 1 = 7

Hi! I'd be happy to help you write the sum in sigma notation. Given the sum: 3 - 3x + 3x^2 - 3x^3 + , + (-1)^n * 3x^n, the sigma notation would be:

Σ[(-1)^k * 3x^k] from k=0 to n

Here's a step-by-step explanation:

1. Identify the pattern in the sum: It alternates between positive and negative terms, and each term has a power of x multiplied by 3.
2. Assign the variable k for the index of summation.
3. Determine the range of k: The sum starts with k=0 and goes up to k=n.
4. Represent the alternating sign using (-1)^k.
5. Combine all components to form the sigma notation: Σ[(-1)^k * 3x^k] from k=0 to n.

The sum can be written in sigma notation as:

\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)

The given series is:

\(3 - 3x + 3x^2 - 3x^3 + ...\)

To write it in sigma notation, we first notice that the terms alternate in sign, and each term is a power of x multiplied by a constant (-3). We can write the general term of the series as:

\((-1)^n * 3 * x^n\)

where n is the index of the term, starting from n = 0 for the first term.

Using sigma notation, we can express the sum of the series as:

\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)

where the summation is over all values of n starting from n = 0.

Learn more about sigma notation

brainly.com/question/27737241

#SPJ11

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4

\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

\[

P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5

\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

know more about probabilities :brainly.com/question/29381779

#SPJ11

The probabilities are calculated assuming independence of each call and that the success probability remains constant throughout the calls. The calculation results in approximately 0.369, or 36.9%.

a. The probability that, among five voters the student calls, exactly one supports candidate Smith can be calculated using the binomial probability formula. With a success probability of 64% (0.64) and exactly one success (k = 1) out of five trials (n = 5), the probability can be calculated as follows:

[P(X = 1) = \binom{5}{1} \times (0.64)^1 \times (1 - 0.64)^4\]

The calculation results in approximately 0.369, or 36.9%.

b. The probability that, among five voters the student calls, at least one supports candidate Smith can be calculated as the complement of the probability that none of the voters support Smith. Using the binomial probability formula, with a success probability of 64% (0.64) and no success (k = 0) out of five trials (n = 5), the probability can be calculated as follows:

[P(X \geq 1) = 1 - P(X = 0) = 1 - \binom{5}{0} \times (0.64)^0 \times (1 - 0.64)^5\]

The calculation results in approximately 0.997, or 99.7%.

c. The probability that the first voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of not reaching a Smith supporter in the first four calls (0.36) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{First Smith Supporter on Fifth Call}}) = (1 - 0.64)^4 \times 0.64

\]

The calculation results in approximately 0.014, or 1.4%.

d. The probability that the third voter supporting candidate Smith is reached on the fifth call can be calculated as the probability of reaching two Smith supporters in the first four calls (0.64 for the first call, 0.36 for the second call, and 0.36 for the third call) multiplied by the probability of reaching a Smith supporter on the fifth call (0.64):

\[

P(\text{{Third Smith Supporter on Fifth Call}}) = (0.64)^2 \times (1 - 0.64) \times 0.64

\]

The calculation results in approximately 0.147, or 14.7%.

know more about probabilities :brainly.com/question/29381779

#SPJ11

1 (7/24) cups of condensed soup were in the can.

Given,

There is a can of condensed soup .

The amount of milk  Alen mixes with the condensed soup = 1 1/3

Subtract amount of milk from total cups of soup:

2 ( 5/8 ) – 1 ( 1/3 )

Make the fraction in same form to make the subtraction easy.

2 ( 5/24 ) – 1 ( 8/24 )

Now solve

2 (15/24 ) – 1 ( 8/24 )= 1 ( 7/24 )

Here, there is 1 ( 7/24 ) cups of condensed soup in the can.

Learn more about fraction calculation here: https://brainly.com/question/644022

#SPJ4

The question is incomplete. And the corrected question is given below.

Alan mixes 1 1/3 cups of milk with a can of condensed soup. he makes a total of 2 5/8 cups of soup. how many cups of condensed soup were in the can?

answer:

x = 29

y = 29

z = 61

step-by-step explanation:

all angles in a triangle must equal 180 degrees.

we were already given the angle degree of 61 degrees so we must include that in our formula to determine the degree of y.

the line in the middle already gives us two more angles because they both are 90 degrees for being a perfect quarter turn.

so to figure out y,

we must add 61+90 and then subtract the sum of that from 180.

so, 61+90 = 150 and 180-151 = 29

therefore,

we can conclude that y = 29

now, to determine the degrees of x and z we do the same thing.

we already know one angle equals 90 degrees.

180-90 = 90

that concludes that x and z must have a sum of 90.

if we use our choices,

39+61 = 100 (no)

39+29 = 68 (no)

29+61 = 90 (CORRECT)

29+29 = 28 (no)

therefore, x = 29 and z = 61

so, in total :

x = 29

y = 29

z = 61

hope this helps :)  

-audrey <3

An arithmetic mean is a calculated central value of a set of numbers.

Statement A: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day.

The arithmetic mean is defined as the average of the numbers for the given set of numbers.

\(m = \dfrac { Sum\;of\;the\;terms}{Number\;of\;terms}\)

Given that Sasha’s daily tips this workweek were $43, $32, $65, $88, $50, and $72.

The mean is calculated as given below.

\(m = \dfrac { 43 + 32+ 65+ 88 + 50 + 72}{6}\)

\(m = \$58.33\)

The mean amount is $58.33.

Statement A: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day.

To know more about the mean, follow the link given below.

https://brainly.com/question/13000783.

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

\(g(f(x)) = 4 - \frac{3}{2} ( \frac{1}{2}x + \frac{3}{2} ) \\ \\ = 4 - \frac{3}{4} x - \frac{9}{4} \\ \\ = \frac{16}{4} - \frac{3}{4}x - \frac{9}{4} \\ \\ = \frac{7}{4} - \frac{3}{4} x\)

We put the equation g(x) and substitute in the place of x the equation f(x) .

I hope I helped you^_^

We can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

Given the triangles EFG and BCD, you can identify that:

By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.

In this case, you can identify that you know two pairs of corresponding sides. Then, you can find that they are in proportion. Set up that:

\(\frac{EF}{BC}=\frac{FG}{CD}\)

Substituting values and simplifying, you get:

\(\frac{18}{90}=\frac{16}{80}\\\\\frac{1}{5}=\frac{1}{5}\)

Notice that they are in proportion.

You can also identify that the corresponding angles F and I are congruent because they have equal measures.

Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).

Hence, the answer is The third option.

learn more about  Side-Angel-Side Theorem (SAS).

https://brainly.com/question/22995265

#SPJ4

According to the triangle, the line of reflection is at the point (0,3)

To start, let's plot the given triangle XYZ on a coordinate plane using the provided vertices X(-2, 4), Y(-9, 3), Z(-10, 7). Once you have plotted the triangle, you can draw the line of reflection that will produce the image of Y'(9, 3).

Here are the steps you can follow to find the line of reflection:

Draw a perpendicular bisector of YY'. This is the line that passes through the midpoint of segment YY' and is perpendicular to it. To find the midpoint of YY', you can use the midpoint formula:

Midpoint of YY' = [(-9 + 9)/2, (3 + 3)/2] = [0, 3]

Draw a line passing through the midpoint of YY' and vertex X. This line will be perpendicular to YY' since it is a perpendicular bisector. To find the equation of this line, we can use the point-slope form:

Slope of line = (3 - 4)/(0 - (-2)) = 1/2

Equation of line: y - 3 = 1/2(x - 0) or y = 1/2x + 3

Extend this line to the other side of YY'. This extended line will be the line of reflection that produces the image of Y'.

To know more about triangle here

https://brainly.com/question/8587906

#SPJ4

Answer:

1/5

Step-by-step explanation:

0.2 is the same as 2/10. you then must reduce the fraction

Step-by-step explanation:

here is the single fraction of it

\( \frac{1}{5} = 0.2\)

Answer:

11

Step-by-step explanation:

how do you know how to read yet not know this

The value of r when 2^(r)=(1)/(32) is -5. This can be derived by taking the logarithm of both sides of the equation. Since log2 (2^r) = r and log2 (1/32) = -5, then r = -5.

In order to work out the value of r when 2^(r) = 1/32, we need to use logarithms. Logarithms are a way of expressing a number as the power of another number. Specifically, the logarithm of a number x is the exponent y to which a given base must be raised to equal x.

In this case, the base is 2, so log2 (2^r) = r. Therefore, to work out the value of r, we need to find the logarithm of 1/32. This can be done by dividing 1 by 32 and taking the logarithm of the result. We get log2 (1/32) = -5. Therefore, r = -5.

Since the question specifies that we should give the answer as an integer or as a fraction in its simplest form, we must conclude that the answer is -5. It is impossible to reduce this fraction any further, so it is already in its simplest form.

For more such questions on Logarithms.

https://brainly.com/question/30085872#

#SPJ11

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

If I were to hypothesize that communication students will have a higher average score on the oral communication measures,

I would have a research hypothesis. A research hypothesis is a statement that is used to explain a relationship between two or more variables,

in this case, the relationship between being a communication student and having a higher score on oral communication measures.

The hypothesis can then be tested through research and analysis of data to determine if there is a significant correlation between the two variables. In order to fully test this hypothesis,

it would be necessary to gather data on both communication students and non-communication students and compare their scores on oral communication measures.

learn more about communication here:brainly.com/question/22558440

#SPJ11

Step-by-step explanation:

Answer:

$24

Step-by-step explanation:

I did this question and got it right.

Answer:

$24

Step-by-step explanation:

got it right on edge

:)

To use the central limit theorem to find the mean and standard error of the mean of the sampling distribution, we need to know the mean (μ) and standard deviation (σ) of the population, as well as the sample size (n).

Given that the monthly rents for studio apartments in a certain city have a mean of μ and a standard deviation of σ, we can use these values to find the mean and standard error of the mean for random samples of size n.

The mean of the sampling distribution will still be μ, as the central limit theorem states that the sampling distribution of the mean will be normally distributed with a mean equal to the population mean.

The standard error of the mean (SE) is calculated by dividing the population standard deviation (σ) by the square root of the sample size (n).

So, SE = σ / √n.

In this case, you haven't provided the values for the mean and standard deviation of the population, nor the sample size. Please provide those values so I can calculate the mean and standard error of the mean for you.

To know more about standard deviation visit:

brainly.com/question/13498201

#SPJ11

Answer: y=1.75

Step-by-step explanation:

STEP 1:

y=40-8.5x

Substitute x for 4.5.

y=40-38.25

STEP 2:

Simplify.

y=1.75

Hope this helps :)