A hair stylist knows that 87% of her customers get a haircut and 40% get their hair colored on a regular basis. Of the customers who get their hair cut, 24% also get their hair colored. What is the probability that a randomly selected customer gets their hair cut and colored?

0.10
0.21
0.35
0.40

The probability that either event will occur is 0.83

From the question, we have the following parameters that can be used in our computation:

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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Answer:

Step-by-step explanation:

Answer:

y = 2x + 2

Explanation:

We can use the following equation to write an equation in slope-intercept form.

Where (x1, y1) is a point in the line and m is the slope. Additionally, the slope can be calculated as:

Where (x2, y2) is another point in the line.

So, replacing (x1, y1) by (0, 2) and (x2, y2) by (3, 8), we get that the slope is equal to:

Finally, replacing m by 2 and (x1, y1) by (0, 2), we get:

Therefore, the equation in slope-intercept form is:

y = 2x + 2

The probability that a worker selected at random makes between $350 and $400 is given as follows:

0.34 = 34%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation for the salaries in this problem are given as follows:

\(\mu = 400, \sigma = 50\)

The probability that a worker selected at random makes between $350 and $400 is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 350, hence:

X = 400:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (400 - 400)/50

Z = 0

Z = 0 has a p-value of 0.5.

X = 350:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (350 - 400)/50

Z = -1

Z = -1 has a p-value of 0.16.

Hence the probability is given as follows:

0.5 - 0.16 = 0.34 = 34%.

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Solution

The measure of the angle

Alternate interior angles are "interior" (between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (next to one another sharing a vertex).

When the lines are parallel,

the alternate interior angles

are equal in measure.

Hence the angle in a parallel lines are said to be corresponding and equal

Therefore the measure of the angle 139°

Step-by-step explanation:

See image

Hey there!

ASSUMING

2(3r + 4) - 3 (r + 1) = 11

IF SO

2(3r + 4) - 3 (r + 1) = 11

2(3r + 4) - 3 (1r + 1) = 11

DISTRIBUTE

2(3r) + 2(4) - 3(1r) - 1(1) = 11

6r + 8 - 3r - 1 = 11

COMBINE the LIKE TERMS

(6r - 3r) + (8 - 3) = 11

6r - 3r + 8 - 3 = 11

3r + 5 = 11

SUBTRACT 5 to BOTH SIDES

3r + 5 - 5 = 11 - 5

SIMPLIFY!

3r = 11 - 5

3r = 6

DIVIDE 3 to BOTH SIDES
3r/3 = 6/3

SIMPLIFY!

r = 6/3

r = 2

Therefore, the answer should be: r = 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

a)Error:multiplied the numerator and denominator by 3 instead of 2.

b)The correct answer to the given expression is 8/15.

In the given image, Sadie made an error in the simplification of the expression.

The error is that she multiplied the numerator and denominator by 3 instead of 2.

She simplified the numerator and the denominator before carrying out multiplication by 2.

This resulted in the final answer being incorrect.

The correct answer would be 8/5.

The correct way to simplify the expression is as follows:

\($$\frac{4}{3} \div \frac{5}{6} = \frac{4}{3} \times \frac{6}{5}$$\)

Now, cross-cancelling can be performed because the numerator of the first fraction and the denominator of the second fraction have a common factor of 2.

\($$=\frac{4 \times 2}{3 \times 5} = \frac{8}{15}$$\)

Therefore, the correct answer to the given expression is 8/15.

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Answer:

Option A

\( {pq}^{2} + {pr}^{2} = {qr}^{2} \)

Step-by-step explanation:

This is because here,

PQ is the Height of the right triangle.

QR is the Base of the right triangle.

PR is the Hypotenuse of the right triangle.

So, as according to Pythagoras Theorem,

\( {base}^{2} + {height}^{2} = {hypotenuse}^{2} \)

Also,

\( {pq}^{2} + {qr}^{2} = {pr}^{2} \)

Not,

\({pq}^{2} + {pr}^{2} = {qr}^{2} \)

Hence, Option A is not correct.

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Okay, so assuming you have set up your division problem, you first have to find a value that will set x = to x^3. This value is x^2. So, put that above the division symbol. Next, multiply (x +4) by x^2. Then, subtract that answer from x^3 + x^2. You should get -3x^2 - 10x. Then, find a value to get x to -x^2. This value is -3x. So, put that above the division symbol. Multiply (x + 4) by -3x. Then, subtract that value from -3x^2 - 10x. You should get 2x + 8 as your answer. Now find a value to get x to 2x. 2 should work. So, put that above the division symbol.  Multiply (x +4) by 2. When subtract your answer from 2x + 8 you get 0. Therefore, the answer is x^2 - 3x +2. Hope this helps!!

Answer:

Simplifying

12x + 2y = 18

Solving

12x + 2y = 18

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

12x + 2y + -2y = 18 + -2y

Combine like terms: 2y + -2y = 0

12x + 0 = 18 + -2y

12x = 18 + -2y

Divide each side by '12'.

x = 1.5 + -0.1666666667y

Simplifying

x = 1.5 + -0.1666666667y

Answer:

Hi

Step-by-step explanation:

First, you need to subtract both sides by 12x

12x+ 2y=18

-12x         -12x

That will give you: 2y= 18-12x

Next, you need to deviede both sides by 2

2y/2= 18-12x/2

That gives you the answer:

y= 18-6x

(im not 100%  sure but i think this is right, feel free to correct me)

Answer:

12 cups

Step-by-step explanation

If the size of the bag decreased by 20%, so will the number of cups held.

Number of cups held before the change = 15 cups

If the number of cups held after the 20% reduction in the size of the bag

= (100 - 20)% × 15

=80% × 15

= 12 cups

The new bags will hold 12 cups.

Answer:

D

Step-by-step explanation:

cause 2/3 of 6 is 4

and 1/2 of 4 is 2

Answer:

C. 418 cm²

Step-by-step explanation:

Rectangle

= s × s

= 19 × 19

= 361 cm²

Triangle

= 1/2 × 6 × 19

= 57 cm²

361 + 57 = 418 cm²

So, therefore your answer is 418 cm²

The area of the triangular yard is 7000 ft².

The entire area enclosed by three sides of a triangle is the area of it.

Given,

The base of the triangle is 200 feet and the height of the triangle is 70 feet.

Therefore, the area of the triangle

= (1/2) × base of the triangle × height of the triangle =  (1/2) × 200 × 70 ft² = 7000 ft².

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Answer:

The function shows negative

Answer:

What's the question?

Step-by-step explanation:

Answer: I also need answer for this question

Step-by-step explanation:

Any body got

Answer:

Probability that a student who passed the test did not  complete the homework = 0.07

Step-by-step explanation:

Given:

Total number of students = 28

Number of students who passed the test = 18

Number of students who completed  the assignment = 23

Number of students who passed the test and also completed the  assignment = 16

To find: probability that a student who passed the test did not  complete the homework

Solution:

Probability refers to chances of occurrence of some event.

Probability = number of favorable outcomes/total number of outcomes

Let A denotes the event that students passed the test and B denotes the event that students completed  the assignment

P(A only) = \(P(A)-P(A\cap B)\)

Here,

\(P(A)=\frac{18}{28}\,,\,P(A\cap B)=\frac{16}{28}\)

So,

\(P(A\,\,only)=\frac{18}{28}-\frac{16}{28}=\frac{2}{28}=\frac{1}{14}=0.07\)

Therefore,

probability that a student who passed the test did not  complete the homework = 0.07

Answer:

2/9

Step-by-step explanation:

The house is 0 miles east of the center of the town.

To determine how far east of the center of the town the house is located, we need more information about the shape of the cell tower's coverage. However, we can make an estimation based on the given information.

Since the house lies on the boundary of the cell tower's coverage, we can assume that the cell tower's coverage area is circular.

Let's consider the following scenario: if the center of the town is the origin of a coordinate system, and the cell tower is located at (0,0), with the house 6 miles north of the town's center, we can represent the house's location as (0,6).

Assuming the cell tower's coverage area is circular, the house must lie on the circumference of this circle. In this case, the radius of the circle is 6 miles (since the house is located 6 miles north of the town's center).

Now, if we want to find the eastward distance of the house from the center of the town, we need to find the x-coordinate of the house. Since the house is directly east of the cell tower, the x-coordinate will be 0.

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We can substitute the value of x = 40 into the cost function and solve for C. Thus;C = (-8/5)(40)^2 - (13/5)(40) + 579.60C = -1280 - 104 + 579.60C = 455.60The cost (in dollars) of producing 40 units, rounded to two decimal places is $455.60. Therefore, option (d) is correct.

(a) Solution:We are given the marginal cost of a product which is modeled by;

16 + 16x + 5(dC/dx) C

= 3

We know that the marginal cost of a product is the derivative of the cost function;Thus, we have;

dC/dx

= 16 + 16x + 5(dC/dx) C

= 3

Rearranging the above equation gives us;

5(dC/dx)

= 3 - 16x - 16

Now;5(dC/dx)

= -16x - 13

Dividing by 5 on both sides, we have;

dC/dx

= (-16/5)x - (13/5)

Integrating with respect to x, we have;

C

= (-16/10)x^2 - (13/5)x + k

where k is a constant. We are given that when x

= 17, C

= 140. Thus;140

= (-16/10)(17)^2 - (13/5)(17) + k140

= -486.2 + 46.6 + kk

= 579.6

Thus the cost function is;C

= (-8/5)x^2 - (13/5)x + 579.6

The constant term rounded to two decimal places is 579.60Therefore, the cost function is given by C

= (-8/5)x^2 - (13/5)x + 579.60

(b) Solution:We are required to find the cost (in dollars) of producing 40 units, given that the cost function is;C

= (-8/5)x^2 - (13/5)x + 579.60

.We can substitute the value of x

= 40 into the cost function and solve for C. Thus;C

= (-8/5)(40)^2 - (13/5)(40) + 579.60C

= -1280 - 104 + 579.60C

= 455.60

The cost (in dollars) of producing 40 units, rounded to two decimal places is $455.60. Therefore, option (d) is correct.

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Answer:

A

Step-by-step explanation:

I hope this helps you out!

Answer:

the circumference is 2.25675833π

simplify how you want

Step-by-step explanation:

(a) The median lifetime of an engine is approximately 2.772 months, which is the value that divides the distribution into two equal halves.

b) The probability of having at least 2 successful engines in a sample of 10 engines is approximately 0.98168, or about 98.17%.

(a) To determine the median lifetime of an engine, we need to find the value of the random variable that divides the distribution into two equal halves.

The Gamma distribution is defined by two parameters: shape (k) and scale (θ). The mean and variance of a Gamma distribution are given by:

Mean = k * θ

Variance = k * θ^2

Given that the mean is 2 months and the variance is 4 months squared, we can equate these values to the corresponding formulas:

2 = k * θ

4 = k * θ^2

We can solve these equations simultaneously to find the values of k and θ:

Dividing the second equation by the first equation, we get:

4/2 = θ/θ^2

2 = 1/θ

θ = 1/2

Substituting this value back into the first equation, we have:

2 = k * (1/2)

k = 4

Therefore, the parameters of the Gamma distribution are k = 4 and θ = 1/2.

To find the median lifetime, we need to solve for the value of x such that the cumulative distribution function (CDF) of the Gamma distribution equals 0.5:

CDF(x) = 0.5

Using a statistical software or tables for the Gamma distribution, we can find that the median lifetime of an engine is approximately 2.772 months.

(b) The probability of at least 2 successful engines in a sample of 10 engines can be calculated using the cumulative distribution function (CDF) of the Gamma distribution. We need to find the probability of getting 2 or more engines with a lifetime exceeding 10 months.

Let X be the number of successful engines in a sample of 10. Since the lifetime of an engine is a continuous random variable, we need to use the cumulative distribution function for X.

P(X ≥ 2) = 1 - P(X < 2)

Using the properties of the Gamma distribution, we can calculate this probability:

P(X < 2) = P(X = 0) + P(X = 1)

The probability mass function (PMF) of the Gamma distribution is given by:

P(X = x) = (k^x * exp(-k)) / (x!)

For x = 0:

P(X = 0) = (4^0 * exp(-4)) / (0!) = exp(-4)

For x = 1:P(X = 1) = (4^1 * exp(-4)) / (1!) = 4 * exp(-4)

Therefore:

P(X < 2) = exp(-4) + 4 * exp(-4) ≈ 0.01832

Finally, we can calculate the probability of at least 2 successful engines:

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.01832 ≈ 0.98168

Therefore, the probability of at least 2 successful engines in a sample of 10 engines is approximately 0.98168, or about 98.17%.

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Answer:

Number of bagels = 10

Number of donuts = 25

Step-by-step explanation:

Let Number of bagels = b

Number of donuts = d

As given,

Each donut cost $0.55 and each bagel cost $1.20

⇒ Cost of d donuts = $0.55d

   Cost of b bagels = $1.20b

Also given,

Jamian bought a total of 35 bagels and donuts

⇒ b + d = 35     ........(1)

Also,

He paid a total of  $25.75.

⇒ 1.20b + 0.55d = 25.75          .........(2)

Now,

Multiply equation (1) by 1.20 , we get

1.20( b + d = 35 )

⇒1.20b + 1.20d = 42               ..........(3)

Now,

Subtract equation (2) from equation (3), we get

1.20b + 1.20d  - ( 1.20b + 0.55d ) = 42 - 25.75

⇒1.20b + 1.20d  - 1.20b - 0.55d  = 16.25

⇒0.65d = 16.25

⇒d = \(\frac{16.25}{0.65}\) = 25

⇒d = 25

Put the value of d in equation (1) , we get

b + d = 35

⇒b + 25 = 35

⇒b = 35 - 25 = 10

⇒b = 10

∴ we get

Number of bagels = b = 10

Number of donuts = d = 25

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Answer:

Laila assumed that the lines that formed the angles x and 18° added up to 90. This is in fact false because of the lack of the square marking to signify it as a right or 90 degree angle.

By using given figure, x=9/4 and the length of GH = 21.75.

What is the length ?

Here, in given figure,

BG≈GF and CH≈HE

now by using these similarities, we can write as,

BG≈GF therfore, \(\frac{GF}{BG}\) = 1:1

\(\frac{GF}{BF}\)=\(\frac{4x+8}{34}\)

1/2=\(\frac{4x+8}{34}\)

8x+16=34

8x= 18

x=9/4

if x=9/4 then,

GH= 7x+6 = 7(9/4)+6 =63/4+6 =\(\frac{63+24}{4}\) = 21.75

What is similarity of sides?

similarity of sides refers to the property of two geometric shapes or figures having the same shape but not necessarily the same size. More specifically, two shapes are said to be similar if their corresponding angles are congruent and their corresponding sides are proportional in length.

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