In a bag are three red marbles and three white marbles. If
two marbles are taken from the bag at the same time,
what is the probability that both marbles will be red?

Answer:

(f • g)(x) = -6x² - 24x

Step-by-step explanation:

The expression (f • g)(x) can be written in an expanded form, f(x) • g(x).

(f • g)(x)                         <----- Original expression

f(x) • g(x)                       <----- Rewritten expression

(- 6 x) • (x + 4)               <----- Insert functions

-6x² - 24x                    <----- Multiply -6x and x, and multiply -6x and 4

Answer:

A

Step-by-step explanation:

His commision was 0.06(160000-20000) = $8400.

His salary was $10,000.

His bonus was $500.

Adding these together, we get $18,900.

The total number of students in the school is calculated as; 600 students

Usually, some figures are expressed as a fraction of a whole as depicted in this case. Thus, when we are given a fraction of a whole to be equal to a particular figure, we will just cross multiply to get the total number.

We are told that;

Number of students that play a team sport at Lincoln high school = 225

Now, we are told that the number above represents a fraction of 3/8 of the total students in that school.

Thus, if the total number of students in the school is x, then we can say that;

(3/8)x = 225

Multiply both sides by 8 to get;

3x = 1800

x = 1800/3

x = 600 students

Thus, we can conclude that if two hundred and twenty five students play a team sport at Lincoln high school and these students represent 3/8 of the total, then we can say that the total number of students in the school is 600 students.

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4x² + 3xy - 7 + (y) = x² -5xy

y = -3x² - 8xy + 7

The correct answer is -3x² -8xy + 7

The solution to the system of inequalities is (-3.375, 1.75)

The system of inequalities is given as:

3y > 2x+12

2x+y ≤ -5

Next, we plot the graph of the system using a graphing tool

From the graph, both inequalities intersect at

(-3.375, 1.75)

Hence, the solution to the system of inequalities is (-3.375, 1.75)

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c. the least squares method.

Regression equation:

In simple linear regression, the predicted value of the dependent variable is given by the equation = b0 + b1x. The values of b0 and b1 are calculated from the data so that the line = b0 + b1X minimizes the total sum of squared errors (error is the difference between the predicted value and the actual value of y).

Least squares method:

The least squares method is a statistical procedure to find the best fit for a set of data points by minimizing the sum of the offsets or residuals of points from the plotted curve.

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Answer:

  yes

Step-by-step explanation:

The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.

The attachment shows a graph of the circle. Its equation is ...

  (x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r

We have (h, k) = (2, 13) and r = 5, so the equation is ...

  (x -2)² +(y -13)² = 25 . . . . graphed equation

The point in question is also graphed, and is shown to lie on the circle.

If the given point satisfies the circle's equation, it lies on the circle.

For (x, y) = (-2, 10), we find ...

  (-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied

Answer:

64

Step-by-step explanation:

evaluate by substituting x = 16 and x = 0 into f(x)

f(16) = 4(16) - 8 = 64 - 8 = 56

f(0) = 4(0) - 8 = 0 - 8 = - 8

then

f(16) - f(0) = 56 - (- 8) = 56 + 8 = 64

Answer:

64

Step-by-step explanation:

f(x) = 4x - 8

First find f(16)

f(16) = 4(16) -8 =64-8=56

Then find f(0) = 4)0) -8 = -8

f(16) - f(0) = 56 - (-8) = 56+8 = 64

The interval in which 99.7% of the sample means fall within 3 standard deviations of the mean is 19,306 to 21,694.

According to the central limit theorem,

Sample mean = Population mean = μ

Sample standard deviation = (Population standard deviation)/√n = σ/√n

where n is at least 30.

It is given that,

The overall population mean = 20,500

Population standard deviation σ = 2180

Sample size n = 30

Since n = 30, the central limit theorem can be applied.

According to the Empirical rule(68-95-99), 99.7% of the sample means fall within the 3 standard deviations of the mean.

So, the interval is calculated by

Sample mean = Population mean = μ = 20500

Standard deviation(sample) = σ/√n

⇒ S = 2180/√30 =398.011 ≅ 398

Thus,

The lower bound  = 20500 - 3 × 398 = 19,306

The upper bound = 20500 + 3 × 398 = 21,694

Therefore, the required interval is from 19,306 to 21,694.

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Answer: y=-(1)/(3)x-3

Please mark brainiest

Answer: [tex]\overline{EL} \cong \overline{HP}[/tex]

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides is a parallelogram.

Answer:

10x-6y-11

Step-by-step explanation:

3(3x+y) = 3(3) +×-3y=-2

9x + 3y = 9 + x -3y =-2

9x+x = -3y-3y =-2-9

10x = -6y =-11

10x-6y-11

The candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

Let x be the quantity of 10% fat-content chocolate.

Fat in 10% fat-content chocolate + Fat in 60% fat-content chocolate = Total fat in 25% fat-content chocolate

0.10x + 0.60(100 - x) = 0.25*100

10x + 60*100 - 60x = 25*100

-50x = 25*100 - 60*100

-50x = 100(25 - 60)

50x = 3500

x = 3500/50

x = 70 kg

This is the quantity of 10% fat-content chocolate required.

100 - x = 30 kg

This is the quantity of 60% fat-content chocolate required.

Therefore, we have found that the candy distributor must use 70 kg and 30 kg of 10% fat-content chocolate and 60% fat-content chocolate respectively.

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There are 430 non square numbers that lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

Given two numbers [tex]215^{2}[/tex] and [tex]216^{2}[/tex] and we are require to find non square numbers that lie between them.

Numbers can be consecutive numbers or non consecutive numbers. In our question we will find the consecutive numbers.

Square numbers are those numbers whos square is in a proper number means decimal should not be there.

First number=[tex]215^{2}[/tex]

Second number=[tex]216^{2}[/tex]

First we have to find the exact value of numbers by finding the square of these numbers.

First number=215*215=46225

Second number=216*216=46656

Numbers that  lie between them=(46656-46225)-1

=431-1

=430

Hence 430 numbers lie between [tex]215^{2}[/tex] and [tex]216^{2}[/tex].

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Answer: The answer is (x+2)(x-4)(x-4)
Or as a short form you can write it as [tex](x+2) (x-4)^{2}[/tex]

Step-by-step explanation:

Answer is very lengthy but I am 100% sure that's the correct answer

Answer:

(x³ - 6x² + 32) = (x - 4)²(x + 2)

Step-by-step explanation:

(x³ - 6x² + 32)/(x - 4) =

           x² - 2x - 8

          ----------------------------------

x - 4    |  x³ - 6x² + 0x + 32

             x³ - 4x²

            ----------

                  -2x² + 0x

                  -2x² + 8x

                 ----------------

                            -8x + 32

                            -8x + 32

                           -------------

                                       0

(x³ - 6x² + 32) = (x - 4)(x² - 2x - 8) = (x - 4)(x - 4)(x + 2) =

= (x - 4)²(x + 2)

a. Surface area = 172 cm²

Volume = 112 cm²

b. The surface area would be needed.

c. The volume would be needed.

Surface area = 2(wl+hl+hw).

Volume = (length)(width)(height)

a. l = 7 cm

w = 2 cm

h = 8 cm

Surface area =2(wl+hl+hw) = 2·(2·7+8·7+8·2) = 172 cm²

Volume = (7)(2)(8) = 112 cm²

b. The surface area would be needed.

c. The volume would be needed to find the amount of juice the box will hold.

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The experimental probability of each event is as follows:

The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.

In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:

Open-sided up: 1

Closed side up 5

On the side: 44.

We are asked to determine the experimental probability of each outcome.

The number of outcomes, when the landing is open-sided up is 1.

The number of outcomes, when the landing is closed-sided up is 5.

The number of outcomes, when the landing is on the side up is 44.

The total number of times the experiment took place is 50.

Thus, the experimental probability of each event is as follows:

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Answer:

5 1/2

Step-by-step explanation:

Rate x Time = Distance.  If you know 2 of the parts, you can figure out the 3rd part.  You know the time and the distance, so plug those in and solve.

Let R = rate

R(1/2) = 2 3/4  Let's change  2 3/4 into a improper fraction.  

R(1/2) = 11/4 Multiply 4x2 and then add 3 that gets you 11 and the bottom number stays the same.  Next, multiply both sides of the equation by 2.

R = 22/4 or 11/2 or 5 1/2 miles per hour.

Answer:

d. 90

Step-by-step explanation:

z = (x - mean)/SD = (15 - 18)/5.4 = - 3/5.4 = -0.55555555... ≈

≈ -0.56

remember the z-table represents the rounded values.

the z-table at -0.56 gives us the p-value of 0.28774.

that is the probability to the left of 15 pounds, so, the probability to have lost 15 pounds or less.

to have lost at least 15 pounds, we have to get the right side of 15 pounds in the bell curve.

and that is 1 - 0.28774 = 0.71226

so, the probability to have lost at least 15 pounds is therefore 0.71226.

how many people are that ?

well, there were in total 128 people (with the total probability of 1 representing everything).

the number of people that lost at least 15 pounds are the proportionate share of 0.71226 of 1 (the whole) :

128 × 0.71226 = 91.16928...

so, the closest answer option is d. 90

Answer: 2x + 6y + 22 units

Step-by-step explanation:

The perimeter of a figure is the total length of all the sides of a figure.

Therefore, the perimeter can be found by adding up all the lengths of the figure.

Suppose that P is the perimeter of this figure, then

[tex]P = x+4+x+4+3y+7+7+3y\\[/tex]

Combining like terms, we get

[tex]P = 2x + 6y + 22[/tex]

Since we do not have any information on what the variables are, this is the perimeter of the figure.

Answer:

Step-by-step explanation:

Discussion

A: incorrect. the minus turns the parabola upside down and you would get a maximum, not a minimum.

B: incorrect. The + 1 moves the parabola upwards not downwards.

C: incorrect. The - 3 turns the parabola upside down. You get a maximum, not a minimum.

D: correct. The parabola moves right (x - 3)^2 which anti intuitive, but it is correct. - 5 moves the parabola down. +8 the plus makes a minimum.

Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

According to the question,

The average household income for a recent year (x₁⁻) = $30,000

The average household income for a recent year (x₂⁻) = $24,500

sample sizes n₁ = n₂ = 34

standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.

Null hypothesis:  There is no evidence to believe that the average household income has increased.

H₀ : μ₁ ≤ μ₂

Alternative hypothesis:  There is evidence to believe that the average household income has increased.

H₁: μ₁ > μ₂  

To check hypothesis we have the formula

Standard error=  [tex]\sqrt{\frac{s_{1} ^{2} }{n_{1} } + \frac{s^{2} _{2} }{n_{2} } }[/tex]

= [tex]\sqrt{2067128.4706}[/tex]

= 1437.7512

Thus, standard error is $1437.7512.

Formula for test statistic = [(x₁⁻ -  x₂⁻) - (μ₁ - μ₂)]/standard error

= [(30000 -  24500) - 0]/1437.7512

= 3.8254

The critical value of z at 5% level of significance is 1.6449.

Here, the calculated value is greater than the critical value so we reject H₀.

Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

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The word problem can be:

"let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?"

And the solution is N = 12.

We want a problem that can be described by 3 divided by 1/4.

So, let's say that you have $3, and there is an item that costs $(1/4), how many of these items can you buy?

The solution to that question is given by:

[tex]N = \frac{3}{1/4}[/tex]

2) To solve this, we can use a really simple model.

In one unit, we have 4 fourts.

Then in 3 units, we have 3*4 = 12 fourts.

Then the answer is 12.

3) How to use multiplication?

Remember that dividing by a fraction is equivalent to multiplying by the inverse of said fraction, then:

[tex]N = \frac{3}{1/4} = 3*(4/1) = 12[/tex]

We got the same thing as above.

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Answer:

3. increasing

4. decreasing

Step-by-step explanation:

well for graph 3 the values are increasing

and for graph 4 the values are decreasing

A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula. In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

How long must a visit be to put a shopper in the longest 20 percent?

Here [tex]\mu=41.8 , \sigma=17.3[/tex]

The 100-20=80th percentile, which is X when Z has p-value of 0.8, so Z=0.84

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

[tex]0.84=\frac{X-41.8}{17.3}[/tex]

14.532=X-41.8

X=14.532+41.8

X=56.33

A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

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The length of AB is 25 units

The given parameters are

AC = 15 cm

BC = 20 cm

The triangle is right -angled at C.

So, we have:

AB^2 = AC^2 + BC^2

This gives

AB^2 = 15^2 + 20^2

Evaluate

AB^2 = 625

Take the square roots

AB = 25

Hence, the length of AB is 25 units

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Answer:

49°

Step-by-step explanation:

Right angled triangle:

This is a type of triangle with one of the angle as 90°

Sum of angles in a Right angled triangle is 90°

Therefore,

y + 41° = 90°

collecting like terms

y = 90 - 41 = 49°

Therefore,

y = 49°

The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.

The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;

Step 1; cos x = cos(2x + x)

Step 2; cos(2x) cosx - sin(2x) sinx

Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx

Step 4; cosx - 2sin²x cosx - 2sin²x cosx

Step 5; cosx - 4sin²x cosx

Step 6; cosx( 1 - 4sin²x)

Step 7; cosx{1 - 4(1 - cos²x)}

Step 8; cosx{-3 + 4cos²x}

Step 9; 4cos³x - 3cosx

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