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Match each rational expression to its simplest form.

The geometric sequence have a common ratio of 2

Geometric progression (GP) is a type of sequence where each next term is gotten by multiplying each previous term by a fixed number, which is called a common ratio.

In this problem, we must write out two equations to find the common ratio.

Let;

The nth term of a GP is given as;

Tn = arⁿ⁻¹

T₈ = ar⁷

256 = ar⁷ ...eq(i)

T₅ = 32

32 = ar⁴ ...eq(ii)

Dividing equation (i) by equation (ii)

256 / 32 = ar⁷ / ar⁴

8 = r⁷⁻⁴

8 = r³

r = ∛8

r = 2

The common ratio of the geometric sequence is 2

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The M(x) or the estimate slope is 20.23X

A regression equation is used in stats to find out what relationship, if any, exists between sets of data. For example, if you measure a child’s height every year you might find that they grow about 3 inches a year. That trend (growing three inches a year) can be modeled with a regression equation.

[tex]Y_i=f(X_i, \beta)+e_i[/tex]        [tex]Y_i[/tex] = dependent variable

[tex]X_i[/tex] = independent variable

[tex]\beta[/tex] = unknown parameters

[tex]e_i[/tex] = error terms

Given here,  Y=20.23*X+516.1

Thus comparing it with the equation above we can deduce that

M(x) = 20.23x

Hence The M(x) or the estimate slope is 20.23X

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Answer:

x represents the number of hours.

(y) distance because the distance depends on the number of hours traveled.

H(x) = 50x

H(5) = 50(5)

H(5) - 250 miles

After 5 hours of driving at 50 miles per hour, the car has traveled 250 miles.

Step-by-step explanation:

Answer:

Reason 5.

All right angles are congruent.

Reason 6.

ASA

(You have 2 angles and the included side of the two triangles, so by ASA (angle-side-angle) the triangles are congruent.)

Answer:

47*

Step-by-step explanation:

Each corner of the square is 90*

angle CBE + angle ABE = 90*

fill in the blanks

43 + x = 90

subtract 43 from both sides

x = 47*

The number of sides of Alexandra's regular polygon is 12.

The number of sides of Maris's regular polygon is 15.

What is a regulars polygon?

A regular polygon is denoted a area. The area bounded by equal length of arms. The angel between any two consecutive arms will same any other pair of consecutive arms.

The number of line of symmetry of a polygon is the same is the number of arm or sides of that polygon.

Thus the number of sides of a polygon that has 12 lines of symmetry is 12.

The angle of rotational symmetry of a polygon is 360°/n, where n is the number of arms.

Therefore,

Angle of rotational symmetry = 360°/n

Putting Angle of rotational symmetry = 24°:

24° = 360°/n

Multiply both sides by n

24n = 360

Divide both sides by 24:

n = 360/24

n = 15

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Answer: 1 [tex]\frac{1}{15}[/tex] miles

Step-by-step explanation:

     We will divide the length of the road, five and one-third miles by the number of groups, five teams, to find the answer to this question.

     (5 1/3) / 5 = (16/3) / 5 = (16/3) * (1/5) = 16/15 = 1 1/15 miles

* Note: We can use "keep change flip" when multiplying with fractions. Keep the first number, change to multiplication, flip to the reciprocal of the second number

The probability that there is at least one car that has no working tires is given as follows:

0.0002 = 0.02%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

For each car, the parameters are given as follows:

p = 0.9, n = 4.

Hence the probability that a car has no working tires is given as follows:

P(X = 0) = (1 - 0.9)^4 = 0.0001.

Hence the probability that two cars have working tires is given as follows:

P(X = 2) = (1 - 0.0001)² = 0.9998.

The probability that at least one has no working tires is given as follows:

P(X < 2) = 1 - 0.9998 = 0.0002 = 0.02%.

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Answer:

Step-by-step explanation:

a = lw

l = a/w

l = (9/10)/(2/5) = (9/4)

l/w = (9/4)/(2/5) = 5 5/8 times greater

Answer:

4.5/2 = 2.25

Dif: 2.25/0.4 = 5.625 times greater

Hope this helps

Answer:

Totally It Would Be 6.48

All of the statements are true.

Here is a breakdown of the set operations:

A U B (the union of A and B) is the set of all elements that belong to either A or B or both. In this case, the elements that belong to

A ∩ B (the intersection of A and B) is the set of all elements that belong to both A and B. In this case, the elements that belong to

A - B (the difference between A and B) is the set of all elements that belong to A but not to B. In this case, the elements that belong to

B - A (the difference between B and A) is the set of all elements that belong to B but not to A. In this case, the elements that belong to

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There is sufficient evidence from the hypothesis test, with a p-value of 0.035 < 0.05, to say that men and women in the United States consume different amounts of calcium.

The evidence for the null and alternative hypotheses, which are two competing statements, are compared using a statistical test. Null hypothesis or population impact does not exist (H0). An alternate hypothesis, or population effect, exists (Ha or H1).

Here,

The proportion between men and women is examined at the null hypothesis as follows:

[tex]H_{0}[/tex] : u1 - u2= 0

If the proportions are different under the alternative hypothesis, then:

[tex]H_{A}[/tex] : u1 - u2 ≠ 0

There is adequate data to determine that men and women in the United States consume different percentages of the necessary calcium levels because the p-value is 0.035 0.05.

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The composite function (f + g)(x) is (f + g)(x) = 9x² - x - 8

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

f(x)=3x²+42-6

g(x)=62-5²-2

Express properly

So, we have the following representation

f(x) = 3x² + 4x -6

g(x) = 6x² - 5x - 2

The composite function is then calculated as

(f + g)(x) = f(x) + g(x)

So, we have

(f + g)(x) = 3x² + 4x -6 + 6x² - 5x - 2

Evaluate

(f + g)(x) = 9x² - x - 8

Hence, the function is (f + g)(x) = 9x² - x - 8

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The amount of the last payment that Elroy will make is $710, which includes the $200 monthly payment and a balance of $510.

The last payment amount is the result of the mathematical operations of subtraction and multiplication.

The first mathematical operation was the subtraction of the down payment from the total cost of the video game system.

Using multiplication, the monthly payments are determined to be $3,400 for 17 months.  This is subtracted from the remaining balance to obtain the last payment amount.

The cost of a custom video game/virtual sound system = $4,210

Down payment = $100

The remaining balance for monthly payment = $4,110 ($4,210 - $100)

Payment period = 18 months (1¹/₂ years)

Monthly payments = $200

Payment for the first 17 months = $3,400 (17 x 200)

Last payment = $710 ($4,110 - $3,400)

Thus, if Elroy makes the minimum monthly payment of $200 till the last payment, then he will pay $710 to settle the account.

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He made a $100 down payment and agreed to pay the entire purchase off in 1 1/2 years The minimum monthly payment is $200 if he makes the minimum monthly payment up until the last payment what will be the amount of his last payment?

The lateral surface area of the walls of the warehouse is 18,000 sq ft.

Area is a measure of the size of a surface or the amount of space that a two-dimensional shape occupies. It is typically measured in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length and width of the shape together.

To find the lateral surface area of the walls of the warehouse, you need to find the combined area of all the exterior walls. To do this, you can use the formula for lateral surface area, which is:

Lateral Surface Area = 2 * (l * h + w * h)

where l is the length of the wall, w is the width of the wall, and h is the height of the wall.

Using this formula, we can find the lateral surface area of each wall and add them together to get the total lateral surface area:

Wall 1: Lateral Surface Area = 2 * (100 ft * 30 ft) = 6,000 sq ft

Wall 2: Lateral Surface Area = 2 * (200 ft * 30 ft) = 12,000 sq ft

Total Lateral Surface Area = 6,000 sq ft + 12,000 sq ft = 18,000 sq ft

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f(x)=-25x^4+3x^2+2 = f'(x)=-100x^3+6x

Take derivation

f'(x)=d/dx(-25x^4+3x^2+2)

Formula

f'(x)=d/dx(-25x^4)+d/dx(3x^2)+d/dx(2)

Formula

f'(x)=-25(4x^3)+3(2x)+0

f'(x)=-100x^3+6x

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Therefore, the five steps are taken to localize the protein dynein in tissue sections of the esophagus and trachea.

Any procedure that involves moving, attaching to, or otherwise maintaining a cell, substance, or cellular entity in one place, like an organelle or protein complex. Substance localisation can also be accomplished through selective degradation.

In this case,

the steps that are done in order to localize the protein dynein in tissue sections of the esophagus and trachea are as follows:

1. Histoclear removes the medium to enable the labeling of the antibodies

2. to rehydrate the sample, add water.

3. Using BSA blocking solution after Triton X- 100, which ruptures membranes and makes antigens more accessible to antibodies

(4) Add the dynein antibody.

5. include a secondary antibody that is likewise peroxidase-active (adds specificity)

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The primary purpose of the passage is to caution against uncritical embrace of nuclear fusion power as a major energy source.

Nuclear fission generates a significant amount of radioactive waste, which can be hazardous and needs to be stored securely for a long period of time. Nuclear fusion waste has a lower radioactivity and decays significantly more quickly. Fossil fuels like gas and oil are not required for nuclear fusion.

Radiation that is released voluntarily is referred to as radioactivity. An atomic nucleus that is unstable for some reason accomplishes this by "wanting" to give up some energy in order to change its configuration to one that is more stable.

The passage begins by classifying as misconceptions favorable views about nuclear fusion power and finishes by recommending the use of current energy sources going forward rather than nuclear fusion power. All of this adds up to the text trying to warn against uncritically embracing nuclear fusion power as a major source of energy.

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Answer:

Step-by-step explanation:

To solve the equation 3(x+1) = 4x-1, we need to use the rules of algebra to isolate the variable "x" on one side of the equation and simplify the other side.

First, we can distribute the 3 on the left side of the equation to obtain 3x + 31 = 4x-1. This gives us 3x + 3 = 4x-1.

Next, we can subtract 3x from both sides of the equation to obtain 3 + 3 = 4x-1-3x. This simplifies to 3 = x-1.

Now we can add 1 to both sides of the equation to obtain 3+1 = x. This gives us the final solution x = 4.

Therefore, the solution to the equation 3(x+1) = 4x-1 is x = 4.

Answer:  5 4/15

Step-by-step explanation:

1 3/5 + 3 2/3 = 8/5 + 11/3

Find the common denominator (5 and 3) = 15

So 8/5 equals to 24/15 because if 5 x 3 = 15 , 8 must also multiply by 3.

11/3 equals to 55/15 because if 3 x 5 = 15 , 11 must also multiply by 5.

Thus 24/15 + 55/15 = 79/15

This is an improper fraction, so converting to mixed number:

79/15 = 5 4/15 because 5 x 15 + 4 = 79

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

Equation: a claim that two expressions with variable- and/or number-filled expressions are equivalent. Mathematical development has been sparked by the desire to find solutions to equations, which are really just questions.

Here,

Part A:

Jamal works as a valet made $10.25 an hour and an additional $50.10 in tips,

Thus number of hours be x

equation : 10.25x + 50.10 =0

or

Jamal works as a waiter made $6.75 an hour and an additional $125 in tips

equation : 6.75x + 125 = 0

Part B:

The total amount he made when both paychecks are same

=> 6.75x + 125 = 10.25x + 50.10

=> 10.25x-6.75x = 125-50.10

=>3.5x = 74.9

=>x=74.9/3.5 =21.4

Thus the total amount he made

10.25(21.4) + 50.1 = 269.45

and

Total amount = 2* 269.45=538.9

Since ,the amount is same in both jobs as valet and waiter thus the total amount of money he made is $538.9

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Answer:

0.07

Step-by-step explanation:

Point (2,10) is not satisfying the linear function y = 10x + 3 thus it will be not the solution of the system of equations.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given point (2,10)

Put it into y = x + 8

10 = 2 +  10 = 10 (satisfy)

Put it into y = 10x + 3

10 = 10 x 2 + 3 = 23 ≠ 10 (Not satisfy)

Hence "Point (2,10) will not be the system of equations' solution since it does not fulfill the linear function y = 10x + 3".

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Answer:

NY: 4cm + 3cm = 7cm

XY: 8cm + 3cm = 11cm

Step-by-step explanation:

1. find the difference between XN and MN

2. use the difference to add to the value LN and LM

The required explanation of probability distribution that has a mean of 0 and a standard deviation of 1 is describe below.

Probability distributions help to show our reality, empowering us to get evaluations of the likelihood that a specific occasion might happen, or gauge the inconstancy of event. They are a typical method for depicting, and potentially foresee, the likelihood of an occasion

The mean of the z-scores is dependably 0. The standard deviation of the z-scores is dependably 1. The chart of the z-score dissemination generally has a similar shape as the first conveyance of test values. The amount of the squared z-scores is dependably equivalent to the quantity of z-score values.

Thus, it is dependable.

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Correct question:

A normal probability distribution can have any value of the mean or must have a standard deviation of 1 and a mean of 0?

The linear functions in this problem are given as follows:

1. y = -x/2 - 4.

2. y = -3x + 7.

Considering the options in these problems, the linear functions are defined in slope-intercept format, given as follows:

y = mx + b.

The coefficients of the function are given as follows:

The slope-intercept definition of the two equations presented in this problem are given as follows:

When two linear functions are parallel, they have the same slope, hence the two functions will be given as follows:

For item 1, when x = 2, y = -5, hence the intercept b is calculated as follows:

-5 = -0.5(2) + b

b = -5 + 1

b = -4.

For item 2, when x = 1, y = 4, hence the intercept b is calculated as follows:

4 = -3(1) + b

b = 7.

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Answer:

please set me in star

The required value of y is obtained as -2.

The given system of equation can either have a unique solution, more than one solutions or no solution.

On this basis they are divided into two parts consistent and inconsistent.

A consistent system has one or more solutions while for an inconsistent system there are no solutions.

The given system of equations is as below,

4x - y = 10             (1)

x - 4 = y               (2)

Substitute the value of y from equation (2) into equation (1) to get,

4x - (x - 4) = 10

=> 3x + 4 = 10

=> 3x = 6

=> x = 2

Then, substitute x = 2 in  x - 4 = y  to get,

y = 2 - 4  = -2

Hence, the value of y for the given system of equations is -2.

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The graph is given below and the value of the function is -0.4 at x = 0.7.

Any equation with a variable difference in it is a difference equation. The following variables affect how different equations are categorized. • The equation's order. The highest order of difference in the equation is represented by the order.

y = Mt (x - 1) + 0

Where Mt = 1/3* 1(0-2)²

Mt = 1/3*4

Mt = 4/3

From equation 1

y = (4/3)(x - 1)

Function at x = 0.7

f(0.7) = 4/3(0.7 -1 )

= 4/3(-0.3)

F(0.7) = -2/5

Let, u = y - 2

du = dy

[tex]\int\limits {1/(y-2)^2} \, dy = \int\limits {x/3} \, dx \\\int\limits{du/ u^2} \, du = 1/3 \int\limits{x} \, dx[/tex]

-1/u = 1/3( x²/2) + c

-1/(y+2)  = x²/6 + c

At point(1 , 0 )

c = 2/6

Thus

-1/(y-2) = x²/ 6  - 1/3

y  = -6/(x² + 2) + 2

Therefore, value of the function is -0.4 at x = 0.7.and function at x = 1 is

y  = -6/(x² + 2) + 2

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Answer:

x would be equal to 5 and the other one to your right would be 3 because O1t is aka known as a linear expression so you would have the multiply by 2 and use and exponent square