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The common factor for the rational expression presented in this problem is given as follows:

A. (x²-1).

The rational expression in this problem is given as follows:

4/(x - 1) - 1/(x² - 1) = 6/(x - 1).

It is called a rational expression as it has the variable x in the denominator.

The common factor, which is the expression that multiplies each term, is obtained considering all the terms that are present in the denominators.

The denominators to each term of the expression are listed as follows:

Hence the two terms present in the denominators of the expression are:

(x - 1)(x + 1) = x² - 1 -> subtraction of perfect squares.

Hence option A gives the correct term.

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The coordinates to the intercepts of the functions are given as follows:

c - i) Point P: P(-4,0).

c - ii) Point Q: Q(0,2).

d - i) Point P: P(-3,0).

d - ii) Point Q: Q(0,9).

The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.

For item c, the function is:

2y = x + 4.

Hence the x-intercept is obtained as follows:

x + 4 = 0

x = -4.

Then the coordinates of point P are:

P(-4,0).

For item d, the function is:

y = 3x + 9

Hence the x-intercept is obtained as follows:

3x + 9 = 0

3x = -9

x = -3.

Then the coordinates of point P are:

P(-3,0).

The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.

For item c, the function is:

2y = x + 4.

Hence the y-intercept is:

2y = 4

y = 2.

The coordinates of Q are:

Q(0,2).

For item d, the function is:

y = 3x + 9.

Hence the y-intercept is:

y = 3(0) + 9 = 9.

The coordinates of Q are:

Q(0,9).

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Answer:

17

Step by step explanation

15-6=21

38-21=17

The example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

According to the question,

We have the following information:

1) 5*(2+5) = 10+25

2) (2+3)+6 = 2+(3+6)

3) 4*(3+6) = 12+24

4) 6*(7*3) = (6*7)*3

5) 12*8 = 8*12

We know that commutative property of multiplication states:

a*b = b*a

So, this applies to 5th one.

Associative property of addition:

(a+b)+c = a+(b+c)

Associative property of multiplication:

(a*b)*c = a*(b*c)

Now, this applies to 2nd and 4th one.

Distributive property:

a*(b+c) = a*b+a*c

This applies to 1st and 3rd one.

Hence, the example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.

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The probability of getting heads twice in a row at some point during three coin flips is 1/8.

Given info;

Assume that a fair coin has an equal chance of coming up heads or tails.

What is the likelihood that three coin flips will result in two consecutive heads at any point?

There is a three-coin flip. The potential results are;

(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)

1 is the number of successful results.

Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8

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Answer:

Answer:The total change in the number of bushels she has for sale after 5 days is 83.125 bushelsStep-by-step explanation:The given parameters are;The initial number pf bushels the farmer has = 120 bushelsThe amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625 The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushelsThe total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 daysThe total change in the number of bushels she has for sale after 5 days = 83.125 bushels.

Step-by-step explanation:

The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.

Corresponding angles are equal.

We have,

Two congruent figures.

Each figure's total sum of the angles must be 360.

The figures are congruent so the corresponding angles must be equal.

From the first figure we get,

∠A = 133 ( Corresponding angles )

∠A + ∠B + ∠C + ∠D = 360

133 + ∠B + 41 + 86 = 360

∠B = 360 - 260

∠B = 100

Now,

∠k = ∠B = 100

∠L = ∠C = 41

∠M = ∠D = 86

Thus,

The measure of the angle that isn't labeled are:

∠B = 100

∠K = 100

∠L = 41

∠M = 86

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Answer:

…………………………………………/,,/,,..,,.,…….

Step-by-step explanation:

Answer:.

Step-by-step explanation: .

We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.

For P, what is the confidence interval at 95 percent?

Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.

What is the 95 percent confidence interval for the population's proportion of smokers?

Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.

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Answer:

u = 2

Step 1: Simplify both sides of the equation.

−7u −u +2u +11u = 10

−7u +−u +2u +11u = 10

(−7u +−u +2u +11u) = 10 (Combine Like Terms)

5u = 10

Step 2: Divide both sides by 5.

5u/5 = 10/5

Hope this helped!

Answer:

x=54.5

Step-by-step explanation:

x+62+x+9=180

2x+71=180

2x+71-71=180-71(subtract 71 from both sides)

2x=109

2x/2=109/2(divide both sides by 2)

x=54.5

Answer:

x=54.5

Step-by-step explanation:

1. Combine like terms

x+62+x+9=180

2x+71=180

You can only combine the x and 62 and 9 in this equation.

2. Subtraction property of equality

2x+71=180

    -71 = -71

2x=109

Subtract 71 from both sides to isolate the variable, x.

3. Division property of equality

2x=109

/2     /2

x=54.5

Hope this helps!

The probability of a type I error is 0.022.

Given,

It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.

The null hypothesis is given as "the individual does not have the disease".

We have to find the probability of type l error if the new blood test is used;

Here,

A: The individual does not have the disease

B: The individual does have the disease

We know that,

Type I Error is rejecting the true null hypothesis

Then, probability;

P (Type I Error) = P(Positive reaction to an individual who does not have the disease)  = 0.022

That is,

The probability of a type I error is 0.022.

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Answer: It does not appear to show a function because the numbers are not multiples of each other

Step-by-step explanation: Hope this helps :-)

Answer:

1. 3  donuts

2.$76.90

Step-by-step explanation:

The value for expression 1 that is 3z+8 is 29 and for expression 2 that is 8y-x is 12 by substituting the values.

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation.

Here,

For expression 1,

3z+8 where z=7

3*7+8=29

For expression 2,

8y-x where x=20 and y=4

8*4-20=12

By substituting the values, the value for expression 1 ,(3z+8) is 29, and the value for expression 2, (8y-x) is 12.

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Answer: 0.865 to (1dp)

Step-by-step explanation:

The Actual Unemployment rate is 7%.

Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.

Cyclical Unemployment Rate = 1%

Natural Unemployment Rate = 6%

The Actual Unemployment rate will be:

= Cyclical Unemployment Rate + Natural Unemployment Rate

= 1% + 6%

= 7%

The unemployment is 7%.

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The speed of the output shaft is 182 rpm.

Given:

Gear index i = 0.33

Input speed = 60 rpm.

Let output shaft speed is x.

we know that:

gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]

i = 60/x

0.33 = 60/x

x = 60/0.33

= 60/033/100

= 60*100/33

= 6000/33

= 181.818 ≈ 182 rpm.

Therefore The speed of the output shaft is 182 rpm.

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The logarithm of 5.238 with solution is  0.71916549409.

= log(5.238)

= log(5238/1000)

= log(5238) - log(1000)

= 3.71916549409 - log([tex]10^{3}[/tex])

= 3.71916549409 - 3log10

= 3.71916549409 - 3

=  0.71916549409.

Therefore the logarithm of 5.238 with solution is 0.71916549409.

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To determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

Rate of Change:

A rate of change describes how an output quantity changes relative to the change in the input quantity. The units on a rate of change are “output units per input units.”

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.

[tex]\frac{\triangle y}{\triangle x} = \frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1}}[/tex]

How to determine:

Given the value of a function at different points, calculate the average rate of change of a function for the interval between two values [tex]x_{1}[/tex] and [tex]x_{2}[/tex].

Hence the answer is to determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].

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Answer:

10.6m

Step-by-step explanation:

height of cylinder:

h= V/pie r^2

h= 48/3.14x1.2^2

h=48/3.14x1.44

h=48/4.5216

h=10.61meter

round to the nearest tenth

= 10.6m

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Answer:

3rd choice

No, it is NOT a linear function because the variable x is in the denominator. x will be multiplied by y.

Answer:

B 1/4

Step-by-step explanation:

f(x) = y = x⁴ + 5

the inverse function is

y - 5 = x⁴

x = 4th root(y - 5)

now we rename y and x to make it a regular function definition :

g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)

because g(6) = 1 (positive), we have

g(x) = (x - 5)^(1/4)

and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.

g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)

because (x - 5)' = 1

g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =

= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4

please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.

The minimum value of the expression is -9

From the question, we have

the expression is 4cosx–3sinx−4.

minimum value of the expression =[tex]c- \sqrt{a^{2} +b^{2} }[/tex]

[tex]=-4- \sqrt{4^{2} +(-3)^{2} }\\=-4-5\\=-9[/tex]

Subtraction:

The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4.

Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers.

The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

The minuend, from which we subtract another number, is the first number in a subtraction process.

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Answer:

see explanation

Step-by-step explanation:

4x + 9 = 16

the error being made is that on dividing both sides by 4 all terms must be divided by 4.

to obtain x + 9 = 4 from 4x + 9 = 16

the term 9 has not been divided by 4

correct solution is

4x + 9 = 16 ( divide through by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( each term being divided by 4 )

x + [tex]\frac{9}{4}[/tex] = 4 ( subtract [tex]\frac{9}{4}[/tex] from both sides )

x = 4 - [tex]\frac{9}{4}[/tex] = [tex]\frac{16}{4}[/tex] - [tex]\frac{9}{4}[/tex] = [tex]\frac{7}{4}[/tex] = 1.75

or

4x + 9 = 16 ( subtract 9 from both sides )

4x = 7 ( divide both sides by 4 )

x = [tex]\frac{7}{4}[/tex] = 1.75

when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.

What is External validity?

The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.

An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.

Question

When you are interrogating the external validity of a sample, which is the most important question to ask?

a. how many people are in the sample?

b. how was the sample collected?

c. how were the participants measured?

d. how many people are in the population?

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