James determined that these two expressions were equivalent expressions using the values of x - 4 and x-6.
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x-2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x-6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x-0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x - 8.

Answer:

Q= 8

The amount emptied is 8 gallons of water

Step-by-step explanation:

First we need to create the equation for the above statement.

Q is directly proportional to the square of d

Q= kd²

Q= 50

d= 5

50= k5²

50 = k25

K = 50/25

K = 2

K is the constant of proportionality.

Now our equation is

Q= 2d²

Where Q = volume in gallons

d = pipe diameters in inch

For a pipe of diameter 2 inch

The amount of gallons of water emptied assuming the same kinf of flow is

Q= 2d²

Q= 2(2)²

Q= 2(4)

Q= 8

The amount emptied is 8 gallons of water

Answer:

Step-by-step explanation:

Hello!

This is an example of a pared sample test, the experiment is based on two dependent variables:

X₁: centimeters on a pain scale before hypnosis

X₂: centimeters on a pain scale after hypnosis

Out of these two variables a new variable is determined Xd= X₁-X₂

If the variables have an approximate normal distribution then the variable resulting from their difference will also have an approximate normal distribution.

The claim is that "hypnosis reduced the pain" if so you'd expect the population mean of the difference to be less than zero, symbolically: μd<0

The statistic for this test is a paired sample t test:

[tex]t= \frac{\frac{}{X_d} - Mu_d}{Sd} ~t_{n-1}[/tex]

To calculate the sample mean and variance you have to calculate the difference between the pairs first.

[tex]\frac{}{Xd}[/tex]= ∑Dif/n

[tex]S_d^2= \frac{1}{n-1} [sumDif^2- \frac{(sumDif)^2}{n} ][/tex]

∑Dif= 6.4

∑Dif²= 12.64

[tex]\frac{}{Xd}[/tex]= 6.4/5= 1.28

[tex]S_d^2= \frac{1}{4} [12.64- \frac{(6.4)^2}{5} ]= 1.112[/tex]

Sd= 1.05

[tex]t_{H_0}= \frac{\frac{}{Xd}-Mu_d }{Sd} = \frac{1.28-0}{1.05} = 1.219= 1.22[/tex]

I hope this helps!

Answer:

third option

Step-by-step explanation:

We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.

Answer:

x^2-10x

Step-by-step explanation:

f(x)-g(x)

(2x^2-4x)-(x^2+6x)

carry through the negative

2x^2-4x-x^2-6x

x^2-10x

Answer:

The correct answer is:

Double-blind (b)

Step-by-step explanation:

A blind/blinded experiment is one in which information which may influence the participant or experimenter is withheld throughout the process of the experiment either by masking (giving false identity) or completely blinded, to avoid biases that may arise from such knowledge by the participant or experimenter.

Blinding is of three types: single-blind, double-blind and triple-blind experiements and this is named with respect to three categories involved in the experiment; participant, researcher or a third party, which may include: analysts, monitoring committees stakeholders etc. The blinding type is explained as follows

Blinding Type              participant       researcher           Third-party

single-blind                   blinded               unblinded           unblinded

double-blind                  blinded               blinded               unblinded

triple-blind                     blinded               blinded                blinded

In this example, the 200 headache sufferers (participants) and the Migrane testing service (researchers) do not know the contents of the bottles being administered, whereas the pharmaceutical company (third-party knows), hence it is a double-blinded experiment.

Answer:

Hey there!

This question is basically asking for the least common multiple, or LCM of the three numbers.

If it is a multiple of 10, it has to be a multiple of 5. Thus, the only thing we need to do now, is find the LCM of 10 and 7, which is 70.

Thus, your answer is 70.

Hope this helps :)

Answer:

I think it is 70.

Step-by-step explanation:

I think that is the Lowest common Multiple of 5, 7 and 10:

10 = 2*5

7 = 7

5 = 5

So the LCM is 2 * 5 * 7 = 70.

Answer:

D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.

Step-by-step explanation:

We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;

X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.

Let [tex]\mu[/tex] = average customer bought worth of shoes.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100      {means that the mean is smaller than or equal to $100}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100      {means that the mean is greater than $100}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4

             s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78

             n = sample of receipts = 10

So, the test statistics =  [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex]  ~  [tex]t_9[/tex]

                                    =  0.991

The value of t-test statistics is 0.991.

Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean is smaller than or equal to $100.

Answer:

The answer is "A'' -2 because anything next to the letter x is the slope

Step-by-step explanation:

The equation to slops is y=mx+b

m= slope

b= y intercept

Slope = -2

Y intercept = ( 0 , -1)

Step-by-step explanation:

Hope this helps. Your answer would be A

Answer:

y = 3.5 + (1/8)x

Step-by-step explanation:

Speed is the ratio of total distance traveled to the total time taken. It is given by the formula:

Speed = distance / time.

The distance Paul Revere traveled from Charlestown to Boston is 3.5 miles.

Paul Revere also traveled from Boston to Lexington by horse at a rate of 1/8 mile per minute. If he traveled for x minutes, the distance covered can be gotten by:

Speed = distance / time

1/8 = distance / x

distance = (1/8)x miles.

y = sum of the distance to Charlestown and the distance from Charlestown to Lexington

y = 3.5 + (1/8)x

Answer:

A. The model under-predicts the price of this diamond because the residual is positive.

Step-by-step explanation:

The diamond seller has listed its 0.8 weighting diamonds at a price of $10,999. The price of the diamond is set as the market maker. The model is used to predict the price of the diamonds. This model has under predicted the value of diamonds and actual price of diamonds must be higher.

Answer:

8w : 3.8974342 ≈ 3.9 or 4 (hope it help)

Step-by-step explanation:

1w : 2

2w : 2 + 10% = 2.2

3w : 2.2 + 10% = 2.42

4w : 2.42 + 10% = 2.662

5w : 2.662 + 10% = 2.9282

6w : 2.9282 + 10% = 3.22102

7w : 3.22102 + 10% = 3.543122

8w : 3.543122 + 10% = 3.8974342

3.8974342 ≈ 3.9 or 4

Answer:

i think is 7

Step-by-step explanation:

Step-by-step explanation:

5 log₅ x − ¼ log₅ (8−x)

log₅ x⁵ − log₅ (8−x)^¼

log₅ x⁵ − log₅ ∜(8−x)

log₅ (x⁵ / ∜(8−x))

The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

A logarithmic expression x = logₐb, implies that aˣ = b.

Some properties used to solve logarithmic expressions are:

In the question, we are asked to condense the expression:

5 log₅ x - 1/4 log₅ (8 - x)

= [tex]log_{5}x^{5} - log_{5}(8 - x)^{1/4}[/tex], (using the power law: logₐ xⁿ = n.logₐ x)

= [tex]log_{5}x - log_{5}\sqrt[4]{8 - x}[/tex], (since, [tex]x^{1/a} = \sqrt[a]{x}[/tex])

= [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , (using the quotient law: logₓ a - logₓ b = logₓ a/b).

∴ The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.

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Answer:

Ok, we have a system of equations:

6*x + 3*y = 6*x*y

2*x + 4*y = 5*x*y

First, we want to isolate one of the variables,

As we have almost the same expression (x*y) in the right side of both equations, we can see the quotient between the two equations:

(6*x + 3*y)/(2*x + 4*y) = 6/5

now we isolate one off the variables:

6*x + 3*y = (6/5)*(2*x + 4*y) =  (12/5)*x + (24/5)*y

x*(6 - 12/5) = y*(24/5  - 3)

x = y*(24/5 - 3)/(6 - 12/5) = 0.5*y

Now we can replace it in the first equation:

6*x + 3*y = 6*x*y

6*(0.5*y) + 3*y = 6*(0.5*y)*y

3*y + 3*y = 3*y^2

3*y^2 - 6*y = 0

Now we can find the solutions of that quadratic equation as:

[tex]y = \frac{6 +- \sqrt{(-6)^2 - 4*3*0} }{2*3} = \frac{6 +- 6}{6}[/tex]

So we have two solutions

y = 0

y = 2.

Suppose that we select the solution y = 0

Then, using one of the equations we can find the value of x:

2*x + 4*0 = 5*x*0

2*x = 0

x = 0

(0, 0) is a solution

if we select the other solution, y = 2.

2*x + 4*2 = 5*x*2

2*x + 8 = 10*x

8 = (10 - 2)*x = 8x

x = 1.

(1, 2) is other solution

Answer:

A)Option D

B)P(X = 15) = 0.1325

Step-by-step explanation:

A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each​ trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of ​another, and the probability of success is the same for each trial.

So option D is correct.

B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66

Let X be the number of adults satisfied with the job. Since 25 are selected,

Thus;

P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)

P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378

P(X = 15) = 0.1325

Answer:

34.26 mm²

Step-by-step explanation:

To find the shaded region we must find the total area of the half-circle and then substract from it the area of the triangle

Let A be the area of the half circle

A = r²*π   where r is the radius

A = 4²π = 16π mm²

Let A' be the area of the triangle

A' = (b*h)/2   where b and h are respectively the base and the the height

A'= (8*4)/2 = 16

Let A" be the area of the shaded region

A" = A-A'

A" = 16π -16 = 34.26 mm²

Answer:

7/44

Step-by-step explanation:

First find the total number of presidents.

2 + 7 + 13 + 12 + 7 + 3 = 44

There were 7 presidents that were 45-49 when elected.  Divide this number by the total number of presidents to find the fraction.

7/44 ≈ 0.159

Answer:

Step-by-step explanation:

Firstly let us calculate the amount of hours you will have to work in a week.

Since you will have to work Mondays through Fridays, hence you will be working 5 days in a week.

Hence in a week you will work 8.5*5= 42.5 hours in a week

Since in 1 hours you are mandated to pick 45 units

Hence in 42.5 hours you will pick 42.5*45= 1912.5 units

Answer and Step-by-step explanation: To find the B-coordinate vector of x:

[tex]b_{1} = \left[\begin{array}{ccc}1\\2\\-3\end{array}\right][/tex] , [tex]b_{2} = \left[\begin{array}{ccc}-4\\-7\\11\end{array}\right][/tex], x = [tex]\left[\begin{array}{ccc}-10\\-17\\27\end{array}\right][/tex]

The augmented matrix will be:

[tex]\left[\begin{array}{ccc}1&-4&-10\\2&-7&-17\\-3&11&27\end{array}\right][/tex]

Transforming into reduced row-echelon form:

= [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&-1&-3\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&-4&-10\\0&1&3\\0&0&0\end{array}\right][/tex]

= [tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\0&0&0\end{array}\right][/tex]

The values for the vector will be:

x = 2

y = 3

The B-coordinate vector is of the form:

V = [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

The B-coordinate vector of x is V = [tex]\left[\begin{array}{ccc}2\\3\end{array}\right][/tex]

Answer:

101.98 yards.

Step-by-step explanation:

Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).

Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).

The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.

tan(22.6) = x / 245

x / 245 = tan(22.6)

x = tan(22.6) * 245

x = 0.4162598242 * 245

x = 101.9836569

So, you are about 101.98 yards from the cabin.

Hope this helps!

66.7

you will get the answer

Answer:

66.7

Step-by-step explanation:

The bicycle shop is 24.1 kilometers west of the train station meaning the distance between them is 24.1 kilometers.

The hardware store is 42.6 kilometers west of the bicycle shop meaning the distance between them is 42.6 kilometers.

Finally, you add both of the distances. (42.6 + 24.1)

You get the answer 66.7 kilometers.

Hope this helps!

Answer:

x=-9

Step-by-step explanation:

6-15=-9

Answer:

-9

Step-by-step explanation:

When you add some thing to a negative that means you are actually subtract that number

Answer:

6

Step-by-step explanation:

We can establish 6 as an upper bound, since 1*2*3 = 6, and 6 is clearly the greatest number that is a divisor of itself.

We can show that the product of any three consecutive numbers is divisible by 6, because out of any three consecutive integers, at least one must be divisible by 3, and at least one must be divisible by 2. Since the product must have factors of 2 and 3, it must also have 6 as a factor.

Answer:

Below

Step-by-step explanation:

The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.

so the equation is:

y= mx+56

m is the slope of the function wich is by how much the function grows.

By analogy, m is the distance added to the road each day.

● y= 3x+56

X is the number of days.

■■■■■■■■■■■■■■■■■■■■■■■■■■

To find the length of the road after 33 days, replace x by 33.

y= 3*33+56 = 155

So after 33 days the road is 155 miles.

Answer:

Step-by-step explanation:

Substitute n = 1, n = 2, n = 3 and n = 4 to the equation f(n) = n² - 1:

f(1) = 1² - 1 = 1 - 1 = 0

f(2) = 2² - 1 = 4 - 1 = 3

f(3) = 3² - 1 = 9 - 1 = 8

f(4) = 4² - 1 = 16 - 1 = 15

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

===============================================

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

Please find attached

thank you

The area of Integral is 19 sq units.

An integral in calculus is a mathematical concept that can be used to represent an area or an expanded version of an area. The basic components of calculus are integrals and derivatives. The terms antiderivative and primal are additional terms for integral.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).

Given:

∫ 3 0 | 8 x − 10 | d x

Now, the graph touches the x axis  

when 8x- 10 = 0

x= 10/8

x= 5/4

and, When x = 0, y = 10.

So, the limit range will be x = 0 to x = 5/4.

Now, Area of First triangle

= 10 x 5/4 x 1/2

= 25/4

and, Area of second triangle

= 14 x (3- 10/8) x 1/2

= 7 x 7/4

= 49/4

Hence, the total Area = 25/4 + 49/4 = 19 sq. units

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see attachment a=400 rpm b and c = 200 rpm d = 40 rpm

Answer:

pulley B 200, pulley C 200, pulley D 160

S = sample space = set of all possible outcomes

S = set of whole numbers 1 through 6

S = {1,2,3,4,5,6}

E = event space = set of outcomes we want to happen

E = set of odd numbers between 1 through 6

E = {1,3,5}

We have 3 items in set E and 6 items in set S. So there are 3 ways to get what we want to happen out of 6 ways total. The probability is therefore 3/6 = 1/2

Answer:

a. Total amount after 65 years = $1179415.39

b. The total contribution to the account  = $288000

Step-by-step explanation:

Given annuity amount = $1800

Total number of years for contribution = 65 – 25 = 40 years

Interest rate  = 6%

a. Total amount after 65 years = Annuity[((1+r)^n -1) / r]

Total amount after 65 years = 1800×((1+.06/4)^(4 × 40) - 1)/(.06/4)

Total amount after 65 years = $1179415.39

b. The total contribution to the account =1800 × 4 Quarter × 40 Years

        The total contribution to the account  = $288000