What is the reason that supports the statement made on line 5?​

Answer:

8m(4 + 7p)

Step-by-step explanation:

Take out the greatest common factor:

8m(4 + 7p)

Answer:

3 √ 13

Step-by-step explanation:

Answer:

3√13

Step-by-step explanation:

We want to find the distance between these two points. To do so, we need to use the distance formula which states that the distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

Here, [tex]x_1=-1,x_2=8,y_1=0[/tex], and [tex]y_2=6[/tex]. So:

d = [tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]

d = [tex]\sqrt{(-1-8)^2+(0-6)^2}=\sqrt{(-9)^2+(-6)^2} =\sqrt{81+36} =\sqrt{117} =3\sqrt{13}[/tex]

Thus, the answer is 3√13.

~ an aesthetics lover

Answer: $57.6

Step-by-step explanation:

Given : A businesswoman sells a bag for $52.32.

Let cuurent selling price : SP = $52.32

As they are making 9% profit now.

That means SP= Cp +0.09 CP , where Cp is the cost price of bag.

i..e [tex]52.32=Cp(1+0.09) \ \text{[Substituted value of SP in LHS and taking Cp common outside in RHS]}[/tex]

[tex]\Rightarrow\ 52.32=Cp(1.09)\Rightarrow\ CP=\dfrac{52.32}{1.09}=48[/tex]

i..e Cost price of bag = 48

Selling price to gain 20% profit = Cp+0.20CP

= CP(1+0.20)

=48 (1.20)

= 57.6

Hence, the  selling price the businesswoman should ask in order to make 20% profit​ = $57.6

Answer:

 The conclusion is that the researcher was correct

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 13[/tex]

    The sample mean is  [tex]\= x = 9.63[/tex]

     The standard deviation is  [tex]s = 0.585[/tex]

      The significance level is  [tex]\alpha = 0.05[/tex]

The Null Hypothesis is  [tex]H_o : \mu = 0[/tex]

The Alternative  Hypothesis  is  [tex]H_a = \mu < 10[/tex]

The test statistic is  mathematically represented as

          [tex]t = \frac{\= x - \mu }{\frac{s}{\sqrt{n} } }[/tex]

Substituting values

          [tex]t = \frac{9.63 - 10 }{\frac{0.585}{\sqrt{13} } }[/tex]

         [tex]t = - 2.280[/tex]

Now the critical value for [tex]\alpha[/tex] is  

     [tex]t_{\alpha } = 1.645[/tex]

This obtained from the critical value table

  So comparing the critical value of alpha and the test value we see that the test value is less than the critical value so the Null Hypothesis is rejected

 The conclusion is that the researcher was correct

Answer:

To find the volume of the pipe, we need to subtract the inside cylinder volume from the outside cylinder volume.

Remember that the volume of a circular cylinder is

[tex]V=\pi r^{2} h[/tex]

Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height.

[tex]V_{outside}=\pi r^{2}h= \pi (6in)^{2} (48in)=1,728 \pi in^{3}[/tex]

[tex]V_{inside}=\pi r^{2}h= \pi (5.75in)^{2} (48in)=1,587 \pi in^{3}[/tex]

Notice that we used the height 4 feet in inches units, that's why the height in the formulas is 48 inches, because each feet is equivalent to 12 inches.

[tex]V_{pipe}=V_{outside} -V_{inside} =1,728 \pi in^{3}-1,587 \pi in^{3} =141 \pi in^{3}[/tex]

(A) Therefore, the volume of metal used to build the pipe is 141π cubic inches.

Now, to know the amount of powder-coat we must use, we need to find the surface area of the pipe, which is basically the sum of the surface area of both cylinders.

[tex]S_{inside}=2\pi r^{2}+2\pi rh=2 \pi (5.75in)^{2}+ 2 \pi (5.75in) (48in)= 66.13 \pi in^{2} +552 \pi in^{2} =618.13 \pi in^{2}[/tex]

[tex]S_{powder}=648 \pi in^{2} + 618.13 \pi in^{2} =1,266.13 \pi in^{2}[/tex]

(B) Therefore, we need 1,266.13π sqaure inches of powder to cover the whole pipe.

Answer:

A. volume of the metal used to build the pipe is 141[tex]\pi[/tex] cubic inches.

B. The total surface area to be powder coated is 1122.125 square inches.

Step-by-step explanation:

The length of the cylinder = 4 feet = 48 inches.

Radius of the outside of the pipe = 6 inches.

Radius of the inside of the pipe = 5.75 inches

A. volume of the metal used to build the pipe = volume of the outside pipe - volume of the inside pipe

volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

volume of the outside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h

                                             = [tex]\pi[/tex] × [tex]6^{2}[/tex] × 48

                                             = 1728[tex]\pi[/tex] cubic inches

volume of the inside pipe = [tex]\pi[/tex][tex]r^{2}[/tex]h

                                          = [tex]\pi[/tex] × [tex]5.75^{2}[/tex] × 48

                                          = 1587[tex]\pi[/tex] cubic inches

volume of the metal used to build the pipe = 1728[tex]\pi[/tex] - 1587[tex]\pi[/tex]

                                                                       = 141[tex]\pi[/tex] cubic inches

B. Total surface area of a hollow cylinder = 2[tex]\pi[/tex] ( [tex]r_{1}[/tex] +  [tex]r_{2}[/tex]) ( [tex]r_{2}[/tex] - [tex]r_{1}[/tex] + h)

where [tex]r_{1}[/tex] is the inner radius and [tex]r_{2}[/tex] is the outer radius.

            =  2[tex]\pi[/tex] (6 + 5.75)(5.75 - 6 + 48)

            =  2[tex]\pi[/tex] (11.75 × 47.75)

           = 1122.125[tex]\pi[/tex] square inches

The total surface area to be powder coated is 1122.125 square inches.

Answer:

Step-by-step explanation:

To find what a digit stands for, make all the other digits zero.

This is substantially what we do when we write the number in "expanded form."

  568,924,126

  = 500,000,000 +60,000,000 +8,000,000 +900,000 +20,000 +4,000 ...

     ... +100 +20 +6

The list of numbers in the sum is the list of numbers the digits stand for.

Answer:

C is the answer

Step-by-step explanation:

If you multiply 58 to 6 gives you 348

Hope this helps

Answer:

C

Step-by-step explanation:

Answer:

[tex]P=\dfrac{\pi r^2+2800}{r} $ ft[/tex]

Step-by-step explanation:

Let the length of the rectangular part =l

The width will be equal to the diameter of the semicircles.

Area of the Skating Rink= [tex]2(\frac{\pi r^2}{2})+(lX2r)[/tex]

Therefore:

[tex]\pi r^2+2lr=2800\\2lr=2800-\pi r^2\\$Divide both sides by 2r\\l=\dfrac{2800-\pi r^2}{2r}[/tex]

Perimeter of the Shape =Perimeter of two Semicircles + 2l

[tex]=2\pi r+2\left(\dfrac{2800-\pi r^2}{2r}\right)\\=2\pi r+\dfrac{2800-\pi r^2}{r}\\=\dfrac{2\pi r^2+2800-\pi r^2}{r}\\=\dfrac{\pi r^2+2800}{r}[/tex]

The perimeter of the rink is given as:

[tex]P=\dfrac{\pi r^2+2800}{r} $ ft[/tex]

Answer:

15 liters

Step-by-step explanation:

60/480= 0.125

0.125*360= 45

60-45= 15

Answer:

Answer: 280,307

Explanation:

The expression

200,000 + 80,000 + 300 + 7

may be expressed as

200 thousand, plus

 80 thousand, plus

300 hundred, plus

  7 ones

Step-by-step explanation:

Answer:

a) [tex] z= \frac{34-34}{2.5}= 0[/tex]

[tex] z= \frac{39-34}{2.5}= 2[/tex]

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

b) [tex] P(X<31.5) [/tex]

[tex] z= \frac{31.5-34}{2.5}= -1[/tex]

So one deviation below the mean we have: (100-68)/2 = 16%

c) [tex] z= \frac{29-34}{2.5}= -2[/tex]

[tex] z= \frac{36.5-34}{2.5}= 1[/tex]

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Step-by-step explanation:

For this case we have a random variable with the following parameters:

[tex] X \sim N(\mu = 34, \sigma=2.5)[/tex]

From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.

We want to find the following probability:

[tex] P(34 < X<39)[/tex]

We can find the number of deviation from the mean with the z score formula:

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

And replacing we got

[tex] z= \frac{34-34}{2.5}= 0[/tex]

[tex] z= \frac{39-34}{2.5}= 2[/tex]

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

For the second case:

[tex] P(X<31.5) [/tex]

[tex] z= \frac{31.5-34}{2.5}= -1[/tex]

So one deviation below the mean we have: (100-68)/2 = 16%

For the third case:

[tex] P(29 < X<36.5)[/tex]

And replacing we got:

[tex] z= \frac{29-34}{2.5}= -2[/tex]

[tex] z= \frac{36.5-34}{2.5}= 1[/tex]

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Answer:

The constant 2.2 in L(D) represent the brightness in lumens per square inch.

Step-by-step explanation:

Answer:

Kate's age now is 30 years old and Jan's age now is 10 years old.

Step-by-step explanation:

Kate age now is 3x

Jan age now is x

3x-6=6*(x-6)

3x-6=6x-36

-3x    -3x

-6=3x-36

+36      +36

30=3x

10=x

x=10

3x=30

Kate's age now is 30 years old and Jan's age now is 10 years old.

Answer:A. is the equilateral triangle because all sides are equal

Step-by-step explanation:

Answer: 25 can be an option.

Step-by-step explanation:

Interquartile range is defined as the difference between the third quartile and the first quartile.

we have 8 values, so the first quartile is the lower 25% of the data:

the  25% of 8 is:

0.25*8 = 2

So the first quartile is 18 + 20 = 38

the third quartile is 30 + 34 = 64.

So we can add any integer that does not affect the first or thid quartile and the interquartile range will remain unchanged, this is if we add a number right in the midle of our data set, for example, we could add a number between 22 and 26 (let's use 25) and the interquartile range will remain unchanged.

Answer:

Step-by-step explanation:

The formula for calculating the nth term of an arithmetic sequence is given as;

Tn = [tex]a+(n-1)d[/tex]

a is the first term

n is the number of terms

d is the common difference

If  two terms of an arithmetic sequence are a12=70 and a30=124 then;

T12 = a+(12-1)d = 70

T12 = a+11d = 70...(1)

T30 = a+(30-1)d = 124

T30 = a+29d = 124...(2)

Solving equation 1 and 2 simultaneously to get a and d;

Taking the difference of both equation we have;

29d - 11d = 124-70

18d = 54

d = 54/18

d = 3

Substituting d=3 into equation 1 to get the value of 'a' we have;

a+11(3) = 70

a+33=70

a = 70-33

a = 37

To get the explicit rule for the nth term of the sequence, we will use the formula Tn = a+ (n-1)d where a = 37, d =3

Tn = 37+(n-1)3

Tn = 37+3n-3

Tn = 34-3n

This gives the required nth term

Answer:

Its A. Medera turned the phone off while playing in the soccer game

Step-by-step explanation:

Answer:

It is A.Medera turned the phone off while playing in a soccer game.

Step-by-step explanation:

got a 100 on the test

Answer:7cm

Step-by-step explanation:

m^3=343

Take the cube root of both sides

m=7

Answer:45.9

Step-by-step explanation:

Circumference=12

Length of arc=8/5=1.6

π=3.14

Circumference=2 x π x r

12=2x3.14xr

12=6.28 x r

Divide both sides by 6.28

12/6.28=(6.28 x r)/6.28

2=r

r=2

Length of arc =Φ/360 x 2 x π x r

1.6=Φ/360 x 2 x 3.14 x 2

1.6=(Φ x 2 x 3.14 x2)/360

1.6=12.56Φ/360

Cross multiply

1.6x360=12.56Φ

576=12.56Φ

Divide both sides by 12.56

576/12.56=12.56Φ/12.56

45.9=Φ

Φ=45.9

Answer:

X ≥ 3   (D)

Step-by-step explanation:

I got it right on Khan Academy :)

Answer:

  none of the above (talk to your teacher about this)

Step-by-step explanation:

If a polynomial has real coefficients, complex roots come in conjugate pairs.

A root of [tex]-5+\sqrt{3} i[/tex] will have a conjugate of [tex]-5-\sqrt{3}i[/tex], which will also be a root.

__

Here, it looks like the given root is [tex]-5+\sqrt{3i}[/tex], which is different from [tex]-5+\sqrt{3}i[/tex]. None of the listed choices is the complex conjugate of this value.

The value of [tex]-5+\sqrt{3i}[/tex] is ...

  [tex]-5+\sqrt{3i}=-5+(\sqrt{\dfrac{3}{2}}+\sqrt{\dfrac{3}{2}}i)[/tex]

so its conjugate is ...

  [tex](-5+\sqrt{3i})^*=-5+\sqrt{\dfrac{3}{2}}-\sqrt{\dfrac{3}{2}}i=\boxed{-5+\sqrt{-3i}}[/tex]

You will note that this is not among the answer choices.

_____

Additional comment

When a problem like this has an error in its presentation, we highly recommend you discuss it with your teacher (to get it corrected or deleted for future students). If you feel you must select one of the (erroneous) answer choices, your computer will probably accept the choice of [tex]-5-\sqrt{3i}[/tex], the first one.

Answer:it’s A

Step-by-step explanation:

I got it right on edg

Answer:

Placebo controlled experiment.

Step-by-step explanation:

The placebo effect is when the effectiveness of a treatment is influenced by the patient’s perception of how effective they think the treatment will be, so a result might be seen even if the treatment is ineffectual. In order to reduce this effect, a dummy treatment (placebo) is given to a control group and the result is compared.

Answer:

24

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

PR5T represents 6754.

P = 6

R = 7

T = 4

Y = 5

Step-by-step explanation:

Let us try to understand the subtraction starting from the unit's digit.

   P R 5 T

-  4 7 Y 6

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

    1 9 9 8

To get 8, 6 should be subtracted from 14

14 - 6 = 8

So, T should be equal unit digit of 14 i.e. T = 4 and 1 should be carried over from the ten's digit of PR5T.

Now, let us move to ten's digit:

   P R 5 4

-  4 7 Y 6

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

    1 9 9 8

To get 9, 6 should be subtracted from 15. But 1 is already carried to unit's place So, we have actually 14 here

14 - Y = 9

So, Y = 5

Moving to hundred's place:

R - carry - 7 = 9

Carry is 1, so R = unit's place of 9 + 8 i.e. R = 7

Moving to thousand's place:

P - carry - 4 = 1

Here carry is 1

So, P = 1 + 4 + 1 = 6

So, the number PR5T is 6754.

Answer:

total distance walked = 11 + 14 = 25 miles

= 50 half miles

so money raised = 50 × 0.25 = 1.25$

Answer:

  see below for a graph

Step-by-step explanation:

To draw a graph on a grid, locate the point (4, -2) and use the slope to find another point. One such point will be 1 to the left and up 3*, at (3, 1). With two points, you can draw the line through them to complete the graph.

__

For a graphing tool that requires an equation, the point-slope form of the equation can be used:

  y -k = m(x -h) . . . . . a line of slope m through point (h, k)

For the given slope and point, the equation of the line is ...

  y +2 = -3(x -4)

  y = -3x +10

_____

* The slope is "rise" over "run". The slope of -3 means that a run of +1 will result in a rise of -3. The given point is already below the x-axis, so we don't really want to find more points farther down. In order to go up on a line with negative slope, we must choose a point to the left of the given one.

Answer:

Step-by-step explanation:

In order to subtract by adding up 65-39, we need to add -39 to the value of 65. This can be rewritten in this way;

65+(-39)

The equation above is similar to the one given because the product of a minus and a plus sign will still give us back a minus sign.

on solving;

65+(-39) = 26

Answer:

He saved 16 dollars

Step-by-step explanation:

6*4=24

24/3=8

8*2=16

the answer is 16