Consider the steps to solve the equation. 2 5 ( 1 2 y + 20 ) − 4 5 = 9 20 (2y − 1) Distribute:  1 5 y + 8 − 4 5 = 9 10 y − 9 20 What is the next step after using the distributive property? Use the multiplication property of equality to isolate the variable term on one side of the equation. Use the multiplication property of equality to isolate the constant on one side of the equation. Combine the like terms on the right side of the equation. Combine the like terms on the left side of the equation.

Answer:

Its D i did the question

Step-by-step explanation:

Answer:

CI=[ 7.1302,7.2698]

we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Step-by-step explanation:

-Given that the sample size, n=1546  the mean is 7.2 hrs and the standard deviation, [tex]\sigma=1.4[/tex]

-The 95% confidence interval can be calculated using the formula:

[tex]CI=\mu\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}\\\\=\mu\pm z_{0.025}\times \frac{\sigma}{\sqrt{n}}\\\\=7.2\pm1.96\times \frac{1.4}{\sqrt{1546}}\\\\=7.2\pm 0.0698\\\\CI=[7.1302, \ 7.2698][/tex]

The confidence intervals is therefore 7.1302,7.2698]

Hence, we are 95% confident that the true mean sleeping time lies between the interval[ 7.1302,7.2698]

Answer:

Number of seconds to reach maximum height = 3 seconds

Maximum height = 144 ft

Step-by-step explanation:

We are given that;

s(t) = -16t² + 96t

Now, s(t) is a function whose graph is an upside-down parabola, so the maximum s value occurs at the vertex.

Thus, the applicable formula for coordinate of vertex is t = -b/(2a) where a is the coefficient -16 and b is 96

Thus,t = -96/(2 x - 16)

t = 96/32

t = 3

Thus maximum height will be at 3 seconds.

Thus;

Max height = s(3) = -16(3)² + 96(3)

Max height = -144 + 288 = 144 ft

The object will reach its maximum height of 144 feet in 3 seconds.

Given information:

An object is projected upward from ground level with an initial velocity of 96 ft per​ sec.

The height in feet after t seconds is given by [tex]s(t)=-16t^2+96t[/tex].

Now, it is required to find the time at which the object will reach its maximum height.

The object will reach maximum height when velocity of the object becomes zero.

So, the velocity of the object can be written as,

[tex]s(t)=-16t^2+96t\\v(t)=\dfrac{d(s(t))}{dt}=-32t+96[/tex]

So, the time at maximum height can be calculated as,

[tex]v(t)=-32t+96=0\\t=3[/tex]

So, after 3 seconds the object will reach its maximum height.

Now, the maximum height of the object will be,

[tex]s(t)=-16t^2+96t\\s(3)=-16\times 3^2+96\times 3\\s(3)=144\rm \; ft[/tex]

Therefore, the object will reach its maximum height of 144 feet in 3 seconds.

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Answer:

Step-by-step explanation:

the answers for "in e^3" is 3

                          "in e^2y" is 2y

                          "e^in 1" is 1

                          "e^in 5x" is 5x

Answer: 3, 2y, 1, 5x.

We have to simplify the given expressions.

We use the formula: [tex]ln(e^a)=a[/tex].

So, [tex]ln(e^3)=3[/tex], here a = 3.

[tex]lne^{2y}=2y[/tex], here a = 2y.

We will use that: ln(1) = 0 and [tex]e^{ln(b)}=b[/tex]

[tex]e^{ln(1)}=e^0=1[/tex]

[tex]e^{ln(5x)}=5x[/tex], here b = 5x.

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Answer:

Step-by-step explanation:

Given

Volume of Cylinder (V)= 480 cm

height (h) = 30 cm

radius (r) = ?

WE KNOW THAT WE HAVE FORMULA

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

           480 = 3.14 * r^2 *30

            480 = 94.2 r^2

             480/94.2 = r^2

               r^2 = 5.1

                 r =[tex]\sqrt{5.1}[/tex]

Therefore r = 2.3 cm

Answer:

7. x = -2 +/- [tex]4i\sqrt{5}[/tex]

8. x = 2 or x = 6

9. x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

10. t = -3 +/- [tex]\sqrt{35}[/tex]

Step-by-step explanation:

7. Subtract 320 from both sides: 4(x + 2)^2 = -320

Divide by 4: (x + 2)^2 = -80

Square root both sides: x + 2 = +/- [tex]\sqrt{-80}[/tex]. We need to add the imaginary i to this: +/- [tex]\sqrt{-80}[/tex] = +/- [tex]i\sqrt{80}[/tex] = +/- [tex]4i\sqrt{5}[/tex]

Subtract 2 from both sides: x = -2 +/- [tex]4i\sqrt{5}[/tex]

8. Add 18 to both sides: 7(x - 4)^2 = 28

Divide by 7: (x - 4)^2 = 4

Square root both sides: x - 4 = +/- 2

Add 4 to both sides: x = 4 +/- 2  ⇒  x = 2 or x = 6

9. Add 5 to both sides: -2(x + 2)^2 = 13

Divide by -2: (x + 2)^2 = -13/2

Square root both sides: x + 2 = +/- [tex]\sqrt{-13/2}[/tex]. We again need i: +/- [tex]\sqrt{-13/2}[/tex] = +/- [tex]i\sqrt{13/2} =[/tex] +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

Subtract 2 from both sides: x = -2 +/- [tex]\frac{\sqrt{26} }{2} i[/tex]

10. Multiply by 5 on both sides: (t + 3)^2 = 35

Square root both sides: t + 3 = +/- [tex]\sqrt{35}[/tex]

Subtract 3: t = -3 +/- [tex]\sqrt{35}[/tex]

Hope this helps!

Answer:

7. -2 + 4sqrt(5) i, -2 - 4sqrt(5) i

8. x = 2, 6

9. x = -2 + sqrt(13/2) i, -2 - sqrt(13/2) i

10. t = -3 + sqrt(35), -3 - sqrt(35)

Step-by-step explanation:

7. 4(x + 2)² + 320 = 0

(x + 2)² = -80

x + 2 = +/- i × sqrt(80)

x + 2 = +/- i × 4sqrt(5)

x = -2 +/- i × 4sqrt(5)

8. 7(x - 4)² - 18 = 10

(x - 4)² = 4

x - 4 = +/- 2

x = 2, 6

9. -2(x + 2)² - 5 = 8

(x + 2)² = -13/2

(x + 2) = +/- i × sqrt(13/2)

x = -2 +/- i × sqrt(13/2)

10. 1/5(t + 3)² = 7

(t + 3)² = 35

t + 3 = +/- sqrt(35)

t = -3 +/- sqrt(35)

Answer:

Step-by-step explanation:

hello :

Ax + 3x = bx + 5

Ax + 3x-bx = bx-bx + 5

x(A+3-b) =5

x= 5/(A+3-b)

Answer:

x/4 + 5 = 7

      -5    -5

x/4 = 2

*4     *4

x=8

Step-by-step explanation:

Answer:

its 8

Step-by-step explanation:

i know so big brains

Answer:

Add 8x to both sides of the inequality

Step-by-step explanation:

took the quiz

Answer:

You would have -31 points left.  :)

196 - 227 = -31

Hope this helped!!

Answer:

-31

Step-by-step explanation:

196 - 227 = -31

Answer:

The balance after 7 years would be $2,548.79

Step-by-step explanation:

We are given the following in the question:

P = $1800

r = 5% = 0.05

t = 7 years

The compound interest is given by:

[tex]A = p\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]

where A is the amount, p is the principal, r is the interest rate, t is the time in years and n is the nature of compound interest.

When compounded quarterly, n = 4

Putting values, we get,

[tex]A = 1800\bigg(1+\dfrac{0.05}{4}\bigg)^{28}\\\\A = \$2,548.79[/tex]

Thus, the balance after 7 years would be $2,548.79

Answer:

The answer to your question is the letter a

Step-by-step explanation:

 |    1    4    -1   |      |  2    -1   |

 |    3   2    2   |      |  0     3  |         Product  = 2 x 3   and 3 x 2  = 2 x 2

                              | 5     2  |          It is possible to do this product,

                                                      the result will be a 2 x 2 matrix

Process

1.- Multiply first row by first column and second row by second column.

2.- Multiply the second row by the first column and second row by the second column.

  = (1 x 2) + (4 x 0) + (-1 x 5) = 2 + 0 - 5 = -3

  = (1 x -1) + (4 x 3) + (-1 x 2) = -1 + 12 - 2 = 9

  = (3 x 2) + (2 x 0) + (2 x 5) = 6 + 0 + 10 = 16

  = (3 x -1) + (2 x 3) + (2 x 2) = -3 + 6 + 4 = 7

Result

             |  3   9  |

             | 16   7  |    

The sample standard deviation of the given data set is approximately 20.72.

To find the sample standard deviation, we can use the following steps:

Answer:

2 grams is bigger than 2.300 mg.

Step-by-step explanation:

1 milligram is equal to 0.001 gram.

1 gram is equal to 1000 milligrams.

If this helped you, Brainliest is appreciated.

Answer:

2 grams is bigger

Step-by-step explanation:

Two grams is bigger than 2.3 milligram . This is because 1 gram is equivalent to 1000 milligrams. To work that out you would multiply 2 by 1000, which is 2000

1 gram=1000 milligram

1) Multiply 2 by 1000.

[tex]1000*2=2000 mg[/tex]

However if it was a misplaced decimal and it was meant to be 2300 milligrams, then 2300 milligrams would be bigger.

Answer:

C

Step-by-step explanation:

You distribute the 11 with the numbers in the parenthesis

Complete Question:

Justify the rationale behind Ms Calcutta's decision to use the circumcenter

Answer:

Check below for the answer and explanations.

Step-by-step explanation:

Ms Calcutta wants every occupant of the three office buildings to have equal easy access to the recycling station. The circumcenter of the three three office buildings, where the recycling station is located, has equal distance from the three offices, this means that all of Ms. Calcutta's workers in the three buildings can have to the recycling station equally without causing unnecessary inconvenience for occupants of any of the buildings.

Answer:

4

Step-by-step explanation:

As you only need the answer (•‿•)

Answer:

5 shirts

Step-by-step explanation:

First, subtract the shipping from her money. 45 - 2.50 = 42.50. Now divide this by the price of each shirt. 42.50 ÷ 8.50 = 5. The shipping fee only applies once because it is for the entire order.

Answer:

20 gallons per 180 miles

Step-by-step explanation:

Answer:

The x-intercepts would be where the line hits the x-axis, so the x-intercepts would be:

-3, 2, and 5.

Step-by-step explanation:

Answer:

q4 is -3,2,5

and for q3 is the start point

Answer:

a) [tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

b) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

Part a

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]    (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.58(1-0.58)}{(\frac{0.05}{2.58})^2}=648.600[/tex]  

And rounded up we have that n=649

Part b

For this case we can use an estimator for p as [tex]\hat p=0.5[/tex]

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{2.58})^2}=665.64[/tex]  

And rounded up we have that n=666

Answer:

communicating results

Step-by-step explanation:

hope this helps

Answer:

[tex]6x+2y=-2\\3x-2y=-5\\-------\\9x=-7[/tex]

Answer:

m= -7

Step-by-step explanation:

using the slope formula, plug in the variables and solve

m=rise/run

m=y2-y1 / x2-x1

(x1, y1) = coordinates of first point in the line

(x2, y2) = coordinates of second point in the line

Answer:

[tex]slope=-7[/tex]

Step-by-step explanation:

Use the slope formula for when you have two points:

[tex]\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]

It is y over x because slope is rise over run : the change in the y-axis over the change in the x-axis. Plug in values:

(-4,6) (-3,-1)

[tex]\frac{-1-6}{-3-(-4)}[/tex]

Simplify

[tex]\frac{-1-6}{-3+4}=\frac{-7}{1}[/tex]

Simplify

[tex]\frac{-7}{1}=-7[/tex]

Done.

Answer:

45.9ft/s

Step-by-step explanation:

Simply plug your given value into the function

[tex]f(26)=9\sqrt{26} = 45.9 (1.d.p.)[/tex]

Answer:

see explanation

Step-by-step explanation:

Using the cosine and tangent trigonometric ratios and the exact values

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{m}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × m = 12 ( divide both sides by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] ← rationalise by multiplying numerator/ denominator by [tex]\sqrt{3}[/tex] )

m = [tex]\frac{12}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{12\sqrt{3} }{3}[/tex] = 4[tex]\sqrt{3}[/tex]

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

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{n}{6}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )

[tex]\sqrt{3}[/tex] × n = 6 ( divide both sides by [tex]\sqrt{3}[/tex] )

n = [tex]\frac{6}{\sqrt{3} }[/tex] ← rationalise the denominator

n = [tex]\frac{6}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] = [tex]\frac{6\sqrt{3} }{3}[/tex] = 2[tex]\sqrt{3}[/tex]

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

Final answer:

The shortest side of the new similar triangle, where the longest side is 9 inches, is found to be 4.8 inches. This is determined by using the scale factor 3/5, obtained from the original triangle with sides 15 inches, 8 inches, and 10 inches.

Explanation:

The student asks for the length of the shortest side of a new triangle similar to the one given, with the length of the longest side being 9 inches. To find this, we need to use the concept of similar triangles. Similar triangles have proportional corresponding sides.

The original triangle has sides of lengths 15 inches (longest side), 8 inches (shortest side), and 10 inches. Given that the longest side of the new triangle is 9 inches, we can find the scale factor by dividing the new longest side by the original longest side: 9 inches / 15 inches = 3/5.

Now, we use this scale factor to find the length of the shortest side in the new triangle: 8 inches (original shortest side) x 3/5 (scale factor) = 4.8 inches.

Therefore, the length of the shortest side of the new triangle is 4.8 inches.

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The front wheel of the bicycle makes approximately 18 complete revolutions.

To find the number of complete revolutions the front wheel makes, we need to know the circumference of the wheel. Let's assume the diameter of the wheel is 0.7 meters. The circumference of the wheel can be calculated using the formula C = πd, where C is the circumference and d is the diameter. Substituting the given values, C = 3.14 * 0.7 = 2.198 meters.

Since the bicycle travels 40 meters, we can divide the distance traveled by the circumference of the wheel to find the number of complete revolutions. 40 / 2.198 = 18.19.

So, the front wheel of the bicycle makes approximately 18 complete revolutions.

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Answer:

[tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Given:

Skylar has 1/2 of her sub left from lunch she wants to cut it into thirds

Question asked:

Find the length of each piece ?

Solution:

Sub left from lunch = [tex]\frac{1}{2}[/tex]

As she want to cut into third, we will divide [tex]\frac{1}{2}[/tex] into [tex]\frac{1}{3}[/tex]

[tex]=\frac{1}{2}\div\frac{1}{3}\\ \\ =\frac{1}{2}\times\frac{3}{1} \\ \\ =\frac{3}{2}[/tex]

Thus, length of each piece will be [tex]\frac{3}{2}[/tex]