Solve: 10(0.5x- 2) = -3x + 20 + 8x

Answer:

53 weeks

Step-by-step explanation:

Given :

Reams of paper used :

3 reams = 4 Week

A case of 5 paper = 8 reams

Hence,

5 cases of paper = (8 * 5) = 40 reams

If :

3 reams = 4 weeks

40 reams = x

Cross multiply :

3x = 40 * 4

3x = 160

x = 160 / 3

x = 53. 333

Approximately 53 weeks (nearest whole number)

Answer:

DL/dt = 1000 miles/hour

Step-by-step explanation:

Let´s call A Point for the airplane at 70 miles from the point O (converging point), and point B for the airplane at 240 miles from point O.

Then the three-points A, B, and O shape a right triangle with legs (distances from each of the airplane to point O, and hypotenuse L distance between the two airplanes

Then according to Pithagoras´theorem:

L²  =  (AO)²  + (BO)²

At the moment t when the airplanes are far away as 70 and 240 miles per hour

L²  = (70)²  + ( 240)²

L²  = 4900 + 57600

L = √62500

L = 250 miles

In general

L²  = x² + y²

That equation is always valid for a right triangle if the airplanes are approaching keeping the right triangle shape then:

L² = x² + y²        where x and y are the legs ( that legs change in time then):

Tacking derivatives on both sides of the equation

2*L*DL/dt = 2*x*Dx/dt + 2*y*Dy/dt

By substitution:    since Dx/dt = 280 m/h   and Dy/dt = 960 m/h

2*(250)*DL/dt = 2*70*280 + 2*(240)*960

500*DL/dt  =  39200 + 460800

DL/dt  =  500000/ 500

DL/dt = 1000 miles/hour

Answer:

B

Step-by-step explanation:

True for all x.

Answer:

y = |x-6|-4

Step-by-step explanation:

If the function is translated left 6, you subtract 6 from the x value. Then if you go down 4, you are subtracting 4 from the y value. Before going down, y = |x-6|. So subtract 4 from that and you get y = |x-6|-4.

Answer:

58 units

Step-by-step explanation:

[tex]7 \times 10 = 70[/tex]

[tex]6 \times 2 = 12[/tex]

[tex]70 - 12 = 58[/tex]

Answer:

972 junior executives should be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

35% of junior executives left their company within three years.

This means that [tex]\pi = 0.35[/tex]

0.95 = 95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

To update this study, how many junior executives should be surveyed?

Within 3% of the proportion, which means that this is n for which M = 0.03. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.35*0.65}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.35*0.65}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.35*0.65}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.35*0.65}}{0.03})^2[/tex]

[tex]n = 971.2[/tex]

Rounding up:

972 junior executives should be surveyed.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

xy3 your welcome tell me if I got it right ✅

Answer:

[tex]y = - \frac{6}{8}x - 3 [/tex]

Answer:

64 ounces of soda

Step-by-step explanation:

for every 8 ounces you need 32 ounces of soda and 16 would be two servings of fruit juice so I multiplied 32 by 2 and got 64

Answer:

Measure of exterior angle ABD = 136°

Step-by-step explanation:

Given:

measure of ∠A = (2x + 2)°

measure of ∠C = (x + 4)°

measure of ∠B = x°

Find:

Measure of exterior angle ABD

Computation:

Using angles sum property

∠A + ∠B + ∠C = 180°

So,

(2x + 2) + (x + 4) + x = 180

4x + 6 = 180

4x = 176

x = 44

So,

measure of ∠B = x°

measure of ∠B = 44°

Measure of exterior angle ABD = 180 - measure of ∠B

Measure of exterior angle ABD = 180 - 44

Measure of exterior angle ABD = 136°

Answer:

B is the answer to the question.

Step-by-step explanation:

Answer:

225°

Step-by-step explanation:

[tex] \frac{5\pi}{4} = \frac{5 \times 180 \degree}{4} = \frac{900 \degree}{4} = 225 \degree \\ [/tex]

The surface area of what shape exactly?

Answer:

Step-by-step explanation:

I'm assumung this is a cube sense cubes will equal the same for all 6 sides we just have to find 1 side then just multiply by 6 to get the answer easy peasy!!! so 4 × 4 = 16 and 16 × 6 = 96 so 96 is our surface area Hope that helps!

Answer:

A and C

Step-by-step explanation:

Edge 2021

The partial sums are correct are Option A and Option C. That is:  (2) and (28/9).

A partial sum (simply put) refers to the sum of the various parts that make up a sequence.

For example, in the above sequence given as:
2 + (2/3) + (4/9) + (8/27) + (16/81) + (32/243) + ...

A partial sum would be:

2 + (2/3).

In this case, thus,

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Answer:

A. 34cm

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:  5 25 14  16

the graph shows the roots of the polymonimal to be

x = 0   and x - 4 = 0     x = 4     when y or f(x) = 0

f(x)   =   x(x-4)   =  x² - 4x

f(x)   =   x² - 4x

when x = 0   f(x) = 0

         x = 2   f(x)  =  2² - 4(2)   =  -4

         x = 4   f(x)  =  4² - 4(4)   =  0

The factorization of the polynomial graphed are,

⇒ y = x (x - 5)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, We have been given graph of polynomial.

This is in parabolic shape.

So, this is graph of quadratic function.

Hence,, there will be two zeroes.

And also number of zeroes of a function is equal to the number of times graphs cuts x-axis

Here, we can see graph cuts at (0,0) and (5,0).

So, the Factors will be:

(x - 0) and (x - 5).

Since, If x = 0 is a zero then it means factor will be (x)

Similarly, If x = 5 is a zero then it means factor will be (x-5).

Thus, the factorization of the polynomial graphed are,

⇒ y = x (x - 5)

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Answer:-18

-6

0

3

9

Step-by-step explanation:

Answer:

The answer is f(x) =√x+4. It would be last one.

Answer:

Step-by-step explanation:

Thales theorem tells us that B is a 90

and therefore from W to o (center) is 45°

we know the total of the arc VoW is 98

180= 8x +1  + 45 +98

36 = 8x

4.5 = x

x = 4.5

Answer:

-3

Step-by-step explanation:

just plug in the points on the line into y2-y1/x2-x1

Answer:

It means that the both sides of the expression in the given equation must be/are congruent.

Hope this helps!

Answer:

12

Step-by-step explanation:

number of bandana that can be made = total yards of fabric ÷ yards needed to make one bandanna

3 ÷ 1 /4

= 3 x 4 = 12

Answer:

B)

Step-by-step explanation:

x+36=102

x=102-36

x=66

Therefore, substitute x in your formula for x+14

66+14

Answer:

[tex]P = 8 - 42x + 56y + 12xy[/tex]

Step-by-step explanation:

Given

[tex]Length = 4 - 7(3x + 4y)[/tex]

[tex]Width = 3x(2y)[/tex]

Required

The perimeter (P)

This is calculated as:

[tex]P = 2 * (Length + Width)[/tex]

[tex]P = 2 * (4 - 7(3x + 4y) + 3x(2y))[/tex]

Open bracket

[tex]P = 2 * (4 - 21x + 28y + 6xy)[/tex]

Open bracket

[tex]P = 8 - 42x + 56y + 12xy[/tex]