What will be the volume of the box?

Answer:

1/4

Step-by-step explanation:

Let a₁, a₂, a₃ and a₄ be the four numbers. Since the geometric mean of the first 3 positive numbers is 4, we have that

∛(a₁a₂a₃) = 4. (1)

Also the geometric mean of the four numbers is 2, we have that ⁴√(a₁a₂a₃a₄) = 2   (2).

So, taking the cube of (1), we have

[∛(a₁a₂a₃)]³ = 4³

a₁a₂a₃ = 64  (3)

Also, taking the fourth power of equation (2), we have

[⁴√(a₁a₂a₃a₄)]⁴ = 2⁴  

a₁a₂a₃a₄ = 16  (4)

Dividing (4) by (3), we have

a₁a₂a₃a₄/a₁a₂a₃ = 16/64

a₄ = 1/4

The fourth value is 1/4

Formulas used :

[tex]loga^ x = x \ log a[/tex]

[tex]logab = log a + logb[/tex]

Steps :

[tex](x+y)^2 = 125xy\\\\log(x+y)^2 = log(125xy)\\\\2log(x+y) = log 125 + log x + log y\\\\2log(x+y) = log 5^3+ log x + log y\\\\2log(x+y) = 3 log 5 + log x + log y\\\\[/tex]

Answer:

33

Step-by-step explanation:

Trust me it'll work.

Answer:

[tex]area = \frac{45}{360} \times \pi {(15)}^{2} \\ = 88.35729338221 \\ = 88.6 \: (3sf)[/tex]

Answer:

40%

Step-by-step explanation:

Amount of money discounted

= $40 - $24

= $16

Percentage of discounted money

= 16/40 x 100%

= 40%

Answer:

she would be able to buy 40 lunches

Step-by-step explanation:

Subtract  100  from both sides of the inequality

Divide each term by   −2  and simplify.

The solution to the inequality 100 – 2x < 20 is x > 40

How to find solution to an inequality?

She set aside $100 to buy school lunches for the year. Each school lunch cost $2.

Therefore, the inequality can be used to find the number of school lunches Gloria can buy before she has less than $20 left.

100 – 2x < 20

The solution of the inequality is as follows;

100 – 2x < 20

subtract 100 from both sides

100 - 100 - 2x < 20 - 100

-2x < - 80

divide both sides by -2

x > 40

learn more on inequality here: https://brainly.com/question/11872626

#SPJ2

Answer:

The answer is "The decimal could be five-tenths".

Step-by-step explanation:

Given value:

[tex]\to 67.5 \times 4. \_= \_ .50[/tex]

Let the decimal value is: (2)

[tex]\to 67.5 \times 4. 2= 283 .50[/tex]

Answer:  Choice C.  [tex]3\sqrt{17}[/tex]

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

Work Shown:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(12-15)^2 + (-21-(-9))^2}\\\\d = \sqrt{(12-15)^2 + (-21+9)^2}\\\\d = \sqrt{(-3)^2 + (-12)^2}\\\\d = \sqrt{9 + 144}\\\\d = \sqrt{153}\\\\d = \sqrt{9*17}\\\\d = \sqrt{9}*\sqrt{17}\\\\d = 3\sqrt{17}\\\\d \approx 12.3693169\\\\[/tex]

I used the distance formula for those steps above.

The two points were (x1,y1) = (12,-21)  and (x2,y2) = (15,-9) but you could swap the order.

As an alternative route, you can plot the two points on the same xy grid. Then form a right triangle such that the hypotenuse is between the two points mentioned. The pythagorean theorem should lead you to the same answer as above. In fact, the distance formula is basically a modified version of the pythagorean theorem.

Answer:

1. The preimage and image are congruent

2. Any line segment connecting the corresponding points between the preimage and image is bisected by the line of reflection

3. Corresponding angles on the preimage and image are congruent

4. Corresponding points of the preimage and image are equidistant from the line of reflection.

Added you

____________

Answer:

Step-by-step explanation:

it has a 50/50 chance if it lands on tailes it is 50/50

Answer:

x= -34/3

Step-by-step explanation:

just solve by multiplying both sides by 15, then distribute 10 and 3 through the parenthesis, multiply both sides by 2, move the variable to the left side and change the sign, move the constant and change the sign, combine like terms, calculate the sum, and finally divide both sides by -3

28000 is the answer.

you count two numbers from front and approximate

Answer:

3 hrs and 20 minutes

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

-4 = 12 - 2x

when plus 12 goes to the left hand side it changes its sign so,

-4 -12 = -2x

- * - is plus so add 4 and 12 but keep the sign - because 12 is the greatest number and its sign is -

-16=-2x

when -2 comes to the left hand side it changes its from multiplication to division.So,

-16/-2=x

8=x

we will get positive 8 because minus and minus also gets cancel.

Answer:

x=8

Step-by-step explanation:−4=12−2x

−4=12−2xSwap sides so that all variable terms are on the left hand side.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16Divide both sides by −2.

−4=12−2xSwap sides so that all variable terms are on the left hand side.12−2x=−4Subtract 12 from both sides.−2x=−4−12Subtract 12 from −4 to get −16.−2x=−16Divide both sides by −2.x=−16÷-2

Divide −16 by −2 to get 8.

Divide −16 by −2 to get 8.x=8

Step-by-step explanation:yo

Answer:

C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer: you would use the last option

For which situations is it appropriate to use a sample? Select three options.

What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?

What is the average number of rainbows each year in Honolulu?

How many pedestrians would use a walkway built over a busy road?

How many police cars are equipped with computers?

What is the most popular car color in the teachers’ parking lot?Answer:

Step-by-step explanation:For which situations is it appropriate to use a sample? Select three options.

What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?

What is the average number of rainbows each year in Honolulu?

How many pedestrians would use a walkway built over a busy road?

How many police cars are equipped with computers?

What is the most popular car color in the teachers’ parking lot?

answers:

3.5

2.875

about 3.0625

Use thing below for answers

Answer:

Starting from

2(-x) = 3x - 5

Distribute

-2x = 3x - 5

add 2x to both sides

0 = 5x - 5

Add 5 to both side

5 = 5x

Flip

5x = 5

Answer:

24.

Step-by-step explanation:

By definition,  factorial 4

= 4!

= 4*3*2*1

= 24.

Answer:

The probability that a worker chosen at random works at least 8 hours is 0.83

Step-by-step explanation:

Given

See attachment for probability distribution

Required

[tex]P(x \ge 8)[/tex]

At least 8 hours means that a worker works for 8 hours or more.

So:

[tex]P(x \ge 8) = P(x = 8) + P(x = 9) + P(x = 10)[/tex]

By reading the probabilities from the graph, we have:

[tex]P(x \ge 8) = 0.61 + 0.14+ 0.08[/tex]

[tex]P(x \ge 8) = 0.83[/tex]

Answer:

vertex point at (-2|11)

f(x)=-2*((x+2)^2+1*-11/2) (simplified)

Step-by-step explanation:

f(x)=-2*x^2+-8*x+3  

f(x)=-2*(x^2+4*x+-3/2) ( Factor out )

f(x)=-2*(x^2+4*x+(2)^2+-1*(2)^2+-3/2) ( Complete the square )

f(x)=-2*((x+2)^2+-1*(2)^2+-3/2) ( Use the binomial formula )

hope this helped, I didn't get much to work with so if i'm wrong i'm sorry

Answer:

Public works administration

Step-by-step explanation:

Roosevelt's public work administration was a part of the new deal in the year 1933. The PWA was intended to cut down on the number of unemployed persons, and to raise the purchasing power of the people through the constructions. Most job seekers that were employed were those that had no formal education. the public works projects included road constructions, bridges, dams as well as public buildings like schools, hospitals

Answer:

y = 18

Step-by-step explanation:

Given y is directly proportional to x² then the equation relating them is

y = kx² ← k is the constant of proportion

To find k use the condition y = 50 when x = 5

50 = k × 5² = 25k ( divide both sides by 25 )

2 = k

y = 2x² ← equation of proportion

When x = 3 , then

y = 2 × 3² = 2 × 9 = 18

Answer:

24000ml or 24L

Step-by-step explanation:

wxhxl = volume

20cm x 30cm x 40cm = volume

volume = 24000cm3

1cm3 = 1ml

24000cm3 = 24000ml

1000ml = 1L

24000ml = 24L

Answer:

Here we do not have the options, so I will answer in a general way.

We have two statements:

p = A number is greater than 25

q = A number is less than 35

We want to have:

p ^ q is true

This means:

p and q are true.

So, we need to find a number such that both conditions are meet, so we need to find a number N such that

The number N is greater than 25  (from p)

The number N is less than 35 (from q)

So N can be any number between 25 and 35

So, some of the possible values of N are:

N = 26

N = 27

N = 28.6

N = 33

N = 34

Concluding, any number N ∈ (25, 35) can be a solution.

(Note that N = 25 and N = 35 are not solutions)