Franco freezes the vegetables he grows in the summer so he can eat them all year long. He packs the vegetables into cube-shaped boxes that each have a volume of one cubic foot. Then, he places the boxes into a freezer that is shaped like a rectangular prism. The bottom of the freezer can be completely covered by a layer of 6 boxes. If the volume of the freezer is 18 cubic feet, what is its height?

Answer:

Step-by-step explanation:

The given expression is

[tex]36,700 - (5,000 + 500m)=0[/tex]

Where [tex]m[/tex] is months.

We need to solve for the variable.

[tex]36,700-5,000-500m=0\\31,700=500m\\m=\frac{31700}{500} \approx 63.4[/tex]

Therefore, Michael needs to save $63.40, approximately.

Answer:

The number representing describing the value of his signing bonus = 5,000.

Step-by-step explanation:

Total debt = $36,700

He pays $500 every month from his monthly salaries, since m = months.

The $5,000 is the amount of his signing bonus, which puts entirely towards paying off his debt.

It is like the fixed payment.  While the 500m is the variable payment per month.

So, at the end of any number of months, you can easily calculate the remaining debt using the expression, 36,700 - (5,000 + 500m)

Answer:

NOOO OYU TYPE INTHE ANSWER

Step-by-step explanation:

Answer:

about 27.42

Step-by-step explanation:

Answer:

1/6a-1/6, a=1

Step-by-step explanation:

Hey there! I can definitely explain :)

-2/3a+5/6a-1/6

Multiply the two terms (the first two), to have common denominators!

The common lowest (easiest to deal with) denominator is 18. So, multiply the first term (-2/3a) by 6/6 and the second term (5/6a) by 3/3!

-12/18a+15/18a-1/6

Now, add those together!

3/18a-1/6

Now simplify!

1/6a-1/6

If you want, you can solve for a!

1/6a=1/6

a=1

Hope this helps! Please mark brainliest :)

Answer:

4

Step-by-step explanation:

1+1+1+1 or 2 + 2

Apple exist in the world. This particular tree only have 4 perfect apples total. Because you only have one friend, they help you pick 2 out of the 4 apples. Then you pick 2 of the other apple. Without dropping or eating them, he gave both of his apple to you . How many apple do you have without dropping or eating them?

Answer:

4

Step-by-step explanation:

Answer:

ZX = 3√2, XY =√10, YZ = 4, Perimeter of ΔXYZ  = 14√5 units

Step-by-step explanation:

1. We can see that if we were to draw an altitude from vertex X to side ZY of this triangle, the length of this altitude would be: 3 units

2. The length of ZX can be determined through Pythagorean Theorem. If this altitude were to be called XW, it would be one of the legs of a mini triangle ZXW, along with leg ZW. ZW clearly = 3, thus ZX^2 = 3^2 + 3^2 = 18, and ZX =  √18 units = 3√2.

3. The same thing can be applied to another "mini" triangle YXW. This triangle would have legs XW (altitude of the triangle ZXY) and YW. Knowing XW to have a length of 3 units, and YW to have length of 1 unit ⇒ XY^2 = XW^2 + YW^2 = 3^2 + 1^2, and XY = √10.

4. YZ is visualized to have a length of 4 units.

5. Knowing that ZX = 3√2, XY =√10, and YZ = 4 ⇒ Perimeter of ΔXYZ = ZX + XY + YZ = 3√2 + √10 + 4 = 14√5 units. To simplify this, it would be that the Perimeter of ΔXYZ  = 14√5 units

Answer:28.26

Step-by-step explanation:

Φ=180 since it's in a straight line

Radius=r=9

π=3.14

Length of arc=Φ/360 x 2 x π x r

Length of arc=180/360 x 2 x 3.14 x 9

Length of arc=0.5 x 2 x 3.14 x 9

Length of arc=28.26

Answer:

(x - 5) (x - 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (-12x) into two terms that can be added to get -12x, and multiplied to get 35:

[tex]x^2[/tex] - 12x + 35

[tex]x^2[/tex] -7x - 5x + 35

Group:

([tex]x^2[/tex] -7x) (-5x + 35)

Take out the GCF (Greatest Common Factor):

x(x - 7)  -5(x - 7)

(x - 5) (x - 7)

Answer:

the answer is D

Step-by-step explanation:

x^2-12x+35=x^2-7x-5x+35=x*(x-7)-5(x-7)=(x-7)(x-5)

Answer:

.16 = 16/100= 8/50= 4/25

Step-by-step explanation:

Answer:

decimal: 0.16

fraction: 4/25

percentage: 16%

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

there are 4 kings in a deck of 52 cards.

4/52 = 1/13

Answer:

A rectangle

Step-by-step explanation

Cutting the rectangular prism diagonally will result in the creation of two triangular prisms taking the two dimensional shape of a rectangle as its cross section.

Diagonal cutting means cutting that passes from the top edge of cuboid to edge on the bottom on opposite sides. This way, a rectangular two dimensional shaped cross section is formed

Answer:

circle, rectangle

Step-by-step explanation:

1. Exponential

2. Linear

3. Exponential

Answer:

[tex]c = \frac{A}{12h} - b[/tex]

Step-by-step explanation:

Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!

Hope this helped! :)

Answer:

Step-by-step explanation:

This problem is a composition of function defined by C(V(r)), now we have the functions [tex]V(r)= \pi r^{3}[/tex] and [tex]C(V)=3.2V[/tex], where the first depends on the radius, and the second dependes on the volume, that means, to find the number of ounce of coffe, we need to determine the volume of the cylinder, that's why we have to replace the volume function inside the ounces function,

[tex]C(V(r))=3.2(\pi r^{3} )[/tex]

Therefore, the right answer is the last choice.

Answer:180.3

Step-by-step explanation:

a=150

b=50

C=120

c^2=a^2+b^2-2 x a x b x cosC

c^2=150^2+50^2-2x150x50xcos120

c^2=150x150+50x50-2x150x50xcos120

c^2=22500+2500-15000cos120

c^2=25000-15000x-0.5

c^2=25000+7500

c^2=32500

c=√(32500)

c=180.3

Answer:

180.3 inches

Step-by-step explanation:

Using cosine law:

c² = 150² + 50² - 1(150)(50)cos(120)

c² = 32500

c = 50sqrt(13)

c = 180.3 (nearest tenth)

Answer:

Difference in the volume = 512 cm³ (Approx)

Step-by-step explanation:

Given:

Radius of cylinder A (r1) = 4 cm

Height of cylinder A (h1) = 18 cm

Radius of cylinder B (r2) = 5 cm

Height of cylinder B (h2) = 5 cm

Find:

Difference in the volume.

Computation:

Difference in the volume = Volume of cylinder A - Volume of cylinder B

[tex]Difference\ in\ the\ volume = \pi (r1)^2(h1)- \pi (r2)^2(h2)\\\\Difference\ in\ the\ volume = \pi (4)^2(18)- \pi (5)^2(5)\\\\Difference\ in\ the\ volume = \pi (16)(18)- \pi (25)(5)\\\\Difference\ in\ the\ volume =905.3-392.5\\\\Difference\ in\ the\ volume = 512.8[/tex]

Difference in the volume = 512 cm³ (Approx)

Answer:

Volume is increased in a factor of 8. The volume is increased from [tex]48\,ft^{3}[/tex] to [tex]384\,ft^{3}[/tex].

Step-by-step explanation:

The formula for the volume of the rectangular prism is:

[tex]V = w\cdot h \cdot l[/tex]

Where:

[tex]w[/tex] - Width

[tex]h[/tex] - Height

[tex]l[/tex] - Length

If dimensions are doubled, then volume is increased in a factor of 8:

[tex]V_{f} = (2\cdot w)\cdot (2\cdot h)\cdot (2\cdot l)[/tex]

[tex]V_{f} = 8\cdot w \cdot h \cdot l[/tex]

[tex]V_{f} = 8 \cdot V_{o}[/tex]

The volume is increased from [tex]48\,ft^{3}[/tex] to [tex]384\,ft^{3}[/tex].

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:

a) H0 : u = 28.5%

H1 : u < 28.5%

b) critical value = - 1.645

c) test statistic Z= - 1.41

d) Fail to reject H0

e) There is not enough evidence to support the professor's claim.

Step-by-step explanation:

Given:

P = 28.5% ≈ 0.285

X = 210

n = 800

[tex] p' = \frac{X}{n} = \frac{210}{800} = 0.2625 [/tex]

Level of significance = 0.05

a) The null and alternative hypotheses are:

H0 : u = 28.5%

H1 : u < 28.5%

b) Given a 0.05 significance level.

This is a left tailed test.

The critical value =

[tex] -Z_0.05 = -1.645 [/tex]

The critical value = -1.645

c) Calculating the test statistic, we have:

[tex]Z = \frac{p' - P}{\sqrt{\frac{P(1-P)}{n}}}[/tex]

[tex]Z = \frac{0.2625 - 0.285}{\sqrt{\frac{28.5(1-28.5)}{800}}}[/tex]

Z = -1.41

d) Decision:

We fail to reject null hypothesis H0, since Z = -1.41 is not in the rejection region, <1.645

e) There is not enough evidence to support the professor's claim that the proportion of obese male teenagers decreased.

Answer:

As shown in the picture, the volume of solid is

V = Rectangular prism - half cylinder

Hope this helps!

:)

Answer:

Last option

Step-by-step explanation:

It's a cuboid/rectangular prism

The curve on top is due to half a cylinder being removed

Answer:

Sum of all the sides.

Step-by-step explanation:

Perimeter is the sum of the distance in length or width, or height or circumference of all the sides of an object.

Therefore the sum total of the given sides V, W, x ,Y, Z are;

15 +20 + 25 + 7 + 22 = 89cm

Since a picture isn't available to know which sides of the objects can be added.

Answer:

Step-by-step explanation:

. if every corresponding internal angles in both shapes are equal

. if all corresponding sides are equal or have same ratio.

more rules but depends on the shape also ( triangle, rectangle, hexagon,...)

Hey there! I'm happy to help out!

As you can see, our number keeps on doubling. It's like 2×2×2×2.... so on and so forth. Whenever we multiply a number by itself, we can model it as an exponent, so if we had 2², it is two twos being multiplied, and 2×2=4. If it was 2³, it would be 2×2×2=8.

However, we have a one. This signifies a starting point and exponents have our back. Anything to the 0th power is always equal to one! So, this situation would look something like this:

[tex]2^0, 2^1, 2^2, 2^3,2^4,... etc.[/tex]

So, for the second square, we are going to the first power. For the fourth square it's going to the third power. Therefore, the 10th square will be the 9th power!

[tex]2^9=[/tex] 2×2×2×2×2×2×2×2×2= 512

However, we want to find how much he has done in total! So, let's find how much he did on the other squares!

[tex]2^8[/tex]= 256

[tex]2^7[/tex]=128

[tex]2^6[/tex]=64

[tex]2^5[/tex]=32

[tex]2^4[/tex]=16

2³=8

2²=4

[tex]2^1[/tex]=2

[tex]2^0[/tex]=1

Now, we add these all up to find the total grains of rice!

512+256+64+32+16+8+4+2+1=895

Therefore, George has placed a total of 895 grains of rice on the chess board.

I hope that this helps! Have a wonderful day!

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

On the first square, George placed 1 grain of rice.

On the second square, he placed 2 grains.

On the third square, he placed 4 grains.

On the fourth square, he placed 8 grains.

In general, on the nth square, he places [tex]2^{n-1}[/tex] grains.

So,

On the first 10 squares,

1 + 2 + 4 + 8 + ... + [tex]2^9[/tex]

This is a geometric series with a first term of 1 and a common ratio of 2.

The sum of the first n terms of a geometric series.

[tex]S_n[/tex] =[tex]a(1 - r^n) / (1 - r)[/tex]

where a is the first term, r is the common ratio, and n is the number of terms.

Substituting the values,

[tex]S_{10}[/tex] = 1(1 - 2^10) / (1 - 2)

    = 1(1 - 1024) / (-1)

    = 1023

Therefore,

Once George has put rice on the 10th square, he has placed a total of 1023 grains of rice on the chessboard.

Learn more about geometric sequence here:

https://brainly.com/question/2321576

#SPJ7

Answer:

  f(x) = 2 - 10 (1 + x) + 12 (1 + x)^2 - 4 (1 + x)^3

Step-by-step explanation:

The general form of the series is shown in the attachment. For the purpose here, we need to evaluate f(-1), f'(-1), f''(-1) and so on.

  f(x) = 2x -4x^3;  f(-1) = 2(-1)(1 -2(-1)^2) = (-2)(-1) = 2

  f'(x) = 2 -12x^2;  f'(-1) = 2 -12(-1)^2 = -10

  f''(x) = -24x;  f''(-1) = -24(-1) = 24

  f'''(x) = -24;  f'''(-1) = -24

So, the series is ...

  f(x) = 2 -10(x +1)/1! +24(x +1)^2/2! -24(x +1)^3/3!

  f(x) = 2 -10(x +1) +12(x +1)^2 -4(x +1)^3 . . . . . . . matches the first choice

Answer:

$[tex]4.48[/tex] is the total price.

Step-by-step explanation:

Mulitply the total by the percentage.

[tex]4 * .12 = .48[/tex]

Add those together.

[tex]4 + .48 = 4.48[/tex]

Total price of mangoes: $[tex]4.48[/tex]

Answer: The numbers are 12, 13, 14, 15, and 16.

Step-by-step explanation:

Write an algebraic equation.

x + (x+1) + (x+2) + (x+3) + (x+4) = 70

5x + 10 = 70

subtract 10 from both sides

5x = 60

divide each side by 5

x = 12

The numbers are 12, 13, 14, 15, and 16.

Answer:

12 to 16 :) hope it helped

Answer:

(32, 42)

Step-by-step explanation:

Answer:

(32,42)

Step-by-step explanation:

Answer:

84mm

Step-by-step explanation:

Formula of a triangle:

A =bh/2

A=14(12)/2

A=168/2

A=84mm

Answer:

Terry made $14 selling cookies.

Step-by-step explanation:

[tex]67-53=14[/tex]

Answer:

$14

Step-by-step explanation:

She made $14 selling cookies.

$67-$53=$14