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Complete Question

A truck is being filled with cube-shaped packages that have side lengths 1/4 ​ foot. The part of the truck that is being filled is in the shape of a rectangular prism with dimensions 8ft × 6 1/4 ft × 7 1/2 ft. Find the number of cubes that can fill that part of the truck

Answer:

1500 cubes

Step-by-step explanation:

Step 1

Find the volume of the cube

V = side length ³

V = (1/4 ft)³

V = 1/64

Step 2

Find the volume of the rectangular prism

= Length × Width × Height

= 8ft × 6 1/4 ft × 7 1/2 ft

= 8 × 25/4 × 15/2

= 375 ft³

Step 3

Number of cubes in the truck

Volume of the Rectangular Prism ÷ Volume of the cube

= 375ft³ ÷ 1/4ft³

= 375 × 4

= 1500 cubes

Therefore, the number of cubes that can fill that part of the truck(Rectangular prism) = 1500 cubes

Answer:

8

Step-by-step explanation:

5x-8 = 2x+16

Move 2x to the left side and you get 3x-8 = 16

Move -8 to the right side and you get 3x = 24

Divide 3 on both sides and you get x = 8

Answer:

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.

A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.

This means that:

[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]

Then

[tex]a_n = a_1q^{n-1}[/tex]

[tex]a_n = 17.5(0.7)^{n-1}[/tex]

First 5 terms:

[tex]a_1 = 17.5[/tex]

[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]

[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]

[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]

[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]

Find the total distance the ball has travelled after it hits the ground the 5th time.

[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]

The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.

Answer:

[tex]351[/tex]

Step-by-step explanation:

[tex]7³ + 8[/tex]

[tex](7 \times 7 \times 7) + 8[/tex]

[tex]343 + 8[/tex]

[tex]351[/tex]

Berapakah hasil 7^3 + 8 = ...

Mari kita coba jawab!

Langkah pertama:

= 7 × 7 × 7

= 49 × 7

= 343 .

Langkah kedua:

= 8

= 8 .

Langkah ketiga:

= 343 + 8

= 351 .

Maka, hasilnya 351 .

Answer:

B. The car's age is the explanatory variable

Step-by-step explanation:

The graph shows a negative linear relationship between car's age and car's value because, as as one variable increases, the other decreases.

Also, data points are close to each other along the line of best fits, therefore, the correlation coefficient would be close to -1, showing a strong negative relationship.

An explanation variable is one that isn't affected or dependent on another variable. In this case, the car's age is the explanatory variable and not the car's value. The car's value is dependent on the car's age, therefore, the car's age is the explanatory variable.

The statement in option B is FALSE.

Answer: Option one i.

Explanation:

Just rewrite √-1 as i.

Answer:

Step-by-step explanation:

The discriminant is used to determine the number and nature of the zeros of a quadratic. If the discriminant is positive and a perfect square, there are 2 rational zeros; if the discriminant is positive and not a perfect square, there are 2 rational complex zeros; if the discriminant is 0, there is 1 rational root; if the discriminant is negative, there are no real roots.

The roots/solutions/zeros of a quadratic are where the graph goes through the x axis. Those are the real zeros, even if they don't fall exactly on a number like 1 or 2 or 3; they can fall on 1.32, 4.35, etc. They are still real. If the graph doesn't go through the x-axis at all, the zeros are imaginary because the discriminant was negative and you can't take the square root of a negative number. As you can see on our graph, the parabola never goes through the x-axis. Therefore, the zeros are imaginary because the discriminant was negative. Choice C.  Get familiar with your discriminants and the nature of quadratic solutions. Your life will be much easier!

Step-by-step explanation:

See you know the area of rectangle that is base x perpendicular

When you cut half the area of rectangle, it becomes a triangle

That is why the formula is 1/2 x base x perpendicular

Answer:

49

Step-by-step explanation:

The average is calculated as

average = [tex]\frac{sum}{count}[/tex] Given the average of 7 numbers is 45 , then

[tex]\frac{sum}{7}[/tex] = 45 ( multiply both sides by 7 )

sum of 7 numbers = 315

Subtract 27, 43 from the sum to obtain the sum of first 5 numbers

315 - (27 + 43) = 315 - 70 = 245 , then

average of first 5 numbers = [tex]\frac{245}{5}[/tex] = 49

Answer:

52

Step-by-step explanation:

f(n) is purely based on the previous value of f(n), or f(n-1), so we can start with f(1) and work our way up. We know f(1) = 2, so to find f(2), we plug f(1) into

f(n-1)²+3 to get

f(1)²+3 = 2²+3 = 4+3=7

Thus, f(2) =7. Similarly,

f(3) = f(3-1)²+3 = f(2)² + 3 -= 7² + 3= 52

Answer with Step-by-step explanation:

We are given that

[tex]3\times (2\div 3)^2+(2\div 3)^2-20\times 2\div 3+12[/tex]

[tex]3\times (\frac{2}{3})^3+(\frac{2}{3})^2-20\times \frac{2}{3}+12[/tex]

[tex]3\times \frac{8}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24}{27}+\frac{4}{9}-\frac{40}{3}+12[/tex]

[tex]\frac{24+12}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{36}{27}-\frac{40}{3}+12[/tex]

[tex]\frac{4}{3}-\frac{40}{3}+12[/tex]

[tex]\frac{4-40}{3}+12[/tex]

[tex]-\frac{36}{3}+12[/tex]

[tex]-12+12[/tex]

[tex]=0[/tex]

Answer:

[tex]{ \bf{ {x}^{2} + 10x - 2400 = 0}} \\ { \bf{ \red{it \: has \: no \: rational \: factors}}} \\ x = - 54.2 \: \: and \: \: 44.2[/tex]

Answer:

One quarter= 1/4

5 3/4= 23/4

Number of quarters in 5 3/4= 23/4 divided by 1/4

23/4 ÷ 1/4

= 23/4 × 4

=23

I hope this helps!

Answer:

23

Step-by-step explanation:

5x4 + 3

5 x 4 = 20

20 + 3 (3 Is the fraction part)

Answer:

-0.6

-0.66267

Step-by-step explanation:

Estimating the product :

Using compatible number :

-3 * 0.2

__ 0.2

* ___-3

______

_ - 0.6

______

-3 * 0.2 = 0.6

The exact product :

-3.33(0.199).

Using calculator :

-3.33(0.199) = - 0.66267

Answer:

-0.66267

Your. Welcome

Answer:

Average rate of change = 0.6

Step-by-step explanation:

Average rate of change of a function between x = a and x = b is given by,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]

From the graph attached,

f(-5) = 0

f(0) = 3

Average rate of change of the graph between x = -5 and x = 0,

Average rate of change = [tex]\frac{3-0}{0-(-5)}[/tex]

                                        = [tex]\frac{3}{5}[/tex]

                                        = 0.6

Therefore, average rate of change of the given function between x = -5 and x = 0 is 0.6.

Answer:

115 + 13w [tex]\geq[/tex] 180

Step-by-step explanation:

[tex]\huge\bold{Given :}[/tex]

Product of two integers = - 112

One of the integer = -8

[tex]\huge\bold{To\:find :}[/tex]

The other integer.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\blue{The \:other \:integer\:is\: 14.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

Let the other integer be [tex]x[/tex].

As per the question, we have

[tex]Product \: \: of \: \: two \: \: integers = - 112[/tex]

➼ [tex] \: - 8 \times x = - 112[/tex]

➼ [tex] \: x = \frac{ - 112}{ - 8} [/tex]

➼ [tex] \: x = 14[/tex]

[tex]\sf\purple{Therefore,\:the\:other\:integer\:x\:is\:14.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex] - 8 \times 14 = - 112[/tex]

➺ [tex] \: - 112 = - 112[/tex]

➺ L. H. S. = R. H. S

Hence verified.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♨}}}}}[/tex]

Answer:

If the product of two integers is -112 and one of them is -8, that means the value of the second integer would be 14.

Step-by-step explanation:

The product of two integers equals -112 means that there are two numbers that, when multiplied, were equivalent to -112. Since you know one of the integers is -8, you can infer that the second integer is both a positive number AND the remainder of [tex]\frac{-112}{-8}[/tex] or 14.

Answer:

[tex]x^4+2x^3+2x^2+2x+1[/tex]

Step-by-step explanation:

Given that,

[tex](x+1)^2 . (x^2+1) = 0[/tex]

We know that, [tex](a+b)^2=a^2+b^2+2ab[/tex]

So,

[tex](x+1)^2=x^2+1+2x[/tex]

So,

[tex](x+1)^2 . (x^2+1) = (x^2+1+2x)(x^2+1)\\\\=x^2\times x^2+x^2+2x^3+x^2+1+2x\\\\=x^4+2x^3+2x^2+2x+1[/tex]

So, the value of the given expression is equal to[tex]x^4+2x^3+2x^2+2x+1[/tex]

Answer:

A)4/5

Step-by-step explanation:

7/9=0.778

so you need to convert the other fractions into decimals as well. The one that's greater than 0.778 will be your answer.

a)4/5=0.8

b)2/3=0.667

c)13/18=0.722

d)3/5=0.6

The decimal that's greater than 0.778 is A=0.8 so that's the answer.

Answer:

24 square cm

Step-by-step explanation:

Answer:

48cm

Step-by-step explanation:

Because 6 times 8= 48cm

Answer:

√13

Step-by-step explanation:

d² = (-3)² + (-2)²

d² = 9 + 4

d² = 13

d = √13

Answer:

[tex](x -y)^2 = -1[/tex]

Step-by-step explanation:

[tex](x - y)^2 = x^2 + y^2 - 2xy[/tex]

           [tex]= (x^2 + y^2 ) - 2(xy)\\\\=(9) - 2( 5)\\\\= 9 - 10 \\\\ = -1[/tex]

The binomial expansion of (x - y)² is

(x - y)² = x² - 2xy + y²

Substitute the given values to the equation

(x - y)² = x² - 2xy + y²

(x - y)² = x² + y² - 2xy

(x - y)² = 9 - 2(5)

(x - y)² = 9 - 10

(x - y)² = -1

Therefore the value of (x - y)² is -1.

#ILoveMath

#ILoveYouShaina

Answer:

60

Step-by-step explanation:

Given: 1/2a + 2/3b =50

(Since b is equal to 30 we will automatically replace b with 30)

Step 1: Simplify both sides of the equation.

1/2a+20=50

Step 2: Subtract 20 from both sides.

1/2a=50-20

1/2a=30

Step 3: Multiply both sides by 2.

2(1/2a) 2(30)

a=60

Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?  

Answer:

a = 15

Step-by-step explanation:

1/2(a) + (2/3 x 30) = 50

2/3 x 30 = 20

1/2(a) + 20 = 50

Rearrange > 20 to -20

-20 + 50 = 30

1/2(a) = 30

Rearrange 1/2 to 2

2 > 30/2

30/2 = 15

a = 15

Hope this helps, and please let me know if it is correct or isn't.

Have a nice day

Answer:

23. c

24.b

25. box 2

26. 48, 26

Step-by-step explanation:

Answer:

B and C

Step-by-step explanation:

fjdjjsngbsnsjf x

Answer:

Step-by-step explanation:

C. The graph of G(x) is the graph of F(x) compressed vertically.

If, for example, x = 1, then F(1) = 1^2 = 1, while G(1) = (4/5)(1^2) = 4/5.

Note that G(1) < F(1); we say G(x) is a vertical compression of F(x).