(a) A box is a cuboid with length 45 cm, width 30 cm and height 42 cm.
The box is completely filled with 90.72 kg of sand.
Calculate the density of this sand in kg/m³.
[Density = mass + volume]

The area of the given trapezoid is 24 square inches.

Area of trapezoid:

Area of the trapezoid is referred as the total space covered by its sides.

The formula to calculate the area of the trapezoid is

A = ½ (a + b) h

where

(A) is the area of a trapezoid,

'a' and 'b' are the bases that are parallel sides,

and 'h' is the height that is the perpendicular distance between a and b

Given,

Here we have the values 8 in, 6 in, and 4 in

Through the given values we have to find the area of the trapezoid.

Let us consider the base values of the trapezoid are 8in and 6 in and the height as 4 in.

Now, we have all the side value of the trapezoid.

Then we have to apply it on the formula,

Then we get,

Area = 1/2 (8 + 6) x 4

Area = 2 x (12)

Area = 24

Therefore, the area of the trapezoid is 24 square inches.

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The number of ways that a nine question true false quiz can be answered is; 512 ways

We are given;

Number of questions = 9

Options for each answer = 2 (True of false)

The power set is defined as the number of subsets of a set of n elements which is expressed as 2ⁿ

There are 2 ways to answer question 1 and as such it means that there are 2 ways to answer question 2.

For question 2; 2² = 4 ways

For question 3; 2³ = 8 ways

For question 4; 2⁴ = 16 ways

For question 5; 2⁵ = 32 ways

For question 6; 2⁶ = 64 ways

For question 7; 2⁷ = 128 ways

For question 8; 2⁸ = 256 ways

For question 9; 2⁹ = 512 ways

Thus we we conclude that, there are 512 ways to answer 9 true-false tests.

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Answer:

The factory makes 12,000 (12k) hats each day

Step-by-step explanation:

4000

× 3

--------

12,000

Answer: K is greater than or equal to 18

Step-by-step explanation:

Answer:k>=-18

Step-by-step explanation:

Rewrite so k

is on the left side of the inequality.

2/5⋅(k−2)≥−8

Multiply each term in

2/5⋅(k−2)≥−8 by 5/2 to eliminate the fractions.

k−2≥−20

Move all terms not containing

k to the right side of the inequality.

k≥−18

The result can be shown in multiple forms.

Inequality Form:

k≥−18

Answer: $9.76

Step-by-step explanation: If you multiply f, the order of fries (5) by the cost of it ($1.08) you would get $5.40 & if you multiply d, the order of drinks (4) by the cost of it ($1.09) you would get $4.36. If you add up both the total numbers, you would get a final answer of $9.76.

Answer:

$9.76

Step-by-step explanation:

1.08f + 1.09d= Total

1.08(5)+1.09(4)= Total

5.40+4.36= Total

The probability of getting 2 yellow apples and 1 red apple is 18/35 which is the D option.

This is a question of permutations and combinations.

Given that:-

Number of yellow apples = 4

Number of red apples = 2

We have to find the probability of getting 2 red apples and 1 yellow apple.

Number of ways of getting 2 yellow apples = [tex]^4C_2=6[/tex]

Number of ways of getting 1 red apple = [tex]^3C_1=3[/tex]

Total number of ways of finding 3 apples from 7 apples = [tex]^7C_3=35[/tex]

Hence,

Probability of getting 2 yellow apples and 1 red apple = 6*3/35 = 18/35.

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When the statement is rewritten as a conditional statement in if-then form, the option that best describes the hypothesis is B. Two lines intersect at a point

A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true whenever P is true.

There is a conditional statement. We will not play if it is raining. Let's say A: it's raining and B: we're not going to play. If A is true (it is raining) and B is false (we played), then the statement A implies B is false.

If the original sentence is restated as an if-then conditional statement, the hypothesis is best described as two lines intersecting at a point. As a result, the statement "Two lines intersect at a point" is the correct option (B) and the best option.

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Complete question

If the statement is rewritten as a conditional statement in if-then form, which best describes the hypothesis?

Two lines in a plane intersect at a point

A. Two lines in a plane intersect

B. Two lines intersect at a point

C. A point exists

D. Points are in a plane

Step-by-step explanation:

-(10x + 2) > 5x - 1 - 8x

combine x terms on right side:

-(10x + 2) > -3x - 1

remove ()'s from left side:

-10x - 2 > -3x - 1

add 10x to both sides:

-10x - 2 + 10x > -3x - 1 + 10x

-2 > 7x - 1

add 1 to both sides:

-2 + 1 > 7x - 1 + 1

-1 > 7x

divide both sides by 7:

-1/7 > 7x /7

-1/7 > x or x < -1/7

in interval notation: (-∞, -1/7)

Answer: 41.2

Step-by-step explanation: The rules of rounding are you round up if the number you're rounding is 5 or higher than five, and you keep the same number if it is 4 or lower. For this problem, the 1 is the digit being rounded, so to round it, look at the number to the right of the 1, which is a 5, which means we would round up.

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Answer:

see the attachment photo!

we use the pooled proportion when we calculate the standard error for the difference in proportions when performing a hypothesis test  whne When the variances of both populations are the same

The standard error for the distinction within the proportions is calculated utilizing the population proportions but in cases where the population proportions are unknown, we utilize the test proportions to calculate the standard error. In the case of hypothesis testing, we are mindful of the population proportions whereas in evaluating the confidence interval for the distinction between the proportions we have no thought of the population proportions. So, the standard error for a hypothesis test of distinction in two proportions is distinctive from the standard error for a certain interval of the difference in two proportion.

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Answer:

(-1,4) (-3,0)

picture below (im assuming you meant x^2.)

if you meant x2, please look at the second image

FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6

SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6

Answer:

8/2 or 4/1

Step-by-step explanation:

To find the slope, you simply count how high up one point is from another (0,0 to 2,8) and then how far over. Since 2,8 is 8 points up from 0,0 the numerator of our slope would be 8; and since 8,2 is two over from 0,0 the denominator is 2. Simplify this to 4/1.

Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).

Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).

What is a coordinate system?

In geometry, a coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the location of points or other geometric elements on a manifold, such as Euclidean space.

In the original figure, we can plot the coordinates, and we get

                     For dark blue dot = (-2, 2)                      

                     For red dot = (-2, 0)

                     For light blue dot = (2, 2)

After applying a scale factor of '2', we get the new coordinates as

                     For dark blue dot = (-4, 4)                      

                      For red dot = (-4, 2)

                      For light blue dot = (4, 4)

Hence,

Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).

Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).

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For the specified requirements, 105 sample size are required.

Given that,

Confidence Interval = 90

Margin of error (m) =0.08

We know , to find Sample size for  estimating a population proportion

n = (Z*/m)² P(1-P)

where , m is margin of error

             P is estimated proportional value.

If we have no preconceived of the value of the population proportion

, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.

for a 90% confidence interval ,

Z* = 1.645 , m=0.08

Using equation we get

n = (1.645/0.08)²(0.5)( 1 - 0.5 )

By solving,

n =105.3 = 105

The necessary sample size is 105

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To simplify the equations so that there would be no fractions, we

1. Multiply both sides by 8

2. Multiply both sides by 12

3. Multiply both sides by 10

4. Multiply both sides by 30

From the question, we are to determine what we could do first to each side of the equations so that there would be no fraction

1. (4x -4)/8 = (x +2)/4

Multiply both sides by the LCM of the denominators

The denominators are 8 and 4

The LCM of 8 and 4 is 8

Thus,

Multiply both sides by 8

8 × (4x -4)/8 = 8 × (x +2)/4

4x -4 = 2(x +2)

2. 3(4 - r)/6 = (4 + r) /4

Multiply both sides by the LCM of the denominators

The denominators are 6 and 4

The LCM of 6 and 4 is 12

Thus,

Multiply both sides by 12

12 × 3(4 - r)/6 = 12 × (4 + r) /4

2 × 3(4 - r) = 3(4 + r)

6(4 - r) = 3(4 + r)

3. (5q + 3)/10 = (q + 2)/5

Multiply both sides by the LCM of the denominators

The denominators are 10 and 5

The LCM of 10 and 5 is 10

Thus,

Multiply both sides by 10

10 × (5q + 3)/10 = 10 × (q + 2)/5

(5q + 3) = 2(q + 2)

4. 4(b - 7)/15 = (b + 3)/10

Multiply both sides by the LCM of the denominators

The denominators are 15 and 10

The LCM of 15 and 10 is 30

Thus,

Multiply both sides by 30

30 × 4(b - 7)/15 = 30 × (b + 3)/10

2 × 4(b - 7) = 3(b + 3)

8(b - 7) = 3(b + 3)

Hence, we will multiply both sides of the equation by 30

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maximum height = 32ft

Given function  h(t) = -16t^2+40t+7

known data:

[tex]h{0}[/tex] = 7 ft

[tex]v_{0}[/tex] = 40 ft/s

we equate the first derivation to zero

and solve for time.

h(t) = -16t^2 + 40t+7

[tex]\frac{dh}{dt} (t)[/tex] = -32t+40 = 0

t = [tex]\frac{40}{32}[/tex] = 1.25s

second derivative and evaluate:

[tex]\frac{d^{2}h}{dt^{2}}[/tex] [tex]\frac{}{}(t)[/tex] = -32

the maximum height of the rocket with the respect to

the ground can be obtained by evaluating the function

h(1.25) = - 16[tex](1.25)^{2}[/tex]+40(1.25)+7 = 32 ft

therefore the rocket reaches maximum height at  h = 32ft.

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Answer:

$18.95

Step-by-step explanation:

5(10.25) + 2x = 89.15

51.25 + 2x = 89.15  Subtract 51.25 from both sides

2x = 37.90  Divide both sides by 2

x = 18.95

Check:

5(10.25) + 2( 18.95) = 89.15

51.25 + 37.90 = 89.15

89.15 = 89.15

89.15 - 5(10.25)

= 37.9

37.9/2

= 18.95 dollars for each parent

Answer:

Step-by-step explanation:

Take the amount, $4.75, multiplied by x will give you the total amount of money raised and just put that into the equation format:

$4.75 (x) = total amount of money raised

The solution to the inequality is X  > 4

Inequality  is a set of mathematical expression which the individual side is not equal to other side

To solve for  x  in the inequality  x - 1 . 5 > 2, we followed the step;

Step 1: Add 1.5 to both sides

x - 1.5 + 1.5 > 2 . 5 + 1.5

X  > 4

Therefore, the solution to the inequality is X  > 4

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The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Divide both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore, the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right r

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Answer:
y = -1/3x + 1

Step-by-step explanation:

1) For a perpendicular line, the slope is the opposite reciprocal. What this means is that, the slope will be the opposite sign and flipped.

~-1/3 will be the new slope

2) Then you have to rewrite the problem using the point slope form which is y - y1 = m(x-x1). The values that we will be plugging in for x1 and y1 will be from the coordinate that you provided.

~ y - (-2) = -1/3(x-9)

3) Now simplify everything you can
~y+2 = -1/3(x-9)

4) Now distribute the -1/3
~y+2 = -1/3x + (9)(1/3)
~y+2 = -1/3x + 3

5) Now we need to subtract 2 from both sides to get y by itself.

~y = -1/3x + 1

Answer:

[tex]x^3-10[/tex]

Step-by-step explanation:

Let the number be x.

"A number cubed" refers to x³.

"Difference" means to subtract, so the answer is [tex]x^3-10[/tex].

The inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The set of integers:

S:{−24, 2, 20, 35}

Plug the value 35 in the inequality:

= 5/6(35 - 5) < 1/2(35 + 3)

= 5/6(30) < 1/2(38)

= 25 < 19  (False)

Thus, the inequality five-sixths m minus five is less than one-half m plus 3 false is false for 35 option (B) is correct.

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Answer:

Step-by-step explanation:

The answer would be 24:600. One student is absent so there are 24 students present. The number of beads is still 600, so the ratio is 24:600 which simplifies to 1:25.