Which of the following represents the prime factorization of 72? (need answer asap please)

2^3 x 3^2 x 4
2^3 x 3 ^2
2 x 3^2 x 4^2
2^2 x 3^3

Answer:

70 square units

Step-by-step explanation:

Since it is half a big rectangle, (10*14)/2=70

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{(5\times10^3) \times (9\times10^7)}[/tex]

[tex]\mathsf{= (5\times 10\times 10\times 10)\times (9\times 10\times10\times10\times 10\times10\times10\times 10)}[/tex]

[tex]\mathsf{= (5\times 100\times 10) \times (9\times 100\times 100\times 100 \times 10)}[/tex][tex]\mathsf{= (5\times 1,000) \times {(9\times 10,000\times 1,000)}}[/tex]

[tex]\mathsf{= (5,000)\times(90,000\times1,000)}[/tex]

[tex]\mathsf{= (5,000)\times (90,000,000)}}[/tex]

[tex]\mathsf{= 5,000\times 90,000,000}}[/tex]

[tex]\mathsf{= 450,000,000,000}[/tex]

[tex]\mathsf{= 4.5\times10^{11}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{4.5\times 10^{11}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The distance of the light travels in 15 seconds is 4500000 kilometers.

It should be noted that a function is simply used to illustrate the relationship between the variables that are given.

In this case, the function is given as d(t) = 300000t. Therefore, it should be noted that the distance of the light travels in 15 seconds will be:

d(t) = 300000t

where t = 15

d(t) = 300,000 × 15

distance = 4,500,000 kilometers

The distance is 4500000 kilometers.

Note that the second question wasn't written properly and hence can't be solved.

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Answer:

Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.

Midpoint = [(3+5)÷2, (-8+(-2.5))÷2]

= (8÷2, -10.5÷2)

= (4, -5.25)

Answer:

x = 76

Step-by-step explanation:

First, distribute -4:

-4x + 104 = -200

Isolate x:

-4x = -200 - 104 = -304

x = -304/-4 = 76

Answer:

Step-by-step explanation:

Find the dividend. ___ ÷ 22 = 1.9

4,180

418

41.8

4.18

x : 22 = 1.9

x = 22 * 1.9

x = 41.8

Answer:

x = 41.8

Step-by-step explanation:

The zeros in the equation  y = 2(x+3)(x+3)-1

[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]

This is further explained below.

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

Set 2(x+3)(x+3)-1 equal to 0 .

2(x+3)(x+3)-1=0

Solve for x.

Simplify [tex]2(x+3)(x+3)-1[/tex]

[tex]$2 x^2+12 x+17=0$[/tex]

Use the quadratic formula to find the solutions.

[tex]\frac{-b \pm \sqrt{b^2-4(a c)}}{2 a}[/tex]

Substitute the values a=2, b=12, and c=17 into the quadratic formula and solve for x.

[tex]\frac{-12 \pm \sqrt{12^2-4 \cdot(2 \cdot 17)}}{2 \cdot 2}[/tex]

Simplify.

[tex]x=\frac{-6 \pm \sqrt{2}}{2}[/tex]

In conclusion, The final answer is the combination of both solutions.

[tex]x=-\frac{6-\sqrt{2}}{2},-\frac{6+\sqrt{2}}{2}[/tex]

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Answer:

x = -7

Step-by-step explanation:

Answer:

x=-7

Step-by-step explanation:

If jimmys saving account makes 0.7% interest every month if he puts 200 in the account 2 months ago, then 202.81  is in therenow round to the nearest cent

Percentage, a relative value indicating hundredth parts of any quantity.

Given

jimmys saving account makes 0.7% interest every month.

The initial deposit is 200 in the account

After two months of time, we need to the find the total amount in account.

0.7% is converted to decimal

0.7/100=0.007

So after two months

A is amount after two months

r is rate of interest

t is time period

[tex]A=P(1+r)^{t}[/tex]

=200(1+0.007)²

=200(1.007)²

=202.8

Hence 202.8  is there now in Jimmys savings accout

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IF YOU CHECK YOU WILL FIND THAT THIS IS A DIFFERENCE OF TWO SQUARES

[tex] = (5 - 3x)(5 + 3x)[/tex]

ATTACHED IS THE SOLUTION

If a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

The original price of the item = $825

The off offered by the store = 1/4

The off offered by the coupon = 1/5

Total off = 1/4 + 1/5

= 9/20

Then the selling price = The original price of the item - The original price of the item× (9/20)

= 825 - 825×9/20

= 825-371.25

= $453.75

Hence, if a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

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The number which is an irrational number as required to.ve identified among the answer choices given is; Choice B; √19.

What is an irrational number?

An irrational number, as the name implies is any real number that cannot be expressed as the quotient of two integers (fraction). It follows that such a number cannot be expressed , a/b, where a and b are both integers.

On this note, the number which cannot be expressed in such form is; Choice B; √19.

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The area of the rectangle will be 512[tex]cm^{2}[/tex] .

let the longer side of the rectangle be "l" and the shorter side of the rectangle be "b".

Hence, the perimeter of rectangle = 2(l+b)

we are given the perimeter =96cm

thus, 2(l+b)=96

l+b = 96/2

l+b =48

also, we are given the condition that the longer side of the rectangle is two times the length of the Shorter side.

Thus, l=2b, substituting this in l+b=48 we get

2b+b=48

3b=48

b=48/3

b=16cm, now substituting this in l=2b,

l=2(16)

l=32cm

area of the rectangle = length x breadth

=l x b

=32 x 16

= 512[tex]cm^{2}[/tex]

What is the difference between perimeter and area?

Area and perimeter are two crucial characteristics of two-dimensional shapes in mathematics. The area of a shape describes the space it occupies, whereas the perimeter describes how far the shape's boundary extends.

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The values of x and y in the system of equations are x = 1 and y = 2

Linear equations are equations that have constant average rates of change.

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

4x + 3y = 10

y - x = 1

Make y the subject in the second equation, by adding x to both sides of the equation

y - x + x = x + 1

This gives

y = x + 1

Substitute y = x + 1 in 4x + 3y = 10

4x + 3(x + 1) = 10

4x + 3x + 3 = 10

Evaluate the like terms

7x = 7

This gives

x = 1

Substitute x = 1 in y = x + 1

y = 1 + 1

Evaluate

y = 2

Hence, the solution for the system of linear equations 4x + 3y = 10 and y - x = 1 are x = 1 and y = 2

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Possible question

Solve for x and y in the following system of equations

y - x = 1

4x + 3y = 10

The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) 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.

The inequality is:

Let the number is x:

-0.96 ≥ 0.3x

0.3x ≤  -0.96

x ≤ -0.96 /0.3

x ≤ -3.2

x ∈ (-∞, -3.2]

As we know, the number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.

The number line (C) represents the solution to the inequality -0.96 ≥ 0.3x

Thus, the number line (C) represents the solution to the inequality -0.96 ≥ 0.3x option (C) is correct.

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Answer:

number is - 2

Step-by-step explanation:

let the number be n then 7 times the number is 7n and 3 times the number is 3n, so

4 - 7n = 12 - 3n ( add 3n to both sides )

4 - 4n = 12 ( subtract 4 from both sides )

- 4n = 8 ( divide both sides by - 4 )

n = - 2

A function is defined as a relation where each input value is paired with exactly one output value. The input -1 has 2 outputs, thus the relation is not a function.

Answer:

1. B

2. D

Step-by-step explanation:

2. 26(2)-2

26(2)=52

52-2=50

Answer:

-35

Step-by-step explanation:

w = 2x^2 + 1

= (2 x -3)^2 +1

= -6^2 + 1

=-36 + 1

= -35

The plane was flying at a height of 706.32 m .

The fundamentals of an object's motion, such as its position, velocity, or acceleration over time, are defined by kinematics equations of motion. An object's motion in one, two, and three dimensions is determined by these three equations of motion. One of three equations of motion can be used to calculate components like displacement (s), velocity (initial and final), time (t), and acceleration (a). The following are the three motion equations:

Initial formula: v = u + at

The second formula is s = ut + 0.5at2.

The third formula is v2 = u2 + 2as.

Let t stand for the package's flight time, s for the plane's altitude, and u for the packet's initial vertical velocity since it is simply dropped.

Given: t = 12 seconds for the delivery to arrive to the ground

With t = 12 and u = 0 in the second equation of motion, we so obtain

s = 0*t + 0.5*9.81*12² = 706.32 m

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Answer:

20

Step-by-step explanation:

The sum of a number and its half is thirty. Find the number​:

the formula would be:

1.5x = 30

divide both sides by 1.5:

1.5x/1.5 = 30/1.5

x = 20

check:

20 = 20

1/2 of 20 = 10

20 + 10 = 30

Answer:

x+0.5x=30

1.5x=30

x=20

Solution :-

2x - 9y = -1

2x = 9y - 1

x = 9y - 1 / 2 _________ (1)

Now, substitute it here!

-4x - 3y = - 19

-4 (9y - 1 /2) - 3y = -19

(-36y + 4 - 6y / 2) = -19

(-42y + 4 / 2) = -19

-42y + 4 = -38

-42y = -38 - 4

-42y = -42

y = 1

Value of x :

Substituting the value of y that is 1 in this equation. x = 9y - 1 / 2

x = 9(1) - 1 / 2

x = 9 - 1 / 2

x = 8 / 2

x = 4

Answer:

Either A or B.

Step-by-step explanation:

Each number in the sequence is being added by 6.

So you can use the equation: x+6

The ninth term in the sequence would be 36 because 30+6=36

Answer:

7

Step-by-step explanation:4*7=28

Therefore 5*7=35

28:35= 4:5

Answer:

60 weeks.

Step-by-step explanation:

10 and 12 both are divisible by 60, thus itll be 60 weeks before she visits them both in the same week again

His grades improved by 2.2 %

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given: Original grades = 75, 85, 90, 90,

100, 75, 80, 100, 90.

And grades after the retake = 85, 85, 100, 90, 100, 85, 80, 100, 90.

So the sum of the original scores = 785.

Thus the percentage can be calculated by 785/ total marks

= 785/ 900 × 100 = 87.2 %

And the sum of the grades after retake= 805

Thus the percentage will become = 805/900 × 100 = 89.4 %

The mean of the first set is 87 and the mean of the second set is 89.

Thus the difference between the two is 2.

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The critical value that is appropriate for a​ 99% confidence level where n​17, is​ unknown, and the population appears to be normally​ distributed is 2.921 (Option B).

A Critical value is the value of the test statistic that establishes the upper and lower boundaries of a confidence interval or the statistical significance threshold in a statistical test.

How did we arrive at the above conclusion?

We are given:

n=17, where n is the size of the set

df = n-1; (df means degree of freedom)

= 17-1

df = 16, at 99% confidence level.

Here we apply the t-test because the data is normally distributed.

∝ = 1-99% [Shere ∝ is the significance level)

= 0.01

∝/2 = 0.01/2

= 0.005

hence,

[tex]t_{\alpha /2} ,df[/tex]  = [tex]t_{0.005}[/tex], 16 = 2.921. this is derived using the T-Table.

The above leads us to conclude therefore that Option B is correct.

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