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The matched pair of rational numbers are as follows;

[tex]\frac{-2}{a^{2}b }+\frac{2}{ab^{2} } = \frac{2(a-b)}{a^{2}b^{2} }[/tex]

[tex]\frac{1}{2ab} +\frac{-1}{4a^{2} b^{2} } =\frac{2ab-1}{4a^{2}b^{2} }[/tex]

[tex]\frac{2}{a^{2} b^{3} } +\frac{-2}{ab} =\frac{2(1-ab^{2} )}{a^{2} b^{3} }[/tex]

[tex]\frac{1}{ab^{3} } +\frac{-1}{a^{2} b} =\frac{a-b^{2} }{a^{2}b^{3} }[/tex]

The matched pair of rational numbers are as follows:

[tex]\frac{-2}{a^{2}b }+\frac{2}{ab^{2} } = \frac{-2b+2a}{a^{2} b^{2} } = \frac{2(a-b)}{a^{2}b^{2} }[/tex]

[tex]\frac{1}{2ab} +\frac{-1}{4a^{2} b^{2} } =\frac{2ab-1}{4a^{2}b^{2} }[/tex]

[tex]\frac{2}{a^{2} b^{3} } +\frac{-2}{ab} =\frac{2 - 2ab^{2} }{a^{2}b^{3} } =\frac{2(1-ab^{2} )}{a^{2} b^{3} }[/tex]

[tex]\frac{1}{ab^{3} } +\frac{-1}{a^{2} b} =\frac{a-b^{2} }{a^{2}b^{3} }[/tex]

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Step-by-step explanation:

A, ×* y = -10 / 9

B, y / x = -8 / 5

C, x / y = -5 / 8

D, x+ y = 1 / 2

E, x- y = - 13 / 6

F, y- x = 13 / 6

Question 1

Question 2

The volume of the given cylinders.

[tex]\huge\boxed{Formula: V=\pi{r}^{2}h}[/tex]

[tex]\huge\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V=3.14×{3}^{2}×9[/tex]

[tex]\large\boxed{V= 254.34 \: {ft}^{3}}[/tex]

Let's work on question 2

Substitute the values according to the formula.

[tex]V=3.14×{13}^{2}×8[/tex]

[tex]\large\boxed{V= 4245.28 \: {yd}^{3}}[/tex]

Step-by-step explanation:

Here is the solution...hope it helps:)

Answer:

51.63 ft

Step-by-step explanation:

Tangent 25 = opposite / adjacent

tan 25 = height/100

Height = 100 tan 25 = 46.63 feet ABOVE the head of the victim

victim head height = 5 ft

46.63 + 5 = 51.63 ft

Answer:

A. Half of

B. Twice

C. greater than

Step-by-step explanation:

The median of the box plot is the middle line of the box, so for set a it is approximately ten and for set b it is approximately 20. 10 is half of 20 and 20 is twice as much as 10.

Hope this helps

Answer:

ok soo

Step-by-step explanation:

45, 56, 61, 75

middle of 56 and 61 add them so 117 then half 117 which is 58.5-

Simplification form of the provided expression is -x⁴-2x³+2x+5 option (B) is correct.

It is defined as the combination of constants and variables with mathematical operators.

The options are:

A) -x⁴ - 2x - x + 2

B) -x⁴ - 2x³ + 2x + 5

C) -2x³ + 1

D) -x - 2x² + 2x + 5

We have an expression:

= (x + 3) - [(x + 2)(x³ - 1)]

[tex]\rm =x+3-\left(x+2\right)\left(x^3-1\right)[/tex]

[tex]\rm =x+3-x^4+x-2x^3+2[/tex]

[tex]\rm =-x^4-2x^3+2x+3+2[/tex]

[tex]\rm =-x^4-2x^3+2x+5[/tex]

Thus, simplification form of the provided expression is -x⁴-2x³+2x+5 option (B) is correct.

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The value of f(-2) in the polynomial is 43

The polynomial function is given as:

f(x) = 10x^2 − 4x − 5;

To calculate f (−2), we substitute -2 for x in f(x).

So, we have:

f(-2) = 10(-2)^2 - 4(-2) - 5

Evaluate the expression

f(-2) = 43

Hence, the value of f(-2) in the polynomial is 43

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Answer:

The answer you selected is correct. Because, [tex]\frac{4}{5} ^{3\\}[/tex]is 4/5, 3 times.

Attached is more explanatory information

Step-by-step explanation:

Answer:

B. [tex]\frac{4}{5}\cdot\frac{4}{5} \cdot\frac{4}{5}=\frac{64}{125}[/tex]

Step-by-step explanation:

(4/5) is raised to a numerical power of 3.

Instead, (4/5) is being multiplied by itself 3 times.

The complete expansion is written as: [tex]\frac{4}{5}\cdot\frac{4}{5} \cdot\frac{4}{5}=\frac{64}{125}[/tex]

You have the correct option selected.

Answer:

16 square units

Step-by-step explanation:

16 square units

719ft

office area=12(20)=240ft

storage=(20-12)(40-(12+15)=8(13)=104ft

home theater=25(15)=375ft

total area= 240+104+375=719ft

Answer:

How?

I don't know

haha

thanks for the points

[tex]~~2^{-5} \cdot 2^8\\\\=2^{-5+8}~~~~~~~~~~~~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\=2^3[/tex]

By decomposing the figure in simpler shapes, we will see that the total area is:

a = 180 cm²

Remember that the area of a rectangle of width W and length L is:

A = L*W

And the area of a triangle with base B and height H is:

A = B*H/2.

Then, the upper part can be seen as a rectangle of length of 6cm and width of 6 cm, with two triangles on the sides, such that each triangle has a base of 3cm and a height of 6cm.

So the area of that part is:

A = 6cm*6cm + 2*(3cm*6cm/2) = 54cm²

Now, the bottom triangle has a base of 12 cm, and a height of:

15cm - 6cm = 9cm

Then its area is:

A' = 12cm*9cm/2 = 54cm²

This means that the total area of the figure is:

total area = 54cm² + 54cm² = 108cm²

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Answer:

Yes

Step-by-step explanation:

1. Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.

2. The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.

3. With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.

4. With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.

Answer:

1) Scalene

2) Equilateral

3) Isosceles

4) Right

5)Obtuse

Step-by-step explanation:

The requried correct match for the given triangle and its sides and angle has been shown.

Following the given characteristic the match of the the properties of triangle is given as:
Type of Triangle:            Characteristics

Scalene:                 all side lengths and angles are different sizes

Equilateral:            all side lengths are equal and all angles are 60°

Isosceles:              two sides and their base angles are equal

Right:                     one angle is 90°

Obtuse:                 one angle is greater than 90°

Thus, the required match shown above is the correct match.

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Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

We know that there's a probability of [tex]p=\frac{40}{50}=\frac{4}{5}=0.8[/tex] of choosing an electronic component that is not defective and a probability of [tex]q=\frac{10}{50}=\frac{1}{5}=0.2[/tex] of choosing an electronic component that is defective:

[tex]\displaystyle P(X\geq4)=P(X=4)+P(X=5)+P(X=6)\\\\P(X\geq4)=\binom{6}{4}(0.8)^4(1-0.8)^{6-4}+\binom{6}{5}(0.8)^5(1-0.8)^{6-5}+\binom{6}{6}(0.8)^6(1-0.8)^{6-6}\\\\P(X\geq4)=\frac{6!}{4!(6-4)!}(0.8)^4(0.2)^2+\frac{6!}{5!(6-5)!}(0.8)^5(0.2)^1+\frac{6!}{6!(6-6)!}(0.8)^6(0.2)^0\\ \\P(X\geq4)=0.90112[/tex]

So, if 6 components are drawn at random from the container, the probability that at least 4 are not defective is 0.90112

Problem 2

[tex]\displaystyle P(X=3)=\binom{8}{3}(0.2)^3(1-0.2)^{8-3}\\\\P(X=3)=\frac{8!}{3!(8-3)!}(0.2)^3(0.8)^5\\ \\P(X=3)\approx0.1468[/tex]

So, if 8 components are drawn at random from the container, the probability that exactly 3 are defective is 0.1468

The probability of exactly 3 of the containers being defective is given as 0.1468

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

to solve for the probability

We have to set p as the  probability of container being non- defective

We have p as the  probability of container being defective 50 - 10 = 40

p = 40/50

= 0.8

q = 10/50

= 0.2

P(3) = 8c3 * 0.2² * 0.8⁵

= 0.1468

Hence the probability that the container has exactly 3 defective containers is 0.1468

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The range of a function is the set of all output values.

A function is a relation where each input value is assigned to only one output value.

The domain of a function is the set of all input values, or x-values, for which the function is defined.

The range of a function is the set of all output values, or y-values, for which the function is defined.

To write the equation y = ax + b in function notation, substitute f(x) for y.

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Answer:

3x - y = 1

Explanation:

Equation formula:

y - y1 = m(x - x1)

where m is slope, (x1, y1) are coordinates

Find Equation:

⇒ y - 2 = 3(x - 1)

⇒ y = 3x - 3 + 2

⇒ -3x + y = -1

⇒ 3x - y = 1

Equation of line in point slope form

Answer:

90

Step-by-step explanation:

The angles are on either side of the line are in proportion.

Hence,

⇒ [tex]\frac{10}{8} = \frac{x}{72}[/tex]

⇒ [tex]\frac{5}{4} = \frac{x}{72}[/tex]

⇒ [tex]x = \frac{5 \times 72}{4}[/tex]

⇒ [tex]x = 5 \times 18[/tex]

⇒ x = 90

Let's see

[tex]\\ \rm\Rrightarrow \dfrac{8}{10}=\dfrac{72}{x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{4}{5}=\dfrac{72}{x}[/tex]

[tex]\\ \rm\Rrightarrow 4x=360[/tex]

[tex]\\ \rm\Rrightarrow x=90[/tex]

The true statement about the pumpkin include:

The median is a value or quantity lying at the midpoint of a frequency distribution of observed values or quantities.

Here, the median pumpkin weight is 35 lb and 75% of pumpkins in the sample have weights higher than the mean.

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Answer:

5

Step-by-step explanation:

6 + 4 is 10

Half of 10 is 5

Answer:

-2.6

Step-by-step explanation:

-1.4+(-1.2)

-1.4-1.2=-2.6

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

volume of a sphere is given by 4/3 × pi × r³

hence, the answer is 523.33

comment if you have any doubts

Work Shown:

[tex]V = (4/3)*\pi*r^3\\\\V \approx (4/3)*3.14*5^3\\\\V \approx 523.33\\\\[/tex]

The system of equations that models the given situation is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

He had 25 customers, hence:

x + y = 25.

He charges $15 for a single lawn and $25 for a front and back lawn, and made a total of $475, hence:

15x + 25y = 475

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Answer: y = 60

the value of y will be 60 when the value of x is 1.

Solution set = (1 , 60)

hope that helps...

[tex]~~~\left(\sqrt 2 + \sqrt 8 \right)^2\\\\=\left(\sqrt 2 \right)^2 + \left(\sqrt 8 \right)^2 +2 \sqrt 2 \sqrt 8\\\\=2+8+2\sqrt{2 \cdot 8}\\\\=10+2\sqrt{16}\\\\=10+2(4)\\\\=10+8\\\\=18[/tex]