solve each compound inequality. drag the correct solution and graph next to the inequality

Answer:

5

028x ·[tex]\frac{1}{5}[/tex]

No. 26 and 65 both have a common factor of 13, since 26 = 2•13 and 65 = 5•13, so GCD(26, 65) = 13 ≠ 1.

We can also arrive at this using Euclid's algorithm.

65 = 58 + 7 = 2•26 + 13

26 = 2•13 + 0

Since the last remainder is zero, the previous remainder is the GCD.

In the quadrilateral KITE,

The value of side KI = [tex]\sqrt{17}[/tex]

The value of side KE = [tex]\sqrt{17}[/tex]

The value of side IT = [tex]3\sqrt{5}[/tex]

The value of side TE = [tex]3\sqrt{5}[/tex]

The quadrilateral KITE is a kite because , KI = KE and IT = TE

How are the values of the quadrilateral sides calculated?

K (0,-2) , I(1,2) ,T(7,5) , E(4, -1)

KI = [tex]\sqrt{17}[/tex]

What is the value of side KE ?

K (0,-2) and E(4, -1)

The distance formula is:

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\KE =\sqrt{(4-0)^{2} + (-1 +2)^{2} }\\\\KE = \sqrt{(4)^{2} + (1)^{2} }\\\\KE = \sqrt{16+1} \\\\KE = \sqrt{17}[/tex]

The value of side KE of the quadrilateral = [tex]\sqrt{17}[/tex]

What is the value of  side IT ?

I(1,2)  and T(7,5)

The distance formula  is:

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\IT =\sqrt{(7-1)^{2} + (5-2)^{2} }\\\\IT = \sqrt{(6)^{2} + (3)^{2} }\\\\IT = \sqrt{36+9} \\\\IT = \sqrt{45} =3 \sqrt{5}[/tex]

The value of  side IT of the quadrilateral =[tex]3\sqrt{5}[/tex]

What is the value of side TE  ?

T(7,5) and E(4, -1)

The distance formula is :

[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\TE =\sqrt{(4-7)^{2} + (-1-5)^{2} }\\\\TE = \sqrt{(-3)^{2} + (-6)^{2} }\\\\TE = \sqrt{9+36} \\\\TE = \sqrt{45} =3 \sqrt{5}[/tex]

The value of side TE of the quadrilateral = [tex]3\sqrt{5}[/tex]

The quadrilateral KITE is a kite because :

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Answer:

The answer is in the picture.

Hope this helps!

Step-by-step explanation:

Answer:

[tex]\frac{3}{8}*\frac{7}{9}=\frac{7}{24}[/tex]

Step-by-step explanation:

Solution with Steps

[tex]\frac{3}{8}*\frac{7}{9}=?[/tex]

For fraction multiplication, multiply the numerators and then multiply the denominators to get

[tex]\frac{3*7}{8*9}=\frac{21}{72}[/tex]

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 21 and 72 using GCF(21,72) = 3

[tex]\frac{21/3}{72/3} =\frac{7}{24}[/tex]

Therefore:

[tex]\frac{3}{8}*\frac{7}{9}=\frac{7}{24}[/tex]

Mathematically we write this as:

=362+(302×q)

The expression is 362+302q

Goodluck.

Answer: x= -16

Step-by-step explanation:

It will cost 140 dollars to buy enough carpet for the living room.

A rectangle is a four-sided figure in which opposite sides are equal and the diagonals are also of the same length.

Given Ed's living room is 4 yards wide and 7 yards long.

We know that the area of a triangle is the product of its length and width.

∴ The area of  Ed's living room is (4×7) sq yards = 28 sq yards.

Also given to install yellow carpet that costs $5.00 per square yard,

∴ For 28 sq yards, the cost of installing a yellow carpet will be,

= (28×5) dollars.

= 140 dollars.

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Answer:

If the variable

y

varies inversely as the variable

x

, then we can write this relationship as:

y

∝

1

x

Removing the proportionality sign and adding a proportionality constant, we have:

y

=

k

x

If the value of y is 18 when the value of x is 5, then:

18

=

k

5

k

=

18

×

5

=

90

Thus, the equation showing the relationship between the two variables is:

y

=

90

x

Using the above equation, the value of y when x = 3 is equal to:

y

=

90

3

=

30

After factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

⇒72a⁹b³-18a⁷b⁵=0  ------(1)

We have to factor in the expression,

⇒72a⁹b³-18a⁷b⁵=0

Take 18a⁷b³ as common,

⇒18a⁷b³(4a²-a²b²)=0

⇒18a⁷b³=0

⇒(4a²-a²b²)=0

⇒4a² = a²b²

⇒b²=4

⇒b=±2

Substitute the value of b in equation 1 we get,

72a⁹b³-18a⁷b⁵=0  

72a⁹(2)³-18a⁷(2)⁵=0

576a⁹-576a⁷=0

a²=1

a=±1

Thus, after factorizing the expression 72a⁹b³-18a⁷b⁵completely we get the value of a and b will be ±1 and ±2.

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The expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .

In the question ,

it is given that

the diameter of the cylindrical metal pipe = 20mm

so the radius of the cylindrical pipe = 10 mm

height of the cylindrical metal pipe = 21mm

Using the formula of Volume of Cylinder = π*r²*h  

the volume of cylindrical metal pipe = π*(10)²*21     .....(i)

the height of smaller cylinder = 21mm

radius of the smaller cylinder = 6mm

So, Volume of the smaller cylinder = π*(6)²*21     .....(ii)

the volume of metal needed to make the pipe = Volume of cylindrical metal pipe - Volume of the smaller cylinder .

Substituting the values from (i) and (ii) , we get

volume of metal needed = π*(10)²*21 - π*(6)²*21

= 21*π*(10)² - 21*π*(6)²

hence , option(a) is correct .

Further Simplifying , we get

= 21*100*π - 21*36*π

= 2100π - 756π

hence , option(c) is also correct

Therefore , the expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .

The given question is incomplete , the complete question is

A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters and the the radius of the smaller cylinder is 6 millimeters.

Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.

(a) 21*π*(10)² - 21*π*(6)²

(b) π*(20)²*(21) – π*(6)²

(c) 2100π - 756π

(d) 7,644π

(e) 1,344

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Answer: A & C

Step-by-step explanation: Just did it

A Type I error occurs in hypothesis testing when one is rejects the null hypothesis and the null hypothesis is true.

To reject the null hypothesis, statisticians conduct hypothesis testing. However, the process is always accompanied by the possibility of making a mistake. These are referred to as hypothesis testing errors.

Type I and Type II errors are the two mutually exclusive errors in hypothesis testing. Type II errors occur when a statistician fails to reject a false null hypothesis, whereas Type I errors occur when a statistician correctly rejects a genuine null hypothesis. So, c is the right response.

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The average income of those who work more and those who work less tends to be equal

The  null hypothesis is a typical statical theory which suggest that no statical relationship and significance exists in a set of given single observed variable , between two sets of observed data and measured phenomena.

The null hypothesis is significant because it offers a rough description of the phenomena inferred from the available evidence. It enables researchers to empirically test the relationship statement in a study.

Example: The null hypothesis is that the population density is the same across all states.

The average income of those who work more and those who work less tends to be equal

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Answer:

4 1/2

Step-by-step explanation: First: Pls just trust <333 and Goodluck!! <3

Answer:

Step-by-step explanation:

Answer:

x-intercept- (-1.2,0)

y-intercept- (0,6)

Step-by-step explanation:

To find the slope-intercept form, we have to find x and y.

First, find x. Get rid of the 2y, and the equation will look like this.

-10x=12

Now, divide both sides by -10.

12/-10=-1.2

The x-intercept would be (-1.2,0)

To find the y-intercept form, do the same thing.

Get rid of the -10x.

2y=12

Divide by 2 on both sides.

y=6

The y-intercept form would be (0,6)

Hope this helps! :D

The value of the quantity after 420 minutes is 1.739

How to calculate the amount of the quantity?

In mathematics, the amount of the quantity can be measured with the help of the exponential function by using its standard equation. But the measured quantity should grow continuously.

According to the question, the growth of the quantity is growing continuously which illustrate the exponential function.

The given parameters are:

Initial value, a = 200;  Rate, r = 55%

An exponential growth function is represented as:

y = a(1 + r)^x

Substitute the value in the equation

y = 200(1 + 55%)^x

After 1.55 minutes, x = 7 * 60

So, we have:

y = 200(1 + 55%)^(7 * 60)

Evaluate the expression

y = 1.739

Hence, the value of the quantity after 420 minutes is 1.739

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The cost of 8 pounds of oranges based on the total cost of 5 pounds bought is 12.00

What is the cost for a pound of oranges?

The cost of a pound of oranges based on the rate at which 5 pounds were bought and 8 pounds would also be bought is determined as the amount paid for 5 pounds of oranges divided by the number of pounds of oranges bought

cost per pound of oranges=cost of 5 pounds/5 pounds

cost per pound of oranges=7.50/5

cost per pound of oranges=1.50

Based on the 1.50 per pound, the cost of 8 pounds is the cost per pound multiplied by 8 pounds

cost of 8 pounds of oranges=1.50*8pounds

cost of 8 pounds of oranges=12.00

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Answer:true

Step-by-step explanation:

Using the inverse operations, the value of h is 54.

An inverse operation can be defined as the operation that undoes what was done by the previous operation.

Therefore, the inverse operation of multiplication is division.

The equation is as follows:

19 = (h/3) - 8

Hence,

add 8 to both sides of the equation

19 = (h/3) - 8

19 + 8 = (h/3) - 8 + 8

27 = h / 3

Multiply both sides of the equation by 3

27 = h / 3

27 × 3 = h / 3 × 3

h = 54

Therefore,

h = 3

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Answer:

Step-by-step explanation:

−1<x+3<5

−1+−3<x+3+ −3<5+−3 (Add -3 to all parts)

Therefore your answer is −4<x<2

The answers to all the equations are:

So, f(x):

(A) f(x) = x + 3 when f(4)

(B) f(x) = 2x - 9 when f(5)

(C) f(x) = -6x + 2 when f(-3)

Therefore, the answers to all the equations are:

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Since the point B is between points A and C, the length BC is 22.25 units

From the question, we have the following parameters that can be used in our computation:

Length AB = 6x - 9

Length BC = 3x + 17

Length AC = 5x + 16

The above implies that the point B is between points A and C

So, we have the following equation

AC = AB + BC

Substitute the known values in the above equation

So, we have the following equation

5x + 16 = 6x - 9 + 3x + 17

Collect the like terms

So, we have the following equation

5x - 6x - 3x = -9 + 18 - 16

Evaluate the like terms

So, we have the following equation

-4x = -7

Divide by -4

x = 7/4

Substitute x = 7/4 in the equation BC = 3x + 17

So, we have the following equation

BC = 3 x 7/4 + 17

Evaluate

BC = 22.25

Hence, the numerical length of BC is 22.25 units

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 m = 1/4  is the slope of the line .

What is slope in plain English?

The slope of a line passing through points ( x₁ , y₁ ) ( x₂ , y₂ )  is defined as

   m = y₂ - y₁/x₂ - x₁

if the x coordinates are not equal. The slope is not defined if the x

coordinates are equal because that would require dividing by zero.

here ,

      ( x₁ , y₁ ) = (0, 5)

      ( x₂ , y₂ ) = ( -12 , 2 )

   m = y₂ - y₁/x₂ - x₁

    m =  2 - 5/-12 - 0

   m = -3/-12

  m = 1/4

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The probability that the box contains exactly one defective motor.

P(X=1)=0.5225

This is further explained below.

Generally, This follows a Poisson distribution and will be solved using:

[tex]P(X=x)=\frac{e^{-u} u^x}{x !}[/tex]

Where

u = Expected number of occurrences, and it is calculated as:

u=n p

u=60 * 4%

u=60 * 0.04

u=2.4

In conclusion,

[tex]P(X=x)=\frac{e^{-u} u^x}{x !}[/tex]

Therefore

[tex]P(X=1)=\frac{e^{-2.4} 2.4^2}{2 !}[/tex]

P(X=1)=0.5225

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The fraction of the total amound he paid for the 11 books is 3/13.

According to our question-

Hence , The fraction of the total amound he paid for the 11 books is 3/13.

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The graph represents the inequality:

The reason we used strictly less than (<) is that the circle is not shaded. Therefore, the correct inequality has to be either the first or last.

We will simplify the inequalities to see which one is equivalent.

First Inequality:

Expanding the brackets using the distributive property, we have:

Subtracting 20x from both sides, we have:

This is not the inequality.

Last Inequality:

Subtract 5x from both sides:

Subtract 10 from both sides:

Divide both sides by -2. Dividing by a negative number will reverse the sign:

Hence, this is the inequality.

ANSWER: The correct inequality is

Answer:

Step-by-step explation:

if the ratio of 9 contains 63 men then what about the ratio of 5 u do cross multiplication it will be 5 ×63 the answer you get multiply by 9 answer will be 35

Answer:

A and D

Step-by-step explanation:

hope this helps