What is a counterexample for the conjecture? if the area of a rectangle is 80 square units, the perimeter must be greater than 35. 9 units.

The value of the expression when evaluated is: -18.

Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.

Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:

4(-3) - |3(-3) + 2(2)|

-13 - |-9 + 4|

-13 - |-5|

-13 - 5

= -18

The value of the expression is: -18.

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The interior angles of the triangle are 43°, 43° and 94°. The exterior angle of the triangle is 86°.

A triangle is polygon with three sides. The sum of angles in a triangle is 180 degrees.

The triangle above is an isosceles triangle. The base angles of a triangle is congruent.

Therefore, the base angles are 5x - 12 and 5x  -12.

The sum of the remote interior angles is equal to the opposite exterior angles.

5x - 12 + 5x - 12 = 8x - 2

10x - 24 = 8x - 2

10x - 8x = -2 + 24

2x = 22

x = 22 / 2

x = 11

Therefore,

5x - 12 = 5(11) - 12 = 43°

Third angle = 180 - 43 - 43 = 94°

Exterior angle =  8x - 2 = 8(11) - 2 = 86°

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Step-by-step explanation:

4z-16z+8=0

[4×8]=32

factors of 32

1,2,4,8,....

The equilibrium quantity is 97 items and equilibrium price is $582

The equation of the price  when quantity demanded

p = 873 - 3q

The equation of the price when quantity supplied

p = 6q

At equilibrium price and quantity

873 - 3q = 6q

Move the like terms to one side

6q + 3q = 873

Add the like terms

9q = 873

q = 873 / 9

Divide the terms

q = 97 items

Substitute the value of q in the equation 2

p = 6q

p = 6 × 97

Multiply the terms

p = $582

Hence, the equilibrium quantity is 97 items and equilibrium price is $582

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Answer:

You can FACTOR x^2-12x+35 by using the AC method

This means the answer will be:

(x-7)(x-5)

I hope this helps!

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The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%

Z- Score gives an idea how far a data point is from mean .

z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .

Given , mean = 80beats/minute

standard deviation = 10 beats/minute

x = 86 beats/minute

Applying z score formula :

z-score = (x-mean)/standard deviation

P(x>86) = P(z > 86-80/10)

=P(z>6/10)

=P(z>0.6) = 1 - P(z<0.6)

= 1 -0.7257

= 0.2742

Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742

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The required value of the given equation when x = 5 is y = 585.5

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.

Given : y = 114.50x + 13

To find ; The value of this equation when x = 5

Thus to find this value we have to simply substitute the value of x in the given equation

Hence, we will get ,

y = 114.50 × 5 + 13

this implies y = 572.5 + 13

which is equal to y  = 585.5

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Answer:

6 feet

Step-by-step explanation:

38-32=6

The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

According to the question,

We have the following expressions:

[tex]49^{-1/2}[/tex]

Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:

[tex]7^{2*(-1/2)}[/tex]

[tex]7^{-1}[/tex]

Or it can be 1/7 because we have positive exponents.

Now, we have another expression:

[tex](\frac{27}{125}) ^{2/3}[/tex]

We will follow the same steps to solve this expression:

[tex](\frac{3}{5}) ^{3*2/3}[/tex]

[tex]\frac{3}{5} ^{2}[/tex]

Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:

9/25

Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.

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The number represented on number line by (A) -13   (B) 26   (C) 65

According to the number line given in part a

there are for parts in between 0 to 52

To find the numbers in one part = 52/4

                                                     = 13

Therefore,

For (A)

0 - 13 = -13

For (B)

0 + 2*13 = 26

For (C)

52 + 13 = 65

Hence, A is -13, B is 26 and C is 65.

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Answer:

Step-by-step explanation:

answer = company b

Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

The graph is shown in the pictures

As we know,

The proportional relationship can be defined as:

y ∝ x

y = kx

k is the constant of proportionality:

y = kx is the equation of the line which passes through the origin.

Graph four passes through origin.

Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.

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Answer:

(x-5)(x+8)

Step-by-step explanation:

Factors of -40:

-1, 40

-2, 20

-4, 10

-5, 8

-5 + 8 =3

x^2+3x-40

x^2 -5x +8x -40

=(x-5)(x+8)

Answer:

4.a)  Broken line.

4.b)  True.

5.a)  Solid line.

5.b)  True.

Step-by-step explanation:

When graphing inequalities:

Given inequality:

[tex]y < -\dfrac{1}{2}x+2[/tex]

a)  As the "<" sign has been used, the line will be a broken line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & < -\dfrac{1}{2}(0)+2\\0 & < 0+2\\0 & < 2\end{aligned}[/tex]

As zero is less than 2, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-2: \quad y &=-\dfrac{1}{2}(-2)+2\\y &=1+2\\y&=3\end{aligned}[/tex]

[tex]\begin{aligned}x=4: \quad y &=-\dfrac{1}{2}(4)+2\\y &=-2+2\\y&=0\end{aligned}[/tex]

Plot the points (-2, 3) and (4, 0).

Draw a broken straight line through the points.

Shade below the line.

Given inequality:

[tex]2x+5y \leq 10[/tex]

a)  As the "≤" sign has been used, the line will be a solid line.

b)  Substitute (0, 0) into the inequality:

[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 2(0)+5(0) &\leq 10\\0+0 &\leq 10\\0 &\leq 10\end{aligned}[/tex]

As zero is less than 10, the solution at (0, 0) is true.

Graphing the inequality

Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:

[tex]\begin{aligned}x=-5: \quad 2(-5)+5y &=10\\-10+5y &=10\\5y &=20\\y&=4\end{aligned}[/tex]

[tex]\begin{aligned}x=5: \quad 2(5)+5y &=10\\10+5y &=10\\5y &=0\\y&=0\end{aligned}[/tex]

Plot the points (-5, 4) and (5, 0).

Draw a solid straight line through the points.

Shade below the line.

Answer:

11 quarters and 4 nickels

Hope this helps! :3

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sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

The value of x is 35°

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cos x° = sin (20° + x°), where 0 < x < 90

We know that,

sin x = cos (90 - x) or cos x = sin (90 - x)

This identity holds when the two angles are complementary

i.e. they sum up to 90 degrees.

x + 90 - x = 90

Now,

cos x = sin (20 + x)

x + 20 + x = 90

2x + 20 = 90

2x = 70

x = 35

Thus,

The value of x is 35°

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Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

The percentage is calculated by dividing the required value with the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Emily:

Each month payment = $250

Each month actual payment = $275

The percentage prediction is off by.

=  (275 - 250) / 275 x 100
= 25/275 x 100

= 9.09%

Enrique:

Each month payment = $200

Each month actual payment = $225

The percentage prediction is off by.

= (225 - 200)/225 x 100

= 25/225 x 100

= 11.11%

Thus,

Emily's prediction was off by 9.09%

Enrique's prediction was off by 11.11%

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The amount of money that is reduced from Tiffany's allowance is $8.75

The amount of allowance reduced every time she forget to clean her room = $1.25

Number of times that she forgets to clean her room = 7 times this month

The amount of money is reduced from Tiffany's allowance =  Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room

Here we have to use the multiplication to find the amount

Substitute the values in the equation

The amount of money is reduced from Tiffany's allowance = 7 × 1.25

Multiply the terms

= $8.75

Hence, the amount of money that is reduced from Tiffany's allowance is $8.75

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The function that represent the given table is f(x) = 2n+1.

In the given question we have to write the correct function for the table given below.

The given table is

x                      y

0                      3

1                       5

2                      7

3                      9

We can write it as

x                      y

0                      3=1+2

1                       5=3+2

2                      7=5+2

3                      9=7+2

So we can see that in each odd number we are adding 2.

So the function should be

f(x) = (2n−1)+2

f(x) = 2n−1+2

f(x) = 2n+1

Hence, the function that represent the given table is f(x) = 2n+1.

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The value of the angle ∠2 = 32° using angle bisector.

What is angle bisector?

In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.

An angle in a triangle is divided into two equal or congruent angles by a straight line known as the angle bisector. Each triangle can have one angle bisector for each of its three vertices. The intersection of these three angle bisectors in a triangle is referred to as the triangle's incenter.

The given angle ∠XVW = 64°

VP is a bisector,

So the angle ∠XVW will be divided equally.

So ∠2 = 32°

Hence the angle of the bisector ∠2 = 32°.

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The sample size required for the true proportion of students who have parents who have remarried is 607.

What is termed the Confidence Interval?

The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.

The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.

The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.

We may also need to consult the table to determine the Z value.

For the given question,

α = 0.5

Consider the Z-table,

Zα/2 = Z (0.1/2)

Z (0.025) = 1.96

Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.

For calculating the margin error 'E' is given 3%.

n = Z² (α/2) / E² × (P°(1 - P°))

Put the given values.

n = (1.96)² / (0.03)²  × (0.28(1 - 0.28))

On solving,

n = 4268.444(0.2016)

n = 860.51

n ≈ 860.51

Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.

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Answer: the answer is  30/11

Step-by-step explanation:

hope it helps:)

The initial value of the function is 75.

The growth factor or growth rate of the function as a percent is 0.25%

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=75(1.0025)ˣ

A = 75 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.0025

1 + r = 1.0025

r = 1.0025 - 1

r = 0.0025

Expressing r as a percentage:

r = 0.0025×100

= 0.25%

Hence we get the required answers.

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it's a Stratified sampling

Answer:

5 km = 5000 m

Hope this helps : )

Answer:

.

Step-by-step explanation:

Jim ate 3/4 part of his lunch is in fraction form then the left part of his lunch is a fraction equal to 1/4 .

Fraction : A fraction represents a part of whole . It is a numerical value. It is evaluated by dividing a whole into number of parts . It has two parts one is called numinator (dividend) and other one is denominator ( divisor) . Denominator tells you how many part of lunch is divided into.

Types : Three types are

We have given in question that,

Jim ate 3/4 of his lunch .

let his lunch be x as a whole number .

Now , 3/4 part of x is ate by Jim i.e 3x/4

left part of x = x - 3x/4 = x/4

so, 1/4 part of x i.e lunch is left .

Hence, after eating the 3/4 of lunch by Jim the left part of lunch is 1/4 .

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The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².

Decibels:

Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.

Given,

Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels

Here we need to find the intensity of the sound of the blender

In order to find the intensity, we have to do the following steps,

First, we have to divide the decibel level by 10.

=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)

Now, we have to use that value as the exponent of the ratio.

=> 8.8 = log (x / 1 x 10⁻¹²)

Finally, we have to use that power of ten to find the intensity in Watts per square meter.

=>  6.3×10⁻⁴ .

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