1 The graph below represents a jogger's speed during her 20-minute jog around her neighbor.
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Answer:

$6.39

Step-by-step explanation:

100-20=80 then divided by 100 which is .80

.8 times 7.99 is 6.39

hope this helps

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

The 4 types of properties are  ;

Melting and boiling temperatures, density, viscosity, solubility, crystal structure, and color are a few examples of distinctive qualities. It is possible to isolate substances having distinctive characteristics. For instance, liquids are separated using the boiling point in fractional distillation.

Let A,B,C  are three integers.

1 Commutative property :

 A+B = B +A

 A.B = B. A

According to the commutative property, a mathematical principle, the product is unaffected by the order in which we multiply the numbers.

2  Associative property :

A + ( B+C ) = (A +B) +C

 A. (B. C) = (A. B) .C

A mathematical principle known as the associative property states that grouping the factors in a multiplication problem does not affect the solution.

3 Distributive property :

A , ( B+C ) =A.B + A.C

When you multiply a value by a sum, the distributive property of multiplication over addition is used.

4 Identity property :

A + 0 = A

A.1 =A

Identity property is defined as the property that a number, known as the identity, can be increased, decreased, multiplied by, or divided into another number without the result changing.

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Answer:

The average yearly replacement cost is approximately $32,211,500

Step-by-step explanation:

 Exponential Distribution

P(X < x) = 1 - e -x/

\(P(X < x) = 1 - e^{\dfrac{-x}{\mu}}\)

For the CPU, μ = 3 years

The probability that a CPU fails in less than 1 year is therefore;

P(C) = \(P(X < 1) = 1 - e^{\dfrac{-1}{3}} \approx 0.2835\)

For the RAM, μ = 2 years

The probability that a RAM fails in less than 1 year is therefore;

P(R) = \(P(X < 1) = 1 - e^{\dfrac{-1}{2}} \approx 0.3935\)

For the hard drive, μ = 5 years

The probability that a hard drive fails in less than 1 year is therefore;

P(H) = \(P(X < 1) = 1 - e^{\dfrac{-1}{5}} \approx 0.1813\)

The probability that either a CPU, or a RAM or a hard drive fails in 1 year so that a replacement is required, P(C ∪ R ∪ H), is given as follows;

P(C ∪ R ∪ H) = P(C) + P(R) + P(H) - P(C∩R) - P(C∩H) - P(R∩H) + P(C∩R∩H)

∴ P(C ∪ R ∪ H) = 0.2835 + 0.3935 + 0.1813 - (0.2835 × 0.3935) - (0.2835 × 0.1813) -(0.3935 × 0.1813) + (0.2835 × 0.3935 × 0.1813) ≈ 0.64423

∴ P(C ∪ R ∪ H) ≈ 0.64423

There is a 0.64423 chance that a laptop will require replacement

For 100,000 laptops sold a year and a replacement cost of $500 per laptop, we have;

The average yearly replacement cost, 'Cost' is given as follows;

Cost = 500 × 100,000 × 0.64423 = 32,211,500

The average yearly replacement cost, Cost ≈ $32,211,500

All of the statements are equivalent to saying that there is a 50% increase in the cost of a movie.

The formula for calculating a percentage increase is:

Percentage increase = (New Value - Original Value) ÷ Original Value x 100

In this case, we can say that the original value is the cost of the movie before the increase, and the new value is the cost of the movie after the increase. Let's say the original cost of the movie is $10. Then the percentage increase is 50%.

We can calculate the new cost of the movie as follows:

New Cost = Original Cost + (Original Cost x Percentage Increase)

New Cost = 10 + (10 x 0.50)

New Cost = 10 + 5

New Cost = 15

Therefore, we can say that the new cost of the movie is 15, which is one and a half times the original cost of $10. The increase in the cost of the movie is 5, which is half the original cost of $10. The cost of the movie did double, from the original cost of $10 to the new cost of 15.

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Answer:Given : Triangle ABC is transformed to triangle A′B′C′

To Find : Which equation shows the correct relationship between the measures of the angles of the two triangles

a  The measure of ∠ABC = The measure of ∠A'B'C'

b  The measure of ∠ABC = The measure of ∠B'C'A '

c  The measure of ∠BCA = The measure of ∠A 'B 'C '

d  The measure of ∠BCA = The measure of ∠C 'A 'B '

Step-by-step explanation:

Triangle ABC is transformed to triangle A′B′C′,

ΔABC  ≅ ΔA'B'C'

Hence

∠ABC = ∠A'B'C'

∠BCA = ∠B'C'A '

The measure of angle ABC = The measure of angle A prime B prime C prime

The measure of ∠ABC = The measure of ∠A'B'C'

option a is correct

Step-by-step explanation:

The solution is, the coordinates of midpoint of AB are (-3/2, -1)

We will use the formula of midpoint ;

(Xm , Ym) = (x₁ + x₂ /2 , y₁ + y₂ /2)

This implies that;

Xm = x₁ + x₂ /2

From the question, x₁ = -4 y₁= 2 and,  x₂ =1, y₂ = -4

substituting the values into;

Xm = x₁ + x₂ /2 and then solve for x_m

x_m = -4 + 1 / 2

x_m = -3/2

Similarly, substituting the values into;

Ym = y₁ + y₂ /2 and then solve for y_m

so. we get,

y_m = 2+ (-4) / 2

or, y_m = -1

Hence the coordinates of midpoint of AB are (-3/2, -1)

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Factor of trinomial 8x+2x-3 is 4x-3(binomial).

The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. Complete factoring is a three-step process: If at all possible, factor a GCF from the expression. Try to factor a trinomial if you can. Factor as many times as you can using a Difference Between Two Squares. Factorizing is the practice of expressing a number or other mathematical object as the sum of a number of other, typically smaller or more basic items of the same kind.

Given Data

8x² + 2x -3

Factorizing,

8x² + 2x -3 =0

8x² - 6x + 4x - 3 = 0

2x(4x -3) +1(4x - 3) =0

(2x + 1) (4x-3) = 0

Binomials are (2x+1) and (4x-3)

Binomial is 4x-3.

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From the dot plot, it can be seen that the median of the sample {1, 20, 5, 0, 5} is 5. This value falls in the range of the medians of samples from Population C. Therefore, it is most likely that this sample was selected from Population C.

The median is a measure of central tendency in a dataset, it is the middle value when a data set is ordered from least to greatest. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values. The median is a useful measure of central tendency when the data set contains outliers or extreme values, which can skew the mean.

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

Answer:

I think its y=8

Step-by-step explanation:

7y-20=3y+12

7y-3y=12+20

4y=32

y=32/4

y=8

Answer:

6,791,240>6,781,204

Step-by-step explanation:

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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Answer:

n>19

Step-by-step explanation:

Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

By using the division property of equality we can divide both sides by -12 to get the solution x = -4

An equation:

A = B

Says that the number A is equal to the number B, so basically, are the same number.

So, if we divide both A and B by the same number C, we will get:

A/C and B/C

And A and B are the same numbers, then A/C and B/C also are the same numbers.

So in an equation, we can divide both sides by the same number (except 0) and the equation will not change.

In this case we have:

-12*x = 48

We could divide both sides by -12, so we will get:

-12*x/-12 = 48/-12

x*(-12/-12) = -4

x = -4

And thus we used the division property of equality to solve the equation.

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The graph of the function y = 1/3x - 2 is added as an attachment

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

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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Answer:

a) Ub = 0,069

b)  CI 99 %  = ( 0,0287 ; 0,069 )

c) n = 2536

Step-by-step explanation:

Confidence Interval (CI) for proportion is

p₀  ±  z(c) * √ ( p₀*q₀ ) /n

Where     p₀  is the sample proportion

n = size of the sample

and z(c)   is z score for the significance level α

As    CI  = 99 %       α = 1%      α = 0,01      α/2 = 0,005

from z-table we find   z(c) = 2,57

p₀ = 12/300      p₀ = 0,04  ;    

n*p₀ = 12  > 10 and  n*q₀  = 300*0,96        n*q₀ = 288 > 10

We can use normal distribution as a valid  aproximation of binomial distibution

Then     z(c) = 2,57

a) upper bound for CI     Ub

Ub = p₀ + z(c) * √ p₀q₀/300

Ub = 0,04  +  2,57 * √ (0,04*0,96)/300

Ub = 0,04 + 0,0113

Ub = 0,069

b) CI at 99%  is

CI  = p₀  ±  z(c) * √ ( p₀*q₀ ) /n

we have already calculated the Ub = 0,069

the Lower bound would be   Lb = 0,04 - 0,0113

Lb = 0,0287

Then     CI 99 %  = ( 0,0287 ; 0,069 )

c) If      CI ≤ 0,02 we can find the minimun n value with the equation:

p₀  ±  z(c) * √ ( p₀*q₀ ) /n = CI   or    p₀  -  z(c) * √ ( p₀*q₀ ) /n = 0,01

For symmetry respect to p₀

z(c) *√ (p₀*q₀) / n  = 0,01

Solving for n

z(c) * √ ( p₀*q₀ ) /n = 0,01

2,57 * √ (0,04*0,96)/n  =  0,01

2,57 * √ 0,0384/n = 0,01

2,57 = 0,01/√ 0,0384/n

Squaring both sides of the equation

6,6049 = (0,01)² *n / 0,0384

0,0384*6,6049 / 0,0001  = n

n = 2536

An object's size in real life and its size on a map or a blueprint are compared using a scale factor, which is a mathematical concept. The scale factor may exceed, fall short of, or be equal to 1.

The size of the object is decreased and becomes smaller if the scale factor is between 0 and 1. This is so because the scale factor only approximates the object's true size. The size of the thing on the map will be half that of the real object, for instance, if the scale factor is 0.5.

When the scale factor is 1, the object's size is said to remain constant. As a result, the map or blueprint is created using the same dimensions.

In other words, the map or blueprint is created at the exact same scale as the final product.

The size of the thing is enlarged and made larger if the scale factor is greater than 1. This is so because the scale factor is a multiple of the object's actual size. The size of an object on a map will appear twice as large as it is in reality, for instance, if the scale factor is 2.

In general, it's crucial to comprehend scale variables in order to appropriately depict an object's size on maps, blueprints, and other scaled representations.

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ANSWER

EXPLANATION

To find the average rate of change of the function, we have to apply the formula:

for a ≤ x ≤ b

This implies that:

Therefore, the average rate of change of the function is:

To find f(2), we have to substitute 2 for x in the given function:

To find f(-6), substitute -6 for x in the given function:

Therefore, the average rate of change of the function is:

That is the answer.

Answer:

Average rate of change = 0.29 million per year

Step-by-step explanation:

Average rate of change in the population from year 1970 to year 1900 is given by the formula,

Average rate of change = \(\frac{\text{Population in year 1990-Population in year 1970}}{1990-1970}\)

                                        = \(\frac{17-11.2}{1990-1970}\)

                                        = \(\frac{5.8}{20}\)

                                        = 0.29 million per year

Therefore, average rate of change in the population from 1970 to 1990 will be 0.29 million per year.                        

\(\sqrt{24}+\sqrt{27} ~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 2\cdot 3\\ 27=3\cdot 3\cdot 3\\ \qquad 3^2\cdot 3 \end{cases}\implies \sqrt{2^2\cdot 2\cdot 3}+\sqrt{3^2\cdot 3} \\\\\\ 2\sqrt{2\cdot 3}+3\sqrt{3}\implies 2\sqrt{2}\cdot \sqrt{3}+3\sqrt{3}\implies \stackrel{\textit{common factoring}}{\underset{ \textit{\LARGE k} }{(2\sqrt{2}+3)} ~~ \sqrt{3}}\)

Answer:

c

Step-by-step explanation:

It makes sense from what you are giving me. And I did the math it all adds up

Answer:

The answer is C) 20,40,4,56

Step-by-step explanation:

I worked each answer out and it was the only one higher than .5.

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Linear equations are two-variable equations that graph as a straight line.

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

Two-variable equations that graph as a straight line are said to be linear equations. The slope and y-intercept of a linear equation allow it to be graphed. Y = mx + b, where m is the slope and b is the y-intercept, is the formula used to represent a line. A graph's straight line can be represented by a linear equation.

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When Kayla was instructed to rewrite the polynomial expression x2 + 6x + 9, she wrote \(x^2+2 x-3+3^2=(x+3)^2\).

Factor \($ x^2+6 x+9: \quad(x+3)^2$\)

\($$x^2+6 x+9$$\)

Rephrase in the manner of \($a^2+2 a b+b^2$\) :

\($9=3^2$\)

\($6 x=2 x \cdot 3$\\$=x^2+2 x \cdot 3+3^2$\)

Using the Perfect Square Formula : \($\quad a^2+2 a b+b^2=(a+b)^2$\)

\($$\begin{aligned}& x^2+2 x-3+3^2=(x+3)^2 \\& =(x+3)^2\end{aligned}$$\)

An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial. x2 4x + 7 is an illustration of a polynomial of one uncertain x.

An expression with a single or a number of terms is referred to as a polynomial. The words "polynomial" and "nomial," which are two distinct phrases, are the origins of the term. Nominal is another word for many, while poly is another word for many. An algebraic expression with two or more algebraic terms is referred to as a polynomial.

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To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result. There you go!