The following are the Consumer Price Index (CPI) for the years 1991-1993. All of the values use a reference year of 1986.

Year CPI
1991 110
1992 120
1993 135


Which of the following is true about the CPI, based on the information?

A.)
$100 in 1992 would have been worth $100 in 1986.
B.)
$100 in 1993 would be equivalent to $120 in 1992.
C.)
$100 in 1986 would be equivalent to $135 in 1993.
D.)
$100 in 1991 would have been worth $110 in 1986

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer: I dont have one for sure but I can explain why this is true.

Step by Step:

sin(x+y)−sin(x−y)=sinxcosy+sinycosx−(sinxcosy−sinycosx)

=sinxcosy+sinycosx−sinxcosy+sinycosx

=sinxcosy+sinycosx−sinxcosy+sinycosx

=sinycosx+sinycosx

=2sinycosx

henceforth proved.

Answer:

52%

Step-by-step explanation:

13×4= 52%

You just multiply by 4 to get the percentage

Answer: 12 people

Step-by-step explanation:

0.30 x 40 = 12

Answer:

9000

Step-by-step explanation:

Answer:

500 and 4.3

Step-by-step explanation:

A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.

5000 × 0.1 = 500

4300 × 0.001 = 4.3

Thus, the answers [in order] are 500 and 4.3

Hope this helps and feel free to ask any questions.

Answer:

  y = 8(50)^t : growth

  y = 8(0.50)^t : decay

Step-by-step explanation:

Whether the exponential function represents growth or decay depends on the magnitude of the base and the sign of the variable in the exponent.

In general, an exponential function will be of the form ...

  y = a·b^x

where 'a' is a scale factor (or "initial value") and 'b' is the base. Any scale factor or translation associated with the variable x can be used to alter the values of 'a' and 'b' appropriately to put the function in this form.

For example, y = a·b^(x+3) = (a·b^3)(b^x).

Similarly, y = a·b^(-x) = a·(1/b)^x

When the value of 'b' is greater than 1, increasing x will increase the value of y. This is the characteristic of a growth function.

When the value of 'b' is less than 1, increasing x will decrease the value of y. This makes it a decay function.

Your function y = 8·50^t has a base of 50, which is greater than 1.

It is a growth function.

On the other hand, y = 8·0.50^t has a base of 0.50, which is less than 1. That function is a decay function.

__

Additional comment

For real values of x and y, we generally require 0 < b. The base can be negative if the domain of the exponent is restricted to integers, or fractions with an odd integer denominator.

Answer:

y+2>y

Step-by-step explanation:

Well, first of all. Adding any sum to y makes it greater then the same variable.

Greater than sign is >. Keeping that in mind now add them. y+2>y is gonna be you’re final answer!

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Answer:

B. (f•g)(x) = 2x³ + 6x² - 4x - 12

Step-by-step explanation:

F(x)  = x +3

G(x) = 2x² -4

(f x g)(x) = f(x)  x  g(x)

(f x g)(x) = (x +3)(2x² -4) =2(x+3)(x²-4)  

(f x g)(x)  = 2x³ + 6x² - 4x -12

Hope this helps! <3

The last number in Row 8 is 56.

The number in Row 12 and column 3 is 80.

The row and column that will contain the number 400 is Row 58 Column 1

The figure shown in the image represents the multiplication table 7.

Each column contains 7 numbers.

Beginning with the first Row and column, 7 numbers are added until the next row. At the end of each row is a multiple of 7.

The last number in Row 8 will be the product of 7 and 8 = 56

The number in Row 12 and Column 3 will be:

7 * 11 + 3 = 80

The row and column that will contain the number 400 will be:

400/7 = 77 remainder 1

Hence, it will be Row 58 Column 1.

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Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

Answer:

b = 5 - 5/4 a

Step-by-step explanation:

a/4 + b/5 = 1

Multiply by 20 to clear the fractions

20*(a/4 + b/5) = 1*20

5a +4b = 20

Subtract 5a from each side

4b = 20 -5a

Divide by 4

4b/4 = 20/4 - 5a/4

b = 5 - 5/4 a

A relative frequency distribution, which is connected to a probability distribution and is widely used in statistics. The relative frequency of people who strongly agree with the statement is 0.70.

A relative frequency distribution, which is connected to a probability distribution and is widely used in statistics, illustrates the proportion of the total number of observations associated with each value or class of values.

The complete question is:

A workplace gave an “Employee Culture Survey” in which 500 employees rated their agreement with the statement, “I feel respected by those I work for.”The relative frequency of people who strongly agree with the statement is?

Assume that there are 350 employees who agrees that they feel respected . Therefore, the number of desired outcomes for the survey will become 350, while the total outcomes will become 500. Therefore, the relative frequency can be written as,

Relative frequency

= Number of desired outcomes/ Total number of outcomes

=  350/500

= 0.70

Hence, The relative frequency of people who strongly agree with the statement is 0.70.

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Answer:

382^2 mod

Step-by-step explanation:

To determine the shared secret key, we need to use the formula (g^a mod p)^b mod p = (g^b mod p)^a mod p, where g is the generator, p is the prime, a is our secret number, and b is the value sent by Aisha. Plugging in the values, we get (7^227 mod 437)^308 mod 437 = (7^308 mod 437)^227 mod 437.

To solve for the shared secret key, we first need to calculate (7^308 mod 437). This can be done by raising 7 to the 308th power and then taking the remainder when divided by 437. We can do this by repeatedly squaring 7 and taking the remainder each time. This results in the following sequence:

7^2 mod 437 = 49

7^4 mod 437 = 161

7^8 mod 437 = 267

7^16 mod 437 = 9

7^32 mod 437 = 49

7^64 mod 437 = 161

7^128 mod 437 = 267

7^256 mod 437 = 9

7^512 mod 437 = 49

Since 512 is greater than 308, we can stop here and use the value 49 as the result of 7^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: (49^227 mod 437)^308 mod 437 = (49^308 mod 437)^227 mod 437.

To solve for the shared secret key, we need to find the value of 49^308 mod 437. This can be done using the same method as before, by repeatedly squaring 49 and taking the remainder each time. This results in the following sequence:

49^2 mod 437 = 67

49^4 mod 437 = 382

49^8 mod 437 = 221

49^16 mod 437 = 67

49^32 mod 437 = 382

49^64 mod 437 = 221

49^128 mod 437 = 67

49^256 mod 437 = 382

Since 256 is greater than 308, we can stop here and use the value 382 as the result of 49^308 mod 437. We can now plug this value into the formula to calculate the shared secret key: 382^227 mod 437 = 382^227 mod 437.

To find the shared secret key, we need to calculate 382^227 mod 437. This can be done using the same method as before, by repeatedly squaring 382 and taking the remainder each time. This results in the following sequence:

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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Answer:

See step by step exlanation

Step-by-step explanation:

Assuming normal distribution

N( μ₀ , σ )

In this case N ( 1000, 200)

From a random sample of 64 accounts we get:

n  = 64

x = sample mean      x = 1040

σ = standard deviation of the population     σ = 200

1.-Test Hypothesis

Null Hypothesis               H₀          x =  μ₀ = 1000

Alternative Hypothesis    Hₐ          x ≠ μ₀    

The alternative hypothesis implies a two tail-test. Given that  n > 30 and σ is known we will use z-table

2.-  z(s) = ( x  - μ₀ ) / σ/√n

z(s) = ( 1040 - 1000 ) / 200/ √64

z(s) = 40*8/200

z(s) = 1,6

3.-P-val for  z (score 1,6)     p-value = 0,0548

4.- If significance level is 0,05  then  α = 0,05  and   α/2 = 0,025

p-value >  α/2        

Then  the z(s) < z(c)      1,6 < 1,96            where  z(c) is z score for α/2

We should accept H₀  

5.-We can claim that at 95 % (of Confidence Interval) the population mean is not significantly  different from 1000 $

The given graph is a parabola, which gives as an idea that AT MOST, there are two zeroes of the function. However, it does not intersect with the x-axis, which means that there are NO REAL zeroes.

We can therefore conclude that the best description of this quadratic function is 2 imaginary zeroes.

The Gini coefficient is 2(−13/30) = -13/15.

The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).

In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.

The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.

The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.

The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=

∫[0,1](p^4/3−p)dp

=(1/15)−(1/2)

= -13/30

The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.

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The number of more hotdog buns than kaya buns there are in the bakery, obtained from the fractions and ratios of the number of buns are 192 hotdog buns

A ratio is a quantitative representation of the number of times one quantity is contained in another quantity.

The fraction of the buns that are coffee buns = 3/11

The amount of the hotdog buns and kaya buns = The rest of the buns

The ratio of the hotdog buns to the kaya buns = 7 : 5

The total number of hotdog buns and kaya buns = 720 more than the number of coffee buns

The difference between the number of hotdog buns and kaya buns are therefore;

Let x represent the number of buns in the bakery

The number of coffee buns = 3·x/11

The number of hotdog buns and kaya buns = x - 3·x/11 = 8·x/11

8·x/11 = 3·x/11 + 720

Therefore;

8·x/11 - 3·x/11 = 720

5·x/11 = 720

5·x = 11 × 720 = 7920

x = 1584

The number of hotdog buns and kaya buns = 8×1584/11 = 1152

The number of hotdog buns = (7/(7 + 5)) × 1152 = 672

The number of kaya buns = (5/(7 + 5)) × 1152 = 480

The difference = 672 - 480 = 192

Part of the question, obtained from a similar question posted on the internet is; How many more hotdog buns than kaya buns are there in the bakery.

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11 x (7 + 5) = 132

(3/11) x 132 = 36 (coffee)

(8/11) x 132 = 96 (hotdog and kaya)

96 – 36 = 60

720/60 = 12

(2/12) x 96 = 16

16 x 12 = 192

Answer:

1/2

Step-by-step explanation:

In a deck of cards, there are 13 hearts and 13 diamonds

13+13 = 26 hearts or diamonds

P( hearts or diamonds) = numbers of hearts or diamonds / total

                                       =26/52

                                       = 1/2

Answer:

y=-2x+5

Step-by-step explanation:

y=-2x+5

Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

Answer:

101.4 floz

Step-by-step explanation:

If I'm correct, you should multiply 16.9 by 6 because there are 6 bottles and each has 16.9 fluid ounces of water.

A water bottle has 16.9 fluid ounces of water, there would be a total of 101.4 fluid ounces of water.

We are given that each water bottle contains 16.9 fluid ounces of water. This is the capacity or volume of a single bottle.

To find the total amount of water in a pack of 6 bottles, we can multiply the amount of water in one bottle by the number of bottles in the pack.

Amount of water in one bottle: 16.9 fluid ounces

Number of bottles in the pack: 6

Total amount of water in the pack: 16.9 fluid ounces/bottle * 6 bottles = 101.4 fluid ounces

Therefore, there would be a total of 101.4 fluid ounces of water in a pack of 6 bottles.

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a. The five-number summary of the data would be:

Minimum: 23; Quartile Q1: 29; Median: 33; Quartile Q3: 42; Maximum: 51

b. The box plot for the data set is given in the diagram attached below.

c. The distribution of the scores based on the box plot is positively skewed.

A box plot represents a data distribution showing the five-number summary which includes, min and max values, lower and upper quartile, and median of the data distribution.

Given the data set:

33, 38, 43, 30, 29, 40, 51, 27, 42, 23, 31

a. The five-number summary of the data would be:

Minimum: 23

Quartile Q1: 29

Median: 33

Quartile Q3: 42

Maximum: 51

b. The box plot for the data set is given in the diagram attached below.

c. The box plot shows that the median is closer to the bottom of the rectangular box, therefore, the distribution of the scores based on the box plot is positively skewed.

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i think is it So if it is

The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

3

Step-by-step explanation:

In this expression, the first term is 2x, then 4y, then 8-2 (which simplifies to 6).

The required rate of return for the stock with a beta of 0.5 is 7.5% and for the stock with a beta of 2 is 15%.

Rate of return is the amount of profit or loss earned on an investment over a certain period of time, expressed as a percentage of the initial investment or total asset value.

A stock is a type of security that represents ownership in a company. Investors buy stocks to become shareholders and share in the company's profits and losses.

According to the given information:

The Capital Asset Pricing Model (CAPM) is expressed as:

R = Rf + beta*(Rm - Rf)

Where:

R = Required rate of return

Rf = Risk-free rate of return

beta = Beta coefficient (systematic risk)

Rm = Expected market return

Using the given values, we can compute the required rate of return for each stock:

Stock with beta of 0.5:

R = 5% + 0.5*(10% - 5%)

R = 7.5%

Stock with beta of 2:

R = 5% + 2*(10% - 5%)

R = 15%

Therefore, the required rate of return for the stock with beta of 0.5 is 7.5%, and the required rate of return for the stock with beta of 2 is 15%.

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