Part III: If a bottle of dishwashing detergent cost $0.31 in 1950, and if the price of
dishwashing detergent increased at the same rate as the CPI from 1950 to 1970,
what was the CPI to the nearest tenth in 1950?

The complete expression is 6 * 1/3 = 1/3 * 6

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

6 x 1/3 _ 6

Express properly

So, we have the following representation

6 * 1/3 = _6

Represent the blank with x

6 * 1/3 = x * 6

So, we have

2 = 6x

Divide by 6

x =1/3

Hence, solution to the expression is 1/3

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Check the picture below.

The probabilities for the standard normal distribution in r or using the standard normal table are

a) P(X<2.18) = 0.9854

b)P(X>2.18)= 0.0146

c) P(<-2.49) = 0.0064

The standard normal table is a mathematical table that allows us to know the percentage of values below the z-score (left) of the standard normal distribution. This is the "bell-shaped" curve of the standard normal distribution. It is a normal distribution with mean 0 and standard deviation 1. Using the Z-table:

Now, we have to determine the probability value for (a) , (b) and (c) .

a) P(X < 2.18) = P( Z< 2.18) = intersection point of row value 2.1 and column 0.08 = 0.9854

b) P(X >2.18) = P( Z> 2.18) = 1 - P( Z< 2.18)

= 1 - 0.9854 = 0.0146

c) P(X < -2.49) = P(Z < -2.49) = intersection point of row value -2.4 and column 0.09 = 0.0064.

Hence, we got all the required probability values.

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Complete question:

Find the following probabilities for the standard normal distribution in R or using the standard normal table. NoteI always recommend drawing the distribution. (Round your answers to four decimal places.) ### Example R code mu = 0; sigma = 1; x = x; # Note you will have to change the value of x. pnorm(x,mu,sigma)

(a) P(X < 2.18)

b) P(X >2.18)

(c) P(X < -2.49)

The width of the front of the aquarium is 30m

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2( l + w)

Given that the parameters are;

From the information given, we have that the values are;

Perimeter = 230m

Length = 85m

Width = w

Substitute the values, we get

230 = 2(85) + 2w

expand the bracket

2w = 230 -170

subtract the values

2w = 60

Make 'w' the subject

w = 30m

Hence, the value is 30m

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Answer:

The function f(x) = 7(3/54*) can be simplified as follows:

Simplified base: 7 * (3/54) * x = (3/54) * 7 * x = (3/54) * 7 * x = (3/54) * 7 * x = 7 * (3/54) * x

Initial value: None provided

Domain: The domain of a function refers to the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, it would depend on the restrictions on x, but typically, real numbers are assumed as the domain unless otherwise stated.

Range: The range of a function refers to the set of all possible output values (y-values) that the function can produce. In this case, the range would be all real numbers since there are no restrictions on the output.

Note: There seems to be some errors or typos in the original function and the question, as the expression (3/54*) does not have a clear mathematical meaning. The information provided is based on the assumptions made from the given information

The change in temperature over the 12-hour period was 50℉ - 10℉ = 40℉.

The population to which it would be most reasonable to generalize the results of the observational study is women who are students at Midwestern colleges in the United States.

This population is well-defined and can be used to make generalizations about the results from the study.

This population can be calculated by taking the total number of college students in the United States and subtracting the number of college students in other regions, as well as the number of male students in the Midwestern region.

The total population of women college students in the Midwestern region of the United States can then be calculated by multiplying the total population by the percentage of female students in the region.

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Answer:

7

Step-by-step explanation: just do it

Answer:

39

Step-by-step explanation:

To find the bearing from the phone to the transmitter, we can use the arctangent function.

The formula to find the bearing is:

θ = atan2(dy, dx)

where dx = difference in x-coordinates and dy = difference in y-coordinates.

Here, dx = -13 km and dy = -21 km, since the transmitter is located to the west and south of the phone.

Therefore, the bearing is:

θ = atan2(-21, -13) = atan2(21, 13) = 63.434948822922° (to the nearest degree)

So the bearing from the phone to the transmitter is approximately 63.4°.

The value of x is 10 and y is -5.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Three parallel lines.

From the diagram,

we have system of equations

6x + 2y + 130 = 180

2x - 4y + 140 = 180

Simplifying both equations,

3x + y = 25....(1)

x - 2y = 20,....(2)

Now, substituting the value of x from the equation 2 to equation 1,

7y = 25 - 60

y = -5.

And x = 10.

Therefore, the value of x is 10 and y is -5.

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The ratio of the areas of the two circles equals the square of the ratio of their radii:  = 1/4

Let O1 be the center of the larger circle and O2 be the center of the smaller circle. T is the tangent point between the two circles.

The distance between their centers, O1O2, is equal to the sum of their radii, i.e., r1 + r2.

The Pythagorean theorem gives us:

(O1O2)^2 = r1^2 + r2^2

By substituting r1, r2, and O1O2 values, we obtain:

(r1 + r2)^2 = r1^2 + r2^2

By broadening and simplifying, we get:

2r1r2 = r2^2

When both sides are divided by r22, we get:

2r1/r2 = 1

So, r1/r2 = 1/2. r2 = 2r1.

The ratio of the areas of the two circles equals the square of the ratio of their radii:

A1/A2 = (r1/r2)^2 = 1/4

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The length of the leg in the triangle is 4 units

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

The length of the other leg using Pythagorean Theorem is

Other Leg = √(Hypotenuse² - One Leg²)

So, we have

Orher Leg = √(5² - 3²)

Evaluate

Other leg = 4

Hence, the other leg is 4 units

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After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.

The amount of ground coffee that Marshall bought for his office machine = 40 ounces

The quantity of coffee he uses per week in his office = 5 ounces.

Therefore for 4 weeks would be= ?

But, 1 week = 5 ounces

4 weeks = X

make X the subject of formula;

X = 5×4 = 20 ounces

The amount of ground coffee that will remain = 40-20 = 20 ounces.

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Answer:

Step-by-step explanation:

The quotient of 2 divided by 1.176 can be calculated as follows:

2 ÷ 1.176 = 1.70860927152318

Therefore, 2 divided by 1.176 is equal to 1.70860927152318.

The number of years that each person would have been employed would be that Nikhil has been with the company for 24 years, while Mae has been there for 4 years. That is option C.

Nikhil has been at the company 6 times as long as Mae.

That is,

x = 6y-----> equation 1

where X= Nikhil

y = Mae

Nikhil's time at the company is 8 more than 4 times Mae's.

That is,

x = 8 + 4y----> equation 2

To solve for each years, substitute for X into equation 2;

6y = 8+4y

8 = 6y-4y

8 = 2y

y = 8/2 = 4

Substitute y into equation 1;

X= 6×4

X= 24

Therefore, Nikhil has been with the company for 24 years, while Mae has been there for 4 years.

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Answer: Option C. Nikhil has been with the company for 24 years, while Mae has been there for 4 years.

Step-by-step explanation:

Answer: 0.32432432432

Step-by-step explanation:

5x7=35

35+2=37

26-14=12

12/37= 0.32432432432

The solution of the given quadratic equation is -2 ± √6.

Quadratic expressions are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Solution of a quadratic equation ax² + b x + c = 0 can be found by,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a, where [tex]b^2-4ac[/tex] is called discriminant.

Given quadratic equation is x² + 4x - 2 = 0.

Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24

x = [-4 ± √24] / 2

  = [-4 ± 2√6] / 2

  = -2 ± √6

Hence the solution of the given quadratic equation is -2 ± √6.

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The number of pounds of ground meat used is 2(13/80).

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

The number of pounds of ground meat bought = 2(9/16).

The number of pounds of ground meat left = 2/5.

Now,

The number of pounds of ground meat used.

= 2(9/16) - 2/5

= 41/16 - 2/5

= (205 - 32) / 80

= 173/80

= 2(13/80)

Thus,

2(13/80) pounds of ground meat were used.

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The total cost of materials used in constructing the box in cents can be given by the function [tex]C(x) = 29x^2 + 24x^2 + 10(4x) = 63x^2 + 40x[/tex].

This formula can be derived by multiplying the cost per square foot of the base, top, and sides with their respective areas. The area of the base and top can both be expressed as [tex]x^2[/tex], while the area of the four sides can be expressed as 4x. Thus, multiplying the cost per square foot of each material with its respective area, we obtain the total cost of materials used in constructing the box in terms of x, which is given by the expression [tex]C(x) = 63x^2 + 40x[/tex].

For example, if x = 4, then the total cost of materials used in constructing the box in cents is [tex]C(4) = 63(4^2) + 40(4) = 1512 + 160 = 1672 cents[/tex].

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The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.

The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.

To calculate the equation, we first need to calculate the slope and the y-intercept. Since we have 5 points, we can calculate the slope using the formula m=(y2-y1)/(x2-x1). For this problem, we'll use (46,250) and (54,410). Plugging the values into the formula, we get m = (410-250)/(54-46) = 4.5.

Next, we need to find the y-intercept, which is 200. The formula for this is b = y-mx. For our problem, we'll use (46,250). Plugging in the values, we get 200 = 250 - 4.5(46), so b = 200.

Therefore, the linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.

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The quartic regression equation is (a) y = -0.04x^4 + 1.06x^3 - 8.99x^2 + 40.05x + 177.92 and the estimated the number of graduates in 1992 is 367

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

(-1,8), (5,-4), (7,8), (2,-6)

Using a graphing calculator, we have the following summary:

The model from the above summary is

y = -0.0402x^4 + 1.0627x^3 - 8.9931x^2 + 40.0522x + 177.9198

Approximate

y = -0.04x^4 + 1.06x^3 - 8.99x^2 + 40.05x + 177.92

In the year 1992, we have

x = 12

So, we have

y = -0.04 * 12^4 + 1.06 * 12^3 - 8.99 * 12^2 + 40.05 * 12 + 177.92

Evaluate

y = 367

The estimated the number of graduates in 1992 is 367

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Answer:

16 divided by the total of x and 4

Step-by-step explanation:

16 / (x+4) can be rewritten as 16 divided by the total of x and 4

Answer:2

Step-by-step explanation:

Number of dogs in the farm of Pisquet is approximately 21.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

If we have two ratio p : q and r : s and if these ratios are proportional, then we can write it as p: q : : r : s.

This is same as p : q = r : s or p/q = r/s

Given that,

On the planet Gespil, there are 5 dogs to every 12 cats.

Number of dogs for 12 cats = 5

Let Number of dogs for 50 cats = x

Using concept of proportion,

12 / 5 = 50 / x

Cross multiplying,

12x = 5 × 50

12x = 250

x = 20.83 ≈ 21

Hence there are approximately 21 dogs for 50 cats.

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Answer:

[tex]\frac{1}{9^{8}}[/tex]

Step-by-step explanation:

When multiplying two numbers with exponents with the same base, you simply add the two exponents together, even if they're negative:

[tex]9^{-5}*9^{-3} =9^{-8}[/tex]

When a number has a negative exponent ([tex]x^{-2}[/tex]) it means that the number is equal to 1/that number ([tex]\frac{1}{x^{2}}[/tex])

[tex]9^{-8}=\frac{1}{9^{8}}[/tex]

The graph shows two functions, f(x) and g(x). So, the statements that describe the resulting graph h(x) is point (-2,2) is on h(x)

A graph is described as the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the question above, we have two functions f(x)=x²-2 and g(x)=x²+2 by adding the function we will get the combined function.

The graph that the function is varying from the coordinates (-2,2) is seen on the attached graph.

Therefore, we can conclude that the graph shows two functions, f(x) and g(x). So point (-2,2) is on h(x)

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Answer:

77

Step-by-step explanation:

1. solve the first part by plugging in 7 for y.

14(7)+37/5

98+37/5

135/5

27

2. then solve the second part by plugging in 7 for y.

8(2(7)-1)

8(14-1)

104

3. then subtract 27 from 104

104-27=77

The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

An arrow is shot vertically upward at a rate of 180ft/s.

Then the equation is given as,

h = −16t² + 180t

The number of seconds when the height is 420 ft will be given as,

420 = −16t² + 180t

16t² - 180t + 420 = 0

4t² - 45t + 105 = 0

t = [-(-45) ± √{(-45)² - 4 × 4 × 105}] / (2 × 4)

t = (45 ± 18.57) / 8

t = 7.95, 3.3 seconds

The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.

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