Consumer Price Index, 1970-2002
Year
1970
1975
1980
1985
1990
1995
2002
Source: World Almanac 2003
CPI
116.3
161.2
248.8
322.2
391.4
456.5
535.8
Describe how the CPI is related to the year.
As the year increases, the CPI decreases and then increases.
As the year increases, the CPI increases and then decreases.
As the year increases, the CPI decreases.
d. As the year increases, the CPI increases.
C.
a.
b.

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

GIVEN :

TO FIND :

USING FORMULA :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

SOLUTION :

Substituting the given values in the formula to find the length of the missing diagonal :

[tex] \longrightarrow{\sf{Area \: of \: rhombus = \dfrac{d_1 \times d_2}{3}}}[/tex]

[tex] \longrightarrow{\sf{20 = \dfrac{10 \times d_2}{2}}}[/tex]

[tex] \longrightarrow{\sf{20 \times 2= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{40= 10 \times d_2}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \dfrac{40}{10}}}[/tex]

[tex] \longrightarrow{\sf{d_2 = \cancel{\dfrac{40}{10}}}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{d_2 = 4 \: miles}}}}[/tex]

Hence, the length of the missing diagonal is 4 miles.

Answer:

The length of the missing diagonal is 4 miles.

Step-by-step explanation:

To find the length of the missing diagonal, we can use the formula for the area of a rhombus, which is:

[tex]\sf\qquad\dashrightarrow Area_{(Rhombus)} = \dfrac{(Diagonal_1 \times Diagonal_2)}{2}[/tex]

We know that the area is 20 square miles and one of the diagonals is 10 miles, so we can substitute these values into the formula as follows:

[tex]\sf\qquad\dashrightarrow20 = \dfrac{(10 \times Diagonal_2)}{2}[/tex]

Simplifying the equation, we get:

[tex]\sf\qquad\dashrightarrow 40 = 10 \times Diagonal_2[/tex]

Dividing both sides by 10, we get:

[tex]\sf\qquad\dashrightarrow \boxed{\bold{\:\:Diagonal_2 = 4\:\:}}\:\:\:\bigstar[/tex]

Therefore, the length of the missing diagonal is 4 miles.

The function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.

What is an inequality equation?

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

The function that is undefined for x = 0 is y = √x+2.

When x = 0, we have:

y = √0+2

y = √2

Since there is no real number whose square is negative, the square root of a negative number is undefined in real numbers.

Therefore, the function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.

To know more about inequality equations visit:

https://brainly.com/question/30238989

#SPJ1

Using the simple interest formula, Whitney earned an interest of $26,000 in 4 years.

The simple interest system does not charge interest on accumulated interest (unlike the compound interest system) but only on the principal for each period.

The formula for computing the simple interest amount for the period is given as I = PRT, where I is the interest earned, P is the principal (starting amount), R is the interest rate expressed as a decimal, and T is the time in years.

Principal = $50,000

Simple interest rate = 13%

Investment period = 4 years

Simple interest earned = $26,000 ($50,000 x 13% x 4)

Learn more about the simple interest system at https://brainly.com/question/30344384.

#SPJ1

In linear equation, 170 adult and 380 children's tickets were sold.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...

 7a + 2(550 -a) = $1950

  7a + 1100 - 2a = 1950

     5a =  1950 -  1100

      5a = 850

        a = 170

 c = 550 - 170  = 380

170 adult and 380 children's tickets were sold.

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Answer:  The solution to the inequality is x is less than or equal to 4. We can write it in interval notation as (-∞, 4].

Step-by-step explanation: To solve the inequality 1/2x + 8 ≤ 10, we need to isolate the variable x on one side of the inequality sign.

Subtracting 8 from both sides, we get:

1/2x ≤ 2

To isolate x, we need to multiply both sides of the inequality by 2:

x ≤ 4

The calculated line of reflection of the graph is y = -3

The given graph is added as an attachment

From the graph, we can see that the shapes are symmetrical about the line y = -3

When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection

This means that the line of reflection is y = -3

Read more about transformation at

brainly.com/question/27224272

#SPJ1

Answer:

The calculated line of reflection of the graph is y = -3

Step-by-step explanation:

The income statement, and stockholders equity are given below.

We have to show the income statement

The income statement for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Income Statement

For the Year Ended December 31, 2024

Service Revenue $55,000

Less: Expenses

Salaries Expense $27,000

Rent Expense $6,000

Utilities Expense $6,000

Interest Expense $5,000

Total Expenses $44,000

Net Income $11,000

The statement of stockholders' equity for Coyote Corporation for the year ended December 31, 2024, is as follows:

Coyote Corporation

Statement of Stockholders' Equity

For the Year Ended December 31, 2024

Retained Earnings, December 31, 2023 $35,000

Add: Net Income for 2024 $11,000

Less: Dividends $0

Retained Earnings, December 31, 2024 $46,000

Classified Balance Sheet:

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

Total Liabilities and Stockholders' Equity $119,000

Therefore, the classified balance sheet for Coyote Corporation as of December 31, 2024, is as follows:

Coyote Corporation

Classified Balance Sheet

As of December 31, 2024

Assets

Current Assets

Cash $27,000

Accounts Receivable $26,000

Prepaid Rent $6,000

Supplies $5,000

Total Current Assets $64,000

Property, Plant, and Equipment

Land $55,000

Total Property, Plant, and Equipment $55,000

Total Assets $119,000

Liabilities and Stockholders' Equity

Current Liabilities

Accounts Payable $90,000

Salaries Payable $375,000

Interest Payable $6,000

Total Current Liabilities $471,000

Long-term Liabilities

Notes Payable (due in two years) $55,000

Total Liabilities $526,000

Stockholders' Equity

Common Stock $35,000

Retained Earnings $46,000

Total Stockholders' Equity $81,000

Learn more about income statement on

brainly.com/question/15169974

#SPJ1

complete question:

Kindly check if the photo below of income statement is wrong and correct which one is wrong in a excel or anything that makes it clear to me.

The probability statement is written below:

The middle 40% of heights fall between the 10th and 90th percentiles of the standard normal distribution.

The z-scores of the 10th and 90th percentiles are -1.28 and 1.28 respectively.

The heights in the given normal distribution are found using the formula:

where

The height of the 10th percentile is:

X = 66 + (-1.28)(2.5)

X = 62.8 inches

The height of the 90th percentile is:

X = 66 + (1.28)(2.5)

X = 69.2 inches

Therefore, the middle 40% of heights fall between 62.8 inches and 69.2 inches and the probability statement will be P(62.8 ≤ X ≤ 69.2) = 0.4

Learn more about normal distribution at: https://brainly.com/question/4079902

#SPJ1

The situation is modeled by the linear equation:

t = $5*x

We know that Brenda earns $5 each week for chores. The variable x represents the number of weeks brenda did her chores, and t represents the total dollars she earned.

Then if she works for x weeks, the amount that she earns is x times $5, then the equation will be a linear one:

t = $5*x

That is the equation.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

The amount (coupon interest) that is earned off the $1,000 bond with 4.3% coupon every 6 months is $21.50.

The coupon interest represents the periodic payment received by a bondholder from the date of issuance until the date of maturity of a bond.

The coupon interest is computed by applying the coupon rate on the face value of the bond.

Face value of the bond = $1,000

Coupon interest rate = 4.3%

Maturity period = 30 years

Coupon (bond) interest for 6 months = $21.50 ($1,000 x 4.3% x 6/12)

Learn more about coupon interests at https://brainly.com/question/30527238.

#SPJ1

Answer:0.125

Step-by-step explanation:

Answer:

x<1

Step-by-step explanation:

looking at the graph, the x values are 0,-1,-2,-3,-4,-5.

therefore, all the values of x are below 1.

x<1 is the suitable inequality that matches the graph.

The interest that have been earned after two years is $25.

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

A = P(1 + r/n)^nt

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

Learn more about compound interest:https://brainly.com/question/14295570

#SPJ1

The required polynomial  [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex].

What is a polynomial ?

A polynomial is a mathematical expression that consists of variables and coefficients, combined by addition, subtraction, and multiplication, but not division by a variable.

To write a polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex], we need to include their conjugates as well. This is because complex roots always come in conjugate pairs.

The conjugate of  [tex]i\sqrt{6[/tex] is  [tex]-i\sqrt{6[/tex], so our polynomial function will have the following zeros: -1, 1,  [tex]i\sqrt{6[/tex], and  [tex]-i\sqrt{6[/tex].

To find the polynomial function, we can use the fact that the product of the factors of a polynomial is equal to the polynomial itself. So, we can start by multiplying out the factors:

[tex](x+1)(x-1)(x-i\sqrt6)(x+i\sqrt6)[/tex]

Expanding this out gives:

[tex](x^2-1)(x^2+6)[/tex]

Multiplying these two expressions gives:

[tex]x^4+5x^2-6[/tex]

So the polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex] is [tex]f(x) = x^4+5x^2-6[/tex]

To verify that this polynomial has the desired zeros, we can factor it using the difference of squares:

[tex]x^4+5x^2-6 = (x^2-1)(x^2+6) = (x-1)(x+1)(x^2+6)[/tex]

And the quadratic factor has no real roots, so it must be the factorization [tex](x-i\sqrt6)(x+i\sqrt6)[/tex].

Therefore, [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex], as required.

To learn more about conjugate pairs visit the link :
https://brainly.com/question/7325000

#SPJ1

The rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.

Explain the term rate

Rate is a measure of the speed or frequency of change of a quantity over time or space. It is expressed as a ratio between two quantities, such as distance travelled per unit of time or number of occurrences per unit of time. Rates are commonly used in mathematics, science, and economics to analyze and compare different phenomena.

According to the given information

Let's let x be the rate of the plane in still air and y be the rate of the wind. When flying against the wind, the plane's effective speed is (x - y) km/h, and when flying with the wind, its effective speed is (x + y) km/h.

From the information given in the problem, we can set up two equations to represent the plane's distance travelled when flying against and with the wind:

6390 = 9(x - y)

2970 = 3(x + y)

Solving for x and y in these equations, we find that x = 810 and y = 90. So the rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.

To know more about rate visit

brainly.com/question/14731228

#SPJ1

The possible values of the random variable P are 0, 1, or 2.

A triangle is a polygon with three straight sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, science, engineering, and art. The sum of the interior angles of a triangle is always 180 degrees, and the length of the sides and the size of the angles determine the shape of the triangle.

Triangles can be classified according to the length of their sides and the size of their angles. A scalene triangle has three unequal sides and three unequal angles. An isosceles triangle has two equal sides and two equal angles. A equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. Triangles can also be classified based on the size of their angles: an acute triangle has three acute angles (less than 90 degrees), a right triangle has one right angle (90 degrees), and an obtuse triangle has one obtuse angle (greater than 90 degrees).

Triangles have many important properties and applications in geometry. For example, the Pythagorean theorem is a fundamental relationship between the sides of a right triangle, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The area of a triangle can be calculated using the formula 1/2 x base x height, and this formula can be used to solve many practical problems involving triangles.

The random variable P can take on four possible values, depending on how many heads are obtained:

P = 0 if both coins show tails.

P = 1 if exactly one of the coins shows heads.

P = 2 if both coins show heads.

Therefore, the possible values of the random variable P are 0, 1, or 2.

To know more about random visit:

https://brainly.com/question/30515377

#SPJ1

An expression which is the simplest form of 4(3x + y) + (2x - 5y) + x² include the following: x² + 14x - 6y.

In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).

In this scenario and exercise, the simplest form of the given expression 4(3x + y) + (2x - 5y) + x² can be determined or calculated by simplifying it as follows;

4(3x + y) + (2x - 5y) + x²

12x + 4y + 2x - 5y + x²

14x + - y + x²

By rearranging, we have;

x² + 14x - 6y.

Read more on expression here: https://brainly.com/question/31442748

#SPJ1

Complete Question:

Which expression is the simplest form of 4(3x+y)+2x-5y)+x²

The original numbers multiplied by 10² are:

968

0.002

3.33

When a number is multiplied by 10², the position of the decimal point will move to the right by 2 steps. If the number does not have decimal point, two zeros is added to the back of the number .

6 * 10³  = 6,000

968 * 10² = 96,800

0.002 * 10² = 0.2

70,000 ÷ 10² = 700

3.33 * 10² = 333

Thus, the original numbers multiplied by 10² are 968, 0.002 and 3.33

Learn more about numbers on:

https://brainly.com/question/20400557

#SPJ1

The two numbers given by the algebraic expressions are x = 5 and y = 2.

A system of equations is a set of two or more equations that are to be solved simultaneously. In other words, a system of equations represents multiple relationships between variables that need to be solved for at the same time. A system of equations can be solved using various methods, such as substitution or elimination. The goal of solving a system of equations is to find the values of the variables that satisfy all of the equations in the system. One common method for solving systems of linear equations is called Gaussian elimination, which involves manipulating the equations in the system to eliminate one variable at a time until a solution is found.

Let us suppose the numbers as x and y.

From the given statement the mathematical expression can be set as:

y = 2x - 8

x + y = 7

Now. substituting the value of y in equation we have:

x + (2x - 8) = 7

3x - 8 = 7

3x = 15

x = 5

Now, for x = 5 the value of y is:

y = 2(5) - 8

y = 2

Hence, the two numbers are x = 5 and y = 2.

Learn more about system of equations here:

https://brainly.com/question/24065247

#SPJ1

The complete question is:

The number y is 8 less than 2 times another number x, their sum is 7. Find the number.

Answer: 96

Step-by-step explanation: There are 16 cups in each gallon. To get how many there are in 6 gallons you would need to multiply 6 and 16.

6*16=96

or

16+16+16+16+16+16= 96

Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

The requried  [tex]\int_a^{oo} g(x) dx[/tex] must be convergent. Option C is correct.

Since f(x) is greater than or equal to g(x) for all x, we know that:

[tex]\int_a^{oo} f(x) dx\geq\int_a^{oo} g(x) dx[/tex]

If [tex]\int_a^{oo} f(x)[/tex]dx is convergent, then by comparison test, [tex]\int_a^{oo} g(x) dx[/tex] must also be convergent. Therefore, the correct answer is (C) g(x)dx is convergent.

Learn more about convergent and divergent functions here:

https://brainly.com/question/15415793

#SPJ1

The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.

The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.

By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.

Read more about expression

brainly.com/question/1859113

#SPJ1

Answer:

C or D it’s hard to see if the bottom of the shape is a square or rectangle.

Step-by-step explanation:

If rectangle C if squared D

I would go with C

A histogram would be the most effective graphic depiction to compare the distribution of the hours spent online among teenagers, young adults, and the elderly.

What is a histogram ?

A histogram is a graph that displays the distribution of a continuous variable. It divides the data into a set of intervals (called bins) and counts the number of data points that fall into each bin.

This creates a bar-like representation of the data, with the height of each bar indicating the frequency of data points in that bin. By using a histogram, we can see the shape of the distribution, as well as any patterns or trends that may exist. We can compare the distribution of the hours spent online by teenagers, young adults, and the elderly by placing the histograms of their data side by side. This will allow us to visually compare the shape, spread, and central tendency of the distributions for each group. Additionally, we can use different colors for each group to make the comparisons even clearer. This will enable us to quickly see if there are any significant differences in the hours spent online among the three groups.

To learn more about central tendency visit the link :

https://brainly.com/question/30218735

#SPJ1

$[tex]240[/tex] is saved by Isaiah from his allowance within the space of [tex]20[/tex] weeks.

The link between two or more variables is depicted using an equation. Mathematical operations may be used in equations.

Isaiah is saving  $[tex]12[/tex] per week from his pay.

Amount of money saved by Isaiah  in [tex]20[/tex] weeks

Money saved [tex]=[/tex] $[tex]12[/tex] ×[tex]20[/tex]

Money saved = $[tex]240[/tex]

Therefore, $[tex]240[/tex] is saved by Isaiah from his allowance within the space of [tex]20[/tex] weeks.

Learn more about allowance, here:

https://brainly.com/question/21478833

#SPJ1

the calculated total savings matches the given total savings of $240, we can say that the statement is true

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

To check whether this statement is true or false, we can use the following formula:

Total Savings = Savings per Week × Number of Weeks

Substituting the given values, we get:

Total Savings = $12/week × 20 weeks = $240

Since the calculated total savings matches the given total savings of $240, we can say that the statement is true.

Learn more about arithmetic, by the following link.

https://brainly.com/question/13181427

#SPJ1

Answer:

Step-by-step explanation:

Area= pi times radius²

The radius in the last one is 7, so 7² is 49.

Multiply 3.14 by 49 and you get 153.86. Round it to the nearest tenth and you get 153.9 as the area

Hope this helps!

F(x) is an antiderivative of f(x) because F'(x) = f(x)

An anti-derivative is the integral of a function

To verify that F is an antiderivative of f where

F(x) = √(3x² - 4) and f(x) = 3x/√(3x² - 4)

This means that F(x) = ∫f(x)

This implies that F'(x) = f(x)

So, we verify as follows

F(x) = √(3x² - 4)

Taking the derivative with respect to x, we have that

dF(x)/dx = d√(3x² - 4)/dx

Let u = 3x² - 4

So, dF(x)/dx = d√u/dx

= d√u/du × du/dx

= 1/(2√u) × du/dx

Now,du/dx = d(3x² - 4)/dx

= 6x

So,

dF(x)/dx  = 1/(2√u) × du/dx

= 1/(2√(3x² - 4)) × 6x

= 1/(√(3x² - 4)) × 3x

= 3x/(√(3x² - 4))

= f(x)

So, F(x) is an antiderivative of f(x) because F'(x) = f(x)

Learn more about antiderivative here:

https://brainly.com/question/27830377

#SPJ1

The x-coordinates of the points on the curve where the tangent line is horizontal will be option A.

(x² + y²)² = 4(x² – y²)

x⁴ + 2x²y² + y⁴ = 4x² - 4y²

y⁴ + 2x^2y² + 4y² - 4x² = 0

Now we can use implicit differentiation to find the derivative of y with respect to x:

4y³(dy/dx) + 4xy² + 4y(dy/dx)x² + 8y(dy/dx) - 8x = 0

Simplifying this expression, we get:

4y³(dy/dx) + 4xy² + 4xy²(dy/dx) + 8y(dy/dx) - 8x = 0

(dy/dx)(4y³ + 4x²y²) + 8y(dy/dx) = 8x - 4xy²

(dy/dx)(4y³ + 4x^2y² + 8y) = 4x(2-y²)

(dy/dx) = 4x(2-y²)/(4y³ + 4x²y² + 8y)

Based on the information, x-coordinates of the points on the curve where the tangent line is horizontal will be option A.

Learn more about coordinate on

https://brainly.com/question/17206319

#SPJ1

The ratio of whites to blacks is 20 to 3 ( or 20/3) in United States in 1990.

From a survey of the population of the United States, a circle graph (or, pie chart) was created on the information,

Population of the United States in 1990 :

White consists of 80%

American Indian, Eskimo, and Aleut consists of 1%

Black consists of 12%

Asian and Pacific Islander consists of 3%

Other Races consists of 4%

Let say the total population of the United States in 1990 was x.

By applying the formula of percentage to numbers we get,

The number of people who were white in 1990 in United States = 80% of x

= [tex][\frac{80}{100} ]x[/tex] = [tex]\frac{4}{5} x[/tex]

The number of people who were black in 1990 in United States = 12% of x

= [tex][\frac{12}{100} ]x[/tex] = [tex]\frac{3}{25} x[/tex]

Thus, we can calculate ratio as,

Ratio of whites to blacks = [tex]\frac{\frac{4}{5} x}{\frac{3}{25} x}[/tex] = 20/3

To know more about ratio here

https://brainly.com/question/1504221

#SPJ1