The length of a rectangle is 2 inches more than 2 times the width. If the area of the rectangle is 40
square inches, find the length and the width.

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 preimage of the quadrilateral is in the second quadrant. The quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

A quadrilateral is a geometric shape that consists of four straight sides and four angles. It is a two-dimensional shape, also known as a 2D polygon, and can be defined as any closed shape that has four sides. There are many different types of quadrilaterals, each with its own unique set of characteristics.

The second quadrant is characterized by negative x-coordinates and positive y-coordinates, while the fourth quadrant has positive x-coordinates and negative y-coordinates.

If the preimage of the quadrilateral is in the second quadrant, then its x-coordinates are negative and its y-coordinates are positive.

When the quadrilateral is reflected across the x-axis, its x-coordinates will remain the same but its y-coordinates will become negative. Therefore, if the preimage is in the second quadrant and the quadrilateral is reflected across the x-axis, the image would lie in the fourth quadrant.

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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: The two lists that are in order from least to greatest are:

C) 0.005, 0.045, 0.102, 0.63

and

E) 7.045, 7.452, 7.599, 7.604

Step-by-step explanation:

To determine which lists are in order from least to greatest, we need to compare the values and arrange them accordingly. Here is the explanation for the two correct answers:

C) 0.005, 0.045, 0.102, 0.63

This list is already in order from least to greatest. Starting from the smallest value of 0.005, each subsequent value increases until we reach the largest value of 0.63.

E) 7.045, 7.452, 7.599, 7.604

This list is also in order from least to greatest. Starting from the smallest value of 7.045, each subsequent value increases until we reach the largest value of 7.604.

For the other options:

A) 117.51, 17.382, 17.38, 17.23 - This list is not in order from least to greatest.

B) 452.8, 45.18, 452.28, 453.71 - This list is not in order from least to greatest.

D) 2.452, 2.749, 2.981, 2.994 - This list is not in order from least to greatest.

Therefore, the two lists that are in order from least to greatest are C (0.005, 0.045, 0.102, 0.63) and E (7.045, 7.452, 7.599, 7.604).

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

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)

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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.

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Answer:0.125

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

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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 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

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If θ=2 rad then the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

In this problem, we are given that when the arc length is equal to the radius (S=r), the angle is 1 radian (θ = 1 rad). Now, we are asked to find the condition when the angle is 2 radians (θ = 2 rad).

If Θ=1 rad when S=r, it means that when the angle subtended by an arc of length r is 1 radian, then the radius of the circle is also r.

Now, if θ=2 rad, we can use the same proportionality to find the arc length S that corresponds to this angle. Since the angle has doubled, we can expect the arc length to double as well. Therefore, we have:

θ/Θ = S/r

2/1 = S/r

S = 2r

Thus, the condition when θ=2 rad is that the arc length S is equal to twice the radius r.

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Answer: the correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,4π3) tell us the radius r=4 and the angle θ=4π3. So the point should be on the circle labeled 4 and form an angle of 4π3 with the positive x-axis. Point B is the correct point.

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.

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Answer:

x = 4√3 y = 8/√2 = 4√2

(4 rad 3) (4 rad 2)

The areas of each figure are 5.6 sq m, 76.8 sq km, 280.8 sq units, 173.88 sq units and 332 sq units

The area of a shape is the amount of space on it

Using the above as a guide, we have the following:

Figure 7:

The area is calculated as

Area = 1/2 * (sum of parallel sides) * height

So, we have

Area = 1/2 * (3.9 + 1.7) * 2

Area = 5.6 sq m

Figure 8:

The area is calculated as

Area = Base * height

So, we have

Area = 9.6 * 8

Area = 76.8 sq km

Figure 9:

The area is calculated as

Area = 6 * 1/2 * Base * height

So, we have

Area = 6 * 1/2 * 9 * 10.4

Area = 280.8 sq units

Figure 10:

The area is calculated as

Area = 7 * 1/2 * Base * height

So, we have

Area = 7 * 1/2 * 6.9 * 7.2

Area = 173.88 sq units

Figure 11:

The area is calculated as

Area = 8 * 1/2 * Base * height

So, we have

Area = 8 * 1/2 * 10 * 8.3

Area = 332 sq units

Figure 12, 13 and 14:

The areas of the figures cannot be calculated with the available details and parameters

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In linear equation., both quantities are different from each other.

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.

Taking LHS

  5 2/3 - 3 3/4= 17/3 - 15/4

  17/3 - 15/4 =  68 - 45/12  = 23/12

now solving RHS

  1+2/3+3/4  = 12 + 8 + 9/12  = 29/12

clearly, LHS≠ RHS

hence both quantities are different from each other.

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Here we have an exponential growth were the increase is of 26%, and it can be written as.

[tex]y = a*(1 + 0.26)^t[/tex]

Here we want to rewrite the function

[tex]y = a*(2)^{t/3}[/tex]

In the given form for the general exponential, so let's do that.

We can expand the product to get:

[tex]y = a*(2)^{t/3}\\\\y = a*((2)^{1/3})^t\\\\y = a*(1.26)^t\\\\y = a*(1 + 0.26)^t[/tex]

To identify if it is a growth or a decay we need to see the sign of r (the thing we are adding to the 1) in this case is +0.26

When it is positive we have a growth, so here we have a growth.

And to get the percentage multiply that number by 100%, we will get:

0.25*100% = 26%

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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.

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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.

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The complete question is:

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

Answer:

  90

Step-by-step explanation:

You want to know the number of times in 360 trials that the same letter will appear twice in a row using a fair 4-letter spinner.

The table shows 4 outcomes of the 16 possible that have the same letter repeated. That's a probability of a repeated letter of 4/16 = 1/4.

The expected number of repeated letters in 360 trials is the number of trials times the probability of a repeat:

  expected repeats = 360 × 1/4 = 90

You predict there will be 90 repetitions in 360 trials.

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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.

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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

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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

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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

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Answer:

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

Step-by-step explanation:

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.

c=25/9 for the given condition of the bionomial.

We can solve this problem by using the technique of completing the square.

First, let's assume that [tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial:

[tex](3x + b)^2 = 9x^2 + 6bx + b^2[/tex]

If we compare the above expression with [tex]9x^2 + 10x + c[/tex], we can see that:

6bx = 10x, which implies that b = 5/3

b^2 = c, which implies that [tex]c = (5/3)^2 = 25/9[/tex]

Therefore, c = 25/9 is the constant that satisfies the condition

[tex]9x^2 + 10x + c[/tex] is equal to the square of a binomial.

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Answer:

16.39 square units.

Step-by-step explanation:

The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.

To see this, we can use the Pythagorean identity for sine and cosine:

sin^2 t + cos^2 t = 1

Multiplying both sides by 9, we get:

9 sin^2 t + 9 cos^2 t = 9

Substituting x = sin t and y = 3 cos t, we get:

9 x^2 + y^2/3 = 9

This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.

The area of an ellipse is given by the formula:

Area = pi * a * b

Substituting the values of a and b, we get:

Area = pi * 3 * sqrt(3) ≈ 16.39

Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.

$[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.

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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.

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Answer:you need to include the expression

Step-by-step explanation:

once you have the expression, substitute the numbers given for each variable and use order of operations to