Jane paid $40 for an item after she received a 20% discount. Jane's friend says this means that the original price of the item was $48. Determine if Jane's friend is correct about the original price of the item.

Answer:

Step-by-step explanation:

A=(b1+b2)h/2

The volume of the candle is approximately 94 cubic inches.

A circular cylinder is a three-dimensional solid object made up of two parallel and congruent circular bases and a curving surface connecting the bases.

The volume of a right circular cylinder is given by the formula:

V = πr²h

Where

Substituting the given values into the formula, we get:

V = 3.14 x 2² x 7.5

V = 3.14 x 4 x 7.5

V = 94.2

Rounding to the nearest cubic inch, we get:

V ≈ 94 cubic inches

Therefore, the volume of the candle is approximately 94 cubic inches.

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Answer:

A) 4%

B) 20%

Step-by-step explanation:

As, A) we will take 60,000/240000 x 100% so that we can find the percentage.

So the answer = 4%

B) for $12,000, 12, 000/240000 x 100%

Answer = 20%

A) The percentage is 4%

B) The percentage is 20%

Given that,

(a)

\(= 60,000\div 240000\)

= 4%

(b)

\(= 12, 000\div 240000\)

= 20%

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Answer:

x=15

Step-by-step explanation:

5x+25=100

Subtract 25 from both sides.

5x+25−25=100−25

5x=75

Divide both sides by 5.

5x÷5=75÷5

x=15

\(5x+25=100\\x=\)

Subtract 25 from both sides:

\(5x+25-25=100-25\\5x=75\)

Divide both sides by 5:

\(\frac{5x}{5} =\frac{75}{5}\)

\(\fbox{x=15}\)

Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Step-by-step explanation:

please make sure that fractions are still in the problem text after scanning it.

because they are missing here, and I have to guess around.

Basically the problem is

x + 1/a × x = 15

that means

ax + x = 15a

(a+1)x = 15a

x = 15a/(a+1)

for a = 2 (so, 1/2 x is added to x), we get

x = 15×2/3 = 30/3 = 10

for a = 4 (1/4 of x is added to x), we get

x = 15×4/5 = 60/5 = 12

these are also the first 2 answer options. so, please pick the one that fits the complete problem definition.

the 3rd and 4th answer options are nonsense anyway, as when you add something greater than 0 to x and get 15, then the initial x cannot be already 15 or even bigger.

Answer: Samantha is 13 years old and Jennifer’s age is 10 years old.

Because it said she was 3 years older, which means 13 +10 = 23.

Step-by-step explanation:

I think.

Samantha age is 7 years and Jennifer age is 4 years.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Samantha is 3 years older than Jennifer.

let Jennifer age be x.

So, Samantha age= x + 3

Now, The square of Jennifer's age plus Samantha's age is equal to 23.

x²+ (x+ 3) = 23

x² + x + 3 = 23

x² + x - 20 = 0

(x- 4) ( x + 5) = 0

x= 4, -5

Hence, Samantha age is 7 years and Jennifer age is 4 years.

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The required length of the rectangle is 89 m.

Given that,
The area of a rectangular field is 6942 m. If the width of the field is 78 m, what is its length is to be determined.

Perimeter is the measure of the figure on its circumference.

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

The area of the rectangle = length * width
                                6942  = length * 78
                                length = 89 m

Thus, the required length of the rectangle is 89 m.

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The required in order for Micaela to end up with ,n = 365 , t = 12, P = $360, and A = $670

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from

A binary relation from A to B is made up of these ordered pairs (a,b),

A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), here the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

According to our question-

r=7.5%

Thus, 7.5% would be required in order for Micaela to end up with $670.

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Answer:

(-2, 1/9)  (-1, 1/3)  (0,1) (1,3) (2,9)

the right graph is graph B

Step-by-step explanation:

To find the y values, input each of the x values in the function and solve them with a calculator. The negative x values may give decimals, but if you start with the positive ones first, you'll notice a pattern in the graph, which will help you figure out what the fraction form of the decimals are.

Once you have the table, use the table to find the points on the right graph.

Answer:

Cumulative Frequency:

The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.

The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.

Step-by-step explanation:

If the function is continuous function and ∫0 to 8 f(u) du = 6, the value of ∫ 1 to 3 xf(x² - 1) dx is B) 3.

Given ∫0 to 8 f(u) du = 6 and we need to find the value of ∫ 1 to 3 xf(x² - 1) dx

We can say, u = x² - 1

Differentiating both sides

du = 2x dx

dx = du/2x

When x = 1,

         u = 1² - 1 = 0

and when x = 3

         u = 3² - 1 = 8

So, ∫ 1 to 3 xf(x² - 1) dx can be written as

           ∫ 1 to 3 xf(x² - 1) dx = ∫ 0 to 8 xf(u)  du/2x

                                          = 1/2∫ 0 to 8 f(u) du

It is given that ∫0 to 8 f(u) du = 6

So, ∫ 1 to 3 xf(x² - 1) dx = 1/2 x 6 = 3

Hence, the value of ∫ 1 to 3 xf(x² - 1) dx is 3.

The question is incomplete. The complete question is

" The function f is continuous and ∫0 to 8 f(u) du=6. What is the value ∫ 1 to 3 xf(x² - 1) dx? (A) 3/2 (B) 3 (C) 6 (D) 12 (E) 24 "

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Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.

Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.

To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.

On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.

Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.

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GIVEN:

We are told that Karen bought 2 jackets, 2 blouses and 2 skirts.

If she wears a jacket-blouse-skirt combination each day,

Required;

How many combinations can she wear using her new items of clothing?

Step-by-step solution;

For the items of cloting that she has, Karen can wear 2 jackets with any blouse-skirt combination. Also, she can wear 2 blouses with any jacket-skirt combination. And then she can wear 2 skirts with any jacket-blouse combination.

In other words, she can combine all items of clothing as follows;

ANSWER:

The correct answer is option D.

Karen has 8 different combinations

The number of ways to replace all the -1s in the array is zero.

The array can be represented as a wave if and only if the number of -1s is even. This is because each -1 must be replaced with a positive integer in order to create a wave, and replacing one -1 with a positive integer will create a new -1 on the opposite side of the wave. Therefore, if there are an odd number of -1s, it is impossible to create a wave.

In the given array, there are 7 -1s, which is an odd number. Therefore, it is impossible to replace the -1s with positive integers in such a way that the resulting array can be represented as a wave.

The number of ways to replace the -1s with positive integers in the range 1 to m is:

(m^7) mod (10^9) = (m^7)

However, since it is impossible to create a wave with this array, the final answer is 0.

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The coordinates 73.355°N and 101.476°E can be converted from decimal degrees (DD) to degrees, minutes, and seconds (DMS) format. The rounded values in DMS are 73°21'18" N and 101°28'34" E.

To convert 73.355°N from DD to DMS, we start by extracting the whole number of degrees, which is 73°. Next, we need to convert the decimal part into minutes and seconds. Multiply the decimal by 60 to get the number of minutes. In this case, 0.355 * 60 = 21.3 minutes. Rounding to the nearest whole number, we have 21 minutes. Finally, to convert the remaining decimal part into seconds, we multiply by 60. 0.3 * 60 = 18 seconds. Rounding to the nearest whole second, we get 18 seconds. Combining all the values, we have 73°21'18" N.

For the coordinates 101.476°E, we follow the same steps. The whole number of degrees is 101°. Multiplying the decimal part, 0.476, by 60 gives us 28.56 minutes. Rounding to the nearest whole number, we have 29 minutes. The remaining decimal part, 0.56, multiplied by 60 gives us 33.6 seconds. Rounding to the whole second, we get 34 seconds. Combining all the values, we have 101°28'34" E.

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The coordinates of P after the circle rotates the given amount counterclockwise around its center include the following:

1/3 of a full rotation = (-1/2, √3/2).

1/2 of a full rotation = (-1, 0).

2/3 of a full rotation = (-1/2, -√3/2).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

For 1/3 of a full rotation, we have the following:

Xp = 1cosθ = 1cos(360/3) = 1cos(120) = -1/2.

Yp = 1sinθ = 1sin(360/3) = 1sin(120) = √3/2.

P' = (-1/2, √3/2).

For 1/2 of a full rotation, we have the following:

P' = (-1, 0).

For 2/3 of a full rotation, we have the following:

Xp = 1cosθ = 1cos(360 × 2/3) = 1cos(240) = -1/2.

Yp = 1sinθ = 1sin(360 × 2/3) = 1sin(240) = -√3/2.

P' = (-1/2, -√3/2).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The equivalent logical expressions are (I) and (III) only. The correct answer is D.

Let's analyze each expression:

1. (x == y && x != z) || (x != y && x == z):

This expression evaluates to true if either (x == y) and (x != z) are both true, or (x != y) and (x == z) are both true. It implies that either x is equal to y and not equal to z, or x is not equal to y and equal to z. This can also be written as (x == y) XOR (x == z), where XOR represents the exclusive OR operation. However, this expression is not equivalent to the other options.

2. (x == y || x == z) && (x != y || x != z):

This expression evaluates to true if both (x == y || x == z) and (x != y || x != z) are true. It implies that either x is equal to y or x is equal to z, and at the same time, either x is not equal to y or x is not equal to z. However, this expression is not equivalent to the others.

3. (x == y) != (x == z):

This expression evaluates to true if (x == y) and (x == z) have different truth values. It implies that x is equal to y and not equal to z, or x is not equal to y and equal to z. This expression is equivalent to expression (I).

Therefore, the correct answer is D. I and III only.

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To find the population of the city, we need to find the total number of people living in the city. We know that there are 1350 people per square mile, so we can find the total number of people by multiplying the number of square miles in the city by the number of people per square mile.

The area of the city is the length times the width, so:

Area = Length x Width

Area = 12 miles x 8 miles

Area = 96 square miles

Now, we can find the population by multiplying the area by the number of people per square mile:

Population = Area x People per square mile

Population = 96 square miles x 1350 people per square mile

Population = 129,600 people

Therefore, the population of the city is 129,600 people.

Hope this helps!

The correct answer is option (a) Not quite - it is a more complicated method than a SRS, but the data is representative of all American adults.

The General Social Survey (GSS) is a nationally representative survey of the adult population of the United States. The GSS uses a multistage area probability sample design, which means that the sample is selected in two or more stages, with the first stage being the selection of primary sampling units (PSUs) and the second stage being the selection of households or individuals within PSUs.

While the GSS does not use a simple random sampling method, the survey design is intended to provide a representative sample of the U.S. adult population. The GSS employs a complex sampling design that takes into account stratification, clustering, and oversampling of certain groups, such as African Americans, Hispanics, and Asian Americans. This design is intended to improve the precision of estimates for these groups, which may be small in number in the overall population.

Therefore, the correct option is (a) Not quite - it is a more complicated method than a SRS, but the data is representative of all American adults.

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Answer: Greater than 10.

The general solution for the given differential equation is:

x(t) = c₁ × \(e^{2/7}\)i × t) + c₂× [\(e^{-1/7}\)t ×cos((3/7)t) + \(e^{-1/7}\)t × sin((3/7)t)]

To solve the given second-order linear ordinary differential equation, we can use the standard method for solving homogeneous equations with constant coefficients. Let's proceed with solving the equation step by step.

The given equation is:

m × d²x/dt² + b × dx/dt + k × x = 0

Step 1: Rewrite the equation in standard form

Divide the entire equation by m to obtain:

d²x/dt² + (b/m) × dx/dt + (k/m) × x = 0

Now, we can substitute the given values:

m = 17500 kg

k = 3500 N/m

b = 5000 N

The equation becomes:

d²x/dt² + (5000/17500) × dx/dt + (3500/17500) × x = 0

Simplifying further:

d²x/dt² + (2/7) × dx/dt + (1/5) × x = 0

Step 2: Find the characteristic equation

Let's assume a solution of the form x(t) = \(e^{rt}\), where r is a constant.

Differentiating x(t) with respect to t, we get:

dx/dt = r\(e^{rt}\)

Differentiating again, we have:

d²x/dt² = r²\(e^{rt}\)

Substituting these expressions into the differential equation, we get:

r²\(e^{rt}\) + (2/7)r\(e^{rt}\)+ (1/5)\(e^{rt}\)= 0

Factoring out \(e^{rt}\), we get:

\(e^{rt}\)(r² + (2/7)r + (1/5)) = 0

Since \(e^{rt}\) is never zero, the expression in parentheses must equal zero:

r² + (2/7)r + (1/5) = 0

Step 3: Solve the quadratic equation

To solve the quadratic equation, we can use the quadratic formula:

r = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 1, b = 2/7, and c = 1/5. Substituting these values into the formula, we have:

r = (-(2/7) ± √((2/7)² - 4(1)(1/5))) / (2(1))

Simplifying further:

r = (-2/7 ± √(4/49 - 4/5)) / 2

r = (-2/7 ± √(4/49 - 40/49)) / 2

r = (-2/7 ± √(-36/49)) / 2

The discriminant is negative, indicating complex roots. Let's simplify further:

r = (-2/7 ± √(-1) × √(36/49)) / 2

r = (-2/7 ± (6/7)i) / 2

Splitting into two cases:

Case 1: r = (-2/7 + (6/7)i) / 2 = (2/7)i

Case 2: r = (-2/7 - (6/7)i) / 2 = -1/7 - (3/7)i

Step 4: General solution

Since we have complex roots, the general solution for the differential equation will involve sinusoidal functions.

Case 1: For r = (2/7)i, the corresponding solution is:

x₁(t) = \(e^{2/7}\)i × t)

Case 2: For r = -1/7 - (3/7)i, the corresponding solution is:

x₂(t) = \(e^{-1/7}\) × t× cos((3/7)t) + \(e^{-1/7}\)t × sin((3/7)t)

The general solution for the differential equation is the linear combination of these solutions:

x(t) = c₁ × x₁(t) + c₂ × x₂(t)

where c₁ and c₂ are arbitrary constants.

Therefore, the general solution for the given differential equation is:

x(t) = c₁ × \(e^{2/7}\)i × t) + c₂× [\(e^{-1/7}\)t ×cos((3/7)t) + \(e^{-1/7}\)t × sin((3/7)t)]

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In the given scenario, the average current produced within the loop is approximately 2.13 A.

We can begin by computing the change in magnetic flux across the loop as it expands to determine the average current generated within the loop.

The following equation provides the magnetic flux across a loop:

Φ = B * A * cos(θ)

ΔΦ = B * ΔA

ΔA = A₂ - A₁ = π * (1.00 m)² - π * (0.40 m)² = π * (1.00² - 0.40²) = π * (1.00 + 0.40)(1.00 - 0.40) = π * (1.40)(0.60) = 0.84π m²

So,

ΔΦ = B * ΔA = (24 mT) * (0.84π m²) = 20.25π m²·T

emf = ΔΦ / Δt = (20.25π m²·T) / (1.0 s) = 20.25π V

As:

emf = I * R

So, again

I = emf / R = (20.25π V) / (30 Ω) ≈ 2.13 A

Thus, the average current produced within the loop is approximately 2.13 A.

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Answer:

120 sq ft.

Step-by-step explanation:

REMEMBER: Area is found by multiplying one side, by the other side that isn't the same length as it.

Multiply 12 by 10 to get 120

120 is the area of the bedroom

Answer:

a. 1.26

b. 0.1038

Step-by-step explanation:

The p-value is 1.0000 (rounded to four decimal places). This means that we fail to reject the null hypothesis, which in this case would be that the population mean is equal to the sample mean of 26.2.

To find the test statistic, we need to use the formula:

test statistic = (sample mean - population mean) / (standard deviation / square root of sample size)

Since the population standard deviation is given as 6, we can plug in the values:

test statistic = (26.2 - population mean) / (6 / √40)

To find the population mean, we can use the fact that the sample mean is an unbiased estimator of the population mean, so:

population mean = sample mean = 26.2

Plugging in the values, we get:

test statistic = (26.2 - 26.2) / (6 / √40) = 0

The test statistic is 0.

To find the p-value, we need to use a t-distribution table or calculator. Since we have a sample size of 40, we can use the t-distribution with 39 degrees of freedom.

Using a calculator or table, we can find that the area to the right of 0 (since the test statistic is 0) is 0.5. Since this is a two-tailed test, we need to double this value to get the p-value:

p-value = 2 * 0.5 = 1.0000
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The volume of the solid S in the given question is 5.48unit³.

A three-dimensional space's occupied volume is measured.

It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.

The definition of length and volume are connected.

So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.

An equilateral triangle's height is determined by:

\(h = sSin60 = \frac{\sqrt{3} }{2} s\)

Consequently, one triangle's area is:

\(A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2\)

The line equation that depicts the diagonal is:

\(\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}\)

This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.

\(\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}\)

Therefore, the volume of the solid S in the given question is 5.48unit³.

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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.

Answer:

16 birds

8 mammals if you need to know.

Step-by-step explanation:

We can set this system of equations up by plugging the 2m from the second equation into where it says r in the first equation. The reason why we do this is because

The 2m is equal to r, so we can replace the r in the first equation with 2m, since they are equal.

Divide both

We can confirm this because

uh

(I like the enter key lol.)

It's the return key on some keyboards in other countries.

Oh yeah.

We can confirm the values.

If there are 16 birds, there is probably going to be a total of 32 legs.

With 8 mammals, it is something like 8 x 4, which is 32

32 + 32 = 64, which is the total.

To obtain the equation that models the balance in Dawn's savings account, the following steps are necessary:

Step 1: Interprete the question in terms of the values provided, as follows: