Grace bought a pair of pants on sale for $24, which is 60% off the original price. What was the original price of the pants?

Step-by-step explanation:

Shift to the L 7 units    ( x+7)^2

Shift down 4       (x+7)^2    - 4  

In a right-angle triangle, a sine function of an angle [tex]\theta[/tex] is equal to the opposite side to [tex]\theta[/tex] divided by hypotenuse.

[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\text{y = f(x)} \rightarrow \text{x}[/tex] in the domain of f. Trigonometric functions are periodic, therefore each range value is within the limitless domain values (no breaks in between). Since trigonometric functions have no restrictions, there is no inverse.

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle. Let’s say [tex]\theta[/tex] is the angle, then:

[tex]\text{Sin} \ \theta = \dfrac{\text{Opposite side to} \ \theta}{\text{Hypotenuse}}[/tex]

[tex]\text{Or} \ \theta = \text{Sin-}1 \ \dfrac{\text{Opposite side to}\ \theta}{\text{Hypotenuse}}[/tex]

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The value of angle ADC is 131⁰.

The value of angle AOC is 262⁰.

The value of angle BAT is 21⁰.

The value of angle ADC is calculated as follows;

The value of the angle at center, AOC = 2 ∠CBA (angle at center is twice angle at circumference)

∠AOC = 2 x 131⁰

∠AOC = 262⁰

The value of arc angle ABC = 262⁰ (intersecting chord theorem)

The value of angle ADC is calculated as;

∠ADC = ¹/₂ arc ABC

∠ADC = ¹/₂ x 262⁰

∠ADC = 131⁰

Angle DAB = 180 - (20 + (131 - 20))

∠DAB = 180 - 131 = 49

The value of angle BAT is calculated as;

∠BAT = 90 - (20 + 49)

∠BAT = 21⁰

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Answer: The answer is A (40 m)

Step-by-step explanation:

Assuming that the person transfers their savings to the highest available account as soon as they reach the required minimum amount, the total amount saved at the end of 25 years can be calculated as follows:

Step:1. For the first year, the person saves $4000 in the ordinary account and earns 6% interest, resulting in a total of $4240.
Step:2 In the second year, the person has $8240 and can transfer it to the 'extra' account to earn a higher interest rate of 7%. After one year, they will have $8816.80.                                                                                                                          Step:3. In the third year, the person has $12816.80 and can transfer it to the 'superextra' account to earn the highest interest rate of 8%. After one year, they will have $13856.22.
Step:4. For the remaining 22 years, the person continues to save $4000 at the beginning of each year and transfers their savings to the 'superextra' account to earn 8% interest. At the end of 25 years, they will have a total of $227,217.97.
Therefore, the total amount saved at the end of 25 years, assuming that the money is transferred to a higher-interest account at the earliest opportunity, is $227,217.97.

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We need additional information, such as a dataset or summary statistics to perform a normality test.

To determine if the data is normally distributed, we need to look at the distribution of the variable of interest. In this case, we are interested in the distribution of social conservatism scores.

If we have access to the data, we can use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to determine if the data is normally distributed. However, since we only have information about the population average and effect size, we cannot directly test for normality.

However, based on the central limit theorem, we can assume that if the sample size is large enough (typically >30), the distribution of the variable of interest will be approximately normal. In this case, since we do not have information about the sample size, we cannot definitively say if the data is normally distributed.

In summary, without more information about the sample size or access to the data, we cannot determine if the data is normally distributed.

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The point estimates for p and q are 0.6636 and 0.3364 respectively, where p is the population proportion for the  condition.

To find the point estimates for p and q, you will need to consider the given information about the population proportion, follow the given steps:

1. The total number of adults in the study is 4374.
2. Out of these, 2903 adults think mainstream media is more interested in making money than in telling the truth.
3. To find the point estimate for p (the proportion of adults who think mainstream media is more interested in making money), divide the number of adults who think this way by the total number of adults in the study:

p = 2903/4374 = 0.6636 (rounded to four decimal places)

4. Now, to find the point estimate for q (the proportion of adults who do not think mainstream media is more interested in making money), subtract p from 1:

q = 1 - p = 1 - 0.6636 = 0.3364 (rounded to four decimal places)

So, the point estimates for p and q are 0.6636 and 0.3364, respectively.

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In order to solve a system by substitution, you want to isolate a variable in one equation and then substitute it into the other equation.

Given that;

To complete the sentence for solving the system of equation.

Now, We know that;

Once you have substituted the variable, you can solve for the remaining variable(s) and find the solution to the system.

Hence, In order to solve a system by substitution, you want to isolate a variable in one equation and then substitute it into the other equation.

Therefore, Option C is true.

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Answer: 225 degree

5/8of full rotation is 225degrees

Answer:

0.625

Step-by-step explanation:

hope the his helping

The volume of the object is  52in³

The formula for the calculating the volume of the cylinder is expressed as;

V = πr²h

Given that the parameters are;

Substitute the values

Volume = 3 × 2² × 3

Multiply the values

Volume = 36 in³

The volume of a sphere is;

Volume = 4/3 ×3 × 2²

Multiply the values

Volume = 16 in³

Total volume = 16 + 36 = 52in³

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Answer:

Step-by-step explanation:

The constant of proportionality between d and h is 3.75

Any function in which the dependent variable (y) is obtained by multiplying the independent variable (x) by a constant value is called the direct proportionality function. This function is also expressed in the form  [tex]( y = m * x)[/tex] and is more commonly called a linear function.

The value m is a constant and is known as the constant of proportionality or the slope of the line. It represents the inclination of the line to the abscissa axis, that is, the x-axis. If we talk about graphic representation, this linear function is a line with slope m that passes through the origin of coordinates, that is, the point 0 in x and 0 in y, which is the point (0,0).

Bethany finds the distance d with the help of equation d = 3.75*h, she travels this distance while walking for h number of hours.  When we compare it with the direct proportionality function y = m * x, then y is represented by the distance d, x is represented by the number of hours h, and slope m or the constant of proportionality is the number 3.75.

So, the constant of proportionality between d and h is 3.75.

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The statistics that is the most appropriate is option 2 from the image I added. [tex]Z = \frac{0.34 - 0.25}{\sqrt{\frac{0.3(1 - 0.3)}{50}+\frac{0.3(1 - 0.3)}{40} } }[/tex]

We have to find the proportion 1

= 17 / 50

= 0.34

Then we find the proportion 2

= 10 / 40

= 0.25

the proprotion = 17 + 10 / 50 + 40

= 27 / 90

= 0.3

Then the value of n1 = 50 and the value of n2 = 40

If we are to find the test statistics

The formula that we would use after inputting the values would be given as

[tex]Z = \frac{P1 - P2}{\sqrt{p(1 - p)\frac{1}{n1}+\frac{1}{n2} } }[/tex]

We will have

[tex]Z = \frac{0.34 - 0.25}{\sqrt{0.3(1 - 0.3)\frac{1}{50}+\frac{1}{40} } }[/tex]

When we expand we will have

[tex]Z = \frac{0.34 - 0.25}{\sqrt{\frac{0.3(1 - 0.3)}{50}+\frac{0.3(1 - 0.3)}{40} } }[/tex]

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The probabilities are: (a) 12/13 (b) 1/13 (c) 0 (d) 1 7/26. (a) The probability of drawing a card above a jack is 48/52 or 12/13. This is because there are 48 cards above a jack and 52 total cards in the deck.

(b) The probability of drawing a card below a 2 is 4/52 or 1/13. This is because there are only 4 cards (A, K, Q, J) that are above a 2, and there are 52 total cards in the deck.

(c) To find the probability that a card is both above a jack and below a 2, we need to find the number of cards that satisfy both conditions. There are no cards that satisfy both conditions, so the probability is 0/52 or 0.

(d) To find the probability that a card is either above a jack or below a 5, we need to find the number of cards that satisfy either condition. There are 48 cards above a jack and 20 cards below a 5 (A, 2, 3, 4), but we need to subtract the overlap (cards that are both above a jack and below a 5), which is only 2 (A and 2). So the total number of cards that satisfy either condition is 48 + 20 - 2 = 66. The probability is then 66/52 or 33/26, which simplifies to 1 7/26.

In summary, the probabilities are:
(a) 12/13
(b) 1/13
(c) 0
(d) 1 7/26

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The pair of points to be used is k and M.

A line of best fit is a straight line which is used to show the relations among non-linear points in a scatter plot. Thus it evenly varies the points on its two sides. This is majorly used when dealing with a cartesian coordinate, or plotted points on a graph.

Considering the given scatter plot, it can be observed that points J, L, M and K on non-linear. Thus the straight line that can be used to as line of best fit is by joining point K and M.

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We cannot get Equation B from Equation A as they are fundamentally different.

Equation A, 5x = 3x, is a linear equation with variables on one side and constants on the other side. To solve this equation for x, we can subtract 3x from both sides to get:

5x - 3x = 2x

Therefore, the solution to Equation A is x = 0 or x = any other real number.

On the other hand, Equation B, 5 = 3, is a statement of equality between two constants. There is no variable in this equation to solve for, and it is always false since 5 is not equal to 3.

Thus, there is no way to derive Equation B from Equation A or vice versa.

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Answer:160

Step-by-step explanation:

multiply the expressions

If Roland has Z-score for his test 0.6, the standard deviation for this set of test scores is 7.5

To find the standard deviation for this set of test scores, we can use the z-score formula:

Z-score = (X - μ) / σ

Where:
- Z-score is 0.6 (given)
- X is Roland's score of 70
- μ is the mean score of 65.5
- σ is the standard deviation we need to find

Now we can plug in the values and solve for σ:

0.6 = (70 - 65.5) / σ

Next, we can rearrange the equation to solve for σ:

σ = (70 - 65.5) / 0.6

Finally, calculate the standard deviation:

σ = 4.5 / 0.6

σ ≈ 7.5

The standard deviation for this set of test scores is approximately 7.5.

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The Laplace transform of the given function f(t) is [tex]L{f(t)} = (2/s^3) ~e^{-s}[/tex]

We have,

The given function can be represented in terms of unit step functions as follows:

f(t) = 0 for 0 ≤ t < 1

f(t) = t² for t ≥ 1

Using the unit step function u(t), we can express f(t) as:

f(t) = 0 x u(t) + t² x u(t - 1)

Apply the linearity property of the Laplace transforms and use the Laplace transform of the unit step function u(t-a), which is [tex]1/s ~e^{-as}:[/tex]

[tex]L{f(t)} = L{0 \times u(t)} + L{t^2 ~ u(t - 1)}\\= 0 \times L{u(t)} + L{t^2} ~ L{u(t - 1)}\\= 0 + L{t^2} ~ e^{-s \times 1}\\= L{t^2} ~ e^{-s}[/tex]

Using the Laplace transform property [tex]L{t^n} = n!/s^{n+1},[/tex] where n is a positive integer,

[tex]L{t^2} = 2!/s^{2+1}\\= 2!/s^3\\= 2/s^3[/tex]

Therefore,

The Laplace transform of the given function f(t) is [tex]L{f(t)} = (2/s^3) ~e^{-s}[/tex]

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It will take time of 33.93 minutes for all of the water to pass through the cone.

To find the volume of the cone-shaped vessel, we need to use the formula for the volume of a cone:

V = (1/3) x pi x r² x h

V = (1/3) x 3.14 x 6^2 x 3

= 339.29 cubic inches

This is the total volume of water that needs to pass through the cone.

If water is dripping out at a rate of 10 cubic inches per minute, we can use the formula:

time = volume / rate

to find how long it will take for all of the water to pass through. Substituting the values we found, we get:

time = 339.29 / 10

=33.93 minutes

Therefore, it will take 33.93 minutes for all of the water to pass through the cone.

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The present value of $9,800 at the end of 4 years with a 6% monthly compounded rate is $7,996.84.

To find the present value of $9,800 at the end of 4 years with a 6% monthly compounded rate, we need to use the present value table.

First, we need to find the monthly compounded rate. The annual interest rate is 6%, so the monthly rate is

6/12 = 0.5%

Next, we need to find the PV factor. From the present value table 12.3, the PV factor for 48 periods at 0.5% monthly rate is 0.8138.

Now, we can calculate the present value:

PV = 9,800 × 0.8138

=7,996.84

Therefore, the present value of $9,800 at the end of 4 years with a 6% monthly compounded rate is $7,996.84.

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Answer:

all yes

Step-by-step explanation:

We can find that this probability is 0.99994, rounded to five decimal places.

Based on the given statistic, we know that 80% of vehicles using the Lincoln Tunnel use E-ZPass. Therefore, we can expect that out of the 12 randomly selected vehicles, 80% or 0.8 * 12 = 9.6 vehicles would use E-ZPass. Rounding to the nearest whole number, we would expect 10 of the 12 vehicles to use E-ZPass.

The mode of the distribution is 10, as this is the most frequently occurring value in the sample.

Since 10 out of 12 vehicles is the mode, the probability associated with the mode is the proportion of vehicles that use E-ZPass in the sample. Therefore, the probability associated with the mode is 10/12 or 0.833, rounded to three decimal places.

The probability of four or more vehicles using E-ZPass can be calculated using the binomial distribution. The probability of a single vehicle using E-ZPass is 0.8, and the probability of a single vehicle not using E-ZPass is 0.2. The probability of four or more vehicles using E-ZPass is the sum of the probabilities of selecting 4, 5, 6, 7, 8, 9, 10, 11, or 12 vehicles that use E-ZPass. Using Excel or a calculator, we can find that this probability is 0.99994, rounded to five decimal places.

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The estimated salary for an employee with 18 years of experience is $65,856.46.

To find the estimated salary for an employee with 18 years of experience using the given regression equation, follow these steps:

1. Identify the regression equation: Estimated Salary = 21,640.90 + 2456.42 (Years of Experience)

2. Substitute the given years of experience (18 years) into the equation:

Estimated Salary = 21,640.90 + 2456.42(18)

3. Multiply 2456.42 by 18: 2456.42(18) = 44,215.56

4. Add 21,640.90 to the result from step 3: 21,640.90 + 44,215.56 = 65,856.46

The estimated salary for an employee with 18 years of experience is $65,856.46.

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Answer: 1.02

Step-by-step explanation:

2.67 - 1.65 =  1.02

Answer: The data is skewed because most text messages are replied to and cause the number to be at least twice what it was originally.

Step-by-step explanation: The data is left-skewed.

The  statement about probability that is true is option The probability of landing on orange is equal to the probability of landing on yellow.

From the  question, the spinner has:

8 sections, with:

So probability of one getting on any section is  = 1/8, or 0.125.

Therefore, the  probability of getting on orange will still be the same as the probability of landing on yellow and as such option C is correct.

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William is currently 15 years old.

Let's start by using algebra to solve for the ages of Jade and Kevin now. Let J be Jade's current age and K be Kevin's current age. We have:

J = 2K - 6 (Jade is 6 years less than twice Kevin's age)

J - 2 = 3(K - 2) (two years ago, Jade was three times as old as Kevin)

We can use the first equation to substitute for J in the second equation:

(2K - 6) - 2 = 3(K - 2)

Simplifying this, we get:

2K - 8 = 3K - 6

K = 2

So Kevin is currently 2 years old, and Jade is:

J = 2K - 6 = 2(2) - 6 = -2

This doesn't make sense as an age, so there may be an error in the problem statement or in our solution method.

Let's use algebra to solve for Amanda's current age, which we can call A. Then we can use that to find her age 3 years from now. We have:

L = 3A - 2 (Len is 2 less than 3 times Amanda's age)

L + 3 = 2(A + 3) + 7 (three years from now, Len will be 7 more than twice Amanda's age)

Substituting the first equation into the second, we get:

(3A - 2) + 3 = 2(A + 3) + 7

Simplifying this, we get:

A = 5

So Amanda is currently 5 years old, and her age 3 years from now will be:

A + 3 = 5 + 3 = 8

Let's use algebra to solve for Faith's current age, which we can call F. Then we can use that to find Janna's and William's ages. We have:

J = 2F (Janna is twice as old as Faith)

W = F + 9 (William is 9 years older than Faith)

J - 3 = 3(F - 3) - 9 (three years ago, Janna was 9 less than 3 times Faith's age)

Substituting the first two equations into the third, we get:

(2F) - 3 = 3(F - 3) - 9

Simplifying this, we get:

F = 6

So Faith is currently 6 years old, Janna is:

J = 2F = 2(6) = 12

and William is:

W = F + 9 = 6 + 9 = 15

Therefore, William is currently 15 years old.

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The number of ways the student can pull 5 integers out of the bucket in increasing order is 15,504.

To determine this, we can use the combination formula, which calculates the number of ways to choose k objects from a set of n objects, regardless of order. In this case, we want to choose 5 integers out of a set of 20 integers in increasing order, which means we can use the combination formula with repetition: C(n+k-1, k-1).

Substituting in our values, we get: C(20+5-1, 5-1) = C(24, 4) = (24232221)/(4321) = 15,504.

Therefore, there are 15,504 ways for the student to pull 5 integers out of the bucket in increasing order.

It is important to note that the order of the integers matters when counting the number of ways in which they can be chosen. In this case, the integers must be chosen in increasing order, which means we cannot count combinations where the integers are chosen in a different order. For example, choosing 1, 2, 3, 4, and 5 is a valid combination, but choosing 5, 4, 3, 2, and 1 is not, since the integers are not in increasing order.

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To express any vector x as a linear combination of an orthogonal basis {u1, u2} or {u1, u2, u3} for R2 or R3, respectively, we can solve a system of linear equations where each equation corresponds to one component of the vector x.

To show that {u1, u2} is an orthogonal basis for R2, we need to prove that u1 and u2 are orthogonal (perpendicular) to each other and that they span the entire space of R2. In other words, any vector in R2 can be expressed as a linear combination of u1 and u2.

Similarly, to show that {u1, u2, u3} is an orthogonal basis for R3, we need to prove that u1, u2, and u3 are pairwise orthogonal and that they span the entire space of R3. Any vector in R3 can be expressed as a linear combination of u1, u2, and u3.

Once we have shown that {u1, u2} or {u1, u2, u3} is an orthogonal basis for R2 or R3, respectively, we can express any vector x in terms of the basis vectors as follows:

For R2:

x = c1u1 + c2u2, where c1 and c2 are constants.

For R3:

x = c1u1 + c2u2 + c3u3, where c1, c2, and c3 are constants.

We can find the values of c1, c2, and c3 by solving a system of linear equations, where each equation corresponds to one component of the vector x. The solution to the system will give us the coefficients that express x as a linear combination of the U.

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