What is the sale price of a $25 shirt first marked down 25% and then marked down another 15%
to the nearest cent? *

Answer:

X=-5

Step-by-step explanation:

Answer:

\(\large\boxed{\tt x = 2}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for x in the given equation.}\)

\(\textsf{We should know that x is cubed, meaning that it's multiplied by itself 3 times.}\)

\(\textsf{We should isolate x on the left side of the equation, then find x by cubic rooting}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{How is this possible?}}\)

\(\textsf{To isolate variables, we use Properties of Equality to prove that expressions}\)

\(\textsf{are still equal once a constant has changed both sides of the equation. A Cubic}\)

\(\textsf{Root is exactly like a square root, but it's square rooting the term twice instead}\)

\(\textsf{of once.}\)

\(\large\underline{\textsf{For our problem;}}\)

\(\textsf{We should use the Subtraction Property of Equality to isolate x, then cubic root}\)

\(\textsf{both sides of the equation.}\)

\(\large\underline{\textsf{Solving;}}\)

\(\textsf{Subtract 1 from both sides of the equation keeping in mind the Subtraction}\)

\(\textsf{Property of Equality;}/tex]

\(\tt \not{1} - \not{1} - x^{3} = 9 - 1\)

\(\tt - x^{3} = 8\)

\(\textsf{Because x}^{3} \ \textsf{is negative, we should exponentiate both sides of the equation by}\)

\(\textsf{the reciprocal of 3, which is} \ \tt \frac{1}{3} .\)

\(\tt (- x^{3})^{\frac{1}{3}} = 8^{\frac{1}{3}}\)

\(\underline{\textsf{Evaluate;}}\)

\(\tt (- x^{3})^{\frac{1}{3}} \rightarrow -x^{3 \times \frac{1}{3} } \rightarrow \boxed{\tt -x}\)

\(\textsf{*Note;}\)

\(\boxed{\tt A^{\frac{1}{C}} = \sqrt[\tt C]{\tt A}}\)

\(\tt 8^{\frac{1}{3}} \rightarrow \sqrt[3]{8} \rightarrow 2^{1} \rightarrow \boxed{\tt 2}\)

\(\underline{\textsf{We should have;}}\)

\(\tt -x=2\)

\(\textsf{Use the Division Property of Equality to divide each side of the equation by -1;}\)

\(\large\boxed{\tt x = 2}\)

The 99% confidence interval estimate of the population mean for sugar packed in 10 ounce bags is approximately 9.88 to 10.02 ounces.

To calculate the confidence interval, we use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / square root of sample size)

Given that the sample mean is 9.95 ounces, the standard deviation is 0.4 ounces, and the sample size is 36, we need to determine the critical value for a 99% confidence level.

Using a t-distribution table or statistical software, we find that the critical value for a 99% confidence level with 35 degrees of freedom is approximately 2.72.

Plugging in the values into the formula, we have:

Confidence Interval = 9.95 ± (2.72 * 0.4 / √36)

Confidence Interval = 9.95 ± (2.72 * 0.0667)

Confidence Interval ≈ 9.95 ± 0.1814

Therefore, the 99% confidence interval estimate of the population mean for sugar packed in 10 ounce bags is approximately 9.88 to 10.02 ounces. This means that we can be 99% confident that the true population mean lies within this range based on the given sample.

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Answer: \(\frac{5}{12}\)

Step-by-step explanation:

      Tangent (tan) is a trigonometry function. It utilizes the opposite side length from the angle divided by the adjacent side length from the angle.

\(\displaystyle tan(30\°) = \frac{\text{opposite side}}{\text{adjacent side}}= \frac{5}{12}\)

Answer:

-3

Step-by-step explanation:

it is the only one without a variable

Answer:

47/30

Step-by-step explanation:

2.35 * 2/3 =

= 2 35/100 * 2/3

= 2 7/20 * 2/3

= 47/20 * 2/3

= 94/60

= 47/30

Answer:

47/30

Step-by-step explanation:

30 ÷ (15÷2.5) + 7

Given: 16 · (4.5 + 3) ÷ 10= ____

First let us do PEMDAS (Parenthesis, Equation, Multiply, Divide. Add, Subtract) upon the given value.

16 · (7.5) ÷ 10 = ____

       120 ÷ 10 = ____

                     = 12

We now understand that the given is equal to the value of 12, now we will calculate each equation with PEMDAS until we find the equivalent value.

20.8 + (3 · 4) ÷ 4 =

   20.8 + 12 ÷ 4   =

          20.8  +  3  =

                            = 23.8

24 ÷ (8 − 4) + 8.2 =

       24 ÷ 4 + 8.2 =

               6 + 8.2 =

                            = 14.2

30 ÷ (15 ÷ 2.5) + 7 =

            30 ÷ 6 + 7 =

                     5 + 7 =

                              = 12

36 ÷ (9 − 4.2) + 3 =

       36 ÷ 4.8 + 3 =

                7.5 + 3 =

                            = 10. 5

It is safe to say the following:

16 · (4.5 + 3) ÷ 10 ≠ 20.8 + (3 x 4) ÷ 4

16 · (4.5 + 3) ÷ 10 ≠ 24 ÷ (8 − 4) + 8.2

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

16 · (4.5 + 3) ÷ 10 ≠ 36 ÷ (9 − 4.2) + 3

Therefore, the answer is:

16 · (4.5 + 3) ÷ 10 = 30 ÷ (15 ÷ 2.5) + 7

Hope this helps =D, happy learning !

Answer:

22 square units

Step-by-step explanation:

Area of a triangle formula:

A = 0.5bh

Given:

b = 11

h = 4

Work:

A = 0.5bh

A = 0.5(11)(4)

A = 5.5(4)

A = 22

The mean of the sample means, also known as the expected value of the sample mean, is equal to the population mean.

When all possible outcomes of size n are selected from a population and the mean of each sample is determined, the sample means to represent a sampling distribution. The mean of this sampling distribution denoted as the expected value of the sample means or simply the mean of the sample means, is equal to the population mean.

This result is derived from the concept of sampling. Each sample is a random selection from the population, and on average, these samples will reflect the characteristics of the population. Therefore, the mean of the sample means represents the average value that would be obtained if an infinite number of samples of size n were taken from the population. Since each sample mean is an unbiased estimator of the population mean, the mean of the sample means will be equal to the population mean. This property holds under certain conditions, such as when the sampling is random and independent.

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Answer:

See below

Step-by-step explanation:

If i recall right when two slopes are perpendicular one slope is supposed to be the negative reciprical of the other slope, because of this I think your answer should be B. -\frac{2}{3}  

Hope this helps

The lines are perpendicular and the slope of the red line is m₂ = -2/3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = 3/2

So , the slope of the green line is m₁ = 3/2

Since the lines are perpendicular to each other , the product of their slopes will be equal to -1

And , m₁ x m₂ = -1

So , ( 3/2 ) x m₂ = -1

Multiply by ( 2/3 ) on both sides , we get

m₂ = ( -2/3 )

Therefore , the slope of the red line is ( -2/3 )

Hence , the slope of the red line m₂ = ( -2/3 )

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The complete question is attached below :

The lines below are perpendicular. If the slope of the green line is 3/2 what is the slope of the red line?

Each box needs to have a minimum space of 576 cubic inches to hold the toy.

What is a cuboid?

A cuboid is a three-dimensional solid shape that has six rectangular faces, where each face meets at right angles with adjacent faces.

To calculate the space required for each box to hold a toy that is 8 inches tall by 12 inches wide and 6 inches deep, we need to calculate the volume of the toy.

The volume of the toy can be calculated as:

Volume = height x width x depth

Volume = 8 inches x 12 inches x 6 inches

Volume = 576 cubic inches

Therefore, each box needs to have a minimum space of 576 cubic inches to hold the toy.

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Answer:

m∠1=111°

Step-by-step explanation:

Since angle 1 is an exterior angle on a straight line, it is the sum of the two outer angles of the triangle.

64+47=111.

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

4.7>a

i think that's correct??

Using a calculator, we get:

√115 ≈ 10.723

On the other hand, 115 can be expressed as 5*23, then:

√115 = √(5*23) = √5*√23

In the given scenario, with an estimated 1000 people visiting the street fair and one information booth available, the percentage of the day the booth will be busy can be determined.

The average waiting time for a person to have their question answered and the average number of people in line can also be calculated. Additionally, if a second person helps at the booth, the impact on waiting time can be assessed.

To determine the percentage of the day the information booth will be busy, we need to calculate the total time spent by people consulting at the booth. With an average consultation time of 2 minutes per person and a standard deviation of 3 minutes, we can use statistical probability distributions such as the normal distribution to estimate the total time.
The average waiting time for a person to have their question answered can be calculated by considering the average consultation time and the average time taken to answer a question. By subtracting the time taken to answer a question from the average consultation time, we obtain the average waiting time.
To determine the average number of people in line, we need to consider the arrival rate of people at the booth and their average consultation time. Using queuing theory, we can calculate the average number of people in line using formulas such as Little's Law.
If a second person helps at the booth, the waiting time can be reduced. By dividing the total arrival rate by the total service rate (considering both employees), we can calculate the new average waiting time.
In conclusion, by applying probability distributions and queuing theory, we can determine the percentage of the day the booth will be busy, the average waiting time, and the average number of people in line. The addition of a second person at the booth will help reduce waiting times.

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The mapping rule for a 180° rotation include the following: D. (x, y) → (-x, -y).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Generally speaking, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y) → (-x, -y)

Where:

In conclusion, (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin.

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Answer:

cost price = $262.57

selling price = $302.48

Explanation:

The selling price is

Selling price = cost + markup

We know that markup is 15.2% of the cost price. Since the markup is $39.91,

dividing both sides by 0.152 gives

The selling price is

cost price + 15.2% of the cost price

= (100% + 15.2%) cost price

=115.2% cost price

Now, 115.2% of the cost price is

Hence the selling price is $302.48.

Therefore, to summerise,

cost price = $262.57

selling price = $302.48

Answer: f(2) = g(2)

Step-by-step explanation:

Well, this is kind of a comparison so you can do this by putting "2" as x value for both functions.

If you do that for both functions:

\(f(x) = 4x^{5}\\f(2) = 128 = (2^{7}) \\----------\\g(x) = 8.4^{x} = 2^{2x + 3}\\g(2) = 128\)

So, this shows that f(2) = g(2).

The value of f(-3) for the function f(a) = -2a² - 5a + 4 is 1. Therefore,  option c is the correct answer.

The given equation = -2a² - 5a + 4

f(a)  = -3

Functions can be defined using different notations, including equations, graphs, tables, and unwritten descriptions.

The value of a should be substituted in the given equation.

f(-3) = -2(-3)² - 5(-3) + 4

f(-3)  = -2(9) + 15 + 4

f(-3)  = -18 + 19

f(-3)  = 1

Therefore, we can conclude that the value of f(-3) for the function f(a) -2a² - 5a + 4 is 1.

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The complete question is:

What is f(a = 3) for the function f(a)=-2a² - 5a + 4?

a. 29

b. 23

c. 1

d. 37

Answer:

$5

Step-by-step explanation:

if you want the cost of 1 pair of colored socks, substitute that into c

5(1) + 3w = 32

5 + 3w = 32

subtract on both sides

3w = 27

this means the amount of pairs of white socks is 9.

multiply by 3

$27

then subtract by 32

$5

he only bought 1 pair of colored socks for $5

Answer:

Wdym

Step-by-step explanation:

wdym

On subtracting 20 from twice a number we get 50, then the number is 35 in this context.

This is referred to as a type of mathematical operation in which one number is taken or deducted from the other and the sign is ( - ). this expression is used in every facet of life for their daily activities.

We were told that 20 was subtracted from twice a number to give 50 which means that twice the number is 70. The exact number will therefore be 70/2 which will then result in 35 and is therefore the most appropriate choice.

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The claim that a drug is effective at 1% is not sufficiently supported by the available data.

Participant 1 2 3 4 5 6

Before 185 220 190 158 227 211

After 175 215 195 155 230 207

Difference = Before - After = 10 5 -5 3  -3 4

Participant 7 8 9 10 11 12

Before 260 156 201 300 180 270

After 258 159 201 290 172 272

Difference = Before - After = 2 -3 0 10  8 -2

Participant 13 14 15 16 17 18

Before 293 183 205 151 291 166

After 290 185 200 146 287 166

Difference = Before - After = -7 -2 5 5  4 0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

10+5-5+3-3+4+2-3+10+8-2+3-2+5+5+4+0 = 44

The mean of d, \(d`\) = Σd / n = 44 / 18 = 2.44

The standard deviation, S.d = 4.45 (using calculator)

The test statistic, T : \(d`\) / (S.d/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

P value = 0.0326

α = 0.01

Since P value < α ; we fail to reject H0

So the claim that a drug is effective at 1% is not sufficiently supported by the available data.

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Answer:

Volume of a cylinder = 225.80 in³ (Approx)

Volume of cone = 75.29 in³ (Approx)

Step-by-step explanation:

Given:

Volume of sphere = 150 in³

Find:

Volume of a cylinder and a cone

Computation:

Volume of sphere = [4/3]πr³

150 = [4/3][22/7]r³

r = 3.3 in (Approx)

Height = 2(3.3) = 6.6

Volume of a cylinder = πr²h

Volume of a cylinder = [22/7]3.3²(6.6)

Volume of a cylinder = 225.80 in³ (Approx)

Volume of cone = [1/3]πr²h

Volume of cone = 75.29 in³ (Approx)

Given:

Number of white roses = 4

Number of red roses = 8

To find:

The ratio of the number of red roses to the number of white roses.

Solution:

Using the given information, the ratio of the number of red roses to the number of white roses is

\(\text{Required ratio}=\dfrac{\text{Number of red roses}}{\text{Number of white roses}}\)

\(\text{Required ratio}=\dfrac{8}{4}\)

\(\text{Required ratio}=\dfrac{2}{1}\)

\(\text{Required ratio}=2:1\)

Therefore, the required ratio is 2:1.

When the number of ounces is 9, the cost per ounce would be 40 cents. To solve , we can use the concept of inverse variation, which states that two variables are inversely proportional if their product remains constant.

Let's denote the cost per ounce as C and the number of ounces as N. According to the problem, we know that when N = 6, C = 60 cents per ounce. Using the inverse variation equation, we have: C × N = k, where k is the constant of variation. Substituting the given values, we get: 60 × 6 = k; k = 360.

Now, we can find the cost per ounce when N = 9: C × 9 = 360. Dividing both sides by 9, we have: C = 360 / 9; C = 40. Therefore, when the number of ounces is 9, the cost per ounce would be 40 cents.

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The annual effective rate of interest is approximately 3.218%.

To find the annual effective rate of interest, we can use the formula for the present value of a perpetuity:

PV = C / i

where PV is the present value, C is the cash flow, and i is the interest rate.

In this case, the present value (PV) is given as 0.5 and the cash flow (C) is 1, as the perpetuity pays 1 at the end of every 6 years. Plugging these values into the formula, we have:

0.5 = 1 / i

Rearranging the equation to solve for i, we get:

i = 1 / 0.5

i = 2

So the annual effective rate of interest (i) is 2.

However, since the interest is paid at the end of every 6 years, we need to convert the rate to an annual rate. We can do this by finding the equivalent annual interest rate, considering that 6 years is the period over which the cash flow is received.

To find the equivalent annual interest rate, we use the formula:

i_annual = \((1 + i)^(^1^ /^ n^)\) - 1

where i is the interest rate and n is the number of periods in one year. In this case, n is 6.

Plugging in the values, we have:

i_annual =\((1 + 2)^(^1 ^/^ 6^) - 1\)

i_annual = \((3)^(^1 ^/^ 6^) - 1\)

i_annual ≈ 0.03218

So the annual effective rate of interest (i_annual) is approximately 3.218%.

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so you write 16 but i don't speak English very good i want help you 2(6+3)-2 ok you you going multiplying 2×6=12+6=18-2=16 so 16

Answer:

32.48 square inches

Step-by-step explanation:

The area of a polygon is \(A=\frac{nsa}{2}\) where \(n\) is the number of sides of the polygon, \(s\) is the side length of the polygon, and \(a\) is the length of the apothem.

We are given the polygon is a heptagon, so it has 7 sides, making \(n=7\)

We are given the heptagon's side length is 3.2 inches, making \(s=3.2\)

We are also given an apothem of 2.9 inches, making \(a=2.9\)

Therefore, by using the formula for the area of a polygon, we get\(A=\frac{nsa}{2}=\frac{7*3.2*2.9}{2}=\frac{64.96}{2}=32.48\)

In conclusion, the area of the heptagon is 32.48 square inches