a tshirt is on sale for 32$ after being marked down by 25% what was the original sale price of the t-shirt before the discount?

The inverse of the function is y = ( 1/5 )x - 6.

An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Consider the function,

y = 5x + 30

To find the inverse of the function we interchange x and y then find the equation for y.

Therefore, after interchanging x and y:

x = 5y + 30

Subtracting 30 from each side of the equation.

x - 30 = 5y + 30 - 30

x - 30 = 5y

Now, dividing the whole equation by 5

( x - 30 ) / 5 = 5y / 5

y = ( 1/5 )x - 30/ 5

y = ( 1/5 )x - 6

Therefore, the inverse of the function y = 5x + 30 is y = ( 1/5 )x - 6.

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The area and circumference of the circle will be 28.26 square units and 18.84 units, respectively.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The circumference of the circle will be

C = 2πr units

From the diagram, the radius of the circle is 3 units. Then the area of the circle will be

A = πr²

A = 3.14 x 3²

A = 3.14 x 9

A = 28.26 square units

Then the circumference of the circle will be

C = 2πr

C = 2 x 3.14 x 3

C = 18.84 units

The area and circumference of the circle will be 28.26 square units and 18.84 units, respectively.

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To calculate the mean fitness of a population, we need to multiply the frequencies of each genotype by their respective fitness values and sum them up.

Let's denote the frequencies of s as f(s) and the corresponding fitness values as w(s).

Given the frequencies: 0, 0.5, 0.1, 0.15, 0.25, 1.
And assuming the corresponding fitness values are: w(0), w(0.5), w(0.1), w(0.15), w(0.25), w(1).

The mean fitness can be calculated as follows:

Mean Fitness = f(0) * w(0) + f(0.5) * w(0.5) + f(0.1) * w(0.1) + f(0.15) * w(0.15) + f(0.25) * w(0.25) + f(1) * w(1)

By substituting the given frequencies and their corresponding fitness values, and performing the calculations, we can determine the mean fitness of the population.

For example, if the fitness values are: w(0) = 0.8, w(0.5) = 0.9, w(0.1) = 0.7, w(0.15) = 0.6, w(0.25) = 0.85, w(1) = 1.0.

Mean Fitness = 0 * 0.8 + 0.5 * 0.9 + 0.1 * 0.7 + 0.15 * 0.6 + 0.25 * 0.85 + 1 * 1.0

Performing the calculations, the mean fitness of the population can be determined.

Please note that the fitness values may vary depending on the specific context or problem at hand.

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Answer:

x = 4

Step-by-step explanation:

I took the test and it was right :)

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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Answer:

  40.4

Step-by-step explanation:

We don't have access to your drawing tools, so we have used our own. The attachment shows the triangle and the angle.

  ∠ABC ≈ 40.4°

Answer: x=43, y=180

Step-by-step explanation: x is 43 because the 43 next to it has the same value. y is 180 because the angle is a straight line.

I assume you're needing to find \((f+g)(x)\) given those two functions you have.

    \(\begin{aligned}(f+g)(x) &= f(x) + g(x) \\[0.5em] &= (5x^3+5x^2-6x+3) + (x^3-4x^2+x-2)\end{aligned}\)

From there, you combine like terms:

    \(\begin{aligned}(f+g)(x) &= f(x) + g(x) \\[0.5em] &= (5x^3+5x^2-6x+3) + (x^3-4x^2+x-2) \\[0.5em] &= 6x^3+x^2-5x+1\end{aligned}\)

Answer: The base is 17 meters long, and the height is 12 meters.

Step-by-step explanation:

The area of a triangle is:

A = b*h/2

where:

b = base

h = height.

For this particular triangle, we have that:

b = 5m + h

A = 102 m^2 = b*h/2

We can replace the first equation into the second one:

b*h/2 = 102 m^2

(5m + h)*h/2 = 102 m^2

(5m + h)*h = 2*102 m^2 = 204m^2

5m*h + h^2 = 204m^2

We can rewrite this as a quadratic equation:

h^2 + 5m*h - 204m^2 = 0

The solutions are given by the Bhaskara formula, the solutions are:

\(h = \frac{-5m +- \sqrt{(+5m)^2 -4*1*(-204m^2)} }{2*1} = \frac{-5m+-29m}{2}\)

Then the two solutions are:

h = (-5m - 29m)/2 = -17 m

This is a negative height, that is not really defined, so this will be discarded.

The other solution is:

h = (-5m + 29m)/2 = 12m

This is positive, so this is the option we will use.

Knowing h, we can find the value of b.

b = 5m + h = 5m + 12m = 17m

Then the area is:

A = 12m*17m/2 = 102m^2

Answer:1.6 hours.

Step-by-step explanation: 11/7=1.57142857 rounding to the tenth you get 1.6

Answer:

50 per hour

Step-by-step explanation:

Answer:

There is no solution

Step-by-step explanation:

\(\frac{1}{4} x-13= \frac{1}{4} x + \frac{13}{4}\)

subrtact 1/4 X from each side

-13=13/4 is not true, so no solution

Step-by-step explanation:

\( - 2 - - 5 \\ \)

\( \div - 3 - - 3\)

Answer:

\(28\sqrt{2}\)

Step-by-step explanation:

To answer this question, you must split 98 into 2 factors:

                                                      98

                                                 2          49

                                                          7       7

2 and 49 can be multiplied to get 98. 49 is also a perfect square, meaning the factors are going to be the same number, which is 7. Since there are two 7's you take that out of the radical, like so:

\((7)4\sqrt{2}\)

\(28\sqrt{2}\)

The 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more is approximately (18.38%, 25.62%).

To calculate the 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more, we can use the following formula:
CI = p ± z*sqrt((p*(1-p))/n)
Where:
p = proportion of voters in the sample who have an income of $150,000 or more = 110/500 = 0.22
z* = z-score corresponding to 95% confidence level = 1.96 (from standard normal distribution)
n = sample size = 500
Plugging in these values, we get:
CI = 0.22 ± 1.96*sqrt((0.22*(1-0.22))/500)
CI = 0.22 ± 0.049
CI = (0.171, 0.269)
Therefore, we can be 95% confident that the percentage of all voters in the population who have an income of $150,000 or more is between 17.1% and 26.9%.
To calculate a 95% confidence interval for the percentage of all voters in the population who have an income of $150,000 or more, we will use the following formula:
CI = p-hat ± Z * √(p-hat * (1 - p-hat) / n)
Where:
- CI represents the confidence interval
- p-hat is the sample proportion (110/500 = 0.22)
- Z is the Z-score for a 95% confidence interval (1.96)
- n is the sample size (500)
Plugging the values into the formula:
CI = 0.22 ± 1.96 * √(0.22 * (1 - 0.22) / 500)
CI = 0.22 ± 1.96 * √(0.1716 / 500)
CI = 0.22 ± 1.96 * 0.01845
CI = 0.22 ± 0.03612

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The appropriate p-value for a t-value of 2.73 with 5 degrees of freedom is approximately 0.05. This indicates that there is a 5% chance of observing a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true.

In statistics, the p-value measures the strength of evidence against the null hypothesis. The null hypothesis states that there is no significant difference or effect in the population being studied. The p-value is calculated by determining the probability of obtaining a test statistic (in this case, the t-value) as extreme as or more extreme than the observed value, assuming the null hypothesis is true.

To determine the appropriate p-value for a t-value, we typically consult a t-distribution table or use statistical software. In this case, with 5 degrees of freedom and a t-value of 2.73, we look up the critical value or use software to find the corresponding p-value. The p-value associated with a t-value of 2.73 and 5 degrees of freedom is approximately 0.05.

The p-value of 0.05 indicates that there is a 5% chance of obtaining a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true. Generally, a p-value of 0.05 or lower is considered statistically significant, implying that the observed result is unlikely to have occurred by chance alone. If the p-value is below a predetermined significance level (often denoted as α, commonly set at 0.05), we reject the null hypothesis in favor of an alternative hypothesis. If the p-value is above the significance level, we fail to reject the null hypothesis.

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Answer:

= 1/5

Step-by-step explanation:

The reciprocal number results from dividing the number 1 by the origial number, by example:

Original number:   a

reciprocal number: 1/a

In this case:

original number: 5

reciprocal number: 1/5

Answer:

7.1

Step-by-step explanation:

All you have to do is divide.

Answer:

Step-by-step explanation:t55

An octagon has 8 sides. If each of them has a length of x, then the perimeter is 8x which is twice the perimeter of the square. (The square has a perimeter of 4x)

A dodecagon is a 12 sided regular polygon. It will have 12 sides all of which are equal to x. Since the square has a perimeter of 4x and the dodecagon has a perimeter of 12x the perimeter of the dodecagon is 3 times that of the given square.

Note that a total of 250 volunteer hours is required to get the silver cord at graduation at cypress bay high school.

The Silver Cord program is a distinguished award available to high school students with the purpose of recognizing their out of school volunteer efforts.

Volunteer efforts are recognized within the context of theSilver Cord program   to acknowledge and celebrate the contributions that high school students make to their communities through volunteer work.

By engaging in voluntary activities outside of school hours, students demonstrate their commitment to   service, leadership, and making a positive impact on society,which aligns with the values promoted by the program.

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The interval is from -10 to 8 on the number line.

What is a number line?

A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided. How a number is used, such as when graphing a point, depends on the question that goes with it.

What are negative numbers?

A negative number in mathematics represents the reverse. A negative number is any number that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.

in the given number line, we can observe that all the numbers from -10 to 8  are -8,-6,-2,0,2,4, and 6 (including -10 and 8).

thus the interval is from -10 to 8,

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Answer:

list in the explanation

Step-by-step explanation:

BOOT x2

SKINNY x2

RELAXED x2

BOOT, SKINNY

BOOT, RELAXED

SKINNY, BOOT

SKINNY, RELAXED

RELAXED, BOOT

RELAXED, SKINNY

The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the equation will be

Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)

He wants to buy 2 pair of pants , and the possible ways of 2 pants are

Set A = { BB , SS , RR , BS , BR , SR }

So , the total number of elements in set A = 6 pairs

Therefore , the value of A is 6 pairs

Hence , the set A is { BB , SS , RR , BS , BR , SR }

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The decimal number that corresponds to the binary number 11111111 is 255.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. A decimal number is made up of two parts: a whole number and a fractional component separated by a decimal point. The decimal point is the dot between the whole number and the fractions. 25.5, for example, is a decimal number.

Here,

In binary, each digit represents a power of 2, starting with the rightmost digit. The rightmost digit in 11111111 represents 2^0, the second digit from the right represents 2^1, and so on. To convert a binary number to decimal, you add up the value of each digit times the corresponding power of 2.

For 11111111, the calculation would be:

=1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

=255

The decimal equivalent of the binary number 11111111 is 255.

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Answer:

≈ 3.9 miles

Step-by-step explanation:

The third angle in the triangle is

180° - (53 + 78)° = 180° - 131° = 49°

Using the Sine rule in the triangle with distance from 2 being x, then

\(\frac{3}{sin49}\) = \(\frac{x}{sin78}\) ( cross- multiply )

x × sin49° = 3 × sin78° ( divide both sides by sin49° )

x = \(\frac{3sin78}{sin49}\) ≈ 3.9 ( to the nearest tenth )

If you wanted to determine if your PSYC210 class performed significantly better than another section on a stats knowledge test, you would use a hypothesis test, specifically a two-sample t-test.

A hypothesis test is a statistical method used to determine whether there is a significant difference between two groups or populations based on their observed data. In this case, you would compare the mean score of your PSYC210 class on the stats knowledge test with the mean score of the other section using a two-sample t-test. The null hypothesis would be that there is no significant difference between the means of the two sections, and the alternative hypothesis would be that there is a significant difference.

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Answer:

a) 79.6

b) 437.8

Step-by-step explanation:

First, you have to do 318.4/4 to find the rate she goes in the duration of an hour. The rate is 79.6, which means she travels at a rate of 79.6 kilometers per hour.

Then, you have to find the distance she takes to travel in 5.5 hours, so you have to do 5.5*79.6 which is 437.8.

So, Hannah travels 437.8 kilometers in 5.5 hours.

The expression (2x + 7)(x - 3) is a factor of 2x^2 - 11x - 21.

Expression is a combination of variables, numbers, and operators (such as +, -, *, /) that represents a mathematical value. For example, 2x + 3, x^2 - 5x + 6, and (x + 2)(x - 3) are all expressions. Expressions can be simplified or evaluated to find their numerical value for a given value of the variable(s).

The expression (2x + 7)(x - 3) is a factor of 2x^2 - 11x - 21.

To see this, we can expand the right-hand side:

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

= 2x^2 + 6x + 7x - 21

= 2x^2 + 13x - 21

As we can see, (2x + 7)(x - 3) is indeed a factor of 2x^2 - 11x - 21.

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