A clothing store is having a clearance sale. All coats are 20% off, and then an additional $10 is taken off the sale price of each. A 7% sales tax is then added. The following functions represent each part of the transaction. Sales price: f(x) = 0.8x Additional amount off: g(x) = x – 10 Final price: h(x) = 1.07x

Answer:

Where are the equations?

Step-by-step explanation:

The present value with interest rate is 14% is $1810.92.

The future value is $4892.

The interest rate is 14% per year.

The time period is 16 years.

To calculate the present value, we can use the following formula:

present value = future value / (1 + interest rate)**number of years

Plugging in the values for the future value, interest rate, and time period, we get:

present value = 4892 / (1 + 0.14)**16 = 1810.92

Therefore, the present value of $4892 if the interest rate is 14% and the number of years is 16 is $1810.92.

In words, the present value is calculated by dividing the future value by the factor that is 1 plus the interest rate raised to the power of the number of years. In this case, the future value is $4892, the interest rate is 14%, and the time period is 16 years. Therefore, the present value is $1810.92.

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Water makes up roughly 60% of your total body weight. This means that if you weigh 150 pounds, about 90 pounds of that is water.

Water is essential for the functioning of our bodies. It plays a vital role in maintaining temperature, transporting nutrients and oxygen, and removing waste products. The percentage of water in the human body varies depending on factors such as age, sex, and body composition. On average, water makes up about 60% of an adult's total body weight. This percentage can be higher in infants and lower in elderly individuals.

For example, a person weighing 150 pounds would have approximately 90 pounds of water in their body. It's important to stay hydrated by drinking enough water to replenish the water that our bodies constantly lose through processes like sweating, urination, and breathing.

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Answer:

B

Step-by-step explanation:

if you drew a line on top of any part of the parabola, you will only touch the line once.

(when drawing a line, they are always vertical, not horizontal)

The p-value for a two-tailed hypothesis test with z stat = 1.49 is approximately 0.136.

The p-value is the probability of obtaining a test statistic as extreme as the observed result, assuming the null hypothesis is true.

In this case, if the null hypothesis is that there is no significant difference between the observed result and the population mean, then the p-value of 0.136 suggests that there is a 13.6% chance of observing a difference as extreme as the one observed, given that the null hypothesis is true.

In statistical hypothesis testing, the p-value is used to determine the statistical significance of the results. If the p-value is less than or equal to the significance level, typically set at 0.05, then the null hypothesis is rejected in favor of the alternative hypothesis.

In this case, the p-value is greater than 0.05, indicating that we do not have enough evidence to reject the null hypothesis.

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Answer: 66

Step-by-step explanation:

1.Split up the figure into smaller rectangles

2.the first bigger rectangle to the left will be 10 multiplied by 4 equaling 40

3. The middle rectangle will be 2 multiplied by 5 equaling 10

4. The last rectangle with be 4 multiplied by 4 equaling 16

5. Finally add it all together 40+10=50 50+16=66

6. The final answer is 66 cm

There are 3 ways to select a senator from a state if you wish to make a 3-senator committee in which no two senators are from the same state.

There are two senators from each of the 50 states, we wish to create a committee of three senators so that no two senators are from the same state.

Therefore, the total number of ways to choose a 3-senator committee is: 2 C 98 + 3 = 2,941 ways.

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Answer: 1/2a-4b

Step-by-step explanation:

When combining like terms you can only combine numbers with the same variables.

So we subtract 3/4a-1/4a=1/2a

And then we subtract the b values

2b-6b=-4b

1/2a-4b

Answer:

distance between (3,7) and (-6,-4) is \(\sqrt{202}\)

Step-by-step explanation:

3rd point = (3, -4)

from (3,7) to (3, -4) is 11 units

from (-6,-4) to (3, -4) is 9 unites

hypothenuse

a^2 + b^2 = c^2

(11)^2 + (9)^2 = c^2

121 + 81 = c^2

c^2 = 202

c = \(\sqrt{202}\)

The factors of the given Quadratic Equation 2x² - x - 120 = 0 is 8 and -15/2.

What are zeros ?

zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.

Now, considering the given Quadratic Equation to find x :

2x² - x - 120 = 0

writing the above equation into two linear factors as :

2x² - 16x + 15x - 120 = 0

2x(x-8) + 15(x-8) = 0

(x-8)(2x+15) = 0

Now, equating each linear equation to zero to find the factors:

(x-8) = 0 and (2x+15) = 0

x = 8 and x = -15/2.

Therefore, the factors of the given Quadratic Equation is 8 and -15/2.

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Answer: The median decreases to

Step-by-step explanation: The median without the added 60 degrees is 79.5, which I double checked using a calculator after using the MEAN formulas. All I had to do was then add 60 to the data set and run the calculator again, and it then changed to 77.

Answer:

X= 6

Step-by-step explanation:

9=2x-3

= -2x= -3-9

-2x=-12 (divide both sides by -2)

X= 6

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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The odds against selecting a 9 are 12:1, while the odds in favor of selecting a 9 are 1:12.

To determine the odds against and in favor of selecting a 9 from a standard deck of 52 cards, first find the total number of cards in the deck, which is 52. There are four nines in the deck since each card rank (Ace, 2, 3,..., Jack, Queen, King) has four cards of each rank (one for each suit).

Odds against selecting a 9: To calculate the odds against, use the following formula:

Odds against = Number of unfavorable outcomes / Number of favorable outcomes

Unfavorable outcomes are the number of cards in the deck that are not 9, which is,

52 - 4 = 48

Since there are 4 nines in a deck of cards. Favorable outcomes are the number of cards that are 9, which is 4.

Odds against selecting a 9 = Number of unfavorable outcomes / Number of favorable outcomes

= 48 / 4

= 12

Therefore, the odds against selecting a 9 are 12:1.

Odds in favor of selecting a 9: To calculate the odds in favor, use the following formula: Odds in favor = Number of favorable outcomes / Number of unfavorable outcomes

Favorable outcomes are the number of cards that are 9, which is 4.

Unfavorable outcomes are the number of cards in the deck that are not 9, which is 52 - 4 = 48

Since there are 4 nines in a deck of cards. Odds in favor of selecting a 9

= Number of favorable outcomes / Number of unfavorable outcomes

= 4 / 48

= 1/12

Therefore, the odds in favor of selecting a 9 are 1:12.

Conclusion: Thus, the odds against selecting a 9 are 12:1, while the odds in favor of selecting a 9 are 1:12.

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Answer:

50% is blue

Step-by-step explanation:

50 spaces, half are colored blue which is 25/50= 50%

Answer: 50%

Step-by-step explanation:

In all, there are 50 blocks, and there are 25 blue blocks. 25/50 to percentage is 50%.

Hope it helps!

Answer:

4=$17.60

1=$17.60/4

1=$4.40

Step-by-step explanation:

Answer:

D. F(x) = |3x| - 4

Step-by-step explanation:

Answer:

His hourly rate is $8.15.

Step-by-step explanation:

The hourly rate is how much he earns in one hour. We know how much he earns in 42 hours ($342.3).

So what we need to do is to divide that amount ($342.3) by 42.

And we get $8.15.

Answer: 3.33

Step-by-step explanation:

Multiplication and division should be solved left to right.

\(37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33\)

Hope it helps <3

Answer:

=37/100×9=.

=divide 37 by 100

=0.37 ×9

=3.33

Answer:

12) x= 21

13) x = 1

14) x = 9

15) x = 1

Step-by-step explanation:

Here, we are being asked to solve the given equations and check our work.

To check the work, we need to substitute the found value of x into the equation to check if it makes a true and correct statement.

12) Solve for x:

\(\sf 12)\ \dfrac{2}{3}x + 2 = 16\ \textsf{[subtract 2 from both sides]}\\\\\implies \dfrac{2}{3}x + 2 - 2 = 16 - 2\\\\\implies \dfrac{2}{3}x = 14\ \textsf{[multiply both sides by 3]}\\\\\implies 3\left(\dfrac{2}{3}\right)x = 14(3)\\\\\implies 2x = 42\ \textsf{[divide both sides by 2]}\\\\\implies \dfrac{2x}{2}=\dfrac{42}{2}\\\\\implies \boxed{\sf x = 21}\)

Check your work:

\(\sf \dfrac{2}{3}x + 2 = 16\ \textsf{[substitute 21 for the value of x]}\\\\\implies \dfrac{2}{3}(21) + 2 = 16\ \textsf{[multiply]}\\\\\implies \dfrac{42}{3} + 2 = 16\ \textsf{[divide]}\\\\\implies 14 + 2 = 16\ \textsf{[add]}\\\\\implies 16 = 16\ \checkmark \textsf{[true statement]}\)

13) Solve for x:

\(\sf 13)\ \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[multiply both sides by 6 - LCM of 2, 3, and 6]}\\\\\implies 6\left(\dfrac{x}{2} + \dfrac{x}{3}\right) = 6\left(\dfrac{5}{6}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{6x}{2} + \dfrac{6x}{3}\right) = \dfrac{30}{6}\ \textsf{[divide]}\\\\\implies 3x+2x=5\ \textsf{[combine like terms]}\\\\\implies 5x = 5\ \textsf{[divide both sides by 5]}\\\\\implies \dfrac{5x}{5}=\dfrac{5}{5}\\\\\implies \boxed{\sf x = 1}\)

Check your work:

\(\sf \dfrac{x}{2} + \dfrac{x}{3} = \dfrac{5}{6}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}\ \textsf{[rewrite the fractions with a common denominator of 6]}\\\\\implies \dfrac{1\times3}{2\times3} + \dfrac{1\times2}{3\times2} = \dfrac{5}{6}\ \textsf{[multiply]}\\\\\implies \dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}\ \textsf{[add]}\\\\\implies \dfrac{5}{6} = \dfrac{5}{6}\ \checkmark \ \textsf{[true statement]}\)

14) Solve for x:

\(\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[multiply both sides by 24 - LCM of 6, 8, and 24]}\\\\\implies 24\left(\dfrac{x-1}{6} - \dfrac{x+1}{8}\right) = 24\left(\dfrac{1}{12}\right)\ \textsf{[multiply]}\\\\\implies \left(\dfrac{24x-24}{6}\right) - \left(\dfrac{24x+24}{8}\right) = \dfrac{24}{12}\ \textsf{[divide]}\\\\\)

\(\sf\\\implies (4x-4)-(3x+3)=2\ \textsf{[distribute the negative sign]}\\\\\implies (4x-4)+(-3x-3)=2\ \textsf{[combine like terms]}\\\\\implies x - 7 = 2\ \textsf{[add 7 to both sides]}\\\\\implies x - 7 + 7 = 2 + 7\\\\\implies \boxed{\sf x = 9}\)

Check your work:

\(\sf 14)\ \dfrac{x-1}{6} - \dfrac{x+1}{8} = \dfrac{1}{12}\ \textsf{[substitute 9 for the value of x]}\\\\\implies \dfrac{9-1}{6} - \dfrac{9+1}{8} = \dfrac{1}{12}\ \textsf{[simplify]}\\\\\implies \dfrac{8}{6} - \dfrac{10}{8} = \dfrac{1}{12}\ \textsf{[rewrite the fractions with a common denominator of 24]}\\\\\implies \dfrac{8\times4}{6\times4} - \dfrac{10\times3}{8\times3} = \dfrac{1\times2}{12\times2}\ \textsf{[simplify]}\\\\\)

\(\sf\\\implies \dfrac{32}{24}-\dfrac{30}{24}=\dfrac{2}{24}\ \textsf{[subtract]}\\\\\implies \dfrac{2}{24}=\dfrac{2}{24}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{12}=\dfrac{1}{12}\ \checkmark\ \textsf{[true statement]}\)

15) Solve for x:

\(\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[multiply both sides by 8 - LCM of 2, 4, and 8]}\\\\\implies 8\left(\dfrac{1}{4}+\dfrac{x+1}{8}\right)=8\left(\dfrac{1}{2}\right)\textsf{[multiply]}\\\\\implies \left(\dfrac{8}{4}+\dfrac{8x+8}{8}\right)=\dfrac{8}{2}\ \textsf{[divide]}\\\\\implies 2 + x + 1 = 4\ \textsf{[add]}\\\\\implies x + 3 = 4\ \textsf{[subtract 3 from both sides]}\\\\\implies x + 3 - 3 = 4 - 3\\\\\implies \boxed{\sf x = 1}\)

Check your work:

\(\sf \dfrac{1}{4}+\dfrac{x+1}{8}=\dfrac{1}{2}\ \textsf{[substitute 1 for the value of x]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1+1}{8}\right)=\dfrac{1}{2}\ \textsf{[simplify]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{2}{8}\right)=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \left(\dfrac{1}{4}+\dfrac{1}{4}\right)=\dfrac{1}{2}\ \textsf{[add]}\\\\\implies \dfrac{2}{4}=\dfrac{1}{2}\ \textsf{[reduce]}\\\\\implies \dfrac{1}{2}=\dfrac{1}{2}\ \checkmark\ \textsf{[true statement]}\)

9514 1404 393

Answer:

Step-by-step explanation:

Angle BAD is an inscribed angle, so is half the measure of the arc it intercepts. Chord BD is on the far side of the circle's center from vertex A, so the arc intercepted by angle BAD is less than 180°. This means angle BAD is less than 180°/2 = 90°.

  ∠BAD < 90°

__

Angles BAD and BCD are supplementary, so if one is less than 90°, the other must be greater than 90°.

  ∠BCD > 90°

Answer: I would say that it is equal to.

Step-by-step explanation: The angle in the bottom corner of the triangle is a right angle if you measure it with a protractor.

Answer:

70

Step-by-step explanation:

|-11| becomes positive cuz its an absolute. so its just 50 +11

Answer:

70

Step-by-step explanation:

The absolute value (the two lines that the -11 are between) refers to a numbers distance from zero. So more or less just remove the negative sign and add like normal.

Answer:

The measure of the obtuse angle marked UVW is 108

Step-by-step explanation:

Here, we want to get the measure of the angle marked UVW

To get this, we refer to the given diagram

From the diagram;

UVW = UVX + XVW

UVW = 68 + 40

UVW = 108 degrees

Answer:

x can be -3, or +3

Step-by-step explanation:

The equation would be

5\(x^{2}\) = 45

Divide both sides by 5

\(x^{2}\) = 9

Take the square root of both sides

x = ± 3

a. The alternative hypothesis (H1) specifies that is greater than 26, indicating a directed alternative, this is a one-tailed test.

b. The alternative hypothesis is one-sided and argues that > 26, hence the critical value is 1.645.

c. The value of the test statistic (z-score) is z ≈ 3.82.

d. We reject the null hypothesis (H0) because the test statistic (z = 3.82) is higher than the crucial value (1.645).

In this case, the p-value is the probability of observing a sample mean of 28 or greater, assuming the population mean is 26.

a. This is a one-tailed test because the alternative hypothesis (H1) states that μ is greater than 26, indicating a directional alternative.

b. The decision rule for a one-tailed test at a significance level of 0.05 is to reject the null hypothesis (H0) if the test statistic is greater than the critical value. In this case, the critical value is 1.645 because the alternative hypothesis is one-sided and states that μ > 26.

c. The value of the test statistic (z-score) can be calculated using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case:

x = 28

μ = 26

σ = 4

n = 34

Substituting the values into the formula:

z = (28 - 26) / (4 / √34) ≈ 3.82

d. Since the test statistic (z = 3.82) is greater than the critical value (1.645), we reject the null hypothesis (H0).

e-1. To calculate the p-value, we need to find the area under the standard normal distribution curve to the right of the test statistic (z = 3.82). We can use a standard normal distribution table or a calculator to find this area.

The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis.

e-2. Interpreting the p-value: The p-value represents the probability of obtaining a sample mean as extreme as the one observed (or more extreme) if the null hypothesis is true.

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The smallest distance of the line to the point is of:

5.36 units.

Suppose the line is defined as follows:

ax + by + c = 0.

The coordinates of the points are as follows:

(x0,y0).

Then the shortest distance of the point to the line is:

D = |a(x0) + b(y0) + c|/sqrt(a²+b²).

In this problem, the line goes through these two points:

(2/7, 3) and (-2,11).

The slope is given by the change in y divided by the change in x, hence:

m = (11 - 3)/(-2 -2/7) = -3.5.

Then:

y = -3.5x + b.

When x = -2, y = 11, hence the intercept is calculated as follows:

11 = -3.5(-2) + b

11 = 7 + b

b = 4.

Then the line is:

y = -3.5x + 4.

3.5x + y - 4 = 0. (standard format, a = 3.5, b = 1).

The coordinates of the point are as follows:

(x0,y0) = (-3,-5).

Then the shortest distance is:

D = |3.5(-3) + 1(-5) - 4|/sqrt(3.5²+1²).

D = 19.5/sqrt(3.5²+1²).

D = 5.36 units.

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Answer:

x = -1

Step-by-step explanation:

I'm not sure I'm reading the problem correctly, the "table" didn't survive formatting changes.

BUT if the question is what input value X produces the same output Y then this is pretty straightforward forward and you don't even need the table.

Basically, the question is asking what number, when substituted for X, produces the same result.

That tells us that x + 7 = 2x + 15

Solve for x:

x = -8

f(x) = {x+7}

g(x)=2x+15

f(-8) = ((-8) + 7) = -1

g(-8) = (2(-8) + 15) = (-16) + 15 = -1

x = -1

a) The probability that both the husband and the wife will be audited is 0.04.

b) The probability that only one of them will be audited is 0.32.

c) The probability that neither one of them will be audited is 0.36.

d) The probability that at least one of them will be audited is 0.36.

(a) The probability that both the husband and the wife will be audited is calculated by multiplying the probability that the husband will be audited by the probability that the wife will be audited. Since the audits are assumed to be independent, we can use the multiplication rule of probability:

P(both audited) = P(husband audited) x P(wife audited)

= 0.2 x 0.2

= 0.04

(b) The probability that only one of them will be audited can be calculated in two ways: either the husband is audited and the wife is not, or the wife is audited and the husband is not. Since these events are mutually exclusive, we can use the addition rule of probability:

P(one audited) = P(husband audited and wife not audited) + P(wife audited and husband not audited)

= (0.2 x 0.8) + (0.8 x 0.2)

= 0.32

(c) The probability that neither one of them will be audited is the complement of the probability that at least one of them will be audited. Using the complement rule of probability, we can write:

P(neither audited) = 1 - P(at least one audited)

We can find the probability that at least one of them will be audited by subtracting the probability that neither of them will be audited from 1. So:

P(at least one audited) = 1 - P(neither audited)

= 1 - (0.8 x 0.8)

= 0.36

(d) The probability that at least one of them will be audited is 0.36, as we found in part (c).

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The expected correlation between the supply of a commodity (x) and the price of a commodity (y) depends on the nature of the commodity and market dynamics. However, in general, we would expect a **negative correlation** between the supply of a commodity and its price. Correct option is C.

The law of supply states that as the supply of a commodity increases, assuming demand remains constant, the price tends to decrease. This is because an increase in supply leads to a higher quantity of the commodity available in the market, potentially causing an excess supply or surplus. In such situations, suppliers may lower prices to attract buyers and reduce their inventory.

Conversely, when the supply of a commodity decreases, assuming demand remains constant, the price tends to increase. A decrease in supply results in a lower quantity available in the market, potentially leading to a scarcity or shortage. In such scenarios, suppliers may increase prices to maximize their profits due to the limited availability of the commodity.

It's important to note that real-world markets can be influenced by various factors, including changes in demand, production costs, technological advancements, government policies, and market competition, which can complicate the relationship between supply and price. Nonetheless, the general expectation is that a decrease in supply tends to lead to an increase in price, and an increase in supply tends to lead to a decrease in price, indicating a negative correlation.

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