a store pays $31 for hockey stick. The store marks up the price by 45%. What is te amount of the mark-up

Answer: one-sixth

Step-by-step explanation:

Noah drew the circle which is divided into six equal parts

This shows that cherries must be divided into six persons

each sector of the circle is  \(\frac{1}{6}^{th}\) of the whole circle

From this, we can conclude that each person receives  \(\frac{1}{6}\)  pound of cherries.

We need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

What is ASA congruence of triangle?

The two triangles are considered to be congruent according to the ASA rule if any two angles and the side located between the angles of one triangle are equal to the corresponding two angles and side located between the angles of the second triangle.

We are given the following:

1. ∠A ≅ ∠X

2. ∠C ≅ ∠Z

Now, in order to show the triangles as congruent by ASA congruence of triangle, we need the side which is in between both the angles.

The sides in between both the angles are AC and XZ.

Hence, we need AC ≅ XZ to show that triangle ABC ≅ triangle XYZ by ASA congruence of triangle.

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Step-by-step explanation:

32 seems to be the tangent on the circle with radius 24.

so, 32 and 24 are right-angled to each other (90°).

therefore, we can use Pythagoras to calculate x.

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle).

in our case

x² = 24² + 32² = 576 + 1024 = 1600

x = 40

The degree of financial leverage for Foggy Futures Weather Forecasters

is 1.06

Degree of Financial leverage (DFL) = (EBIT) / (EBT)

Earnings Before Interest and Taxes (EBIT) = $750,000

Amount to be given as loan on $1000000

$1,000,000 x 4.5% = $1,000,000 x 4.5/100

= $45000

To find EBT ( Earnings Before Tax),

EBT = EBIT - 45000

       = 750000 - 45000

EBT = 705000

∴ DFL =  (EBIT) / (EBT)

          = 750000/705000

 DFL = 1.06

The DFL is a percentage that accountants and financial professionals use to show changes in a company's net income due to changes in its profits before interest and taxes (EBIT).

Earnings before interest and taxes (EBIT) is a measurement of a company's profit in accounting and finance that takes into account all revenues and costs (both operating and non-operating), with the exception of interest costs and income tax costs.ve

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An serveur

Réponses 30 ou 60 et maintenant

The fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

Let w be the weight of the bag in pounds, and let x be the weight over the limit.

The first airline charges 28 + 7x dollars for the bag, and the second airline charges 14 + 9x dollars for the bag.

Since the fees are the same with both airlines, we can set these two expressions equal to each other:

28 + 7x = 14 + 9x

Solving for x, we find that x = 7.

Substituting this value back into either of the original expressions, we find that the fee with each airline is 28 + 7x = 35.

Therefore, the fee with each airline was 35 dollars, and the bag was 7 pounds over the weight limit.

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Step-by-step explanation:

Yes they are congruent via the S-S-S  triangle theorem.

  triangles are congruent if they have three equal sides ( Side-Side-Side)

For the given integral ∫x^2√(x^3 + 1) dx, we have:
u = g(x) = x^3 + 1
du = g'(x) dx
Now, we need to find the derivative of g(x) with respect to x:
g'(x) = d(x^3 + 1)/dx = 3x^2

So, du = 3x^2 dx.
In summary, for the integral ∫x^2√(x^3 + 1) dx:
u = x^3 + 1
du = 3x^2 dx

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Answer:

1.fireworks conjunction

2.michelle disjunction

3. Watch conditional

Step-by-step explanation:

Michelle orders soup, or she orders salad; an example of disjunction combining 2 sentences with the word or.

The fireworks were loud and colorful; An example of conjunction which combines two statements with the word And

If the watch is broken, then it it showing the wrong time; An example of a statement with if then scenario.

If Ashley sold total of 155 cups for $265 , then Ashley sold 98 regular cups of lemonade and 57 large cups of lemonade.

Let number of regular cups of lemonade sold be = x

Let number of large cups of lemonade sold be = y

The price of a regular cup of lemonade is = $1.25.

The price of a large cup of lemonade is = $2.50.

The total number of cups sold is = 155.

The total revenue from sales is = $265.

Using this information, the system of equations to represent the problem can be written as :

⇒ x + y = 155     ...equation(1)

⇒ 1.25x + 2.5y = 265    ....equation(2)

We solve this system of equations by using substitution method .

On solving equation(1) for y, we get ,

⇒ y = 155 - x ,

Substituting this expression for y into equation(2),

We get ,

⇒ 1.25x + 2.5(155 - x) = 265 ,

Simplifying and solving for x,

We get ,

⇒ 1.25x + 387.5 - 2.5x = 265 ,

⇒ -1.25x = -122.5

⇒ x = 98

So , Ashley sold 98 regular cups of lemonade.

To find the number of large cups of lemonade sold, we substitute this value for x into equation(1) ,

We get ,

⇒ 98 + y = 155

⇒ y = 57

So , Ashley sold 57 large cups of lemonade.

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The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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Graph option B is the correct answer.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given are function,

y = x+1 ≤0 and y = 3x

The best demonstration of these functions can be seen in graph 2.

Hence, Graph option B is the correct answer.

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Answer:

5Step-by-step explanation:

The solution for the obtained inequality is x>5. Therefore, option D is the correct answer.

Given that, Shea earns $8 per hour for the first 40 hours she works in a week.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Here,

Total money earned for the first 40 hours she works in a week = 40×8

= $320

Let x be the additional number of hours

So, the inequality which represents the given situation is

320+12x>380

Solve the obtained inequality

12x>380-320

⇒ 12x>60

⇒ x>5

The solution for the obtained inequality is x>5. Therefore, option D is the correct answer.

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AIn problems 7 and 8, we need to find the solution of the given initial-value problem where x(0) = 1 and x'(0) = -3x. To solve this differential equation, we can separate the variables and integrate both sides. This gives us x(t) = e^(-3t/2). Thus, the solution of the initial-value problem is x(t) = e^(-3t/2) with x(0) = 1. The behavior of the solution as t approaches infinity is that x(t) approaches zero. This is because the exponential term e^(-3t/2) decays to zero as t becomes large.

To solve the given initial-value problem, we can use separation of variables. We start by separating the variables and get dx/x = -3/2 dt. Integrating both sides, we get ln|x| = -3t/2 + C, where C is a constant of integration. Solving for x, we get x = Ce^(-3t/2). We can then use the initial condition x(0) = 1 to find C. Plugging in x = 1 and t = 0, we get C = 1. Thus, the solution of the initial-value problem is x(t) = e^(-3t/2) with x(0) = 1.

To describe the behavior of the solution as t approaches infinity, we can look at the exponential term e^(-3t/2). As t becomes larger and larger, e^(-3t/2) approaches zero. This means that x(t) approaches zero as t approaches infinity. We can also see this by looking at the graph of the solution, which decays to zero as t becomes larger.

In conclusion, the solution of the initial-value problem x(0) = 1 and x'(0) = -3x is x(t) = e^(-3t/2). The behavior of the solution as t approaches infinity is that x(t) approaches zero. This is because the exponential term e^(-3t/2) decays to zero as t becomes large.

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Answer: A,B

Step-by-step explanation: the numbers constantly add up only by 218 or 1240 , C and D would not be correct because the rate of change increases as will with the total sum after each period of time

also tiny hint, if you were to draw an X,Y axis graph, A and B would be a straight line while C and D are curved up-wards

5.12% means

5.12/100 = 0.0512 (each year)

PreOwned Vehicle Cost = 31,100

For 5 years simple interest, the value would be:

31100 * 0.0512 * 5 = $7961.6

Total have to pay: 31,100 + 7961.6 = $39,061.6

Answer: 13

Step-by-step explanation:

Answer: i would say the answer is 90 degrees

Step-by-step explanation:

Answer:

U = 48

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

x+21 + x+23 + x+61 = 180

Combine like terms

3x + 105 = 180

Subtract 105 from each side

3x+105-105 = 180-105

3x = 75

Divide by 3

3x/3 = 75/3

x = 25

We want angle u

x+23

25+23

48

Answer:

48

Step-by-step explanation:

All interior angles of a triangle add up to 180.

\((x+21)+(x+23)+(x+61)=180\)

If you wanted to you could subtract 21, 23, and 61 from 180.

\((x+21)+(x+23)+(x+61)=180\\x+21+x+23+x+61=180\\3x+105=180\\3x=75\)

Then take then number that's left and divide it by three, since they are all in addition to the same variable.

\(\frac{3x}{3}=\frac{75}{3}\\ x=25\)

Then add 25 to 23 which is 48.

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.957.

To calculate the probability of the customer being a good risk, we need to divide the total number of good risk customers (7732) by the total number of customers (11,102). This gives us 7732/11102 = 0.7000. To calculate the probability of the customer not being a poor risk, we can subtract the total number of poor risk customers (949) from the total number of customers (11,102). This gives us 11102-949 = 10,153. We then divide this number by the total number of customers, giving us 10,153/11,102 = 0.9571. Therefore, the probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.9571.

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The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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To approach this type of problem, you have to make a couple of reasonable assumptions - first, that each worker works at the same pace, and second, that the effort to build each wall is the same.

Next, figure out how much effort is required to build one wall. The effort is measured in “working days”. So, how many days does one worker need to build one wall, or how many workers would be required to build one wall in one day? We can calculate this by dividing the 25 worker days used to build five walls by the number of walls (5). So we need five worker days per wall.

(5 workers) x (5 days) = 25 worker-days;

25 worker days/5 walls = 5 worker days per wall.

With 100 workers, it will take five days to build 100 walls. Each worker will build one wall in 5 days. So it will also take 5 days for all 100 workers to build all 100 walls.

100 x 5 = 500 worker days;

500 worker-days / 100 workers = 5 days (answer)

Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

The roots of the system of equations are x = 3.38586 and y = 2.61414, the error converges to 0 after the third iteration.

To solve this system of equations, we can use the Newton-Raphson method. This method starts with an initial guess and then uses a series of iterations to converge on the solution. In this case, we can use the initial guess x = y = 4.

The following table shows the results of the first few iterations:

Iteration | x | y | Error

------- | -------- | -------- | --------

1 | 4 | 4 | 0

2 | 3.38586 | 2.61414 | 0.06414

3 | 3.38586 | 2.61414 | 0

As you can see, the error converges to 0 after the third iteration. Therefore, the roots of the system of equations are x = 3.38586 and y = 2.61414.

The Newton-Raphson method is a relatively simple and efficient way to solve systems of equations.

However, it is important to note that it is only guaranteed to converge if the initial guess is close enough to the actual solution. If the initial guess is too far away from the actual solution, the method may not converge or may converge to a different solution.

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Answer:

second one

Step-by-step explanation:

it is the second one , it has three expression starts with 5

when n=0 :2n+5=2(0)+5=5

n=1 : 2n+5=7

n=2: 2n+5=4+5=9

n=3: 2n+5=11

Answer: B

Step-by-step explanation:

The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The possible outcomes are there on Ryan's first turn flipping two cards is

The cards are 52 in number in which 13 cards are different. Each card is four in quantity.

Ryan is playing a multiplication game with a pile of 26 cards, each with a number on them.

Each turn, he flips over two of the cards and has to  multiply the numbers.

The  number of ways in which two cards can be selected  from 26 cards, at the same time. The order of those are important.

Then, the number of possible outcomes on each flip of two cards

= 26 p(2)

= 26 x 25

=650

Thus, the possible outcomes are there on Ryan's first turn flipping two cards.

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Answer:

3/4

Step-by-step explanation:

thy shalt have the answer