5 /4 6 5
Find the quotient.

The cost of purchasing the number of shirts after discount and sale tax is $40.3125.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

The discount is 25%.

The total price before the coupon is $50.

The sale tax is 7.5%

The cost of purchasing the number of shirts after discount will be

\(\rm Cost = 50*(1-0.75 )\\\\Cost = 97.5\)

The cost of purchasing the number of shirts after the sale will be

\(\rm Cost = 37.5*(1.075)\\\\Cost = 40.3125\)

The cost of purchasing the number of shirts after discount and sale tax is $40.3125.

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Answer:

43.98 cm

Step-by-step explanation:

\(C=2\pi r\) where r is the radius

Plug the radius 7 cm into the equation as r

\(C=2\pi (7)\\C=14\pi \\C=43.98\)

Therefore, the circumference of the circle is approximately 43.98 cm.

I hope this helps!

The present value of $102,000 in 10 years, given a long-term interest rate of 9 percent, is $43,229. This means that if Delia were to receive $102,000 in 10 years, it would be equivalent to receiving $43,229 today.

Therefore, Delia should choose to take the $38,000 today instead of waiting 10 years to receive $102,000. The present value of $102,000 is less than the amount offered today, so it is a better choice financially.
Explanation:
To calculate the present value, we use the formula: Present Value = Future Value / (1 + Interest Rate)^n, where n is the number of periods.

Using Appendix B, we can find the present value factor for 10 years at a 9 percent interest rate, which is 0.423.
To calculate the present value, we multiply the future value ($102,000) by the present value factor (0.423): $102,000 * 0.423 = $43,229.
Comparing the present value of $43,229 to the $38,000 offered today, we can see that the latter is the better choice financially. Delia should choose to take the $38,000 today instead of waiting 10 years to receive $102,000.

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Answer:

A

Explanation:

To determine which sequence of transformation will map figure K onto figure K', we test each of the options using the point (6,5) in Figure K.

Option A

Reflection across x=4, 180° rotation about the origin, and a translation of (x+8,y)

Option B

Reflection across x=4, 180° rotation about the origin, and a translation of (x-8, y)

Option C

Reflection across y=4, 180° rotation about the origin, and a translation of (x+8,y)

Option D

Reflection across y=4, 180° rotation about the origin, and a translation of (x-8,y)

We can see that Option A is the one which maps point (6,5) to (6,-5).

Therefore, it is the sequence of transformations will map figure K onto figure K'.

Answer:

x = 4

Step-by-step explanation:

perpendicular lines have opposite and reciprocal slopes

the line y = 2 is a horizontal line, which means the slope is zero

also, y = 2 intersects the y-axis at 2

a line perpendicular to a horizontal line is a vertical line and, if it passes through the point (4,5) will intersect the x-axis at 4

therefore, the equation would be x = 4

Answer:

D

Step-by-step explanation:

Let's look at each option:

A. Distance =600 ✓

This is because the graph is a distance- time graph. To find the distance between her house and the post office, look at the y value of the point at the end of her journey. In this case, at t=24 mins, the y -value is 600 and thus the statement is correct.

B. ✓ correct

First 9 mins is from t=0 to t=9. Speed can be found by taking the gradient of the line of a distance- time graph.

Gradient can be found by taking rise/ run, which is also the difference in the y- coordinates divided by the difference in the x -coordinates.

\(\boxed{ gradient = \frac{y1 - y2}{x1 - x2} }\)

\(gradient \\ = \frac{315}{9} \\ = 35\)

Thus, the speed in the first 9 minutes is indeed 35m/min.

C. ✓correct

Since distance remained at 315m from t=9 to t=13mins, she stopped for that period of time.

Time stopped

= 13 -9

= 4 minutes

D. Incorrect

Average speed= total distance/ total time

Total distance= 600m

Total time= 24 mins

Thus, average speed

= 600 ÷24

= 25m/min

We have a 98% confidence that the actual percentage of consumers who click on mobile ads is between 0.363 and 0.537.

Using the following calculation, we can determine the 98% confidence interval for the actual percentage of consumers who click on mobile ads:

point estimate ± margin of error

where the sample proportion (0.45) serves as the point estimate and the following formula is used to get the margin of error:

z * standard error of the proportion

where the standard error of the proportion is determined by the formula below, and z is the z-score for a 98% confidence level.

the standard deviation of the proportion = square root of (sample proportion * (1 - sample proportion) / sample size)

With the values entered, we obtain:

standard deviation of the proportion= square root of (0.45 * (1 - 0.45) / 150) = 0.037

The z-score at a 98% confidence level, according to a z-table, is 2.33.

Therefore, the error margin is:

2.33 * 0.037 = 0.087

The 98% confidence interval for the actual percentage of consumers who click on mobile ads is as follows:

0.45 ± 0.087 = (0.363, 0.537)

Thus, We have a 98% confidence level that the actual percentage of consumers that click on mobile ads is between 0.363 and 0.537.

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Answer:

91677.9415 milliliters

Step-by-step explanation:

Answer:

28%

Step-by-step explanation:

38.40 - 30 = 8.40

x : 100 = 8.40 : 30

x = 8.40 * 100 / 30

x = 840/30

x = 84/3 = 28%

Answer:

y = 5

Step-by-step explanation:

Isolate x to plug in to other equation

y   =   x  +  2

-y-x     -y-x

(- x = -y + 2) / -1

x = y - 2

Plug into other equation

y = 3(y-2) - 4

Distribute

y = 3y-6-4

y = 3y-10

-3y  -3y

(-2y = -10)/-2

y = 5

With x = 9 and y = 9, the minimum value of q is 729.

We have,

The concept used to solve the problem is substitution.

By substituting the given values of x and y into the function

\(q = 6x^2 + 3y^2\), we can evaluate the expression and find the minimum value.

Substitution allows us to replace the variables with their specific values and simplify the equation to obtain the result.

To minimize the function q = \(6x^2 + 3y^2\) with the constraint x = 9 and y = 9, we substitute the given values into the function.

Substituting x = 9 and y = 9 into q, we have:

\(q = 6(9)^2 + 3(9)^2\)

= 6(81) + 3(81)

= 486 + 243

= 729

Therefore,

With x = 9 and y = 9, the minimum value of q is 729.

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The total vertical distance traveled by the ball is 50 feet.

The ball is dropped from a height of 6 feet, so the first bounce covers a distance of 6 feet.

For subsequent bounces, the ball rebounds up to 0.88 times the height of the previous bounce. Let's calculate the distances for the subsequent bounces:

First bounce: 6 feet

Second bounce: 0.88 * 6 feet

Third bounce: 0.88 * (0.88 * 6) feet

Fourth bounce: 0.88 * (0.88 * (0.88 * 6)) feet

...

Nth bounce: \(0.88^{N-1} * 6\) feet

To find the total distance traveled, we need to sum up all these distances. Since the ball continues bouncing indefinitely, we have an infinite geometric series.

The sum of an infinite geometric series is given by the formula:

Sum = a / (1 - r)

where:

a is the first term of the series (6 feet in this case),

r is the common ratio (0.88 in this case).

Using the formula, we can calculate the total distance traveled:

Sum = 6 feet / (1 - 0.88)

Sum = 6 feet / 0.12

Sum = 50 feet

Therefore, the total vertical distance traveled by the ball is 50 feet.

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Therefore, the value of x is 7.2.

Hoped this helped.

\(BrainiacUser1357\)

If each chip chosen from the shipment has a 0.05 probability of being defective, then the probability of a chip working properly is 1 - 0.05 = 0.95.

Since each chip is chosen independently, the probability that all 16 chips in a car will work properly is the product of the individual probabilities of each chip working properly.

Probability of a chip working properly = 0.95

Number of chips in a car = 16

Probability that all 16 chips will work properly = (0.95)^16 ≈ 0.544

Therefore, the probability that all 16 chips in a car will work properly is approximately 0.544, or 54.4%.

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Answer: $1114.91

Step-by-step explanation:

The formula for compound interest is

\(A= P(1+\frac{r}{n})^{nt} \\\)

Where

A = final amount

P = initial principal balance (1030 for this)

r = interest rate (0.04 for this)

n = number of times interest applied per time period (2 for this)

t = number of time periods elapsed (2 for this)

\(A= 1030(1+\frac{.04}{2})^{(2)(2)} \\\\A= 1030(1+0.02)^{4} \\A=1030(1.02)^4\\A=1114.905125\)

This rounds up to $1114.91

The z-score for a person who received a score of 62 is -2.1053.

To calculate the z-score, we use the formula:

z = (x - μ) / σ

Where:

x is the individual score,

μ is the mean of the distribution, and

σ is the standard deviation of the distribution.

In this case, the class mean (μ) is 71 and the standard deviation (σ) is 3.8. The individual score (x) is 62.

Plugging these values into the formula, we get:

z = (62 - 71) / 3.8

z = -9 / 3.8

z ≈ -2.3684

Rounding the z-score to four decimal places, we get -2.1053.

The negative z-score indicates that the person's score of 62 is below the class mean. A z-score measures the number of standard deviations an individual's score is above or below the mean. In this case, the score is approximately 2.1053 standard deviations below the mean.

The z-score allows us to compare the person's score to the rest of the class by standardizing it with respect to the mean and standard deviation. It provides a standardized measure of how far the person's score deviates from the average performance in the class.

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The fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

Ryan grew \($\frac{1}{2}$\) feet in a year.

1. To express the fraction \($\frac{9}{12}$\) as a sum of smaller fractions, we can simplify it by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of \(9\) and \(12\) is \(3\).

So, we can rewrite \($\frac{9}{12}$\) as:

\($\frac{9}{12} = \frac{3 \times 3}{3 \times 4} = \frac{3}{4}$\)

Therefore, the fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

2. To find how much Ryan grew in a year, we need to calculate the difference between his height this year and his height last year.

Let's convert the mixed fractions to improper fractions for easier computation:

Last year's height: \($4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}feet\)

This year's height: \($5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} feet\)

To determine the growth, we subtract last year's height from this year's height:

\($\frac{21}{4} - \frac{19}{4} = \frac{21 - 19}{4} = \frac{2}{4} = \frac{1}{2}feet\)

Therefore, Ryan grew \($\frac{1}{2}$\) feet in a year.

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Calculate the area of the floor:

Area = 1.6 x 2.3 = 3.68 square meters

Using the given formula: Pressure = force/area

200 = force / 3.68

Solve for force by multiplying both sides by 3.68

Force = 200 x 3.68

Force = 736 N/m^2

Correct to the nearest 5N/m^2 = 735 N/m^2

First of all we need to calculate the area of the floor and then we will find the pressure using the formula for pressure...

\(\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}\)

Area of floor ↯

\( \sf \: area = length \times breadth\)

\( \sf \: area = 1.6 \times 2.3\)

\( \sf \: area = 3.68 \: {m}^{2} \)

\(\purple{ \rule{300pt}{3pt}}\)

Finding force ↯

\( \tt \: pressure = \frac{force}{area} \)

\( \tt \: 200 = \frac{force}{3.68} \)

\( \tt \: force = 200 \times 3.68\)

\( \tt \: force = 736 \: newton\)

Thus, The maximum force is 736 Newton...~

Answer:

22

Step-by-step explanation:

Do 83.58 divided by 3.799

The state income tax is $2,214.

To calculate the state income tax owed on a $50,000 per year salary, we need to apply the progressive tax rate.

First, we find the amount of income that falls into each tax bracket. Since $50,000 falls into the highest tax bracket, we can ignore the first two tax brackets.

Amount subject to 5.4% tax rate

= $50,000 - $9,000

= $41,000

Next, we calculate the tax owed on each portion of income and add them together.

Tax owed on amount subject to 5.4% tax rate

= 5.4% x $41,000

= $2,214

Therefore, the state income tax owed on a $50,000 per year salary is $2,214.

Rounded to the nearest whole dollar amount, the answer is $2,214.

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Answer:

The answer is apple

Step-by-step explanation: If you break it out correctly, whenever the sky tastes like watermelon its a sign of the birth of apples.

Answer:

the answer is simply 14

Step-by-step explanation:

its ez dum baby brain

To find the area of the region enclosed by the curves y = 2x and y = x2 - 4x, we have to follow these steps.

Step 1: Find the intersection point between y = 2x and y = x2 - 4x.

To find the intersection point between the curves, we have to set y = y and solve for x.2x = x2 - 4x ⇒ x2 - 6x = 0 ⇒ x(x - 6) = 0So, either x = 0 or x = 6. But y = 2x will always give us positive values. Hence the intersection point is (0, 0) and (6, 12).

Step 2: Find the integral expression for the area of the region enclosed by the curvesThe region enclosed by the curves can be represented in two parts. One part is between the curve y = 2x and the x-axis. Another part is between the curve y = x2 - 4x and the x-axis.

Area of the region =

∫0^6(2x)dx + ∫0^6[(x2 - 4x) - (2x)]dx= ∫0^6(x2 - 6x)dx= [x3/3 - 3x2]06= 72Now we will conclude that the area of the region enclosed by the curves y = 2x and y = x2 - 4x is 72 square units.

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Answer:

V≈6.93

Step-by-step explanation:

AB=s(s﹣a)(s﹣b)(s﹣c)

V=ABh

s=a+b+c

2

Solving forV

V=1

4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1

4·4·﹣24+2·(2·2)2+2·(2·2)2﹣24+2·(2·2)2﹣24≈6.9282

D. At the end of 20 years, the policy's cash value will equal $100,000 is INCORRECT regarding a $100,000 20-year level term policy.

A $100,000 20-year level term policy is a type of life insurance policy that provides a fixed amount of coverage for a set period of time. The premiums for this policy will remain level for the entire 20 years and, if the insured dies during that time, the beneficiary will receive the full $100,000. However, the policy will expire at the end of the 20-year period and the cash value will not equal the $100,000. As a result, it is untrue to say that $100,000 will be the policy's cash value after 20 years.

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Answer:

y=-2x+15

Step-by-step explanation:

Hi there!

We are given that m=-2, b=15, and we want to write the equation of the line, given these values

We can write the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept, since we are given the values of both m and b.

Since we know the values of m and b (-2 and 15 respectively), we can substitute those numbers in as the variables they equal to.

Substitute -2 as m:

y=-2x+b

Substitute 15 as b:

y=-2x+15

Hope this helps!

The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.

To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:

A = x^2 + 4xh

Solving for h, we get:

h = (A - x^2) / 4x

The volume V of the box is given by:

V = x^2 * h

Substituting the expression for h, we get:

V = x^2 * (A - x^2) / 4x

Simplifying, we get:

V = (Ax^2 - x^4) / 4

The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.

To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).

To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = (2Ax - 4x^3) / 4

Setting this equal to 0 and solving for x, we get:

x = sqrt(A) / sqrt(2)

Plugging this value of x into the formula for V, we get:

V = A^1.5 / (4sqrt(2))

Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).

To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:

V = (10x^2 - x^4) / 4

Simplifying, we get:

V = 2.5x^2 - 0.25x^4

Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.

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At the base of the ramp, the box is moving at a speed of roughly 2.21 m/s.

On the uneven horizontal surface, the box will move around 0.508 meters before stopping.

To analyze the motion of the box, we can break it down into different stages:

Stage 1: Box sliding down the ramp (height = 0.25m)

Stage 2: Box sliding on the rough horizontal surface (friction coefficient = 0.50)

Determine the box's final velocity after sliding on the uneven horizontal surface by computing the motion of the object at each stage.

Stage 1: Box sliding down the ramp :-

Using the principle of energy conservation, we can determine the box's speed when it reaches the bottom of the ramp.

Since there is no energy loss due to friction, the original potential energy at the top of the ramp will be transformed into kinetic energy at the bottom.

The potential energy at the top of the ramp is given by:

\(\mathrm{PE_{top} = m \times g \times h}\)

where m = mass of the box = 2.0 kg (given)

g = acceleration due to gravity = 9.81 m/s² (approximate value on Earth)

h = height of the ramp = 0.25 m (given)

\(\mathrm {PE_{top}} = \mathrm {2.0 \ kg \times 9.81 \ m/s^2 \times 0.25 \ m \approx 4.905\ J}\)

The kinetic energy at the bottom of the ramp will be equal to the potential energy at the top:

\(\mathrm {KE_{bottom} = PE_{top} = 4.905 \ J}\)

The kinetic energy is given by:

\(\mathrm {KE = (1/2) \times m \times v^2}\)

where v is the velocity of the box at the bottom of the ramp.

\(\mathrm {4.905 \ J = (1/2) \times 2.0 \ kg \times v^2}\)

\(\mathrm{v^2 = 4.905 \ J \times 2 / 2.0 \ kg}\)

\(\mathrm{v^2 = 4.905 \ m^2/s^2}\)

v ≈ 2.21 m/s

So, the velocity of the box at the bottom of the ramp is approximately 2.21 m/s.

Stage 2: Box sliding on the rough horizontal surface :-

The friction coefficient is denoted by the symbol = 0.50.

Let's now determine the slowdown brought on by friction on the uneven horizontal surface.

The friction force can be calculated using the equation:

friction force = μ × normal force

Since there is no vertical acceleration (the box doesn't lift off the ground), the normal force acting on the object is equal to its mass (mg).

normal force = \(\mathrm {m \times g = 2.0\ kg \times 9.81 m/s^2 \approx 19.62\ N}\)

friction force = \(\mathrm {0.50 \times 19.62 \ N \approx 9.81 \ N}\)

The friction force operates against the direction of motion, causing the box to decelerate (have a negative acceleration).

Newton's second law provides the net force in the horizontal direction:

net force = mass × acceleration

acceleration = net force / mass

acceleration = -9.81 N / 2.0 kg

≈ -4.905 m/s²

The opposite of the initial motion is being accelerated, as indicated by the negative sign.

Now, we can find the distance the box travels on the rough horizontal surface.

The final velocity (\(\mathrm{v_{final}}\)) on the rough surface can be found using the following kinematic equation:

\(\mathrm{(v_{final})^2 = (v_{initial})^2 + 2 \times acceleration \times distance}\)

Since the box starts from rest (\(\mathrm{v_{initial} = 0 \ m/s}\)) on the rough surface, the equation simplifies to:

\(\mathrm{v_{final} = \sqrt{ (2 \times acceleration \times distance)}}\)

Plugging in the values:

\(\mathrm{2.21 \ m/s = \sqrt{(2 \times (-4.905 \ m/s^2) \times distance)}}\)

Solving for distance:

\(\mathrm{distance = \frac{(2.21 \ m/s)^2}{2 \times (-4.905 m/s^2)} \approx 0.508 \ m}\)

Thus, the box will move around the uneven horizontal surface for about 0.508 meters before stopping.

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Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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Phase 5: The system of implementation is conversion.

Option B is the correct answer.

We have,

Phase 5 of the system development life cycle is commonly referred to as "Conversion" or "Systems Implementation."

During this phase,

The focus shifts from planning and designing the system to actually implementing it.

This phase involves the conversion of the old system to the new system, which includes activities such as data conversion, software installation, hardware setup, user training, and system testing.

The term "Conversion" is used because it signifies the transition from the old system to the new system.

It involves migrating data, processes, and operations from the existing system to the new system.

This phase ensures that the newly developed system is successfully integrated into the organization and becomes fully operational.

Thus,

Phase 5: The system of implementation is conversion.

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The geometric mean radius of the unconventional conductors in terms of the radius r of an individual strand is 1.583r.

To find the geometric mean radius of the unconventional conductors, we need to understand the concept of geometric mean. The geometric mean of two numbers is the square root of their product. In this case, we are looking for the geometric mean radius of multiple strands.

First, we need to determine the number of strands in the unconventional conductors. The question does not provide this information explicitly, so we assume there are at least two strands.

We know that the geometric mean radius is the square root of the product of the individual strand radii. Let's assume there are n strands, and the radius of each strand is r. Therefore, the product of the individual strand radii would be r^n.

Now, we can calculate the geometric mean radius by taking the square root of r^n. Mathematically, it can be expressed as (r^n)^(1/n) = r^((n/n)^(1/n)) = r^1 = r.

Therefore, the geometric mean radius in terms of the radius r of an individual strand is 1.583r.

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