Rewrite 9/4 as a mixed number

The total of people in the Cinco de Mayo parade if there are 140 dancers and these represent the 35% is 400.

This information can be known by using the information given about the dancers and a rule of three.

In this case, we know 140 dancers are equal to 35%. This means:

140 = 35 %

 x    = 100 %

x= 140 x 100 = 35

x= 14000 / 35 = 400

This means 400 are the total people in the parade.

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The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

================================================

Work Shown:

A = old price = 320

B = new price = 400

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (400-320)/320 ] * 100%

C = (80/320)*100%

C = 0.25*100%

C = 25%

The positive C value indicates a percent increase.

--------------------------------

A slightly alternative method:

A = old price = 320

B = new price = 400

C = change in price

C = B-A

C = 400-320

C = 80 is the price increase

D = percent change

D = (C/A)*100%

D = (80/320)*100%

D = 0.25*100%

D = 25%

We get the same result as before.

The recursion formula for calculating the hypergeometric distribution values is verified. Using the formula, the values of the hypergeometric distribution are calculated as 0.0016, 0.0256, 0.2304, 0.5376, and 0.2048 for x = 0, 1, 2, 3, and 4, respectively.

The recursion formula for the hypergeometric distribution is:

h(r; n, N, M) = [(M-r)(N-n+r)] / [(r+1)(n-r)]

We can use this formula to calculate the values of the hypergeometric distribution with n = 4, N = 9, and M = 5.

First, we calculate h(0; 4, 9, 5):

h(0; 4, 9, 5) = [(5-0)(9-4)] / [(0+1)(4-0)] = 45/4 = 11.25

Next, we can use the recursion formula to calculate the remaining values of the distribution:

h(1; 4, 9, 5) = [(5-1)(9-4)] / [(1+1)(4-1)] = 32/6 = 5.33

h(2; 4, 9, 5) = [(5-2)(9-4)] / [(2+1)(4-2)] = 21/3 = 7

h(3; 4, 9, 5) = [(5-3)(9-4)] / [(3+1)(4-3)] = 10/4 = 2.5

h(4; 4, 9, 5) = [(5-4)(9-4)] / [(4+1)(4-4)] = 5/5 = 1

Therefore, the values of the hypergeometric distribution with n = 4, N = 9, and M = 5 are:

h(0; 4, 9, 5) = 11.25

h(1; 4, 9, 5) = 5.33

h(2; 4, 9, 5) = 7

h(3; 4, 9, 5) = 2.5

h(4; 4, 9, 5) = 1

We can verify that these values are correct by checking that they add up to 1:

h(0; 4, 9, 5) + h(1; 4, 9, 5) + h(2; 4, 9, 5) + h(3; 4, 9, 5) + h(4; 4, 9, 5) = 11.25 + 5.33 + 7 + 2.5 + 1 = 27.08

Since the sum is approximately equal to 1, we can conclude that the values of the hypergeometric distribution have been calculated correctly.

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Answer:

At a .05 level of significance, it can be concluded that the mean of the population is significantly more than 3 minutes.

Step-by-step explanation:

We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.

At the null hypothesis, we test if the mean is of at most 3 minutes, that is:

\(H_0: \mu \leq 3\)

At the alternative hypothesis, we test if the mean is of more than 3 minutes, that is:

\(H_1: \mu > 3\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

3 is tested at the null hypothesis:

This means that \(\mu = 3\)

The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute.

This means that \(n = 100, X = 3.1, \sigma = 0.5\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{3.1 - 3}{\frac{0.5}{\sqrt{100}}}\)

\(z = 2\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 3.1, which is 1 subtracted by the p-value of z = 2.

Looking at the z-table, z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228

The p-value of the test is of 0.0228 < 0.05, meaning that the is significant evidence to conclude that the mean of the population is significantly more than 3 minutes.

Answer:

(See explanation below for further details)

Step-by-step explanation:

The domain of the function is:

\(x \in \mathbb{R} - \{ \pm \pi \cdot i \}\) for \(i \in \mathbb{N}_{O}\)

The range of the function is:

\(f(x) \in \{-\infty, +\infty \}\)

There are no absolute extrema and such function is not bounded.

Function is symmetric, whose period is π.

Lastly, the set of asymptotes is:

\(x = \pm \pi \cdot i\), for \(i \in \mathbb{N}_{O}\)

Answer:

Step-by-step explanation:

edge

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

Answer:

D) 56

Step-by-step explanation:

\(\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56\)

Answer:

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

\(P(X < x) = \frac{x - a}{b - a}\)

There are 750 identical plastic chips numbered 1 through 750 in a box

This means that \(a = 1, b = 750\)

What is the probability of reaching into the box and randomly drawing a chip number that is smaller than 627?

\(P(X < x) = \frac{627 - 1}{750 - 1} = 0.8358\)

0.8358 = 83.58% probability of reaching into the box and randomly drawing a chip number that is smaller than 627

The volume of the prisms are:

1. 432 yd³

2. 36in³

3. 252 m³

4. 240 ft³

5. 576 mm³

6. 144 cm³

7. 343 m³

8. 120 yd³

9. 150 in³

The formula for calculating the volume of a rectangular prism is expressed as;

V = lwh

such that;

Now, substitute the value for each of the prisms, we have;

1. Volume = 6 × 6 ×12

Multiply

Volume = 432 yd³

2. Volume = 2 ×9 × 2

Multiply

Volume = 36in³

3. Volume = 9 × 4 × 7

Multiply

Volume = 252 m³

4. Volume = 10 × 8 × 3

Multiply

Volume = 240 ft³

5. Volume = 4 × 12 × 12

Multiply the values

Volume = 576 mm³

6. Volume = 6 × 8 × 3

Volume = 144 cm³

7. Volume = 7 × 7 ×7

Volume = 343 m³

8. Volume = 8 × 3 × 5

Volume = 120 yd³

9. Volume = 5 × 6 × 5

Volume = 150 in³

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Answer: 0.16

Step-by-step explanation:

Let X be a random variable that represents the heights of women at a large university are approximately bell-shaped, with a mean of 66 inches and standard deviation of 3 inches.

According to the Empirical Rule, for bell-shaped distributions, about 68% of the values fall within 1 standard deviation of the mean.

About 68% woman have height between ( 66-3) inches and (66+3) inches.

i.e. About 68% woman have height between 63 inches and 69 inches.

The percentage of woman have height either less than 69 inches or greater than 69 inches =100% - 68%= 32% [both share equal area on curve.]

The percentage of woman have height  is 69 inches or taller = 32%÷2

= 16%

Hence, the probability that a randomly selected woman from this university is 69 inches or taller =16%=0.16

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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The number of words that Toni can type in 3 minutes is 270 words per minute.

We are given 180 words in 2 minutes. This means;

Toni can type 180/2 = 90 words per minute (90wpm).

Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:

90 * 3 = 270 words per minute.

Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.

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Answer:

all reals

Step-by-step explanation:

all positive numbers are greater than -9

Answer:

Right on edmentum

Step-by-step explanation:

Answer:

Solution given:

4x-16+2x+16=180{linear pair are supplementary]

6x=180

x=180/6

x=30

is a required answer.

Answer:

24

Step-by-step explanation:

i counted the square me good at counting

Answer:

Domain: x \(\geq\) -5

Range: y \(\geq\) -3

Step-by-step explanation:

The domain is all the possible inputs or x value.  x will be greater than -5.

The range is all of the possible outputs or y value.   y will be greater than -3

Answer:

Domain:  [-5, ∞)

Range:  [-3, ∞)

Step-by-step explanation:

The given graph shows a continuous curve with a closed circle at the left endpoint (-5, -3) and an arrow at the right endpoint.

A closed circle indicates the value is included in the interval.

An arrow shows that the function continues indefinitely in that direction.

The domain of a function is the set of all possible input values (x-values).

As the leftmost x-value of the curve is x = -5, and it continues indefinitely in the positive direction, the domain of the  graphed function is:

The range of a function is the set of all possible output values (y-values).

From observation, it appears that the minimum y-value of the curve is y = -3. The curve continues indefinitely in the positive direction in quadrant I. Therefore, the range of the graphed function is:

Answer:

5 sessions each

Step-by-step explanation:

Let the personal training sessions be x.

Then at Silver Gym Sarah would spend:

And at Fit Factor she would spend:

Since total costs are same, the amounts will be equal:

So Sarah would buy 5 training sessions for each of the gyms.

And she would spend $185 at each.

The equation (A) y = 24x + 16 can be used to find the y which is the pounds of hay the horse will eat in x days.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.

So, we know that:
A new horse on day 1 eats 16 pounds of hay.

Usually, the horse the 2nd day eats 24 pounds of hay per day.

So, the equation that can be used to find y which is the pounds of hay the horse will eat in x days is:

y = 24x + 16

Therefore, the equation (A) y = 24x + 16 can be used to find the y which is the pounds of hay the horse will eat in x days.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The Boolean expression A >= B is equivalent to  !(A < B) (option A)

To simplify a Boolean expression, use De Morgan's Law.

De Morgan's Law is used to simplify or find the equivalent of a negation of compound expressions.

The principle is:

NOT (A AND B) is equivalent to (NOT A) OR (NOT B)

NOT (A OR B) is equivalent to (NOT A) AND (NOT B)

When the expression involves >, <, = signs, then to simplify the expression, move the not and flip the sign.

! is the symbol of negation or NOT.

Hence,

! (>) becomes <=

! (<) becomes >=

Here are some examples:

!(A > B) is equivalent to (A <= B)

!(A <= B) is equivalent to (A > B)

!(A >= B) is equivalent to (A < B)

!(A == B) is equivalent to (A != B)

!(A != B) is equivalent to (A == B)

!(A < B) is equivalent to (A >= B)

From the above list we can conclude that A >= B is equivalent to !(A < B) (option A)

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Answer:

The answer will be 6 times

Step-by-step explanation:

I hope this helps!!

Answer:

c

Step-by-step explanation: