Find the value of each variable.

UCF students pay an average of 1,236 dollars for books. The standard deviation of costs of books is sigma = 101 dollars. Select 36 UCF students at random.

The probability is 0.025.

Explanation:

To find the probability that the mean cost of books for 36 UCF students exceeds 1,236 + 1.96(101/6), follow these steps:

1. Calculate the target mean:

1,236 + 1.96(101/6) = 1,236 + 32.99 ≈ 1,268.99.

2. Determine the standard deviation of the sample mean:

σ_sample = σ/√n = 101/√36 = 101/6 ≈ 16.83.

3. Calculate the z-score

: z = (target mean - population mean) / σ_sample =

(1,268.99 - 1,236) / 16.83 ≈ 1.96.

4. Use a standard normal table or a calculator to find the probability that the z-score is greater than 1.96.

This is 1 - P(Z ≤ 1.96) = 1 - 0.975 = 0.025.

So, the probability that the mean cost of books for 36 UCF students exceeds 1,236 + 1.96(101/6) is 0.025 or 2.5%.

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Answer:

c = 0.3

Step-by-step explanation:

c = √0.5² - 0.4² = √0.09 = 0.3

Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..

What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i

This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.

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Answer: 15 oatmeal cookies.

Step-by-step explanation:

There were 25 cookies baked.

Out of these, 3/5 are oatmeal cookies.

The amount of actual oatmeal cookies is:

= fraction of oatmeal cookies * total number of cookies

= 3/5 * 25

= 75 / 5

= 15 oatmeal cookies.

The margin for the runners is 50% and the Margin percentage is 33.33% (to the nearest percent).

When the shop sells runners at a mark-up of 50%, we need to find out the margin for these runners.

What is markup?

The mark-up is a percentage that you add to the cost price of a product to get the selling price. The mark-up percentage is calculated based on the cost price of the product.

Let the cost price of the runner be CP and the markup percentage be M%

Since the shop is selling the runners at a 50% markup, the selling price of the runners would be 150% of their cost price.

Selling price = (100 + M)% × Cost priceSelling price = (100 + 50)% × CP = 150% × CP = 1.5 × CP

Therefore, the margin for the runners can be calculated as follows:

Margin = Selling price - Cost price

Margin = 1.5 × CP - CP = 0.5 × CP

Clearly, the margin on runners is 50% of their cost price.

The percentage of margin can be calculated as follows:

Margin percentage = (Margin / Selling price) × 100Margin percentage = (0.5 × CP / 1.5 × CP) × 100Margin percentage = (1/3) × 100Margin percentage = 33.33%

Therefore, the margin for the runners is 50% and the margin percentage is 33.33% (to the nearest percent).

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Answer:

∠ABC = 162

Step-by-step explanation:

Since you have ∠ABD and ∠DBC, add the two angles to find ∠ABC.

28 + 134 = 162

Answer:

huh

Step-by-step explanation:

Answer:

slope = 25

y -intercept = 525

equation : y = 25x + 525

Step-by-step explanation:

An investor invests $525 in stock

It means the initial price of stock is $525

In 1 month increase in value of stock = $25

thus,

In x month increase in value of stock = $25x

Total cost of stock in x months = initial investment + increase in value of stock in x months

Total value of stock in x months = 525 + 25x

as Total value of stock in x months = f(x)

f(x) = 525 + 25x

it can be also written as

y =  25x   + 525

____________________________________________

we know that slope intercept form of linear relationship is

y = mx + c

where m is the slope

and c is the y intercept

thus

comparing  y =  25x   + 525 with y = mx + c

we have m = 25

c = 525

Answer:

12(2-(4-a²)÷7+b

12(2-(4-(5)²)÷7+1

12(2-(4-25)÷8

12(2-(-21)÷8

12(2+21)÷8

12(23)÷8

276÷8

34.5

The population size after four days is 121.

Given that,

a population of protozoa with a constant relative growth rate of 0.8603 per member per day

let P be the population size and let t be the time interval then the given system modeled by the differential equation

\(\frac{dP}{dt}\) = 0.8603

by solving the separable equation and expifying both sides we get,

P = A \(e^{0.8603t}\)

From the condition that on day zero the population consist of four members,

i.e. P(0) = 4, A = 4

Therefore population size after four days is

P(4) = 4\(e^{4(0.8603)}\)

      = 4 \(e^{3.441}\)  

      = 4 × 30.295

P(4) =  121.2

nearest whole number is 121

i.e P(4) = 121

Hence the population size after four days is 121.

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Answer:

d. x = 14; angle measurement is 28 degrees

Step-by-step explanation:

2x is equivalent 28 so divide 28 by 2 to get 14

The expression that shows time, t, it will now take Rashid to make the trip relative to the speed, v with which he slows down is t = (240 - (v/120) * 240) / (120 - v)

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity.

The relation between time, t, and the speed at which Rashid slows down, v, is given by the formula:

t = (240 - (v/120) * 240) / (120 - v)

t = time

v= speed.

This formula can be derived by using the distance formula (distance = speed x time) and the fact that the distance traveled is constant (240 km).

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The average velocity of Gwen over the time interval 0 < t is zero. We need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer.

Given that Gwen runs back and forth along a straight track and her velocity, in feet per second, is modeled by the function v(t) during the time interval 0 < t < 45 seconds; We are to determine the first time at which Gwen changes direction and find her average velocity over the time interval 0 < t.Firstly, we know that velocity is a vector quantity and has both magnitude and direction.

Since she is running back and forth along a straight track, her displacement at any given time t is given by the function s(t), which is the integral of her velocity function v(t).That is, s(t) = ∫v(t)dtWe can find the displacement by taking the definite integral of v(t) from 0 to t. Since Gwen is running back and forth, her displacement will be zero at the times when she changes direction.

Therefore, we need to solve the equation:250sin(πt/45) = 0Solving for t, we get:πt/45 = nπwhere n is an integer. Therefore,t = 45n/πwhere n is an integer. Since we are looking for the first time at which Gwen changes direction, we need to take the smallest positive value of n, which is n = 1.

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S + R represents the total trips done by these trucks.

Volume is defined as the amount of space occupied by an object that is bound by a boundary. It must be noted that the volume is a mathematical term that is only applicable to 3D (three-dimensional) objects or spaces. As such, the units commonly used for volume are cubic units, that is, m3, cm3, in3, etc.

Two dump trucks hauling rock to a construction site is given by the expression. xS + yR

S +R

Truck 1 can haul x cubic yards

Truck 2 can haul y cubic yards.

Truck 1 makes P trips to the construction site, while truck 2 makes R trips.

Hence the trips made by truck 1 and truck 2 should be the addition of the trips made by the trucks individually.

So the total trips is represented by S + R

Therefore, S + R represents the total trips done by these trucks.

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Answer:

h(0) = 10

h(4) = 16

Step-by-step explanation:

h(0) = 2(0)² - 3(0) + 10 = 10

h(4) = 2^4 = 16

The coefficients of the identical terms in both polynomials are added or subtracted to determine the sum or difference of two polynomials. For instance, when the coefficients of x and y are added together, the sum of (2x + 3y) + (4x + 9y) + (4x + 12y) is equal to 6x + 12y.

1. (2x + 3y) + (4x + 9y)

2x + 3y + 4x + 9y = 6x + 12y

2. (6s + 5t) + (4t + 8s)

6s + 5t + 4t + 8s = 10s + 9t = 14s + 9t

3. (5a + 9b) - (2a + 4b)

5a + 9b - 2a - 4b = 3a + 5b

4. (11m - 7n) - (2m + 6n)

11m - 7n - 2m - 6n = 9m - 13n

5. (m2 - m) + (2m + m2 )

m2 - m + 2m + m2 = 3m2 + m = 2m2 + m

Find each product.

1. (3x + 4y)(2x - 9y) 6x2 - 33xy + 8y2

2. (2a + 5b)(a - 7b) 2a2 - 19ab + 35b2

3. (7s - 4t)(s + 2t) 7s2 + 10st - 8t2

4. (4m + 6n)(m - n) 4m2 - 2mn + 6n2

5. (3x2 + 2x)(5x + 7) 15x3 + 31x2 + 14x

By adding or removing the coefficients of the identical terms in both polynomials, one can determine the sum or difference of two polynomials. Finding the similar terms in both polynomials is the first step in accomplishing this. The corresponding words, for instance, are x and y in the case of (2x + 3y) + (4x + 9y). The sum of the x coefficients is 2 + 4 which equals 6, and the y coefficients is 3 + 9 which equals 12. Because of this, the expression (2x + 3y) + (4x + 9y) = 6x + 12y. Two polynomials can be subtracted using the same procedure

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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1x - 13y + 475

Step-by-step explanation:

\(3x \: + \: 4y \: - \: 2(4y \: - \: 8) \: - \: 25y \: + \: 485\)

3x + 4y - 2x - 2 + 8y - 8 - 25y + 485

3x - 2x + 4y + 8y - 25y - 2 - 8 + 485

1x + 4y + 8y - 25y - 2 - 8 + 485

1x + 12y - 25y - 2 - 8 + 485

1x - 13y - 2 - 8 + 485

1x - 13y - 10 + 485

1x - 13y + 475

HOPE THIS HELPS YOU

When a validity coefficient exceeds 0.90, it is considered to be in the very high range.

Validity coefficients greater than 0.90 are considered in the very high range.

Validity coefficients measure the strength of the relationship between a test or measurement and the construct it is intended to assess. The coefficients range from -1.00 to +1.00, where higher values indicate stronger validity.

When a validity coefficient exceeds 0.90, it is considered to be in the very high range. This suggests that the test or measurement has a high degree of accuracy in assessing the intended construct, demonstrating a strong relationship between the two. Validity coefficients in this range provide strong evidence that the test is measuring what it is intended to measure.

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Answer:

k=3

Step-by-step explanation:

Answer:

k = 3

Step-by-step explanation:

Given

3 - 2k - 3k = - 12, simplifying left side

3 - 5k = - 12 ( subtract 3 from both sides )

- 5k = - 15 ( divide both sides by - 5 )

k = 3

Answer:

\(\textsf{C.} \quad C = \$10 + \$5h\)

Step-by-step explanation:

Given information:

Given variables:

The Park admission fee of $10 is independent of the fee charged per hour per sport.  Therefore, it is represented by a constant in the equation.

The fee per hour of sledding is dependent on the number of hours spent.  Therefore, it is represented by the cost of the specific sport multiplied by the given variable for time (h).

Therefore the equation that represents the cost of sledding per hour is:

C = $10 + $5h

\(\huge \boxed{\sf C}\)

Each hour costs 5 dollars for sledding and an extra fee of 10 dollars.

\(\sf C = 5h + 10\)

An equation contains variables and integers.

C and h are variables which means the value changes.

5 and 10 are integers.

Answer:

70

Step-by-step explanation:

triangle xbc is an isosceles triangle.

there are 180 degrees in a triangle.

angle xbc=55.

so that means angle xcb is also 55.

55+55=110

180-110=70

hope this helps

Lex will need approximately 18.96 units of tile to surround his pool. The perimeter of the quadrilateral is the sum of these lengths.

To find the number of units of tile Lex will need to surround his pool, we can calculate the perimeter of the quadrilateral ABCD.
Given the coordinates of the vertices on the coordinate plane, we can calculate the lengths of the sides:
AB = \(\sqrt((3-0)^2 + (5-4)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
BC = \(\sqrt((5-3)^2 + (-1-5)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
CD = \(\sqrt((2-5)^2 + (-2+1)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
DA = \(\sqrt((2-0)^2 + (-2-4)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
The perimeter of the quadrilateral is the sum of these lengths:
Perimeter = AB + BC + CD + DA = 3.16 + 6.32 + 3.16 + 6.32 = 18.96 units (rounded to the nearest hundredth)
Therefore, Lex will need approximately 18.96 units of tile to surround his pool.

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Lex will need approximately 20.46 units of tile to surround his pool. To find the number of units of tile needed to surround the pool, we need to calculate the perimeter of the pool.

Given the coordinates of the four vertices of the pool:
    A(0, 4)
    B(3, 5)
    C(5, -1)
    D(2, -2)

We can find the length of segment AB using the distance formula:
    \(AB = \sqrt{(3-0)^2 + (5-4)^2} = \sqrt{9 + 1} = \sqrt{10} = 3.16\)units (rounded to the nearest hundredth).

The length of diagonal BD can also be found using the distance formula:
    \(BD = \sqrt{(2-3)^2 + (-2-5)^2} = \sqrt{1 + 49} = \sqrt{50} = 7.07\) units (rounded to the nearest hundredth).

Since angles A and C are right angles, we know that the opposite sides AB and CD are parallel. Similarly, the opposite sides AD and BC are parallel.

The perimeter of the pool is the sum of the lengths of all four sides:
    Perimeter = AB + BC + CD + AD
                      = 3.16 + BD + 3.16 + BD
                      = 6.32 + 7.07 + 7.07
                      = 20.46 units (rounded to the nearest hundredth).

Therefore, Lex will need approximately 20.46 units of tile to surround his pool.

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Answer:

The number of days is at most 5 days

= d ≤ 5 days

Step-by-step explanation:

A rental car company charges $31 per day to rent a car and $0.13 for every mile driven. Jocelyn wants to rent a car, knowing that:

She plans to drive 500 miles.

• She has at most $220 to spend.

At most means Less than or equal to $220

The inequality for expressing this = ≤

Hence, the inequality which can be used to determine d, the number of days Jocelyn can afford to rent while staying within her budget.

$31 × d + $0.13 × 500 miles ≤ $200

The inequality is given as:

31d + 65 ≤ 220

Solving further

31d ≤ 220 -65

31d ≤ 155

d ≤ 155/31

d ≤ 5

Therefore, the number of days is at most 5 days

The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.

Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
 To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.

Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25

Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211

Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709

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Answer:

x^2+5x+6

Step-by-step explanation:

\(\left(x+2\right)\left(x+3\right)\\\\\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\\\a=x,\:b=2,\:c=x,\:d=3\\\\=xx+x\times\:3+2x+2\times \:3\\=xx+3x+2x+2\times\:3\\\\\mathrm{Simplify}\:xx+3x+2x+2\times\:3:\\\quad x^2+5x+6\)

The graph of h against m is plotted in form of a curve.

Given:

A tree branch is observed to bend as the fruit growing on it increases in size.

The height h in metres of the branch end above the ground is closely approximated by the function \(h=2-0.2*1.60^{0.2m}\) where m is the estimated mass, in kilograms, of fruit on the branch.

We have to sketch the graph of h against m.​

The x-axis represents the mass in kg while the y-axis represents the height of the branch above the ground in metres.

Hence a curved graph is obtained by plotting the function.

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During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:

$80,000

Step-by-step explanation:

40%___$32,000

100%___X=$80,000

(100*32,000)/40 = 80,000

Answer:

i have no clue

Step-by-step explanation:

bbbbbbbbbbbbbbb bbbbbbbbbbbbbb