given a normal distribution with a mean of 100 and a standard deviation of 10, what is the probability that x > 75?

Using proportions, if a contractor hired 18 workers to complete the construction of a road in 60 days, to complete the construction work 15 days earlier, the additional workers he should hire is 6.

We can use proportions to determine the number of workers needed to complete the work 15 days earlier, which is in 45 days.

Proportions are ratios equated to one another.

The number of workers needed to complete a road construction in 60 days = 18

If the contractor wants to complete the work 15 days earlier, he must complete it in 45 days (60 - 15).

The number of workers needed to complete the construction in 1 day = 1,080 (60 x 18)

The number of workers needed to complete the construction in 45 days = 24 (1,080/45)

The difference between completing the work in 60 days and 45 days = 6 workers (24 - 18).

Thus, proportionately, it will take 6 additional workers to complete the construction work 15 days earlier.

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Graph of the equation y-4=0.75(x-1) is in the attachment.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given  equation is y-4=0.75(x-1)

y-4=0.75x-0.75

Add 4 on both sides

y=0.75x+3.25

The slope is 0.75 and y intercept is 3.25.

The graph is given in the attachment.

Hence, graph of the equation y-4=0.75(x-1) is in the attachment.

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The table that represents a proportional relationship is given as follows:

x −3 0 3

y −2 0 2

(which is the last option).

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the definition, we have that a proportional relationship is a linear function with an intercept of zero, meaning that when x = 0, y = 0.

The last option is the only option for which the intercept of zero condition is satisfied, hence it is the correct option.

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it A

Step-by-step explanation:

The estimates that is led from the data from a poll conducted by Travelocity , then the percentages are "computed from a sample"  .

The Data from the poll conducted by Travelocity was computed from a sample of travelers and was used to estimate the proportion of travelers

The travelers have certain habits or behaviors, such as checking work email (44%) taking a cell phone (32%) , or bringing a laptop computer on vacation (26%) .

The sample estimates are used to make inferences about the population.

Therefore , the given percentages are that they were  "computed from a sample" .

The given question is incomplete , the complete question is

Data from a poll conducted by Travelocity led to the following estimates:

Approximately 44% of travelers check work email while on vacation, about 32% take cell phones on vacation in order to stay connected with work, and about 26% bring a laptop computer on vacation.

Are the given percentages "population values" or were they "computed from a sample" ?

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Answer:

[tex]2.28*10^7[/tex]

Step-by-step explanation:

[tex](2.4*10^3)(9.5*10^3)=(2.4*9.5)(10^3*10^3)=22.8*10^6=2.28*10^7[/tex]

Answer:

228,000

Step-by-step explanation:

(2.4x10^3) x (9.5x10^3)

(2.4x100) x (9.5x100)

240x950

228,000

The probability that after servicing twelve of these phones, phones of only two of the three types remain to be serviced can be calculated using combinatorics.

The number of ways to choose two types of phones out of three and the number of ways to arrange twelve phones of these two types need to be determined. The probability can then be calculated as the number of favorable outcomes divided by the total number of possible outcomes. This method can help determine the likelihood of a specific event happening in a given scenario.

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Answer:

10

Step-by-step explanation:

Use the pythagorean theorem/distance formula.

AB = \sqrt{(4-(-2))^2+(7-(-1))^2} = \sqrt{36+64} = \sqrt{100} = 10

Answer:

The marginal profit function can be found by subtracting the marginal cost from the marginal revenue. The marginal cost is given by the derivative of the cost function, and the marginal revenue is given by the derivative of the revenue function.

The derivative of the cost function is:

C'(x) = dC(x)/dx = 0.9

The derivative of the revenue function is:

C'(x) = dC(x)/dx = 0.9

The derivative of the revenue function is:

R'(x) = dR(x)/dx = 9 - 0.04x

Therefore, the marginal profit function is:

P'(x) = R'(x) - C'(x) = 9 - 0.04x - 0.9 = 8.1 - 0.04x

Point that represents height after 10 years is (10 , 8.25).

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

Given points

C(3, 3) and D(11, 9) are on a directed line segment that represents height of tree over 16 years.

Equation of the line segment

(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x ₋ x₁)

(y - 3) = [(9 - 3)/(11 - 3)](x - 3)

y - 3 = (6/8)(x - 3)

y - 3 = (3/4)x - 9/4

y = (3/4)x - 9/4 + 3

y = (3/4)x + 3/4

y is height, x is number of years

In 10 years,

= (3/4)10 + 3/4

y = 30/4 + 3/4

y = 33/4 = 8.25

Point is (10 , 8.25)

Hence, (10, 8.25) is point for height of tree after 10 years.

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Answer:

length=9

width=4m

Step-by-step explanation:

Let the width of the rectangle be, x and the length be, x+5

perimeter=2(L+W)

26 m=2(x+5+x)

26=2x+10+2

26-10=4x

16=4x

x=

length=9m

width=4m

The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base is 10

The length of the dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base is 14.87

The interior diagonal is solved using the Pythagoras theorem is applicable to right angle triangle.  the formula of the theorem is

hypotenuse² = opposite² + adjacent²

For same base

opposite = 6

adjacent = 8

plugging the values as in the problem

let x be the required distance

x² = 6² + 8²

x² = 36 + 64

x² = 100

x = √100

x = 10

dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base

opposite = 11

adjacent = 10

let y be the required distance

y² = 10² + 11²

y² = 100 + 121

y² = 221

y = √221

y = 14.87

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It will take 14 weeks for the insect population to exceeds 10,000 insects.  It will take 17 weeks for the insect population to exceeds 10,000 insects when 40% of the insect is killed by a disease every 4 week.

The code for this function of Java is : class InsectPopulation {

   public static void main(String[] args) {

       int week = 1;

       double population = 2;

       System.out.println("Week 1: 2 insects");

       while (population <= 10000) {

           population = population * 2;

           week++;

           if (week % 4 == 0) {

               population = population - (population * 0.4);

           }

           System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");

       }

   }

}

The second function for the loop is : class InsectPopulation {

   public static void main(String[] args) {

       int week = 1;

       double population = 2;

       System.out.println("Week 1: 2 insects");

       do {

           population = population * 2;

           week++;

           if (week % 4 == 0) {

               population = population - (population * 0.4);

           }

           System.out.println("Week " + week + ": " + String.format("%.2f", population) + " insects");

       } while (population <= 10000);

   }

}

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The expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given that, an expression (8+√12) / (5+√3) we need to convert it into

(a+√3) / b, where, a and b are integers.

The given expression is (8+√12) / (5+√3)

Rationalizing the expression by multiplying the numerator and denominator by changing the sign of the denominator, (5-√3)

Therefore, (8+√12) / (5+√3)

= (8+√12) / (5+√3) × (5-√3) / (5-√3)

= (40 - 8√3 + 5√12 - √36) / 5²-√3²   [a²-b² = (a+b)(a-b)}

= (40 - 8√3 + 5× 2√3 - 6) / (25-3)

= (40 - 8√3 + 10√3 - 6) / 22

= (36 + 2√3) / 22

= (18 + √3) / 11

Hence, the expression (8+√12) / (5+√3) in the form of (a+√3) / b is given by (18 + √3) / 11, where a = 18 and b = 11

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The probability that in an hour there will be at least 10 requests for parts is P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9) . The probability that the 10th request in the morning requires at least 2 hours of waiting time is P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) .

i) Poisson Distribution: The Poisson distribution can be used to model the number of requests for parts in a given time period, assuming that the average rate of requests is constant. The Poisson distribution with parameter λ is given by the following formula:

P(k requests in a time period) = (e^-λ * λ^k) / k! , where k is the number of requests, e is the mathematical constant approximately equal to 2.71828, and λ is the average rate of requests.

a) Using Poisson distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(X ≥ 10) = 1 - P(X < 10) = 1 - (Σ P(X = k) for k = 0 to 9)

b) To find the probability that the 10th request in the morning requires at least 2 hours of waiting time, we need to find the distribution of the time between requests. Since the requests are modeled as a Poisson process, the time between requests is modeled as an exponential distribution with parameter λ.

ii) Gamma Distribution: The gamma distribution is a continuous probability distribution that can be used to model the sum of k independent and identically distributed exponential random variables. In this case, the distribution of the time between requests is exponential, and the sum of 10 independent exponential random variables gives us the distribution of the time until the 10th request.

a) To find the probability that in an hour there will be at least 10 requests for parts using the gamma distribution, we need to first find the distribution of the number of requests in an hour.The sum of 10 independent exponential random variables with rate λ follows a gamma distribution with shape parameter k = 10 and scale parameter 1/λ.

Using the cumulative distribution function of the gamma distribution, the probability that in an hour there will be at least 10 requests for parts is given by:

P(number of requests ≥ 10) = 1 - P(number of requests < 10)

b) Using Gamma distribution, the probability that the 10th request in the morning requires at least 2 hours of waiting time is given by:

P(time until the 10th request ≥ 2 hours) = 1 - P(time until the 10th request < 2 hours) , where the cumulative distribution function of the gamma distribution can be used to calculate the probability.

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Answer:

Each person gets .36 quarts of vegetable soup.

Step-by-step explanation:

If Suzie makes 9 quarts of vegetable soup to serve among 25 people, you must divide 25 by 9, doing so you get .36 .

If Judy's refund is $535, to pay for furniture worth $800, she will have to come up with $265, which is the difference.

The difference is the result of the subtraction operation.

The subtraction operation is one of the four basic mathematical operations.

Subtraction operations involve the minuend, subtrahend, the subtraction operator (-), the difference, and the equal symbol (=).

The cost of furniture = $800

Expected credit refund = $535

The difference between the cost and refund = $265 ($800 - $535)

Thus, Judy will bring $265 to make up for the purchase of the furniture.

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When two finite populations are connected by migration , then (b) Fst decreases to 0 .

The Fixation Index denoted as Fst ,  is a measure of population differentiation, which is used to quantify the level of genetic differentiation between two populations.

The Fst ranges from 0 to 1, where 0 indicates complete gene flow between two populations and 1 indicates complete genetic isolation.

If the migration rate is 2% per organism per generation, over time this will lead to a reduction in genetic differentiation between the populations, and the Fst value will decrease towards 0.

This is because the exchange of genetic material will reduce the amount of variation that is unique to each population, which leads to an increase in the genetic similarities between the populations.

The given question is incomplete , the complete question is

What happens to Fst when two finite populations are connected by migration (say 2% chance of migration per organism per generation, and no selection) ?

(a) Fst increases to 1

(b) Fst decreases to 0

(c) Fst stays moderate, near 0.5

(d) Fst wanders around randomly between 0 and 1 forever  .

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The fourth vertex of the rectangle is given as follows:

(g,g).

A rectangle is composed by two dimensions, which are given as follows:

A rectangle has four sides, meaning that two dimensions are equal, and the coordinates for this problem are given as follows:

The missing combination of one coordinate of x and one coordinate of y is given as follows:

(g,g).

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The given statement: The standard deviation is a resistant measure of spread is true.

Standard deviation is the measure of how spread out numbers are. It is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.

When outliers are included, resistant statistics don't change (or vary very little). Resistance does not imply that anything is immobile; that would be "immovable." It implies that your results could fluctuate a bit, but not much.

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The total sales in week 20 after the beginning of the advertising campaign was $3297.03

An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic

Her sales in the first week were $86. After starting an online advertising campaign, her sales increased 20% the following week. This expression can be represented in the form of an exponential function:

y = abˣ

Where a is the initial value and b is the multiplication factor

Let y represent the total sales after x weeks. Comparing with the expression:

a = $86, b = 100% + 20% = 1.2. Hence:

y = 86(1.2)ˣ

After 20 weeks:

y = 86(1.2)²⁰ = 3297.03

The total sales was 3297.03

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Equation can use to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

As per the given data, Naomi's carries a bin of water balloons outside for the balloon toss, she trips and breaks 13 balloons.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The number of water balloons w in the bin before Naomi trips.

She counts the remaining water balloons, and there are 15 left.

According to the question, the equation is

w - 13 = 15

⇒ w = 15 + 13

⇒ w = 28

Hence, equation which is used to find the number of water balloons w in the bin before Naomi trips is w - 13 = 15.

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The cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

The formula to calculate the cost of carpeting a rectangular floor is Area of the floor x Cost of carpet per square yard.

The area of the floor is calculated by multiplying the length and the width, which in this case is 9 feet x 18 feet = 162 square feet.

To convert 162 square feet into square yards, divide 162 square feet by 9, which equals 18 square yards.

Therefore, the cost of carpeting a rectangular floor measuring 9 feet by 18 feet is 18 square yards x 12.75 = 228.50.  If needed, this can be rounded to the nearest penny, which is 228.50.

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The number of bricks that will be used for the entire job would be = 1000 bricks.

The amount of bricks which will be used by the Carmona Construction Company for brick patio can be calculated as follows;

The amount of rows that has been installed = 30 rows

The amount of bricks that makes up the installed rows = 600 bricks.

The amount of uninstalled rows = 20

The amount of bricks that would be required to install the remaining 20 rows ;

30 rows = 600

20 rows = X

Make X the subject of formula

X = 20×600/30

X = 12000/30

X= 400 bricks

Therefore, the total brick that will be required = 400+600 = 1000 bricks.

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Answer:

Step-by-step explanation:

The volume of a solid obtained by rotating a two-dimensional region about an axis can be found using the method of cylindrical shells.

The region in question is bounded by the parabolic curve y = x^2, the vertical line x = 5, and the x-axis. We can find the volume of the solid obtained by rotating this region about the x-axis by adding up the volumes of an infinite number of infinitely thin cylindrical shells with radius equal to the distance from the axis to the boundary of the region at each y-value.

The formula for the volume of a cylindrical shell is given by V = 2 * pi * y * dV, where y is the distance from the x-axis to the boundary of the region at each y-value, and dV is the incremental volume at that y-value.

To find the volume, we need to find the incremental volume dV, and integrate the cylindrical shell formula over the region bounded by y = x^2 and x = 5. The incremental volume is given by dV = pi * (R^2 - r^2)dy, where R is the outer radius, r is the inner radius, and dy is the incremental change in y.

In this case, the outer radius R is equal to the value of x = 5 when y = x^2, and the inner radius is equal to zero. Thus, the incremental volume is given by: dV = pi * (5^2 - 0^2)dy = 25 * pi * dy.

The bounds of the integration are from 0 to 5^2 = 25. Integrating the cylindrical shell formula over this range, we find that the volume of the solid obtained by rotating the region bounded by y = x^2, x = 5, and y = 0 about the x-axis is:

V = 2 * pi * integral from 0 to 25 of (y * 25 * pi)dy = 2 * pi * (25^2 * 25 / 2) = 15625 * pi cubic units.

So, the volume of the solid is approximately 49,093 cubic units.

Answer:

4 inches

Step-by-step explanation:

Let b = base length

h = height

A = area

[tex]A = \dfrac{1}{2}\cdot b \cdot h\\\\[/tex]

Multiply throughout by 2

[tex]2 \cdot A = 2\cdot \dfrac{1}{2}\cdot bh\\\\2A = bh\\\\h = \dfrac{2A}{b}[/tex]

We are given A = 16 in² and b = 8 inches

So, h = 2(16)/8 = 32/8 = 4 inches

Check to see if this is correct

A = (1/2)(8)(4) = (4)(4) = 16

Answer:

3/2 of a mile

Step-by-step explanation:

The equation is 1/2 times something = 3/4 (because length times width is area)

you would divide 1/2 on both sides to get an unknown number(that represents the width)

3/4 divided by 1/2 is 3/2 of a mile !

The length of the rectangle in centimeters is 15.60 cm.

The correct way to report the length of the rectangle in centimeters is 15.60 cm. To calculate the length of the rectangle, we must first calculate the distance between the two edges of the rectangle. To do this we can use the formula Distance = Final Position - Initial Position. Therefore, the distance between the two edges of the rectangle is 15.600 cm - 0 cm = 15.600 cm. This is the length of the rectangle, so the correct way to report the length of the rectangle in centimeters is 15.60 cm.

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Answer:

The mean is 8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

add all numbers together and divide by how many numbers there are so:

8+12+4+3+14+1+9+13=64

64÷8=8

Feel free to ask me any questions if you don't understand it :)

Answer:

the answer is 330000

Step-by-step explanation:

just do 22,000 divided by 4 and that 5, 500 so its 5,500 miles a month and then do 5,500 x 60= 330000