each year, francesca earns a salary that is 2 % 2%2, percent higher than her previous year's salary. in her first 5 55 years at this job, she earned a total of $ 187 , 345 $187,345dollar sign, 187, comma, 345. what was francesca's salary in her 1 st 1 st 1, start superscript, start text, s, t, end text, end superscript year at this job? round your final answer to the nearest thousand.

Answer:

Step-by-step explanation:

Equation of circle: [tex](x-a)^2+(y-b)^2=r^2[/tex]  where (a,b) is center and r is radius.

This is a circle with center [tex](\frac{5}{2} ,4)[/tex] and radius [tex]\sqrt{60}[/tex].

Diameter [tex]=2 \times radius=2\sqrt{60} =4\sqrt{15}[/tex]

a) The probability that the demand will exceed 200 cfs during the early after- noon on a randomly selected day is 0.1353.

b)  The water-pumping capacity that the station should maintain during early afternoons is 460.52 cfs, so that the probability that demand will exceed capacity on a randomly selected day is only 0.01.

a) The given probability distribution of the demand for water during the early afternoon hours is given as exponentially distributed with a mean of 100 cfs. Therefore, the random variable X, representing the demand for water during early afternoon hours, follows exponential distribution with parameter λ = 1/100. We are required to find the probability that the demand will exceed 200 cfs during the early afternoon on a randomly selected day. By definition of probability density function of exponential distribution, the probability that the demand for water during early afternoon hours will exceed 200 cfs on a randomly selected day is:  

P(X > 200) = e-2  ≈ 0.1353

b) Given that the probability that demand will exceed capacity on a randomly selected day is only 0.01, we can write this in terms of the probability density function of exponential distribution as:

P(X > c) ≤ 0.01, where c is the water-pumping capacity that the station should maintain during early afternoons.

If X ~ Exponential distribution with parameter λ, the probability density function is given by:

f(x) = λ e-λx;  x > 0

For the probability P(X > c) ≤ 0.01, we have:

P(X > c) = e-λc ≤ 0.01 (probability distribution function of exponential distribution)

⇒ e-λc = 0.01

⇒ λc = ln(100) = 4.6052

⇒ c = 4.6052 * 100 = 460.52 cfs

Therefore, the station should maintain a pumping capacity of 460.52 cfs.

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Answer: 70km

Step-by-step explanation: 280/4=70

Let's have a couple of examples:

You're going to drive at an average of 70km/h for 4 hours. Distance is speed multiplied by time, so: 70km/h * 4 hours = 280km.

You are going to run for 80km in 6 hours  80/6=13.33. You will run 13.33 km an hour 13.33x6= 80km

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If all three dimensions of a pyramid are multiplied by a factor of 2, the volume of the pyramid increases by a factor of 8, meaning the new volume is eight times the original volume.

If all three dimensions of a pyramid are multiplied by a factor of 2, the new pyramid will be twice as long, twice as wide, and twice as tall as the original pyramid. Therefore, the volume of the new pyramid will be 2 x 2 x 2 = 8 times the volume of the original pyramid.

In other words, if V1 is the volume of the original pyramid, and V2 is the volume of the new pyramid, we can write:

V2 = 8 x V1

So the volume of the pyramid increases by a factor of 8.

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Answer:

1/110

Step-by-step explanation:

Probability of selecting a rose is 3/12, probability of selecting a tulip is 4/11, and probability of selecting a carnation is 1/10.

[tex]\frac{3}{12} *\frac{4}{11} *\frac{1}{10} \\=\frac{1}{110}[/tex]

Jake interpreted the mean as the mode. Half the cats weighed less than pounds and half weighed more.

What is mean and mode?

In statistics, mean and mode are two common measures of central tendency used to describe a set of data:

Mean: The mean, also known as the average, is calculated by adding up all the values in a data set and dividing the sum by the total number of values. It is a measure of the central location of the data, and it gives us an idea of the typical value of the data set. For example, the mean weight of a group of cats can tell us the typical weight of a cat in that group.

Mode: The mode is the value that appears most frequently in a data set. It is a measure of the most common value or values in the data, and it is useful for describing the shape of the distribution of the data. For example, the mode of the weights of a group of cats can tell us the most common weight among the cats in that group. It is possible for a data set to have more than one mode (bimodal or multimodal).

Jake's error is that he interpreted the mean as the mode, which is the most frequent value in a data set. The mean, however, is the average value of a data set and is calculated by adding all the values and dividing by the total number of values. Therefore, his interpretation that half the cats weighed less than the mean and half weighed more is incorrect. In reality, the mean only tells us the average weight of all the cats in the data set, but it does not indicate anything about the distribution of weights.

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The height of a cone with a diameter of 12 m whose volume is 340 m^3 is 9m

The height of a cone is calculated using the formula:

h = 3V/πr 2

Where h = height of the cone

V = volume of the cone

r = Radius of the cone

But note that radius, r = diameter divided by 2

r = 12 ÷ 2 = 6m

Volume = 340 m^3

Substitute the values into the formula

h = 3 × 340 ÷ 3.14 × 6 × 6

h = 1020 ÷ 113.04

h = 9m

Therefore, the height of a cone with a diameter of 12 m whose volume is 340 m^3 is 9m

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This equation involves a cosine function shifted to the right by pi/2 units [tex]y = cos(x - \pi /2) - 1[/tex]

Explain about cosine function ?

The cosine function is a mathematical function that describes the relationship between the angles and the adjacent sides of a right triangle. It is defined as the ratio of the adjacent side of a right triangle to its hypotenuse.

In trigonometry, the cosine function is often represented as cos(θ), where θ is the angle of interest. The value of the cosine function for a given angle θ can range from -1 to 1, depending on the angle's position relative to the x-axis.

According to the question:
Based on the description you provided, it seems like option (c) is the correct answer:

[tex]y = cos(x - \pi /2) - 1[/tex]

This equation involves a cosine function shifted to the right by pi/2 units, which causes the wave to start below the x-axis. The additional -1 at the end of the equation causes the entire graph to be shifted downward by one unit.

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Step-by-step explanation:

BRO I USE TO DO THIS IN 7TH GRADE I GOT YOU.

Answer:

[tex]y = - 3x {}^{ - 12x - 1} [/tex]

Step-by-step explanation:

Hope that's help your answer

The percentage of students who have grade point averages between 1.28 and 3.92 is therefore 99.7%.

Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.44.

Using the empirical rule, the percentage of the students who have grade point averages between 1.28 and 3.92 is 99.7%.

The empirical rule, which is often known as the three-sigma rule, states that in any normal distribution of data, the following percentage of data will be within one, two, or three standard deviations of the mean:-

68.27% of the data will lie within one standard deviation of the mean.- 95.45% of the data will lie within two standard deviations of the mean.- 99.73% of the data will lie within three standard deviations of the mean.

For this question, we want to know what percentage of students have grade point averages between 1.28 and 3.92, which is two standard deviations below and above the mean.

Using the empirical rule, we know that approximately 95% of the data will fall within two standard deviations of the mean, so 95% of the students will have grade point averages between (2.6 - 0.88) = 1.72 and (2.6 + 0.88) = 3.48. However, we want to know what percentage of students fall within the range of 1.28 to 3.92, which is slightly beyond two standard deviations from the mean. Since the empirical rule only provides estimates, we can assume that the additional percentage of students who fall beyond two standard deviations from the mean is roughly 2.5% on each side.

Therefore, the percentage of students who have grade point averages between 1.28 and 3.92 is approximately 95% + 2.5% + 2.5% = 99%.

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Answer:

Step-by-step explanation:

b

Answer: When dividing a polynomial by a monomial, we can simply divide each term in the polynomial by the monomial.

So, dividing (8zy² - 28z¹y5 + 12z³y7) by (4z¹y³) gives:

(8zy²)/(4z¹y³) - (28z¹y5)/(4z¹y³) + (12z³y7)/(4z¹y³)

Simplifying each term by canceling out any common factors gives:

2y^(-1)z^(1-1) - 7y^(5-3)z^(1-1) + 3y^(7-3)z^(3-1)

which simplifies to:

2yz^0 - 7y^2z + 3y^4z^2

Therefore, (8zy² - 28z¹y5 + 12z³y7) ÷ (4z¹y³) = 2yz^0 - 7y^2z + 3y^4z^2.

Step-by-step explanation:

The sales tax rate is 7% in Allegheny County. The sales tax rate in Warren County is 6%. And the book was bought in Allegheny County.

A math teacher bought a book for $ 24.99, and the sales tax on the book was $ 1.75. The teacher was able to determine whether the book was purchased in Allegheny County or Warren County by figuring out the sales tax rate. Because the total sales tax on the book was $1.75, which is equivalent to 7% of the purchase price of $24.99, the book was purchased in Allegheny County.

Sales tax rate = Total sales tax / Purchase price

Using the above formula,

Total sales tax = Sales tax rate * Purchase price

Let's calculate the sales tax using the above formula;

For Warren County, Sales tax rate = 6% = 0.06

Total sales tax = Sales tax rate * Purchase price= 0.06 * 24.99= $1.4994 ≈ $1.50

For Allegheny County,Sales tax rate = 7% = 0.07

Total sales tax = Sales tax rate * Purchase price= 0.07 * 24.99= $1.7493 ≈ $1.75

As we can see, the total sales tax on the book was $1.75, which corresponds to the sales tax rate of 7%. Therefore, the book was bought in Allegheny County.

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The number is -14 because it is even and less than -12. The absolute value of -14 is between 9 and 15. These conditions fulfill all the given clues.

Jia has given three clues about the number she's thinking of. The first clue is that the number is even, which means it is a multiple of 2. The second clue is that the number is less than -12. This means that the number is a negative number and it lies between -12 and -9 (because the absolute value of a number between -12 and -9 is between 9 and 12). The third clue is that the absolute value of the number is between 9 and 15. This condition is only satisfied by the number -14, which is even, negative, and has an absolute value between 9 and 15. Therefore, the answer is -14.

Based on the given clues, the number Jia is thinking of must be an even number that is less than -12 and whose absolute value is between 9 and 15. The only number that meets all three criteria is -14, which is an even number, less than -12, and has an absolute value of 14, which falls between 9 and 15. Therefore, we can conclude that Jia's number is -14.

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Yes, there is a correlation between the number of hours per week a student works outside of school and how many units the student takes in a quarter.

The cluster sample of 482 students is chosen in order to examine the relationship between these two variables. The statistical relationship between two variables is known as correlation.

The correlation coefficient r is used to determine the degree and direction of the correlation between two variables. The correlation coefficient is a numerical value that ranges from -1 to +1.

A negative correlation exists when one variable decreases as the other variable increases. A positive correlation exists when both variables increase or decrease together.

In this case, if the number of hours per week a student works outside of school increases, the number of units the student takes in a quarter may decrease, indicating a negative correlation between the two variables. Similarly, if the number of hours per week a student works outside of school decreases, the number of units the student takes in a quarter may increase, indicating a positive correlation between the two variables.

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Polynomial functions can only have 2 terms which is true.

Monomials are polynomials that contain only one term. Examples: 15x 2, 3b, and 12y 4 Binomials are polynomials that contain only two terms. Examples: x + y, 4x – 7, and 9x + 2

Therefore, Polynomial functions can only have 2 terms which is true.

Answer:

False

Step-by-step explanation:

Polynomial functions contain two or more terms.

Hope this helps

Answer: To sketch all the possible rectangles that Kay could make with 16 small squares and 1 large square, we can arrange them in different configurations. For example:

One possible rectangle could have a length of 8 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

 8 small squares

8 small squares

1 large square

The area of this rectangle is (8)(2) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 17(1).

Another possible rectangle could have a length of 4 small squares and a width of 4 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 4 small squares

4 small squares 4 small squares

1 large square

The area of this rectangle is (4)(4) + 1 = 17. We can write this in standard form as 17 and in factored form as 17 = 1(17).

A third possible rectangle could have a length of 8 small squares and a width of 1 small square. The large square would be used to fill in the empty space at one end of the rectangle.

8 small squares

1 large square

The area of this rectangle is (8)(1) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 9(1).

A fourth possible rectangle could have a length of 4 small squares and a width of 2 small squares. The large square would be used to fill in the empty space at one end of the rectangle.

4 small squares 2 small squares

4 small squares 2 small squares

1 large square

The area of this rectangle is (4)(2) + 1 = 9. We can write this in standard form as 9 and in factored form as 9 = 3(3).

So, there are four possible rectangles that Kay could make with 16 small squares and 1 large square, and the area of each rectangle can be expressed in both standard form and factored form as shown above.

Step-by-step explanation:

Considering the definition of perpendicular line, the correct answer is option 2.: the equation of a line perpendicular to y = 2x + 5 and passing through the point (8,2) is y= -1/2x +6.

A linear equation o line can be expressed in the form y = mx + b

where

Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 2x +5

where:

If you multiply the slopes of two perpendicular lines, you get –1. So:

2× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 2

slope perpendicular line= -1/2

The line passes through the point (8, 2). Replacing in the expression for perpendicular line:

2= -1/2× 8 + b

2= (-4) + b

2 +4 = b

6= b

Finally, the equation of the perpendicular line is y= -1/2x +6.

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There are 12 coins, such that 6 are real, weighing 10 grams each, and 6 are fake, weighing 9 grams each. you have a scale that shows the exact weight of the coins on it. one of the two coins that were left out is heavier and the other is lighter.

Take 4 coins out of the pile and put them on one side of the balance scale. Take another 4 coins out of the pile and put them on the other side of the balance scale.

If both sides of the scale are equal, you know the remaining 4 coins contain the two coins of different weights you are looking for. In that case, take two coins out of the remaining 4 and weigh them on the balance scale. If they balance each other, the other two coins must be the ones of different weight. On the other hand, if the two coins on the balance scale don’t balance, you can be certain that one is real and the other is fake. In that case, you have already found the two coins you were looking for.

If the balance scale does not balance in the first weighing, you will know that the two coins of different weights must be contained in the group of 4 that is heavier or the group of 4 that is lighter. Remove two coins from the heavier pile, and place them on one side of the scale, and keep the other two on the other side. If the balance scale is still unbalanced, it means that the coin that is heavier is one of the two coins on the heavier side of the scale, and the coin that is lighter is one of the two coins on the lighter side. If the balance scale is now balanced, it means that one of the two coins that were left out is heavier and the other is lighter.

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Step-by-step explanation:

'x + 5' under the sqrt sign cannot be less than zero

so   x values (domain) must be greater than or equal to -5  to + inf

  the resulting y values (range)  will go from   0 to + inf

D    [-5, +∞)

R    [0, +∞)

Answer:

C.

Step-by-step explanation:

FOIL

3x*2x^2=6x^3

3x*-7x=-21x^2

3x*1=3x

-6*2x^2=-12x^2

-6*-7x=42x

-6*1=-6

Combine like terms

6x^3   -21x^2   +3x   -12x^2   +42x   -6

3x+42x=45x

-21x^2-12x^2=-33x^2

So the answer=6x^3  -33x^2  +45x  -6

C.

Have a good day :-)

Answer: .54 4 points away from 0.5, 0.62 2 points away from 0.6

Step-by-step explanation: nice prodigy

The function that represents the amount of money in the account t years after it is opened is c(t) = $63,000 × (1 + 0.0255/12)^(12t)

To calculate the amount of money in the account after a certain number of years, we can use the formula for compound interest

A = P × (1 + r/n)^(nt)

where

A = the amount of money in the account after t years

P = the initial investment (in this case, $63,000)

r = the annual interest rate (2.55%)

n = the number of times the interest is compounded per year (12, since it is compounded monthly)

t = the number of years

Substituting the values given

c(t) = $63,000 × (1 + 0.0255/12)^(12t)

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The largest possible volume of the box is 480 cm³.

Given that 2400 square centimeters of material is available to make a box with a square base and an open top.

To find the largest possible volume of the box, we need to maximize the volume. We can express the volume of the box in terms of its side length.

Let's say the side length of the square base is x cm. The area of the square base will be x² square cm. Since the box has no top, we can say that its height is also x cm. So, the volume of the box can be expressed as,

V(x) = x² × x = x³ cubic cm

We know that 2400 square cm of material is available to make the box. The material is used to create the sides of the box. The box has 5 sides - four walls and a base. The area of the four walls will be the same. So, the total area of the four walls can be expressed as, 4xh = 4x², where h is the height of the box.

Subtracting this area from the total available material, we get the area of the base, which is equal to the area of the remaining material, 2400 - 4x² = x²

Simplifying, 5x² = 2400x² = 480

Volume of the box, V(x) = x³cubic cm

Substituting x = 12 in the expression for V(x), we get the maximum volume of the box, 480 cm³. Therefore, there is a maximum volume of 480  cm³ for the box.

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Answer:

234

Step-by-step explanation:

The area of the shaded region of the ring is approximately 1600.36 square feet.

A circle's size may be determined using both its radius and diameter. The circumference of a circle, measured from centre to centre, is its diameter. The radius is the separation between any point on a circle's perimeter and its centre. In other words, the diameter is equal to the radius's length times two. This connection may be mathematically expressed as d = 2r, where d is the diameter and r is the radius. While the radius is frequently employed in computations involving circles, such as determining the area or circumference, the diameter is frequently used to describe the size of a circle.

The area of the circle is given by the formula:

A = πr²

For the inner circle we have:

radius = 36/2 = 18

A = π(18)²

For the outer circle we have:

radius = 44/2 = 22 ft.

A = π(22)²

Now, the area of the shaded portion is:

A = π(22)² - π(18)²

A = π(484) - π(324)

Substituting 3.14 for π we have:

A = 1600.36 square feet

Hence, the area of the shaded region is approximately 1600.36 square feet.

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The complete question is:

The cost per game ticket is 0.75. The solution has been obtained by using the linear equations.

What is a linear equation?

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. Several variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables.

We are given that Clayton and Iris purchase admission to a carnival plus a number of game tickets.

Let the admission cost be 'x' and cost per game ticket be 'y'.

Since, Clayton purchases 10 game tickets and spends $19.50 so, we get an equation in two variables as:

x + 10y = 19.50

Similarly, Iris purchases 15 game tickets and spends $23.25 so, we get first order equation as:

x + 15y = 23.25

Now, on subtracting the first equation from the second, we get

⇒ 5y = 3.75

⇒ y = 0.75

Hence, the cost per game ticket is 0.75.

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The measure of angle B is in the given cyclic quadrilateral is 140 ⁰.

The measure of angle B is calculated by applying the principle of circle geometry for cyclic quadrilateral.

From the given figure, we will have the following equation;

angle D + angle B = 180 (opposite angles of a cyclic quadrilateral are supplementary)

x + ( 4x - 20 ) = 180

5x - 20 = 180

5x = 200

x = 200/5

x = 40

The measure of angle B is calculated as;

∠B = 4x - 20

∠B = 4 (40) - 20

∠B = 160 - 20

∠B = 140 ⁰

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