An 800 investment that earns 3% annual interest compound yearly for 4 years

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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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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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:

2x is equals to 100

x is equals to 100 / 2

x is equals to 50

therefore x=50

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]

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:

She spent 7 minutes on her math homework.

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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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:

Step-by-step explanation:

b

Answer:

x²+y²=58

Step-by-step explanation:

(x-x₁)²+(y-y₁)²=r²

(0,0)=(x₁,y₁) [centre of the circle)

x²+y²=r²

The point (3,7) belongs to the circle.

3²+7²=r²

r²=9+49

r²=58

x²+y²=58

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 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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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:

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

Step-by-step explanation:

Hope that's help your answer

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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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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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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A. The length of its edge is 512 cubic units, B. The volume of the sphere is 268.08 cubic units and C. The fraction of the cube is 67 / 128 and the percentage is 52.34%.

A. We are given that the volume of the cube is 512 cubic units.

We are required to find the length of its edge. So, Let the length of an edge of a cube be a units.

Then, the volume of the cube = (length of edge)3

We have the volume of the cube = 512 cubic units.

So, (length of edge)3 = 512 cubic units

Now, we can find the length of the edge by finding the cube root of 512.

So,Length of edge = Cube root of 512 cubic units = 8 units

Now, we need to find the volume of the sphere which fits snugly inside the cube. When a sphere is inscribed in a cube, its diameter is equal to the edge of the cube.

Thus, the diameter of the sphere = 8 units.

Hence, the radius of the sphere = 8 / 2 = 4 units

B. volume of the sphere = (4 / 3)πr3

= (4 / 3) × π × 43

= 4/3 × 3.14 × 64= 268.08 cubic units

C. The fraction of the cube that is taken up by the,

sphere = volume of sphere/volume of cube

= 268.08 / 512= 67 / 128

So, the percentage of the cube taken up by the sphere is,

percentage of cube taken up by sphere = (67 / 128) × 100= 52.34% (approx)

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1. 4

2.2

3.0,5

IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS

Answer: help me pleaz

Step-by-step explanation:

Answer: The transformation r y=x reflects the point (x, y) across the line y = x, and the transformation T -3,3 translates the point (x, y) three units to the left and three units up. To find the image point of (-8, 2) after these transformations, we can follow these steps:

Apply the reflection r y=x to the point (-8, 2):

(-8, 2) reflects to (2, -8).

Apply the translation T -3,3 to the reflected point (2, -8):

(2, -8) translates to (-1, -5).

Therefore, the image point of (-8, 2) after the transformation r y=x T -3,3 is (-1, -5).

Step-by-step explanation:

Answer:

234

Step-by-step explanation:

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

Step-by-step explanation: nice prodigy

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 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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