What is the simple interest on $360 borrowed for 30 months at 12.3%?

PLEASE SHOW HOW YOU SOLVEDIT!!! :D

For part a,

we are rotating the region enclosed by y = 4 – x^2 and y = -2x +4 about the x-axis. We will use the disc, washer, and shell method to find the volume of the resulting solid.

Disc method: We can slice the solid into thin discs perpendicular to the x-axis. The radius of each disc is given by y = 4 – x^2, and the thickness is dx. The volume of each disc is πr^2h, where h = dx and r = 4 – x^2. Thus, the integral for the disc method is:

∫[from -2 to 2] π(4 – x^2)^2 dx

Washer method: We can also slice the solid into thin washers perpendicular to the x-axis. The outer radius of each washer is given by y = 4 – x^2, and the inner radius is given by y = -2x + 4. The thickness is again dx. The volume of each washer is π(R^2 – r^2)h, where h = dx, R = 4 – x^2, and r = -2x + 4. Thus, the integral for the washer method is:

∫[from -2 to 2] π((4 – x^2)^2 – (-2x + 4)^2) dx

Shell method: Alternatively, we can slice the solid into thin vertical shells parallel to the y-axis. The radius of each shell is given by x, and the height is given by y = 4 – x^2 – (-2x + 4) = 6 – x^2 + 2x. The thickness is dy, so the volume of each shell is 2πrh dy, where r = x and h = 6 – x^2 + 2x. Thus, the integral for the shell method is:

∫[from 0 to 4] 2πx(6 – x^2 + 2x) dy

For part b,

we are rotating the same region about the line x = 3. We will use the same methods to find the volume of the resulting solid.

Disc method: The radius of each disc is given by x – 3, and the thickness is dx. The volume of each disc is again πr^2h, where h = dx and r = x – 3. Thus, the integral for the disc method is:

∫[from 1 to 5] π(x – 3)^2 dx

Washer method: The outer radius of each washer is given by y = 4 – x^2 – 3, and the inner radius is given by y = -2x + 4 – 3 = -2x + 1. The thickness is again dx. The volume of each washer is π(R^2 – r^2)h, where h = dx, R = 4 – x^2 – 3, and r = -2x + 1. Thus, the integral for the washer method is:

∫[from 1 to 5] π((4 – x^2 – 3)^2 – (-2x + 1)^2) dx

Shell method: The radius of each shell is given by y + 3, and the height is given by x – (4 – y) = y – x + 4. The thickness is dy, so the volume of each shell is again 2πrh dy, where r = y + 3 and h = y – x + 4. Thus, the integral for the shell method is:

∫[from -2 to 2] 2π(y + 3)(y – x + 4) dy

Note: In part b, we integrate with respect to x instead of y in the disc and washer method, but the limits of integration and the setup are still the same.

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The value of angle x in decimal place is 57.8°.

A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.

Draw the altitude of the triangle

We know that

sinθ =  Opposite / Hypotenuse

sin 38° = y/11

y = 11 sin 38°

y = 6.77

sin(x) = y/8

sin(x) = 6.77/8

sin(x) = 0.84625

sin(x) = 57.8°

Thus, the value of angle x in decimal place is 57.8°.

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Taking a difference, we can see that the trip to city C is 482.6 mi longer.

Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles

To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.

That means that we need to take the distance to city c and subtract the distance to city b.

We will get:

739.4 mi -  256.8 mi = 482.6 mi

The trip to city C is 482.6 mi more than the trip to city B.

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The quadratic function y = -(x + 3)² - 5 is a maximum

The maximum or minimum of a function are the maximum or minimum values of the function.

Since we have the quadratic function y = -(x + 3)² - 5, this is the vertex form of a quadratic polynomial.

The vertex form y = a(x - k) + h with vertex (h, k)

So, we have the vertex of the function at (3, -5).

To determine if there is a maximum or a minimum,it will follow these conditions at the vertex

So, differentiating y twice to get d²y/dx², we have

y = -(x + 3)² - 5

dy/dx = d[-(x + 3)² - 5]/dx

=  d[-(x + 3)²]/dx - d5/dx

= -2(x + 3) - 0

= -2x - 6

differentiating again, we get d²y/dx². So,

d(dy/dx)/dx = d(-2x - 6)/dx

d²y/dx² = d(-2x)/dx - d6/dx

= -2 - 0

= -2

Since d²y/dx² = -2 < 0.  The quadratic function y = -(x + 3)² - 5 is a maximum

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The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Answer:

When k(x) is 2x² - 5x + 3, k(-3) = 36.

Step-by-step explanation:

k(x) = 2x² - 5x + 3

Substitute the input of x.

k(-3) = 2(-3)² - 5(-3) + 3

Square -3.

k(-3) = 2(9) - 5(-3) + 3

Multiply 2 and 9.

k(-3) = 18 - 5(-3) + 3

Multiply -5 and -3.

k(-3) = 18 + 15 + 3

Add 18 and 15.

k(-3) = 33 + 3

Add 33 and 3.

k(-3) = 36.

A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.

Given,

Number of credit card holders

n = 450

x = 127

p = 127/450

Proportion:

p = 0.2822

99% confidence interval:

C I = 0.2822 ± 2.576 × 0.2122

CI = 0.2822 ± 0.05465

CI = 0.282 + 0.055

A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.

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The duration of this event is 4 hours

This function is a quadratic one

let Δ be the discriminant :

a = -16

b = 48

c= 64

Δ = 48²-4*(-16)*64 = 6400

So there are two values that satisfy -16t²+48t+64 = 0  x and y

x= (-48+80)/-16*2 = -1

y= (-48-80)/-16*2= 4

x<0 so w won't take it since time is a positive value here

so t = y = 4h

What is a quadratic equation meaning?

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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The P-value for the hypothesis test H₀: p = 0.9 against H₁: p ≠ 0.9, at α = 0.056, is less than 0.056.

What is hypothesis test?

A hypothesis test is a statistical procedure used to make inferences or draw conclusions about a population based on sample data. It involves formulating two competing hypotheses, the null hypothesis (H₀)

In this hypothesis test, we are interested in determining if the proportion (p) of customers who are satisfied or very satisfied with a corporation's products and services is different from 0.9.

The null hypothesis (H₀) states that the proportion is equal to 0.9, while the alternative hypothesis (H₁) states that the proportion is not equal to 0.9.

To test these hypotheses, we use a binomial proportion test. From the given information, we have a sample of 1000 customers, and 850 of them are satisfied or very satisfied.

Using the sample proportion calculated as 850/1000 = 0.85, we can calculate the test statistic, which follows an approximately standard normal distribution under the null hypothesis.

Since the P-value is less than 0.056, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion of satisfied or very satisfied customers is different from 0.9.

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The inequality that best describes the value of the gift card is v ≥ 12.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

The inequality above states that the gift card, v could have $12 or possibly more on it because we know the most expensive app his gift card can buy is $12.

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Francine received a gift card to buy cell phone apps. She says that the card’s value is enough to buy any of the apps:

recipes-$9.50, W02 sports-$10.50, or

Remote desktop-$12.00. Let v be the dollar value of the gift card. Write an inequality that best describes the value of the gift Card.

Answer:

12.7=s

Step-by-step explanation:

First, write the equation and combine like terms.

7-45=-3s

-38=-3s

Next, divide both sides by 3.

-38=-3s

/-3  /-3

12.7=s (I rounded the answer.)

Hope this helps! Have a great day C:

Answer:

Domain

Step-by-step explanation:

The set of input values is called the domain of the function.

Hope I helped! Please mark Brainliest!

Answer: the domain is the set of inputs for a function

so domain.

Answer:

A

Step-by-step explanation:

5/8=0.625

0.42=0.42^2

Answer:

is in the point x = 1, y = -5

Step-by-step explanation:

The absolute minimum of a graph is the point that is the most far below the x-axis.

Such that if we draw a horizontal line parallel to this point, this line should not intersect the graph in another point. It is usually associated with the lowest value of the variable y.

In the graph, we can see that in the extremes we have dots, so the graph does not continue.

Then we can be sure that the absolute minimum is at the bottom of the large curve, that is in the point x = 1, y = -5

Answer: 31 7/8

Step-by-step explanation:

Firstly, we add the whole part which is 31 into the fraction making it an improper fraction. Then solve the problem by making a common denominator of 3/4  from the whole fraction into 6/8 and adding it to the previous fraction, then subtracting the spilled amount. To make the improper fraction a whole fraction/normal, just divide by the denominator. That's all!

31 x 8 = 248

248 + 6 = 254

254 - 7 = 247

247 ÷ 8 = 31 + \(\frac{7}{8}\)

OR 31 \(\frac{7}{8}\)

Answer:5^15

Step-by-step explanation: I am Smart :>

Answer:

\(5^{15}\)

Step-by-step explanation:

\(\frac{(5^3)^9}{5^{12}} \\\\\frac{5^{27}}{5^{12}} \\\\5^{15}\)

3 x 9 = 27

27 - 12 = 15

Answer:

(4,4)

Step-by-step explanation:

The solution set of the system of equations can be found by setting the two equations equal to each other and solving for x.

x^2 - 6x + 12 = 2x - 4

x^2 - 8x + 16 = 0

(x - 4)^2 = 0

x = 4

Since both equations in the system are equal to y, we can substitute x = 4 into either equation to find the corresponding value of y.

y = 2x - 4 = 2(4) - 4 = 4

Therefore, the solution of this system of equations is (4, 4).

Therefore, the correct answer is (4, 4).

Answer:

Step-by-step explanation:

Both pools were filled 6 inches from the top.

12 inches = 1 feet

6 inches = 6/12 = 0.5 foot

Considering Theresa's pool, it is rectangular. The formula for determining the volume if the rectangular pool is

Volume = length × width × height

Height filled is 4 - 0.5 = 3.5 feet

Volume = 30 × 15 × 3.5 = 1575 ft³

Recall, 1 cubic feet = 7.48 Us gallons

Therefore,

1800 cubic feet = 1575 × 7.48 = 11781 gallons of water

Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water. It means that the amount she paid to fill her pool is

3.95 × 11781/100 = $465.35

Considering Nancy's pool, it is cylindrical. The formula for determining the volume if the cylindrical pool is

Volume = πr²h

Diameter = 24

Radius = diameter/2 = 24/2 = 12 ft

Volume = 3.14 × 12² × 3.5 = 1582.56 ft³. Converting to gallons, it becomes

1582.56 × 7.48 = 11837.55 gallons of water.

Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.

It means that the amount she paid to fill her pool is

200 × 11837.55/6000 = $394.59

Therefore, Theresa paid more to fill her pool.

By algebraic handling and factor rules, the polynomial (x - 2) · (x - 5) · (x - √3) · (x + √3) is equivalent to the expanded form x⁴ - 7 · x³ + 7 · x² + 21 · x - 30.

Herein we must transform a polynomial of the form (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄) to the form a · x⁴ + b · x³ + c · x² + d · x + e by algebraic handling, especially factor rules:

(x - 2) · (x - 5) · (x - √3) · (x + √3)

(x² - 7 · x + 10) · (x² - 3)     Factor rules

x² · (x² - 3) - (7 · x) · (x² - 3) + 10 · (x² - 3)     Distributive and commutative properties

x⁴ - 3 · x² - 7 · x³ + 21 · x + 10 · x² - 30     Distributive property/Definition of power

x⁴ - 7 · x³ + 7 · x² + 21 · x - 30      Distributive property/Definition of addition

By algebraic handling and factor rules, the polynomial (x - 2) · (x - 5) · (x - √3) · (x + √3) is equivalent to the expanded form x⁴ - 7 · x³ + 7 · x² + 21 · x - 30.

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Answer:

I want to say 12:50 pm but please tell me if I'm wrong

Answer:its 2.5 quarts

Step-by-step explanation:5 pints=2.5 quarts 1 pint is 0.5 quarts

Answer:

2.5

Step-by-step explanation:

The required measure of the angle ∠spq of a rhombus is 110°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
For rhombus,
m∠spr=(2x + 15)°
m∠qpr=(3x−5)°

And,
m∠spr = m∠qpr
2x + 15 = 3x - 5
x = 20

Now,
∠spq = m∠spr + m∠qpr
        = 2x + 15 + 3x - 5

        = 5x + 10
        = 5(20) + 10
        = 110°

Thus, the required measure of the angle ∠spq of a rhombus is 110°.

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5cm

Step-by-step explanation:

volume of cube= l³

125 =l³

3root over 125 =l

l = 5

Answer:

So the length of the edge of a cube with a volume of 125 is 5.

Step-by-step explanation:

Answer:

??????????//

Step-by-step explanation:

Answer:

whole = 67.75

Step-by-step explanation:

In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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