Please help as well:
Solve for X

Answer: PV= $ 2292.10

Step-by-step explanation:

A= P(1+r/100)^n*r

where FV is the Future vale, PV is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years

5000 = PVe^(0.065*12)

PV = 5000/e^0.78

PV = 2292.10

a. The radius of circle P is 5 inches.

b. The side length of the large square is 25 cm.

c. The side length of the large equilateral triangle is 26 feet.

a. The area of circle N is π\(r^2\) = π(\(3^2\)) = 9π square inches.

The area of circle O is π\(r^2\) = π(\(4^2\)) = 16π square inches.

The area of circle P is the sum of the areas of circles N and O, so it is 9π + 16π = 25π square inches.

The formula for the area of a circle is A = π\(r^2\), so we can rearrange it to find the radius:

r = √(A/π)

Plugging in the area of circle P, we get:

r = √(25π/π) = √25 = 5

b. The area of the small square is \(7^2 = 49\) square cm.

The area of the medium square is \(24^2 = 576\) square cm.

The area of the large square is the sum of the areas of the small and medium squares, so it is 49 + 576 = 625 square cm.

The formula for the area of a square is A =\(s^2\), so we can rearrange it to find the side length:

s = √A

Plugging in the area of the large square, we get:

s = √625 = 25

c. The area of the small equilateral triangle is \((\sqrt{3} )/4)\times 10^2 = 25\sqrt{3}\)square feet.

The area of the medium equilateral triangle is \((\sqrt{3} /4)\times 24^2 = 144\sqrt{3}\)square feet.

The area of the large equilateral triangle is the sum of the areas of the small and medium equilateral triangles, so it is \(25\sqrt{3} + 144\sqrt{3} = 169\sqrt{3}\) square feet.

The formula for the area of an equilateral triangle is\(A = (\sqrt{3} /4)\times s^2\), so we can rearrange it to find the side length:

\(s = \sqrt{(4A/\sqrt{3} )}\)

Plugging in the area of the large equilateral triangle, we get:

\(s = \sqrt{(4(169\sqrt{3} )/\sqrt{3} )} = \sqrt{676} = 26\)

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The null hypothesis will be same as the claim value which is 75%.

What is null hypothesis?

The null hypothesis is a statistical claim that no statistical significance can be found in a set of given observations. To determine the validity of a theory, hypothesis testing is carried out using sample data. Its symbol is H₀, and it is occasionally referred to as simply "the null".

We are given that the claim is that the proportion is less than 75%.

So, the statement of the null hypothesis states that the population value is the same as the claim value.

So,

H₀ : p = 75% = 0.75

If this null hypothesis is correct, then 75% of all students at the researcher's school finished their homework assignments last night.

Hence, this will mean that the null hypothesis is true.

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Question: No homework? Refer to Exercise 1. The math teachers inspect the homework assignments from a random sample of 50 students at the school. Only 68% of the students completed their math homework. A significance test yields a P-value of 0.1265.

Explain what it would mean for the null hypothesis to be true in this setting.

The measurement that gives you the difference between the points on the scatterplot and the prediction line for the same value of x is the residual. Therefore, the correct answer is C. Residual.

In regression analysis, the residual represents the vertical distance between the observed data points and the corresponding predicted values on the regression line. It is calculated by taking the difference between the actual observed value and the predicted value for a specific value of the independent variable (x). The residuals provide a measure of how well the regression line fits the data, with smaller residuals indicating a better fit.

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Answer: The answer is D. 17.9

Step-by-step explanation: Use the equation \(c = \sqrt{a^2 +b^2}\) where c represents the triangles hypotenuse and a and b represent the legs of the triangle.

I hope this helps have a great day!

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

So first you should remember that....

\(a^{2} +b^{2} =c^{2}\)

then you should plug in...

\(8^{2}+16^{2}\)

that should equal...

\(c^{2}=320\)

Then you should solve the equation now by doing the inverse of the square which is the square root of both sides...

\(\sqrt{c^{2} } =\sqrt{320}\)

\(c=17.88854382...\)

Then you have to round it to the nearest tenths, which'll give you...

\(17.9\)

choice D

The surface integral given is evaluated using the Gauss formula. The result is determined by calculating the divergence of the vector field and integrating it over the surface of the solid.

To evaluate the surface integral using the Gauss formula, we need to compute the divergence of the vector field. The given vector field is F = (x²dy Adz + y²dz / dx + z²dx Ady). The divergence of F, denoted as div(F), can be found by taking the partial derivatives of each component of F with respect to its corresponding variable and summing them up.

Taking the partial derivative of x²dy Adz with respect to x yields 2x dy Adz, the partial derivative of y²dz/dx with respect to y gives dz/dx, and the partial derivative of z²dx Ady with respect to z results in 2z dx Ady. Summing these partial derivatives gives div(F) = 2x dy Adz + dz/dx + 2z dx Ady.

Now, according to the Gauss formula, the surface integral of a vector field F over a closed surface S is equal to the triple integral of the divergence of F over the volume enclosed by S. Since the problem statement specifies that the surface S is the outside of the surface of the solid, we can use this formula.

The result of the surface integral is obtained by integrating the divergence div(F) over the volume enclosed by the surface S. However, without additional information about the shape and limits of the solid, it is not possible to determine the exact numerical value of the integral. To obtain the final answer, the specific characteristics of the solid and its boundaries need to be provided.

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The additive counterpart of given expressions are (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

When two numbers may be added together or multiplied, regardless of the order in which they are entered, the result is said to be commutative. There are different formulas available for the conversion of multiplicative expressions to their additive counterparts.

a) The first expression is a²b³. This expression is written as aabbb. This is of the form ab and its corresponding additive counterpart is of the form a+b.

Then, a+a+b+b+b=2a+3b.

b) The second expression is a⁻²(b⁻¹c)². This expression is of the form a⁻¹ and its corresponding additive counterpart is of the form -a.

Then,

\(\begin{aligned}a^{-2}(b^{-1}c)^2&=a^{-1}a^{-1}(b^{-1}c)(b^{-1}c)\\&=-a-a-b+c-b+c\\&=-2a+2(-b+c)\end{aligned}\)

c) The third expression is (ab²)⁻³c²=e. This expression is first expanded as, (ab²)⁻¹(ab²)⁻¹(ab²)⁻¹c²=e. Using property, (xy)⁻¹=y⁻¹x⁻¹.

Then,

\(\begin{aligned}((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})((b^2)^{-1}a^{-1})c^2&=e\\(b^{-2}a^{-1})(b^{-2}a^{-1})(b^{-2}a^{-1})c^2&=e\end{aligned}\)

Also, the additive identity to e is zero. And, aⁿ=na.

Then,

(-2b-a)+(-2b-a)+(-2b-a)+2c=0

Simplifying we get,

-3(a+2b)+2c=0.

The answers are  (2a+3b), -2a+2(-b+c), and -3(a+2b)+2c=0.

The complete question is -

Translate each of the following multiplicative expressions into its additive counterpart. assume that the operation is commutative

a. a²b³

b. a⁻²(b⁻¹c)²

c. (ab²)⁻³c²=e

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1. x³ - 1 = (x - 1)(x² + x + 1)

2. The possible rational roots of the function are ±1.

3. 1 and -1 are the root.

4. The factorization of 999 will involve the numbers 3 and 37, as they are factors of 1, 24, and 666

1. To factorize x³ - 1, we can use the difference of cubes formula

a³ - b³ = (a - b)(a² + ab + b²).

In this case, a = x and b = 1.

So, x³ - 1 = (x - 1)(x² + x + 1)

2. To factorize 25 - 1, we can use the difference of squares formula,

a² - b² = (a - b)(a + b).

In this case, a = 5 and b = 1. Applying the formula, we have:

25 - 1 = (5 - 1)(5 + 1)

      = 4 x 6

      = 24

3. The possible rational roots of the function are ±1.

4. To determine which of those are actually roots, we can substitute them into the function and see if the result is zero:

When x = 1, we have 1³ - 1 = 1 - 1 = 0

So, 1 is a root.

When x = -1, we have (-1)³ - 1 = -1 - 1 = -2.

So -1 is not a root.

3. To factorize x⁷ - 1,  The difference of cubes formula and difference of squares formula are still applicable. Using the same numbers as before (a = x and b = 1), we have:

x⁷ - 1 = (x - 1)(x⁶ + x⁵ + x⁴ + x³ + x² + x + 1)

4. Based on the pattern we observed in the previous factorizations, we can predict that the factorization of 999 will involve the numbers 3 and 37, as they are factors of 1, 24, and 666.

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Answer:

1/5 is the answer

Step-by-step explanation:

Answer:

1 gallon?

Step-by-step explanation:

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

Answer:

Put a Greater than symbol >

Step-by-step explanation: That question is showing absolute value which is basically the amount it takes to get there from zero.

-5 with absolute value becomes a regular 5

Answer:

its >

Step-by-step explanation:

The probability of Bob winning is (3)/(10), which means the probability of him losing is (7)/(10). The odds in favor of Bob winning the raffle are 3 to 7.

To calculate the odds in favor of Bob winning the raffle, we need to divide the probability of his winning by the probability of his losing.

Step 1: Determine the probability of winning:

Bob's probability of winning is given as (3)/(10). This means that out of all possible outcomes, there is a probability of (3)/(10) that Bob will win.

Step 2: Determine the probability of losing:

The probability of losing is complementary to the probability of winning. Since the sum of all possible outcomes must equal 1, we can subtract the probability of winning from 1 to find the probability of losing:

Probability of losing = 1 - Probability of winning

Probability of losing = 1 - (3)/(10)

Probability of losing = (10)/(10) - (3)/(10)

Probability of losing = (7)/(10)

Step 3: Calculate the odds in favor:

The odds in favor of winning can be found by dividing the probability of winning by the probability of losing:

Odds in favor = Probability of winning / Probability of losing

Odds in favor = (3)/(10) / (7)/(10)

Odds in favor = (3)/(10) * (10)/(7)

Odds in favor = 3/7

Therefore, the odds in favor of Bob winning the raffle are 3 to 7.

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Answer:

Step-by-step explanation:

(1/2)(x+3)(2x+4)

= x^2 + 5x + 6

a=1

b=2

c=5

d=1

e=6

=======================================================

Explanation:

The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.

------------

A slightly longer alternative path would be to do this:

The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...

20+20+c = 180

40+c = 180

c = 180-40

c = 140

Then angle b is supplementary to this

b+c = 180

b+140 = 180

b = 180-140

b = 40

This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.

In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.

Therefore ,the solution to the given problem of interquartile range of the concert tickets sold is 72. (the second option).

An analysis of the distribution and level of a set of scores is done using a box plot, which is a graph. Two whiskers plus a box make up the box plot. The minimum and maximum numbers are represented by the first and last whiskers, respectively.

The lower (first) quartile is represented by the first line on the box. The median is indicated by the following line on the box. The third line from the top on the box denotes the third quartile.

The distance between the third quartile and the first quartile is known as the interquartile range.

Third-to-first quartile difference is the interquartile range.

369 - 297 = 72

Therefore ,the solution to the given problem of  interquartile range of the concert tickets sold is 72. (the second option).

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Answer:

center: (-5,6)

Radius: 7

Step-by-step explanation:

Answer:

I think its C

Step-by-step explanation:

Answer:

the answer is c. I took the test and got it right!

The population in this scenario consists of all employees in the firm, which totals 4,500 individuals. The sample is a subset of the population, specifically 60 randomly selected employees who are part of a committee evaluating the implementation of sensitivity training.

the population refers to the entire group of employees in the firm, which consists of 4,500 individuals. The sample, on the other hand, is a smaller group of 60 employees who have been randomly selected to form a committee. This committee's purpose is to evaluate the proposal of implementing sensitivity training online instead of the current in-person format.

The sample of 60 employees is chosen in a random manner to ensure representativeness and minimize potential bias. By selecting a subset of the population, the committee can provide insights and perspectives that are representative of the larger employee base. Each committee member will have the opportunity to vote "yes" or "no" on the proposal, and their votes will be used to determine the overall sentiment of the committee regarding the implementation of online sensitivity training.

It's important to note that the sample of 60 employees is being used as a representative group to make inferences about the entire population.

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Answer:

50 new fish in total

so lets say 25 per month

Rate: 25 fish per month

Step-by-step explanation:

The rate is the population increasing is  0.135 or 13.5% .

Growth rates refer to the percentage change of a specific variable within a specific time period.

Growth rate= \(\frac{Present value - Past value}{Past value}\)

According to the question

The population of fish increased from 370 to 420

i.e

Present value = 420

Past value = 370

over the months of March and April

By using Growth rate formula :

Growth rate= \(\frac{Present value - Past value}{Past value}\)

Now,

Substituting values in formula

Growth rate= \(\frac{420 - 370}{370}\)  

                    = \(\frac{50}{370}\)

                    = 0.135 or 13.5%

Hence, the rate is the population increasing is  0.135 or 13.5% .

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Answer

55

Step-by-step explanation:

5w+25= c

5(6)+25=55

Answer:

f(g(x)) = x^4 + 12x^3 + 14x^2 -132x + 123

Step-by-step explanation:

Here, we simply will place g(x) into f(x)

So every x in f(x) is replaced by g(x)

Thus, we have;

(x^2 + 6x + 11)^2 + 2

= (x^2+6x-11)(x^2 + 6x -11) + 2

= x^4 + 6x^3 -11x^2 + 6x^3 + 36x^2 - 66x -11x^2 -66x + 121 + 2

= x^4 + 12x^3 + 14x^2 -132x + 123

Using Scientific notation, the expression (6.1 * 10⁴) + (5.2 * 10⁴) can be written as;  11.3 * 10⁴

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 × 10⁸.

Now, we want to use scientific notation to simplify;

(6.1 * 10⁴) + (5.2 * 10⁴)

Using distributive property of equality, we can say that the expression can be broken down as;

10⁴(6.1 + 5.2)

= 11.3 * 10⁴

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The volume of the solid is approximately 1.04 x 10⁻¹⁰ cubic units.

To find the volume of the solid obtained by rotating the region bounded by the y=1/x⁵, y=0, x=1, x=9 about the y axis, we can use the Disk Method.

The Disk Method can be used when rotating a function around an axis. It requires integration to find the volume of the solid. The formula for the Disk Method is: V=π∫aᵇ(R(x))²dx where R(x) is the radius of the disk.

In this case, the y-axis is our axis of revolution and the function is given as y=1/x⁵ and the limits of integration are 1 and 9. Thus, the formula becomes V=π∫1⁹(1/x⁵)²dx. After simplifying, this becomes V=π∫1⁹ 1/x¹⁰ dx.

Evaluating this integral, we get V=π[1/(-9x⁹)] from 1 to 9. This simplifies to V=π[1/(-9(9)⁹) - 1/(-9(1)⁹)] or V=π[1/3,025,611,125].

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The flight-path angle is equal to 45' when v =90' on all parabolic trajectories is proved using the trajectories.

Using trajectories equation :

r = p/(1+cosv)     at v= 90 degrees

r{90} = p/ (1+cos90°)

        = p       since, cos 90 = 0

also, v= √2mue/r

        v{90} = √2mue/p

where r {90}  and v{90} are radius and velocity at v = 90 degrees.

the angular momentum is given as , h = r.v cosФ

and at periapsis on a parabolic trajectory , rp = p/2

  v{90} = √2mue/p

applying the concentration of angular momentum,

rp.vp = r90.v90.cosФ

p/2.√2mue/p = p.√2mue/p.cosФ

cos Ф = 1/√2

therefore,Ф = 45

hence the flight-path angle is equal to 45' when v =90' on all parabolic trajectories is proved.

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Answer:

x=30°

Step-by-step explanation:

x +2x+3x=6x

since triangles are 180° in total. 6/180=30

so 30° is your answer.

answer:

I forgot how to do this haven't done it in a while.

Step-by-step explanation:

Sorry I couldn't help.

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{10}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-5)}}}\implies \cfrac{-6}{-3+5}\implies \cfrac{-6}{2}\implies -3\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{10}=\stackrel{m}{-3}(x-\stackrel{x_1}{(-5)})\implies y-10=-3(x+5) \\\\\\ y-10=-3x-15\implies y=-3x-5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

as you can see, the "b" part is -5, or namely the y-intercept is at (0 , -5).

The probability of not winning the coupon at the grocery store given the probability of winning the coupon is 23/25.

Probability determines the likelihood of the occurence of an event. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability of not winning the coupon = 1 - probability of winning

1 - 2/25 = 23/25.

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Answer:

x= 5 ........................ .......