Franklin deposited $75 in a no-interest bank account when he opened it. After that, he deposits $50 per month in the account. Assume he makes no other withdrawals or deposits. The equation below can be used to find m , the number of months it will take him to save a total of $175.

75 + ?m = 175

What number should he use as the coefficient of m?

The Reduction in the Price of Computer is $56.25

What is Percentage?

A percentage is a figure or ratio that may be stated as a fraction of 100 in mathematics. If we need to compute the percentage of a number, divide it by the entire and multiply by 100. As a result, the percentage denotes a part per hundred. The term 100% refers to one hundred percent. It is denoted by the sign "%".

Solution:

To solve this problem we need to find 15% of $375

15 * 375 / 100 = 56.25 $

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Evaluate this integral over the appropriate interval [a, b] to find the volume V of the solid. V = ∫[a, b] π(64x² - 64x⁴) dx

To find the volume, we can use the washer method, which involves rotating a vertical strip between the curves y=8x and y=8x² around the x-axis. The first step is to sketch the region bounded by the curves. The region is a shape between two parabolas, with the x-axis as its base.

In the second step, we consider a typical disk or washer within the region. The inner radius of the washer is determined by the lower curve, which is y=8x². The outer radius of the washer is determined by the upper curve, which is y=8x. Therefore, the inner radius is r₁ = 8x² and the outer radius is r₂ = 8x.

To find the volume of each washer, we need to integrate the difference in the areas of the outer and inner circles. The volume of the entire solid is obtained by integrating this difference over the range of x values that define the region.

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Answer:

-5+3....................

Transformation involves changing the position of a shape

The transformations performed are (c) translation, rotation

From the question, we understand that she shifts the triangle, and then spins it

Shifting implies translation, while spinning implies rotation

Hence, the transformations performed are (c) translation, rotation

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Answer:

The answer is 7, 8 and 9. The Two-digit numbers are: ab, ac, ba, bc, ca, cb

The Sum of them is: 10a + b + 10a + c + 10b + a + 10b + c + 10c + a + 10c + b = 528

22a + 22b + 22c = 528

a + b + c = 528/22

a + b + c = 24      The only option of three different digits with the sum of 24 is 7, 8 and 9.

Hope this helps, stay safe, and merry christmas!

According to the statement the correct answer is option C - yes, the data are distributed evenly around the line of fit.

To determine if a model is a good fit for a data set, one needs to evaluate how closely the data points align with the line of fit. The line of fit represents the best possible straight line that can be drawn through the data points. If the data points are too far from the line of fit or too close to the line of fit, then it is an indication that the model is not a good fit for the data.
Option A states that the data points are too far from the line of fit, indicating that the model is not a good fit for the data. Option B states that the data points are too close to the line of fit, which is not necessarily a good or bad thing as it depends on the level of accuracy required for the analysis. Option C states that the data points are evenly distributed around the line of fit, which indicates that the model is a good fit for the data. Lastly, option D states that the line of fit touches at least one point in the data set, which is not sufficient to determine if the model is a good fit for the entire data set.
Therefore, the correct answer is option C - yes, the data are distributed evenly around the line of fit.

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Answer:

c

Step-by-step explanation:

nine over twenty i think i dont remember i did this last year

Answer:

C. nine over twenty

Step-by-step explanation:

First we should do all of the dividing of the fractions

8/20 =  .4       =   40%

9/25 =  .36     =   36%

9/20 =  .45     =   45%

8/25 =  .32     =   32%

then turn them into percentages

180 times

45 cups can wash 180 times

Answer:

3/8,5/8,9/16,7/16,11/16,5/16,3/4,1/2

Step-by-step explanation:

An annuity is a financial product in which the buyer deposits a sum of money in exchange for a series of payments to be made at regular intervals. These payments are usually made over a specified period of time or for the remainder of the annuitant's life.

An annuity that pays a fixed amount for a specified period of time is known as an ordinary annuity. A typical example of an ordinary annuity is a retirement fund, where a worker makes regular contributions to an investment account over the course of their career, and then receives regular payments from the fund after retirement.

Given that quarterly deposits of $800 are made for 6 years into an annuity that pays 8.5% compounded quarterly, the rate per period (i) and the number of periods (n) can be calculated as follows:

Firstly, we need to calculate the effective quarterly interest rate. The effective quarterly interest rate is calculated using the formula:

i = (1 + r/n)ⁿ - 1

Where:
r = annual interest rate = 8.5%
n = number of compounding periods per year = 4 (quarterly)
i = effective quarterly interest rate

Substituting the given values, we have:

i = (1 + 0.085/4)⁴ - 1
i = 0.0206 or 2.06%

Therefore, the rate per period (i) is 2.06%.

To calculate the number of periods (n), we need to convert the 6-year term into quarterly periods. Since there are 4 quarters in a year, the number of periods will be:

n = 6 x 4 = 24 quarters

Therefore, the number of periods (n) is 24.

Hence, i = 2.06% and n = 24.

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Answer:

cliches idioms

Step-by-step explanation:

a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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Answer: 140 km

Step-by-step explanation:

240 km in 3 hours

1 3/4 hours = (1 3/4 / 3) x 240

= (7/4 / 3) x 240

= 7/12 x 240

= 7 x 20 = 140

Radius of the semicircle is 8 km and diameter is 16 km.

What is area of the semicircle?

The area of the semicircle can be determined using the formula,\(A = 1/2 * \pi * r^2\)

The area of a semicircle is given by the formula:

\(A = 1/2 * \pi * r^2\)

where A is the area and r is the radius.

We are given that the area of the semicircle is 32π km². So, we can set up the equation:

\(32\pi = 1/2 * \pi * r^2\)

Simplifying this equation, we get:

r² = (2 × 32π) / π = 64

Taking the square root of both sides, we get:

r = 8 km

So, the radius of the semicircle is 8 km.

The diameter of the semicircle is twice the radius, so:

d = 2r = 2 × 8 km = 16 km

Therefore, the diameter of the semicircle is 16 km.

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The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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From the graph of the parent logarithmic function f and transformed function, to produce g

It is clear from the given graph that, the function g has a graph that is the stretch of f by a factor of 2.

For instance, for X=4, Y is 2 for f and 4 for g.

This proofs that, the g function is double to that of f function.

Therefore,

To produce g , function f was vertically stretched or expand by a factor of 2.

Function g is defined as 2f.

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stretched, 2, g(x)=2f(x)

Equation of a tangent to the surface is \(-4x+54y+18z+524=0\) and equation for normal line is \(\frac{x+4}{-4}= \frac{y+9}{54}=\frac{z+3}{18}\)

Tangent is a line which touches only  one point of a curve.

Given, the equation of the surface is \(x=3y^2+3z^2-274\) can be rewritten as \(f(x,y,z)=x-3y^2-3z^2+274=0\)

The tangent plane can be calculated by determining the gradient vector

\(\nabla f=(\partial f/\partial x)i+(\partial f/\partial y)j+ (\partial f/\partial z)k=i-6yj-6zk\) at point (-4,-9,-3) is (-4,54,18). Tangent plane to the equation is

\(-4(x+4)+54(y+9)+18(z+3)=0\\-4x+54y+18z+524=0\)

\(\frac{x-x_{0}}{\partial f_{x}}= \frac{y-y_{0}}{\partial f_{y}}=\frac{z-z_{0}}{\partial f_{z}}\)

On substituting, the normal line will be as follows:

\(\frac{x+4}{-4}= \frac{y+9}{54}=\frac{z+3}{18}\)

Hence, tangent to the surface is \(-4x+54y+18z+524=0\) and equation for normal line is \(\frac{x+4}{-4}= \frac{y+9}{54}=\frac{z+3}{18}\)

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The complete question is given below:

Find equations of the tangent plane and normal line to the surface \(x=3y^2+3z^2-274\) at point (-4, -9, -3).

<GIH:-

Now

So

Option A

In this case, we have a parallelogram:

  --> that means all the corresponding sides are parallel

         GJ -- parallel to -- HI

         GH -- parallel to -- JI

That means we can implement the alternate angle theorem

      * look at the diagram that I uploaded. The angles in there serve to

        show what angles are congruent

In this case, parallel lines GH and JI are cut by a transversal, GI, and thus we can implement the alternate angle theorem

   --> ∠GIJ = 40 degrees

Hope that helps!

Answer:

it marked the bike up by 69 percent

Step-by-step explanation:

Answer:

The shape of the Earth's surface - unevenness of the land surface - heights and slopes

Answer:

0.50 :)

Step-by-step explanation:

The probability of the union of being either a freshman or junior is 0.50

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes,

n(S) is the total number of events in the sample space.

For given example,

Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

⇒ P(freshman) = 0.25

⇒ P(sophomores) = 0.25

⇒ P(juniors) = 0.25

⇒ P(seniors) = 0.25

We know for event A and B,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Assuming event A : student is a freshman

event B : student is junior

P(A) = 0.25

P(B) = 0.25

The number of students who are freshman as well as junior = 0

⇒ n(A ∩ B) = 0

⇒ P(A ∩ B) = 0

Now, the probability of the union of being either a freshman or junior would be,

⇒ P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(A ∪ B) = 0.25 + 0.25 - 0

⇒ P(A ∪ B) = 0.50

Therefore, the probability of the union of being either a freshman or junior is 0.50

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Answer:

D

Step-by-step explanation:

f(x) = 3x² + 5x – 2

g(x) = 5x³ - 4x² + 4

We want to find

(f+g)(x)

We need to add the two functions, making sure to line up the powers of x

f (x) = 3x² + 5x – 2

+g(x) = 5x³ - 4x² + 4

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

(f+g)(x) = 5x³ - x²+ 5x+2

The answer choice is choice D

D. (f+g)(x) = 5x³ - x² + 5x+2

To find the missing sides and angles of a right triangle with side b = 32 and side c = 51, we can use the Pythagorean theorem and trigonometric ratios.

Let's denote the missing side as a and the angles as A and B, with B being the right angle.

Using the Pythagorean theorem, we know that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c):

a^2 + b^2 = c^2

Plugging in the given values, we have:

a^2 + 32^2 = 51^2

a^2 + 1024 = 2601

a^2 = 1577

a ≈ 39.73

Therefore, the length of the missing side a is approximately 39.73.

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The can's minimum surface area should have a height of 8 cm and a radius of 4 cm.

Given:

The volume of closed right circular cylindrical cans = 128π cm³

As we know the volume of a cylinder = πr²h

By equating;

πr²h = 128π

h = 128/r²

To get the dimensions of a can with minimum surface area;

S = 2πrh + 2πr

Put h = 128/r²;

Therefore, S(r) = 256π/r + 2πr²

                 S'(r) =  -256π/r² + 4πr

                S''(r) = -(2*256π)/r³ + 4π

Now, for S(r) = 0;

               r = 4cm

         for S''(4) > 0 at r = 4 is minimum point.

Hence,

h = 128π/(π*4*4)

h = 8cm

Therefore, the minimum surface area of the can should have a radius of 4 cm and a height of 8 cm.

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Answer:

500 sq. ft

Step-by-step explanation:

20 ft x 25 ft = ? ft

500 ft = ? sq. ft

25x0=0

25x2= 50

25x20=500

Answer:

Cindy's backyard has an area of 20 feet x 25 feet = 500 square feet. Therefore, Cindy needs 500 square feet of sod to cover her entire backyard.

Answer:

Step-by-step explanation:

Important Comment

Instead of writing What is y when x = - 3, the question writes f(-3) which means exactly the same thing. f(-3) mean what is y when x = whatever is in the brackets (-3) in this case.

Answer

f(-3) = - 1