Combine like terms in the equation f(x)=-f(x)_______=0

The Equation to represent the "total-cost", "t", for purchasing "5 hardcover books", 8 "paperback-books", and 6 music CDs during the sale is t = 4h + 6.4p + 6m - 1.

The cost of the hardcover-book is = $h,

The cost of the paperback-books is = $p,

The cost for one music-CD is = $m,

In the sale, the price of each book is reduced by 20%, and

The price of music-CD is reduced by $1,

So, the cost of 5 hardcover books during the sale is:

⇒ 5h - 0.2(5h) = 4h     ...because 20% = 0.2;

and the cost of 8 paperback books during the sale is:

⇒ 8p - 0.2(8p) = 6.4p,

The cost of 6 music CDs during the sale is ⇒ 6m - 1;

So, the total cost, "t", for buying 5 hardcover books, 8 paperback books, and 6 music CDs during the sale is:

⇒ t = 4h + 6.4p + 6m - 1,

Therefore, the required equation of "total-cost" is t = 4h + 6.4p + 6m - 1.

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Question Completion:

California (population about 40 million) has about twice as many people as New York State (population about 20 million). Without calculation, pick the correct option and explain your choice.

If the underlying population SDs are equal, a simple random sample of 1000 people in California is

(i) about half as accurate

(ii) about 1/V2 times as accurate

(iii) about as accurate

(iv) about V2 times as accurate

(v) about twice as accurate

as a simple random sample of 1000 people in New York State.

Answer:

If the underlying population SDs are equal, a simple random sample of 1000 people in California is

(i) about half as accurate

as a simple random sample of 1000 people in New York State.

Step-by-step explanation:

Since the population of California is about 40 million, which is twice as many people as in New York State (approximately 20 million), in taking a sample size, that of California supposed to be as twice as New York's.

Therefore, if the random sample of 1,000 people is taken from California, just as a random sample of 1,000 people is also taken from New York State, we can conclude that the accuracy of population standard deviation of California will be about half as accurate as the standard deviation of New York's population.

This is because accuracy is enhanced by a larger sample size.  This means that if the sample size of California is 2,000, the SD would have been equally as accurate as New York's.

Answer:

the process of isolating a variable in these literal equations is similar to solving a one-step equation because after isolating a variable you solve the rest of the equation,it is different from solving a one-step equation because it is more than one step so it takes longer to solve

Answer:

2

Step-by-step explanation:

To determine the number of real solutions of the quadratic equation `y = -3x^2 + x + 12`, we can use the discriminant formula `b^2 - 4ac`.

First, we identify the values of a, b, and c:

a = -3

b = 1

c = 12

Next, we substitute these values into the discriminant formula:

b^2 - 4ac = (1)^2 - 4(-3)(12) = 145

Since the discriminant is positive (and not equal to zero), the quadratic equation has two distinct real roots. Therefore, the number of real solutions is 2.

The expressions that will correctly calculate what percent 19 is of 20 are:

A.19/20 .100

D.19.100/20

The concept that will be used here is percentage. A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.

From the options we can see that to find the percentage of 19  of 20, iot can be expressed mathematically as :

(19/20) *100 and this can as well be expressed as (19*100)/20 becausethey will still give use the same value which is 95%

Therefore, option A and D are correct.

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The minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".

Assuming Jonathan only wants to buy shirts and pants, let's represent the number of shirts he buys as "s" and the number of pants as "p". Then we have two equations:

1. The total cost of Jonathan's purchase:

35s + 50p >= 350

2. Jonathan wants to spend at least $350:

s, p >= 0

To solve this problem, we can start by finding the minimum number of pants Jonathan needs to buy to meet his spending requirement.

When s = 0, 50p >= 350, so p >= 7.

Therefore, Jonathan needs to buy at least 7 pants.

If Jonathan buys 7 pants, the total cost of his purchase is 35s + 50(7) = 35s + 350. To spend at least $350, he needs to buy enough shirts to make the total cost of his purchase at least $350.

35s + 350 >= 350

35s >= 0

s >= 0

Since s must be a non-negative integer (you can't buy a fractional part of a shirt), Jonathan needs to buy at least 0 shirts.

So the minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.

Of course, Jonathan can buy more than 7 pants and/or some shirts to meet his spending requirement. For example, he could buy 5 pants and 4 shirts, which would cost him $375.

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The sum we want is

\(\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots\)

where \(T_n=\frac{n(n+1)}2\) is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as

\(\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)\)

For convenience, I'll use the abbreviations

\(S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}\)

\({S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}\)

for m ∈ {1, 2, 3, …, 7}, as well as the well-known series

\(\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}\)

We want to find \(S_1-S_3-S_5+S_7\).

Consider the periodic function \(f(x) = \left(x-\frac12\right)^2\) on the interval [0, 1], which has the Fourier expansion

\(f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}\)

That is, since f(x) is even,

\(f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)\)

where

\(a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}\)

\(a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}\)

(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)

Expand the Fourier series to get sums resembling the \(S'\)-s :

\(\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)\)

which reduces to the identity

\(\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'\)

Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution

\(\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}\)

It turns out that

\({S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7\)

so we're done, and the sum's value is \(\boxed{\dfrac{\pi^2}{8\sqrt2}}\).

Answer:

24

Step-by-step explanation:

The common multiple that 8 and 12 have in common is 24. This is because 24 is the first multiple of 8 and 12 that is shared

Answer:

The multiples of 8 are: 8, 16, 24, 32, 40, … .

The multiples of 12 are: 12, 24, 36, 48, 60, … .

LCM = 24

Step-by-step explanation:

(PLATO answer)

Step-by-step explanation:

hope you understand.

first simplify it by arranging correct signs then it's just subtraction or addition.

Answer:

x=50

Step-by-step explanation:

2x+15+3x-20+x+15+x=7x+10=360

7x=350

x=50

This is not a prime factorization.

The correct prime factorization is \(2^5*3*5^4*11^2\)

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

Further Explanation:

The expression your teacher gave you is not a prime factorization because the 8 isn't prime.

8 = 2*2*2 = \(2^3\)

If we replace 8 with \(2^3\), then we go from

\(2^2*3*5^4*8*11^2\)

to

\(2^2*3*5^4*2^3*11^2\)

and that rearranges to

\(2^2*2^3*3*5^4*11^2\)

Then we can simplify the \(2^2*2^3\) portion to get \(2^5\) since we add the exponents while keeping the base '2' the same.

We therefore end up with

\(2^5*3*5^4*11^2\)

as the correct prime factorization. Each base (2,3,5,11) is a prime number.

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

As a check, use your calculator to type in

2^2*3*5^4*8*11^2

and also

2^5*3*5^4*11^2

and you should get the result of 7,260,000 each time. Since we get the same result, this confirms 2^2*3*5^4*8*11^2 = 2^5*3*5^4*11^2

The required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

A rational expression is a mathematical expression that is the ratio of two polynomial expressions. That is, a rational expression is formed by dividing one polynomial expression by another polynomial expression.

Here,
The given rational expression,
= 1/x²  - 1/4x² + 12x

In the question, we have been asked to determine the least common denominator for the given rational expression.

Since least common denominator is given expression,
= x² (4x² + 12x)
= 4x³(x + 3)

Thus, the required least common denominator for the given expression is  4x³(x + 3). Option C is correct.

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Answer:

A

Step-by-step explanation:

Cosine X= adjacent /hypotenuse

where adjacent=5 and hyp=13

Cos X=5/13

Given the expression :

The answer will be as following:

So, the error of Sadie is that: she didn't take the square root of a^5

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

B. -3

Step-by-step explanation:

check image for reference. <3

(this is what I am learning so I have some other pictures as well.)

Answer:

Answer B is correct

Step-by-step explanation:

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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Answer:

The measure of angle N is 58 degrees (58°).

Step-by-step explanation:

If angle M is a right angle, it means it measures 90 degrees (90°) since a right angle is always 90 degrees.

In a triangle, the sum of the angles is always 180 degrees (180°). So, we can find the measure of angle N by subtracting the measures of angles L and M from 180 degrees.

Angle L is given as 32 degrees (32°) and angle M is 90 degrees (90°).

Angle N = 180° - angle L - angle M

Angle N = 180° - 32° - 90°

Angle N = 58°

Therefore, the measure of angle N is 58 degrees (58°).

Answer:n= 58 degrees

Step-by-step explanation:

so all u do is 90 “right angle” minus 32 which is 58! Hope this helped!

..

The variables 8 observations have x2 values of 2 or greater.

Two variables, x1 and x2, are present in the supplementary data set. There are a total of 20 observations in this data set. The x2 values for 8 of these 20 observations are equal to 2. Thus, x2 values of two were present in eight out of twenty observations, or 40%. The following 12 observations' x2 values do not add up to 2. Thus, 8 of the 20 observations in the data set have x2 values of 2 or higher.8 of these 20 observations have x2 values that are equal to 2. Thus, eight out of twenty observations, or 40 percent, had x2 values equal to two. The x2 values for the next 12 observations are not equal to 2. Consequently, 8 of the data set's 20 observations have x2 values of 2 or above.

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When we conduct time series forecasting it is safest to utilize regression analysis, because then we will not be extrapolating the above statement is False.

Regression analysis is a group of analytical techniques used to measure the relationships between a dependent variable and one or more independent variables. It may be used to simulate the long-term link between variables and gauge how strongly the relationships between them are related.

Models that evaluate the connection between a dependent variable and an independent variable include simple linear regression. The following equation represents the simple linear model:

Y = a + bX + ϵ

Regression analysis is the most secure method for time series forecasting since it involves extrapolation.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:

166 2/3 meters/sec.

Step-by-step explanation:

1/1 =1  12 inches/1 foot =1  you are looking for equivalents that will cancel out the unit until you can get to meters and seconds.  See work in the picture.

Answer:

225 students

Step-by-step explanation:

Total number of students = 900 students

percent that bring lunch to school everyday = 25%

Number of student that bring lunch to school = 25% of 900

Number of student that bring lunch to school = 0.25 * 900

Number of student that bring lunch to school = 225

Hence 225 students bring lunch to school everyday

The circle on a graph by drawing the center point and then drawing a circle around it with a radius of 6.

To graph the circle with the equation (x - 3)² + (y + 3)² = 36, we can start by finding the center and radius of the circle.

The equation of a circle in standard form is (x - h)² + (y - k)² = r² (h, k) represents the center of the circle and r represents the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (3, -3) and the radius is √36 = 6.

Using this information, we can proceed to plot the circle on a graph:

Plot the center point: (3, -3).

From the center point, move 6 units in each direction (up, down, left, and right) to determine the points on the circle.

Up: (3, -3 + 6) = (3, 3)

Down: (3, -3 - 6) = (3, -9)

Left: (3 - 6, -3) = (-3, -3)

Right: (3 + 6, -3) = (9, -3)

Connect the plotted points to form a circle.

The resulting graph should look like this:

    |            • (3, 3)

    |  

    |    •

    |                     •

__|_____________________________

    |

    |

    |

    |  

    |    • (3, -3)

The center of the circle is denoted by a solid dot (•) in the graph and the other points lie on the circumference of the circle.

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Answer:

see Image below:)

Step-by-step explanation:

Go here for steps