Given f(x) = 3VX and g(x) = 2x, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (f of)(1) (d) (gog)(0) (a) (fog)(4) = _____ (Type an exact answer, using radicals as needed. Simplify your answer.)

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=8\\ y=30 \end{cases} \\\\\\ 30=\cfrac{k}{8}\implies 240=k\hspace{9em}\boxed{y=\cfrac{240}{x}} \\\\\\ \textit{when y = 20, what's "x"?}\qquad 20=\cfrac{240}{x}\implies x=\cfrac{240}{20}\implies x=12[/tex]

The value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.

At the unit place of both numerals, there is a digit 4. The place value of a digit determines how valuable it is in a number. The position of the digit from the number's rightmost side determines its place value.

The value of the digit 4 in the tens place of the number 4,670 is 4 x 10 = 40.

The value of the digit 4 in the thousands position of the number 5,040 is 4 x 1000, or 4000.

Therefore, As 4000/40 = 100, the value of the digit 4 in 5,040 is 100 times more than that of the digit 4 in 4,670.

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Answer:

Step-by-step explanation:

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Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

The terms of the polynomial are -5s^(7), -8s^(4), 6s^(3), 4s, and -6. The degree of each term is 7, 4, 3, 1, and 0, respectively. The degree of the polynomial is the highest degree of any of its terms, which is 7.

The leading term is the term with the highest degree, which is -5s^(7). The leading coefficient is the coefficient of the leading term, which is -5. The constant term is the term with a degree of 0, which is -6.

So, the terms are -5s^(7), -8s^(4), 6s^(3), 4s, and -6; the degree of each term is 7, 4, 3, 1, and 0; the degree of the polynomial is 7; the leading term is -5s^(7); the leading coefficient is -5; and the constant term is -6.

Terms: -5s^(7), -8s^(4), 6s^(3), 4s, and -6

Degree of each term: 7, 4, 3, 1, and 0

Degree of the polynomial: 7

Leading term: -5s^(7)

Leading coefficient: -5

Constant term: -6

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Answer:

C

Step-by-step explanation:

I think its c because it said x = 3 less than 6, what is three less than 6? 3 so if you were to plug in 3 for x so bc = 3 and ab = 6 you multiply those two together but when you are doing area for a triangle its 1/2 bh so how i do this is i multiply 6 and 3 and get 18 and divide that by 2 and my final answer is 9. Hope this works, let me know if it doesnt!

Answer:

Step-by-step explanation:

lets take the top part as 1 and the seconds part as 2

so for the first part

1 Area= L*B

so 8*5 =40

2 Area=L*B

so 11*4=44

44+40=84cm2

The measure of the height of the tin in mm can be found using the steps below.

What are Measurements?

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Here, the activity is to measure the height of a tin.

Height of the tin is the vertical distance from the base of the tin to the top of the tin.

The height of the tin is the exact straight line measurement when the tin is placed upright on a flat surface.

The measurement has to be in millimeters.

So the best tool is the ruler.

Place the ruler vertically with point 0 at the baseline of the tin.

Mark the point in millimeters that the ruler coincides with the top of the tin.

Read the height to the nearest millimeter.

Hence, the height of the tin can be measured as above.

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The complete Question:

Measure the height of the tin in the mm and write down the real height in mm

The inequalities that represent the regular price of eyeglass frames will be 0.4r ≤ 120 and r ≥ 4(360/5).

If we let r represent the regular price of the eyeglass frames, then we can write the following two inequalities based on the given information:

0.4r ≤ 120

This inequality represents the fact that the lowest regular price for the eyeglass frames is $120. We use 0.4 because a 60% discount means that the price paid is 40% of the regular price.

Also, r ≥ 4(360/5) as this inequality represents the fact that the highest regular price for the eyeglass frames is $360. We use 4(360/5) because a 75% discount means that the price paid is 25% of the regular price, which is equivalent to multiplying the regular price by 0.25. Then, 4 times that amount gives us the regular price, which is $360 in this case.

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The equation that gives the cost of each juice bottle is 24j + 2.19 = 40.83

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let j represent the cost of each juice.

Sophie bought a popcorn for $2.19 and 24 juice bottles for a total of $40.83.

The equation that represents this problem is:

24j + 2.19 = 40.83

The equation is 24j + 2.19 = 40.83

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The complex solutions to the given equation are -1 + i√2 and -1 - i√2.

To determine the complex solutions to the equation, we can first simplify the quadratic equation by dividing each term by 2. This gives x² + 2x + 3 = 0.

The discriminant (b² - 4ac) can be calculated to find the nature of roots.

b² - 4ac = 2² - 4(1)(3) = 4 - 12 = -8

As the discriminant is less than 0, the roots are imaginary roots. That is, the roots are complex numbers.

To find the roots of this quadratic equation, the following steps can be followed.

Since the coefficient of x² is 1, the quadratic formula can be used to solve the given quadratic equation. The quadratic formula is given by

x = [-b ± √(b² - 4ac)] / 2a

Substitute the given values into the formula.

x = [-2 ± √(-8)] / 2

On simplifying the above expression,

x = [-2 ± 2i√2] / 2= -1 ± i√2

Therefore, -1 + i√2 and -1 - i√2 are the complex roots or solutions of the given quadratic equation.

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Given- A sequence as -6,-9,-12,-15

To find- The equation for the nth term of the arithmetic sequence and to find the value of [tex]a_{10}[/tex].

Explanation- The common difference is [tex]-9-(-6)=-3[/tex]

We know the arithmetic sequence formula is

[tex]a_n=a_1+(n-1)d\\a_n=-6+(n-1)(-3)[/tex]

When n=10

[tex]a_{10}=-6+(10-1)(-3)\\a_{10}=-6+9(-3)\\a_{10}=-6-27\\a_{10}=-33[/tex]

Final answer- The value of 10th term is -33.

Answer:

A

[tex]2y {}^{4} \div x {}^{4} [/tex]

Step-by-step explanation:

Divide 14 by 7 it will be 2.

Now divide the variables.

X variable will give you X{}^{-4} and y{}^{4}.

So bring X variable in the denominator to make it positive.

So your answer will be option A.

Answer:

A

Step-by-step explanation:

It was right for me

When f(x) = 4, then, the value of x = 2 (domain = 2, range = 4).

According to the mapping above, the given relationship is bijective (one-to-one and onto or one-to-one correspondence) because each element of the range is mapped to by exactly one element of the domain.

When we say a relationship is bijective, it means the satisfies both the injective (one-to-one function) and surjective function (onto function) properties. Therefore, as a result, f(x)=4 implies f(2)=4 or simply x=2.

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The correct answer is C. the probability of incorrectly rejecting the null hypothesis.

A P-value is used in hypothesis testing to determine the likelihood of observing a test statistic as extreme as the one observed under the null hypothesis. It is a measure of the strength of evidence against the null hypothesis.

A small P-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis. A large P-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

It is important to note that a P-value is not the same as the significance level (option E), which is the threshold used to determine whether to reject or fail to reject the null hypothesis.

The P-value is also not the same as the correlation between two variables (option A), which measures the strength of a linear relationship between two variables.

The P-value is also not the ratio between the test statistic and the standard error (option B), which is used to calculate the P-value but is not the same thing.

Therefore, the correct answer is option C, the probability of incorrectly rejecting the null hypothesis.

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The solution of the given expression is y = -12 and there are no extraneous solutions.

A solution to an equation that appears during the solving process but does not fulfil the original problem is known as an extraneous solution. In other words, it is a solution that, when inserted back into the original equation, yields an untrue assertion. Extraneous solutions typically result from certain algebraic operations, such squaring an equation's two sides, which might introduce new solutions that don't truly satisfy the original problem.

The given expression is:

7y+3−6y+9=0

y = -12

Substitute y = -12 back into the original equation:

7y + 3 - 6y + 9 = 0

7(-12) + 3 - 6(-12) + 9 = 0

-84 + 3 + 72 + 9 = 0

The left-hand side simplifies to:

0 = 0

Hence, the solution of the given expression is y = -12 and there are no extraneous solutions.

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Answer: C

Step-by-step explanation:

replace n=1 with f(n)= 5n-2 we have

f(1)=3 => remove answers B and D

f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7

Try with answers C and D to see if it satisfies this

f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct

The first five terms of the sequence whose general term is given as a_(n)=2n-8 are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.

To explain this in more detail, the general term for a sequence is given by an equation in the form a_(n)= some expression. In this case, the expression is 2n-8, so it can be read as “2 times the term number minus 8”.

To calculate the first term, we substitute n=1 into the equation and solve, so a_1=2*1-8=-6. To calculate the second term, we substitute n=2 into the equation and solve, so a_2=2*2-8=-4. Continuing in this manner, we calculate the third term as a_3=2*3-8=-2, the fourth term as a_4=2*4-8=0, and the fifth term as a_5=2*5-8=2.

Therefore, the first five terms of the sequence are a_1=-6, a_2=-4, a_3=-2, a_4=0, and a_5=2.

In conclusion, to find the first five terms of a sequence given by a general term a_(n)= some expression, substitute the values n=1, n=2, n=3, n=4, and n=5 into the expression and solve to get the desired terms.

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The length and width of the toolbox are 8 feet and 5 feet respectively.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length.

Given that the volume of the toolbox is 80 cubic feet, so we can write:

V = w × h × l = 80ft³

Next, we know that the width is 3 feet less than the length, so we can write:

w = l - 3

Now we can substitute the second equation into the first equation to get an equation with just one variable:

V =  w × h × l = l(l - 3)(2) = 80

Simplifying this equation, we get:

2l² - 6l - 80 = 0

We can solve this quadratic equation using the quadratic formula:

l = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = -6, and c = -80. Plugging in these values, we get:

l = (6 ± √(6² - 4(2)(-80))) / 4

l = (6 ± √(676)) / 4

We take the positive value of l since the length must be positive, so we get:

l = (6 + 26) / 4

l = 8

Now we can use the second equation (w = l - 3) to find the width:

w = l - 3

w = 8 - 3

w = 5

Therefore, the length of the toolbox is 8 feet and the width is 5 feet.

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The graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

For the first inequality, 2x + 3y < 9, we will start by graphing the line 2x + 3y = 9, which is the boundary line of the inequality.

To do this, we will solve for y:

2x + 3y = 9

3y = -2x + 9

Divide both sides by 3

y = (-2/3)x + 3

For the second inequality, Y≥ - 2/3x-4

Hence, the graph of 2x + 3y < 9 and y≥ - 2/3x-4 is given in the attachment.

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Yes, this word problem is solvable using exponential functions.

To solve this problem, we need to use the formula for exponential growth:

P(t) = P0 * e^(rt)

where P(t) is the population after t hours, P0 is the initial population, r is the growth rate, and e is the mathematical constant approximately equal to 2.71828.

In this problem, we are given that the population doubles in size every 25 hours. This means that the growth rate is 1/25, since the population is multiplying by 2 each time.

We are also given that there are about 1.35 million infections every year. Since there are 365 days in a year, this means there are about 1.35 million/365 = 3699.18 infections per day.

We can now use this information to find the initial population:

P0 = 3699.18 / e^(1/25 * 24 * 365)

P0 ≈ 2135.05

So the initial population is about 2135.05 bacteria.

To find the population after one year, we can use the formula again:

P(365 * 24) = 2135.05 * e^(1/25 * 24 * 365)

P(365 * 24) ≈ 3.89 x 10^18

Therefore, there are approximately 3.89 x 10^18 bacteria present after one year.

radius of the circle is sqrt(3)x.

The radius of the circle can be found by using the Pythagorean Theorem. The side lengths of each equilateral triangle created by the diagonals is 2x, so the hypotenuse of the triangle is sqrt(3)x. Since the hypotenuse of each triangle is the same as the radius of the circle, the radius of the circle is sqrt(3)x.

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Answer:

a) The digit in the hundredths place in 0.453 is 3. Therefore, the value of the digit in color is 3/100.

b) The digit in the tenths place in 43.1 is 1. Therefore, the value of the digit in color is 1/10.

c) The digit in the thousandths place in 92.303 is 3. Therefore, the value of the digit in color is 3/1000.

d) The digit in the ten-thousandths place in 2.3214 is 1. Therefore, the value of the digit in color is 1/10,000.

15 - 60%

x - 100%

1500 = 60x

x = 25

∴ There are 25 students in the class in all.

Answer:

35 miles.

Step-by-step explanation:

A=3x+65

B=2x+100

3x+65=2x+100

x+65=100

x=35

Answer:

if I'm correct it's 3(4x5)

BUT RECHECK JUST INCASE

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

To solve this, we need to combine like terms.
(9c-8d) + (2c-6) + (-d+3)
9c + 2c - 8d - d - 6 + 3
11c - 8d - d - 6 + 3
11c - 9d - 6 + 3
11c - 9d - 3

Yes, H is a subgroup. We can prove this by using the subgroup criterion, which states that a subset H of a group G is a subgroup if and only if it satisfies the following three conditions:

1. The identity element of G is in H.

2. If h1 and h2 are in H, then h1*h2 is in H.

3. If h is in H, then h^(-1) is in H.

Let's check if these conditions are satisfied for H:

1. The identity element of ???? is the zero function, f(x) = 0, which is differentiable. Therefore, the identity element is in H.

2. If h1 and h2 are in H, then they are both differentiable functions. The sum of two differentiable functions is also differentiable, so h1 + h2 is in H.

3. If h is in H, then it is a differentiable function. The inverse of a differentiable function under addition is its negative, which is also differentiable. Therefore,[tex]h^{-1} = -h[/tex] is in H.Since all three conditions are satisfied, H is a subgroup.

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According to the Synthetic Division, the Quotient is equal to  7x² -4x + 5 and the Remainder is equal to 8.

Synthetic division can divide two polynomials more quickly than the standard long division algorithm.

With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.

Given:

(7x³-25x² +17x -7) ÷ (x-3).

So, Synthetic Division for this is as follows:                                    

                      (x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5

                                                    7x³-21x²

                                                 _________

                                                           -4x² + 17x

                                                           -4x² + 12x        

                                                    _______________

                                                                        5x - 7              

                                                                        5x - 15

                                                                      ________

                                                                               8

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Answer:

1 / 625

Step-by-step explanation:

To write 5^-24 without exponents, simplify.

5^-4

1 / 5^4

1 / 625 or .0016

Answer:

The outputs are in order:

5

2

1

2

5

Answer:

5.2.1.2.5

Step-by-step explanation: