25, 8, 10, 35, 5, 45, 40, 30, 20 What is the median of the given data set?

The mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y

The solution of the equation is given as

10x - 3y = 6

      +3y     +3y

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

10x = 3y + 6

-6           -6

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

(10x - 6)/3 = 3y/3

10x - 2 = y

In the above steps, we have the following equation

(10x - 6)/3 = 3y/3

When the above equation is expanded, we have

10x/3 - 6/3 = 3y/3

Evaluate the quotient in the above equation

So, we have

10x/3 - 2 = y

The abvoe equation is different from Mike's result

Hence, the mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y

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The solution of the compound inequality are:

| x - 3  | < 4              -1 < x < 7

| x + 2 | > 8             -10 < x or  x >6

Given data

| x - 3  | < 4 and | x + 2 | > 8

Solution the first inequality | x - 3  | < 4

| x - 3  | < 4

x < 4 + 3  OR  x >  - 4 + 3

x < 7        OR  x >  - 1

-1 < x < 7

Solution for the second inequality  | x + 2 | > 8

| x + 2 | > 8

x < -8 - 2  OR  x >   8 - 2

x < - 10        OR  x >  6

-10 < x or  x >6

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The standard form will be

1/10 x⁴-2x²-4x-1

Polynomials in standard form can also be referred to as the standard form of a polynomial which means writing a polynomial in the descending order of the power of the variable. To write a polynomial in a standard form, the degree of the polynomial is important as in the standard form of a polynomial, the terms are written in decreasing order of the power of x. The standard form of polynomial is given by, f(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a1x + a0, where x is the variable and ai are coefficients.

A mathematical expression of one or more algebraic terms in which the variables involved have only non-negative integer powers is called a polynomial. The terms have variables, constants, and exponents. The standard form polynomial of degree 'n' is

aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+.......

To write a polynomial in standard form ,simplyfy and then arrange the terms in descending order.

ax²+bx+c

move -1

-4x+x⁴/10-2x²-1

Reorder terms

1/10x⁴-2x²-4x-1

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Answer: 5y^2

Step-by-step explanation: hope this helps

Answer: it is the third option

Explanation: as any number with a negative power will be the reciprocal

----> y^-2 = 1/y^2

----> 5 x 1/y^2

----> 5/y^2

i hope this helps

The account balance invested at 6. 5% annual interest compounded annually will take 19.1 years to reach $50,000.

Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:

B = P(1 + r/n)^t

where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year

Using this formula, find t, the time it will take the account to reach $50,000 when

B = $15,000

r = 6.5% = 0.065

n = 1

B = P(1 + r/n)^t

$50,000 = $15,000(1 + 0.065/1)^t

(1 + 0.065)^t = $50,000/$15,000

1.065^t = 10/3

t = 19.1 years

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Answer: the product is 1816.08

Step-by-step explanation:

The required product of the expression is 1816.08.

Given that,
To determine the product and simplified value of the expression (134−2.4)⋅[0.5⋅(25+2.6)]

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

Given expression,
= (134−2.4)⋅[0.5⋅(25+2.6)]

= (131.6) * [0.5 * 27.6]
= 131.6 * 13.8
= 1816.08

Thus, the required product of the expression is 1816.08.

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The domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).

Domain of function f(x) :

√ (x - 1) ≥ 0

So, we get that:

x ≥ 1

= [1, ∞)

Range = (0, ∞) as square of a number is always positive.

Domain of function g(x):

√ x ≥ 0

on adding 1 both sides we get

x ≥ 0

= (0,∞)

Range = [-1, ∞).

Therefore, the domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).

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Answer: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)

                              J(-3, 1) = J'(4, 0)

                              F(-2, 3) = F'(5, 2)

                              N(-2, 0) = N'(5, -1)

Step-by-step explanation:

If you want to translate a point 7 units right, you'll need to add 7 to its x-coordinate. If you want to translate a point 1 unit down, you'll need to subtract 1 from its y-coordinate. Do both of these things to perform a translation 7 units right and 1 unit down.

So, we can write,

            7 units right means add the +7

             1 unit down means subtract the -1

Then,

                  J(-3, 1) = J'(-3 + 7, 1 - 1)

                  J(-3, 1) = J'(4, 0)

                  F(-2, 3) = F'(-2 + 7, 3 - 1)

                  F(-2, 3) = F'(5, 2)

                  N(-2, 0) = N'(-2 + 7, 0 - 1)

                  N(-2, 0) = N'(5, -1)

Therefore,

These points to make sure they have shifted 7 units right and 1 unit down.

   7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)

                              J(-3, 1) = J'(4, 0)

                              F(-2, 3) = F'(5, 2)

                              N(-2, 0) = N'(5, -1)

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Answer:

a,b,c and no d

Step-by-step explanation:

welcome

Answer:

a, b, and c.

Step-by-step explanation:

Use the line test. :)

Answer:

[tex]\frac{5}{1}[/tex]

Step-by-step explanation:

45 : 9

= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )

= [tex]\frac{5}{1}[/tex] ← in simplest form

Step-by-step explanation:

2,250 was made in a month

Answer: y=kx

Step-by-step explanation:

Answer:

The sum is the third answer

Step-by-step explanation:

you add together the numbers that are in the same spot in both matrixes.

-3 + -4              0 + 2

5 + -1                 -7 + 8

That would give you

-7    2

4      1

The intercepts and the standard form of each polynomial are listed below:

In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.

Now we proceed to find each element:

Case 1

x-Intercept

x = - 4 or x = 6

Standard form

f(x) = (x + 4) · (x - 6)

f(x) = x² - 2 · x - 24

y-Intercept

f(0) = - 24

Case 2

x-Intercept

x = 1 / 4 or x = 3

Standard form

f(x) = (2 · x - 4) · (x - 3)

f(x) = 2 · (x - 2) · (x - 3)

f(x) = 2 · (x² - 5 · x + 6)

f(x) = 2 · x² - 10 · x + 12

y-Intercept

f(0) = 12

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Answer:

x = 30

Step-by-step explanation:

To find the x intercept, you need to substitute [tex]y = 0[/tex], as all points on the x axis's y-coordinate is 0.

[tex]0 = 30000 - 1000x\\ \\ \to 0 + 1000x = 30000 \cancel{- 1000x + 1000x} \\\\ \to 1000x = 30000 \\ \\\to \frac{1000x}{1000} = \frac{30000}{1000} \\ \\\to x = 30[/tex]

Answer: Its x= 30

Step-by-step explanation:

55 ounces of honey will need to mix with 11 ounces of strawberries.

Question is not complete so lets suppose that,

For each ounce of mix, we use honey five times of a ounces of strawberry.

And then we will find that how many ounces of honey we would to mix with 11 ounces of strawberries.

According to above statement

 one ounce of strawberries = 5 ounce of honey

So, for the mix we will need to add honey which will we equal to five times of strawberries.

If we have 11 ounces of strawberries then,

the amount of honey will be = 5 × 11 = 55 ounces

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Answer:

4.27

Step-by-step explanation:

1 bundle= $0.56

7bundles=o.56x7=$3.92

Tax=0.35

3.92+0.35=4.27

The values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.

it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc. When it comes to integers, even numbers can be divided by two exactly while odd numbers cannot. 2, 6, 10, 20, 50, and other even numbers serve as examples.

Suppose the value of the three consecutive even integers is n, n + 2, and n + 4

The sum of the integers is 6000.

Sum = n + n + 2 + n + 4

Sum = 3n + 6

Sum=6000

3n + 6 = 6000

3n =  5994

n = 5994/3

n = 1998

The three consecutive even integers are,

n=1998

n+2=1998+2=2000

n+4=1998+4=2002

Thus, the values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.

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y=5x 7.5w+7.5d Answer:

Step-by-step explanation:

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week is , w + d ≤ 15 .

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

here, we have,

Given that w is the number of hours for washing a car and d is the number of hours to walking dogs.

The work hours  at most 15 hours altogether between both jobs in a given  in a week.

Hence, w + d ≤ 15 is the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.

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The total change in the stock market from the beginning of the day to the end of the​ day is [tex]40\frac{1}{4}[/tex]

When the value of the stock market goes down, its value has decreased. The decrease in the value of the stock market would be represented with a negative number. A negative number is a number that is less than 0. The sign that is used to represent a negative number is -.

When the value of the stock market goes up, its value has increased. The increase in the value of the stock market would be represented with a positive number. A positive number is number that is greater than 0.

The total change in the stock market is the sum of the decrease and the increase in the stock market.

Total change = increase in the stock market - decrease in the stock market

[tex]110\frac{1}{2} - 70\frac{1}{4}[/tex]

[tex]40\frac{2-1}{4}[/tex] = [tex]40\frac{1}{4}[/tex]

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The equation of the translated graph from the parent function is g(x) = |x + 2| + 1

The parent function is given as

f(x)= |x|

From the graph, we can see that the parent function f(x) is translated as follows:

The above sequence of translation is represented as

(x, y) = (x + 2, y + 1)

So, we have

g(x) = |x + 2| + 1

Hence, the equation of the translated graph is g(x) = |x + 2| + 1

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The option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.

What is a collateral asset ?

An asset that a borrower pledges to a lender as a guarantee that the loan will be repaid is known as collateral asset.

We know that the assets that a lender accepts as security for a loan are referred to as collateral. That meant lenders are protected by the collateral in this way. To put it another way, if the borrower stops making loan payments, the lender may be able to sell the collateral to collect some or all of its losses.

So , let's check which of the given option falls under category of collateral.

A.

This is not collateral asset because for a credit card there is no security money given to bank. We only need to pay a maintenance charge and nothing else.

B.

This is a collateral asset.

For an antique vase whose value is $125000 , if the person has purchased this by taking a loan then he would have paid some security money as deposits. If any case he is not able to pay the loan by time the property or the asset becomes collateral which meant the lender may sell the asset to some or all of his losses.

C.

This is not collateral asset because if the loan is repaid in full there will be no extra charges liable on the asset and it can't be categorized as collateral.

Therefore , the option B , that is , an antique vase valued at $125,000 can be categorized as collateral asset.

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1. He is spending more money than he makes.

2. He has to cut back on other expenses.

3. It is a listing of what an individual owns minus what they owe.

4. an antique vase valued at $125,000

5. capital

Explanation: I took the same quick check and got 100%, hope this helps!

The inverse of the function is f ⁻¹(x) = 10ˣ

Given the function is y = log₁₀ x

In relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain. By replacing (x, y) with (y, x) with reference to the line y = x, one can obtain the graph of the inverse function.

steps to find the inverse of the function:

now replace y with x.

x = log₁₀ y

change the dependent variables.

f ⁻¹(x) = 10ˣ

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The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

It follows from the task content that the expression which is equivalent to that given in the task content be determined.

On this note, by distributing the coefficient of.tne parents; we have;

-1/2 ( 1/4x - 3/8)

= {(-1/2) × (1/4)x} + {-1/2 × -3/8}

= (-1/8)x + 3/16

Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.

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Option C: Samantha is correct because when using x=2, the resulting values in both expressions are equal.

Consider, 4x + 2

When x = 2,

=> 4x + 2 = 4*2 + 2

=> 10

Now consider, x + 17 + 3x - 15

When x = 2,

=> 2 + 17 + 3*2 - 15

=> 10

Therefore, Samantha is correct as both expressions equal 10 when x=2.

In other words, if we consider, x + 17 + 3x - 15

=> x + 17 + 3x - 15

=> x(1+3) + 17 - 15

=> 4x + 2

This shows that for any value of x, the expression x + 17 + 3x - 15, simplifies to 4x + 2.

Therefore, both the expressions, 4x + 2 and x + 17 + 3x - 15, are equal.

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Answer:

50 meters

Step-by-step explanation:

Width is x

So length will be x + 20

Perimeter = 2 (W + L) = 2 (x + x + 20) = 2 (2x + 20) = 4x + 40

so 4x + 40 = 160

4x = 120

x = 30

so length = x + 20 = 30 + 20 = 50

Given that Angles A and B are complementary to each other, the numerical value of x is 15.

Complementary angles are angles that sum up to 90 degrees.

Given the data in the question;

Since Angles A and B are complementary to each other, the sum of angle A and B is 90 degrees.

Measure of angle A + Measure of angle B = 90°

Plug in the given values and solve for x.

41 + (2x + 19) = 90

41 + 2x + 19 = 90

2x + 60 = 90

2x = 90 - 60

2x = 30

x = 30/2

x = 15

Given that Angles A and B are complementary to each other, the numerical value of x is 15.

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Answer: A is the answer

Step-by-step explanation: i took the test and got it right

log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.

Now,

log (x) - log (3) = 8

=> log (x) = 8 + log (3) = 8 + 0.477

=> log (x) = 8.477

Since, generally the base of log is 10, raising them to 10.

=> [tex]10^{log_{10}x} = 10^{8.477}[/tex]

=> x = 299916251.899 (as  [tex]a^{log_a(x)} = x[/tex])

Hence, log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.

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