Simplify completely.a.4x212 xwhen x +0.b. (2t)(3t)(t)c. (3x² - 4x +8)+(x² +6x-11)d. (3x² + 4x – 8) - (x² + 6x +11)

Given:

650 lb of coffee is sold when the price is $4 per pound,

400 lb of coffee is sold at $8 per pound.

To find:

A) List the data points

B) The slope of line joining the points

C) Interpretation of meaning of slope of line

D) linear equation of data using point slope form

E) Using the function we need to predict the number of consumers buying at $6 per pound

Step-by-step solution:

A) Data points of the given data:

Data points:

(4,650) and (8,400)

B) The slope of the line joining the points:

C) Interpretation of meaning of slope of line:

Slope here means that:

When there is an increase in the price of coffee then the weight of coffee decreases.

Weight per dollar of coffee decreases at the rate of 62.5

D) linear equation of data using the point-slope form:

Applying point-slope form:

y - y1 = m(x - x1)

y - 650 = -62.5(x - 4)

y = -62.5x + 900

In function notation it can be represented as:

S(P) = -62.5P + 900

E) Using the function we need to predict the number of consumers buying at $6 per pound

To predict that, we will simply put the value of P equal to 6 in the given function:

S(P) = -62.5P + 900 At P = 6

S(P) = -62.5(6) + 900

S(P) = 525

Thus we can say that 525 customers will buy at $6 per pound.

Steve's taxable social security benefits is zero.

Since Steve declares himself as the head of the home, his social security payments, which range from $25,000 to $34,000, will be subject to a 50% tax.

Retirement income, interest income, and dividend income are not considered social security benefits for determining the limit. Nevertheless, in the case at hand, the social security benefits total $23,000, which is less than the maximum of $25,000 and is thus not taxable.

As a result, Steve's Social Security benefits are not taxable.

Hence the taxable amount on Steve on social security benefits is Zero.

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Debbie's checkbook balance is $-3,297.23, which shows an overdraft.

An overdraft occurs when the money (deposits) in Debbie's account does not exceed her payments or withdrawals.

While Debbie had a positive beginning balance, the ending balance shows an overdraft of $-3,297.23.

By this overdraft, Debbie's bank is extending her some short-term credit, which she should pay back with interest.

Beginning balance on checkbook =  $2,715.50

Checks for the month =                     $-5,298.13

Deposits for the month =                       $250.16

Payroll check =                                 $-2,980.66

IRS check =                                          $2,550

Auto insurance and utilities =               $-534.10

Ending balance on checkbook =     $-3,297.23

Thus, Debbie's ending checkbook balance will show an overdraft of $-3,297.23.

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The number 8.26 10^0 is shown in scientific notation.

Its standrad form is: 8.26 since we know that any base different from zero raised to the power "0" (zero) gives "1" (one).

Answer:

yes

Step-by-step explanation:

if y = -6,

3x = -6

x = -2

Answer:

yes

Step-by-step explanation:

y = 3x?

Let x = -2 and y = -6

-6 = 3(-2)

-6 = -6

This is a true statement so (-2,-6) is a solution to the equation y = 3x

The critical value (tα/2) for a 99% confidence interval for the sample size 15 is 2.977 .

We have to find the critical value tα/2 for 99% confidence interval, we are given the sample size.

First we will find the alpha value to get the critical value.

=100%-99%

=1-0.99

=0.01

α=0.01

α/2=0.01/2

α/2=0.005

degrees of freedom(df)= n-1=15-1=14

We will use degrees of freedom and α/2 values to find the critical value that is tα/2.

By using the t table we get the critical value  of tα/2=2.977.

Therefore, the critical value for 99% confidence interval with sample size 15 is 2.977.

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the selling price of each card is = 28 $

let she sold x number of cards,

so, the equation is,

28x = 224

x = 224/28

x = 8

thus, the answer is number of cards sold by nandita is 8

so, the equation is

28x = 224

Data:

Equation as a function of D of P

Answer (6):

• Domain

To know how many shirts per month will be demanded if the price is $27, we have to use P = $27:

Answer (7): $37.80

'the sum of a number and four' means

And three times that is

Then, that 'equals to five times a number'

'decreased by two':

So, the statement is translated into the equation:

The correct answer is option A

Answer:

4 19/24

Explanation:

First, we need to convert the mixed numbers into a fraction, so:

Then, we can add the fractions as follows:

Finally, we can simplify the fraction and write the fraction as a mixed number as:

Because when we divide 115 by 24, we get 4 as a quotient and 19 as a remainder.

Therefore, the answer is: 4 19/24

Given,

The weight of candies normally distributed ;

Mean  weight of candies = 0.8543 g

Standard deviation, σ = 0.0519 g

Sample of candy came from a packet of 469 candies

Net weight of the packet = 400.3 g

Average weight of the candies in the packet;

[tex]x_{avg} =[/tex] ∑xi/n = 400.3/469 = 0.8535

The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).

z = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002

P(X > 0.8536) = P(z > 0.002) = 0.4992

A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.

z = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288

P(X > 0.8543) = P(z > 0.3288) = 0.37115

A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.

z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89

P(X > 0.8556) = P(z > 0.89) = 0.18673

Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.

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Answer:

[tex]w \leq 1.9[/tex]

Step-by-step explanation:

The picture itself measures 6" by 8". Therefore, the area is 6 * 8 = 48 square inches.

All of the pieces of wood have the same width, and we know that two of them will be 6 inches long and two will be 8 inches long.

Therefore, the combined area of the pieces of wood will be 2 * 6w and 2 * 8w. This gives us 12w + 16w.

Now we can set up an inequality:

48 (area of picture) + 12w + 16w <= 100 (maximum area).

Simplify the left side of the equation to give us this:

[tex]48+28w\leq 100.[/tex]

We can move the 48 over to the other side to get [tex]28w \leq 100 - 48[/tex], which simplifies to [tex]28w \leq 56[/tex]. Now, you just have to divide both sides by 28 to get [tex]w\leq 1.857[/tex].

Rounding to the nearest tenth of an inch gives us 1.9 as the maximum width of the pieces of wood.

Let x be the length of the rectangle and y be the width of the rectangle, then we can set the following equations:

Solving the first equation for x we get:

Substituting x=20-y in the second equation we get:

Now, we will use the first and second derivative criteria to find the maximum.

The first and second derivatives are:

Since the second derivative is a negative number that means that A(y) reaches a maximum when A´(y)=0.

Solving A´(y)=0 for y we get:

Now, substituting y=10 in x=20-y, we get:

Answer:

Length 10 yards.

Width 10 yards.

By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.

Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.

Based on this, you know that:

Knowing that:

You get that:

The Pythagorean Theorem states that:

Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.

So you can identify that, for this case:

Where "CD" is the altitude of the triangle.

Therefore, substituting values and solving for "CD", you get this result:

The answer is: Option (1)

Answer:

It's average speed is 48 km per hour

Step-by-step explanation:

Answer:

60 km/hr

Step-by-step explanation:

150 km / 2.5 hr =  60 km/hr

The given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

First, we have to find the whole number,

Determine how many times the denominator enters the numerator. Divide 60 by 25 and preserve just the numbers to the left of the decimal point:

⇒ 60 / 25 = 2.4000 = 2

Then, find a new numerator :

Multiply the result by the denominator and subtract it from the original numerator.

⇒ 60 - (25 x 2) = 10

Now, put together

To obtain this, keep the original denominator and use the solutions from Steps 1 and 2:

⇒ 2 10/25 ⇒ 2 2/5

Thus, the given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.

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We have the next inequality

First we need to isolate the y

The boundary line need to be dashed because the sign is less than

Two points of the boundary line can be calculated using the next equality y=-x

x=0

y=0

Point (0,0)

x=-5

y=5

Point (-5,5)

The area will be the area below the boundary line because we have a sign less than

An inequality that represents the given graph is; 2 < x < ∞.

For the given question.

The inequality is given by the values of the number line.

The value is starting from 2 and goes up to infinity.

But, It is a hollow dot at 2 means 2 is with open interval, as 2 will not be taken for the value of x.

The values lies between, (2, ∞)

Thus, the inequality that represents the given graph is; 2 < x < ∞.

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The factored expression of 4x^3 + 12x^2 + 3x + 9 is (4x^2 + 3)(x + 3)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

4x^3 + 12x^2 + 3x + 9

Group the expression in 2's

So, we have

4x^3 + 12x^2 + 3x + 9 = (4x^3 + 12x^2) + (3x + 9)

Factor each group

So, we have

4x^3 + 12x^2 + 3x + 9 = 4x^2(x + 3) + 3(x + 3)

Rewrite as

4x^3 + 12x^2 + 3x + 9 = (4x^2 + 3)(x + 3)

Hence, the factored expression is (4x^2 + 3)(x + 3)

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Thee values of the functions are;

(f . g)(x) = √(-2x + 3)

(g . f)(x) = - 2√x + 3

A function can simply be defined as a law, rule or expression showing the  relationship between two variables in an equation or expression.

The two variables are given;

Given the functions;

To determine the function (f . g)(x), substitute the value of x as g(x) in the function, we have;

(f . g)(x) = √(-2x + 3)

To determine the function  (g . f)(x), substitute the values of x  in the function g(x), we have;

(g . f)(x) = - 2√x + 3

Hence, the functions are √(-2x + 3) and  - 2√x + 3

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Given:

To find:

The interval at which the function is increasing, decreasing and constant.

Explanation:

We know that,

For a function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function.

For a function, y = F(x), if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.

According to the graph,

The function is increasing in the interval,

Because, if x increases from 2, the value of y increases.

The function is decreasing in the interval,

Because, if x increases from negative infinity, the value of y decreases.

As we know, a constant function is a function whose output value is the same for every input value.

Here, the function is not constant at any of the intervals.

Final answer:

Increasing:

Decreasing:

Constant: DNE.

The solution to the system of equations represented by the matrix is (x, y, z) = (6, 7, 6).

Maybe your matrix is ...

[tex]$\left[\begin{array}{ccc|c}3 & -1 & 7 & 53 \\ 1 & 7 & 1 & 61 \\ 9 & 1 & 1 & 67\end{array}\right]$[/tex]

A calculator can tell you the solution is ...

 (x, y, z) = (6, 7, 6)

The third variable in systems of equations with more than two variables can be defined in terms of the other two (as for solution by substitution). This can be used to create two equations with two unknowns by substituting it into the remaining equations. The value of the third variable can then be determined using that answer. The use of this technology is demonstrated in the attached.

The last equation served as a definition, which was then applied to the first two equations. An algebraic solution can be solved using the same strategy.

The answer is (x, y, and z) = (6, 7, 6).

Complete question: Find the solution to the system of equations represented by the matrix shown below. 3 -1 7 53 1 7 1 61 9 1 1 67​

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Given the function of the rate of change of the population:

The integral of this function will be the value of the population growth of the town from 1990 to 2010. This is because P(t) is the rate of change of population, its integral will be the antiderivative, that is the population of the town.

To calculate the change in population we have to find the integral from 5 to 10 of P(t):

The change in population can not be a decimal number, so we can round it to 1162.

To calculate the population in 2020 we have to find the integral from 0 to 30 of P(t) and then add it to 10000 which was the initial population (we already know the integral so we're just going to evaluate it):

It means that the population in 2020 is 18221 (Remember that we round it because it is not possible to have a decimal value for the population of the town).

Solution

For this case we can do the following:

m < X = 60

One angle in a right triangle needs to be 90º

So then we can find the measure of the other angle like this.

180 -90-60 = 30º

We can find the following identity:

And solving for thw leg opposite we got:

Answer:

-1/2, -1/4, 3/4.

Explanation:

If we draw the number in a number line, we get:

So, if we order them from least to greatest, we get:

-1/2, -1/4, 3/4.

Answer:

-1/2, -1/4, 3/4

Step-by-step explanation:

After rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)

Upon rotation of this hexagon by 180

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .

After rotation, the co- ordinates change from

(0, -8) → (0, 8)

(3, -8) → (-3, 8)

(6,-5) → (-6, 5)

(6, 1) → (-6, -1)

(3, 2)  → (-3, -2)

(0, 2)​ → (0, -2)

Therefore, after rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)

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Answer:

Step-by-step explanation:

The rent is 420 a year.

6 months is half a year.

The rent for 6 months is half the rent for a year:

It is important to know that horizontal lines are represented by the equation y = k, where k is a real numbers.

In this case, if the equation passes thorugh (2,7), then the equation would be y = 7.