From 1982 to 2004, the number
B
of federally insured banks could be approximated by
B
(
t
)
=
−
326.6
t
+
13783
where t is the year and t=0 corresponds to 1982.

How many federally insured banks were there in 1987?


Find the slope of the graph of B.

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.

The value of the expression 8! is 40320.

It should be noted that an expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, 8! will be:

= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40320

This illustrates the concept of multiplication.

Therefore, it is 40320.

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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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Answer:

x and y is 59 degrees

Step-by-step explanation:

You can find the angle next to 121 which is 59 degrees considering linear pair. Then, you can figure out y by doing corresponding angles and so this means that y is also 59 degrees. To find x, we know that x is vertical to y and that they are the same value. So, this means that x is 59 degrees as well. Hope this helps!

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

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

'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

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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Given:

The equation is:

Required:

Find the area enclosed by the region.

Explanation:

The given equation is:

Find the intersecting point of the curve.

The enclosed area is:

Ok, so

The answer is that there's 1,000 grams in a Kilogram. That's the equivalence.

Answer:

Step-by-step explanation:

Ascending is least to greatest.

We can convert the fractions into decimals.

SO,

7/10 can be 0.7 and 9/10 can be 0.9

In least to greatest order, it would be:

0.4, 0.7, 0.9 ANSWER

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

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

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).

The value of P is 1 and value of V is 5 .

In this addition, each letter represents a single digit.

Now, Given that

       1   7    2

       2   9   4

+     7    V   6

= P   2    P    2

To find the value of P

To solve this addition:

       1   7    2

       2   9   4

+     7    5   6

= 1   2    1    2

Hence, The value of P is 1 and value of V is 5 .

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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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Given:

let u = x+5

so, the equation will become:

so, the equation is quadratic in form because the substitution u = x+5

The answer is the first statement

Note:

the second statement is wrong, because when the equation expanded, it will be a second degree polynomials not fourth degree

Also, the last 2 statements are wrong, because it is quadratic equation.

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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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.

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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The Solution:

Given:

We are asked to find the value of x.

By applying the Trigonometrical Ratio, we have:

Cross multiplying, we get

Therefore, the correct answer is 14.20

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.

n+1< -3

n< -3 -1

n<-4

-4n< - 8

n>-8/-4

n > 2

so, the solution is,

n < - 4 or n > 2

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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You can use multiplication to generate an equivalent ratio by multiplying both sides of the ratio by the same factor, this way:

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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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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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.

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).