From 1980 to 2008, the number of federally insured banks could be approximated by B(t)=-328.2t+13716 where t is the year and t=0 corresponds to 1980.
How many federally insured banks were there in 1985?


Find the slope of the graph of B.


Interpret this slope as a rate of change. Choose the correct answer below.
The number of banks increased by 13716 banks per year
The number of banks decreased by 12075 banks per year
The number of banks increased by 328.2 banks per year
The number of banks increased by 12075 banks per year
The number of banks decreased by 328.2 banks per year
The number of banks decreased by 13716 banks per year


Find the y-intercept of the graph of B.
The y-intercept is


Interpret the y-intercept. Choose the correct answer below.
The y-intercept is the number of banks in 1985
The y-intercept is the maximum number of banks allowed in the country
The y-intercept is the minimum number of banks allowed in the country
The y-intercept is the number of banks in 2008
The y-intercept is the number of banks in 1980

The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol

The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.

The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.

The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.

The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.

The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.

To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.

Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.

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Answer: put it in a caculator

Step-by-step explanation:

Combine 18x^3 and 5x^3.

Combine x^2 and 6x^2.

Combine 9x and −14x.

Add −3 and 11.

Therefore , the solution of the given problem of volume comes out to be where V₀ = (4/3)πr₀³  represents the balloon's initial volume at time

t = 0.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The cubic units cm3 and in3 are two examples. Contrarily, mass is a measure of how much stuff is in an object. It is usual practise to convert an object's weight into mass units like pounds or kilogrammes.

Here,

(a) We may express the radius of a balloon as follows because it is growing at a constant pace of 10 cm/s:

r(t) = r₀ + 10t

where r0 represents the balloon's initial radius at time t = 0.

(b) The following formula determines the volume of a sphere with radius r:

=> V(r) = (4/3)πr³

By replacing component (a) with r(t), we obtain:

=> V(t) = (4/3)π(r₀ + 10t)³

By enlarging and condensing the expression, we obtain:

=> V(t) = (4/3)π(r₀³ + 3r₀²(10t) + 3r₀(10t)² + (10t)³)

=> V(t) = (4/3)πr₀³ + 4πr₀²(10t) + (4/3)π(10t)²r₀ + (4/3)π(10t)³

=> V(t) = V₀ + 4πr₀²(10t) + (4/3)π(10t)²r₀

where V₀ = (4/3)πr₀³  represents the balloon's initial volume at time t = 0

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Answer:

A table can be made to to identify relationships between numerical patterns

Step-by-step explanation:

A numerical pattern refers to a sequence of numbers that arranged following some rule. This rule is known as a pattern rule. Relationship between consecutive numbers in the patterns can be described using one or more mathematical operations

A table can be made to identify relationships between numerical patterns. When data is organized in a table, it is easier to find the patterns between numbers or the terms.

Answer:

5

Step-by-step explanation:

15-3= 12

12+8 =20

20/4 =5

Step-by-step explanation:

26*2 1/2

26*3/2

13*3

39 is answer

make mae brain liest

The inequality equation given is,

Solve for x

Multiply both sides by 2

Collect like terms

Since, x ≤ -2 the values that are the solutions for x from the options are -2 and -3.

Therefore, the correct options are Option 1 and Option 2.

The critical value, given the sample size of 5 and the confidence level of 99. 0 percent would be 16. 812.

The critical values for the chi-squared (χ^2) distribution depend on the degree of freedom and the level of significance.

The degree of freedom for a chi-squared distribution typically equals the sample size minus 1 so the degrees of freedom here is:

= 5 - 1

= 4

The level of significance would be:

= 1 - 99. 0 %

= 0. 01

The critical value of the sample would therefore be found on a chi -squared distribution table for df = 4 and α = 0.01 to be 16. 812.

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Answer:

DE= 39°

Step-by-step explanation:

(4w+ 4 )+(4w+8)= 180

Solve for w

8w + 12 = 180

8w = 180-12

8w = 168

W= 21°

(4w+ 4)+(2w+11)+DE = 180

But w= 21°

((4*21 )+4)+((2*21)+11)+DE = 180

88 + 53 + DE = 180

DE = 180-88-53

DE= 39°

Answer:

true

Step-by-step explanation:

Answer:

It's true bro

Step-by-step explanation:

Answer: $1312.5 is the amount of interest earned in 5 years.

Answer:

C≈31.42

Step-by-step explanation:

Using the formulas

C=2πr

d=2r

Solving for C

C=πd=π·10≈31.41593

Answer:

The center of the circle is (3, -2) ((three, negative two)).

The radius of the circle is 5 (five).

Answer:

The inequality that represents this situation is 15x + 10y ≥ 1100, since Ezra needs to earn at least $1100 to buy the laptop.

To check if (60, 20) is a solution to this inequality, we need to substitute x = 60 and y = 20 into the inequality and see if it is true:

15(60) + 10(20) ≥ 1100

900 + 200 ≥ 1100

1100 ≥ 1100

Since 1100 ≥ 1100 is true, this means that (60, 20) is a solution to the inequality. This means that if Ezra works 60 hours mowing lawns and 20 hours walking dogs, he will earn enough money to buy the laptop.

The point (60, 20) represents the combination of hours worked for mowing lawns (x) and walking dogs (y) that will result in Ezra earning enough money to buy the laptop. The x and y values are the inputs or variables, while the inequality 15x + 10y ≥ 1100 is the constraint that must be satisfied. The solution (60, 20) is the output or result of the system of inequalities, and represents the combination of hours worked that will satisfy the constraint.

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

\(y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x\)

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

\(y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12\)

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

\(y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x\)

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

\(y=-4}x\\ 4=-4x\\x=-1\)

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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The option that represents shapes of the sampling distribution of p hat  is:

c. Because n (1 minus p) = 20 (1 minus 0.87) = 2.6 less-than 10 , the sampling distribution of p hat is not approximately Normal. Because p = 0.87 is closer to 1 than 0, the sampling distribution of p hat is skewed to the left.

Normal distribution is defined as the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

Because the requirement for normal is greater than 10, n×p is greater than 10 and nx(1-p) is also greater than 10.

This situation is abnormal because it is not valid. If p is close to 1 in a normal graph, then p is left skewed.

Thus, the option third is correct because nx(1-p)=2.6 less than equal to 10 then the sampling distribution  is not approximate normal because p=0.87 is closer to 1 than zero. Sampling distribution  is skewed to the left.

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9514 1404 393

Answer:

  all real numbers

Step-by-step explanation:

The arrows on the ends of the curve indicate that the graph extends to infinity horizontally. The domain is the horizontal extent, so is all real numbers.

__

Additional comment

Apparently, y=-7 is a horizontal asymptote, so the range is y > -7.

Answer:

what? i really dont understand

Step-by-step explanation:

Answer:

huh idrk what your asking but uhm

Answer:

\(\$1342.64\)

Step-by-step explanation:

We can represent the value \(A\) of a quantity \(P\) compounded continuously for \(t\) years at \(r\) rate of interest as:

\(A = P\cdot e^{rt}\)

This formula uses the mathematical constant \(e\) (approx. 2.72), which is the theoretical limit for continuous compounding.

Plugging the given values into the formula:

\(A = \$900 \cdot e^{(0.04 \, \cdot \, 10)}\)

We can now solve for \(A\).

↓ simplifying \(e\)'s exponent

\(A = \$900 \cdot e^{0.4}\)

↓ plugging into a calculator

\(A \approx \$1342.64222788\)

↓ rounding to the nearest cent

\(\boxed{A \approx \$1342.64}\)

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

The overall percent increase after 4 hours is 21% if the number of bacteria in a colony increases by 10% every 2 hours option (G) is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

The number of bacteria in a colony increases by 10% every 2 hours.

Let there be 100 bacteria in the starting

In the first 2 hours :

= (100×10%) + 100

= 10 + 100

= 110

Again after 2 hours:

= (110×10%) + 110

= 11 + 110

= 121

= (121 - 100)

= 21

Thus, the overall percent increase after 4 hours is 21% if the number of bacteria in a colony increases by 10% every 2 hours option (G) is correct.

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The probability that the first part is suitable is 0.83, and if the first part is suitable, the probability that the second part is also suitable is 0.8255, while the probability that the second part is not suitable is 0.1745.

a. The probability that the first part is suitable is 40/48 = 0.83.

b. If the first part is suitable, the probability that the second part is also suitable is 39/47 = 0.8255. This is because if the first part is suitable, that means there are only 39 parts left in the shipment that are suitable.

c. If the first part is suitable, the probability that the second part is not suitable is 8/47 = 0.1745. This is because if the first part is suitable, that means there are only 8 parts left in the shipment that are not suitable.

To calculate the probabilities, we used the formula P(A) = n(A)/n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of outcomes.

For part a, the event A is the first part being suitable, n(A) is 40, and n(S) is 48.

For part b, the event A is the second part being suitable, n(A) is 39, and n(S) is 47.

For part c, the event A is the second part not being suitable, n(A) is 8, and n(S) is 47.F

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

The volume of the closet space = 207,936 in³

The volume of the one roll of toilet paper = 141.3in³

To calculate the volume of the closet, the formula that should be used is the formula for the volume of a rectangle = length×width×height.

Where;

length = 57 in

width = 57

height = 64

volume = 57×57×64 = 207,936 in³

The volume of the toilet paper with the shape of a cylinder would be = πr²h

where;

radius = diameter/2= 6/2=3in

height = 5 in

volume of cylinder = 3.14×3×3×5 =141.3in³

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Answer:

B.  P(A|B) = P(A).

Step-by-step explanation:

Question

If a and b are independent events then it must be true that P(A|B)=P(A). TRUE OR FALSE.

Answer

The correct answer is:True.Explanation:P(A|B) is read as “the probability of A given B.” If A and B are independent, this means that B has no effect on A. This means the probability of A given B would be the same as the probability of A, since B has no effect.This means that P(A|B) = P(A).

Answer:

B. P(A|B) = P(A)

Step-by-step explanation:

I got it right on edge 2023 :)