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

Answer:

n = 19

Step-by-step explanation:

2n > 36 ( divide both sides by 2 )

n > 18

and

5n < 100 ( divide both sides by 5 )

n < 20

so n > 18 and n < 20

thus n = 19

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

Answer:

  {3, 4, 5}

Step-by-step explanation:

You want the integer values that satisfy the inequality 3 ≤ x < 6.

The interval of interest has an open circle at 6, which means x=6 is not included in the solution set. (The "or equal to" condition is missing there.) The integers that are included are shown in the attachment.

  {3, 4, 5} . . . . possible integer values of x

<95141404393>

In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation

For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.

1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.

2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.

Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.

3. Level of Significance: α = 0.05

4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).

Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.

Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.

It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.

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Answer: The answer is A.

Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.

Answer:

Step-by-step explanation:

Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.

Corresponding angles are congruent, so we have ...

  ∠K≅∠P = 100°

  ∠M≅∠R = 85°

Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.

  JK : NP = 12 : (x+4)   ⇒   x+4 = 6   ⇒   x = 2

  KL : PQ = ? : 7   ⇒   KL = 14

  LM : QR = (5y+1) : 8   ⇒  5y+1 = 16   ⇒   y = 3

  MJ : RN = 20 : 10 . . . . . establishes the ratio for the others

The true statements are ...

__

Additional comment

It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).

<95141404393>

The equation for the circle is

(x - 1)² + (y + 2)² = 9

Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.

Remember that for an equation for a circle of radius R and center (a, b), the equation is:

(x - a)² + (y - b)² = R²

Here we have the equation of the circle:

x² + y² - 2x + 4y - 4 = 0

We need to complete squares, we will get:

(x² - 2x) + (y² + 2*2y)  = 4

Now we can add in both sides (-1)² and (2)², then we will get:

(x² - 2x + (-1)²) + (y² + 2*2y +  (2)²)  = 4 +  (2)² + (-1)²

(x - 1)² + (y + 2)² = 4 + 4 + 1

(x - 1)² + (y + 2)² = 9 = 3²

Then we can see that the center is (1, -2), and the radius is 3.

The graph of this circle is on the image at the end.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

see explanation

Step-by-step explanation:

using any of the tangent, sine, cosine ratios in the right triangle.

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then

Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )

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

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]

cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]

With f(1), we're being given an x-value of 1.

Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.

f(1) = 1 - 2 = -1

Answer:

70 cm³

Step-by-step explanation:

let the total volume be x

copper : zinc = 3:2

copper ==>

3/5 *x = 42

make x the subject if formula

x = 42*5/3

:. x = 70 cm³✅✅

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The data set is not approximately periodic. The correct option is A.

The values do not repeat after a certain interval. For example, the value of 36 is not repeated after 6 days, 12 days, or any other interval. Therefore, the data set is not periodic.

A periodic function is a function that repeats its values after a certain interval. For example, the function f(x) = sin(x) is periodic with a period of 2π. This means that the values of f(x) repeat every 2π units of x.

The data set in the question does not repeat its values after a certain interval. Therefore, the data set is not periodic.

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Answer:

Step-by-step explanation:

The exact value of cos(2θ) given the information and using trigonometric identity is 1519.

To find the exact value of cos(2θ), we can use the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

First, let's find the values of sin(θ) and cos(θ) using the given information about θ:

Given:

tan(θ) = 9/40

θ : lies in the fourth quadrant (3π/2 < θ < 2π).

In the fourth quadrant, both sin(θ) and cos(θ) are negative.

Since:

tan(θ) = sin(θ)/cos(θ),

we can write:

9/40 = sin(θ)/cos(θ)

Using the properties of trigonometric functions, we can rewrite this as:

sin(θ) = -9

cos(θ) = -40

Now, let's calculate cos²(θ) and sin²(θ):

cos²(θ) = (-40)² = 1600

sin²(θ) = (-9)² = 81

Finally, we can substitute these values into the double-angle formula for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

        = 1600 - 81

        = 1519

Therefore, the exact value of cos(2θ) is 1519.

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The number of boxes of lawn seed that will be needed will be 4.

From the information, an area is formed by a square, ABCB, and a semi circle. BD is the diameter of the semi circle.The radius of the semi circle is 4m. The area is going to be covered completely with lawn seed.

The area of the square is s²

= 4²

= 16 m²

The area of the semi-circle is (πr²)/2:

= (π*4²)/2

= 8π m²

The total area is 16 + 8π m²

The number of boxes of lawn seed needed is (16 + 8π)/25 = (8 + 4π)/25

≈ 3.44 boxes

≈ 4 boxes

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A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384

B) first divide 384 from 18 which should give you 18, so the answer is 18

Answer:

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

In ΔNOP, we are given:

Use the law of cosines to find side o:

Now, use the law of sines to find ∠N:

So,  ∠N is approximately 10°.

Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.

It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.

When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.

It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.

The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.

If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.

Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.

By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.

The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.

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a. The two-digit number  is 19

b. The number is 22

C. The number is 44

(a) To solve this problem, we are looking for a two-digit number less than 20, odd  and with a sum of digits equal to 10.

the only number that satisfies these conditions is 19.

(b) We need to find a two-digit even number

the only number that meets these criteria is 22.

(c) We are searching for a two-digit number less than 80, even, with identical digits and a multiple of 4.

the only number that satisfies all these conditions is 44

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The distance from X to Z will be 386 km when rounded to 3 significant figures.

The distance from Y to XZ will be 141 km when rounded to 3 significant figures.

To obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.

y/Sine Y = z/Sine Z

y/Sine 105° = 200/Sine 30°

y = 200 × 0.966/0.5

386 km to 3 significant figures

Also for the distance from Y to XZ,

We assume that the distance from Y to XZ is d

Sine 45°/1 = d/200

d = 200 sine 45°

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Answer:

Step-by-step explanation:

A) Area of figure is,

⇒ A = 3π (3 + √73) + 4.5π

B) Area of figure is,

A = 89 feet²

We can simplify as;

A) In figure A,

It is make with one cone and one semicircle.

Hence, Area of cone is,

A = πr (r + √h² + r²)

A = π × 3 (3 + √8² + 3²)

A = 3π (3 + √64 + 9

A = 3π (3 + √73)

And, Area of semicircle is,

⇒ A = 1/2 (π × 3²)

⇒ A = 4.5π

Hence, Total area is,

⇒ A = 3π (3 + √73) + 4.5π

B) Figure B is make with a trapezoid and triangle.

Area of trapezoid is,

A = 1/2 (7 + 13) × 5

A = 20 × 5 / 2

A = 50 feet²

And, Area of triangle is,

A = 1/2 × 6 × 13

A = 39 feet²

Hence, We get;

Area of figure is,

A = 50 + 39

A = 89 feet²

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a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

We have,

a)

The composite figure has a cone and a semicircle.

So,

Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³

Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²

b)

The composite figure has a trapezium and a triangle.

Area of the trapezium

= 1/2 x ( sum of the parallel side) x h

= 1/2 x (7 + 13) x 5

= 1/2 x 20 x 5

= 10 x 5

= 50 ft³

Area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 8

= 3 x 8

= 24 ft²

Thus,

a)

Shape 1 area is 753.8 cm³.

Shape 2 area 14.13 cm².

b)

Shape 1 area is 50 ft³.

Shape 2 area is 24 ft².

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Answer:

a) .12 × $2,400 = $288

b) $2,400 + $288 = $2,688

Answer:

please see answers below

Step-by-step explanation:

In a right-angled triangle, a ² + b ² = c ².

angles in a triangle add up to 180°.

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C

angle C = 90° (little square means 90).

if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.

using the Sine rule:

a/Sin A  =  c/Sin C

multiply both sides by Sin A:

a = (c Sin A) / Sin C

= (12 Sin 30) / Sin 90

= 6.

so a = 6.

Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),

c² = a² + b²

b² = c² - a²

= 12² - 6²

= 144 - 36

= 108

so b² = 108

b = √108

angle B is correct

Answer:

The answer James

Step-by-step explanation:

James=2/5hours

J=2/5×60=2×12=24 minutes

Sandle=4/12×60=4×5=20 minutes

The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.

Given an equation,

3√2 sec θ + 7 = 1

We have to find that whether 3π/4 is a solution for the given equation or not.

Solving the given equation, we get,

3√2 sec θ + 7 = 1

3√2 sec θ = 1 - 7

3√2 sec θ = -6

sec θ = -6 / 3√2

sec θ = -2 / √2

sec θ = -√2

Now, we know that, sec θ = 1/ cos θ

So the equation becomes,

1/ cos θ = -√2

cos θ = -1/√2

Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.

cos 3π/4 =  cos (π - π/4) = -cos (π/4) = -1/√2

So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.

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