An aeroplane flies from a town X on a bearing of N45°E to another town Y, a distance of 200 km. It then changes course and flies to another town Z on a bearing of S60°E. If Z is directly east of X, calculate, correct to 3 significant figures, a the distance from X to Z by the distance from Y to XZ. ​

Answer:

--6a^6b^5+12a^5b^4+60a^2b^4+42ab^3

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

a

the sum of the interior angles of a polygon is calculated as

sum = 180° (n - 2) ← n is the number of sides

here n = 73 , then

sum = 180° × (73 - 2) = 180° × 71 = 12,780°

b

here sum of interior angles = 2700° , then

180° (n - 2) = 2700° ( divide both sides by 180° )

n - 2 = 15 ( add 2 to both sides )

n = 17

number of sides is 17

c

the sum of the exterior angles of a polygon = 360°

given the polygon is regular then each exterior angle is congruent , so

number of sides = 360° ÷ 7.2° = 50

Answer:

a)  12870°

b)  17

c)  50

Step-by-step explanation:

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

The number of sides of a 73-gon is n = 73. Therefore, the sum of its interior angles is:

[tex]\begin{aligned}\textsf{Sum of the interior angles of a 73-agon}&=(73-2) \cdot 180^{\circ}\\&=71 \cdot 180^{\circ}\\&=12870^{\circ}\end{aligned}[/tex]

Therefore, the sum of the interior angles of a 73-gon is 12870°.

[tex]\hrulefill[/tex]

The Polygon Interior Angle-Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is (n - 2) · 180°.

Given the sum of the interior angles of a regular polygon is 2700°, then:

[tex]\begin{aligned} \textsf{Sum of the interior angles}&=2700^{\circ}\\\\\implies (n-2) \cdot 180^{\circ}&=2700^{\circ}\\n-2&=15\\n&=17\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 17.

[tex]\hrulefill[/tex]

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find the number of sides of a regular polygon given its exterior angle is 7.2°, divide 360° by the exterior angle.

[tex]\begin{aligned}\textsf{Number of sides}&=\dfrac{360^{\circ}}{\sf Exterior\;angle}\\\\&=\dfrac{360^{\circ}}{7.2^{\circ}}\\\\&=50\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 50.

For the given function:

Vertex is at (-2, -4) and range is −4 ≤ y < ∞

Hence, Option b is correct.

The given function is

y = |3x + 6| − 4

We can see that it is consist of absolute value function or mod function.

Since we know that,

An absolute value function is an algebraic function in which the variable is contained inside the absolute value bars.

The absolute value function is also known as the modulus function, and its most frequent form is f(x) = |x|,

where x is a real integer. In general, the absolute value function may be represented as f(x) = a |x - h| + k,

where a denotes how far the graph extends vertically, h represents the horizontal shift, and k represents the vertical displacement from the graph of f(x) = |x|.

If the value of 'a' is negative, the graph opens downwards; otherwise, it opens upwards.

The appropriate method of finding range and vertex both is to plot its graph:

Therefore after plotting graph we get,

Vertex is at (-2, -4)

And range is (-4 , ∞) ⇒ −4 ≤ y < ∞

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Answer:

BOYS = 30.

GIRLS = 12.

Step-by-step explanation:

Boys: B

Girls: G

B = (2/5)G

B + G = 42.

(2/5)G + G = 42

2G + 5G = 210

7G = 210

G = 210/7

G = 30.

B = (2/5)G

B = (2/5)(30)

B = 60/5

B = 12.

Answer:

[tex]\Huge \boxed{\bold{\text{12 Boys}}}[/tex]

[tex]\Huge \boxed{\bold{\text{30 Girls}}}[/tex]

Step-by-step explanation:

Let the number of girls be [tex]g[/tex] and the number of boys be [tex]b[/tex].

According to the problem: [tex]b = \frac{2}{5} \times g[/tex]

We also know that the total number of students is 42, so [tex]b + g = 42[/tex].

Now, we have two equations with two variables:

We can solve these equations to find the values of [tex]b[/tex] and [tex]g[/tex].

Step 1: Solve for [tex]\bold{b}[/tex] in terms of [tex]\bold{g}[/tex]

From the first equation, we have[tex]b = \frac{2}{5} \times g[/tex]

Step 2: Substitute the expression for [tex]\bold{b}[/tex] into the second equation

Replace [tex]b[/tex] in the second equation with the expression we found in step 1.

[tex]\frac{2}{5} \times g + g = 42[/tex]

Step 3: Solve for [tex]\bold{g}[/tex]

Now, we have an equation with only one variable, [tex]g[/tex]:

[tex]\frac{2}{5} \times g + g = 42[/tex]

To solve for [tex]g[/tex], first find a common denominator for the fractions:

[tex]\frac{2}{5} \times g + \frac{5}{5} \times g = 42[/tex]

Combine the fractions:

[tex]\frac{7}{5} \times g = 42[/tex]

Now, multiply both sides of the equation by [tex]\frac{5}{7}[/tex] to isolate [tex]g[/tex]:

Step 4: Find the value of [tex]\bold{b}[/tex]

Now that we have the value of [tex]g[/tex], we can find the value of [tex]b[/tex] using the first equation:

So, there are 12 boys and 30 girls in the class.

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

Answer:

a = 4

b=2

x=18

QR =16+1=17

Angle QRS =59

Step-by-step explanation:

4a+1 = 2a + 9

2a = 8

a = 4

6b = 11b-10

-5b=-10

-b= -2

b=2

6x+13 = 7x - 5 (opposite angles are equal)

-x=-18

x=18

QR =16+1=17

Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)

The value of y is 2 * √3.

In the second right triangle, we have a 60-degree angle and a leg opposite to that angle labeled y. The hypotenuse of the first right triangle is equal to the leg of the second right triangle.

Let's denote the hypotenuse of the first right triangle as h. From the first right triangle, we know that the vertical leg is equal to the square root of 2.

Using trigonometric ratios, we can relate the sides of a right triangle as follows:

sin(angle) = opposite/hypotenuse

In the first right triangle, the angle is 45 degrees, and the opposite side is the square root of 2. Therefore, we have:

sin(45 degrees) = √2 / h

By rearranging the equation, we can solve for h:

h = √2 / sin(45 degrees)

Using the value of sin(45 degrees) = 1/√2, we can simplify the equation:

h = √2 / (1/√2) = √2 * √2 = 2

Now, we can find the value of y in the second right triangle. Since the hypotenuse of the first right triangle is equal to the leg of the second right triangle, we have:

y = 2 * √3

Therefore, the value of y is 2 * √3.

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The angle relationship between DCA and BCA is that they are congruent.

In Mathematics and Geometry, an angle bisector is a type of line, ray, or segment, that typically bisects or divides a line segment exactly into two (2) equal and congruent angles.

Generally speaking, the diagonals of a rhombus are angle bisectors. In this context, we can logically deduce that the two (2) angles that would result from the bisection of angle C by a straight line are congruent.

By applying the angle bisector theorem to the given square sign (rhombus ABCD) below, we would have the following congruent angles;

∠DCA ≅ ∠BCA

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Missing information:

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

The job A is the best job based on pay scale

Given data ,

a) Job A:

Hours per week: 40

Hourly rate: $15

On simplifying the equation , we get

Gross pay per week: 40 hours * $15/hour = $600

b) Job B:

Hours per week: 30

Hourly rate: $5

On simplifying the equation , we get

Gross pay per week: 30 hours * $5/hour = $150

In addition to the base pay, Job B also offers tips averaging $350 per week.

Considering the total compensation for each job:

Total compensation for Job A: $600 per week (base pay)

Total compensation for Job B: $150 per week (base pay) + $350 per week (tips) = $500 per week

Based on the total compensation, Job A offers a higher gross pay of $600 per week, while Job B offers a total compensation of $500 per week.

Hence , if the decision is solely based on pay, Job A would be the better choice.

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Note that his is solved using the principle of Combination, and there are 771, 891, 120 different ways to form the groups for the first division soccer league tournament in Mexico.

Let 's compute the number of ways to form the groups using combinations.

First group - 5 teams

C(18, 5) = 18! / (5! * (18-5)!) = 8568

Second group - 5 teams

C(13, 5) = 13! / (5! * (13-5)!) = 1,287

Third group - 4 teams

C(8, 4) = 8! / (4! * (8-4)!) = 70

Fourth group - 4 teams

C(4, 4) = 4! / (4! * (4-4)!) = 1

Now, applying the product rule

Total ways =  8568 x 1,287 x 70 x 1 = 771891120

Therefore, there are 771, 891, 120  different ways to form the groups for the first division soccer league tournament in Mexico.

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Translation

In how many ways is it possible to form the groups of the first division soccer league tournament? Let's remember that 18 teams participate in the first division of soccer in Mexico, and for the league tournament, two groups of five teams and two groups of 4 teams are formed. It is suggested that when solving it, the number of teams that have been considered for the first group be subtracted, then for the second group and so on for each group. Finally apply the product rule to find the different shapes.​

Answer:

608 in²

Step-by-step explanation:

To figure out how much wrapping paper we need to cover the box, we can find its surface area.

The surface area of a rectangular prism (a box) is defined as:

[tex]SA = 2A + (P \cdot d)[/tex]

where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.

From the diagram, we can identify the following values for these variables:

[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]

[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]

[tex]d = 4\text{ in}[/tex]

Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.

[tex]SA = 2A + (P \cdot d)[/tex]

[tex]SA = 2(192) + (56 \cdot 4)[/tex]

[tex]SA = 384 + 224[/tex]

[tex]SA = 608 \text{ in}^2[/tex]

So, we need 608 in² of paper to cover the box.

When selecting 2 letters from the set {A, B, C, D}, considering that the order matters, we can use the concept of permutations to calculate the number of possible arrangements.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of items (in this case, 4) and r is the number of items being selected (in this case, 2).

Using this formula, the number of ways to arrange 2 letters from A, B, C, D is:

P(4, 2) = 4! / (4 - 2)!

= 4! / 2!

= (4 x 3 x 2 x 1) / (2 x 1)

= 24 / 2

= 12

Therefore, there are 12 possible ways to arrange 2 letters selected from A, B, C, D when considering that the order matters.

~~~Harsha~~~

Answer:

Step-by-step explanation:

When selecting 2 letters from the set {A, B, C, D} and considering that the order matters, we can determine the number of possible arrangements using the concept of permutations.

The number of ways to arrange 2 letters from a set of 4 can be calculated using the formula for permutations:

P(n, r) = n! / (n - r)!

where P(n, r) represents the number of permutations of r objects chosen from a set of n objects.

In this case, we have n = 4 (the total number of letters) and r = 2 (the number of letters to be selected).

Using the formula, we can calculate:

P(4, 2) = 4! / (4 - 2)!

       = 4! / 2!

       = (4 × 3 × 2 × 1) / (2 × 1)

       = 24 / 2

       = 12

Therefore, there are 12 different ways to arrange 2 letters chosen from the set {A, B, C, D} when the order matters.

Answer:

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

Given function:

In order to find its inverse, first swap x and y:

Then solve for y:

The inverse function is y= √x.

The solution of the System of equation are,

⇒ x = 1

⇒ y = 5

We have to given that;

System of equation are,

⇒ 3x - 5y = - 22

⇒ 4x + 2y = 14

Now, We can simplify as;

From (ii);

2x + y = 7

y = 7 - 2x

Put above value in (i);

3x - 5 (7 - 2x) = - 22

3x - 35 + 10x = - 22

13x = - 22 + 35

13x = 13

x = 1

From (i);

⇒ 3x - 5y = - 22

⇒ 3 - 5y = - 22

⇒ 3 + 22 = 5y

⇒ 25 = 5y

⇒ y = 5

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Answer:

[tex]A =[/tex] 95.45

Step-by-step explanation:

[tex]A=s(s﹣a)(s﹣b)(s﹣c)[/tex]

[tex]s=a+b+c[/tex]

Solving for A

A=1

4﹣[tex]a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1[/tex]

4-[tex]124+2·(12·16)2+2·(12·21)2﹣164+2·(16·21)2﹣214≈95.45123[/tex]  

≈ 95.45123

Answer:
-328

Step-by-step explanation:

Simply use BODMAS or BIDMAS; this is the order of your operations. It is an acronym that tells you what to do in what order

Brackets: there are no brackets, move on to indices/order

Indices/Order: for the first step, do 5^2, which is 25, and √49, which is 7. The equation is no 12-5*9(7)-25

Division/Multiplication: For this step, multiply 5, 9 and 7 to get 315. The equation is now 12-315-25

Addition/subtraction: For the final step, just solve 12-315-25 in the traditional left to right way, which is -328.

I have grouped addition and subtraction as well as division and multiplication together because they are done at the same time; if a question has either both addition and subtraction or division and multiplication, just solve these parts from left to right. Division is not superior to multiplication and, likewise, addition is not above subtraction.

To determine which company offers the better deal, we compare the total costs for different amounts of fencing. Company 1 has a better deal for less than 608 ft of fencing, while Company 2 is more cost-effective for 608 ft or more.

To determine which company offers the better deal for fencing, we need to compare the total cost for a specific amount of fencing between the two companies.

Let's consider the amount of fencing required as "x" feet.

Company 1 charges $200 for the first 150 ft of fencing and $18 for each additional foot. So, the total cost for x feet of fencing with Company 1 can be calculated as:

Cost1 = $200 + $18 × (x - 150)

Company 2 charges $450 for the first 75 ft of fencing and $15 for each additional foot. Thus, the total cost for x feet of fencing with Company 2 is:

Cost2 = $450 + $15 × (x - 75)

To determine which company offers the better deal, we need to find the range of x values for which Cost1 is less than Cost2. Let's set up the inequality:

Cost1 < Cost2

$200 + $18 × (x - 150) < $450 + $15 × (x - 75)

Now, we can solve this inequality to find the range of x values where Company 1's cost is less than Company 2's cost.

$200 + $18x - $2700 < $450 + $15x - $1125

Combining like terms:

$18x - $2499 < $15x - $675

Subtracting $15x from both sides:

$3x - $2499 < - $675

Adding $2499 to both sides:

$3x < $1824

Dividing both sides by $3 (since x represents feet, we can ignore the currency):

x < $1824 / $3

x < 608

Therefore, for any value of x less than 608 feet, Company 1 has a better deal. However, when x is equal to or greater than 608 feet, Company 2 offers a better deal.

To provide evidence supporting this answer, let's consider an example:

Suppose we need 200 feet of fencing.

Using Company 1:

Cost1 = $200 + $18 × (200 - 150)

Cost1 = $200 + $18 × 50

Cost1 = $200 + $900

Cost1 = $1100

Using Company 2:

Cost2 = $450 + $15 × (200 - 75)

Cost2 = $450 + $15 × 125

Cost2 = $450 + $1875

Cost2 = $2325

In this example, Company 1's cost is $1100, while Company 2's cost is $2325. Hence, for 200 feet of fencing, Company 1 provides the better deal.

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The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.

To calculate the volume of a cylinder, you can use the formula:

Volume = π * (radius²) * height

Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:

radius (r) = 8 cm / 2 = 4 cm

The height (h) of the cylinder is 12 cm.

substitute these values into the formula:

Volume = π * (4 cm)² * 12 cm

Volume = π * 16 cm² * 12 cm

Volume ≈ 602.19 cm³ (rounded to two decimal places)

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The meaning of ran R = { v : there exist u, (u, v) ∈ R} is,

⇒ Defined as v, there exist u such that an order pair (u, v) is belon in relation R

We have to given that;

The meaning of,

⇒ ran R = { v : there exist u, (u, v) ∈ R}

Since, WE know that;

''ran R'' is stand for range of relation R.

Which is defined as,

⇒ ran R = { v : there exist u, (u, v) ∈ R}

That's mean,

Let us defined as v, there exist u such that an order pair (u, v) is belon in relation R.

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Answer:

[tex]-2x^{-2} \ \text{or} \ -\frac{2}{x^2}[/tex]

Step-by-step explanation:

Find [tex]\frac{d}{dx}[\frac{2}{x} ][/tex].

(1) - Pull out the constant

[tex]\frac{d}{dx}[\frac{2}{x} ]\\\\\Longrightarrow 2\frac{d}{dx}[\frac{1}{x} ][/tex]

(2) - Flip the fraction

[tex]2\frac{d}{dx}[\frac{1}{x}]\\\\\Longrightarrow 2\frac{d}{dx}[x^{-1}][/tex]

(3) - Apply the power rule]

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Power Rule:}}\\\\\frac{d}{dx}[x^n]=nx^{n-1} \end{array}\right}\\\\\\2\frac{d}{dx}[x^{-1}]\\\\\Longrightarrow 2[(-1)x^{-1-1}]\\\\\Longrightarrow 2[-x^{-2}]\\\\\therefore \boxed{\boxed{\frac{d}{dx}[\frac{2}{x} ] =-2x^{-2} \ \text{or} \ -\frac{2}{x^2}}}[/tex]

Thus, the problem is solved.

The function is a good model for the data.

The retail sales in the U.S. in 2016 is estimated to be 282.24 billion dollars.

The year that corresponds to retail sales of $241 billion is 2020.

The function F(t)= 9.44 t +84.182 is a linear model for the data. This means that the graph of the function is a straight line.

The scatter plot shows that the data points are close to a straight line. This means that the function is a good model for the data.

To estimate the retail sales in the U.S. in 2016, we need to find the value of F(11). F(11) = 9.44 * 11 + 84.182

= 282.24.

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Answer:

The answer is 69.63cm²

Step-by-step explanation:

d=18

r=d/2=18/2=9cm

Area of shaded portion =Area of square -Area of circle

A=18²-pi×9²

A=69.53cm²

Answer:

69.53 centimeters squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:

Inserting 18 as our side length:

Therefore, the area of the square without the circular gap is 324 [tex]cm^{2}[/tex].

To solve for the area of a circle, we can use the formula:

But wait, we are given the diameter, not the radius!

No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.

Inserting 9 into the formula for the radius:

Now we can subtract this from the squares area.

The closest to match this approximation is [tex]69.53cm^{2}[/tex].

Answer:

670

We can use the pythagorus theorum which says

The square of hypotenuse is equal to the square of perpendicular added to sq of base

Step-by-step explanation:

Use h2=p2+b2

H=6.708

Rounding to the hundredth place the answer is 670.8

Using Pythagoras Theorem (since the triangle is a right angled triangle)

[tex]( {hyp}^{2}) = ( {base}^{2} ) + ( {per}^{2} )[/tex]

[tex]( {hyp}^{2} ) = ( {3}^{2} ) + ( {6}^{2}) [/tex]

[tex]( {hyp}^{2} ) = 9 + 36[/tex]

[tex] {hyp}^{2} = 45[/tex]

Taking under root on both sides

[tex]hyp = 6.7[/tex]

Hence the missing side is 671

The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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The average speed of Sophie in miles per hour is 5.04 miles per hour.

The speed in feet per second is 7.39 feet per second.

Given that,

Sophie recently ran a marathon.

It took her 5.2 hours to run the 26.2 miles required to complete a marathon.

Total distance ran = 26.2 miles

Total time taken = 5.2 hours

Speed = Total distance / Total time

           = 26.2 / 5.2

           = 5.04 miles per hour

Speed in feet per second = (5.04 × 5280 feet) / 3600 seconds

                                           = 7.39 feet per second

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Answer:

  B.  2

Step-by-step explanation:

You want the predicted number of missed shots after 8 weeks if the trend line equation is ...

  y = -1/2x +6

Using x=8 in the given equation, we find the prediction to be ...

  y = -1/2(8) +6 = -4 +6 = 2

The number of missed shots is predicted to be 2.

__

Additional comment

We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.

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Answer:

1) 5/6
2) 19/30
3) They are mutually exclusive.

Step-by-step explanation:

Let's break the diagram down.
We have four types of smoothies:

Contains apple but not blueberry - 12
Contains blueberry but not apple - 7
Contains both blueberry and apple - 3
Doesn't contain either - 8

From here, we find that there are 30 smoothies in total.

In addition, we know that the number of smoothies containing an apple is 15, and the number of smoothies containing blueberry is 10.

Therefore,

[tex]P(\text{contains apple}) = \frac{\text{contains apple}}{\text{total}} = \frac{15}{30} = \frac12\\\\P(\text{contains blueberry}) = \frac{\text{contains blueberry}}{\text{total}} = \frac{10}{30} = \frac13\\\\\text{a) } P(\text{contains apple}) + P(\text{contains blueberry}) = \frac12 + \frac13 = \frac36 + \frac26 = \frac56[/tex]

Now, the probability of getting apple OR strawberry is given by adding the probabilities of getting one of the flavors but not the other.

[tex]P(\text{apple, no blueberry}) = \frac{12}{30}\\\\P(\text{blueberry, no apple}) = \frac{7}{30}\\\\P(\text{apple or blueberry}) = \frac{12}{30} + \frac7{30} = \frac{19}{30}[/tex]

We can check if the events are mutually exclusive using the formula:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In our case, A means contains apple, and B means contains blueberry.
[tex]P(A \cup B)[/tex] resembles the case for exclusively apple or exclusively blueberry (AKA our answer for b).

[tex]P(A \cap B)[/tex] resembles the case for both apple and blueberry (AKA the intersection), which is equal to 3/30 = 1/10.

If the two sides are equal, the cases are not mutually exclusive.

[tex]\frac{19}{30} = \frac{15}{30} + \frac{10}{30} - \frac{3}{30}\\\\\frac{19}{30} \ne \frac{22}{30}[/tex]

Therefore, the events are mutually exclusive.

Answer:

The inequality |x – 4| > –3 represents an absolute value inequality.

The absolute value of any real number is always non-negative, meaning it is greater than or equal to zero. Therefore, the left side of the inequality, |x – 4|, will always be greater than or equal to zero.

Since the right side of the inequality, -3, is also greater than or equal to zero, this means that the inequality |x – 4| > –3 holds true for all real numbers x. In other words, there are no restrictions on the value of x.

The solution set for this inequality is the set of all real numbers, often represented as (-∞, +∞).

Answer:

(−∞,∞)

Step-by-step explanation:

|x – 4| > – 3

Since |x – 4| is always positive and - 3 is negative, |x – 4| is always greater than - 3, so the inequality is always true for any value of x.

All real numbers

The result can be shown in multiple forms.

All real numbers

So, the answer is (−∞,∞)

Answer:

To find the number of federally insured banks in 1985, we need to substitute t = 1985 into the equation B(t) = -328.2t + 13716:

B(1985) = -328.2 * 1985 + 13716

B(1985) = -648537 + 13716

B(1985) = 7122

So, there were approximately 7122 federally insured banks in 1985.

The slope of the graph of B represents the rate of change. From the equation B(t) = -328.2t + 13716, we can see that the slope is -328.2. Therefore, the interpretation of the slope as a rate of change is: "The number of banks decreased by 328.2 banks per year."

The y-intercept of the graph of B represents the value of B when t = 0, which corresponds to the year 1980. From the equation B(t) = -328.2t + 13716, the y-intercept is 13716. Therefore, the interpretation of the y-intercept is: "The y-intercept is the number of banks in 1980."