Write the equation of the line of best fit using the slope-intercept formula y=mx+b. Show all your work, including the points used to determine the slope and how the equation was determined.

Answer:

108°

Step-by-step explanation:

We know for a theorem that A = B, so:

4x + 28 = 2x + 68

Isolating the x:

2x = 40

x = 20

Now let's plug in the equation for A:

4(20) + 28 = 108°

The expected value for the person buying the insurance is -25.

The expected value is the average gain or loss of an event if the event is repeated a number of times.

Expected value = ∑xP(x)

It is given that,

The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179

The death benefit = $100,000 - $204 = $99,796

The loss from living = -204

Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25

Therefore, the expected value for the person buying the insurance is -25.

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The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).

It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.

It follows from observation that one of the zeros of the polynomial expression is at; x = -2.

Consequently, one of the factors of the polynomial in discuss is; (x+2).

x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)

= (x+2)(x+2i)(x-2i)

Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).

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Answer:

2.603 degrees

Step-by-step explanation:

This word problem is talking about a triangle. 500 meters high would be the height and 11 Kilometers would be the base. We should convert kilometers to meters in order to make this easier. 11 kilometers = 11,000 meters.

Height = 500

Base = 11,000

The hypotenuse ends up being 11,011.35777

in order to find the angle of depression (assuming it is a constant rate) we would measure the angle where the hypotenuse meets the base. (11,000 & 11,011.35777) the angle comes out at 2.603 degrees. Hope this helped!

The function which compares the growth of both functions is; The function y = 3x is growing slower than y = 3^x.

The graphs in the task content are given as y=3x which is a linear graph, and y=3^x which is the exponential graph.

Hence, it follows that although both graphs are growing, the graph of function y = 3x is growing slower than y = 3^x.

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Answer:

The answer to your question is m = 6

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

36^12 - m = 6^2m

6^2(12 - m) = 6^2m

24 - 2m = 2m

24 = 4m

m = 6

Answer:

Step-by-step explanation:

-10x-16

Answer:

distribute the -2 so your answer is -10x-16

Step-by-step explanation:

The area of the triangle is 1000 unit square

The area of a triangle is half the base multiplied by the height

The formula is given as;

Area = 1/2 × b × h

From the information given, the base is given as 50 and the height is 40

Area = 1/ 2 × 50 × 40

Area = 1/ 2 × 2000

Area = 1000 unit square

Thus, the area of the triangle is 1000 unit square

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The answer choice which sin(x + y) - sin(x - y) simplifies to is; 2(cos x)(sin y).

It follows from the task content that the expression given in the task content can be simplified by trigonometric identities as follows;

sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy -cosxsiny)

= 2cosxsiny.

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The bearing angle exists 53.49°.

A bearing of 36° corresponds to the corresponding angle of

θ = 90 -36 = 54°

The (x, y) values for the position of the ship after achieving its first heading exist:

[tex]x_1[/tex] = 12.1 Cos 54° = 7.11 m

[tex]y_1[/tex] = 12.1 Sin 54° = 9.78 m

Our second displacement exists a simple 4.6 mi due east, that exists, the positive x-direction. The components exist therefore

[tex]x_2[/tex] = 6.1 mi

[tex]y_2[/tex] = 0 mi

To find the total displacement from the port, we'll add these two vectors' components and use the distance formula:

Δx [tex]= x_1+x_2[/tex]

= 7.11 mi + 6.1 mi = 13.21 mi

Δy [tex]=y_1+y_2[/tex]

= 9.78 mi + 0 mi = 9.78 mi

[tex]$r=\sqrt{(x_{total})^2+(y_{total})^2}[/tex]

[tex]=\sqrt{(13.21mi)^2+(9.78mi)^2}[/tex]

= 16.43 mi

The direction of the displacement vector exists given by

tan θ = Δy/Δx

θ = arc tan (Δy/Δx)

= arc tan (9.78/13.21)

= 36.51°

The question requested for the bearing angle, which exists just this angle subtracted from 90°:

90° - 36.51° = 53.49°.

Therefore, the bearing angle exists 53.49°.

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Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

You can the distance between P(10,-7) and Q(7,-10) by using 'PQ=

[tex] \sqrt{(10 - 7) ^{2} } + \sqrt{ ( - 7 + 10) ^{2} } [/tex]

Also, for example the distance between A(a,b) and B(c,d)

is

[tex] \sqrt{(a - c)^{2} } + \sqrt{(b - d) ^{2} } [/tex]

Answer:

[tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

Step-by-step explanation:

To find the distance between two points, we can use the Distance Formula.

Distance Formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given:

P (10, -7) ⇒ x₁ = 10, y₁ = -7

Q (7, -10) ⇒ x₂ = 7, y₂ = -10

Substitute the given values into the formula and simplify.

[tex]\\\implies d=\sqrt{\bold{(7-10)}^2+\bold{(-10-(-7))}^2}\\\\\implies d=\sqrt{\bold{(-3)}^2+\bold{(-10+7)}^2}\\\\\implies d=\sqrt{9+\bold{(-3)}^2}\\\\\implies d=\sqrt{\bold{9+9}}\\\\\implies d=\sqrt{\bold{18}}\\\\\implies d=\sqrt{\bold{9}\times2}\\\\\implies d=3\sqrt{2}[/tex]

The distance between points P and Q is [tex]\sqrt{18}[/tex] or [tex]3\sqrt{2}[/tex] units.

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Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart

Step-by-step explanation:  On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches

x = child tickets

y = adult tickets

x + y = 141

5.60x + 9.30y = 974.60

y = 141 - x

5.60x + 9.30 ( 141 - x ) = 974.60

5.60x + 1311.3 - 9.30x = 974.60

-3.70x + 1311.3 = 974.60

-3.70x = 974.60 - 1311.3

-3.70x = -336.7

x = 91

91 child tickets were sold that day

The function that will have a horizontal asymptotes are function B, C and D

A function is said to have a horizontal asymptotes of the degree of the numerator is less or equal to that of the denominator.

From the rational expression given, the function A and E wil have no horizontal asymptotes since the power of the numerator is greater abd equal to the denominator,

The function that will have a horizontal asymptotes are function B, C and D

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Answer:  30 miles

Work Shown:

2 in : 6 mi

5*2 in : 5*6 mi

10 in : 30 mi

Answer:

4.5 tablets.

Step-by-step explanation:

We just divide 9 by 2.

13. The tablets needed is 4 and a half.

14. There are 10 half-gram doses available from the 5 gram vials of medication.

15. Pat's heart beats approximately 58.5 times in 3/4 of a minute.

Given are words problems based on the mixed numbers:

13. To determine the number of tablets needed, we divide the total dosage required by the dosage per tablet.

In this case, the nurse needs to administer 9 milligrams of medication, and each tablet contains 2 milligrams.

So, the number of tablets needed is:

9 milligrams / 2 milligrams per tablet = 4.5 tablets

Hence, the tablets needed is 4 and a half.

14. If the pharmacy has 5 gram vials of medication, we can calculate the number of 1/2 gram doses available by dividing the total amount of medication by the dose size.

The total amount of medication in grams is 5 grams.

To find the number of 1/2 gram doses available, we divide the total amount of medication (5 grams) by the dose size (1/2 gram):

5 grams / (1/2 gram) = 5 grams x (2/1 gram)

= 5 x 2 = 10 doses.

Therefore, there are 10 half-gram doses available from the 5 gram vials of medication.

15. To calculate how many times Pat's heart beats in 3/4 of a minute, you can use a simple proportion:

1 minute = 78 beats

3/4 minute = ? beats

Let's solve for the number of beats in 3/4 of a minute:

Number of beats in 3/4 minute = (3/4) x 78

= 0.75 x 78

= 58.5

So, Pat's heart beats approximately 58.5 times in 3/4 of a minute. Since you can't have half a heartbeat, the closest whole number is 58 beats.

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well, we know the suits are all reduced by 20%, so the man saved 20% of 231.20

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of 231.20}}{\left( \cfrac{20}{100} \right)231.20}\implies 46.24[/tex]

It would cost $72,000 for 7 units of that product.

The term “discount” refers to the pricing system in which the price of a commodity (goods or services) is lower than its marked price listed price. It is simply to say, 'discount' is a percentage of the listed price. A discount is a kind of price deduction in products that is noticed in consumer transactions, where the buyers have proposed a percentage of rebates on various products in order to boost sales. This rebate offered by the seller to buyer is known as a discount.

Original cost of product = $15,000.

For the second product there is a discount of 15%, thus selling price for the second product = $15,000 x 0.85 = $12750

For the fourth product and on there is a discount of 30%, thus selling price for the fourth product and on = $15,000 x 0.70 = $10500.

Thus total price of 7 units =  $15,000 + $12750x2 + $10500x3

=   $15,000 +   $25,500 + $31500

= $72,000

Thus it would cost $72,000 for 7 units of that product.

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Answer:

on a coordinates plane :

The point of coordinates (h , k) is the center of the circle.

Step-by-step explanation:

by definition the expression:

(x-h)² + (y-k)² = r²

is the equation of the circle (in standard form)

Where r is the radius and (h , k) is the center of the circle.

It is the general equation of a circle

Correct answer:

The general equation of a circle is [tex](x - h)^2 + (y - k)^2 = r^2,[/tex]where (h, k) represents the location of the circle's center, and r represents the length of its radius. if we take some entities as [tex]h=4,k=-3[/tex] first has the equation of [tex](x - 4)^2 + (y + 3)^2 = 29[/tex]. This means that its center must be located at (4, –3), and its radius is √29.

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In the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Thus, identifying the values of a, b, and c, is the first step in using the quadratic formula to find a solution(s)/root(s) to a quadratic equation.

In the question, we are asked to find the values of a, b, and c, in the given quadratic equation - 3x² - 5x + 9 = 0.

To find the values of a, b, and c, we compare the given equation, to the standard form of a quadratic equation, ax² + bx + c = 0.

On comparing, we get a is the coefficient of x², that is, a = -3.

On comparing, we get b is the coefficient of x, that is, b = -5.

On comparing, we get c is the constant term, that is, c = 9.

Thus, in the given quadratic equation, - 3x² - 5x + 9 = 0, we have the values, a = -3, b = -5, and c = 9. Hence, option C is the right choice.

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The provided question is incomplete.

The complete question is:

"Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

What are the values a, b, and c in the following quadratic equation?

- 3x² - 5x + 9 = 0

Answer:

6. Quadrant four

7. Quadrant three

8. Quadrant one

Step-by-step explanation:

These questions give you points to graph and then asks which quadrants they are graphed in. Here is a visual.

Answer: A = JIH

B = GJH

C = GH

D = 300

E = 60

Step-by-step explanation:

A) <JIH is a inscribed angle

B) GJH is a major arc

C) GH is a minor arc

D) m GH = m<GFh = 60

A single card is drawn from each of two decks of 52 cards. The probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.

Probability means possibility.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

There are 52 cards in a standard deck.

So, the total number of possible outcomes=52

We have to pick a single card from each of decks of 52 cards.

In a deck of 52 cards there are 13 heart cards and 13 diamond cards.

Therefore the probability of getting a heart from the first deck=13/52

And the probability of getting a diamond from the second deck=13/52

Hence the probability of getting a heart from the first deck and then a diamond on the second deck=(13/52)×(13/52)=6.25%

Thus, the probability of getting a heart from the first deck and then a diamond on the second deck is 6.25%.

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Answer:

6.25%

Step-by-step explanation:

I got it right on the test.

The statement that most clearly shows an example of ethos is C. As the CEO of a major technology company, I am constantly making tough hiring decisions.

An ethos statement establishes the credibility, knowledge, and good moral character of the speaker or writer.

The use of ethos is meant to sound fair or to demonstrate credibility, expertise, education, or pedigree.

Thus, an example of ethos is when this CEO claims they constantly make tough hiring decisions.

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The common difference based on the sequence given is 15.

It should be noted that the sequence given Isa arithmetic sequence.

The common difference will be the second term minus the first term. This will be:

= 101 - 86

= 15

In conclusion, the difference is 15.

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