Based on historical data, an insurance company estimates that a particular customer has a 3.3% likelihood of having an accident in the next year, with the average insurance payout being $1500.

If the company charges this customer an annual premium of $120, what is the company's expected value of this insurance policy?

$

Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

The circle E with diameter CD and radius EA having the length of AC is approximately 4.2 units.

What is Pythagoras' Theorem?

In a right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.

Since EA is a radius of circle E, and AB is tangent to E at A, we know that AB is perpendicular to EA. Thus, triangle EAB is a right triangle.

Let x be the length of AC. Then, by the Pythagorean Theorem in triangle EAC, we have:

[tex]AC^{2} = EA^{2} +EC^{2}[/tex]

[tex]AC^{2} = 3^{2} + 3^{2}[/tex]

[tex]AC^{2} = 18[/tex]

AC ≈ 4.2 (rounded to the nearest tenth)

Therefore, the length of AC is approximately 4.2 units.

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Answer:

∠w = 50°

∠y = 130°

Step-by-step explanation:

Angles ∠w and ∠y are supplementary angles, which means their sum is 180.

4x + 6 + 12x - 2 = 180

16x + 4 = 180

16x = 176

x = 11

To find the angle measures replace x with 11

∠w = 4x + 6

∠w = 4*11 + 6

∠w = 50°

Now, ∠y

∠y = 12x - 2

∠y = 12*11 - 2

∠y = 130°

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]

Therefore, knowing the slant height is important in calculating the lateral area of the pyramid, which is one component of the total surface area.

by the question.

Option 2 is the correct response. Knowing the slant height is helpful because it represents the height of the rectangle that makes up each lateral face of the pyramid. The lateral faces are made up of triangles and rectangles, and the slant height is used to find the height of these rectangles.

Knowing the slant height helps because it represents the height of the rectangle that makes up each lateral face. So, the slant height helps you to find the area of each lateral face. The formula for the lateral area of a pyramid involves the slant height, the perimeter of the base, and the apothem (the distance from the center of the base to the midpoint of a side). Once you know the lateral area, you can add it to the area of the base to find the total surface area of the pyramid.

The slant height of a pyramid is the height of each triangular lateral face, which is an essential component in calculating the lateral surface area of a pyramid. Knowing the slant height is used in the formula for finding the lateral area of a pyramid, which is the sum of the areas of all the triangular lateral faces. Additionally, the base area of the pyramid is also needed to find the total surface area of the pyramid. So, knowing the slant h

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Answer:

20.8

Step-by-step explanation:

Let h be the height of the ladder. We know that the distance BC is 8 ft, and the angle of elevation BAC is 69 degrees. Therefore, we have:

tan(69) = h/8

Multiplying both sides by 8, we get:

8*tan(69) = h

Using a calculator, we get:

h ≈ 20.8 ft

Therefore, the height of the top of the ladder from the ground is approximately 20.8 feet.

The wire can be divided into five equal parts, where one portion is one-fifth of the total length and the other four parts are four-fifths of the total length. the measure of the longer part of the wire after cutting is 2 meters.

If the wire was cut in a ratio of 1:4, then the total length of the wire can be divided into 5 parts, where one part is 1/5 of the total length, and four parts are 4/5 of the total length. Let's call the length of one part "x".

So, the total length of the wire is:

 [tex]5x = 2.5[/tex] meters

To find the length of the longer part of the wire, we need to find how many parts are in the longer portion. Since the wire was cut in a 1:4 ratio, the longer portion has four parts.

Therefore, the length of the longer part of the wire is:

[tex]4x = 4/5 \times 2.5 meters = 2 meters[/tex]

Therefore, the measure of the longer part of the wire after cutting is 2 meters.

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Answer:

To find the coordinates of A' after the translation, we need to apply the motion rule to the coordinates of A:

(x, y) → (x + 2y - 5, y - 6)

Substituting the coordinates of point A, which is (4, -4), into this motion rule, we get:

A' = (4 + 2(-4) - 5, -4 - 6) = (-3, -10)

Therefore, the coordinates of A' after the translation are (-3, -10).

Answer:

3x + 4 < 13

2y - 5 > 7

6n - 1 ≤ 23

8m + 2 ≥ 18

4a - 7 < 5a + 2

9b + 3 > 6b + 10

Step-by-step explanation:

I dunno if this is what you're asking for

Answer:

ok.....

x + 2 < 5

|x - 4| > 4

x + 7 [tex]\geq[/tex] 8

-x < -5

x - 5 < 9

5x + 18 > 2

|3x - 1| < 8

The amount of time needed for this capital to triple would be 50 months, the letter "d" being correct. We arrive at this result using simple interest.

Simple interest is a type of financial calculation that is used to calculate the amount of interest on borrowed or invested capital for a given period of time.

In order to find the amount of time required for the principal to be equal to three times the redemption, we have to note that the amount will be equal to three times the principal, using this information in the formula. Calculating, we have:

M = C * (1 + i * t)

3C = C * (1 + 0.04t)

3 = 1 + 0.04t

0.04t = 3 - 1

0.04t = 2

t = 2/0.04

t = 50

The exponential equation represents a growth, and the rate of increase is 9%.

The general exponential equation is written as:

y = A*(1 + r)^x

Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).

Here we have:

y = 38*(1.09)^x

We can rewrite this as:

y = 38*(1 + 0.09)^x

So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:

100%*0.09 = 9%

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Therefore, cos(K) = √(17)/9, sin(L) = 8/9, and cos(K) and sin(L) together are (√(17)/9, 8/9) are trigonometric ratios as fractions in simplest terms.

It is possible to calculate trigonometric ratios for various orientations. However, we memories the trigonometric ratios of a few particular angles, such as 0°, 30°, 45°, 60°, and 90°, to make computations easier. The numbers of the ratios at these angles can be found in the trigonometric ratios table.

The Pythagorean formula can be applied to the illustration to determine the length of the third side:

c²= a²+ b²

c²= 8² + √(17)²

c²= 64 + 17

c² = 81

c = 9

We can now calculate the trigonometry ratios of angles K and L:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

Using the same hypotenuse number of 9, we can calculate both cos(K) and sin(L) as follows:

cos(K) = adjacent/hypotenuse = √(17)/9

sin(L) = opposite/hypotenuse = 8/9

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Answer:

260

Step-by-step explanation:

First you find the area of the triangle

1/2×base×height

1/2×20×10

=100

Then you find the area of the rectangle

A=l×b

=20×8

=160

Then you add the area of the triangle with the area of the rectangle

160+100=260

Answer: 3

Step-by-step explanation:

Answer:  3

Step-by-step explanation:

16/4=unit rate =4

1 in 4 hour

3 for 12 hours

Answer: it depends; if exam day, no

Step-by-step explanation:

Answer:

linear

Step-by-step explanation:

this is a linear function!

linear functions follow y = mx+b, where m is the slope and b is the y-intercept

let's write our y = mx+b equation

for each value that x increases, y increases by DOUBLE that amount. slope is y/x, so since y increases by 2 and x increases by 1, the slope is 2/1 which is 2.

the y-intercept is where the line passes the x axis, or when x is 0. in this table, it gives you your y-intercept, which is -6

your equation is y=2x+(-6); which simplified to y=2x-6

if you plug in the y and x values, you'll get the same thing. i hope this helped!

Problems:

Solve for x: 2x - 5 > 9x + 2

Solve for x: 3x + 2 < 7x - 5

Solve for x: 4x + 3 < 2x - 1

Solve for x: -2x - 4 > -8x + 3

Solve for x: 5x + 1 < 2x + 7

Answers:

x < -0.7

x > 1.75

x < -1

x < 0.875

x < 1.2

Answer:  

Example 1

Solve 3x − 5 ≤ 3 − x.

Solution

We start by adding both sides of the inequality by 5

3x – 5 + 5 ≤ 3 + 5 − x

3x ≤ 8 – x

Then add both sides by x.

3x + x ≤ 8 – x + x

4x ≤ 8

Finally, divide both sides of the inequality by 4 to get;

x ≤ 2

Example 2

Calculate the range of values of y, which satisfies the inequality: y − 4 < 2y + 5.

Solution

Add both sides of the inequality by 4.

y – 4 + 4 < 2y + 5 + 4

y < 2y + 9

Subtract both sides by 2y.

y – 2y < 2y – 2y + 9

Y < 9 Multiply both sides of the inequality by −1 and change the inequality symbol’s direction. y > − 9

Solving linear inequalities with subtraction

Let’s see a few examples below to understand this concept.

Example 3

Solve x + 8 > 5.

Solution

Isolate the variable x by subtracting 8 from both sides of the inequality.

x + 8 – 8 > 5 – 8 => x > −3

Therefore, x > −3.

Example 4

Solve 5x + 10 > 3x + 24.

Solution

Subtract 10 from both sides of the inequality.

5x + 10 – 10 > 3x + 24 – 10

5x > 3x + 14.

Now we subtract both sides of the inequality by 3x.

5x – 3x > 3x – 3x + 14

2x > 14

x > 7

Solving linear inequalities with multiplication

Let’s see a few examples below to understand this concept.

Example 5

Solve x/4 > 5

Solution:

Multiply both sides of an inequality by the denominator of the fraction

4(x/4) > 5 x 4

x > 20

Step-by-step explanation:

Hope this helps :3

The radius of the circle with given circumference is 13.

What is circumference?

In mathematics, the circumference of any shape determines the path or boundary that surrounds it. In other words, the perimeter, also referred to as the circumference, helps determine how lengthy the outline of a shape is.

We are given that the circumference of a circle is 81.64 miles.

We know that circumference of a circle is given by 2πr.

So, using this we get

⇒ C  = 2πr

⇒ 81.64  = 2 * 3.14 * r

⇒ 81.64  = 6.28 * r

⇒ r  = 13

Hence, the radius of the circle with given circumference is 13.

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Answer:

Step-by-step explanation:

modal weight:  the weight that appear most often

4.5 kg  appears 3 times

6-sided polygon:  even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720

therefore, angle f = 720 - 576 = 144      (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)

modal score:  read this right off the graph.  The score with the highest frequency is the modal score:  14   (meaning, 9 contestants got this score)

Answer:

22

Step-by-step explanation:

first you would add all books from the book store to get 66

Then you would divide that by 3 to get

66÷3=22

Answer:

x=66 and y=63

Step-by-step explanation:

The middle triangle is isosceles

57+57+x=180

114+x=180

x=66

Left triangle is equilateral (all angles =60)

60+57+?=180

117+?=180

?=63

Right triangle is isosceles

?=y

y=63

Answer:

$25

Step-by-step explanation:

You round 44.95 to 45 and 68.49 to 70. 70 - 45 = 25.

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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Answer: top two goes together, middle left goes to bottom right, bottom left goes to middle right

Step-by-step explanation:

Substitute x for an easy number like 2 and solve.

x - 2/3 - 1/2x = 1/2x - 2/3

x - 1/2 - 3/4x = 1/4x- 1/2

1/3x - 3/4 - 2/3x = -1/3x - 3/4

Answer: yes, no, yes, no

Step-by-step explanation:

The inequality can be solved to get 2 > x, and the graph on the number line can be seen in the image at the end.

Here we have an inequality and we want to sole it, to do so, we just need to isolate the variable in the inequality.

Here we have:

10 > 5x

To isolate the variable we can divide both sides of the inequality by 5, then we will get:

10/5 > 5x/5

2 > x

So x is the set of all values smaller than 2.

That is the inequality solved, to graph this, drawn an open circle at x = 2 and a line that goes to the left. The graph is the one you can see in the image below.

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The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.

It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.

Here we have

The cumulative area is 0.3897

Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:

1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.

2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.

3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.

Therefore,

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

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