Solve for the unknown variable. Give all of the exact general solutions.

cosθ = sinθ

1 + sinθ = 2cos^2 (θ)

sin3θ = -1

The proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

What is proportion?

A proportion is a statement that two ratios or fractions are equal. It is commonly written in the form of two fractions separated by an equal sign, such as a/b = c/d.

To write a proportion comparing the rise to the run for each of the similar slope triangles, we can use the fact that the ratio of corresponding sides of similar triangles is the same.

Let's say we have two similar triangles with corresponding sides of length a, b, and c, and a', b', and c', respectively. Then we can write the following proportion:

a / a' = b / b' = c / c'

Now, let's apply this to finding the proportion of the rise to the run for each of the similar slope triangles.

In a right triangle, the slope is defined as the ratio of the rise (vertical change) to the run (horizontal change). Let's say we have two similar right triangles with slopes m and m', respectively, and the rise and run of the first triangle are h and b, respectively. The rise and run of the second triangle are then mh and mb', respectively.

We can write the proportion of the rise to the run for each triangle as:

h / b = mh' / mb'

Simplifying this proportion, we can cancel out the common factor of b:

h / b = mh' / mb'

h / 1 = mh' / m'

h = bmh'

Therefore, the proportion of the rise to the run for each of the similar slope triangles is given by:

h / b = mh' / mb' = mh / b

The numeric value of this proportion will depend on the specific values of the rise and run for each triangle and the slope of the triangles.

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For instance: Let f(x) = 2x + 1 and g(x) = x^2. Find (f ∘ g)(3). First, we need to find g(3) which is 3^2 = 9. Then we plug this value into f: f(g(3)) = f(9) = 2(9) + 1 = 19. Therefore, (f ∘ g)(3) = 19.

Function composition is a mathematical concept that is used to combine two or more functions into a single function. This concept is widely used in real life situations, such as in computer programming, engineering, and physics.

For example, in computer programming, function composition is used to break down complex programs into smaller, more manageable parts. By using function composition, programmers can create complex programs that are easier to read and maintain. Therefore, function composition is a powerful tool that is used in various fields to simplify complex problems and create more accurate models of the world around us.

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The surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.

To calculate the surface area and volume of the frustum of a pyramid, we first need to determine the slant height of the frustum, which we can do using the Pythagorean theorem.

Calculate the slant height of the frustum:

Let s1 and s2 be the side lengths of the top and bottom squares, and h be the height of the frustum.

The slant height (l) can be calculated using the Pythagorean theorem:

l = sqrt(h^2 + ((s2 - s1)/2)^2)

l = sqrt(5^2 + ((6 - 3)/2)^2)

l = sqrt(25 + 1.5^2)

l = sqrt(25 + 2.25)

l = sqrt(27.25)

l ≈ 5.22 cm

Calculate the surface area of the frustum:

Surface area = top square area + bottom square area + lateral surface area

Top square area = s1^2 = 3^2 = 9 cm^2

Bottom square area = s2^2 = 6^2 = 36 cm^2

Lateral surface area = 0.5 * (s1 + s2) * l = 0.5 * (3 + 6) * 5.22 ≈ 23.49 cm^2

Total surface area ≈ 9 + 36 + 23.49 = 68.49 cm^2

Calculate the volume of the frustum:

We can use the following formula to calculate the volume of a frustum:

Volume = (h/3) * (A1 + A2 + sqrt(A1 * A2))

Where A1 and A2 are the areas of the top and bottom squares, respectively:

A1 = 3^2 = 9 cm^2

A2 = 6^2 = 36 cm^2

Volume = (5/3) * (9 + 36 + sqrt(9 * 36))

Volume = (5/3) * (45 + sqrt(324))

Volume = (5/3) * (45 + 18)

Volume = (5/3) * 63

Volume ≈ 105 cm^3

So, the surface area of the frustum is approximately 68.49 cm^2 and the volume is approximately 105 cm^3.

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The areas of the two cross-sections would be proportional to k².

If a new cross-section was created in each solid, both at the same height using a scale factor k, the areas of the two cross sections would be proportional to k².

The reason for this is that when a scale factor is applied to a two-dimensional figure, the area of the resulting figure increases by a factor of k². This is because the linear dimensions of the figure (length and width) are multiplied by k, and since the area is calculated by multiplying length and width, the area of the figure is multiplied by k².

Therefore, if the two cross sections are created at the same height and are scaled by the same factor k, their areas will be proportional to k². For example, if k=2, the area of each cross-section will be four times the original area; if k=3, the area of each cross-section will be nine times the original area, and so on.

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The price of Groupon for revenue of $300 is $4 if the expected revenue is at least $390 per day.

Probability is assigned as

x =30, 60, 120, 180

P(x) = 0.10,0.40, 0.40, 0.10

Expected sales volume:

Number of tubes x =30, 60, 120, 180

Probability P(x)= 0.10,0.40, 0.40, 0.10

Expected values are 3, 24,48,18

Total = 93 tubes

Groupon price = $390/$93 = $4.19

Jane's price for each Groupon is the daily rental income divided by the expected number of tubes rented per day. The expected number of tubes is derived by multiplying the expected number of each tube by its probability and then summing the results. 

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The range wοuld stay the same value οf 8 inches.

Let's lοοk at the average fοrmula in mοre detail in this part and use sοme examples tο illustrate hοw it may be used. The fοllοwing is an example οf the average fοrmula fοr a specific set οf data οr οbservatiοns: Average = (Sum οf Observatiοns) ÷ (Tοtal Numbers οf Observatiοns).

In the οriginal data set, the maximum value is 22 inches and the minimum value is 14 inches, sο the range is:

22 - 14 = 8 inches

If anοther plant with a height οf 14 inches is added tο the data, the minimum value will still be 14 inches, but the maximum value will nοw be 22 inches (since there are twο plants with a height οf 22 inches).

Therefοre, the range will increase:

22 - 14 = 8 inches

Sο the cοrrect answer is: The range wοuld stay the same value οf 8 inches.

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Answer:

7 hours and 2 hours longer

The answer is C) +18 ÷ +3 = +6. Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

Measure of how far an object travels in a certain amount of time. Speed is calculated by dividing the distance traveled by the time it took to travel that distance.

The answer is C) +18 ÷ +3 = +6.

This is because Alvin decreased his training by 18 miles over a period of 3 weeks.

Dividing the decrease by the number of weeks gives us 6 miles, which is the average weekly change in his training.

That is 18/3= 6.

To answer the second question, Micheal's 50-meter freestyle was 24.73 meters faster than his 100-meter freestyle.

To calculate this, we subtract the time of the 50-meter freestyle (23.04 seconds) from the time of the 100-meter freestyle (47.77 seconds) to get 24.73 seconds.

We then multiply this time by the speed of a meter per second (1 meter/second) to get 24.73 meters.

Therefore, Micheal's 50-meter freestyle time was 24.73 meters faster than his 100-meter freestyle time.

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Answers and explanation:

[tex]3x^{2} +12x+9=(3x+3)(x+3)[/tex]

Factored form:

[tex](3x+3)(x+3)=0[/tex]

First zero:

[tex]3x+3=0[/tex]

[tex]3x=-3[/tex]

[tex]x=\frac{-3}{3} =-1[/tex]

Second zero:

[tex]x+3=0[/tex]

[tex]x=-3[/tex]

Ordered pair:

[tex]x=-1, x= -3[/tex]

Hope this helps.

Answer: We can use the fact that the sum and product of the roots of a quadratic equation are related to its coefficients, and use this relationship to find the values of p and q.

Given the equation ²-13x - 30 = (x+p)(x+q), we can see that the coefficient of the x^2 term is 1, the coefficient of the x term is -13, and the constant term is -30.

By comparing the coefficients with the formula for the sum and product of the roots of a quadratic equation, we have:

p + q = -(-13)/1 = 13

p*q = -30/1 = -30

Since the absolute value of p is greater than the absolute value of q, we know that either p is positive and q is negative, or p and q are both negative. We can eliminate the possibility of p being positive and q being negative, since their product would be negative, and we know that p*q = -30. Therefore, both p and q must be negative integers.

We also know that the sum of p and q is 13, which means that the absolute value of q is less than the absolute value of p. Since p and q are both negative, this means that q has a larger absolute value (i.e., is farther from zero) than p. Therefore, q is the negative integer in this case.

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

just look at the picture.

what must have happened to figure A to turn into figure B ?

is B more to the right or to the left of A ?

well, right. isn't it obvious ?

and when you look at the coordinates of a vertex, it is 3 units to the right of A.

and if the shift to the right had not happened - the 2 figures would be a mirrored image of each other with the x-axis being the mirror.

that is why A) is the right answer.

The relation between the area (a) and the side length (s) in the table is:

A. a = s²

What is an area?

To see this relationship, we can observe that the areas of the poster boards are the square of their respective side lengths. For example, when the side length is 2 feet, the area is 4 square feet (2²).

Similarly, when the side length is 4 feet, the area is 16 square feet (4²). This pattern holds true for all the side lengths listed in the table. Therefore, we can conclude that the area of each poster board is equal to the square of its side length.

Calculation:

Side Length (s)    |       Area (a)

  1                         |        1

  2                        |        4

  3                        |        9

  4                        |        16

As we can see, the area of each poster board is equal to the square of its side length. Thus, the relation between the area (a) and the side length (s) in the table is a = s².

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Answer:

A

Step-by-step explanation:

[tex]a = s {}^{2} \\ 1. \: + - \sqrt{a = s} \\ 2. \: s = + - \sqrt{a} [/tex]

The probability that the married couple will have adjacent desks is 0.72.

Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say it will happen or not. The result often has good applications in sports, business as a result of forecasting, and the result is also widely used in the field of new intelligence.

Mathematically, the number of ways to assign 6 desks to 6 employees is equal to 8!

Now,

the number of ways the couple can interchange their desks is just 2 ways

Thus,

the number of ways to assign desks such that the couple has adjacent desks is 2(6!)

The number of ways to assign desks among all six employees randomly is 7!

Thus, the probability that the couple will have adjacent desks would be ;

2(6!)/7! = 2/7

This means that the probability that the couple have non adjacent desks is 1-2/7 = 5/7 = 0.71428 ≈ 0.72

Which is 0.72 to the nearest tenth of a percent

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Answer:

Let's use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we are given that one leg (let's call it the shorter leg) is twice the length of the other leg. So, if we let x represent the length of the shorter leg, then the longer leg has a length of 2x.

We are also given that the length of the hypotenuse is √45 centimeters. We can simplify this by noticing that √45 = √(9 × 5) = √9 × √5 = 3√5. So the length of the hypotenuse is 3√5 centimeters.

Now we can write the Pythagorean Theorem equation:

x^2 + (2x)^2 = (3√5)^2

Simplifying, we get:

x^2 + 4x^2 = 45

5x^2 = 45

x^2 = 9

x = 3

So the shorter leg has a length of 3 centimeters, and the longer leg has a length of 2x = 2(3) = 6 centimeters.

D

I graphed each one and then compared the graphs to the one in the question

[tex]log_2(100)[/tex] is apprοximately 6.64 when evaluated using the change οf base fοrmula with base 10.

The change οf base fοrmula is used in lοgarithmic functiοns tο change the base οf the lοgarithm frοm οne value tο anοther.

The fοrmula states that fοr any base b, and any pοsitive numbers x and y, the fοllοwing equatiοn hοlds true:

[tex]log_b(x) = log_y(x) / log_y(b)[/tex]

Here,[tex]log_b(x)[/tex] represents the logarithm of x with base b, and [tex]log_y(x)[/tex]represents the logarithm of x with base y.

Tο evaluate the change οf base fοrmula, we need tο substitute the given values οf x, y, and b in the fοrmula and simplify the expressiοn. Fοr example, let's say we want tο find [tex]log_2(100)[/tex] using the change οf base fοrmula with base 10. We can write:

[tex]log_2(100)[/tex] [tex]= log_{10}(100) / log_{10}(2)[/tex]

Here, we know that log_10(100) = 2, as 10^2 = 100, and log_10(2) is approximately 0.301. Therefore, we can simplify the expression as:

[tex]log_2(100)[/tex]  = 2 / 0.301

This gives us:

[tex]log_2(100)[/tex]  ≈ 6.64

Therefore, [tex]log_2(100)[/tex] is approximately 6.64 when evaluated using the change of base formula with base 10.

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Complete Question:

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log₂1 ?

a. The probability density function of the random variable generated using rand in Excel is:1:b. The probability of generating a random number between 0.2 and 0.8 can be found by calculating the area under the probability density function between those values:P(0.2 ≤ X ≤ 0.8) = ∫0.8 0.2 f(x) dxP(0.2 ≤ X ≤ 0.8) ≈ 0.6Therefore, the probability of generating a random number between 0.2 and 0.8 is approximately 0.6.c. The probability of generating a random number with a value less than or equal to 0.5 can be found by calculating the area under the probability density function up to that value:P(X ≤ 0.5) = ∫0.5 0 f(x) dxP(X ≤ 0.5) ≈ 0.5Therefore, the probability of generating a random number with a value less than or equal to 0.5 is approximately 0.5.d. The probability of generating a random number with a value greater than 0.8 can be found by calculating the area under the probability density function above that value:P(X > 0.8) = ∫1 0.8 f(x) dxP(X > 0.8) ≈ 0.1Therefore, the probability of generating a random number with a value greater than 0.8 is approximately 0.1.e. Using the given random numbers, we can calculate the mean and standard deviation as follows:Mean:μ = (0.931806 + 0.398110 + 0.216843 + ... + 0.545347 + 0.159312) / 50μ ≈ 0.464257Therefore, the mean of the given random numbers is approximately 0.464257.Standard deviation:s = sqrt([(0.931806 - μ)^2 + (0.398110 - μ)^2 + ... + (0.545347 - μ)^2 + (0.159312 - μ)^2] / (50 - 1))s ≈ 0.316221Therefore, the standard deviation of the given random numbers is approximately 0.316221.

a. The probability density function is 1.

b. The probability of generating a random number between 0.2 and 0.8 is 0.6.

c. The probability of generating a random number with a value less than or equal to 0.5 is 0.5.

d. The probability of generating a random number with a value greater than 0.7 is 0.3.

e. The mean is 0.472817 and the standard deviation is 0.316211.

Answer: I do not understand this question

Step-by-step explanation: Enjoy your day today

To solve this problem, we use the rule of conditional probability which states that the probability of the joint event A and B happening is equal to the probability of A happening multiplied by the probability of B happening given that A has already happened.

So, the probability of drawing a green marble on the first draw is 4/15, since there are 4 green marbles out of a total of 15 marbles.

If the first marble drawn is green and not replaced, there are now 14 marbles remaining in the bag, out of which 3 are green.

Thus, the probability of drawing another green marble given that the first one was green is 3/14.

Therefore, the probability of drawing two green marbles without replacement is:

(4/15) * (3/14) = 2/35

So the answer is 2/35.

Answer:

The answer to your problem is, B. mAngleA + 60° + 55° = 180°

Step-by-step explanation:

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle 

if a² + b² > c² , it is an acute triangle

Let the triangle be represented as ABC:

Now , the first measure of angle = 55

The second measure of angle = 60

The angle of the first ∠A = 180

Thus the answer to your problem is, B. mAngleA + 60° + 55° = 180°

Answer:

29

Step-by-step explanation:

Given:

P = 88

Let's assume, that the length is x and the width is y

x = (2y - 1)

Let's write an equation for the perimeter:

2x + 2y = 88

2 × (2y - 1) + 2y = 88

4y - 2 + 2y = 88

6y = 88 + 2

6y = 90 / : 6

y = 15

We found the width, now we can find the length:

x = 2 × 15 - 1 = 30 - 1 = 29

Answer:

0.4 meters.

Step-by-step explanation:

The ratio of centimeters to meters is 100:1.

That means if there are 100 centimeters, there is 1 meter.

So:

centimeters divided by 100 is a meter.

In this case, we have 40 centimeters.

Since there are less than 100 centimeters, we can't divide by 100, so we go into the decimals.

40 divided by 100 is

40/100

simplified to:

4/10

turned into decimal:

0.4 meters.

Hope this helps :)

The answer is 0.4 meters

The given ratio of centimeters to meters is 100:1. The rope Laura has is 40 cm long. To determine how long the rope is in meters, we need to divide 40 cm by 100 to convert it to meters.

Therefore, the length of the rope in meters is 0.4 meters (40/100 = 0.4).Answer: 0.4 meters

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The absolute value equation | x - (-5) | = 3 has a solution set corresponding to a straight horizontal line with marked points -8, -2, and x in left to right manner.

How to write an absolute value equation that has the following solution set?

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

Explanation:

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Answer:

Ok

Step-by-step explanation:

Y = mx + c

Slope is for the gradient =m therefore we have +3 as our gradient

Now we are going to substitute pont - 8mac- 8 on the above equation

Y = mx +c

-8=3(-8) +c

-8=-24 +c

-8+24 =c

16=c

This means that the y intecept of this straight line is 0 mac 16

Meaning that when the line touches the y axis at 16 x will be equal to zero

Therefore our equation is

Y =3x +16

Answer:

Angle A = Angle L

Angle D = Angle M

Angle C = Angle N

Segment AB = Segment LB

Segment CD = Segment NM

Segment DA = Segment ML

2nd part

Quadrilateral URST has moved by a translation of (x-5,y+2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the probability that the average of 25 randomly selected claims exceeds 20,000, we need to first determine the mean and standard deviation of the sample distribution.

Given:
- Mean of the population (μ) = 19,400
- Standard deviation of the population (σ) = 5,000
- Sample size (n) = 25

Step 1: Calculate the mean of the sample distribution (μ_sample)
Since the sample mean is an unbiased estimator of the population mean, μ_sample = μ = 19,400.

Step 2: Calculate the standard deviation of the sample distribution (σ_sample)
σ_sample = σ / √n = 5,000 / √25 = 5,000 / 5 = 1,000

Now, we need to find the probability that the sample mean exceeds 20,000. We can do this using the Z-score formula:

Z = (X - μ_sample) / σ_sample

where X is the sample mean we want to find the probability for (20,000 in this case).

Step 3: Calculate the Z-score
Z = (20,000 - 19,400) / 1,000 = 600 / 1,000 = 0.6

Step 4: Find the probability
Now, we need to find the area to the right of the Z-score in the standard normal distribution table or use a calculator/software that provides the probability.

The area to the right of Z = 0.6 is approximately 0.2743. So, the probability that the average of 25 randomly selected claims exceeds 20,000 is approximately 0.2743 or 27.43%.

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Answer: -64

Step-by-step explanation:

Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.

A linear equation is a one-variable equation of such a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.

All values which it make this equation true are included in the solution set. All real numbers make up the solution set for this equation because, when a real number is used in place of x, the equation is proved to be true.

Given one variable linear equation :

3x + 8 = 5x - 9

Isolate the variable and the constants on the different sides;

5x - 3x = 8 + 9

2x = 17

x = 17/2

x = 8.5

Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.

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Complete question:

What is the value of x? The given equation is: 3x + 8 = 5x - 9.

The value of the indicated sides of the shape given above are as follows:

Scale factor = 1.67

X = 15

Y = 9

Z = 9

To call the scale factor of a given shape the formula used is given below;

Scale factor = Dimension of new shape(bigger)/dimension of the old shape(smaller).

Dimension of new shape = BC = 30

Dimension of old shape = FE = 18

scale factor = 30/18 = 1.67

X = AD/1.67

X = 25/1.67

X = 15 (approximately)

Y = DC/1.67

Y = 15/1.67

Y = 9 (approximately)

Z = AB/1.67

Z = 15/1.67

Z = 9(approximately)

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Answer:

c/0.5= 2.6+3.2

c= 5.8×0.5

c=2.9