A certain cosine function has an amplitude of 5 which functional rule could model this situation

Using the Poisson distribution, the probabilities are given as follows:

a) P(X < 10) = 0.9682.

b) P(X = 10) = 0.0181.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are given as follows:

On average, 1 computer in 800 crashes, hence the mean number of crashes for 4000 computers is given by:

\(\mu = 1 \times \frac{4000}{800} = 5\)

Then the probability that less than 10 computers crash is:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9).

All these values are found using the probability mass function given at the beginning of the answer. Using a calculator, with parameter \(\mu = 5\), we have that:

P(X < 10) = 0.9682.

For item b, the probability is:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 10) = \frac{e^{-5}5^{10}}{(10)!} = 0.0181\)

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There are many shapes of a star. It depends on the shape of the star. If you’re referring to this star, then the number of triangles is 5.

Hope this answers your question!

Answer:

Let us make the last unknown interior angle be "b"

b+a+36=180

b=180-36-a

b=144-a

for the main triangle,

a+144-a+a-28=180

2a+116=180

2a=180-116

2a=64

a=32

so a=32

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

\(\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}\)

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

\(\implies (0-80)^2=4p(0-20)\)

\(\implies (-80)^2=4p(-20)\)

\(\implies 6400=-80p\)

\(\implies p=-80\)

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

\(\implies (x-80)^2=4(-80)(y-20)\)

\(\implies (x-80)^2=-320(y-20)\)

Given:

\(\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}\)

\(\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}\)

\(\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}\)

A triangle is shown with its exterior angles and the interior angles of the triangle are angles 2, 3, 5. The true statements are m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. The correct answers are B, C, and E.

We know that the sum of the measures of the interior angles of a triangle is always 180 degrees. We can use this fact, along with the properties of exterior angles of a triangle, to determine which statements are always true regarding

m∠5 + m∠3 = m∠4 This statement is not always true. It is only true in this case because angle 4 is an exterior angle at vertex 3, which means that m∠4 = m∠3 + m∠5. Therefore, m∠5 + m∠3 = m∠3 + m∠5, which simplifies to m∠5 = m∠5. However, in general, this statement is not always true.

m∠3 + m∠4 + m∠5 = 180° This statement is always true, because the sum of the measures of the three exterior angles of a triangle is always 360 degrees. Therefore, m∠3 + m∠4 + m∠5 = 360°, which simplifies to m∠3 + m∠4 + m∠5 = 180°.

m∠5 + m∠6 = 180° This statement is always true, because the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, m∠5 + m∠6 = m∠1 (because angle 1 is an exterior angle at vertex 2), and m∠1 + m∠2 + m∠3 = 180° (because the sum of the measures of the interior angles of a triangle is 180 degrees). Therefore, m∠5 + m∠6 = m∠2 + m∠3, which is equal to 180° (because m∠2 + m∠3 = m∠1, and m∠5 + m∠6 = m∠1).

m∠2 + m∠3 = m∠6 This statement is not always true. It is only true in this case because angle 6 is an exterior angle at vertex 5, which means that m∠6 = m∠5 + m∠3. Therefore, m∠2 + m∠3 = m∠2 + m∠5 + m∠3, which simplifies to m∠2 + m∠3 = m∠5 + m∠3. Then, by subtracting m∠3 from both sides, we get m∠2 = m∠5. However, in general, this statement is not always true.

m∠2 + m∠3 + m∠5 = 180°: This statement is always true, because the sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, m∠2 + m∠3 + m∠5 = 180°.

Based on the above analysis, the statements that are always true regarding the diagram are

m∠3 + m∠4 + m∠5 = 180°

m∠5 + m∠6 = 180°

m∠2 + m∠3 + m∠5 = 180°

Therefore, the correct options are B, C, and E.

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The equations are y = 30x + 13 and y = 28x + 15. And the charge less for cleaning 4 mattresses is $127 given by company B. Then the amount of money saved to clean 7 mattresses is $22.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Let 'x' be the number of mattresses and 'y' be the total cost. Then the equations are given as,

Company A: y = 30x + 13

Company B: y = 28x + 15

The amount for x = 4 is given as,

Company A: y = 30 (4) + 13 = $133

Company B: y = 28 (4) + 15 = $127

The amount for x = 4 is given as,

Company A: y = 30 (7) + 13 = $223

Company B: y = 28 (7) + 15 = $211

Then the amount of money saved is given as,

⇒ $233 - $211

⇒ $22

The amount of money saved to clean 7 mattresses is $22.

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using the law of sines the results are:

Angle B = 70°

Side a = 7.97 cm

Side c = 12.31 cm

To solve the triangle using the law of sines, we have the following information:

Angle A = 42°

Angle C = 68°

Side b = 12 cm

We want to find Angle B, side a, and side c.

First, we can find Angle B using the fact that the sum of the angles in a triangle is 180°:

Angle B = 180° - Angle A - Angle C

Angle B = 180° - 42° - 68°

Angle B = 70°

Next, we can use the law of sines to find side a and side c:

sin(A)/a = sin(B)/b = sin(C)/c

We know b = 12 cm and angles A, B, and C. Let's focus on finding side a:

sin(A)/a = sin(B)/b

We have:

sin(42°)/a = sin(70°)/12

To find side a, we rearrange the equation:

a = (sin(42°) × 12) / sin(70°)

a ≈ 7.97 cm

Now, let's find side c using the same law of sines equation:

sin(C)/c = sin(B)/b

We have:

sin(68°)/c = sin(70°)/12

Rearranging the equation, we can solve for side c:

c = (sin(68°) × 12) / sin(70°)

c = 12.31 cm

So, the results are:

Angle B = 70°

Side a = 7.97 cm

Side c = 12.31 cm

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Gail height increased by 24 is 50 is g + 24 = 50

Before we begin, note the following:

a increased by b means that we will add a and b, In other words, the expression would be a + b

Now, for our problem:

We have "g" as Gail's height.

The given information is as follows:

i. Gail's height increased by 24 means that we will add g and 24.

ii. Gail's height increased by 24 is 50 means the increased height is equal to 50.

Hence, Based on the above, the expression is: g + 24 = 50

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Answer:

f(x) = x^(1/2) + 3

Step-by-step explanation:

Translating to the right 3 units would change these:

0^(1/2) = 0 /// 3 units to the right would be (0,3)

1^(1/2) = 1 //// 3 units to the right would be (1,4)

4^(1/2) = 2 //// 3 units to the right would be (4,5) etc

Telling Marvin the number 18 should get us into the museum.

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse of multiplication, and is used to find out how many times one number is contained within another number.

To get into Marvin's Magic Museum, we need to figure out which number Marvin likes based on the given information.

Marvin likes the number 14, but not 15. This suggests that he likes even numbers, since 14 is even and 15 is odd.

Marvin likes the number 21, but not 26. This suggests that he likes numbers that are divisible by 3, since 21 is divisible by 3 and 26 is not.

Marvin likes the number 35, but not 39. This suggests that he likes numbers that are not divisible by 4, since 35 is not divisible by 4 and 39 is.

Putting these clues together, we can see that the number Marvin likes must be even, divisible by 3, and not divisible by 4. The only number in the list that meets these criteria is 18, since it is even, divisible by 3 (6 times), and not divisible by 4.

Therefore, telling Marvin the number 18 should get us into the museum.

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Answer:

1.7578071e+26

Step-by-step explanation:

Answer:

Let's use option C to represent the relationship between the number of bags of dog food sold and the profit made:

Profit per bag of dog food = $5.50

Total expenses per day = $2,500

The store wants to make a profit of at least $5,225 per day.

If d represents the number of bags of dog food sold, then the profit made can be represented as:

Profit = Revenue - Expenses

Revenue = Profit + Expenses

Revenue = $5.50d + $2,500

To make a profit of at least $5,225 per day, we can set up the following inequality:

$5.50d + $2,500 ≥ $5,225

Simplifying:

$5.50d ≥ $2,725

Dividing both sides by $5.50:

d ≥ 500

Therefore, the store must sell at least 500 bags of dog food per day to make a profit of at least $5,225 per day.

The correct inequality that represents this relationship is option C: 5.50d +2,500 ≥ 5,225.

Answer:

OK, Here is your answer

Step-by-step explanation:

Let's assume the capacity of the drum be C litres.Since the drum is initially 3/4 full, the amount of water in it is 3/4 × C = (3/4)C liters.When 9 liters of water are drawn from the drum, the remaining amount of water is (3/4)C - 9 liters.Since the drum is now half full, the amount of water remaining in it is (1/2)C liters.Therefore, we can write the equation: (3/4)C - 9 = (1/2)CTo solve for C, let's first get rid of the fractions by multiplying both sides by 4.(3/4)C - 9 = (1/2)C → 3C - 36 = 2C → C = 36Therefore, the capacity of the drum is 36 liters.Hence, the drum holds 3/4 × 36 = 27 liters of water initially and after 9 liters of water are drawn, the remaining amount of water in it is 27 - 9 = 18 liters.

Answer:

18 Lieters.

Step-by-step explanation:

found the answer in his answer. ↑↑↑↑

Answer:

2nd one is a

Step-by-step explanation:

it is true that the expression (36⁴−6⁹)(38⁹−38⁸) is divisible by 30 and 37

Carl Friedrich Gauss introduced the fundamental principle of number theory in 1801, which states that any integer higher than one can be expressed as the product of prime numbers only in one way. Number theory is also referred to as arithmetic. Addition, subtraction, multiplication, and division are the four foundational operations in mathematics. Below, a quick discussion of all these operations is provided.

The expression is given as:

(36⁴−6⁹)(38⁹−38⁸)

Express 36 as 6²

(36⁴ - 6⁹) = (6²)⁴ - 6⁹

= 6⁸ - 6⁹

= 6⁷(6 - 6²)

= 6⁷(6 - 36)

= 6⁷(-30)

=(38⁹ - 38⁸)

= 38⁸(38 - 1)

= 38⁸(37)

=(36⁴−6⁹)(38⁹−38⁸)

=6⁷(-30) × 38⁸(37)

=(30)(37)(-6⁷)(38⁸)

Clearly, 30 and 37 are factors, so divisible by them.

The complete question is-

Prove that the value of the expression: b (36^5−6^9)(38^9−38^8) is divisible by 30 and 37.

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Answer:

x-10

Step-by-step explanation:

ten is less than x

follow me for more answer

Answer:

1404.81

Step-by-step explanation:

1277.1 +127.71 =  i read it wrong the first time sorry

The total amount paid to harry in past week, is 299.28.

Amount is the sum or the total value.

For example, if A purchase 2 kg rice at the price of 40 rs/kg, the amount will be 40×2= 80 rs.

Given that,

The amount paid to Harry for 1 hour = $8.60

Since, Harry worked for 33 hours,

So, The amount paid to Harry for 33 hours = 8.60×33=283.8

Harry gets half times more amount than hourly rate and also gets bonus for last 3 days

So for last 3 days the extra amount paid to Harry

= 3×1/2×8.60+3×1/10×8.60

= 12.9+2.58

=15.48

So the total amount paid to harry = 283.8+15.48=299.28

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Answer: I believe it is 108 good luck girl

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

i believe it would be the last option.

Step-by-step explanation:

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

633637e7sysuy

Step-by-step explanation:

ee7wuqhqwhj

Answer:

3/4 X 8 = 6 pounds of potatoes.

Step-by-step explanation:

You need to attach the but based on my estimation I got 6lb potatoes.

Step-by-step explanation:

Find the difference

3,621 - 1,836 = 1,785

They payed $1,785 dollars in the second installment.

Answer:

a) 37º

b) 143º

c) 2x - 5 = 143

Step-by-step explanation:

a) Angles 5 and 7 are vertical angles and therefore have the same measurements.

b) Angles 5 and 6 form a straight line and are therefore supplementary (add up to 180º). 180 - 37 = 143.

c) We found the measure of angle 6 is 143º in part b. We can set that equal to 2x - 5. Therefore the equation is 2x - 5 = 143.

Answer:

2

Step-by-step explanation:

a. The probability that a yellow disk will be selected is 1 out of 5.

b. It is **likely** that a yellow disk will be randomly selected from the bag.

a. The probability that a yellow disk will be selected can be calculated by;

P = 5 / 25

P = 1/5

The probability of randomly selecting a yellow disk is calculated by dividing the number of yellow disks by the total number of disks. In this case, there are 5 yellow disks and 25 total disks, so the probability is 5/25 = 1/5. This means that there is a 20% chance of randomly selecting a yellow disk.

b. The likelihood of randomly selecting a yellow disk is described as "likely" because the probability is greater than 1/10. A probability of 1/10 or less is considered "unlikely", while a probability of greater than 1/10 is considered "likely".

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Answer:

you would have to add it up

Step-by-step explanation:

when you add the part that you have to add you get your answer

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Answer: False study.

Explanation: This is not true, and is purely by chance.

I hope this helped!

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- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:it might be A