if the lengths of the legs of a right triangle are labelled x and y, and if its hypotenuse length is labelled z, then the pythagorean theorem states

old version of which the answer may be

Therefore, the probability that there will be at most 71 visitors at this national park in one weekend is 0.9887.

The Poisson distribution is a probability distribution that describes the probability of a certain number of independent events occurring within a fixed interval of time or space, given that the events occur at a constant average rate and are randomly distributed throughout the interval.

Given that the number of visitors at a national park in one weekend follows a Poisson distribution with a mean of 55.

We need to find the probability that there will be at most 71 visitors in one weekend, that is, P(X ≤ 71).

We can use the cumulative distribution function (CDF) of the Poisson distribution to calculate this probability:

P(X ≤ 71) = F(71) = Σ(k=0 to 71) [e^(-λ) * λ^k / k!]

Where λ is the mean of the Poisson distribution, which is 55 in this case.

Using a calculator or software, we can compute this probability to be:

P(X ≤ 71) = F(71) = 0.9887 (rounded to 4 decimal places)

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Answer:

Probability that there will be at most 71 visitors in one weekend, Assuming variable follows poisson distribution is 0.9887

Probability:

Probability means occurence of an event in respect of another event .

suppose a coin is tossed one time , the probability of getting heads is 1/2

Poisson distribution:

Poisson distribution is also called discrete probability distribution which helps to find the probability of an event happening a certain number of times (k) within a given interval of time. The Poisson distribution has only one parameter, λ (lambda), which is also  the mean number of events.

According to the information:

Given: No. of visitors follows a poisson distribution with a mean of 55

To calculate the probability that there will be at most 71 visitors λλλλin one weekend , cumulative distribution is used:

P[X≤71]=F[71]=∑[k=0 to 71][\(e^{λ}\)*\(λ^{k}\)/k!]

After calculating P[X≤71] = F[71] = 0.9887

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Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

20 feet

Step-by-step explanation:

The horse is running 4 feet per second faster than horse B so you multiply that 5 times because it's after 5 seconds

Hope this helps!

Answer:

254

Step-by-step explanation:

bcDSHWDJHgvshjg

Answer:

More than likely no full answer key however there might be answers for each individual question.

Solving provided question, we can say that The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.

The least common multiple, or the least common multiple of the two integers a and b, is the smallest positive integer that is divisible by both a and b. LCM stands for Least Common Multiple. Both of the least common multiples of two integers are the least frequent multiple of the first. A multiple of a number is produced by adding an integer to it. As an illustration, the number 10 is a multiple of 5, as it can be divided by 5, 2, and 5, making it a multiple of 5. The lowest common multiple of these integers is 10, which is the smallest positive integer that can be divided by both 5 and 2.

To compare the proportion of each notebook covered with stickers, we need to find a common denominator for the fractions.

The least common multiple (LCM) of 6 and 8 is 24. So, we can rewrite Kayla's fraction as 20/24 and Kevin's fraction as 15/24.

So, Kayla covered more of her notebook with stickers, as 20/24 is greater than 15/24.

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Answer:

Step-by-step explanation:

From the given information:

x = number of ads in sports illustrated

y = number of ads in Man's health

Thus, the total ads read by z = (4x +y) million people

The objective function to maximize Z (millions) is:

Z = 4x + y

To determine x & y; constraint to,

x  ≥ 3,  y  ≥  4

Budget constraint:  2000x + 1000y ≤ 14000

By approaching the graphically

If we draw the line x = 3 , y = 4

Then;

2000x + 1000y = 14000

2x + y = 14

Corner points are A (3,4), B(5,4), C(3,8)

At A(3,4):

Z = 4(3) + 1 (4) = 16

At B(5,4):

4(5) + 1 (4) = 24

At C(3,8):

4(3) + 1(8) = 20

Thus, Z = 24 million.    x = 5, y = 4

Therefore;

they should place 5 ads in sports illustrated.

4 ads in man's health to maximize the number of 24 million readers.

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Therefore, 15.95 centimeters represents the top limit of the rope's maximum length.

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.

Since the ruler used to measure the length of the rope has some uncertainty or error, the actual length of the rope could be slightly larger than the measured value.

To find the upper bound of the largest possible length of the rope, we can add the uncertainty or error to the measured value.

Let's assume that the ruler used to measure the rope has a precision of 0.1 cm, which means that the measured value could be off by up to 0.05 cm in either direction.

Therefore, the upper bound of the largest possible length of the rope can be found by adding the maximum possible error of 0.05 cm to the measured value of 15.9 cm:

Upper bound = 15.9 cm + 0.05 cm = 15.95 cm

So the upper bound of the largest possible length of the rope is 15.95 cm.

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Answer-

B) 18a3 is the highest common factor

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Thanks for the hint

Step 1

3+(-7)+9  Equation/Question

Step 2

3+(-7)+9  Remove parenthesis

3-7+9

Step 3

3-7+9  Add and subtract

-4+9

Step 4

-4+9  Simplify

5

Answer

5

Hope this helps

Answer:

12 because it is repeat which means multiple kindergarteners have a size 12 shoe

Step-by-step explanation:

Answer:

The last set.

Step-by-step explanation:

The first 3 sets  contain  'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set  3 , so they are not functions.

The last set does not have any of these and is a function.

The least to greatest of the ratio is 18 : 32, 5 : 8, and 11 : 16

Least to greatest arrangement can also be referred to as ascending order. Ascending order is the order such that each element is greater than or equal to the previous element.

5 : 8

= 5/8

= 0.625

11 : 16

= 11/16

= 0.6875

18 : 32

= 18/32

= 0.5625

Therefore, the ratio can be arranged as 18 : 32, 5 : 8, and 11 : 16 in ascending order.

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Substitute the c for 3 and the d for 6 and evaluate the expression:

Answer:

The diagonals are perpendicular.

The diagonals are congruent to each other.

The diagonals bisect the vertex angles.

The statements that are true of squares include:

It should be noted that a square simply means a shape that has four sides equal. The angles are also 360° since they're 90° each.

In squares, the diagonals are perpendicular and the diagonals are congruent to each other.

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Work Shown:

x^2 - 9 = 0

x^2 - 3^2 = 0

(x-3)(x+3) = 0 ..... difference of squares rule

x-3=0 or x+3=0

x = 3 or x = -3

\( \frac{1}{2} \: to \: the \: power \: of \: 5 \: is \: \frac{1}{32} or \: 0.03125 \)

Answer:

\( \ {\boxed{ \tt ( \frac{1}{2}) ^{5} = \frac{1}{32} }}\)

Step-by-step explanation:

\( \\ \tt( \frac{1}{2} )^{5} \)

\( \\ \tt= \frac{ {1}^{5} }{ {2}^{5} } \)

\( \\ \tt = \frac{1 \times 1 \times 1 \times 1 \times 1}{2 \times 2 \times 2 \times 2 \times 2} \)

\( \\ \tt = \frac{1}{32} \)

Answer:

Step-by-step explanation:

11. 7 × 8 = 8 × 7 [commutative property]

12. 5 × 0 = 0 × 5 [commutative property]

13. 5 × (0 + 8) = (5 × 0) + (5 × 8) [[distributive property]

14. (7 × 1) + (7 × 9) = 7(1 + 9) [distributive property]

15. 6 × 1 = 6 [Identity property of multiplication]

16. 9 × (10 × 1) = (9 × 10) × 1 [[commutative property]

17. 1 × 10 = 10 [Identity property]

18. 7 × 1 = 7 [Identity property]      

19. 4 × 8 = 8 × 4 [commutative property]

20. 4 × (1 × 2) = (4 × 1) × 2 [commutative property]

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

Answer:

15 feet

Step-by-step explanation:

The amount we have is 80 feet, so basically we need to find a width that is under the width. That makes it easier for me saying that the width cant be anything over 40. We also need to make sure that we don't use material that we don't have also.  so that makes it to anything smaller then 20.

P.S- This is probably wrong; it's just my guess.

Answer: 15

Step-by-step explanation:

plato

Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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The rational function will have the next form:

where x1 and x2 are the x-coordinates of the x-intercepts, x3 and x4 are the vertical asymptotes and a is some coefficient.

The x-intercepts are (2,0) and (3,0), then x1 = 2, and x2 = 3

The vertical asymptotes are x = – 7 and x = -8, then x3 = -7 and x4 = -8.

Substituting this information we get:

The y-intercept at (0,12) means when x = 0, f(x) = 12. Substituting this information into the previous formula and solving for a:

Finally, the equation for the rational function is:

Answer:

A

Step-by-step explanation:

Guess

Answer:

I think y and z = 45