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Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.

Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.

In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.

In doing so, we would use the previous formula given as;

x² = y² + z²

In a Pythagorean triple, the largest side is the hypothenuse.

17² = 8² + 15²

289 = 64 + 225

289 = 289

The numbers are equal and they're Pythagorean triple.

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Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

2 times

According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:

Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts.

Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country.

Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy.

Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths.

Regularly update the data: As the situation evolves, keep track of new data releases and updates.

Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:

Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts. Examples include official government health agencies, international health organizations (e.g., WHO), and reputable databases (e.g., Worldometer, Johns Hopkins University).

Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country. Ensure the data is recent and covers a comprehensive list of countries.

Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy. Different sources may have slight variations, so it's important to verify the data and use the most reliable figures.

Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths. Use a spreadsheet or calculator to perform the calculations accurately.

Regularly update the data: As the situation evolves, keep track of new data releases and updates. Update the total number of deaths accordingly to maintain accuracy.
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The question probable may be:

How to calculate the total number of deaths for all the countries?

​

The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.

We can solve for x by taking the logarithm of both sides with base 5:

[tex]5^{(\frac{-x}{16})} = 5[/tex]

[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]

(-x/16)log₅(5) = 1

-x/16 = 1/log₅(5)

x = -16/log₅(5)

Using a calculator, we get:

x ≈ -4.4431

Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex]  in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

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Area of the figure is 402.8 ft².

We have,

Rectangle area = Length x Width

Area of sector = π r² x angle / 360

Now,

There are two rectangles and one sector.

So,

Area of one rectangle.

= 8 x 2

= 16 ft²

Area of another rectangle.

= 5 x 2

= 10 ft²

Area of the sector.

= π x r² x {360 - (150 + 90 + 90)}

= 3.14 x 2² x 30

= 376.8 ft²

Now,

The area of the figure.

= 16 + 10 + 376.8

= 402.8 ft²

Thus,

The area of the figure is 402.8 ft².

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The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

We have,

Assuming that the line of best fit represents the trend between the number of hours students study and their quiz grades,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

In other words,

If a student studies for this amount of time, they are predicted to achieve a quiz score of 100 based on the trend shown by the line of best fit.

Thus,

The x-value on the line when y = 100 represents the estimated number of hours a student would need to study to achieve a quiz grade of 100.

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The measure of the angles is c = 37. 5 degrees

d = 15 + 37.5 = 52. 5 degrees

To determine the value, we need to know what complementary angles are;

Complementary angles are defined as pair of angles whose sum is equal to 90 degrees

From the information given, we have that;

Angle c and d are both complementary angles

Also, the measure of angle d is 15 degrees greater than the measure of angle c

Then, we have;

d = 15 + c

Substitute the values

c + 15 +c = 90

collect like terms

2c = 90 - 15

2c = 75

Divide both sides by the coefficient

c = 37. 5 degrees

Substitute the value for angles d

d = 15 + 37.5 = 52. 5 degrees

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The area of the figure is 183.5 ft².

We have,

The figure has two types of shapes.

Two rectangles and one triangle.

Now,

Area of rectangle = Length x Width

Area of triangle = 1/2 x base x height

Now,

Rectangle 1:

Area = 7 x 5 = 35 ft²

Rectangle 2:

Area = 4 x (4 + 5) = 4 x 9 = 36 ft²

Triangle:

Area = 1/2 x (11 + 4) x 15 = 1/2 x 15 x 15 = 112.5 ft²

Now,

The area of the figure.
= 35 + 36 + 112.5

= 183.5 ft²

Thus,

The area of the figure is 183.5 ft².

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The logarithmic expressions when expanded are

1. [tex]\log2^{8yz}[/tex] = 8xyz log(2)

2. [tex]\log9^{81x/y}[/tex] = 81x/y log(9)

3. [tex]\log5^{x^3}[/tex] = x³ log(5)

4. [tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)

From the question, we have the following parameters that can be used in our computation:

The logarithmic expressions

The logarithmic expressions can be expanded using power rule of logarithm which states that

logaᵇ = b log(a)

Using the above as a guide, we have the following:

[tex]\log2^{8yz}[/tex] = 8xyz log(2)

[tex]\log9^{81x/y}[/tex] = 81x/y log(9)

[tex]\log5^{x^3}[/tex] = x³ log(5)

[tex]\log6^{\sqrt[3]{x}}[/tex] = ∛x log(6)

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We can conclude that cosθ = sin(90° - θ) for any right triangle with angle θ and its complementary angle (90° - θ).

To prove that cosθ = sin(90° - θ), we can use the properties of right triangles and their angles.
Consider a right triangle ABC, where angle A is θ, angle B is (90° - θ), and angle C is 90°.
According to the definition of trigonometric functions in a right triangle:
- cosθ = adjacent side (AB) / hypotenuse (AC)
- sin(90° - θ) = opposite side (AB) / hypotenuse (AC)
From the given definitions, we can see that both cosθ and sin(90° - θ) have the same ratio of side lengths, which is AB/AC.
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Answer:6

Step-by-step explanation:

Answer:

Step-by-step explanation:

hoop 132

1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

To find Daniela's Season 3 pay in terms of p, we need to calculate the pay increase for each season.

In Season 2, her pay increases by 5 percent, which means she will receive 105 percent (or 1.05) of her Season 1 pay.

In Season 3, her pay increases by 10 percent from Season 2, so she will receive 110 percent (or 1.10) of her Season 2 pay.

To express Daniela's Season 3 pay in terms of p, we multiply the Season 1 pay (p) by the pay increase factors for Season 2 and Season 3:

Season 2 pay = 1.05p

Season 3 pay = 1.10(1.05p) = (1.10)(1.05)p

Simplifying the expression, we get:

Season 3 pay = 1.155p

Therefore, 1.15p is the expression which  represents Daniela's Season 3 pay in terms of p

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The graph could be the graph of exponential function of option b)

[tex]F(x) = 2 • (0.5)^{x} [/tex]

The general form of an exponential function is

[tex]f(x) = {ab}^{x} [/tex]

Here, a is the function's starting value and b is its growth factor.

F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function

The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.

Given that the graph indicates that the function is decreasing, b must be less than 1.

It indicates that the necessary function is in the form of

[tex]f(x) = 2(b)^{x} [/tex]

Where it is b<1

By checking option B, b=0.5<1. Hence, option B is the correct answer

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Note that the full question is:

(check the attached image)

Answer:

Step-by-step explanation:

Hi, im gonna try my best to explain.
First we solve what X could be, since it doesnt say; we make x = 1
3 x 1 = 3.
now we take both 3's and multiply which would be 9
2 to the power of 3 is 8.
8 + 9 is 17
then, minus 2 is 15
and lastly; 15 + 1 = 16

(hope this helped!)

The spread of the data is not relevant to determining which class used the most paper overall.

Mrs. Potter's class used the most paper overall based on the data displayed because it has a larger median value of 16 pieces of paper. The median value of Mr. Howard's class is 11 pieces of paper.

The spread of the data is not relevant to determining which class used the most paper overall.

Therefore, the correct answer is Mrs. Potter's class; it has a larger median value of 16 pieces of paper.

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Answer:

your answer is c=y=1/6x

The probability of randomly choosing two boys is 0.174

If the selection is done at random, then the probability of choosing a boy is equal to the quotient between the number of boys and the total number of people.

There are 12 boys and 16 + 12 = 28 students in total, then the probability is:

P = 12/28

Now, for the second selection the probability is computed in the same way, but now there are 11 boys and 27 students (one was already choosen), then:

P = 11/27

the joint probability (for the two selections) is given by the product between the individual probabilities, we will get:

P = (12/28)*(11/27)

P = 0.174

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The meaning of the statement is if you take n distinct numbers, x₁, ..., xₙ, and permute them in all possible ways, the number of different values that the function f(x₁, ..., xₙ) can take on will be a divisor of n!.

This assertion is a specific instance of a broader concept known as the Principle of Inclusion-Exclusion in the field of combinatorics. The Principle of Inclusion-Exclusion asserts that when dealing with a set comprising n elements and aiming to determine the number of possible subsets that can be selected, one can arrive at this figure by summing up the number of options for choosing 0, 1, 2, and up to n elements from the set.

Regarding the aforementioned assertion, the collection of components comprises every potential arrangement of the numerical values x₁, ..., xₙ. There is only one possible way to choose 0 elements, there are n options for choosing 1 element, selecting 2 elements can be done in n(n-1)/2 ways, and the pattern continues.

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a. The values of k for which points A, B, and C are collinear are k = 3 and k = -2.

b. The value of k for which AB is parallel to CD is k = 13.

a. slope AB = (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of AC is:

slope AC = (k+3-9)/(2k-0) = (k-6)/(2k)

Since A, B, and C are collinear, slope AB = slope AC. Therefore, we have:

(k-5)/(k+1) = (k-6)/(2k)

2k(k-5) = (k+1)(k-6)

2k^2 - 10k = k² - 5k - 6

k = 3 or k = -2

(b)  The slope of AB is:

= (k+4-9)/(k+1-0) = (k-5)/(k+1)

The slope of CD is:

= (k+6-k-3)/(2k+2-2k) = 3/2

Since AB is parallel to CD, slope AB = slope CD. Therefore, we have:

(k-5)/(k+1) = 3/2

2(k-5) = 3(k+1)

k = 13

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The side length x and y of the right triangle are  [tex]\frac{8\sqrt{3} }{3}[/tex] and  [tex]\frac{16\sqrt{3} }{3}[/tex] respectively.

The figure in the image is a right triangle.

Angle θ = 60°

Opposite to angle θ = 8

Adjacent to angle θ = x

Hypotenuse = y

To solve for side lengths x and y, we use the trigonometric ratio.

Note that:

sine = opposite / hypotenuse

cosine = adjacent / hypotenuse

tangent = opposite / adjacent

First, we determine the value of x.

tanθ = opposite / adjacent

tan( 60 ) = 8/x

x = 8/tan( 60 )

x = [tex]\frac{8\sqrt{3} }{3}[/tex]

Next, solve for y:

sinθ = opposite / hypotenuse

sin( 60 ) = 8/y

y = 8/sin( 60 )

y = [tex]\frac{16\sqrt{3} }{3}[/tex]

Therefore, the value of x is  [tex]\frac{8\sqrt{3} }{3}[/tex] and the value of y is  [tex]\frac{16\sqrt{3} }{3}[/tex].

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Answer: 60

Step-by-step explanation: If you subtract then you will continue to get 60

The function of the graph is f(x) = x²-3x -10

A quadratic function is a function in which the highest power of it's variable is 2. quadratic equation is given in the form f(x) = ax²+ bx +c

To form the quadratic function from a graph, we need to find the roots of the function from the graph. The root is the point where the curve intercept the x axis.

Therefore the roots are -2 and 5.

f(x) = x² -( z+y)x +zy

where z and y are the roots

z+y = -2 +5 = 3

zy = -2 × 5 = -10

f(x) = x²-3x -10

therefore the function of the graph is f(x) = x²-3x -10

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The area of the given rectangle is 121/16 square inches.

As know that the area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

To find the area of the rectangle, we need to multiply the length by the width. We have:

Length = 2 3/4 inches = 11/4 inches

Width = 2 3/4 inches = 11/4 inches

Area = Length x Width

Area = (11/4) inches x (11/4) inches

Area = 121/16 square inches

Therefore, the area of the rectangle is 121/16 square inches.

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Note that based on the volume  calculations,  the manager's statement is NOT correct. The given area of 2m × 2m is insufficient to store all 80 crates.

To verify if the manager's statement is correct, we need to derive the volume of each crate and the total volume required to store all 80 crates.

Volume = Length × Width × Height

Recall that

Length (L) = 690 mm

Width (W) = 445 mm

Height (H) = 180 mm

Thus, the Volume of one crate is

Volume = 690 mm × 445 mm × 180 mm

Converting mm to meters we have,

Volume = (690 / 1000)  × (445 / 1000)  × (180 / 1000)

= 0.690  × 0.445 × 0.180

= 0.055269 m³

Next , we calculate the total volume required for 80 crates as

Total Volume = Volume of one crate × Number of crates

= 0.055269 m³ × 80

= 4.42152 m³

Recall that the manager stated that all 80 crates can be packed in a 2m × 2m area in the store room.

Since area of store room is

Area = 2 m × 2 m

Area = 4 m²

Comparing the total volume required (4.380208 m³) with the available area (4 m²), we see that the volume exceeds the area. Tus, the manager's statement is incorrect.

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Full question:

Manager states that all 80 crates can be packed in a 2m x 2m area e store room. (Assume that the height of the store room is adequate stacked crates) y if this statement is correct. Show all your calculations.​

See attached Image.

Step-by-step explanation:

7!  =  7 P 7 = 5040 ways

7 choices for first

6 choices for 2nd

5 choices for 3rd

4 chouces for 4th

3

2

1

           7 x 6 x 5 x 4 x 3 x 2 x 1 = 7!