Work out length AC.

Answer:

0

Step-by-step explanation:

First, you have to plug it into the formula to find the slope.

\(\frac{rise}{run}\) =\(\frac{y2-y1}{x2-x1}\)

\(\frac{8-8}{-5-10} =\frac{0}{-15}\)

Since 0 divided by anything is 0, that gives us 0 as a slope and it would be horizontal.

Answer:

There are 6,840 possible outcomes for these awards.

Step-by-step explanation:

Given that a group of 20 people are going to run a race, and the top three runners earn gold, silver, and bronze medals, to determine how many outcomes are possible for these awards, the following calculation must be performed:

20 x 19 x 18 = X

380 x 18 = X

6.840 = X

Therefore, there are 6,840 possible outcomes for these awards.

Total outcomes that are possible for these awards are 6840 outcomes, calculated using permutation.

Total number of people=20

permutation means the arrangement of items while the combination is all about the selection of some out of many.

let us say start with the gold medal

no of ways a gold medal can be given = ²⁰C₁ = 20

Now, the number of people left is 19

no of ways a silver medal can be given = ¹⁹C₁ = 19

Now, the number of people left is 18

no of ways a bronze medal can be given = ¹⁸C₁ = 18

possibility of total outcomes=20*19*18 = 6840ways

Therefore, total outcomes that are possible for these awards=6840

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At the top of Mount Aconcagua, the air pressure is around 31.8% of the pressure at sea level.

This is because the air pressure decreases as we move upwards, due to the decrease in the number of air molecules per unit volume at higher altitudes. This decrease is significant at the summit of Mount Aconcagua, which is one of the highest peaks in the world.

To calculate the percentage of air pressure at the summit, we divide the air pressure at the top by the air pressure at sea level and multiply by 100. Therefore, the air pressure at the top of Mount Aconcagua is approximately 31.8% of the pressure at sea level, rounded to one decimal place.

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The distance between the points (−3,−5) and (2,7) on the coordinate plane is given as 52+t2. Therefore, the value of t is 13.4 units.

Coordinate Planes:

The coordinate plane is a two-dimensional plane formed by two numerical axes. It forms when a horizontal line (X axis) and a vertical line (Y axis) intersect at a point called the origin. The numbers on the coordinate grid are used to locate the points. Coordinate planes can be used to draw points, lines, etc. It acts like a map and provides precise directions from one point to another.

Based on the Question:

Points(−3,-5)and(2,7)

Distance between points=

=    \(\sqrt{(2+3)^2(7+5)^2}\)                     [by distance formula (x−a)² + (y−b)²]

​= \(\sqrt{ 36+ 144}\)

= √180

= 13.4

​Distance points = 13.4unit

Therefore, t = 13.4

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Answer:

\(f(g(-3))=-25\)

Step-by-step explanation:

\(g(-3)=2(-3)^2+7(-3)-3=2(9)-21-3=18-24=-6\\f(g(-3))=4(-6)-1=-24-1=-25\)

Answer:

The each have to place 2 subscriptions

Step-by-step explanation:

Adriana

E (earnings) = 6 + 2*x where x is the number of subscriptions

Sophie

E (earnings) = 4 + 3x

For them to earn the same amount, their right sides must be equated.

4 + 3x = 6  + 2x                    Subtract 2x from both sides

4 + 3x - 2x = 6+ 2x  - 2x       Combine

4 + x = 6                                Subtract 4 from both sides

4 - 4 + x = 6 - 4

x = 2

1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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There will be 10 confidence intervals obtained in a Tukey multiple comparison of 5 populations.

In a Tukey multiple comparison, the confidence intervals are constructed to compare the means of all pairs of groups. To calculate the number of confidence intervals, we use the following formula:

C = n(n-1)/2

Where C is the number of confidence intervals, and n is the number of groups. In this case, there are five populations being compared, so n=5. Plugging this into the formula, we get:

C = 5(5-1)/2 = 10

Each confidence interval will provide information about the difference between the means of two groups, with a certain level of confidence. These confidence intervals can be used to identify which pairs of groups have significantly different means.

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The answer of the given question based on the  Runge-Kutta 4th order method is , the equation is , y(1.25 + 0.005) = 1 + (k1 + 2k2 + 2k3 + k4)/6.

To use the Runge-Kutta 4th order method with a step size h=0.005, we need to calculate the value of y at x=1.25 for the given initial value problem.

The formula for the Runge-Kutta 4th order method is as follows:

k₁ = h * f(x, y)
k₂ = h * f(x + h/2, y + k₁/2)
k₃ = h * f(x + h/2, y + k₂/2)
k₄ = h * f(x + h, y + k3)

y(x + h) = y(x) + (k₁ + 2k₂ + 2k₃ + k₄)/6

Now, let's calculate the values using the given initial conditions:

x = 1.25
y = 1
h = 0.005

k₁ = 0.005 * (2 * x * cos(x²) * exp(-y))
k₂ = 0.005 * (2 * (x + 0.005/2) * cos((x + 0.005/2)²) * exp(-(y + k₁/2)))
k₃ = 0.005 * (2 * (x + 0.005/2) * cos((x + 0.005/2)²) * exp(-(y + k₂/2)))
k₄ = 0.005 * (2 * (x + 0.005) * cos((x + 0.005)²) * exp(-(y + k3)))

y(1.25 + 0.005) = 1 + (k₁ + 2k₂ + 2k₃ + k₄)/6

Now, substitute the calculated values into the equation above and round the final result to three decimal places.

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A vertical 1-meter stick casts a shadow of 0.4 meters , then the height of the tree is 30 meters , the correct option is (c) .

We use the concept of proportions to find the height of the tree .

We know that , A vertical stick of 1 meter casts a shadow of 0.4 meters.

We have to find the height of tree which casts a shadow of 12 meter at the same time ,

Let x =  the height of the tree in meters.

So , we can write ,

⇒ 1/0.4 = x/12 ,

Simplifying this proportion:

We get ,

⇒ 0.4x = 12 ,

⇒ x = 12/0.4

⇒ x = 30

Therefore, the height of the tree is Option(c) 30 meters.

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The given question is incomplete , the complete question is

A vertical 1-meter stick casts a shadow of 0.4 meters. If a tree casts a shadow of 12 meters at the same time, how tall is the tree?

(a) 13.4 meters

(b) 12.6 meters

(c) 30 meters

(d) 4.8 meters.

Answer:

r³ + 15r² - 10r - 4

Step-by-step explanation:

First, note you can remove the brackets, in this case they contribute nothing at all.

Then, group the like terms and add them, e.g., we have 3r³ and -2r², they add up to r³.

Finally, order them from greatest power of r to smallest power of r.

That's all!

The negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

here,
As a person climbs a mountain, the temperature drops 4°F for every thousand feet climbed.

Change in temperature  = -4°F

Thus, the negative integer -4°F  represents the change in temperature for every thousand feet a person climbs.

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Answer:

X< -5

Step-by-step explanation:

Answer: x<−5

Step-by-step explanation: hope this help

Answer:

Length is 7 units

Step-by-step explanation:

width- w

L- length

W+3=L
(w)(l)=28

hopes this helps

Answer:

That is correct, The answer IS 5. Good job

Step-by-step explanation:

I know how A.P.E.X can be confusing, but keep trying!

I believe the answer is 5 because that has to add up to 30 because it is a triangle.

PLEASE MARK BRAINLIEST

Answer:

its 90 degrees

Step-by-step explanation:

The equation of the new graph is y = -(1/4)|(x + 3)| - 4.

The transformation steps provided in the question describe how to transform the graph of y = |x| to obtain a new function that represents the transformed graph.

Starting with the original graph of y = |x|, the first transformation applied is a vertical compression by a factor of 1/4. This means that each y-coordinate of the graph is multiplied by 1/4, resulting in a shorter and narrower version of the original graph. The equation of this transformed graph is y = (1/4)|x|.

Next, the transformed graph is reflected across the x-axis. This means that every point on the graph is mirrored across the x-axis, resulting in an upside-down version of the previous graph. The equation of the reflected graph is y = -(1/4)|x|.

After reflecting the graph, it is translated 3 units to the left. This means that every point on the graph is shifted 3 units to the left. The equation of the translated graph is y = -(1/4)|(x + 3)|.

Finally, the translated graph is moved 4 units down. This means that every point on the graph is shifted 4 units downward. The equation of the final transformed graph is y = -(1/4)|(x + 3)| - 4.

Therefore, starting with the original graph of y = |x|, we can apply these four transformations in sequence to obtain the equation of the new transformed graph.

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Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

Step-by-step explanation:

is this a bot or girl

The solutions to the equation x² = 4x + 12 are x = 6 and x = -2.
In conclusion, by factoring the quadratic expression x² - 4x - 12, we found that the solutions to the equation x² = 4x + 12 are x = 6 and x = -2.

To solve the equation x² = 4x + 12 by factoring, we need to rearrange the equation to bring all terms to one side of the equation, making it equal to zero.

x² - 4x - 12 = 0

Next, we factor the quadratic expression x² - 4x - 12.

To factor the expression, we need to find two numbers that multiply to give -12 and add to give -4. The numbers are -6 and 2.

(x - 6)(x + 2) = 0

Now, we set each factor equal to zero and solve for x.

x - 6 = 0    or   x + 2 = 0

For the first equation, we add 6 to both sides to isolate x.

x = 6

For the second equation, we subtract 2 from both sides to isolate x.

x = -2

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The measures of the angles are: 64°  and 26°.

Recall: Two angles are complement of each other if they add up to the sum of 90° .

Thus,

Let \(x\) represent the first angle

The second angle = \((x-38)^{o}\)

Therefore:

\(x + (x - 38) = 90\)

Solve for x

\(x + x - 38 = 90\\2x - 38 = 90\\2x - 38 + 38 = 90 + 38\\2x = 128\\x = 64\)

The first angle, x, is 64°

The second angle = \(x - 38\)

Plug in the value of x

\(= 64 - 38\\= 26\)

Therefore, the measures of the two angles are 64°  and 26°

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Answer:

A. X = 3 and x = 6

Step-by-step explanation:

Since graph is intersecting x-axis at 3 and 6, therefore 3 and 6 are zeros of this function.

The zeros of the function are x = 3 and x = 6

The zeros of the function are the x values where the graph crosses the x-axis

From the figure, the graph crosses the x-axis at:

x = 3 and x = 6

Hence, the zeros of the function are x = 3 and x = 6

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The number of hours Sue spends in each class is  \(1\frac{23}{48}\) hours.

Sue spends 6 and 2/3 hours in a school each day .

Her lunch period is 1/2 hour long and she spends a total of 15 minutes switching rooms between classes .

The rest of the time sue spends in her four classes that are the same length of time.

Therefore, the number of hours she spends in each class can be calculated as follows;

6 2 / 3 hours = 20 / 3 hours

Hence,

total remaining hours for classes = 20 / 3 - 1 / 2  - 1 / 4

total remaining hours for classes = 71 / 12 hours

Therefore,

time used in each classes  = 71 / 12 ÷ 4

time used in each classes  =  71 / 12 × 1 / 4

time used in each classes  = 71 / 48 = \(1\frac{23}{48}\)  hours

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The complete sufficient statistic for the pdf f(x|θ) = (1+x)¹+0¹ is T(x₁, x₂, ..., xn) = (1+x₁)(1+x₂)...(1+xn).

To find a complete sufficient statistic for the given probability density function (pdf), we need to determine a statistic that contains all the information about the parameter θ (in this case, θ = 0) and also satisfies the condition of completeness.

A statistic T(X₁, X₂, ..., Xn) is said to be sufficient if it captures all the information in the sample about the parameter θ. Completeness, on the other hand, ensures that no additional information about θ is left out in the statistic.

In this case, we have the pdf f(x|θ) = (1+x)¹+0¹, where θ = 0. We can rewrite the pdf as f(x|θ) = (1+x).

To find a sufficient statistic, we can use the factorization theorem. We express the pdf as a product of two functions, one depending on the data and the other depending on the parameter:

f(x₁, x₂, ..., xn|θ) = g(T(x₁, x₂, ..., xn)|θ) * h(x₁, x₂, ..., xn),

where T(x₁, x₂, ..., xn) is the statistic and g(T(x₁, x₂, ..., xn)|θ) and h(x₁, x₂, ..., xn) are functions.

In this case, we can see that the pdf f(x₁, x₂, ..., xn|θ) = (1+x₁)(1+x₂)...(1+xn). Thus, we can factorize it as:

f(x₁, x₂, ..., xn|θ) = g(T(x₁, x₂, ..., xn)|θ) * h(x₁, x₂, ..., xn),

where T(x₁, x₂, ..., xn) = (1+x₁)(1+x₂)...(1+xn) and h(x₁, x₂, ..., xn) = 1.

Now, to check for completeness, we need to determine if the function g(T(x₁, x₂, ..., xn)|θ) is independent of θ. In this case, g(T(x₁, x₂, ..., xn)|θ) = 1, which is independent of θ. Therefore, the statistic T(x₁, x₂, ..., xn) = (1+x₁)(1+x₂)...(1+xn) is a complete sufficient statistic for the given pdf.

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The prediction of the value of the dependent variable outside the experimental region is called

extrapolation. So, the option(a) is right one.

A dependent variable is defined as the variable which is tested and measured in a scientific experiment. It is always depends on other variables. That's why it is called dependent variable and other variable is independent variable. Because it is a variable so it's value always change according to situation. So, there are two processes for predicting the values of dependent variable. These are defined as below :

Hence, the prediction of the value of the dependent variable outside the experimental region is known as extrapolation.

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Answer:

Two expressions are relatively prime if their greatest common divisor is one.

Given the terms: \(n^3 + 2n$ and n^4 +3n^2 +1\), \(n \in N|\{0\}}\)

\(n^3 + 2n=n(n^2+2)\\n^4 +3n^2 +1$ is not factorizable\\\)

Therefore, the greatest common divisor of the two expressions is 1.

Therefore, for all n in the set of natural numbers, (where n cannot be zero.) The two expressions are relatively prime.

Answer:

nth term is;

0.5n-0.5

Step-by-step explanation:

As we can see, the first term is 0

The common difference is 0.5-0= 1-0.5 = 1.5-1 = 0.5

Formula for nth term of an arithmetic sequence is;

a + (n-1)d

So we have

0 + (n-1) 0.5

= 0.5n-0.5

Answer:

Step-by-step explanation:

find the two points and do "rise over run" to fins the slope.

the y-intercept is the point on the y-axis

(0, 3) and (-5, 5)

slope is 2/5

y-intercept is 3

y = 2/5x + 3

Answer:

93° (to the nearest degree)

Step-by-step explanation:

sum of the interior angles of a triangle = 180°

Find angle C first, then subtract angle C and angle B from 180° to find angle A.

Use the sine rule \(\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\) to find angle C:

Therefore,

              \(\frac{sinB}{b}=\frac{sinC}{c}\)

              \(\frac{sin38}{9}=\frac{sinC}{11}\)

         angle C = 48.80523914...°

Angle A = 180 - 38 - 48.80523914...°

              = 93.19476086..°

              = 93° (to the nearest degree)