2. An isosceles right triangle whose legs are 6 is rotated about one of its legs to generate a
right circular cone What is the volume of that cone?

Answer:

If sin 115 degrees≈ 0.91 and cos 115 degrees = -0.42, then sin -115 = -0.91 and cos -115 degrees = 0.42

Step-by-step explanation:

To determine which method can be used to prove the similarity of the given triangles, use SAS, SSS, and AA.

To determine which method can be used to prove the similarity of the given triangles, let's briefly discuss each method:

a) SAS~ (Side-Angle-Side Similarity): If two sides of a triangle are proportional to two sides of another triangle, and their included angles are congruent, then the triangles are similar.

b) SSS~ (Side-Side-Side Similarity): If all three sides of a triangle are proportional to the corresponding sides of another triangle, then the triangles are similar.

c) AA~ (Angle-Angle Similarity): If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar.

Unfortunately, I cannot see the given triangles in your question, but based on the provided information, you can use these explanations to determine which method (SAS~, SSS~, or AA~) can be used to prove their similarity. If none of these methods apply, then similarity cannot be proved for the triangles.

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Answer:

14 gallons of gasline

Step-by-step explanation:

I think this is right atleast

When the radius is 10 feet, the rate at which the area of the circle is increasing is 20π square feet per second.

10 seconds after the boy drops the stone, the rate at which the area of the circle is increasing is still 20π square feet per second.

Boy sitting on a pier,

Height of the pier above water drops = 16 feet

Apply the formulas for the area of a circle and the relationship between the radius and time.

To find the rate at which the area of the circle is increasing when the radius is 10 feet,

Differentiate the area formula with respect to time,

A = πr²

Differentiating both sides with respect to time (t),

dA/dt = 2πr × dr/dt

dr/dt = 1 foot per second (since the radius expands at a rate of 1 foot per second),

and we want to find the rate when the radius is 10 feet, we substitute these values,

r = 10 ft

dr/dt = 1 ft/s

dA/dt

= 2π(10) × 1

= 20π

To find the rate at which the area of the circle is increasing 10 seconds after the boy drops the stone,

Determine the radius at that time and differentiate the area formula accordingly.

The radius expands at a rate of 1 foot per second, after 10 seconds, the radius will be,

r = initial radius + (rate × time)

= 0 + (1 × 10)

= 10 ft

Now, differentiate the area formula with respect to time and substitute the values,

A = πr²

⇒dA/dt = 2πr × dr/dt

⇒dA/dt = 2π(10) × 1

             = 20π

Therefore, rate at which area of the circle increasing,

For the radius 10 feet and 10 seconds after which boy drops the stone increase in area pf the circle by 20π square feet per second.

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The relationship between the type 1 error rate (α) and statistical power is inversely proportional. A type 1 error occurs when we reject a true null hypothesis, and statistical power is the ability to correctly reject a false null hypothesis. When we set a lower α value (e.g., 0.01 instead of 0.05), we decrease the chances of making a type 1 error, but we also decrease statistical power. On the other hand, setting a higher α value (e.g., 0.1 instead of 0.05) increases the chances of making a type 1 error, but also increases statistical power. Therefore, researchers must strike a balance between these two values to ensure their study has sufficient power while also minimizing the risk of making false conclusions.

The relationship between type 1 error rate (α) and statistical power is an important concept in statistical hypothesis testing. A type 1 error occurs when we reject a null hypothesis that is actually true. The probability of making a type 1 error is represented by the α level. Statistical power, on the other hand, is the probability of correctly rejecting a false null hypothesis. In other words, it is the ability of a study to detect a significant effect if one exists.

The relationship between α and statistical power is inversely proportional. This means that as α increases, statistical power decreases, and vice versa. If a study sets a lower α value (e.g., 0.01 instead of 0.05), the chances of making a type 1 error decrease. However, this also means that the study may have less statistical power because it is more difficult to reject the null hypothesis. Conversely, if a study sets a higher α value (e.g., 0.1 instead of 0.05), the chances of making a type 1 error increase, but statistical power may increase as well because it is easier to reject the null hypothesis.

In summary, researchers must balance the α level and statistical power when conducting hypothesis testing. A lower α level decreases the chances of making a type 1 error, but also decreases statistical power. A higher α level increases the chances of making a type 1 error, but may increase statistical power. Researchers must consider the importance of minimizing the risk of false conclusions while also maximizing the ability to detect a significant effect.

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The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer:

Think of 2 pizzas being cut to make 10 slices. Each pizza will be 5 parts.

Step-by-step explanation:

2 ÷ 10 = .2

Answer:

=2574+1287i

Step-by-step explanation:

Transformations

We are given the coordinates of point A=(-1,4).

A transformation (x-4,y+1) is applied. This means the x-coordinate is subtracted 4 and the y-coordinate is added 1 to get the point A' = (-1-4,4+1) = (-5, 5)

Now it's required to reflect A' over y=4

The vertical distance from the point to y=4 is 5-4 = 1.

Thus, we subtract 2*1 = 2 to the y-coordinate to get A'' = (-5,5-2) = (-5,3)

The final coordinates of the original point are (-5,3)

Answer:

\(\boxed{\textsf {The given polynomial is a quadratic polynomial. }}\)

Step-by-step explanation:

A polynomial is given to us and we need to make the polynomial by its degree . Here the given polynomial is 3x² + 5x -3 .

\(\sf\implies p(x)= 3x^2+5x-3 \)

So here we can see that the highest power of the variable in the given polynomial is 2 . So the polynomial is a quadratic polynomial .

★ More to Know :-

When we equate this quadratic polynomial with 0 , it becomes a quadratic equation.

That is ,

\(\sf\implies p(x)= 3x^2+5x-3=0\)

This is done in order to find the zeroes of the polynomial. The zeroes of the polynomial are the values for which the polynomial becomes 0 .

If two lines form congruent adjacent angles, it indicates that the lines are perpendicular to each other.

This is known as the Perpendicular Adjacent Angles Theorem. According to this theorem, if two lines intersect and the adjacent angles formed by the intersection are congruent, then the lines are perpendicular to each other.

Congruent adjacent angles are angles that have the same measure and share a common vertex and a common side. When two lines intersect to form congruent adjacent angles, it implies that the lines are forming a right angle at their point of intersection. Thus, the lines are perpendicular to each other.

In summary, if two lines form congruent adjacent angles, it indicates that the lines are perpendicular.

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The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)

An equation is an expression that shows the relationship between two or more variables and numbers.

The surface area of  pyramid = sum of individual area of the surface

Surface area = (2 * 2) + 4(0.5 * 2 * 3)

The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)

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Answer: n + 2n - 6 = 12

Step-by-step explanation:

The number is n.

Six less than twice the number can be expressed as = 2n - 6

Adding those together will be; n + 2n - 6

They add up to 12 so the equation is;

n + 2n - 6 = 12

You said I don't need to solve but the number is 6 just in case.

Answer:

68

Step-by-step explanation:

Let The first number = X

& the Second one = X + 16

Sum of these two numbers = 120

X + X + 16 = 120

2X = 120 - 16

2X = 104

X = 52

So , the first number = 52

& Second one = 52 + 16 = 68

Answer:

The numbers are 52 and 68.

Step-by-step explanation:

Let x be the first number and y be the second. The question tells us that:

1) x = y + 16

2) (x + y) / 2 = 60

2 equations, 2 unknowns. Solve the system. Plug equation 1 into equation 2:

(y + 16 + y) / 2 = 60

2y + 16 = 120

y + 8 = 60

y = 52

Now plug the value of y back into either original equation. I'll use the first:

x = 52 + 16

x = 68

The probability of Thuy rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

We know that:

Thuy rolls a number cube 7 times,

so the total outcomes are: 6.

Also, it is asked to find the probability of rolling a 4 exactly 2 times.

So it could be done by the method that:

1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6,

where 1/6 denotes the probability of rolling a 4 and 5/6 denotes the probability of rolling a number other than 4

therefore we know that, the probability of rolling a 4 exactly 2 times is 1/6 × 1/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 × 5/6 = 5⁵/6⁷

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Alonzo used 68.5 pounds of type B coffee in his blend.

Let x be the number of pounds of type B coffee used.

As the total cost of the blend is $708.95, we set up the equation which is as follows:

5.95x + 4.40x = 708.95

10.35x = 708.95

x = 708.95 / 10.35

= 68.5.

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The probability that a patient will not be given a placebo is approximately 0.5294 or 52.94%.

To calculate the probability that a patient will not be given a placebo, we need to consider the total number of patients and the number of patients who are not given a placebo.

Given that 30 patients are given Drug A, 60 patients are given Drug B, and 80 patients are given a placebo, the total number of patients is:

Total number of patients = 30 (Drug A) + 60 (Drug B) + 80 (placebo) = 170

To find the probability that a patient will not be given a placebo, we need to calculate the number of patients who are not given a placebo:

Number of patients not given a placebo = 30 (Drug A) + 60 (Drug B) = 90

Now, we can calculate the probability by dividing the number of patients not given a placebo by the total number of patients:

Probability = Number of patients not given a placebo / Total number of patients

Probability = 90 / 170

Simplifying the fraction, we get:

Probability ≈ 0.5294

As a result, the likelihood that a patient won't receive a placebo is roughly 0.5294, or 52.94%.

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Given

One of the zeros of 14² − 42² − 9 is the negative of the other.

To find the value of k.

Explanation:

It is given that,

One of the zeros of 14² − 42² − 9 is the negative of the other.

That implies,

Let α, -α be the zeros of the polynomial f(x) = 14² − 42² − 9.

Then,

Also,

Subtracting (1) and (2) implies,

Hence, the value of k is 0.

False, a binary (categorical) predictor should not be used along with nonbinary (numerical) predictors

It is important to note that binary and non-binary predictors can both be utilized.

Categorical variables with two possible outcomes, such as yes/no or true/false, are represented by binary predictors. On the other hand, nonbinary predictors indicate numerical variables that can have a variety of values.

It is feasible to capture the links between several sorts of variables and enhance the predictive ability of a model by using both types of predictors. Utilizing methods like logistic regression and

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Answer:

(-8,4)

Step-by-step explanation:

System of Equations:

Solve the following system of equations by the substitution method:

5x - 6y = -64      [1]

y = 20 + 2x        [2]

Substituting y from [2] in [1]:

5x - 6(20 + 2x) = -64

Operating:

5x - 120 - 12x = -64

Simplifying:

-7x - 120 = -64

Adding 120:

-7x = -64 + 120 = 56

x = 56/(-7) = -8

x = -8

From [2]:

y = 20 + 2(-8) = 4

Solution (-8,4)

Based on an equation, the number of Cadbury eggs that Teddy bought was 11.5.

An equation is an algebraic statement of the equality of two or more mathematical expressions.

The differentiating factor of an equation from an algebraic expression is the equal symbol (=).

Let the number of eggs Teddy bought = x

Let the number of eggs Elena bought = x + 4

Let the number of eggs Sharon bought = 2x

The total number of Cadbury eggs that the trio bought = 50

Therefore, x + x+4 + 2x = 50

4x + 4 = 50

4x = 46

x = 11.5

Thus, Teddy bought 11.5 eggs, Elena bought 15.5 eggs, while Sharon bought 23 eggs, making a total of 50 eggs.

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The equation is

Approximately 1575

Answer:

approximately 1,575 insects

Step-by-step explanation:

We can model this as an exponential equation.

General form of an exponential equation:  \(y=ab^x\)

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the population falls by 10% each year, then each year the population will be 90% of the previous year (since 100% - 10% = 90%)

Convert 90% into a decimal:  90/100 = 0.9

Therefore, the base of the exponential function is 0.9

Given:

\(\implies y=2400(0.9)^x\)

To find how many insects there will be in 4 years, substitute x = 4 into the equation and solve for y:

\(\begin{aligned}x=4 \implies y & =2400(0.9)^4\\& = 1574.64\end{aligned}\)

Therefore, there will be approximately 1,575 insects remaining in 4 years.

0 because there is no 7 on a fair 6-sided die

Answer:

The probability of rolling a "7" on a fair 6-sided die is 0/6 or 0% because there is no value of 7 to be rolled on such a die. The probability of flipping a tails on a  fair coin is 1/2 or 50% because there are only two sides to a coin and tails is one of those sides.

Answer:

Answer is c hope this helps :)

Step-by-step explanation:

The probability of not rolling a 5 when rolling a fair 6-sided die is 0.83, or 83%. This means that in repeated rolls of the die, we can expect to see a 5 about 17% of the time.

When rolling a fair 6-sided die, each face has an equal chance of landing. Since we want to find the probability of not rolling a 5, we need to determine the number of favorable outcomes (i.e., the number of outcomes that are not a 5) and divide it by the total number of possible outcomes.

Out of the six faces of the die, only one face represents the number 5. Therefore, there are five favorable outcomes (1, 2, 3, 4, and 6) out of six possible outcomes. Dividing the number of favorable outcomes by the total number of outcomes gives us 5/6, which is approximately 0.83 when rounded to two decimal places.

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Answer:

ROC= -3

Step-by-step explanation:

X    f(x)

0   59

3   58

6   57

9   56

12  55

ROC= change in y/change in x

3/-1

The rate of change is -3

Answer:

73.85

Step-by-step explanation:

30% off of 100 is 30$

100-30=70

5.5% of 70 is 3.85

70+3.85=73.85