Use the methods from this lesson to write the expression in simplest form. Assume x > 0.

Enter the correct answer in the box.

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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Answer: Formula is 2πr^2

Step-by-step explanation:

plug in and it is 196*π

Answer: A= 196\(\pi\)  

Step-by-step explanation:

The area of a circle formula:

A=\(\pi r^{2}\)                       >r=14   substitute in

A=  \(\pi( 14^{2} )\)                >simplify 14²

A= 196\(\pi\)                   > leave pi  like a variable x to leave in terms of pi, do

                                      not multiply by 3.14

Given the sequence:

6, 10, 14, 18,...

We will find the 75th term

The given sequence is an arithmetic sequence

Because there is a constant common differnce

d = 18 - 14 = 14 - 10 = 10 - 6 = 4

The first term = a = 6

The general formula of the arithmetic sequence is as follows:

Where: n is the nth term

To find the 75th term, substitute with n = 75 and a = 6, d = 4

So, the answer will be the 75th term = 302

Using the secant theorem, the value of x is obtained as 19.

What is secant theorem?

According to the intersecting secants theorem, the product of one whole secant segment and its external segment is equal to the product of the other whole secant segment and its external segment when two secants cross at an exterior point. The secant theorem or secant power theorem are other names for this.

The intersecting secant theorem states that for the two secant AB and CD intersecting a circle, there is relationship between

the lengths of the segments as follows -

OA × OB = OC × OD

Substitute the known and given quantities in the equation -

8 × (8 + x) = 9 × (9 + 15)

Apply the addition operation on right hand side -

8 × (8 + x) = 9 × (24)

Apply the multiplication operation -

64 + 8x = 216

Apply the subtraction operation -

8x = 216 - 64

8x = 152

Apply the division operation -

x = 152 / 8

x = 19

Therefore, the value of x is obtained as 19.

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Answer: The value of x is 38.4

Answer:D

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{\dfrac{h}{2} + 21 - k\ if\ h=20\ and\ k=89}\)

\(\textsf{If h = 20 and k = 89, the SUBSTITUTE it for where they are in the equation}\)

\(\mathsf{\dfrac{10}{2}+21 - 89}\)

\(\mathsf{\dfrac{20}{2}= \bf 10}\)

\(\mathsf{\bold{10}+21 - 89}\)

\(\mathsf{10+21=\bf 31}\)

\(\mathsf{\bold{31}-89= \underline{ANSWER}}\)

\(\mathsf{= \bf -58}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf -58}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma(\(\alpha ,\beta\))

E(X)= \(\alpha \beta\)                 \(\beta\)= \(12^{2}/24\)=6 weeks

V(x)= \(\alpha \beta ^{2}\)                \(\alpha\)=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, \(\alpha\), \(\beta\), False)

P(\(12\leq X\leq 24\))

P(\(12/6\leq G\leq 24/6\))

P(\(2\leq G\leq 4\))

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

There isnt even a graph shown to graph on.

Answer:

attached

Step-by-step explanation:

1/4x ≤ 2   same as

x ≤ 8

Number line and 2 dimension graphs

The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is \(1/144\)

The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.

Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:

P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)

\(= (1/6) \times (1/6) \times (1/2) \times (1/2)\)

\(= 1/144\)

Therefore, the probability that Kyle wins the prize is ,\(1/144\) or approximately  \(0.0069\) (rounded to four decimal places).

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Answer:

I cannot answer this question because it is not complete. Please use complete sentences and questions.

Answer:

101

Step-by-step explanation:

the tenth term of the sequence would be 10x10 (10 squared), which equals 100. add 1 to that you get 101.

Answer:

101

Step-by-step explanation:

10 X 10 + 1 = 101

nth term = n^2 + 1

Answer:

a) 2x+(x+36)=90

Step-by-step explanation:

b) A1+A2=90°. (A=angle)

2x+(x+36)=90

2x+x+36=90

3x+36=90

3x=90-36

x=54/3

x=18

then A1=2x=2*18=36°

A2=x+36=18+36=54°

Answer:

Below

Step-by-step explanation:

18 - 4x^2 + 23x is a second degree polynomial since the highest power is 2.

The leading coefficient is -4 since it's the number multiplied by x^2

Answer:

ok, here is your answer

Step-by-step explanation:

The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-

Answer:

y = 2x + 2

Step-by-step explanation:

First solve for the slope using \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

\(\frac{8-2}{3-0}\) = 2

Plug the slope into the slope intercept form equation y = mx + b

y = 2x + b

To solve for b, plug in any (x, y) point on the table.

2 = 2(0) + b

2 = b

Now you can plug the b value into your equation.

y = 2x + 2

The probability for the dots 10 and fewer shots to get a successful shot is 0.85.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

The probability that Gerald makes a three-point shot in basketball is 20%.

He simulated 40 trials of three-point shots where each shot had a 0.2 probability of being successful, and in each trial, he counted how many shots it took to get the first successful shot.

All the dots that are greater than 10 = 6 dots.

we need to find for the dots 10 and fewer there are 40 dots in total

So,

40-6= 34

Then,

P(E) = \(\frac{34}{40}\)

P(E) = 0.85

Hence, The probability for the dots 10 and fewer shots to get a successful shot is 0.85.

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Answer:

1/3=2/6

Step-by-step explanation:

1*2=2

3*2=6

Answer: 1/3=2/6

Step-by-step explanation: the numerator (1) in the first fraction is half it is in the second (2). This means the denominator in the first question (unknown) will be half the second (6). Half of (6) is (3). Your answer is 3.

0.05093 is the probability that exactly 13 students will take up application development in the coming year .

Describe probability using an example?

Average rate (number) of students who chose to study Application Development (λ)= 18

Poisson random variable(number of students taking up Application Development in the coming year)(x)=13

Poisson distribution = P(X = x) = e^−λ (λ)^x/ x!

Here, probability of 13 students choosing application development next year= P(X=13)

               =   ^(−18 ) 18^13/  13!

P(X=13) = 0.0509286= 0.05093

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Answer:

1.35764501988

Step-by-step explanation:

tan:opposite/adjacent

tan(x)=32/21

tan^-1(32/21)=x

x=56.7

Answer:

The last one

Step-by-step explanation:

an exponential function always has the x as an exponent

Answer:

B, D, F

Step-by-step explanation:

Got it right

The z-score associated with a 95% confidence level is approximately 1.96.

The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.

Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.

Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula

z = invNorm(1 - α/2)

where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:

z = inv Norm(1 - 0.05/2)

= inv Norm(0.975) ≈ 1.96

Therefore, the z-score is 1.96

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Answer:

30 apples

Step-by-step explanation:

600 is the total number of apples (adding all numbers in the apples*frequency column). Dividing this by 20, the number of boxes, we get 30 apples as the mean number in a box.

The mean number of apples is the result of dividing the product of frequency and number of apples and f in the table given. Hence, the mean number of apples is 30

The sum of frequency = (2 + 4 + 8 + 4 + 2) = 20

The sum of fx = (56 + 116 + 240 + 124 + 64) = 600

The mean number of apples can be calculated using the values obtained thus :

Mean = fx ÷ f

Mean = 600 ÷ 20

Mean = 30

Therefore, the mean number of apples in a box is 30

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Answer: (1, -10)

Step-by-step explanation:

Substituting the coordinates of each of the points into the given inequalities, we see that (1, -10) is the only point that results in two true statements.

The values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

The expression p(- x ≤ t22 ≤ x) represents the probability of a t-distribution with 22 degrees of freedom lying between - x and x.

We want to find the values of x such that this probability is 0.98.

We can use a table of t-distribution probabilities or a calculator to find the value of t for which the probability of a t-distribution with 22 degrees of freedom lying between −t and t is 0.98.

This value is , 2.518.

Therefore, we need to solve the inequalities:

-2.518 ≤ -x ≤ 2.518

Solving for x, we get:

-2.518 ≤ -x x ≤ 2.518

Therefore, the values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.

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David can best improve his investigation by including a control group. A control group is a group that does not receive any treatment or intervention and is used as a benchmark to compare the results of the experimental group. In this case, the control group would be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well.

In scientific research, it is important to include a control group to ensure that the results of the experimental group are due to the treatment or intervention and not due to other factors. In this case, David is investigating the factors that affect plant growth, and he is manipulating the amount of water and fertilizer that the two elm trees receive. However, there could be other factors that affect plant growth, such as soil quality, sunlight exposure, temperature, and pests. If David only measures the height and trunk girth of the two elm trees that receive water and fertilizer, he cannot be sure if any changes in their growth are due to the treatment or due to other factors.

To improve his investigation, David can plant a third young elm tree near the other two and not give it any water or fertilizer. This third tree will serve as the control group, and David can measure its height and trunk girth every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

David can best improve his investigation by including a control group, which will serve as a benchmark to compare the results of the experimental group. The control group should be a third young elm tree that is planted near the other two but does not receive any water or fertilizer. David can measure the height and trunk girth of the control tree every week for a year as well. By comparing the growth of the experimental group (the two elm trees that receive water and fertilizer) to the growth of the control group (the third elm tree that receives nothing), David can be more confident that any changes in the growth of the experimental group are due to the treatment and not due to other factors.

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The sample space in the tree diagram regarding the probability will be HR, HY, HB, TR, TY, TB.

It should be noted that probability simply means the likelihood of the occurence of an event.

In this case, the sample space in the tree diagram will be HR, HY, HB, TR, TY, TB where,

H= head

T = tail

B = blue

r = red

y = yellow

The number of outcomes are in the event "Toss a tails, spin yellow will be 1.

The probability of tossing tails and spinning yellow will be:

= 1/2 × 1/3

= 1/6

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