Find the area of the region determined by the intersections of the curves. 1) y = x2 – 1, y = 7 – x2 y .Compute the volume of the solid formed by revolving the given region about the given line. 20 = = 0 about (a) the Region bounded by y = (x, y = 2 and x y-axis; (b) x = 4

Answer:

5n + 1

Step-by-step explanation:

Increase by 5.

Variable term is 5n.

Number term is +1

5n + 1 :)

Hope this helps!

Answer:

Tn=5n+1

Step-by-step explanation:

T9=5*9+1

T9=45+1

T9=50

To be 95% positive that the population proportion is within 0.02 percentage points, we would need to survey at least 2,450 drivers.

To determine the minimum sample size needed to estimate a population proportion with a certain level of confidence and a given margin of error, we use the following formula:

n = [Z² * p * (1-p)] / E²

where:

- n is the sample size

- Z is the Z-score corresponding to the desired level of confidence

- p is the estimated population proportion

- E is the desired margin of error

Assuming we do not have any prior information about the population proportion, we can use a conservative estimate of 0.5 for p, which maximizes the sample size needed. Also, for a 95% confidence level, the Z-score is approximately 1.96.

Plugging in the values, we get:

n = [1.96² * 0.5 * (1-0.5)] / 0.02²

n = 2.45 * 10³

Rounding up to the nearest whole number, we get:

n = 2,450

Therefore, we would need to survey at least 2,450 drivers to be 95% confident that the population proportion is estimated to within 0.02.

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Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

The following illustrate the examples of Qualitative data: (1) the eye color of children participating in after-school activities and (2) the traits of various bird species.

Data that cannot be quantified or expressed in numbers are referred to as qualitative data.

Now,

(1) The time, in minutes, it took students to finish their exams: It is quantifiable data since the number of minutes it took pupils to complete their tests can be measured.

(2) The eye color of students involved in after-school activities: Since the eye color of students participating in after-school activities cannot be quantified, the information is qualitative.

(3) The characteristics of different types of birds: The characteristics of many bird species can never be quantified quantitatively; therefore, the information is qualitative.

(4) The scores on the last exam: It is quantitative data since the results of the last exam may be quantified and expressed in numbers.

(5) The weights of different books: It is quantifiable data because it is possible to measure the weights of various books.

Hence, the eye color of children participating in after-school activities and the traits of various bird species are examples of qualitative data.

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Answer:

$3600

Step-by-step explanation:

To find the total budget, you need to divide the amount money for the mortgage payment by the percentage is is of the budget.

21% = 0.21

756/0.21 = 3600

$3600 is the total family budget.

Answer:

1 & 2

1 & 8

2 & 7

Step-by-step explanation:

Any two angles that add up to 180 degrees (aka a straight line) are supplementary angles.

Step-by-step explanation:

12a2 +18a

6a(2a+3).

hope it helps

The minimum score needed to receive a grade of 'a' is 87.92

Given that,

At a nearby university, a professor noticed that her students' exam results were regularly distributed, with a mean of 73 and a standard deviation of 11. 8.75 percent of the professor's students achieved grades of A, she told us.

Mean = μ = 73

Standard deviation = σ =  11

Using the standard normal table,

⇒ P(Z > z) = 8.75%

⇒ 1 - P(Z < z) = 8.75%

= 1 - P(Z < z) = 0.0875

= P(Z < -1.36) =1- 0.0875

= P(Z < 1.3563) =0.9125

∴ Z = 1.3563                              ( Using standard normal z-table )

Using z-score formula ;

x= z * σ + μ

x=1.3563 * 11 + 73

x=87.92

So, the minimum score needed to receive a grade of 'a' is 87.92

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Answer:

7.07070707E15

Step-by-step explanation:

Step-by-step explanation:

ur answer....here u gi

Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

The zero of the function is at 33.69 degree , the graph is plotted and attached with the answer.

A function is a law that relates a dependent variable and an independent variable with each other

It is given that

y = 2tan (x - π/2) +3

To find the zeroes of a function that function has to be equated to zero.

2tan (x - π/2) +3 = 0

2tan (x - π/2)  = -3

tan (x - π/2)  = -3/2

x - 90 = -56.31

x = 33.69 degree

The zero of the function is at 33.69 degree

For finding the maxima /minima

the derivative is

dy/dx = 2 sec² (x - π/2)

the point at which the slope is zero is substituted in the second derivative to find maxima/minima

d²y/dx² = 4 sec² (x - π/2) tan (x - π/2)

if the value is negative then it is a maxima and if it is positive it is a minima.

The vertical asymptote is found by finding the values that make the function undefined

x = 0+ πn

No horizontal or oblique asymptote

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The function f(x) = 150,000(0.85)^x can be used to determine the number of tickets the Houston Ballet Company will sell over time. In this function, the 150,000 represents the initial number of tickets sold before any time has passed (when x = 0).

It serves as the starting point or baseline for the exponential decay of ticket sales over time. As x increases, the function evaluates the number of tickets sold at a particular time, where each subsequent value of x represents a subsequent unit of time (such as days, weeks, months, etc.). The term (0.85)^x represents the decay factor, as it is less than 1 (0.85). Thus, the function models a situation where ticket sales decrease exponentially over time from the initial value of 150,000.

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Ximena wants to design a test for applicants for a statistician position that solely focuses on g factors. Which of the following would it most likely test

Answer: A. Performance of general maths skills The test designed by Ximena for applicants for a statistician position that solely focuses on g factors would most likely test the performance of general maths skills.

A g factor is a concept in psychology that refers to a general intelligence factor that is widely accepted. It is often defined as a mental capacity that is responsible for a person's overall performance on intellectual tasks.

Because general math skills are an essential component of general intelligence, a test for applicants for a statistician position that solely focuses on g factors would most likely test performance of general maths skills.

Therefore, Option A - Performance of general maths skills is the correct answer.

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Answer:

the answer for this one is B

Answer:

The answer would be B.

Step-by-step explanation:

Just substitute x for 5.

For example, A is 2+x=3.

Just put 5 instead of x.

It would be 2+5=3.

But that isn't the answer because 2+5 is 7, not 3.

For B, sub the x for 5 just like we did for A.

It would usually be 3x=15

But sub the x with 5.

It would turn into 3x5=15

And that is right, because if you multiple 5 three times, it would be 15.

I hope this helps, I did my best. Have a great day!

The solution to the system of equations, using the elimination method, is given as follows:

(6,1).

The system of equations for this problem is defined as follows:

The elimination method means that we can add the two equations, thus eliminating the variable y and obtaining the value of x as follows:

3x = 18

x = 18/3

x = 6.

Then the value of y is obtained replacing the value of x into one of the two equations, as follows:

12 + 3y = 15

3y = 3

y = 1.

Hence the coordinates are:

(6,1).

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Answer:

y = 4x

Hope that helps!

Step-by-step explanation:

Answer:

x=3/5

Step-by-step explanation:

Answer:

x = 3/5

Step-by-step explanation:

Given equation,

→ 5(x + 2/5) = 5

Now the value of x will be,

→ 5(x + 2/5) = 5

→ 5x + (10/5) = 5

→ 5x + 2 = 5

→ 5x = 5 - 2

→ 5x = 3

→ [ x = 3/5 ]

Hence, the value of x is 3/5.

The probability that at least one sensor detects the pollutant is 0.9.The probability that either only S1 or only S2 detects the pollutant is 0.5.The probability that S1 does not detect the pollutant, and S2 detects the pollutant is 0.2.The probability that S2 fails to detect the pollutant is 0.3.

The event "at least one sensor detects the pollutant" refers to the scenario where either S1 or S2 (or both) detect the excessive pollution. This can be visualized as the union of the two events: S1 detecting the pollutant (event A) and S2 detecting the pollutant (event B). The probability of event A is 0.7, the probability of event B is 0.8, and the probability of both events A and B occurring together is 0.6. By applying the principle of inclusion-exclusion, we can calculate the probability of the union as P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.7 + 0.8 - 0.6 = 0.9.

The event "either only S1 or only S2 detects the pollutant" can be represented as the exclusive OR (XOR) of the two events: S1 detecting the pollutant without S2 detecting it (event A) and S2 detecting the pollutant without S1 detecting it (event B). Since the probabilities of events A and B are not explicitly given, we assume that they are equal. Let's denote this probability as p. Therefore, the probability of either event A or event B occurring is 2p. Given that the sum of probabilities of all possible outcomes is equal to 1, we have 2p + P(A ∩ B) = 1. We are also given that P(A ∩ B) = 0.6. Solving these equations simultaneously, we find that p = 0.2. Hence, the probability of the event "either only S1 or only S2 detects the pollutant" is 2p = 2 × 0.2 = 0.4.

The event "S1 does not detect, and S2 detects the pollutant" is the complement of S1 detecting the pollutant (event A) intersected with S2 detecting the pollutant (event B). The probability of event A is 1 - P(S1 detects) = 1 - 0.7 = 0.3. The probability of event B is P(S2 detects) = 0.8. The probability of both events A and B occurring together is given as P(A ∩ B) = 0.6. Therefore, the probability of the event "S1 does not detect, and S2 detects the pollutant" is P(A' ∩ B) = P(A ∩ B') = P(A) - P(A ∩ B) = 0.3 - 0.6 = 0.2.

The event "S2 fails to detect the pollutant" is the complement of S2 detecting the pollutant. Therefore, the probability of this event is 1 - P(S2 detects) = 1 - 0.8 = 0.2.

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Answer: Heyy Bestie Your answer would be 22.7%

Love ya and stay sliving ❤️

Step-by-step explanation:

The base of the ladder must be placed 3 ft from the base of the building. The total length of the ladder is 15 ft.

1. The ladder must reach 12 ft up the wall, so we need to calculate the distance from the base of the building to 12 ft.

2. The total length of the ladder is 15 ft.

3. Subtract the length of the ladder (15 ft) fromthe desired height (12 ft) to get the distance from the base of the building.

4. 12 ft - 15 ft = -3 ft

5. Since the distance cannot be negative, the base of the ladder must be placed 3 ft away from the base of the building.

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Answer:

y=5

Step-by-step explanation:

RS  +    ST   =    RT

9y+2     +     2y+3       =   60

11y         +      5         = 60

11y   =     55

Y = 5

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Answer:

The values are 13 and 1

I hope this is correct

Answer:

B. cos(x+y) + cos(x-y)= 2cosx.cosy

Step-by-step explanation:

cos(x+y) + cos(x-y)

= cosx.cosy - sinx.siny + cosx.cosy + sinx.siny

=cosx.cosy + cosx.cosy

=2cosx.cosy

Answer:

Step-by-step explanation:

The answer is D. The graph to the left of x = 1 has an open hole at the x value of 1, and the graph does not continue on past the x value of 1. Therefore, the domain of that function is all values of x that are to the left of x = 1. The hole is open because the inequality statement doesn't have a line under the inequality symbol that says we have to include it. It is, however, included at the x value of 1 on the line.

Answer:

\( (-7)^{10} \)

Step-by-step explanation:

When you multiply equal bases, add the exponents.

\( (-7)^4 \times (-7)^6 = (-7)^{4 + 6} = (-7)^{10} \)

To approximate the value of the definite integral ∫[0, 8] 3x dx using the Trapezoidal rule and Simpson's rule, we need to divide the interval [0, 8] into smaller subintervals and evaluate the function at specific points within each subinterval.

Let's calculate the approximations for different values of n:

Trapezoidal Rule:

The formula for the Trapezoidal rule is:

Approximation = h/2 * [f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(xn)]

where h is the width of each subinterval.

For n = 1:

h = (8 - 0) / n = 8

Approximation = 8/2 * [f(0) + f(8)] = 4 * [0 + 24] = 96

Simpson's Rule:

The formula for Simpson's rule is:

Approximation = h/3 * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + ... + 2f(xn-2) + 4f(xn-1) + f(xn)]

where h is the width of each subinterval.

For n = 1:

h = (8 - 0) / n = 8

Approximation = 8/3 * [f(0) + 4f(4) + f(8)] = 8/3 * [0 + 48 + 24] = 8/3 * 72 = 192

Exact Value of the Definite Integral:

The exact value of the definite integral ∫[0, 8] 3x dx can be obtained by evaluating the antiderivative F(x) of the integrand 3x and then taking the difference between F(8) and F(0).

F(x) = (3/2)\(x^2\)

Exact Value = F(8) - F(0) = (3/2)(\(8^2\)) - (3/2)(\(0^2\)) = 96

Comparing the Results:

Trapezoidal Rule Approximation: 96

Simpson's Rule Approximation: 192

Exact Value of the Definite Integral: 96

As we can see, in this case, the exact value of the definite integral matches the result obtained using the Trapezoidal rule. The approximation from Simpson's rule is double the exact value, which suggests that the choice of n might not be appropriate for Simpson's rule. To get a more accurate approximation using Simpson's rule, a smaller value of n (such as n = 2) could be used.

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The situations that can be modeled by uniform distribution include;

Option 2) is: When each discrete value is

equally likely to occur.

Option 3) is:  When each value of a continuous random variable is equally likely to occur.

Since each value has an equal chance of occurrence, thus this situation can be  modelled by Uniform distribution.

Since each value of a continuous random variable is equally likely to occur, that it follows a continuous uniform distribution.

A uniform distribution is a type of probability distribution in statistics in which all outcomes are equally likely. A deck of cards has uniform distributions because the chances of drawing a heart, a club, a diamond, or a spade are all equal. When you sample a random element, you do so according to some distribution.

The term "uniformly" refers to sampling from a uniform distribution, i.e., from a set in which drawing each element is equally likely. In statistics, it is a type of probability distribution in which every possible outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

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