Given are the first three terms of a sequence that is either arithmetic or geometric. If the
sequence is arithmetic, find the common difference. If the sequence is geometric, find
the common ratio.
4, 8, 16

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The mean greater than median when skewed right, because the median is not affected by having much larger values.

We know that the skewness is nothing but the measure of the asymmetry of a distribution.  A distribution can have right skewness (also called positive skewness), left skewness (or negative), or zero skewness. A distribution is said to be asymmetrical when its left and right side are not mirror images.

As we know, in a perfectly symmetrical distribution, the mean and the median are the same.

In case of right skewness, the mode is often less than the median, which is less than the mean. It's because the median is not affected by having much larger values but there would be increase in the mean.

For example {1, 2, 3, 4, 5} both the mean and the median equal 3  

But in case of {1, 2, 3, 4, 50} the median is still 3 and the mean is 12

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Answer: C

Step-by-step explanation:

For our unknown value x, the opposite side = 10 and the adjacent side = 18, using this information you can use SOH CAH TOA.

TOA refers to opposite over adjacent, which would be

tan x = 10/18.

Hope this helps!

Answer:12

Step-by-step explanation:

Given

The function is given by

\(F(t)=t^2-8t+12\)

at t=0

\(F(0)=0^2-8\times 0+12=12\)

Graph of this function is given below

The sine of 0 radians is 0.

In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse of a right-angled triangle.

When the angle is 0 degrees (or 0 radians), the opposite side has a length of 0, and thus the ratio is also 0. Therefore, the sine of 0 radians is 0.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 0 is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

Note that, the sine function maps an angle to a value which is between -1 and 1, with a periodic nature, meaning that the values repeat in a cycle as the angle increases.

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Answer:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

Step-by-step explanation:

we want to integrate the following integration:

\( \displaystyle \int {x}^{2} \cdot {e}^{x} dx\)

notice that, the integrand is in the multiplication of two different function in that case we can consider integration by parts given by:

\( \rm \displaystyle \int u \cdot v \: dx = u \int vdx - \int u' \left( \int v dx \right)dx\)

where u' can be defined by the differentiation of u

now we have to choose our u and v

which can be chosen by using the guideline:ILATE Inverse trig. , Logarithm, Algebraic expression, Trigonometry, Exponent.

since x comes first thus,

\( \displaystyle u = {x}^{2} \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u,we acquire:

\( \displaystyle u' = 2x\)

altogether we get:

\( \rm \displaystyle \int {x}^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int 2x \left( \int {e}^{x} dx \right)dx\)

by figuring out the parentheses integration

we get:

\( \rm \displaystyle \int x^2 \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \int2x \cdot {e}^{x} dx\)

now we again have integration of two different functions so let's choose our u and v once again which can be done using the guideline

\( \displaystyle u = 2x \quad\text{and} \quad v = {e}^{x} \)

by figuring out the defferentiation of u

we acquire:

\( \displaystyle \: u' = 2\)

altogether we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x \int{e}^{x} dx- \int2 \left( \int{e}^{x}dx \right) dx \right)\)

by solving parentheses we get

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} \int {e}^{x} dx - \left( 2x {e}^{x} - 2 e^{x} dx \right)\)

by figuring out the integral we get:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- \left( 2x {e}^{x} - 2 e^{x} \right)\)

remove parentheses:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} \)

at last we of course have to add constant of integration:

\( \rm \displaystyle \int x ^{2} \cdot {e}^{x} \: dx = {x}^{2} {e}^{x}- 2x {e}^{x} + 2 e^{x} + \rm C\)

and we are done!

Answer:

\(\displaystyle \int {x^2e^x} \, dx = e^x(x^2 - 2x + 2) + C\)

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)

Basic Power Rule:

Integration

Integration by Parts:                                                                                               \(\displaystyle \int {u} \, dv = uv - \int {v} \, du\)

Step-by-step explanation:

*Note:

The answer below me is correct, but there is a simpler method of obtaining the answer.

Step 1: Define

Identify

\(\displaystyle \int {x^2e^x} \, dx\)

Step 2: Integrate

Use tabular integration.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer:

6

Step-by-step explanation:

Hayden uses 3 cups of water to make a broth for soup

He uses 3 times as many cups of milk

Therefore the number of broth ounces made by Hayden can be calculated as follows

= 3+3

= 6

I assume you mean the product of mixed numbers,

3 1/2 × 3 1/2

If we write this as

(3 + 1/2) × (3 + 1/2) = (3 + 1/2)²

we can use the identity

(a + b)² = a² + 2ab + b²

so that

3 1/2 × 3 1/2 = 3² + (2 × 3 × 1/2) + (1/2)²

3 1/2 × 3 1/2 = 9 + 3 + 1/4

3 1/2 × 3 1/2 = 12 1/4

Alternatively, we can first write 3 1/2 as a mixed number:

3 + 1/2 = 6/2 + 1/2 = (6 + 1)/2 = 7/2

Then

3 1/2 × 3 1/2 = 7/2 × 7/2 = (7 × 7) / (2 × 2) = 49/4

and

49/4 = (48 + 1)/4 = ((4 × 12) + 1)/4 = 12 + 1/4

The area of the figure shown in the question diagram is 207 cm².

Area is the region bounded by a plane shape.

To calculate the area of the figure below, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

2996

Step-by-step explanation:

5x + 4x = 6741

9x = 6741

x = 6741/9

x = 749

to get the no votes,

4x i.e 4*749

=>  4*749 = 2996

hope this helps :)

Answer:

2996

Step-by-step explanation:

Answer:

1.40

Step-by-step explanation:

yea

Answer:

below

Step-by-step explanation:

3 lbs  X  .454 kg/lbs = 1.362 =~ 1.4 kg

This is a logical statement, of the form

where p is the statement "the test is today" and q is the statement "the party is tonight". The DeMorgan's Law indicates that:

Therefore the equivalent statement is " the test is not today and the party is not tonight".

Answer:

\( \frac{2}{35} \)

Step-by-step explanation:

\( \frac{ \binom{1}{1} }{ \binom{7}{1} } \times \frac{ \binom{2}{1} }{ \binom{5}{1} } = \frac{2}{35} \)

of course it can easily be simplified, but the logic is shown here!

first you have to draw 1 checker marble out of the seven marbles.

at the top is the ideal draw where you draw the one checker marble out of that one, and the bottom is all the options to draw 1 marble out of the 7 marbles.

3 is the prime number.

again, at the top you draw obe 3 out of the two, and the bottom is all the options to draw one out of the five numbers.

First, we have to acknowledge that the marble draw's outcome is independent from the card being drawn.  Because of this independence, we can multiply the two individual probabilities.

For the marble, there are 7 outcomes (7 marbles we could draw) and only 1 of which is checkered  We have a 1/7 chance of picking a checkered marble.

For the cards, there are 5 possible outcomes (5 cards we could drawa) and 2 are prime (there are two "3" cards).  We have a 2/5 chance of drawing a card with a prime number.

For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:

   1/7 · 2/5 = 2/35

We have a 2/35 (about 5.714%) chance of drawing a checkered marble and then picking a card with a prime number.

Answer:

y = 5x - 3, so M = 5 and C = -3.

The account increases in value by 1% every quarter, which is equivalent to 1/4% every month.

Savings interest is calculated on a daily basis and deposited into the account on the first day of the next quarter. The interest rate will depend on the balance in the account. Now it's between 3% and 3.5%.

To find the increase in value for an account with an APR of 4% and quarterly compounding, we'll first need to convert the APR to a quarterly interest rate.
1. Divide the APR by the number of compounding periods in a year: 4% / 4 = 1%.
2. The account increases in value by 1% every quarter.

Your answer: a. 1%

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The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.

We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it

=> x = 3 + 2 + 3456

Substracts 45 from above expression

=> x = 3 + 2 + 3456 - 45

Dividing the above expression of x by 20

=>

\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)

\(= \frac{3416}{20}\)

= 17.8

Hence, required simplify value is 17.8.

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There is insufficient evidence to conclude that those with the high incomes are the ones that have the more credit scores.

We have the bar x = 705.9

The value of n = 34

mean = 724 . 1

standard deviation = 83.4

the level of significance = 5 percent level

The Hypothesis formulation

The null hypothesis H0 = u 705.9

alternative hypothesis = H1 u > 705.9

The t test is given as x - u / s /√n

= (724.1 - 705.9) / (83.4 / √34)

= 1.2725

The degree of freedom = 34 - 1 = 33

The test that we have here is a right tailed test

The p value for the test is given as probability of p (t33 > t)

= 0.1064

From the solution that we have here, we can see that the p value that has been calculated is greater than the level of significance.

Given that this is the case, the decision rule would be for us not to reject the null hypothesis.

There is insufficient evidence to the claim that the high income persons have the greater credit scores.

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Answer:

Step-by-step explanation:

The system of equations is:

x^2 = y

x^2 + y^2 = 9

Substituting the first equation into the second, we get:

x^2 + (x^2)^2 = 9

x^4 + x^2 - 9 = 0

Using the quadratic formula, we can solve for x^2:

x^2 = (-1 ± sqrt(37))/2

Taking the positive root, we get:

x^2 = (-1 + sqrt(37))/2

Substituting this back into the first equation, we get:

y = (-1 + sqrt(37))/2

So the solution is the point (sqrt((-1 + sqrt(37))/2), (-1 + sqrt(37))/2)

Looking at the graphs, only graph (d) contains the point (sqrt((-1 + sqrt(37))/2), (-1 + sqrt(37))/2), so the answer is (d).

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QUESTION: Which graph shows the system (x^2 = y =2 x^2 + y^2 = 9

    |     /|

    |    / |

    |   /  |

    |  /   |

    | /    |

    |/     |

_____|______|______

    |

    |

    |

    |

    |

    |

Answer:

About .9332

Step-by-step

This tells us that the probability that a z value is less than or equal to 1.5 is about .9332. Thus, the shaded region is about 93.32% of the entire curve. Let's try another example.

Option C. which corresponds to the probability of approximately 0.0771 that there will be 8 occurrences within a period of ten minutes.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

This problem follows a Poisson distribution, where the mean and variance of the distribution are equal to λ. Here, λ = 5, and we need to find the probability of having 8 occurrences in 10 minutes. The probability mass function of Poisson distribution is:

P(X = k) = (e⁽⁻λ⁾ * λᵏ) / k!

Substituting the given values, we get:

P(X = 8) = (e⁽⁻⁵⁾ * 5⁸) / 8!

P(X = 8) ≈ 0.0771

Therefore, the probability that there are 8 occurrences in ten minutes is approximately 0.0771, which corresponds to option C.

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A) If the triangle is a right triangle

The first step of an indirect proof of the phrase:

If the triangle is a right triangle. The correct statement is A.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

The Conditional statement:

If one of the angles of a triangle equals 90, then the triangle is classified as a right triangle.

The first step of an indirect proof of the phrase:

If the triangle is a right triangle.

That means, the triangle have an angle equals to 90°.

Therefore, the correct statement : If the triangle is a right triangle.

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Answer:

60

Step-by-step explanation:

5(a + 2) + 6(2a - 3)

Expand the brackets.

5a + 10 + 12a - 18

Add or subtract like terms.

17a - 8

Plug a = 4 and evaluate.

17(4) - 8

68 - 8

= 60

The given statement "Establishing evaluation criteria often gives rise to subjectivity issues during the systems development life cycle (SDLC) process." is True. Because in SDLC it  processes as helps to assess the effectiveness and quality of the system being developed.

There can be subjectivity issues that arise during this process as different stakeholders may have different perspectives, preferences, and priorities. For example, what one stakeholder considers to be a critical feature may not be as important to another stakeholder.

Additionally, the criteria themselves may be subjective, such as user experience or ease of use. It is important for the development team to consider these subjectivity issues and engage in open communication with stakeholders to ensure that the evaluation criteria are well-defined, consistent, and aligned with the system's goals and objectives.

This can help to minimize subjectivity issues and improve the overall quality of the system. So, the given statement is True.

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Answer:

Step-by-step explanation:

According to definition of the function, each input must have exactly one output.

One of the given relationships - T-shirt prices reveals two outputs.

All the rest show one-to-one relationship.

The domain and range of the function shown on the graph are (a) Domain is x ≥ 0, and range is y ≥ 0

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

The graph

On the graph, we can see that the line is a straight line

This means that the graph is a linear function

However, the function only covers the positive axes

This means that

Domain is x ≥ 0, and range is y ≥ 0

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There is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

To find the probability that a group of 10 persons will exceed the load limit of the elevator, we need to calculate the probability that the total weight of the group exceeds 2000 lb.

Since the weights of the people are normally distributed with a mean of 185 lb and a standard deviation of 22 lb, we can use the properties of the normal distribution to solve this problem.

First, we need to calculate the mean and standard deviation of the total weight of the group. The mean of the total weight is simply the mean weight of a person multiplied by the number of persons, which is 185 lb * 10 = 1850 lb.

The standard deviation of the total weight is calculated by taking the square root of the sum of the variances of each person's weight. Since the weights are independent, the variance of the total weight is equal to the sum of the variances of each person's weight. So, the standard deviation of the total weight is sqrt(10) * 22 lb ≈ 69.296 lb.

Next, we can use the normal distribution to calculate the probability that the total weight exceeds 2000 lb. We standardize the value using the formula z = (x - mean) / standard deviation, where x is the threshold value of 2000 lb.

Calculating the z-score: z = (2000 - 1850) / 69.296 ≈ 1.81

Finally, we look up the probability corresponding to this z-score in the standard normal distribution table or use a calculator to find the area under the curve to the right of the z-score. The probability that the group of 10 persons will exceed the load limit of the elevator is approximately 0.0351, or 3.51%.

Therefore, there is a 3.51% probability that a group of 10 persons will exceed the load limit of the elevator.

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Answer:

0.875

Step-by-step explanation:

The student's mark can be expressed as 65%.

To express the student's mark as a percentage, you need to divide the number of marks obtained by the possible marks and multiply by 100.

In this case, the student got 78 marks out of a possible 120.

Percentage = (Marks Obtained / Possible Marks) * 100

Percentage = (78 / 120) x 100

Percentage = 0.65 x 100

Percentage = 65%

Therefore, the student's mark can be expressed as 65%.

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