In a certain triangle, one angle has a measure of 42° and another angle has a measure of 96°. If the triangle is isosceles, then which of the following could be the measure of the third angle?
A.
60°
B.
42°
C.
96°
D.
69°

a. The probability that a randomly selected American worker does not take a single nap during a month is approximately 0.0183, or 1.83%.

b. The probability that the total number of naps for two randomly selected American workers during a month is zero is approximately 0.0336, or 3.36%.

In the first step, the probability of a randomly selected American worker not taking a single nap during a month is calculated. Since the mean number of naps per month is four, the probability of not taking a nap can be found by using the Poisson distribution with a mean of four.

The formula for the Poisson distribution is P(x; μ) = (e−μ * μx) / x!, where x is the number of naps and μ is the mean. Plugging in x = 0 and μ = 4 into the formula, we get P(0; 4) = \((e^(^-^4^) * 4^0) / 0!\) ≈ 0.0183.

In the second step, the probability of the total number of naps for two randomly selected American workers being zero is calculated. This can be done by finding the probability of each worker not taking a nap and then multiplying those probabilities together. Since the probability of a worker not taking a nap is 0.0183, the probability of both workers not taking a nap is 0.0183 * 0.0183 ≈ 0.0336.

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Step-by-step explanation:

Answer:

do you just add and multiply all of them?

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

The center is at (3, -5) and the radius is 3

Answer:

The first one is the correct answer!

Step-by-step explanation:

A similarity statement is a statement used in geometry to prove exactly why two shapes have the same shape and are in proportion.

In the second year, the APR (Annual Percentage Rate) will increase quite substantially.

What is Introductory APR?

a temporary promotional interest rate that is lower than the card's standard APR, occasionally as low as 0% APR. Purchases, balance transfers, or both may be covered. After the introductory period has been over, your balance will be subject to the standard APR.

Any outstanding balances will begin to accrue interest once the promotional period is expired. Not just new charges, but also any amounts you charged or transferred to the credit card within the promotional APR period.

Your APR will transition from your promotional interest rate to a standard variable APR rate decided by your lender once it expires.

So, in this case, Trina's credit card has an introductory APR of 7.99-8.99%, but from the second year onwards the APR will increase.

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Following the conclusion of the promotional period, interest will start to be charged on any unpaid balances. Not only fresh charges, but also any sums you added to the credit card or transferred within the promotional APR period.

When the promotional period is up, your APR will change from the promotional interest rate to a standard variable APR rate chosen by your lender.

Thus, Trina's credit card in this instance has an introductory APR of 7.99–8.99%; but, in the second year, the APR will rise.

Answer:

2/3

Step-by-step explanation:

Bag A: WWB

Bag B: B

The investment of $2,000 at 7% compound interest will be worth $2,489.31 at the end of 3 years.

To find the value of an investment at compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the principal (initial investment), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period (in years).

In this case, we have P = $2,000, r = 0.07 (since the interest rate is given as 7%), n = 1 (since the compounding is not specified), and t = 3. Plugging these values into the formula, we get:

A = 2000(1 + 0.07/1)^(1*3) = $2,489.31 (rounded to the nearest cent)

Therefore, the investment of $2,000 at 7% compound interest will be worth $2,489.31 at the end of 3 years.

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Answer:

y = 2x-3

Explanation:

By definition, two lines are parallel if they have the same slope.

Given the equation for a line:

Comparing the given line with the slope-intercept form of a line:

Thus, we want to find the equation of the line with the following properties:

• Slope: m = 2

• Point: (x1,y1)=(2,1)

In order to do this, we employ the use of the point-slope form of the equation of the line:

We then simplify:

The equation of the parallel line is y=2x-3.

The main answer to the question is: None of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative. The explanation to support the answer is given below:

Normal distribution is a statistical distribution that depicts how values are dispersed in a dataset. It is also known as Gaussian distribution or bell curve because of its bell-shaped pattern. It is described by two parameters, i.e., mean and standard deviation.The mean of a normal distribution specifies the location of the center of the distribution. The variance of a normal distribution indicates the amount of variation from the mean. Variance is always positive, no matter whether the mean is positive or negative.

Therefore, if the mean of a normal distribution is negative, the variance must not be negative.Hence, none of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative.

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5 km = 5000 meters

66 minutes = 3960 seconds

Meters per second = 5000/3960 = 1.26

The answer is A.1.26

To determine if the proportion of successes with cream A is different from cream B in treating warts, the researcher conducted a comparative study. To conduct this test, the researcher will define a level of significance (e.g., 0.05) to determine the threshold for statistical significance. If the p-value (the probability of observing a difference as extreme as the one observed, assuming no true difference) is less than the chosen significance level, it indicates a significant difference between the two creams.

Here's a step-by-step explanation:
1. Selecting the sample: The researcher identified individuals who had two warts. These individuals will be included in the study.
2. Assigning treatments: One wart was treated with cream A, while the other wart was treated with cream B. This ensures that each individual serves as their own control, eliminating potential confounding factors.
3. Applying the creams: The researcher applied cream A on one wart and cream B on the other wart according to the assigned treatments.
4. Observing the results: The researcher will monitor the progress of the warts over a specified period of time. They will record the number of successful outcomes for each cream.
5. Analyzing the data: Using statistical methods, the researcher will compare the proportion of successes with cream A and cream B. This analysis will determine if there is a significant difference between the two creams.
6. Testing for significance: The researcher will perform a significance test to determine if the observed difference in success rates between the two creams is statistically significant. This test will provide evidence as to whether the proportion of successes with cream A is different from cream B.

In conclusion, the researcher will analyze data collected from the study to determine if there is a significant difference in the effectiveness of cream A and cream B in treating warts. The significance test will provide the main answer as to whether the proportion of successes with cream A is different from cream B at the chosen level of significance. This analysis will help evaluate the effectiveness of the new cream in comparison to the standard treatment.

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Answer:

0.64 is a decimal and 64/100 or 64% is the percentage for 64/100.

Step-by-step explanation:

Answer:

64/100 = 0.64

Step-by-step explanation:

64/100=0.64

(i don't know how to explain it)

To find the number when 28 is the geometric mean of 13 and that number, we'll use the formula for the geometric mean: √(a * b) = GM, where a and b are the two numbers, and GM is the geometric mean. In this case, a = 13, GM = 28.

Step 1: Substitute the given values into the formula:
√(13 * b) = 28

Step 2: Square both sides to get rid of the square root:
(√(13 * b))^2 = 28^2
13 * b = 784

Step 3: Divide both sides by 13 to isolate b:
b = 784 / 13
b ≈ 60.31

So, the other number is approximately 60.31 when rounded to the nearest hundredth. In summary, 28 is the geometric mean of 13 and 60.31, as √(13 * 60.31) ≈ 28.

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Let input be x

\(\\ \bull\tt\dashrightarrow 2(x+2)-3=21\)

\(\\ \bull\tt\dashrightarrow 2(x+2)=21+3\)

\(\\ \bull\tt\dashrightarrow 2(x+2)=24\)

\(\\ \bull\tt\dashrightarrow x+2=\dfrac{24}{2}\)

\(\\ \bull\tt\dashrightarrow x+2=12\)

\(\\ \bull\tt\dashrightarrow x=12-2\)

\(\\ \bull\tt\dashrightarrow x=10\)

Answer:

• let the number be x:

\(• { \tt{ \dashrightarrow \: 2(x + 2)}}\)

\(• \dashrightarrow{ \tt{2x + 1}}\)

\(• \dashrightarrow{ \tt{ 2x + 1 = 21}} \\ \\ { \tt{2x = 20}} \\ \\ • \: { \boxed{ \tt{output : \: \: x = 10 \: \: }}}\)

The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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The function that represents the graph is the second option;

f(x) = 5·sin(3·θ)

A function assigns or maps the values in the set of input variables unto the set of the output variables.

The general form of a sinusoidal function is; y = A·sin(B·(x - C)) + D

Where;

A = The amplitude

The period, T = 2·π/B

D = The vertical shift of the graph of the function

The peak and midline coordinates of the graph are (π/6, 5), and (π/3, 0)

The amplitude of the graph is therefore; 5 - 0 = 5

The period of the graph is the distance between successive peaks, which can be found as follows;

Period, T = 5·π/6 - π/6 = 4·π/6 = 2·π/3

Therefore; T = 2·π/3 = 2·π/B

B = 3

The point (0, 0), on the graph indicates that when the function is a sine function, and sin(0) = 0, the horizontal shift is; C = 0

The location of the midline on x-axis indicates that the vertical shift of the function is; D = 0

The function is therefore;

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Answer:

answer is d

Step-by-step explanation:

just did it

Answer:

its D

Step-by-step explanation:

Answer:

\(f^{-1}(x)=2^x+3\)

Step-by-step explanation:

Given:

\(y=\log_2(x-3)\)

To find the inverse of the given function, make x the subject.

\(\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b\)

\(\implies 2^y=x-3\)

Add 3 to both sides:

\(\implies x=2^y+3\)

Swap x for \(f^{-1}(x)\) and y for x:

\(\implies f^{-1}(x)=2^x+3\)

Answer:

8(x+3)

Explanation:

"The product of 8 and" means 8 is going to be multiplied times another quantity. "...the sum of a number x and 3" means that 8 is going to be multiplied times (x+3).

This is represented by 8×(x+3), which simplifies to 8(x+3).

The weight that is left when 18759 grams of bricks are removed is 3.241 kg

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

Pile of bricks = 22 kg

The weight removed from the pile = 18759 grams

The remaining weight can be calculated using the following subtraction equation

Remaining weight = Pile of bricks - The weight removed from the pile

Substitute the known values in the above equation, so, we have the following representation

Remaining weight = 22 kg - 18759 grams

Convert grams to kg

This gives

Remaining weight = 22 kg - 18.759 kg

Evaluate the difference in the above equation

Remaining weight = 3.241 kg

Hence, the remaining weight is 3.241 kg

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It will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

To find out how long it will take, we can use the formula for compound interest:

A = P(1 + r)^t

Where A is the final amount, P is the principal amount, r is the interest rate, and t is the number of years.

In this case, we want to find out how long it will take for $100 to reach $500 when it grows at 10 percent per year. So we can plug in the values and solve for t:

500 = 100(1 + 0.10)^t

5 = (1.10)^t

Taking the natural logarithm of both sides:

ln(5) = t ln(1.10)

t = ln(5) / ln(1.10)

t = 14.87 years

So it will take 14.87 years for $100 to reach $500 when it grows at 10 percent per year.

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a) Domain of the function 0 ≤ d ≤ 21 (0,21)

Range of the function 0 ≤ B ≤ 400 (0,400)

b) Estimate to the nearest hundreds for B(0) is 200

c) Ebony's bank balance first reached $0 on day 12 can be shown as functional notation as - we can add the number 12 below the first point reaching the horizontal axis.

d) Ebony's bank balance remained $0 from day 12 through day 15. The segment which represents the information is - segment 4.

(a) Domain: the collection of values used as input or arguments for the function.

Range: Either the codomain or the function's image is mentioned.

For three weeks, Ebony's bank account was active (21 days). then the domain is 0 ≤ d ≤ 21 (here 'd' refers to day)

Her highest balance was $400 and her lowest was zero, so the range is  0 ≤ B ≤ 400. (Here, 'B' refers to Balance)

(b) When d = 0, the graph's highest point, which represents her highest balance of $400, is displayed. This means that on the first day, the point will probably only be half as high as the highest point. Therefore, we may calculate the nearest hundred for B(0) is about equal to 0.5 * 400 = 200.

(c) In other words, the line of the function first touches the horizontal axis at d = 12; the balance first reached $0 on day 12. Below the first point that reaches the horizontal axis, we can add the number 12.

(d) From day 12 through day 15, the bank balance stayed at zero dollars; this is shown by the vertical axis of segment 4 of graph 4.

COMPLETE QUESTION:

The amount in Ebony's bank account B(d)  is a function of the number of days(d) since she opened the account. The graph shows segments representing her day-by-day bank balance. Although there are no labeled tick marks on the graph, you can answer the questions by using the additional given information as well as your general knowledge of graphs of functions. (Score for Question 1;_ of 4 points) 1. Ebony kept her bank account open for only 3 weeks, and the graph shows the entire 3 weeks. During that time, her greatest balance was $400.

(a) Give the domain and range of the function. 0 ≤ d ≤ 21  domain; 0 ≤ B ≤ 400  

(b) Give an estimate to the nearest hundreds for B(0). Explain how you determined your estimate and tell what B(0) means in the context of the situation.

(c) Ebony's bank balance first reached $0 on Day 12. How would you show that information in function notation? B(12) = 0  

(d) Ebony's bank balance remained at $0 from Day 12 through Day 15. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain how you know. 4th segment

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Since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

If every term of the sequence is either greater than or equal to (≥) some number M or less than or equal to (≤) some number N (finite numbers), then the sequence is said to be bounded.

Otherwise, the sequence is said to be unbounded. And, if a sequence has a convergent subsequence, then the sequence is called bounded.

Let’s look at the example to answer the question.

Example of an unbounded sequence that has a convergent subsequence:

Let {an} = 1, 2, 3, 4, 5, 6, 7, …It is an unbounded sequence since there is no number that can be defined as M or N, that will make every term of the sequence less than or equal to (≤) or greater than or equal to (≥) this number (M or N).

However, {an} = 1, 2, 3, 4, 5, 6, 7, … has a convergent subsequence which is {an} = 1, 2, 3, 4, 5, 6, 7, … itself.

And, since the subsequence {an} = 1, 2, 3, 4, 5, 6, 7, … is convergent to the limit ∞, thus the original sequence {an} = 1, 2, 3, 4, 5, 6, 7, … must also be unbounded.

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Answer:

Step-by-step explanation:

 y^2 - 3y + 12

It has 3 terms (y^2) and (-3y) and (12)...therefore, it is a trinomial.

The degree of a polynomial with 1 variable is the highest exponent...so it has a degree of 2. But if it had more then 1 variable, it would be different.

answer is : trinomial with a degree of 2

The polynomial y² – 3y + 12 is trinomial with a degree of 2. Therefore, option C is the correct answer.

The given polynomial is y² – 3y + 12.

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Here, the polynomial y² – 3y + 12 is trinomial with a degree of 2

Therefore, option C is the correct answer.

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Answer:

x = 6, -6

Step-by-step explanation:

-x^2 = -36

~Take the square root of both sides

x = ±6

Best of Luck!

Answer:

x=4

Step-by-step explanation:

a) The distribution is roughly symmetric and bimodal. b) The histogram has two modes, which may be due to the different shoe size scales used for men and women in the U.S. but not in Europe.

The histogram of European shoe sizes of 269 male and female college students converted from their reported US shoe sizes is not visible based on the information provided, but the questions are clear.

a) The shape of the distribution is not visible, but it is mentioned that it is "roughly symmetric and bimodal".

b) There are two modes in the histogram. This could be because shoe sizes in the United States are defined differently for men and women, but not in Europe. As a result, the histogram of the distribution of European shoe sizes for both men and women may show two distinct peaks.

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