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Evaluate 8 − 12 ÷ 2 + 3. 1 −1 4 5

Answers

Answer 1

Answer:

According to the order of operations, multiplication and division are performed before addition and subtraction.

... 8 - 12 ÷ 2 + 3

... = 8 - 6 + 3 . . . . . . 12÷2 = 6

... = 2 + 3 . . . . . . . . . 8-6 = 2

... = 5

Answer 2

Answer:

Answer:-13

Step-by-step explanation:

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Determine whether or not the given procedure results in a binomial distribution. For those that are not binomial, identify at least one requirement that is not satisfied.a) Treating 863 subjects with Lipitor (Atorvastatin) and recording whether there is a "yes" response when they are each asked if they experienced a headache.b) Treating 863 subjects with Lipitor (Atorvastatin) and asking each subject "How does your head feel?" c) Twenty different Senators are randomly selected from the 100 Senators in the current Congress, and each was asked whether he or she is in favor of abolishing estate taxes.d) Fifteen different Governors are randomly selected from the 50 Governors currently in office and the sex of each Governor is recorded.

The image shows a geometric representation of the function f(x) = x2 + 2x + 3 written in standard form. An algebra tile configuration. Only the Product spot is shown. 6 tiles are in the Product spot in 4 columns with 2 rows. First row: 1 + x squared, 1 + x. Second row: 1 + x, 3 +. What is this function written in vertex form? f(x) = (x + 2)2 + 3 f(x) = (x2 + 2x)2 + 3 f(x) = (x + 1)2 + 2 f(x) = (x + 3)2 + 2x

Answers

The function written in vertex form; f(x) = (x + 3)^2 + 2x. Hence, correct option is D.

What is a quadratic equation?

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

x² + 2x + 3 = 0 is a quadratic equation.

An algebra tile configuration showing Only the Product spot is shown. 6 tiles are in the Product spot in 4 columns with 2 rows.

First row: 1 + x squared, 1 + x.

Second row: 1 + x, 3 +.

Then,

The factors of the polynomial are;

(2x + 3) (x + 1)

Thus, the function written in vertex form;

f(x) = (x + 3)^2 + 2x

Hence, correct option is D.

More about the quadratic equation link is given below;

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Answer:

The factors of the polynomial are (2x + 3) (x + 1)

Step-by-step explanation:

Select the correct answer.What is the current value of a future sum of money called?
А.
current value
B.
present value
С. .
future value

Answers

Answer:

b. present money

Step-by-step explanation:

the concept that States an amount of money today is worth more than that sum amount in the future. future money is not worth much then the amount received today.

Answer is B, Present Value

Adrian shops for school clothes and spends a total of $93.42. If the local tax rate is 8%, how much was the cost without taxes?

Answers

Based on the amount that Adrian spent in total, the cost without taxes was $86.50.

The cost of the clothes was $93.42 including tax.

Assuming the original cost is x, the equation is:

Total cost = Original cost x ( 1 + tax)

Solving would give:

93.42 = x × (1 + 8%)

93.42 = 1.08x

x = 93.42 / 1.08

= $86.50

In conclusion, the cost without taxes was $86.50.

Find out more at brainly.com/question/17836987.

Answer:

85.95

Step-by-step explanation:

If the local tax was 8% and we want to know what is was without the tax then we need to do 93.42 times .92

$93.42*.92=85.9464$

Since money only goes to the hundredths place we need to round there

$85.95$

The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and the standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. Interpret the interval!

Answers

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{(\alpha)/(2)}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{(\alpha)/(2)}\frac{\sigma}√(n)$

= $110\pm z_(.01)\frac{7.1}√(50)$

= $110\pm 2.33\frac{7.1}√(50)$

First we take + sign

$110 + 2.33\frac{7.1}√(50)$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}√(50)$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

Your flight has been delayed: At Denver International Airport, 85% of recent flights have arrived on time. A sample of 14 flights is studied. Round the probabilities to at least four decimal places.(a) Find the probability that all 12 of the flights were on time.(b) Find the probability that exactly 10 of the flights were on time.(c) Find the probability that 10 or more of the flights were on time.(d) Would it be unusual for 11 or more of the flights to be on time?

Answers

Analyzing a sample of 14 flights at Denver International Airport, the probability of 10 or more flights arriving on time is 0.3783, and the probability of 11 or more flights arriving on time is 0.2142, which is not considered unusual.

(a) All 12 of the flights were on time.

(b) Exactly 10 of the flights were on time.

(d) Would it be unusual for 11 or more of the flights to be on time?

We can use the binomial probability formula to solve this problem. The binomial probability formula is:

P(k successes in n trials) = (n choose k) * $(p)^k$ * $(q)^(^n^-^k^)$

where:

n is the number of trials

k is the number of successes

p is the probability of success

q is the probability of failure

In this case, n = 14, p = 0.85, and q = 0.15.

(a) To find the probability that all 12 of the flights were on time, we can plug k = 12 into the binomial probability formula:

P(12 successes in 14 trials) = (14 choose 12) * $(0.85)^1^2$ * $(0.15)^2$

Using a calculator, we can find that this probability is approximately 0.0032.

(b) To find the probability that exactly 10 of the flights were on time, we can plug k = 10 into the binomial probability formula:

P(10 successes in 14 trials) = (14 choose 10) * $(0.85)^1^0$ * $(0.15)^4$

Using a calculator, we can find that this probability is approximately 0.1022.

(c) To find the probability that 10 or more of the flights were on time, we can add up the probabilities of 10, 11, 12, 13, and 14 successes:

P(10 or more successes) = P(10 successes) + P(11 successes) + P(12 successes) + P(13 successes) + P(14 successes)

Using a calculator, we can find that this probability is approximately 0.3783.

(d) To determine whether it would be unusual for 11 or more of the flights to be on time, we can find the probability of this event and compare it to a common threshold for unusualness, such as 0.05.

P(11 or more successes) = P(11 successes) + P(12 successes) + P(13 successes) + P(14 successes)

Using a calculator, we can find that this probability is approximately 0.2142. This probability is greater than 0.05, so it would not be considered unusual for 11 or more of the flights to be on time.

Final answer:

This problem can be approached as a binomial distribution. The probability of a particular number of flights on time is calculated using the binomial probability formula. Determining 'unusual' can be subjective but normally a probability less than 0.05 is considered unusual.

Explanation:

This problem is a binomial probability problem because we have a binary circumstance (flight is either on time or it isn't) and a fixed number of trials (14 flights). The binomial probability formula is P(X=k) = C(n, k) * (p^k) * ((1 - p)^(n - k)) where n is the number of trials, k is the number of successful trials, p is the probability of success on a single trial, and C(n, k) represents the number of combinations of n items taken k at a time.

(a) For all 12 flights on time, it seems there's a typo; there are 14 flights in the sample. We can't calculate for 12 out of 14 flights without the rest of the information.

(b) For exactly 10 flights, we use n=14, k=10, p=0.85: P(X=10) = C(14, 10) * (0.85^10) * ((1 - 0.85)^(14 - 10)).

(d) For determining whether 11 or more on-time flights is unusual, it depends on the specific context, but we could consider it unusual if the probability is less than 0.05.

Learn more about Binomial Probability here:

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a radio station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.7 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for this amount of advertising time

Answers

Answer:

z-score for 11 minutes of advertising time is $z=(-6)/(2.7)\approx -2.222$

Step-by-step explanation:

Z-scores measure the distance of any data point from the mean in units of standard deviations and are useful because they allow us to compare the relative positions of data values in different samples.

The z-score for any single data value can be found by the formula:

$z=(data \:value- \:mean)/(standard \:deviation)$

From the information given we know:

Data value = 11 minutes
Mean = 17 minutes
Standard deviation = 2.7 minutes

$z=(11-17)/(2.7) = (-6)/(2.7)\approx -2.222$

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