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4 years ago

Write and simplify an expression to model the following phrase: "15% off the original price of a purchase"

2 answers:

7 0

There are a couple of equations u can use

x = original price

15% off the original price of the purchase :
x - 0.15x

OR

if u get 15% off, then u are paying for 85%
0.85x

Inessa [10]4 years ago

4 0

Answer:

The required expression to the model is 0.85x.

Step-by-step explanation:

Consider the provided information.

15% off the original price of a purchase.

Let the original price of the product is x.

If you are getting an off of 15% that means that you need to pay 100%-15%=85% of the original price.

85% of the original price (x) can be written as:

$85\% \times x$

$\frac{85}{100}\times x$

$0.85\times x$

$0.85x$

Thus, the required expression to the model is 0.85x

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What is the prime factorization of 89u^3 and 11u

Alchen [17]

Answer:

Socratic app

Step-by-step explanation:

it will help you

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3 years ago

A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = probability of obtaining head.

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago

Rewrite 4 6/7 as an improper fraction.

natima [27]

Im pretty sure its 34/7

4 0

4 years ago

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Anestetic [448]

Answer:

The size of a sundae and the amount of calories it contains.

Step-by-step explanation:

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When a car travels, gas is used and it depletes. As a snowball does when it melts. And "the temperature on Tuesday" has no correlation involved at all

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3 years ago

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umka2103 [35]

I’m not sure I only answer these for the points :)

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3 years ago

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