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3 years ago

Eight times the sum of a number and 16 is at least -28 Use the variable w for the unknown number

Mathematics

1 answer:

Genrish500 [490]3 years ago

8 0

Answer: (w+16)8 ≥ -28

*≥ means greater than or equal to. Since the value of the expression is AT LEAST -28, the number could be -28 or anything greater.

Hope this helps,

LaciaMelodii :)

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Use set-builder notation to describe the following sets: (a) {1,2,3,4,5,6,7} (b) {1, 10, 100, 1000, 10000} (c) {1,1/2, 1/3, 1/4,

Alja [10]

Answer:

A) The set builder notation is: {n | n∈Z, 1≤n≤7}.

B) The set builder notation is: $\{10^x | x=0,1,2,3,4\}$

C) The set builder notation is: $\{\frac{1}{n} | n\in z\}$

D) The set builder notation can be: $\{x\ \in R | x=x^3\ and\ x\neq 1\}$

Step-by-step explanation:

Consider the provided information,

We need to use set-builder notation to describe the following sets.

(a) {1,2,3,4,5,6,7}

Here, the number are integer starting from 1 to 7.

Thus, the set builder notation is: {n | n∈Z, 1≤n≤7}.

(b) {1, 10, 100, 1000, 10000}

The above set can be written as:

$\{1, 10, 100, 1000, 10000\}=\{10^0, 10^1, 10^2, 10^3, 10^4\}$

Thus, the set builder notation is: $\{10^x | x=0,1,2,3,4\}$

(c) {1, 1/2, 1/3, 1/4, 1/5, ...}

Here the numerator is 1 for each term but denominator is natural number.

Thus, the set builder notation is: $\{\frac{1}{n} | n\in z\}$

(d) {0}

The set builder notation can be: $\{x\ \in R | x=x^3\ and\ x\neq 1\}$

8 0

3 years ago

Explain why any of the four operations (+x +) placed between the two terms 5 and-3/(radical sign) 8 will result in an irrational

kompoz [17]

To answer this question we will have to understand the nature of $\sqrt{8}$ .

$\sqrt{8}$ can be rewritten as: $\sqrt{2\times 2\times 2} =2\sqrt{2}$ . Now, $\sqrt{2}$ is an irrational number and thus any of the four operations of addition, multiplication, subtraction or division placed anywhere between any of these terms will always result in an irrational number.

The only way irrational numbers can be made rational is by dividing or multiplying the given irrational number by the same irrational number.

8 0

2 years ago

In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alc

Fynjy0 [20]

Answer:

We conclude that the proportion of adults who totally abstain from alcohol has changed.

Step-by-step explanation:

We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"

Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in

Let p = proportion of adults who totally abstain from alcohol.

where, p = $\frac{429}{1100}$ = 0.39

So, Null Hypothesis, $H_0$ : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}

Alternate Hypothesis, $H_A$ : p $\neq$ 39% {means that the proportion of adults who totally abstain from alcohol has changed}

The test statistics that would be used here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who totally abstain from alcohol = $\frac{352}{1100}$ = 0.32

n = sample of adults surveyed = 1100

So, test statistics = $\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }$

= -4.976

The value of z test statistics is -4.976.

Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.

4 0

3 years ago

katrin2010 [14]

Answer:

230 - 151 + 180 + (43 - 12) = 290

Step-by-step explanation:

Use PEMDAS.

Evaluate the expression in the parentheses:

230 - 151 + 180 + (43 - 12)

43 - 12 = 31

230 - 151 + 180 + 31

Add and Subtract From Left to Right:

230 - 151 + 180 + 31

79 + 180 + 31

259 + 31

290

None of the given options are correct. 

6 0

3 years ago

An amount of 41,000 is borrowed for 15 years at 8.5% interest, compounded annually. If the loan is paid in full at the end of th

bazaltina [42]

Answer: $139390 must be paid back.

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = amount to be played back at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount borrowed.

From the information given,

P = 41000

r = 8.5% = 8.5/100 = 0.085

n = 1 because it was compounded once in a year.

t = 15 years

Therefore,

A = 41000(1 + 0.085/1)^1 × 15

A = 41000(1 + 0.085)^15

A = 41000(1.085)^15

A = $139390

3 0

2 years ago

Read 2 more answers