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3 years ago

Simplify 3{[3(9 – 2)] + [7(8 – 1)]}

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

6 0

Answer:

210

Step-by-step explanation:

Use the order of operations pemdas( parenthesis, exponent, multiply, divide, add, subtract)

first do everything within the parenthesis.

3 ( ( 3 (9-2) ) + ( 7 (8-1) ) )

3 ( ( 3 (7) + ( 7 ( 7 ) ) )

3 ( ( (21) + (49) ) ) )

3 ( ( 21 + 49 ) )

3 ( 70 )

3 (70) = 70 + 70 + 70 = 140 + 70 = 210

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Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the l

yawa3891 [41]

Well, it goes 5 inches per second so after 4 seconds it is 4 times 5 =20 inches under the surface, add that to 5 feet and you get 6 ft and 8 inches

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3 years ago

Complete this equation 2 2/3 +4/5= 40/? + 12/? = ?/?

OlgaM077 [116]

Answer:(7/8 - 4/5)^2 = 9

1600

= 0.005625

Step-by-step explanation:

Subtract: 7

- 4

= 7 · 5

8 · 5

- 4 · 8

5 · 8

= 35

- 32

= 35 - 32

= 3

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(8, 5) = 40. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 5 = 40. In the next intermediate step the fraction result cannot be further simplified by cancelling.

In words - seven eighths minus four fifths = three fortieths.

Exponentiation: the result of step No. 1 ^ 2 = (3

) ^ 2 = 32

402

= 9

1600

In words - three fortieths squared = nine one-thousand six-hundredths.

6 0

3 years ago

2. The National Safety Council routinely analyzes the benefit of seat belt use on driver safety. Their data showed that among 28

JulijaS [17]

Answer:

We conclude that there is difference in the proportion of deaths between the 2 groups.

Step-by-step explanation:

We are given that among 2823 drivers not wearing seat belts, 31 died as a result of injuries, and among 7765 drivers wearing seat belts 16 were killed.

Let $p_1$ = proportion of deaths when drivers were not wearing seat belts.

$p_2$ = proportion of deaths when drivers were wearing seat belts.

So, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the proportion of deaths between the 2 groups}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is difference in the proportion of deaths between the 2 groups}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of deaths when drivers were not wearing seat belts = $\frac{31}{2823}$ = 0.011

$\hat p_2$ = sample proportion of deaths when drivers were wearing seat belts = $\frac{16}{7765}$ = 0.002

$n_1$ = sample of drivers not wearing seat belts = 2823

$n_2$ = sample of drivers wearing seat belts = 7765

So, the test statistics = $\frac{(0.011-0.002)-(0)}{\sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} } }$

= 4.438

The value of z test statistics is 4.438.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic 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 there is difference in the proportion of deaths between the 2 groups.

Also, Margin of error (E) = $1.96 \times \sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} }$

= $1.96 \times \sqrt{\frac{0.011(1-0.011)}{2823}+\frac{0.002(1-0.002)}{7765} }$

= 0.00397

5 0

3 years ago

What is the total amount for an investment of $1600 invested at 4.25% for 20 years and compounded continuously?

galina1969 [7]

Answer:

$3743.43

Step-by-step explanation:

The amount is given by the formula ...

A = Pe^(rt)

where P is the principal, r is the annual rate compounded continuously, and t is the number of years. Filling in the values, we get ...

A = $1600·e^(0.0425·20) = $1600·e^0.85

≈ $1600·2.33964685 ≈ $3743.43

The amount in the account will be $3743.43.

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3 years ago

Find the inequality represented by the line. Need help immediately. Explain if you can

Debora [2.8K]

Answer:

ok fine 1.3x+4y<10

Step-by-step explanation:

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3 years ago

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