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3 years ago

Britney is solving a quadratic equation. Her first

2 answers:

8 0

Britney used commutative property of addition and distributive property of multiplication over addition to get to step

The answer is II and IV ⇒ answer 4

Step-by-step explanation:

The quadratic equation is:

3x² - 8 - 10x = 3(2x + 3)

Britney's step is:

3x² - 10 x - 8 = 6x + 9

Lets explain the meaning of:

1. Commutative property of addition is: you can add a and b or b and a

both give the same answer

2. Distributive property of multiplication over addition is: when the

number a is multiplied by the sum of two numbers (b + c), the

first number a can be distributed to both b and c and multiplied

by each of them separately, then adding the two products ab and

ac together for the same result as multiplying the first number a by

the sum (b + c) ⇒ a(b + c) = ab + ac

3. Addition property of equality is: the property that states if you

add the same number to both sides of an equation, the sides

remain equal

4. Multiplication property of equality is: The property that states if

you multiply both sides of an equation by the same number, the

sides remain equal

Now let us explain Britney's step

∵ She change the places of the terms - 10x and - 8

- She arranges the terms of the left hand side from greatest power

of x to the numerical term

∴ She used the commutative property of addition

∵ She multiplied 3 by 2x and multiplied 3 by 3

- She multiplied the number out side the bracket by each of the

two terms in the bracket

∴ She used the distributive property of multiplication over addition

Britney used commutative property of addition and distributive property of multiplication over addition to get to step

The answer is number 4) II and IV

Learn more:

You can learn more about quadratic equation in brainly.com/question/8196933

#Learn withBrainly

KiRa [710]3 years ago

5 0

Answer:

4) II and IV

Step-by-step explanation:

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A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selecti

Andrews [41]

Answer:

(a) Null Hypothesis, $H_0$ : p = 0.50

Alternate Hypothesis, $H_A$ : p > 0.50

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed.

(e) The value of z test statistics is 0.96.

(f) The P-value is 0.1685.

(g) At 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.

(h) We conclude that the proportion of baby girls is equal to 0.50.

Step-by-step explanation:

We are given that a 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender selection, the proportion of baby girls is greater than 0.5.

Assume that sample data consists of 78 girls in 144 births.

Let p = population proportion of baby girls

(a) So, Null Hypothesis, $H_0$ : p = 0.50 {means that the proportion of baby girls is equal to 0.50}

Alternate Hypothesis, $H_A$ : p > 0.50 {means that the proportion of baby girls is greater than 0.50}

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed as in the alternative hypothesis we are concerned for proportion of baby girls that is greater than 0.50.

(e) The test statistics that would be used here One-sample z test for proportions;

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

where, $\hat p$ = sample proportion of baby girls = $\frac{78}{144}$ = 0.54

n = sample of births = 144

So, the test statistics = $\frac{0.54-0.50}{\sqrt{\frac{0.54(1-0.54)}{144} } }$

= 0.96

The value of z test statistics is 0.96.

(f) The P-value of the test statistics is given by;

P-value = P(Z > 0.96) = 1 - P(Z < 0.96)

= 1 - 0.8315 = 0.1685

(g) Now, at 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.

(h) Since our test statistic is less than the critical value of z as 0.96 < 1.282, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region (which was to the right of value of 1.282) due to which we fail to reject our null hypothesis.

Therefore, we conclude that the proportion of baby girls is equal to 0.50.

7 0

3 years ago

There are 3 red and 9 blue counters in a box. A counter is chosen and then replaced. If you did this 144 times, how many times w

anygoal [31]

If you do it 144 times that is (3+9)*12
This means that 12 times 3 red and 9 blue counters will be chosen that means that 9 blue counters will be chosen 12 times. 9*12 is 108.
This means blue counters will be chosen 108 times.
This can be checked as 108/3 would give you the number of red counters which is 36 and 108+36 is 144

3 0

3 years ago

Two parallelograms are similar. The base of the first is 12cm, and its height is 8 cm. Find the base of the second parallelogram

bearhunter [10]

Answer:

The base of the second parallelogram is 51cm.

Step-by-step explanation:

If the parallelograms are similar, it means by applying the same scale factor to all the sides in one gives you the other. The question tells us the height of the first shape is 8cm and the height of the second shape is 34cm. That means the scale factor is:

$\frac{34}{8}=4.25$

Apply this same scale factor to the base of the first shape to find the base of the second:

$12 \times 4.25=51$

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3 years ago

Triangle ABC = Triangle ADF, AD = 18, BC = 17, DF= [?]

snow_lady [41]

The value of the length DF is 17

<h3>How to determine the length DF?</h3>

The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.

So, we have:

AB = AD

AC = A F

BC = DF

Given that BC = 17;

The equation BC = DF becomes

17 = DF

Rewrite as:

DF = 17

Hence, the value of the length DF is 17

Read more about congruent triangles at:

brainly.com/question/1675117

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the answer is A couse divide all 5

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