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3 years ago

Find the product (3a4+4)2

Mathematics

2 answers:

geniusboy [140]3 years ago

5 0

Answer:

The product is 9a^8+24a^4+16

Step-by-step explanation:

Since we have given that (3a^4+4)^2

As we know that (a+b)^2=a^2+2ab+b^2

So, it becomes, (3a^4 + 4)^2=(3a^4)^2+2\times 3a^4\times 4+(4)^2\\\\=9a^8+24a^4+16

Hence, the product is 9a^8+24a^4+16

asambeis [7]3 years ago

4 0

The result is

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The reason is the following:

The problem is an example of a notable product: "the sum multiplied by the diference is equal to the difference of squares", that is to say:

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By applying this to our question, we obtain that:

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Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pound

cluponka [151]

Answer:

The test statistic value using the VLBW babies as group 1 is z=-2.76±0.01 and the P-value for the test (±0.0001) is 0.0030.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

Then, the null and alternative hypothesis are:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0$

The significance level is 0.05.

The sample 1 (VLBW group), of size n1=244 has a proportion of p1=0.77049.

$p_1=X_1/n_1=188/244=0.77049$

The sample 2 (control group), of size n2=247 has a proportion of p2=0.79757.

$p_2=X_2/n_2=197/247=0.79757$

The difference between proportions is (p1-p2)=-0.02708.

$p_d=p_1-p_2=0.77049-0.79757=-0.02708$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{188+197}{244+247}=\dfrac{385}{491}=0.988$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.988*0.012}{244}+\dfrac{0.988*0.012}{247}}\\\\\\s_{p1-p2}=\sqrt{0.00005+0.00005}=\sqrt{0.0001}=0.0098$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.02708-0}{0.0098}=\dfrac{-0.02708}{0.0098}=-2.76$

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=P(t$

As the P-value (0.0030) is smaller than the significance level (0.05), the effect issignificant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of persons with normal birth weight that graduates from high school is significantly greater than the proportion of persons with very low birth weight that graduates from high school.

3 0

3 years ago

Savanna works as a sales rep and receives $23.80 for every $140 she sells. What is her rate of commission?

REY [17]

This is actually quiet easy!

(23.80/140) x 100 = (0.17) x 100 = 17%

That's how you do it! Hope this helps!

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3 years ago

Each beehive on Larson's Honey Farm usually produces 85 pounds of honey per year. About how many pounds of honey will 1000 hives

never [62]

85000 pounds of honey

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3 years ago