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3 years ago

Using the ratio of perfect squares method, what is the square root of 96 rounded to the nearest hundredth?

1 answer:

4 0

When the square root is a whole number, it is called a perfect square. For instance, 25 is a perfect square whose square root is 5.

We have a list of perfect squares that we can generate by squaring the natural numbers, e.g., $1^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25$ . Now, there are two perfect squares in particular that we want to look at: $9^2=81$ and $10^2=100$ .

Why? Well, 96 is between 81 and 100, therefore, it's square root is between 9 and 10. In fact, since 96 is a lot closer to 100, its square root is closer to 10.

If we want to approximate it, we first guess. Knowing its square root is closer to 10, we can guess that it is 9.6. Let's check the square of 9.6.
$9.6^2=9.6 \times 9.6 = 92.16\\92.16\ \textless \ 96$
The square of 9.6 is less than 96, so we try a bigger number. Let's try 9.7.
$9.7^2=9.7 \times 9.7 = 94.09\\94.09\ \textless \ 96$
We're closer, but not quite there yet. Let's try 9.8.

$9.8^2=9.8 \times 9.8 = 96.04\\96.04\ \textgreater \ 96$
We are very close now, but our answer seems a little bit too big. We know we can't go down to 9.7 again, so we go out to a second decimal place. Let's try 9.78.
$9.78^2=9.78 \times 9.78 = 95.65 \\ 95.65 \ \textless \ 96$
We want something bigger, so let's try 9.79.
$9.79^2=9.79 \times 9.79 = 95.84 \\ 95.84 \ \textless \ 96$

Now it looks like we need to go up again, and while we could now move out to the thousandth place, your question asks us to round to the hundredths place. So it looks like 9.8 was accurate after all, but rounded to the hundredths place, it's 9.80.

We can confirm on a calculator that indeed the square root of 96 is about 9.80.

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PLz help me this is 7th grade math

UkoKoshka [18]

Answer:

g = 118°, h = 62°, k = 140°, m = 40°

Step-by-step explanation:

g = 118°

h = 180 - 118 = 62°

k = 140°

m = 180 - 140 = 40°

5 0

3 years ago

The number of rows in an auditorium can be represented by the function f(x) = 80x. the number of seats in each row can be repres

Dominik [7]

Applying multiplication of functions, the total number of seats in the auditorium is given by:

h(x) = 80x² + 560x.

<h3>How polynomial functions are multiplied?</h3>

They are multiplied applying the distributive property, that is, all the terms are multiplied and then the common terms are added.

In this problem, the functions are given as follows:

f(x) = 80x.

g(x) = x + 7.

Then the multiplication is:

h(x) = f(x)g(x) = 80x(x + 7) = 80x² + 560x.

More can be learned about multiplication of functions at brainly.com/question/13136492

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4 0

2 years ago

Which are equivalent to 3^2 x 3^4? check all that apply.

Andreas93 [3]

equivalent

1) 3^6

4) 3^-4 · 3^10

8) (3 · 3) · (3 · 3 · 3 · 3)

Step-by-step explanation:

$= {3}^{2} \times {3}^{4}$

$= {3}^{(2 + 4)}$

$= {3}^{6}$

equivalent

1) 3^6

4) 3^-4 · 3^10

8) (3 · 3) · (3 · 3 · 3 · 3)

8 0

2 years ago

Read 2 more answers

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,

REY [17]

Answer:

a) 217

b) 1351

c) 5403

Step-by-step explanation:

Given that:

confidence interval (c) = 0.95

$\alpha =1-0.95=0.05\\\frac{\alpha }{2} =\frac{0.05}{2}=0.025$

The Z score of $\frac{\alpha }{2}$ is from the z table is given as:

$Z_{\frac{\alpha }{2} }=Z_{0.025}=1.96$

Range = $45000 - $30000 = $15000

The standard deviation (σ) is given as:

$\sigma=\frac{Range}{4} =\frac{15000}{4}=3750$

Sample size (n) is given as:

$n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2$

a) E = $500

$n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{500} )^2$ ≈ 217

b) $n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{200} )^2$ ≈ 1351

c) $n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{100} )^2$ ≈ 5403

7 0

3 years ago

Read 2 more answers

When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were aske

12345 [234]

Answer:

The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0$

where μ1: mean calorie estimation for the cheesecake group and μ2: mean calorie estimation for the organic salad group.

There is enough evidence to support the claim that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first (P-value=0.0000002).

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>"Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first.</em>

<em>At the 0.01 level of significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first?"</em>

<em />

This is a hypothesis test for the difference between populations means.

The claim is that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0$

The significance level is 0.01.

The sample 1 (cheese cake), of size n1=20 has a mean of 780 and a standard deviation of 128.

The sample 2 (organic salad), of size n2=20 has a mean of 1041 and a standard deviation of 140.

The difference between sample means is Md=-261.

$M_d=M_1-M_2=780-1041=-261$

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

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{128^2}{20}+\dfrac{140^2}{20}}\\\\\\s_{M_d}=\sqrt{819.2+980}=\sqrt{1799.2}=42.417$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-261-0}{42.417}=\dfrac{-261}{42.417}=-6.153$

The degrees of freedom for this test are:

$df=n_1+n_2-1=20+20-2=38$

This test is a left-tailed test, with 38 degrees of freedom and t=-6.153, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.0000002) is smaller than the significance level (0.01), the effect is significant.

The null hypothesis is rejected.

3 0

3 years ago