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4 years ago

How do you write 23 2/8 in decimal

Mathematics

1 answer:

Setler79 [48]4 years ago

4 0

First, simplify 2/8 to its smallest form, which is 1/4, or 25%
You could then right it as 23.25

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Two numbers have a difference of 24. What is the sum of their squares if it is a minimum?

seraphim [82]

Let "a" and "b" be some number where:

a - b = 24

We want to find where a^2 + b^2 is a minimum. Instead of just logically figuring out that the answer is where a=b=12, I'll just use derivatives.

So we can first substitute for "a" where a = b+24

So we have (b+24)^2 + b^2 = b^2 +48b +576 + b^2
And that equals 2b^2 +48b +576

Then we take the derivative and set it equal to zero:

4b +48 = 0
4(b+12) = 0
b + 12 = 0
b = -12

Thus "a" must equal 12.

So:
a = 12
b = -12

And the sum of those two numbers squared is (12)^2 + (-12)^2 = 144 + 144 = 288.

The smallest sum is 288.

3 0

3 years ago

Sanjay let me finish his box of mints.

AVprozaik [17]

Answer:

Sanjay had eaten 60 mints.

Step-by-step explanation:

Given 5/8th part had eaten by Sanjay

then 3/8th part is left which equals to 36 mints

If 3/8 = 36,the 1/8 = 12

then 5/8 = 12 × 5

=60.

7 0

2 years ago

Please solve this question based on integeration chapter

Olenka [21]

Answer: -ln |cos x| - ln |sin x| + C

<u>Step-by-step explanation:</u>

$.\quad \int\dfrac{sin^2x-cos^2x}{sin\ x\ cos\ x}dx\\\\\\=\int \dfrac{sin^2x}{sin\ x\ cos\ x}dx-\int \dfrac{cos^2x}{sin\ x\ cos\ x}dx\\\\\\=\int \dfrac{sin\ x}{cos\ x}dx-\int \dfrac{cos\ x}{sin\ x}dx\\\\\\=\int tan\ x\ dx - \int cot\ x\ dx\\\\=-ln |cos\ x|-ln|sin\ x| + C$

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3 years ago

Help!!!Geometry chapter three

leonid [27]

Answer: 50

Step-by-step explanation:

3(50)-14=136

7 0

4 years ago

A sample of 200 observations from the first population indicated that X1 is 170. A sam- ple of 150 observations from the second

nikitadnepr [17]

Answer:

a. If the P-value is smaller than the significance level, the null hypothesis is rejected.

b. Pooled proportion = 0.8

c. z = 2.7

d. As the P-value (0.0072) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

We will use the P-value approach, so the decision rule is that if the P-value is lower than the significance level, the null hypothesis is rejected.

The claim is that the proportions differ significantly.

Then, the null and alternative hypothesis are:

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

The significance level is 0.05.

The sample 1, of size n1=200 has a proportion of p1=0.85.

$p_1=X_1/n_1=170/200=0.85$

The sample 2, of size n2=150 has a proportion of p2=0.7333.

$p_2=X_2/n_2=110/150=0.7333$

The difference between proportions is (p1-p2)=0.1167.

$p_d=p_1-p_2=0.85-0.7333=0.1167$

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

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{170+110}{200+150}=\dfrac{280}{350}=0.8$

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

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.8*0.2}{200}+\dfrac{0.8*0.2}{150}}\\\\\\s_{p1-p2}=\sqrt{0.0008+0.00107}=\sqrt{0.00187}=0.0432$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.1167-0}{0.0432}=\dfrac{0.1167}{0.0432}=2.7$

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

$P-value=2\cdot P(z>2.7)=0.0072$

As the P-value (0.0072) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportions differ significantly.

6 0

3 years ago