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4 years ago

Which is the BEST estimate for the product of 3.1*10^4

Mathematics

1 answer:

masya89 [10]4 years ago

6 0

Answer:

31000

Step-by-step explanation:

3.1 * 10^4 or 3.1 * 10000= 31000

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Fill in the Blank:

arsen [322]

Answer:

The exponent of the second term (b) starts with 0 (b0 = 1) and then increases by one in each following term until it is equal to the exponent of the binomial (5).

Step-by-step explanation:

6 0

3 years ago

5. Solve 2(1 - x) > 2x.

Mrrafil [7]

Answer:

I do not know for sure but i think it might be B.

Step-by-step explanation:

Im not the smartest so yeah hopefully that is the answer you are looking for tho :D

4 0

3 years ago

In the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37

djyliett [7]

Answer:

More than 50% would germinate

Step-by-step explanation:

Given that in the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated

Let us check whether more than 50% will germinate using hypothesis test

$H_0: p = 0.50\\H_a: p>0.50\\$

(right tailed test)

Sample proportion p = $\frac{37}{60} =0.617\\q = 0.383\\Std error = \sqrt{\frac{pq}{n} } =0.0628$

p difference = 0.117

Test statistic Z = p difference/std error = 1.864

p value =0.0312

Since p value <0.05 our significance level of 5% we reject null hypothesis

It is possible to claim that most of the seed will germinate (i.e. more than 50%)

7 0

3 years ago

Andrey is making a garden box and wants to know how much dirt is needed to fill the box. A prism has a length of 8 feet, height

olga_2 [115]

Answer:

The space inside the box is the volume, which is 128 ft3

Step-by-step explanation:

Given the dimensions of the box as 8ft by 2ft by 8ft. We calculate it's volume and surface area to validate the statements;

$V=lwh\\\\=8\times 2\times 8\\\\=128 \ ft^3\\\\Area=2lw+2lh+2hw\\\\=2(8*2)+2(8*8)+2(2*8)\\\\=192 \ ft^2$

The volume of the box is 128 ft^3 and its surface area 192 ft^2. Hence, the correct statement is The space inside the box is the volume, which is 128 ft3

4 0

4 years ago

Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))

Sonja [21]

Answer:

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

Let $a=\sin^{-1}(\frac{2}{3})$ .

With some restriction on $a$ this means:

$\sin(a)=\frac{2}{3}$

We need to find $\tan(a)$ .

$\sin^2(a)+\cos^2(a)=1$ is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

$(\frac{2}{3})^2+\cos^2(a)=1$

$\frac{4}{9}+\cos^2(a)=1$

Subtract 4/9 on both sides:

$\cos^2(a)=\frac{5}{9}$

Take the square root of both sides:

$\cos(a)=\pm \sqrt{\frac{5}{9}}$

$\cos(a)=\pm \frac{\sqrt{5}}{3}$

The cosine value is positive because $a$ is a number between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ because that is the restriction on sine inverse.

So we have $\cos(a)=\frac{\sqrt{5}}{3}$ .

This means that $\tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}$ .

Multiplying numerator and denominator by 3 gives us:

$\tan(a)=\frac{2}{\sqrt{5}}$

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

$\tan(a)=\frac{2\sqrt{5}}{5}$

Let's continue on to letting $b=\cos^{-1}(\frac{1}{7})$ .

Let's go ahead and say what the restrictions on $b$ are.

$b$ is a number in between 0 and $\pi$ .

So anyways $b=\cos^{-1}(\frac{1}{7})$ implies $\cos(b)=\frac{1}{7}$ .

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of $b$ .

$\cos^2(b)+\sin^2(b)=1$

$(\frac{1}{7})^2+\sin^2(b)=1$

$\frac{1}{49}+\sin^2(b)=1$

Subtract 1/49 on both sides:

$\sin^2(b)=\frac{48}{49}$

Take the square root of both sides:

$\sin(b)=\pm \sqrt{\frac{48}{49}$

$\sin(b)=\pm \frac{\sqrt{48}}{7}$

$\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}$

$\sin(b)=\pm \frac{4\sqrt{3}}{7}$

So since $b$ is a number between $0$ and $\pi$ , then sine of this value is positive.

This implies:

$\sin(b)=\frac{4\sqrt{3}}{7}$

So $\tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}$ .

Multiplying both top and bottom by 7 gives:

$\frac{4\sqrt{3}}{1}= 4\sqrt{3}$ .

Let's put everything back into the first mentioned identity.

$\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}$

$\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}$

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

$\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}$

$\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}$

4 0

3 years ago