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4 years ago

70 POINTS!!!!!!!!!!!!!! HELP PLEASE

Mathematics

2 answers:

Dovator [93]4 years ago

7 0

Answer:

$\boxed{\mathrm{view \: explanation}}$

Step-by-step explanation:

When bases are same in multiplication, add exponents.

1) a. 4^1 × 4^2

4^(1+2)

4^3

b. 5^3 × 5^-6

5^(3+-6)

5^(-3)

c. 3^2 × 3^1

3^(2+1)

3^3

d. 6^5 × 5^-7

0.0995328

2. I added the exponents. For the last one, I evaluated by calculator.

TEA [102]4 years ago

5 0

4^1 * 4^2 = 4^(1 + 2) = 4^3 = 64

5^3 * 5^-6 = 5^(3 - 6) = 5^-3 = 1/125

The third one down is rather sneaky. It's also kinda neat.
31 = 32 - 1 = 2^5 - 1
32 * 31
= 32 (2^5 - 1)
= 2^5(2^5 - 1)
= 2^10 - 2^5
= 1024 - 32
= 992

I don't see any math tricks to solve this. Use brute force.
6^5 * 5^-7 = 6^5 / 5^7 = 7776 / 17125 = 0.00953

2. Just pick a couple of questions out of the four above. The last one is a good example for division. The first one would be good for multiplication. I've explained all you need.

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What statements are there? (If there are 3 batches, you'd have 1 cup of milk, just FYI).

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3 years ago

(3-4i)(6i+7)-(2-3i)

Sergeu [11.5K]

Answer:

43-7i

Step-by-step explanation:

We are given the expression:

$\displaystyle \large{(3 - 4i)(6i + 7) - (2 - 3i)}$

First, expand 3-4i in 6i+7. To expand binomial with binomial, first we expand 3 in 6i+7 then expand -4i in 6i+7.

$\displaystyle \large{[(3 \cdot 6i) + (3 \cdot 7) + ( - 4i \cdot 6i) + ( - 4i \cdot 7)]- (2 - 3i)} \\ \displaystyle \large{[18i + 21 - 24 {i}^{2} - 28i]- (2 - 3i)}$

Now combine like terms.

$\displaystyle \large{[ - 10i+ 21 - 24 {i}^{2} ]- (2 - 3i)}$

Imaginary Unit

$\displaystyle \large{i = \sqrt{ - 1} } \\ \displaystyle \large{ {i}^{2} = - 1 }$

Therefore:-

$\displaystyle \large{[ - 10i+ 21 - 24 ( - 1) ]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 21 + 24]- (2 - 3i)} \\ \displaystyle \large{[ - 10i+ 45]- (2 - 3i)}$

Then expand negative sign in 2-3i; remember that negative times negative is positive and negative times positive is negative.

$\displaystyle \large{- 10i+ 45 - (2 - 3i)} \\ \displaystyle \large{- 10i+ 45 - 2 + 3i}$

Combine like terms.

$\displaystyle \large{43 - 7i}$

5 0

3 years ago

PLEASE DONT ANSWER IF YOU NOT GONNA PUT THE RIGHT ANSWER PLZZ!!!!

Verizon [17]

Yes; the corresponding angles are congruent. You can see that that triangle EFGH is a dilation from triangle ABCD. To be exact, if you multiply each side on triangle ABCD by 2.5, you get triangle EFGH. If it is a dilation, this means that the angles will stay the same.

7 0

3 years ago

Read 2 more answers

What line model matches the expression

SVETLANKA909090 [29]

Answer:

Step-by-step explanation:

You would distribute the negative sign in front of -3. -3 would then become 3.

-6 (3)

Then you would place them on a line.

Please mark as brainliest! If you need anymore help just let me know! :D

3 0

3 years ago

estimate the number of first-year students at an assembly meeting. He surveys 60 students and finds that 24 of them are first-ye

bogdanovich [222]

Answer:

The values needed to calculate a confidence interval at the 95% confidence level are $z = 1.96, n = 60, \pi = \frac{24}{60} = 0.4$

The 95% confidence interval for the proportion of first-year students at an assembly meeting is (0.276, 0.524).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 60, \pi = \frac{24}{60} = 0.4$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The values needed to calculate a confidence interval at the 95% confidence level are $z = 1.96, n = 60, \pi = \frac{24}{60} = 0.4$

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4*0.6}{60}} = 0.276$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4*0.6}{60}} = 0.524$

The 95% confidence interval for the proportion of first-year students at an assembly meeting is (0.276, 0.524).

6 0

3 years ago