Which law would you use to simplify the expression
(P/q)^3?

power of a power
power of a quotient
quotient of powers
power of a product

Answer:

15.5⁰ or approximately 16⁰

Step-by-step explanation:

let unknown side be x

cos x= 53/55

cos x= 0.9636

x=cos inverse of 0.9636

x=15.5⁰

Answer:

[tex]cosx = \frac{53}{55} \\ x = {cos}^{ - 1} ( \frac{53}{55} ) \\ x = 15.4987[/tex]

Answer:

C.3-6

Step-by-step explanation:

Every complex number has a complex conjugate.

Examples is a+bi the conjugate is a-bi,if your adding the two conjugate its going to be 2a and if your subtracting the result is 2bi.And if multiplied it is seen as complex number which are a²+b²

Answer:

[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]

a+2b-3c+(-3a+b+2c) +(2a-3b+c)

=a+2b-3c-3a+b+2c+2a-3b+c

=a-3a+2b+2b+b-3b-3c++2b+c

=0a+0b+0c

=0

Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.

To know more about algebraic expressions

https://brainly.com/question/28307605

Step-by-step explanation:

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Answer: Distance: 2250

Step-by-step explanation:

Find GCF of 450 and 250

9514 1404 393

Answer:

  0.2807

Step-by-step explanation:

The relationship between the effective annual yield (e) and the nominal annual interest rate (r) compounded n times per year is ...

  e = (1 +r/n)^n -1

  e = (1 +0.25/12)^12 -1 = 0.2807 . . . . . . about 28.07%

Answer:

D. Find the cost of 1 week of guitar lessons for each store and compare.

Step-by-step explanation:

Find the cost for 1 week of guitar lessons by finding the slope of the data.

[tex]\frac{y_2-y_1}{x_2-x_1}\\\\ A.)\frac{132-66}{6-3}=\frac{66}{3}=22\\\\ B.)\frac{168-84}{8-4}=\frac{84}{4}=21[/tex]

Therefore, Store B would be the best choice.

Answer:

hope this answer helps.

Answer:

88 hours

Step-by-step explanation:

Ian = 132

Daniel + Ian = 44

Daniel = Ian - 44

= 132-44 = 88 hours

Answer:

0.0286 = 2.86% probability that today is Monday.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Dressed correctly

Event B: Monday

Probability of being dressed correctly:

100% = 1 out of 4/7(mom dresses).

(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So

[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]

Probability of being dressed correctly and being Monday:

The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:

[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]

What is the probability that today is Monday?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]

0.0286 = 2.86% probability that today is Monday.

Answer:

0.6827

Step-by-step explanation:

Given that :

Mean, μ = 3

Standard deviation, σ = 0.1

To produce an acceptable cork. :

P(2.9 < X < 3.1)

Recall :

Z = (x - μ) / σ

P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]

P(2.9 < X < 3.1) = P(-1 < Z < 1)

Using a normal distribution calculator, we obtain the probability to the right of the distribution :

P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827

Hence, the probability that the first machine produces an acceptable cork is 0.6827

Answer:

y=-2/3x+3

Step-by-step explanation:

the equation of line J is y=3/2x-5

perpendicular slope would be -2/3

you want it at point (6, -1) so sub the points into y=-2/3x+b

-1=-2/3(6)+b

-1=-4+b

3=b

y=-2/3x+3

Answer:

5

Step-by-step explanation:

Calculate the square root of 25 and get 5.

Answer:

No solution.

Step-by-step explanation:

[tex]{ \sf{y = ±∞ \: \: and \: \: x = ±∞}}[/tex]

Answer:

x=30°

hopefully this answer can help you to answer the next question

Answer:

The value 138 means that this height (138cm) is less than the average height of a 4th grader.

Answer: No credit wanted

Step-by-step explanation:

The other guy is completely right.

Answer:

-5+3=-2

1/4 of 24 = 6

Step-by-step explanation:

Answer:

a) The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

b) The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Step-by-step explanation:

Question a:

The resistors produced by a manufacturer are required to have an average resistance of 0.150 ohms.

At the null hypothesis, we test if this is the average resistance, that is:

[tex]H_0: \mu = 0.15[/tex]

We are interested in testing the hypothesis that the resistors conform to the specifications.

At the alternative hypothesis, we test if it is not conforming, that is, the mean is different of 0.15, so:

[tex]H_1: \mu \neq 0.15[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.15 is tested at the null hypothesis:

This means that [tex]\mu = 0.15[/tex]

Sample mean of 0.152, sample of 10, population standard deviation of 0.005.

This means that [tex]X = 0.152, n = 10, \sigma = 0.005[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.152 - 0.15}{\frac{0.005}{\sqrt{10}}}[/tex]

[tex]z = 1.26[/tex]

P-value of the test and decision:

The p-value of the test is the probability of the sample mean differing from 0.15 by at least 0.152 - 0.15 = 0.002, which is P(|z| > 1.26), given by two multiplied by the p-value of z = -1.26.

Looking at the z-table, z = -1.26 has a p-value of 0.1038.

2*0.1038 = 0.2076

The p-value of the test is 0.2076 > 0.05, which means that the sample indicates that the resistors are conforming.

Question b:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.005}{\sqrt{10}} = 0.003[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.15 - 0.003 = 0.147.

The upper end of the interval is the sample mean added to M. So it is 0.15 + 0.003 = 0.153.

The 95% confidence interval for the average resistance is (0.147, 0.153). 0.152 is part of the confidence interval, which means that as the test statistic in item a), it indicates that the resistors are conforming.

Answer:

54ft

Step-by-step explanation:

if 3foot is 4ft tall

then a shadow of 72 ft will be how tall?= x

4x =3ft by 72ft

4x= 216ft

x= 216/4

×=54

Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC

=> EF // và bằng 1/2 AB

=> AB = 16

Step-by-step explanation:

Answer:

AB=16

Step-by-step explanation:

Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.

AD=DB

AD+DB=AB=2EF

AB=2×8=16

Answer:

YWX = DFE

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

we have 1 side and one angle confirmed.

so, we need one of the other two angles (W or Y vs. F or D) confirmed.

they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.

Notice that

6 + 7 = 13

13 + 7 = 20

so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is

a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1

The last term in the series is 111, which means the series consists of 16 terms, since

7k - 1 = 111   ==>   7k = 112   ==>   k = 16

Then in summation notation, we have

[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]

Answer:

FACTORING THE NUMBERS :-

well u didnt say to prime factors so i am writing all factors

1) 48 => 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48    ( all are plus and minus )

2) 36 => 1, 2, 3, 4, 6, 9, 12, 18 and 36    ( all are plus and minus )

3) 28 => 1, 2, 4, 7, 14 and 28    ( all are plus and minus )

4) 100 => 1, 2, 4, 5, 10, 20, 25, 50, and 100  ( all are plus and minus )

5) 125 => 1, 5, 25, 125   ( all are plus and minus )

is it worth brainliest...

yes ofc

Hi! I'm happy to help!

To find the answer we first have to find the distance between the x and y values.

From the first point, we travel from the x point -9, to the x point, -2. This means that we traveled 7 units.

From the first point, we also travel from the first y point, -6, to the second y point, 2. This means we traveled 8 units.

From here we use the Pythagorean Theorem.

The Pythagorean Theorem says that: a²+b²=c²

We can use a and b (the 7 and 8 units we traveled) to find c (the distance between).

Let's insert our values.

7²+8²=49+64=113=c²

To find c, we need to find the square root of c².

√113

This is 10.6301..., if you want to round the the hundredth, or thousandth, your answer would be 10.63, rounding to the nearest tenth, it would be 10.6, and rounding to the nearest whole number would be 11.

I hope this was helpful, keep learning! :D

Answer:

A. 671*3

B. 67*13

C. 3*1*7*6

D. 1*80

Step-by-step explanation:

you know that you can copy and paste and give the answer

Answer:

348 frogs

Step-by-step explanation:

ratio = 3:7

total of ratio = 10

frogs = 3/10 × 1280 = 348 frogs

Answer:

let the ratio be 3x and 7x.

3x+7x=1280

10x=1280

x=128

Now

frogs =3x=3*128=384

toads =7x=7*128=896

Answer:

180 Feet Per Minute

Step-by-step explanation:

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