which law would you use to simply the expression 3^10/3^4 quotient power power of a quotient product of powers power of a product

Answer:

  You can work no more than 10 hours teaching, and must work at least 5 hours cashiering. The remaining hours can be worked at the other job until the goal is reached.

Step-by-step explanation:

The restrictions give rise to two inequalities. If we  ...

  let x represent teaching hours

  let y represent cashiering hours

then the restrictions are ...

  x + y ≤ 15 . . . . total hours cannot exceed 15

  6x +8y ≥ 100 . . . . you want to earn at least $100

The solution set for these inequalities is a triangular area on a graph with vertices at ...

  (x, y) = (10, 5), (0, 12.5), (0, 15)

You must work at least 5 hours cashiering, and the remainder of necessary time at teaching.

Answer:

7.33333333333 I think. Hope this helped.

Answer:

Step-by-step explanation:

a circle will satisfy the conditions of Green's Theorem since it is closed and simple.

Let's identify P and Q from the integral

[tex]P=x^2 y[/tex], and [tex]Q= xy^2[/tex]

Now, using Green's theorem on the line integral gives,

[tex]\oint\limits_C {x^2ydx-xy^2dy } =\iint\limits_D {y^2-x^2} \, dA\\\\[/tex]

Answer:

Step-by-step explanation:

From the given question;

Given that:

Jan's All You Can Eat Restaurant charges ​$9.10 per customer to eat at the restaurant.

Distribution  is skewed and and has a mean of $8.10 and a standard deviation of ​$4.

A.  If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.

the mean by using the central limit theorem is 8.10

the standard error of the sampling distribution  = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

the standard error of the sampling distribution = [tex]\dfrac{4}{\sqrt{100}}[/tex]

= 4/10

= 0.4

B.  

P(X > $8.95) = P (Z > 8.95 - 8.10/0.4)

P(X > $8.95) = P (Z > 2.1)

P(X > $8.95) = 1 - P (Z < 2.1)

P(X > $8.95) = 1 - 0.9821

P(X > $8.95) = 0.0179

Answer:

D

Step-by-step explanation:

3/40 * 2.5/2.5 = 7.5/100 = 0.075

Answer: 178 1/4 or 713/4

Step-by-step explanation:

178.25 = 178+0.25 = 178+25/100

gcd(25,100) = 25

178.25 = 178+(25/25)/(100/25) = 178+1/4 = 713/4

Answer:

2

Step-by-step explanation:

1+9+2 = 12

12/3= 4

Answer:2

Step-by-step explanation:9+2+1=12

So 12/3=4

ANSWER=2

Answer:

Pre-image ABCD has been shifted 2 units right and 1 unit upwards.

Step-by-step explanation:

Coordinates of the points A,B,C and D of the pre-image ABCD,

A(-4, 4), B(-1, 4), C(-5, 1), D(-2,1)

Coordinates of the points A', B', C' and D' of the image A'B'C'D'.

A'(-2, 5), B'(1, 5), C'(-3, 2), D'(0, 2)

Now we choose points A from the pre-image and A' from the image,

A(-4, 4) → A'(-2, 5)

Rule for the translation will be,

A(-4, 4) → A'(-4+2, 4+1)

Or A(x, y) → A'(x+2, y+1)

Therefore, pre-image ABCD has been shifted 2 units right and 1 unit upwards to form image A'B'C'D'.

Answer: It's D

Step-by-step explanation:

the last one I just took the quiz

Answer:

A = 19.6 ft²

Step-by-step explanation:

A = πr²            Use this equation to find the area of the circle

A = π(2.5)²      Multiply

A = π(6.25)     Multiply

A = 19.6 ft²

Answer:

174

Step-by-step explanation:

l x w

5x20

8x4

6x7

174

Answer:

X=1

Step-by-step explanation:

6x+12-3=15

6x+9=15

6x+9-9=15-9

6x=6

X=1

Answer:

see below

Step-by-step explanation:

15=3(2x+4)-3

Distribute

15 = 6x +12 - 3

Combine like terms

15= 6x +9

Subtract 9 from each side

15 -9 = 6x+9-9

6 = 6x

Divide each side by 6

6/6 = 6x/6

1 =x

Answer:

Rectangle

Step-by-step explanation:

Count the units. For the triangle, A=0.5bh. 0.5(4)(6)=A. A=12

Now, for the rectangle, A=bh. A=(3)(5). A=15. The rectangle is larger

Answer:

63 metres

Step-by-step explanation:

A rectangle has 4 sides

2 of these sides are the lengths

The other 2 sides are the width

If the length of one side is 97 metres, the other side length must also be 97 metres

The two lengths then add together (97 + 97) to become 194 metres

Now we can use this information to calculate the width

320 (the total perimeter) subtract 194 (The total length) = 126 metres

This means that 126 metres is the total width

Because there are two sides which add up to the total width we divide 126 by 2

This allows us to get the measurement of the width

126 divided by 2 = 63 metres

Answer:

[tex]\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}[/tex]

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ([tex]N[/tex]) of subsets of a set containing [tex]n[/tex] elements: N = [tex]2^{n}[/tex]

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = [tex]2^{4} = 16[/tex]

(same result as using counting method)

Brief proof of formula: N = [tex]2^{n}[/tex]

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means  that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are [tex]n[/tex] elements in total. => There are [tex]2^n}[/tex] ways to select, or in other words, there are [tex]2^{n}[/tex] subsets.

Hope this helps!

:)

Answer: 3/20

Step-by-step explanation:

p(A)=the day selected in Monday =1/5

p(B)=student is absent

P(A∩B)=it is Monday AND a student is absent =3/100

Events A and B are independent so

P(A∩B) = P(A) · P(B)

3/100=1/5*p(B)

p(B)=3/20

Answer:

  ∠F ≈ 43.9°

Step-by-step explanation:

The Law of Cosines is used to find an angle when all triangle sides are known.

  f² = d² +e² -2de·cos(F)

  cos(F) = (d² +e² -f²)/(2de) = (25² +28² -20²)/(2·25·28) = 1009/1400

  F = arccos(1009/1400)

  F ≈ 43.9°

Answer:

D.

Step-by-step explanation:

The base of a log is also the base of an exponent. So 7 to the c power, our 7 would be the base. To find c, we simply just do log base 7 of 49, which comes out to be 2.

Answer:

x = 1/9

Step-by-step explanation:

3^ (x+1) = 9 ^ (5x)

Replace 9 with 3^2

3^ (x+1) = 3^2 ^ (5x)

We know that a^b^c = a ^(b*c)

3^ (x+1) = 3^(2 * (5x))

3^ (x+1) = 3^(10x)

The bases are the same so the exponents are the same

x+1 = 10x

Subtract x from each side

x+1-x = 10x-x

1 = 9x

Divide each side by 9

1/9 = 9x/9

1/9 =x

Answer: 7/6

Step-by-step explanation:

If he is writing sixths, then we have multiples of 1/6.

this is:

0*(1/6) = 0

1*(1/6) = 1/6

.

.

.

5*(1/6) = 5/6 (the numer he wrote at the left of 1)

6*(1/6) =  6/6 = 1

7*(1/6) = 7/6

So the number next to 1, (at the right of 1) must be 7/6.

You also can find it by adding 1/6 to 1.

1/6 + 1 = 1/6 + 6/6 = 7/6.

Answer:

[tex]7/6[/tex]

Explanation:

[tex]1/6 \approx 0.16666[/tex]

[tex]2/6 \approx 0.33333[/tex]

[tex]3/6 = 0.5[/tex]

[tex]4/6 \approx 0.66666[/tex]

[tex]5/6 \approx 0.83333[/tex]

[tex]6/6=1[/tex]

[tex]7/6 \approx 1.16666[/tex]

Answer:

x = -30/7

Step-by-step explanation:

-7x+3y=30

Let y=0

-7x +0 = 30

Divide by -7

-7x /-7 = 30/-7

x = -30/7

Answer:

[tex]-\frac{30}{7}[/tex]

Step-by-step explanation:

y equals zero => y = 0

-7x+3y=30

-7x +3.0 = 30

-7x + 0 = 30

-7x = 30

-7x/-7 = 30/-7

x = -30/7

Hope this helps ^-^

Answer:

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

Step-by-step explanation:

[tex]-5[(x^{3} +1)(x+4)][/tex]

Use the FOIL method for the last two groups.

[tex]-5(x^{4} +4x^{3} +x+4)[/tex]

Now, distribute the -5 into each term.

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

Answer:

Option 2

Step-by-step explanation:

The first statement is false because the price for 10 gallons is about $37 from the graph. Using this same reasoning, the third statement is also false. The last statement doesn't make sense because the graph has nothing to do with the amount of miles driven. Therefore, the answer is the second statement. We can prove it by looking at the point (4, 15). This means that it costs $15 for 4 gallons, so then the price for one gallon will be 15 / 4 = $3.75.

Answer:

solution

Step-by-step explanation:

x=5

y=4

Answer:

The percentage of the employee will experience a lost-time accident in both years is 0.0%

Step-by-step explanation:

Let A denote events that employees suffered lost-time accidents during the last year

Let B denote events that employees suffered lost-time accidents during the current year

P(A) = 5% = 0.05

P(B) = 4% = 0.04

P(B | A) = 15% = 0.15

(a) P (A ∩ B) = P(B | A) × P(A)

= 0.15 × 0.05

= 0.0075

= 0.0 (1 decimal place)

The probability that an employee will experience a lost- time accident in both years is 0.0

Answer:

8 hours

Step-by-step explanation:

We can use a ratio to solve

12 hours    x hours

----------   = ------------

93 dollars    62 dollars

Using cross products

12 * 62 = 93x

Divide each side by 93

12*62/93 = 93x/93

8 = x

8 hours

Answer:

The mass of the grains = 120 ± 1 g

Step-by-step explanation:

we are given the following:

Total mass of container + grains = 185 grams

Mass of container = 65 grams

Therefore, mass of grains is calculated as follows:

Mass of grains = ( Mass of container + grains) - mass of container

= 185 - 65 = 120 grams.

since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g

Answer:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Step-by-step explanation:

We have the following info given:

n1 = 150 n2 = 275

[tex]\bar x_1 = 72.86, \bar x_2 = 67.34[/tex]

s1 = 15.98 s2 = 35.67

We want to test the following hypothesis:

Null hypothesis: [tex]\mu_1 \leq \mu_2[/tex]

Alternative hypothesis: [tex]\mu_1 > \mu_2[/tex]

The statistic is given by:

[tex]t= \frac{\bar X_1 -\bar X_2}{\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}}[/tex]

And replacing we got:

[tex] t=\frac{72.86-67.34}{\sqrt{\frac{15.98^2}{150} +\frac{35.67^2}{275}}}=2.194[/tex]

And the best option would be:

2.19

Answer:

  a) 11

  b) 16

  c) between 5 and 6

  d) 16

Step-by-step explanation:

[tex]\text{a. }\quad\sqrt{121}=\sqrt{11^2}=\boxed{11}\\\\\text{b. }\quad 8\sqrt{4}=8\sqrt{2^2}=8\cdot 2=\boxed{16}\\\\\text{c. }\quad\sqrt{35}\ \dots\ \sqrt{25}<\sqrt{35}<\sqrt{36}\\\\\text{ }\qquad\sqrt{5^2}<\sqrt{35}<\sqrt{6^2}\\\\\text{ }\qquad \boxed{5<\sqrt{35}<6}\\\\\text{d. }\quad\dfrac{.8}{.05}=\dfrac{0.80\cdot 20}{.05\cdot 20}=\dfrac{16}{1}=\boxed{16}[/tex]

Answer:

numerators:      11  7. 12. 0

                          _  _   _.  _

denominators.  12 512. 10. 78

Step-by-step explanation:

Answer:

11/12 n:11 d:12

7/512 n:7 d:512

12/10 n:12 d:10

0/78 n:0 d:78

Step-by-step explanation:

n=numerator

d=denominator