Solven/6 =24/36, for the unknown quantity,n.
n=192
n=144
n=108
n=4

By "number of Power set of A" I wonder if you mean the cardinality of the power set.

For any finite set with [tex]n[/tex] elements, its power set contains [tex]2^n[/tex] elements.

Here [tex]|A| = 5[/tex], so the power set will contain [tex]|\mathcal P(A)| = 2^5 = \boxed{32}[/tex] elements.

Recall that the power set is the set of all subsets of a given set

• subsets of [tex]A[/tex] of size 0 (1):

[tex]\emptyset[/tex]

• subsets of size 1 (5):

[tex]\{a\}\\ \{b\}\\ \{\{a\}\}\\ \{3\}\\ \{\{3\}\}[/tex]

• subsets of size 2 (10):

[tex]\{a,b\}\\ \{a,\{a\}\}\\ \{a, 3\}\\ \{a, \{3\}\}\\ \{b,\{a\}\}\\ \{b,3\}\\ \{b,\{3\}\}\\ \{\{a\},3\}\\ \{\{a\}, \{3\}\}\\ \{3,\{3\}\}[/tex]

• subsets of size 3 (10):

[tex]\{a,b,\{a\}\}\\ \{a,b,3\}\\ \{a,b,\{3\}\}\\ \{a,\{a\},3\}\\ \{a,\{a\},\{3\}\} \\ \{a,3,\{3\}\}\\ \{b,\{a\},3\}\\ \{b,\{a\},\{3\}\}\\ \{\{a\},3,\{3\}\}[/tex]

• subsets of size 4 (5):

[tex]\{a,b,\{a\},3\}\\ \{a,b\{a\},\{3\}\}\\ \{a,b,3,\{3\}\}\\ \{a,\{a\},3,\{3\}\}\\ \{b,\{a\},3,\{3\}\}[/tex]

• subsets of size 5 (1):

[tex]\{a,b,\{a\},3,\{3\}\}[/tex]

Answer:

(x-4)² + y² = 100

Step-by-step explanation:

The only circles that have a center at (4 , 0) are :

(x-4)² + y² = 100

(x-4)² + y² = 10

……………………

•  (-2 - 4)² + 8² = (-6)² + 64 = 36 + 64 = 100 ≠ 10

Then

The circle (x-4)² + y² = 10 doesn’t contain the point (-2, 8)

•  (-2 - 4)² + 8²  = 100

Then

The circle (x-4)² + y² = 100 contains the point (-2, 8)

Answer:

the x value is 13 and the y value is 10. x=13 and y=10

Answer:

2 miles

Step-by-step explanation:

6X + 10 = 22

X = (22-10)/6 = 12/6 = 2 miles

Answer:

(x/0.2)(7)-2.8=-499.8

x=-14.2

Step-by-step explanation:

(x/0.2)(7)-2.8=-499.8

7x/0.2 -2.8 = -499.8

35x -2.8 = -499.8

35x = -499.8 +2.8

35x = -497

35x/35 = -497/35

x = -14.2

you probably already got it solved, but at least this can help anyone else!

Answer:

Ordinal, 3,355th. This number as US currency, three thousand three hundred fifty-five dollars ... 3355 is NOT a triangle number ... Base 6

The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.

An equation is an expression that shows the relationship between two or more numbers and variables.

60 km/h = 1 km/min

Hence:

9 km/h = 9 km/h * (1 km/min) / ( 60 km/h) = 0.15 km/min

In 15 minutes, distance = 0.15 km/min * 15 min = 2.25 km

The rate of 9 kilometers per hour in kilometers per minute is 0.15 km/min. The cyclist would travel 2.25 km in 15 minutes.

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Step-by-step explanation:

[tex]\sqrt{35} =\sqrt{5} *\sqrt{7};[/tex]

all the details are in the attachment.

The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.

Given The factor included in lease is 0.00354.

Interest is the amount that a bank or person who gives loan charges from loan taker.

Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.

Money factor=0.00354.

So the interest rate that Cindy will charge is equal to 2400*0.00354

The interest rate Cindy will be charged =8.496%

=8.5%

Hence the interest rate charged is approximately 8.5%.

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Answer: [tex]f(x) > 0[/tex]

Step-by-step explanation:

The range of all exponential functions without a vertical shift is the set of positive real numbers.

Answer:

Actual distance=187.5miles

Step-by-step explanation:

1cm=30miles

6.25cm=6.25*30miles

=187.5miles

The distance between the two towns using the map scale is 187.5 miles.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The distance between the towns on map is 1 cm.

And, the scale of map is 1 cm = 30 miles.

As per the problem the actual distance can be found by using the scale of the map as follows,

The distance between two towns is 6.25 × 30 = 187.5 miles.

Hence, the actual distance between the two towns is 187.5 miles.

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Answer: 8 pieces

Step-by-step explanation:

- if there are 24 pieces of sushi in 6 packages then 24/6 = 4 so there’s 4 pieces of sushi in each package

- since there’s 4 pieces of sushi in each pack just do 4 x 2 = 8

- so there’s 8 pieces of sushi in 2 packages

hope this helps :)

Answer:

t = 4.0

Step-by-step explanation:

1.) P(t) = 1578

2.) Divide both sides by 1400

3.) Take the natural log of both sides (to remove the "e")

4.) Divide both sides by 0.03

5.) Properly round to the 1st decimal place

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = -16 [/tex]

[tex]\qquad \tt \rightarrow \: y =4 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 27 + yi = 11 - x + 4i[/tex]

[tex]\qquad \tt \rightarrow \: yi + x = 11 + 4i - 27[/tex]

[tex]\qquad \tt \rightarrow \: x + yi = - 16 + 4i[/tex]

By equating both equations we get :

[tex]\qquad \tt \rightarrow \: x = - 16[/tex]

[tex]\qquad \tt \rightarrow \: y = 4[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

480 Hectares potatoes, 340 Hectares corn

Step-by-step explanation:

Let x be the land used to plant potatoes in hectares.

Let y be the land used to plant corn in hectares.

Given the information from the question, we know that:

x + y = 820 - Equation 1

and

x - y = 140 - Equation 2

as you can see here we have 2 equations, means we can solve them simulteanously to solve for both. We will use elimination method.

We will use Equation 1 - Equation 2.

x-x+y-(-y)=820-140

2y = 680

y = 680 ÷ 2 = 340 hectares

We substiture y into equation 1 to find x

x + 340 = 820

x = 820 - 340

= 480 hectares

Therefore, 480 hectares of potatoes and 340 hectares of corn were planted.

Answer:

It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

The number is written in the form  [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]

Scientific notations have some of the profits as:

Better readability due to compact representation

Its value in terms of the power of 10 is known, which helps in the easy comparison of quantities differing by a large value.

A comet is about  [tex]5.1 \times 10 ^9[/tex] km from the sun.

Light travels at about [tex]3.0 \times 10 ^5[/tex] km per second.

[tex]\dfrac{5.1 \times 10 ^9}{3.0 \times 10 ^5}[/tex]

= [tex]1.7 \times 10 ^4[/tex]

Hence, It takes 1.7 x 10 ^4 for light from the sun to reach the comet.

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According to the empirical rule, the percent of the data points that are above 76 is; 2.28%

We are given;

Mean; μ = 88

Standard deviation; σ = 6

Sample mean; x' = 76

Formula for z-score is;

z = (x' -  μ)/σ

z = (76 - 88)/6

z = -2

Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%

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The sentence that best supports the reason for youth recreational sports is (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day.

Recreational sports are competitive physical games played for fun and physical exercise with friends or as part of extra-curricular activities.

They do not involve professional sports persons.

Read this source of information. (1) American youth have school commitments and extracurricular activities. (2) Many also enjoy leisure activities, such as reading and playing video games. (3) The US Department of Agriculture recommends that young people ages 6–17 should engage in 60 minutes of physical activity each day. (4) The specific amount of activity needed for a healthy lifestyle depends on daily caloric intake.

Thus, the sentence that best supports the reason for youth recreational sports is Sentence 3.

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Answer:

ez 3

Step-by-step explanation:

The transformation was a 180° rotation about the origin.

We can solve this question by plotting the points R (1, 1)

S (3, 1) T (1, 6) and R' (–1, –1) S' (–3, –1) T' (–1, –6) on the graph as shown below.

As we can see from the graph, the original triangle RST which was in quadrant 1, now becomes triangle R’S’T’ in quadrant 3. Thus, when triangle RST was transformed using the rule (x, y) → (–x, –y), from quadrant 1 to quadrant 3 it is a 180° rotation about the origin.

Hence, the transformation was a 180° rotation about the origin.

Your question was incomplete. Please check below for full content.

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown. R (1, 1) S (3, 1) T (1, 6) R' (–1, –1) S' (–3, –1) T' (–1, –6)

Which best describes the transformation?

The transformation was a 90° rotation about the origin.

The transformation was a 180° rotation about the origin.

The transformation was a 270° rotation about the origin.

The transformation was a 360° rotation about the origin.

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Answer:

  k ≠ -14/3

Step-by-step explanation:

A square matrix is invertible if and only if its determinant is not zero.

The determinant of a 2×2 matrix is the difference of the products of the diagonal terms and the off-diagonal terms:

  det = (6)(k) -(-7)(4) = 6k +28

The requirement that the determinant is not zero places a restriction on k.

  6k +28 ≠ 0

  k +14/3 ≠ 0 . . . . . . divide by 6

  k ≠ -14/3 . . . . . . . . subtract 14/3

For the matrix to be invertible, the value of k must not be -14/3.

Answer:

see image

Step-by-step explanation:

I did two different problems depending on whether the 4 beside the log is a base or not.

If the log IS the base, I got x = 1 as you did. But if the 4 is not the base then there is no base written and that means the base is 10.

For log problems that have log on one side of the equation only, then a good strategy is to change the equation from logarithmic form to exponential form. See image for work. Hope this helps.

Answer: 4

Step-by-step explanation:

[tex]f(4)=\frac{1}{4} \cdot 2^{4}=\frac{1}{4} \cdot 16=4[/tex]

The first three terms of the sequence are 10, 20, and 30.

The function given is 10n. In this case, the terms will be:

First term = 10n = 10 × 1 = 10

Second term = 10 × 2 = 40

Third term = 10 × 3 = 30

In this case, the first three terms of the sequence are 10, 20, and 30.

It an arithmetic sequence as there is a common difference of 10.

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The function that is a  tangent to the graph of f is [tex]f(x) = (5/4)x^4+60[/tex]

The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.

Knowing that :

therefore, f'(x)|x=a = -40, so only look for a we have:

[tex]5a^3 = -40\\a^3 = -8\\a = -2[/tex]

if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:

[tex]f'(x) = 5x^3\\f(x) = (5/4)x^4 + c\\80 = (5/4)(-2)^4 + c\\c = 60[/tex]

Therefore,

[tex]f(x) = (5/4)x^4+60[/tex]

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The graph of the exponential function in discuss whose base is; e would have a y-intercept t at point (0, 1), with a domain as the set of all real numbers and its range as the set of all positive numbers.

It follows from the task content that the function in discuss can be written as;

y = e^x.

Consequently, the y-intercept of the graph which corresponds to x= 0 is; (0, 1).

The domain and range of the graph as with other exponential functions are therefore given as the set of all real numbers and all real positive numbers respectively.

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Answer:

no

Step-by-step explanation:

there are somethings you need to know. The given height is the combined height of the cylinder and hemisphere. but we need to use the height of cylinder in the formula so we subtract the original height by radius.

Next thing is that the formula 2πrh is for C.S.A of the cylinder but we need the base area as well for surface area of this combined solid. So we add base area (i.e πr²) to 2πrh.