Form the intersection for the following sets.
R={10, 15, 20}
S = {20, 25}
R ∩S=

{10,15,25}

{10,15,20,25}

{20}

{}

Answer:

$4

Step-by-step explanation:

If 1 carton is $4 than 12 cartons would be 48 dollars because 12*4 is 48. So each carton is $4. Please give brainliest Thanks

Answer:

This report is valid

Step-by-step explanation:

We use this z score formula to solve for a question where a random number of samples is given:

z-score is z = (x-μ)/σ/√n

where x is the raw score

μ is the population mean

σ is the population standard deviation

n = number of samples

When σ/√n = Standard error

From the above question,

x = $48,574

μ = $48,432

σ = 2000

n = 400 families

z = $48, 574 -$48,432/(2000/√400)

= $48, 574 -$48,432/(2000/20)

= $48, 574 -$48,432/100

= 1.42

The z score is 1.42

H0 = μ = $48,432

At 0.05, we reject H0 if z < - 1.96 or > 1.96

z = 1.42

Therefore, H0 cannot be rejected.

The central limit theorem also holds because a sufficiently large amount of random samples (400) where taken from the population and replaced and this causes the mean to be randomly distributed.

Therefore, from the above z score, what we can conclude about the validity of the report is that the REPORT IS VALID because H0 cannot be rejected and the central limit theorem holds.

Answer:

  21.9

Step-by-step explanation:

The altitude of an isosceles triangle bisects the base. So, x represents the hypotenuse of a right triangle with legs of 9 and 20. It can be found using the Pythagorean theorem:

  x^2 = 9^2 +20^2 = 81 +400

  x = √481 ≈ 21.932

The length x is about 21.9 units.

Answer:

Value in $= 3x -600

Step-by-step explanation:

Let the value of the stock before investment= x

At the first year , the value tripled

Value after first year=3x

The second year , the stock reduces by $600.

So

The value of the stock after the second year

Value in $= 3x -600

Answer:

2x + 2 > 10

2x > 10 - 2

2x > 8

x > 8

B. x > 4.

Answer:

B. x>4

Step-by-step explanation:

2x + 2 > 10

In order to solve this inequality, we must isolate the variable, x , on one side of the inequality.

2 is being added to 2x. The inverse of addition is subtraction. Subtract 2 from both sides of the inequality.

2x+ (2-2) > 10-2

2x > 10-2

2x > 8

x is being multiplied by 2. The invers of multiplication is division. Divide both sides of the inequality by 2.

2x/2 > 8/2

x > 8/2

x > 4

The solution to the inequality 2x+2 > 10 is x > 4 and the correct answer is B.

Answer:

9 + (-4i) = 9 - 4i

Answer:

a. around 36.36 hours; around 28.57 hours

b. $134.21; $159.38

Step-by-step explanation:

a. The driving time at 70 miles per hour is  28.57 hours

b The gasoline cost for this trip would be $159.38.

a. At an average speed of 55 miles per hour:

Time = 2000 miles / 55 miles per hour = 36.36 hours

At an average speed of 70 miles per hour:

Time = 2000 miles / 70 miles per hour = 28.57 hours

b. At an average speed of 55 miles per hour:

The car averages 38 miles per gallon on the highway.

Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 38 miles per gallon = 52.63 gallons

The gasoline cost for this trip would be: 52.63 gallons * $2.55 per gallon = $134.13.

At an average speed of 70 miles per hour:

The car averages 32 miles per gallon on the highway.

Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 32 miles per gallon = 62.50 gallons.

The gasoline cost for this trip would be: 62.50 gallons * $2.55 per gallon

= $159.38.

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Answer:

See below

Step-by-step explanation:

21. Name 8 different rays.

22. Name 2 pairs of opposite rays.

23. Name 2 lines that intersect at point Z.

24. Draw three noncollinear points A, B, and C. Sketch. AB Then add a point D and  sketch CD so that CD intersects AB at point B.

Answer:

54 cm^2.

Step-by-step explanation:

Area = 1/2 * altitude * base

= 1/2 * 6 * 18

= 54 cm^2.

Answer:

P(A) ∪ P(B) ⊆ P(A ∪ B) can be proved when [tex]X[/tex] ∈ P ( A U B )

Step-by-step explanation:

To  Prove that P(A) ∪ P(B) ⊆ P(A ∪ B) is attached below and also a counter example to prove that we do not always get an equality is attached below as well

Answer:

  ∠DAB = 80°

  ∠BAC = 105°

Step-by-step explanation:

You are given ...

  ∠DAC = 25° = (x -20)°

Adding 20°, we have ...

  x° = 45°

Then the measures of the other angles are ...

  ∠DAB = (2x -10)° = 2(45°) -10°

  ∠DAB = 80°

and

  ∠BAC = ∠DAB +∠DAC = 80° +25°

  ∠BAC = 105°

_____

Nothing in this problem statement defines a circle.

I hope this helps you

Answer:

(3x-2y)(3x+2y)

Step-by-step explanation:

Proof:

(3x-2y)(3x+2y)-use FOIL method (First, Outer, Inner, Last)

3x*3x+2y3x-2y3x-2y*2y

9x^2+0-4y^2

9x^2-4y^2

The answer is (3x-2y)(3x+2y).

Answer:

1

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

integer has no decimal point.

The 2 integer seemingly that is present is 7 and 8.

HOWEVER, 7 is less than 7.2, so it is not the answer

7.2<8<8.8

So it fits in the range

Hope this helps!! :)

Please let me know if you have any question

Answer:

BC=6

Step-by-step explanation:

The perimeter is the sum of all the side lengths.

Thus, add up all the sides.

And we already know the perimeter is 64. Thus:

[tex](3z)+(10)+(z-1)+(2z+3)+(10)=64[/tex]

Combine like terms and add the numbers:

[tex]6z+22=64[/tex]

Subtract 22 from both sides:

[tex]6z=42[/tex]

Divide by 6:

[tex]z=7[/tex]

So, z is 7.

BC is z-1. Therefore:

[tex]BC=z-1\\BC=7-1=6[/tex]

So, BC is 6.

Answer:

m and n are variables whereas 4 and 5 are constant terms or coefficient.

Step-by-step explanation:

hope it will help ^_^

Answer:

Below

Step-by-step explanation:

● 4 and 5 are constants since their values don't change.

● m and n are variables since they can take any value.

Answer:

C. [tex]5 (\frac{x}{z}) ^1^0[/tex]

Step-by-step explanation:

Hey there!

Given

[tex]\frac{15 x^-^3 z^5}{3 x^7 z ^-^5}[/tex]

Well to solve this we first need to do 15 ÷ 3

= 5

When dividing exponents we actually subtract.

-3 - 7 = -10

5 - -5 = 10

[tex]5 x^-^1^0 z^1^0[/tex]

Hope this helps :)

Answer:

D.   5 (z/x)^10.

Step-by-step explanation:

15/3 = 5

x^-3 / x^7 = x^-10 = 1/x^10

z^5 / z^-5 = z ^10

So the answer is 5 * z^10 * 1/x^10

= 5 z^10 / x^10

= 5 (z/x)^10.

Answer:

24 inches

Step-by-step explanation:

Because we know that Pablo drew a square, we can correctly assume that all sides have equal lengths. There are four sides to a square, so taking the number 6, 4 times (6*4) gives us 24!

Answer:

width = 18 cm

Step-by-step explanation:

perimeter of rectangle = 2(length + width)

then:

90 = 2(27+w)

90/2 = 27+w

w = width

45 = 27+w

45 - 27 = w

18 = w

Check:

90 = 2(27+18)

90 =2*45                                       =

Answer:

A number increased by 9.

Step-by-step explanation:

A number= can be denoted by any letter.

increased= +

by 9= 9

Hope this helps ;) ❤❤❤

One way to determine this is to take the difference of numbers.

If the difference results in 0 then we can assume numbers that we subtracted are the same, mathematically:

[tex]a-a=0\implies a = a[/tex]

So,

[tex]9324-9234=90\implies 9324\neq9234[/tex].

Hope this helps.

Step-by-step explanation:

9,324 have a different value than 9,234 because 9,324 is greater than 9,234.

9,324-9,234=90

9,324 is 90 more than 9,234.

Answer:

97

Step-by-step explanation:

Given the following conditions :

board measuring 1x100, each square is numbered from 1 to 100

Three colors are used to paint the squares from left to right in the sequence :

one blue, two reds and three green squares in a repeated pattern.

What is the highest numbered square that is painted blue?

The sequence of painting is repeated after :

(1 + 2 + 3) = 6 successive squares

Since the number of squares = 100

Maximum complete repetition possible :

100 / 6 = 16 remainder 4

Hence 16 * 6 = 96 (the highest complete sequence terminates on the square numbered 96)

On the 97th square, another sequence begins which is a blue and the 100th square is painted the first of the 3 green colors.

Hence, the highest numbered square that is painted blue is 97

Patterns are simply the rules that guide the formation of elements in a dataset. The highest numbered square that is painted blue is 97.

The sequence is given as:

[tex]Blue = 1[/tex]

[tex]Red = 2[/tex]

[tex]Green = 3[/tex]

The number of squares is given as:

[tex]n = 100[/tex]

First, we calculate the number of complete iteration of the sequence of squares.

[tex]Total = Blue + Red + Green[/tex]

[tex]Total = 1+2+3 =6[/tex]

So, the complete iteration (k) is:

[tex]k = \frac{n}{Total}[/tex]

[tex]k = \frac{100}{6}[/tex]

[tex]k = 16.67[/tex]

Remove decimal (do not approximate)

[tex]k = 16[/tex]

Next, calculate the position of the last element in the iteration.

[tex]Position = k \times Total[/tex]

[tex]Position = 16 \times 6[/tex]

[tex]Position = 96[/tex]

The blue square is the first on each iteration.

So, the highest numbered blue square is:

[tex]Highest = Position + Blue[/tex]

[tex]Highest = 96 + 1[/tex]

[tex]Highest = 97[/tex]

Hence, the highest numbered square that is painted blue is 97.

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calculate the percentage increase,work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100.  

520-500 = 20

20÷500 =.04

.04 ×100= 4%

Answer:

9/2π

=14.13716694

Step-by-step explanation:

The equation of the volume of the sphere:

V=4/3πr^3

If the diameter is 3cm, the radius is divided by 2, so 1.5cm.

Plug that in, 4/3π1.5^3

Use a calculator:

9/2π

=14.13716694

[tex]14,14~cm^{3}[/tex]

d = 3cm = 2r => r = d/2 = 3cm/2 = 1,5 cm

[tex]V=\frac{4}{3}\pi*r^{3}\\\\=\frac{4}{3}*\frac{22}{7}*3.375cm^{3}\\ \\=\frac{4*22*3.375}{21}cm^{3}\\ \\=\frac{297}{21}cm^{3}\\ \\[/tex]

≈ [tex]14,14~cm^{3}[/tex]

Answer:

The system has 4 solutions

Step-by-step explanation:

When the two lines meet at a point it means that the point is a solution, in this case the lines meet 4 times.

Answer:

[tex]Area = 72in^2[/tex]

Step-by-step explanation:

Your question is incomplete without an attachment (See attachment)

Required

Determine the area of the shaded part

From the attachment;

Assume that the shaded portion is closed to the right;

Calculate  the Area:

[tex]Area_1 = Length * Width[/tex]

[tex]Area_2 = 8in * (6in + 6in)[/tex]

[tex]Area_2 = 8in * 12in[/tex]

[tex]Area_1 = 96in^2[/tex]

Next;

Calculate the Area of the imaginary triangle (on the right)

[tex]Area_2 = \frac{1}{2} * base * height[/tex]

[tex]Area_2 = \frac{1}{2} * (6in + 6in) * 4in[/tex]

[tex]Area_2 = \frac{1}{2} * 12in * 4in[/tex]

[tex]Area_2 = \frac{1}{2} * 48in^2[/tex]

[tex]Area_2 = 24in^2[/tex]

Lastly, calculate the Area of the Shaded Part

[tex]Area = Area_1 - Area_2[/tex]

[tex]Area = 96in^2 - 24in^2[/tex]

[tex]Area = 72in^2[/tex]

Hence,

The area of the shaded part is 72in²

Answer:

137

Step-by-step explanation:

Given the following :

Margin of Error (E) = 7% = 0.07

Confidence level = 90% = 0.9

Prior study (p) = 54% = 0.54

Using the sample size formula:

([Z/E]^2) × p × (1 - p)

(1 - p) = 1 - 0.54 = 0.46

Z score at 90% confidence interval. = 1.645

[(1.645 / 0.07)^2] * 0.54 * 0.46

(23.5^2) * 0.54 * 0.46

552.25 * 0.54 * 0.46

= 137.1789

= 137

Sample size = 137

Answer:

[tex]56[/tex]

Step-by-step explanation:

[tex]-7*(-8)[/tex]

The only one thing we have to do on this question is simplify.

[tex](-7)(-8)[/tex]

And this equals

[tex]56[/tex]

Now you got your answer!

Hope this helps!

The solution to the expression -7 times (-8) is 56

From the question, we have the following parameters that can be used in our computation:

-7 times (-8)

Express using product expression

So, we have

-7 times (-8) = -7 * -8

Evaluate all the products in the expression

so, we have the following representation

-7 times (-8) = 56/1

Evaluate all the quotients in the expression

so, we have the following representation

-7 times (-8) = 56

Lastly, we have

-7 times (-8) = 56

Hence, the solution is 56

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