What is the probability of rolling a 2 and then a 4? Answer choices are in the form of a percentage, rounded to the nearest whole number.

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:

7458

Step-by-step explanation:

I hope this helps you

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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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:

So we have the equation:

[tex]7m+11=-4(2m+3)[/tex]

Distribute the right:

[tex]7m+11=-8m-12[/tex]

Add 12 to both sides:

[tex]7m+23=-8m[/tex]

Subtract 7m from both sides:

[tex]23=-15m[/tex]

Divide by -15:

[tex]m=-23/15\approx-1.5333[/tex]

Answer:

2

Step-by-step explanation:

9= 18 ÷x

Multiply each side by x

9x = 18

Divide each side by 9

9x/9 = 18/9

x = 2

Answer:

[tex]2[/tex]

Step-by-step explanation:

[tex]9=18[/tex] ÷ [tex]?[/tex]

Let's solve your equation and make it true.

[tex]9+9=18[/tex]

Since we added 9 twice, it would be *2. So now it would be 9*2 = 18. So 18 divided by 9 would be 2.

So, [tex]9=18[/tex] ÷ [tex]2[/tex]

So now you got your answer!

Hope this helps!

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:

24 marbles

Step-by-step explanation:

P( purple) = 2/3 = purple/total

                   2/3 = 16/total

Using cross products

                  2 * total = 3 *16

                    2 * total  = 48

                            total = 24

There are 24 marbles

Step-by-step explanation:

Average Cost to Mow a Lawn Per Square Foot

Most mowing pros do not charge by the square foot. For smaller properties, expect to pay between $0.01 and $0.04 per square foot.

National Average: $132

Typical Range: $49 - $219

Low End - High End: $30 - $520

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.

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:

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:

[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:

[tex]Probability = \frac{18}{1860480}[/tex]

Step-by-step explanation:

Given

Soda = 10

Sprite = 4

Dr. Pepper = 3

Cherry Coke = 3

Required

Determine the probability of picking Dr. pepper the fourth and fifth

First, we need to sum up the number of drinks

[tex]Total = 10 + 4 + 3 + 3[/tex]

[tex]Total = 20[/tex]

First Selection: Dr. Pepper

[tex]P_1= \frac{3}{20}[/tex]

Since its probability without replacement;

At this stage: Dr. Pepper = 2 and Total = 19

Second Selection: Cherry Coke

[tex]P_2= \frac{3}{19}[/tex]

At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18

Third Selection: Cherry Coke

[tex]P_3= \frac{2}{18}[/tex]

[tex]P_3= \frac{1}{9}[/tex]

At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17

Fourth Selection: Dr. Pepper

[tex]P_4= \frac{2}{17}[/tex]

At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16

Fifth Selection: Dr. Pepper

[tex]P_5= \frac{1}{16}[/tex]

Multiply the calculated probabilities, to give the required probability

[tex]Probability = P_1 * P_2 * P_3 * P_4 * P_5[/tex]

[tex]Probability = \frac{3}{20} * \frac{3}{19} * \frac{1}{9} * \frac{2}{17} * \frac{1}{16}[/tex]

[tex]Probability = \frac{3 * 3 * 1 * 2 * 1}{20 * 19 * 18 * 17 * 16}[/tex]

[tex]Probability = \frac{18}{1860480}[/tex]

Answer:

Equation 1 = Equation 2

165 - 4x = 145 - 3.50x

Step-by-step explanation:

Let x represent the number of 30-day periods.

Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.

Therefore the equation =

$165 -$4 × x

= 165 - 4x.......... Equation 1

He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.

$145 -$3.50 × x

= 145 - 3.50x........... Equation 2

Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together

So, we have

Equation 1 = Equation 2

165 - 4x = 145 - 3.50x

We simplify further:

165 - 145 = -3.50 + 4.0x

20 = 0.5x

x = 20/0.5

x = 40

Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40

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 ;) ❤❤❤

Answer:

Step-by-step explanation:

For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.

fraction remaining = 55% = 0.55

0.55 = 0.5n

log 0.55 = n log 0.5

-0.2596 = -0.301 n

n = 0.8625 = # of half lives elapsed

0.8625 half lives x 2.5 billion years/half live = 2.16 billion years have elapsed = age of the rock

b)  0.15 = 0.5n

log 0.15 = n log 0.5

-0.824 = -0.301 n

n = 2.74 half lives

2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock

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:

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:

9/2π

=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:

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:

16 inches

Step-by-step explanation:

Note: it should say 56π inches instead of 56 inches otherwise no option is correct

Given

Full circumference of the wheel

Bike moves

The wheel turns:

We only consider her 0.5 of full turn of the wheel to identify the screw position

Since we consider the turns from the ground level as the initial position of the screw, the screw position in the end will be half turn opposite to ground level.

This is the full diameter length, which is 16 inches

So correct answer option is 16 inches

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:

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:

The answer is B.

Step-by-step explanation:

HOPE THIS HELPS U!!!

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.

Given :

[tex]F(x)=3(x^2-1)[/tex]

To Find :

the absolute minimum and absolute maximum values of f on the given interval

[-1,2] .

Solution :

Now , getting first order differential equation and equating its equal to zero.

[tex]\dfrac{d(3x^2-3)}{dx}=0\\\\6x=0\\x=0[/tex]

So , x=0 is critical point .

Now , coefficient of [tex]x^2[/tex] is positive .

Therefore , it is increasing function after  x=0 .

So , min value will be at , x=0.

[tex]Min = (0^2-1)\times 3=-3[/tex]

And maximum value will be the maximum at the x=2 because it is increasing function .

[tex]Max=(2^2-1)\times 3=9[/tex]

Therefore , max and min value is 9 and -3 respectively .

Hence , this is the required solution .

I hope this helps you

Answer:

F test = 2.54

Step-by-step explanation:

We are given two samples

Standard deviation of the first sample = 3.9288

Standard deviation of the second sample = 6.2597

F test statistic = Variance of the Larger sample/ Variance of the smaller sample

Variance = (Standard deviation)²

Variance for the first sample = 3.9288²

= 15.43546944

Variance for the second sample = 6.2597² = 39.18384409

F test = 39.18384409/15.43546944

= 2.5385586258

Therefore, the F test approximately = 2.54

Answer:

2.539

Step-by-step explanation:

Standard deviation of sample 1 = 3.9288

Standard deviation of sample 1 = 6.2597(

Standard deviation = √variance

Variance = (standard deviation)^2

Variance of sample 1 = (3.9288)^2 = 15.43546944

Variance of sample 2 = (6.2597)^2 = 39.18384409

For two samples:

F stat = (variance 1) / (variance 2)

Since the variance of sample is large, we place it in th e numerator

F stat = (39.18384409) / (15.43546944)

F stat = 2.5385586

F stat = 2.539