|2x + 4| less than or equal to 5

Answer:

a)   [tex]S=50[/tex]

    [tex]P(X)=0.02[/tex]

b)  [tex]P(W,M,C)=8*10^-^6[/tex]

c)  [tex]P(W_2_3)=1.18*10^-^3[/tex]

Step-by-step explanation:

From the question we are told that

Sample space S=50

Sample size n=30

a)Generally the sample space S is

[tex]S=50[/tex]

The probability measure is given as

[tex]P(X)=\frac{1}{50}[/tex]

[tex]P(X)=0.02[/tex]

b)

Generally the probability that  the class hangs Wisconsin’s flag on Monday, Michigan’s flag on Tuesday, and California’s flag on Wednesday is mathematically given as

Probability of each one being hanged is

[tex]P(X)=\frac{1}{50}[/tex]

Therefore

[tex]P(W,M,C)=\frac{1}{50} *\frac{1}{50}* \frac{1}{50}[/tex]

[tex]P(W,M,C)=\frac{1}{125000}[/tex]

[tex]P(W,M,C)=8*10^-^6[/tex]

c)Generally the probability that Wisconsin’s flag will be hung at least two of the three days is mathematically given as

Probability of two days hung +Probability of three days hung

Therefore

[tex]P(W_2_3)=^3C_2 (1/50) * (1/50) * (49/50) +^3C_3 (1/50) * (1/50) *(1/50)[/tex]

[tex]P(W_2_3)=148 / 125000[/tex]

[tex]P(W_2_3)=1.18*10^-^3[/tex]

Answer:

The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.

Step-by-step explanation:

We have that 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 Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

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{5}{\sqrt{64}} = 1.225[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes

The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes

The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.

The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.

Given :

The following steps can be used in order to determine the 95% confidence interval for the mean installation time:

Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.

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

where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.

Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.

[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]

[tex]M = 1.225[/tex]

Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).

The 95% confidence interval for the mean installation time is (40.775, 43.225).

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Answer:

7,6

Step-by-step explanation:

So in total Peyton must buy 10 items. Since she's already buying 4 drinks. We need to find the amount of tacos the max amount of tacos she can buy are 7 tacos and the minimum is 6 because if we bought less than 6 it wouldn't have met the criteria for 10 items minimum. And if we passed 7 tacos it would go past the limit of how much money Peyton has. I hope this helped:)

Step-by-step explanation:

[tex] = 2\pi \times r = 2\pi \times \frac{16}{2} = 2\pi \times 8 = 50.265 = 50.27[/tex]

Answer:

x=–/-4

Step-by-step explanation:

Let's solve your equation step-by-step.

5(2)(1)+4(x+1)=x+2

Step 1: Simplify both sides of the equation.

5(2)(1)+4(x+1)=x+2

5(2)(1)+(4)(x)+(4)(1)=x+2(Distribute)

10+4x+4=x+2

(4x)+(10+4)=x+2(Combine Like Terms)

4x+14=x+2

4x+14=x+2

Step 2: Subtract x from both sides.

4x+14−x=x+2−x

3x+14=2

Step 3: Subtract 14 from both sides.

3x+14−14=2−14

3x=−12

Step 4: Divide both sides by 3.

3x

3

=

−12

3

x=−4

Answer:

x=−4

Answer:

The two triangles are related by AAS, so the triangles are congruent.

Step-by-step explanation:

Two angles and a non-included side of one triangle are congruent to corresponding two angles and an included side in the other triangle. Therefore, we can conclude that the two triangles are related by the AAS Congruence Criterion. Hence, both triangles congruent to each other.

Answer:

At least 75% of these commuting times are between 30 and 110 minutes

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean of 70 minutes, standard deviation of 20 minutes.

Since nothing is known about the distribution, we use Chebyshev's Theorem.

What percentage of these commuting times are between 30 and 110 minutes

30 = 70 - 2*20

110 = 70 + 2*20

THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes

Answer:

A= 2pirh +2pir^2

972=2 x pi x x x 5x + 2 x pi x x^2

972= 31.4x^2 + 6.28x^2

972=37.68x^2

x^2= 972/37.68

x^2=25.796

x= 25.796 square root

x= 5

The value of x is 5 cm.

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The surface area of a cylinder = 972 cm²

The surface area of a cylinder.

= 2πrh + 2πr²

Diameter = 2x

Radius = x

Height = 5x

Now,

2πrh + 2πr² = 972

2π (rh + r²) = 972

2π (5x² + x²) = 972

2π x 6x² = 972

6x² = 972/(2 x 3.14)

6x² = 154.78

x² = 25.79

x = √25.79

x = 5.08

x = 5

Thus,

x value is 5.

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Answer:

D. 27

Explanation:

First you solve parentheses by solving the exponent 2^3 and adding 4, and you will get 12. Then you'll solve the exponent 3^2 which will give you 9. Then you will multiply 9 by 12 to get 108. Then you will solve the exponent 2^2 which will get you 4. Finally divide 108 by 4 which will give you 27. Hope this helps!

Answer:

Expression

Step-by-step explanation:

Answer: Expression

Got this right!!!

Hope this helps!!!

Answer:

Step-by-step explanation:

Cross multiply on both sides

= (x + 1) (21) = 15(x + 3)

= 21x + 21 = 15x + 45

Bringing like terms on one side

21x - 15x = 45 - 21

= 6x = 24

x = 24/6 = 4

Option A is the correct answer

[tex] =\tt (a) \: 4[/tex]

[tex] = \frac{x + 1}{x + 3} = \frac{15}{21} [/tex]

[tex] =( x + 1 )\times 21 = (x + 3 )\times 15[/tex]

[tex] = 21x + 21 = 15x + 45[/tex]

[tex] = 21x + 21 - 15x = 45[/tex]

[tex] = 6x + 21 = 45[/tex]

[tex] = 6x = 45 - 21[/tex]

[tex] = 6x = 24[/tex]

[tex] = x = \frac{24}{6} [/tex]

[tex] =\color{plum} \bold{x = 4}[/tex]

Let us now place 4 in the place of x and see if the substitution is equivalent to [tex] \frac{15}{21} [/tex] :

[tex] = \frac{4 + 1}{4 + 3} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15÷3}{21÷3} [/tex]

[tex] = \frac{5}{7} = \frac{5}{7} [/tex]

Therefore, the value of x in this proportion = 4

Answer:

I think it's true

Step-by-step explanation:

Answer: this is true

Step-by-step explanation:

The term out of is express as a fraction

Example:

1/2

This is 1 out of 2

Hope this helps ;)

Answer:

Step-by-step explanation:

Brayden's car travels 37.1 miles per gallon.

Dylan's car travels 48.4 miles/(2 gallons) = 24.2 miles per gallon.

37.1 - 24.2 = 12.9

Dylan's car gets 12.9 miles per gallon less than Brayden's car.

Answer:  4

Step-by-step explanation:

I got it right when i did my math

The equation which represents the given situation is 5(y + 2) = 30 and the value of y = 4.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Total number of volunteers = 5

Mai gave each of them the same number of stickers.

Let y be the number of stickers she gave to each of them.

Then she gave 2 more stickers to each of them.

Then number of stickers each has = y + 2

Total number of stickers = 30

5(y + 2) = 30

5y + 10 = 30

5y = 20

y = 4

Hence the number of stickers each one has is 4.

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Answer:

$625

Step-by-step explanation:

If Todd has to pay $14,000 in tuition for his school each year and uses $6,500 in financial aid each year all for 2 years, the money he needs to save can be modeled by:

2(-$14000 + $6500) + 2(12x) = 0.

x is the minimum amount of money he needs to save in order to cover this expense without debt.

Thus 2(-$14000 + $6500) + 2(12x) = 0 →

2(-$7500) + 24x = 0 → -$15000 + 24x = 0 →

24x = $15000 → x = $625

Answer:

$625

Step-by-step explanation:

If Todd has to pay $14,000 in tuition for his school each year and uses $6,500 in financial aid each year all for 2 years, the money he needs to save can be modeled by:

2(-$14000 + $6500) + 2(12x) = 0.

x is the minimum amount of money he needs to save in order to cover this expense without debt.

Thus 2(-$14000 + $6500) + 2(12x) = 0 →

2(-$7500) + 24x = 0 → -$15000 + 24x = 0 →

24x = $15000 → x = $625

Answer:

x=6

Step-by-step explanation:

Answer:

y=15x+35

Step-by-step explanation:

15 every month and 35 for instant charge

Answer:

0.30

Step-by-step explanation:

Probability of stopping at first signal = 0.36 ;

P(stop 1) = P(x) = 0.36

Probability of stopping at second signal = 0.54;

P(stop 2) = P(y) = 0.54

Probability of stopping at atleast one of the two signals:

P(x U y) = 0.6

Stopping at both signals :

P(xny) = p(x) + p(y) - p(xUy)

P(xny) = 0.36 + 0.54 - 0.6

P(xny) = 0.3

Stopping at x but not y

P(x n y') = P(x) - P(xny) = 0.36 - 0.3 = 0.06

Stopping at y but not x

P(y n x') = P(y) - P(xny) = 0.54 - 0.3 = 0.24

Probability of stopping at exactly 1 signal :

P(x n y') or P(y n x') = 0.06 + 0.24 = 0.30

Answer:27.1c

Step-by-step explanation:

18.6 + 8.5 =27.1

Answer:

27.1

Step-by-step explanation:

Answer:HI

Step-by-step explanation:HI

Answer:

A. Cendric is correct because he used the inverse of subtraction and added 4.5

Step-by-step explanation:

To solve for x, all we needed to do was to make x stand alone. To do this, we have to apply addition property of equality. This means we would add 4.5 to both sides for the equation to balance. Thus, we would have z standing alone which equals 3.

Therefore, Cendric was correct because he used the inverse of subtraction of -4.5, which is 4.5 that was later added to both sides of the equation.

Answer:

72 cm³ (see below)

Step-by-step explanation:

First, refer to the volume formula:

V = l · w · h

If you plug in all of your values and simplify, you'll get the volume:

l = 6 cm

w = 3 cm

h = 4 cm

V = (6) (3) (4)

V = 18 (4)

V = 72 cm³

Because this is volume, the measurements are units cubed, meaning it's cm³.

Answer: D 35/100

Step-by-step explanation: if you divide 35/100, the answer would be .35, which is the decimal form of 35%.

Answer:

B 4 1/4

Step-by-step explanation:

Answer:

Its B. 4 1/4

Step-by-step explanation:

How it helps!

UmmmmAnswer:

Step-by-step explanation:

Answer:

1

Step-by-step explanation: