Which are correct representations of the inequality -3(2x-5) <5(2 - x)? Select two options.

Answer:

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 50 minutes and a standard deviation of 10 minutes.

This means that [tex]\mu = 50, \sigma = 10[/tex]

Class size of 30 students

This means that [tex]n = 30, s = \frac{10}{\sqrt{30}}[/tex]

What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes.

This is the p-value of Z when X = 48.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{48.5 - 50}{\frac{10}{\sqrt{30}}}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a p-value of 0.2061

0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes

Answer:

Step-by-step explanation:   7  3  13  31

3 × 1.8      long pieces                                  Calculate the ratios

2 × 1.44    9  tall vertical piece                     1.44 / 9  = x / 9      x = 1.44

5 × ___    8  medium vertical pieces          1.44 / 9  = x / 8      x = 1.28

6 × ___    7  short vertical pieces                1.44 / 9  = x / 7       x = 1.12

3 × 1.8      long pieces

2 × 1.44    9  tall vertical piece                     1.44 / 9  = x / 9      x = 1.44

5 × 1.28    8  medium vertical pieces          1.44 / 9  = x / 8      x = 1.28

6 × 1.12    7  short vertical pieces                1.44 / 9  = x / 7       x = 1.12

3 × 1.8      long pieces                                 =  5.4 m

2 × 1.44    9  tall vertical piece                   =  2.88  m

5 × 1.28    8  medium vertical pieces        =  6.4 m

6 × 1.12    7  short vertical pieces              =   6.72 m                  

                                                Total           =  21.4  m

Answer:

0.0069

Step-by-step explanation:

According to the Question,

We have, μ=22 , σ= 5 , P(X<9.7)=Area to the left of 9.7.

Z = (x-μ)/σ

Z = (9.7-22) / 5 ⇒ -2.46

Thus,

Answer:

They all test relationship when it involves two variables

Explanation:

All of the statistical methods listed above all measure the relationship between two variables.

The Chi Square test tests the relationship between two nominal/categorical variable groups.

The Pearson correlation test tests relationship between two continuous variables using the Pearson correlation coefficient to determine statistical relationship between them.

The simple linear regression measures relationship between two variables: dependent/response variable and independent/explanatory variable, to see if a relationship exists between by way of influence of the independent variable on the dependent variable.

Answer:

x < -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x/-2 > 5

Step 2: Solve for x

[tex]\large {\mathsf {\red{\underbrace {\overbrace{\blue{ {\pink}{Answєr}}}}}}} \: [/tex]

x > - 10

[tex] \large \mathtt \green{Step-by-step \: explanation : }[/tex]

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

Solve for x

[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]

common denominator is 2

[tex]\small \sf ➪ \frac{2x}{ - 2} >2 \times 5 \\ [/tex]

[tex]\small \sf ➪ \frac{ \cancel{2}x}{ - \cancel{ 2}} >2 \times 5 \\ [/tex]

➪ - x > 2 × 5

➪ - x > 10

multiply by - 1

➪ - x × - 1 > 10 × - 1

x > - 10

Answer:

Percent error=1.23%

Step-by-step explanation:

We are given that

Estimate length of room=20 feet

Actual length of room=20.25 feet

We have to find the percent error.

To find the percent error we will find the difference between the estimate length and actual length of room.

Difference=Actual length of room-Estimate length of room

Difference=20.25-20

Difference=0.25 feet

Now,

Percent error=[tex]\frac{Difference}{actual\;length}\times 100[/tex]

Percent error=[tex]\frac{0.25}{20.25}\times 100[/tex]

Percent error=1.23%

Answer:

P(red and blue) = 1/12

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of independent events:

If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each event happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

P (red and blue).

Probability of choosing a red marble, then a blue marble. The marbles are replaced, so the trials are independent.

Probability of a red marble:

3 out of 3 + 5 + 4 = 12. So

[tex]P(A) = \frac{3}{12} = \frac{1}{4}[/tex]

Probability of a blue marble:

4 out of 12, so:

[tex]P(B) = \frac{4}{12} = \frac{1}{3}[/tex]

P (red and blue).

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{4} \times \frac{1}{3} = \frac{1}{4*3} = \frac{1}{12}[/tex]

So

P(red and blue) = 1/12

Answer:

60 degrees

Step-by-step explanation:

So we see there's a 90 degree angle and a 150 degree larger angle including it.

So to find out the part that the 150 degree large angle that's not a part of the 90 angle we would do: 150 - 90, and we get 60.

So the bottom right angle is 60 degrees.

Now since we have a straight line from the left to right horizontally, we know that one side has to equal 180 degrees. On the side which the x is on, we already have 2 angles: 90 and 30. 90 + 30 = 120.

Since a straight line equals 180, x + 120 has to equal 180.

So now we do simple algebra.

x + 120 = 180

x = 180 - 120

x = 60

So x is equal to 60 degrees.

Answer:

8.35714285714

Step-by-step explanation:

Hope it help you

Answer:

-x^4, and (2√x)/x

Step-by-step explanation:

4. [tex]- \sqrt{ x^{8} } = - \sqrt{x^{4} *x^{4} } = -x^{4}[/tex]

x^8 = x*x*x*x*x*x*x*x = (x*x*x*x)(x*x*x*x) = (x^4)(x^4)

5.

[tex]\sqrt{\frac{4}{x} } = \frac{\sqrt{4} }{\sqrt{x} } = \frac{2}{\sqrt{x} } \\\\\\\frac{2}{\sqrt{x} } * \frac{\sqrt{x} }{\sqrt{x} } = \frac{2\sqrt{x} }{x}[/tex]

Answer:

28

Step-by-step explanation:

We know that ,

Answer:

Top left: not a function

Top right: not a function

Bottom left: function

Bottom right: not a function

Step-by-step explanation:

A function is a relationship where each x value has it's own y value ( note that domain = x values and range = y values)

For the one on the top left.

S and n have more than one y value.

Because s and n have more than one y value the relation is not a function

For the one of the top right.

There x value "c" has multiple y values therefore the relation is not a function

For the one on the bottom left

Each x value has it's own y value therefore it is a function ( note that the y values can repeat. It's only the x values that can't repeat. )

For the one on the bottom right

The x value "-5" has multiple y values therefore the relation is not a function

Answer:

x=−40

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x4−3x8=5

14x+−38x=5

(14x+−38x)=5(Combine Like Terms)

−18x=5

−18x=5

Step 2: Multiply both sides by 8/(-1).

(8−1)*(−18x)=(8−1)*(5)

x=−40

Answer:

x=−40

Hello!

x/4 - 3x/8 = 5

2x - 3x = 40

-x = 40

x = -40

Good luck! :)

Answer:

B

Step-by-step explanation:

The definition of a function is that any input will only have one output. Here, the input is the number of years, and the output is the value of the car. We know this because the question is asking why the value of the car is a function of the number of years. Therefore, based on the number of years, the value of the car is given.

Going back to the definition of a function, we can apply this year to say that any number of years will only have one car value. Another way to say this is that each time is associated with exactly one car value.

Answer:

DK = 10.23 units (approx)

Step-by-step explanation:

(DK * (CK + KE))/2 = 29

DK * CK = 29

180 - 31 = 149

149/2 = 74.5 --> degree of other angles

tan 74.5 = DK/CK

CK * tan 74.5 = DK

CK * CK * tan 74.5 = 29

CK = 2.83591462

2.83591462 * tan 74.5 = DK

DK = 10.22597776

So DK is approximately 10.23 units.

Hope this helps!

Answer:

8275382+9162672(7263382) 615-41+8162(71818)

Answer:

6280m

Step-by-step explanation:

6.28×1000m

=6280m

Answer:

The correct answer is:

        30 = 10 + 3h - 6

        26 = 3h

        h = 8.67

Step-by-step explanation:

We're gonna calculate by our part the hours a new costumer can rent a bike and pay a total of $30, using the original function:

Where:

We know The total money spent must be $30, by this reason, the function change to:

Now, we must clear the h variable, by this reason, we multiply 3 by h and 2:

We pass the 10 and the -6 to the left side of the equality:

Finally, we pass the 3 to the left side of the equality:

26 / 3 = h (the 3 pass to divide because is multiplying the x)

If we just use two decimals, the number of hours is:

How the third option is the one that shows this calculation and result, that is the correct answer.

Answer:

(3, 0)

Step-by-step explanation:

Given the inequality y > -2x + 3 and y ≤ x - 2

The graph of the inequalities are plotted using the geogebra graphing online calculator.

The portion of the graph that is shaded with dark blue, represents the portion that supports the equation.

All the ordered pair points given in the question are also labelled in the graph.

From the graph we can see that only point (3, 0) falls in the area that supports the equation. Hence (3, 0) makes both inequalities true.

Answer:

The last choice: 68/5 - 22/5 = 9 1/5

Step-by-step explanation:

Solve each problem:

9 3/7 = 10 3/7

The fractions are the same so look at the whole numbers.

Does 9 equal 10? No, it doesn't so this is a false statement.

332/4 = 1/83

Simplify 332/4:

332/4 = 83/1

83 does not equal 1/83 so this is a false statement.

37/5 = 5 2/5

Convert the improper fraction into a mixed number:

7 2/5 = 5 2/5

These numbers do not equal each other so this is a false.

68/5 - 22/5 = 9 1/5

Subtract the numerators on the left side of the equation:

46/5 = 9 1/5

Convert the improper fraction into a mixed number:

9 1/5 = 9 1/5

These numbers equal each other so this is a true statement!

Answer:

Step-by-step explanation:

the equation has the form of  y = mx + b  (slope intercept form)

where  m = - 1/5

start with the point-slope form and work it to the slope-intercept form

y-y1 = m(x-x1)     (point-slope form)

y-5 = -1/5(x-(-5))

y-5 = -1/5(x+5)

y-5 = -1/5(x) +  -1/5(5)

y-5 = -x/5 + - 5/5

y-5 = -[tex]\frac{1}{5}[/tex] X -1

y = -[tex]\frac{1}{5}[/tex] X - 1 +5

y = -[tex]\frac{1}{5}[/tex] X +4

there you go :)

Answer:

22.7 pounds

Step-by-step explanation:

Simply just subtract 42.7 with 37 (5/8) to get the answer. If done correctly, you should get 22.7 pounds.

So, the final answer is 22.7 pounds.

Hope this helped!

Answer: The answer is b

Answer:

The mean is to the right of the median

Step-by-step explanation:

Given

Skewed right distribution

Required

Relationship between the mean and the median

The question would be better answered if there are options available. Since there are none, I will provide a general answer/explanation.

For a distribution that is right skewed, the mean is always on the right side of the median.

Step-by-step explanation:

Let us assume his monthly salary as x. According to the question,

➝ Money spent on rent + Money spent for utility bill + Remaining money = His salary

[tex]\longrightarrow\sf {\dfrac{1}{3}x + \dfrac{1}{7}x + 759 = x} \\ [/tex]

[tex]\longrightarrow\sf {\dfrac{7x + 3x + 15939}{21}= x} \\ [/tex]

[tex]\longrightarrow\sf {\dfrac{10x+ 15939}{21}= x} \\ [/tex]

[tex]\longrightarrow\sf {10x+ 15939= 21x} \\ [/tex]

[tex]\longrightarrow\sf {15939= 21x - 10x} \\ [/tex]

[tex]\longrightarrow\sf {15939= 11x} \\ [/tex]

[tex]\longrightarrow\sf {\cancel{\dfrac{15939}{11}}= x} \\ [/tex]

[tex]\longrightarrow\underline{\boxed{\bf {1449= x}}} \\ [/tex]

Therefore, his monthly income is $1449.

Answer:

16 √(3)

and then the decimal form if needed is: 27.7128129211

Step-by-step explanation:

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

To learn more about Value of the expression refer to:

https://brainly.com/question/13961297

#SPJ2

Answer:

option c

Step-by-step explanation:

becoz for inverse the number that is negative changes into positive like wise for the positive number it changes into negative , just opposites

Answer:

C

Step-by-step explanation:

here in the question it is given that it is four times as long as wide and its area is 36 square inches

now as we onow 3×4 =12

therefore here the side becomes four time

now area of rectangle is equal to 12 ×3 =36