let x be a random variable with c.dj. f(x). find the c.d.f. of ax b first for a > 0, then for a < o.

Answer:  60

Step-by-step explanation:

9514 1404 393

Answer:

  d.  f(2) < g(2)

Step-by-step explanation:

The attached table and graph shows how the functions relate for the various x-values of interest. The true statement is ...

  f(2) < g(2)

  -3 < 0

Answer:

The range of values from one job is between $50 and $650.

Step-by-step explanation:

An electrician charges y amount to work x hours on a job. The electrician charges a $50 service fee and $30 per hour.

This means that his earnings in a job can be modeled by the following function:

\(y = 30x + 50\)

The electrician works maximum of 20 hours on any job. What is the range of values for one job?

Minimum, he works 0 hours, and earns:

\(y(0) = 30(0) + 50 = 50\)

Maximum, he works 20 hours, and earns:

\(y(20) = 30(20) + 50 = 650\)

The range of values from one job is between $50 and $650.

The measure of the angles formed between parallel lines and their transversals indicates;

9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°

Parallel lines are lines that  maintain the are equidistant from each other and have the same slope on the coordinate plane.

The angles formed between the parallel lines and their transversal are;

1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e);  ∠15 & ∠11

3. Alternate interior angles (a); ∠10 & ∠15

4. Vertical angles (d); ∠12 & ∠15

5. Corresponding angles (b); ∠9 & ∠11

6. None (f); ∠9 & ∠15

7. Supplementary angles (e); ∠13 & ∠14

8. Alternate interior angles; ∠14 & ∠11

9. The alternate interior angles theorem indicates that we get;

(a + 28) = 2·a

Therefore; 2·a - a = 28

2·a - a = a, therefore;

a = 28

∠MNP = (a + 28)° = (28 + 28)° = 56°

10. The alternate interior angles theorem indicates that we get;

5·y° = (2·y + 78)°

Therefore;

5·y - 2·y = 78

3·y = 78

y = 78/3 = 26

The measure of the angle WXZ, m∠WXZ = 5·y°

Therefore; m∠WXZ = 5 × 26 = 130

m∠WXZ = 130°

9. ∠2 ≅ ∠3 (Vertical angles theorem)

m∠2 = m∠3

Therefore; m∠3 = m∠2 = 97°

m∠5 + m∠6 = 180° (Linear pair angles theorem)

m∠5 + 83° = 180°

m∠5 = 180° - 83° = 97°

∠10 and ∠2 are corresponding angles, therefore;

m∠10 = m∠2 = 97°

∠7 and ∠6 are vertical angles, therefore;

m∠7 = m∠6 = 83°

∠9 and ∠3 are same side interior angles, therefore;

m∠9 + m∠3 = 180°

m∠9 = 180° - m∠3

m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°

∠16 and ∠6 are same side exterior angles, therefore;

m∠16 + m∠6 = 180°

m∠16 = 180° - 83° = 97°

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Answer:

Step-by-step explanation:

To create a frequency distribution with a first class of 13-19 and a class width of 7, we need to determine the boundaries for each class. The first class has a lower boundary of 13 and an upper boundary of 19. The upper boundary of each subsequent class is obtained by adding 7 to the previous upper boundary.

Using these boundaries, we can count how many values fall into each class:

Class Boundaries Tally Frequency

1             13-19  

2            20-26  

3            27-33  

4           34-40  

5           41-47  

6          48-54  

7          55-61  

8         62-68  

9         69-75  

To obtain the frequency, we count the number of values that fall into each class. The tally column is used to keep track of the values as they are counted.

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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The length of the 180° arc as required in the task content is; 22/21 inches.

Recall that the length of an arc is given by the formula;

Length of arc = theta / 360 × 2 π r

Therefore, for a radius of 3 inches;

Length of arc = 180/360 × 2 × 22/7 × 3

Length of arc = 22/21 inches.

Ultimately, the length of the arc in discuss is; 22/21 inches.

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The time Ann finished playing in the backyard is 12 : 15 pm

Total time = 9:38 + 41 minutes + 1 hour 56 minutes

= 10:19 + 1 hour 56 minutes

= 12 : 15 pm

Therefore, the time Ann finished playing in the backyard is 12 : 15 pm

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Answer:

I got 571

Step-by-step explanation:

not sure but best bet

The fails to dismiss the null hypothesis, so he's unable to conclude that there's enough proof to back up his faith that there are greater than \(30\)% coloured jelly beans for each bag.

Chance is simply how probable an event is to happen. If we are unsure of how an incident will come out, we might debate the probability of various outcomes, and how likely they are. The examination of occurrences regulated by probability is termed statistics.

French mathematician as well as philosopher Blaise Pascal made significant contributions to many branches of mathematics. In correspondence with Fermat, he started working on conic sections as well as spatial geometrical and laid the groundwork again for probability theory.

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The p-value is not less than the significance level, Ramon fails to reject the null hypothesis.

What is null hypothesis?

In statistical hypothesis testing, the null hypothesis is a statement that there is no significant difference between two specified populations, or that a proposed relationship between two variables does not exist.

Ramon used the following null and alternative hypotheses:

H0: p = 0.30 (The proportion of blue jelly beans is 30%)

Ha: p > 0.30 (The proportion of blue jelly beans is greater than 30%)

Ramon calculated a p-value of 0.256, which is greater than his significance level of 0.1.

Since the p-value is not less than the significance level, Ramon fails to reject the null hypothesis.

Therefore, he does not have enough evidence to conclude that the proportion of blue jelly beans is greater than 30%.

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The percent extension and lengthening (in meters) for the deformed rock layers is 20%.

Percent extension refers to the amount of stretching that has occurred in a rock layer, expressed as a percentage of its original length.

To calculate percent extension, we would subtract the original length from the current length (120 - 100 = 20) and then divide that difference by the original length (20/100 = 0.2).

Finally, we would multiply by 100 to get the percent extension (0.2 x 100 = 20%).

Therefore, the percent extension of the rock layer would be 20%.

In summary, percent extension and lengthening are important concepts in geology that help us understand how rocks have been deformed over time.

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Answer:

the probability is:

P(A) 2/6 =1/3

Now let's take rolling a prime number:

A prime number is a natural number greater than 1 which can only be divided without a remainder by 1 and itself. So from the numbers on the cube prime numbers are:

2, 3 and 5. The probability of getting a prime number in a single roll is:

P(B) =3/6=1/2

Now to calculate the probability of A and B

you have to multiply both probabilities:

P(A-B)=P(A) . P(B) = 1/3 . 1/2 = 1/6

Step-by-step explanation:)

Answer:

\(\frac{2}{45}\)

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

I don't know I'm sorry (◞‸◟ㆀ)

Answer:

The mode are: 7, 8

Step-by-step explanation:

Given

\(7, 11, 8, 7, 8, 7, 8, 11, 8, 10, 7\)

Required

Determine the mode

We start by arranging the given data in ascending order

The ordered data are:

\(7,7,7,7, 8,8,8,8, 10, 11, 11\)

From the above data.

7 has a frequency of 4

8 has a frequency of 4

10 has a frequency of 1

11 has a frequency of 2

The data with the highest frequency is the mode.

We can see that 7 and 8 both have frequencies of 4

Hence, the mode are: 7, 8

Answer:

The mode are: 7, 8

Step-by-step explanation:

This sounds like an answer....

Answer:

4/5 would be at the 8th line, and 3/10 would be on the 3rd

Step-by-step explanation:

Answer:

The point that could represent the numbers of adults and child haircuts that meet the stylist goals is 25, 0.

Since the hairstylist change $15 for an adult haircut and $9 for a child haircut, then using 25, 0 will be:

= 15(25) + 9(0)

= 375 + 0

= $375

Therefore, she has earned at least 360 dollars and cut about 25 haircuts this week.

In conclusion, the correct option is A.

Answer:

THE FRIST ONE

!Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Plug in both point values into each of the equations and see if the LHS = RHS.

Only eq A satisfies for both points

eq B satisfies for point (5,6) but not for (1,1)

Equations C and D satisfy for neither point

The equation of the straight line passing through the points (1, 1) and (5, 6) is 4y = 5x - 1.

The general equation of a straight line is -

y = mx + c

Here {m} is the slope which also denotes the unit rate. Unit rate is the rate at which the value of {y} changes per unit change in the value of {x}.

Given is the table as shown in the figure.

The line passes through the points (1, 1) and (5, 6). We can write the slope of the line as -

m = (6 - 1)/(5 - 1)

m = 5/4

So, we can write the equation as -

y = 5x/4 + c

For the point (1, 1), we can write -

1 = 5/4 + c

c = 1 - 5/4

c = (4 - 5)/4

c = -1/4

So, the equation will be -

y = 5x/4 - 1/4

y = (5x - 1)/4

4y = 5x - 1

Therefore, the equation of the straight line passing through the points (1, 1) and (5, 6) is 4y = 5x - 1.

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Answer:

$5000

Step-by-step explanation:

20% = 1,000.00

1% = 1,000.00 ÷ 20 = 50

100% = 50 x 100 = 5000

The transformed equation of \(y = x^{3}\) is \(y = -\frac{1}{7} (x + 8)^{3}\).

Given equation ;  \(y = x^{3}\)

Applying the given transformations, we have:

To have a vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by  \(\frac{1}{7}\). So, we have:

\(y =\)  \(\frac{1}{7}\) \(x^{3}\)

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

\(y = \frac{1}{7} (x + 8)^{3}\).

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

\(y = -\frac{1}{7} (x + 8)^{3}\).

Therefore, the transformed equation is  \(y = -\frac{1}{7} (x + 8)^{3}\).

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46 minutes is the elapsed time :)

Answer:

46 minutes

Step-by-step explanation:

In order to find the time elapsed, you must subtract 10:51 and 10:05 which equals 46 minutes.

Answer:

 5.93 years

Step-by-step explanation:

The continuous compounding formula tells you the amount after t years will be ...

  A = Pe^(rt) . . . . principal P compounded continuously at annual rate r for t years

  7400 = 5500e^(0.05t)

  ln(7400/5500) = 0.05t . . . . divide by 5500, take natural logs

  t = 20×ln(74/55) ≈ 5.93

It will take about 5.93 years for $5500 to grow to $7400.

It's important to know that the domain refers to the x-values of the function, and the range refers to the y-values of the function. Graphically, the domain would be the x-axis and the range would be the y-axis, that is, their values.

As you can observe in the given graph, the function doesn't have any interruption or restriction horizontally, it goes from the negative x-axis to the positive x-axis, this means the domain is all real numbers from negative infinity to positive infinity, as follows

On the other hand, the range of the given function is from y = -2 to positive infinity, it's important to know that y = -2 is excluded from the range because as you can observe the function curves there without crossing y = -2. So, the range is

For the second question of the problem, we have to select two y-values from x = 0 and x = 1, which is the given interval. From the graph, we can identify that x = 0 belongs to y = -1, and x = 1 belongs to y = 1. So, we have the points (0,-1) and (1,1). Now, we use the following formula to find the average rate of change.

Where a = 0, f(a) = -1, b = 1, and f(b) = 1, note that these values are the coordinates of the two points we selected. Let's use these values to find the rate.

Answer:

the average rate of change over the interval [1,0] is 2.

Step-by-step explanation:

\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

The quadratic equation with roots -7, 3/4 in standard form is

4x² + 25x - 21 = 0.

A quadratic equation is an algebraic equation of degree two and has exactly two roots real or imaginary or complex.

We know the roots of a quadratic equation are also factors of a quadratic equation.

If x = a and x = b are two roots of a quadratic equation then x - a = 0 and

x - b = 0 are the factors of a quadratic equation that can be formed by multiplying the two factors (x - a)(x - b) = 0.

Given that -7 and 3/4 are the roots.

∴ { x - (-7)}{ x - 3/4) = 0.

(x + 7)(x - 3/4) = 0.

x² + 7x -(3/4)x - 21/4 = 0.

x² + (25/4)x - 21/4 = 0.

4x² + 25x - 21 = 0.

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Answer:

the answer is 17