Line segment is reflected about the y-axis to form C’D’. Which is statement describes C’D’?

Every point in the interval [2, 6] has an equal probability of occurring, 1/(6 - 2) = 1/4. So the PDF of X is

[tex]f_X(x) = \begin{cases} \frac14 & \text{if } 2 \le x \le 6 \\ 0 & \text{otherwise} \end{cases}[/tex]

Compute the CDF by integrating the PDF.

• If [tex]x<2[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^x 0 \, dt = 0[/tex]

• If [tex]2\le x< 6[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^x \frac{dt}4 \\\\ ~~~~~~~~~~~~~~~~~ = 0 + \frac14 \int_2^x \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \frac{x-2}4[/tex]

• If [tex]x\ge6[/tex], we have

[tex]\displaystyle \int_{-\infty}^x f_X(t) \, dt = \int_{-\infty}^2 f_X(t) \, dt + \int_2^6 f_X(t) \, dt + \int_6^x f_X(t) \, dt \\\\ ~~~~~~~~~~~~~~~~~ = \int_{-\infty}^2 0 \, dt + \int_2^6 \frac{dt}4 + \int_6^x 0 \, dt \\\\ ~~~~~~~~~~~~~~~~~ = 0 + 1 + 0 \\\\ ~~~~~~~~~~~~~~~~~ = 1[/tex]

Putting the pieces together, we find the CDF to be

[tex]\boxed{F_X(x) = \begin{cases} 0 & \text{if } x < 2 \\\\ \dfrac{x-2}4 & \text{if } 2\le x < 6 \\\\ 1 & \text{if } x\ge6 \end{cases}}[/tex]

Compute the expectation of X.

[tex]\Bbb E[X] = \displaystyle \int_{-\infty}^\infty x\,f_X(x)\,dx \\\\ ~~~~~~~ = \int_{-\infty}^2 0 \, dx + \int_2^6 \frac x4 \, dx + \int_6^\infty 0 \, dx \\\\ ~~~~~~~ = 0 + \frac{6^2 - 2^2}8 + 0 \\\\ ~~~~~~~ = \boxed{4}[/tex]

Answer: -6.25, -2, 3/4, 3, 5, 6, 67/10 would be the soliton

Answer:

D

Step-by-step explanation:

an = 3/4 × an-1

let's see for n = 2

a2 = 3/4 × a1 = 3/4 × 4

n = 3

a3 = 3/4 × a2 = 3/4 × 3/4 × a1 = 3/4 × 3/4 × 4 = 9/16 × 4

so, we see, we multiply 3/4 one time less than n by itself and then by 4.

that makes D the correct answer.

the multiplication by (n - 1) in answer C would add 3/4 n-1 times instead of multiplying it n-1 times.

to apply n-1 multiplications we need to use n-1 as exponent.

Answer:

6.  ∠PVU = 58°

7.  y = 74°

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ ∠USP + ∠PSV = 180°

⇒ 148° + ∠PSV = 180°

⇒ 148° + ∠PSV - 148° = 180° - 148°

⇒ ∠PSV = 32°

The interior angle of a rectangle at each vertex is 90°.

⇒ ∠VPS = 90°

Interior angles of a triangle sum to 180°.

⇒ ∠PVS + ∠PSV+ ∠VPS = 180°

⇒ ∠PVS + 32° + 90° = 180°

⇒ ∠PVS + 122° = 180°

⇒ ∠PVS + 122° - 122° = 180° - 122°

⇒ ∠PVS = 58°

From inspection of the given diagram:

⇒ ∠PVU = ∠PVS

⇒ ∠PVU = 58°

Opposites sides of a rectangle are parallel.

Therefore, GF is parallel to AB:

⇒ ∠CFG = ∠CBA = 32°

Interior angles of a triangle sum to 180°.

⇒ ∠FGC + ∠GCF + ∠CFG = 180°

⇒ y + 74° + 32° = 180°

⇒ y + 106° = 180°

⇒ y + 106° - 106° = 180° - 106°

⇒ y = 74°

The scale from a playground to this drawing is 5 ft to 1 cm. The scale from the same playground to another drawing is 8 ft to 1 cm. What are the side lengths of the playground in the other scale drawing?

The side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].

By using geometry we answer this question.

Geometry is nothing but  the branch of mathematics which deals with measurements of shapes.

Here, we take the scale from a playground to this drawing as "a" and The scale from the same playground to another drawing as "b".

First, we see the scale from a playground to this drawing.

[tex]\frac{a}{l}= \frac{1}{5}[/tex]

[tex]l=5a[/tex]

Now we see the scale from the same playground to another drawing.

[tex]\frac{b}{l} =\frac{1}{8}[/tex]

[tex]b=\frac{l}{8}\\[/tex]

Here, l=5a then

[tex]b=\frac{5a}{8}[/tex]

Therefore, the side lengths of the playground in the other scale drawing is [tex]\frac{5a}{8}[/tex].

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Step-by-step explanation:

The function f was shifted 8 units to the right to obtain g.

Answer:

  see attached

Step-by-step explanation:

You want the truth table for a logical implication that involves other logical expressions with up to three variables.

A truth table is conveniently produced using the logical operations available on a spreadsheet. The AND (∧), OR (∨), and NOT (¬) functions are built-in to the spreadsheet. The implication (→) function must use the equivalent:

  p → q ≡ ¬p∨q

If p, q, and r are in columns A, B, C, respectively, then the formulas in columns D through G are ...

The formulas are filled to the following rows.

The values of p, q, and r are entered manually. The spreadsheet computes the truth values for the formulas.

The value of the given functions are:

(i) f + g = x² + x - 6

(ii) f - g = -x² + x - 4

(iii) f . g = x³ - 5x² - x + 5

(iv) f/g = ( x - 5)/(x +1)(x - 1)

(v) g(f(x)) = x² - 10x + 24

The two functions are given that

f(x) = x - 5

g(x) = x² - 1

We have to find

(i) f + g

f(x) + g(x) = ( x-5)  + (x² - 1)

                = x² + x -5 -1

               = x² + x -6

(ii) f - g

f(x) - g(x) = (x-5)- (x² - 1)

              = -x² + x -5 +1

              = -x² + x -4

(iii) f . g

f(x) . g(x) = (x-5)(x²-1)

              =x(x² - 1) -5(x² - 1)

              = x³ - x - 5x² + 5

              = x³ - 5x² - x + 5

(iv) f/g

f(x) / g(x) = (x-5) / ( x² - 1)

              = (x - 5) / (x+1)(x-1)

(v) g(f(x)) = - 1 + ( -5 + x )²

              = -1 + 25 + x² - 10x

              = x² - 10x + 24

Therefore we get the value of the function, (i) f + g = x² + x - 6, (ii) f - g = -x² + x - 4,(iii) f . g = x³ - 5x² - x + 5, (iv)f/g = ( x - 5)/(x +1)(x - 1), (v) g(f(x)) = x² - 10x + 24.

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The complete question is:

F(x)=x-5 and g(x)=x2 - 1 find (i) f + g , (ii) f-g, (iii) f. g (iv) f/g (v) g(f(x)).

Answer:

12

Step-by-step explanation:

15:10

15/10=1.5g/min

1.5x8=12.

A camel can drink 12L in 8 minutes.

Using proportions, it is found that the cat has to go 9/16 further to reach the gate.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

An entire distance is represented by the proportion of 1 = 100%. The cat has gone 7/16 of the distance, hence the fraction corresponding to the remaining distance that he has to go is given by:

1 - 7/16 = 16/16 - 7/16 = 9/16.

Hence the cat has to go 9/16 further to reach the gate.

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Answer:

£30

Step-by-step explanation:

Elvis is paying for 2/3 of 3 kg, so the cost is:

[tex]\frac{2}{3}(45)=30[/tex]

Answer:

its 4

Step-by-step explanation:

[tex] \bf\longrightarrow \large\frac{ \frac{ \frac{a( {r}^{4} - 1)}{ \cancel{r - 1}} }{a( {r}^{2} - 1) } }{ \cancel{r - 1}} = 10 \\ [/tex]

[tex]\bf\longrightarrow {r}^{4} - 1 = {10r}^{2} - 10[/tex]

[tex]\bf\longrightarrow {r}^{4} - {10r}^{2} + 9 = 0[/tex]

[tex]\bf\longrightarrow \: {a}^{2} - 10 {a}^{2} + 9 = 0[/tex]

[tex]\bf\longrightarrow \: a = \frac{10± \sqrt{100 - 36} }{2} = \frac{10±8}{2} [/tex]

r = 3 or r = 1 but r ≠ 1

[tex]\therefore[/tex] r = 3

[tex]\bf\longrightarrow \: a_3 = 54 \\ \bf\longrightarrow \: a {r}^{2} = 54 \\ \bf\longrightarrow \: a = \frac{54}{9} = 6[/tex]

Answer:

2, 4 6, 8

Step-by-step explanation:

The counting numbers are the set of numbers: 1,2,3,4,... It follows that pattern forever.  No, 1/2 or .0745.

Answer:

2 4 6 8 is the answer for your question

Answer:

28.26 inches^2

Step-by-step explanation:

The area of a circle is given by the formula [tex]A = \pi r^2[/tex].
We know that the diameter of the circle is 6 inches, therefore, its radius 3 inches (the radius is exactly one half of the circle's diameter).

Substituting into the formula

[tex]A = \pi r^2 \\ \\\to A = \pi \times 3^2 \\ \\\to A = \pi \times 9 = 28.26[/tex]

Answer:

30 000

Step-by-step explanation:

30 000   if underlined digit is >= 5 round thousands up 1 ...o/w leave as is

30 000

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Domain : All values of x, for which function is defined.

i.e [tex]\boxed{\sf 0\leqslant x\leqslant 12} [/tex]

Range : All possible values of y, that can be obtained by putting value of x in the equation of function

i.e [tex]\boxed{\sf 0\leqslant y\leqslant 900} [/tex]

Step-by-step explanation:

when a line intersects with 2 (or more) parallel lines, the angles at the intersection points are the same for each parallel line.

therefore,

5 + 10x = 85

10x = 80

x = 8

so, B is the right answer option.

Answer: 13/12 times 12/4 is the answer

Answer:

Step-by-step explanation:

Discussion

Let's consider an rational number for a moment. If I tell you that the fraction you used was 1/3 and gave you the first couple of numbers as in

1/3 = 0.33333.....

and asked you what the next number is, you should be able to tell me that the number to write down is 3.

Even something like 1/7 is well behaved.

1/7 = 0,142857142857142857 .... and tell you I want the next number, you should be able to see it as 1.

But an irrational number can't be handled that way. If I ask for the next digit after 5 when taking the square root of 2, you would have no idea what I was talking about without the help of a calculator.

Now if you multiply a rational by an irrational, you just get a bigger irrational, but it remains irrational.

The statement is false.

Answer:

[tex]2 \frac{5}{8} [/tex]

Step-by-step explanation:

[tex]1. \: \frac{1 \times 6 + 1}{6} \times 2 \frac{1}{4} \\ 2. \: \frac{6 + 1}{6} \times 2 \frac{1}{4} \\ 3. \: \frac{7}{6} \times 2 \frac{1}{4} \\ 4. \: \frac{7}{6} \times \frac{2 \times 4 + 1}{4} \\ 5. \: \frac{7}{6} \times \frac{8 + 1}{4} \\ 6. \: \frac{7}{6} \times \frac{9}{4} \\ 7. \: \frac{7 \times 9}{6 \times 4} \\ 8. \: \frac{63}{6 \times 4} \\ 9. \: \frac{63}{24} \\ 10. \: \frac{21}{8} \\ 11. \: 2 \frac{5}{8} [/tex]

After rounding, we can say that there are about 1,140 candles in the 22 packets.

First let's get the exact number, and then round it as we need to do.

We know that each packet contains 52 candles, and there are 22 packets, so the total number of candles is given by the product between these two values, which gives:

C = 52*22 = 1,144 candles.

Now we want to round it to the nearest ten, to do so, we need to look at the digit at the right of the tens unit (in this case the ones digit) and see, if it is 5 or more, we round up, if it is 4 or less, we round down.

We can see that it is a 4, so we round down here:

C = 1,140

There are about 1,140 candles in the 22 packets.

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Answer:

Step-by-step explanation:

A triangle has a base of 7.2 centimeters and height of 10.24 centimeters. A large triangle has a base of question mark centimeters and a height of 25.6 centimeters.

The diagram represents the process of creating a scale drawing from an original using a scale factor of 0.4. The base of the original drawing must be:

17.6 cm

18 cm

33.5 cm

45 cm

--------------------

1st solution (using an equation)

10.24 : 7.2 = 25.6 : x

x = 7.2 * 25.6 : 10.24

x = 18cm

------------------------------------

2nd solution (using the scale factor)

7.2 : 0.4 =

18 cm

Answer: 18cm

Step-by-step explanation:

The rate of change of the cost in dollars with respect to the number of t-shirts printed is $0.75 per shirt.

An equation is an expression that shows the relationship between two or more numbers and variables.

A linear function is in the form:

y = mx + b

Where m is the rate of  change and b is the initial value of y.

Given that the cost f(x) in dollars for printing x, t-shirts is given by:

f(x) = 100 + 0.75(x - 50)

f(x) = 0.75x + 62.5

Comparing with linear function, the rate of change is 0.75

The rate of change of the cost in dollars with respect to the number of t-shirts printed is $0.75 per shirt.

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Considering the definition of an equation and the way to solve it, the smallest four integers are 8, 10, 12, 14.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.

The members of an equation are each of the expressions that appear on both sides of the equal sign.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" n any integer, and knowing that:

So, the equation in this case is:

(2n + 2n +2 + 2n +4 + 2n + 6)÷ 4= 11

Solving:

(8n +12)÷ 4=11

8n +12= 11× 4

8n +12= 44

8n= 44 -12

8n= 32

n= 32 ÷ 8

n= 4

Then, the smallest four integers can be calculated as:

Finally, the smallest four integers are 8, 10, 12, 14.

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The average balance of the account is $1126.37.

An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any set of data:

Mean, [tex]\overline X=\frac{\sum X}{n}[/tex]

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is:

[tex]Average{~}balance=\frac{1285.12+961.36+1132.63}{3}[/tex]

[tex]Average{~}balance=\frac{3379.11}{3}[/tex]

Average balance = $ 1126.37

So, the account's average balance is $1126.37.

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The complete question is mentioned below:

The table shows the balance (in dollars) of a bank account each month for three months. What is the average balance of the account?

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

The average balance of the account is $1126.37

Average: An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.

Consider the table that shows the balance (in dollars) of a bank account for three months.

Months            Account Balance

1                       $1285.12

2                       $961.36

3                       $1132.63

As we are aware, the following formula for the mean or average of any

set of data,

Mean,

where,  ∑X is the sum of all the observations in the data and n  is the number of observations in the data

Therefore, the average balance in the account is,

Average balance of the account = $ 1126.37

So, the account's average balance is $1126.37

The complete question is mentioned below,

The table shows the balance (in dollars) of a bank account each month for three months.

Table:

Month 1, account balance: $1285.12

Month 2, account balance: $961.36

Month 3, account balance: $1132.63

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The one time fee is -$17 and the one-time fee cannot not be applicable to this scenario because it is negative

The given parameters are

Hourly rate, r = 20.00

Number of hours, h = 5.5

Total amount = 93.00

The total amount is calculated as:

Total amount = One time fee + Hourly rate * Number of hours

So, we have

93.00 = One time fee + 20.00 * 5.5

Evaluate the product

So, we have

93.00 = One time fee + 110

Subtract 110 from both sides

So, we have

One time fee = 93.00 - 110

Evaluate the difference

So, we have

One time fee = -17

Hence, the one time fee is -$17

Amount cannot be negative.

This means that the one-time fee cannot not be applicable to this scenario

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