A student takes a 10-question, multiple-choice exam with three choices for each question and guesses on each question. Find the probability of guessing exactly 4 out of 10 correctly.

The value of E(Y) and Var(Y) are 50 and 178/5 respectively

Given the formula for temperature conversion expressed as:

Y = (9/5)*X + 32

where:

X stands for a temperature in degrees Celsius,

Y the same temperature in degrees

If E(X) = 10, then;

Y = (9/5) * 10 + 32

Y = (9*2) + 32

Y = 18 + 32

Y = 50

Hence E(Y) = 50

If Var(X) = 2

Y = (9/5) * 2 + 32

Y = 18/5 + 32

Y =  178/5

Hence Var(Y) = 50

The value of E(Y) and Var(Y) are 50 and 178/5 respectively

Learn more on temperature here: https://brainly.com/question/894531

Answer:

4x² + 4x + 1

Step-by-step explanation:

to evaluate (g ￮ f)(x) , substitute x = f(x) into g(x)

g(f(x))

= g(2x + 1)

= (2x + 1)² ← expand using FOIL

= 4x² + 4x + 1

Answer:

Just add the 2 fractions that were mentioned

Step-by-step explanation:

turn 6 1/2 into an improper fraction and then add it to 5/8 by finding a common denominator

so it would be like -

13/2 + 5/8    =      52/8 + 5/8   =   57/8   =   7  1/8

Answer:

6 1/2 + 5/8 = 57/8 = 7 1/8 = 7.125

Step-by-step explanation:

Conversion a mixed number 6 1/2

to a improper fraction: 6 1/2 = 6 1/2 = 6 · 2 + 1/2 = 12 + 1/2 = 13/2

To find a new numerator:

a) Multiply the whole number 6 by the denominator 2. Whole number 6 equally 6 * 2/2 = 12/2

b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 2.

Six and one half is thirteen halfs

Add: 13/2 + 5/8 = 13 · 4/2 · 4 + 5/8 = 52/8 + 5/8 = 52 + 5/8= 57/8

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - thirteen halves plus five-eighths = fifty-seven eighths.

(43 + 4x) / 2 = 32

43 + 4x = 64

4x = 21

x = 21 / 4

x = 5.25

Answer:a hope this helps

Step-by-step explanation:

Answer:

13.5m/s

Step-by-step explanation:

formula is v=u + at

as given:

u=3m/s

a=1.5m/s²

t=7secs

v=3+1.5(7)

v=3 + 10.5

v = 13.5m/s

The unit for velocity is m/s

Answer:

a) 87

b) 13.5

Step-by-step explanation:

for the first question we've been given the equation and the parameters needed

so we just input the parameters

3a+4b when a is 17 and b is 9

therefore the answer is 3*17 + 4*9

51+36=87

second question

that's an equation of motion and we've been given all the parameters we also need so we just input the parameters In the equation

v=u+at

v=3+1.5*7

v= 3+10.5

v=13.5

Answer:

x > -6  or  x > 4

Answer: B. x = –8

Step-by-step explanation:

Answer:

6,16

Step-by-step explanation:

The histogram for the data is given at the end of this answer.

An histogram is a graph that shows the number of times each element of x was observed.

In this problem:

Hence, the graph given at the end of this answer is the histogram.

You can learn more about histogram at https://brainly.com/question/2962546

Answer:

(Q.1) No solution

(Q.2) True

(Q.3)  x = 4 - 2y

(Q.4) True

Step-by-step explanation:

(Q.1) As shown in the first attached figure.

By graphing.   x + 2y = 8   &   x + 2y = -4

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

===================================================

(Q.2) As shown in the second attached figure.

By graphing the system of inequalities  y> -3x+2  &  y<2x+1

The Shaded area represents the solution of the system of inequalities

And the point (4,2) is inside the shaded area

So, The ordered pair (4,2) is a solution to the system of inequalities.

====================================================

(Q.3) solving the system { x+2y=4  &  2x+2y=6 } by substitution

From the first equation x + 2y = 4

we will find x in terms of y then plug it into the second equation

So, x + 2y = 4 ⇒  x = 4 - 2y

=====================================================

(Q.4) As shown in the third attached figure.

By graphing.   2x + 4y = 8  &  x + 2y = 6

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

Answer:

(x³+2x²-2x)-(-3x³+4x²-x)

(x³+2x²-2x)+(3x³-4x²+x)

(x³+3x³)+(2x²-4x²)+(-2x+x)

4x³-2x²-x ----you may write till here.

But, if not satisfied, factorize it

x(4x²-2x-1)

please mark brainliest

Answer:

The General Sherman Tree is the world's largest tree, measured by volume. It stands 275 feet (83 m) tall and is over 36 feet (11 m) in diameter at the base. Sequoia trunks remain wide high up. Sixty feet above the base, the Sherman Tree is 17.5 feet (5.3 m) in diameter.

Step-by-step explanation:

Answer:

[1] [tex]\frac{3}{22}[/tex]

[2] [tex]\frac{4}{9}[/tex]

[3] [tex]\frac{1}{8}[/tex]

[4] [tex]\frac{9}{25}[/tex]

[5] [tex]\frac{2}{3}[/tex]

[6] [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

[1] Using the given fractions,

3/8×4/11

Applying the fractions formula for multiplication,

=3×4/8×11

=12/88

Simplifying 12/88, the answer is

=3/22

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋ

[2] Using the given fractions,

8/15×5/6

Applying the fractions formula for multiplication,

=8×5/15×6

=40/90

Simplifying 40/90, the answer is

=4/9

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[3] Using the given fractions,

7/12×3/14

Applying the fractions formula for multiplication,

=7×3/12×14

=21/168

Simplifying 21/168, the answer is

=1/8

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[4] Using the given fractions,

9/20×4/5

Applying the fractions formula for multiplication,

=9×4/20×5

=36/100

Simplifying 36/100, the answer is

=9/25

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[5] Using the given fractions,

7/10×20/21

Applying the fractions formula for multiplication,

=7×20/10×21

=140/210

Simplifying 140/210, the answer is

=2/3

ˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊˋˏˎˊ

[6] First:

Reduce fractions where possible.

Then your initial equation becomes:

4/9×9/20

Applying the fractions formula for multiplication,

=4×9/9×20

=36/180

Simplifying 36/180, the answer is

=1/5

[RevyBreeze]

Your most trustful answer

Answer:

  594 in²

Step-by-step explanation:

There are several ways to do this.

Given the way the figure is dimensioned, the last strategy is the easiest.

A rectangle that surrounds the entire figure will be 36 inches wide and 22 inches high. The white space rectangle in the lower right corner is shown to be 18 inches wide and 11 inches high.

The area of a rectangle is the product of its length and width:

  A = LW

So the difference in area between the "bounding" rectangle and the whitespace rectangle is ...

  shaded area = (36 in)(22 in) -(18 in)(11 in) = 792 in² -198 in²

  shaded area = 594 in²

_____

Additional comment

You can also recognize that the dimensions of the cut out corner are each half the overall dimensions. That means the shaded area is 3/4 of the overall "bounding" rectangle. There are several ways you can make use of that fact.

Answer: $1.44

Step-by-step explanation:

Answer:

10³⁰

Step-by-step explanation:

firstly working out without the power of 3

[tex]( \frac{10 {}^{15} }{10 {}^{5} } )[/tex]

this is the same as 10¹⁵ ÷ 10⁵

here the bases are the same and it's division so we subtract the powers

15 - 5 = 10

10¹⁵ ÷ 10⁵ = 10¹⁰

we are left with (10¹⁰)³, multiply the powers

10 × 3 = 30

final answer = 10³⁰

Hey there!

(10^15/10^5)^3

10^15

= 1,000,000,000,000,000

10^5

= 10 * 10 * 10 * 10 * 10

= 100 * 100 * 10

= 10,000 * 10

= 100,000

(1,000,000,000,000,000/100,000)^3

= (10,000,000,000)^3

= 10,000,000,000 * 10,000,000 * 10,000,000

= 100,000,000,000,000,000 * 10,000,000

= 10^30

Therefore, your answer is: 10^30

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

y=x+14

Step-by-step explanation:

Let us check if this is the answer:

the first numbers in the table are 0 and 14

0 plus 14 equals 14.

Now the next two numbers on the table:

1 plus 14 equals 15

And one more:  the third numbers on the table:

2 plus 14 equals 16

-----does this make sense? need more explination? then let me know

Answer:

5000 meters

Step-by-step explanation:

kilometers to meters=1km to 1000m

so 5km to 5000m

The total meters did ed hike and swim on Saturday and Sunday 5000 meters.

We have given,

Ed hiked 3 kilometers on Saturday and

Swam 2 kilometers on Sunday.

Kilometers to meters

1km = 1000m

We have to find the total distance Ed hiked and swam on Sunday and Saturday,

Total distance=3km +2km

=3km +2km

=5km

1km=1000m.

So 5km to 5000m.

To learn more about the distance visit:

https://brainly.com/question/17273444

By iteratively substituting, we have

[tex]a_n = a_{n-1} + n[/tex]

[tex]a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)[/tex]

[tex]a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)[/tex]

and the pattern continues down to the first term [tex]a_1=0[/tex],

[tex]a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))[/tex]

[tex]\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)[/tex]

[tex]\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k[/tex]

Recall the formulas

[tex]\displaystyle \sum_{n=1}^N 1 = N[/tex]

[tex]\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2[/tex]

It follows that

[tex]a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2[/tex]

[tex]\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1[/tex]

[tex]\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}[/tex]

Answer:

a) odd

b) even

Step-by-step explanation:

a) It is an odd symmetry because it is symmetric about the origin, meaning if you rotate an odd function 180° around the origin, you will have the same function you started with.

b) It is an even symmetry because it reflects over the y-axis. The left and right looks the same.

Answer: The answer is 50

Step-by-step explanation:

I did the test

Answer:

[tex]V = \frac{1}{2} LBH \\ \\ \\ LH =V \div ( \frac{1}{2} B) \\ \\ LH =V \times \frac{2}{B} \\ \\ \\LH = \frac{2V}{B} [/tex]

Answer:

[tex]\frac{2}{9\pi}ft^3/min[/tex]

Step-by-step explanation:

Given

[tex]\frac{dV}{dt}=2ft^3/min\\ \\\frac{dh}{dt}=?\\ \\V_{cone}=\frac{1}{3}\pi r^2h\\\\d=2r=3h\\\\\frac{d}{2}=r=\frac{3}{2}h\\\\h=2[/tex]

Calculation

[tex]V=\frac{1}{3}\pi r^2h\\ \\V=\frac{1}{3}\pi(\frac{3}{2}h) ^2h\\\\V=\frac{1}{3}\pi(\frac{9}{4}h^2)h\\ \\V=\frac{9}{12}\pi h^3\\ \\V=\frac{3\pi}{4}h^3\\ \\\frac{dV}{dt}=\frac{9\pi}{4}h^2\frac{dh}{dt}\\ \\2=\frac{9\pi}{4}(2)^2\frac{dh}{dt}\\ \\ 2=9\pi\frac{dh}{dt}\\ \\ \frac{2}{9\pi} =\frac{dh}{dt}[/tex]

Therefore, the rate that the height of the pile is changing when the pile is 2 feet high is [tex]\frac{2}{9\pi}ft^3/min[/tex].

Answer:

the awnser is 19,500

Step-by-step explanation:

you multiply 325 × 2=650 then you multiply 30×650=19,500

Answer:

$60

Step-by-step explanation:

40 text messages × .25 each = $10. Plus the $50 per month is $60.

Answer:

it should be $60 a month

Answer:

y = 4x - 2

Step-by-step explanation:

slope = (10 - 2)/(3 - 1) = 8/2 = 4

Let the equation be y = 4x + b

Sub (1, 2) into it,

2 = 4*1 + b

so b = 2 - 4 = -2

The equation is y = 4x - 2

[tex]\textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ A=48\\ b=8 \end{cases}\implies 48=8h\implies \cfrac{48}{8}=h\implies 6=h[/tex]

Answer:

6a

Step-by-step explanation:

replace x with -a

-2a -6(-a)

-2a +8a

6a

Answer:

Step-by-step explanation:

Given equation:

Simplify:

Solve:

He is wrong.

He was off by 3 digits.