the table displays the scores of students on a recent exam find the mean of the scores to the nearest tenth

The Table Displays The Scores Of Students On A Recent Exam Find The Mean Of The Scores To The Nearest

Answers

Answer 1

In this case, the number of students refers to frequencies.

To find the mean, we have to use the following formula

[tex]\begin{gathered} \bar{x}=\frac{\Sigma(x\cdot f)}{N}=\frac{65\cdot4+70\cdot1+75\cdot7+80\cdot5+85\cdot8+90\cdot3+95\cdot4+100\cdot1}{33} \\ \bar{x}=\frac{260+70+525+400+680+270+380+100}{33} \\ \bar{x}=\frac{2685}{33} \\ \bar{x}\approx81.4 \end{gathered}[/tex]Hence, the mean is 81.4.

Related Questions

Which is an x-intercept of the graphed function?
O (0, 4)
(-1, 0)
(4, 0)
(0, -1)

Answers

       A line's x-intercept and y-intercept are the points at which the x axes- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

We set y = 0 and solve the equation for x to determine the x-intercept.

The graphed function derived from the choices has the x-intercept  (-1, 0)

How do you calculate the x-intercept?

      A graph's x-intercept is the location where the graph crosses the x-axis.

The graph in the accompanying image crosses the x-axis at:

(-2, 0), (-1, 0), (1, 0) and (2, 0) (2, 0)

Consequently,  the x-intercept of the graphed function derived from the alternatives (-1, 0)

To Learn more About  x-intercept, Refer:

https://brainly.com/question/17932786

#SPJ13

eleven is fifteen more than four times a number.

translate to an equation. let x be the unknown number . solve for x

Answers

The equation is 15+4x= 11 and the value for x= -1

what are equations?

An equation is a mathematical statement between two expressions that have equal values. For example, 15+4x= 11. The symbol = shows that 11 and 15+4x are the same

Word problems can be translated into equation with variables.

Representing the unknown with x,

4×x= 4x

the word problem is therefore translated to

11= 15+4x

collecting like terms

4x= 11-15

4x= -4

divide both side by 4

x=-1

learn more about equations from

https://brainly.com/question/2972832

#SPJ1

Find the value of a.

Answers

The value of a is √10/2 if |x| =  2√2 and a|x| = 2√5 in the given Functions respectively.

What is function?

Functions are the foundation of calculus in mathematics. The functions are the various types of relationships. In mathematics, a function is represented as a rule that produces a unique output for each input x.

In mathematics, mapping or transformation is used to denote a function. These functions are usually represented by letters like f, g, and h. The domain is defined as the set of all possible values for which the function can be defined.

We have given that f(x) = |x|

Where x is hypotenuse the triangle made by the line

The formula for hypotenuse = c² = a² + b²

Here each side = 2 units

so hypotenuse  is

c² = 4² + 4²

c² = 16 + 16

c² = 32

c = 4√2

Thus,  f(x) = 2√2

In f(x) = a|x|

The blue lines with the base and side also makes a right angles triangle and the  blue line is the hypotenuse

c² = 4² + 2²

c² = 16 + 4

c² = 20

c = 2√5

Thus,  f(x) = 2√5

Now, if |x| =  2√2 and a|x| = 2√5

Taking |x| in common we get the equation

2√2 =  (2√5)/a

a = (2√5)/(2√2)

a = √5/√2

a = √10/2

Thus, the value of a is √10/2 if |x| =  2√2 and a|x| = 2√5 in the given Functions respectively.

Learn more about function

https://brainly.com/question/11624077

#SPJ13

If f(x) = 5x+27, find the instantaneous rate of change of f(x) at x=9

Answers

The instantaneous rate of change refers to the derivative of f(x), so let's find that first, following the power rule, we have.

[tex]f^{\prime}(x)=1\cdot5x^{1-1}=5x^0=5\cdot1=5[/tex]

As you can observe, the instantaneous rate of change is a constant, which means we don't have to evaluate it at x=9.

Therefore, the instantaneous rate of change is f'(x) = 5.

Express the statement in symbolic form and construct the truth table for the statement. "Cheap Trick does not play at the White House and Jacque is the president."Use the symbolic representationsp: cheap trick plays at the White Houseq: Jacque is the president(May complete on your paper or in the space provided)

Answers

Answer:

Explanation:

Here, we want to express the statement in symbolic form and construct the truth table for the statement

From what we have, the symbolic form is as follows:

[tex]\text{ \textasciitilde p }\wedge\text{ q}[/tex]

Now, let us complete the truth table as follows:

The Jurassic Zoo charges $5 for each adult admission and $3 for each child. The total bill for the 243 people from a school trip was $823. How many adults and how many children went to the zoo? There were adults and children on the trip

Answers

Let x be the number of adult and let y be the number of children

5x + 3y = 823 --------------------------(1)

x + y = 243 ----------------------------(2)

We can now solve simultaneously

Multiply through equation (2) by 3

3x + 3y =729 -----------------(3)

subtract equation (3) from equation (1)

2x =94

Divide both-side of the equation by 2

x =47

substitute equationx = 47 into equation (2) and then solve for y

47 + y = 243

subtract 47 from both-side of the equation

y = 243 - 47

y = 196

Hence

Jonathan needs to buy some food for his dog. At the nearest store, 6 bags of dog food cost $30.72. How much would Jonathan spend on 4 bags?

Group of answer choices

$15.36

$20.48

$25.60

$22.40

Answers

Answer: B

Step-by-step explanation: find the amount for one bag, by doing 30.72/6, to get 5.12. Then multiply that by 4 to get $20.48

Answer: $20.48

Step-by-step explanation:

first divide the total ( 30.72) by six and you will get 5.12 which is how much it cost to by one bag now since they want to know how much it would cost if you bought four bags multiply that by four and you will get 20.48 which is the correct answer

Im stuck on question 5-91 in cpm geometry the question asks me to find the area of a triangle... I figured out the 30 60 90's are but i still have triangle left over ill send a photo of the triangle

Answers

Answer

Area of the triangle = 72 square units

Explanation

For a triangle whose two sides (a and b) are given, and an angle that exists between them is also given, the area of that triangle is given as

Area of the triangle = ½ ab Sin θ

For this question,

a = 12 units

b = 24 units

θ = 30°

Area of the triangle = ½ ab Sin θ

Area of the triangle = ½ (12) (24) (Sin 30°)

Sin 30° = 0.5

Area of the triangle = ½ (12) (24) (Sin 30°)

Area of the triangle = ½ (12) (24) (0.5) = 72 square units

Hope this Helps!!!

What is the slope of BC in the simplest form?

Answers

Explanation:

The slope of BC can be calculated

Slope = rise/run

In this case, the rise is the height of the blue triangle and the run is the base of the blue triangle, so

Slope = 2/6 = -2/6

To simplify the slope, we need to divide by 2, so

[tex]\text{Slope}=-\frac{2\div2}{6\div2}=-\frac{1}{3}[/tex]

A rectangular backyard has a length of of 68 feet and a width if 40 1/2 feet. the owner wants to play 75% of the yard with grass seed the planting rate for the seed is 1.5 pounds per 1000 square feet of area.To the nearest tenth of a pound ,how much grass seed will tye owner need to plant

Answers

We have the following:

The first thing to do is calculate the area of the backyard

[tex]\begin{gathered} A=l\cdot w \\ l=68 \\ w=40\frac{1}{2} \\ \text{replacing:} \\ A=68\cdot40\frac{1}{2}=2754 \end{gathered}[/tex]

Now, they tell us it is 75% of the backyard therefore

[tex]2754\cdot0.75=2065.5[/tex]

Now we calculate the amount in pounds knowing that for each square foot of area 1.5 pounds are needed

[tex]2065.5\cdot\frac{1.5}{1000}=3.1[/tex]

The answer is 3.1 pounds

What is the volume of the pyramid shown below?A. 294 cu. unitsB. 1008 cu. unitsC. 112 cu. unitsD. 196 cu, units

Answers

Step 1

Write an expression for the volume of a square-based triangular pyramid

[tex]\text{Volume(V) =}\frac{1}{3}\times base\text{ area(b)}\times height[/tex]

height= 12

Step 2

Find the base area

[tex]\begin{gathered} \text{Base area = length }\times\text{ width} \\ \text{Length = 7} \\ \text{Width = 7} \\ \text{Base area = 7}\times7=49unit^2 \end{gathered}[/tex]

Step 3

Find the volume of the shape

[tex]\begin{gathered} V\text{ = }\frac{1}{3}\times49\times12 \\ V\text{ =}196unit^3 \end{gathered}[/tex]

Write an inequality for the following problem. Use M for your variable.
22 less than 5 times a number is greater than 65.



Helppp

Answers

Answer:

5m - 22 > 65

I hope this helps!

The mean of a set of data is 25 with a standard deviation of 2. What is the interval about the mean of the data within one standard deviation? Where is my answer?

Answers

Mean = 25

Standard deviation= 2

The interval about the mean is

Thus the interval will be

(mean - SD) to (mean + SD)

(25-2) to ( 25 +2)

23 to 27

The interval will be between 23 - 27

In parallelogram FGHJ if m^GHJ=55° find m ^ FGH. I

Answers

Given:

[tex]m\angle GHJ=55^o\text{ and m}\angle FGH=x^o[/tex]

Recall that the adjacent angles of the parallelogram are supplementary.

[tex]\begin{gathered} m\angle GHJ\text{ and m}\angle FGH\text{ are adjacent angles of the given parallelogram and these are supplementary.} \\ \end{gathered}[/tex]

We know that the sum of the supplementary angles is 180 degrees.

[tex]m\angle GHJ+\text{m}\angle FGH=180^o[/tex][tex]55^o+x^o=180^o[/tex]

[tex]x^o=180^o-55^o[/tex]

[tex]x^o=125^o[/tex]

Hence the answer is

[tex]\text{ m}\angle FGH=125^o[/tex]

Three. 5 m away from the base of the building. How I is window B?

Answers

Explanation

Given that each ladder is 3.5 meters away from the base of the building, we are asked to find the height of the building. This can be seen below,

Number 1:

The height of ladder A is 5.5 meters. We can then use the Pythagoras theorem to find the height of the window.

[tex]\begin{gathered} 5.5^2=3.5^2+A^2 \\ A^2=5.5^2-3.5^2 \\ A=\sqrt{5.5^2-3.5^2}=\sqrt{30.25-12.25} \\ A=4.24m \end{gathered}[/tex]

Answer: Height of window A =4.24m

Number 2

The height of ladder B is 8.8 meters. We can then use the Pythagoras theorem to find the height of the window.

[tex]\begin{gathered} 8.8^2=3.5^2+B^2 \\ B^2=8.8^2-3.5^2 \\ B=\sqrt{8.8^2-3.5^2}=\sqrt{77.44-12.25}=\sqrt{65.19} \\ B=8.07 \end{gathered}[/tex]

Answer: Height of window B =8.07m

Number 3

The height of ladder B is 9.3 meters. We can then use the Pythagoras theorem to find the height of the window.

[tex]\begin{gathered} 9.3^2=3.5^2+C^2 \\ C^2=9.3^2-3.5^2 \\ C=\sqrt{9.3^2-3.5^2}=\sqrt{86.49-12.25}=\sqrt{74.24} \\ C=8.62 \end{gathered}[/tex]

Answer: Height of window C =8.62m

Number 4

The height of ladder B is 7.9 meters. We can then use the Pythagoras theorem to find the height of the window.

[tex]\begin{gathered} 7.9^2=3.5^2+D^2 \\ D^2=7.9^2-3.5^2 \\ D=\sqrt{7.9^2-3.5^2}=\sqrt{62.41-12.25}=\sqrt{50.16} \\ D=7.08 \end{gathered}[/tex]

Answer: Height of window D = 7.08m

Please help it’s due tonight I will give a brainlist

Answers

The percentage of the markdown amount is approximately 30%.

What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.

So, the percentage of markdown amount:

The total amount is $54.88.The markdown amount is $16.38.

So, the markdown percentage is calculated as follows:

16.38/54.88  × 1000.2984 × 10029.84

Rounding off: 30%

Therefore, the percentage of the markdown amount is approximately 30%.

Know more about percentages here:

https://brainly.com/question/24877689

#SPJ13

The circle below is centered at (10,4) and has a radius of 4. What is itsequation?101010O A. (x - 10)2 + (y - 4)2 = 16O B. (x-4)2 + (-10)2 = 4O C. (x-4)2 + (-10)2 = 16OD. (x-10)2 + (x-4)2 = 4

Answers

The general equation of a circle with centre (h,k) and radius r is given as

[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where,} \\ (h,k)=(10,4) \\ r=4 \end{gathered}[/tex]

By substitution, we will have,

[tex]\begin{gathered} (x-10)^2+(y-4)^2=4^2 \\ =(x-10)^2+(y-4)^2=16 \end{gathered}[/tex]

Hence,

The correct answer is OPTION A

change the height for Ramp 2 to make a smooth slide

Answers

First answer:

If you look carefully to the measures of the three triangles that are the ramps of the exercise, you will notice they are similar after comparing them.

• Ratio of Ramp 1 = 2/3

,

• Ratio of Ramp 2 = 4/6

,

• Ratio of Ramp 3 = 6/9

Second answer

The information is given on the image and we can calculate the missing measures for make a smooth slide:

• Ramp 1 - Base 10 - Height 12

,

• Ramp 2 - Base 15 - Height 18

,

• Ramp 3 - Base 30 - Height 36

We used the ratio 2/3 for answering the first question, now we have the ratio

5/6, as follows:

• Ramp 1 - 5/6 * 2/2 = 10/12

,

• Ramp 2 - 5/6 * 3/3 = 15/18

,

• Ramp 3 - 5/6 * 6/6 = 30/36

What is 1/4 x 3
Give it's answer in its simplest form

Answers

Answer:   3/4

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

Explanation:

Think of 3 as 3/1. Then multiply the numerators together separate from the denominators being multiplied together

(1/4)*(3/1) = (1*3)/(4*1) = 3/4

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

An alternative route

1/4 x 3 means we have 3 copies of 1/4 being added

1/4 + 1/4 + 1/4 = (1+1+1)/4 = 3/4

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

If you are a visual learner, draw a circle and split it into 4 equal pizza slices. Shade 1 out of the 4 to represent 1/4.

Imagine that you did this 3 times. That would mean you have 3 shaded slices. Each slice represents 1/4, so you would have 3/4 of the total pizza.

Put another way: you have 3 friends who get 1/4 of a pizza each. That shades 3 out of the 4 total slices to get 3/4.

Which statements are true for the function y= \xi - 2? Select all that apply. The value of the function is never negative. Its graph has a V-shape There is only one input for which the output is 0. There are two inputs for which the output is 5 The vertex. of ts graph 13 81 (0.-2).

Answers

Explanation:

We need to check out each of the options to determine which of the statements are true:

The given function: y = |x| - 2

a) The symbol '| |' means absolute. So any number you put in it either positive or negative number,becomes positive after it is removed.

For example: if x = -2, y = |-2| - 2 = 2 -2 = 0

if x = -1, y = |-1| -2 = 1 -2 = -1

Hence from the example above, the value of the function can be negative.

Statement is wrong

b) Yes, the graph has a V shape: (statement is correct)

c) For the output to be 0, it means y = 0

Let's find out the value of x when y= 0

y = |x| -2

0 = |x| -2

0 + 2 = |x|

|x| = 2

|x| = x or -x

From the above we have only one x value (the input) which is 2

Statement is correct

d) For the output to be 5, y = 5

5 = |x| -2

|x| = -2 -5

|x| = -7

|x| = x or -x

x = -7 or -x = -7

x = -7 or x = 7

Find the intersection points when the line y = 12-4x meets the curve y =12-x^3. Hence, sketch in the same diagram, the line y = 12 - 4x and the curve y=12-x^3 Calculate the area of the region bounded by the curve and the line

Answers

The equations of the line and the curve are

[tex]\begin{gathered} y=12-4x \\ y=12-x^3 \end{gathered}[/tex]

We will equate their right sides to find the values of x

[tex]12-4x=12-x^3[/tex]

Subtract 12 from both sides

[tex]\begin{gathered} 12-12-4x=12-12-x^3 \\ -4x=-x^3 \end{gathered}[/tex]

Divide both sides by -1

[tex]\begin{gathered} \frac{-4x}{-1}=\frac{-x^3}{-1} \\ 4x=x^3 \end{gathered}[/tex]

Subtract 4x from both sides

[tex]\begin{gathered} 4x-4x=x^3-4x \\ 0=x^3-4x \end{gathered}[/tex]

Switch the two sides

[tex]x^3-4x=0[/tex]

Take x as a common factor

[tex]\begin{gathered} x(\frac{x^3}{x}-\frac{4x}{x})=0 \\ x(x^2-4)=0 \end{gathered}[/tex]

Factor the bracket using the rule of the difference between two squares

[tex](a^2-b^2)=(a+b)(a-b)[/tex][tex]\begin{gathered} (x^2-4)=(x+2)(x-2) \\ x(x+2)(x-2)=0 \end{gathered}[/tex]

Now, equate each factor by 0

[tex]\begin{gathered} x=0 \\ x+2=0,x-2=0 \\ x=-2,x=2 \end{gathered}[/tex]

Substitute the values of x in the equation of the line to find their corresponding values of y

[tex]\begin{gathered} y=12-4(0)=12 \\ y=12-4(-2)=12+8=20 \\ y=12-4(2)=12-8=4 \end{gathered}[/tex]

The points of intersection between the line and the curve are

(0, 12), (-2, 20), (2, 4)

Let us draw the graph

The red line represents the equation of the line

The blue curve represents the equation of the curve

To find the area bounded between the line and the curve we will use the integration

Since the line is above the curve at the point (-2, 20), then

We will subtract the curve from the line and use the values of x -2 and 2 as the limits of integration

[tex]A=\int_{-2}^2[(12-4x)-(12-x^3)]dx[/tex]

Simplify the terms inside the brackets first.

[tex]\begin{gathered} A=\int_{-2}^2[12-4x+12+x^3]dx \\ A=\int_{-2}^2[-4x+x^3]dx \end{gathered}[/tex]

In integration, we will add the power by 1 and divide the term by the new power

[tex]A=[\frac{-4x^{1+1}}{1+1}+\frac{x^{3+1}}{3+1}]_{-2}^2[/tex]

Simplify it

[tex]\begin{gathered} A=[\frac{-4x^2}{2}+\frac{x^4}{4}]_{-2}^2 \\ A=[-2x^2+\frac{x^4}{4}]_{-2}^2 \end{gathered}[/tex]

Substitute x by 2 and -2, then subtract the answer

[tex]A=[-2(2)^2+\frac{2^4}{4}]-[-2(-2)^2+\frac{(-2)^4}{4}][/tex]

Solve each bracket

[tex]A=8[/tex]

The area of the region bounded between the line and the curve is 8 square unit

Which relation is a function?

Answers

Answer:

The V (Bottom left)

Step-by-step explanation:

The top left is NOT a function because it fails the vertical line test. In fact, it is a vertical line.

The top right is NOT a function because it also fails the vertical line test. This graph may be considered as an inverse of a different function but it will not be a true inverse.

The bottom left IS a function because it passes the vertical line test. It has 1 x value for every y value.

The bottom right is NOT a function because it fails the vertical line test. At most x values, it has 2 y values.

The vertical line test is an imaginary line that you draw to test a function. If only 1 point hits the vertical line, then it is a function. The vertical line can be placed at any point in the graph.

Hope that helps

You are reducing a map of dimensions 24 in. by 36 in. to fit onto a piece of paper 8 in. by 10 in. What are the dimensions of the largest possible map that can fit on the page?

Answers

We have

scale factor

[tex]\frac{24}{36}=\frac{2}{3}[/tex]

The largest side 10 in

Then we need to obtain the shortest side

[tex]\frac{2}{3}=\frac{x}{10}[/tex][tex]x=\frac{2\cdot10}{3}=\frac{20}{3}=6\frac{2}{3}[/tex]

Therefore the dimensions of the largest possible map are

6 2/3 in by 10 in

(x-8)(2x+5)=0 solve the equation

Answers

Solution:

Given the equation:

[tex](x-8)(2x+5)=0[/tex]

To solve the equation, we use the zero factor principle.

From the zero factor principle, we have

[tex]\begin{gathered} When\text{ } \\ ab=0 \\ \Rightarrow a=0\text{ or b=0} \end{gathered}[/tex]

Thus, we have

[tex]\begin{gathered} x-8=0\text{ or 2x+5 =0} \\ when \\ x-8=0 \\ add\text{ 8 to both sides of the equation} \\ x-8+8=0+8 \\ \Rightarrow x=8 \\ when \\ 2x+5=0 \\ add\text{ -5 to both sides of the equation,} \\ 2x+5-5=0-5 \\ \Rightarrow2x=-5 \\ divide\text{ both sides by the coeffient of x, which is 2} \\ \frac{2x}{2}=\frac{-5}{2} \\ \Rightarrow x=-\frac{5}{2} \end{gathered}[/tex]

Hence, the solution to the equation is

[tex]x=8,\text{ x=-}\frac{5}{2}[/tex]

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Zoe is making greeting cards, which she will sell by the box at an arts fair. She paid $22 for a booth at the fair, and the materials for each box of cards cost $4. She will sell the cards for $15 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take? How much will the sales and expenditures be?

Answers

Let x be the number of box cards

Expenditures: $22 plus $4 times x

[tex]E=22+4x[/tex]

Sales: $15 times x

[tex]S=15x[/tex]

At some point, she will sell enough cards so that her sales of her cover her expenditures of her: Equal E and S

[tex]E=S[/tex]

Substitute the values of E and S:

[tex]22+4x=15x[/tex]

Solve x:

[tex]\begin{gathered} 22+4x-4x=15x-4x \\ 22=11x \\ \frac{22}{11}=\frac{11}{11}x \\ 2=x \\ \\ \\ x=2 \end{gathered}[/tex]

Use the value of x to find the sales and expenditures:

[tex]\begin{gathered} S=15x \\ S=15(2) \\ S=30 \\ \\ E=22+4x \\ E=22+4(2) \\ E=22+8 \\ E=30 \end{gathered}[/tex]Then, It takes to Zoe sell 2 box cards to cover the expenditures, the sales need to be $30 to cover the expenditures

Complete the description of how to find the sums −4 + 1 and −4 + (−1) on a number line.

To find −4 + 1, start at −4 and move 1 unit to the _____ to _____.
To find the sum −4 + (−1), start at −4 and move 1 unit to the ______ to ______

Answers

Integer Sums on a Number Line,

Start in the location that the first number denotes. Move the equivalent amount of units to the left if the second number is negative. Move that many units if it's affirmative.

How can I calculate the total on a number line?

Result for an image Fill in the blanks to describe how to locate the sums 4 + 1 and 4 + (1) on a number line. Start at 4, then move one unit to the ____ to ____ to find 4 + 1. Start at 4, then move 1 unit to the _____ to _____ to find the sum 4 + (1).

Utilizing a number line, combine two integers:

Make a number line first.

Next, locate the first integer's position on the number line.

To learn more about Integer sum on a number line refer to:

https://brainly.com/question/18731042

#SPJ9

the measure of an interior angle of a regular polygon is given. find the number of sides in a polygon. show work. Number 8.

Answers

Given the following interior angle of a regular polygon:

[tex]120\degree[/tex]

You need to remember that, by definition, a regular polygon is a polygon whose sides have all equal lengths.

Therefore, you can apply the following formula:

Where "n" is the number of sides of the polygon and β is the measure of one interior angle of the polygon.

Knowing that, in this case:

[tex]\beta=120\degree[/tex]

Therefore, you can substitute this value into the formula and solve for "n":

[tex]\begin{gathered} 120=\frac{(n-2)\cdot180}{n} \\ \\ 120n=180n-360 \end{gathered}[/tex][tex]\begin{gathered} 120n-180n=-360 \\ \\ -60n=-360 \\ \\ \\ n=\frac{-360}{-60} \end{gathered}[/tex][tex]n=6[/tex]

Hence, the answer is:

[tex]n=6[/tex]

I need to use factorials and doing it step-by-step for the bio normal probability formula Please help me figure this A through C step-by-step they want the factorial symbol! When showing my workGiven the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)n = 15, p = 0.4, find P(4 successes) n = 12, p = 0.2, find P(2 success ) n = 20, p = 0.05, find P(at most 3 successes) (hint for c. P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)I just got disconnected from my tutor who said it would take 20 minutes to song and help me go over it step-by-step so if you were that tutor or any tour available please contact

Answers

Binomial distribution formula:

[tex]P(x)=\frac{n!}{(n-x)!x!}*p^x*q^{n-x}[/tex]

________

n = 15, p = 0.4, find P(4 successes)

[tex]\begin{gathered} n=15 \\ x=4 \\ p=0.4 \\ q=1-0.4=0.6 \\ \\ P(x=4)=\frac{15!}{(15-4)!*4!}*0.4^4*0.6^{15-4} \\ \\ P(x=4)=\frac{15!}{11!*4!}*0.4^4*0.6^{11} \\ \\ P(x=4)=\frac{15\times14\times13\times12\times11!}{11!*4!}*0.4^4*0.6^{11} \\ \\ P(x=4)=\frac{15\times14\times13\times12}{4\times3\times2\times1}*0.4^4*0.6^{11} \\ \\ P(x=4)=1365*0.4^4*0.6^{11} \\ \\ P(x=4)=0.1268 \end{gathered}[/tex]

__________________

n = 12, p = 0.2, find P(2 success )

[tex]\begin{gathered} n=12 \\ x=2 \\ p=0.2 \\ q=1-0.2=0.8 \\ \\ P(x=2)=\frac{12!}{(12-2)!*2!}*0.2^2*0.8^{12-2} \\ \\ P(x=2)=\frac{12!}{10!*2!}*0.2^2*0.8^{10} \\ \\ P(x=2)=\frac{12\times11\times10!}{10!*2!}*0.2^2*0.8^{10} \\ \\ P(x=2)=\frac{12\times11}{2\times1}*0.2^2*0.8^{10} \\ \\ P(x=2)=66*0.2^2*0.8^{10} \\ \\ P(x=2)=0.2835 \end{gathered}[/tex]

_________________________

n = 20, p = 0.05, find P(at most 3 successes)

Find each part (P(x=0), P(x=1), P(x=2), P(x=3)) and then sum the results

[tex]\begin{gathered} n=20 \\ p=0.05 \\ q=1-0.05=0.95 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} P(x=0)=\frac{20!}{(20-0)!0!}*0.05^0*0.95^{20-0} \\ \\ P(x=0)=\frac{20!}{20!*0!}*1*0.95^{20} \\ \\ P(x=0)=\frac{20!}{20!*1}*1*0.95^{20} \\ P(x=0)=1*1*0.95^{20} \\ P(x=0)=0.3585 \end{gathered}[/tex][tex]\begin{gathered} P(x=1)=\frac{20!}{19!*1!}*0.05^1*0.95^{19} \\ \\ P(x=1)=\frac{20\times19!}{19!*1}*0.05*0.95^{19} \\ \\ P(x=1)=20*0.05*0.95^{19} \\ P(x=1)=0.3774 \\ \end{gathered}[/tex][tex]\begin{gathered} P(x=2)=\frac{20!}{18!*2!}*0.05^2*0.95^{18} \\ \\ P(x=2)=\frac{20\times19\times18!}{18!*2\times1}*0.05^2*0.95^{18} \\ \\ P(x=2)=190*0.05^2*0.95^{18} \\ P(x=2)=0.1887 \end{gathered}[/tex][tex]\begin{gathered} P(x=3)=\frac{20!}{17!*3!}*0.05^3*0.95^{17} \\ \\ P(x=3)=\frac{20\times19\times18\times17!}{17!*3\times2\times1}*0.05^3*0.95^{17} \\ \\ P(x=3)=1140*0.05^3*0.95^{17} \\ P(x=3)=0.0596 \end{gathered}[/tex][tex]P(x\leq3)=0.3585+0.3774+0.1887+0.0596=0.9842[/tex]

a right triangle ABC is shown below the area of the triangle above will equal 1/2 of the rectangle that is 5 units long and underscore units wide

Answers

for the ahe area of triangle

Height of the triangle = 2 units, base= 5 unit

Area of triangle =1/2 Breadth x height

Susbtitute the value and simplify:

[tex]\begin{gathered} \text{ area of triangle=}\frac{1}{2}\times2\times5 \\ \text{ area of triangle= }5\text{ units} \end{gathered}[/tex]

Answer =5 units

A home has a triangular backyard. The second angel of the triangle is 3 more than the first angel. The third angel is 9 more than four times the first angel.

Answers

The measure of three angles of triangular backyard are 28°, 31°  and 121°.

Given that, a home has a triangular backyard.

What is the angle sum property of a triangle?

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the measure of first angle be x.

The second angel of the triangle is 3 more than the first angel = x+3

The third angel is 9 more than four times the first angel = 4x+9

Using angle sum property of a triangle

x+x+3+4x+9 = 180°

⇒ 6x + 12 = 180

⇒ 6x = 168

⇒ x = 28°

So, x+3 = 31° and 4x+9 = 121°

Therefore, the measure of three angles of triangular backyard are 28°, 31°  and 121°.

To learn more about the angle sum property of a triangle visit:

https://brainly.com/question/8492819.

#SPJ1

Other Questions
Using the internet, research tools for identifying misinformation.Resources might refer to misinformation as fake news, myth, or fiction. There are excellent online articles designed to help you learn how to separate fact from fiction.2 Number and explain your tools.Type or handwrite the tools for identifying misinformation. Number them 1 through 5, and include a detailed description of how to apply each tool.3 Find an article related to fitness or nutrition.4 Use the tools identified in Step 2 and use them to evaluate the selected article.This will likely require learning more about the author, analyzing the claims, and assessing motive.5 Write a 1-page report summarizing the validity of the information in the article.Explain whether the article was truthful or contained misinformation. Often articles are mostly true but contain a few claims that are inaccurate or false. If the article seems entirely factual, describe why, making reference to the tools you applied. If you believe you have identified misinformation, describe why, making reference to the tools you applied. 8 Select the correct answer. Which inequality represents all the solutions of 10(3x + 2) > 7(2x - 4)? . X> 4 OB. X After Tybalt is killed, Romeo is most worried that: None of the choices are correct.Friar Laurence will not be able to help him find a place to hide.Mercutio will try to kill him for revenge.Juliet will no longer love him because he killed her cousin.the Prince will force him to work as a slave. The building and tearing apart of the supercontinent __________ hundreds of millions of years ago created reverse and tensional faulting that has made the eastern United States susceptible to earthquakes today. 7ReturnPreviousNe10 pointsA cylindrical can holds 28 in of soup. If the can is 4 in. tall, what is the radius of the can to the nearest tenth of an inch?Round your answer to the nearest hundredth. Only numbers in your answer.(Hint: V = rh)V =type your answer...h =type your answer...r =type your answer... Bekah has a rectangular garden. The length and width are different odd numbermeasures, and the perimeter is 12 feet. What is the area of her garden? What were the problems europeans faced during the 18th and 19th century in Africa Which personality trait allow you to admit your mistakes and accept feedback from others? 23. The cell has ahighlowconcentration of watercompared to the solution. I70% Water30% Solute If the frequency of homozygous dominant individuals in a population is 0.25, then p = _______. Which of the following was a major goal of Progressives during the Progressive Era?regulating business practicesrestructuring the court systemrestructuring farming practicesregulating the press Which of the following is the most important function of the skin? separating the body from its environmentB.storing fat for energy useC.sweating to keep body temperature warmD.absorbing sunlight for energy at lone star middle school 2 out of 5 randomly selected students participate in the school science fair if there are 800 students at the middle school how many students will be expected to participate in the science fair. A roll of gasket material is 16 in wide. What length is needed to obtain 21 sq ft of the material? the answer has to be as a mixed number 8. in the cladogram below, which letter represents the unique history of organism B? Select the equivilent expression(4 ^ 3 / 5 to the negative power of two) ^ 5 if an amplifier needs a low input resistance and a low output resistance, then it is a transresistance amplifier.a. Trueb. False Can you please help with 8 I need to finish 8 more packets by tonight Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Yesterday a chef used 32 eggs to make 2 chocolate souffles and 6 lemon meringue pies. The day before, he made 2 chocolate souffles and 10 lemon meringue pies, which used 48 eggs. How many eggs does each dessert require? A chocolate souffle requires __ eggs and a lemon meringue pie requires __ eggs. What is Aunt Alexandra's opinion on breeding a family.