Mathematics College

## Answers

**Answer 1**

To solve this problem, we need to calculate the midpoint for the two points in each option and check if it corresponds to the given midpoint (-3,4).

Calculating the midpoint for the two points of option A.

We have the points:

[tex](-1,7)and(2,3)[/tex]

We label the coordinates as follows:

[tex]\begin{gathered} x_1=-1 \\ y_1=7 \\ x_2=2 \\ y_2=3 \end{gathered}[/tex]

And use the midpoint formula:

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Substituting our values:

[tex](\frac{-1_{}+2_{}}{2},\frac{7_{}+3_{}}{2})[/tex]

Solving the operations:

[tex](\frac{1_{}}{2},\frac{10_{}}{2})=(\frac{1_{}}{2},5)[/tex]

Since the midpoint is not the one given by the problem, this option is not correct.

Calculating the midpoint for the two points of option B.

We have the points:

[tex](-2,6)and(-4,2)[/tex]

We follow the same procedure, label the coordinates:

[tex]\begin{gathered} x_1=-2 \\ y_1=6 \\ x_2=-4 \\ y_2=2 \end{gathered}[/tex]

And use the midpoint formula:

[tex]\begin{gathered} (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \text{Substituting our values} \\ (\frac{-2-4_{}}{2},\frac{6+2_{}}{2}) \\ \text{Solving the operations:} \\ (\frac{-6}{2},\frac{8}{2}) \\ (-3,4) \end{gathered}[/tex]

The midpoint for the two points in option B is (-3,4) which is the midpoint given by the problem.

**Answer: B (-2,6) and (-4,2)**

## Related Questions

I need help This is from my trig prep guide

### Answers

From the question given, we have the following data;

Height of the tree = 80 feet

Angle of elevation to the top of the tree = 68 degrees

Distance from Corey to the tree = unknown

We shall now call the unknown variable x.

With that we shall have the following diagram;

We now have a diagram detailing the triangle and the dimensions showing Corey, the tree and the eagle at the tree top.

To get a better look, Corey moves several steps away from the tree and now determines his new angle of elevation to be 41 degrees.

This can now be illustrated as follows;

From triangle EDC, we shall calculate the distance from point C to point D using trigonometric ratios. The reference angle is at point C, which means the **opposite** side is side ED. The **adjacent** side is side CD (labeled x). Using trig ratios we have;

[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 68=\frac{80}{x} \end{gathered}[/tex]

We cross multiply and we now have;

[tex]\begin{gathered} x=\frac{80}{\tan 68} \\ U\sin g\text{ a calculator, we have tan 68 as 2.475086}\ldots \\ x=\frac{80}{2.475086} \\ x=32.322109\ldots \\ \text{Rounded to the nearest hundredth of a foot;} \\ x=32.32ft \end{gathered}[/tex]

Looking at triangle EDB;

The reference angle is 41 which makes the **opposite** side ED and the **adjacent** side BD. To calculate the distance BD, we'll have;

[tex]\begin{gathered} \tan \theta=\frac{\text{opp}}{\text{adj}} \\ \tan 41=\frac{80}{BD} \\ We\text{ cross multiply and we now have;} \\ BD=\frac{80}{\tan 41} \\ BD=\frac{80}{0.869286} \\ BD=92.02955\ldots \\ \text{Rounded to the nearest hundredth;} \\ BD=92.03 \end{gathered}[/tex]

Take note that the distance Corey moved before he had a new angle of elevation is line segment CD which is indicated as y. Note also that

[tex]\begin{gathered} BC+CD=BD \\ CD=x=32.32ft \\ BC+32.32=92.03 \\ \text{Subtract 32.32 from both sides;} \\ BC=59.71 \end{gathered}[/tex]

The distance Corey stepped back is indicated as y (line segment BC).

**ANSWER:**

Corey stepped back **59.71 feet**

Identify the graph that has a vertex of (-1,1) and a leading coefficient of a=2.

### Answers

To determine the vertex form of a parabola has equation:

[tex]f(x)=a(x-h)^2+k[/tex]

where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.

From the question, we have that, the vertex is (-1, 1)

and the leading coefficient is a = 2

We substitute the vertex and the leading coefficient into the vertex form to

get:

[tex]\begin{gathered} f(x)=2(x+1)^2\text{+}1 \\ f(x)=2(x+1)^2+1 \end{gathered}[/tex]

**The graph of this function is shown in the attachment.**

**Hence the equation of parabola is**

[tex]f(x)=2(x+1)^2+1[/tex]

Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side?

### Answers

**SOLUTION **

From the triangle inequality theorem, the sum of the lengths any two sides must be greater than the length of the third side

So, looking at the options and looking at 4 and 5, it means that 5 is the longest side. So

[tex]\begin{gathered} 4+2=6>5 \\ 4+4=8>5 \\ 4+1=5=5 \\ 4+3=8>5 \end{gathered}[/tex]

So since 4 + 1 = 5 and 5 is not greater than 5, hence 1 cannot be the length of the 3rd side.

**The answer is option C**

A pile of cards contains eight cards, numbered 1 through 8. What is the probability of NOT choosing the 6?

### Answers

The **probability **of NOT choosing the 6 is 7/8.

What is the probability?

**Probability** is used to calculate the likelihood that a random event would happen. The chances that the random event happens is a **probability **value that lies between 0 and 1. The more likely it is that the event occurs, the closer the probability value would be to 1. If it is equally likely for the event to occur or not to occur, the probability value would be 0.50.

The **probability **of NOT choosing the 6 = number of cards that are not 6 / total number of card

Cards that do not have a value of 6 = 1, 2, 3, 4, 5, 7, 8

Total is 7

The **probability **of NOT choosing the 6 = 7 / 8

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You want to build a sandbox that can hold50,445 cubic inches of sand. If the sandbox is to be59 in. long and57 in. wide, how tall will it need to be?

### Answers

**Volume** of sandbox (to be built) = 50,445 cubic inches

A sandbox is the shape of a **cuboid** and is calculated by the formula

[tex]\text{volume = length }\cdot\text{ wi}\differentialD tth\text{ }\cdot\text{ height }\Rightarrow\text{ v = l }\cdot\text{ w }\cdot\text{ h}[/tex]

Volume = Length * Width * Height

Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?

50,445 = 59 * 57 * h

Make **h **the subject of the formula, we have:

h = 50445 / (59 * 57) = 15 in

Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.

### Answers

**Answer:**

45.1

**Step-by-step explanation:**

96 x .47 = 45.12

Rounded to the nearest tenth is 45.1

Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.

x+3y=6 2x+6y=-18 solve

### Answers

The system of **equation **x + 3y = 6 and 2x + 6y = -18 has **no solution**.

What is the solution to the given system of equation?

Given the system of **equation **in the question;

x + 3y = 6

2x + 6y = -18

To find the solution to the **system **of **equation**, first solve for **x **in the first equation.

x + 3y = 6

Subtract 3y from both sides

x + 3y - 3y = 6 - 3y

x = 6 - 3y

Now, replace all occurrence of x in the second equation with 6 - 3y and solve for **y**

2x + 6y = -18

2( 6 - 3y ) + 6y = -18

Apply distributive property to remove the parenthesis

12 - 6y + 6y = -18

-6y and +6y cancels out

12 = -18

Since 12 equal -18 is not true, there is **no solution **to the system of **equation**.

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(a) The perimeter of a rectangular parking lot is 340 m.If the width of the parking lot is 77 m, what is its length?Length of the parking lot: 0m(b) The area of a rectangular pool is 7410 m².If the length of the pool is 95 m, what is its width?Width of the pool: Im

### Answers

Part a)

Perimeter = 340 = 2•77 + Length doubled

then

Length x 2 = 340 - 154 = 186

Length= 186/2 = 93

ANSWER IS Length of parking lot is= 93 meters

Part b)

Area = 7410 = Width x Length

. 7410 = Width x 95

. 7410/95 = Width

THEN Width of the pool IS

78 square meters

Tony is a hiring director at a large tech company in Chicago, and he gets hundreds of resumes each week. How long does Tony MOST likely spend looking over each resume?30 seconds50 seconds3 minutes30 minutes

### Answers

The time needed to look over the resumes depends on how many papers is the resume

But it is convenient to have a speed looking on each one

so, the answe will be 50 seconds

Timothy ran a lemonade stand for 6 days. on the first day he made $5. Each day after that he made $2 more than the previous day. How much money did Marcus make, , after the 6 days?A) $60B) $15C) $12D) $30

### Answers

Step `1;

Total number of days = 6

Step 2:

First day = $5

Second day = $5 + $2 = $7

Third day = $7 + $2 = $9

Fourth day + $9 + $2 = $11

Fifth day = $11 + $2 = $13

Sixth day = $13 + $2 = $15

Step 3:

Marcus made = $5 + $7 + $9 + $11 + $13 + $15

= $60

**Second method**

Use the sum of nth terms of arithmetic progression.

first term a = $5

Common difference = 2

n = 6

[tex]\begin{gathered} S\text{um of the 6 terms = }\frac{n}{2}(\text{ 2a + (n-1)d)} \\ =\text{ }\frac{6}{2}\text{ ( 2}\times5\text{ + (6 -1) }\times\text{ 2)} \\ =\text{ 3( 10 + 5}\times2\text{ )} \\ =\text{ 3( 10 + 10 )} \\ =\text{ 3 }\times\text{ 20} \\ =\text{ \$60} \end{gathered}[/tex]

Final answer

**Marcus made = $60 Option A**

Determine the sum of the infinite geometric series

1/2-1/3+2/9-…

A. -1/2

B. the sum cannot be determined

C. 1/3

D. 3/10

### Answers

We (B) cannot determine the sum of the given **infinite geometric series** (1/2-1/3+2/9-…).

**What is infinite geometric series?**A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the **summation index. **The **ratio **is a rational function of the summation index in a more general sense creating what is known as a** hypergeometric series.**The result of an infinite geometric sequence is an **infinite geometric series. **There would be no conclusion to this series. The infinite geometric series has the general form a₁ + a₁r + a₁r² + a₁r³ +..., where r is the common ratio and a1 is the first term.

So, the sum of 1/2-1/3+2/9-…

We can easily observe that the terms of the following given series are not in a series or in a particular **sequence**.Then, it is not possible to find the sum of this given **series**.

Therefore, we (B) cannot determine the sum of the given **infinite geometric series** (1/2-1/3+2/9-…).

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5|x +1| + 7 = -38

Solve for x

### Answers

**Answer: No solutions**

**Step-by-step explanation:**

[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]

However, as absolute value is non-negative, there are no solutions.

Choose the best description of its solution. If applicable, give the solution.

### Answers

Given:

[tex]\begin{gathered} -x-3y=-6\ldots\text{ (1)} \\ x+3y=6\ldots\text{ (2)} \end{gathered}[/tex]

Adding equation(1) and equation(2)

[tex]\begin{gathered} -x-3y+x+3y=-6+6 \\ 0=0 \end{gathered}[/tex]

**The system has infinitely many solution .**

**They must satisfy the equation:**

[tex]y=\frac{6-x}{3}[/tex]

Find a standard form of the equation for the circle with the following property

### Answers

**Solution:**

**Given:**

[tex]Endpoints\text{ }(-7,5)\text{ and }(-5,-1)[/tex]

To get the equation of the circle, the center of the circle and the radius are needed.

The center of the circle is the midpoint of the endpoints.

Using the midpoint formula;

[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \end{gathered}[/tex]

Thus,

[tex]\begin{gathered} M=(\frac{-7+(-5)}{2},\frac{5+(-1)}{2}) \\ M=(\frac{-12}{2},\frac{4}{2}) \\ M=(-6,2) \end{gathered}[/tex]

Hence, the coordinates of the center of the circle is (-6,2)

The length of the diameter can be gotten using the distance between two points formula;

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\begin{gathered} where: \\ x_1=-7,y_1=5 \\ x_2=-5,y_2=-1 \\ Hence, \\ d=\sqrt{(-5-(-7))^2+(-1-5)^2} \\ d=\sqrt{2^2+(-6)^2} \\ d=\sqrt{4+36} \\ d=\sqrt{40} \end{gathered}[/tex]

The diameter is twice the radius. Hence, the radius is;

[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{\sqrt{40}}{2}=\frac{2\sqrt{10}}{2} \\ r=\sqrt{10} \end{gathered}[/tex]

Hence, the equation of the circle with center (-6,2)

[tex]with\text{ radius }\sqrt{10}[/tex]

Using the standard form of the equation of a circle;

[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ where: \\ (h,k)\text{ }is\text{ }the\text{ center} \\ r\text{ is the radius} \\ h=-6 \\ k=2 \\ r=\sqrt{10} \end{gathered}[/tex]

Hence, the equation is;

[tex]\begin{gathered} (x-(-6))^2+(y-2)^2=(\sqrt{10})^2 \\ (x+6)^2+(y-2)^2=10 \end{gathered}[/tex]

**Therefore, the equation of the circle is****;**

[tex](x+6)^{2}+(y-2)^{2}=10[/tex]

Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?

### Answers

Margie used a total of 264** inches** of lace for the 24 pillows

**How to calculate the total inches of lace used ? **

Margie used 36** inches** of lace for one pillow

She needs to make 24 pillows

The total** inches** of lace that was used for the 24 pillows can be calculated as follows

= 36 × 24

= 864

Hence Margie used 864** inches** of lace for 24 pillows

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Apply the product rule to rewrite the product below using a single base and exponent then simplify: 3^2 *3^3 our base is Answerour exponent is Answerthis simplifies to Answer

### Answers

[tex]undefined[/tex]

Explanation:

[tex]3^2\text{ }\times3^3[/tex][tex]\begin{gathered} \text{The expression has same base.} \\ \text{Base = 3} \\ We\text{ take one base and bring the exponents together} \\ \text{The sign betw}en\text{ them changes from multiplication to addition} \end{gathered}[/tex][tex]\begin{gathered} 3^2\text{ }\times3^3\text{ = }3^{2\text{ + 3}} \\ \text{Exponent = 2 + 3} \\ \text{Exponent = 5} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplifying:} \\ 3^{2+3}=3^5 \\ 3^5\text{ = 243} \end{gathered}[/tex]

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

### Answers

The correct **representations** of the** inequality** -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an **open circle** is at 5 and a bold line that starts at 5 and is pointing to **the right**" , the correct option is (c) and (d) .

In the question ;

it is given that

the **inequality -**3(2x-5)<5(2-x)

on solving this inequality further , we get

-3(2x-5)<5(2-x)

-6x+15<10-5x

which is option (c) .

Further solving

Subtracting 15 from both the sides of the **inequality** , we get

-6x + 15 -15 < 10 -5x -15

-6x < -5 -5x

-6x +5x < -5

-x < -5

multiplying both sides by (-1) ,

we get

x > 5 .

x> 5 on **number line** means an open circle is at 5 and a bold line starts at 5 and is pointing to the right .

Therefore , the correct **representations **of the** inequality** -3(2x-5)<5(2-x) are -6x + 15 < 10 - 5x and "an **open circle** is at 5 and a bold line that starts at 5 and is pointing to **the right**" , the correct option is (c) and (d) .

The given question is incomplete , the complete question is

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

(a) x < 5

(b) –6x – 5 < 10 – x

(c) –6x + 15 < 10 – 5x

(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.

(e) A number line from negative 7 to 3 in increments of 1, An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.

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While at college orientation, Kate is buying some cans of juice and some cans of soda for the dorm. The juice is $0.60 per can while the soda is $0.75. ￼￼Kate has $24 of dorm funds all to be spent. What is an equation that represents all the different combinations of juice and soda Kate can buy for $24￼ and how many different combinations of drinks are possible?￼

### Answers

From the question the following can be derived:

(a)

Let x cans of juice and y cans of soda be purchased for the dorm. Then the cost of the juice and soda is 0.60x + 0.75y. The equation of all the combinations of juice and soda is **0.60x + 0.75y = 24**.

(b)

The cost of exactly 24 cans of juice is $24 * 0.60 = $14.40. After this purchase, the remaining sum of money available is $24 - $14.40 = $9.60. This will suffice to buy 12 cans of soda, leaving a balance of $0.80. Thus. the entire money cannot be spent if exactly 24 cans of juice are purchased.

(c)

Below is a graph of the line 0.6x + 0.75y = 24 or 4x + 5y = 160 is plotted. All possible cimbinations of juice and soda will lie on this line. The x-intercept is 40 and the y-intercept is 32. Since neither of x and y can be negative, hence the lower and upper bounds for x are 0 and 40 and the lower ad upper bounds for y are 0 and 32. Also , x has to be multiple of 5 and y has to be a multiple of 4. As may be observed from the graph, only 9 combinations are possible which are (x, y):

(0, 32), (5, 28), (10, 24), (15, 20), (20, 16), (25, 12), (30, 8), (35, 4), (40, 0).

Graph:

A tee box is 48 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation 0 = -16t^2+ 32t +48 givesthe time t in seconds when a golf ball is at height 0 feet on the fairway.What is the height of the ball at 1 second and is the ball at its maximum height at 1 second (explain)?

### Answers

**Answer:**

**Step by step explanation:**

A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure.What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.

### Answers

**Solution**

For this case we can do the following:

We can find the value of s on this way:

[tex]s=\sqrt[]{6^2+4^2}=\sqrt[]{52}=7.21[/tex]

And solving for r we got:

[tex]r=\sqrt[]{6^2+3^2}=\sqrt[]{45}=6.71[/tex]

Then the answer for this case would be:

[tex]\sqrt[]{52}=7.21[/tex]

Consider these functions:/(=) =-{=2 + 51g(I) = =2 + 2What is the value of fg(-2))?

### Answers

**Answer**: Provided the two functions, **f(x)** and **g(x)**, we have to find the composite of these two functions at** x = - 2:**

[tex]\begin{gathered} f(x)=-\frac{1}{2}x^2+5x \\ \\ g(x)=x^2+2 \end{gathered}[/tex]

The composite function is as follows**:**

[tex]\begin{gathered} f(g(x))=-\frac{1}{2}(x^2+2)^2+5(x^2+2) \\ \\ \\ f(g(x))=-\frac{1}{2}[x^4+4x^2+4]+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ f(g(x))=-\frac{x^4}{2}-2x^2-2+5x^2+10 \\ \\ \\ f(g(x))=-\frac{x^4}{2}+3x^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8 \\ \\ \\ f(g(-2))=-\frac{(-2)^4}{2}+3(-2)^2+8=-8+12+8=12 \\ \\ \\ f(g(-2))=12 \end{gathered}[/tex]

The answer is **12**.

Find all x-intercepts of the following function. Write your answer or answers as

coordinate points. Be sure to select the appropriate number of x-intercepts.

f(x)

3x + 30

25x2 - 49

### Answers

**Given:** The function below

[tex]f(x)=\frac{3x+30}{25x^2-49}[/tex]

**To determine:** All x-intercepts of the given function

The x-intercept is a point where the graph crosses the x-axis

We would substitute the function equal to zero and find the value of x

[tex]\begin{gathered} f(x)=\frac{3x+30}{25x^2-49},f(x)=0 \\ \text{Therefore} \\ \frac{3x+30}{25x^2-49}=0 \\ \text{cross}-\text{ multiply} \\ 3x+30=0 \end{gathered}[/tex][tex]\begin{gathered} 3x=-30 \\ \frac{3x}{3}=\frac{-30}{3} \\ x=-10 \end{gathered}[/tex]

**Therefore, the coordinate of the x-intercept is ****(-10, 0)**

Jaylen used a 20% discount on a pair of jeans that cost $70 before tax. The sales tax is 6%. How much does the pair of jeans cost after tax? Show your work

### Answers

If Jaylen used a 20% discount on a pair of jeans that cost $70 before tax, then the price of the jeans will be $70 - 20%.

Let's calculate the 20% of $70.

[tex]70\times20\%=14[/tex]

*So, the discounted price of the jeans before tax is $70 - $14 = $56***.**

Generally, sales tax is applied to the discounted price, so let's calculate the 6% of $56.

[tex]6\%\times56=3.36[/tex]

*The sales tax is $3.36.*

**Therefore, the cost of the pair of jeans after tax is $59.36.**

[tex]56+3.36=59.36[/tex]

The figure below is made up of a triangle and a circle. The ratio of the area of the triangle to the area of the circle is 5:6. If 1/5 of the area of the triangle is shaded, what is the ratio of the shaded area to the area of the figure?

### Answers

**ANSWER**

[tex]\begin{equation*} 1:10 \end{equation*}[/tex]

**EXPLANATION**

The ratio of the area of the triangle to the area of the circle is:

[tex]5:6[/tex]

Let the area of the triangle be T.

1/5 of the area of the triangle is shaded i.e. 1/5 T

The total area of the figure is the sum of the area of the triangle that is not shaded and the area of the circle.

The area of the triangle that is not shaded is:

[tex]\begin{gathered} T-\frac{1}{5}T \\ \frac{4}{5}T \end{gathered}[/tex]

Let the area of the circle be C. The ratio of the area of the triangle to that of the circle is 5/6. This implies that:

[tex]\begin{gathered} \frac{T}{C}=\frac{5}{6} \\ \Rightarrow C=\frac{6T}{5} \end{gathered}[/tex]

And so, **the area of the figure is in terms of T is**:

[tex]\begin{gathered} \frac{4}{5}T+\frac{6}{5}T \\ 2T \end{gathered}[/tex]

Therefore, **the ratio of the shaded area to the area of the figure is:**

[tex]\begin{gathered} \frac{1}{5}T:2T \\ \Rightarrow\frac{1}{5}:2 \\ \Rightarrow1:10 \end{gathered}[/tex]

That is the answer.

A Geiger counter counts the number of alpha particles from radioactive material. Over a

long period of time, an average of 16 particles per minute occurs. Assume the arrival of

particles at the counter follows a Poisson distribution. Round your answers to four decimals.

a) Find the probability of exactly 21 particles arrive in a particular one minute period.

0.0426053 O

b) Find the probability of exactly one particle arrives in a particular one second period.

0.20424755689724

### Answers

a) The **probability** of exactly 21 particles arrive in a particular **one minute **period is 0.0426

b) The **probability** of exactly one particle arrives in a particular **one second **period is 0.2042

What is probability?

**Probability** is the ratio of the total number of **conceivable outcomes** to the** number of outcomes** in an exhaustive set of equally likely alternatives that result in a particular occurrence.

The probability is given by:

**P(X=x) = (e⁻ⁿ nˣ)/x!**

a) The probability of exactly 21 particles arrive in a particular one minute period is given by :

P(X=21) = (e⁻16 × 16²¹)/21!

P(X=21) = (2.176746853×10¹⁸)/51090942171709440000

P(X=21) = 0.0426

b) The probability of exactly one particle arrives in a particular one second period is :

1 min = 16 particles

1 sec = 16/60 particles

1 sec = 0.2667 particles

P(X=1) = (e⁻⁽¹⁶/⁶⁰⁾ × (16/60)¹)/1!

P(X=1) = 0.2042

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Rewrite the expression 3(12 - 10) using the distributive property of multiplication over subtraction.

### Answers

The resulting expression using the** distributive property** of multiplication over subtraction is 3(12) - 3(10).

What is distributive property of multiplication?

The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.

For instance, given the expression;

A(B - C)

We will have to** distribute A over B **and C to have;

A(B - C) = AB - AC

**Applying the rule** to the given expression

3 (12 - 10)

3(12) - 3(10)

This shows that the **given expression **can also be written as 3(12) - 3(10)

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Hello! I need some assistance with this homework question, pleaseQ12

### Answers

**Answer:**

A(-1,4) and B(2,0)

**Step-by-step explanation:**

The quadratic parabola equation is represented as;

[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the vertex of the parabola} \end{gathered}[/tex]

Therefore, if the given vertex (2,-5) and the other given point (-1,-1), substitute into the equation and solve for the constant ''a'':

[tex]\begin{gathered} -1=a(-1-2)^2-5 \\ -1=9a-5 \\ 9a=4 \\ a=\frac{4}{9} \end{gathered}[/tex]

Hence, the equation for the parabola:

[tex]f(x)=\frac{4}{9}(x-2)^2-5[/tex]

Now, for the line since it is a horizontal line, the equation would be:

[tex]g(x)=5[/tex]

Then, for (f+g)(x):

[tex]\begin{gathered} (f+g)(x)=\frac{4}{9}(x-2)^2-5+5 \\ (f+g)(x)=\frac{4}{9}(x-2)^2 \end{gathered}[/tex]

Then, the graph for the composite function and the points that lie on the graph:

A(-1,4) and B(2,0)

Somebody please answer asap for brainlist please

### Answers

The thing that the change that takes place in Ulrich and **Georg** suggested that the authors theme may be A. Wild **anger** can lead to wild deaths.

What is the story about?

The Interlopers is a story about two men who met in a forest and we're fighting over a **land**. They were trapped under a tree. In the end, they wee killed by a **wolf**.

It should be noted that the theme was illustrated in the story. This was that **anger** can bring about death. This was depicted ad **Georg** and rich fired due o their anger.

In conclusion, the correct option is A.

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you bought a car for $5000. each year it depreciates by 8.5%. Which equation can be used to find the value, v, of the car, x years after it was purchased?

### Answers

We have the following:

In this case, we have the following formula:

[tex]v=C\cdot(1-r)^x[/tex]

Where C is the original value of the car, r is the depreciation rate and x is the time in years

If np ≥5 and nq≥5, estimate P(at least 6) with n=13 and p = 0.5 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the

normal approximation is not suitable.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

O A. P(at least 6) =

(Round to three decimal places as needed.)

O B. The normal distribution cannot be used

### Answers

Using** normal distribution **we know that the value is P(at least 6) = 0.866.

What is Normal Distribution?A continuous **probability **distribution for a real-valued random variable in statistics is known as a** normal distribution** or a Gaussian distribution.

The mean is 8.4 according to the **formula**:

q = 1 - p = 1 - 0.5 = 0.5Np = (13)(0.5) = 6.5 > 5Nq = (13)(0.5) = 6.5 > 5

Consequently, the normal distribution will indeed resemble the **binomial**.

sqrt(Npq) = sqrt(13*0.5*0.5) = 1.802 is the standard deviation.Since it's ≥ and not > and to the right, we use 6-0.5 = 5.5

Because going right from 5.5 includes 6.

P(x > 5.5) with μ = 6.5 and σ = 1.802

Either find the z-score and use the table or use **technology **to find

Hence, Answer = 0.866

Therefore, using** normal distribution **we know that the value is P(at least 6) = 0.866.

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