The volume of a cylinder is given by
V = pi r^2 h where r is the radius and h is the height
We are given the diameter is 5
r = d/2 = 5/2 = 2.5 in
V = pi ( 2.5)^2 (7)
V =pi ( 6.25)*7
V = 43.75 pi
Assuming a value for pi of 3.14
V =137.375 in ^3
Rounding to the nearest hundredth
V = 137.38 in ^3
Assuming a value for pi by using the pi button
V = 137.44468
Rounding to the nearest hundredth
V = 137.44 in ^3
which of these is closest to the unit distance between points M and M' ?
the coordinate of M is (-3, -5)
it is given that M is translated 6 unit right , and 5 unit up.
so the coordinate of M' is (-3+6 , -5 + 5) = (3, 0)
so, the distance between M and M' is,
[tex]d=\sqrt[]{(3-(-3))^2+(0-(-5))^2}[/tex][tex]\begin{gathered} d=\sqrt[]{6^2+5^2} \\ d=\sqrt[]{36+25} \\ d=\sqrt[]{61} \end{gathered}[/tex]d = 7.81
so, the closest to the unit distance is 8
thus, the answer is option D
I'll send you the pic a
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
Please help me with my Calc hw, it is not outside scope of brainly tutor. I am following along diligently, thanks!
ANSWER
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]EXPLANATION
To solve this integral we have to use the substitution method. Let u = 1 + cos(x), then du is,
[tex]du=-\sin (x)dx[/tex]Thus, dx is,
[tex]dx=\frac{du}{-\sin (x)}[/tex]Replace the function and the differential in the integral,
[tex]\int \frac{\sin(x)}{\sqrt[]{1+\cos(x)}}dx=\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin (x)}[/tex]The sin(x) cancels out,
[tex]\int \frac{\sin(x)}{\sqrt[]{u}}\cdot\frac{du}{-\sin(x)}=-\int \frac{1}{\sqrt[]{u}}du[/tex]We have to find a function whose derivative is 1/√u. This function is √u since its derivative is,
[tex]\frac{d}{du}(\sqrt[]{u})=\frac{1}{2\sqrt[]{u}}[/tex]Note that a coefficient 1/2 is missing, so to cancel it out, we have to multiply by 2. Don't forget the constant of integration,
[tex]-\int \frac{1}{\sqrt[]{u}}du=-2\sqrt[]{u}+C[/tex]Finally, we have to replace u with the function we substituted before,
[tex]-2\sqrt[]{u}+C=-2\sqrt[]{1+\cos (x)}+C[/tex]Hence, the result of the integral is,
[tex]-2\sqrt[]{1+\cos(x)}+C[/tex]An inspector found 18 defective radios during an inspection. If this is 0.024% of the total number of radios inspected, how many radios were inspected?
Total number of defected radios is 18
Let the total number of defective radios be taken as y
If 0.024% of the total number of radios inspected are defective, i.e 0.024% of y
[tex]\frac{0.024}{100}y=18[/tex]Solve for y, by cross multiplying
[tex]\begin{gathered} \frac{0.024}{100}y=18 \\ 0.024y=18\times100 \\ \text{Divide both sides by 0.024} \\ \frac{0.024y}{0.024}=\frac{1800}{0.024} \\ y=75000 \end{gathered}[/tex]Hence, the number of radios inspected, y, is 75000
wich choice shows the correct solution to 2544÷8?
ANSWER:
318
STEP-BY-STEP EXPLANATION:
We have the following operation:
[tex]2544÷8[/tex]So the answer is 318
Find the areas of the figure. Area of Parallelogram, Trapezoid and Composite figure. Round to the nearest hundredth where necessary.
Let
A₁ be the area of the parallelogram
A₂ be the area of the trapezoid
Solving for the area of the parallelogram
Given the following dimensions
b = 23 cm
h = 14 cm
The area is solved using
[tex]\begin{gathered} A_1=bh \\ A_1=(23\text{ cm})(14\text{ cm}) \\ A_1=322\text{ cm}^2 \end{gathered}[/tex]The area of the parallelogram therefore is 322 square centimeters.
Solving for the area of the trapezoid.
Given the following dimensions
b₁ = 15 cm
b₂ = 34 cm
h = 19 cm
The area is solved using
[tex]\begin{gathered} A_2=\frac{b_1+b_2}{2}\cdot h \\ A_2=\frac{15\text{ cm}+34\text{ cm}}{2}(19\text{ cm}) \\ A_2=\frac{49\text{ cm}}{2}(19\text{ cm\rparen} \\ A_2=(24.5\text{ cm})(19\text{ cm}) \\ A_2=465.5\text{ cm}^2 \end{gathered}[/tex]The area of the trapezoid is 465.5 square centimeters.
Solving for the area of the composite figure.
Get the sum of the two areas to get the area of the composite figure, we have
[tex]\begin{gathered} A_{\text{total}}=A_1+A_2 \\ A_{\text{total}}=322\text{ cm}^2+465.5\text{ cm}^2 \\ A_{\text{total}}=787.5\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the composite figure is 787.5 square centimeters.
A publisher for promising new novel figures fixed costs at $61,000 and variable cost at $1.50 for each book produced if the book is sold to distributors for $15 each how many must be produced and sold for publisher to break even?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given information
[tex]\begin{gathered} For\text{ the cost price function:} \\ Fixed\text{ cost=\$61,000 = constant} \\ Variable\text{ cost = \$1.50 }\times\text{ number of books} \\ Let\text{ x be the number of books produced} \end{gathered}[/tex]The function for the cost price becomes:
[tex]61000+1.5x[/tex]STEP 2: Get the function for the selling price
The function for the selling price becomes:
[tex]\text{ \$}15x[/tex]STEP 3: Calculate the number of books required to break even
To get the breakeven, the cost price will be equal to selling price. Therefore,
[tex]\begin{gathered} 61000+1.5x=15x \\ Subtract\text{ 1.5x from both sides} \\ 61000+1.5x-1.5x=15x-1.5x \\ 61000=13.5x \\ Divide\text{ both sides by 13.5} \\ \frac{61000}{13.5}=\frac{13.5x}{13.5} \\ 4518.518519=x \\ x\approx4519 \end{gathered}[/tex]Hence, the number of books that must be produced and sold to get a breakeven is approximately 4519
Sharel spent the day at the mall. First, she bought five phones for $35each. Later, she found two five dollar bills. Write the total change to
if Sharel bought 5 phenes for 35 each, se spent 5 times 35 = $175
And when she found two $5 bills, it is like she received 2 times 5 = $10
Normally, expenses are negative numbers and earning are positive numbers, in this case
-$175 + $10 = - $165
Sothe answer is -165
Help please I’ll give 10 points
Choose the right symbol for the following
What are Symbols?
Many operations in mathematics are carried out using mathematical symbols. Mathematical quantities are easy to refer to thanks to the symbols. It's interesting to consider how entirely dependent mathematics is on numbers and symbols. In addition to referring to various amounts, math symbols also show how two quantities relate to one another. The primary purpose of all mathematical symbols is to carry out mathematical operations under distinct conceptions.
1) 0.02 > 0.002
2) 0.05 < 0.5
3) 0.74 < 0.84
4) 0.74 > 0.084
5) 1.2 < 1.25
6) 5.130 = 5.13
7) 3.201 > 3.099
8) 0.159 < 1.590
9) 8.269 > 8.268
10) 4.60 > 4.060
11) 302.026 > 300.226
12) 0.237 > 0.223
13) 3.033 < 3.303
14) 9.074 < 9.47
15) 6.129 < 6.19
16) 567.45 > 564.75
17) 78.967 > 78.957
18) 5.346 < 5.4
19) 12.112 < 12.121
20) 26.2 = 26.200
21) 100.32 > 100.232
To learn more about Symbols click on the link
https://brainly.com/question/25421984
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Tiffany deposited two checks into her bank account this month.One check was for $50, and the second check was for $22.Her balance at the end of the month was $306, and she made no withdrawals.Which expression shows Tiffany's balance at the beginning of the month?
Tiffany's balance at the beginning of the month = $229
Explanations:First Deposit = $50
Second Deposit = $22
End of the month balance = $306
Balance at the beginning of the month = End of the month balance - (First Deposit + Second deposit)
Balance at the beginning of the month = 306 - (50 + 22)
Balance at the beginning of the month = 306 - 77
Balance at the beginning of the month = $229
If a number with two places to the right of the decimal place is added to a number with three places to the right of thedecimal place then the answer should be reported as having how many numbers to the right of the decimal place
Let the number with two places to the right of the decimal place be represented as 20.45 and the number with three places to the right of the decimal place be 20.456
Required:
When we add the two numbers, how many numbers to the right of the decimal place is it going to have?
We can know this by adding the two fictitious numbers:
[tex]20.45\text{ + 20.456 = 40.906}[/tex]Here we can see that
Last month, Ebony had 110 dollars in achecking account. The current balance is146 dollars. What is the percent change inthe account balance from last month to thismonth? Round your answer to the nearest whole percent.
Problem
Last month, Ebony had 110 dollars in a
checking account. The current balance is
146 dollars. What is the percent change in
the account balance from last month to this
month? Round your answer to the nearest whole percent.
Solutiion
For this case we can use the following formula:
[tex]\text{Change}=\frac{\text{Actual}-\text{Before}}{\text{Before}}\cdot100[/tex]And replacing we got:
[tex]\text{Change}=\frac{146-110}{110}\cdot100=32.72[/tex]And then the answer wounded to the nearest percent would be:
33%
4) Using the number line to help you, decide which fraction is larger or if they are equal: one/twos or three/fifths. Label each fraction on the number line.
Explanation:
The number line is between 0 to 1. There are 10 smaller lines in between
Each of the small lines represent 1/10 or 0.1
one/twos is the same as 1/2 = 0.5
three/fifths is the same as 3/5 = 0.6
From the above, 0.6 is greater than 0.5
Showing both numbers on the number line:
Pedro can't decide which size pizza to order. The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza, the total price will be divided among 3people. If he chooses the 12-inch pizza, then the total price will be divided among 4 people. Which is the better buy? How much will each person pay? (Use 3.14 for r.)A. 10-inch pizza; $1.50B. 12-inch pizza; $1.50C. 10-inch pizza; $1.66 D. 12-inch pizza; $1.66
Answer: The better buy is the the 12-inch deluxe for $5.99.
B. 12-inch pizza; $1.50
Explanation:
From the information given, the 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99. If he gets the 10-inch pizza. We would calculate the area of both pizzas by applying the formula for calculating the area of a circle which is expressed as
Area = πr^2
where
π = 3.14
r is the radius of the circle
For the 10-inch cheese and sausage pizza,
diameter = 10
r = 10/2 = 5
Area = 3.14 x 5^2 = 78.5
If it is divided among 3 people,
each person gets 78.5/3 = 26.2 in^2
Amount that each person pays = 4.99/3 = $1.66
This means that each person pays $1.66 for 26.2 in^2
For the 12-inch cheese and sausage pizza,
diameter = 12
r = 12/2 = 6
Area = 3.14 x 6^2 = 113.04
If it is divided among 4 people,
each person gets 113.04/4 = 28.26 in^2
Amount that each person pays = 5.99/4 = $1.5
This means that each person pays $1.5 for 28.26 in^2
Thus, the better buy is the the 12-inch deluxe for $5.99.
The amount that each person pays is
B. 12-inch pizza; $1.50
what is 2^-3 as a fraction
Answer:
Solution below.
Step-by-step explanation:
The question tests on the concept of indices.
We know the following indices rule:
[tex] {x}^{ - y} \\ = \frac{1}{ {x}^{y} } [/tex]
Which means by inversing the power, we will multiply the power by -1.
So in the case of this question, we can:
[tex] {2}^{ - 3} = \frac{1}{ {2}^{3} } \\ = \frac{1}{8} [/tex]
Trini bought some jeans that she had been saving up for. She purchased them for $88 but has wornthem 4 times already. So far, what is the cost of wear for the jeans?
In order to find the cost of wear for the jeans, we just need to divide the cost of the jeans by the number of times Trini worn it.
So we have:
[tex]\frac{88}{4}=22[/tex]Therefore the cost of wear so far is $22.
Use the quadratic formula to solve the problems. Then state whether the roots are real number roots or complex number roots.
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Solving the quadratic equation using the quadratic formula, we have that:
From the solution above, we can see that the roots are complex.
[tex]\begin{gathered} \text{The roots of the equation are:} \\ x\text{ = }\frac{-5}{4}\text{ + i }\frac{\sqrt[]{31}}{4}, \\ x\text{ =}\frac{-5}{4}-i\frac{\sqrt[]{31}}{4} \end{gathered}[/tex]A sample of 7 students was taken to see how many pencils they were carrying.2, 3, 2, 5, 7, 1, 41. Calculate the sample mean.2. Calculate the standard deviation.
Sample mean = 3.43
sample standard deviation = 2.07
Explanation:
Given: 2, 3, 2, 5, 7, 1, 4
Total numbers = 7
1) Sample mean is calculated by finding the average of the data set
[tex]\begin{gathered} \text{Sample mean = }\frac{su\text{ m of data set}}{number\text{ of data set}} \\ \text{sample mean = }\frac{2+3+2+5+7+1+4}{7} \\ \text{sample mean = 24/7 } \\ \text{sample mean = }3.43 \end{gathered}[/tex]2) We have sample standard deviation and population standard deviation.
SInce the question asked for sample mean, we will be calculating sample standard deviation.
Standard deviation is calculated as:
[tex]\begin{gathered} s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum^{}_{}(x_1-mean)^2}{N-1}} \\ \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{\sum ^{}_{}(2-3.43)^2+(3-3.43)^2+(2-3.43)^2+(5-3.43)^2+(7-3.43)^2+(1-3.43)^2+\mleft(4-3.43\mright)^2}{7-1}} \\ s\tan dard\text{ deviation = }\sqrt[]{\frac{25.7143}{6}}\text{ = }\sqrt[]{4.2857} \\ s\tan dard\text{ deviation = }2.07 \end{gathered}[/tex]
x+y=22x+7y=9can u help me solve this equation
Keeping Od, this is the solution:
x + y = 2
2x + 7y = 9
___________
Step 1: Let's isolate x in equation 1, as follows:
x + y = 2
x = 2 - y
__________________
Step 2: Let's substitute x and solve for y in equation 2, this way:
2x + 7y = 9
2 (2 - y) + 7y = 9
4 - 2y + 7y = 9
4 + 5y = 9
Subtracting 4 at both sides:
4 + 5y - 4 = 9 - 4
5y = 5
Dividing by 5 at both sides:
5y/5 = 5/5
y = 1
_______________________
Step 3: Let's substitute y and solve for x in the first equation, as follows:
x + y = 2
x + 1 = 2
Subtracting 1 at both sides:
x + 1 - 1 = 2 - 1
x = 1
_____________________
Step 4: Let's write the solution as an ordered pair, this way:
(1, 1)
If f(x)=x squared + 3x - 10 then over which of the following intervals is f(x)<0 ?
Given data:
The given function is f(x)= x^2 +3x-10.
The given inequality is,
[tex]\begin{gathered} f(x)<0 \\ x^2+3x-10<0 \\ x^2+5x-2x-10<0 \\ x(x+5)-2(x+5)<0 \\ (x+5)(x-2)<0 \\ -5Thus, the value of x is -5In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.
Solution
We will equate the two values
[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]The answer is
What is the mean for the data shown in the dot plot?
We will determine the mean as follows:
[tex]x=\frac{1(4)+4(5)+3(6)+2(7)+1(10)}{11}\Rightarrow x=6[/tex]So, the mean will be 6.
the vertices of ABC and the endpoints of DE have coordinates that are integers. Determine the coordinates of point F so That ABC≈DEFOPTIONS:(-7, 1)(-5, 3)(-7, -8)(-2, -8)
We want figure EDF≈ABC.
We can see that if we rotate figure ABC we will obtain the following:
If we rotate it we can see that the segment AB is exactly as the segment ED.
We can now find the answer if we look how far is the point C, we see it is three unities up from B and 5 unities to its left. Then F must be 3 unities up from E and 5 unities to its left.
Since E is located :
at y = -2 if we go up 3 unities
-2 + 3 = 1
at x = -2 if we go at its left 5 unities then
-2 - 5 = -7
Then, F must be at x = -7 and y = 1.
Answer: (-7, 1).. Find the values indicated. For g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)} g(-3) = g(-9) = g(-7)=
Given:
g = {(-1,0), (-3,3), (-5, 6), (-7,9), (-9, 12)}
So,
To find g(-3), we need to find the term that contains -3 in the location of x of the order pair
So, g(-3) = 3
And by the same manner, we will find the others
So,
g(-9) = 12
g(-7) = 9
Please help with the question below (please try to answer in maximum 10/15 minutes).
Solution:
Given the dimensions of the composite figure below
[tex]\begin{gathered} For\text{ the cuboid:} \\ l=12\text{cm} \\ w=4\text{ cm} \\ h=3cm \\ For\text{ the triangular prism:} \\ a=3\text{ cm} \\ b=4\text{ cm} \\ c=13\text{ cm} \\ h=5\text{ cm} \end{gathered}[/tex]To find the surface area, SA, of the composite figure, the formula
[tex]SA=2(lh)+2(wh)+(lw)+2(\frac{1}{2}lh)+(bc)+(ah)[/tex]
Substitute the values of the variables into the formula above
[tex]\begin{gathered} SA=2\left(12\cdot3\right)+2\left(3\cdot4\right)+\left(12\cdot4\right)+2\left(\frac{1}{2}\left(12\cdot5\right)\right)+\left(13\cdot4\right)+\left(4\cdot5\right) \\ SA=2(36)+2(12)+(48)+(60)+(52)+20 \\ SA=72+24+48+60+52+20 \\ SA=276\text{ cm}^2 \end{gathered}[/tex]Hence, the surface area, SA, is
[tex]276\text{ cm}^2[/tex]Dee, Sarah, Brett, and Betsy are splitting their dinner bill. After the tip, the total is $30.08. How muchdoes each owe if they split the bill four ways?
The four individuals Dee, Sarah, Brett and Betsy split their dinner bill four ways, which means its divided into four parts. Hence, after splitting, each person owes;
[tex]\begin{gathered} \text{Per person=}\frac{Total}{4} \\ \text{Per person=}\frac{30.08}{4} \\ \text{Per person=7.52} \end{gathered}[/tex]This shows that when paying the bill, each of the four individuals will have to pay $7.52
using first principles to find derivatives grade 12 calculus help image attached much appreciated
Given: The function below
[tex]y=\frac{x^2}{x-1}[/tex]To Determine: If the function as a aximum or a minimum using the first principle
Solution
Let us determine the first derivative of the given function using the first principle
[tex]\begin{gathered} let \\ y=f(x) \end{gathered}[/tex]So,
[tex]f(x)=\frac{x^2}{x-1}[/tex][tex]\lim_{h\to0}f^{\prime}(x)=\frac{f(x+h)-f(x)}{h}[/tex][tex]\begin{gathered} f(x+h)=\frac{(x+h)^2}{x+h-1} \\ f(x+h)=\frac{x^2+2xh+h^2}{x+h-1} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^2+2xh+h^2}{x+h-1}-\frac{x^2}{x-1} \\ Lcm=(x+h-1)(x-1) \\ f(x+h)-f(x)=\frac{(x-1)(x^2+2xh+h^2)-x^2(x+h-1)}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} f(x+h)-f(x)=\frac{x^3+2x^2h+xh^2-x^2-2xh-h^2-x^3-x^2h+x^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^3-x^3+2x^2h-x^2h-x^2+x^2+xh^2-2xh-h^2}{(x+h-1)(x-1)} \\ f(x+h)-f(x)=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)} \end{gathered}[/tex][tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{x^{2}h+xh^{2}-2xh+h^{2}}{(x+h-1)(x-1)}\div h \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2h+xh^2-2xh+h^2}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(x^2+xh^-2x+h^)}{(x+h-1)(x-1)}\times\frac{1}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{x^2+xh-2x+h}{(x+h-1)(x-1)} \end{gathered}[/tex]So
[tex]\lim_{h\to0}\frac{f(x+h)-f(x)}{h}=\frac{x^2-2x}{(x-1)(x-1)}=\frac{x(x-2)}{(x-1)^2}[/tex]Therefore,
[tex]f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2}[/tex]Please note that at critical point the first derivative is equal to zero
Therefore
[tex]\begin{gathered} f^{\prime}(x)=0 \\ \frac{x(x-2)}{(x-1)^2}=0 \\ x(x-2)=0 \\ x=0 \\ OR \\ x-2=0 \\ x=2 \end{gathered}[/tex]At critical point the range of value of x is 0 and 2
Let us test the points around critical points
[tex]\begin{gathered} f^{\prime}(x)=\frac{x(x-2)}{(x-1)^2} \\ f^{\prime}(0)=\frac{0(0-2)}{(0-1)^2} \\ f^{\prime}(0)=\frac{0(-2)}{(-1)^2}=\frac{0}{1}=0 \\ f^{\prime}(2)=\frac{2(2-2)}{(2-1)^2}=\frac{2(0)}{1^2}=\frac{0}{1}=0 \end{gathered}[/tex][tex]\begin{gathered} f(0)=\frac{x^2}{x-1}=\frac{0^2}{0-1}=\frac{0}{-1}=0 \\ f(2)=\frac{2^2}{2-1}=\frac{4}{1}=4 \end{gathered}[/tex]The function given has both maximum and minimum point
Hence, the maximum point is (0,0)
And the minimum point is (2, 4)
Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=
Find out the division
3x^4-6x^3-8x+16 : (x-2)
3x^3-8
-3x^4+6x^3
-----------------------
-8x+16
8x-16
------------
0
The remainder is zero
that means
The expression (x-2) is a factor of the polynomial
so
3x^4-6x^3-8x+16=(x-2)(3x^3-8)
A shoe salesman earns a commission of 30%
of all shoe sales made.
Yesterday he sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80
each. How much did he earn in commission yesterday?
Answer: $111 is earn by shoe salesman as commission .
Step-by-step explanation:
As given the statement in the question be as follow.
Shoes salesman sold 3 pairs of shoes for $70 each and 2 pairs of shoes for $80 each.
Total cost of the pair of shoes = 3 × 70 + 2 × 80
= 210 + 160
= $ 370
As given
shoe salesman earns a commission of 30% of all shoe sales made.
30% is written is decimal form
= 0.30
Commission earns = 0.30 × Total cost of the pair of shoes .
= 0.30 × 370
= $ 111
Therefore $111 is earn by shoe salesman as commission .
Boris's cat will be having four kittens. Boris performs asimulation by tossing a coin to model whether thesekittens will be male or female.• Let'heads (H) = female kitten• Let tails (T) = male kittenThe results of the simulation are:
Given:
Boris performs a simulation by tossing a coin to model whether these kittens will be male or female.
The total number of sample space is, N = 10.
Head for female kitten
T for male kitten.
The objective is to find the probability that at least three of the kittens will be male.
Fromthe obtained simulation, the number of sample space with at least thee tail (T) is, n(T)=4
Now, the probability of at least three of the kittens will be male can be calculated by,
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