Solution:
If the outer diameter is 7, then the outer radius is b=7/2.
On the other hand, if the inner diameter is 3, then the inner radius is a= 3/2.
Now, the surface area of a torus (glazed donut) with inner radius a and outer radius b is given by
[tex]SA=\pi^2\mleft(b+a\mright)\mleft(b-a\mright)\text{ =}\pi^2(b^2-a^2)[/tex]Then, applying the data of the problem to the above equation, we can conclude that the surface area of the given glazed donut would be:
[tex]SA=\pi^2(b^2-a^2)=\pi^2((\frac{7}{2})^2-(\frac{3}{2})^2)=98.69[/tex]so that, the correct answer is:
[tex]SA=98.69\approx98.7[/tex]
2) A seat has a speed of 15 mph in seicher travels downstream from Greentown to Glenevon in 2/5 of an hour. It then goes back upstream from Glenevon to Colombia, which is 2 miles downstream, in 3/5 of an hour. Find the rate of the current.
Rate of the current = 5 mph
Explanations:The time taken to travel downstream from Greentown to Glenevon = 2/5 hours
The time taken to travel upstream from Glenevon to Columbia = 3/5 hours
Rate = Distance /time
Let the distance traveled = y miles
Rate of the downstream travel:
Rate = y ÷ 2/5
Rate = y x 5/2
Rate = 5y / 2
Rate of the upstream travel
Since the travel upstream from Glenevon to Columbia is 2 meters downstream:
Distance = y - 2
Rate = (y-2) ÷ 3/5
Rate = (y-2) x 5/3
Rate = 5(y-2)/3
Let the current rate be represented by k
The rate of the downstream travel will be:
15 + k = 5y/2...........(1)
The rate of the upstream movement will be:
15 - k = 5(y-2)/3............(2)
Add equations (1) and (2)
(15 + k) + (15 - k) = [5y/3] + [5(y-2)/3]
[tex]\begin{gathered} 30\text{ = }\frac{5y}{2}+\text{ }\frac{5y-10}{3} \\ 30\text{ = }\frac{15y+10y-20}{6} \\ 30(6)\text{ = 15y + 10y - 20} \\ 180\text{ = 25y - 20} \\ 180\text{ + 20 = 25y} \\ 25y\text{ = 200} \\ y\text{ = 200/25} \\ y\text{ = 8} \end{gathered}[/tex]Substitute the value of y into equation (1)
[tex]\begin{gathered} 15\text{ + k = }\frac{5y}{2} \\ 15\text{ + k = }\frac{5(8)}{2} \\ 15\text{ + k = }\frac{40}{2} \\ 15\text{ + k = 20} \\ k\text{ = 20 - 15} \\ k\text{ = 5} \end{gathered}[/tex]The rate of the current = 5 mph
Find the mean: 16,12,15,10,7,916
You can calculate the mean by using the formula:
Mean=sum of values/number of values
Then,
[tex]undefined[/tex]Question 2(Multiple Choice Worth 2 points)
(01.06 MC)
Simplify 31.
1
0-1
-1
Answer:
[tex]-i[/tex]
Step-by-step explanation:
Imaginary numbers
Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].
Given expression:
[tex]i^{31}[/tex]
Rewrite 31 as 30 + 1:
[tex]\implies i^{30+1}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies i^{30} \cdot i^1[/tex]
[tex]\implies i^{30}i[/tex]
Rewrite 30 as 2 · 15:
[tex]\implies i^{(2 \cdot 15)}i[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left(i^2\right)^{15}i[/tex]
[tex]\textsf{Apply\:imaginary\:number\:rule}\quad \:i^2=-1:[/tex]
[tex]\implies \left(-1\right)^{15}i[/tex]
As -1 to the power of an odd number is -1:
[tex]\implies -1 \cdot i[/tex]
[tex]\implies -i[/tex]
Elsie is moving to iowa city iowa, with her three-year-old daughter. The table shows the results of a family budget estimator for iowa City for Elsie and her daughter."If Elsie earns $45,000 per year at her new job, can she stay on budget in lowa City? A. Yes, because she can easily afford $4020 per month.B. Yes, because she will not actually need all the items that the family budget estimator includes. C. No, because she will only make $3750 per month before taxes are taken out. D.No, because she will not be able to find housing as low as $853 per month?
In order to determine what is the correct statement, calculate the amount of money Elsie can spend per month, based on her earnings per year.
Divide 45,000 by 12:
45,000/12 = 3,750
You can notice that the amount of money Elsie can spend per month is lower than the total expenses shown in the table.
Hence, the correct statement is:
C. No, because she will only make $3750 per month before taxes are taken out.
2. A car travels a distance of 250 miles, 700 miles and 325 miles at the rate of 50
miles/hour, 35 miles/hour and 13 miles/hour respectively. Find the average speed
of the car in miles/hr.
(A) 50
(B) 42.5
(C) 30
(D) 25.5
(E) 13
Answer:a
Step-by-step explanation:can i get brainiest
Which of the following natural phenomena follows an elliptical motion?Question content area bottomPart 1Choose the correct answer below.A.A ball thrown from one person to anotherB.The path of marbles when rebounding from a curved surfaceC.Sound wavesD.The motion of the planets around the sun
The natural phenomena that follows an elliptical motion is:
D.
The motion of the planets around the sun
R'Find the composition of transformationsthat map APQR to APQ'R'.QT RRotate [?] degrees aboutthe origin and then translate(unit(s) [ ].90180
For a transformation like the one shown in the graph, note that the points have switched as follows;
[tex]P(x,y)\Rightarrow P^{\prime}(-y,x)[/tex]This is a 90 degree anticlockwise rotation about the origin.
That means point P would now be translated as follows;
[tex]\begin{gathered} P(1,1)\Rightarrow P^{\prime}(-1,1) \\ Q(2,1)\Rightarrow Q^{\prime}(-1,2) \\ R(2,3)\Rightarrow R^{\prime}(-3,2) \end{gathered}[/tex]After this rotation, the coordinates have now moved from their position one unit upwards. That now makes the final coordinates;
[tex]undefined[/tex](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
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
What is the opposite of the given number?-10.1
According to the given data we have the following number:
-10.1
Therefore, the opposite of this given number would be the number 10.1
Instead of -10.1 the opposite would always be with the contrary sign. In this case is the opposite is a positive number.
In this case is -10.1. but for example if we the have to find the opposite number of 1 that would be the -1.
All real number would have and opposite number, except for the number 0.
Determine which relation is a function.Question 1 options: {(–3, 2), (–1, 3), (–1, 2), (0, 4), (1, 1)} {(–3, 2), (–2, 3), (–1, 1), (0, 4), (0, 1)} {(–3, 3), (–2, 3), (–1, 1), (0, 4), (0, 1)} {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}
Answer
{(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}
Step-by-step explanation
The options have the form:
[tex]\lbrace(input_1,output_1),(input_2,output_2),...\rbrace[/tex]In a function, every input can be related to only one output.
In the case of the first option, the input -1 is related to two outputs, 3 and 2, then it is not a function.
In the case of the second and third options, the input 0 is related to two outputs, 4 and 1, then they are not a function.
The actual time it takes to cook a ten pound turkey is a normally distributed. Suppose that a random sample of 19 ten pound turkeys is taken. Given that an average of 2.9 hours and a standard deviation of 0.24 hours were found for a sample of 19 turkeys, calculate a 90% confidence interval for the average cooking time of a ten pound turkey. (10 points)
19 ten pound tukeys
average of 2.9 hours
standar deviation 0.24
90% confidence
Interval with 90% confidence is 2.42961–3.37039
The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certainday, 252 people entered the park, and the admission fees collected totaled 728 dollars. How many childrenand how many adults were admitted?Your answer isnumber of children equalsnumber of adults equalso
Answer: Number of children = 112, number of adult = 140
Let the number of children = x
Let the number of adult =
According to the question, 252 people entered the park
Mathematically, the number of adult and children that entered the park sum up to 252
x + y = 252 ------- equation 1
$1.5 is charged for children for the admission fee into the park
$4 is charged for adult for the admission fee into the park
A totaled of $728 was realized from both children and adult that were admitted into the park
This implies that the total amount realized is equal to the number of children and adults inside the park per amount charged respectively
1.5* x + 4 * y = 728
1.5x + 4y = 728 -------- equation 2
Equation 1 and 2 can be solve simultaneously using substitution method
x + y = 252 ----- 1
1.5x + 4y = 728 ------ 2
Make x the subject of the formula in equation 1
x + y = 252
x = 252 - y ----- equation 3
Substitute equation 3 into equation 2
1.5(252 - y ) + 4y = 728
Open the parenthesis
1.5 x 252 - 1.5 x y + 4y = 728
378 - 1.5y + 4y = 728
Collect the like terms
-1.5y + 4y = 728 - 378
2.5y = 350
Divide both sides by 2.5
y = 350/2.5
y = 140
To find x, put the value of y into equation 1
x + y = 252
x = 252 - y
x = 252 - 140
x = 112
The number of children = 112
The number of adults = 140
true or false16. The y-intercept of the equation, = −7^2 + 11 − 12 is 12
For us to be able to determine if it is true or false, let's evaluate the given equation:
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex]In order to find the y-intercept of a function, we substitute x equals to 0. A y-intercept always has an x-coordinate of 0.
Thus, we get,
[tex]\text{ y = -7x}^2\text{ + 11x - 12}[/tex][tex]\text{ y = -7(0)}^2\text{ + 11(0) - 12}[/tex][tex]\text{ y = -7(0)}^{}\text{ + 0 - 12 = 0 + 0 - 12}[/tex][tex]\text{ y = -12}[/tex]The y-intercept of the given equation is -12.
Therefore, the answer is FALSE.
Using the area formula A=LW (where A is the area L is the length and W is the width ) which of the following formulas would you use to solve for width ?
Answer:
W = A/L
Step-by-step explanation:
We are given the following formula:
A = LW
We want to solve for the width W. So
LW = A
L multiplies W, so it can go to the other side of the equality dividing. Then:
W = A/L
Type the correct answer in each box. Use numerals instead of words.Consider the quadratic equation x2 + 10x + 27 = 0.Completing the square leads to the equivalent equation (x +__ )^2 = __
Given:
[tex]x^2+10x+27=0[/tex]Required:
To complete the square that leads to the equivalent equation (x +__ )^2 = __.
Explanation:
Consider
[tex]\begin{gathered} x^2+10x+27=0 \\ \\ x^2+10x+25+2=0 \\ \\ x^2+10x+25=-2 \\ \\ x^2+5x+5x+25=-2 \\ \\ x(x+5)+5(x+5)=-2 \\ \\ (x+5)(x+5)=-2 \\ \\ (x+5)^2=-2 \end{gathered}[/tex]Final Answer:
[tex](x+5)^{2}=-2[/tex]turn 5 7/10 into a decimal and a percent
It is a mixed number:
[tex]5\frac{7}{10}[/tex]THe whole part, 5, is going to stay 5.
Now, let's work with the fractional part.
7/10 into a decimal would require for division.
7 divided by 10 is 0.7
Thus,
IN Decimal, it will be "5.7"
To find percentage from decimal, we multiply by 100 and tag along a % sign.
So,
[tex]5.7\cdot100=570[/tex]The number, in percentage, is 570%
You are purchasing a snack at the store for $3.50. The sales tax is 6%. How much is the sales tax?
price = $3.50
Sale tax = 6%
Multiply the price by the tax percentage in decimal for ( divided by 100)
3.50 x (6/100) = 3.50 x 0.06 = $0.21
Find the equation for the line that passes through the points (-9, 8) and (-4,-4). Give youranswer in point-slope form. You do not need to simplify.
Given:
The points are (-9,8) and (-4,-4).
Required:
We need to find the line equation in point-slope form.
Explanation:
Consider the slope equation.
[tex]slope,\text{ m=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitute\text{ }y_2=-4,y_1=8,x_2=-4,\text{ and }x_1=-9\text{ in the formula to find the slope of the equation.}[/tex][tex]Slope,\text{ m=}\frac{-4-8}{-4-(-9)}[/tex][tex]Slope,\text{ m=}\frac{-12}{-4+9}[/tex][tex]Slope,\text{ m=}\frac{-12}{5}[/tex]Consider the point (-9,8).
Consider the point-slope form of the equation.
[tex](y-y_1)=m(x-x_1)[/tex][tex]Substitute\text{ }m=-\frac{12}{5},y_1=8,\text{ and }x_1=-9\text{ in the equation.}[/tex][tex](y-8)=-\frac{12}{5}(x-(-(-9))[/tex][tex](y-8)=-\frac{12}{5}(x+9)[/tex]Final answer:
[tex](y-8)=-\frac{12}{5}(x+9)[/tex]Which of the following is the solution to the compound inequality below?5 + x>3or6x +1 -29O A. x2 - 7or14X<-3O B. *)-2orx 5C. x22 or x<5OD. x 814or X-3O
we will need to solve the first inequality,
5+x>=-3 , we will subtract -5 from both sides and the solution is
x>=-2
for the second inequality
6x+1<-29, we will subtract 1 from bothe sides and get
x<-5
is your choice B
Answer this question and show me how to check it
We write numbers that are very small or very large in standard form. Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form
Given that the length and thickness as
[tex]\begin{gathered} l=8\times10^4 \\ t=5\times10^{-6} \end{gathered}[/tex]The ordinary form of the wire is
[tex]\begin{gathered} l=8\times10^4m=8\times10000m=80000m \\ t=5\times10^{-6}m=5\times\frac{1}{1000000}m=0.000005m \end{gathered}[/tex]From the defination of standard form, taking the length, 8 is a number between 1.0 and 10.0 and 10⁴m is a power of 10.
Also, the width, 5 is a number between 1.0 and 10.0 and 10 ⁻⁶ is a power of 10.
Hence, the standard form of the length and thickness of the wire is
length = 8.0 x 10⁴m
thickness = 5.0 x 10 ⁻⁶m
explain two ways to evulate 32(16-6)
There are two ways to evaluate the expression:
32(16 - 6)
WAY 1
Evaluate the expression in the bracket first, then multiply the result by the content outside the bracket.
32(10)
= 320
WAY 2
Remove the bracket straight, without simplifying the content inside the bracket by multiplying 32 by each element in the bracket.
32*16 - 32*6
= 512 - 192
= 320
And those are the two ways.
Noah has a coupon for 30% off at his favorite clothing store he uses it to buy hitting and a pair of jeans Noah paid $28 for jeans after using the coupon what is the regular price of the jeans
$28 after 30% off
28 = regular price * (100 - 30)/100
28 = regular price * 70/100
28 = regular price *0.70
regular price = 28/0.70 = 40
Answer:
Regular price = $40
calculate the slope of a line passing through the given points (5,-2) and (5,-3)
Given the points (5,-2) and (5,-3), we can find the slope of the line that passes through them with the following formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-3-(-2)}{5-5}=\frac{-1}{0} \end{gathered}[/tex]since we have that the slope is not defined, the line that passes through the points (5,-2) and (5,-3) is the vertical line x=5
The side-by-side boxplots show consumer ratings of name brand and store brands of peanut butter.
name brands
al The median of name brands peanut butter is
grester thas the median of store
brands. (Hint* greater than or less than)
b) Approximately
% of name brands peanut butter data values are
greater than the median of the store brands peanut butter data values.
a. Median for name brands is greater than the median for store brands data values in the boxplots given.
b. Approximately 75% of the data values of name brands is greater than the median of the data values of store brands.
How to Find the Median of a Data in a Boxplot?A boxplot displays the distribution of a data such that the median is represented by the vertical line that divides the rectangular box.
25% of a data distribution is represented by the beginning of the edge of the box, while 50% is represented by the median, and 75% is represented by the point at the end of the edge of the box in the boxplot.
Therefore:
a. The median of name brands peanut butter is approximately 82-83.
The median of store brands is approximately less than 80.
Thus, we can conclude that, the median for name brands is greater than the median for store brands.
b. The median for store brands is approximately below 25% of the data values for name brands. Therefore, we would conclude that, approximately 75% of name brands data value are greater, compared to the median of the store brands data value.
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Palge counted the number of items in other people's shopping carts while waiting in line at the grocery store. Palge counted the following items in seven carts: 13, 24, 17, 43, 38, 22, and 35. What is the median number of items in the shopping carts? items
ANSWER
24
EXPLANATION
The median of a data set is the middle number of the set - when they are arranged from least to greatest. If the amount of numbers in the data set is even, the median is the average of the two middle numbers.
In this case, there are 7 charts. To find the middle number we have to arrage the set from least to greatest: 13, 17, 22, 24, 35, 38, 43
The middle number is 24. This is the median.
Round 36,236 to the nearest ten thousand
We have to round the number 36,236 to the nearest ten thousand (10,000).
Then, the number 36,236 is between 3 and 4 ten thousands. As 36,236 is over 35,000 we round it to 40,000.
Answer: 40,000
Describe 4 types of Quadrilaterals
Answer:
Parallelograms, Squares, Rectangles, and Rhombuses
Step-by-step explanation:
use pie=3.14 to estimate the unknown measures for each circle.c=132 ind=r=A=I'll upload a picture
Problem N 25
we know that
C=132 in
Remember that
The formula to calculate the circumference is given by
[tex]C=pi*D[/tex]using pi=3.14
C=132 in
substitute given values in the formula
[tex]\begin{gathered} 132=3.14*D \\ solve\text{ for D} \\ D=\frac{132}{3.14} \\ D=42.04\text{ in} \end{gathered}[/tex]The diameter D=42.04 in ( with pi=22/7 the diameter is 42 in exact)
Find out the radius r
r=D/2=42.04/2=21.02 in -----> the radius is half the diameter
Find out the area of the circle
The area is given by the formula
[tex]A=pi*r^2[/tex]we have
r=21.02 in
pi=3.14
substitute
[tex]\begin{gathered} A=3.14*21.02^2 \\ A=1,387.38\text{ in}^2 \end{gathered}[/tex]therefore
the answer isd=42.04 inr=21.02 inA=1,387.38 in2At a company meeting, there were 40 people in attendance. 70% of them were managers. How many managers were in the meeting?
TELL ANSWER ASAP PLS WHAT IS 15.5 MULTIPLIED BY 3.75??????
Multiplied by 15.5 to 3.75 is 58.125.
To solve the:
15.5 is multiplied by 3.75
Now,
15.5 × 3.75
= 58.125
What is the process of Multiplication ?
Multiplication is the process of calculating the total of one number multiplied by another. There will be simple tests in addition, subtraction, multiplication and division. 2. uncountable noun. The multiplication of things of a particular kind is the process or fact of them increasing in number or amount.
Hence, Multiplied by 15.5 to 3.75 is 58.125.
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