Answers
A graph of triangle CAT is shown below.
A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.
ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (x, -y)
C (-1, 2) → (-1, -(2)) = C' (-1, -2)
A (-1, 4) → (-1, -(4)) = A' (-1, -4)
T (3, 2) → (3, -(2)) = T' (3, -2)
Read more on reflection here: brainly.com/question/27912791
#SPJ1
Related Questions
Problem 5:
Find the missing side using
trigonometry:
52
18 H
AWO
Drag&Drop the correct trig function:
Cos
Tan
Rati
Circle which shortcut you use.
Multiply
Round your answer to the nearest tenth:
Give Feedback to Micrones
Sin
%
or
IN
Divide
Ans
Ans
Answers
The missing length is 11.0818 unit.
We have,
Angle = 52 degree
H = 18
Using Trigonometry
cos 52 = B/H
cos 52 = x / 18
0.615661 = x /18
x = 11.0818 unit
Thus, the missing length is 11.0818 unit.
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ2
Examine the equation below used for determining the capital gain made on a stock.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05
Answers
This capital gain problem that can be modelled using this equation is one that relates to the price of a stock or share.
How can the problem be crafted?It can be writen as follows.....
Suppose that one purchased 900 shares of a stock at a price of $ 12.55 per share .
After a year, the stock price rose to $ 13.25 per share, but you sold the shares at a price of $8. 14 per share due to financial difficulties.
You also incurred a transaction cost of $25.
What is the capital gain or loss made on the stock?
given the above question, if we solved for for the problem, we would get....
Solving for x, we get:
((900 )(x )-(900 )(x)(.01))-(900) (x-4) +25)
= 15,740
Simplifying this expression, we get:
(0.99900x) - (36 x 900) + 25
= 15,740
0.99900 x = 15,655
x = 17.39
Therefore, the current stock price is $17.39
Learn more about Capital Gain:
https://brainly.com/question/27880977
#SPJ1
Full Question:
1. Examine the equation below used for determining the capital gain made on a stock. Look through this chapter and your notes to help you write a problem that could be modeled by this equation.
.((900)(12.55)-(900)(12.55)(.01))-(900)(8.14)+25)=3,831.05
The box plots display the scores that two different groups of students got on their last math quiz.
Answers
The correct option is A.
The interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
Given that, the box plots display the scores that two different groups of students got on their last math quiz.
We need to find the interquartile range of each data set.
So, the interquartile range of data set A = 80-65 = 15
the interquartile range of data set B = 90-80 = 10
Hence, the interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
The correct option A.
Learn more about interquartile range click;
https://brainly.com/question/29204101
#SPJ1
HELP PLS ASAP DETERMINE THE RANGE
Answers
Answer:
-7≤y≤2
Step-by-step explanation:
The range measures the highest and lowest numbers up and down on the y-axis for a line. In order to determine range, start with the smallest number (the farthest place the line touches going down) then write less than or equal to. This is because the two dots are closed, meaning they include what the line touches. Afterward, add another less than or equal to, and then add the biggest number (the highest place the line touches going up). The range basically gives you your boundaries, and tells you how high or low the line you are describing is. And after that, you're done!
I hope this helps :)
Last year, the rates of return on the investments in a large portfolio had an approximately mound-shaped distribution, with a mean of 20% and a standard deviation of 10%. What proportion of the investments had a return of between 10% and 30%? What proportion of the investments had a return of between -10% and 50%? b. What proportion of the investments had a return that was either less than 10% or more than 30%? What proportion of the investments had a positive return? (Hint: A mound-shaped distribution is symmetrical.)
Answers
a) The proportion of the investments had a return of between 10% and 30% is given as follows: 0.68 = 68%.
b) The proportion of the investments had a return of between -10% and 50% is given as follows: 0.997 = 99.7%.
c) The proportion of the investments had a return either less than 10% or more than 30% is given as follows: 0.32 = 32%.
d) The proportion of the investments had a positive return is given as follows: 0.9985 = 99.85%.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.Hence the percentages for this problem are given as follows:
Item a -> 68% -> within one standard deviation of the mean.Item b -> 99.7% -> within three standard deviation of the mean.Item c -> 32% -> More than one standard deviation of the mean.Item d -> all above the mean, 99.7% of the 50% below the mean -> 0.997 x 0.5 + 0.5 = 0.9985 = 99.85%.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
#SPJ1
PLEASE HELP HURRY FAST PLEASE THANK YOU! please put answers as either a b c or d thank you and please help me on every single one ill give brainiest if completed thanks
4. Find the rational roots of x^4+5x^3+7x^2-3x-10=0
A. -2,1
B. 2,1
C. -2,-1
D. 2,-1
5. Find all the zeros of the equation 3x^2-4=-x^4
A. 1,2i
B. -1,-2i
C. 1,-1,2i,-2i,0
D. 1,-1,2i,-2i
6. What is a polynomial function in standard form with zeros 1,2,-2, and -3?
A. x^4+2x^3+7x^2-8x+12
B. x^4+2x^3-7x^2-8x+12
C. x^4+2x^3-7x^2+8x+12
D. x^4+2x^3+7x^2+8x+12
7. Which correctly describes the roots of the following cubic question.
x^3-3x^2+4x-12=0
A. three real roots, each with a different value
B. one real root and two complex roots
C. three real roots, two of which are equal in value
D. two real roots and one complex root
8. What is the solution of 5^3x=900. Round your answer to the nearest hundredth
A. 1.24
B. 1.41
C. 4.23
D. 0.69
9. x= 1,2,4,6,8,10,11 y= 0,-1,0,4,8,9,8 <--- Table is right here
Which of the following questions best represents the regression line for the data given in the table above.
A. y=x+2
B. y=2x-2
C. y=-x-2
D. y=x-2
10. Is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is a direct or inverse variation, write a function to model it. ---> Table x= 2,5,12,20 y= 30,12,5,3
A. direct variation; y=15x
B. inverse variation; y=60/x
C. direct variation; y=2x+2
D. neither
11. A drama club is planning a bus trip to New York City to see a Broadway play. the cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 55 people go on the trip. Round your answer to the nearest cent if necessary
A. $48.00
B. $12.50
C. $24.00
D. $33.00
12. What is the simpler form of the radical expression? 4sqrt2401x^12y^16
A. 49|x^9|y^16
B. 49x^9|y^16|
C. 7|x^3|y^4
D. 7x^3|y^4|
13. Simplify. 125^1/3
A. 125
B. 5
C. 25
D. sqrt125
14. Graph the function. y=sqrtx+3
15. An initial population of 293 quail increases at an annual rate of 6%. Write an exponential function to model the quail population. What will the approximate population be after 4 years?
A. f(x)=(293 x 1.06)^x; 930
B. f(x)=293(0.06)^x; 379
C. f(x)=293(1.06)^x; 370
D. f(x)=293(6)^x; 190
16. Evaluate the logarithm
log3 2187
A. 5
B. 6
C. 7
D. -7
17. Estimate the value of the logarithm to the nearest tenth
log4 22
A. 2.2
B. 0.4
C. -0.7
D. 3.2
18. Solve 1n 4 + 1n (3x)=2. Round your answer to the nearest hundredth
A. 1.13
B. 0.18
C. 1.41
D. 0.62
19. Write an equation for the translation of y= 4/x that has the asymptotes x=7 and y=6.
A. y= 4/x-6 +7
B. y= 4/x+7 +6
C. y= 4/x-7 +6
D. y= 4/x+6 +7
20. What is the graph of the rational function?
y=(x-5)(x-3)/(x+4)(x-4)
21. What are the points of discontinuity?
y=(x-3)/x^2-12x+27
A. x=4,x=9,x=1
B. x=-9,x=-3
C. x=-9,x=-3,x=-1
D. x=9,x=3
22. What is the quotient 6-x/x^2+2x-3/x^2-4x-12/x^2+4x+3 in simplified form? State any restrictions on the variable.
23. Simplify the complex fraction x+3/ 1/x+1/x+3
A. x^2/2x+3
B. x^2/2x
C. x^2/x+3
D. x^2+2x+3/2x+3
24. Simplify the difference
x^2-x-56/x^2+6x-7 - x^2+2x-15/x^2+9x+20
A. x-71/(x-1)(x+4)
B. 2x^2-8x-29/(x-1)(x+4)
C. -8x-35/(x-1)(x+4)
D. -35/(x-1)(x+4)
25. Solve the equation 1/x-3+1/x+5=1/3
A. x=1,x=7
B. x=3,x=-5
C. x=-3,x=1
D. x=-3,x=7
Answers
Answer:
Step-by-step explanation:
4. A. Im not sure but that seems like the most logical.
5. D.
6. B.
7. B.
8. I think it's A. maybe-
9.- id-k sorry-
10. i--dk..]
11. C
12. D
13. B.
15. C.
16. C
17. A.
18. D
19. C.
21. D.
22. -(x+1)/(x-1)(x+2) x does not equal -3, -2, 1, and 6
23. i d-ksorry
24.i-d-k sorry
25. D.
Hope this helped sorry i culdn't get them all-
The answers to all parts are shown below.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
1. x⁴ + 5x³ + 7x² -3x - 10 = 0
= (x-1)(x+2)(x² + 4x + 5)
Thus, the rational roots are 1 and -2.
2. 3x² -4 = - x⁴
x⁴ + 3x² -4 = 0
(x-1)(x+1)(x² + 4) =0
Thus, the zeroes are 1, -1, -2i, +2i.
3. We can write the zeroes as
p(x)=(x-1)(x-2)(x+2)(x+3).
So, p(x) = x⁴ + 2x³ -7x² -8x +12
4. x³ -3x² +4x- 12=0
(x-3)(x²+4) =0
x= 3, -2i, 3i
5. x= 1,2,4,6,8,10,11
y= 0,-1,0,4,8,9,8
So, equation of line
(y- 0) = (-1-0)/(2-1)(x-1)
y = -1(x-1)
y + x +1=0
6. x= 2,5,12,20 and y= 30,12,5,3
k = 30/2
k = 15
So, the relationship is y= 15x.
7. cn = constant(k)
n= 44
then, c= 30/44 = 0.68
and, k = 44 x 0.68
k = 30
So, c = 1.5 dollars per person.
8. 125¹/³
= (5³)¹/³
= 5
9. y = 293(1.06)⁴ = 370
10. log₃ 2187
= log₃ 3⁷
= 7
11. log₄ 22
= 2.29
12 . y= 4/x
The new equation is y = 4/(x - 7) + 6.
13. (6-x)/ (x² + 2x - 3) / (x² -4x- 12)/ (²x² + 4x + 3)
= - (x+1)/ (x+1)(x+2)
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ5
Drag and drop to complete the proof below:
Given: DE←→
is tangent to circle C, at point F
Prove: ∠FEC and ∠ECF are complementary
Answers
To complete the proof below, we have;
<EFC is right angle; definition of a right angle
m<EFC = 90 degrees; definition of a tangent line
m<EFC + m<FEC + m<ECF = 180; Triangle sum theorem
90° + m<FEC + m<ECF = 180; Substitution property of equality
m<FEC + m<ECF = 90; Subtraction property of equality
<FEC + <ECF are complementary angles; definition of complementary angles
How to match the statementsTo match the statement with their corresponding equations, we need to know the following;
The sum of the angles in a triangle is 180 degreesThe measure of the angle at right angle is 190 degreesComplementary angles are pair of angles that sum up to 90 degreesLearn more about angles at: https://brainly.com/question/25716982
#SPJ1
Problem 3
Draw the pictures to compute 1 ÷ 11 in a base ten system, and show the answer is 0.09.
Answers
The result of 1/11 in the base 10 system is given as is 0.09.
How to solveTo visualize the long division of 1 ÷ 11 in a base ten system:
Set up the long division: 11 outside and 1.00 inside the division bracket.
Place the decimal point in the quotient above the dividend's decimal point.
Bring down the first digit (0) and divide 11 into 10; it goes 0 times.
Subtract the product (0) from 10, leaving 10.
Bring down the next digit (0) and divide 11 into 100; it goes 9 times.
Subtract 99 from 100, leaving a remainder of 1.
The result is 0.09.
Read more about base ten here:
https://brainly.com/question/26668177
#SPJ1
Ana's lawn is shaped like a square with an area of 224.9 .
Which measurement is closest to the side length of his lawn in feet?
Answers
The square root of 224.9 is approximately 14.99 feet.
Therefore, the measurement closest to the side length of Ana's lawn in feet is 15 feet.
Help need help now
A beaker is shaped like a cylinder with a radius of 1.8 inches and a height of 4.6 inches. It is filled to the top with a solution. Caleb wants to pour it into a different beaker with a radius of 1.25 inches. What is the minimum height the second beaker must be so it does not overflow? Round to the nearest tenth.
Answers
The minimum height the second beaker must be so it does not overflow is 9.55 inches.
Given that a beaker has a radius of 1.8 inches and height of 4.6 inches. we need to find the height of another beaker which has the radius of 1.25 in and has same volume,
Volume of a cylinder = π × radius² × height
= 3.14 × 1.8² × 4.6
= 46.8 in³
Now, the second beaker =
46.8 = 3.14 × 1.25² × h
h = 46.8 / 3.14 × 1.25²
h = 9.55
Hence, the minimum height the second beaker must be so it does not overflow is 9.55 inches.
Learn more about volumes, click;
https://brainly.com/question/1578538
#SPJ1
what is the surface area of the capsule ? round your answer to the nearest hundredth
Answers
I'm sorry, but I cannot answer this question without additional information about the dimensions of the capsule. Please provide me with the necessary information so that I can assist you.
Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answers
Answer:
check attachment
Step-by-step explanation:
First write in point-slope form:
y-y1=m(x-x1)
Now substitute:
y-(-1)=3/4(x-(-4))
And then just solve. You should get a y-intercept of 2.
Corellian Engineer needs to develop a new navigation system for its YT-1300 Freighter. They opened the process to competitive bids. The best bid gave the following numbers. (All numbers in millions).
Working -
Total cost estimate for thos project = Programming + Beta Testing + Installation + Final shake down.
= 5,000 + 3,500 + 2,000 + 7,000
= 17,500.
the total cost estimate for this project is $17,500.
What process did Corellian use for this estimate? Choose one.
1.Top down (Macro)
2.Balanced
3.Bottom up (Micro)
4.OMG, my head hurts
Answers
Corellian Engineer used the Bottom up (Micro) approach to estimate the total cost of developing a new navigation system for its YT-1300 Freighter. The total cost estimate of $17,500. So, the correct option is C).
The process that Corellian used for this estimate is the Bottom up (Micro) approach, which involves estimating costs for each component or task in the project and then summing them up to get the total cost estimate.
In this case, they estimated the costs for programming, beta testing, installation, and final shake down, and then added them up to get the total cost estimate of $17,500.
So, the correct answer is C).
To know more about navigation system:
https://brainly.com/question/13894678
#SPJ1
Please help, due tonight!
Answers
The area of the trapezoid with parallel sides of 8 meters and 7 meters, and a height of 4 meters, is 30 square meters.
To find the area of a trapezoid, we use the formula:
Area = (a + b)h/2
where "a" and "b" are the lengths of the parallel sides of the trapezoid, and "h" is the height of the trapezoid.
In this case, we are given that the parallel sides are 8 meters and 7 meters, and the height is 4 meters.
Substituting these values into the formula, we get:
Area = (8 + 7) x 4 / 2
= 15 x 4 / 2
= 60 / 2
= 30 square meters
To learn more about the trapezoid;
https://brainly.com/question/8643562
#SPJ1
b) The Median and Mode of the following wage distribution are known to be $33.5 and $34 respectively. Three frequency values from the table are, however, missing. Find the missing values. Wages (in $) 0-10 10 - 20 20 - 30 30 - 40 40 - 50 50-60 60-70 Frequencies (f) 10 10 ? ? ? 6 230 repsectively
Answers
The missing values are 60, 100 and 40 if the Median and Mode of the wage distribution are known to be $33.5 and $34 respectively
Wages (in Rs)_freq____ CF
0-10________4___________4
10-20_______16________20
20-30_______x________20+x
30-40______y_________20+x+y
40-50______z________20+x+y+z
50-60______6_______26+x+y+z
60-70______4______30+x+y+z
Since total 230
So, 30+x+y+z=230
x+y+z=200
Mode =34
Median = 33.5
By solving the equations we get x=60, y=100 and z=40
Hence, the missing values are 60, 100 and 40
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ1
i nedddddddd help on thisssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss
Answers
b) the answer is -9,8
Help please on this one i need help
Answers
∠ AFE is supplementary to ∠ AFB and the measure of ∠ AFE = 102⁰.
option A.
What is a supplementary?Supplementary angles are the two angles that sum up to 180 degrees.
That is, if the sum of two angles is equal to 180 degrees, then the two angles are supplementary.
From the given diagram we can form the following equation;
∠ AFE + ∠ AFB = 180 (sum of angles on a straight line is equal to 180⁰ )
∠ AFE = 180 - ∠ AFB
∠ AFE = 180 - 78
∠ AFE = 102⁰.
Learn more about supplementary angles here: https://brainly.com/question/12919120
#SPJ1
Convert 135° from degrees to radians.
Answers
Answer:
Answer:Radians = Degrees × 3.14/180
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174
Answer:Radians = Degrees × 3.14/180Step-by-step explanation:145× (3.14/180)3.14/180= 0.0174135×0.0174 = 2.355
Find the volume of the composite solid. Round your answer to the nearest hundredth.
6 ft
-12 ft
The volume is about
cubic feet.
Answers
(4/3) Pi r^3 -formula for sphere\/\/\/
2/3 Pi r^3- formula for hemisphere*
Going to use these two, substitute and add together
Cone- 144 pi
Hemisphere- 144pi
Cone + hemisphere =288pi OR about 904.78
You save $8,500.00. You place 40% in a savings account earning a 4.2% APR compounded annually and the rest in a stock plan. The stock plan decreases 3% in the first year and increases 7.5% in the second year.
A. What is the total gain at the end of the second year for both accounts combined?
B. If you had invested 60% in the savings account and the rest in the stock plan, what is the difference in the total gain compared to the original plan?
Answers
The total gain at the end of the second year for both accounts combined is $509.09.
We have,
Amount saved = $8500
40% of 8500 is saved in saving account = 0.4 x 8500 = $3400
Remainder amount in stock plan = 8500 - 3400 = 5100
Working for savings plan
A = P(1 + r/n[tex])^{nt[/tex]
A = 3400(1 + 0.042/1)²
A = $3691.60
So, we gain = 3691.6 - 3400 = $291.6
Working for stock plan:
The stock plan decreases 3% in the first year
= 5100 x 0.97
= $4947
and increases 7.5% in the second year.
= 4947 x 1.75
= $5318.03
So, we gain = 5318.03 - 5100 = $218.03
Thus, the total gain is
= 291.06 + 218.03
= $509.09
Learn more about Compound Interest here:
https://brainly.com/question/14295570
#SPJ1
The graph of which equation passes through the
point
Answers
Answer:
The answer is A.
A graph passes through a point if its equation is equal to the coordinate of this point. In this exemple:
5x+4y=8
we replace the variables with 4 and -3 (x with 4 and y with -3):
5(4)+4(-3)=8
20-12=8
8=8 so it passes.
NOW , for the slope:
slope = - 5/4 ( the equation is 5x+4y=8 , the cartesian equation is 5x+4y-8=0. THE cartesian equation with variables is ax+by+c=0) NOW this is linked with the slope bcz the slope is linked to the director vector (-b;a) that gives (-4;5), this is the director vector's formula that we're going to call U. THEN with this formula you get the slope: Y of U / X of U = 5/-4 = - 5/4 (bcz you dont leave the denominator with a negative sign).
THAT'S it thats the answer.
The volume of 1,000 drops of a liquid is 10 fluid ounces. What is the volume of 10 drops?
Answers
Answer:
0.1 oz
Step-by-step explanation:
1000=10 oz
10 drops
1000/100=10
10/100=O.1 oz
Question attached. You dont need to send working out just and answer to 2dp
Answers
The value of length of AG is,
AG = 157.02
We have to given that;
AD = 31 cm
DC = 22 cm
Hence, We get;
AC = √31² + 22²
AC = √961 + 484
AC = √1445
AC = 38
Thus, We get;
cos 76° = AC / AG
0.242 = 38 / AG
AG = 38/0.242
AG = 157.02
Therefore, The value of length of AG is,
AG = 157.02
Learn more about the cuboid visit:
https://brainly.com/question/26403859
#SPJ1
A normal distribution has a mean of 85.5 and a standard deviation of 4.8 to find the data value corresponding to the value of the given
Answers
The data value corresponding to z = 0.55 is approximately 87.6075.
How to solve for the data valueTo find the data value corresponding to a given z-score, we need to use the formula:
z = (x - μ) / σ
where z is the standard score, x is the data value, μ is the mean, and σ is the standard deviation.
Rearranging this formula, we get:
x = z * σ + μ
Substituting the given values, we get:
x = 0.55 * 4.85 + 85.3
x = 87.6075
Therefore, the data value corresponding to z = 0.55 is approximately 87.6075.
Read more on normal distribution here:https://brainly.com/question/4079902
#SPJ1
A normal distribution has a mean of 85.3 and a standard deviation of 4.85. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.) z = 0.55
What are the coordinates of the image of the point (8,1) after a dilation by a scale factor of 2 with the origin as the center of dilation, followed by a translation over the y-axis
Answers
The point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).
Given is a point, (8, 1) we need to find the coordinates of a point which is dilated from the origin by the scale factor of 2 and translation over the y-axis,
So, the coordinates of after dilation by k scale factor =
(x, y) = (kx, ky)
So, (8, 1) = (16, 2)
Now, the translation over the y-axis gives,
(x, y) = (-x, y)
Therefore, (16, 2) = (-16, 2)
Hence, the point after a dilation by a scale factor of 2 with the origin as the center of dilation, and a translation over the y-axis is (-16, 2).
Learn more about transformation, click;
https://brainly.com/question/13801312
#SPJ1
A cylinder has a base radius of 6ft and a height of 18ft. What is its volume in cubic ft, to the nearest tenths place?
Answers
Answer:
2035.8 ft³
Step-by-step explanation:
You want to know the volume of a cylinder with radius 6 ft and height 18 ft.
VolumeThe volume of a cylinder is given by the formula ...
V = πr²h
For the given dimensions, the volume is ...
V = π(6 ft)²(18 ft) ≈ 2035.8 ft³
The volume of the cylinder is about 2035.8 cubic feet.
__
Additional comment
If you use 3.14 for π, you get 2034.7 cubic feet.
<95141404393>
explicit formula for an, the nth term of the sequence 6, 0, -6, ....
Answers
Answer:
12 - 6n
Step-by-step explanation:
As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.
Nth term = a1 + d(n-1)
= 6 + -6(n-1)
= 6 - 6n + 6
= 12-6n
Mark is running in a 13-mile race.He has run 5miles so far
Answers
The required Mark has completed 38.46% of the race.
To calculate the percentage of the race completed by Mark, we can divide the number of miles he has run by the total length of the race and then multiply by 100 to convert the result to a percentage.
So, Mark has run 5 miles out of a total of 13 miles:
Percentage of race completed = (5/13) x 100%
Calculating this expression, we get:
Percentage of race completed = 38.46%
Therefore, Mark has completed 38.46% of the race.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
nd the interest on the loan using the Banker's ru P = $4800, r= 8.8%, t = 105 days! The interest on the loan using the Banker's rule
Answers
The interest on the loan using the Banker's Rule is $139.20.
How to find the interest on the loan using the Banker's ruleThe formula for calculating interest using the Banker's Rule is:
Interest = Principal x Rate x Time / 360
where:
Principal is the amount of the loan
Rate is the interest rate as a decimal
Time is the time period in days
Using this formula, we can calculate the interest on the loan as:
Interest = 4800 x 0.088 x 105 / 360
Interest = 139.20
Therefore, the interest on the loan using the Banker's Rule is $139.20.
Learn more about interest at https://brainly.com/question/25793394
#SPJ1
You will purchase 700 frozen treat's the cost to you should be at most 400 your goal is to make a profit of at least $800. Explain to Omar how your decision meets each of the criteria. Include the number of each type of treat in your explanation
Answers
The decision meets each of the criteria by: Buying 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each enables the purchase of 700 frozen delights within the $400 budget and satisfies the objective of producing at least $800 in profit.
How did your decision meets each of the criteria?I have made the decision to buy 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each in order to fulfil the requirement of buying 700 frozen delights at a price of no more than $400.
Cost of purchasing 500 popsicles = (500 * $0.50)
Cost of purchasing 500 popsicles = $250
Cost of purchasing 200 ice cream sandwiches =(200 * $1.50)
Cost of purchasing 200 ice cream sandwiches = $300
So, Total cost of purchasing all 700 frozen treats is $550 ($250 + $300) which is within the budget of $400.
I intend to sell the popsicles for $1.50 each and the ice cream sandwiches for $3.00 each in order to meet the requirement of turning a profit of at least $800. This would bring in $1350 in income for the ice cream sandwiches and $750 for the popsicles (500 * $1.50 and 200 * $3.00 respectively).
The objective of producing a profit of at least $800 is met after deducting the expense of buying the frozen treats from the overall income.
Net profit =($1350 - $550)
Net profit = $800
Therefore purchasing 500 popsicles at $0.50 each and 200 ice cream sandwiches at $1.50 each satisfies the objective of producing at least $800 in profit.
Learn more about profit here:https://brainly.com/question/29785281
#SPJ1