Answer:
252 ft²
Step-by-step explanation:
A triangular prism has three rectangles and two triangles, to find the surface area, first find the surface area of thee rectangles and then the surface area of the triangles. After that add all the surface area.
For rectangle 1, surface area = 20 × 3 = 60 ft²
For rectangle 2, surface area = 20 × 4 = 80 ft²
For rectangle 3, surface area = 20 × 5 = 100 ft²
The triangle has height, base and hypotenuse. 5 ft is the hypotenuse and the height and base are 3 ft and 4 ft.
5² = 3² + 4²
For the triangle, the surface area = 1/2 × base × height = 1/2 × 3 × 4 = 6 ft²
Total surface are = 60 + 80 + 100 + 2(6) = 252 ft²
Find the area of the semicircle? Helpppp
Answer:
14.135
Step-by-step explanation:
6 divided by 2 (half) = 3, π·32≈28.27433 dived by 2 (half) equals 14.135
Answer:
14.13 units ^2
Step-by-step explanation:
A= 3.14 (3)^2 (area of a circle)
A= 28.26 / 2 (divide to find half of the circle)
A=14.13 units ^2
2.) The equation yˆ=−8.74x2+50.57x+39.02 models the number of customers in a store x hours after opening.
Q 2 Options -Which number is the best estimate for the number of customers in the store 3 hours after opening?
A. 86
B. 47
C. 105
D. 112
3.The table shows the number of mobile cellular subscriptions per 100 people in Australia for different years.
Year 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011
Cellular subscriptions / 100 people 4 12 25 33 57 72 90 101 101 108
The quadratic regression equation using the years since 1990 for the input variable and the number of cellular subscriptions for the output variable is yˆ=−0.107x2+9.008x−28.851.
What is the predicted number of cellular subscriptions per 100 people in Australia in 2030?
Round your answer to the nearest whole number. Enter your answer in the box.
4. Determine the equation of the quadratic regression curve for the data.
x 0 1 2 3 4 5 6
y 4.1 −0.9 −3.9 −5.1 −4.1 −1.1 4.1
Enter your answer in the box
5.The table shows the average number of miles traveled per person in the United States for different years.
Year 1915 1925 1935 1945 1955 1965 1975 1985 1995 2005
Average miles traveled per person 194 1056 1796 1788 3650 4569 6147 7460 9099 10,181
Find the quadratic regression equation using the years since 1900 for the input variable and the average number of miles for the output variable. Round each coefficient in the equation to the nearest thousandth.
Using the regression equation with rounded values, what is the best estimate for the average number of miles traveled per person in 1961?
Question 5 options:
A. 4324
B. 1885
C. 4191
D. 2398
Answer:
2. The correct option is;
D. 112
3. The predicted number of cellular subscription per 100 people in Australia in 2030 is 217 subscriptions
4. The equation of the quadratic regression curve is y = x² - 6×x + 4.1
5. The closest option is;
C. 4191
Step-by-step explanation:
2. The equation for the number of customers in a store is presented as follows;
y = -8.74·x² + 50.57·x + 39.02
Where:
x = Number of hours after opening
∴ When x = 3 hours
y = -8.74×3² + 50.57×3 + 39.02 = 112.07 ≈ 112 people
The correct option is D. 112
3. The expression of the regression equation is presented as follows
y = -0.107·x² + 9.008·x +28.851
Where:
x = Number of years since 1990, hence
When x = 2030 - 1990 = 40 Years
Hence, the predicted number of cellular subscriptions per people in 2030 is presented as follows;
y = -0.107×40² + 9.008×40 +28.851 = 217.971 Subscribers
To round down to the nearest whole number as y = 217 subscribers
4. The general form of a quadratic equation is presented as follows;
y = a·x² + b·x + c
When x = 0, y = 4.1, therefore;
4.1 = a×0² + b×0 + c = c
∴ c = 4.1
When x = 1, y = -0.9, therefore;
-0.9 = a×(1)² + b×1 + c = c
-0.9 = a + b + 4.1
∴ a + b = -0.9 - 4.1 = -5.0
When x = 2, y = -3.9, therefore;
-3.9 = a×(2)² + b×2 + c = c
-3.9 = 4·a + 2·b + 4.1
∴ 4·a + 2·b = -3.9 - 4.1 = -8.0
Thus we have two equations;
a + b = -5.0..................(1) and
4·a + 2·b = -8.0 ..........(2)
Multiply equation (1) by 2 and subtract it from equation (2), we have
4·a + 2·b - 2×(a + b) = *8.0 - (2 ×-5.0)
∴ 2·a = 2
a = 1
From equation (1,) we have;
a + b = -5.0..................(1)
Therefore, where a = 1 we have, 1 + b = -5.0
Hence, b = -5.0 - 1 = -6.0
Therefore, the equation of the quadratic regression curve is presented as follows;
y = x² - 6×x + 4.1
5. The quadratic regression equation is found as follows;
The general form of a quadratic equation is presented as follows;
y = a·x² + b·x + c
When x = 55, y = 3650, therefore;
3650= a×55² + b×55+ c................(1)
When x = 65, y = 4569, therefore;
4569= a×65² + b×65+ c ...........(2)
When x = 75, y = 6147, therefore;
6147= a×75² + b×75+ c............(3)
Solving the system of equation;
3650= a×55² + b×55+ c................(1)
4569= a×65² + b×65+ c ...........(2)
6147= a×75² + b×75+ c............(3)
Subtracting equation (1) from (2), we obtain;
4569 - 3650 = a×65² + b×65 + c - (a×55² + b×55 + c)
919 = 1200·a + 10·b...........(4)
Subtracting equation (2) from (3), we obtain;
6147 - 4569 = a×75² + b×75 + c - (a×65² + b×65+ c)
Which gives;
1578 = 1400·a + 10·b...........(5)
Subtracting equation (4) from equation (3), we obtain;
1578 - 919 = 1400·a + 10·b - (1200·a + 10·b)
659 = 200·a
a = 659/200= 3.295
Substituting the value of a in equation (4), we have;
919 = 1200×3.295 + 10·b = 3954 + 10·b
∴ 10·b = 919 -3954 = -3035
b = -3035/10 = -303.5
Substituting the value of a and b in equation (1), we have;
3650 = (3.295)×55² + (-303.5)×55+ c
3650 = -6725.125 + c
∴ c = 3650 - (- 6725.125)= 10375.125
Therefore, the quadratic regression equation is presented as follows;
y = 3.295·x - 303.5·b +10375.125
Hence, in 1961, x = 1961 - 1900 = 61, we have
y = 3.295×61² - 303.5×61 10375.125= 4122.32
Therefore, the closest option is C. 4191.
Answer:
Step-by-step explanation: I took the test and here are the answers
Jake and Becky measured the circle-shaped part of a sun they drew on the sidewalk.
The diameter of the circle is 70 centimeters. What is the approximate area of the circle?
(Use 3.14 for Pi)
Answer:
3847
Step-by-step explanation:
To get your radius
diameter/2= 70/2=35.
Radius=35
Area=πr^2 =3.14x 35x35= 3846.5
approximately=3847
I don’t understand how to do this problem. How would I solve it?
Answer:
About 2.569 seconds
Step-by-step explanation:
To solve this problem, you can separate it into two half parabolas. The beginning part is initial upward rising. To calculate the amount of time that this part of the dive takes, you can use the formula [tex]v_f=v_o+at[/tex], where [tex]v_f[/tex] is the final velocity, [tex]v_o[/tex] is the initial velocity, a is the acceleration due to gravity, and t is the amount of time it takes. You know that the final velocity is 0, since the diver is reaching the terminal of their dive. Therefore, you can set up the following equation (assuming that the acceleration due to gravity is 32ft/s^2):
[tex]0=5+(-32)t[/tex]
[tex]t=5/32[/tex] seconds
To find the height that this indicates the diver has risen, you can plug this time into the following formula: [tex]d=v_o t+\frac{1}{2}at^2[/tex]
[tex]d=5(5/32)+\frac{1}{2}\cdot 32\cdot (5/32)^2\approx 1.172[/tex] feet
For the second part, you can use the equation [tex]d=v_o t+\frac{1}{2}at^2[/tex] again. Since the initial velocity for this part is 0, you can set up the following equation:
[tex]92+1.172=\frac{1}{2}\cdot 32 \cdot t^2[/tex]
[tex]t \approx 2.413[/tex]
Adding this to the time that the first part of the dive takes, you get a total of about 2.569 seconds. Hope this helps!
1. Express as a unit rate
a) Serena walks 4 km in 1 h.
Answer:
Step-by-step explanation:
Serena walks 4 km in 1 h.
That means:
1) She walks 4 km per hour.
2) She spends 1/4 = 0.25 hour per mile.
Have a good day.
We can write this as:
4 kilometers/1 hour
The unit rate is already simplified so there is nothing else to do.
Answer: 4km/1hr
Best of Luck!
3 POINSSSSSS
The bar graph shows the results of rolling a number cube (a die) 50 times. What is the probability of rolling an odd number? How does this compare with the theoretical probability of rolling an odd number?
Experimental Probability. Theoretical Probability
P(odd) = % P(odd) = %
Answer:
see below
Step-by-step explanation:
Experimental means what actually happened
P(odd) = (number of 1 + number of 3 + number of 5) / total
= (10+8+8) / 50
= 26/50
= 13/25 = 52%
Theoretical means what we expect to happen
P (odd) = (number of 1 + number of 3 + number of 5) / total
=(1+1+1)/6
=1/2 = 50%
We rolled an odd just a little more than the expected amount of times
Answer:
yes
Step-by-step explanation:
If y varies inversely as x and y = 8 when x = 9, find x when y = 12.
Answer:
x = 6
Step-by-step explanation:
An inverse variation is
xy = k where k is the constant of variation
8*9 = k
72 = k
xy = k
Let y = 12
x*12 = 72
Divide each side by 12
12x/12 =72/12
x = 6
6. David leaves the house to go to school He walks 200 m west and 125 m
north. Calculate how far he is from the sting point.
Answer:
~235.8
Step-by-step explanation:
200^2 +125^2= distance traveled^2
55625= distance traveled^2
235.849528301
it costs $12 to attend a golf clinic with a local pro. Buckets of balls for practice during the clinic costs $3 each. How many buckets can you buy at the clinic if you have $30 to spend?
Answer: If you take out the price of the golf clinic with a local pro, you could buy 6 buckets.
Step-by-step explanation:
12 inches is a feet :))
i’m with the gàng, I’m with the fleet >:)
Answer:
12 inches is a foot * ;)
Step-by-step explanation:
PLZZZZZZZZZZ HELP MEEEEEEEE
Answer:
D
Step-by-step explanation:
[tex]2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2[/tex]
The correct answer is choice D. Hope this helps!
Answer:
{-5, 2}
Step-by-step explanation:
[tex]2x^{2} + 2x + 12 = 3x^{2} -x + 2[/tex] move everything to the right side
[tex]-2x^{2} -2x-12=-2x^{2} -2x-12[/tex] add line 1 and 2 to get the below equation
[tex]0 = x^{2} -3x -10[/tex] find multiples of -10 that add to give you -3
to get -10 we have to have (+)(-)
{-5, 2}
Kayla says that the point labeled C in the diagram below is the center.
Raymond says that point C is the radius.
Who is correct and why?
A.Kayla is correct; the center is a fixed point in the middle of the sphere.
B.Kayla is correct; the center is a line segment from the center to the surface of the sphere.
C.Raymond is correct; the radius is the fixed point in the middle of the sphere.
D.Raymond is correct; the radius is a chord that is from the center to the surface of the sphere.
HURRY I WILL GIVE U THE BRAINLYEST BECAUSE I AM IN A TIMER PLZ!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
HELP PLEASE:
I am not understanding on how to solve this problem, and a step by step explanation would help a lot.
A random sample of 120 is taken from a population of 10000. From a previous survey, it is believed that 62% of the population has an Instagram account. Find the mean and standard deviation of the sample proportion. Give the standard deviation to two nonzero decimals (such as .012 and not .01).
(mean subscript p-hat) μˆp =
(standard deviation subscript p-hat) σˆp=
Answer: Mean of the sample proportion = 74.4
Standard deviation of the samnple proportion is 5.32.
Step-by-step explanation:
Given : A random sample of 120 is taken from a population of 10000.
Let n = 120
Also, from previous survey, it is believed that 62% of the population has an Instagram account.
i.e, population proportion : p = 0.62
Now , the mean of the sample proportin would be :
[tex]\text{Mean}=\mu_{\hat{p}}=np\\\\=120\times0.62=74.4[/tex]
i.e. Mean of the sample proportion = 74.4
The standard deviation of the samnple proportion would be :
[tex]\text{standard deviation}=\sigma_{\hat{p}}=\sqrt{np(1-p)}\\\\=\sqrt{120(0.62)(1-0.62)}\\\\=\sqrt{28.272}\\\\=5.31714208951\approx5.32[/tex]
Thus , the standard deviation of the samnple proportion is 5.32.
The drop that riders experience on Dr. Doom’s Free Fall can be modeled by the quadratic function, h(t) = −9.8t2−5t + 39
where h is height in meters and t is time in seconds.
Determine the actual solution to the questions below. Use the previous question to assist you.
(a) What is the starting height of the riders?
The starting height of the riders is meters.
(b) According to the function, when will the height of the riders equal 0? Round to the nearest tenths place. *hint: find the solution(s).
The height of the riders will equal 0 at seconds.
Answer:
a) 39 meters
b) t = 1.8 seconds
Step-by-step explanation:
a)
To find the starting height of the riders, we just need to use the value of t = 0 in the equation of h(t):
h(0) = -9.8*0^2 - 5*0 + 39
h(0) = 39 meters
b)
To find when the height will be equal 0, we just need to use the value of h(t) = 0 and then find the value of t:
0 = -9.8*t^2 - 5*t + 39
Delta = b^2 - 4ac = 25 + 4*39*9.8 = 1553.8
sqrt(Delta) = 39.418
t1 = (5 + 39.418)/(-2*9.8) = -2.2662 s (A negative value for the time is not suitable for the problem)
t2 = (5 - 39.418)/(-2*9.8) = 1.756 s
Rounding to nearest tenth, we have t = 1.8 s
Tamara stacked two cubes, as shown. 2 stacked cubed. One cube has side lengths of 24 inches, and the second cube has side lengths of 12 inches. What is the total volume of the cubes? 1st cube volume: V = Bh V = (12)(12)(12) 2nd cube volume V = Bh V = (24)(24)(24) The total volume of the cubes is cubic inches.
Answer:
15 552 in³
Step-by-step explanation:
Since cubes have the same side lengths all around, to find the volume, you need to have one side length and cube it.
Cube 1 : 24³ = 24 x 24 x 24 = 13 824 in³
Cube 2 : 12³ = 12 x 12 x 12 = 1 728 in³
Now, to find the total, just add the volumes.
13 824 + 1 728 = 15 552 in³
The total volume of the cubes is V = 15,552 cubic inches
What is the Volume of a Cube?The formula of volume of the cube is given by:
Volume of Cube = a x a x a
Volume of Cube = a³
where a is the length of its sides or edges
Given data ,
The volume of the first cube with side length of 24 inches is given by:
V1 = (24 inches)³ = 13,824 cubic inches
The volume of the second cube with side length of 12 inches is given by:
V2 = (12 inches)³ = 1,728 cubic inches
The total volume of the two cubes is the sum of their volumes:
Total volume = V1 + V2 = 13,824 + 1,728 = 15,552 cubic inches
Hence , the total volume of the cubes is 15,552 cubic inches
To learn more about volume of cube click :
https://brainly.com/question/27770332
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A cow can give 5 gallons of milk if it eats 2 pounds of grass. Express x in terms of y, where y is the number of gallons of milk the cow gives, and x is the number of pounds of grass it eats.
Answer:
x = 2.5y
Step-by-step explanation:
If a cow can give 5 gallons of milk after eating 2 pounds of grass.
Let's consider 'x' is the number of pounds of grass it eats and 'y' is the number of gallons of milk the cow gives.
Hence,
5y = 2x
We will simplify it to get what x equal to y by dividing 2 on both side we find,
x = 2.5y
x is equal to 2.5 y
By eating 1 pound of grass cow can give 2.5 gallons of milk.
Answer:
26xy
Step-by-step explanation:
#THANKMELATER
This is a very important opinion question. Answer however you want to lol
1. Whats the best burger place, ice cream place, and groceery store you have ever been to?
2. Whats the best sugary treat and where can you buy it.
3. Your favorite word (ex. potato)
Answer:
1. In & Out, Jeremiah's Ice cream, and Costco
2. Circus Peanuts, at a local grocer (Publix, Winn-Dixie)
3. Irrationally
Step-by-step explanation:
The radius of a cylindrical water tank is 6.5 ft, and its height is 11 ft. What is the volume of the tank? Use the value 3.14 for pie, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:Idon't say you have to mark my ans as brainliest but my friend if it has helped you don't forget to thank me...
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
What is a cylinder?
A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Radius r = 6.5ftHeight h = 11ftConstant pi π = 3.14Volume of the cylindrical water tank V = ?We substitute our values into the expression above.
V = π × r² × h
V = 3.14 × (6.5ft)² × 11ft
V = 3.14 × 42.25ft² × 11ft
V = 1459ft³
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
Learn more on volume of cylinder here: brainly.com/question/16788902
Simplify the following expression (6x2 + 8x - 3) - (3x2 - 6)
Answer:
3x^2 +8x +3
Step-by-step explanation:
(6x^2 + 8x - 3) - (3x^2 - 6)
Distribute the minus sign
(6x^2 + 8x - 3) - 3x^2 + 6
Combine like terms
3x^2 +8x +3
what is the slope of the line that passes through the points (-4,-4) and (-4,-9)? Write your answer in simplest form
Answer:
undefined
Step-by-step explanation:
We can find the slope of a line using two points by
m = (y2-y1)/(x2-x1)
= (-9- -4)/(-4 - -4)
= (-9+4)/(-4+4)
= -5/0
When we divide by zero, our solutions is undefined
The slope is undefined
What the simplified radical form is
Answer:
3√7
Step-by-step explanation:
√63
√3x21
√3x3x7
3√7
Students measure objects in their desks and the data are shown in the line plot below. If the objects are to be connected end to end,what would be the total length?
This question is incomplete because it lacks the diagram of the line plot. Find attached to the answer, the diagram of the scatter plot.
Answer:
35/8 inches or 4 3/8 inches.
Step-by-step explanation:
Reading the line plot, the number of objects is plotted vertically while the length of the object is arranged horizontally on the line plot.
The total length is calculated as: summation of the (Number of objects × Length of the objects)
= [(1/8 ×0) + (1/4×0) + (3/8 × 2) + (1/2 ×3) + (5/8 × 1) + (3/4 × 2) +(7/8 × 0)] inches
=[ 0 + 0 + 3/4 + 3/2 + 5/8 + 3/2 + 0] inches
= 35/8 inches or 4 3/8 inches.
Therefore, the total length of the objects if they are connect end to end is 35/8 inches or 4 3/8 inches.
UV and RV are secant segments that intersect at point V.
Circle C is shown. Secants U V and R V intersect at point V outside of the circle. Secant U V intersects the circle at point T, and secant R V intersects the circle at point S. The length of U V is 12, the length of T V is a, the length of R S is 5, and the length of S V is 4.
What is the length of TV?
1 unit
1Two-thirds units
2One-half units
3 units
Answer:
(D)3 units
Step-by-step explanation:
To find the value of a, we use the Theorem of Intersecting Secants.
Applying this to the diagram, we have:
UV X TV = RV X SV
12 X a=(5+4)*4
12a=9*4
12a=36
Divide both sides by 12
a=3 units.
The correct option is D.
By applying the Theorem of Intersecting Secants, the length of TV (a) is equal to: D. 3 units.
What is the Theorem of Intersecting Secants?The Theorem of Intersecting Secants states that the product of a secant and its external secant is equal to the product of the other secant and its external secant, when two (2) secants are drawn to a circle from an exterior (outside) point:
How to determine the length of TV?In order to determine the length of TV (a), we would apply the Theorem of Intersecting Secants as follows:
UV × TV = RV × SV
12 × TV = (5 + 4) × 4
12TV = 9 × 4
12TV = 36
TV = 36/12
TV = 3 units.
Read more on Intersecting Secants here: https://brainly.com/question/1626547
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please please help me
Answer:
a) 22, b) i. 5/11, ii. 5/11, iii. 7/11
Step-by-step explanation:
a) 3+6+3+5+4+1 = 22 total number of students
b)
i. Number of girl/total number of students= 10/22 = 5/11
ii. blond hair/total number of students = 10/22 = 5/11
iii.
Number of girl/total number of students= 10/22 = 5/11
red hair/total number of students = 4/22 = 2/11
P(a girl or red hair) = 5/11 + 2/11 = 7/11
can anyone give me some brainliest please, I need it to move on at least one?
Answer:
sure
Step-by-step explanation:
To be marked as brainiest,you should answer the questions asked by the people.If the answer is more helpful than the another person then the asker will mark your answer as brainliest .
I hope I removed your confusion..
The answer to 7/12 divided by 2
Answer: 7/24
Step-by-step explanation: Think of the 2 as 2/1.
When dividing by a fraction, we can simply change, we can simply change the multiplication sig to division and take the reciprocal of the second fraction or flip the second fraction.
So our problem can be rewritten as [tex](\frac{7}{12})[/tex] [tex]x[/tex] [tex](\frac{1}{2})[/tex].
Now multiplying across the top and bottom we get 7/24.
Answer:
7/24
Step-by-step explanation:
the guy was right! (also khan said so)
John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at a speed of 42mph. On the way back the rain was over so his speed was 54mph. What was John's average speed, for the whole trip?
The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. Why are the events are not independent?
Answer:
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Step-by-step explanation:
Independent events:
Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question, we have that:
[tex]P(A) = 0.4, P(B) = 0.2, P(A \cap B) = 0.1[/tex]
However
[tex]P(A)P(B) = 0.4*0.02 = 0.08[/tex]
Since [tex]P(A \cap B) \neq P(A)P(B)[/tex], these events are not independent.
Answer:
C
Step-by-step explanation:
edg 2020
Which change can be made to correct the chart
Answer:
what chart
Step-by-step explanation:
which explains how to find the radius of a circle whose equation is in the gorm x^2+y^2=z
if you could show us the picture then maybe i can help you
