In the diagram shown,
ABCE is a trapezium,
AD is parallel to BC,
DE = 4cm,
Area of ABCE = 60cm^2,
Area of ABCD = 48cm^2,
Work out the values of f and g.
You must show all your working.
Answers
The values of f and g are;
f = 6
f = 6g = 8
We are given the trapezium ABCE where;
AD is parallel to BC
DE = 4 cm
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
f and g are sides of the rectangle ABCD. Thus;
fg = 48 - - - (eq 1)
Also,for the trapezium ABCE;
½(g + g + 4)f = 60
(2g + 4)f = 120 - - - (eq 2)
From eq 1, f = 48/g
Thus;
(2g + 4) × (48/g) = 120
96 + 192/g = 120
192/g = 120 - 96
192/g = 24
g = 192/24
g = 8
Thus;
8f = 48
f = 48/8
f = 6
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Related Questions
Points are plotted at (-2, 2), (-2,4), and (2,-4). A fourth point is drawn such that the four points can be connected to form
a rectangle. What is the area of this rectangle?
8 square units
12 square units
16 square units
24 square units
Answers
The area is 24 square units
Help my please please
Answers
Answer:
Rectangle:6+5=11(Odd)
Triangle:6+6=12(even)
Star:4+3=7(odd)
Pentagon:9+8=17(odd)
Hexagon:6+6+12(even)
Circle:4+4=8(even)
Step-by-step explanation:
Hope this helps:)
Answer:
odd, even
odd, odd
even, even
Step-by-step explanation:
Number the pictures starting from left to right and the down, then pictures 1, 3 4 are odd
2, 5, 6 are even.
I will give brainliest answer and upvote
Answers
Answer:
397.39
Step-by-step explanation:
steps are all stated in the picture, basically use area of circle minus area of rectangle will give you the shaded area
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A. A graph shows the average daily temperature on the x-axis, and number of years on the y-axis, from 1 to 4. The average temperature was 18 for 2 years; 19 for 3 years; 20 for 2 years; 21 for 3 years; 22 for 2 years; 23 for 4 years; 24 for 3 years; 25 for 3 years; 26 for 5 years; 27 for 2 years; 28 for 1 year; 29 for 2 years; 30 for 2 years; 31 for 1 year. The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean? 18° 19° 22° 30°
Answers
The temperature which is within one standard deviation of the mean is 22 degree Celsius of the graph of average daily temperatures.
What is the mean and standard deviation of data?The mean of the data is the average value of the given data.The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
The graph below in the attached image shows the average daily temperatures on January 1 from 1900 to 1934 for city A.
A graph shows the average daily temperature on the x-axis, and number of years on the y-axis, from 1 to 4.
Interval within 1 standard deviation of the mean when the mean is μ and standard deviation σ can be given as,
[tex][\mu-\sigma, \mu+\sigma][/tex]
The mean of the temperatures in the chart is 24°, with a standard deviation of 4°. Put these values,
[tex][\mu-\sigma, \mu+\sigma]\\\ [24-4, 24+4]\\\ [20, 28][/tex]
The temperatures in the options given will be correct, which lies in the above range.
Thus, the temperature which is within one standard deviation of the mean is 22 degree Celsius of the graph of average daily temperatures.
Learn more about the mean here;
https://brainly.com/question/14532771
Answer:
C
Step-by-step explanation:
Took the quiz got a 100%
What is 25% of $4007
Answers
Answer:
$1001.75
Step-by-step explanation:
Do 4007 x 0. 25 on a calculator
Since it is a ratio of two integers,
6/4 is irrational
Answers
Answer:
is this a question? also, 6/4 is not irrational, it is rational, and an irrational number is a number that cannot be expressed as a ratio of two integers, aka a simple fraction
Give the domain and range.
Answers
Answer:
Domain is {-2,0,2}
Range is {4,6,8}
Step-by-step explanation:
The domain is the input or x values
Domain is {-2,0,2}
The range is the output or y values
Range is {4,6,8}
Use the following information for #18
Connor makes $120 for every 10 hours he works.
#18 How much does Connor make per hour?
Answers
Answer:
$12
Step-by-step explanation:
u do 120 divided by 10 which gives u 12 which gives u per hours
hope this helps
Which equation describes the circle with center (5, -1) and
radius 4?
Answers
Answer:
[tex](x-5)^2+(y+1)^2=4^2[/tex]
Step-by-step explanation:
The equation is: [tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) = center.
[tex](x-5)^2+(y+1)^2=4^2[/tex]
Twice a certain number is tripled. The resulting number is _____. 2x + 3 2x - 3 (2x)3 (2x)
Answers
Answer:
(2x)3
Step-by-step explanation:
Twice a certain number is tripled. Use x as the unknown number and double it.
2x
Now triple the whole answer
(2x)3
Answer:
[tex](2x)3[/tex]
Step-by-step explanation:
Let's say [tex]x[/tex] is the number.
Our answer would be:
[tex]2x*3[/tex] or [tex](2x)3[/tex]
You can assign [tex]x[/tex] a value and it will get you double the number, then triple of that number.
Sorry if it seems like I'm copying the other person.
Which statement describes the graph of h (x)?
Answers
Answer:
The 4th option
Step-by-step explanation:
-3 will make you go down
Simplify.
(3.8w+ 4) – 1.5w+8
2.3 w+ 12
5.3 w+ 12
2.3 w-12
5.3 w-12
Answers
Answer:
2.3w +12
Step-by-step explanation:
(3.8w+ 4) – 1.5w+8
Combine like terms
3.8w-1.5w +4+8
2.3w +12
Answer:
2.3w+12
Step-by-step explanation:
Parentheses do not matter for this question.
(3.8w+ 4)–1.5w+8=
3.8w+4-1.5w+8=
Subtract 1.5w from 3.8w
2.3w+4+8=
Add 4 and 8 together
2.3w+12
plsssssss on thissss i need someone helppp plssss helppp
Answers
Answer:
B
Step-by-step explanation:
A is incorrect, the y-axis represents the distance, not time
answers ? Idk how to do this
Answers
Answer:
Step-by-step explanation:
ghjikop0987trsxzcvbhtrdxc vbhgfc
Two numbers are in the ratio 3:5 . If their sum is 64 , then the numbers are-
24 and 40
20 and 44
30 and 34
14 and 50
Answers
Answer:
The two numbers are 24 and 40
At 1:00 p.m., the temperature is 12°F. If the temperature steadily decreases by 2°F per hour, then what the temperature at 08:00 p.m
Answers
Answer:
-2
Step-by-step explanation:
There’s a decrease over 7hrs 7•-2= -14
12-14=-2
Answer:
-2
Step-by-step explanation:
A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities. [4×5 marks] A box contains 24 transistors, 4 of which are defective. If 4 are sold at random, find the following probabilities.
a) Exactly 2 are defectives.
b) None is defective.
c) All are defective.
d) At least 1 is defective.
Answers
Answer:
a) 10.73%
b) 45.60%
c) 0.0094%
d) 54.4%
Step-by-step explanation:
The probability of one transistor being defective is equal the number of defective transistors over the total number of transistors
a)
The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. The probability of the third one being not defective is 20/22, and the fourth one not being defective is 19/21. We also multiply the final probability by a combination of 4 choose 2, because the defective transistors can be any 2 of the group of 4:
C(4,2) = 4! / (2! * 2!) = 6
P = 6 * (4/24) * (3/23) * (20/22) * (19/21) = 0.1073 = 10.73%
b)
Similar to the letter a), we have:
First one not defective: P = 20/24
Second one not defective: P = 19/23
Third one not defective: P = 18/22
Fourth one not defective: P = 17/21
P = (20/24) * (19/23) * (18/22) * (17/21) = 0.4560 = 45.60%
c)
First one defective: P = 4/24
Second one defective: P = 3/23
Third one defective: P = 2/22
Fourth one defective: P = 1/21
P = (4/24) * (3/23) * (2/22) * (1/21) = 0.000094 = 0.0094%
d)
If we want at least 1 defective, we just need to subtract 100% from the case where all 4 are not defective:
P = 1 - 0.4560 = 0.5440 = 54.4%
In this exercise we have to use the knowledge of probability to calculate each of the requested probabilities, so we can say that:
a) [tex]10.73\%[/tex]
b) [tex]45.60\%[/tex]
c) [tex]0.0094\%[/tex]
d) [tex]54.4\%[/tex]
a)The probability of the first one being defective is 4/24, and then the probability of the second one being defective is 3/23, because we have one less defective transistor. So the combination will be:
[tex]C(4,2) = 4! / (2! * 2!) = 6\\P = 6 * (4/24) * (3/23) * (20/22) * (19/21) = 0.1073 = 10.73%[/tex]
b)So find the not defective, we have:
First one: P = 20/24 Second one: P = 19/23 Third one: P = 18/22 Fourth one: P = 17/21
[tex]P = (20/24) * (19/23) * (18/22) * (17/21) = 0.4560 = 45.60%[/tex]
c)So find the defective, we have:
First one: P = 4/24 Second one: P = 3/23 Third one: P = 2/22 Fourth one: P = 1/21
[tex]P = (4/24) * (3/23) * (2/22) * (1/21) = 0.000094 = 0.0094%[/tex]
d)We just need to subtract 100% from the case where all 4 are not defective:
[tex]P = 1 - 0.4560 = 0.5440 = 54.4%[/tex]
See more about probability at brainly.com/question/743546
5. A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the
Earth model?
Solve each problem. Use 3.14 for p.
Answers
Answer:
the length of the radius of the Earth Model = 9cm
Step-by-step explanation:
The volume of the model of Earth is approximately 3052.08 cubic centimeters.
It has been discovered that the Earth is spherical in shape, hence this model is spherical as well.
The formula for the Volume of a Sphere = 4/3 πr³
Where r = radius or the length of the radius
The Volume of the Earth Model = 3052.08 cm³
We are told to use π = 3.14
To find the length of the radius, we have derive the formula
V = 4/3 × π × r³
V = 4πr³/3
Cross multiply
3V = 4πr³
Divide both side by 4π
3V/4π = r³
We find the cube root of both sides =
∛(3V/4π) = r
Substituting our given values in the question, we have:
∛(3 × 3052.08/ 4 ×3.14) = r
r = ∛9156.24÷12.56
r = ∛729
r = 9cm
Therefore, the length of the radius of the Earth Model = 9cm
What is the answer I need the answer
Answers
Answer:
The correct choice is A
Step-by-step explanation:
the definition of inverse is the opposite of something or different in direction so that would mean they want you to switch what they gave you so that would mean the answer is choice A
I need help with this guys
Answers
Answer:
25:53
Step-by-step explanation:
75:159 have a common factor of 3
75/3=25
159/3=53
Rewrite using a negative exponent.
1/a ^4
Answers
Answer: a^-4
Step-by-step explanation:
[tex]\frac{1-4}{a^4-4}[/tex] = a^-4
Does (7, 1) make the equation y = x true?
Answers
Answer:
No.
Step-by-step explanation:
The point (7,1) contains a x-value of 7 and a y-value of 1. 7 does not equal 1.
Answer:
The equation is true.
Step-by-step explanation:
While on the golf course last weekend Marc hit into the rough landing the ball behind a tall tree. His best option was to get it high enough to get over the tree and hopefully come down in the fairway for his next shot. So with a mighty swing he hit the ball into the air and was surprised to see the ball hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is: h(x)= -16x^2+120 where h is the height of the ball and x is the number of seconds the ball is in the air.
Question 1. How high did Marc actually hit the ball?
Later during that same golf outing, Marc decided to show off by trying to hit the green in one shot. So with his macho swing, he said he hit the green as the ball hung in the air for 15 seconds. The formula for this shot is: h(x)= -16x^2+200x
Question 2. How long did the ball actually hang in the air?
Answers
Answer:
120 ft at 0 seconds
Question 2: 12.5 seconds in the air
Step-by-step explanation:
h(x)= -16x^2+120
We want to find the vertex
The vertex is at
h = -b/2a = 0/-32 = 0
The maximum is at 0
h(0) = 0+120 = 120
it occurs at 0 seconds and a height of 120 ft
h(x)= -16x^2+200x
We want to find the zeros of the function
0= -16x^2+200x
Factor out -8x
0 = -8x(2x -25)
Using the zero product property
-8x=0 2x-25 =0
x =0 2x =25
x=25/2
The ball starts on the ground at 0 seconds and lands at 12.5 seconds
wiil mark bianleast
Which figure is a translation of the gray shape?
Figure A.
Figure B.
Figure C.
Figure D.
Answers
Figure C
Do you need an explanation?
Betty bought two bags full of books at an annual library book sale. If she
pays a total of $12.90 for both bags, of which $0.90 is tax, how much did
each bag of books cost?
Answers
Answer:
12.90= .90+ 2x
12=2x
6=x
Each bag of books cost was $6
Answer: the answer is $6
Step-by-step explanation:
Since Betty payed .90 cents on tax we can subtract this from the equation because we are just trying to focus on how much she spent on one bag. Now all we have left is $12. Then we would have to divide 12 by the number of bags she bought, so 2. 12 divided 2 equals 6, meaning Betty spent $6 per bag.
Simplify 2(x - 4) + 7(x + 2). 9x + 6 9x - 4 9x - 6
Answers
Answer:
-The final answer is [tex]9x + 6[/tex] .
Step-by-step explanation:
Simplify the following equation:
[tex]2(x - 4) + 7(x + 2)[/tex]
-Use Distributive Property:
[tex]2(x - 4) + 7(x + 2)[/tex]
[tex]2x - 8 + 7x + 14[/tex]
-Combine [tex]2x[/tex] and [tex]7x[/tex] together:
[tex]2x - 8 + 7x + 14[/tex]
[tex]9x - 8 + 14[/tex]
Add [tex]-8[/tex] and [tex]14[/tex] together:
[tex]9x - 8 + 14[/tex]
[tex]9x + 6[/tex]
So, the final answer is [tex]9x + 6[/tex] .
2x+7x+9x+69x-49x+14-6
38x+8
Plz mark brainiest
Hope this helpers
The number of bricklayers needed to build a brick wall varies inversely as the number of hours needed. Four bricklayers can build a brick wall in 30 hours. How long would it take 5 bricklayers to build a wall?
Answers
Answer: 24 hours
Step-by-step explanation:
You multiply 30 by 4/5, since this is inverse.
If it took 4 bricklayers to build a brick wall in 30 hours, then it would 24 hours for 5 bricklayers to build a brick wall.
The amount of time is reduced down to 4/5 of the first time because there are now 5 bricklayers instead of four.
Answer:
It would take 24 hours for 5 bricklayers to build a wall.
Step-by-step explanation:
We can deduce the number of hours the bricklayers needed to build a wall because they are inversely proportional.
In other words, more bricklayers will result in fewer work hours.
4 bricklayers × 30 hours = 120 bricklayers hours
120 bricklayers hours / 5 bricklayers = 24 hours
Therefore, it would only take 24 hours for 5 bricklayers to build a wall. (Which is 6 hours faster since one person joined the workforce to help the others).
I hope this helps!
plz help with this question
Answers
Answer:
3cm ,4cm,5cm,and 8 centimetres
If Lebron can run 12 laps in 2 hours, approximately how long will it take him to run 60 laps?
Answers
Answer:
10 hours
Step-by-step explanation:
Let's set up a proportion using the following setup.
hours/laps=hours/laps
We know that it takes him 2 hours to run 12 laps. We don't know how long it will take him to run 60 laps, so we can say it takes x hours to run 60 laps.
2 hours/12 laps=x hours/60 laps
2/12=x/60
We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
x is being divided by 60. The opposite of division is multiplication, so multiply both sides by 60.
60*2/12=x/60*60
60*2/12=x
10=x
It will take Lebron 10 hours to run 60 laps.
question in attachment
Answers
Answer:
[tex]a_{1}=6[/tex]
Step-by-step explanation:
It is sum of arithmetic progression
[tex]$S_{20}=\frac{20}{2} [2a_{1}+(20-1)\cdot 4]$[/tex]
[tex]$880=10[2a_{1}+(19)\cdot 4]$[/tex]
[tex]$880=10[2a_{1}+76]$[/tex]
[tex]880=20a_{1}+760[/tex]
[tex]120=20a_{1}[/tex]
[tex]a_{1}=6[/tex]