Answers
Answer:
11. 78
12. 4x² - 3x - 1
Step-by-step explanation:
11. Sum of n whole numbers = ½(n² + n)
Multiply
½*n² + ½*n
= n²/2 + n/2
To find the sum of the first 12 whole number, substitute 12 for n into the equation.
= 12²/2 + 12/2
= 144/2 + 12/2
= 72 + 6
= 78
12. Area of trapezoid = ½(a + b)*h
Where,
a = 5x - 4
b = 3x + 2
h = x + 1
Area = ½(5x - 4 + 3x + 2)*(x + 1)
Area = ½(8x - 2)*(x + 1)
Area = ½[8x(x + 1) -2(x + 1)]
= ½[8x² + 8x - 2x - 2]
Add like terms
= ½(8x² - 6x - 2)
= ½(8x²) - ½(6x) - ½(2)
= 4x² - 3x - 1
Related Questions
Use synthetic division to evaluate f(x) = x^3-4x^2+x-8 when x = 2.
Answers
Answer:
=-14
Step-by-step explanation:
Substitute 2 in for x:
Before- x^3-4x- + x-8 ; Now- 2^3 - 4* 2^2 + 2-8=-14
What is the value of a?
Answers
Answer:
your answer will be option B
Step-by-step explanation:
[tex]\frac{10}{12} =\frac{a}{38} \\\\a=\frac{(10) (38)}{12} \\\\=31.6[/tex]
A complex electronic system is built with a certain number of backup components in its subsystems. One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours. The subsystem will operate if any two of the four components are operating. Assume that the components act independently.a) Find the probability that exactly two of the four components last longer than 1000 hours.b) Find the probability that the subsystem operates longer than 1000 hours.
Answers
Answer:
a) 0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.
b) 0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.
Step-by-step explanation:
For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The probability of a component failing in less than 1000 hours is independent of any other component. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One subsystem has four identical components, each with a probability of 0.2 of failing in less than 1000 hours.
Four components means that [tex]n = 4[/tex]
Probability of 0.2 of failling means that 1 - 0.2 = 0.8 probability of not failling, so [tex]p = 0.8[/tex]
a) Find the probability that exactly two of the four components last longer than 1000 hours.
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]
0.1536 = 15.36% probability that exactly two of the four components last longer than 1000 hours.
b) Find the probability that the subsystem operates longer than 1000 hours.
It will operate if at least two compoents last longer than 1000 hours. So
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.8)^{2}.(0.2)^{2} = 0.1536[/tex]
[tex]P(X = 3) = C_{4,3}.(0.8)^{3}.(0.2)^{1} = 0.4096[/tex]
[tex]P(X = 4) = C_{4,4}.(0.8)^{4}.(0.2)^{0} = 0.4096[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.1536 + 0.4096 + 0.4096 = 0.9728[/tex]
0.9728 = 97.28% probability that the subsystem operates longer than 1000 hours.
Convert the following angle from degrees to radians. Express your answer in simplest form. 435^
Answers
Answer:
29π/12.
Step-by-step explanation:
Multiply by π/180
= 435π/180
= 29π/12 radians.
Combine like terms to simplify; (5x + 2) + (4x + 5). 1 point 9x - 7 9x + 7 -9x - 11 X + 7
Answers
(5x + 2) + (4x + 5)
= 5x + 2 + 4x + 5
= 5x + 4x + 5 + 2
= 9x + 7
The picture shows the top view of a piece of glass. A rectangular piece of glass is shown. The length is measured as 4 feet. The width is measured as 2 and one-half feet. Which equations can be used to find the area, in square feet, of the piece of glass? Select all that apply. A. A = 2 1 2 × 4 B. A = 5 2 + 4 C. A = ( 2 1 2 + 2 1 2 ) + ( 4 + 4 ) D. A = 5 2 × 4 E. A = ( 2 × 2 1 2 ) + ( 2 × 4 ) F. A = 2 1 2 + 4 answer and u get brainlyest
Answers
Answer:
d. and e.
Step-by-step explanation:
i did the test
Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that A rectangular piece of glass is shown.
The length is measured as 4 feet.
The width is measured as 2 and one-half feet.
We have to find the equations can be used to find the area of the piece of glass.
Area=Length×width
Area=4 feet × 2 and one-half feet
=4×[tex]2\frac{1}{2}[/tex]
=4×5/2
Hence, Option A and Option D represents the equation of area of rectangular piece which are A=4×[tex]2\frac{1}{2}[/tex] and A=4×5/2.
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What is the answer
7(2m+5)
Answers
Answer:
14m+35 is your answer ☺️☺️☺️
Answer:
14m+35
Step-by-step explanation:
7(2m+5)
7(2m)+7(5)
14m+35
plzz help me solve this question i need correct question i will mark you as a brainliest and I will give 5.0 rating anf thanks if ur answer will be correct
Answers
Answer:
I. p = 7
II. 17 litres
Step-by-step explanation:
I. Determination of the value of p
Mean = 17.7
p =.?
Let the number of litre be L
Let the number of motorist be M
Mean = summation LM / summation M
Summation of LM = (16×11) + (17×10) + (18×p) + (19×4) + (20×8)
= 176 + 170 + 18p + 76 + 160
= 582 + 18p
summation M = 11 + 10 + P + 4 + 8
= 33 + p
Mean = summation LM / summation M
17.7 = 582 + 18p / 33 + p
Cross multiply
17.7(33 + p) = 582 + 18p
584.1 + 17.7p = 582 + 18p
Collect like terms
584.1 – 582 = 18p – 17.7p
2.1 = 0.3p
Divide both side by 0.3
p = 2.1 / 0.3
p = 7
II. Determination of the median number of litre.
Let the number of motorist be M (i.e the frequency)
summation M = 11 + 10 + P + 4 + 8
p = 7
summation M = 11 + 10 + 7 + 4 + 8
summation M = 40
The median is the middle term i.e
Median = (summation M / 2)ᵀʰ motorist
Median = (40 / 2)ᵀʰ motorist
Median = 20ᵀʰ motorist
Considering the table in the question above, the 20ᵀʰ motorist has 17 litres.
Therefore, the median number of litres is 17 litres.
Plzzz help. Giving everything.
Answers
Answer:
d. 260. is the answer.
Solve the inequality:
8+4x≥12
Select one:
x≤1
x≥5
x≥1
x≤5
Answers
Answer:
x≥1
Step-by-step explanation:
You go to Trader Joes with your older sister to pick up avocados to make guacamole. Trader Joes sells 4 avocados for $3.50 or 6 avocados for $5.00. Which is a better deal?
Answers
can somebody help me
Answers
3x4=12
———
40 cups
28 mango and 12 cranberry
If m = 27 and n = 4, what is the value of the following expression?
Answers
Answer:
2
Step-by-step explanation:
m - 5 • n + 5
plug it in
27- 5 * 4+5
well, we gotta follow PEMDAS (there are no parentheses)
5*4
20
now we have
27-20+5
20+5
25
27-25
2
Students picked 144 ounces of strawberries to make strawberry jam. How many pounds of strawberries did they pick
Answers
Answer:
9 pounds
Step-by-step explanation:
I converted it
If Figure F is rotated 180° and dilated by a factor of , which new figure could be produced?
Hurry please!
Answers
Answer:
2nd answer choice :)
Step-by-step explanation:
The new figure produced is given below.
Option C is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
Let the figure be in the first quadrant.
Now,
Rotation of 180-degree means,
The figure will be in the third quadrant.
Now,
Dilation with a factor of 1/2.
This means,
The figure will shrink by 1/2.
Thus,
The new figure is given below.
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A satellite television company charges a one-time installation fee of $55 and a monthly service charge of $46. Elizabeth was installed this year and has spent a total of $285.00 on her satellite connection. The equation 55 + 46x = 285 can be used to represent her expenses so far. What does the variable x represent in this situation?
Answers
Answer:
The monthly service charge
Step-by-step explanation:.
Which one is greater?
4 yd or 144 in.
Answers
Answer:
4yd
144
Step-by-step explanation:
because 4yd is greater than 144
Enter the unknown value in the equation.
35.7−□=11.23
Answers
Answer:
24.47
Step-by-step explanation:
First, 35.7 - 11.23 = 24.47, which is your answer
Hope this helps!
I got 18 can someone double check me please?
Answers
Answer:
It's correct, it is 18 because ur adding
Answer:
28!
Step-by-step explanation:
this is because its 8 + 8 + 6 + 6 = 28. They're asking to add the outline of the perimeter.The perimeter is the length of the outline of a shape.
A theater sells t tickets at a price of p dollars each. The theater conducts a survey and predicts that if the price of each ticket is changed by $2, the number of tickets sold will change by 15 tickets. If n is the number of times the theater changes the ticket price by $2, the expression (p+ 2n) (t-15n) can represent the theaters's total revenue, in dollars. In this expression, what does (t-15n) represent?
A. the number of tickets that the theater will sell If the ticket price is increased by $2
B. the number of tickets the theater will sell if the ticket prices increased by $2n
C.the number of tickets the theater will sell if the ticket price is decreased by $15
Answers
Answer:
B
Step-by-step explanation:
You have to look at the second term to be sure of the meaning of t - 15n
What the given term says is that the total number of tickets sold (p) will decrease by 15 times the number of increases that there are.
The other term says that the cost of 1 ticket will increase that each ticket will increase by 2 dollars for each change in the ticket prices providing that change is 2 dollars.
C is out of the question. The information talks about 2 dollars per increase which is the first term.
A is not quite correct. It implies there is exactly 1 ticket increase. The crorect answer is the ticket increases can be a number of times (n)
The answer is B
Answer:
The answer is B
Step-by-step explanation:
A rectangle’s length is three times its width, w. Its area is 243 square units. Which equation can be used to find the width of the rectangle?
w2 = 3(243)
3w2 = 243
4w2 = 243
3w2 = 3(243)
Answers
Answer:
the second option because it's three times the width so it would be time the W
Step-by-step explanation:
Answer:
the guy above me is correct
Step-by-step explanation:
just did the test got a 100%
The table shows the number of hours spent practicing
singing each week in three samples of 10 randomly
selected chorus members.
Time spent practicing singing each week (hours)
Sample 1 12 13 11 8 9 7 4
8 9 10 Mean = 9.1
Sample 2 7 12 11 8 9 8 12 8 9 10 Mean = 9.4
Sample 3 11 9 8 12 8 10 7 8 7 9 Mean = 8.9
Which statement is most accurate based on the data?
A. A prediction based on the data is reliable, because the means of
the samples are close together.
OB. A prediction based on the data is reliable, because each sample
has 10 data points.
O C. A prediction based on the data is not completely reliable, because
the means are not the same.
D. A ediction based on the data is not completely reliable, because
the means of samples 1 and 2 are greater than 9 and the mean of
sample 3 is less than 9.
PREVIOUS
Answers
Answer:
A prediction based on the data is reliable, because the means of the samples are close together.
Step-by-step explanation:
Test approved
The most accurate statement is A. A prediction based on the data is reliable, because the means of the samples are close together.
What is Mean?Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.
Given three data sets.
All the samples have 10 data points.
Number of data points = 10
Mean of sample 1 = 9.1
Mean of sample 2 = 9.4
Mean of sample 3 = 8.9
We can see that the mean of the three samples is so close to each other.
So the data is reliable.
Hence the option is A.
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In the expression, x^2 + 6x + 9, which is the coeffcient?
Answers
The coefficient is the number next to the letter.
Although the x squared term has a coefficient of 1, it is not listed in the answer choices. However, the coefficient of the middle term 6x is listed.
Answer: 6
HELP QUESTION IS IN THE PHOTO ILL GIVE YOU EXTRA POINTS
Answers
WILL GIVE BRAINLEST !
hAVE A GOOD DAy :)!
Answers
Natalena drives a moving van. She travels 372 mi in 6 h. At what speed does
Natalena drive, in miles per hour? Draw a model. Show your work.
Answers
Answer:
62 mph
Step-by-step explanation:
62 mph
372 divided by 6 = 62
I cant draw on this so you make the model. :)
hope this helps!!!!!!!!!!
What is the difference of the polynomials:
(3x2 + 4x + 8) - (2x2 + 2x + 5)
a x^2 + 2x + 3
b x^2 + 6x + 3
c x^4 + 2x^2 + 3
d x^4 + 6x^2 + 13
Answers
Answer:
(6+4x+8)-4-2x-5
6-4+4x-2x+8-5
2+2x+3.
Find the slope of the line that passes through (9, 6) and (6, 2).
Answers
Answer:
4/3 not sure
i hope its hepls
Answer:
y2 - y1/ x2 - x1
6 - 6/2 - 6 = 0/-4 = 0
Step-by-step explanation:
Which model shows 1/4 divided by 3 ? A B C D
Answers
Answer:
You didn't attach a picture of the models?
Answer:
b or d
Step-by-step explanation:
Which is the graph of the inequality: y is less than (1/2x - 2)^3
Answers
Answer:
A
Step-by-step explanation: