Answer:
x = 5+6y
Step-by-step explanation:
Let x represents the age of the father and y represents the present age of the son.
ATQ,
The present age of the father is 5 more than 6 times the age of the son. We can write it in the form of equation as follows :
6 times the age of the son means 6y. So,
x = 5+6y
Hence, the mathematical equation is "x = 5+6y".
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.
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.
7
T
S
U
The triangle STU has been drawn on to a centimetre grid.
Calculate the area of triangle STU *
(2 Points)
Enter your answer
Answer:
12 square units
Step-by-step explanation:
The area of a given figure is the measure of space occupied by the figure on a 2 dimensional plane.
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
From the given grid, the following can be observed for triangle STU.
base SU = 6 units
height = 4 units
Thus,
area of triangle STU = [tex]\frac{1}{2}[/tex] x base x height
= [tex]\frac{1}{2}[/tex] x 6 x 4
= 3 x 4
area of triangle STU = 12 square units
The required area of triangle STU is 12 square units.
The sum of two numbers is 58. Twice the second
number subtracted to four times the first number is
28. Find the two numbers.
Answer:
Step-by-step explanation:
a+b=58 and 4a-2b=28 is the system of equations
solving the first for a, a=58-b, using this value for b in second equation is
4(58-b)-2b=28
232-4b-2b=28
232-6b=28
-6b=-204
b=34, and since a=58-b
a=58-34
a=24
So the two numbers are 24 and 34
put the following equation on a line into slope intercept form simplified all fraction 12 x + 3 Y equals -18
Which shows how to add 6 + 4+ 5?
6 = 6 and 4 + 5 = 9
1) 6+4 = 10 and 10 + 5 = 15
<» 6+4 = 10 and 4 + 5 = 9
Answer:
6+4=10 and 10+5=15
Step-by-step explanation:
Combine like terms to simplify; (5x + 2) + (4x + 5). 1 point 9x - 7 9x + 7 -9x - 11 X + 7
(5x + 2) + (4x + 5)
= 5x + 2 + 4x + 5
= 5x + 4x + 5 + 2
= 9x + 7
Can someone help me with these two for brilliant please
Answer:
its A
Step-by-step explanation:
Answer:
A. y=5.50x
Step-by-step explanation:
Brainlist plz
What is the factored form of 18+12
6(3+2)
Step-by-step explanation:
that xas factor of 18+12
Answer:
30:)
Step-by-step explanation:
I think it's 30!!!!!
Can someone help me with these questions and show work please and thank you
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
Please answer and explain I’ll mark brainliest!!!!!!!!!!!!
Answer:
A. x^2−x+6
B. 2x^2−11x+12
C. x^2−4
Step-by-step explanation:
Hope it helps
A. Distribute:
=(x)(x)+(x)(−3)+(2)(x)+(2)(−3)
=x2+−3x+2x+−6
Combine Like Terms:
=x2+−3x+2x+−6
=(x2)+(−3x+2x)+(−6)
=x2+−x+−6
B. I can't find an explanation
C. I can't find an explanation
Answer:
So we apply the distributive property to get
a) x^2 - 3x + 2x - 6
b) 2x^2 - 8x - 3x + 12
c) x^2 - 2x + 2x - 4
then we add like terms to get
a) x^2 - x - 6
b) 2x^2 - 11x + 12
c) x^2 - 4
brainliest please?
The answer choices are 10, 15, 30, 35.
Lets us start with finding the inner angles of the triangle. The bottom right angle shall be 70 degrees as it is opposite. The 100 degrees shall add together to make 200. 360-200 = 160. 160 / 2 = 80. So, Now we know bottom left angle (80) and bottom right (70). 80 + 70 = 150. In a triangle, angles add to 180 so 180 - 150 = 30. 30 = 2x which means that x = 15
15
Find the sum of all numbers 1 to 1000
Answer:
it is 500500
Step-by-step explanation:
learned this fact a few years ago and it stuck with me.
Find the missing number in each sequence.
40, ___ , 37 1/3 , 36
help!!!!! will give big brain
PLEASE HELP WILL MARK BRAINLIEST
Answer:
D
Step-by-step explanation:
Answer:
[tex]\boxed {\boxed {\sf D. \ 64x^{12}y^6z^2}}[/tex]
Step-by-step explanation:
This is an example of a power to a power. The exponents inside the parentheses are being raised to another power outside the parentheses. We multiply the exponents and take the coefficients (number in front of the variables) to the power.
[tex](8x^6y^3z)^2[/tex]
Remember that a variable without an exponent has an implied exponent of 1.
[tex]8^2x^{6*2}y^{3*2}z^{1*2}[/tex]
Solve the coefficient's exponent.
8²= 8*8= 64[tex]64x^{6*2}y^{3*2}z^{1*2}[/tex]
Multiply the exponents.
[tex]64x^{12}y^{6}z^{2}[/tex]
So, the expression given is equal to Choice D: 64x¹²y⁶z²
will give brianlist
Jennifer has a hair ribbon that is 12 centimeters long. What is the length of the ribbon in millimeters? Use the number of zeros of the product when multiplying a number by a power of 10 to help you.
120 millimeters
12 millimeters
1,200 millimeters
1.2 millimeters
Joel rides bikes in his city There are 4 lengths of race tracks.
Answer:
21
Step-by-step explanation:
asdawda
Solve the inequality:
8+4x≥12
Select one:
x≤1
x≥5
x≥1
x≤5
Answer:
x≥1
Step-by-step explanation:
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?
Answer:
The monthly service charge
Step-by-step explanation:.
A person on a moving sidewalk travels 6 feet in 3 seconds. The moving sidewalk has a length of 60 feet. How long will it take to move from one end of the sidewalk to the other?
Answer:
Speed = distance / time
= 6/3 =2 ft/sec
Time = distance / speed
= 60/2
= 30 seconds
Helpp guyss left with this one onlyy!!!!
Answer:
[tex]m=\frac{2}{5}[/tex]
Step-by-step explanation:
1. To find the slope we need to use the slope formula, [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
2. The points that were given were (0,0) and (5,2). Let's plug those into the formula.
[tex]\frac{2-0}{5-0}[/tex]
[tex]\frac{2}{5}[/tex]
So, your slope would be [tex]m=\frac{2}{5}[/tex]
Hope this helped! C:
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
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.
To learn more on Area of Rectangle click:
https://brainly.com/question/20693059
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Can someone please solve this for me btw I’m suppose to be dividing that question using long division
Answer:
0.343
Step by step explanation:
0. 3 4 3
8 2. 7 5 0
− 0
2 7
− 2 4
3 5
− 3 2
3 0
− 2 4
6
What is the value of a?
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]
suppose that grade point averages of undergraduate students at one university bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.4 describe where approximately 99.7% of a grade point averages lie
Answer:
2.57-0.4-0.4-0.4=1.37
2.57-0.4-0.4=1.77
so the answer is 1.37 between 3.77
Step-by-step explanation:
1. How many triangle make a trapezoid
A trapezoid consists of two triangles.
A trapezoid does indeed contain two triangles within its structure. A trapezoid is a quadrilateral with one pair of parallel sides.
The other two sides, known as the legs, are not parallel and meet at a point. These legs, along with the two parallel sides, form two triangles within the trapezoid.
One triangle is formed by connecting the two legs and one of the parallel sides. The other triangle is formed by connecting the two legs and the other parallel side.
So, a trapezoid consists of two triangles.
Learn more about Trapezoid here:
https://brainly.com/question/19340938
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Belle deposited money into a savings account. This table gives the value of her account for the first 14 months after the initial deposit. The data can be modeled using an exponential function.
Years 2 4 6 8 10 12 14
Account value $106 $113 $119 $126 $135 $143 $152
Based on the data, which amount is closest to the value of the account 24 months after the initial deposit?
$180
$200
$240
$280
Answer:
The answer is B 200
Step-by-step explanation:
i just took the test so yah :)
If ABCD is a parallelogram, m
A
B
(3x + 4)º
D
xº
C
Equation:
X=
(PLEASE HELP)
Answer:
x is 44 because
3x+4+x=180
4x=180-4
4x=176
x=44
A parking garage owner wants to collect $2,250.00 in parking fees. If he charges $15.00 for each car, how many cars are needed to meet his goal?
A 150 cars
B 168 cars
C 169 cars
D 301 cars
Laura kept a list of her expenses and income for one month. If she started the month with no money, how much money did she have left at the end of the month?
Answer:
$25
Step-by-step explanation:
she received$12 five times
12×5=60 ...(1)
she earned$5 two times for yard work
5×2=10....(2)
(1)+(2).... 60+10=70
Bought dog food and ticket
30+15=45
70-45=25
Answer $25 is what she is left with at the end of the month
Answer:
She would have 5 dollars left
Step-by-step explanation: