Answer: fx + gx
f(x) =x^2 -13x + 36
g(x) = x - 9
Let the random variable X be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. Here are the distributions of the number of rooms for owner-occupied units and renter-occupied units:
Rooms 1 2 3 4 5
Owned 0.003 0.002 0.023 0.105 0.218
Rented 0.008 0.027 0.287 0.362 0.165
Rooms 6 7 8 9 10
Owned 0.225 0.198 0.149 0.053 0.024
Rented 0.095 0.033 0.013 0.003 0.004
Required:
a. Express "the unit has 7 or more rooms" in terms of X. x≥7. What is the probability of this event?
b. Express the event {X > 7} in words.
c. What important fact about discrete random variables does comparing your answers to (a) and (b) illustrate?
Answer:
Part a:
"The unit has 7 or more rooms" in terms of X is given by the unit which has 7, 8, 9 or 10 rooms.
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. .
Part C:
A continuous random variable is given by intervals of numbers
A discrete random variable is the variable that is obtained by counting.
Step-by-step explanation:
Part a:
"The unit has 7 or more rooms" in terms of X is given by
{ X≥7} = {x=7} + {x=8} + {x=9} + {x=10}
the unit which has 7, 8, 9 or 10 rooms.
The probability of this event is given by
P{ X≥7} =P {x=7} + P {x=8} + P {x=9} + P {x=10}
P{ X≥7} = 0.198 + 0.149+ 0.053 + 0.024
P{ X≥7}= 0.424
Part b:
The event {X > 7} in words is that the unit has more than 7 rooms. This does not include the unit having 7 rooms.
Part C:
A continuous random variable takes all the values in the given interval as in part a.The random variable X takes the values between 7 and 10 inclusive of 7.
A discrete random variable is the variable that is obtained by counting as in part b. The variable X takes the values of the units with 8 , 9 or 10 rooms.
A car traveled 11.5 miles in 15 minutes. How many miles per hour was it traveling?
Answer:
46 miles per hour
Step-by-step explanation:
ِAn hour has 60 minutes. In 60 minutes, there is four 15 minutes (4*15 = 60).
So, if it travelled 11.5 miles in 15 minutes, in an hour, it travelled 11.5 * 4 = 46 miles per hour.
The miles per hour he was travelling is 46 miles.
What is the miles per hour travelled?
The first step is determine the average speed. Average speed is the total distance travelled per time.
Average speed = total distance / total time
11.5 / 15 = 0.766667 miles / per minutes
Miles travelled = average speed x time
Miles travelled = 0.766667 x 60 = 46 minutes
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Express the series using sigma notation. 1 + 4 + 16 + ... + 256.
a.
c.
b.
d.
Please select the best answer from the choices provided
A
B
C
D
Answer:
D
Step-by-step explanation:
By looking at the terms, we can notice that each term is 4 times the previous term. This means the series is geometric and we can rule out options A and B because of this. We can find the first terms of both options C and D to get:
first term c: 4
first term d: 1
The first term of our series is one, so that must mean D is the answer.
what is a lineary equation
Answer:
In mathematics, a linear equation is an equation that may be put in the form are the coefficients, which are often real numbers.
Step-by-step explanation:
Hope this helped Mark BRAINLIEST!!!!
Solve for x.
x = [?]
4x - 16
2x + 16,
Answer:
Solution given:
4x-16+2x+16=180{linear pair are supplementary]
6x=180
x=180/6
x=30
is a required answer.
6 cm = ______ mm *
50 mm = ______ cm
100 mm=_______cm
20 mm = ______ cm
5kg = ______ g *
800g = _____kg *
6000mg = ______kg *
2lit = _____ml *
75ml = ____lit *
82km = ____m
Answer:
6 cm = __6*10=60____ mm *
50 mm = _[tex] \frac{50}{10} [/tex]__=5___ cm
100 mm=__[tex] \frac{100}{10} [/tex]=10____cm
20 mm = __[tex] \frac{20}{10} [/tex]_=2_____ cm
5kg = _5*1000=5000_____ g *
800g = ____[tex] \frac{800}{1000} [/tex]=0.8___kg
6000mg = ___[tex] \frac{6000}{1000000} [/tex]=0.006___kg *
2lit = _2*1000=2000_ml *
75ml = __[tex] \frac{75}{1000} [/tex]=0.075_lit *
82km = 82*1000=82000__m
What is the shape of the cross-section formed when a cylinder intersects a
plane as shown in the drawing?
O A. circle
B. oval
C. rectangle
OD. square
Answer: circle
Step-by-step explanation:
The shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
As we know, the circle is a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
As we can see in the picture the cylinder is cut by a plane that is parallel to the base of the cylinder.
The base of the cylinder is a circle.
the shape of the cross-section is formed when a cylinder intersects a
the plane is a circle.
Thus, the shape of the cross-section is formed when a cylinder intersects the plane is a circle option (A) is correct.
Learn more about the cylinder here:
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If the square of a positive integer is added to four times to integer the result is 117 find the integer.
Answer:
x = -2 ± 452i
Step-by-step explanation:
x² + 4x = 117
x² + 4x - 117 = 0
if you solve this quadratic by using the quadratic formula you get:
x = -2 ± 452i
452i is an imaginary number that equals [tex]\sqrt{-452}[/tex]
Find the measure of an angle in standard position for each reference angle.
Step-by-step explanation:
1. 90+65= 155°
2. π+ π/6 = 7π/6 or 210°
3. 24+180=204°
4. 3π/2 + 2π/9 = (27π+4π)/18 = 31π/18
or 310°
PLZZZ HELP!!! Brainliest to whoever can help!!! T^T
Answer:
I think it B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
h=2x^2
b=5x^2+4x
we know that
area of triangle (A)=1/2×b×h
=1/2×2x^2×(5x^2+4x)
=x^2(5x^2+4x)
=5x^4+4x^3 square units
please help, seventh grade math problem
Answer:
12
Step-by-step explanation:
divide into two shapes. the first one being 2 x 4 units and the second being 2 x 2.
2 x 4 = 8
2 x 2 = 4
8 + 4 = 12
The answer is 12 square units.
Please mark brainliest if it was correct and helped!
Answer:
12
Step-by-step explanation:
just count the blocks
brainliest please???
write in algebraic expression the difference between a number m and the product of m and n. If you can help it would mean a lot
Answer:
m - mn
Step-by-step explanation:
The two numbers are denoted by m and n respectively.
From the question, we can deduce the following points;
- the difference between m and another variable (mn).
- product or multiplication of m and n.
Translating the word problem into an algebraic expression, we have;
m - (m*n)
m - mn
Can the surface area of a sphere and the volume of a sphere be the same numerical value if the units are measured relative to the same unit of length?
A. Yes; the radius would need to be the unit radius, 1.
B. Yes; the radius would need to be 3.
C. No, the surface area would always be greater than the volume.
D. No, the volume would always be greater than the surface area.
Answer:
Volume = surface area
[tex]\frac{4}{3}\pi r^3 = 4\pi r^2\\\\\frac{r}{3} = 1\\r = 3[/tex]
option B
TERM 2: WEEK 8
CLASSWORK 1
1.
Solve the simultaneous equations using elimination method
4x - 3y = 1
x + 3y = 19c
a.
9514 1404 393
Answer:
(x, y) = (4, 5)
Step-by-step explanation:
We notice that the coefficients of y are opposites, so we can eliminate y by adding the two equations together.
(4x -3y) +(x +3y) = (1) +(19)
5x = 20 . . . . . . simplify
x = 4 . . . . . . . . .divide by 5
Substituting into the second equation gives ...
4 +3y = 19
3y = 15 . . . . . . . subtract 4
y = 5 . . . . . . . . . divide by 3
The solution is (x, y) = (4, 5).
What is the area of the triangle?
Answer:
Area of triangle 12 ft^2 Area of shaded region 84 ft^2
Step-by-step explanation:
area of triangle 6 x 4 / 2 =12
Shaded region 96-12= 84 ft^2
please help will mark brainlist!!
Answer:
x=28
y=28
Step-by-step explanation:
Equation 1:
Dived both sides by 0.75 to remove 3/4 from x.
(x-12)=16
Now, add 12 to both sides.
x=28
Equation 2:
Same here, divide both sides by 0.75.
y-12=16
Add 12 to both sides.
y=28
9 - x < - 11
Show steps please
Answer: x > 20
Step-by-step explanation:
9 - x < - 11
In this scenario, we've to collect like terms in order to.wolve for x. This will be:
9 - x < - 11
- x < - 11 - 9
- x < - 20
Divide both side by -1
-x/-1 < -20/-1
When we divide by a coefficient with minus sign, the sign changes too from less than to greater than
-x/-1 < -20/-1
x > 20
Colin is buying dirt to fill a garden bed that is a 9 ft by 18 ft rectangle. If he wants to fill it to a depth of 4
in, how many cubic yards of dirt does he need? If necessary, round to the nearest cubic yard. If dirt costs
530 per yd, how much will the project cost?
The project will require
|yd of dirt, and will costs
The estimated difference of 3209 and 1893, when rounded off to the nearest ten is
o(a) 1300
(b) 1310
(c) 1320
0 (d) 1000
Answer:
[tex] = (3209) - (1893) \\ = 1.32 \times {10}^{3} \\ = 1320[/tex]
[tex] \small{ \star{ \underline{ \blue{becker}}}}[/tex]
Answer:
1320
Step-by-step explanation:
round off
3209 ≈ 3210
1893 ≈ 1890
estimated difference = 3210 - 1890 = 1320
Find the sum of each of the following polynomials.
a) [tex]x^3+5x^2+2, 3x^2-4x+7[/tex]
b) [tex]2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3[/tex]
c) [tex]5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3[/tex]
d) [tex]2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4[/tex]
Answer:
[tex](a)\ Sum = x^3+8x^2-4x+9[/tex]
[tex](b)\ Sum =3x^3-7x^2+6x +16[/tex]
[tex](c)\ Sum = x^3-x^2+10x+6[/tex]
[tex](d)\ Sum = 3x^4 -3x^3+ 6x^2-x+2[/tex]
Step-by-step explanation:
Required
Sum of the polynomials
[tex](a)\ x^3+5x^2+2, 3x^2-4x+7[/tex]
[tex]Sum = x^3+5x^2+2+3x^2-4x+7[/tex]
Collect like terms
[tex]Sum = x^3+5x^2+3x^2-4x+2+7[/tex]
[tex]Sum = x^3+8x^2-4x+9[/tex]
[tex](b)\ 2x + 5x^3-2x^2+7, 9+4x-5x^2-2x^3[/tex]
[tex]Sum =2x + 5x^3-2x^2+7+ 9+4x-5x^2-2x^3[/tex]
Collect like terms
[tex]Sum =5x^3-2x^3-2x^2-5x^2+4x+2x +7+ 9[/tex]
[tex]Sum =3x^3-7x^2+6x +16[/tex]
[tex](c)\ 5x^3+2x^2+4, 2x^2+7x-5, 7-5x^2 +3x-4x^3[/tex]
[tex]Sum = 5x^3+2x^2+4+ 2x^2+7x-5+ 7-5x^2 +3x-4x^3[/tex]
Collect like terms
[tex]Sum = 5x^3-4x^3+2x^2+ 2x^2-5x^2+7x+3x-5+ 7 +4[/tex]
[tex]Sum = x^3-x^2+10x+6[/tex]
[tex](d)\ 2x^4-3x^2+4x^3-5, 9x^2-7x^3-2x^4, 7-x+3x^4[/tex]
[tex]Sum = 2x^4-3x^2+4x^3-5+ 9x^2-7x^3-2x^4+ 7-x+3x^4[/tex]
Collect like terms
[tex]Sum = 2x^4-2x^4+3x^4 +4x^3 -7x^3-3x^2+ 9x^2-x-5+ 7[/tex]
[tex]Sum = 3x^4 -3x^3+ 6x^2-x+2[/tex]
. if 3, 2, y, 10 are in proportion, find the value of y
Answer:
y = 15
Step-by-step explanation:
Given :
3, 2, y, 10
If the numbers are in proportion :
We can thus say :
3/2 = y/10
Cross multiply
3 * 10 = 2 * y
30 = 2y
Divide both sides by 2
30 / 2 = 2y / 2
15 = y
19 POINTS the answer is not the first or second option I’m maybe think the last one
The perimeter of a rectangular field is 332 yards. If the length of the field is 92 yd what is the width?
Answer:
The width of the rectangular field is equal to 74 yards.
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityTerms/Coefficients
Geometry
Perimeter Formula [Rectangle]:
[tex]\displaystyle P = 2l + 2w[/tex]
Step-by-step explanation:
Step 1: Define
Identify given variables.
P = 332 yds
l = 92 yds
Step 2: Find Width
[Perimeter Formula - Rectangle] Substitute in variables:∴ the width of the field is equal to 74 yards.
___
Learn more about Geometry: https://brainly.com/question/27795993
___
Topic: Geometry
5 bricklayers can lay a total of 50 bricks in 30 minutes. How many bricklayers will
be required to lay a total of 60 bricks in 18 minutes?
Answer:
First look at the number of bricks alone.
Going from 50 bricks to 60 bricks is more work, thus it will require more people. The number of people would be the ratio of the 2. Since the number must be larger, you know the numerator must be the larger of the 2 numbers, so you get 60/50
Next look at the time alone.
Going from 30 minutes to 20 minutes is more work, thus it will require more people. The number of people would be the ratio of the 2. Since the number must be larger, you know the numerator must be the larger of the 2 numbers, so you get 30/20
Now you can just multiply everything.
= 5*60/50*30/20
= 5*6/5*3/2
= 90\10
= 9.
In 2017, you are starting to plan for retirement. You decide to deposit
$2.000 into a mutual fund that compounds quarterly and earns 4.2% annual interest.
Find the balance in 2027.
Answer:
10,369.04
Step-by-step explanation:
Sorry if i'm wrong i got a little confused with this
Use an exponential inequality to determine the number of years, t, after which the area covered by purple loosestrife will
exceed 850 acres.
Type the correct answer in the box. Use numerals instead of words.
The area covered by purple loosestrife will be greater than 850 acres for t > ___ years.
Answer: t>3
Step-by-step explanation:
PLATO
Answer:
t > 5
Step-by-step explanation:
How to solve Solve 3!
Answer:
by solving 3
Step-by-step explanation:
Help will give 20 points
Answer:1/3 divided by 6 equals 18
Step-by-step explanation: If you have a cloth that is 1/3 long then divide it by 6 it would look like 1/3 divided by 1/6 which would then equal 1/18.
Get brainly if right !!
John and Jack divided their math homework. John solved twice
as many problems as Jack, plus one more problem. How many
problems did each boy solve if there are 28 assigned problems?
Answer:
Jack=9, John= 19
Step-by-step explanation:
28/3=9 1/3, counting as nine, as thats what got the right answer in my homework.
9 *2) +1= 19, no idea why the plus one, thats just what showed up
J1=19
J2=9
How to solve 4x - 5 = 2x + 19?
Answer:
x = 12
Step-by-step explanation:
4x - 5 = 2x + 19
First subtract the 2x from 4x.
2x - 5 = + 19
Then add the 5 to the 19.
2x = 24
Divide 24 by 2 in order to get x by itself.
x = 12