a recent survey shows that 16% of college students have dogs and 38% have an HBO subscription. assuming these two events are independent, what is the probability that a randomly selected college student has neither a dog nor HBO
Answer: [tex]0.939\ or\ 93.9\%[/tex]
Step-by-step explanation:
Given
Survey shows that 16% of college students have dogs and 38% have HBO subscription
Probability that a random person have both is
[tex]\Rightarrow P_o=0.16\times 0.38\quad [\text{As both events are independent}]\\\Rightarrow P_o=0.0608[/tex]
The probability that the random person has neither of the two is
[tex]\Rightarrow P=1-P_o\\\Rightarrow P=1-0.0608\\\Rightarrow P=0.939[/tex]
Write the equation of the line in point-slope form given the information:
Slope = -1/5
Y intercept = -3
point slope form:
y + 3= -1/5 x (x+0)
Step-by-step explanation:
-use the point slope form equation: y - y1 = m (x - x1).
-using the given information we know that m = -1/5 and that the y intercept is (0,-3).
- y and x will be kept as a variable.
-plug in the y1 and x1 from the y intercept:
y + 3 = m(x + 0)
-once you've plugged in the y intercept then plug in the slope which gives you the answer:
y + 3= -1/5 x (x+0)
Find the product of these complex numbers.
(8 + 5)(6 + 3) =
Solve and check
y − 5 = −5
Answer:
Its -0
Step-by-step explanation:
-0-5=-5
Hope thia helps I believe its right check on a calculator
Classify the type of angle.
A: Acute
B: Right
C: Straight
D: Obtuse
Answer:
obtuse angle that's the answer
Solve the inequality (help please)
Answer:
v<1 23/25
Step-by-step explanation:
The inequality simplifies to 48/25, which is equivalent to 1 23/25.
The diameter of the base is the cone measured 8 units. The height measures 6 units.
What is the volume of the cone?
A) 24 π cubic units
B) 32 π cubic units
C)48 π cubic units
D)64 π cubic units
PLEASE PLEASE HELP ASAPPPP IM BEING TIMEDDD
6x2y − 3xy − 24xy2 + 12y2
Rewrite the expression completely factored. Show the steps of your work.
Answer:
3y(2x-1)(x-4y)
Step-by-step explanation:
Apply exponent rule:
6x^2y-3xy-24xyy+12yy
Rewrite 12 as 4*3
Rewrite -24 as 8*3
Rewrite 6 as 2*3
2*3x^2y-3xy+8*3xyy+4*3yy
Factor out common term 3y:
3y(2x^2-x-8xy+4y)
Factor 2x^2-x-8xy+4y:
3y(2x-1)(x-4y)
Your Answer Is 3y(2x-1)(x-4y)
Two planes are the same altitude. From the airport , one plane is 50 km away in the direction of N°60 E and another is 80 km away in the direction of S50° E .How far apart are the two planes
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Answer:
78.5 km
Step-by-step explanation:
Measured at the airport, the angle between the two planes is ...
180° -60° -50° = 70°
The law of cosines tells us the distance between the planes is ...
d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km
The planes are about 78.5 km apart.
A rocket is fired upward with an initial velocity v of 80 meters per second. The quadratic function S(t)=−5t2+80t can be used to find the height s of the rocket, in meters, at any time t in seconds. Find the height of the rocket 8 seconds after it takes off. During the course of its flight, after how many seconds will the rocket be at a height of 270 meters?
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Answer:
a) 320 m
b) 4.838 seconds, or 11.162 seconds
Step-by-step explanation:
a) S(8) = -5(8^2) +80(8) = -320 +640 = 320
The height 8 seconds after takeoff will be 320 meters.
__
b) S(t) = 270
270 = -5t^2 +80t
-54 = t^2 -16t . . . . . . divide by -5
10 = t^2 -16t +64 . . . . add 64
±√10 = t -8 . . . . . . . . . . take the square root
t = 8 ±√10 ≈ {4.838, 11.162}
The rocket will be at a height of 270 meters at 4.838 and 11.162 seconds after takeoff.
Help me with this please!!
Answer:
[tex]y=\sqrt{x} -2[/tex]
Step-by-step explanation:
If you were to replace x with 0 in each of the equations, you would get
from top to bottom choices:
[tex]\sqrt{2}[/tex]
[tex]\sqrt{-2}[/tex]
2
-2
Since we can see that the line touches the y-axis on the number -2, we know that it is the last choice that is the answer
4. Five cards are randomly chosen from a deck of 52 (13 denominations with 4 suits). a. How many ways are there to receive 5 cards from a deck of 52
Answer:
There are 2,598,960 ways to receive 5 cards from a deck of 52.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[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]
a. How many ways are there to receive 5 cards from a deck of 52?
[tex]C_{52,5} = \frac{52!}{5!(47)!} = 2598960[/tex]
There are 2,598,960 ways to receive 5 cards from a deck of 52.
Which equation is equivalent to
1
3
= 27X+22
O 3*-3-3x+2
O 3* = 33x+6
O 3-* - 33x+2
O 3-* = 33x+6
Answer:
[tex]3^{-x} = 3^{3x + 6}[/tex]
Step-by-step explanation:
Required
Which is equivalent to [tex](\frac{1}{3})^x = 27^{x + 2}[/tex]
Express base as 3
[tex](3^{-1})^x = 3^3^{x + 2}[/tex]
Open brackets
[tex]3^{-x} = 3^{3x + 6}[/tex]
Given the triangle below, what is m 2A, rounded to the nearest tenth?
B
18
11
309
A
C
Triangle not drawn to scale
A. 17.8
OB. 20.4
O C. 24.2
D. 26.8
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Answer:
A. 17.8°
Step-by-step explanation:
We have an angle and an opposite side, so we can use the law of sines to find the angle of interest.
sin(A)/a = sin(C)/c
A = arcsin(a/c·sin(C)) = arcsin(11/18·1/2) = arcsin(11/36)
A ≈ 17.7916° ≈ 17.8°
Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary
Write each equation in standard form:
3x + y + 3z = 11
x + 2y + z = 7
-x + y + z = 0
In matrix form, this is
[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]
and in augmented matrix form,
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]
Now for the row operations:
• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]
• Multiply row 2 by -1/5:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]
• Add -4 (row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]
• Multiply row 3 by 1/6:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Add -1 (row 2) and -3 (row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Mutiply row 1 by 1/3:
[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).
What is the range for the following set of numbers?57, -5, 11, 39, 56, 82, -2, 11, 64, 18, 37, 15, 68
so
82-(-2)
=84
then ur answer is 84
821) The integon which is 15 more than - 55 is
Answer:
-40
Step-by-step explanation:
-55 + 15 = x
-40 =x
Blood pressure values are often reported to the nearest 5 mmhg (100, 105, 110, etc.). the actual blood pressure values for nine randomly selected individuals are given below.
108.6 117.4 128.4 120.0 103.7 112.0 98.3 121.5 123.2
Required:
a. What is the median of the reported blood pressure values?
b. Suppose the blood pressure of the second individual is 117.7 rather than 117.4 (a small change in a single value). What is the new median of the reported values?
c. What does this say about the sensitivity of the median to rounding or grouping in the data?
Answer:
Step-by-step explanation:
Arranging the data in the ascending order:
108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4
The median is the middle value of the data set:
a)
Hence,
median = 117.4
b)
When the value of blood pressure is 117.7 instead of 117.4 then the median will be:
Median = 117.7
c)
This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.
What is the value of the expression 10(n-6) when 4=14
Answer:
it's going to be 4n so its going to be 4...
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Assuming you meant when n=14
10(n-6)
plug in 14 for n
10(14-6)
work out parenthesis first
10(8)=
80
If someone knows the answer that will be greatly appreciated :)
[tex]a. \: 8 = 2 + 2a \: and \: 3 = a[/tex]
Step-by-step explanation:
Set up equation as we know both weights are equal.Subtract two from both sides and divide by 2 to isolate the variable a.3 = aIf 400 patrons visit the park in March and 550 patrons visit in April, the total number of patrons who
visited the park over the two months falls into all of the following categories except
O real numbers
O rational numbers
o irrational numbers
900 d 180 nd the SP when: CP = Rs. 950, gain = 6 1%4
Respuesta:
????????????,,,???
Step-by-step explanation:
THERE ARE STEPS TO THIS
Y
X
Pls help me you’ll get 29 points
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+x+x = 180
3x = 180
Divide by 3
3x/3 =180/3
x = 60
Matt buys a new fish tank. The fish tank is in the shape of a cuboid. The diagram shows water in the tank. 30 cm 30 cm 100 cm Matt knows 1000 cm' = 1 litre 1 gallons = 4.5 litres He can keep 2 small fish in the tank for every 1 gallon of water in the tank. Matt thinks he can keep more than 36 small fish in the tank. Is Matt correct?
Answer: Yes, but only if he houses 37, 38, 39, or 40 fish
Anything larger than 40 and he'll need more room.
==========================================================
Explanation:
The tank is 30 cm by 30 cm by 100 cm. The volume is 30*30*100 = 90,000 cm^3 which is shorthand for "cubic centimeters".
We're told that 1000 cm^3 = 1 liter, which means the 90,000 cm^3 converts to (90,000)/(1000) = 90 liters.
The fish tank is 90 liters.
Since 1 gallon = 4.5 liters, this means the 90 liter tank converts to 90/(4.5) = 20 gallons
----------------------------
Your teacher mentions "He can keep 2 small fish for every 1 gallon".
Since the tank is 20 gallons, that means he can keep 20*2 = 40 fish. This value is larger than 36, so Matt is correct to a point. If Matt is thinking 37, 38, 39, or 40 fish then he would be correct. If Matt is wanting more than 40 fish, then he'll need a bigger tank.
In short, he can't have any number over 36 and can only have 4 specific values (the four values mentioned earlier).
So technically, Matt is correct, but strong clarification is needed.
Abu is trying to decide which pet–sitting service he wants to use . Your Pets charges a $15 fee, plus $1 .75 per hour . Sit Pets charges an $11 fee, plus $2 .25 per hour . At how many hours will both services ...
Answer:I did not see the entire question but is assuming the question is asking how many hours for both services to cost the same.
Your Pets Cost =15+1.75x
Sit Pets Cost =11+2.25x
set both equations equal to each other
15+1.75x=11+2.25x
15-11 = (2.25-1.75)x
4=0.5x
x=8
Step-by-step explanation:
A class of 24 students is planning a field trip to a science museum. A nonrefundable deposit of $50 is required for the day-long program, plus a charge of $4.50 per student.
Determine a linear function that models the cost, c, and the number of students, s.
Answer:
c = 4.50s + 50
Step-by-step explanation:
50 is a flat rate so it is a constant. 4.50 is the charge per student so it would be multiplied by the total number of students s.
Answer:
This is the linear function: c = 4.5s + 50
This is the cost if all 24 students came along: $158.00
Step-by-step explanation:
C is the total cost, it is $4.50 per student coming, and there is a $50 non refundable deposit for the program. So, if all 24 students came along for the trip, you would do 24 times $4.50 which is $108 and then add the additional $50 for the nonrefundable deposit, making the total $158.
what is the completely factored form of this expression?
y^2-12y+32
a.(y+4)(y+8)
b.(y-4)(y-8)
c.(y+18)(y+2)
d.(y-18)(y-2)
Answer:
[tex]y^2-12y+32[/tex]
[tex]=(x - 4)(x - 8)[/tex]
------------------------
Hope it helps...
Have a great day!!
How would I find the area of this?
Answer:
Read below v
Step-by-step explanation:
First you would find the area of the semi circle by turning it into a circle and then dividing your answer by two. Then you would find the area of the triangles.
Answer:
26.13 [tex]ft^{2}[/tex]
Step-by-step explanation:
Half circle :
Area of a circle = [tex]\pi r^{2}[/tex]
A = 3.14 ([tex]3^{2}[/tex]) = 9(3.14) = 28.26
That's a full circle. We want half. Divide by 2 = 14.13
Triangles. Both are same.
A = [tex]\frac{(b)(h)}{2}[/tex] = [tex]\frac{(3)(4)}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
There are two of them, so area of triangles is 12
12 + 14.13 = 26.13
I need help:/ I’m in college
Step-by-step explanation:
Amount of acid = 14.9% of 331 mL solution
= 0.149×(331 mL)
= 49.3 mL acid
Answer question below
Answer:
edge of cube = root 13.5/6 = 1.5
volume of cube = (Edge of cube)^3= (1.5)^3 = 3.37500 m^3
