Answer:
0 ≤ t ≤ 4.5.
Step-by-step explanation:
Since the volume of the tub, V is increasing at a rate of 8 gallons per minute, the volume of the bathtub at any time, t is V = 8t.
Now, to find the domain of the function, V, we know that the minimum value for V is zero and the maximum value is 36. Now, at V = 0,
V = 8t
0 = 8t
t = 0 and at V = 36 gallons,
V = 8t
36 = 8t
t = 36/8
t = 4.5 minutes
Since 0 ≤ V ≤ 36, 0 ≤ t ≤ 4.5.
So, the domain of the function V is 0 ≤ t ≤ 4.5.
Is this graph continuous or discontinuous?
For a recent evening at a small, old-fashioned movie theater, 35% of the moviegoers were female and 65% were male. There were two movies playing that evening. One was a romantic comedy, and the other was a World War II film. As might be expected, among the females the romantic comedy was more popular than the war film: 70% of the females attended the romantic comedy. Among the male moviegoers, the romantic comedy also was more popular: 60% of the males attended the romantic comedy. No moviegoer attended both movies. Let F denote the event that a randomly chosen moviegoer (at the small theater that evening) was female and ¯F denote the event that a randomly chosen moviegoer was male. Let R denote the event that a randomly chosen moviegoer attended the romantic comedy and ¯R denote the event that a randomly chosen moviegoer attended the war film. Fill in the probabilities below, and then answer the question that follows. Do not round any of your responses
P(F)=0.35
P(F and R)=
P(F and ¯R)=
P(¯R|F)=
P(R|¯F)=0.60
P(¯F and R)=
P(¯F and ¯R)=
P(¯F)=
What is the probability that a randomly chosen moviegoer attended the romantic comedy?
Answer:
[tex]P(F\ and\ R) = 0.21[/tex]
[tex]P(F\ and\ R^{-}) = 0.14[/tex]
[tex]P(R^{-}|F)= 0.40[/tex]
[tex]P(F^{-} and\ R) = 0.39[/tex]
[tex]P(F^{-}\ and\ R^{-}) =0.26[/tex]
[tex]P(F^{-}) =0.65[/tex]
Step-by-step explanation:
The variables have been defined in the question as:
[tex]F = Female\ Moviegoer[/tex]
[tex]F^{'} = Male\ Moviegoer[/tex]
[tex]R = Romantic\ Comedy[/tex]
[tex]R^{'} = War\ File[/tex]
Also, we have the following given parameters:
[tex]P(F) = 0.35[/tex]
[tex]P(F^{-}) =0.65[/tex]
[tex]P(R) =0.60[/tex]
[tex]P(R^{-}) = 0.40[/tex]
The solution is as follows:
[tex]a.\ P(F\ and\ R)[/tex]
[tex]P(F\ and\ R) = P(F) * P(R)[/tex]
Substitute values for P(F) and P(R)
[tex]P(F\ and\ R) = 0.35 * 0.60[/tex]
[tex]P(F\ and\ R) = 0.21[/tex]
[tex]b.\ P(F\ and\ R^{-})[/tex]
[tex]P(F\ and\ R^{-}) = P(F) * P(R^{-})[/tex]
Substitute values for P(F) and P(R-)
[tex]P(F\ and\ R^{-}) = 0.35 * 0.40[/tex]
[tex]P(F\ and\ R^{-}) = 0.14[/tex]
[tex]c.\ P(R^{-}|F)[/tex]
[tex]P(R^{-}|F)=\frac{P(R^{-}\ and\ F)}{P(F)}[/tex]
[tex]P(R^{-}|F)=\frac{P(R^{-})\ *\ P(F)}{P(F)}[/tex]
Substitute values for P(F) and P(R-)
[tex]P(R^{-}|F)=\frac{0.40 * 0.35}{0.35}[/tex]
[tex]P(R^{-}|F)= 0.40[/tex]
This implies that both events are independent
[tex]d.\ P(F^{-} and\ R)[/tex]
[tex]P(F^{-} and\ R) = P(F^{-}) * P(R)[/tex]
Substitute values for P(F-) and P(R)
[tex]P(F^{-} and\ R) = 0.65 * 0.60[/tex]
[tex]P(F^{-} and\ R) = 0.39[/tex]
[tex]e.\ P(F^{-}\ and\ R^{-})[/tex]
[tex]P(F^{-}\ and\ R^{-}) =P(F^{-}) * P(R^{-})[/tex]
Substitute values for P(F-) and P(R-)
[tex]P(F^{-}\ and\ R^{-}) =0.65 * 0.40[/tex]
[tex]P(F^{-}\ and\ R^{-}) =0.26[/tex]
[tex]f.\ P(F^{-})[/tex]
[tex]P(F^{-}) =0.65[/tex] --- Given
Find the mean, median, and mode of the data set 8 2 7 2 6 5
Answer:
Mean is 6, median 5.5, mode 2
Step-by-step
Answer:
mean=8+2+7+2+6+5
=30
30÷6=5
note: divide the total with it's sum.
median=7+2
=9
9÷2= 4.5
note: median is the middle no. since there is no middle no. so just add those two no. and divide it by 2.
mode= 2
since it occurs twice
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
Which statement is true?
Select each correct answer.
The maximum height of the water balloon occurs at x = 0.
The water balloon is in the air for 2 s.
The water balloon hits the ground in 64 s.
The water balloon rises above 64 ft before falling toward the ground.
The maximum height of the water balloon is 64 ft.
Answer:
O The maximum height of the water balloon occurs at x = 0.
O The water balloon is in the air for 2 s.
O The maximum height of the water balloon is 64 ft.
Step-by-step explanation:
Firstly, by simply looking at the x axis on the graph (time), you will see that it starts at 0 and the 64 ft maximum height is aligned with the starting point of 0 seconds.
The graph also shows (x axis) the 'time' represented, and as the height rapidly decreases the graph eventually reaches the 2 second mark, going no further and no lower.
Finally, the graph shows (y axis) the peak of the water balloon's height is 64 ft, as it is the highest number reached while the water balloon was airborne.
The correct options are (A) The maximum height of the water balloon occurs at x = 0, (B) The water balloon is in the air for 2 s, and (5) The maximum height of the water balloon is 64 ft are correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
The water balloon follows a path such that it makes half parabola.
From the graph:
At x = 0
Height(h) = 64 feet
Which is the maximum height of the water balloon.
After t = 2 seconds
The water balloon hits the ground
The correct options are:
The maximum height of the water balloon occurs at x = 0. The water balloon is in the air for 2 s. The maximum height of the water balloon is 64 ft.Thus, the correct options are (A) The maximum height of the water balloon occurs at x = 0, (B) The water balloon is in the air for 2 s, and (5) The maximum height of the water balloon is 64 ft are correct.
Learn more about the parabola here:
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Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time
he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training
times this week
Step-by-step explanation:
Given that,
Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. This week, he spent more than 6 hours training for the race.
Let x represent no. of times Dominick runs per week and y represents no. of times that Dominick swims per week.
ATQ,
0.75x + 1.5y > 6
The graph represent the scanario for the given data.
Answer:
picture A
Step-by-step explanation:
I know because I just took a quiz and i got it right
one and two-thirds divided by 3
Answer:
5/9
Step-by-step explanation:
Carrie has 18 pens. Carrie has 2 more than 4
times the number of pens that Patricia has.
Exactly how many pens does Patricia have?
Answer: ( sorry I misread the problem)
I'm not sure what I'm supposed to be multiplying with
but I'll try my best
subtract 2 with 18 and divide 4 with the remaining
18 -2 = 16
then it is 16/4= 4
Pat has a total of 4pens
Thee questionn is beloww
Given:
[tex]m\angle ABC=60[/tex]
To find:
The [tex]m\angle ADC[/tex].
Solution:
In circle B, [tex]\angle ABC[/tex] is central angle and [tex]\angle ADC[/tex] is inscribed angle from two points A and C.
According to central angle theorem, central angle is always twice of inscribed angle.
[tex]m\angle ABC=2(m\angle ADC)[/tex] [Central angle theorem]
[tex]60=2(m\angle ADC)[/tex]
Divide both sides by 2.
[tex]\dfrac{60}{2}=m\angle ADC[/tex]
[tex]30=m\angle ADC[/tex]
Therefore, [tex]m\angle ADC=30[/tex].
Solve the equation.
W+3/3 = - 4
Answer:
W=−5
r=3
hope this helps!!
A local hamburger shop sold combined total 500 hamburgers and cheeseburgers the number of cheeseburgers old was three times the number of hamburger sold how many hamburgers were sold?
Answer:
125 hamburgers
Step-by-step explanation:
Let x be the number of hamburgers sold and 3x the number of cheeseburgers sold.
So:
x+3x=500
4x=500
x=125
So there are 125 hamburgers sold.
pls help!!!!!!!!!!!!!!
Answer:
C) √221 units
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-7, 7)
Point (7, 2)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute [DF]: [tex]d = \sqrt{(7+7)^2+(2-7)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(14)^2+(-5)^2}[/tex]Exponents: [tex]d = \sqrt{196+25}[/tex]Add: [tex]d = \sqrt{221}[/tex]What is the value of the expression expression 9 – m. If m = –3, n = 8, and p = –1?
Answer:
Step-by-step explanation:
i do believe you didn't write the whole problem
if m=-3
9-m=9-(-3)=9+3=12
Alfie is cooking a 0.6kg jaunt of steak for dinner. calculate the total time he needs to cook for it
Answer: This is a tough question
Depends on if you wanna cook it medium rare, rare, medium well, well done, or do you just wanna eat it raw :D
Step-by-step explanation:
What is the reciprocal of 1/5?
5/1
4
1/5
And this is Ari, signing off
Answer:
Byeee again haha
Step-by-step explanation:
Yea I'm answering this question again
A specific moderator deleted a lot of my answers almost all at once and for the reason that I didn't answer the question the people were asking, it's pretty weird as all the questions were either free points or very extremely straightforward questions like "what dynasty started the great wall" and usually when a moderator sees those they delete them but they just deleted my answer for almost no reason haha
Well if u see this then have a great day!
Answer:
ok :)
Step-by-step explanation:
Determine whether the relationship is a function. Complete the explanation.
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Answer:
the relationship is not a function
Step-by-step explanation:
it's not a function because two of the domains are the same.
The relationship represented by these ordered pairs is not a function.
We have,
To determine whether the relationship is a function, we need to check if each input (x-value) is associated with exactly one output (y-value).
If there is any x-value that is associated with multiple y-values, then the relationship is not a function.
Let's analyze the given set of ordered pairs:
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Here, we can see that the x-value 8 is associated with both y-values 8 and 7.
Therefore, the relationship is not a function because one input (x-value) is mapped to multiple outputs (y-values).
In a function, each input must have a unique output, but in this case, the x-value 8 is associated with both 8 and 7 as the corresponding y-values.
Thus,
The relationship represented by these ordered pairs is not a function.
Learn more about functions here:
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Which graph has x-intercept (-5,0) and y-intercept (0,-2)?
The top one is x-intercept, and the bottem one is y-intercept. Also the gray boxes are your answer
The graph of the x-intercept at x = -5 and y-intercept at y = -2 is given below.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
x-intercept = (-5, 0)
This means,
It is a vertical line at x = -5.
y-intercept = (0, -2)
This means,
It is a horizontal line at y = -2.
Thus,
The graph is given below.
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Which equation has a slope of 2 and y-intercept of -3
y = 2x -3
fhfjdydtsfxbnpurwsgh
Which choices are solutions to the following equation?
Check all that apply.
X2-7x = -24/4
A. X=1
B. X=2
C. X=12
D. X=6
Which expression would the model be most helpful in solving?
An area model has 5 shaded parts and 1 unshaded part.
This question is awfully vague without any images of the equation to back it up, sorry
Find the recipricol of -b/3
Answer:
-0.333333333
Step-by-step explanation:
What is 63 divided by 36?
Answer:
1.75
Step-by-step explanation:
used a calculator
Answer:
63÷36=1.75
Step-by-step explanation:
itz easy
mark me as a brainlist
Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 bags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.
Answer:
The value is [tex]UCL = 10.8[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 9 \ ounce[/tex]
The sample size is n = 25
The standard deviation is [tex]\sigma = 3 \ ounce[/tex]
Given that the sample size is not large enough i.e n< 30 we will make use of the student t distribution table
From the question we are told the confidence level is 99.7% , hence the level of significance is
[tex]\alpha = (100 -99.7 ) \%[/tex]
=> [tex]\alpha = 0.003[/tex]
Generally the degree of freedom is [tex]df = n- 1[/tex]
=> [tex]df = 25 - 1[/tex]
=> [tex]df = 24[/tex]
Generally from the student t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24[/tex] is
[tex]t_{\frac{\alpha }{2} , 24 } = 3.0 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 24} * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 3.0 * \frac{3 }{\sqrt{25} }[/tex]
=> [tex]E =1.8 [/tex]
Gnerally the upper control chart limit for 99.7% confidence is mathematically represented as
[tex]UCL = \= x + E[/tex]
=> [tex]UCL = 9 + 1.8[/tex]
=> [tex]UCL = 10.8[/tex]
A hiker starts hiking at the beginning of a trail at a point which is 20 feet below sea level. He hikes to a location on the trail that is 58 feet above sea level
and stops for lunch
What is the vertical distance between 200 feet below sea level and 580 feet above sea level?
Answer:
780 feet below sea level
Step-by-step explanation:
a farmer grows 128 red tomato plants and 102 yellow tomato plants each plant produces about 32 tomatoes the farmer plans to sell each tomato for$2
Answer:
14720$ he will make and there are 7360 tomatoes
Step-by-step explanation:
A net of a storage trunk is shown. Which is the trunk's surface area?
2. A spider can walk at a certain speed and run at
another speed. If she walks for 10 seconds and runs for 9
seconds, she travels 85m. If she walks for 30 seconds and
runs for 2 seconds, she travels 130m. Find her speeds of
walking and running.
Answer:
The answer is below
Step-by-step explanation:
Speed is the ratio of distance covered to the time taken. Speed is given by the formula:
speed = distance / time.
Let us assume the spider walking speed is x and its running speed is y.
If the spider walks for 10 seconds and runs for 9 seconds, she travels 85m. distance = speed * time, hence:
Total distance = distance covered walking + distance covered running
10x + 9y = 85 (1)
Also if she walks for 30 seconds and runs for 2 seconds, she travels 130m. Hence:
30x + 2y = 130 (2)
Solving equation 1 and 2 simultaneously by mutiplying equation 1 by 3 and subtracting equation 2 from the result:
25y = 125
y =5 m/s
Put y = 5 in eqn. 2
30x + 2(5) = 130
30x = 120
x = 4 m/s
The spider walks at 4 m/s and runs at 5 m/s
this app is bad its s lie
Which table represents a function with a slope of 1/2 and a y-intercept of 4
Answer:D
Step-by-step explanation: trust me ima sophomore use this for help y=1/2x+4 then x value change it to the number in the x section then if the y appears just like in the box the y section it’s correct
pls help asap i will give brainliest 16 POINTS!!!!