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Anna71 [15]
1 year ago
5

A graph has minutes on the x-axis and ounces of popcorn on the y-axis. A curve goes through points (0, 0), (50, 12), and (110, 1

8).
Rachel had a popcorn machine at her party. Determine whether the relationship between time and the amount of popcorn popped is directly proportional.
Yes, for every 10 minutes there were 4 ounces of popcorn popped.
Yes, the input is time and the output is the amount of popcorn popped.
No, the graph does not make a straight line.
No, the graph does not go through the origin.
Mathematics
2 answers:
NARA [144]1 year ago
8 0

Answer:

C - No, the graph does not make a straight line.

Step-by-step explanation:

Just did on edg

butalik [34]1 year ago
5 0

Answer:

No :)

Step-by-step explanation:

the graph does not make a straight line. :)

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A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $100,00
serg [7]

Answer:

a) 68%

b) 95%.

c) 2.5%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 100,000, standard deviation of 10,000.

a. Approximately what percentage of the salaries fall between $90,000 and $110,000?

90,000 = 100,000 - 10,000

110,000 = 100,000 + 10,000

Within 1 standard deviation of the mean, so approximately 68%.

b. Approximately what percentage of the salaries fall between $80,000 and $120,000?

80,000 = 100,000 - 2*10,000

120,000 = 100,000 + 2*10,000

Within 2 standard deviations of the mean, so approximately 95%.

c. Approximately what percentage of the salaries are greater than $120,000?

More than 2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean, so approximately 5% are more than 2 standard deviations from the mean.

The normal distribution is symmetric, which means that 2.5% are more then 2 standard deviations below the mean, and 2.5% are more than 2 standard deviations above the mean, which means that 2.5% of the salaries are greater than $120,000.

7 0
1 year ago
Let S(x) denote "x has a good attitude," where the domain is the set of people in the class. Express the negation of the proposi
user100 [1]

Answer:

See below

Step-by-step explanation:

Remember, we have two quantifiers, the existential quantifier ∃, and the universal quantifier ∀. The existential ∃ translates to English as "for some" or "there exists", whereas ∀ means "for all" or "every". We will also use the negation operator ¬.

First, let's write the proposition using quantifiers. "There is someone in this class who does not have a good attitude" translates to "(∃x)(¬S(x))". ∃x means that there exists a person in this class x. ¬S(x) means that x, the person that exists because of the quantifier, does not have a good attitude.

The negation is "¬(∃x)(¬S(x))" or equivalently "(∀x)(S(x))". To negate a proposition using quantifiers, change the quantifier (existential to universal and viceversa) and negate the predicate (in this case we negated ¬S(x)).

In English, "(∀x)(S(x))" means "Every person in this class has a good attitude".

8 0
1 year ago
You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?
lana66690 [7]

Answer:

3.706 liters

Step-by-step explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

V=\pi r^{2} h

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

V=\pi r^{2} h\\V=\pi (3in)^{2} (8 in)\\V=\pi *72 \ in^{3} \\\\V=72\pi\ in^{3} \\\\

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro =  1000 cubic centimeters

if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^{3} =(2.54\ cm)^{3}\\\\1\ inch^{3}=16.3870\ cm^{3}

1 cubic inch = 16.3870 cubic centimeters

1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=\frac{72\pi \cubic \ inch\ \*16.3870 }{1\ cubic\ inch} \\\\x=3706.65\ cubic\ centimeters

Step 4

Finally, convert cubic centimeters into liters1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=\frac{3706.65 \cubic \ centimeters\ \*1 liter}{1000 cubic centimeters} \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters

I can put 3.706 liters in the thermos

Have a good day

4 0
2 years ago
This figure has two intersecting lines and a ray. What is the value of x?
Evgen [1.6K]
The answer is 37 degrees
7 0
1 year ago
For the scotch yoke mechanism shown, the acceleration of point a is defined by the relation a = −1.08sinkt − 1.44coskt, where a
julia-pushkina [17]
<span>Position at t=0.35s is 0.2 m Velocity at t = 0.35s is -0.2 m/s Since this is college level mathematics, the use of the word "acceleration" should indicate to you that you've been given the 2nd derivative of a function specifying the location of point a. And since you've been asked for the velocity, you know that you want the 1st derivative of the function. And since you've also been asked for the position, you also want the function itself. So let's calculate the desired anti-derivatives. f''(t) = -1.08 sin(kt) - 1.44 cos(kt) The integral of f''(t) with respect to t is: f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C In order to find out what C is, we know that at time t=0, v = 0.36 m/s. So let's plug in the values and see what C is: f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C 0.36 = (1.08 cos(3*0) - 1.44 sin(3*0))/3 + C 0.36 = (1.08 cos(0) - 1.44 sin(0))/3 + C 0.36 = (1.08*1 - 1.44*0)/3 + C 0.36 = 0.36 + C 0 = C So the first derivative will be f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k Now to get the actual function by integrating again. Giving: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C And let's determine what C is: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C 0.16 = (1.08 sin(3*0) + 1.44 cos(3*0))/3^2 + C 0.16 = (1.08 sin(0) + 1.44 cos(0))/9 + C 0.16 = (1.08*0 + 1.44*1)/9 + C 0.16 = 1.44/9 + C 0.16 = 0.16 + C 0 = C So C = 0 and the position function is: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 So now, we can use out position and velocity functions to get the desired answer: Position: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 f(t) = (1.08 sin(3*0.35) + 1.44 cos(3*0.35))/3^2 f(t) = (1.08 sin(1.05) + 1.44 cos(1.05))/9 f(t) = (1.08*0.867423226 + 1.44*0.497571048)/9 f(t) = (0.936817084 + 0.716502309)/9 f(t) = 1.653319393/9 f(t) = 0.183702155 So the position of point a at t=0.35s is 0.2 m Now for the velocity: f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k f'(t) = (1.08 cos(3*0.35) - 1.44 sin(3*0.35))/3 f'(t) = (1.08 cos(1.05) - 1.44 sin(1.05))/3 f'(t) = (1.08*0.497571048 - 1.44*0.867423226)/3 f'(t) = (0.537376732 - 1.249089445)/3 f'(t) = -0.711712713/3 f'(t) = -0.237237571 So the velocity at t = 0.35s is -0.2 m/s</span>
4 0
2 years ago
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