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3 years ago

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A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 ce

ntimeters. Uma is a middle school student with a height of 165 centimeters. What proportion of student heights are higher than Uma's height?

1 answer:

dybincka [34]3 years ago

5 0

Answer:

0.2266

Step-by-step explanation:

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If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct charac

mezya [45]

There are $\binom{52}4$ ways of drawing a 4-card hand, where

$\dbinom nk = \dfrac{n!}{k!(n-k)!}$

is the so-called binomial coefficient.

There are 13 different card values, of which we want the hand to represent 4 values, so there are $\binom{13}4$ ways of meeting this requirement.

For each card value, there are 4 choices of suit, of which we only pick 1, so there are $\binom41$ ways of picking a card of any given value. We draw 4 cards from the deck, so there are $\binom41^4$ possible hands in which each card has a different value.

Then there are $\binom{13}4 \binom41^4$ total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is

$\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761$

4 0

2 years ago

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker

Lynna [10]

For this case, the first thing we must do is define variables.
We have then:
t: number of tarts
p: number of pies
We now write the system of equations:
Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day:
8p + t ≤ 184
the baker makes no more than 40 tarts per day:
t ≤ 40
Answer:
A system of inequalities that can be used to find the possible number of pies and tarts the baker can make is:
D. t ≤ 40
8p + t ≤ 184

5 0

3 years ago

Read 2 more answers

When y = 35,x = 2.5. If the value of y varies directly with x what is the value of y when the value of xis 3.25

leonid [27]

Answer:

The value of y would be 45.5

Step-by-step explanation:

To solve this problem, start with the base form of direct variation.

y = kx

Now we can use our original values to model the equation and find k.

35 = k(2.5)

14 = k

Now we can model the equation as:

y = 14x

Now to find y, when x = 3.25, simply put 3.25 into the equation.

y = 14(3.25)

y = 45.5

8 0

3 years ago

Explain how 7/12 is greater than 1/3 but less than 2/3

cupoosta [38]

Think if you had 7/12 of a pie witch is 7 tiny piece opposed to 1 huge piece

3 0

3 years ago

An Air Conditioner uses 850 Watts of electricity and local emissions from electricity produce 1.37 pounds of CO2 per kWh. If you

Zina [86]

Answer: 6,987,000 pounds fo CO₂ per kWh.

Step-by-step explanation: <u>Quilowatt</u>-<u>hour</u> <u>(kWh)</u> is a unit of energy that measures the amount of energy expended in 1 hour.

The AC uses 850 Watts, which in kW is 850,000 kW

If you leave the AC on for 6 hours, it will consume

850,000(6) = 5,100,000 kWh

Eletricity produces 1.37 pounds of CO₂ per kWh, then in 5,100,000 kWh:

1.37 $\frac{pounds}{kWh}$ .(5,100,000kWh) = 6,987,000 pounds

If you open a window for 6 hours, you would keep 6,987,000 pounds of CO₂ for entering the atmosphere.

7 0

3 years ago