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2 years ago

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For the upcoming holiday season, Dorothy wants to mold 20 bars of chocolate into tiny pyramids. Each bar of chocolate contains 6

cubic inches of chocolate. Dorothy plans to make chocolate pyramids with a square base of 1 square inch and a height of 2 inches. What is the largest number of pyramids she can make from the 20 bars of chocolate?

2 answers:

gizmo_the_mogwai [7]2 years ago

3 0

So each bar contains 6 and she has 20 so 6 times 20=120

pyramid volume=legnth times width times height times 1/3
v=base times height times 1/2
v=1 times 2 times 1/3
v=2/3
volume of 1 pyramid is 2/3 cubic inches

divide 120 by 2/3 to find out how many pyrimds will fit into amount given
120/1 divide by 2/3=120/1 times 3/2=360/2=180

she can make 180 pyramids

algol [13]2 years ago

3 0

Answer:

20 x 6 = 120 in³

V ( pyramid ) = 1/3 B h

= 1/3 · 1 · 2 = 2/3 in³

120 : 2/3 = 120 · 3/2 = 180

Step-by-step explanation:

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A mercury thermometer records a temperature of 8 degrees Fahrenheit at 10:00am.If the Temperature drops by 3 degrees Fahrenheit

AysviL [449]

Given:

Temperature at 10:00 am = 8 degrees Fahrenheit

Temperature drops by 3 degrees Fahrenheit every hour.

To find:

The temperature by 2:00pm of the same day.

Solution:

Let y be the temperature after x hour after 10:00 am.

The temperature at 10:00 am is the initial temperature.

So, y-intercept of the linear function is 8.

Temperature drops by 3 degrees Fahrenheit every hour.

So, slope of linear function is -3. Here, negative sign represents the decrease in the temperature.

Slope intercept form of a linear function is

$y=mx+b$

where, m is slope and b is y-intercept.

Substitute m=-3 and y=8 in the above equation.

$y=-3x+8$

Difference between 2:00pm and 10:00 am is 4 hours. So, substitute x=4 in the above equation.

$y=-3(4)+8$

$y=-12+8$

$y=-4$

Therefore, the temperature by 2:00pm of the same day is -4 degrees Fahrenheit.

5 0

2 years ago

Jose is applying to college. He receives information on 7 different colleges. He will apply to all of those he likes. He may lik

marta [7]

Answer:

128 posibilities

Step-by-step explanation:

We have 7 colleges (A,B,C,...,H) which form a set with seven elements.

What you are asking is the number of elements (or cardinality) of the set that contains all possible sets formed by those 7 elements (or the "power set").

It is known that if n is the number of elements of a given set X, then the cardinality of the power set is $2^n$ .

Therefore, there are $2^7$ or 128 possibilities (or elements) for the set of colleges that he applies to.

6 0

2 years ago

A popcorn container is the shape of an inverted cone. It is 9 inches tall, and the circular opening has a diameter of 4 inches.

stealth61 [152]

Answer:

<u>The volume of the container is 37.7 cubic inches and the equation is π * r² * h/3, where r is the radius and h is the height of the cone.</u>

Step-by-step explanation:

Let's recall that the formula for finding out the volume of a cone is:

Volume of a cone = π * r² * h/3

Replacing with the real values, we have:

diameter = 4 inches ⇒ radius = 2 inches

Volume of a cone = 3.1416 * 2² * 9/3

Volume of a cone = 3.1416 * 4 * 3

Volume of a cone = 37.7 cubic inches

5 0

2 years ago

Read 2 more answers

If a cow has a mass of 9×102 kilograms, and a blue whale has a mass of 1.8×105 kilograms, which of these statements is true?

lana66690 [7]

Answer:

The mass of the Blue whale is 200 times the mass of the cow

Step-by-step explanation:

Given

Mass of Cow = 9 * 10² kg

Mass of Blue Whale = 1.8 * 10⁵ kg

Required

Determine the relationship between both weights

Represent the mass of the cow with C and the mass of the whale with B

$C = 9 * 10^2kg$

$C = 9 *100kg$

$C = 900kg$

$B = 1.8 * 10^5kg$

$B = 1.8 * 100000kg$

$B = 180000kg$

Divide the bigger weight by the smaller weight

$\frac{B}{C} = \frac{180000kg}{900kg}$

$\frac{B}{C} = \frac{180000}{900}$

$\frac{B}{C} = {200}{}$

Multiply both sides by C

$C * \frac{B}{C} = {200}{} * C$

$B = {200}{} * C$

$B = 200}C$

<em>From the expression above, it can be concluded that the mass of the Blue whale is 200 times the mass of the cow</em>

7 0

2 years ago

A probability calculator is required on this problem; answer to six decimal places. Suppose we will spin the wheel pictured 400

KiRa [710]

Answer:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=400, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

We need to check the conditions in order to use the normal approximation.

$np=400*0.2=80 \geq 10$

$n(1-p)=400*(1-0.2)=320 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=400*0.2=80$

$\sigma=\sqrt{np(1-p)}=\sqrt{400*0.2(1-0.2)}=8$

So then we can approximate the random variable as $X \sim N(\mu = 80, \sigma = 8)$

And we want this probability:

$P(90< X< 110)$

We can use the z score formula given by:

$z = \frac{x -\mu}{\sigma}$

And replacing we got:

$P(90< X< 110)= P(\frac{90-80}{8}$

And we can find this probability with this difference:

$P(90< X< 110)=P(z$

And we can find the real value with the following excel code using the binomial distribution:

"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"

And we got 0.118 a very close value from the value obtained using the normal approximation

8 0

2 years ago