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2 years ago

A box of cereal states that there at 90 calories in 3/4 cup serving. How many calories are there in 4 cups of cereal?

Mathematics

2 answers:

babymother [125]2 years ago

6 0

If there are 90 calories in 3/4 cup serving, we can multiply both sides by 4/3 to get

$90 \text{ calories} \mapsto \dfrac{3}{4}\text{ cups} \iff \dfrac{4}{3}\cdot 90=120\text{ calories} \mapsto 1\text{ cup}$

So, in 4 cups there are

$120\cdot 4=480$

calories.

Artist 52 [7]2 years ago

4 0

Answer:

480 calories

Step-by-step explanation:

this should be correct divide 4 cups by .75 (3/4 cups) you'll get 5.3 repeater then you multiply that by 90 to get 480 calories

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Convert 4x=1+2y from standard form to slope intercept form

gregori [183]

Answer:

3x=2y

Step-by-step explanation:

subtract on from each side 4x-1=1-1+2y=3x+2y

7 0

3 years ago

Consider the probability that greater than 26 out of 124 software users will call technical support. Assume the probability that

Mekhanik [1.2K]

Answer:

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

100% probability that greater than 26 out of 124 software users will call technical support.

Step-by-step explanation:

Test if the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.

It is needed that:

$np \geq 10$ and $n(1-p) \geq 10$

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Out of 124 software users

This means that $n = 124$

Assume the probability that a given software user will call technical support is 97%.

This means that $p = 0.97$

Conditions:

$np = 124*0.97 = 120.28 \geq 10$

$n(1-p) = 124*0.03 = 3.72 < 10$

Since $n(1-p) = 3.72 < 10$ , the normal curve cannot be used as an approximation to the binomial probability.

Consider the probability that greater than 26 out of 124 software users will call technical support.

The lowest possible probability of those is 27, so, if it is 0, since it is considerably below the mean, 100% probability of being greater. We have that:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 27) = C_{124,27}.(0.97)^{27}.(0.03)^{97} = 0$

1 - 0 = 1

100% probability that greater than 26 out of 124 software users will call technical support.

3 0

3 years ago

PLEASE HELP! 40 POINTS

Vedmedyk [2.9K]

I'd start with setting up the equations. Calling x the number of students in most popular country 1, and y in country 2.

x + y = 44740

x - y = 5672

now solve for x1 and x2. You can subtract second from first:

0 + 2y = 39068

y = 19534

x = 5672 + 19534 = 25206

Add a sentence to answer it in words.

7 0

2 years ago

Read 2 more answers

The circumference of the tree trunk is 7.85

Nadusha1986 [10]

Answer:

2.5 feet

Step-by-step explanation:

Since circumference is just pi(we're using 3.14 in this case) * diameter, which is our answer, we need to divide the circumference(which is 7.58) BY 3.14, which is pi. This leaves us with the diameter, which is 2.5. The unit is already feet, so we needn't do anything about that.

4 0

2 years ago

If Y varies directly as X and Y= 79 when X= 49, Find Y if X = 9

ryzh [129]

Answer:

y = 14.5

Step-by-step explanation:

given that y varies directly as x

mathematically,

y ∝ x

y = kx .............................................. where k is the constant of proportionality.

k = y /x

given that

y = 79

x = 49

k = 79/49

k = 1.61

to find y when x = 9

from

y = kx

y = 1.61 × 9

y = 14.5

therefore the value of y when x = 9 in ths variation is evaluated to be equals to 14.5

7 0

3 years ago