How much water must be added to 1 litre of 5% cordial mixture to produce a 4% cordial mixture?

A science class is tracking the progress of plant growth. The class starts the experiment with a plant five centimeters high. Th

Sedaia [141]

Answer: the y-intercept is the starting height of the plant

Step-by-step explanation:

3 0

2 years ago

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Carla can choose two of her three pairs of sneakers to take to a track meet. If the pairs of sneakers are called A, B, and C, wh

Semenov [28]

Number of ways of choosing two pair of sneakers from three pairs named A, B, C is given by 3C2 (3 combination 2) = 3! / 2!(3 - 2)! = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3.

Therefore, the sample space is given by S = {AB, AC, BC}

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2 years ago

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Ice cream usually comes in 1.5-quart boxes (48 fluid ounces), and ice cream scoops hold about 2 ounces. However, there is some v

Troyanec [42]

Answer:

(a) The expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b) The expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c) Because the variance of each variable is dependent on the other.

Step-by-step explanation:

The random variable X and Y are defined as follows:

X = amount of ice cream in the box

Y = amount of ice cream scooped out

The information provided is:

E (X) = 48

SD (X) = 1

V (X) = 1

E (Y) = 2

SD (Y) = 0.25

V (Y) = 0.0625

(a)

The total amount of ice-cream served at the party can be expressed as:

X + 3Y.

Compute the expected value of (X + 3Y) as follows:

$E(X+3Y)=E(X)+3E(Y)\\= 48+(3\times2)\\=48+6\\=54$

Compute the variance of (X + 3Y) as follows:

$V(X+3Y) = V (X)+3^{2}V(Y)+2\times 3Cov (X,Y)\\=1+(9\times0.0625)+0\\=1.5625$

Then the standard deviation of (X + 3Y) is:

$SD(X + 3Y) =\sqrt{V(X + 3Y)}\\\sqrt{1.5625}\\=1.25$

Thus, the expected value and standard deviation of the amount of ice cream served at the party are 54 ounces and 1.25 ounces respectively.

(b)

The amount of ice-cream left in the box after scooping out one scoop is represented as follows:

X - Y.

Compute the expected value of (X - Y) as follows:

$E(X-Y)=E(X)-E(Y)\\=48-2\\=46$

Compute the variance of (X - Y) as follows:

$V(X - Y) =V(X)+V(Y)-2Cov(X,Y)\\=1+0.0625-0\\=1.0625$

Then the standard deviation of (X - Y) is:

$SD(X-Y) =\sqrt{V(X -Y)}\\\sqrt{1.0625}\\=1.031$

Thus, the expected value and standard deviation of the amount of ice cream left in the box after scooping out one scoop are 46 ounces and 1.031 ounces respectively.

(c)

The variance of the sum or difference of two variables is computed by adding the individual variances. This is because the variance of each variable is dependent on the others.

7 0

2 years ago

Rewrite the expression (3a^2b^3c^5)/(8x^4y^3z)so that it has no denominator. (note: do not use a fraction line in your answer. a

Gemiola [76]

Use:

$\dfrac{1}{a}=a^{-1}\\\\\dfrac{1}{a^n}=a^{-n}$

$\dfrac{3a^2b^3c^5}{8x^4y^3z}=3a^2b^3c^5\cdot8^{-1}x^{-4}y^{-3}z^{-1}$

Answer: 3"8^-1a^2b^3c^5x^-4y^-3z^-1

5 0

2 years ago

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Prof. okamoto selects 3 different students to report on 3 different current events. if there are 27 students in the class, in ho

kenny6666 [7]

Consider this option:
C³₂₇=27!/(3!*24!)=25*13*9=2925 ways to select 3 students.

8 0

2 years ago