there is 3/5 liter of milk left in a container. A child drinks 2/3 of it. How many liters of milk does the child drink

The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, x and y vary directly and y is 44 when x is 11.

Let, y ∝ x.

y = kx.

44 = 11k.

k = 44/11.

k = 4.

Now x = 9.

y = 4×9.

y = 36.

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Answer:

9400.32 square inches

Step-by-step explanation:

The area of one floor tiles is 92.16

The area of a kitchen floor covered with 102 floor tiles can be calculated as follows

= 102 × 92.16

= 9400.32 square inches

Hence the area is 9400.32 square inches

Answer:

98°

Step-by-step explanation:

x = 53° + 45° { exterior angle of a triangle is equal to the sum of two opposite interior angles }

x = 98°

Answer: 0.28157

Step-by-step explanation:

Given, The proportion of the community favored building a police substation in their neighborhood: p= 0.75

Number of citizens are chosen: n= 10

Let x be the binomial variable that represents the number of citizens favor the building of the police substation.

Then, the probability that exactly 8 of them favor the building of the police substation will be :

\(P(x=8)=\ ^{10}C_8(0.75)^8(1-0.75)^2\)

 [Using binomial probability function \(P(X=x)=^nC_xp^x(1-p)^{n-x}\)]

\(=\dfrac{10!}{8!2!}(0.100113)(0.0625)\\\\=0.2815678125\approx0.28157\)

Hence, the probability that exactly 8 of them favor the building of the police substation =0.28157

The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

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Answer:

5

Step-by-step explanation:

To prove angle abd and angle cbd are congruent using a proof by contradiction, the assumption statement that starts the proof is Angle abd and angle cbd are not congruent.

Proof by contradiction is a technique used in logic and mathematics to verify the truth or validity of a claim by demonstrating how presuming the proposition to be incorrect results in a contradiction.

A proof by contradiction first starts with the negation, or opposite of the hypothesis.

In context of the problem, the proof by contradiction will start by the opposite . Since we are to prove that angle abd and angle cbd are congruent, the opposite is Angle abd and angle cbd are not congruent.

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Answer:

0.65

Step-by-step explanation:

To reduce a quantity by 35%, multiply it by 100% - 35% = 65% = 0.65

Think of it like this:  if 35% of a quantity is gone, 65% remains.

This applies to all sorts of situations.  One example is discount or sale prices.

A $250 item goes on sale at a 35% discount.  The sale price is 0.65 x 250 = 162.5  ($162.50).  If you DON'T pay 35% of something, you DO pay 65%.

The random number 0.23, when interpreted in the given frequency distribution of demand, would correspond to a demand of 1.

In order to interpret the random number 0.23, we need to refer to the frequency distribution of demand. A frequency distribution provides information about the different values of a variable and their corresponding frequencies or probabilities. However, since the frequency distribution of demand is not provided, we cannot determine the exact values and frequencies for each demand level.

Nevertheless, assuming that the demand levels in the frequency distribution are discrete and start from 0, it is likely that the random number 0.23 falls within the range of the cumulative probabilities for a demand level of 1. The cumulative probability represents the probability of observing a value less than or equal to a particular demand level.

To interpret the random number, we can compare it to the cumulative probabilities associated with each demand level. If the random number falls within the cumulative probability range of a specific demand level, then that demand level would be the interpretation. Since the random number 0.23 falls within the range for a demand of 1, we can conclude that the demand corresponding to the random number 0.23 is 1.

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Answer:

17

Step-by-step explanation:

Hope it helps!

The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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The required answer is f(x) = x + 4 and f(x) = 2x - 5

The group of answer choices, both f(x) = x + 4 and f(x) = 2x - 5 have well-defined inverses as they are both one-to-one and onto functions.

To select the function that has a well-defined inverse from the group of answer choices, we need to look for the function that satisfies the horizontal line test. The horizontal line test states that a function has a well-defined inverse if no horizontal line intersects the graph of the function more than once.

The company raised a $6 million Series A funding in 2016, led by Crosslink Capital with participation from Bertelsmann Digital Media Investments.
Out of the four answer choices, the only function that satisfies the horizontal line test is f:→f(x)=|x|. Therefore, the function f:→f(x)=|x| has a well-defined inverse.

To select the function that has a well-defined inverse, we need to identify the function that is both one-to-one and onto. Here are the given functions:

1. f(x) = |x|
2. f(x) = x + 4
3. f(x) = ⌈x/2⌉
4. f(x) = 2x - 5

the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by, \(f-1\)
Now let's analyze each function:

1. f(x) = |x| is not one-to-one because f(1) = f(-1) = 1.
2. f(x) = x + 4 is one-to-one and onto, as every input has a unique output and every output can be achieved by a unique input.
3. f(x) = ⌈x/2⌉ is not one-to-one because f(1) = f(2) = 1.
4. f(x) = 2x - 5 is one-to-one and onto, as every input has a unique output and every output can be achieved by a unique input.
the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers.

Among the group of answer choices, both f(x) = x + 4 and f(x) = 2x - 5 have well-defined inverses as they are both one-to-one and onto functions.

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T he joint moment generating function of x and y is M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

Let X be the value of the first die, which takes on values {1, 2, 3, 4, 5, 6} with equal probability of 1/6 each. Let Y be the sum of the values of two dice, so Y takes on values {2, 3, ..., 12}.

The joint moment generating function of X and Y is given by:

M(t1, t2) = E[e^(t1X + t2Y)]

To compute this, we can use the law of total probability and conditioning on the value of X:

M(t1, t2) = E[e^(t1X + t2Y)]

= Σx P(X=x) E[e^(t1X + t2Y) | X=x]

= (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

Now we need to compute E[e^(t1x + t2Y) | X=x]. We can use the fact that the sum of two dice is the sum of two independent uniform random variables on {1, 2, 3, 4, 5, 6}:

E[e^(t1x + t2Y) | X=x] = E[e^(t1x + t2(x+Z))]

= E[e^(tx) e^(t2Z)]

= MZ(t2) e^(tx)

where Z is a uniform random variable on {1, 2, 3, 4, 5, 6} and MZ(t2) is its moment generating function, which is:

MZ(t2) = E[e^(t2Z)]

= (1/6)Σz=1^6 e^(t2z)

Substituting this back into the expression for M(t1, t2), we get:

M(t1, t2) = (1/6)Σx=1^6 E[e^(t1x + t2Y) | X=x]

= (1/6)Σx=1^6 MZ(t2) e^(tx)

= (1/6)Σx=1^6 [(1/6)Σz=1^6 e^(t2z)] e^(tx)

Simplifying the expression, we get:

M(t1, t2) = (1/36)Σx=1^6Σz=1^6 e^(t1x + t2z)

This is the joint moment generating function of X and Y.

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Answer:

I don't think so, regular triangle sizes are 3, 4,5. If I am wrong please tell me.

Step-by-step explanation:

Answer:

-2x=30y-6

2x+30y-6=0

Step-by-step explanation:

Answer:

5 x 10⁰

Step-by-step explanation:

-15 / -3 = 5

5 in standard form is 5 x 10⁰

Answer: 5

Step-by-step explanation:

-15/-3

negative signs cancel out each other to make positive

⇒15/3

⇒5/1

⇒5 answer.

hope that helps...

Answer: 9

Step-by-step explanation: All you have to do to find the sum is simply add 6 and 3

Answer: Part 1: DC=2 units

BC=13 units

Part  2: AB=40 units

DE=26

Step-by-step explanation:

Answer:

48.10 dollars

Step-by-step explanation:

I think JDJDKDIDID

Answer:

250

Step-by-step explanation:

Multiply 100 by 65 and divide that by 26.

Answer:

\(4^{-5}\)

Step-by-step explanation:

The given expression is :

\(4^{-3}\times (\dfrac{1}{4})^2\)

We know that, \(x^{-a}=\dfrac{1}{x^a}\)

So,

\(4^{-3}\times (\dfrac{1}{4})^2=\dfrac{1}{4^3}\times (\dfrac{1}{4})^2\\\\=\dfrac{1}{4^3}\times \dfrac{1}{4^2}\\\\=\dfrac{1}{4^3\times 4^2}\\\\=\dfrac{1}{4^{3+2}}\\\\=\dfrac{1}{4^5}\\\\=4^{-5}\)

So, the answer of the given expression is equal to \(4^{-5}\).

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²  

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

Answer:

m<DBC = 109

Step-by-step explanation:

8x-27=6x+7

8x=6x+34

2x=34

x=17

8(17)-27= 109

Answer: 109

Step-by-step explanation:

i'm not entirely sure of this answer as its been a while since ive done problems like this, however, i think the steps to solve are setting (8x-27) equal to (6x+7). Once you do that, you can solve for x. Substitute x into angle DBC to find the answer.

Answer:

Step-by-step explanation:

m - 3.8 - 0

m = 3.8 + 0

m = 3.8

Step-by-step explanation:

I'm sorry, but the statement you provided is not correct. The transitive property of angle congruence actually states that if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then ∠QRS ≅ ∠XYZ. In other words, if two angles are congruent to a third angle, then they are congruent to each other.

So, in your statement, if ∠QRS ≅ ∠PQR and ∠PQR ≅ ∠XYZ, then you can conclude that ∠QRS ≅ ∠XYZ.

We swap the x- and y-coordinates of the translated point, and then shift the x-coordinate 3 units to the right and the y-coordinate 5 units down.

The formula for translating 3 units right and 5 units down if we start at a position (x, y) is:

(x, y) → (x + 3, y - 5)

In other words, we multiply the x-coordinate by 3 and the y-coordinate by 5.

We switch the point's x- and y-coordinates in order to reflect the generated image across the line y = x. Finally, the rule is:

(x, y) → (y - 5, x + 3)

This entails switching the x- and y-coordinates of the translated point, followed by a 3 unit rightward and a 5 unit downward translation.

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Answer:

Carson earns $21 for each hour of yard work. After doing a total of 2 hours of yard work, how much money will Carson have earned?

42 Dollars is the correct Answer!

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Happy Labor day!