37. A juice pitcher holds 1.5 gallons of liquid. How many 8-ounce glasses of juice can be poured from a full pitcher? (1 gallon 128 ounces) Explain your answer by writing or describing the steps you used to solve the problem.

To solve this problem, what we have to do is to calculate for the z scores of each condition then find the probability using the standard normal probability tables for z.

The formula for z score is:

z = (x – u) / s

where,

x = sample value

u = sample mean = 23 days

s = standard deviation = 1 day

A. P when x < 21 days

z = (21 – 23) / 1

z = -2

Using the table,

P = 0.0228

Therefore there is a 2.28% probability that the hatching period is less than 21 days.

B. P when 23 ≥ x ≥ 22

z (x=22) = (22 – 23)  / 1 = -1

P (z=-1) = 0.1587

z (x=23) = (23 – 23) / 1 = 0

P (z=0) = 0.5

P = 0.5 - 0.1587 = 0.3413

Therefore there is a 34.13% probability that the hatching period is between 22 and 23 days.

C. P when x > 25

z = (25 – 23) / 1

z = 2

P = 0.9772

This is not yet the answer since this probability refers to the left of z. Therefore the correct probability is:

P true = 1 – 0.9772

P true = 0.0228

Therefore there is a 2.28% probability that the hatching period is more than 25 days.

The initial value of a function is the value of the function when x = 0

 o when x = 0, y = 2 so the initial value is 2

Answer:

2

Step-by-step explanation:

The initial value is what you start off with, so it is 2! :)

Answer:

∠TSR = 93°

Step-by-step explanation:

In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]

∠S = [tex]\frac{131+43}{2}[/tex]

     = [tex]\frac{174}{2}[/tex]

     = 87°

Now we have to find the measure of ∠RST

Since ∠QSR + ∠TSR = 180° [ supplementary angles]

87° + ∠TSR = 180°

∠TSR = 180 - 87 = 93°

Therefore, m∠TSR = 93° is the answer.

Final answer:

The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.

Explanation:

The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.

Now, subtract the smallest value from the largest value to determine the range:

Range = Largest value – Smallest value

Range = 182 cm – 132 cm

Range = 50 cm

Therefore, the range of the given set of heights is 50 cm.

Answer:

216

Step-by-step explanation:

i think

To answer this question you will have to combine like terms.

3z-5+2z=25-5z

Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z

Now you have -5+5z=25-5z

Now you will go ahead and distribute since you can't combine anymore on certain sides.

You can add 5 to 25 on the other side: 25+5=30

Then add 5z to 5z on the other side: 5z+5z=10z

So now your equation should look like this: 10z=30

From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3

So your solution should come to: z=3

Answer:

B

Step-by-step explanation:

Edg 2020

Answer:

Step-by-step explanation: Answer B

If

N = a (mod 10)

N = b (mod 13)

gcd(10,13) = 1

then

N = 10 bx + 13 ay (mod 130)

Where

10x + 13y = 1

-> (10x + 13) (mod 2) = 1 (mod 2)

-> y (mod 2) = 1

y = -3, x = 4

-> N = 40b – 39a (mod 130)

It is given that  ra + sb should be non-negative:

N = 40b – 39a (mod 130)

N = 40b + (130 – 39)a (mod 130)

N = 40b + 91a (mod 130)

Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).

Final answer:

To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.

Explanation:

To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:

n = 10k + a, where k is some integer

n = 13l + b, where l is some integer

Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.

Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

[tex]\frac{r^9}{r^3}[/tex]

According to the property of exponent,

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Using this property of exponent, we get

[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]

[tex]\frac{r^9}{r^3}=r^{6}[/tex]

The expression [tex]r^{6}[/tex] is equivalent to the given expression.

Therefore the correct option is B.

You can rearrange formulas to highlight a specific quantity of interest by identifying it and isolating it using inverse operations.

In mathematics, you can rearrange formulas to highlight a specific quantity of interest using the same reasoning as in solving equations. The goal is to isolate the variable or the quantity you want to highlight on one side of the formula. Here are the steps to do it:

Identify the quantity of interest you want to highlight.

Apply inverse operations to isolate that quantity on one side of the equation/formula.

Simplify or solve for the highlighted quantity if needed.

For example, if you have the formula for the area of a rectangle, A = L * W, and you want to solve for the length of the rectangle, you can rearrange the formula as L = A / W, highlighting the length as the quantity of interest.

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Equations:
8c + 4t = 45
3c + 2t = 20

Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40

Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)

Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20

2t=12.50

T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)

 Table = 6.25 each

Chair = 2.50 each

Check:

3(2.50) + 2(6.25) =

7.50 +12.50 = 20

8(2.50) + 4(6.25) =

20.00 + 25.00 = 45.00

Answer:

[tex](2+x)+3y[/tex]

Step-by-step explanation:

In associative property , when we add the numbers we can group the numbers in any combination.

for example : [tex]a+(b+c)= (a+b)+c[/tex]

[tex]2 + (x + 3y)[/tex] can be written as [tex](2+x)+3y[/tex] using associative property.

The terms can be grouped in any combination

[tex](2+x)+3y[/tex]

The probability is 0.1  (or 10%).

It is required to find  the probability.

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes.

Given that:

The favorable count is determined as follows: considering Green marbles. There are 7 of them in the box, so 7 possible picks at the first draw.

Since you don't replace the pick, at the next drawing there are only 6 Green ones. So for each of the 7 possible first picks, there are 6 possible second picks: number of possibilities is 7 by 6 = 42.

The total number of possible drawings, irrespective of color is determined as follows: there are 21 marbles in total at first drawing, and 20 at second. So, for each first pick there are 20 possibilities, i.e., total number is 21 by 20 = 420

The probability is P = 42 / 420 = 1 / 10 = 0.1  (or 10%)

So, the probability is 0.1  (or 10%).

Learn more about probability here:

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