A scientist mixes water (containing no salt) with a solution that contains 20% salt. she wants to obtain 120 ounces of the mixture that is 15 % salt. How many ounces of water and how many ounces of the 20% salt solution should she use?

Part (a)

Answer: Constant of proportionality = 5/8

Reason:

The general template equation is y = kx where k is the constant of proportionality. It is the slope of the line.

The direct proportion line must pass through the origin. In other words, the y intercept must be zero.

=====================================

Part (b)

Answer: Not Proportional

Reason:

The y intercept isn't zero.

Plug x = 0 into the equation to find y = 1 is the y intercept. This graph does not pass through the origin.

Answer:

x≤20

Step-by-step explanation:

x+5≤25

 -5.  -5

x≤20

Hopes this helps please mark brainliest

Answer:

The answer is B

Step-by-step explanation:

20+5=25 and x can be greater than or equal to 25

         Ensuring that each person has an equal chance to maximize their potential is what equality is all about.

Proof: Given that A = B and B = C, we can infer that A = C according to the transitive principle. A = C and C = D are both true if we also know that C = D. We shall ultimately get at A = D after one more transitive property application.

The symmetrical attribute of equality

This fact, which states that if  

18 + 10 =28,

then

28 = 10 + 18,

Serves as an example of the equality's symmetric property. The symmetric property of equality in mathematics is actually fairly straightforward. According to this principle, if a = b, then b =a.

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Answer:

just go with your heart

\(perimeter = 17 + 19 + 7 + 11 + 10 + 8 \\ \)

\(perimeter = 72 \: \: cm\)

Answer:

55

Step-by-step explanation:

You just need to divide 220 ÷ 4 = 55

Hope this helps :)

Pls brainliest...

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

Step-by-step explanation:

Answer:

hi!

Step-by-step explanation:

Answer:

1119744

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out expression

\(\frac{6^{14}}{(2^5)(3^7)}\)

Step 2: Evaluate exponents

6¹⁴ = 78365164096

2⁵ = 32

3⁷ = 2187

Step 3: Replace

\(\frac{78364164096}{32(2187)}\)

Step 4: Multiply

\(\frac{78364164096}{69984}\)

Step 5: Divide

1119744

In an equilateral triangle, each angle of 60 degrees. Then the value of x is 20.8 units, then the correct option is B.

Trigonometry deals with the relationship between the sides and angles of a triangle.

The triangle ΔDEF is an equilateral triangle.

Then each angle is 60 degrees.

Then by the sine rule, we have

\(x = 24 \times \sin 60^o \\\\x = 24 \times 0.866\\\\x = 20.78\approx 20.8\)

The value of x is 20.8 units.

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Answer:

0.273

Step-by-step explanation:

Can you please give me brainliest?

Answer:

3/11 written as a decimal would be 0.2727 which would then be 0.273.

Step-by-step explanation:

Hope this was helpful. Have a good day.

Answer:

72.

Step-by-step explanation:

Given a group of 6, 9 and 12.

We are to determine the least number of patties that will be shared equally among the groups.

This we do by determine the Least common multiple of the three numbers.

\(6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72\)

Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.

we have that

the probability is equal to

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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Answer:

should be 2.24. I am sorry if I am wrong

Step-by-step explanation:

31.36÷14=2.24

Answer:

2:1

Step-by-step explanation:

Think of ratios like fractions.

8:4 is a ratio.

If you turn that ratio into a fraction, it will be ---> 8/4

Now, simplify 8/4.

The numerator and denominator share a greatest common factor of 4.

Divide 8 and 4 by 4, which makes the fraction: 2/1

Finally, to put your answer as a ratio again, 2/1 equals to 2:1

You have the following equation:

1) -4(x - 24) + 1/2(x + 4) = x + 15

in order to solve for x the previous equation, proceed as follow:

-4(x - 24) + 1/2(x + 4) = x + 15 multiply by 2 both sides

-8(x - 24) + (x + 4) = 2x + 30 apply distribution property

-8x + 192 + x + 4 = 2x + 30 simplify like terms both sides

-7x + 196 = 2x + 30 subtract 2x and subtract 196 bot sides

-7x - 2x = 30 - 196

-9x = -166 divide by -9 both sides

x = -166/(-9)

x = 18.44

2)

12(x + 2) - 4x = 4(2x + 11) - 20 apply distribution property

12x + 24 - 4x = 8x + 44 - 20

8x + 24 = 8x + 24

0 = 0

In this case, you have infinite solutions

The correct option regarding the transformations of the functions is given as follows:

B. For f(kx), there will be a vertical stretch by a factor of 1/k. For kf(x),there will be a vertical compression by a factor of k.

The stretching and compression can be either horizontal or vertical, as follows:

The constant k is the factor of the stretch or of the compression. In this problem, the constant assumes values with an absolute value less than 1, hence:

Hence the correct option regarding the transformations is given by option b.

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Answer:

115

Step-by-step explanation:

The opposite angles (115degree angle and angle 4) are equal.

Angle 3=65

Angle 4=115

Angle 5=115

Angle 6=65

Angle 7=65

Angle 8=115

Brainliest please~

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

It must be number 2.

1 and 3 number is wrong as parallelogram don't need have right angle

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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The angles COA and POC are 22.5 and 67.5 degrees respectively as POA is a right angled triangle.

POA is a right angle so it is 90 degrees.

POC +COA = 90  .....(1)

Also, POC is 3 times as large as COA.

Let's take COA, "x"

POC = 3x

Substituting the values in equation (1) as follows:

x + 3x = 90

4x = 90

x= 22.5

Therefore,

COA = 22.5°

POC = 22.5*3 = 67.5°

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Answer:35.09

Step-by-step explanation:From the question given above, the following data were:Opposite = 12Hypothenus = X Angle θ = 20 °

Answer:

T' (-3,5)

U' (-4,3)

V' (-1,2)

Answer:

Option (1)

Step-by-step explanation:

Each cake requires cups of milk = \(1\frac{1}{2}\) cups ≈ 1.5 cups

6 cakes will require milk = 6 × 1.5

                                         = 9 cups

Anne has milk = 5 pints

∵ 1 pint = 2 cups

∴ 5 pints = 10 cups

Therefore, Anne has milk = 10 cups

Extra amount of milk Anne has = 10 - 9 = 1 cup

Hence, Answer is yes, she has enough milk. She will have 1 extra cup of milk.

Option 1 will be the answer.

Answer:

3rd option

Step-by-step explanation:

One of our exponent rules tells us that \((\frac{x}{y} )^{z}\) =  \(\frac{x^{z} }{y^{z} }\). So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?

We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.

Let me know if you have any questions!

The answer can be seen on the attachment that I have given.

The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.

Given :

The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:

x = 60 - 2(y + z)  --- (1)

The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:

x = 2z + 20  --- (2)

Therefore, the correct option is A) and E).

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