If 52 is added to a number, it will be
3 times as large as it was originally. Find the number

In order to solve these problems, we will use the standard normal distribution and convert the given values to z-scores using the formula:

In order to solve these problems, we will use the standard normal distribution and convert the given values to z-scores using the formula:

z = (x - mu) / sigma

where x is the observed value, mu is the mean, and sigma is the standard deviation.

a. Highest 30 percent:

To find the weight corresponding to the highest 30 percent, we need to find the z-score that corresponds to the 70th percentile (100% - 30% = 70%). Using a standard normal distribution table or Excel function, we find that the z-score corresponding to the 70th percentile is approximately 0.52. Therefore, we can solve for x:

0.52 = (x - 395) / 22

x - 395 = 11.44

x = 406.44

Therefore, the weight that corresponds to the highest 30 percent is approximately 406.44 grams.

To find the weight range corresponding to the middle 70 percent, we need to find the z-scores that correspond to the 15th and 85th percentiles. Using a standard normal distribution table or Excel function, we find that the z-scores are approximately -1.04 and 1.04, respectively. Therefore, we can solve for x1 and x2:

-1.04 = (x1 - 395) / 22

x1 = 371.72

1.04 = (x2 - 395) / 22

x2 = 418.28

Therefore, the weight range that corresponds to the middle 70 percent is approximately 371.72 to 418.28 grams.

To find the weight corresponding to the highest 90 percent, we need to find the z-score that corresponds to the 10th percentile (100% - 90% = 10%). Using a standard normal distribution table or Excel function, we find that the z-score corresponding to the 10th percentile is approximately -1.28. Therefore, we can solve for x:

-1.28 = (x - 395) / 22

x - 395 = -28.16

x = 366.84

Therefore, the weight that corresponds to the highest 90 percent is approximately 366.84 grams.

To find the weight corresponding to the lowest 20 percent, we need to find the z-score that corresponds to the 20th percentile. Using a standard normal distribution table or Excel function, we find that the z-score corresponding to the 20th percentile is approximately -0.84. Therefore, we can solve for x:

0.84 = (x - 395) / 22

x - 395 = -18.48

x = 376.52

Therefore, the weight that corresponds to the lowest 20 percent is approximately 376.52 grams.

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The equation to compute José's age (j) given Mario's age (m) is y = m + 7.

An equation is a mathematical statement that claims that two mathematical expressions are equal or equivalent in value.

Equations are written with the equation symbol (=) to confirm the equality of two mathematical expressions or values.

José's age (years)  j        10    11    12    13

Mario's age (years) m      3     4     5     6

Common difference        7     7      7     7

Thus, using the common difference between José's age and Mario's age as 7, we can write the equation for computing José's age given Mario's age as y = m + 7.

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Answer:

j=m+7

Step-by-step explanation:

Answer:

11331 non fiction books

Step-by-step explanation:

Given :

Total books = 67982

Childrens section = 1/3 of total

Number of children's books :

(1/3 * 67982) = 22660 books (approximately)

Books left :

67982 - 22660 = 45,322 books

Fiction books:

75% of remaining

0.75 * 45322

33991.5

= 33991 books

If the only section left is non - fiction, then

Non - fiction books = (45322 - 33991) = 11331

Answer:

D

Step-by-step explanation:

For the graphed function the domain is D: (-∞, 4] and the range is R: [0, ∞)

For any function y = f(x), we define the domain as the set of the inputs (that is, the set of the possible values of x) and the range as the set of the outputs (possible values of y).

To identify the domain, we need to look at the horizontal axis.

We can see that the maximum value of x is x = 4, and there is no minimum value (there is an arrow that points to the right) then the domain is:

D: (-∞, 4]

For the range, we look at the vertical axis, and we can see a minimum at y = 0 and that it goes upwards (so there is no maximum) then the range is:

R: [0, ∞)

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The mass per cup for the objects will be 320g and 272g respectively.

Mass simply means the weight that an object contains.

The mass of a teapot and 4 cups is 1,280 grams. The mass per cup will be:

= Mass / Number of cups

= 1280 / 4

= 320g

The mass of the same teapot and 10 cups is 2,720 grams. The mass per cup will be:

= 2720 / 10

= 272g

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Answer:

w - 7.4 ≥ 11

Step-by-step explanation:

If it's no less than, then it has has to be greater than or equal to

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

–x² + 12x + 5

Step-by-step explanation:

x² + 3x

–2x² + 9x + 5

The sum of the above expression can be obtained as follow:

.... x² + 3x

+ –2x² + 9x + 5

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

–x² + 12x + 5

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Thus, the sum of x² + 3x and –2x² + 9x + 5 is –x² + 12x + 5

The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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Answer:

D. 118°

Step-by-step explanation:

90 + 28 = 118

good luck, i hope this helps :)

Answer:

D

Step-by-step explanation:

give them brain, they're correct.

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

The magnitude of the vector is 9.165 and it's direction is 40.6°

Step-by-step explanation:

A vector quantity is a quantity that has both size (magnitude) and direction. Examples of vector quantities are force, velocity and impulse.

Magnitude of vector v is given by

|v| = √6²+7²

= √36+49

= √84

= 9.165

Direction of vector v is obtained by:

\( \tan( \theta) = \frac{x}{y} \)

\(\theta = {tan}^{ - 1} ( \frac{6}{7}) \)

\(\theta = {40.6°}\)

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Answer:

Increase by 10% of students that bought lunch.

Step-by-step explanation:

I think the percent change was by 10%. Because 10% of those students who packed lunched on Monday did not pack lunch on Tuesday, and assuming that they either buy or pack it that means that 10% more students bought lunch.

Answer:A school bus provides a safe way of transportation for your child. Learn resources to talk to your child about school bus and bus stop safety.

Step-by-step explanation:

Answer:

\(\huge \boxed{\mathrm{\$ \ 7,533.33}}\)

Step-by-step explanation:

There are 12 months in one whole year.

In one year, the person earns $96,600 with bonus.

The person gets a bonus of $6,200 during Christmas.

96,600 - 6,200 = 90,400

The person earns $90,400 yearly.

\(\frac{90,400}{12}\) = 7,533.3333

Each month, the person earns $7,533.33, to the nearest cent.

the answer is 2

Solution:

32⅕

(2⁵)⅕

Answer is 2

Answer:The answer is no they are slower by 20%

Step-by-step explanation:divide 12 by 5 then divid the answer of 12 by 5 by 2 then you get the answer of 20%

Answer:

I think its B but I'm not 100% sure

Answer:

Its 20 buckets.

Step-by-step explanation:

2r+r+s+2s =2×r + r×1 + s×1 + 2×s

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

2r+r+s+2s

=2×r + r×1 + s×1 + 2×s

Hence,

each sum as the product of two factors 2r+r+s+2s =2×r + r×1 + s×1 + 2×s

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The point (1,0) is a solution to the system of linear equations.

What is a linear system of equations?

A system of linear equations consists of two or further equations made up of two or further variables similar that all equations in the system are considered contemporaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

We are given a system of linear equations i.e. y = -x + 1 and 3x - y = 3.

In order to check that which point is a solution to the system of linear equations, we need to put the values in the given system.

1. (3/2 , -1/2)

Here, x = 3/2 and y = -1/2

Putting these values in the equations, we get

y = -x + 1

1/2= -3/2+1

1/2=1/2

3x - y = 3

3(3/2)-(-1/2) ≠ 3

9/2+1/2 ≠ 3

5 ≠ 3

Thus, it is not a solution to the system of linear equations.

2. (1 , 0)

Here, x = 1 and y = 0

Putting these values in the equations, we get

y = -x + 1

0= -1+1

0=0

3x - y = 3

3(1)-(0) = 3

3=3

Thus, it is a solution to the system of linear equations.

3. (-1/2, 3/2)

Here, x = -1/2  and y = 3/2

Putting these values in the equations, we get

y = -x + 1

3/2= -(-1/2)+1

3/2=1/2+1

3/2=3/2

3x - y = 3

3(-1/2)-(3/2) ≠ 3

-3/2-3/2 ≠ 3

-3 ≠ 3

Thus, it is not a solution to the system of linear equations.

4. (0, 1)

Here, x = 0  and y = 1

Putting these values in the equations, we get

y = -x + 1

1= -0+1

1=1

3x - y = 3

3(0)-(1) ≠ 3

0-1 ≠ 3

-1 ≠ 3

Thus, it is not a solution to the system of linear equations.

Hence, the point (1,0) is a solution to the system of linear equations.

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Answer:

False

Step-by-step explanation:

Sorry for the lat reply hopefully you still have that question ready. But basically in order for these equations to be considered inverses of one another it has to map its domain value and switch it to the range value and in this case it does not match the inverse when graphed.

6 and 1/2 minus 5 and 3/4 mathematically is equivalent to 3/4 .

Given, 6 and 1/2 minus 5 and 3/4 .

Solve for:

1. First off, convert both of these mixed number fractions into improper fractions.

6 and 1/2 minus 5 and 3/4

= \(\frac{13}{2} - \frac{23}{4}\)

2. Find a common denominator

Multiply the numerator and denominator of the first fraction both by 2.

= \(\frac{13}{2} - \frac{23}{4}\)

=\(\frac{26}{4} - \frac{23}{4}\)

3. Subtract the fractions.

= \(\frac{26}{4} - \frac{23}{4}\)

= \(\frac{3}{4}\)

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Answer:

y intercept = 30

slope = 40

four points on the line would include..

(0, 30)

(1, 70)

(3, 150)

Step-by-step explanation:

y = mx + b

Answer:

Slope = ½

Step-by-step explanation:

Find the slope using two points on the line, (-4, 0) and (0, 2):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (-4)} = \frac{2}{4} = \frac{1}{2} \)

Slope (m) = ½

Answer:

x = 36 degrees

Step-by-step explanation:

The sum of a triangle's interior angles is 180 degrees.

We know that 2 of the angles measure 90 degrees (right angle) and 54 degrees. Add those together and you get 144. Now all you have to do is subtract 144 from 180 to get

36 degrees.

180 - 90 - 54 = x

Answer:

36

Step-by-step explanation:

The conner shows a thin square. That means it is a 90-degree angle. You know that x is going to be smaller than the 54- degree angle and 90-degree angle. So the angle x will be a smaller number. You would need to subtract 90 from 54. Therefore the answer is 36.

a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)

b. The increase in cost between 12 noon and 3 pm is $2.

c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.

The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.

We can represent it as (8am, 9am) U (11am, 12pm).

It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).

And stays constant at : (9am, 10am) U (10am, 11am)

We simply deduct the 12pm's cost from 3pm's cost.

So, we have

Cost increase = $3.5 - $1.5

Evaluate the difference

Cost increase = $2

Hence, the cost increase is $2

When you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)

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A relation that has more than one output of each input. That is not a function. A function only has one output of each input. Function a and function b are linear functions. Function a is represented by the table values. function b is represented by the equation y=3x+4.

Domain, is a term that is used to measure the independent variable’s values. Also known as the “x” values. It tells you what values of “x” are applicable in the function. What values will satisfy the function.

Range, is a term used to measure the dependent variable’s values. Also known as the “y” values. It tells you what values of why does the graph of the function extends till.

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