Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?

Answer: The answer is D.

Step-by-step explanation: Because I use a graphing calculator

When the fraction n/12 is between 1/4 and 2/3, the possible values of n will be 4, 5, 6, and 7.

It should be noted that a fraction simply means a number that isn't whole. It can be illustrated as a/b where a is the numerator and b is the denominator.

It should be noted that 1/4 is equivalent to 3/12.

It should be noted that 2/3 is equivalent to 8/12.

Therefore, the values of n will be numbers between 3 and 8. They are 4, 5, 6, and 7.

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The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.

If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.

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Answer: 20 is the answer

Step-by-step explanation:

Answer: 20 students

Step-by-step explanation

40% of 20 can be written as 40% × 20.

= 40/100 × 20

= 8

After conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.

So, pounds of Almonds Lisa purchased:

Now, calculate the pounds of almonds Lisa purchased as follows:

(Refer to the image attached below for calculation)

Therefore, after conducting some mathematical operations, we conclude that Lisa purchased 7 pounds of almonds.

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The correct question is given below:

Lisa purchased almonds for $3.50 per pound. She spent a total of $24.50. How many pounds of almonds did she purchase?

A cash flow statement is divided into three sections: operating activities, investments, and financial activities.

The net balance of money coming into and going out of a business at a particular period is referred to as cash flow. A firm constantly receives and expends cash. For instance, when a retailer buys merchandise, money leaves the company and goes to its suppliers.

According to question:

A cash flow statement is divided into three sections: operating activities, investments, and financial activities.

Operating activities: Cash flow activities that either produce income or keep track of the funds used to produce a good or service are referred to as operating activities. Inventory transactions, interest and tax payments, employee paychecks, and rent payments are all examples of operational business activity. This section does not cover any additional sources of cash flow, such as investments, debts, or dividends.

Investment activities: The cash flow statement's second column lists profits and losses resulting from investments in assets like property, plant, or equipment (PPE), demonstrating how the company's overall cash position has changed. Analysts look for changes on a cash flow statement when they want to determine the company's investment in PPE.

Financial activities: The cash flow between the company's owners and creditors is tracked in the third section of the cash flow statement. Transactions involving debt, stock, and dividends are all considered financial operations. In these transactions, the receipt of capital (from lenders or investors, for example) triggers the recording of incoming cash, and the payment of dividends triggers the recording of outgoing cash.

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Okay, here we have this:

Considering the provided information, we are going to analize whether it is better to use a sample or the population in the proposed situation, so we obtain the following:

To know the most popular song in an entire country, it is necessary to use the entire population, since the result of the favorite song if only one sample is used will not give results with certainty, considering that the population that is not covered could generate changes in the result.

The variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.

It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

P(male) = 45% = 0.45

P(female) = 55% = 0.55

Variance = SD²

Variance  = nP(male)xP(male)

Variance  = 30x0.45x0.55

Variance = 7.42

Thus, the variance of the number of male students is 7.42 if the university has 10,000 students of which 45% are male and 55% are female.

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We can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.

So, first, we need to find the LCM of all the denominators:

Now, the fractions will be:

So, ascending to descending order will be:

Therefore, we can conclude that the ascending to descending order of the given fractions are, 7/5, 3/2, 11/4, 15/4, and 13/3.

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Answer:

$45

Step-by-step explanation:

Charles meets with customers on a daily basis. He uses the function f(x) = 5| x - 8| + 20 to calculate how many dollars he charges, per hour, for his time. How much does Charles charge per hour if a customer hires him for 3 hours?

f(x) = 5| x - 8| + 20

solve for when x = 3

f(3) = 5| 3 - 8| + 20

f(3) = 5| -5| + 20

f(3) = 25 + 20

f(3) = 45

By using the method subtraction, the indicated Z score the graph depicts IS 0.30501

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1 and it is given by the probability density function and distribution function

Areas of the normal distribution are often represented by tables of the standard normal distribution.

Shaded area is 0.80501 according to the attachment. Then the lookup area is

Find the indicated z score.

z=x-μ/ σ

where Z is the value on the standard normal distribution, X is the value on the original distribution, μ is the mean of the original distribution, and σ is the standard deviation of the original distribution.

According to the picture below z is

z=0.80501- 0.5/1 = 0.30501

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Answer:

324

Step-by-step explanation:

20%-> 0.2

0.2(270)= 54

270+54=324

Answer:The answer is 324

Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer

The value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.

How to round off any decimal number to one decimal place?

When you round to the first decimal place, or to the nearest tenth, the number in the hundredth point place will determine whether you round up or down. If the hundredths digit is a number between 5 and 9, round up to the nearest whole number. If it's a number between 0 and 4, you would "round down" by keeping the tenths place the same.

We have 30/cos40°

Value of 30/cos40° = 30/0.766044 = 39.162241 (cos40° = 0.766044)

Since the number in the hundredths place is 6, which is between 5 and 9, we would round the tenth decimal point up to 2.

Therefore, the value of 30/cos40° rounded to 1 d.p. (decimal point) is 39.2.  

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Answer:

x = 5, y = 13

Step-by-step explanation:

Solve for x:
42 = 8x + 2

40 = 8x

x = 5

This is solved using the alternate interior angles theorem, which states that alternate interior angles (in this case, the 42-degrees and 8x + 2 degree angles) are the same.

Solve for y:

180 = 42 + 6(2y - 3)

180 = 42 + 12y - 18

180 = 24 + 12y

156 = 12y

y = 13

This is solved using the same-side interior angles theorem, which states that same-side interior angles (in this case, the 42-degrees and 6(2y-3)-degree angles) add up to 180 degrees.

Answer:

E' will be at (2, -6)

Step-by-step explanation:

Here we are given point E at (2, 6).

A reflection over the x-axis will keep the x coordinate the same while changing the y value to become the additive inverse (the number in which adding to the current value will get you zero). In this case, it is -6.

E (2,6) --> E' (2, -6)

Another way of thinking of it is reflecting on the x-axis while change the value from (x, y) to (x, -y).

The coordinates of D' are (4,0)

A Trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.

The coordinates of the given trapezoid are:

A = (-6,2)

B = (-5,4)

C = (-2,4)

D = (1,2)

It is given that the trapezoid is moved to the points of (x+3, y-2) on the graph.

Now, consider A = (-6,2)

A' = (-6+3, 2-2)

A' = (-3,0)

Consider B = (-5,4)

B' = (-5+3, 4-2)  

B' = (-2,2)

Consider C = (-2,4)

C' = (-2+3, 4-2)  

C' = (1,2)

Consider D = (1,2)

D' = (1+3, 2-2)  

D' = (4,0)

Therefore, D' has the coordinates (4,0)

Refer to the full question given in the following image.

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The area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.

What is area?

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Area of a square is side × side.

Let the area of Desert A = x square miles

and the area of Desert B = y square miles

Given that, the area of Desert A is five times the area of Desert B,

i.e. x = 5y                         ...(1)

and the sum of their areas is 600,000 square miles,

i.e.  x + y = 600,000  square miles                  ...(2)

Putting equation (1) in (2), we get

         5y + y = 600,000

or        6y = 600,000  or      y =  100,000  square miles

Using equation (1),

  x = 5 × 100,000 = 500,000  square miles

Hence, the area of Desert A is 500,000 square miles and the area of Desert B is 100,000 square miles.

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The equation of the line in slope intercept form is y = -5 / 9x + 2 / 9

The slope intercept form of the equation of a line  can be represented as follows:

y = mx + b

where

Let's find the slope using the points (4, -2)(-5, 3)

Hence,

m = y₂ - y₁ / x₂ - x₁

x₁ = 4

x₂ = -5

y₁ = - 2

y₂ = 3

m = 3 + 2 / -5 - 4

m = 5 / -9

m = - 5 / 9

Therefore, let's find the y-intercept using (4, -2).

-2 = - 5 / 9 (4) + b

-2 = - 20 / 9 + b

b = -2 + 20 / 9

b =  -18 + 20/  9

b = 2 / 9

Therefore, the equation is y = -5 / 9x + 2 / 9

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The best estimate for the pigeon population is 540.

Finding an estimate or approximation—a value that may be used for a purpose despite the possibility of incomplete, ambiguous, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.

Counting a small sample of something and extrapolating that number to a wider population is how estimation is frequently done. Calculating how many sweets of a certain size are contained in a glass jar is an example of estimation.

380 x 27/19

= 540

So the answer is

540

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Answer:

5 degree Celsius

Explanation:

Using the formula for conversion included in the image attached, we have:

Therefore, 41 degrees Fahrenheit is equivalent to 5 degrees Celsius

Answer:

x = 10

The interior angles measure 93°, 126°, 60°, and 81°.

Step-by-step explanation:

[tex]9x + 3 + 12x + 6 + 6x + 8x + 1 = 360[/tex]

[tex]35x + 10 = 360[/tex]

[tex]35x = 350[/tex]

[tex]x = 10[/tex]

9(10) + 3 = 90 + 3 = 93°

12(10) + 6 = 120 + 6 = 126°

6(10) = 60°

8(10) + 1 = 80 + 1 = 81°

Given the rigth triangle, you have to determine the length of the missing side marked with an x.

To do so you have to apply the trigonometric functions, these are calculated as:

Where

θ is one of the inner angles of the triangle.

"opposite" indicates the opposite side to than angle

"adjacent" is the side in contact or next to the angle

and "hypotenuse" is the longest side of the triangle.

In this exercise we know the measure of the angle and the hypotenuse, the trigonometric function you have to use to determine the length of "x" is the Sine:

Replace with:=46º

hypotenuse=14

opposite=x

Correct option is b. 10.1

The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.

Let l = distance further away at which they'll meet. This will be illustrated as:

l = ✓13² - ✓5²

= ✓169 - 25

= ✓144

= 13m

Assuming that each bus drives a constant 55mph. The passes towards each other will be:

= -(55 + 55)

= -110m/h

Therefore, h² + l² = b².

Differentiate

2hdh/dt + 2ldl/dt = 2bdb/dt

= 2 × 5 × 0+ 2 × 12 (-110)

= 3 × 13db/dt

= -101.54 m/h

The rate is 101.54 m/h.

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The surface area of the triangular prism is 224 square units.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area. The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given Data

Surface area = ( S₁ + S₂ + S₃) × Length

S₁ = 6

S₂= 8

S₃ = 2

L = 14

Surface area = ( 6+8+2)14

Surface area = 16(14)

Surface area = 224

The surface area of the triangular prism is 224 square units.

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Answer:

  x = 8

Step-by-step explanation:

You want to know the value of x in an expression for an angle measure at parallel lines.

Where at transversal crosses parallel lines, all acute angles created are congruent, all obtuse angles created are congruent, and the acute angles are supplementary to the obtuse angles.

The angle marked 83° is acute. The angle marked (12x+1)° is obtuse, so these angles are supplementary:
  83° +(12x +1)° = 180°

  12x +84 = 180 . . . . . . . divide by ° and simplify

  12x = 96 . . . . . . . . . . subtract 84

  x = 8 . . . . . . . . . . . . divide by 12

The value of x is 8.

The integers that are in order from least to greatest will be C. -13, -2, 6, 20.

It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.

In this case, the numbers will be illustrated as thus:

The smallest number is -13.

The biggest number is 20.

Therefore, the arrangement is -13, -2, 6, 20.

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$17.85

Explanation

you can easily solve this by using a rule of three.

Let

x represents the maximum vale

then

if

Step 2

the proportion is the same, so