Ms. Maynard grates 23/30 of a block of cheese. Mr. Connor then eats another 3/30 of the cheese. What fraction of the cheese is left over?

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

Explanation:

x = number of cups

y = total height

We have these ordered pairs

(x1,y1) = (2,16)

(x2,y2) = (4,20)

Let's find the slope of the line through those points.

[tex](x_1,y_1) = (2,16) \text{ and } (x_2,y_2) = (4,20)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{20 - 16}{4 - 2}\\\\m = \frac{4}{2}\\\\m = 2\\\\[/tex]

A slope of 2, aka 2/1, means each time x goes up by 1, the y value goes up by 2.

It means each time we add a cup, the total height goes up by 2 cm.

This isn't the final answer, but it helps get us there.

------------

We'll then use point-slope form to determine the equation.

[tex]y-y_1 = m(x - x_1)\\\\y-16 = 2(x - 2)\\\\y = 2(x - 2)+16\\\\y = 2x - 4+16\\\\y = 2x + 12\\\\[/tex]

The last step is to plug x = 1 into that equation to determine the height of 1 cup.

So,

[tex]y = 2x + 12\\\\y = 2*1 + 12\\\\y = 2 + 12\\\\y = 14\\\\[/tex]

We have x = 1 cup lead to a total height of y = 14 cm.

The final answer is 14 cm.

-----------------

Notice that adding on 2 cm (the slope) gets us to 14+2 = 16 cm which is the height of two cups stacked together. A lot of the 2nd cup's height is part of the 1st cup's height. Only the 2 cm at the top is going to be added.

We could see that if we used x = 2.

[tex]y = 2x + 12\\\\y = 2*2 + 12\\\\y = 4 + 12\\\\y = 16\\\\[/tex]

That confirms the left-most part of the diagram.

Now try x = 4.

[tex]y = 2x + 12\\\\y = 2*4 + 12\\\\y = 8 + 12\\\\y = 20\\\\[/tex]

That works as well. It helps confirm we have the correct equation, and also confirms the final answer is correct. Another way to confirm is to either graph or use a table.

If you wanted to find the height of 8 cups, then,

[tex]y = 2x + 12\\\\y = 2*8 + 12\\\\y = 16 + 12\\\\y = 28\\\\[/tex]

The chart has been completed and the information has been given below:

Annually $9200 6% 15 9200(1+0.06)15 $22084.34

Semi-Annually $9200 6/2 = 3% 15*2 = 30 9200(1+0.03)30 $22330.81

Quaterly $9200 6/4 = 1.5% 15*4 = 60 9200(1+0.015)​​​​​60 $22477.62

Monthly $9200 6/(12*15) = 1/30 %

15*12*15 = 2700

9200(1+1/(30*100))2700

$22624.96

Weekly $9200 6/(15*52) = 1/130 15*52*15 = 11700

9200(1+1/(130*100))11700

$22627.57

Daily $9200 6/(15*365) = 2/1825

15*365*15 = 82125

9200(1+2/(1825*100))82125

$22628.24

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Answer:

10

Step-by-step explanation:

according to the formula of y = P(1-r)^x, P is the initial value, and in this case it looks like it is 10 :)

Answer:

14x14= 196

Step-by-step explanation:

196cm^2

Answer:

56cm²

Step-by-step explanation:

If its a square, all sides are the same.

A = 14 x 4 = 56cm²

Answer:

107 degrees

Step-by-step explanation:

since the two angles are on a straight line, and a straight line is 180 degrees,
180-73=x

x=107

 The value of the investment after 3.5 years is $ 2000.

What is the interest rate?

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

Here, we have

Given: if $2000 is invested at 4% interest compounded monthly, the value of the investment after t years is given by 2000(12.04/12)¹²ⁿ.

We have to find the value of the investment after 3.5 years.

= 2000(12.04/12)¹²ⁿ

n = 3.5

= 2000(12.04/12)¹²⁽³°⁵⁾

= = 2000(12.04/12)⁴²

= 2000(1)

= $ 2000

Hence,  the value of the investment after 3.5 years is $ 2000.

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We can start by using the formula for the mean (average):

Mean = (sum of numbers) / (number of numbers)

We are given that the mean of 3, 15, and another number is 40, so we can set up an equation:

40 = (3 + 15 + x) / 3

Multiplying both sides by 3 yields:

120 = 3 + 15 + x

Simplifying this equation gives:

102 = x

Therefore, the missing number is 102.

The minimum sample size required for the estimate, considering the z-distribution, is given as follows:

560.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is modeled as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

The parameters for this problem are given as follows:

[tex]M = 0.16, \sigma = \sqrt{5.29} = 2.3, z = 1.645[/tex]

Hence the sample size is obtained as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.16 = 1.645\frac{2.3}{\sqrt{n}}[/tex]

[tex]0.16\sqrt{n} = 1.645 \times 2.3[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 2.3}{0.16}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 2.3}{0.16}\right)[/tex]

n = 560. (rounded up).

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Debt payments relate to gross income in terms of the debt-to-income (DTI) ratio by total debt payments are divided by total. gross income.

How do debt payments relate to gross income?

The debt-to-income (DTI) ratio is a financial measurement used by lenders to assess a borrower's ability to manage debt payments. It is calculated by dividing the borrower's total debt payments by their total gross income. The resulting ratio is expressed as a percentage and indicates the portion of the borrower's income that goes towards paying their debt obligations.

For example, if a borrower has total debt payments of $1,000 per month and a gross income of $4,000 per month, their DTI ratio would be 25% ($1,000 divided by $4,000). A lower DTI ratio indicates that a borrower has more disposable income available after paying their debts and is generally viewed as a positive factor by lenders when considering a borrower for a loan or credit.

So, correct option is total debt payments are divided by total gross income.

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Answer:

D. total debt payments are divided by total gross income

Step-by-step explanation:

D. total debt payments are divided by total gross income

Answer:

  (x, y) = (-2, -1) or (1, 2)

Step-by-step explanation:

You want to find the algebraic solutions to the system of equations ...

The x-value of the solutions will be the solutions to ...

  f(x) = g(x)

  f(x) -g(x) = 0

  (x² +2x -1) -(x +1) = 0 . . . . substitute for f(x) and g(x)

  x² +x -2 = 0 . . . . . . . . . simplify

  (x +2)(x -1) = 0 . . . . . factor

The zero product rule says the solutions will be values of x that make one or the other of the factors zero.

  x = -2 or +1 . . . . . . . values that make the factors zero

  y = x +1 = -1 or +2 . . . . from the equation for g(x)

Solutions are (x, y) = (-2, -1) or (1, 2).

We already know that g(x) is satisfied by these x- and y-values.

  f(x) = x² +2x -1 = (x +2)x -1

  f(-2) = (-2 +2)(-2) -1 = 0 -1 = -1 . . . . . (-2, -1) is a solution

  f(1) = (1 +2)(1) -1 = 3 -1 = 2 . . . . . . . . . (1, 2) is a solution

These values agree with the above, so we have shown the solutions satisfy both equations in the system of equations.

If the skills have a choice of making a model plane or a model proposed the materials for plane cost $2 in the materials for the boat cost $4. The relationship between the cost of making planes (y) and the number of planes made (x) is D. y = 2x

Let's assume that x is the number of planes and y is the cost of making the planes.

According to the problem, the cost of making one plane is $2, so the cost of making x planes would be:

Cost of making planes = 2x

Therefore, the relationship between the cost of making planes (y) and the number of planes made (x) can be represented as:

y = 2x

Therefore  the correct answer is D) y=2x.

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As the confidence in the "interval-estimate" increases, the width of the interval (a) decreases.

The width of a confidence interval is a measure of precision of the estimate. A wider interval indicates less precision, while a narrower interval indicates greater precision.

As the confidence level increases, the corresponding critical value z* also increases it means that we are including more of the distribution in the confidence interval, resulting in a wider interval.

Therefore, the width of interval decreases as our confidence in the interval estimate increases, the correct option is (a).

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The given question is incomplete, the complete question is

As our confidence in an interval estimate increases, the width of the interval :

Select One:

(a) decreases

(b) increases

(c) remains the same

(d) increases or decreases depending on the alpha level.

Answer:

0

Step-by-step explanation:

if f is an even function, it means that:

f(x) = f(-x) for every x of the domain

So, because 7 is in f's domain, f(7) = f(-7),

and so f(7) - f(-7) = 0

Answer:

9.2(x- 7) = 9

Step-by-step explanation:

I tried my best to solve this sorry if it is wrong.

Have a good day  :)

After answering the presented question, we can conclude that  it will function take 36 months for the total cost to reach $2005.

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

inverse function

[tex]c(x) = 55x + 25\\c(x) - 25 = 55x\\x = (c(x) - 25) / 55\\c^(-1)(x) = (x - 25) / 55\\c(x) = 55x + 25 = 2005\\55x = 1980\\x = 36\\[/tex]

it will take 36 months for the total cost to reach $2005.

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Answer:

Min = -1

Max = 3

Step-by-step explanation:

Evaluate the values on the ends of the interval

[tex]f(-10) = \sqrt[3]{-10+9}[/tex]

[tex]f(-10)=\sqrt[3]{-1}[/tex]

[tex]f(-10)= -1[/tex]

[tex]f(18)=\sqrt[3]{18+9}[/tex]

[tex]f(18)=\sqrt[3]{27}[/tex]

[tex]f(18)=3[/tex]

The values of g(-4) = 0

                        g(-2) = 2

                        g(0) = 2

                        g(3) = -1

                        g(4) = -2

What is a function?

In mathematics, a function is a rule which assigns a unique output value to each input value in a given set. It shows a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Functions are typically represented by an equation or a graph, and they play an important role in various fields of mathematics, science, engineering, and technology.

Using the given piecewise defined function:

g(x) = x + 4, −5 ≤ x ≤ −1

         2 − x, −1 < x ≤ 5

We can evaluate g at different values in its domain as follows:

g(−4) = (-4) + 4 = 0

g(−2) = (-2) + 4 = 2

g(0) = 2 - 0 = 2

g(3) = 2 - 3 = -1

g(4) = 2 - 4 = -2

Therefore:

g(-4) = 0

g(-2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

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A random sample of 30 employees of a local company has been taken to measure the systolic blood pressure (mm hg). using only the sample information, a 99% confidence interval estimate for the mean systolic blood pressure (mm hg) for all employees of the company is 113.206 to 126.794. The value of the sample standard deviation (mm Hg) is approximately 2.639.

To find the sample standard deviation (mm Hg), we need to use the given information. Here is the solution:

Given information:

Sample size, n = 30

Confidence interval = 99%

Confidence interval limits = 113.206 to 126.794

Formula to find standard deviation:

σ = (CI width) / (2 × Zα/2)

Whereσ = Sample standard deviation

CI = Confidence interval width

Zα/2 = Z-score for a given confidence interval

Let's calculate the confidence interval width:

CI width = Upper Limit - Lower Limit

CI width = 126.794 - 113.206

CI width = 13.588

To find the z-score for a 99% confidence interval, we can use a z-table or calculator.

The z-score for a 99% confidence interval is 2.576. So,

substituting the values in the formula, we get:

σ = 13.588 / (2 × 2.576)σ = 13.588 / 5.152σ ≈ 2.639 mm Hg

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The integer that describes 50 feet below sea level is -50.

The integer that describes 50 feet below sea level is -50. Negative integers are used to represent values below zero.

In this case, the value of 50 feet below sea level is represented by a negative integer because it is below the reference point of sea level, which is typically defined as zero.

Sea level is the average height of the surface of the sea, and is often used as a reference point for measuring elevations and depths.

When a location is above sea level, positive integers are used to represent the height or elevation, while negative integers are used to represent depths or elevations below sea level.

In summary, the integer -50 represents 50 feet below sea level because it is a negative integer that describes a depth below the reference point of sea level.

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Complete question

What integer describes 50 feet below sea level

Answer: The last one

Step-by-step explanation: there is two zeros and every input (x) can only have one output.

Answer:

The last one

Step-by-step explanation:

zero and every input (x) can only have one out put

The calculated length of r is 27.18 meters

From the question, we have the following parameters that can be used in our computation:

The right triangle

Using the tangent of angle 63 degrees, we have

tan(63) = r/13.85

So, we have

r = 13.85 * tan(63)

When evaluated, we have

r = 27.18

Hence, the length of r is 27.18

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There are approximately 31 quarters in a jar of 250 coins.

The probability of picking a quarter from a jar of coins is 0.125. To calculate the number of quarters in a jar of 250 coins, we need to use the following formula:

Number of Quarters = Total Number of Coins * Probability of Picking a Quarter

Number of Quarters = 250 * 0.125

Number of Quarters = 31.25

So, there are approximately 31 quarters in a jar of 250 coins.

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The volume of a pyramid is 2.4 cm^3.

Let's begin by finding the area of the square base. Since the perimeter of the base is 4.7 cm, the length of one side of the square is 4.7 cm / 4 = 1.175 cm. The area of the square base is then

Area = (side length)^2 = (1.175 cm)^2 = 1.38 cm^2

Now, we can use the formula for the volume of a pyramid

Volume = (1/3) x Base Area x Height

Substituting the values we found, we get

Volume = (1/3) x 1.38 cm^2 x 4.7 cm

Volume = 2.3974 cm^3

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 2.4 cm^3.

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The given question is incomplete, the complete question is:

Find the volume of a pyramid with a square base, where the perimeter of the base is

4.7 cm and the height of the pyramid is 4.7 cm. Round your answer to the nearest tenth of a cubic centimeter

The location of Connor's work place with respect to his home is √10 units.

The location of Vikram's martial art school with respect to his home is √34 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Next, we would determine Connor's location with respect to his home as follows;

Distance = √[(-2 - 1)² + (2 - 3)²]

Distance = √[(-3)² + (-1)²]

Distance = √[9 + 1]

Distance = √10 units.

For Vikram, we have:

Distance = √[(-2 - 3)² + (4 - 1)²]

Distance = √[(-5)² + (3)²]

Distance = √[25 + 9]

Distance = √34 units.

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Therefore , the solution of the given problem of probability comes out to be 0 0.015, 0.018, 0.045 , 0.061 and 0.045.

Every procedure's criteria-based approaches have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from one to one, where 0 typically represents chance and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.

Here,

The formula below can be used to calculate the likelihood of drawing precisely k red balls in 4 draws:

=> P(b = k) =  (C(6, k) * C(5, 4-k))/C.(11, 4)

By applying this method, the probability distribution for b can be determined as follows:

=> P(b = 0) = (C(6, 0) * C(5, 4-0)) / C(11, 4) = (1 * 5) / 330 = 0.015

=> P(b = 1) = (C(6, 1) * C(5, 4-1)) / C(11, 4) = (6 * 1) / 330 = 0.018

=> P(b = 2) = (C(6, 2) * C(5, 4-2)) / C(11, 4) = (15 * 1) / 330 = 0.045

=> P(b = 3) = (C(6, 3) * C(5, 4-3)) / C(11, 4) = (20 * 1) / 330 = 0.061

=> P(b = 4) = (C(6, 4) * C(5, 4-4)) / C(11, 4) = (15 * 1) / 330 = 0.045

As a result, the following is the probability distribution for the random variable b that represents the number of red balls pulled in 4 subsequent draws from the box:

b P(b)

0 0.015

1 0.018

2 0.045

3 0.061

4 0.045

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area of trapezium is 30 in².

A trapezium is a four-sided geometric figure that has only one pair of parallel sides. It is also known as a trapezoid in some countries. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The height (or altitude) of a trapezium is the perpendicular distance between the two bases.

The area of a trapezium is given by the formula:

A =½(a×b)h

where "a" and "b" are the lengths of the parallel sides of the trapezium, and "h" is the height (or perpendicular distance) between the parallel sides.

Length of two parallel side

a=7.7in

b=2.3in

Height of trapezium, h=6in

Area of trapezium=½(a×b)h

=½(7.7+2.3)×6

=3×10

=30in²

Hence, area of trapezium is 30 in².

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There are 8 cutting machines and each machine can cut 4 cases every 15 seconds, or 16 cases per minute (4 cases/15 seconds x 60 seconds/minute = 16 cases/minute). Therefore, all 8 machines can cut a total of 8 x 16 = 128 cases per minute.

If 25% of the machines are removed for maintenance, then 2 machines (25% of 8) will be taken out of service. This leaves 6 machines to continue cutting phone cases.

The 6 remaining machines can cut 6 x 16 = 96 cases per minute (since each machine still cuts 16 cases per minute). Therefore, the 6 remaining machines cut 128 - 96 = 32 fewer cases per minute than all 8 machines together.

So the answer is that the remaining machines cut 32 fewer cases per minute when compared to the number of cases per minute all 8 machines cut.

By applying the quadratic formula to simplify the following statement, it is possible to find the value of x, which is 3, 5.

The problem is asking us to find all values of $c$ that satisfy the given equation:

[tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex]

To solve for $c$, we can start by cross-multiplying:

[tex]c(c-4)= 4(c-5)[/tex]

Expanding both sides gives:

[tex]c^2-4c=4c-20[/tex]

Simplifying and rearranging terms, we get:

[tex]c^2-8c+20=0[/tex]

We can now calculate $c$ using the quadratic formula:

[tex]c=[/tex] -b ±[tex]\sqrt{b^2-4ac}[/tex]/2a

Plugging in the values $a = 1$, $b = -8$, and $c = 20$, we get:

c= 8 ± [tex]\sqrt{8^2-4(1)(20)}[/tex]/2(1)

Simplifying, we get:

c = 8 ±[tex]\sqrt{64-80}[/tex]/2

c = 8±[tex]\sqrt{-16}[/tex]/ 2

c = 8 ±[tex]\sqrt{4}[/tex]/2

c = 8± 2/2

c = 4±1

So the solutions are:

c= 3,5

Therefore, the values of $c$ that satisfy the equation are $c = 3$ and $c = 5$.

The complete question is:-

Find all values of [tex]'x'[/tex] such that [tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex].

If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in [tex]$a + bi$[/tex] form.

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