The **midpoint** of the fourth **class** interval is 0.51

The range of the **fourth** class is 0.48-0.54

So, to find the middle point of the class we use the following formula:

The average of the top and lower values of a specific class interval is referred to as the class midpoint (also known as the class mark). The class midpoint substitutes a range of values with a single value in a frequency distribution table. We can create a line graph for our data using the frequency and the class midpoint.

**Midpoint** = Upper limit+Lower limit/2

Upper limit = 0.54

Lower limit = 0.48

Substituting the values in the formula we get:

Midpoint = (0.54+0.48)/2

= 0.51

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What is answer????????

Answer is 6

9 - 6 = 3

The difference of a number and 9 means to subtract said number from 9.

Review and evaluate the following: By the given y = 2x + 1 ÷ x, what is the value of y when: 1. x=0 2. x = 1 3. x = 2.5 4.x = 1/3 5. x=a

**ANSWER**

**EXPLANATION**

We want to find the value of y:

[tex]y=\frac{2x+1}{x}[/tex]for the values of x.

To do this, for each value of x, substitute the values of x into the equation and simplify.

1. x = 0:

[tex]\begin{gathered} y=\frac{2x+1}{x} \\ \\ y=\frac{2(0)+1}{0}=\frac{0+1}{0}=\frac{1}{0} \\ \\ y=\text{ Undefined} \end{gathered}[/tex]The value of y is undefined for x = 0 since any value divided by 0 is undefined.

2. x = 1:

[tex]\begin{gathered} y=\frac{2(1)+1}{1}=\frac{2+1}{1} \\ \\ y=\frac{3}{1} \\ \\ y=3 \end{gathered}[/tex]3. x = 2.5:

[tex]\begin{gathered} y=\frac{2(2.5)+1}{2.5}=\frac{5+1}{2.5} \\ \\ y=\frac{6}{2.5} \\ \\ y=2.4 \end{gathered}[/tex]4. x = 1/3:

[tex]\begin{gathered} y=\frac{2(\frac{1}{3})+1}{\frac{1}{3}}=\frac{\frac{2}{3}+1}{\frac{1}{3}} \\ \\ y=\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}*\frac{3}{1} \\ \\ y=5 \end{gathered}[/tex]5. x = a:

[tex]\begin{gathered} y=\frac{2(a)+1}{a}=\frac{2a+1}{a} \\ \\ y=2+\frac{1}{a} \end{gathered}[/tex]That is the answer.

Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?

**Compound Interest**

It occurs when the interest is reinvested rather than paying it out.

When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Harry deposited an initial amount of P = $1500.

The savings account gives r = 6% = 0.06 interest

Since the interest is compounded monthly, n = 12 (there are 12 months in a year)

The time is t = 10 years.

Now we apply the formula:

[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:

A = $2729.095

Rounding to two decimals,

A = $2729.10

**Harry will have $2729.10 in his account after 10 years**

Now for t = 20 years:

[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:

A = $4965.31

**Harry will have $4965.31 in his account after 20 years**

Assume that 600 births are randomly selected and 309 of the births are girls. Use subjective judgment to describe the

number of girls as significantly high, significantly low, or neither significantly low nor significantly high.

Choose the correct answer below.

A. The number of girls is significantly low.

B. The number of girls is neither significantly low nor significantly high.

C. The number of girls is significantly high.

D. It is impossible to make a judgment with the given information.

**Option b. **The number of girls is **neither significantly low nor significantly high.**

**How is the subjective judgement given?**

Total number of births selected= 600

Half of the total number = 300

Number of girls = 309

As we can see, the number of girls is**What is subjective judgement ?**

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Find the equation of the line that passes through (-1,5) and (0,1)

We have to find the equation of the line that passes through the points (-1,5) and (0,1). We will write the equation **in the slope-intercept form**, which is given by:

Where m represents the slope of the function, and b the y-intercept. We will find the slope, and then the y-intercept.

**1. Finding the slope**

For finding the slope we will use the formula:

[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where (x₁,y₁) and (x₂,y₂) are two points that passes through the line. In this case, the points (-1,5) and (0,1).

Replacing, we obtain:

[tex]m=\frac{1-5}{0-(-1)}=\frac{-4}{1}=-4[/tex]Thus, **the slope is -4.**

**2. Finding the y-intercept**

For doing this step, we want to know the value of the function when x equals zero. But, as we have that the line passes through (0,1), this means that this value will be 1. This is, **the y-intercept is 1. **

**3. Putting all together**

Now, we just have to put the values obtained in the slope-intercept form:

[tex]\begin{gathered} y=mx+b \\ y=-4x+1 \end{gathered}[/tex]And this means that the **equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.**

1.)Based on the average.how many people will usethe ramp each week? Setup ratio.2.) What will the surface areaof the ramp be? Writeequation & solve. Roundto the nearest hundredth.3.) What percentage of thepeople do not need theramp?4.) How high will the ramp be9 feet from the front walk?Draw a diagram & solve.5.) How high will the ramp be6 feet fromthe front walk?Draw a diagram & solve.Please help with these questions.thank you.

1)

Let:

N = Total people every week = 207

r = People which needs a ramp = 1:9 = 1/9

So:

[tex]N\cdot r=207\cdot\frac{1}{9}=23[/tex]Answer: 23 people

2)

[tex]\begin{gathered} SA=b\cdot h+pw \\ _{\text{ }}where\colon \\ b=18ft \\ h=4ft \\ p=b+h+l \\ l=\sqrt[]{h^2+b^2} \\ l=\sqrt[]{340} \\ w=4.75ft \end{gathered}[/tex]Therefore:

[tex]\begin{gathered} SA=72+192.09 \\ SA=264.09ft^2 \end{gathered}[/tex]3)

The percentage of the people that don't need the ramp will be given by:

[tex]1-r=1-\frac{1}{9}=\frac{8}{9}\approx0.89[/tex]Answer: Approximately 89%

4)

[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-9^2} \\ h=\sqrt[]{259} \\ h\approx16.09ft \end{gathered}[/tex]5)

[tex]\begin{gathered} h=\sqrt[]{(\sqrt[]{340})^2-6^2} \\ h=\sqrt[]{340} \\ h\approx17.44ft \end{gathered}[/tex]in 2018, the population of los Angeles county, California, was 10,137,915. if los Angeles County covers 4,751 square miles, what's the average population density in the county?

The average population density in the county is:

10,137,915 people / 4,751 square miles = 2133.84 people / square mile

Rounding to nearest integer, we have: 2134 people / square mile

Sarah is working towards paying off the rest of her student loan. The graph models the amount owed, in dollars, for x months. What does the slope represent?

The **slope** of the **graph** that **models** the amount Sarah owed after a given number of *x *months, represents the monthly payment Sarah makes to repay the loan

**Monthly payment** on a **loan** is the payment made each month within the period specified in the loan, to repay the loan and the **interest** on the loan.

The given parameters of the graph are;

Information on the graph = The **amount owed** for a number of *x ***months**

Taking the y–axis (Vertical axis) of the graph as specifying the amount owed given in Dollars, and the x–axis as the number of months of payment, we have;

[tex] \displaystyle{Slope = \frac{\Delta y}{\Delta x}} [/tex]

Where;

∆y = Change in the amount Sarah owes

∆x = Change in the time

Which gives;

[tex] \displaystyle{Slope = \frac{Change\: in\: the\: amount \:owed}{Change\: in\: time }}[/tex]

Whereby the graph is a **straight line graph**, we have;

The slope = **Constant**

Therefore, the change in the amount owed over a given time frame such a month, is constant

Which gives;

The slope represents the amount by which the Sarah's student **loan** **changes each **month, which is equivalent to and therefore;

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11. At Outdoor Adventures Clothing Company, all items are marked up to maximize

profit. Life preservers cost $25 to buy from the manufacturer. They sell for $35. What

is the percent increase on life preservers, to the nearest whole percent?

Using the **percentages **formula, we conclude that the percentage increase in life preserves is 40%.

So, the **percentage **increase in life preserves:

Now, substitute the values in the formula as follows:

(selling value - cost)/cost ×100(35 - 25)/25×10010/25×1000.4×10040%Therefore, using the **percentages **formula, we conclude that the percentage increase in life preserves is 40%.

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A data set has a correlation coefficient of 0.013. Which statement about the data is true? a. The data has little or no linear correlation. b. The data has a strong positive linear correlation. c. The data has a weak negative linear correlation. d. The data has a strong negative linear correlation.

**Answer: Choice A**

**The data has little or no linear correlation**

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

Explanation:

r = correlation coefficient

The r values are within the interval [tex]-1 \le r \le 1[/tex]

In other words, r is between -1 and 1 inclusive of both endpoints.

r = -1 is the strongest negative correlationr = 1 is the strongest positive correlationr = 0 means there's no linear correlation at all. The data points are either randomly scattered about, or they perhaps fit on some kind of curve.For the case r = 0.013, it's very close to r = 0. This suggests there is very weak positive correlation or practically no linear correlation at all.

Apples are 99 cents a pound and pears are $1.25 a pound. Write an expression thatrepresents the total cost, in dollars, of a pounds of apples and p pounds of pears.

**Answer**

$(0.99 + 1.25p)

**Explanation**

Note: 100 cents = $1

Apples cost $(99/100) = $0.99 a pound

Pears cost $1.25 a pound

Since 1 pound of pears cost $1.25,

∴ p pounds of pears will cost $1.25p

Now total cost in $ of a pound of apples and p pound of pears = $(0.99 + 1.25p)

Hence, the expression that represents the total cost is $(0.99 + 1.25p)

6

The exchange rate between pounds and US dollars is £1 = $1.27

a) Annie goes on holiday to the USA.

She buys £500 worth of dollars

She spends $550 and converts the rest back to £ at the same rate.

How much money does she receive?

**Annie** will **receive** 66.92 **euros** after **converting** the **dollars** into euros post her **trip**

The **exchange** **rate** between **pounds** and **US **dollars: 1 Euro = $1.27

Exchange rate: An exchange rate determines the **price** at which one **currency** will be **exchanged** for another and has an **impact** on international **trade** and money **transfers**.

Euro **Annie** spends to **buy** dollars = 500

Equivalent dollars received by Annie for 500 euros = 500*1.27

= $635

The money she **spent** in dollars = $550

Dollars remaining = 635-550 = $85

Euro she will receive after conversion = Dollars remaining/**Conversion** rate 85/1.27 = 66.92 Euros

So, After **changing** the dollars into euros after her **vacation**, Annie will receive 66.92 euros.

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What is a formula for the nth term of the given sequence 15,24,33

**Answer:**

87

**Step-by-step explanation:**

the whole sequence would be 15, 24, 33, 42, 51, 60, 69, 78, 87

Which value must be added to the expression x² - 8x to make it a perfect-square trinomial?

04

O-16

O-4

O 16

**Answer: 16**

**Step-by-step explanation:**

The standard form of a perfect square trinomial is:

[tex](x-a)^{2} = x^{2}-2ax+a^{2}[/tex]

Put the equation into standard form:

[tex]x^{2} -8x+c[/tex]

Compare to to the form of a perfect square trinomial:

[tex]-8x=-2ax\\\frac{-8x}{-2x}=a\\a=4[/tex]

Plug a back into the equation to get **c**:

[tex]c=a^{2}=4^{2}\\c=16[/tex]

Putting everything back together gives you:

[tex](x-4)^{2} = x^{2}-8x+16[/tex]

The required, we need to add 16 to the **expression **x² - 8x to make it a perfect square **trinomial**. Option D is correct.

A **polynomial function **is a function that applies only integer dominions or only positive integer powers of a value in an **equation **such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

To make the expression x² - 8x a perfect-square trinomial, we need to add the square of half of the coefficient of x to the expression.

The coefficient of x is -8, so half of it is -4. The square of -4 is 16.

Therefore, we need to add 16 to the **expression **x² - 8x to make it a perfect square **trinomial**.

Answer: 16.

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Write the equation of the line that is parallel

to y = x-7 and passes through the point

(-3, 1)

Equation **paralle**l to **y = x+4, **

How do you write an equation for a parallel line?Equations that are

** y = mx + b**

where m is your slope and b is the y intercept

So, in the equation provided, 1 is the slope.

To write an equation when given a slope and points, you use point slope form, which is

**y −y1 =m(x−x1)**

y1 is the y in the set of points you are given, same with x1

So,

y1 =1 and x1= -3

As stated before, m is the slope, and the slope is given as 1

Plug in the numbers into the equation

y −1 =1 (x+3)

y= x +4 ;

And there you have a equation **paralle**l to

**y=x +4**

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The value of the ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.

The value of the **independent variable **does not rely on the values of the other variables in an expression or function, and its value **determines** the values of the other variables.

An **independent variable** can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.

It is termed “independent” because it's not affected or changed by other variables in an experiment or study.

It is known as a variable that is **unaffected** in a function and cannot be determined by the other variables in that function.

Other names for an independent variable includes;

Explanatory variableInput variableExposure variableControlled variablePredictor variableHence, the** variable **is** independent**.

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Question 8 of 15

Triangle ABC with vertices A(-1, 2), B(-1, -2), and C(-4,-2) is dilated by a scale factor of 2 to form triangle A'B'C'.

у

A

C

4321

-4-3-2-10 이 1234

1

OHN 3 +

B

+2+

-3+

Submit Test

-4-

What is the length, in units, of side A'B'?

units

2223 Math Grade 8 IA1

X

The formula that most accurately captures the dilatation that **Triangle ABC** underwent to produce **A'B'C** will be:

**(x, y) → (1/2x, 1/2y)**

**Detailed explanation?**

A **triangle's vertices** are given.

A(-2, -4) (-2, -4)

B(2, -4) (2, -4)

C(-8, -4) (-8, -4)

The vertices of an image triangle should be after the dilatation

A' (-1, -2) (-1, -2)

B '(1, -2) (1, -2)

C' (-4, -2) (-4, -2)

If we look attentively, we can see that the vertices of the image triangle, A'B'C', make up half of the original **triangle ABC.**

For example,** (x, y) (1/2x, 1/2y)**

verification

A(-2, -4) → A'(-2/2, -4/2) = A'(-1, -2) (-1, -2)

B(2, -4) → B'(2/2, -4/2) = B'(1, -2) (1, -2)

C(-8, -4) → C'(-8/2, -4/2) = C'(-4, -2) (-4, -2)

As a result, it is confirmed, and we come to the conclusion that the rule that best captures the dilatation that Triangle ABC underwent to form **A'B'C**' will be:

**(x, y) → (1/2x, 1/2y)**

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Solve the system of equations

-2x - 6y + 8z = 14

3x + 2y - z = 4

2x - y + 2z = 10

726 819 yep that’s the answer

Can u please help me solve this problem

Given that the initial point of vector "u" is:

[tex](4,8)[/tex]And the terminal point:

[tex](-12,14)[/tex]You need to find the Component Form of the vector with this formula:

[tex]u=\langle x_2-x_2,y_2-y_1\rangle[/tex]In this case:

[tex]\begin{gathered} x_2=-12 \\ x_1=4 \\ y_2=14 \\ y_1=8 \end{gathered}[/tex]Then, you get:

[tex]u=\langle-12-4,14-8\rangle=\langle-16,6\rangle[/tex]Find the Magnitude using this formula:

[tex]||u||=\sqrt{x^2+y^2}[/tex]In this case:

[tex]\begin{gathered} x=-16 \\ y=6 \end{gathered}[/tex]Therefore, by substituting values and evaluating, you get:

[tex]||u||=\sqrt{(-16)^2+(6)^2}\approx17.088[/tex]In order to find the direction of the vector "u", you need to use this formula:

[tex]\theta=tan^{-1}(\frac{y}{x})[/tex]Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:

[tex]\theta=tan^{-1}(\frac{6}{16})\approx20.556°[/tex]Hence, the answer is:

What is the unit rate for the situation represented in the table?

Hours 3 5 7 9

Wages $35.25 $58.75 $82.25 $105.75

a $7.05/hour

b $2/hour

c $11.75/hour

d $16.45/hour

**Answer:**

c $11.75/hour

**Step-by-step explanation:**

You want the **unit rate** represented by the table of (**hours, wages**) = (**3, $35.25**), (**5, $58.75**), ....

The unit rate of dollars per hour is found by dividing dollars by hours:

$35.25/(3 hour) = **$11.75/hour**

You can check the other table values to see if they represent the same unit rate. (They do.)

Can anyone help me with this problem please and thank you !

**Answer:**

d = 7

For step by step explaintion I am so sorry but I don't rember enough of my geometry class to properly explain this, but triangles BDC and ABD are congruent (I swear I can prove this if I dig up my old notes but I really do not feel like doing that) so these 2 equations (sides) are equal. So we just solve for d!

6d + 3 = 10d - 25

(we all know how to solve something this simple so I won't bore you with the details of inverse operations and such)

d = 7

There are 4 corners at an intersection. A pole at each corner holds 2 traffic light, 1 streetlight, and 2 crosswalk light. How many lights are at the intersection in all ?

Using **multiplication **we calculate that there are 56 lights in the cross-section.

When two **integers **are **multiplied **together in mathematics, the result is a product, or an **expression **that describes the factors to be **multiplied**.

Total number of lights in each pole = 2 + 1 + 2 = 5 lights

There are 4 corners

Total number of poles = 5 × 4 = 20

So by **multiplication **we get there are 20 lights in the intersection.

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Given that log 2 = a and log 3 = b, express the following in terms of a and b:

a) log 72

Answer:

Step-by-step explanation:

=a, log 3 = b Log 2 log 1.5= log 23/20 год 1.5 = = log 3-log 2 b-a The other terms log 1.2 log 0.24, log 0.5, log 0.836 cannot be expressed only. of in terms a or bor both. [Answer: Log 1.5 Option A

**Answer:**

[tex]\log 72=3a+2b[/tex]

**Step-by-step explanation:**

Given:

[tex]\log 2 = a[/tex][tex]\log 3 = b[/tex]Rewrite 72 as a product of 2s and 3s.

[tex]\implies 72 = 2 \times 2 \times 2 \times 3 \times 3[/tex]

[tex]\implies 72=2^3 \times 3^2[/tex]

Therefore:

[tex]\implies \log 72=\log(2^3 \times 3^2)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log xy=\log x + \log y[/tex]

[tex]\implies \log 72=\log(2^3)+\log(3^2)[/tex]

[tex]\textsf{Apply the log power law}: \quad \log x^n=n\log x[/tex]

[tex]\implies \log 72=3\log2+2\log3[/tex]

Substitute the given values of log 2 and log 3:

[tex]\implies \log 72=3a+2b[/tex]

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Indira finds that on a typical day, 4 out of every 5 students at her school eat a

cafeteria lunch. The rest of the students bring their lunch from home. Indira's

school has 495 students. On a typical day, how many students at her school bring

their lunch from home? Show your work.

By using **fractions**, we can conclude that 99 students bring their lunch from home.

So, the Fraction of students eating a cafeteria lunch at her school = 4/5

A **fraction **of students bring their lunch from home:

495 students attend her school in total.

Several students bring their lunch from home, including:

1/5 × 49599Therefore, by using **fractions**, we can conclude that 99 students bring their lunch from home.

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f(x)=-3x^2+3x, find f(f)x))

The value of the **composite function **f(f(x)) is -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)

The **functions **are given as

f(x) = -3x^2 + 3x

The definition of the **composite function **is given as

f(f(x))

This **composite function **is calculated using the following composite function formula

f(f(x))= (f o f)(x)

Substitute the known values in the above equation

So, we have the following equation

f(f(x)) = -3f(x)^2 + 3f(x)

So, we have

f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)

Hence, the **composite function **is f(f(x)) = -3(-3x^2 + 3x)^2 + 3(-3x^2 + 3x)

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How to find the range of data. 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

Answer:

22

Step-by-step explanation:

To find the rage, you subtract the smallest number from the largest number in the set of numbers.

So...

26 - 4 = 22

Resting body temperatures are normally distributed with an average of 98.25 degreesFahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)A)0.97B)0.11542313C)0.99D)Sample size is not larger than 40 so we cannot compute probability

Resting body temperatures are normally distributed with an average of 98.25 degrees

Fahrenheit and a standard deviation of 0.73 degrees Fahrenheit. A nurse examines 40 patients in one hour. What is the probability the average temperature of the 40 patients is between 98.0 degrees Fahrenheit and 98.50 degrees Fahrenheit? (Round to the hundredths)

A)0.97

B)0.11542313

C)0.99

D)Sample size is not larger than 40 so we cannot compute probability

step 1

Find the z-scores

For x=98.0 degrees

z=(98-98.25)/0.73 --------> z=-0.3425

For x=98.50

z=(98.50-98.25)/0.73 ------> z=0.3425

using a Z-score Calculator

we have that

P=0.26803

step 2

we have that

If X - N(-3,4), find the probability that x is between -6 and 6. Round to 3 decimal places.

The **probability **that x is between **-6 **and 6 is 18.84%.

For the given question;

The probability of x should line between -6 and 6.

The formula for calculating the z-score is;

z = (x - μ)/σ

μ = mean (-3)

σ = **standard deviation** (4)

Put the values in the formula.

For x = -6

z = (-6 - (-3))/4

z = -3/4

z = -0.75

Now, x = 6

z = (-6 - 3)/4

z = -9/4

z = -2.25

P(-6 < x < 6) = P(-0.75 < x < -2.25)

Find the probability using **negative z score**.

P(-6 < x < 6) = 0.197 - 0.0122

P(-6 < x < 6) = 0.1848

P(-6 < x < 6) = 18.84%

Thus, the** probability **that x is between -6 and 6 is 18.84%.

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A coffee shop currently sells 440 lattes a day at $2.50 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 60 less lattes a day.

a). Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.

N(p)= (blank)

b). Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.

R(p)= (blank)

c). The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).

p= (blank) which will give a maximum revenue of $ (blank)

Show your work!

Explain your answer!

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Using **linear function **concepts, it is found that:

**a)** The amount of lattes sold **function **is: N(p) = -240p + 1040.

**b) **The **revenue **function is: R(p) = -240p² + 1040p.

**c) **The revenue is **maximized **when p = $2.17.

A linear function, in **slope-intercept** format, is modeled according to the following rule:

y = mx + b

In which:

The coefficientFor this problem, we have a linear function with the points having the following **format**:

(price, lattes sold).

Hence **two points **are given as follows:

(2.50, 440), (2.75, 380).

The **slope **is given by change in y divided by change in x, hence:

m = -60/0.25 = -240.

Then:

N(p) = -240p + b.

When p = 2.50, N(p) = 440, hence we **solve for b** as follows:

440 = -240(2.5) + b

b = 1040.

Thus the **function **is:

N(p) = -240p + 1040.

The **revenue **function is:

R(p) = pN(p)

Hence:

R(p) = p(-240p + 1040)

R(p) = -240p² + 1040p.

Which is a **concave down** quadratic function, with a = -240 and b = 1040. A concave down quadratic function is **maximized **when:

p = -b/2a

Hence:

p = -1040/2(-240) = $2.17.

More can be learned about **linear functions** at https://brainly.com/question/24808124

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Four friends have $525 that they want to share equally. To start, they divide the money so that each friend gets a $100 bill. What is the most useful next step?

If four friends have $525 that they want to share equally and they **divide** the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25

**Total money** the have = $525

they divide the money so that each friend gets a $100 bill

The amount of money they **split equally **= 4×100

= $400

**Remaining money** = 525-400

= $125

Split the remaining money into 4 = 125/4

= $31.25

Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25

Learn more about **division** here

brainly.com/question/2273245

#SPJ1

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