Carlo and Anita make mailboxes and toys in their craft shop near Lincoln. Each mailbox requires 4 hours of work from
Carlo and 4 hours from Anita. Each toy requires 2 hours of work from Carlo and 4 hours from Anita. Carlo cannot work
more than 20 hours per week and Anita cannot work more than 28 hours per week. If each mailbox sells for $15 and
each toy sells for $24, then how many of each should they make to maximize their revenue? What is their maximum
revenue?

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

And the terminal point:

You need to find the Component Form of the vector with this formula:

In this case:

Then, you get:

Find the Magnitude using this formula:

In this case:

Therefore, by substituting values and evaluating, you get:

In order to find the direction of the vector "u", you need to use this formula:

Then, when you substitute the values of "x" and "y" into the formula and evaluate, you get:

Hence, the answer is:

Answer is 6

9 - 6 = 3

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

Equation parallel to y = x+4,

                         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 parallel to

y=x +4

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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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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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Answer : -4/9 , -4/7 , -3/5 , -5/6

The x and y solution of the system  is x = -3 and y = -6

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

6 = −4x + y

− 5x − y = 21

Make -y the subject in the second equation, by adding 5x to both sides of the equation

5x − 5x − y = 21 + 5x

This gives

−y = 21 + 5x

Substitute −y = 21 + 5x in 6 = −4x + y

6 = −4x - 21 - 5x

Evaluate the like terms

5x + 4x = -6 - 21

This gives

9x = -27

So, we have

x = -3

Substitute x = -3 in −y = 21 + 5x

−y = 21 + 5 * -3

Evaluate

−y = 6

So, we have

y = -6

Hence, the solution for the system of linear equations 6 = −4x + y and − 5x − y = 21 is x = -3 and y = -6

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Answer:

Total price including tax: $ 1,092.00

Sales tax rate: 5%

Step-by-step explanation:

Brainlest, Please!

if we take 1040 to be the 100%, what is 52 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1040 & 100\\ 52& x \end{array} \implies \cfrac{1040}{52}~~=~~\cfrac{100}{x} \\\\\\ 20=\cfrac{100}{x}\implies 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]

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:

For 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.

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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)

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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Answer:

y = mx

Step-by-step explanation:

It depends on what form of the line that you want.  Usually the slope intercept form is wanted.

y = mx + b  We need to have the m (slope) and the b (the y-intercept)

The slope is the change in y over the change in x.

Ordered pairs are in the form (x,y)

(0,0) and (4,4)  Have x's of 4 and 0, and y's of 4 and 0.  We subtract these to find the changes in y and x.

[tex]\frac{4-0}{4-0}[/tex]  This is [tex]\frac{4}{4}[/tex] which is the same as 1. The slope (m) is 1.

Now we need to find the y -intercept.  The y intercept is the point where x is 0  (0,b).  They give us this point (0,0,)  So the y -intercept is zero.

y = 1m + 0

or y =mx

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

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:

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

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Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:

The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.

The mean is given as follows:

[tex]E(X) = np[/tex]

The standard deviation is given as follows:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:

n = 200, p = 0.8.

Hence the mean is:

[tex]E(X) = np = 200 \times 0.8 = 160[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66[/tex]

The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.

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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:

Therefore, by using fractions, we can conclude that 99 students bring their lunch from home.

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ANSWER

EXPLANATION

We want to find the value of y:

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:

The value of y is undefined for x = 0 since any value divided by 0 is undefined.

2. x = 1:

3. x = 2.5:

4. x = 1/3:

5. x = a:

That is the answer.

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:

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:

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:

Calculating again:

A = $4965.31

Harry will have $4965.31 in his account after 20 years

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;

Hence, the variable is independent.

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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

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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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

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:

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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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.

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.

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

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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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:

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:

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:

And this means that the equation of the line that passes through (-1,5) and (0,1) is y=-4x+1.

Given -

a = 2.5 cm

b = 3.6 cm

∠A = 43°

To Find -

Remaining angles and sides =?

Step-by-Step Explanation -

We will start by drawing the diagram:

Now, we know

By, sine rule:

Now, we know N

A + B + C = 180 c°°

43 + B + 79° = 180°°

B = 180° - 799 - 43°°

B = 58°

Now, Side b =

Final Answer -

∠B = 58B°

∠C = 797°

Side, b = 3.1 cm

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.)