Evalúe the limit. Show steps

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)

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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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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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

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

Answer:

87

Step-by-step explanation:

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

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.)

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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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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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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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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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 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

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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.

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: 25 ft

Step-by-step explanation:

Let the shortest side be s. Then, the other two sides are 2s and s+21.

[tex]s+2s+s+21=121\\\\4s+21=121\\\\4s=100\\\\s=25[/tex]

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

What is subjective judgement ?

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Conclusions that can be made about the line in the table include:

The slope of a line is found by the formula:

= Change in y / Change in x

Two points from the table:

(-6, -7) (2, -3)

Slope is:
= (-3 - (-7)) / 2 - (-6))

= 4 / 8

= 1/2

The y-intercept is:

y = Slope (x) + y-intercept

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

y-intercept  = -3 - 1

y-intercept  = -4

Points on the line as shown on the table:

(-2, -5) and (8,0)

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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 is 6

9 - 6 = 3

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

The function exists a Power function. The power of function is 3 and the constant variation is - 1/3

Any function where y = x n, where n is any real constant integer, is referred to be a power function. In reality, many of our parent functions, including linear and quadratic functions, are power functions. A few other power functions are y = x³, y = 1/x, and y = x squared.

A parameter function used in statistical testing that represents the likelihood of rejecting the null hypothesis for a given value of the parameter, assuming that value is true.

Therefore, the power of function is 3 and the constant variation is - 1/3.

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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.

Answer:

para hacer la repuesta xd

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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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:

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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1)

Let:

N = Total people every week = 207

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

So:

Answer: 23 people

2)

Therefore:

3)

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

Answer: Approximately 89%

4)

5)

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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Answer:

B. Diagonals that are congruent