In college, we study large volumes of information- information that, unfortunately, we go not often retain for very long. The function f(x) = 80e +20 describes the percentage of information, fx), that a particular person remembers x weeks after learning the information. a. Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned. b. Substitute 1 for x and find the percentage of information remembered after 1 week C. Find the percentage of information that is remembered after 4 weeks. d. Find the percentage of information that is remembered after 1 year.

Recall the area of a rectangle is determined by the formula

Given the following

w = 4 3/4 ft

l = 6 4/5 ft

Convert the following given into improper fraction first

Next, substitute those values to the given formula for solving the area of the rectangle

AS shown in the figure:

The measure of arc RT = 27

The measure of arc FN = 105

The measure of angle FUN will be as follows:

So, the answer is option C. 66

So,

We're going to multiply:

Multiplying numerators and denominators together, we obtain:

Now, to simplify, what we're going to do is to reduce the fraction dividing by a common number. Let's begin dividing by 2:

As you can see, we can't divide by a common number more times, so, the simplified fraction is 5/36.

Solution

We are given the expression

The image below shows the definition of a polynomial and some examples as well

Thus, given

Here;

Degree = 0

Leading coefficient = 3

Answer:

-54

Step-by-step explanation:

Finding a value means you will get a number answer. Since they said x

x = -2

fill in -2 in place of the x.

also they said

y = 6

so fill in 6 wherever you see a y.

2(3x - 6) - 5y

fill in -2 for x and 6 for y.

= 2(3•-2 - 6) - 5•6

Work on parentheses first. Multiply before adding or subtracting.

= 2(-6 - 6) - 5•6

= 2(-12) - 5•6

Again, multiply before adding or subtracting.

= -24 - 30

= -54

For the information given in the statement you have

Using the elimination method, multiply by -1 the equation (2) and then add the equations to eliminate one of the variables

Now plug the value of x found into any of the initial equations to find the value of y. For example in equation (1)

Therefore, the solutions of the system of equations are

Answer:

Volume = 2268 ft³

1814.4 bushels of corn

Explanation:

The volume of the corn crib can be calculated as:

Volume = Length x Width x Height

Then, the volume is equal to:

Volume = 21 ft x 9 ft x 12 ft

Volume = 2268 ft³

Finally, to know the number of bushels of corn that can be stored, we need to divide the volume of the corn crib by the volume of each bushel of corn. So:

Therefore, the volume of the corn crib is 2268 ft³ and it can store 1814.4 bushels of corn.

Two lines are parallel is they have the same slope. In this case:

Solving the equation for y, and obtaining the slope-intercept equation for the line equation, we have:

Then,

To simplify the expression above, simply combine similar terms.

The similar terms in the expression above are 8c and -3c as well as 6 and -2.

Let's combine the pairs of similar terms.

So, 8c - 3c = 5c and 6 - 2 = 4. Hence, the answer is:

The answer is 5c + 4. (Option A)

A parallelogram has rotational symmetry of order 2. This means that rotation transformation maps a parallelogram onto itself 2 times during a rotation of 360 degrees about its center.

And that is at 180 degrees and 360 degrees.

Hence, the only correct option is a rotation of 180 degrees clockwise about the center.

Answer:

Option D

Answer:

(1, -2)

Step-by-step explanation:

Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

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Answer:

There are 126 months in 10 years and 6 months.

Explanation:

In a year there are 12 months.

Then, to know how many months are in 10 years, we multiply by 10:

Now we add the additional 6 months:

The answer is 126.

a.

Given that a health club charges a one-time initiation fee of $120.00 plus a membership fee of $30.00 per month.

The total cost will be equal to the fixed one-time charge plus the charge per month times the number of months.

It can be represented by the expression C(x);

b.

Graphing of the function, we would have;

c.

If the health club decided to give its members an option of a higher initiation fee but a lower monthly membership charge. If the initiation fee is $420 and the monthly membership fee is $10, we will have the function as;

graphing the above function, we have;

the first plan is represented by the blue line while the second plan is represented by the red line.

d.

The number of months after which the second plan is less expensive is the value of x when the two lines meet.

the two lines meet at point;

The value of the x coordinate is 15.

So, The number of months after which the second plan is less expensive is

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

A square is a quadrilateral in geometry that has four equal sides and four right angles (90-degree angles). It is a unique kind of both a rhombus and a rectangle. A square is made up of four equal-length sides, two equal-length diagonals, and right-angle diagonal cuts. A square's area and perimeter can be calculated by multiplying one of its sides by itself (squared), and one of its sides by four, respectively. Because of their symmetry and regularity, squares are frequently employed in mathematics and building.

given

By multiplying the first lawn's length by its breadth, one may determine its area: 56 square metres is the size of the first lawn, which is 8 metres by 7 metres.

The second lawn's breadth is six times that of the first lawn's, so:

The second lawn's width is equal to 6 × 7 metres, or 42 metres.

The second lawn is the same length as the first one, so:

The second lawn is 8 metres long.

The second lawn's area is calculated by multiplying its length by its width:

The second lawn is 336 square metres in size (8 metres by 42 metres).

The first and second lawns' combined areas make up the overall area of the two lawns:

Total area equals the sum of the first and second lawns.

56 square metres + 336 square metres make up the total area.

Area overall is 392 square metres. The two lawns' combined area is therefore 392 square metres.

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Yes, the given figure has the horizontal symmetry.

Line symmetry is a type of symmetry about reflections. When there is at least one line in an object that divides a figure into two halves such that one-half is the mirror image of the other half, it is known as line symmetry or reflection symmetry. The line of symmetry can be in any direction - horizontal, vertical, slanting, diagonal, etc.

The horizontal line of symmetry divides a shape into identical halves, when split horizontally, i.e., cut from right to left or vice-versa.

The given figure has horizontal symmetry.

Yes, the given figure has the horizontal symmetry.

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The values for the composition of the functions are:

(f o g)(x) = 9x² + 5

(g o f)(x) = 3x² + 15

To evaluate the composition of a function, the first thing to do is to evaluate the inner function, then use the output as an input to evaluate the outer function of the composition.

Given the following functions:

f(x) = x² + 5

g(x) = 3x

We are required to find (f o g)(x) and (g o f)(x).

To find (f o g)(x), replace g(x) for x in the outer function f(x):

(f o g)(x) = (3x)² + 5

(f o g)(x) = 9x² + 5

To find (g o f)(x), replace f(x) for x in the outer function g(x):

(g o f)(x) = 3(x² + 5)

(g o f)(x) = 3x² + 15

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A composite number is defined as a whole number that have more than two factors; from this definition we conclude that all whole numbers that are not prime are composite numbers.

Since all even numbers are not prime we conclude that Larry is correct; all numbers that have a 2 in the one's place are composite. In fact all even numbers are composite with exception of 2 itself.

a) The yield to maturity of the IOU Corporation's bond is -0.39%.

b) The current yield of the IOU Corporation's bond is 5.58%.

The bond's yield to maturity (YTM) is the total rate of return earned by a bondholder with all interest payments and the original principal repaid.

We can compute the yield to maturity using the following YTM formula:

Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]

Where:

FV = Face Value of the Bond

Price = Current Market Price

Maturity = Maturity Period.

Bond's face value = $2,000

Current date = April 19, 2021.

Company (Ticker)  Coupon  Maturity  Last Price  Last Yield  EST volume

                                                                                                      (000s)

IOU            (IOU)       6.3    April 19, 2037  112.97         ??            1,857

Annual interest = $126 ($2,000 x 6.3%)

Maturity period = 16 (2037 - 2021)

Price = $2,259.4 ($2,000 x 112.97/100)

Yield to Maturity = [Annual Interest + {(FV-Price)/Maturity}] / [(FV+Price)/2]

= [$126 + {($2,000 - $2,259.4)/16}] / [($2,000 + 2,259.4)/2]

=  [$126 -$259.4)/16] / [($4,259.4)/2]

= -8.3375/2,129.7

= -0.39%

Current yield = Annual Coupon/Current Price

= 5.58% ($126/$2,259.4 x 100)

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Based on the increase in CPI, the amount that would be required at year end to have the same purchasing power at the beginning of the year is $1,024.46.

First, find the inflation rate:

= (Current CPI - Beginning CPI) / Beginning CPI

= (108.9 - 106.3) / 106.3

= 2.446%

This means that the amount of money at the beginning of the year has lost a value of 2.446%.

In order to remain the same as the value of $1,000, a person would need:

= 1,000 x (1 + 2.446%)

= $1,024.46

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The number of solutions that this equation have is: A. zero solutions.

Generally speaking, an equation is said to have zero solution or no solution when the left hand side and right hand side of the equation are not the same or equal. This ultimately implies that, an equation would have zero solution or no solution when both sides of the equal sign are not the same and the variables cancel out.

In order to determine the number of solutions that this equation have, we would simplify the equation by opening the bracket and then compare both sides of the equation as follows:

6(c+4) = 6c + 30

6c + 24 = 6c + 30

6c - 6c = 30 - 24

0 = 6 (no solution).

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From 1 to 10, there are 3, 6, and 9 are divisible by 3

Then we have 3 choices out of 10 numbers

Since the probability = an event/outcomes

Since the event is 3

Since the outcomes are 10, then

This is the probability for spinning the spinner one time

But we need to spin it 70 times

We will multiply 3/10 by itself 70 times, which means make it to the power of 70

The answer is (3/10)^70 OR (0.3)^70

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

What is transforming coordinates?

Polar coordinates (r,θ) are transformed into Cartesian coordinates (x, y) using the formulas x = r cos(θ), and y = r sin(θ).

This problem is under the concept of transforming polar coordinates (r,θ) to cartesian coordinates  (x, y).

For this problem the polar coordinates  are r = 18 and θ = 190°.

Convert these polar coordinates into a cartesian coordinates as,

x = r cos(θ) = 18 cos(190°) = -17.73

y = r sin(θ) = 18 sin(190°) = -3.13

The coordinates of a point on a circle with radius 18 corresponding to an angle of 190° are (-17.73, -3.13).

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Standard deviation is an important measure of spread or dispersion. It tells us how far, on average the results are from the mean.

The smallest standard deviation belongs to the dataset with the smallest range and almost no outliers. Closer the values are to the mean, less the value of the standard deviation.

Comparing those datasets, the one that fits this description is the third one.

Given:

Betty and Theresa together complete a job in 20 hours.

Betty alone does a work in 60 hours.

The aim is to find the time Theresa will take to complete the job alone.

Therefore,

Betty and Theresa's 1 day work:

Betty's 1 day work when he works alone:

Now, Theresa's 1 day work when he works alone is given by:

Hence, Theresa can do the job in 30 hours working alone.

Answer:

[tex]x + ( - 9) = - 21[/tex]

[tex]x - 9 = - 21[/tex]

[tex]x = - 12[/tex]

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]

[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]

[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]

how much will it be in interest alone?

well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned

[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]

ANSWER

Let x = liters of drink A

Let y = liters of drink B

System:

EXPLANATION

We know that of the liters of drink A, 20% is real juice: 0.2x

and that of the liters of drink B, 15% is real juice: 0.15y

The sum of the amounts of real juice in each drink is 100.5, because it is said that 100.5 liters of real juice are use to make both drinks.

Also it is said that they make 30 more liters of drink A than of drink B, so the liters of drink A are 30 more than drink B: x = y + 30

The system is:

Explanation

Step 1

Aya sold printed T-shirts for $7.50 each at a carnival. She earned

$187.50.

then

let x represents the number of T-shirts Aya sold.so, if she made $187.5 and the cost per T-shirt is $7.50

therefore, for part A , the answer is

Step 2

What is the number of T-shirts Aya sold at the carnival?

to figure out this,we need to solve for x

it means she sold 25 T-shirts at the carnival

I hope this helps you

Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm