Victoria and her children went into a grocery store and she bought $9 worth of applesand bananas. Each apple costs $1.50 and each banana costs $0.50. She bought a totalof 8 apples and bananas altogether. Determine the number of apples, x, and thenumber of bananas, y, that Victoria bought.Victoria boughtapples andbananas.

Given:

There are given the equation:

Explanation:

To find the factor of the given equation, first, we need to take a common variable from the given equation:

Then,

Final answer:

Hence, the factor of the given equation is shown below:

[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]

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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ANSWER

1058 grams

EXPLANATION

Each day she eats 46 grams of protein. In 23 days of training, she will eat 23 times that amount,

Hence, in 23 days she will eat 1058 g of protein.

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.

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

Remember that the volume of a rectangular pyramid is given by the expression:

Where:

• a ,and ,b ,are the lenght of the sides of the rcetangle (base)

• h, is the height of the pyramid

Using this, and the data given, we'll get that:

The volume of the pyramid is 665 cubic feet

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.

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.

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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Given:

It is given that you roll a die 96 times.

Required:

We have to find the expectation of landing on 3 or 4.

Explanation:

If you roll a die then there are 6 possibilities (1-6) and the possibility of landing on 3 or 4 is 2.

Then the probability of landing on 3 or 4 is

If you roll the die 96 times then the probability of landing 3 or 4 is

Final answer:

Hence the final answer is:

You could expect it to land on 3 or 4 is

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:

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.

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:

He took 3 1/4 hours to clean the bathroom and then he took 1/8 hours to clean the kitchen.

First, we can convert the mixed number 3 1/4 into a fraction:

3 1/4 = 3/1 + 1/4 = 13/4

Now, we can sum both times:

13/4 + 1/8 = ((13*8)+(4*1)) / (4*8) = (104 +4)/ 32 = 108/32 = 27/8

Finally, we need to convert the total of hours 27/8 as a mixed number:

If 27/8 = 3.375

We take the whole number and then convert the decimal remaining into a fraction:

3 - whole number

0.375* (1000/1000) = 3/8

Hence, the mixed number for the total time that Ali spent cleaning both rooms is 3 3/8

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 most appropriate choice for square root will be[tex]\sqrt{19}[/tex] lies between 4 and 5

What is square root of a number?

A number's square root is a value that, when multiplied by itself, yields the original number. The opposite way to square a number is to find its square root. Squares and square roots are therefore related ideas. Assuming that x is the square root of y, the equation would be written as x=y or as x2 = y. The radical symbol for the number's root is "" in this instance. When multiplied by itself, the positive number represents the square of the original number. The original number is obtained by taking the square root of a square of a real integer. For instance, the square of 3 is 9, the square root of 9 is 9, and 9 squared equals 3. Finding the square root of 9 is simple because it is a perfect square.

[tex]\sqrt{p} = p^{\frac{1}{2}}[/tex]

[tex]\sqrt{19} = 4.36\\[/tex]

4.36 lies between 4 and 5

[tex]\sqrt{19}[/tex] lies between 4 and 5

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Answer:

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

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

[tex]x = - 12[/tex]

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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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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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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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

Wholesale price for a pair of shoes = $3.50.

Wholesale price by 60%.

Find

price of the pair of shoes in the department store

Explanation

Price in deparrtmental store is 60% more than wholesale

so ,

Final Answer

Therefore , the price of the pair of shoes in the department store is $5.60.

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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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)

Let's find the vertex for the following equation:

y = x² - 2x - 3

As you can see, we found graphically that (1, -4) is the vertex for this equation.

Now, let's find the intercept form, as follows:

x-intercept:

0 = -1² -2 * - 1 - 3

0 = 1 + 2 - 3

Then, (-1, 0)

0 = 3² - 2 * 3 - 3

0 = 9 - 6 - 3

Then (3, 0)

y-intercept:

yy

The z - score of the normal deviation will be 0.8.

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

A normal distribution has the mean = 62

Standard deviation = 20

Since, The formula for the z - score will be;

z = (x - μ) / σ

Where, σ is the standard deviation and  μ is the mean of normal distribution.

Substitute all the values in above equation, we get;

z = (x - μ) / σ

z = (46 - 62) / 20

z = - 16 / 20

z = - 0.8

Therefore,

The z - score of the normal deviation will be 0.8.

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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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Answer:

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

Use arc length formula:

Substitute the values and calculate:

The matching answer choice is C.