02: Pretest CR Algebra 2 A / 2:Equations and Functions

Answer: Area = 4x^2 + 24x + 32

Step-by-step explanation:

Area = length x width

Length = x + 6 + x + 2 = 2x + 8

Width = x + 4 + x = 2x + 4

area = 2x + 8 * 2x + 4

multiply each term by each term

Area = 4x^2 + 24x + 32

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An expression which does not represent the perimeter of the rug in feet include the following: C. 2(6 7/8) + w.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W) or P = 2L + 2W

Where:

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

P = 2(6 7/8 + W)

P = 2(6 7/8) + 2W = 2W + 13 6/8

P = 6 7/8 + W + 6 7/8 + W

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Answer:

50.1

Step-by-step explanation:

let the height = h

so because that angle is 62 so it's supplemental angle in left triangle is 28°

in any triangle, the tangent of an angle is opposite/adjacent

so height/28 = tan28° =0.53

so height = 14.8

in any triangle, the sine of an angle is opposite/hypotenuse

so height / x = sin 38°

so x = 14.8 / sin 38° = 14.8/0.296 =50.1

At the end of 24 hours, 48 cupcakes will have grown. Every 8 hours, two cupcakes are grown, so after 24 hours, 24 sets of two cupcakes have been grown. Therefore, 48 cupcakes have grown.

At the end of 24 hours, 48 cupcakes will have grown. This is because every 8 hours, two cupcakes are grown. After 24 hours, 24 sets of two cupcakes have been grown. This means that in the 24 hours, two cupcakes were grown a total of 24 times. When this total is multiplied by two, it results in 48 cupcakes being grown. Therefore, after 24 hours, 48 cupcakes have grown. It is important to note that this is only the number of cupcakes that have grown in the 24 hour period, and not the total number of cupcakes. This number includes any cupcakes that were already present at the beginning of the 24 hour period, so the total number of cupcakes at the end of the 24 hour period could be higher than 48.

1. Calculate the number of sets of cupcakes grown in 24 hours: 24 hours divided by 8 hours = 3 sets

2. Calculate the number of cupcakes grown in 24 hours: 3 sets multiplied by 2 cupcakes = 6 cupcakes

3. Calculate the total number of cupcakes grown in 24 hours: 6 cupcakes multiplied by 4 sets = 24 cupcakes

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The distances of the following places are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Places traveled:

Camp → waterfall → meadow → camp.

We are assuming the time taken as follows:

Camp → waterfall = 30 minutes = 0.5 hour

waterfall → meadow = 1 hour

meadow → camp = 2 hours.

Now,

Speed = 4.5 km per hour.

Speed = Distance / Time

So,

The distance between camp → waterfall.

= 4.5 x 0.5

= 2.25 km

The distance between the waterfall → meadow.

= 4.5  x 1

= 4.5 km

The distance between the meadow → camp.

= 4.5 x 2

= 9 km.

Thus,

The distances are:

Camp → waterfall = 2.25 km

waterfall → meadow = 4.5 km

meadow → camp = 9 km

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pr(z < 2.3) is =NORMSDIST(2.3) which equals 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

The probability that a standard normal random variable is less than 2.3 can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. This function gives us the probability that a standard normal random variable is less than or equal to a given value.

In Excel, you can use the NORMSDIST function to calculate the CDF of the standard normal distribution. The syntax for this function is:

=NORMSDIST(x)

where x is the value for which you want to calculate the CDF.

In this case, to calculate the probability that a standard normal random variable is less than 2.3, we would use the following formula in Excel:

=NORMSDIST(2.3)

This gives us the result of 0.9893 or a probability of 0.9893 that a standard normal random variable is less than 2.3.

Note: The cumulative distribution function can also be approximated using tables or calculators that have the function built in. The result obtained using these methods may have some slight differences compared to the result obtained using Excel.

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The size of the population after 15 hours is 6400 bacteria.

The size of the population after 15 hours can be found using the exponential growth formula. The formula for exponential growth is P = P₀ × 2^(t/k), where P₀ is the initial population, t is the time elapsed, k is the time it takes for the population to double, and 2^(t/k) is the exponential growth factor.

In this case, the initial population is 200, the time elapsed is 15 hours, and the time it takes for the population to double is 3 hours. Putting these values in the formula, we get:

P = 200 × 2^(15/3)

P = 200 × 2⁵

P = 200 × 32

P = 6400

So, the size of the population after 15 hours is 6400 bacteria.

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In any case, the solution (2,5) is a specific point that satisfies both equations in the system. It tells us that at this particular point, whatever the equations are describing about trees is true.

A location in the coordinate plane that satisfies both equations is typically what a solution to a system of equations in two variables refers to.

If the set of equations in this case has anything to do with trees, we could interpret the answer (2,5) as indicating that there are two different types of trees and five of each type. As an alternative, the equations can reflect the development or health of trees, and the answer (2,5) might point to a certain period of time or place when both varieties of trees are at a given stage of development or health.

In any case, the system's solution (2,5) is a particular location that satisfies both of the system's equations. It indicates that whatever the equations' descriptions of trees are at this specific time are accurate. The answer can shed light on how the system of equations behaves and how it connects to trees, but it does not always reveal information about other locations or circumstances.

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Answer:

288/720 or simplified to its lowest is 2/5

Charlie would consume 30 units of bananas if he chose the bundle that maximized his utility function subject to his budget constraint There for the answer is option A

Charlie's utility function is given by U(A, B) = AB, where A is the number of apples he consumes and B is the number of bananas he consumes. The price of apples is $1, and the price of bananas is $2.

If Charlie's income is $120, he has a budget constraint given by:

1A + 2B = 120

To maximize his utility subject to this budget constraint, Charlie must use his income to purchase the combination of apples and bananas that gives him the greatest value of U(A, B).

The solution to this problem can be found by using the method of Lagrange multipliers. From the budget constraint, we can solve for A in terms of B:

A = 120 - 2B

Substituting this into the utility function, we have:

U(B) = (120 - 2B)B = 120B - 2B^2

To maximize U(B), we must find the value of B that maximizes this expression. Taking the derivative of U(B) with respect to B and setting it equal to zero, we find that:

dU/dB = 120 - 4B = 0

Solving for B, we find that:

B = 30

Thus, if Charlie chose the bundle that maximizes his utility subject to his budget constraint, he would consume 30 units of bananas. The answer is therefore a. 30.

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Answer:

12

Step-by-step explanation:

45 total

2/3 * 45 = 30 gave speeches

so 15 remaining

1/5 *15 = 3 gave speeches

remaining 12 didn't

Your mom had the better/lower unit price.

A unit price is the cost of a single unit of a product or item, usually expressed per unit of weight, volume, or length. It represents the cost per unit of measurement and allows for comparison of the cost of different products on an equal basis.

For example, the unit price of a bag of apples could be given as the cost per pound, so that a consumer can compare the cost of a 5-pound bag of apples at different stores.

The unit price for your mom's books is $19.85/8 books = $2.48 per book.

The unit price for your dad's books is $15.00/6 books = $2.50 per book.

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The equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 6/5a + 2/3b - 7/6b + 1/8.

Expression is a mathematical phrase that can contain numbers, variables, and operators.

An equivalent expression is a different expression that has the same value as the original expression. In this question, we need to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.

Let's start by simplifying the fractions in the expression. We can see that 4/5a and 2/5a have a common denominator of 5a. We can add these two fractions by finding a common denominator and then adding the numerators. The equivalent fraction to 4/5a + 2/5a is 6/5a.

Next, we can simplify the expression by combining like terms, which are terms that have the same variable and coefficient.

The equivalent expression to

=> 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a = 6/5a + 2/3b - 7/6b - 3/4 + 1/8.

Finally, we can simplify the expression by combining the constants, which are terms without variables. The equivalent expression to

=> 6/5a + 2/3b - 7/6b - 3/4 + 1/8

after combining constants is

=> 6/5a + 2/3b - 7/6b + 1/8.

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$615.9 is the spending per person per year on the internet in 2007.

percentage, a relative value indicating hundredth parts of any quantity.

Consumer spending per person per year or the internet was $13.24. t

The spending increased by about 36% per person per year from 1996 to 2002.

36% of 13.24

36/100×13.24

0.36×13.24

4.7664

[tex]A=Pe^{rt}[/tex]

[tex]A=13.24e^{0.34(6)}[/tex]

[tex]A=13.24e^{2.04}[/tex]

A=101.82

Now the total amount is 101.82

From 2002 to 2007, the number of years are 5.

[tex]A=101.82e^{0.36(5)}[/tex]

[tex]A=101.82e^{1.8}[/tex]

A=101.82×6.049

A=615.9

Hence, $615.9 is the spending per person per year on the internet in 2007.

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The rate of the westbound train is 85miles per hiur

Velocity is the rate of change of displacement with time. It is measured in meter per second. It is a vector quantity.

Since the two trains move at the same time and in opposite directions, then the total displacement (d) = d1 - d2

900 = (vt)1 - (Vt)2

if v1 is the eastbound train velocity and v2 is the westbound train velocity

v1 = v2+10

they have thesame time of 5hours

therefore;

900 = (v2+10-(-v2)(5)

900 =( 2v2+10)5

divide both sides by 5

180 = 2v2 +10

2v2 = 170

v2 = 170/2

v2 = 85

therefore the rate of the westbound train is 85 miles per hour

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The USB stick contains 6 whole GB

Given is that the capacity of a USB stick is 49/8 GB.

Given is the expression as -

49/8

Dividing, we get -

6.125

6 + 0.125

where 6 is a whole number while 0.125 is a decimal.

Therefore, the USB stick contains 6 whole GB.

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{Question in english -

Aid:

The capacity of a USB stick is 49\8 GB. How many whole GB does it contain?}

Hi there, here's your answer:

We have -1 < x ≤ 2 and -2 ≤ x < 3

Let's first solve both the inequalities one at a time.

Case 1:

-1 < x ≤ 2

The solution set for this inequality is (-1 , 2]

Case 2:

-2 ≤ x < 3

The solution set for this inequality is [-2 , 3)

Now, the values that satisfy both these inequalities can be taken from the solution set of case 1.

Thus, we get a new solution set for the satisfactory values.

New solution set = (0,2]

The required integer values are:

0, 1 and 2.

Hope this helps!

Answer: 0, 1, 2

Step-by-step explanation:

0 is less then 2 and 3 and greater than -1 and -2

Same for 1 and 2, but for 2 in the first equation it is equal but look at these signs [tex]\leq \geq[/tex]

It means equal or less/greater than.

2 is = 2 so it satsifys the first equation.

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Answer:

no

Step-by-step explanation:

A: 360 -150 = 210 * (1+7%) = 224.7

B: 360 * 1.07  -150 =385.2 -150 =235.2

He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

What is simple interest?

The simple interest method, which always adds interest to the starting principal amount at the same rate for each time cycle, is a quick and easy way to calculate interest on money. Any bank where we deposit money will return our investment with interest. Simple interest is one of the several forms of interest that banks charge. Now, before going into any detail on the concept of fundamental curiosity,

The formula for simple interest is:

S = p*t*r/100

The part-time receptionist's taxable income would be calculated by deducting their exemptions and standard deduction from their gross income. The person's gross income was $9101.99. A $3650 exemption was requested by the person. They also qualified for a $5700 standard deduction.

We can figure out their taxable income by deducting the exemption and standard deduction from their gross income. $9101.99 - $3650 - $5700 = $-748.01 would be used to compute the taxable income.

Hence He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.

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Answer:

Below

Step-by-step explanation:

From 10 am to 1 pm is three hours

  the boys covered distance =  68 miles in 3 hours  

x = rate1

x+3 = rate2

rate  X   time   = distance

(x   +    x+3)  X  3  = 68

6x+9 = 68

6x = 59

x = 9  5/6 mph     then the other rate is x+3 = 12  5/6 mph

Answer: 9.833...

Step-by-step explanation:

The boys traveled a combined 68 miles in 3 hours (difference between 10am and 1pm). This makes their combined speed equal to 68/3.

We can make this equation to model how that combined speed breaks down between them:

68 miles/3 hours = (3 + x) miles/1 hour + x miles/1 hour

To solve:

68/3 = (3 + x) + x

68 = (3 + 2x) * 3

68 = 9 + 6x

59/6 = x

9.833... = x

Here are three different equations that relate C and B:

1. B = (2/7) * C

2. B/C = 2/5

3. 5C = 2B

1. B = (2/7) * C

Since the ratio of cocoa to cocoa butter is 5:2, we can write 5 + 2 = 7, which represents the total number of parts. Dividing 2 by 7, we get 2/7, which represents the fraction of cocoa butter in the mixture. To find the number of grams of cocoa butter needed for C grams of cocoa, we multiply C by 2/7.

2. B/C = 2/5

Dividing the number of grams of cocoa butter (B) by the number of grams of cocoa (C), we get the ratio of cocoa butter to cocoa, which is 2/5.

3. 5C = 2B

Since the ratio of cocoa to cocoa butter is 5:2, we can write the equation 5 * C = 2 * B, which represents the number of parts of cocoa to the number of parts of cocoa butter. Solving for B in terms of C, we get B = (2/5) * C.

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The required probability is 0.112 × [tex]10^-^1^3[/tex]

In the combination, ordering of items does not consider important when we need to determine the number of ways to select the _k_ items from the total _m_ items. There will be two cases in selecting the items- one in which repetition allowed, and the other is repetition not allowed.

Total Number of US senators (n) =100

Number of politicians to be chosen (r) = 50

Total number of ways in which 50 politicians can be chosen from 100 senators is:

[tex]C^n_r = C^1^0^0_5_0[/tex]

Number of senators in each US state = 2.

The number of ways in which senator can be chosen such that each state is represented = [tex]2_C_1[/tex]

Thus, the number of ways in which senator can be chosen for 50 states is:

[tex](2_C_1)^5^0[/tex]

Let A be an event that a politician is chosen such that each state is represented.

P(A) = [tex]\frac{2^5^0}{100_C_5_0}[/tex]

By solving, we get:

P(A) = 0.112 × [tex]10^-^1^3[/tex]

Hence, the required probability is 0.112 × [tex]10^-^1^3[/tex]

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To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

The number of socks chosen at random will be denoted by the letter "n." Given by: The anticipated number of blue socks in "n" pairs

Expected number of blue socks = n * 1/4

In order for there to be four blue socks as expected, we need to determine the value of "n." Thus, we can construct the equation:

n * 1/4 = 4

And solving for n:

n = 4 / (1/4) = 4 * 4 = 16

So, To get 4 pairs of blue socks, on average, you would need to choose 16 pairs of socks at random.

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Addition And Subtraction

1.) -27+68-56+61= 46

2 ) 4.17-9.42+0.2= -5. 05

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

5 ) 6 5/12 - (-4 2/3)8 + (-2 3/4)= 5/12

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

1.) -27+68-56+61=

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

2 ) 4.17-9.42+0.2= -5. 05

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

3 ) 3.1+(-4.72)+(-8.12)-(-0.96)=-8.78

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the number (-0.96) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is . positive.

4 ) -18.31-6.27+(-8.44)-(-31.67)=-1. 35

Because in this arithmetic operation there is only addition and subtraction, it can be calculated starting from anywhere.

But it should be noted that before the numbers (-8.44) and (-31.67) there is a negative sign (-) so you need to multiply the sign with the number in brackets. In this case the result is positive.

5 ) 6 5/12 - (-4 2/3) + (-2 3/4)= 5/12

In question number 5, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

6 ) 4 1/8 - 6 2/9+ (-3 1/6) - (-5 3/4)= -49/72

In question number 6, it involves mixed fractions. To do this, you can change mixed fractions to improper fractions.

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Answer:

7 miles

Step-by-step explanation:

Let's call the distance from point C to point D as "x".

We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.

Using the Pythagorean Theorem, we can find the distance from C to D:

(x)^2 + (4)^2 = (8)^2

Expanding and simplifying the equation:

x^2 + 16 = 64

x^2 = 48

x = sqrt(48) = 6.928

So the distance from the third tower to point D is approximately 6.9 miles (rounded to the nearest tenth of a mile).

Answer:

6.9 miles

Step-by-step explanation:

Since the distance between points A and B is 8 miles, and point C is equidistant from points A and B, triangle ABC is an equilateral triangle with side lengths of 8 miles.

As point D is 4 miles from point A, point D is the midpoint of AB.

Therefore, the distance between point C and point D is the altitude of the triangle.

The formula for the altitude of an equilateral triangle is:

[tex]h=\dfrac{\sqrt{3}}{2}s[/tex]

where s is the the side length.

Therefore, the altitude of an equilateral triangle with side length 8 miles is:

[tex]\implies h=\dfrac{\sqrt{3}}{2} \cdot 8[/tex]

[tex]\implies h=4\sqrt{3}[/tex]

[tex]\implies h=6.9\; \sf miles\;(nearest\;tenth)[/tex]

Therefore, the distance from the third tower C to point D is 6.9 miles to the nearest tenth of a mile.

The value of x of the parallelogram is x = 38

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be represented as ABCD

Now , the diagonals of the parallelogram are AC and BD

The measure of DE = 31

The measure of EB = x - 7

Now , Each diagonal of a parallelogram separates it into two congruent triangles where the measure of AC = BD

So , substituting the values in the equation , we get

BD = BE + DE and BE = DE

On simplifying the equation , we get

31 = x - 7

Adding 7 on both sides of the equation , we get

x = 31 + 7

x = 38

Hence , the measure of x of parallelogram is 38

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The number of different outfits cory can make is 270 ways.

Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangements is called a combination. The various ways in which objects from a set may be selected, generally without replacement to form subsets is known as combination.

Given;

He has 5 pairs of pants to pick from, 18 shirts , and 3 pairs of shoes

Now, the combination;

=5*18*3

=270

Therefore, the combinations will be 270.

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