3. Lizbeth has a lunch box in the shape of a rectangular prism that
measures 11.5 inches in length and 7.2 inches in width. If the lunch box is 4
inches tall, calculate its volume in cubic inches.

The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

For more related questions on rational expressions:

https://brainly.com/question/30968604

#SPJ8

Answer:

distribute 3/4 of x-8 would be the correct first step

Step-by-step explanation:

guy above me

The sum of the measures of the angle of a triangle is 180 degrees.

The given triangle is a type of triangle and the type of triangle a scalene triangle.

For a scalene triangle, the measure of the three sides are unequal and the sum of the interior angle of a triangle is 180 degrees.

Hence the measure of the angles <A, <B and <C are all less than 90 degrees since they are all acute angles.

We can therefore conclude that:

m<A + m<B + m<C = 180 degrees

Learn more on triangle sum theorem here: https://brainly.com/question/30870203
#SPJ1

Answer:

A) $87.5

B) $164

Step-by-step explanation:

A) Marked Price (Original Price)

= \(\frac{Sale Price}{1 -Discount}\)

=\(\frac{77}{1-0.12}\)

=87.5

B) Marked Price (Original Price)

=\(\frac{Sale Price}{1 -Discount}\)

=\(\frac{123}{1-0.25}\)

=164

Answer:

  $344.05

Step-by-step explanation:

The markdown multiplies the price by (1 -40%) = 0.60.

  $521.28×0.60 = 312.768 ≈ $312.77

The tax multiplies the price by (1 +10%) = 1.10.

  $312.77×1.10 = $344.047 ≈ $344.05

The total cost of the surfboard was $344.05.

The marginal cost of purchasing the French fries for Aaron would be 25 cents

The marginal cost refers to the additional cost of consuming one more unit of a particular item.

Aaron is considering whether to purchase the French fries in addition to the cheeseburger and drink.

Given that the value meal contains a cheeseburger, drink, and French fries for $3, we can compare the cost of purchasing the cheeseburger and drink separately with the cost of the value meal.

The cheeseburger costs $2, and the drink costs 75 cents, so the total cost of purchasing them separately is $2 + $0.75 = $2.75.

The cost of the value meal is $3, which includes the cheeseburger, drink, and French fries.

Therefore, the additional cost of purchasing the French fries in the value meal would be $3 - $2.75 = $0.25.

To learn more on Total cost click:

https://brainly.com/question/31443323

#SPJ4

Answer:

{4}

Step-by-step explanation:

first move 7 to RHS in addition

then 4 in RHS in division

Answer:

{-1/2,4}

Step-by-step explanation:

The temple is described with a central tower and stepped towers symbolizing Mount Meru is Angkor Wat.

The temple is described with a central tower over the main shrine and four stepped towers symbolizing Mount Meru is Angkor Wat. Angkor Wat is a massive temple complex located in Siem Reap, Cambodia, and is one of the most important and iconic archaeological sites in Southeast Asia.

Built-in the 12th century by the Khmer Empire, Angkor Wat is a UNESCO World Heritage Site and is known for its intricate architectural design and religious significance. The central tower stands at a height of 215 feet and is surrounded by four smaller stepped towers, forming a symbolic representation of Mount Meru, which is considered a sacred mountain in Hindu mythology.

Angkor Wat is not only a significant religious site but also attracts visitors from around the world due to its historical and cultural importance, as well as its impressive architectural beauty.

To learn more about “temple” refer to the https://brainly.com/question/24219203

#SPJ11

(a) To find the 5-number summary of the dataset, we need to arrange the data in ascending order and find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

Arranging the data in ascending order:

56 61 62 63 64 66 67 68 69 71 72 73 74 76 77 78 79 81 81 82 83 84 84 88 106

The 5-number summary is as follows:

Minimum: 56

Q1: 68

Median (Q2): 74

Q3: 81

Maximum: 106

(b) To find the mean, we sum up all the values and divide by the total number of values:

Mean = (56 + 61 + 62 + 63 + 64 + 66 + 67 + 68 + 69 + 71 + 72 + 73 + 74 + 76 + 77 + 78 + 79 + 81 + 81 + 82 + 83 + 84 + 84 + 88 + 106) / 25

Mean ≈ 76.56

(c) The range is the difference between the maximum and minimum values:

Range = Maximum - Minimum

Range = 106 - 56

Range = 50

(d) The interquartile range (IQR) is the difference between the first quartile (Q1) and the third quartile (Q3):

IQR = Q3 - Q1

IQR = 81 - 68

IQR = 13

(e) The lower fence for a boxplot is calculated using the formula:

Lower fence = Q1 - 1.5 * IQR

Lower fence = 68 - 1.5 * 13

Lower fence = 68 - 19.5

Lower fence = 48.5

(f) The upper fence for a boxplot is calculated using the formula:

Upper fence = Q3 + 1.5 * IQR

Upper fence = 81 + 1.5 * 13

Upper fence = 81 + 19.5

Upper fence = 100.5

(g) The boxplot represents the 5-number summary graphically. It consists of a box with a line inside representing the median, and lines (whiskers) extending from the box indicating the minimum and maximum values within a certain range. Outliers may also be represented as individual points beyond the whiskers.

(h) To determine if there are any outliers, we can use the concept of fences. Any data point below the lower fence or above the upper fence is considered an outlier.

In this case, we have:

Lower fence = 48.5

Upper fence = 100.5

Observing the dataset, we can see that there is an outlier with a value of 106, which is above the upper fence. Hence, there is one outlier in the dataset.

Learn more about boxplot from :

https://brainly.com/question/14277132

#SPJ11

The mean of the dependent variable R can be found by taking the expected value of R, which is equal to the square root of the sum of the expected values of X squared and Y squared. Since X and Y are normally distributed and independent, the mean of R can be calculated as follows:

Mean(R) = sqrt(E[X^2] + E[Y^2])

To find the variance of R, we need to use the properties of independent random variables. Since X and Y are independent, the variance of the sum of two independent random variables is equal to the sum of their variances. Therefore, the variance of R can be calculated as:

Var(R) = Var(X^2) + Var(Y^2)

To find Var(X^2), we can use the formula for the variance of a function of a random variable:

Var(X^2) = E[X^4] - (E[X^2])^2

Similarly, for Var(Y^2):

Var(Y^2) = E[Y^4] - (E[Y^2])^2

know more about dependent variable :brainly.com/question/9254207

#SPJ11

Answer:

310 rows

Step-by-step explanation:

The length of side AB of the isosceles triangle is 8x + 5.

The formula for finding the length of a isosceles triangle side is given by:

Length of side = √x² +  y²

Where x and y are the lengths of the other two sides.

To find the length of the side AB, we need to first calculate x and y. We know that BC = 4x + 4 and CA = 3x + 9.

Therefore, \(x = BC - CA = 4x + 4 - 3x - 9 = x + -5\)

And \(y = CA - BC = 3x + 9 - 4x - 4 = -x + 5\)

Substituting these values in the formula, we get:

Length of side AB = √((x + -5)² + (-x + 5)²)

= √((x² + 25) + (x² + 25))

= √(2x² + 50)

= √(2(8x + 5)²)

= √(16x2 + 80x + 25)

= 8x + 5

Therefore, the length of side AB is 8x + 5.

Learn more about isosceles triangle here:

https://brainly.com/question/2456591

#SPJ4

Following are all of the subparts' solutions using the probability formula:

Red ball (A) P: 5/8

(B) P: 7/8 (NOT Yellow)

(C) P(yellow or white): 3/8

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

Probability formula: P(E) = favorable events/Total events

(A) P(red ball):

P(E) = favorable events/Total events

P(E) = 5/8

(B) P(NOT Yellow)

P(E) = favorable events/Total events

P(E) = 7/8

(C) P(white or yellow)

P(E) = favorable events/Total events

P(E) = 3/8

Therefore, the answers to all the subparts using the probability formula are shown:

(A) P(red ball): 5/8

(B) P(NOT Yellow): 7/8

(C) P(white or yellow): 3/8

To Know more about probability visit:

https://brainly.com/question/11234923

#SPJ4

Answer: Where inequality?

Step-by-step explanation:

Answer:

A is correct

Step-by-step explanation:

You have to find the rate of change for each one.

Divide the price with the amount

Hope this helps!

Answer:

The mean of this test is 36.'

RATE 5 STARS NALANG PARE MARK BRAINLIEST NADEN

Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

To find out how much of each leftover paint Josh should mix to achieve a medium pink color (50% red), we can set up a system of equations based on the percentages of red in the paints.

Let's assume that Josh needs x gallons of dark pink paint and y gallons of light pink paint to achieve the desired color.

The total amount of paint needed is 3 gallons, so we have the equation:

x + y = 3

The percentage of red in the dark pink paint is 80%, which means 80% of x gallons is red. Similarly, the percentage of red in the light pink paint is 30%, which means 30% of y gallons is red. Since Josh wants a 50% red mixture, we have the equation:

(80/100)x + (30/100)y = (50/100)(x + y)

Simplifying this equation, we get:

0.8x + 0.3y = 0.5(x + y)

Now, we can solve this system of equations to find the values of x and y.

Let's multiply both sides of the first equation by 0.3 to eliminate decimals:

0.3x + 0.3y = 0.3(3)

0.3x + 0.3y = 0.9

Now we can subtract the second equation from this equation:

(0.3x + 0.3y) - (0.8x + 0.3y) = 0.9 - 0.5(x + y)

-0.5x = 0.9 - 0.5x - 0.5y

Simplifying further, we have:

-0.5x = 0.9 - 0.5x - 0.5y

Now, rearrange the equation to isolate y:

0.5x - 0.5y = 0.9 - 0.5x

Next, divide through by -0.5:

x - y = -1.8 + x

Canceling out the x terms, we get:

-y = -1.8

Finally, solve for y:

y = 1.8

Substitute this value of y back into the first equation to solve for x:

x + 1.8 = 3

x = 3 - 1.8

x = 1.2

Therefore, Josh should mix 1.2 gallons of dark pink paint and 1.8 gallons of light pink paint to achieve the desired medium pink color.

for such more question on medium

https://brainly.com/question/14532771

#SPJ8

6x + 18, that is the answer

The 95% confidence interval for the true population mean age of Camden County College students is (22.8, 25.2) years.

To calculate a confidence interval for the true population mean, we can use the t-distribution and the t-interval function on a TI 83 or TI 84 calculator.

The t-distribution is a distribution of values that are used to estimate the mean of a population when the standard deviation of the population is unknown and the sample size is small (typically n < 30). The t-interval function on a TI 83 or TI 84 calculator calculates a confidence interval for the mean of a population based on a sample of data, using the t-distribution to account for the uncertainty due to sampling error.

To use the t-interval function on a TI 83 or TI 84 calculator to calculate a 95% confidence interval for the true population means the age of Camden County College students, we need to enter the following values:

The sample mean (24 years)

The sample size (21 students)

The standard deviation of the sample (4 years)

The confidence level (95%)

The t-interval function will then calculate the 95% confidence interval for the true population mean age, which in this case is (22.8, 25.2) years. This means that we can be 95% confident that the true population means the age of Camden County College students is within this range.

Learn more about Standard deviation here:

https://brainly.com/question/475676

#SPJ4

Answer:

A:33

B:22

C:74

Step-by-step explanation:

A:

2x2x2=8

5x5=25

8+25=33

B:

7x7=49

3x3x3=27

49-27=22

C:

8x8=64

square root of 100 is 10

64+10=74

i hope this helps :)

Step-by-step explanation:

11/4 X 5/12

Lcm of denominators= 12

11 3 33

X =

4 3 12

33/12 X 5/12 = 165/12

Hope it's correct

Please mark as brainliest

The letter on the number line that stands in for the numerals after it On the number line, B stands for -38.

The number line that displays negative numbers is presented to us. On the number line, we are aware that the number rises as we travel to the right.

As per the data given in the above question are as bellow,

The details provided are as bellow,

We can observe that the number line has a grading scale of 1, meaning that each subsequent mark is separated by one unit.

B is four points away from a 42.

This suggests that to get B, we just need to add 4 to -42.

So:

B = -42 + 4

B = -38

For such more question on number line

https://brainly.com/question/24644930

#SPJ4

Note : The complete question would be as bellow,

What integer does the letter B represent on the number line above?

What integer does the letter B represent on the number - 1

Answer: 28:4

Step-by-step explanation:

If you divide 224 by 32 you’re going to get 7. If you also divide 28 and 4 you’re going to get 7. Hope that helps!

Answer:

option 28:4 is the answer

The factor that provides the basis for the grading of newly diagnosed malignant tumours is degree of differentiation.

The level of differentiation impacts an individual's capacity to control their emotions, thoughts, individuality, and connections to others. The degree of any differential equation can be obtained when it is expressed as a polynomial; otherwise, the degree cannot be defined.

The mechanisms by which immature cells develop into mature cells with particular roles are described in biology. This indicates the degree to which tumour tissue resembles the healthy tissue from which it originated in the context of cancer. Compared to poorly or undifferentiated cancer cells, well-differentiated cancer cells resemble normal cells more and grow and spread more slowly. Tumour grading systems, which vary for each form of cancer, use differentiation.

To know more about degree of differentiation, visit:

https://brainly.com/question/28104656

#SPJ4

Answer:

\(3\frac{1}{3}\) or \(\frac{10}{3}\)

Step-by-step explanation:

We could use the combined rate equation to find the combined rate of work.

Combined rate of work formula: \(\frac{1}{t_{b}} = \frac{1}{t_{1} } + \frac{1}{t_{2} }\), where \(t_{1}\) is the individual time for object A, \(t_{2}\) the individual time for object B and \(t_{b}\) is the time for A and B together.

The time it takes Irina to paint the room alone, \(t_{1}\) = 5 hours

The time it takes Paulo to paint the room, \(t_{2}\) = 10 hours

1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change \(t_{b}\) into an \(x\).

\(\frac{1}{{x}} = \frac{1}{5 } + \frac{1}{10 }\)

2) Add the fractions.

\(\frac{1}{x} = \frac{3}{10}\)

3) Solve for the \(x\).

\(x(3) = 1(10)\\3x = 10\\x = \frac{10}{3} \\\)

4) Change them into a mixed fraction.

\(3\frac{1}{3}\)

Note: \(\frac{10}{3}\) or \(3\frac{1}{3}\) are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose \(3\frac{1}{3}\).

Answer:

70° and 110° .

Step-by-step explanation:

Answer: Graphing

Step-by-step explanation:

Graphing is the best method to use when introducing a new student to solving systems of two equations in two variables, because it gives them a visual to recognize what they are looking for. Graphing is less exact and often takes more time than the other methods.

* Hopefully this helps!

At the time when we have to decide whether the system of equations has a solution so here we do the graphing.

It is considered to be the best method at the time when it introduced to the new student for solving the system of 2 equations  in 2 variables as it provides the visual to record what actually they have looking.

Also, graphing is considered to be less exact and taken more time as compared to the other methods.

Learn more about graph here: https://brainly.com/question/24299008

We can solve for r using numerical methods or trial and error. One possible way is to use Excel's goal seek function, which gives us a discount rate of approximately 16.5%. Therefore, at a discount rate of 16.5%, the NPV of the project is zero, and we would be indifferent between accepting the project and rejecting it.

Using the formula for NPV, we have:

\(NPV = -Cost + (CF1 / (1+r)^1) + (CF2 / (1+r)^2) + ... + (CFn / (1+r)^n)\)

where CF is the annual cash flow, r is the required rate of return, and n is the number of years.

Plugging in the given values, we get:

At a required return of 9%:

\(NPV = -9100 + (2200 / (1+0.09)^1) + (2200 / (1+0.09)^2) + ... + (2200 / (1+0.09)^9)\\NPV = -9100 + 1704.13 + 1562.30 + ... + 653.89\\NPV = $404.19\)

At a required return of 25%:

NPV = -9100 + (2200 / (1+0.25)^1) + (2200 / (1+0.25)^2) + ... + (2200 / (1+0.25)^9)

\(NPV = -9100 + 1548.28 + 1179.08 + ... + 160.69\\NPV = -$1,489.91\)

To find the discount rate at which we would be indifferent between accepting the project and rejecting it, we can use the NPV formula and set it equal to zero:

\(0 = -9100 + (2200 / (1+r)^1) + (2200 / (1+r)^2) + ... + (2200 / (1+r)^9)\)

To know more about  discount rate here

https://brainly.com/question/9841818

#SPJ4

The indefinite integral of √\(x^{11\) × sin(3\(x^{(13/2)\)) dx is -2/39 × cos(3\(x^{(13/2)\)) + C, where C represents the constant of integration.

To evaluate the indefinite integral of √\(x^{11\) × sin(3\(x^{(13/2)\)) dx, we can use substitution. Let's substitute u = \(x^{(13/2)\):

Step 1: Find du/dx:

Differentiating both sides with respect to x:

du/dx = (13/2) × \(x^{(11/2)\)

Step 2: Solve for dx:

Rearrange the equation to solve for dx:

dx = (2/13) × du / \(x^{(11/2)\)

Step 3: Substitute the values in the integral:

∫ √\(x^{11\) × sin(3\(x^{(13/2)\)) dx = ∫ √\(x^{11\) × sin(3u) × (2/13) × du / \(x^{(11/2)\)

Step 4: Simplify the integral:

∫ √\(x^{11\) × sin(3\(x^{(13/2)\)) dx = (2/13) × ∫ sin(3u) du

Step 5: Integrate with respect to u:

∫ sin(3u) du = - (1/3) × cos(3u) + C,

where C is the constant of integration.

Step 6: Substitute back the value of u:

∫ √\(x^{11\) × sin(3\(x^{(13/2)\)) dx = (2/13) × (-1/3) × cos(3u) + C

= -2/39 × cos(3\(x^{(13/2)\)) + C.

Learn more about indefinite integral at

https://brainly.com/question/28036871

#SPJ4