8th Grade Math Homework Thursday, January 28th
Simplify. Combine like terms.
1. 12y - 18y
2. 4(y + 5)
3. 3x + 6y - 9x + 4
4. 6(x - 9) + 10 - 3x
5. Is 4 a solution of 5(2 - x) = -10? Show work to justify your answer.
Solve and check the following equations. Show all steps.
6. 4x + 20 = 0
7. 5x - 3 = 2x - 27
8. 6x - 8 = 2x + 16
9. 12 - 3x = 22 + 2x
10. x + 7x - 12 = -20
11. 7x+4 - 13x = -1 + 23

Answer:

{x:x is having odd number}

Answer:

3:1      &     54:18

Step-by-step explanation:

Answer: 9:3 and 3:1

Step-by-step explanation:

Glad I could help!

No ,the team will not make the first down.

The definition of a yard is an outdoor area of a house or other building. An example of a yard is the lawn in front of your house; a front yard. An example of a yard is the area around a train repair center where trains are stored; a rail yard.

the first of a series of usually four downs in which a football team must net a 10-yard gain to retain possession of the ball.

If the team with the ball can pick up one yard or more on the third-down play, then they will be given a first down, which means they get to start all over with a new set of four downs. A team can continue moving the football down the field as long as they continue to pick up first downs.

we have been given that -

the ball forward at least 10 yards from its starting point to make a first down if the team has 2 losses of 2 yards each and a gain of 12 yards

Here are the integers that are represented by the scenario.

-2 + -2  = -4

-4 + 12 =8 yard gain.

There are 2 yards less of the first down.

Hence, the team will not make the first down.

To learn more about first down in football

visit - https://brainly.com/question/25146419

#SPJ9

option  1.) and 3.) are correct.

What is congruent ?

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles. The circles below may be put perfectly over one another and have the same radius, hence they are considered to be congruent.

These two statements are true:

Figure 1 and 4 are not congruent because figure 1 cannot be maped into figure for using a sequence of rigid transformations because figure 1 and 4 don't have same length of the sides.  

Figure 1 and 3 are not congruent because figure one cannot be mapped on to figure 3 using a sequence of rigid transformations becuase figure 3 is large than by figure 1 by its sides.

To know more about congruent https://brainly.com/question/27848509

#SPJ1

The value of n that satisfies each equation are fractions or integers  n = 5/2, n = (log3(4/9) + 2)/(-4) and n = 7/4.

What is fraction ?

A fraction is a mathematical expression that represents a part of a whole or a ratio of two quantities. It consists of two numbers, one on top of the other, separated by a horizontal or diagonal line. The number above the line is called the numerator and the number below the line is called the denominator.

According to the question:
a. \(4\sqrt(2) = 2 ^ n\)

We can write \(4\sqrt(2)\) as \(2^2 * \sqrt(2)\). Therefore, we can rewrite the equation as:

\(2^2 * \sqrt(2) = 2^n\)

We can simplify this to:

\(2^{2 + 1/2} = 2^n\)

\(2^{5/2} = 2^n\)

To solve for n, we can take the logarithm of both sides of the equation with base 2:

\(log2(2^(5/2)) = log2(2^n)\)

5/2 = n

Therefore, n = 5/2.

b. \(1/( \sqrt[4]{9} ) = 3 ^ n\)

We can simplify root(9, 4) to:

\(\sqrt[4]{9} = (4/9) ^ {1/4}\)

Substituting this into the equation gives:

\(1/((4/9)^{1/4}) = 3^n\)

Taking the reciprocal of both sides of the equation gives:

\((4/9)^{1/4} = 3^{-n}\)

Raising both sides of the equation to the fourth power gives:

\(4/9 = 3^{-4n}\)

Multiplying both sides of the equation by 9 gives:

\(4 = 9 * 3^{-4n}\)

Dividing both sides of the equation by 9 gives:

\(4/9 = 3^{-4n-2}\)

Taking the logarithm of both sides of the equation with base 3 gives:

\(log3(4/9) = -4n - 2\)

Solving for n gives:

\(n = (log3(4/9) + 2)/(-4)\)

Therefore, n = (log3(4/9) + 2)/(-4).

c.\(\sqrt[4]{32} * \sqrt[4]{8} = 2 ^ n\)

We can simplify root(32, 4) and root(8, 4) to:

\(\sqrt[4]{32} = 2\)

\(\sqrt[4]{8} = 2^{3/4}\)

Substituting these values into the equation gives:

\(2 * 2^{3/4} = 2^n\)

Multiplying the two terms on the left-hand side of the equation gives:

\(2^{7/4} = 2^n\)

To solve for n, we can take the logarithm of both sides of the equation with base 2:

\(log2(2^{7/4}) = log2(2^n)\)

7/4 = n

Therefore, n = 7/4.


To know more about fraction visit:
https://brainly.com/question/29766013
#SPJ1

The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

Visit here to learn more about probabilities:

brainly.com/question/29381779

#SPJ11

The expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these.

A single term or a collection of phrases can be used to create an algebraic expression.

For instance, 4x and y are the two terms in the formula 4x + y.

So, we have a square as a figure.

The side of the figure is (n - 6).

Now, the expression to find the area of the square will be:

A = (n-6)²

Now, evaluate when n = 11 as follows:

A = (n-6)²

A = (11-6)²

A = (5)²

A = 25 units²

Therefore, the expression that will help to calculate the area of the figure is A = (n-6)² and the area will be 25 units² when n = 11.

Know more about expressions here:

https://brainly.com/question/28934492

#SPJ1

The mathematical expression that Katherine requires to know the price of the objects that she is going to buy is 8 * ($20.75) + 120 * ($5/12) = $216

To find a mathematical expression for this procedure we must take into account the values that we know.

For example, we know that it requires 15 pansies for each tree. This can be expressed like this:

On the other hand, we must calculate the price of each tree and the pansies that are going to be used to surround each one as shown below.

According to the above, the final expression, in which all the necessary data for Katherine is included, is:

Learn more about mathematical expression in: https://brainly.com/question/1703934

#SPJ1

Answer:

Answer From Edge 2023

Step-by-step explanation:

The total cost of the trees must be added to the total cost of the pansies. The tree cost is the cost of one tree times eight. The pansy cost is the cost for 15 pansies multiplied by 8 trees, then divided by the number of pansies in a pack: 20.75(8) + 2.50(15)(8) ÷ 6.

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

For more such questions on center

https://brainly.com/question/1506955

#SPJ8

The estimated length of the ramp is in meters  \(30^2/100^2+3^2\).

The length of the hypotenuse in a right triangle is,

\(a^2+b^2a^2+b^2\)

The square root of, a, squared, plus, b, squared, end square root where a and b are the lengths of the triangle's sides (this formula is derived from the Pythagorean theorem).

From the side, a certain ramp has a right-triangular shape.

Its height is,

30.3030 centimeters and its horizontal length are 333 meters.

To learn more about the Pythagorean theorem visit:

https://brainly.com/question/343682

#SPJ1

Mean is when you sum up all the numbers in a data set and divide that sum with the total amount of numbers in the data set.

Median is the middle number of a data set.

Mode is the number that shows up the most in a data set.

Best of Luck!

Answer:

The mean is the average of a data set. The mode is the most common number in a data set. The median is the middle of the set of numbers.

Step-by-step explanation:

i hope you get it.

The producers' surplus at a price level of $53, given the price-supply equation p = 5 + 0.1x + 0.0003x², is approximately $506.

To calculate the producers' surplus, we need to find the area between the supply curve and the price line up to the quantity supplied at the given price level. First, we need to determine the quantity supplied (x) at a price of $53 by substituting p = 53 into the equation p = 5 + 0.1x + 0.0003x²:

53 = 5 + 0.1x + 0.0003x²

Simplifying this equation and solving for x, we get x² + 333.33x - 48000 = 0. By applying the quadratic formula, we find two possible solutions: x ≈ -359.94 and x ≈ 133.61. Since the quantity supplied cannot be negative, we discard the negative value.

Therefore, the quantity supplied at a price of $53 is approximately 133.61. Now we can calculate the producers' surplus by integrating the supply function S(x) from 0 to 133.61:

Producers' Surplus = ∫(0 to 133.61) (53 - (5 + 0.1x + 0.0003x²)) dx

Evaluating this integral numerically gives us approximately $506. Thus, the producers' surplus at a price level of $53 is approximately $506.

Learn more about equation here:

https://brainly.com/question/32645495

#SPJ11

i) Michaelangelo's sells small, medium, large, and jumbo pizzas. - Not nominal data.

Nominal data refers to a type of categorical data where values are assigned to distinct categories or labels without any inherent order or numerical significance. In the given options, both i) and ii) involve categorical information, but only option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") describes nominal data.

In option i), the sizes of pizzas (small, medium, large, and jumbo) can be considered ordinal data as they have a specific order and imply a relative size difference. Ordinal data possesses a sequential arrangement where the categories have a meaningful relationship or hierarchy.

On the other hand, option ii) presents toppings (pepperoni, black olives, and mushrooms) as distinct categories without any inherent order or hierarchy.

Each topping represents a separate label or category, making it an example of nominal data.Therefore, option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") accurately describes nominal data.

Learn more about nominal data

brainly.com/question/31918425

#SPJ11

Answer:

6:2

Step-by-step explanation:

Answer:6:2 I hope this is helpful

Step-by-step explanation:

6 apples to 2 mangos is 6:2

Answer:270,000

Step-by-step explanation:

Answer:-3/2

Step-by-step explanation:

a. To determine the maximum wait time that would result in at most 1.5% of customers receiving a free meal, we need to find the z-score associated with the 1.5% probability. Using a standard normal distribution table or calculator, we find that the z-score is approximately -2.33.

From the formula for a z-score:

z = (x - mu) / sigma

where x is the wait time we want to find, mu is the mean wait time (19 minutes), and sigma is the standard deviation (3.3 minutes), we can solve for x:

-2.33 = (x - 19) / 3.3

x - 19 = -7.689

x = 11.311

Therefore, we should advertise a maximum wait time of 11.3 minutes to ensure that no more than 1.5% of customers receive a free meal.

b. See attached graph.

The normal distribution is a continuous probability distribution that describes the probability of a random variable taking on a range of values. It is characterized by its mean and standard deviation and has a bell-shaped curve.

The normal distribution might apply to this situation because it is a common model for many real-world phenomena that exhibit random variation. In this case, the waiting times of customers are likely to be influenced by a variety of factors, including the time of day, the number of customers, and the efficiency of the staff. These factors may produce a random variation in waiting times that can be modeled using a normal distribution.

The specific normal distribution for this situation has a mean of 19 minutes and a standard deviation of 3.3 minutes. This means that the majority of customers can expect to wait around 19 minutes for their meal, with some variability around this average.

The graph created in part b represents the waiting times of the customers by showing the distribution of waiting times and highlighting the area corresponding to the 1.5% of customers who would receive a refund. The graph is centered at the mean of 19 minutes and has a spread of 3.3 minutes, which reflects the variability in waiting times.

The answer to part a suggests that we should advertise a maximum wait time of 11.3 minutes to ensure that no more than 1.5% of customers receive a free meal. For customers who do not receive a free meal, this wait time represents a reasonable expectation for their wait time. For customers who do receive a free meal, the wait time would be longer than expected but would still be within the realm of reasonable expectations. In practice, the company may choose to round this number up to a "nice" wait time, such as 10 minutes or 15 minutes, to make it more appealing to customers.

The proposal will not result in a loss of profit for the company because the maximum wait time advertised is well within the expected range of waiting times. By offering a refund for customers who wait longer than this time, the company is incentivizing its staff to work more efficiently and reduce waiting times overall. The cost of a few free meals is likely to be offset by increased customer satisfaction and loyalty, as well as reduced negative reviews and complaints. Additionally, the company can control the maximum refund rate by adjusting the advertised wait time as needed.

Learn more about z-score

https://brainly.com/question/15016913

#SPJ4

Full Question ;

Suppose that you are working for a chain restaurant and wish to design a promotion to disabuse the public of notions that the service is slow. You decide to institute a policy that any customer that waits too long will receive their meal for free.

a. Determine an estimate of an advertised maximum wait time so that 1.5% of the customers would receive a free meal. Round to one decimal place.

b. Include a graph illustrating the solution. For the graph do NOT make an empirical rule graph, just include the mean and the mark off the area that corresponds to the 1.5% who would receive the refund. There is a Normal Distribution Graph generator linked in the resources area. Combine the above into as single file and upload using the link below.

c. Write a response to the vice president explaining your prescribed maximum wait time. Structure your essay as follows:

1. An advanced explanation of the normal distribution

2. Why the normal distribution might apply to this situation

3. Describe the specific normal distribution for this situation (give the mean and standard deviation)

4. Explain how the graph created in part b. represents the waiting times of the customers.

5. Explain the answer to part a. in terms of both the customers who get a free meal and those who do not. Feel free to use the accurate answer in part a to determine a "nice" wait time to be used in the actual advertising campaign.

6. Use the answers to parts a. and b. to explain how the proposal will not result in a loss of profit for the company.

The dimensions of the rectangle is 25m × 25m.

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth.

The three dimensions of a three-dimensional shape are length, width, and depth.

It is given that

Perimeter of the rectangle = 100m

Area is as large as possible if both the values are the same number.

The measurements must be equivalent for the rectangle to attain its maximum area.

Consider the dimensions as x

So perimeter can be written as

2 (x + x) = 100

2 (2x) = 100

By additional computation

4x = 100

Divide both sides by 4

x = 25

Therefore, the dimensions of a rectangle is 25m × 25m.

To learn  more about dimension of a rectangle visit:

https://brainly.com/question/15225905

#SPJ4

Answer:

31/20

Step-by-step explanation:

write all numerators above the LCD 20

45-14/20

subtract the numbers

31/20

Answer:

31/20

Step-by-step explanation:

a) A random family is chosen and then a random child within that family is chosen the mean is 1.45 and the variance is 0.38.

b) A random child is chosen in the town, the mean is 1.579 and the variance is 0.454.

For part A:

A random family is chosen and then a random child within that family.

P(X=1)= P(X=1 | family with one child). P(family with one child)

             + P(X=1 | family with two children).P(family with two children)

             +P(X=1 | family with three children).P(family with three children)

           = 1.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 37/60

P(X=2)=P(X=2 | family with one child). P(family with one child)

             + P(X=2 | family with two children).P(family with two children)

             +P(X=2 | family with three children).P(family with three children)

           = 0.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 19/60

P(X=3)=P(X=3 | family with one child). P(family with one child)

             + P(X=3 | family with two children).P(family with two children)

             +P(X=3 | family with three children).P(family with three children)

           = 0.30/100 + 0 . 50/100 + 1/3 . 20/100 = 4/40

hence, using these probabilities we can find,

E(X) = 1(37/60) + 2(19/60) + 3(4/60) = 1.45,

therefore, Var(x) = 149/60 − \(1.45^{2}\) = 457/1200 ≈ 0.38

hence, the mean of the child's birth is 1.45 and the variance of the child's birth ranks 0.38.

For part B,

When a random child is chosen in the town with equal probabilities.

There are 1 x 30 + 2 x 50 + 3 x 20 = 190 children in the town where 100 of them are first born, 70 of them are second born, and 20 of them are third born. Let X be a random variable that marks the birth rank of a child.

Hence,

E(X) = 1(100/190) + 2(70/190) + 3(20/190) ≈ 1.579

and

Var(X) = 2.947 − \(1.579^{2}\) ≈ 0.454

For a random child chosen, the mean of the child's birth is 1.579 and the variance of the child's birth ranks 0.454.

Read more about the mean and variance:

brainly.com/question/28562949

#SPJ4

Step-by-step explanation:

all regular polygons have (n-2)*180 this formula can use here. n= no of sides

Answer:

M = (n-2)*180 degrees for polygons with n sides.

Step-by-step explanation:

As already noted, there is no description of the polygon in question.  However, the formula for the sum of the measure of the interior angles of a regular polygon is M = (n-2)•180 where n is the number of sides.  A triangle has 3 sides, so M = (3-2)*180 = 180 degrees.

A hexagon has 6 sides, so M = (6-2)*180 = 720.

To find the length of the model, we need to use the given scale, which states that 1 inch on the model represents 1.5 feet in reality.

The length of the actual object is given as 18 feet. Let's calculate the length of the model:

Length of model = Length of actual object / Scale factor

Length of model = 18 feet / 1.5 feet/inch

Length of model = 12 inches

Therefore, the length of the model is 12 inches. Therefore, the correct option is (a) 12 inches.

Learn more about Length here :

https://brainly.com/question/29133107

#SPJ11

Answer:

-60/72 = -5/6

-24/36 = -2/3

91/364 = 45/182

To rank data sets from the smallest to largest standard deviation, we need to look at the spread of the data in each histogram. The standard deviation is a measure of how spread out the data is. If the data is closely clustered around the mean, the standard deviation will be small. If the data is spread out over a wider range, the standard deviation will be larger.

To determine the standard deviation of each data set, we can look at the width of the histogram. A narrower histogram indicates a smaller standard deviation, while a wider histogram indicates a larger standard deviation.

Based on this information, we can rank the data sets from smallest to largest standard deviation by looking at the width of the histograms and ordering them from narrowest to widest.

In conclusion, to rank data sets from the smallest to largest standard deviation, we need to look at the spread of the data in each histogram and order them from narrowest to widest. This will give us the ranking of the data sets from smallest to largest standard deviation.

Learn more about histogram: https://brainly.com/question/25983327

#SPJ11

The Least Common Multiplier of \($q(2-4), r(-6-8), s(-102), t(-26)$\) is \($-9282 q r s t$\).

What is Least Common Multiplier ?

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm), lowest common multiple (lcm), or smallest common multiple of two numbers a and b in mathematics and number theory.

Lowest Common Multiplier (LCM)

The LCM of a, b is the smallest multiplier that is divisible by both a and b

Factor \($q(2-4): \quad-2 q$\)

Factor \($r(-6-8): \quad-2 \cdot 7 r$\)

Factor \($s(-102): \quad-17 \cdot 2 \cdot 3 s$\)

Factor \($t(-26): \quad-13 \cdot 2 t$\)

Multiply each factor with the highest power:

\($$-13 \cdot 17 \cdot 2 \cdot 3 \cdot 7 \cdot q \cdot r \cdot s \cdot t$$\)

Simplify

\($-9282 q r s t$\)

Complete question: Find the Least Common Multiplier  of Q(2, -4), R(-6, -8), S(-10, 2), T(-2, 6) is:

To learn more about Least Common Multiplier visit:https://brainly.com/question/27962046

#SPJ1

Answer: 9.0x10^-6

Step-by-step explanation:

Scientific notation is writing a given number, as a product of a unit number (that can and usually has digits after the decimal point) and a given power of the number 10.

In this case we have:

0.9x10^-5.

This is almost correct, the "correct" way to write this is having a number in the unit place:

So we want to move our number to te left, then we can multiply and divide by 10, because this will not change the value of our number:

(0.9x10^-5)*10/10 = 9.0x10^-5/10 = 9.0x10^-6

The present value of the cash flows is approximately $11,754.04.

To calculate the present value of the cash flows, we need to discount each cash flow to its present value using the appropriate discount rate. The present value (PV) can be calculated using the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + ... + CFn / (1 + r)^n

where CF is the cash flow and r is the discount rate.

Using the given discount rate of 9.89 percent per year, we can calculate the present value as follows:

PV = 2,200 / (1 + 0.0989)^1 + 2,600 / (1 + 0.0989)^2 + 4,800 / (1 + 0.0989)^3 + 5,400 / (1 + 0.0989)^4

Calculating each term and summing them up:

PV = 2,200 / 1.0989 + 2,600 / 1.0989^2 + 4,800 / 1.0989^3 + 5,400 / 1.0989^4

PV ≈ 1,999.64 + 2,271.89 + 3,622.82 + 3,860.69

PV ≈ 11,754.04

know more about present value here:

https://brainly.com/question/28304447

#SPJ11

Answer:

Y=1/2x-3

Step-by-step explanation:

Down 3 at the y-axis and up 1 right 2.

Answer:

20 feet.

Step-by-step explanation:

Pythagoreans theorem states that a^2 + b^2 = c^2

a = 12, squared = 144

b = 16, squared = 256

144 + 256 = 400

√400 = 20

20 feet is the answer.

Hope this helps.