As a town gets smaller, the population of its high school decreases by 7% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write
an equation. Then solve the equation without graphing.
Write an equation to represent this situation. Let n be the number of years before the class will have 100 students.
(Type an equation using n as the vanable. Use integers or decimals for any numbers in the equation)
Help again please

a) The total number of marbles is 6 + 12 = 18.P(a red marble) = 6/18 = 1/3

b) There are 12 odd-numbered marbles in total. P(an odd-numbered marble) = 12/18 = 2/3

The probability that the marble drawn from the jar is red can be found using the formula for probability. The probability formula can be written as the ratio of the number of favorable outcomes to the total number of possible outcomes. P(a red marble) = number of red marbles / total number of marbles. In this case, there are 6 red marbles and 12 blue marbles in the jar. Therefore, the total number of marbles is 6 + 12 = 18.P(a red marble) = 6/18 = 1/3(b) The probability that the marble drawn from the jar is odd-numbered can be found using the formula for probability. The probability formula can be written as the ratio of the number of favorable outcomes to the total number of possible outcomes. P(an odd-numbered marble) = number of odd-numbered marbles / total number of marbles. In this case, there are 6 red marbles numbered 1 to 6 and 12 blue marbles numbered 1 to 12 in the jar. Therefore, the total number of marbles is 6 + 12 = 18.To find the number of odd-numbered marbles, we need to count the number of red and blue marbles numbered 1, 3, 5, 7, 9, 11. There are 6 odd-numbered red marbles and 6 odd-numbered blue marbles. Therefore, there are 12 odd-numbered marbles in total. P(an odd-numbered marble) = 12/18 = 2/3

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The power dissipated by the heater is 1260 watts (W).

What is a polynomial?

A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.

Given:

Current (I) = 10.5 A

Potential Difference (V) = 120 V

Unknown:

Power (P) = ?

The formula to calculate the power is:

P = VI

Substituting the given values:

P = 120 V × 10.5 A

P = 1260 W

It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:

P = 1260 W (rounded to three significant digits).

Therefore, the power dissipated by the heater is 1260 watts (W).

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The subject with the maximum average is Mathematics, while the subject with the minimum average is Social studies; moreover, there is a difference of 6 between Hindi and English.

Based on the graph and the values given about each subject, it can be concluded that the subject with the maximum average is Mathematics which has an average of 91, while the subject with the minimum average is social studies with an average of 55.

English average: 62

Hindi average: 56

62 - 56 = 6

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Answer:

10 units

Step-by-step explanation:

Here, legs = base and perpendiculars.

So, Clearly given Base = 6 units Perpendicular = 8 cm

Square's Side = Hypotenuse.

By Pythagoras theorem,

H² = B²+P²

H ² = 6²+8²

H² = 36+64 = (10)²

H = 10 units.

Square's Side length = 10 units

Roy purchased whole pizzas for P 190.00 each. To determine the number of whole pizzas he bought, we can divide the total cost of the pizzas by the cost of each pizza. Therefore, the calculation P 950.00 / P 190.00 results in 5, indicating that Roy bought five whole pizzas.

Roy spent a total of P 1070 for pizza with 3 sets of additional toppings. Since each set of additional toppings costs P 40.00, then the total cost of the toppings is 3 x P 40.00 = P 120.00. Subtracting this from the total amount spent gives us P 950.00, which is the cost of the pizzas alone.

Since each whole pizza costs P 190.00, we can divide the cost of the pizzas by the cost of each pizza to find the number of whole pizzas Roy bought. Therefore, P 950.00 / P 190.00 = 5.

Thus, Roy bought 5 whole pizzas.

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Answer:

Step-by-step explanation:

Given:

Side a and Side b are 6 and 5.

The angle C is 131.

This is an obtuse scalene triangle as identified.

Area = ab * sin (C)/2  = 11.32064

According to Moore's Law, the number of transistors that can be placed inexpensively on a silicon chip doubles every two years, a typical CPU contained about 1,000,000 transistors in 1990.

Let’s first calculate the number of doublings from 1990 to 2000. Number of years from 1990 to 2000 = 2000 - 1990 = 10 yearsDoublings from 1990 to 2000 = [tex]$\dfrac{10 \text{ years}}{2 \text{ years per doubling}} = 5$[/tex] doublingsNow, we can calculate the number of transistors in a typical CPU in the year 2000:

[tex]$$\begin{aligned} \text{Number of transistors in 2000} &= \text{Number of transistors in 1990} \times 2^{\text{number of doublings}} \\ &= 1,\!000,\!000 \times 2^5 \\ &= 32,\!000,\!000 \end{aligned}$$[/tex]

Therefore, a typical CPU contained about 32,000,000 transistors in the year 2000.

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The 90% confidence interval for the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is: resulting in a confidence interval of (4.337, 6.263) pounds.

To construct a 90% confidence interval to estimate the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not, we can use a two-sample t-test with unequal variances.

The null hypothesis is that the true difference between the mean amounts of weight lost by the two groups is zero, and the alternative hypothesis is that the true difference is not zero.

We can use the following formula to calculate the confidence interval:

CI = (x_1 - x_2) ± tα/2 * √((s_1)²/n_1 + (s_2)²/n_2)

where

x_1 = 15.6 (mean amount of weight lost by group a)

x_2 = 10.3 (mean amount of weight lost by group b)

s_1 = 1.2 (standard deviation of group a)

s_2 = 1.9 (standard deviation of group b)

n_1 = n_2 = 26 (sample size of both groups)

tα/2 = t0.05/2,24 = 1.711 (degrees of freedom = n_1 + n_2 - 2 = 50)

Plugging in the values, we get:

CI = (15.6 - 10.3) ± 1.711 * √(1.2²/26 + 1.9²/26)

CI = 5.3 ± 0.963

CI = (4.337, 6.263)

Therefore, with 90% confidence, we can estimate that the true difference between the mean amounts of weight lost by dieters who supplement with calcium and those who do not is between 4.337 and 6.263 pounds.

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Answer:

Let's use the formula for the volume of a right circular cone to solve this problem:

V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.

Using the chain rule of differentiation, we can express the rate of change of the volume as follows:

dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)

To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:

dV/dr = (2/3)πrh

dV/dh = (1/3)πr^2

Substituting the given values and their rates of change, we have:

dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)

dV/dt = 55,742.4 - 1,994,598.4

dV/dt = -1,938,856 in^3/s

Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.

Step-by-step explanation:

The player should be willing to pay up to $1.33 to play this game and not lose money in the long run.

The expected value is the sum of the products of each possible outcome and its probability. Let's calculate the expected value of the game:

E(X) = (1/6) * $4 + (5/6) * (-$2)

E(X) = $0.67

This means that on average, the player can expect to win $0.67 per game. Since it costs $2 to play, the player should not be willing to pay more than $2 - $0.67 = $1.33 to play the game and not lose money in the long run.

Probability theory is based on axioms, which are basic assumptions about the nature of probability. It is used to quantify uncertainty and to make predictions based on the available information. Probability is expressed as a number between 0 and 1, with 0 meaning an event is impossible, and 1 meaning an event is certain.

The concept of probability is used in a variety of fields, including statistics, economics, engineering, and physics. In statistics, probability is used to model random variables, estimate parameters, and test hypotheses. In economics, probability is used to model financial risks and decision-making under uncertainty. In engineering and physics, probability is used to model complex systems and predict the behavior of particles.

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The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.

Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:

1/4(4 + x) = 4/3

4 * 1/4(4 + x) = 4 * 4/3

Simplifying:

4 + x = 16/3

Subtract 4 from both sides of the equation:

4 + x - 4 = 16/3 - 4

Simplifying:

x = 16/3 - 12/3

x = 4/3

A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.

Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.

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Let's break this problem down step by step.

First, we can work out the weight of one white ball by subtracting the weight of 6 white and 3 orange balls (20 pounds) from the weight of 2 white and 5 orange balls (8 pounds):

Weight of 1 white ball = 8 - 20 = -12

Next, we can work out the weight of one orange ball by subtracting the weight of 2 white and 5 orange balls (8 pounds) from the weight of 6 white and 3 orange balls (20 pounds):

Weight of 1 orange ball = 20 - 8 = 12

Now that we know how much one white and one orange ball weigh, we can work out the weight of 4 white and 4 orange balls together:

Weight of 4 white and 4 orange balls = (4 x -12) + (4 x 12) = 0

Therefore, the weight of 4 white and 4 orange balls together is 0 pounds.

By solving two given simultaneous equations using algebra, we find that the combined weight of 4 white balls and 4 orange balls is 16 pounds.

The subject matter of this question pertains to simultaneous equations. The equations in question are, 2w + 5o = 8 and 6w + 3o = 20, where w stands for the weight of a white ball and o stands for the weight of an orange ball. We can solve these equations to find the individual weights of these balls. After finding these values, we substitute these into a new equation, 4w + 4o, to find the total weight of 4 white and 4 orange balls together. By solving these equations, we find that the weight of 4 white balls and 4 orange balls together is 16 pounds.

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3

Step-by-step explanation:

you can see the ratio of flour to sugar is 3:1 so for every 3 cups of flour is 1 cup of sugar so if you have 5 sugar cups you must have 3 times that of flour so 5×3=15 so 15 cups

Answer: At 250 miles, plan B is the most cost effective.

Step-by-step explanation:

Answers are under the questions below.

I. In complete sentences, translate each function into a verbal model describing the total cost of the rental in terms of the number of miles that the car is driven.

Plan A will charge .12 per mile plus a one time fee of $75.

Equation is y = .12x + 75 with the $75 being the y intercept or one time fee.

Plan B will charge .35 per mile with no one time fee.

Equation is y = .35x with the y intercept being (0) zero.

II. For each function, determine how the rate of change will affect the total cost of a car rental.

Initially the Plan A will be more expensive because of the one time fee, even though the rate is .12 per mile, which is much less than Plan B.

Plan B charges .35 per mile, but will eventually catch up in cost.

At approximately 326 miles the cost of each plan will equal at $114.13.

After 326 miles, Plan B will cost more than Plan A.

III. For a car rental that will include a maximum of 250 miles for the duration of the rental, which plan is the most cost effective?

Plan A, substitute 250 miles for x

Cost = .12 (250)  + 75

Cost = $105

Plan B, substitute 250 miles for x

Cost = .35 (250)

Cost = $87.50

At 250 miles, plan B is the most cost effective, saving $17.50.

graph is attached.

The probability that the flip results in a head is given as Pr[H] = 23. Therefore, the probability that the flip results in a tail is Pr[T] = 1 - Pr[H] = 1 - 23 = 13.

Let A be the event that a white marble is selected. We need to find the conditional probability Pr[H|A], i.e., the probability that the flip resulted in a head given that a white marble was selected.

Using Bayes' theorem, we have:

Pr[H|A] = (Pr[A|H]*Pr[H]) / Pr[A]

Pr[A|H] is the probability of selecting a white marble given that the flip resulted in a head. This is given by (9/25), since there are 9 white marbles out of 25 in the first urn.

Pr[A] is the total probability of selecting a white marble, which can be found using the law of total probability:

Pr[A] = Pr[A|H]*Pr[H] + Pr[A|T]*Pr[T]

= (9/25)*0.23 + (1/11)*0.13

= 0.0888 + 0.0118

= 0.1006

Pr[A|T] is the probability of selecting a white marble given that the flip resulted in a tail. This is given by (1/11), since there is only 1 white marble out of 11 in the second urn.

Therefore,

Pr[H|A] = (9/25 * 0.23) / 0.1006 = 0.6508

Hence, the probability that the flip resulted in a head given that a white marble was selected is 0.6508 (or approximately 0.65).

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Jenny works at Sammy's Restaurant and is paid according to the rates in the following

table.

Jenny's weekly wage agreement

Basic wage $600.00

PLUS

$0.90 for each customer served.

In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by

the formula

W = 600+ 0.90n.

(i) Determine Jenny's weekly wage if she served 230 customers.

(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number

of customers that Jenny must serve in order to have a good week?

(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for

each customer she serves.

If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's

weekly wage when she serves m customers.

(iv) In a certain week, Jenny and Shawna received the same wage for serving the same

number of customers.

How many customers did they EACH serve?

3 / 3

(i) If Jenny serves 230 customers, her weekly wage is

W = 600 + 0.90n = 600 + 0.90(230) = $807.00

Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.

(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,

600 + 0.90n ≥ 1,000

0.90n ≥ 400

n ≥ 444.44

Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.

(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:

W = 270 + 1.50m

Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.

(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:

Jenny's wage = 600 + 0.90x

Shawna's wage = 270 + 1.50x

Setting these two expressions equal to each other, we get:

600 + 0.90x = 270 + 1.50x

330 = 0.60x

x = 550

Therefore, Jenny and Shawna each served 550 customers.

The probability of someone returning exactly 1 of the 3 packages can be calculated as:P(1 out of 3 packages is returned) = C(3, 1) × P(0 or 1 diskette is defective)¹ × (1 - P(0 or 1 diskette is defective))²P(1 out of 3 packages is returned) = C(3, 1) × (0.9043820371)¹ × (0.0956179629)²P(1 out of 3 packages is returned) = 0.2448700124Therefore, the required probability of someone returning exactly 1 of the 3 packages is 0.2448700124.

The given data from the question is that the company produces diskettes which have the probability of being defective as 0.01. The packages that are sold have a size of 10 and the guarantee says that there can be at most one defective diskette in the package. Now, the question is to find the probability of someone returning exactly 1 of the 3 packages that they have bought.  So, the given data can be summarized as:Given:Probability of the diskette being defective, p = 0.01Guarantee: At most one diskette in the package of size 10 is defective.Now, let's solve the problem using probability theory

Probability of 1 diskette being defective in a package of size 10 can be calculated as:P(defective) = p = 0.01P(non-defective) = 1 - p = 0.99Using the given guarantee, probability of at most one defective diskette in a package of size 10:P(0 or 1 diskette is defective) = P(0 defective) + P(1 defective)P(0 or 1 diskette is defective) = C(10, 0) × (0.99)¹⁰ + C(10, 1) × (0.99)⁹ × (0.01)P(0 or 1 diskette is defective) = 0.9043820371Using the above probability

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2/7 + 1/4 = 15/28 ≅ 0.5357143

Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28 

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.

The smallest possible values for "a" and "b" that satisfy these conditions are when a = 1 and b = 3. This is because 1 is the smallest factor of 15, and 3 is the smallest multiple of 3.

What is integers?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

Let's call the two unknown numbers as "a" and "b"

Since "a" is a factor of 15, the possible values for "a" are 1, 3, 5, and 15.

Since "b" is a multiple of 3, the possible values for "b" are 3, 6, 9, 12, 15, and so on.

The smallest possible values for "a" and "b" that satisfy these conditions are when a = 1 and b = 3. This is because 1 is the smallest factor of 15, and 3 is the smallest multiple of 3.

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The intercept value in multiple linear regression is the value of Y when all the values of all input variables are zero. i.e., option (A) is correct

Multiple linear regression (MLR) is a statistical technique that determines the relationship between two or more independent variables and a single dependent variable. MLR is a statistical technique that is more general than simple linear regression, which can only handle two variables.

The intercept term is critical in Multiple linear regression (MLR) models since it represents the value of the dependent variable when all independent variables are equal to zero, indicating the baseline value of the dependent variable. It also influences the slope of the regression equation because its slope varies across different regression coefficients.

The intercept value is used to calculate the predictions for Y based on various combinations of X values in the model. When all independent variables are equal to zero, the intercept value is equivalent to the constant term or bias term in the model equation.

Therefore, Option (A) is correct, it is critical to have a solid understanding of the intercept value and its interpretation when working with Multiple linear regression (MLR) models.

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All parts are define in the below points.

A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.

a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.

b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.

c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.

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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.

b). Its p-value would be 0.00015.

c). The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex].

A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.

A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration [tex](\mu=0.31g/m^2)[/tex]. Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration [tex](\mu\neq 0.31g/m^2)[/tex] in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.

B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than [tex]0.31g/m^2[/tex]. Its p-value would be 0.00015.

C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than [tex]0.31g/m^2[/tex]. The safe concentration of [tex]0.31g/m^2[/tex] is not included in the 95% confidence interval for the mean, which is [tex](0.2457g/m^2,\ 0.3105g/m^2)[/tex]. As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.

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Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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By answering the presented question, we may conclude that Sanderson amount Equipment Company owes $42,000 Galaxy Furniture Supply owes $13,360. $55,360 in total liabilities

aggregate attempting to determine the time required, total number or amount. The quantity at sight or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, or a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity signifies how much there still is, how often you have, the amount you require, or the amount that you get. He needs that quantity of cash to get by.

The following figures would appear on Dr. Ortiz's balance sheet:

Assets:

Cash: $31,000

$11,300 for dental supplies

$57,100 for dental equipment

$20,000 for office furnishings

The total value of the assets is $119,400.

Liabilities:

Sanderson Equipment Company owes $42,000

Galaxy Furniture Supply owes $13,360.

$55,360 in total liabilities

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Answer:

1. first, add the amount of people who cannot swim. they need swim lessons.

2.  add up the people in 5th grade who can swim and the people who cannot. same with the 4th graders.

4.  the students that cannot swim, add up the 5th and 6ths graders that cannot swim.

5. add up all of the SOHO swimmers.

6. subtracts SOHO swimmers from swim academy.

set up an equation like this for #7

total number of students that can swim/ total amount of 5th graders = x/100

use the fraction on the left and multiply it by 100.

same with number 8

Step-by-step explanation:

Answer:

Step22-by-step explanation:

In total, the knockout stage of the UEFA champions league includes players from 79 different nationalities.

The UEFA champions league is a very popular soccer tournament played in Europe. This tournament includes 16 different teams in the knockout stage. Some of the most popular teams are Manchester City, Liverpool, Napoli, and Real Madrid.

Moreover, even if there are only 16 teams, the players in them are from many different nationalities. Indeed, this year there are players from 79 different countries.

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Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,

    determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.

The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.

Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9

The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.

When a ball falls from height, it gains potential energy.

Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height

PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules

Initial kinetic energy (KE) = PE of Basketball

KE of Basketball = 18.4 J

Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.

Using the coefficient of restitution (e) we can find the velocity of the balls after collision

   v1 - v2 = -e(u1 - u2)

Initial momentum (P) = Final momentum (P)

before the collision  P = m1u1 + m2u2

after collision  P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P

                           = (0.625 kg * v1) + (0.0585 kg * v2)

        Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)

     Here, m1 = mass of basketball

                     = 0.625 kg,

                m2 = mass of tennis ball

                      = 0.0585 kg,

  u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)

Also given that the time taken by the balls to meet is 0.15 seconds

Let h be the height to which the tennis ball bounces after the collision.

When the tennis ball bounces to height h, it gains potential energy.

KE + PE = Total energy

             = Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h

              = (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²

              = (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²

              = (1/2) * u2² - g * h

Substituting the values of u1, u2, m1, m2, e, t and g, we get:

v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1

   = 1.96 m/sv2

    = (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2

    = 5.5 m/s

Here, u1 = u2 = 0.

Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J

                = -0.286 J - 0.572 h0.572 h

                = -12.83 J / 2h

                = -12.83 J / (2 * 0.572)

                = 11.2 m

Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.

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Learn more about basketball is dropped and the coefficient of restitution at: https://brainly.com/question/19339515

Answer:

if it's for 1-6 just put a 1 at the bottom and multiply 8×5 and 1×12 for the first question and if u need to divide do that if your looking for answers I can help you but there's that for now :)

Step-by-step explanation:

(a) Parameter being estimated in the given information is the difference between two proportions (p_1 - p_2).

(b) A 95% confidence interval is given by  (0.075, 0.225)

(a) The parameter being estimated is the difference between two population proportions, which is denoted by (p_1 - p_2).

(b) The margin of error for a 95% confidence interval is 5%, which means that the critical value of z is 1.96 (obtained from a standard normal distribution table). Using the formula for the margin of error, we can write:

1.96 * √(p_1_hat*(1-p_1_hat)/n_1 + p_2_hat*(1-p_2_hat)/n_2) = 0.05

where p_1_hat and p_2_hat are the sample proportions from the two samples, and n1 and n2 are the sample sizes.

Solving for p_1_hat - p_2_hat, we get:

p1_hat - p2_hat = ±0.075

Since we are interested in a 95% confidence interval, we can subtract and add this value from P1 - P2 to obtain the interval:

P_1 - P_2 ± 0.075

Substituting the given value of P_1 - P_2 = 0.15, we get:

95% Confidence Interval: (0.075, 0.225)

To know more about the "confidence interval" concept: https://brainly.com/question/17097944

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Answer:

-0.5x[tex]x^{2}[/tex]+3x=0

Step-by-step explanation: