A survey asked stamp collectors how many stamps they have in their collection. The box-and-whisker plot summarizes the responses. Between what 2 numbers do the middle half of the responses fall

Answers

Answer 1

Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

What is data plotting?

A graph illustrating the correlation between two extra variables is the most common way to present data using a chart. It is also permitted to use diagrams that were manually or digitally drawn. starting at the origin, go 3 units up, then 2 units to the right. It is necessary to display the numbers for the positions 2, 3, and 4 on the reference system. Make your points really clear. 2.3 is represented by the pinkish dot with letter P. For each value in a data collection, you must first create a number line before you can create a line chart.

Here,

The boxplot, in its most basic version, visualizes five sample statistics: the minimum, the smallest value, the mean, the upper quartile, and the maximum.

The plot's box is a rectangle with ends at each quartile that encloses the sample's middle half. Therefore, the box's length represents the sample's interquartile range.

Nothing specific is represented by the box's other dimension. At the sample median, a line is drawn from across box.

Up until they hit the sampling maximum and minimum, whiskers extend from the box's two ends.

Each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

Therefore , the solution of plotting data comes out to be each whisker has a crossbar at the very end that is optional and has no significance in terms of length.

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Related Questions

shane made a scale drawing of a house and its lot. the scale of the drawing was 11 millimeters : 7 meters. if the lawn in the backyard is 66 millimeters long in the drawing, how long is the actual lawn?

Answers

Each piece of room or house length and width should be inverted to be scaled. For instance, a rectangle measuring 66" by 7" might be used to depict a dresser that is 5' by 2' at a scale of 14" = 1'.

A table that is 4' by 4' would also be 1" by 1" in size. [7] When measuring furniture that isn't square or rectangular, make the smallest square or rectangle the item might possibly fit and then use those dimensions. For instance, to represent a wingback chair that is 2' 6" wide and 2' deep, use a 5/8" by 1" rectangle.

Next, draw a rough outline of the chair inside the rectangle. On a piece of graph paper that is blank, draw the furnishings. Use graph paper without the room's floor plan drawn on it.

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In the triangle shown, for $\angle A$ to be the largest angle of the triangle, it must be that $m

Answers

The least possible value of n−m, expressed as a common fraction is 17/6.

By Triangle Inequality Theorem,

(x + 4) + 3x > x + 9

So 4x + 4 > x + 9

3x > 5

x > 5/3

If angle A is the largest angle, the side opposite to angle A will be the largest length, so

x + 9 > x + 4 (which is possible for all values of x)

and x + 9 > 3x

2x < 9

x < 9/2

Therefore 5/3 < x < 9/2. So m = 5/3 and n = 9/2

So calculating value of n - m

n - m = 9/2 - 5/3

= 27/6 - 10/6

= 17/6

--The question is incomplete, the complete question is as follows--

"In the triangle shown, for ∠A to be the largest angle of the triangle, it must be that m<x<n. What is the least possible value of n−m, expressed as a common fraction?"

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steve wants to download a selection of new music. how many ways can steve select three rock songs, five alternative songs, and six rap songs from a list of five rock songs, six alternative songs, and nine rap songs?

Answers

Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of ways.

1. To select three rock songs from a list of five, use the formula for combinations: nCr = 5Cr = 5!/ (3!*2!) = 10

2. To select five alternative songs from a list of six, use the formula for combinations: nCr = 6Cr = 6!/ (5!*1!) = 6

3. To select six rap songs from a list of nine, use the formula for combinations: nCr = 9Cr = 9!/ (6!*3!) = 84

4. To find the total number of selections, multiply the individual combinations: 10 x 6 x 84 = 11,250

Steve can select three rock songs, five alternative songs, and six rap songs in 11,250 number of  ways.

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Water is poured into the top half of a spherical tank at a constant rate. If W(t) is the rate of increase of the depth of the water, then W is: O constant O linear and increasing O linear and decreasing O concave up

Answers

The rate of increase of the depth of the water (W(t)) is constant.

What is rate ?

In mathematics and physics, the rate is a measure of change of a certain quantity with respect to another quantity. The rate can be a number, a ratio or a derivative. It is often represented by the symbol "d" or "dx/dt" or "dy/dt" and it measures how fast a quantity is changing.

Water is poured into the top half of a spherical tank at a constant rate, this means that the rate of increase of the depth of the water (W(t)) is constant.

In this case, W(t) is constant.

It is important to keep in mind that the rate of change of the function doesn't indicate the shape of the function, it just tells us the change of the dependent variable with respect to the independent variable. The shape of the function can be visualized by creating a graph of the function.

So , The rate of increase of the depth of the water (W(t)) is constant.

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The list shows numbers in order from least to greatest. -15, -3 4/5, -1.5, ____, 2.3, 5 2/3Which is an integer that can be inserted on the blank line in the list?a.-2 b. -1 1/3 c. 0 d. 1.2

Answers

An integer that can be inserted on the blank line in the list from the given options is 0.

Therefore the answer is c) 0.

The list shows numbers in order from least to greatest, that is ascending order -15, -3 4/5, -1.5, ____, 2.3, 5 2/3

The integer that can be inserted on the blank line in the list is c. 0, because it is greater than -1.5 and less than 2.3 and it is an integer.

-2 is less than -1.5. So they cannot be the answer. -1 1/3 is equal to -4/3 and 1.2 is greater than -1.5 and less than 2.3, but they are not integers.  

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If 7 girls each own 7 dresses and each
of the 7 dresses has 7 different hats to
go with it, how many hats are there?

Answers

7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are 49.

What is multiplication?

Calculating the sum of two or more numbers is the process of multiplication. It is stated as "a multiplied by b" when two numbers, let's say "a" and "b," are multiplied.

Multiplication in mathematics is essentially just adding a number repeatedly in relation to another number.

What are word problems?

A word problem is a type of mathematics exercise where the majority of the problem's context is supplied in spoken language as opposed to mathematical notation. Most word problems incorporate some type of narrative, hence they are sometimes called "story problems," and the quantity of technical jargon they employ can vary.

Given that 7 girls own 7 dresses, and each dress has 7 different hats to go with it then the total number of hats are:

Hats = (7)(7) = 49.

Hence, there are a total of 49 hats.

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(WILL GIVE BRAINIEST) A collage artist makes art out of real-life objects. She has three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. If she makes a triangle out of the pieces will it be right, acute or obtuse triangle?

Answers

If the artist makes a triangle from three pieces of bamboo that measure 4 inches, 5 inches and 7 inches. The triangle will not be a right triangle because the values are not Pythagorean triple

What is Pythagorean triple?

Pythagorean triples are b² + a² = c² where b, a and c are all positive integers.

These triples are represented as (b, a, c).

Here, b is perpendicular (or right angel) to a, a is the base and the hypotenuse of the right - angled triangle is labeled .

The most known and smallest triplets are (3, 4, 5).

In the problem, the values  4 inches, 5 inches and 7 inches cannot make a Pythagorean triple since

c² = 4² + 5²

c² = 16 + 25

c² = 41

c = √41 ≠ 7

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Melissa purchased a new car. the car had a list price of $20,540. melissa made a down payment of $3,900 and financed the rest, paying 8.6% interest compounded monthly over a payment period of 5 years. if melissa also had to pay 8.25% sales tax, a $995 vehicle registration fee, and a $57 documentation fee, what is her monthly payment?

Answers

Melissa's monthly payment is $450 if the down payment is $3,900.

To calculate the monthly payment, we first need to calculate the total amount financed. This is done by adding the list price of the car ($20,540), the sales tax (8.25% of $20,540 = $1,690.35), the registration fee ($995), and the documentation fee ($57) for a total of $23,282.35.

We then need to calculate the total amount of interest that Melissa will pay over the 5-year loan period. This is done by multiplying the interest rate (8.6%) by the total amount financed ($23,282.35) and multiplying that by the number of years (5).

This gives us a total interest payment of $7,634.84. We then add the total amount financed ($23,282.35) and the total interest payment ($7,634.84) and subtract the down payment ($3,900), which gives us the total amount that Melissa will pay over the 5-year loan period: $27,016.99.

We then divide this total amount by the number of months in the loan period (60) to get the monthly payment: of $450

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!!!!!!!!!!!!Sorry im just so tired from so much work but I need some help with this one quickly while I finished other assignments!!!!!!Question How do you graph an inequality? Use 2 or more sentences

Answers

Answer: To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.

Step-by-step explanation:

2. maria has 3 more than 4 times how much money josh has in savings. if josh has $505, how much does maria have?

Answers

Answer:

2023

Step-by-step explanation:

3 + 4x = y

y = 3 + 4(505)

y = 3 + 2020

y = 2023

please answer this i dont understand

Answers

The possible solution would be 10 bags of popcorn and 3 pretzels.

What are inequalities and their types?

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 'x' represents the number of bags of popcorn purchased and 'y' represents the number of bags of pretzels purchased.

Therefore,

x + y ≥ 13 and 7x + 5y ≤ 85.

The possible solution to these inequalities is where the graph of two intersects which is at (10, 3).

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Ekene was curious if sample range was an unbiased estimator of population range. She placed ping pong ballsnumbered from 0 to 32 in a drum and mixed them well. Note that the range of the population is 32.
She then took a random sample of 5 balls and calculated the range of the sample. She replaced the balls and
repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot
represents the sample range from a sample of 5 balls.
.
ea
8
12
16
20
24
28
32
Sample range
Based on these results, does sample range appear to be a biased or unbiased estimator of population range?
Hint: The population range is 32.

Answers

The graph provided in the exercise must be used in this task, together with our statistical understanding, so that we can state: correct option is A

What is statistics?

Statistics is a discipline of applied mathematics concerned with the gathering, description, analysis, and derivation of inferences from quantitative data. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics provide us the knowledge we need to understand how things operate. To conduct research, assess results, foster critical thinking, and make wise judgements, statistics are utilized. Almost any subject of study may benefit from the application of statistics to explore the causes, timing, and predictability of events.

The maximum points on the graph are at 21 and 31, and the sample ranges appear to be centered below 32, so we may claim so the option A is more appropriate.

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The complete question is as follows:

I. The sum of the probabilities in a probability distribution can be any number between 0 and 1. II. The probability of the union of two events is the sum of the probabilities of those events. III. The probability that an event happens is equal to 1 minus the probability that the event does not happen.

Answers

None of the above gives the complete set of true responses for the probability that the event does not happen.

What is probability?

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

None of the above provides the entire set of accurate replies for the likelihood that the event does not occur.

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Which is true about the legs of a 45 − 45 − 90 triangle?

A. The legs of a 45-45-90 triangle are congruent.
B. Now, a 45-45-90 triangle will be a right triangle because one of the angles is 90°.
C. Further, it will also be an isosceles triangle since the two angles are equal and the sides opposite to equal angles in a triangle are always equal.
D. Since it becomes an isosceles triangle, the two of its legs will definitely be equal, or congruent to each other.

Answers

A 45-45-90 triangle is a right and isosceles triangle, whose legs are congruent or equal, and have one right angle of 90°. Thus all the statements are correct.

A 45-45-90 triangle is a special kind of triangle, which has the following characteristics:

It’s isosceles with two congruent or equal sides and two congruent anglesIt has one right angle of 90° and two acute angles of 45°The length of the hypotenuse is √2 times the length of a leg. Thus the ratio of the length of sides is 1 : 1 : √2

The attached picture gives a better understanding of these characteristics.

If we take a look at the given problem, we can conclude that all the given statements are correct.

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The expression -250+12.1m represent a submarine that begins at a depth of 250 feet below sea level and ascended at a rate of 12.1 ft.per min. what was the depth of the submarine after six minutes 

Answers

Answer:

Step-by-step explanation:

The depth of the submarine after 6 minutes would be -182.9 ft. below sea level. This is calculated by taking the starting depth of -250 ft. and adding 12.1 ft. for each minute (6 minutes x 12.1 ft. = 72.6 ft.). Therefore, -250 + 72.6 ft. = -182.9 ft. below sea level.

identify the inequality that represents the given graph

Answers

The inequality, [tex]y < -3x+6[/tex] represents the following graph.

What three instances of inequality?

Income gap, gender inequality, access to health care, and social class are some of the most prominent examples of social inequality. Some people receive better and more skilled care in the medical field than others.

What are the two inequalities' rules?

Rule 1: An inequality symbol remains unchanged when the same amount is added to or subtracted from both sides. Rule 2: The inequality symbol remains unchanged when both sides are multiplied or divided by a positive number.

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Which data outcome of the number of customers in line would best support opening another cash register? Homework Help 1DF. Range/variance/standard deviation (population and sample) and shape of distribution, examples 2 (DOCX) High mean with high standard deviation Low mean with high standard deviation High mean with small standard deviation Low mean with small standard deviation

Answers

High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

What is standard deviation?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

We have to find from the given options which data outcome of the number of customers in line would best support opening another cash register.

The number of customer in the line having high mean with small standard deviation means deviation in data small and data cluster around mean. High mean I'm play high number of customer in line. This help to opening another cash register.

Hence, High mean with small standard deviation data outcome of the number of customers in line would best support opening another cash register.

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Which formula describes the range?

Answers

On solving the provided question, we can say that a function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

What is range?

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution. The solution provides the list's range.

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range (x).

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A student took a test which had 6 questions. He would score 8 points on the test if all his answers are correct. If y represents the student's score when he got x questions incorrect, which graph best represents this situation? (1 point)

A. graph of line going through ordered pairs 0, 8 and 6, 0
B. graph of line going through ordered pairs negative 6, 0 and 0, 8
C. graph of line going through ordered pairs 0, negative 6 and 8, 0
D. graph of line going through ordered pairs 0, 6 and 8, 0

Answers

Answer: Chart A best represents this situation: Pairs (0,8) and (6,0).

Step-by-step explanation: If y represents the students score and x represents the number of questions that the student has answered incorrectly, then if the student has answered 0 questions incorrectly, they should have the highest possible score. This would mean that at no mistakes (x=0), the student would have the maximum score (y=8). This would create the ordered pair (0,8).

Following that logic, if the student has made a mistake on every single question (x=6), then they would have the lowest possible score (y=0). This would then make the ordered pair (6,0). Hope this helps!

the mass of a grain of salt is around 0.06 mg. how many grains of salt would be in 100 grams of sand?

Answers

Answer:

1,666,667

Step-by-step explanation:

1000 milligrams is equal to one gram.

First, convert the mass of the grain of salt in milligrams to grams by dividing the mass in milligrams by 1000:

[tex]\implies \dfrac{0.06}{1000}=0.00006\; \rm g[/tex]

To calculate how many grains of salt would be in 100 grams of sand, divide 100 g by 0.00006 g:

[tex]\implies \dfrac{100}{0.00006}=1,666,666.6666...[/tex]

Therefore, there are 1,666,667 grains of salt in 100 grams of sand (to the nearest whole number).

A homeowner needs two loads of gravel for a driveway to their new house. One load of gravel weighs 7 tons and the second load weighs 8,000 pounds . What is the total weight of the gravel, in tons, used for the driveway?l1 toas87 tons7,8 tons

Answers

12 tons of gravel has been used for the driveway.

Weight of first load = 7 tons

Weight of second load = 8000 pounds

There are 2000 pounds (lb) in one US customary ton (t). Both tons and pounds are measurements of mass/weight in the US customary and imperial systems of measurement. However, the definitions of the ton vary in both systems. For example, there are 2240 pounds in an imperial ton, and 2204.6226 pounds in a metric ton.

The US ton is mostly used in the United States and Canada. The imperial ton was mostly used in the UK, and still is to a degree, but since the UK began the process of metrication, the metric ton is also used in the UK.

Convert pounds to tons:

1 pound = 0.0005 ton

8000 pounds = 4 ton

Then,

Weight of second load = 4 ton

Total weight of the gravel, in tons = Weight of first load + Weight of second load

= 8 tons + 4 tons

= 12 tons

Thus, 12 tons of gravel has been used for the driveway.

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What are the x- and y-intercepts of the equation?
y = log (3x + 4) + 2
Round only the final answers to the nearest hundredth.
Enter your answers in the boxes.
x-intercept: =
y-intercept =

Answers

x- intercept:  x = -1.33, y- intercept: y = log 4 + 2

How to find where does a function crosses x or y-axis?

Suppose that the line considered be of the form  y=f(x)

The equation for y-axis is x = 0

Thus, intersection between both the curves is obtained by putting x = 0 in the considered function.

We get x=0 and y=f(0)

Thus, the coordinate point of intersection with y-axis is (0,f(0))

And the equation for x-axis is y=0

Thus, its intersection with given function is at y= 0 and y such that

f(x)=0

Given equation,

y = log (3x+4) + 2,

For x - intercept,

y = 0,

0= log(3x+4) +2

-2= log(3x+4)

10^-2= 3x+4 ([tex]log_{m}[/tex]a=b => a=m^b)

0.01= 3x+4

0.01-4=3x

x= -3.99= -1.33

For y-intercept,

x = 0,

y=log(3(0)+4)+2= log4+2

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Write the equation of the circle centered at (6, 2) with radius 1. Fully simplify the equation.

Answers

Answer:

[tex]x^2-12x+y^2-4y+39=0[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given:

center = (6, 2)radius = 1

Substitute the given values into the equation of a circle formula:

[tex]\implies (x-6)^2+(y-2)^2=1^2[/tex]

Simplify by expanding:

[tex]\implies (x-6)(x-6)+(y-2)(y-2)=1[/tex]

[tex]\implies x^2-12x+36+y^2-4y+4=1[/tex]

[tex]\implies x^2-12x+y^2-4y+39=0[/tex]

which of the following outliers would most likely be the easiest to correct? a. a typographical error in data transfer b. a measurement error in instrument calibration c. a heavily skewed distribution d. a correctly measured anomalous result

Answers

a. a typographical error in data transfer outliers would most likely be the easiest to correct.

What is typographical error?

Typo, often known as a misprint, is short for a typographical error. Typos are mistakes created during the typing process that editors and proofreaders failed to catch.

When the writer means to enter the wrong term, the error is referred to be a typo. The majority of the time it is spelt wrongly. It's possible for a word to be incomplete, to have an extra letter, or to be missing a letter, which can occasionally result in the creation of a new term with a completely different meaning. A typographical error in material that has been written or printed.

Thus, correct option is: a

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Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.

Beth’s father asked her to buy party favors for her little brother’s birthday party. Party hats cost $1.60 each, balloons cost $.75 each, and noisemakers cost $.89 each. If each of the nine children receives one of each of the favors, find a reasonable estimate of the total cost of the party favors by rounding each amount to the nearest dollar.

Answers

Answer:

29$

Step-by-step explanation:

1.60+0.75+0.89=3.24 - dollars per one kid
3.24 * 9 = 29.16 - dollars total
round 29.16 to the nearest dollar - 29$

Some please help me with this: 2y - z + z^2

Answers

2y - z + z^2 is an algebraic expression. It represents a mathematical operation that includes three different terms: 2y, -z and z^2. It can be simplified depending on the context and the values of y and z.

In the given expression, 2y is the coefficient of y, which is multiplied by y. -z is subtracted from 2y and z^2 is added to the result.

In order to simplify this equation, you could combine like terms, which means combining the same variable or powers of the same variable with each other.

This expression does not have any like terms, so it can't be simplified anymore.

It can be evaluated by replacing y and z with specific values and then performing the mathematical operations in the given order.

When full, one of the pools at Sapphire Island will hold 43,000 gallons of water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute. Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level. Explain the steps you used to write your equation.

Answers

The equation to determine the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity can be found using the following steps.

To write an equation that can be used to find the number of hours it will take to fill the pool from its current level, we need to use the following information:

The pool's capacity: 43,000 gallons

The current level of the pool: 20,000 gallons

The rate of filling the pool: 130 gallons per minute

We can start by using the formula:

time = (amount needed to fill)/(rate of filling)

The amount needed to fill the pool is the difference between the pool's capacity and the current level of the pool.

amount needed to fill = 43,000 - 20,000 = 23,000 gallons

Now we can substitute this value in the formula above:

time = (23,000 gallons)/(130 gallons/minute)

To convert the time to hours, we divide the time in minutes by 60

time = (23,000 gallons)/(130 gallons/minute) × (1 hour/60 minutes)

So, the equation that can be used to find h, the number of hours it will take to fill the pool from its current level is:

h = (23,000 gallons) / (130 gallons/minute) × (1 hour/60 minutes)

Note that this equation is not simplified, you can simplify it by canceling out common factors, you'll get:

h = (23000 / 130) × (1/60)

This equation can be used to find the number of hours it will take to fill the pool, given the current level of the pool, the rate at which the pool is being filled, and the pool's capacity.

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What type of triangle has side lengths of 8cm 8cm and 10cm?

Answers

A triangle with the given measure of side length 8cm, 8cm , and 10cm is an isosceles triangle with two sides of equal measure.

As given in the question,

In the given triangle,

Measure of side length of a triangle is given by :

8cm, 8cm , and 10cm

Longest side = 10cm.

But ( 8)² + (8)² ≠ (10)²

It is not right angled triangle as does not satisfied the Pythagoras theorem.

8cm = 8cm.

Here in the given triangle two side length of the triangle are of same measure.

It represents it is an isosceles triangle.

Therefore, the given triangle side length represents it is an isosceles triangle with two sides of equal measure.

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A: -4p²q²-3pq
B: 4c²-12c to the 4th
C: 3m²+9m³
D: c³+c to the 7th
E:-24x to the 4th -16x to the 8th
PLEASE WRITE ALL AS A PRODUCT QUICK HELP

Answers

The required product are as follows,
A: -4p²q²-3pq = 4c²[1 - 3c²]     B: 4c²-12c⁴ = 4c²[1 - 3c²]    
C: 3m²+9m³ = 3m²{1 + 3m}       D: c³+c⁷ = c³[1 + c⁴]
E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
(a)
Given expression,
-4p²q²-3pq = -pq (4pq + 3)

Similarly,
B: 4c²-12c⁴ = 4c²[1 - 3c²]

C: 3m²+9m³ = 3m²{1 + 3m}

D: c³+c⁷ = c³[1 + c⁴]

E: 24x⁴ - 16x⁸ = 8x⁴[3 - 2x²]

Thus, the required products has be illustrated above.

Learn more about simplification here:

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Answer:

3.20

Step-by-step explanation:

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