A rectangular container 6.5 ft long, 3.2 ft wide, and 2 ft high is filled with sand to a depth of 1.3 ft. How much sand is in the container?

I'll give thanks or mark as brainliest if you can figure out how much more sand the container can hold

Let's think of this number as T|U where T is the tens position digit and U is the units position digit.

Original number has value 10T+U.  U=3T (first sentence).

Second sentence deals with U|T, which has value ('new number') 10U+T.

Half the new number is 21 < twice the original means:

 ½(10U+T) = 2(10T+U) - 21

There you have a system of two equations in two unknowns.  You may now solve it.

Check the answers for reasonableness and correctness. (Also check my work producing the last equation)

Note I have used the vertical separation symbol "|" to segregate the two digits of a 2-digit number.

However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem .

To solve this problem, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Let's first find the measure of angle P:

m∠P + m∠Q + m∠R = 180

Substituting in the given measures:

(x + 13) + (10x + 13) + (2x - 2) = 180

Simplifying and solving for x:

13x + 24 = 180

13x = 156

x = 12

So m∠P = (x + 13) = 25 degrees.

Next, we can use the fact that the angles opposite equal sides in a triangle are congruent. Since we know that PR and QR are equal, we have:

m∠P = m∠R

So m∠R = 25 degrees.

Finally, we can find m∠Q:

m∠Q = m∠P + m∠R - 180

Substituting in the values we found:

m∠Q = 25 + 25 - 180 = -130

However, this answer does not make sense, as angles in a triangle cannot be negative. This means that there is no solution to this problem.

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The length of each leg of a right triangle given that one angle is 22° and the length of the hypotenuse is 10 inches are 3.75 and 9.27 inches respectively.

In order to determine the length of the opposite side and adjacent side, we would apply both the cosine and sine trigonometry ratio because the given side lengths represent the hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the parameters into the sine trigonometry ratio formula, we have the following;

sin(θ) = Opp/Hyp

sin(22) = y/10

y = 10sin(22)

y = 3.75 inches.

For the adjacent side, we have:

cos(θ) = Adj/Hyp

cos(22) = x/10

x = 10cos(22)

x = 9.27 inches.

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The experimental probabilities have their values to be P(3) = 1/12, P(6) = 1/4 and P(Less than 4) = 1/2

Experimental probability of 3

From the table of values, we have

n(3) = 1

Total = 12

So, we have

P(3) = 1/12

Experimental probability of 6

From the table of values, we have

n(6) = 3

Total = 12

So, we have

P(6) = 3/12

P(6) = 1/4

Experimental probability of less than 4

From the table of values, we have

n(Less than 4) = 6

Total = 12

So, we have

P(Less than 4) = 6/12

P(Less than 4) = 1/2

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The below list represents the years from driest to wettest

2012, 2011, 2009, 2008, 2010  

The average rainfall in Phoenix is 8.29 inches per year

The table shows recent data on the difference in annual rainfall from the average.  

Phoenix Annual Total Rainfall  Year compared to average yearly rainfall

2008     +6.57 inches

2009   –2.68 inches

2010     +12.26 inches

2011      –4.38 inches

2012     –4.46 inches

Driest   –4.46 inches       2012

Then  –4.38 inches in 2011    

–2.68 inches                    2009

+6.57 inches                    2008

+12.26 inches    Wettest  2010

The below list represents the years from driest to wettest

2012, 2011, 2009, 2008, 2010  

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The solution of the  expression 6 × [tex]\frac{1}{4}[/tex] × (12 - 3) using order of operations rule BODMAS/PEMDAS is 13.5.

What is BODMAS?

BODMAS is acronym for B is for Bracket, O is for Of, D is for Division, M is for Multiplication, A is for Addition, and S is for Subtraction. This rule is used to explain the order of operation of a mathematical expression and solve the expression in case it has more than one operational signs. BODMAS is same as PEDMAS which i acronym for P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, and S-Subtraction.

Here the expression is:

6 × [tex]\frac{1}{4}[/tex] × (12 - 3)= 6 × [tex]\frac{1}{4}[/tex] × (9) {solving the brackets}

                      = 54 × [tex]\frac{1}{4}[/tex]

                      = 13.5

The value of given expression is 13.5

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The solution of the  expression is using order of operations rule BODMAS/PEMDAS is 13.5.

BODMAS stands for Bracket, Of, D, Multiplication, Multiplication by One, Addition by One, and Subtraction by One. This rule is used to specify the order of operations in a mathematical equation as well as to solve expressions with multiple operational signs. P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, & S-Subtraction are collectively referred to as PEDMAS. BODMAS stands for the same thing.

The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems.

Here the expression is:

6 × 1/4 × (12 - 3)= 6 × 1/4 × (9) {solving the brackets}

                     = 54 × 1/4

                     = 13.5

The value of given expression is 13.5

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Answer:

3=0

Step-by-step explanation:

There are 92 observations that are less than or equal to 50.

To calculate the cumulative frequency, we need to add up the frequencies of all the bins up to and including the bin in question. This can be calculated by adding up the frequency values for the bins that include values less than or equal to 50:

4 (from bin 15) + 62 (from bin 20) + 101 (from bin 25) + 70 (from bin 30) + 83 (from bin 35) + 20 (from bin 40) + 45 (from bin 45) + 9 (from bin 50) = 394

So, the cumulative percentage for the bin containing 50 is 92.71%. Therefore, the number of observations less than or equal to 50 is approximately 92.

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according to the question, the selling price of each book is $13.18.

When the quantity supplied and wanted are equal, prices are in equilibrium. The quantity provided and demanded are equal at the price of equilibrium.

Let's denote the selling price of each book as "x". The markup for each book is 56% of its selling price, so the profit that Binder's Bookstore makes on each book is:

0.56x

If we add this profit to the cost of the book, we get the selling price:

x = 5.80 + 0.56x

Solving for x, we can simplify as follows:

0.44x = 5.80

x = 13.18

Therefore, the selling price of each book is $13.18.

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Answer:

20

Step-by-step explanation:

So there is a total of 1/5 chance of getting an answer right, because there are 5 possibilities and only 1 is correct.

Now because there are 100 Questions, we will multiply our probability with the total value (in this case its a 100).

So 1/5 = .2

.2 × 100 = 20

The standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.

The standard deviation of the number of questions answered correctly in a multiple-choice test of 100 questions with 5 possible answers for each question, assuming random selection of one answer per question, can be calculated using the formula for the binomial distribution, which is the square root of n times p times q, where n is the total number of trials, p is the probability of success on each trial, and q is the probability of failure on each trial.

Using the formula for the binomial distribution, the standard deviation of the number of questions answered correctly can be calculated as follows:

n = 100 (total number of trials)

p = 1/5 (probability of success on each trial, i.e., selecting the correct answer)

q = 4/5 (probability of failure on each trial, i.e., selecting one of the incorrect answers)

Therefore, the standard deviation is:

√(100 x 1/5 x 4/5) = √16 = 4

Therefore, the standard deviation of the number of questions answered correctly is 4. This means that on average, the number of questions answered correctly will be within 4 of the expected value.

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Answer:

Step-by-step explanation:

x = 7

To find the measure of angle B, we can use the inverse tangent function:

tan(B) = opposite / adjacent = a / b

tan(B) = 500 / 300

B = arctan(500 / 300)

B ≈ 59.0 degrees

Therefore, the measure of angle B is approximately 59 degrees (rounded to the nearest degree).

Answer: 13/100

Step-by-step explanation:

The value of three times the number plus 17 - that same number is found to be 7.

It is provided that if twice a number is equal to that number minus then we have to find what is three times that number plus 17 minus that number.

Let's say that the number we are talking about his x.

From the given condition we can write at the twice of x will equal to x minus x - 5.

2x = x-5

Solving this simple algebraic equation.

x = -5.

Now, to find the answer,

3x + 17 - x

Putting values,

= 3(-5) + 17 -(-5)

= -15 + 17 + 5

= 7.

So, the value of thrice the number added to number minus from 17 is 7.

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When graphed on a scatter plot, the data has a generally decreasing trend. Therefore, the basketball coach was correct in thinking that his players are not scoring as many points as they were in the previous weeks.

Based on the scatter plot, we can observe the trend that the number of game points decreases as the week progresses.

The points on the scatter plot are generally trending downwards, indicating a decrease in the number of points scored over time.

Therefore, the basketball coach was correct in his observation that his players are not scoring as many points as they were in the previous weeks.

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Answer:

5

Step-by-step explanation:

Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.

One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.

Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.

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This relationship shows that the diameter of the central circle (2R) is twice the diameter of each outer circle (2r).

In this configuration, four outer circles are placed around a central circle, such that they are all tangent to the central circle and tangent to each other.
To determine the relationship between the diameter of the outer circles and the diameter of the inner circle, follow these steps:
1. Let the radius of the outer circles be r and the radius of the central circle be R.
2. In this arrangement, the distance between the centers of any two adjacent outer circles is equal to the sum of their radii, which is 2r.
3. Now, draw a straight line connecting the centers of these two adjacent outer circles.

This line will pass through the center of the central circle.
4. The length of this line is the sum of the radii of the outer circle, the central circle, and another outer circle, which is

r + R + r = 2r + R.
5. Observe that the line connecting the centers of the two adjacent outer circles, along with the radii connecting the center of the central circle to the points of tangency, forms a right-angled isosceles triangle.
6. Since it is an isosceles triangle, the length of the line connecting the centers of the two adjacent outer circles (2r + R) is also the length of the other side of the triangle, which is equal to the diameter of the outer circle (2r).
7. Therefore, the relationship between the diameter of the outer circles and the diameter of the inner circle is:

2r = 2r + R.
8. Simplify the equation to find the relationship: R = 2r.

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Answer:

diameter = 2× radius

circumference = [tex]2\pi r[/tex]

Area = [tex]\pi r^{2}[/tex]

use this formulas and put the given values and you will get the answers

Step-by-step explanation:

From the given coordinates geometry function will be y=-3x+1.

Plotting points on a coordinate plane will provide the graph of the function y = -3x + 1. To accomplish this, we can select various x values, enter them into the equation, and then solve for y. As an illustration, if x = 0, then y = -3(0) + 1 = 1. We now get the graph's point (0, 1) thanks to this. Similar to the previous case, if we select x = 1, then y = -3(1) + 1 = -2. This results in the graph's point (1, -2) for us. By repeating this procedure, we can identify more points, which we can then join with a straight line to create the function's graph. A straight line with a slope of -3 and the point appears on the graph as a result (0, 1).

from graph we can write coordinates ,

(-1,4),(0,1),(1,-2),(2,-5)

so from these coordinates ,function will be

y=-3x+1.

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Step-by-step explanation:

4x^2 + 16x -4       factor out a '4'

4 ( x^2 + 4x -1)     Done.  

                  There isn't anything else you can factor out of the three terms

Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.

Once someone outlines their solution and how they approached the challenge, clarifying questions should be asked.

List the parallels and differences between several approaches to solving the issue.

Find the mistake in a wrong response, and then provide proof to support your claim.

Create strong arguments and evaluate other people's reasoning.

What It Means: When kids can give us the right answer and explain how they arrived at it, we know they fully understand a topic.

So, in the given situation the red dot represents the value of 1/3, and thus Craig is correct that the given number line represents the value of 1/3.

Therefore, Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.

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We multiply the base's area by the prism's height to get the volume of the structure. In this case, the height of the prism is also 9 feet. Therefore, the volume of the triangular prism is 162 cubic feet.

By dividing the base's area by the prism's height, one can determine the volume of a triangular prism. The area of the triangular base can be calculated by using the formula

area of a triangle = [tex]\frac{1}{2}[/tex] × base × height.

In this case, the base of the triangular prism is 4 feet and the height is 9 feet. Hence, the triangle's base's area is:

[tex]\frac{1}{2}[/tex] × 4 ft × 9 ft = 18 square feet

Multiplying the area of the base by the height of the prism gives us the volume of the triangular prism:

Volume = Area of triangle × height of the triangle

18 sq ft × 9 ft = 162 cubic feet

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The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

To calculate the mean value, we add up all the values and divide by the

number of values:

(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000

So the mean value is 1000 rpm.

To calculate the standard deviation, we need to first calculate the

variance:

Variance =[tex][(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6[/tex]

Variance = 12000 / 6 = 2000

So the variance is [tex]2000 (rpm)^2[/tex].

The standard deviation is the square root of the variance:

Standard deviation = √(2000) = 44.7 rpm

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

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In order to print out a deck of 52 cards, and each card having its suit and value displayed on the same line, 13 columns were used for each of the  card.

In Illustration 3, assuming that the deck contains 52 cards, each card in the deck was printed using 13 columns. This is because a standard deck of playing cards contains four suits (clubs, diamonds, hearts, and spades), and each suit has 13 cards (Ace, 2-10, Jack, Queen, King).

Therefore, to print out a deck of 52 cards, with each card having its suit and value displayed on the same line, 13 columns were used for each card.

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The complete question is :

In Illustration 3, a deck of cards was shuffled and printed out. Line 35 shuffles the deck. How many columns were used for each card in the deck, assuming that the deck contains 52 cards?

As per the given data, Mark is buying different nuts to make a mixed nut platter to serve at a party. the total weight in grams of the nuts Mark purchased is 4000.

He buys 1.5 kilograms of peanuts, 500 grams of almonds and 200 dekagrams of cashews. We need to calculate the total weight in grams of the nuts he purchased.Calculation:Total weight in grams of peanuts = 1.5 × 1000 = 1500 grams. Total weight in grams of almonds = 500 grams. Total weight in grams of cashews = 200 × 10 = 2000 grams. . Adding all the weights: Total weight = 1500 + 500 + 2000 = 4000. Therefore, the total weight in grams of the nuts Mark purchased is 4000. The gross weight is the total weight of the goods carried, including all packaging but excluding the tare weight of the transport unit. The tare weight is the weight of a transport unit before any cargo is loaded.

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The level of significance in a hypothesis test is the maximum allowable probability of a Type I error. A Type I error occurs when you reject a null hypothesis that is actually true.

The level of significance is usually denoted by the symbol α (alpha) and is expressed as a percentage or a decimal value, such as 5% or 0.05. This means that if the level of significance is set at 5%, there is a 5% chance of making a Type I error when the null hypothesis is true.
To answer the student question, the level of significance is not the same as the confidence coefficient or the p-value. The confidence coefficient is related to the confidence interval, which is a range of values within which the true population parameter is likely to fall. The confidence coefficient (1 - α) represents the probability that the true population parameter lies within the confidence interval.
The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is less than or equal to the level of significance, you reject the null hypothesis and accept the alternative hypothesis.
Lastly, the maximum allowable probability of a Type II error (denoted by β) is not the same as the level of significance. A Type II error occurs when you fail to reject a null hypothesis that is actually false. The power of a test is defined as (1 - β) and represents the probability of correctly rejecting a false null hypothesis.

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Answer:

Step-by-step explanation: