a swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its deepest point. a cross-section is shown in the figure. if the pool is being filled at a rate of 0.9 ft 3 /min , how fast is the water level rising when the depth at the deepest point is 5 ft ? (round your answer to five decimal places.)

Samantha needs to mix 10 milliliters of the 40% alcohol solution with 90 milliliters of the 60% alcohol solution to create 100 milliliters of a 58% solution.

Let x be the number of milliliters of the 40% alcohol solution that Samantha needs to mix, and let y be the number of milliliters of the 60% alcohol solution. Since Samantha needs to create 100 milliliters of a 58% solution, we can write the following system of equations:

x + y = 100 (equation 1: total volume)

0.4x + 0.6y = 0.58(100) (equation 2: alcohol concentration)

In equation 1, we see that the total volume of the resulting mixture must be 100 milliliters. In equation 2, we convert the concentration of the 58% solution into a decimal and set it equal to the weighted average of the concentrations of the two solutions.

We can solve this system of equations to find the values of x and y:

x + y = 100

0.4x + 0.6y = 58

Multiplying the first equation by 0.4, we get:

0.4x + 0.4y = 40

Subtracting this equation from the second equation, we get:

0.2y = 18

y = 90

Substituting y = 90 into equation 1, we get:

x + 90 = 100

x = 10

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Answer:

The integers you seek are:

759, 761, 763, 765

since

759 + 761 + 763 + 765 = 3048.



Hope this helps!

The given measure of ∠ DEC = 80 degrees

We have the following details

m ∠BAC = 46 degrees

m ∠ CBA = 54 degrees

We are to find the measure of angle DEC

This is a question that shows us two similar triangles

We have ∠BAC = DCE

∠ CBA = ∠ EDC

then ∠ DEC  = ∠ BCA

The measure of the angles that are in a triangle is given as 180 degrees

we have ∠BAC + ∠ CBA + ∠ BCA = 180

46 + 54 + ∠ BCA = 180 degrees

∠ BCA = 180 - 100

∠ BCA = 80 degrees

We know that corresponding angles are equal when we have parallel lines

since ∠ DEC  = ∠ BCA

∠ DEC = 80 degrees

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Check the picture below.

The coordinates of the image of the triangle and the rules that can be used to transform the triangle are;

1. A' is located at (-3, 3)

B' is located at (-2, -1)

C' is located at (2, 1)

Second part; The rules are;

(x, y) → (x + 5, -y)

(x, y) → (5·x, 5·y)

A transformation of a figure is the reorientation of the figure to change the size and position of the figure.

1. The coordinates of the triangle ABC following the transformation (x, y) → (-x, y) are;

A(3, 3) (x, y) → (-x, y) A'(-3, 3)

B(2, -1) (x, y) → (-x, y) B'(-2, -1)

C(-2, 1) (x, y) → (-x, y) C'(2, 1)

2. The coordinates of the vertices of the triangle are; (1, 1), (4, 1), and (0, 4)

Translating the triangle five units right, we get;

(1 + 5, 1) = (6, 1), (4 + 5, 1) = (9, 1), and (0 + 5, 4) = (5, 4)

The coordinates of the triangle following a translation 5 units right are therefore;  (6, 1), (9, 1), and (5, 4)

The coordinates of the image of the point (x, y) following a reflection across the x-axis is the point (x, -y), therefore;'

The coordinates of the image of the triangle obtained from the previous transformation following a reflection across the x-axis is therefore;

(6, 1) reflection across the x-axis → (6, -1)

(9, 1) reflection across the x-axis → (9, -1)

(5, 4) reflection across the x-axis → (5, -4)

A rule that takes the triangle to a congruent triangle right five units and reflected over the x-axis is therefore;

The transformation of a triangle by a dilation by a scale factor of five, such that the triangle is five times larger can be obtained by the expression for a dilation transformation as follows;

(x, y) → (a·x, a·y)

Therefore, we get;

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Answer: A) Likely

Step-by-step explanation: Without further context, it's hard to tell what 0.999 represents.

Answer: The number 0.999 is a valid number that exists between the values of 0 and 1 on the number line. Therefore, it is possible and not unlikely or impossible. The correct answer is option C, which is "Neither unlikely nor likely".

Step-by-step explanation: The number 0.999 is the decimal representation of a fraction that is very close to 1 but not relatively equal to 1. However, it is still an important number found between 0 and 1 on the number line and is commonly used in math and science.

The statement "0.999 is probable" or "0.999 is unlikely” suggests that the number is somehow unique or rare, which it is not. In fact, 0.999 is a standard number used in many calculations and applications.

So the correct answer is option C, which means that 0.999 is neither particularly probable nor improbable. It only exists as a valid number between 0 and 1.

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The condition that must be satisfied to use a chi-square goodness-of-fit test is D. The expected count for each category is at least 5.

A chi-square goodness-of-fit test is a statistical test used to determine whether the observed frequencies of categorical data match the expected frequencies. This test is often used to analyze categorical data, such as determining if the distribution of colors in a bag of candies matches the expected proportions.

The reason behind this condition is that the chi-square test is based on the assumption that the data follow a specific distribution. When the expected count for each category is less than 5, the test might not accurately represent the true distribution, and the results may be misleading. By having an expected count of at least 5 in each category, the test can better approximate the true distribution and provide more reliable results. Therefore, option D is correct.

The Question was Incomplete, Find the full content below :

which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?

A. The sample size is greater than 30.

B. The number of categories is less than 10% of the number of observations.

C. The expected count is the same for each category. the population distribution is approximately normal.

D. The expected count for each category is at least 5.

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The probability of selecting a football card and then a basketball card is 0.16 or 16%. The probability of selecting a football card and then a basketball card can be calculated by multiplying the probability of selecting a football card on the first draw and the probability of selecting a basketball card on the second draw.

Since the first card is replaced before the second draw, the probability of selecting a football card or a basketball card remains the same on both draws.

The probability of selecting a football card on the first draw is 2/10, or 0.2, since there are 2 football cards in a total of 10 cards in the bag. The probability of selecting a basketball card on the second draw is 8/10, or 0.8, since there are 8 basketball cards left after the first draw.

Therefore, the probability of selecting a football card and then a basketball card can be calculated as follows:

P(Football and Basketball) = P(Football on 1st draw) x P(Basketball on 2nd draw)

= (2/10) x (8/10)

= 0.16

So, the probability of selecting a football card and then a basketball card is 0.16 or 16%.

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The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588

We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.

The standard error of the mean can be calculated as

SE = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size

Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.

SE = 90 / sqrt(72) = 10.6066

Next, we need to standardize the sample mean using the z-score formula

z = (X - μ) / SE

where X is the sample mean, μ is the population mean.

Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.

z = (1173.8 - 1192) / 10.6066 = -1.7356

We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.

Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.

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The fractions [tex]\frac{-2}{5}[/tex] and the fraction [tex]\frac{-4}{10}[/tex] , both are equal [tex]\frac{-2}{5} =\frac{-4}{10}[/tex], which means the "=" sign makes the statement true.

A mathematical relationship between two expressions is called inequality, and it is expressed using one of the following:

"less than or equal to": [tex]\leq[/tex]

"greater than" :>

"greater than or equal to" : [tex]\geq[/tex]

"less than": <

"not equal to": [tex]\neq[/tex]

To compare the fraction, make the denominator of both fractions the same.

Given:

Fraction 1 = [tex]\frac{-2}{5}[/tex]

Fraction 2 = [tex]\frac{-4}{10}[/tex]

To make the same denominator we can multiply by 2 to the numerator and denominator of the fraction 1.

[tex]\frac{-2}{5} =\frac{-2 * 2}{ 5*2}[/tex]

[tex]\frac{-2}{5} =\frac{-4}{10}[/tex]

Hence from the above calculation, the given fractions are equal.

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Answer: B

Step-by-step explanation:

The answer is 9x^2 + 14xy -19y^2

The width of the confidence interval increases as the sample size increases and decreases as the confidence interval decreases. The confidence interval decreases as the sample size increases and increases as the confidence level increases.

Sample size is defined as the number of observations used to determine

an estimate of a particular population. The size of the model is drawn by people. Sampling is the process of selecting a group of individuals from a population to estimate the characteristics of the entire population. Select the number of establishments in a population group for analysis.

The sample size increases with the square of the standard deviation and decreases with the square of the difference between the mean under the alternative hypothesis and the mean under the null hypothesis.

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Answer: 3.71

Step-by-step explanation:

The distance a car travels varies directly with the amount of gasoline it uses. If a car uses 28 gallons of gasoline to travel 924 miles, the car can travel 627 miles with 19 gallons of gasoline.

We can set up a proportion to solve the problem:

distance / gasoline = constant

Let's use x to represent the distance the car can travel with 19 gallons of gasoline:

924 / 28 = x / 19

Simplifying and solving for x:

x = (924 / 28) * 19 = 627 miles

Therefore, the car can travel 627 miles with 19 gallons of gasoline.

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Answer:

522/9=58

11-9=2

58*2=116

522+116=638

Step-by-step explanation:

Answer:

638

Step-by-step explanation:

Answer: 9 and 1/3

Step-by-step explanation:

First of all, you have to find the unit rate. So 28 divided by 2 = 14.

The bird flies at a unit rate of 14 miles in 1 hour.

Next, we need to find out what fraction of an hour is 40 minutes.

How many minutes in an hour? 60... so 40 would be 40/60 of an hour or 4/6 or 2/3 of an hour.

Next, remember the formula D=rt which is distance= rate multiplied by time

We can use this formula here: 14 times 2/3 = 9 and 1/3

180º-110º = 70º

m∠7 = 70°

Answer:

Step-by-step explanation:

cost of the phone = 150

sale is 35% off

Multiply the original cost $150.00 time the percent off as a decimal.

35% = . 35 (drop the sign and move the decimal two places left.)

150 X .35 = 52.50 off the price

He will save $52.50 off the cell phone during the sale.

Answer: 9 - i

Step-by-step explanation:

The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

We have to give that,

The sum of numbers 12 - 5i and - 3 + 4i.

Now, we can find the sum of complex numbers as,

(12 - 5i) + (- 3 + 4i)

12 - 5i - 3 + 4i

Combine like terms,

12 - 3 - 5i + 4i

9 - i

Therefore, The sum of numbers 12 - 5i and - 3 + 4i is, (9 - i)

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Answer:

for the firsts ones :

1. 12 x 2 x 5

2. 4 x 11 x 2,25

3. 6.5 x 22.6 x 10

Step-by-step explanation:

The value that is NOT greater than [-4.2] is D. [-4.5]

The values [-4.2], [3.5], and [4.1] are all greater than [-4.5]. To determine which value is the greatest, we can use a number line or compare the numbers directly. On a number line, we can see that [-4.5] is located to the left of [-4.2], [3.5], and [4.1]. This means that [-4.2], [3.5], and [4.1] are all greater than [-4.5].

Alternatively, we can compare the values directly. We know that -4.5 is less than -4.2 since -4.5 is farther to the left on the number line. We also know that 3.5 and 4.1 are positive values, which are greater than any negative value. Therefore, the answer is [-4.5] is not greater than [-4.2]. Hence, option D is correct.

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Answer:

If I did this right it should be: A)720g flour B)(i) 480g (ii) 2

Step-by-step explanation:

So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

What does an expression mean?

It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.

Let's solve this equation step by step:

100000+1X2

This is a simple expression which involves addition and multiplication.

100000+1X2 = 100000 + 2 (since 1X2 equals 2)

Therefore, 100000+1X2 = 100002

222+222+22222222222x111111111111111111111

This expression involves addition and multiplication as well.

We need to multiply 22222222222 by 111111111111111111111 first, and then add 222+222 to the result.

22222222222 x 111111111111111111111 = 24,691,358,024,691,358,024,691,358

222+222 = 444

So, 222+222+22222222222x111111111111111111111 = 24,691,358,024,691,358,024,691,802

222222222222222222

This is a simple number.

So, 100000+1X2 + 222+222+22222222222x111111111111111111111+222222222222222222 = 24,691,458,024,691,358,024,691,826

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Assuming the black and red squares are equally likely and there is no bias in the coin, the probability that it will land heads up on a black square is 1/2, or 50%.

Probability is a branch of mathematics that studies the likelihood of a random event occurring. When a coin is tossed into the air, for example, the possible outcomes are Head and Tail.

We will have a probability of 50%; this is because there are two equally likely outcomes when flipping a coin - heads or tails - and each square on the checkerboard has an equal chance of being landed on.

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Answer:15

You multiply 6 and 5. That equals 30 then divide the 30 by 2 and that equals 15

The largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.

what is quadrilateral?

A quadrilateral is a four-sided polygon, which is a two-dimensional closed shape with straight sides. In other words, a quadrilateral is a geometric figure that has four sides, four vertices, and four angles. The sum of the interior angles of a quadrilateral is always equal to 360 degrees. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and kites.

From the given information, we have:

angle P = 3p

angle Q = 4q

angle R = 5r

Since PQRS is a cyclic quadrilateral, the sum of opposite angles is equal to 180 degrees. Therefore, we have:

angle P + angle R = 180 degrees

3p + 5r = 180 degrees

Similarly, we have:

angle Q + angle S = 180 degrees

4q + S = 180 degrees

S = 180 - 4q

To find the largest angle, we need to find the largest angle measure among angles P, Q, R, and S.

Let's substitute the expression for S in terms of q into the equation for angle Q and simplify:

angle Q = 4q

angle Q + angle S = 180 degrees

4q + (180 - 4q) = 180 degrees

4q - 4q + 180 = 180 degrees

180 = 180 degrees

This equation is true, but it does not provide any information about the largest angle in PQRS.

Let's now substitute the expressions for angles P, Q, and R in terms of p and r into the equation for angle P + angle R = 180 degrees:

3p + 5r = 180 degrees

We want to find the largest angle, so we need to find the largest value of p or r that satisfies this equation. One way to do this is to try different values of p and r that satisfy the equation and see which one yields the largest value for angle P or angle R.

Let's try p = 10 and r = 30:

3p + 5r = 3(10) + 5(30) = 150

This satisfies the equation, so we can calculate angle P and angle R:

angle P = 3p = 30 degrees

angle R = 5r = 150 degrees

Therefore, the largest angle in quadrilateral PQRS is angle R with a measure of 150 degrees.

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Answer:

x = -4,

y = -1

Step-by-step explanation:

{-3x - 8y = 20,

{-5x + y = 19;

Make x or y the subject from either the 1st or the 2nd equation (I chose to make x the subject from the 2nd equation, because after division, the numbers can be written as a finite decimal fraction):

-5x = 19 - y / : (-5)

x = -3,8 + 0,2y

Replace x in the 1st equation with its value from the 2nd one (the underlined expression):

-3(-3,8 + 0,2y) - 8y = 20

Multiply every term inside the bracket by the term on the outside:

11,4 - 0,6y - 8y = 20

Collect like terms and add them together:

-8,6y = 20 - 11,4

-8,6y = 8,6 / : (-8,6)

y = -1

y = -1x = -3,8 + 0,2 × (-1) = -4

The solution to the system of equations is p = 4 and q = 2

The substitution method is a way to solve a system of linear equations. In this method, we solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. This produces a new equation with one variable, which we can then solve for its value. Once we know the value of one variable, we can substitute it back into one of the original equations to find the value of the other variable.

To solve the system of equations using the method of substitution, we need to solve one of the equations for one of the variables, and then substitute the resulting expression into the other equation. We can start by solving the second equation for p:

p + 2q = 8

p = 8 - 2q

Now we can substitute this expression for p in the first equation:

2p - 3q = 2

2(8 - 2q) - 3q = 2

16 - 4q - 3q = 2

16 - 7q = 2

-7q = -14

q = 2

We can now substitute q = 2 into the expression we found for p:

p = 8 - 2q

p = 8 - 2(2)

p = 4

Therefore, the solution to the system of equations is p = 4 and q = 2.

correct question  Solve the equations 2p – 3q = 2 and p + 2q = 8, using the method of substitution.

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Answer:

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]

Step-by-step explanation:

[tex]m = \frac{79 - ( - 20)}{9 - ( - 2)} = \frac{99}{11} = 9[/tex]

[tex]y - ( - 20) = 9(x - ( - 2))[/tex]

[tex]y + 20 = 9(x + 2)[/tex]