an empty swimming pool is in the shape of a rectangle meters long, meters wide and meters deep. a child starts to fill the pool using a saucepan with a circular base having a diameter of and a depth of . the child can fill the saucepan and empty it into the pool twice per minute. how many days would it take the child (working 24 hours per day) to fill the pool? don’t round to the nearest day.

1. The inequality for the statement is C. f minus 7 over 8 is greater than negative 2 over 3

2. The value of the expression is C. 43 over 24 times j plus 1 over 12.

3. −0.28x − 15.3 = 1.92 will be B. -61.5.

1. The difference between a number and seven eighths exceeds negative two thirds is:

Let the number be f.

This will be:

f - 7/8 > -2/3

2. The expression negative one eighth j plus two thirds minus the expression five thirds j plus nine twelfths will be:

= -1/8j + 2/3 - 5/3j + 9/12

= -1/8j - 5/3j + 9/12 - 8/12

= -3/24j - 40/24j + 1/12

= -43/24j + 1/12

3. −0.28x − 15.3 = 1.92

Collect like term

−0.28x = 1.92 + 15.3

-0.28x = 17.22

x = 17.22 /- 0.28

x = -61.5

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Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.

The exponential probability distribution, with mean m, is described by the following probability mass function:

[tex]f(x) = \mu e^{-\mu x}[/tex]

[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

The integral has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

Hence the probability of finding a value higher than x is given by:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In the context of this problem, the mean and the decay parameter are given, respectively, by:

[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]

Hence the probability that a truck will be loaded in 20 minutes or more is:

[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]

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The product of 3.7x x 6x = (3.7 x 6) x (x x x) = 22.2x².

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Joan walked 20 brown dogs.

As per the question, the 40% of total number of dogs are brown. So, finding 40% of the number 50 will give us the number of brown dogs.

Number of brown dogs = 50×40%

Converting Percentage to fraction

Number of brown dogs = 50×40/100

Cancelling zero as it is common

Number of brown dogs = 5×4

Performing multiplication to find the number of brown dogs

Number of brown dogs = 20

Thus, out of 50 dogs, Joan walked 20 brown dogs.

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Answer:

{-4; -5}

Step-by-step explanation:

just put any integer from set S in place of p and you will know. the inequality is false with -2 and -3, but with other two numbers is true

The empty table should be completed with the coordinates of the transformed graph after a dilation with a scale factor of 3 as follows;

x              m(x)

4              -2

2              -1

0              0

-2              1

-4              2

The equation of the resulting line in slope-intercept form is y = -0.5x + 3.

Based on the given coordinates of the graph of function f(x), the dilation with a scale factor of 3 from the origin (0, 0) or center of dilation would be calculated as follows:

Point 1 (-2) → Point 1' (-2 × -2) = Point 1' (4).

Point 2 (-1) → Point 2' (-1 × -2) = Point 2' (2).

Point 3 (0) → Point 3' (0 × -2) = Point 3' (0).

Point 4 (1) → Point 4' (1 × -2) = Point 4' (-2).

Point 5 (2) → Point 5' (2 × -2) = Point 5' (-4).

Next, we would translate the graph of function f(x) 3 units up as follows:

Point 1 (-2) → Point 1' (-2 + 3) = Point 1' (1).

Point 2 (-1) → Point 2' (-1 + 3) = Point 2' (2).

Point 3 (0) → Point 3' (0 + 3) = Point 3' (3).

Point 4 (1) → Point 4' (1 + 3) = Point 4' (4).

Point 5 (2) → Point 5' (2 + 3) = Point 5' (5).

Now, we can determine the slope of the transformed graph:

Slope, m = Δy/Δx

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (2 - 1)/(2 - 4)

Slope, m = -1/2 or -0.5

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (2, 2) and y-intercept c = 3, we have:

y = mx + c

y = -0.5x + 3

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The range of the function f (x) = -3x are (0, -3, 6).

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

The domain of f(x) = -3x is (0, 1, 2).

Now, Domain of the function are the values of x.

So, We find the Range of the function as;

Substitute all the values of domain (x) in the given function as;

The function is;

f (x) = -3x

For x = 0

Range = f (x) = - 3 × 0 = 0

For x = 1;

Range = f (x) = - 3 × 1 = -3

For x = 2

Range = f (x) = 3 × 2 = 6

Thus, Range of the function are (0, -3, 6)

Therefore, The range of the function f (x) = -3x are (0, -3, 6).

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Complex number :

[tex]i^{99}[/tex]= - i.

here,

i = [tex]\sqrt{-1}[/tex]

If the power is

99 is odd so now is

-i if (99+1)/2 is even or is

i is (99+1)/2 is odd

Now check (99+1)/2= 100/2= 50,

50 is even so

i^99 = -i

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Answer:

2

9c and a

Step-by-step explanation:

Answer:

2, (a and c)

Step-by-step explanation:

When the spacecraft launched, it was 254 miles away from the Earth and its distance away from the Earth is increasing at a rate of 270 miles per hour.

The equation that represents the distance of the space craft is known as a linear equation. A linear equation is an equation that has only one variable that is raised to the power of one.

A linear equation increases or decreases at a constant rate. When drawn on a graph, a linear equation is a straight curve that slopes either upward or downward.

A linear equation usually has this form y = mx + b

Where:

D = 254 + 270t

Where:

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they seem to be right :p

Step-by-step explanation:

Answer:

g + 1199 / 8

Step-by-step explanation:

3/4+65/8-23+78+92-6+g

1199/8+g

Answer:

p(x) is a function, and a polynomial of degree 3, then

By remainder theorem and factor theorem,

p(0) = p(1) = p (-1) = 0 if and only if

x = 0, 1, -1 are zeroes if and only if

p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx

p(2) = k(2)^3 - k(2) = 6

8k - 2k = 6

6k = 6

k = 1

Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x

p(-x) = (-x)^3 - (-x) = x^3 + x

-p(x) = -(x^3 - x) = -x^3 + x

As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,

because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0

p(x) = x(x - 1)(x + 1)

If x < -1, then x < 0, x - 1 < 0, x + 1 < 0

That means p(x) < 0

If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1

That means p(x) > 0

If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2

That means p(x) < 0

If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0

That means p(x) > 0

Thus p(x) < 0 if x < -1 or 0 < x < 1

Answer:

Both the lights will flash 1440 times a day. Proof: Red light flashes after every 30 seconds and green light flashes after every 20 seconds.

Step-by-step explanation:

The value of f(3) for the given expression is 8.

What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.

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Answer:

88.6000 = 88.622

It is not possible to create a complex number in which b = 0, as it would be equivalent to a real number.

The general format of a complex number is given as follows:

z = a + bi.

The meaning of the parameters a and b are given as follows:

If the coefficient b has a value of zero, then the complex number is written as follows:

z = a + 0i.

z = a.

Which is equivalent to a real number, that is, the number would have only a real component, hence it is not possible to find an imaginary number with b = 0.

Basically, any real number can be represented as a complex number with imaginary part 0, but then the number would not be complex.

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If Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

The scores she scored on test = 69, 74, 79, 62

Consider the final score she must make on the final exam as x

Sum of the scores = 69+74+79+62+2x

= 284+2x

Consider the average of score = Sum of scores / Number of subjects

= (284+2x)/6

She need average of 71 or higher

Then the inequality equation will be

(284+2x)/6 ≥ 71

284+2x ≥ 426

2x ≥ 426-284

2x ≥ 142

x ≥ 71

Hence, if Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

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The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the y-intercept, we set x = 0

So, we have

g(0) = 7⁰ + 2

Evaluate the exponent

g(0) = 1 + 2

Evaluate the sum

g(0) = 3

So, we have

(x, y) = (0, 3)

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the horizontal asymptote, we set 7ˣ

So, we have

y = 0 + 2

Evaluate the sum

y = 2

Hence, the solution is (a) (0, 3) ; y = 2

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The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.

Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3

Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y =  0 + 2
y = 2

Thus,  the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

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Answer:

Angle 1 & 2 are both 100 degrees

Step-by-step explanation:

In the picture,

angles on the same side of the line must add up to 180degrees.

Angles directly opposite of each other(same vertices) must be equal.

with parallel lines, angles that are made by the same intersecting line are also equal.

image really helps :( sry its hard to explain in words

Answer:

Step-by-step explanation:

Zero exponent numbers = 1

When you try to multiply an exponent by zero, it equals one.

Negative exponents is just a 1/x

Negative just flips over the equation.

For example, 9^-1

1/9^1

1/9

Answer:

Step-by-step explanation:

Zero Exponent Property: The zero exponent rule states that when a nonzero number is raised to the power of zero, it equals 1.

Example:  x^0 = 1

Negative Exponent Properties: the negative exponent rule tells us that a number with a negative exponent should be put to the denominator, and vice verse. It also describes how many times we have to multiply the reciprocal of the base.

An example of negative exponents is [tex]3^{-2}[/tex].

Answer:

4

Step-by-step explanation:

2/5 divided by 1/10

Division of fractions

Use copy dot flip

2/5 * 10/1

20/5

4

To determine a compound Interest

The above formular is for solving compound interest

Hence the compound interest = 612.10 (nearest cent)

The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.

1 egg = M/N cups of flour.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let M cups of flour be needed for N eggs.

This can be written as:

N eggs = M cups of flour

Divide both sides by N.

1 egg = M/N cups of flour

Thus,

The division expression to find the number of cups of flour Max needs to use if he has only 1 egg is M ÷ N cups of flour.

1 egg = M/N cups of flour.

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The cups of sugar needed is 2.5 cups.

The cups of flour needed is 3.75 cups

The cups of butter needed is 1.25 cups.

Given the information in the question, the ratio of sugar to flour to butter is 1 : 1.5 : 0.5

Cups of sugar needed = (ratio representing sugar / sum of ratios) x total number of cups

Sum of ratios = 1 + 1.5 + 0.5 = 3

Cups of sugar needed = (1 / 3) x 7.5 = 2.5 cups

Cups of flour needed = (ratio representing flour / sum of ratios) x total number of cups

Cups of flour needed = (1.5 / 3) x 7.5 = 3.75 cups

Cups of butter needed = (ratio representing butter / sum of ratios) x total number of cups

Cups of butter needed = (0.5 / 3) x 7.5 = 1.25 cups

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Answer:

11) 7d + 28 and 7(d+4)

12) y^2 + 3y and y(y+3)

Step-by-step explanation:

The corresponding values of the lower and upper bounds of m - n are 41.41 and 41.59.

What are the values of the lower and upper bounds of m - n?

Upper and lower bounds are the possible maximum and minimum values of a number before it was rounded.

The upper and lower bounds can be expressed using the error interval

The lowest value of m is 48.15

The highest value of m is 48.24

The lowest value of n is 6.65

The highest value of n is 6.74

Therefore, lower bound of m - n = 48.15 - 6.74 = 41.41

Also, the upper bound of m - n = 48.24 - 6.65  = 41.59

So values of the lower and upper bounds of m - n are 41.41 and 41.59 respectively.

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When a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and  the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1

The perimeter of the square is equal to the perimeter of the rectangle.

The length of a side of the square=4x-1

The perimeter of the square=4a

Where a is the side of the square

Substitute the values in the equation

The perimeter of the square=4(4x-1)=16x-4

The length of the rectangle=2x+1

The width of the rectangle=x+2

The perimeter of the rectangle=2(l+w)

where l is the length and w is the width

The perimeter of the rectangle =2(2x+1+x+2)

=2(3x+3)

= 6x+6

A square and a rectangle have equal perimeters

16x-4=6x+6

16x-6x=6+4

10x=10

x=1

Hence, when a square and a rectangle have the same perimeters. If the length of a side of the square is 4x-1 and  the length of the rectangle is 2x+1 and the width is x+2. then the value of x=1

The complete question is

A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2, Write and solve an equation to find x

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