Work the problem using the three-step method. Show your work.
The sum of three consecutive integers is 18. Find the integers.
WRITER

With speed = 10 m/s, the rope will hit ground after 3.36 seconds.

Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.

Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:

Speed = Distance / Time

where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.

Now,

To find when the rope will hit the ground, we can use the kinematic equation:

y = vi * t + (1/2) * a * t²

where:

y = 50 m (the height of the cliff)

vi = 10 m/s (the initial velocity of the rope)

a = 9.8 m/s² (the acceleration due to gravity, acting downward)

t = time it takes for the rope to hit the ground

We can solve for t by setting y=50 and solving for t:

50 = 10t + (1/2) * 9.8 * t²

50 = t(10 + 4.9t)

t = 50/14.9=3.36 s

Therefore, the rope will hit the ground after 3.36 seconds.

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At least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

What is standard deviations?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Chebyshev's theorem states that for any distribution (not just the normal distribution), regardless of shape, at least 1 - 1/k^2 of the data values will be within k standard deviations of the mean, where k is any number greater than 1.

In this case, we want to know the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean. So we need to use Chebyshev's theorem with k = 2.

At least 1 - 1/2^2 = 1 - 1/4 = 0.75, or 75%, of the healthy adults have body temperatures within 2 standard deviations of the mean.

To find the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean, we can use the formula:

Minimum = Mean - k * Standard deviation

Maximum = Mean + k * Standard deviation

Plugging in the values for this problem, we get:

Minimum = 98.33 - 2 * 0.67 = 96.99°F

Maximum = 98.33 + 2 * 0.67 = 99.67°F

Therefore, we can say that at least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

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The statement g(5) = 33.75 represents total cost of $33.75 when the purchase of a stuffed giraffe added to 5 accessories to it, the total cost

From the question, we have the following parameters that can be used in our computation:

g(x) = the cost of a stuffed giraffe.

The giraffe costs $15 and accessories cost $3.75 each.

This means that

g(5) = 33.75

Using the above as a guide, we have the following:

The statement g(5) = 33.75 means that if we purchase a stuffed giraffe and add 5 accessories to it, the total cost will be $33.75.

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The answer of Caroline is 19.33 years old and Cameron is 53.67 years old

Let's start by assigning variables to represent Caroline's age and Cameron's age. We'll use C for Caroline's age and M for Cameron's age.

According to the problem, the sum of their ages today is 73, so we can write the equation:

C + M = 73

Five years ago, Cameron was 2 times older than Caroline. so we can write the equation:

M - 5 = 2(C - 5)

Now we can use the first equation to solve for one of the variables. Let's solve for C:

C = 73 - M

Next, we can substitute this value of C into the second equation:

M - 5 = 2(73 - M - 5)

Simplifying the equation gives us:

M - 5 = 146 - 2M - 10

3M = 161

M = 53.67

Now we can use this value of M to find C:

C = 73 - 53.67

C = 19.33

So Caroline is 19.33 years old and Cameron is 53.67 years old.

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The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:

Where L = 400, A [tex]\approx[/tex] 12.82

Where L = 700 A [tex]\approx[/tex] 44.43

Where L = 1,100 A [tex]\approx[/tex]  86.13

The length of the pipe is given by the function:

L =  111.25√A.

Where a = (L/111.25)²

Thus, for L = 400inches

A =  (400/111.24)²

(400/111.24)² = (400²)/(111.24)²

(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:

(160000)/(12369.5776) = 12.820128200735

Therefore, A = 12.820128200735,

A [tex]\approx[/tex] 12.82

Thus:

Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43

Where L = 1,100
A = 86.129479

A [tex]\approx[/tex] 86.13

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The equation that represents the line of best fit for the scatterplot is given as follows:

B. y = -10x + 100.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, we have that:

Hence option B is correct.

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The antenna's height is 12.1 meters, as stated throughout the announcement.

Building type refers to a grouping of buildings according to their purpose, location, and style that serves as the standard for evaluating and categorizing variants. Buildings must be categorized as either support, civic, commercial, industrial, or residential. Any kind of fella construction is a structural. It could be anything: a dam or a bridge, for instance. In contrast, a building is a closed construction with walls and a roof. Once more, the more precise phrase is "building," although "structure" is far more generic.

Based on the graph.

[tex]$$\begin{aligned}& \overline{O H}=\overline{C D}=1.51 \mathrm{~mm} . \\& \overline{O C}=24 \mathrm{~m} . \\& \angle O C A=20^{\circ} . \quad \angle O C B=41^{\circ} .\end{aligned}$$[/tex]

In RT [tex]$\triangle A O C_,$[/tex]

[tex]$$\begin{aligned}& \tan 20^{\circ}=\frac{A_0}{O C}=\frac{A_0}{24} \\& \text { So } A_0=\tan 20^{\circ} \times 24=8.74 \mathrm{~m}\end{aligned}$$[/tex]

In Rt ΔOBC.

[tex]$$\begin{aligned}\tan 41^{\circ} & =\frac{O B}{O C}=\frac{O B}{24} \\O B & =\tan 41^{\circ} \times 24=20.86 \mathrm{~m} .\end{aligned}$$[/tex]

[tex]A B=O B-O A=20.86-8.74=12.12 \mathrm{~m} \approx 12.1 \mathrm{~m} .[/tex]

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Answer:

12.1

Step-by-step explanation:

I got the question right

Answer:

Part A: To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length multiplied by width. We have the expression for the area as 8x² - 12x, and the expression for the width as 4x. So, we can write:

Area = Length × Width

8x² - 12x = Length × 4x

Simplifying the right side by multiplying, we get:

8x² - 12x = 4x × Length

2x² - 3x = Length

Therefore, the expression for the length of the rectangular space is 2x² - 3x.

Part B: To prove that the expression for the length from Part A is correct, we can multiply it by the expression for the width and simplify:

Length × Width = (2x² - 3x) × (4x)

= 8x³ - 12x²

= 4x(2x² - 3x)

= 4x(2x(x - 3))

This is in fact the same as the expression for the area of the rectangular space, 8x² - 12x, in standard form.

Answer:

Rational numbers are those that can be expressed as a ratio of two integers whereas irrational numbers are those which cannot be expressed as a ratio of two integers.

Rational numbers can be written in the form of a fraction whereas irrational numbers cannot be written in the form of fractions.

Rational numbers comprise of those perfect squares whereas irrational numbers comprise of surds.

The least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6) is 14(x-3).

To find the least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6), we need to find the least common multiple of the denominators 7x-21 and 2x-6.

Step 1: Factor the denominators.
7x-21 = 7(x-3)
2x-6 = 2(x-3)

Step 2: Identify the common factors.
Both denominators have the factor (x-3).

Step 3: Multiply the unique factors together.
7 * 2 * (x-3) = 14(x-3)

Step 4: The least common denominator is 14(x-3).

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Y= 3.2

When \( y \) varies directly as \( x \) and inversely as \( z \), the equation is given by:
\( y = \frac{kx}{z} \)

Where \( k \) is a constant.

Substituting the given values of \( x \), \( y \) and \( z \), we get:
\( 24 = \frac{k(120)}{16} \)

Solving for \( k \):
\( k = \frac{24*16}{120} = 4.8 \)

Substituting the values of \( k \), \( x \) and \( z \) into the equation, we get:
\( y = \frac{(4.8)*4}{15} \)

Therefore, the value of \( y \) when \( x=4 \) and \( z=15 \) is \( 3.2 \).

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The equation which represents the total length of the siding is given by A , where A = 50 x 4 = 200 meters

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total length of the siding be represented as A

Now , the value of A is

Let the number of pieces be n = 48 pieces

Let the length of each piece be l = 3.7 meters

Now , total length of the siding A = number of pieces x length of each piece

On simplifying the equations , we get

The total length of siding A = 48 x 3.7 = 177.6 meters

Now , n ≈ 50 pieces

l ≈ 4 meters

So , total length of siding A = 50 x 4 = 200 meters

Hence , the equation is A = 50 x 4 = 200 meters

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The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.

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Answer:

I'm sorry, but it is not clear what you are asking for. Can you please provide more information or a specific question?

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

Adding/subtracting radical expressions and simplifying can be done as follows:

(a) \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}} \)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\) = \( -14 y \sqrt{7 x^{3}}+3 x \sqrt{63 x y^{2}}\)

(b) \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

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The value of x for the given pentagon will be 125 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Given the values exterior angles of the pentagon such that, 70°, 60°, 65°, 40°, x°.

To calculate the value of x.

Since the Sum of all exterior angles of a pentagon is 360°,

Thus,

70 + 60 + 65 + 40 +x = 360

x + 235 = 360

x = 360 - 235

x = 125°

Therefore, the value of x for the given pentagon will be 125 degrees.

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Answer:

the paper is too blurry i would help if i could.

Step-by-step explanation:

Answer: Y=-3X+5

Step-by-step explanation:

Slope intercept form is Y=mx+b where m is slope and b is slope intercept to graph you can use desmos which is a free graphing calculator just punch in the equation exactly as I gave it. since m is slope it is -3 and b is y intercept so 5 so Y=-3x+5

Answer:

y = -3x + 5

Step-by-step explanation:

y = mx + b  The m is the slope and the b is the y intercept.  Substitute in the slope and the y-intercept

y = -3x + 5

First, graph the y-intercept.  That will be at the point (0, 5).  From that point, go down 3 units and then go one unit right.  You will be back on the line.  That is the slope.

Helping in the name of Jesus.

In response to the given query, the result we have is Hence, each expressions container contains 1/2 gallon of paint.

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

The remaining paint would be as follows if the art teacher had 8 gallons and the students had used 3/4 of it:

8 x 1 - 3/4 = 8 x 1/4 = 2 gallons.

The 4 bottles of the remaining 2 gallons of paint each contain the following amounts of paint:

1/2 gallon is equal to 2/4.

Hence, each container contains 1/2 gallon of paint.

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Answer:

The answer is [tex](u + 3)(5u^{2} - 1)[/tex]

The exponential function that models the percentage as a function of P is given as follows:

P(t) = 100(0.705)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function that models the data in the table is defined as follows:

P(t) = 100(0.705)^t.

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The value of f(3) using synthetic division is 72.

To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).

Write the coefficients of the polynomial in a row: 12 -40 4 17 21

Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21

Bring down the first coefficient: 3 | 12 -40 4 17 21
          ------------------
             12

Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
          ------------------
             12  36

Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
          ------------------
             12  -4

Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51

The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51  72

So, f(3) = 72.

Therefore, the value of f(3) using synthetic division is 72.

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The two values of x that are roots of the given equation are approximately 3.618 and 1.382.

What is quadratic equation ?

Quadratic equations are used to model a wide range of phenomena in many areas of science and engineering, including physics, biology, economics, and finance. They are also used extensively in mathematics for their elegant properties and applications in algebra, geometry, and calculus.

We start with the quadratic equation:

[tex]$x^2 - 5x + 5 = 0$[/tex]

To find the roots of this equation, we use the quadratic formula:

[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

where [tex]$a$, $b$,[/tex] and [tex]$c$[/tex] are the coefficients of the quadratic equation.

In this case, we have [tex]a = 1$, $b = -5$, and $c = 5$.[/tex] Substituting these values into the quadratic formula, we get:

[tex]$x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(5)}}{2(1)}$[/tex]

Simplifying the expression under the square root, we get:

[tex]$x = \frac{5 \pm \sqrt{5}}{2}$[/tex]

Therefore, the two roots of the equation are:

[tex]$x = \frac{5 + \sqrt{5}}{2} \approx 3.618$[/tex]

[tex]$x = \frac{5 - \sqrt{5}}{2} \approx 1.382$[/tex]

Hence, the solutions to the equation [tex]$x^2 - 5x + 5 = 0$[/tex] are approximately 3.618 and 1.382.

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Answer:

The answer to your problem is, $0.60

Step-by-step explanation:

1 banana and 1 orange = 1.20.

We divide next:

1.20 / 2 = 0.60.

We know that because in the question it says one banana and one orange is 1.20. Next we divide because two items are sharing the same number.

1.20 / 2 = ? ( ? = 0.60 or 0.6 )

Thus the answer to our problem is, $0.60

The equation of line is y = -4x - 3 and the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 5 )

Let the second point be Q ( -1 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 5 ) / ( -1 - ( -2 ) )

On simplifying , we get

Slope m = ( -4 ) / 1

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = -4 ( x - ( -2 ) )

y - 5 = -4 ( x + 2 )

y - 5 = -4x - 8

Adding 5 on both sides , we get

y = -4x - 3

Hence , the equation of line is y = -4x - 3

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The relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

What is frequency ?

In statistics, frequency refers to the number of times a particular observation or value occurs in a given dataset or sample. It is often represented in a frequency table, which organizes the data by category or value and shows the number of occurrences for each.

To find the relative frequency for the total number of boys in this survey, we need to divide the number of boys who prefer math or social studies by the total number of students in the survey, which is 120.

Relative frequency of boys who prefer math = 43/52 ≈ 0.83

Relative frequency of boys who prefer social studies = 9/52 ≈ 0.17

Relative frequency of total number of boys = 52/120 ≈ 0.43

Therefore, the relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

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To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle.

In this case, we are given the lengths of the two legs of the triangle, 11 inches and 24 inches.
We can plug these values into the formula and solve for the hypotenuse:
c^2 = 11^2 + 24^2
c^2 = 121 + 576
c^2 = 697
c = √697
c ≈ 26.4 inches

Therefore, the hypotenuse of the triangle is approximately 26.4 inches.

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The missing side of the triangle is 16 mm.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.

As per the given diagram:

The sides and angles of the right-angled triangle is given:

To find v using the trigonometric ratio:

sinθ = (P/H) {P is perpendicular and H is hypotunese}

for θ = 30°

sin30° = (8/v)

1/2 = 8/v

v = 16 mm

Hence, the missing side of the triangle is 16 mm.

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Precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

To make a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point, follow these steps:

1. Draw the given circle using a compass.
2. Mark the given point on the paper with a pencil.
3. Place the point of the compass at the given point and extend the compass until it touches the edge of the circle.
4. Draw a circle with the compass. This circle will intersect the given circle at two points.
5. Use a ruler to draw a line from the given point to each of the intersection points. These lines are the tangent lines to the given circle that pass through the given point.
6. Label the tangent lines and the given point for clarity.

By following these steps, you can create a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point. Remember to be precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

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