Turner helped his grandfather build a raised garden bed for Tanner’s grandmother. The bed is shaped like a rectangular prism that is 4 1/2 feet wide and a half of a foot tall. Turner and his grandfather use 18 bags of topsoil, each containing three force of a cubic foot, to feel the bed completely. How long is the garden?

The empirical rule to determine the interval middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds

Given data ,

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Since the middle 99.7% of data falls within three standard deviations of the mean, we can calculate the upper and lower limits of this interval as follows:

Lower limit = Mean - (3 x Standard Deviation)

Upper limit = Mean + (3 x Standard Deviation)

Plugging in the values for mean and standard deviation:

Lower limit = 68 - (3 x 1.5) = 68 - 4.5 = 63.5 seconds

Upper limit = 68 + (3 x 1.5) = 68 + 4.5 = 72.5 seconds

Hence , the interval of times that represents the middle 99.7% of Caroline's finishing times in the 400 meter race is 63.5 seconds to 72.5 seconds

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Answer:

Step-by-step explanation:

The value of angle t is 126⁰.

The value of angle x is 70⁰.

The value of angle 5 is 85⁰.

The value of each of the missing angles is calculated as follows;

angle b = 27⁰ (vertical opposite angles are equal)

The value of angle t is calculated as follows;

b + t + 27 = 180 ( sum of angles on a straight line)

27 + t + 27 = 180

54 + t = 180

t = 180 - 54

t = 126⁰

The value of angle x is calculated as follows;

x + 30 + 80 = 180 (sum of angle in a triangle and vertical opposite angles)

x + 110 = 180

x = 180 - 110

x = 70⁰

The value of angle 5 is calculated as follows;

65 + 70 + (180 - 40) + ∠5 = 360 (sum of angles in a quadrilateral)

65 + 70 + 140 + ∠5 = 360

275 + ∠5 = 360

∠5 = 360 - 275

∠5 = 85⁰

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Answer:

To find the distance between a point and a line in a plane, we can use the formula:

distance = |Ax + By + C| / √(A^2 + B^2)

where A, B, and C are the coefficients of the general form of the line equation (Ax + By + C = 0), and (x,y) are the coordinates of the point.

First, we need to rewrite the given line equation in the standard form (y = mx + b):

2x - 3y = -2

-3y = -2x - 2

y = (2/3)x + 2/3

Now we can identify the slope (m) and y-intercept (b) of the line:

m = 2/3

b = 2/3

Next, we can find the equation of the perpendicular line that passes through the point (1,2), since the distance between the point and the line will be the length of the segment connecting the point to the intersection of these two lines. The slope of a line perpendicular to a line with slope m is -1/m, so the equation of the perpendicular line passing through (1,2) is:

y - 2 = (-3/2)(x - 1)

y = (-3/2)x + (7/2)

Now we need to find the intersection of the two lines by solving the system of equations:

y = (2/3)x + 2/3

y = (-3/2)x + (7/2)

(-3/2)x + (7/2) = (2/3)x + 2/3

(-13/6)x = -5/6

x = 5/13

y = (2/3)(5/13) + 2/3

y = 11/13

So the intersection point of the two lines is (5/13, 11/13). Now we can use the distance formula to find the distance between this point and the given point (1,2):

distance = √[(5/13 - 1)^2 + (11/13 - 2)^2]

distance = √[(36/169) + (25/169)]

distance = √(61/169)

distance = √61/13

The closest answer choice is (A) √13, but the simplified expression is actually √61/13. Therefore, none of the answer choices provided are completely accurate.

Step-by-step explanation:

Answer:

171.76 Pounds

Step-By-Step Explanation:

So the explanation to how I got the answer is in the link below.

The given expression is

[tex]2x+x^2[/tex]

So we can write the general rule for the sequence as

[tex]T_x=2x+x^2[/tex]

Recall that the domain of a sequence is the set of natural numbers.

Let us plug in some first few natural numbers to generate the sequence.

When [tex]x=1[/tex], we obtain,

[tex]T_1=2(1)+(1)^2[/tex]

[tex]\rightarrow T_1=2+1[/tex]

[tex]\rightarrow T_1=3[/tex]

When [tex]x=2[/tex], we obtain,

[tex]T_2=2(2)+(2)^2[/tex]

[tex]\rightarrow T_2=4+4[/tex]

[tex]\rightarrow T_2=8[/tex]

When [tex]x=3[/tex], we obtain,

[tex]T_3=2(3)+(3)^2[/tex]

[tex]T_3=6+9[/tex]

[tex]T_3=15[/tex]

When [tex]x=4[/tex], we obtain,

[tex]T_4=2(4)+(4)^2[/tex]

[tex]T_4=8+16[/tex]

[tex]T_4=24[/tex]

Therefore the number sequence produced by the given expression is,

[tex]\boxed{\bold{3, 8, 15, 24.}}[/tex]

The range of the function is y = {11, 13, 17, 25}.

In mathematics, the range of a function refers to the set of all possible output values that the function can produce when given a set of input values. It is also known as the image of the function. The range of a function can be found by evaluating the function for all possible input values, or by analyzing the properties of the function.

To find the range of the function, we need to substitute each value of the domain into the function and record the corresponding output values.

For x = 2, f(2) = 2(2) + 7 = 11.

For x = 3, f(3) = 2(3) + 7 = 13.

For x = 5, f(5) = 2(5) + 7 = 17.

For x = 9, f(9) = 2(9) + 7 = 25.

Therefore, the range of the function is y = {11, 13, 17, 25}.

The answer is A. y = {9, 10, 12, 16} is not the correct range for this function with the given domain.

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Answer:

9/5x+7

Step-by-step explanation:

You can keep the slope the same, because it is parallel, but the y-intercept must change to plus seven in order to go through (-5, -2)

Answer:

The total cost, C (in dollars), for driving x miles is given by:

C = 0.06x + 10.75

where x is the number of miles driven.

To find the total cost for driving a certain number of miles, simply substitute that value for x in the equation and solve for C.

The limiting value or horizontal asymptote of the function y = 2x/4x-5 is y = 0.5

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

y = 2x/4x-5

The limiting value or horizontal asymptote can be calculated by graph

So, we start by plotting the graph of y = 2x/4x-5

See attachment for the graph

From the graph, we can see that

The function does not have a defined value at y = 0.5

This means that the limiting value or horizontal asymptote is y = 0.5

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The canoe traveled approximately a distance of 21.9ft.

let the distance the canoe travels be "d".

Initial position = 65 ft

After  7s,

The Final position is 40ft away

From the given information the canoe moves =(65-40)=25ft closer

Let x=25ft

Using the tangent function

we know that, tan(50degree)=x/d

therefore, d=25/tan(50 degree)

d=21.9ft

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Answer:

Your calculator should be in radian mode.

a)

[tex]f(x) = 56 \sin( \frac{2t\pi}{12} + \frac{\pi}{2} ) + 4[/tex]

b)

[tex]f(x) = 56 \cos( \frac{2t\pi}{12} - \frac{\pi}{2} ) + 4[/tex]

c)

The height of the wheel's central axle is 32 meters.

f(x) = 56sin((2(x + 4)π/12) - (π/2)) + 4

the three friends spent L.120.00, L.240.00, and L.360.00, respectively.

How to solve the problem?

Let's denote the amount that Alicia spends as "x". According to the problem statement, we know that Juan spends twice as much as Alicia, which means he spends 2x. Similarly, we know that Ana spends three times as much as Alicia, which means she spends 3x.

We also know that the three friends together have spent L.720.00. So, we can set up an equation to represent this:

x + 2x + 3x = 720

Simplifying this equation, we get:

6x = 720

Dividing both sides by 6, we get:

x = 120

So, Alicia spent L.120.00, Juan spent twice as much as Alicia, which is L.240.00, and Ana spent three times as much as Alicia, which is L.360.00.

Therefore, the three friends spent L.120.00, L.240.00, and L.360.00, respectively.

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To calculate the expected value of playing this game, we need to multiply the probability of winning each amount by the corresponding payout and then sum them up.

Let's start by calculating the probability of selecting each type of marble:

   Probability of selecting a gold marble: 3/34

   Probability of selecting a silver marble: 8/34

   Probability of selecting a black marble: 23/34

Now, let's calculate the expected value of playing the game:

E(x) = (3/34) * $3 + (8/34) * $2 + (23/34) * (-$1)

E(x) = $0.26

So the expected value of playing this game is $0.26. This means that over many plays of the game, we would expect to win an average of $0.26 per play. However, it's important to remember that this is just an average, and in any individual play of the game, you could win more or less than this amount.

Answer:

First, we need to find out how many people are male and female in the town:

Step-by-step explanation:

Male population = 48% of 42800 = 20544

Female population = 100% - 48% = 52% of 42800 = 22256

To find out how many more females there are than males, we need to subtract the male population from the female population:

Female population - Male population = 22256 - 20544 = 1712

Therefore, there are 1712 more females than males in the town.

Answer:

Step-by-step explanation:

There is no correlation between the two.

The graph provided is a scatter plot and the dots are to spread out to have any time of coloration

Juan traveled approximately 288.24 miles.

The direct road would be approximately 288 miles long.

Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.

We have,

a.

Here is a diagram illustrating Juan's trip:

    Grand Canyon

         |

         |

         |

Juan's    |       x

house --------->

         y

b.

To find the total distance Juan traveled, we can use the Pythagorean theorem:

distance² = x² + y²

Juan drove 280 miles south (y direction) and 64 miles east (x direction), so we have:

distance² = 280² + 64²

distance² = 78,976 + 4,096

distance² = 83,072

Taking the square root of both sides, we get:

distance ≈ 288.24 miles

c.

To find the length of the direct road, we can use the Pythagorean theorem again:

distance² = x² + y²

The direct road forms a right triangle with legs of 280 miles and 64 miles, so we have:

distance² = 280² + 64²

distance² = 78,976 + 4,096

distance² = 83,072

Taking the square root of both sides, we get:

distance ≈ 288.24 miles

d.

To find how much shorter Juan's trip would be if he took the direct route, we can subtract the distance he traveled from the direct road distance:

288 - 288.24 ≈ -0.24

Thus,

Juan traveled approximately 288.24 miles.

The direct road would be approximately 288 miles long.

Juan's trip would be approximately 0.24 miles shorter if he was able to take the direct route.

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The values of x, y and  z of the given parallelogram are: x = 12, y = -20 and z = -32

A quadrilateral has two pairs of sides are parallel to each and the four angles at the vertices are not equal to the right angle, and then the quadrilateral is called a parallelogram. Also, the opposite sides are equal in length.

The key properties of angles of a parallelogram are:

- If one angle of a parallelogram is a right angle, then all the angles are right angles

- Opposite angles of a parallelogram are equal (or congruent)

- Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees)

Consecutive angles are supplementary and as such:

85 + 8x - 1 = 180

8x = 181 - 85

8x = 96

x = 96/8

x = 12

Opposite angles are equal and as such:

85 = -4y + 5

-4y = 80

y = -20

Similarly:

85 - 3z - 4 = 180

3z = -96

z = -96/3

z = -32

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Answer:

Use Formula nPr, to solve the following question

6P4 = 360

Answer:

Step-by-step explanation:

26/7

The height of the building is given by h = 93.5 m

Given data ,

Let the proportion be represented as A

Now , the value of A is

The height of the pole is 3.3 meters and its shadow is 1.71 meters long. We can set up a proportion to find the height of the building:

Height of pole / Length of pole's shadow = Height of building / Length of building's shadow

3.3 m / 1.71 m = x / 48.25 m

Now we can cross-multiply and solve for "x":

3.3 m * 48.25 m = 1.71 m * x

159.825 m² = 1.71 m * x

x = 159.825 m² / 1.71 m

x ≈ 93.5 m

Hence , the height of the building is approximately 93.5 meters

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A number with eight tens and one one is  = 81.

A  number with five tens and five ones is  = 55.

A number with eight tens and nine ones is 89.

A number with five tens and eight ones = 58.

A number with one ten and seven ones is 17.

A number with five tens and two ones is 52.

A  number with six tens and two ones is 62.

A number with three tens and zero ones  is 30.

A number with four tens and five ones is 45.

The phrase "eight tens and one one" denotes a numerical value featuring the digit 8 in the tens position and 1 in the ones position. This is equal to the sum of 80 and 1, resulting in a total value of 81.

Therefore "a numerical figure composed of 5 tens and 5 units" indicates a number where 5 is in the tens position while 5 is in the ones position, resulting in a total of 50 + 5, which equals 55.

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It is not appropriate to generalize the findings of the survey to the entire school population.

What is survey?

The conclusion that about 8.6% of the students in the school have a January birthday is not necessarily valid based on the information provided.

The sample size of the survey is too small (only 3 students with January birthdays) and limited to one math class, so it may not be representative of the whole school population. Additionally, the sample is not randomly selected, which introduces the possibility of selection bias.

Therefore, it is not appropriate to generalize the findings of the survey to the entire school population. A more reliable way to determine the percentage of students with a January birthday would be to collect data from a larger, randomly selected sample of students across the entire school population.

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Plotting the graph of the function h(x) = [tex](x^2 - 3x - 4) / (x - 4)[/tex], we get y- intercept = 1, vertical asymptotes at x=4 and  horizontal asymptotes at y=1.

The connection between a function's input values (usually written as x) and output values (often indicated as y) is represented by the function's graph. It gives insights on the function's characteristics, including its domain, range, intercepts, asymptotes, and general form, as well as a visual representation of how the function acts.

Steps to plot the graph of the give function h(x) =[tex](x^2 - 3x - 4) / (x - 4)[/tex]:

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The total number of different ways that the student can be assigned during a 4-day work week is 81 different ways.

A student is a person who is enrolled in an educational institution, such as a college, university, or trade school. Students are typically required to attend classes and complete assignments to gain knowledge and develop skills related to their field of study. Depending on their level of education, students may also be required to participate in research or internships in order to gain practical experience.

There are 3 possible floors that the student can be assigned to, so for each day of the 4-day week, there are 3 possible assignments.
Therefore, the total number of different ways that the student can be assigned during a 4-day work week is 3 x 3 x 3 x 3
= 81 different ways.

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Standard form of the equation for the circle with the following properties is (x + 7)² + (y + 6)²= 104.

A line segment through the center of a circle with its ends on the circle's circumference. Its value is twice of the radius.

An equation is a mathematical statement that asserts the equality between two expressions, typically containing one or more variables. It consists of two sides separated by an equals sign (=), indicating that the expressions on both sides have the same value. Equations are used to describe relationships, solve problems, and make predictions in various branches of mathematics, science, engineering, and other fields. They can be linear or nonlinear, and may involve arithmetic, algebraic, trigonometric, exponential, or other mathematical operations. Solving an equation involves finding the values of the variables that make the equation true.

To find the standard form of the equation for a circle, we can start by finding the center and radius of the circle using the given endpoints of a diameter.

The center of the circle is the midpoint of the diameter, which can be found by averaging the coordinates of the two endpoints. Let's denote the coordinates of the endpoints of the diameter as (x1, y1) and (x2, y2) respectively.

In this case, the coordinates of the endpoints are (x1, y1) = (-6, -1) and (x2, y2) = (-8, -11). Using the midpoint formula, we can find the center of the circle:

Center = ((x1 + x2)/2, (y1 + y2)/2)

Plugging in the values, we get:

Center = ((-6 + (-8))/2, (-1 + (-11))/2)

Center = ((-14)/2, (-12)/2)

Center = (-7, -6)

So, the center of the circle is (-7, -6).

The radius of the circle is half the length of the diameter, which can be found using the distance formula between the two endpoints of the diameter. Let's denote the distance between the endpoints as d.

The distance formula is given by:

d = sqrt((x2 - x1)² + (y2 - y1)²)

Plugging in the values, we get:

d = sqrt((-8 - (-6))² + (-11 - (-1))²)

d = sqrt((-2)² + (-10)²)

d = sqrt(4 + 100)

d = sqrt(104)

So, the radius of the circle is sqrt(104).

Now that we have the center and radius of the circle, we can write the standard form of the equation of the circle as:

(x - h)² + (y - k)²= r²

where (h, k) is the center of the circle and r is the radius of the circle.

Plugging in the values, we get:

(x - (-7))² + (y - (-6))² = (sqrt(104))²

(x + 7)² + (y + 6)²= 104

So, the standard form of the equation for the circle with endpoints of a diameter at (-6, -1) and (-8, -11) is (x + 7)² + (y + 6)² = 104

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Without seeing the graph of the linear function, it is impossible to determine if Tom's answer of 12 is correct or incorrect. However, it is important to understand the concept of slope and how it is calculated for a linear function.

The slope of a linear function represents the rate at which the y-coordinate changes for each unit increase in the x-coordinate. In other words, it measures the steepness of the line. Mathematically, the slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

To calculate the slope of a line given its graph, one can choose any two points on the line and find the difference in their y-coordinates and x-coordinates. The slope is then the ratio of the change in y-coordinates to the change in x-coordinates. This can be expressed as:

slope = (change in y-coordinate) / (change in x-coordinate)

Now, if Tom has correctly identified two points on the line and calculated the difference in their y-coordinates and x-coordinates, and if he has obtained a ratio of 12 for the change in y-coordinate to the change in x-coordinate, then his answer of 12 for the slope would be correct.

However, it is also possible that Tom made an error in his calculation, or that he misread the graph, and obtained an incorrect answer. Therefore, it would be necessary to verify his calculations by checking the points he used and the formula he applied.

In conclusion, without further information about the graph of the linear function and the points chosen by Tom to calculate the slope, it is impossible to determine if his answer of 12 is correct or incorrect.

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The table is completed as below

                             Interested in            NOT Interested in      Total

                             Athletics                   Athletics

Interested in

Academic Clubs        26                              58                          84

Not Interested in

Academic Clubs        118                              38                          156

Total                         144                               96                         240

To fill in the table, we start with the total number of students, which is 240.

We know that 35% of students are interested in athletics, so we can find the number of students interested in athletics as:

0.35 x 240 = 84

Similarly, we know that 3/5 of students are interested in academic clubs, so we can find the number of students interested in academic clubs as:

(3/5) x 240 = 144

We also know that 26 students are interested in both athletics and academic clubs, so we can fill in that cell as 26.

To fill in the remaining cells, we can use the fact that the row and column totals must add up correctly. For example, in the "Interested in athletics" row, we know that there are a total of 84 students interested in athletics. We also know that 26 of these students are interested in both athletics and academic clubs. Therefore, the number of students interested in athletics but not academic clubs is:

84 - 26 = 58

We can use similar reasoning to fill in the remaining cells. For example, in the "Not interested in athletics" column, we know that there are a total of 214 students who are not interested in athletics. We also know that 144 students are interested in academic clubs. Therefore, the number of students who are not interested in athletics but are interested in academic clubs is:

144 - 26 = 118

Let x represent "not interested in academics club" and "not interested in athletic". Using the total in the horizontal (bottom row) we have:

144 + 58 + x = 240

x = 240 - 202

x = 38

Hence 58 + 38 = 96 and 118 + 38 = 156

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Answer:

The same, Congruent

Step-by-step explanation:

The measures of alternate exterior angles are equal when two parallel lines are intersected by a transversal line. That is, if we have two parallel lines l and m intersected by a transversal line t, then the alternate exterior angles are congruent, which means that they have the same measure. More formally, if angle 1 and angle 2 are alternate exterior angles, then:

angle 1 = angle 2

The reason for this is that when the parallel lines are intersected by the transversal line, they form a Z-shape pattern, and the alternate exterior angles are located on opposite sides of the transversal line, but outside of the two parallel lines. The angles are congruent because they are formed by a pair of corresponding angles and a pair of vertical angles.

-

Answer:

D

Step-by-step explanation:

The domain of a function refers to the set of all possible input values (independent variable) for which the function is defined. In this case, the graph has points (6,80) and (11,40), which means that the function is defined for the values of g (the independent variable) between 6 and 11. Therefore, the domain of the function is:

D. 6≤g≤11

The domain of the function in the given graph is 6≤h≤11, as it includes all possible values of h between and including 6 and 11 on the horizontal (h) axis. So the correct option is D.

The domain of a function refers to the set of all possible input values for the function. In the given graph, which is plotted on the h-g axis and includes points (6, 80) and (11, 40), we are interested in determining the valid range for the independent variable, h.

The lowest h-value on the graph is 6, corresponding to the point (6, 80), and the highest h-value is 11, corresponding to the point (11, 40). These are the boundaries that define the domain of the function. Any value of h that falls within this range is a valid input for the function, and any value outside this range is not represented on the graph.

Therefore, the domain of the function is 6≤h≤11, as it includes all values of h between and including 6 and 11. This range encompasses all possible inputs for this function as depicted in the graph.

In summary, the domain represents the valid input values, and in this case, it is limited to the interval from 6 to 11 on the h-axis.

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