How many pairs of shoes does a typical teenage boy own? To find out, a group of statistics
students surveyed a random sample of 20 male students from their large high school. Then
they recorded the number of pairs of shoes that each boy owned. Here are the data:
4
5
5
Ол
5
6
7
7
7
7
00
10
10
10
10
11
12
14
22
35
38
Luis is at the first quartile Q1 of the distribution. How many pairs of shoes does
Luis own?

SOLUTION

The equation of a parabola in a vertex form is given

since the parabola is on the x-axis.

From the diagram given, we have

Substituting into the formula above, we have

We have

Since the parabola is a reflection from the parent function, then

The equation of the parabola becomes

Answer; x = -2(y + 2)^2-4

\(\frac{11z}{z+3}=13-i,z\in\mathbb{C}\)

First, multiply both sides by \(z+3\),

\(11z=(13-i)(z+3)\)

\(13z+39-iz-3i=11z\)

Collect terms and put z on the left,

\(2z-iz=3i-39\)

\(z(2-i)=3i-39\)

\(z=\frac{3i-39}{2-i}\)

Division of complex numbers is defined by multiplying both denominator and numerator with complex conjugate of the denominator,

\(z=3\frac{(i-13)(2+i)}{(2-i)(2+i)}\)

Multiply out,

\(z=3\frac{2i-1-26-13i}{5}\)

\(z=3\frac{-11i-27}{5}\)

The result is,

\(z=-\frac{81}{5}-\frac{33}{5}i\)

Hope this helps :)

Check the picture below.

so the hexagonal prism is really just a hexagon with six 8x27 rectangles, let's simply get the area of all and sum them up.

\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} p=perimeter\\ a=apothem\\[-0.5em] \hrulefill\\ p=\stackrel{8\times 6}{48}\\ a=6.9 \end{cases}\implies A=\cfrac{1}{2}(6.9)(48)\implies A=165.6 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{six rectangles} }{(6)(8)(27)}~~ + ~~\stackrel{ \textit{hexgonal face} }{165.6}}\implies 1296+165.6\implies \text{\LARGE 1461.6}~in^2\)

The coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the Coordinates of Luke's house on the coordinate grid.

The grid representing Kyle's house. However, based on the given information, we can determine the coordinates of Kyle's house relative to Luke's house.

If Luke's house is located at the point (x, y), then Kyle's house is located 4 units to the left of Luke's house, which means the x-coordinate of Kyle's house is (x - 4). Similarly, Kyle's house is located 2 units up from Luke's house, which means the y-coordinate of Kyle's house is (y + 2).

Therefore, the coordinates of Kyle's house would be (x - 4, y + 2) relative to Luke's house, where x and y represent the coordinates of Luke's house on the coordinate grid.

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Answer:

A = 228 tickets

Step-by-step explanation:

We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.

Because the number of adult and student tickets together equals 506, we have A + S = 506.

Because there are 56 more student tickets than adult tickets we have A + 56 = S

And the way the system is already set up allows us to use substitution.

Thus, we have:

\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)

The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.

Answer:

-13

Step-by-step explanation:

-2x6 = -12

-9+8= -1

-1+-12=-13

Hope this helps

In a direct variation, y = 16 when x = 4. The direct variation equation shows the relationship between x and y will be y=4x.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

y = 16 when x = 4

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

In the given equation x is the independent variable while y is the dependent variable.

16 = 4(4)

y=4x

Thus, in a direct variation, y = 16 when x = 4. The direct variation equation shows the relationship between x and y will be y=4x.

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A function in the form that would match the graph that is given is

y(x)=(6/5)(x-1)²(x-5)².

An example of a rule is a function, which creates one output from one input. Alex Federspiel is the photographer. y=x² serves as an illustration of this. There is just one output for y if you enter anything for x. Considering that x is the input value, we can infer that y is a function of x. a formula, rule, or piece of legislation that specifies the relationship between the independent and dependent variables (the dependent variable). The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).

From the graph, the curve turns at the points

x=1 and x=5

The equation becomes,

y(x)=a(x-1)²(x-5)²

The above curve passes through (0, 30)

y(0)=a(1-0)²(0-5)²=30

a(-1)²(-5)²=30

a=30/25

a=6/5

y(x)=(6/5)(x-1)²(x-5)²

A function in the form that would match the graph that is given is

y(x)=(6/5)(x-1)²(x-5)².

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Answer:

80 marbles

Step-by-step explanation:

8 times 2=16

40 times 2=80

Answer:

393.75

Step-by-step explanation:

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

2 games

Step-by-step explanation:

First, find how many that won this year by multiplying 24 by 3/4

24(3/4)

= 18

Find how many they won last year by multiplying 24 by 2/3

24(2/3)

= 16

Find the difference:

18 - 16

= 2

So, they won 2 more games this year than last year

Answer:

2 more games

Step-by-step explanation:

this year

24/4 = 6

6*2 = 18

last year

24/3 = 8

8*2 = 16

18-16=2

Answer:

5 green marbles.

Step-by-step explanation:

20* 1/4 = 5

Relative interest refers to the comparison of interest rates between different financial instruments or investment opportunities. It allows individuals or investors to assess and evaluate the attractiveness of various options based on their potential returns.

1. Understand the basic concept: Interest is the cost of borrowing money or the return earned on invested funds. Relative interest involves comparing the interest rates of different financial instruments or investments to determine which one offers a more favorable return.

2. Identify the investment options: Start by identifying the different investment opportunities or financial instruments available. These can include savings accounts, certificates of deposit (CDs), bonds, stocks, or other investment vehicles.

3. Research interest rates: Research and gather information about the current interest rates offered by each investment option. This information can usually be found on financial websites, through financial institutions, or by consulting with a financial advisor.

4. Compare interest rates: Once you have the interest rates for each investment option, compare them side by side. Look for the differences in rates and identify which options offer higher or lower returns.

5. Assess risk and return: Consider the level of risk associated with each investment option. Higher returns often come with higher risk, so it's essential to evaluate the risk-reward tradeoff.

6. Make an informed decision: Based on the comparison of interest rates and the risk-reward assessment, make an informed decision on which investment option aligns with your financial goals and risk tolerance.

Always remember to consider your financial goals, risk tolerance, and consult with a financial advisor if needed.

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Answer:

2.01 ounces

Step-by-step explanation:

684 grams ÷ 12 servings =

57 grams in a serving

1 gram (g) = 0.03527396195 ounces (oz)

57 grams (g) ≈ 2.01 ounces (oz)

The z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

The sample scores are given as:

2, 3, 5, 5, 6.

Calculate the mean and the standard deviation using a statistical calculator.

From the statistical calculator, we have:

\(\bar x = 4.2\) --- mean

\(\sigma_x = 1.64\) --- standard deviation

The z-score is then calculated using

\(z= \frac{x - \bar x}{\sigma}\)

Where:

x = 2, 3, 5, 5, 6.

So, we have:

\(z_1= \frac{2 - 4.2}{1.64} = -1.34\)

\(z_2= \frac{3 - 4.2}{1.64} = -0.73\)

\(z_3= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_4= \frac{5 - 4.2}{1.64} = 0.48\)

\(z_5= \frac{6 - 4.2}{1.64} = 1.10\)

Hence, the z-scores of the scores are -1.34, -0.73, 0.48, 0.48 and 1.10

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The relation given is a function since each of the input value only maps to a single output value.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are set of coordinate values of a relation.

We have to determine whether the relation is function or not.

The points are,

{(-3, -8), (3, 6), (5, -5), (7,-6), (10, 6)}

Domain of the relation are {-3, 3, 5, 7, 10}

Range of the relation are {-8, 6, -5, -6, 6}

We can see that each of the input value only maps to a single output value.

So the relation is a function.

Hence the relation is a function.

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It is not possible to calculate the area accurately. If you could provide more details about the figure, such as its shape or a diagram, I would  to help you calculate the area.

Based on the information provided, it seems you are asking for the area of a figure with sides 4, 8, 4, 4, 8, and 16 meters.

However, without knowing the specific shape of the figure,  In general, calculating the area of a shape involves using formulas specific to that shape,

such as length × width for rectangles or base × height × 0.5 for triangles. Once you provide more information about the figure, I can guide you through the appropriate calculation.

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The image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).

Dilation is a process for creating similar figures by changing the size.

Rotation of a point P(x, y) 180 counterclockwise about the origin produces an image at P'(-x, -y).

Here, the point counterclockwise about the origin → (-(-9), -7).

Therefore, the image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).

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c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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The garden store was able to sell a total of 1,960 bags of potting soil on Saturday and Sunday.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

In order to find the number of bags of potting soil sold over those two days, the first step is find out the number of pallets store sold there potting soil :

= 17( on Saturday) + 23 (Sunday)

= 40 palettes

Each palettes has 7 flats so the total number of flats sold is:

= 40 x 7

= 280 flats

Each flat then contains 7 bags so the total number of bags sold is:

= Number of flats sold x 7

= 280 x 7

= 1960 bags

In conclusion 1,960 bags of potting soil were sold.

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The confidence interval for the proportion of millennials that care about Jobs/Economy is (0.22, 0.28).

The term confidence interval refers statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall.

Here we have given that Jobs/Economy 25%, Immigration 17%, Healthcare 16%, Education 16%, Environment 12%.

And we need to find the confidence interval for the proportion of millennials that care about Jobs/Economy.

As per the formula of confidence interval,

CI = x ± Z× s/√n

CI = 25 ± 1.9600 × 0.03/ √50

CI = 25 ± 0.00832

When we simplify this one then we get the confidence interval for the proportion of millennials that care about Jobs/Economy as

=> (0.22, 0.28)

Therefore, option (3) is correct.

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Answer:

If f(x) = +4, which of the following is the inverse of f(x)?

O A. ƒ˜¹(x) = 2(2+4)

B. ƒ˜¹(x) = 7(2-4)

C. ƒ˜¹(x) = 7(2+4)

D. f¯¹(x) = ²(2-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer:

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Step-by-step explanation:

We are given the following differential equation:

\(\frac{dP}{dt} = kP - h\)

Solving by separation of variables:

\(\frac{dP}{kP-h} = dt\)

Integrating both sides:

\(\int \frac{dP}{kP-h} = \int dt\)

On the left side, by substitution, u = kP - h, du = kDp, Dp = du/k. Then

\(\frac{1}{k} \ln{kP-h} = t + K\)

In which K is the constant of integration.

\(\ln{kP-h} = kt + K\)

\(e^{\ln{kP-h}} = e^{kt + K}\)

\(kP - h = Ke^{kt}\)

\(kP = Ke^{kt} + h\)

\(P(t) = \frac{Ke^{kt} + h}{k}\)

The general solution to this differential equation is \(P(t) = \frac{Ke^{kt} + h}{k}\)

Answer:

 =6mx^4−7x^4

Step-by-step explanation:

(6m−7)(x^4)

=(6m+−7)(x^4)

=(6m)(x^4)+(−7)(x^4)

\(\huge\text{Hey there!}\)

\(\mathsf{(6m - 7)\times4}\)

\(\mathsf{= (6m - 7)(4)}\)

\(\mathsf{= (6m - 7) 4}\)

\(\mathsf{= 4(6m - 7)}\)

\(\mathsf{= 4(6m) - 4(-7)}\)

\(\mathsf{= 6m(4) + (-7)(4)}\)

\(\mathsf{= 6m(4) - 7(4)}\)

\(\mathsf{= 6m - 28}\)

\(\huge\textbf{Therefore, your answer should be:}\)

\(\huge\boxed{\frak{24m - 28}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer: choice A

Step-by-step explanation:

the transposed matrix would be

5 3

2 -1

so

5*5+2*2=29

3*5+2*-1=13

5*3-2*-1=13

3*3+-1*-1=10

which gives us the answer

29 13

13 10