[tex]\frac{2}{3}a + 2 = \frac{1}{3}(4a + 1)[/tex]


solve for "a"

Answer:

0.5 feet or 6 inches

Step-by-step explanation:

To find the height of the ball on the 10th bounce, we need to use the given equations. Let h be the height of the ball in feet after n bounces (including the initial drop), and k be a constant that depends on the coefficient of restitution. We also have a starting height of 10 feet and a height of 2 feet after 5 bounces, so:

10 = k * 5h

4 = k * 10h

We can solve these two equations for k, then use them to solve for h:

k = (10 - 4) / (5 * 4) = 0.5

Substituting this value into the original height equation, we get:

h = k^2 * 2 = 0.25 * 2 = 0.5

So, the height of the ball on the 10th bounce is 0.5 feet, or 6 inches.

Answer: 0.09766 feet (0.10 rounded to the nearest tenth)

Step-by-step explanation:

Answer:

  715 mL

Step-by-step explanation:

You want the total volume in two containers that have the volume ratio 4:7 and a difference in volumes of 195 mL.

Considering the question in terms of "ratio units," we see the difference of ratio units is 7-4 = 3, and the total of ratio units is 7+4 = 11. Then the total volume will be 11/3 times the difference in volume:

  total volume = (11/3)(195 mL)

  total volume = 715 mL

__

Additional comment

Though it is not necessary, as a check you can work out the volumes of the containers. The smaller will be 4/3 times the difference: 260 mL, and the larger will be 7/3 times the difference: 455 mL. The total is ...

  455 +260 = 715 . . . mL

and the difference is ...

  455 -260 = 195 . . . mL

If you prefer to work with equations for the volume, you can let x and y represent the volumes of the smaller and larger containers. Now you have ...

  x/y = 4/7

  y -x = 195

Substituting for y gives ...

  x/(195 +x) = 4/7

  7x = 4(195) +4x

  3x = 4(195)   ⇒   x = (4/3)·195 . . . . as above

Then the total volume is ...

  x+y = 195 +2x = 195(1 +2·4/3) = 11/3·195 . . . as above

Answer:

To calculate the net profit for each of the listed stocks, you can use the formula:

Net Profit = (Current Price - Purchase Price) * Number of Shares

Assuming you invested $500 in each stock 5 years ago, the purchase prices would be as follows:

Chipotle: $649.85 (based on the current price of $1,708.29)

Nike: $71.45 (based on the current price of $122.64)

Amazon: $45.60 (based on the current price of $103.29)

Snap Inc.: $15.49 (based on the current price of $11.21)

To calculate the number of shares you would have purchased at the time, you would divide $500 by the purchase price. For example, for Chipotle:

Number of Shares = $500 / $649.85 = 0.769 shares

Using this formula, the net profit for each stock would be:

Chipotle: (1,708.29 - 649.85) * 0.769 = $764.28

Nike: (122.64 - 71.45) * 7.006 = $359.62

Amazon: (103.29 - 45.60) * 10.920 = $630.58

Snap Inc.: (11.21 - 15.49) * 32.281 = -$137.31 (assuming you bought fractional shares)

Therefore, your total net profit would be $1,616.17.

Note that this calculation does not take into account any transaction fees or taxes that may be incurred in buying and selling the stocks.

I made a long explanation because you wanted me to explain step by step.

For Nike:

1.5 years ago the stock was at 63.59 USD, so buying $500 of Nike stock would give me 7.85 stocks (Purchase amount/stock price) or (500/63.59:7.85).

Stock is now valued at $122.64 USD, so I own $963.78 in stock (Stock price x Stock owned) or (7.85 X 122.64 = $963.78).

Net profit is $463.78 (Total of current owned stock - initial investment) or ($963.78 - $500 = $463.78).

For Amazon:

1.5 years ago the stock was at $1,765.13 USD, so buying $500 of Amazon stock would give me 0.283 stocks (Purchase amount/stock price) or (500/1,765.13:0.283).

Stock is now valued at $3,369.19 USD, so I own $953.63 in stock (Stock price x Stock owned) or (0.283 X 3,369.19 = $953.63).

Net profit is $453.63 (Total of current owned stock - initial investment) or ($953.63 - $500 = $453.63).

For Snap Inc.:

1.5 years ago the stock was at $17.46 USD, so buying $500 of Snap Inc. stock would give me 28.63 stocks (Purchase amount/stock price) or (500/17.46:28.63).

Stock is now valued at $11.21 USD, so I own $321.36 in stock (Stock price x Stock owned) or (28.63 X 11.21 = $321.36).

Net loss is $178.64 (Total of current owned stock - initial investment) or ($321.36 - $500 = -$178.64).

Based on the net profit, Chipotle and Amazon have performed well over the past 5 years, with net profits of $1,230.51 and $453.63 respectively. Nike has also performed well with a net profit of $463.78. However, Snap Inc. has decreased in price over the past 5 years and resulted in a net loss of $178.64.

Answer:

The image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

Step-by-step explanation:

To prove that triangle ABC is isosceles, we need to show that at least two of its sides have the same length. We can use the distance formula to calculate the length of each side:

AB = sqrt[(−7−(−2))^2 + (−1−4)^2] = sqrt[25 + 25] = 5sqrt(2)

AC = sqrt[(−3−(−2))^2 + (−3−4)^2] = sqrt[1 + 49] = sqrt(50)

BC = sqrt[(−7−(−3))^2 + (−1−(−3))^2] = sqrt[16 + 4] = 2sqrt(10)

Since AB and AC have different lengths, triangle ABC cannot be equilateral. However, if we compare AB and BC, we see that they have the same length, 5sqrt(2). Therefore, triangle ABC is isosceles.

To find the coordinates of A'B'C' after the translation 5 units to the right and 5 units down, we simply add 5 to the x-coordinates and subtract 5 from the y-coordinates of each vertex. Thus:

A' = (-2+5, 4-5) = (3, -1)

B' = (-7+5, -1-5) = (-2, -6)

C' = (-3+5, -3-5) = (2, -8)

Therefore, the image of triangle ABC after the translation 5 units to the right and 5 units down is A'B'C' with vertices at (3, -1), (-2, -6), and (2, -8).

To calculate how many sheets of graph paper each of the 26 students in Mr. Ramirez's math class will get if they all get the same number, we need to divide the total number of sheets by the number of students:

Number of sheets per student = Total number of sheets / Number of students

Number of sheets per student = 250 / 26

Number of sheets per student ≈ 9.615

So each student will get approximately 9 sheets of graph paper.

To calculate how many sheets will be left over, we can use the modulo operator (%), which returns the remainder of a division:

Sheets left over = Total number of sheets % Number of students

Sheets left over = 250 % 26

Sheets left over = 12

So there will be 12 sheets of graph paper left over after each of the 26 students has received approximately 9 sheets.

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

The complete table of trigonometric functions:

Row 1: θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

Row 2: θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

Row 3: θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

In this problem we must complete a table with three angles, measured in radians, and three kinds of trigonometric functions (two fundamental function and a derivate function). The procedure to complete the table is shown below:

Now we proceed to complete the table of trigonometric functions:

θ = π / 3, sin θ = √3 / 2, cos θ = 1 / 2, tan θ = √3

θ = 5π / 4, sin θ = - √2 / 2, cos θ = - √2 / 2, tan θ = - 1

θ = 7π / 6, sin θ = - 1 / 2, cos θ = √3 / 2, tan θ = - √3 / 3

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Answer:

25%

Step-by-step explanation:

8/32=0.25 as in percentage it would be 25%

i hope you find it helpful

The probability that the jury makes the correct decision that the defendant is guilty is 0.7063.

In order to resolve this issue, we must determine the likelihood that the jury would find the defendant guilty. Let's divide the issue into more manageable components.

We are aware that there is a 0.80 chance that a single juror would choose correctly. If the defendant is found guilty, there is still an 80 percent chance that the jury will reach the right verdict. Consequently, if the defendant is found guilty, there is an 80 percent chance that one jury will reach the right verdict.

The likelihood that at least 10 out of 12 jurors will choose the right course of action may be calculated using the binomial distribution formula. The equation is:

[tex]P(X \geq k) = 1 - \sum (i=0, k-1) [\frac{i!}{(i!(n-i)!)} ]p^i*(1-p)^(^n^-^i^)[/tex]

where:

P(X ≥ k) is the probability of at least k successes

n is the total number of trials (in this case, 12 jurors)

p is the probability of success in a single trial (in this case, 0.80)

k is the number of successes we want to find the probability of (in this case, 10)

Using a calculator or software, we can calculate this to be approximately 0.7063.

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Therefore , the solution of the given problem of triangle comes out to be  Cosine B = 9/41 is the solution (b).

A polygon is a hexagon if it has a minimum of one extra segment. It has a simple rectangular shape. Only the edges A and B can differentiate something like this from a regular triangle. Despite the exact collinearity of the borders, Euclidean geometry only produces a part of the cube. Three edges and three angles make up a triangle.

Here,

Using the cosine definition:

=> adjacent/hypotenuse = cos(B)

We are aware that AB is the hypotenuse, with a length of 41, and that the neighboring side, BC, has a length of 9. Therefore:

=> cos(B) = 9/41

=> Cosine B = 9/41 is the solution (b).

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[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{w}-\underset{x_1}{(-9)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ -8 }\implies \cfrac{3+5}{w+9}=-8\implies \cfrac{8}{w+9}=-8 \\\\\\ \cfrac{8}{-8}=w+9\implies -1=w+9\implies -10=w[/tex]

The author develops the connection between Mourne Textiles and the history and culture of Ireland by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs. Additionally, the author highlights the significance of the landscape and natural resources in Northern Ireland to the design and production of the textiles.

Hence, the correct answer is option B.

In the article, the author describes how Gerd Hay-Edie learned traditional weaving techniques from local weavers in Northern Ireland, and how she incorporated these techniques into her designs. The author also emphasizes the importance of the Mourne Mountains and the surrounding natural resources in shaping the textiles produced by the company.

Furthermore, the author highlights how the designs and techniques used by Mourne Textiles are rooted in Irish tradition and history. Through these details and examples, the author establishes a strong connection between Mourne Textiles and the history and culture of Ireland.

Hence, the correct answer is option B.

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--The question is incomplete, answering to the question below

"How does the author develop the connection between Mourne Textiles and the history and culture of Ireland?

A. by explaining major historical events in Ireland and how Gerd Hay-Edie took part in them

B. by mentioning that local Irish weavers taught Gerd Hay-Edie how to weave and make the designs

C. by describing Gerd Hay-Edie’s career and how events in Ireland impacted the company

D. by comparing the Norwegian fjords to the Irish landscape and Gerd Hay-Edie’s fashion sense to the typical Irish style" --

The required time the cyclist would take to ride 156 miles with a rate of 24 mph is 6.5 hours.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,

To find the time it takes a cyclist to cover a certain distance at a constant rate, you can use the formula:

time = distance/speed.

Plugging in the given values, you get:

[tex]\text{time} = 156 \ \text{miles} \div 24 \ \text{mph} = 6.5 \ \text{hours}[/tex].

So it would take the cyclist 6.5 hours to ride 156 miles at a constant rate of 24 mph.

The ordered pair that describes the location of V" is (5, -2).

In mathematics, reflection is a transformation in which a geometric figure is mirrored or flipped over a line, plane or point. It is a type of transformation that changes the position of an object without changing its shape or size. Reflection can occur in any number of dimensions, including two-dimensional space (plane), three-dimensional space (solid objects), or even higher dimensions.

The reflection of point V over the x-axis will change the sign of the y-coordinate, so point V' will be located at (-5, -2).

The reflection of point V' over the y-axis will change the sign of the x-coordinate, so point V" will be located at (5, -2).

Therefore, the ordered pair that describes the location of V" is (5, -2).

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The complete question is:

Point V is located at (-5,2) on the coordinate plane. Point V is reflected

over the x-axis to create point V'. Point V' is then reflected over the y-axis

to create point V". What ordered pair describes the location of V"?*

Answer:

x = 4√2

Step-by-step explanation:

This is a normal square with side length x. You can break this down into 2 right triangles connected by the diagonal. Given that both side lengths are equal, we can infer that this is a 45-45-90 triangle. The pattern for side lengths for this type of triangle is s - s - s√2. This means that 8, corresponds to the hypotenuse s√2.

s corresponds to the side length, in this case, x. So if we find the value of s, it will give us the value of x.

[tex]s\sqrt{2} = 8\\ s = \frac{8}{\sqrt{2} }\\ s = \frac{8}{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2}} \\s = \frac{8\sqrt{2} }{2}\\ \\s = 4\sqrt{2}[/tex]

So now we know that x = 4√2.

The slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here the given line coordinates are [tex](x_1,y_1) = (2,3)[/tex] and [tex](x_2,y_2)=(-4,0)[/tex].

Now using slope formula , slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{0-3}{-4-2}=\frac{-3}{-6}=\frac{1}{2}[/tex]

Now using equation formula then [tex]y-y_1=m(x-x_1)[/tex]

=> y-3= [tex]\frac{1}{2}[/tex] (x - 2)

=> 2y-6 = x-2

=> 2y = x-2+6

=> 2y = x+4

=> y = [tex]\frac{1}{2}x+2[/tex]

Hence the slope intercept form of the equation is y = [tex]\frac{1}{2}x+2[/tex].

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Answer:

0.125

Step-by-step explanation:

[tex] \frac{1}{2} \div 4[/tex]

[tex] \frac{1}{2} \times \frac{1}{4} [/tex]

[tex] \frac{1}{8} \: or \: 0.125[/tex]

Answer:

0.125

Step-by-step explanation:

The expression that represents this real-world situation is: c x 2 + 6

The expression that represents the real-world situation of Sam having 6 cookies and being given 2 more packs of cookies, each containing c cookies, is c x 2 + 6. This expression indicates that Sam received two packs of cookies, each with c cookies, and he already had 6 cookies before that. Multiplying c by 2 represents the two packs of cookies he received, and adding 6 to the result gives the total number of cookies Sam has now. The expression simplifies to 2c + 6. Therefore, to find the total number of cookies Sam has, we need to know the value of c, which represents the number of cookies in each pack.

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Answer:

6 hours - 5 = 2, so 15 = 6 , as its constant

I think they are all correct except for the last one

I think the last one should be b

Answer:

Step-by-step explanation:

(a)   [tex]5\frac{1}{8} =\frac{41}{8}[/tex]

      So we get

          [tex]5\frac{1}{8}\% =\frac{41}{8}\div100[/tex]

                   [tex]= \frac{41}{8} \times \frac{1}{100}[/tex]

                   [tex]=\frac{41}{800}[/tex]  

(b)    [tex]91.4=91\frac{4}{10} =91\frac{2}{5} =\frac{457}{5}[/tex]  

       So we get

               [tex]91.4\%=\frac{457}{5} \div100[/tex]

                          [tex]=\frac{457}{5} \times \frac{1}{100}[/tex]

                          [tex]=\frac{457}{500}[/tex]                

The baseball game lasted 2 hours and 10 minutes.

To calculate how long the baseball game lasted, we must begin by taking the start time of 7:05. We can convert this time to a numerical value by adding 7 hours and 5 minutes, which equals 705 minutes. Next, we must do the same with the end time of 9:15. Adding 9 hours and 15 minutes gives us a total of 915 minutes. Subtracting the start time from the end time gives us a difference of 210 minutes. Finally, we must convert the minutes back to hours and minutes, which gives us 2 hours and 10 minutes. Therefore, the baseball game lasted 2 hours and 10 minutes.

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Check the picture below.

ANSWER 1: The supplementary angle measures 58 degrees.

A=S+64=58+64=122

ANSWER 2: The angle measures 122 degrees.

double checking

A+S=180

122+58=180

180=180

Therefore, the probability that the student plays neither tennis nor netball is 1/5 = 0.2 or 20%.

There are 40 students in a class. 19 students play tennis, 20 students play netball, and 8 students play neither of these sports.

A student is chosen randomly from the class, and we need to determine the probability that the student: Plays tennis If a student is randomly chosen from the class, the probability that the student plays tennis is: Probability of playing tennis= (Number of students playing tennis) /

(Total number of students in the class) Probability of playing tennis= 19 / 40Plays netball if  a student is randomly chosen from the class, the probability that the student plays netball is: Probability of playing netball= (Number of students playing netball) / (Total number of students in the class)Probability of playing netball= 20 / 40 = 1/2Plays neither of these sports a student is randomly chosen from the class, the probability that the student plays neither tennis nor netball is

:Probability of playing neither tennis nor netball= (Number of students who do not play either of the two sports) / (Total number of students in the class)Probability of playing neither tennis nor netball= 8 / 40Probability that the student plays tennis and netball

Probability of playing tennis and netball = (Number of students playing both tennis and netball) / (Total number of students in the class)We are given that none of the students play both tennis and netball, so the probability of playing both tennis and netball is 0.

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Given the quadratic equation the condition that must apply to the constants a and c is c < 9a.

A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.

1) Remember, a quadratic function can have either a maximum or minimum value and that the value of the function at the vertex (i.e., the maximum or minimum point) is given by [tex]-b/2a[/tex].

In this case, the coefficient of x is 6, so the x-coordinate of the vertex is [tex]-6/2a = -3/a[/tex].

Since the function is always negative, the vertex must be a maximum, and the value of the function at the vertex must be negative.

Therefore, this gives us:

[tex]ax^2 + 6x + c < 0[/tex] for all x

The x-coordinate of the vertex is[tex]-3/a[/tex], so the value of the function at the vertex is:

[tex]a(-3/a)^2 + 6(-3/a) + c = 9a/a - 18/a + c = c - 9a/a[/tex]

Since the value of the function at the vertex must be negative, we thus have:

[tex]c - 9a/a < 0[/tex]

Simplifying further, we get:

[tex]c < 9a[/tex]

Therefore, we can conclude that the condition for the constants a and c to satisfy the given inequality is [tex]c < 9a.[/tex]

ii) We can choose [tex]a = 1[/tex] and [tex]c = -8[/tex].

Then, the function [tex]ax^2 + 6x + c = x^2 + 6x - 8[/tex] has a maximum value at [tex]x = -3[/tex],

Therefore, this example shows that [tex]a = 1[/tex] and [tex]c = -8[/tex]  satisfies the conditions found in part (i).

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Answer:

Step-by-step explanation:

function

slope

x value

y value

Answer:

180°

Step-by-step explanation:

The functions from the graph are x = -10, y = x + 5 and y = x² + 6x + 10, while the identities are listed below

Constant function

This is a function that does not change its value irrespective of the input and/or the output

From the graph, we have the vertical line

x = -10

This is a constant function with the following identities

Domain: x = -10

Range: 0 ≤ y ≤ 12.25

Linear function

This is a function that changes constantly with x and y

From the graph, we have the points

(-4, 1) and (-2, 3)

The equation is calculated as

y = mx + c

So, we have

-4m + c = 1

-2m + c = 3

This gives

2m = 2

m = 1

So, we have

-2(1) + c = 3

-2 + c = 3

c = 5

This means that the function is y = x + 5 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 3

Quadratic function

This function is represented as

y = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have

(h, k) = (-3, 1) and (x, y) = (-2, 2)

So, we have

y = a(x + 3)² + 1

Also, we have

2 = a(-2 + 3)² + 1

a + 1 = 2

a = 1

So, we have

y = (x + 3)² + 1

y = x² + 6x + 10

This means that the function is y = x² + 6x + 10 with the following identities

Domain: -4 ≤ x ≤ -2

Range: 1 ≤ y ≤ 2

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