What is the average rate of change of the function from x = 1 to x = 3?

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

I think they are all correct except for the last one

I think the last one should be b

In the triangle , the value of x is 57.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here in the given triangle , SD=99 , SF=44 , RF = 76 and FE = 76+3x

RE = FE - RF

=> RE = 76+3x-76 = 3x

Now using triangle proportionality theorem then,

=> [tex]\frac{SF}{SD}=\frac{RF}{RE}[/tex]

=> [tex]\frac{44}{99}=\frac{76}{3x}[/tex]

=> 3x = [tex]\frac{76\times99}{44}[/tex] = 171

=> x = 171/3 = 57

Hence the value of x is 57.

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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:

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.

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.

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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The minimum length the ramp will need to be so that it is safe for hand-powered wheelchairs is approximately 19.7 feet.

To calculate the minimum length of the ramp, we can use trigonometry. We know that the height of the ramp is 1.5 feet and that the angle of elevation should be no greater than 4.8°. Let's call the length of the ramp L.

The tangent of 4.8° is given by:

[tex]$$\tan(4.8\degree) \approx 0.084$$[/tex]

We can use this to set up an equation:

[tex]$$\frac{1.5}{L} \leq 0.084$$[/tex]

Solving for L, we get:

[tex]$$L \geq \frac{1.5}{0.084} \approx 17.9$$[/tex]

So the minimum length the ramp will need to be is approximately 17.9 feet. However, we should round up to ensure that the angle of elevation is no greater than 4.8°. Therefore, the minimum length the ramp will need to be so that it is safe for hand-powered wheelchairs is approximately 19.7 feet.

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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:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

Answer:

(-11, -14)

Step-by-step explanation:

Point (-8, -9)

Translation left 3 units

(-8, -9) → (-11, -9)

Down 5 units

(-11, -9) → (-11, -14)

So, the final point will be at (-11, -14)

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

[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 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 fraction comes out to be  a = 2/9.

Any arrangement of parts or pieces that are the same dimension can represent the whole. Quantity is referred to in standard English as "a portion" in a given measure. 8, 3/4. Fractions are included in wholes. In mathematics, integers are represented by the ratio which is the divisor to the ratio. These are all examples of basic fractions that are divided by whole integers. The residue is a difficult fraction even though the fraction itself includes a fraction.

Here,

We can begin by separating out the variable component (a + 6) on one side of the equation and simplifying to find a:

=> 9/10 = 8/(a + 6)

Adding (a + 6) to both edges results in:

=> 9/10 * (a + 6) = 8

As the left edge is widened:

=> 9a/10 + 54/10 = 8

54/10 from both groups subtracted:

=> 9a/10 = 2/10

By 9/10ths dividing both sides:

=> a = (2/10)/(9/10)

=> a = 2/9

The answer is therefore a = 2/9.

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Step-by-step explanation:

Given that:

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select three options. The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.

Solution:

1) The vertex of the function is at (–4,–15).

Ans.This is false.

2) The vertex of the function is at (–3,–16).

Ans. This is true. from the graph it is clearly shown A is vertex of graph.Which is (-3,-16)

3)The graph is increasing on the interval x > –3.

Ans. This region is located in graph with red colour,here it is easily shown that in this region graph continuously increasing.

This is true.

4)The graph is positive only on the intervals where x < –7 and where x > 1.

Ans: Yes,it is true.

Because when x<-7 graph is decreasing but have positive values and when x>1,graph is increasing and have positive values.

5)The graph is negative on the interval x < –4.

Ans:Yes,yellow part is shown the region of x<-4

here value of graph continuously decreasing.

Hope this helps!

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:

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:

180°

Step-by-step explanation:

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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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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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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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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Answer:

10.8 miles

Step-by-step explanation:

Use Pythagorean Theorem

[tex]a^{2} +b^{2} = c^{2}[/tex]

[tex]9^{2} +6^{2} = c^{2}[/tex]

[tex]c^{2} = 117[/tex]

[tex]c=\sqrt{117}[/tex]

Rounded to 10.8

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.

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).

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"?*

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.

Answer:

25%

Step-by-step explanation:

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

i hope you find it helpful

Answer: (i) The length of the wire is 2147.76 cm.

(ii) The volume of the wire is 43.16 cm^3.

Step-by-step explanation:

Given : Diameter of copper wire = 8mm = 0.08cm

length of the cylinder = 24 cm

diameter of the cylinder = 49 cm

(i) To calculate the length of the wire.

As we know, surface area of the cylinder = πrl = 3.14*28.5*24 = 2147.76cm.

Hence, the surface area of the cylinder will be the length of the wire, as the wire is evenly wrapped n the surface of the cylinder.

Therefore, the length of the wire is 2147.76 cm.

(ii) To calculate the volume of the wire.

As we know, the formula for the volume of the cylinder = πr^2h

now the volume of the wire is = 3.14*0.08*0.08*2147.76 = 43.16 cm^3.

Therefore, the volume of the wire is 43.16 cm^3.

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