Question 7Incorrect2 tries left. Please try again.Jodi surveyed her friends about the number of calls they made over the weekend. The responses were 20, 23, 18, 4, 17, 21, 15, and 25. Use therange and interquartile range to describe how the data vary.The data vary by a range ofcalls. The middle half of the data values vary bycalls

The final rule for g(x) is g(x) = 3|3x| + 12.

To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.

So, the rule for g(x) is g(x) = 3f(x).

Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:

g(x) = 3f(x)

g(x) = 3(-|3x| - 4)

g(x) = -3|3x| - 12

This is the expression for g(x), which represents the transformed graph.

To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.

Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.

Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.

The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).

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Answer:\(x^{2}+\frac{11x}{5}-\frac{12}{5}\)

Step-by-step explanation:

The roots are really just what x is when the equation is equal to zero. So, an equation with these roots would look like this:

(x+3)(x-4/5)=y

however, this is not standard form. To get standard form we will need to expand the equation using FOIL.

x^2+3x-4x/5-12/5=

x^2+11x/5-12/5

and that would be your answer.

This stuff is a bit tricky and it get annoying with those pesky fractions. If you have any questions just comment.

a. The value of the definite integral \(\int\limits^7_{3.5} {f(x)} \, dx = - 1\)

b.  The value of the definite integral \(\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5\)

To answer the question, we need to know what definite integrals are.

These are integrals which are evaluated between two values of the variable.

\(\int\limits^7_{3.5} {f(x)} \, dx = - 1\)

Given that \(\int\limits^{10.5}_0 {f(x)} \, dx = 9, \int\limits^{3.5}_0 {f(x)} \, dx = 7 and \int\limits^{10.5}_7 {f(x)} \, dx = 3\)

We require  \(\int\limits^7_{3.5} {f(x)} \, dx\)

So,  \(\int\limits^{10.5}_0 {f(x)} \, dx = \int\limits^{3.5}_0 {f(x)} \, dx + \int\limits^7_{3.5} {f(x)} \, dx + \int\limits^{10.5}_7 {f(x)} \,dx\)

So,  \(\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx\)

Substituting the values of the variables into the equation, we have

So,  \(\int\limits^7_{3.5} {f(x)} \, dx = \int\limits^{10.5}_0 {f(x)} \, dx - \int\limits^{3.5}_0 {f(x)} \, dx - \int\limits^{10.5}_7 {f(x)} \,dx\)

 \(\int\limits^7_{3.5} {f(x)} \, dx = 9 - 7 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = 2 - 3\\\int\limits^7_{3.5} {f(x)} \, dx = - 1\)

So, \(\int\limits^7_{3.5} {f(x)} \, dx = - 1\)

\(\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5\)

\(\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = \int\limits^7_{3.5} 5{f(x)}\, dx - \int\limits^7_{3.5} 3\, dx\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = 5\int\limits^7_{3.5} {f(x)}\, dx - 3(7.5 - 3)\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= 5 X (-1 ) - 3 X 4.5 \\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx= -5 - 13.5\\\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5\)

So,  \(\int\limits^7_{3.5} (5{f(x)} - 3)\, dx = -18.5\)

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The probability is P = 0.135

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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Given statement solution is :- It  would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

To find the cost of installing tile in the dining room and carpet in the bedroom, we need to calculate the areas of both rooms first.

Given:

Every 2 centimeters on the floor plan represents 1 meter of the house.

Dining Room:

On the floor plan, the dining room is 8 cm by 10 cm.

Converting this to meters, the dimensions of the dining room are 8 cm / 2 = 4 meters by 10 cm / 2 = 5 meters.

The area of the dining room is 4 meters * 5 meters = 20 square meters.

Bedroom:

On the floor plan, the bedroom is 6 cm by 10 cm.

Converting this to meters, the dimensions of the bedroom are 6 cm / 2 = 3 meters by 10 cm / 2 = 5 meters.

The area of the bedroom is 3 meters * 5 meters = 15 square meters.

Now, let's calculate the costs.

Cost of Tile:

The cost of installing tile is $34 per square meter.

The area of the dining room is 20 square meters.

Therefore, the cost of installing tile in the dining room is 20 square meters * $34/square meter = $680.

Cost of Carpet:

The cost of installing carpet is $21 per square meter.

The area of the bedroom is 15 square meters.

Therefore, the cost of installing carpet in the bedroom is 15 square meters * $21/square meter = $315.

Therefore, it would cost $680 to install tile in the dining room and $315 to install carpet in the bedroom.

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Answer:

60 mph

Step-by-step explanation:

1 min to go 1 mile, 60 minutes per hour, 60 x 1=60

Answer:

y = 3x + 10

Step-by-step explanation:

Answer:

im pretty sure it is (0,5) or (10,0)

Step-by-step explanation:

The time he start shopping is 2 : 00 PM

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

Time spent = 25 minutes

Time he left the store = 2 : 25PM

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

Time he started = Time he left the store - Time spent

substitute the known values in the above equation, so, we have the following representation

Time he started = 2 : 25PM - 25 minutes

Evaluate

Time he started = 2 : 00 PM

Hence, the time he start shopping is 2 : 00 PM

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The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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Answer:

Please double check the question

y = 2√2 is not on the unit circle

The exact measure of the angle is 45°. If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=2√2,

A Unit circle is defined as a circle having a radius of 1 unit and having its center at the origin.

We know that the terminal side passes through a point of the form (√2/2, y).

Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:

\(1=\sqrt{(\dfrac{\sqrt{2}}{2})^2+y^2}\)

\(1^2=\dfrac{2}{4}+y^2\)

\(1-\dfrac{1}{2}=y^2\)

\(Y=\dfrac{1}{\sqrt{2}}\)

We know that y is positive because the point is on the first quadrant.

Now, we know that our point is:

(√2/2, 1/√2)

And we can rewrite:

√2/2 = 1/√2

So the point is:

( 1/√2,  1/√2)

Finally, remember that a point (x, y), the angle that represents it is given by:

θ = Atan(y/x).

Then in this case, we have:

θ = Atan(1/√2/1/√2) = Atan(1) = 45°

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Answer:

8.62% probability that all have the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the marbles are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

What is the probability that all have the same color?

Desired outcomes:

Either all red(from a set of 9), all white(from a set of 9) or all blue(from a set of 8). So

\(D = C_{9,3} + C_{9,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{9!}{3!6!} + \frac{8!}{3!5!} = 224\)

Total outcomes:

3 marbles, from a set of 9 + 9 + 8 = 26. So

\(T = C_{26,3} = \frac{26!}{3!23!} = 2600\)

Probability:

\(p = \frac{D}{T} = \frac{224}{2600} = 0.0862\)

8.62% probability that all have the same color

The equation which represents the relationship between X values and Y values can be found by deriving the equation of line using slope intercept form. The equation of line is 3x - 5y = 25.

How to find equation of line using slope intercept form?

Equation of line using slope intercept form is y = mx + b

where m is slope of the line and b is y-intercept

The slope intercept can be used to form equation of line using two points on the line.

According to the given question:

The two points which lie on the line are (x, y) = (5, -2) and (x', y') = (0, -5)

Slope of the line m = y' - y/x' - x

                               = (-5 +2)/(0 - 5)

                               = 3/5

Now y intercept b = y - mx

                              = -2 - (3/5. 5)

                              = -5

Therefore the required equation of line is y = 3/5x - 5

On simplifying further 3x - 5y = 25

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The side length of the equilateral triangle is 29 inches.

What is perimeter?

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides. Area is the portion of the plane that a closed form occupies, whereas perimeter is the space surrounding the closed figure.

Here in equilateral triangle all side of the triangle is equal . Then

Perimeter of triangle = 3× side. = 3s

Now perimeter of square = 4×side = 4a

Here perimeter of an equilateral triangle is 9 inches more than the perimeter of a square

=> Perimeter of square = perimeter of triangle + 9

=> 4a = 3s+9 ---------> 1

Now side of the triangle is 5 inches longer than the side of the square.

=> s = a+5-------> 2

=> a = s-5 --------> 3

Now put 3 into 1 then,

=> 4(s-5) = 3s+9

=> 4s-20 = 3s +9

=> 4s-3s = 20+9

=> s = 29 inches.

Hence side length of the equilateral triangle is 29 inches.

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Answer:

16/25 (B)

The complete question related to thus found on brainly (ID: 10153234) is stated below:

The two triangular prisms shown are similar. The dimensions of the larger prism were multiplied by a scale factor of to create the smaller prism.

When the large prism was reduced, the surface area changed by a factor of

A. 64/125

B. 16/25

C. 4/5

D. 10/8

Find attached the diagram

Step-by-step explanation:

In dilation, two figures have same shape but different size.

The triangular prism was dilated to create a new prism.

The larger triangular prism is the original shape

The smaller triangular prism is the new shape

Let the scale factor = p

For larger prism: the length = breadth = height = 10unit

For smaller prism: the length = breadth = height = 8unit

Surface area of smaller triangular prism = p × surface area of larger triangular prism

p = (Surface area of smaller triangular prism)/(surface area of larger triangular prism)

In similar shapes, the ratio of their areas = square of the ratio of their corresponding sides.

Let's take the height of each shape

Ratio of their corresponding sides (height) = 8/10

p = ratio of areas = (8/10)²

p = 64/100

p = 16/25

Answer:

16/25

Step-by-step explanation:

edge 2021

Answer:

1. 0.445 or 0.5

2. 0.167 or 0.2

3. Yes and No

Step-by-step explanation:

2 coins are fair and the 3rd is two-headed

So there are 2 tails and 4 heads altogether.

(A) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?

The probability that the coin is a fair one is: Probability of a fair coin x Probability of obtaining a head

= 2/3 x 4/6 = 0.445 to 3 decimal places

(B) He randomly picks one and flips it twice. Compute the probability that he gets 2 tails

This is = [the sum of the probability that each coin produces a tail 2 times when flipped twice] divided by 3.

For Coin 1,  0.5 is the probability of getting tails. For two consecutive tails, the probability would be 0.5 x 0.5 = 0.25

Same goes for Coin 2 which is the second fair coin.

For Coin 3, the probability of getting a tail at all is 0.

So [0.25 + 0.25 + 0] / 3  = 0.167 to 3 d.p.

(C) Suppose B = the event that the first result is head

Suppose C = the event that the second result is also head

- Are B and C independent (if the two-headed coin wasn't picked)?

YES

- Are B and C independent (if the two-headed coin was picked)?

NO

Given that Franklin has three coins, two fair coins (head on one side and tail on the other side) and one two-headed coin, to determine 1) if he randomly picks one, flips it and gets a head, what is the probability that the coin is a fair one; 2) if he randomly picks one, and flips it twice, what is the probability that he gets two tails; and 3) if he randomly picks one and flips it twice, supposing B stands for the event that the first result is head, and C represents the event that the second result is also head, if B and C are independent, the following calculations must be made:

1)

The probability that the coin is a fair one is 50%.

2)

The probability that he gets two tails is 11.11%.

3)

B and C will be independent as long as it is a fair coin.

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Answer:

14 million dollars

Step-by-step explanation:

We notice that there's a pattern on the graph. The company has a loss of 2 million then it gains 4 million and so on. Given this rule, we notice that in 2007 that the company gained 4 million that time and was at 16 million. So, in 2008, the company should lose 2 million, thus giving a total of 14 million dollars.

Answer:

P (4,-4) Q (2,-3) R(5,-2)

Step-by-step explanation:

Any coordinates that is rotated by 180 degrees is going to be opposite of the number, for example 4 will become -4 and -7 will be 7.

65%

Convert fraction (ratio) 13 / 20 Answer: 65%

Answer:

At a map scale of 1:100000, 1 millimeter on the map is equivalent to 1 kilometer on the ground

Answer:

1000 or 1/1000

Step-by-step explanation:

The scale is 1000 or 1/1000 as there are 1000 cm in 1 km

Answer:

So Alex paid 9 dollars for 6 candy bars, we can convert it to a fraction

so, the fraction is 9/6 dollars per candy bar

hence, Alex paid $1.5 for each candy bar

Answer:

a=20

Step-by-step explanation:

7+13=20

20-7=13

Answer:

90 miles

Step-by-step explanation:

1erhhjbcfikbv

Answer:

90

Step-by-step explanation:

180/2 = 90 (divided by 2 basically is saying half of 100% and in this case 180 is the 100%)

Answer:

\((x-5-\sqrt{19})(x-5+\sqrt{19})\)

Step-by-step explanation:

1) In general, given \(ax^2+bx+c\), the factored form is:

\(a(x-\frac{-b+\sqrt{b^2-4ac} }{2a} )(x-\frac{-b-\sqrt{b^2-4ac} }{2a})\)

2) In this case, \(a=1\), \(b= -10\) and \(c=6\).

\((x-\frac{10+\sqrt{(-10)^2-4\times6} }{2} )(x-\frac{10-\sqrt{(-10)^2-4\times6} }{2} )\)

3) Simplify.

\((x-\frac{10+2\sqrt{19} }{2} )(x-\frac{10-2\sqrt{19} }{2} )\)

4) Factor out the common term \(2\).

\((x-\frac{2(5+\sqrt{19)} }{2} )(x-\frac{10-2\sqrt{19} }{2} )\)

5) Cancel \(2\).

\((x-(5+\sqrt{19} ))(x-\frac{10-2\sqrt{19} }{2} )\)

6) Remove parentheses.

\((x-5-\sqrt{19} )(x-\frac{10-2\sqrt{19} }{2} )\)

7) Factor out the common term \(2\).

\((x-5-\sqrt{19} )(x-\frac{2(5-\sqrt{19}) }{2} )\)

8) Cancel \(2\).

\((x-5-\sqrt{19})(x-(5-\sqrt{19}))\)

9) Remove parentheses.

\((x-5-\sqrt{19})(x-5+\sqrt{19})\)

Thanks,
Eddie Echevarria

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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Answer: 1/2

Step-by-step explanation:

This is straight from Khan

ample size and margin of error

In a one-sample

z

zz interval for a proportion, the

margin of error

margin of errorstart text, start color #11accd, m, a, r, g, i, n, space, o, f, space, e, r, r, o, r, end color #11accd, end text is how far our interval extends above and below the sample proportion:

(

statistic

)

±

(

margin of error

)

p

^

±

z

∗

p

^

(

1

−

p

^

)

n

(statistic)

p

^

​

​

±(margin of error)

±z

∗

n

p

^

​

(1−

p

^

​

)

​

​

​

Since the sample size

n

nn is in the denominator, increasing the sample size will lead to a smaller margin of error.

Hint #22 / 3

Comparing sizes of margins of error

Let's look at each margin of error in terms of its sample size.

Smaller sample,

n

=

200

n=200n, equals, 200:

=

z

∗

p

^

(

1

−

p

^

)

200

error

margin of

=z

∗

200

p

^

​

(1−

p

^

​

)

​

​

start text, e, r, r, o, r, end text, start superscript, start text, m, a, r, g, i, n, space, o, f, end text, end superscript, equals, z, start superscript, times, end superscript, square root of, start fraction, p, with, hat, on top, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, divided by, 200, end fraction, end square root

Larger sample,

n

=

800

n=800n, equals, 800:

=

z

∗

p

^

(

1

−

p

^

)

800

=

z

∗

p

^

(

1

−

p

^

)

4

⋅

200

=

z

∗

1

4

⋅

p

^

(

1

−

p

^

)

200

=

1

2

⋅

z

∗

p

^

(

1

−

p

^

)

200

error

margin of

​

=z

∗

800

p

^

​

(1−

p

^

​

)

​

​

=z

∗

4⋅200

p

^

​

(1−

p

^

​

)

​

​

=z

∗

4

1

​

⋅

200

p

^

​

(1−

p

^

​

)

​

​

=

2

1

​

⋅z

∗

200

p

^

​

(1−

p

^

​

)

​

​

​

Even though

800

800800 is

4

44 times larger than the smaller sample, the margin of error from the larger sample is

1

2

2

1

​

start fraction, 1, divided by, 2, end fraction the margin of error from the smaller sample.

Equivalently, the margin of error from the smaller sample is

2

22 times the margin of error from the larger sample.

Hint #33 / 3

Answer

The margin of error from the larger sample will be

1

2

2

1

​

start fraction, 1, divided by, 2, end fraction the margin of error from the smaller sample.

Answer:

1/2

Step-by-step explanation:

Answer:

Figure 1 does not have perimeter 8x +8

Step-by-step explanation:

Perimeter of  shape is the sum of all the sides.

Perimeter of figure 1 = 2x +2 + x + 2x + 2 +x

                                  = 2x + 2x + x + x + 2 + 2   {Combine like terms}

                                  =6x + 4

Answer:

there is 50% of vitamins

Step-by-step explanation:

Answer:

Step-by-step explanation:

80 milligrams

The line touches -x axis at 3 and touches y axis at 3

P(x,y) = (-3,3)

α+ β = -3

α β = 3

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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