How does the average change if the minimum number is
removed from the list below? Round your answer to the nearest hundreths.
24 36 10 56 12 6 41 28
A
Increase by 2.95
B
Decrease by 2.95
Increase by 0.75
D Decrease by 0.75
E
Decrease by 3.12

Answer:

D

Step-by-step explanation:

360h+6,400 >8,020, with a solution is h> 4.

Answer:

4(2x - 1) + 3(2x + 5)

Step-by-step explanation:

4(2x - 1) + 3(2x+5)

Multiply 4 with 2x - 1 and multiply 3 with 2x + 5,

8x - 8 + 6x + 15 = 0

Arrange x and constant,

8x + 6x = 8 - 15

14x = - 7

14x = - 7

x = -7/14

x = -1/2

x = -0.5

Hope this helps! Recheck the answers.

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Comparing the median of each box-and-whisker plot, the type of transportation that is LEAST likely to take more than 30 minutes is: d. train.

How to Interpret a Box-and-whisker Plot?

In order to determine the transportation that is LEAST likely to take more than 30 minutes, we have to compare the median of each data set represented on the box-and-whisker plot for each transportation.

The box-and-whisker plot that has the lowest median would definitely represent the the transportation that is LEAST likely to take more than 30 minutes, since median represents the typical minutes or center of the data.

Therefore, from the box-and-whisker plots given, the one for train has the lowest median. Therefore train would LEAST likely take more than 30 minutes.

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Answer:

B. 4|−25| = $100

Step-by-step explanation:

Hope this helps!

Answer: f(3) = 145 ==> 1st option

Step-by-step explanation:

f(p) = 7p³ - 5p² + 1/3p

f(p) = 7p³ - 5p² + p/3

f(3) = 7(3)³ - 5(3)² + (3)/3

f(3) = 7(27) - 5(9) + 1

f(3) = 189 - 45 + 1

f(3) = 144 + 1

f(3) = 145 ==> 1st option

Answer:

x=-9

Step-by-step explanation:

\(13-x=21\\\\12-x+x=21+x\\\\12+0=21+x\\\\21+x=12\\\\21-21+x=12-21\\\\0+x=-9\\\\x=-9\)

Answer:

- 8

Step-by-step explanation:

13 - x = 21

-x = 8             Subtract 13 from both sides

x = -8             Divide both sides of -1 since x still has a negative.

the awnser: is 960 inches

To solve the differential equation, proceed as follows:

Integrate each side of the equation:

Solve for y:

Substitution method:

Answer:

\(\displaystyle\text{Slope: } -\frac{4}{3}\)

Point (4,1)

Step-by-step explanation:

The Equation of the Line

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

The given line is:

\(\displaystyle y-1=-\frac{4}{3}(x-4)\)

If we compare the equation of this line, both the slope and the point through which is passes are clearly identifiable:

Slope:

\(\mathbf{\displaystyle -\frac{4}{3}}\)

Point (4,1)

Answer:

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b) $34.50

(c) 356

Step-by-step explanation:

Let x = number of minutes.

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b)

Here, x = 350, so x > 200.

f(x) = 0.03(x - 200) + 30

f(350) = 0.03(350 - 200) + 30

f(350) = 0.03(150) + 30

f(350) = 4.5 + 30

f(350) = 34.5

$34.50

(c)

f(x) = 0.03(x - 200) + 30

0.03(x - 200) + 30 = 34.68

0.03(x - 200) = 4.68

x - 200 = 156

x = 356

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

What is the area of the triangle?

To calculate the area of a triangle, use the formula area = 1/2 * base * height.

We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:

\(Area = {\sqrt{(s(s-a)(s-b)(s-c))}\)

where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:

s = (a + b + c)/2

In this case, we have:

a = AB = 154

b = BC = 346

c = AC = 349

So the semiperimeter is:

s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5

Now we can use Heron's formula to find the area of the triangle

\(Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3\)

Therefore, the area of the triangle ABC is approximately 18096.3 square units.

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Answer:

  71.6°

Step-by-step explanation:

The angle can be found from the dot product of PQ and PR.

  PQ·PR = |PQ|×|PR|×cos(α)

where α is the angle between the two segments.

  cos(α) = (Q -P)·(R -P)/(|Q -P|×|R -P|)

  = ((0, 1, 0) -(1, 0, 0))·((0, 0, 2) -(1, 0, 0))/(|Q -P|×|R -P|)

  = (-1, 1, 0)·(-1, 0, 2)/(√(((-1)² +1²)((-1²) +2²)) = (1+0+0)/√10

  α = arccos(1/√10) ≈ 71.6°

The angle at P is about 71.6°.

_____

Additional comment

The side lengths of the triangle are √2, √5, √5. As we have seen, the angle at P is bounded by the sides of length √2 and √5. The law of cosines can also be used to arrive at the angle between these sides.

Answer:

36

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

because am very good at math

Answer:

radius

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The total time taken for the entire journey is 2.8 hours.

To calculate the total time taken for the entire journey, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:

Time1 = 112 km / 70 km/h = 1.6 hours

For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:

Time2 = 60 km / 50 km/h = 1.2 hours

To find the total time for the entire journey, we sum up the times for both parts:

Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours

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The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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Answer:

f(-8) = -2

Step-by-step explanation:

f(x)=x/4

Let x = -8

f(-8)=-8/4

f(-8) = -2

Using the height and radius given, the surface area of the cylinder is 408.2m²

The surface area of a cylinder is the combined area of its curved surface (lateral surface) and its two circular bases. The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

where:

In the given question, the data are;

Substituting the value into the formula

A = 2π(5 * 8) + 2π(5)²

A = 408.2m²

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In this case we have a translation of 8 units to the left and 11 units upwards.

To find the translation, we just need to compare the two known vertices before and after the translation.

If we have a translation of a units in the x-axis and b units in the y-axis, we will get:

T(a, b)L ---> L'

We know that L = (7, -3) and L' = (-1, 8)

Then we can write:

(7 + a, -3 + b) = (-1, 8)

Then we have two equations:

7 + a = -1 ---> a = -1 - 7 = -8

-3 + b = 8 ---> b = 8 + 3 = 11

Then we have a translation of 8 units to the left and 11 units up-.

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Complete question:

"Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Find the translation done"

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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Answer:

Step-by-step explanation:

Answer:

21.3 cm

Step-by-step explanation:

first find the rate of change (RISE/RUN)

\(\frac{19.8-25.2}{24-6}\) which gives you -0.3

Next, create an equation. You can choose any point, but I chose (6,25.2) because it is given.

y - 25.2 = -0.3(x-6)

y - 25.2 = -0.3x + 1.8

y = -0.3x + 27

Finally, plug in 19 for x...

y = -0.3(19) + 27 = 21.3 cm

Answer:

Reflection across the x-axis: (-4,2)

Reflection across the y-axis: (4,-2)

Step-by-step explanation:

Going based off of what I see, a reflection across the x axis changes "y" & the same rule applies to the y axis.

It should be an L shape.

Answer:

5

Step-by-step explanation:

Margo bought 7 pens for $23.

Some pens are $3 and some $4.

We need to find how many $3 pens she bought.

Let the number of $3 pens be represented by p and let the number of $3 pens be represented by r. So:

p = $3  and r = $4

Now we know 7 pens were purchased so is we add the number of $3 pens purchased to the number of $4 pens purchased, we will get 7.

p + r = 7

We know that the total cost of the pens is $23 so that equation would be found by takign the $3 pen multiplied by the number of $3 pens purchsed added to the $4 pen multiplied by the number of $4 pens purchsed, which equals $23.

$3p + $4r = $23

Now we have 2 equations and 2 unknowns.

p + r = 7

$3p + $4r = $23

Let's solve for r in the first equation.

p + r = 7     Subtract p from both sides.

p - p + r = 7 - p   The p on the left cancels.

r = 7 - p

Now that we know r, we can substitute it into the second equation and solve for p.

$3p + $4r = $23

3p + 4( 7 - p) = 23       Multiply it out.

3p + 4*7 - 4*p = $23

3p + 28 - 4p = 23      Combine like terms.

3p  - 4p + 28 = 23

- 1p + 28 = 23       Subtract 28 from both sides.

- p + 28 - 28 = 23 - 28  

- p = - 5   Divide each side by -1

- p/- 1 = - 5/ - 1       The negative cancels on each side.

p = 5

We can see Margo bought 5 $3 pens.

For fun, let's solve for how many $4 pens she bought. We know p, so we plug it in the first equation and solve for r.

p + r = 7

5 + r = 7  Subtract 5 from each side

5 - 5 + r = 7 - 5

r = 7 - 5

r = 2

So Margo bought 5 $3 pens and 2 $4 pens!