20 x 20 x 20 x 20 × 15 × 15 ×15
​

Answer:

i) Increasing on:

(−∞,2), (6,∞)

Decreasing on:

(2,6)

ii) ( 6,4) is the local minima

 [tex](2, \frac{44}{3} )[/tex] is the local maxima

iii) Concave down on

(−∞,4) since f''(x) is negative

Concave up on

(4,∞) since f''(x) is positive

iiii)

Find where the second derivative is equal to 0

[tex](4, \frac{28}{3})[/tex]

The theoretical probability of winning any prize is 0.111.

The theoretical probability is calculated as follows:

Probability = number of favorable outcomes/total number of possible outcomes

The probabilities of winning each prize are given as:

First Prize: 1 in 1000 = 1/1000

Second Prize: 1 in 100 = 1/100

Third Prize: 1 in 10 = 1/10

The probability of winning any prize is the sum of the probabilities of winning each prize:

Probability of winning any prize = (1/1000) + (1/100) + (1/10)

Probability of winning any prize = 0.001 + 0.01 + 0.1

Probability of winning any prize = 0.111

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The volume of the figures are

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

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Answer:

18% = Jan's percentage of error

Step-by-step explanation:

The percentage error (PE) formula

% error = (|measured value - actual value| / actual value) x 100%

Thus, we can find Jan's percentage of error using the following steps:

Step 1:  Convert Jan's estimated (measured) time of 5 hours to minutes by multiplying by 60:

5 hours x 60 minutes/hour = 300 minutes

Step 2:  Convert Jan's actual time of 4 hours and 15 minutes to minutes by adding the number of minutes (15) to the number of hours (4) converted to minutes:

4 hours x 60 minutes/hour + 15 minutes = 255 minutes

Step 3:  Find the difference and between Jan's estimated (measured) time and actual time.  Then take the absolute value of this value:

300 minutes - 255 minutes = 45 minutes

The absolute value of 45 is 45

Step 4:  Express the difference as a percentage of the actual time:

(45 minutes / 255 minutes) x 100% = 17.64705882% = 18%

Therefore, Jan's percentage of error is 18%. This means that her actual time was about 18% faster than her estimated time.

The equation of the conic in standard form is (x + 1)² + (y - 4)² = 16.

In this problem we find the equation of the conic in general form, that is, an equation of the form:

A · x² + B · x + C · y² + D · y + E = 0

Where A, B, C, D, E are real coefficients.

And we are asked to find the standard form of the previous formula and this can be found by completing the square:

x² + 2 · x + y² - 8 · y + 1 = 0

(x² + 2 · x) + (y² - 8 · y) = - 1

(x² + 2 · x + 1) + (y² - 8 · y + 16) = 16

(x + 1)² + (y - 4)² = 16

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The matrix has one solution.

The solutions of the matrix are, x = -3.21, y = -5.1 and z = 4.8.

The solution of the matrix is calculated by applying Cramer's rule as follows;

[-2   6   -7]   = [-47]

[2    -7  -3]      [22]

[6   -4   -6]      [-10]

The determinant of the matrix is calculated as;

Δ = -2[42 - 12]  -6[-12 + 18]  -7[-8 + 42]

= -208

The x determinant of the matrix is calculated as;

Δx = -47[42 - 12] -6[-132- 30] - 7[-88 - 70]

= 668

The y determinant of the matrix is calculated as;

Δy = -2[-132 -30] + 47[-12 + 18] -7[-20 - 44]

= 1054

The z determinant of the matrix is calculated as;

Δz = -2[70 + 88] - 6[-20 - 132] - 47[-8 + 42]

= -1002

The x, y and z values are calculated as follows;

x = Δx/Δ = 668/-208 = -3.21

y = Δy/Δ = 1054/-208 = -5.1

z = Δz/Δ = -1002/-208 = 4.8

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A distance of x miles is represented by √10 inches on this map. The exact value of √10 is approximately 3.16 Option D.

To determine the number of inches on the map that represent a distance of x miles, we need to consider the given scale, which states that one inch on the map represents an actual distance of 10 miles.

If we set up a proportion using this information, we can solve for the unknown number of inches. The proportion would be:

1 inch (on the map) / 10 miles (actual distance) = x inches (on the map) / x miles (actual distance)

To simplify the proportion, we can cross-multiply:1 inch * x miles = 10 miles * x inches

This simplifies to:

x inches * x miles = 10 miles

Rearranging the equation, we get:

[tex]x^2 = 10[/tex]

To solve for x, we take the square root of both sides:

[tex]\sqrt{(x^2)} = \sqrt{10}[/tex]

Simplifying further, we have:

x = √10

Therefore, a distance of x miles is represented by √10 inches on this map. The exact value of √10 is approximately 3.16. Hence, the closest answer choice that corresponds to this is  3.

In summary, the number of inches on the map that represents a distance of x miles is approximately √10 inches, which is closest to 3 inches. So Option D is correct.

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Answer: Therefore, the rate of the slower bus is 54 mph, and the rate of the faster bus is 69 mph.

Step-by-step explanation: Let's use the following variables to represent the rates of the two buses:

- Let x be the rate of the slower bus

- Then, x + 15 is the rate of the faster bus

Using the formula: Distance = Rate * Time

After 2 hours, the distance traveled by the slower bus is:

Distance = Rate * Time

Distance = x * 2

And the distance traveled by the faster bus is:

Distance = Rate * Time

Distance = (x + 15) * 2

The sum of the distances is equal to 246 miles:

Distance of slower bus + Distance of faster bus = 246

2x + 2(x + 15) = 246

Solve for x:

2x + 2x + 30 = 246

4x = 216

x = 54

Therefore, the rate of the slower bus is 54 mph, and the rate of the faster bus is 69 mph.

Answer:

-----------------------

Triangular faces have a base of 7 cm and height of 9 cm.

The area of one face is:

The area of one of the triangular faces in this square pyramid is

1.5 square cm

The area of a triangular face in the figure displaying net of square pyramid is achieved by using the formula for re of triangle

The formula for area of triangle is given by

= 1/2 base * height

= 1/2 * 7 * 9

= 1/2 * 63

= 31.5 square cm

We can therefore say that the e area of one of the triangular faces in this square  pyramid is 31.5 square cm

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Answer:

50

Step-by-step explanation:

A+B=90+40

90+40 = 130

130(0.75) = 97.5

130-97.5 = 32.5

32.5x2 = 65

Now

65 - 15 = 50

Check the picture below.

so let's use those two points from it to get the equation.

[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ (2~~,~~1.6)\hspace{5em}1.6=ab^2\implies 1.6=abb \\\\[-0.35em] ~\dotfill\\\\ (3~~,~~6.4)\hspace{5em}6.4=ab^3\implies 6.4=abbb\implies \stackrel{\textit{substituting from above}}{\cfrac{6.4}{abb}=b\implies\cfrac{64}{1.6}=b} \\\\\\ \boxed{4=b}\hspace{6em}1.6=a(4)(4)\implies \cfrac{1.6}{(4)(4)}=a\implies \boxed{\cfrac{1}{10}=a} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=\frac{1}{10}(4)^x \end{array}}~\hfill[/tex]

Answer 19

Step-by-step explanation:

i tried my best in bath but not sure still 5 and a half+9+4=19 but round it to 19

The solutions of the function in coordinate form are (0.5,0) , (2.5, 0 ) and (5, 0)

The given equation is,

4x³ - 32x² + 65x - 25

Since it is a cubic equation,

So it has degree 3

Then it cuts the x axis at three points.

And these points  are nothing but solution of the given polynomials.

Now after plotting the graph of the given function

We get three points at which graph cuts the x axis as following;

(0.5,0) , (2.5, 0 ) and (5, 0)

Hence the solutions of the given functions are:

x =0.5 or x = 2.5 or x = 5.

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The solutions to the quadratic equation x² - 3x + 9/10 = 0 are

x₁ = (3 + 3√(3)/√(5)) / 2 and x₂ = (3 - 3√(3)/√(5)) / 2

To find the solutions to the quadratic equation x² - 3x + 9/10 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, the quadratic equation is in the form ax² + bx + c = 0. Comparing it to our given equation x² - 3x + 9/10 = 0, we can see that:

a = 1

b = -3

c = 9/10

Substituting these values into the quadratic formula, we have:

x = (-(-3) ± √((-3)² - 4(1)(9/10))) / (2(1))

x = (3 ± √(9 - 36/10)) / 2

x = (3 ± √(90/10 - 36/10)) / 2

x = (3 ± √(54/10)) / 2

x = (3 ± √(27/5)) / 2

To simplify the square root further, we can rationalize the denominator:

x = (3 ± √(27)/√(5)) / 2

x = (3 ± 3√(3)/√(5)) / 2

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Answer:

c=0 .1x² + 2.4x +25= 430=52.56

The volumes of the right prism are, respectively:

Case 6: V = 703.72 mm³

Case 7: V = 57905.84 mm³

Case 8: V = 3744 ft²

Case 9: V = 475.20 mm³

The volume of the sphere is:

Case 10: V = 18816.57 cm³

In this problem we find four cases of right prisms, whose volumes must be computed. This can be done with the help of following formulas:

Volume

V = A · h

Area formula - Rectangle

A = w · l

Area formula - Triangle

A = 0.5 · w · l

Area formula - Circle

A = π · r²

In addition, we need to determine the volume of a sphere:

V = (4π / 3) · r³

Where:

Now we proceed to determine the volume for each case:

Case 6

V = π · (16 mm)² ·  (14 mm)

V = 703.72 mm³

Case 7

V = π · [(40 mm)² - (32 mm)²] · (32 mm)

V = 57905.84 mm³

Case 8

V = (12 ft) · (8 ft) · (39 ft)

V = 3744 ft²

Case 9

V = 0.5 · (11 mm) · (5.4 mm) · (16 mm)

V = 475.20 mm³

Case 10

V = (4π / 3) · (16.5 cm)³

V = 18816.57 cm³

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The perpendicular line equation is y = -1/2x + 17/2. The parallel line equation is: y = 2x - 9.

Recall the following:

Parallel lines have the same slope value.

Perpendicular lines have slope value that are negative reciprocals to each other.

Given the equation of a line as, y = 2x - 2, the slope is 2. Therefore, we have:

Substitute m = -1/2 and (a, b) = (7, 5) into y - b = m(x - a) to find the perpendicular line equation:

y - 5 = -1/2(x - 7)

Rewrite in slope-intercept form:

y - 5 = -1/2x + 7/2

y = -1/2x + 7/2 + 5

y = -1/2x + 17/2

Substitute m = 2 and (a, b) = (7, 5) into y - b = m(x - a) to find the parallel line equation:

y - 5 = 2(x - 7)

y - 5 = 2x - 14

y = 2x - 14 + 5

y = 2x - 9

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Answer:

B. - 18

Step-by-step explanation:

-2 ║n + 6 ║                                     n = -15

= -2 ║ - 15 + 7 ║

= -2 ║-9 ║

= -2 · 9

= -18

So, the answer is B. - 18

It can be seen that f(t) ≥ f(1) = 0 for t ≥ 1, which establishes the inequality.

In order to establish the inequality when t is greater than or equal to 1, it is necessary to examine the function.

f(t) = (t + 1)(t³ - 1)/[3t(t² + 1)] - log(t).

It will be demonstrated later in the text that f(t) is positive when t is equal to or greater than 1.

One can start by noting that the value of f at 1 is equal to 0.

Next, compute the derivative f'(t) and simplify to obtain:

f'(t) = (2t² - t - 1)/(t²(t² + 1)²)

For t ≥ 1, the denominator is always positive.

The numerator is a quadratic with roots 1 and -1/2.

Since t ≥ 1, the value in the top part of the fraction is positively positioned.

f'(t) > 0 for t ≥ 1.

Since f'(t) is positive for t ≥ 1, f(t) is non-decreasing.

Thus, f(t) ≥ f(1) = 0 for t ≥ 1, which establishes the inequality.

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Answer:

  see attached for a sketch

  area = 5 1/3 square units

Step-by-step explanation:

You want the area under the square root curve, above y=0, from x=0 to x=4.

The area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...

  dA = (√x)dx

  A = ∫(√x)dx

The power rule can be used for the integration:

  [tex]\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}[/tex]

The area of the region is 5 1/3 square units.

__

Additional comment

You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.

This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.

#95141404393

Examining the figure the questions are solved to be

Common internal tangent = line HJ

point of tangency = G

Center = A

chord = line GK

secant = line CD

diameter = EF

common external tangent = line KF

radius = line BF

semi-circle = arc EGF

Major arc = arc CDK

Minor arc = arc CK

A major arc refers to the arc that is more than 180 degrees while minor arc is below 180 degrees.

considering the figure the arc CDK is above 180 degrees hence the major arc other major arcs are

DKG

GCD and so on.

while some of the minor arcs are

arc DG

arc DK

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The volume of the rectangular prism is 22.5 cubic meters.

To find the volume of a rectangular prism, we multiply its length, width, and height together.

Given that the length is 2.5 meters, the width is 4 meters, and the height is 2.25 meters, we can calculate the volume.

Volume of the rectangular prism = Length [tex]\times[/tex] Width [tex]\times[/tex] Height

Volume = 2.5 meters [tex]\times[/tex] 4 meters [tex]\times[/tex] 2.25 meters

Simplifying the calculation:

Volume = 22.5 cubic meters.

Imagine a rectangular-shaped solid object with the following measurements:

Length: 2.5 meters

Width: 4 meters

Height: 2.25 meters

The length is the longer side of the rectangle, the width is the shorter side, and the height represents the vertical dimension.

The object has six faces: two rectangular faces with dimensions 2.5 meters by 4 meters, two rectangular faces with dimensions 2.5 meters by 2.25 meters, and two rectangular faces with dimensions 4 meters by 2.25 meters.

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Answer:

  (x, y) = (4, -9)

Step-by-step explanation:

You want to solve this system of equations by elimination:

The coefficients of x are not integer multiples of each other, but the coefficient of y in the first equation is 4 times the coefficient in the second equation. To eliminate y, we can multiply the second equation by -4 and add the result to the first equation:

  (-8x -4y) -4(-5x -y) = (4) -4(-11)

  12x = 48

  x = 4

Using the second equation to find y, we have ...

  -5x +11 = y

  -5(4) +11 = -9 = y

The solution is (x, y) = (4, -9).

<95141404393>

Answer: Other point = 4/5

Step-by-step explanation:

(2/5)*2=4/5

The number of candles that the company make on an average each hour is 38.

Given that,

BeeBright is a company that makes wax candles in the shape of a solid sphere.

Diameter of each candle = 15 cm

We have to find the volume of each candle.

Since the candles are in the shape of a solid sphere,

Volume of the candle = Volume of the sphere

                                    = 4/3 π r³, where r is the radius of the candle.

Radius of candle = Diameter / 2 = 7.5 cm

Volume of a candle = 4/3 π (7.5)³

                                 = 562.5π

                                 = 1767.14586764 cm³

Number of candles make in an hour = Total wax used / Wax used for 1 candle

= 67650 cm³ / 1767.14586764 cm³

= 38.28

≈ 38 candles

Hence 38 candles are made on an average.

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Answer:

The equation that represents the number of books (b) a student reads each week (w) if the student reads 3 books each week is:

B) b = 3w

Now, to find out how many books the student will read in 18 weeks, we can substitute the value of w as 18 into the equation:

b = 3 * 18

b = 54

Therefore, the student will read 54 books in 18 weeks.

The correct answer is D) w = 3b; 54.

Step-by-step explanation:

Matching each quotient with its answer when expressed in the form of a + bi will be:

1. i/i

Let's rewrite as (0 + i)/(0 + i)

(0 + i)/(0+i) * (0 - i)/(0 - i)

= (0*0 + 0*i - 0*i - i^2)/(0*0 + 0*i - 0*i - i^2)

= (0 - -1)/(0 - -1)

= 1/1

= 1 + 0i which is option "D"

2. 3+4i/3-4i

3+4i/3-4i * 3+4i/3+4i

= (9 + 12i + 12i + 16i^2) / (9 - 12i + 12i - 16i^2)

= (-7 + 24i) / 25

= -7/25 + 24/25i, which matches option "A"

3. 1/3-4i

1/3-4i * 3+4i/3+4i

= (3 + 4i)/(9 + 12i - 12i - 16i^2)

= (3 + 4i)/(9 - -16)

= (3 + 4i)/25

= 3/25 + 4/25i,

4. 3-4i/1

3-4i/1 * 1/1 = 3-4i, which matches option "F"

5. 1/3+4i

1/3+4i * 3-4i/3-4i

= 3-4i/(9 + 12i - 12i - 16i^2)

= 3-4i/25

= 3/25 - 4/25i,

6. 3-4i/3+4i

3-4i/3+4i * 3-4i/3-4i

= (9 - 12i - 12i + 16i^2) / (9 - 12i + 12i - 16i^2)

= (9 - 12i - 12i + -16) / (9 - 12i + 12i - -16)

= (-7 - 24i) / 25

= -7/25 -24/25i

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Match each quotient with its answer when expressed in the form of a + bi.

1. i/i

2. 3+4i/3-4i

3. 1/3-4i

4. 3-4i/1

5. 1/3+4i

6. 3-4i/3+4i

A. -7/25+24/25i

B. 3/25+4/25i

C. -7/25-24/25i

D. 1+0i

E. 3/25+4/25i

F. 3-4i

Answer: 141.4

Step-by-step explanation:

(π)(1.5)(30)= 141.37

141.37 rounded to the nearest tenth is 141.4

Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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