Find the area of the region between the curve y= 2ln(x) and the horizontal axis for 1<= x <= 4

Answer:

D

Step-by-step explanation:

3x - 4 < 8

Add 4:

3x - 4 + 4 < 8 + 4

3x < 12

Divide by 3:

3x / 3 < 12 / 3

x < 4

Answer:

D. x<4

Step-by-step explanation:

3x-4<8

3x<8+4

3x<12

x<4

Hope this helps ;) ❤❤❤

Answer:

m = -3

b = 0

equation of line

y = -3x

Step-by-step explanation:

in the  the equation in the form y = mx +b

m is the slope

b is the y intercept.

__________________________________________________

given slope = -3

thus,

m = -3

the required equation of line is

y = mx +b  

put m = -3

y = -3x + b

to find b , we put x = -2, y = -6 as this equation contains point (-2,-6).

-6 = -3*-2 + b

=> -6 = -6 + b

=> b = -6 + 6 = 0

thus. m = -3

b = 0

equation of line

y = -3x

Answer:

1.37

Step-by-step explanation:

The student can give only 0.139 % answer correctly.

The first and second questions have four answer choices,

Probability of first and second question answer correctly is,

                [tex]P_{1}=\frac{1}{4}*\frac{1}{4} =\frac{1}{16}[/tex]

The third and fourth questions have three answer choices,

Probability of third and fourth question answer correctly is,

           [tex]P_{2}=\frac{1}{3} *\frac{1}{3}=\frac{1}{9}[/tex]

The last question has five answer choices.

Probability of fifth question answer correctly is,

              [tex]P_{3}=\frac{1}{5}[/tex]

The probability of corrected answer is,

        [tex]P=P_{1}*P_{2}*P_{3}\\\\P=\frac{1}{16} *\frac{1}{9}*\frac{1}{5}=\frac{1}{720}[/tex] = 0.139 %

Hence, The student  can give only 0.139 % answer correctly.

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Answer:

Q  has coordinates (qx+5, qy-5)

Step-by-step explanation:

Q  has coordinates (qx, qy)

we move 5 units to the right so add 5 to the value of x

Q  has coordinates (qx+5, qy)

we move 5 units down so subtract 5 from the value of y

Q  has coordinates (qx+5, qy-5)

Answer:

x = -1/2

Step-by-step explanation:

Step 1: Write out equation

9 - 8x - 8 - 2x = 4

Step 2: Combine like terms (x)

9 - 10x - 8 = 4

Step 3: Combine like terms (constants)

-10x - 1 = 4

Step 4: Add 1 to both sides

-10x = 5

Step 5: Divide both sides by -10

x = -5/10

Step 6: Simplify

x = -1/2

Answer:

25/36

Step-by-step explanation:

Solved in steps:

Simplest fraction is 25/36

Answer:

D

Step-by-step explanation:

Given

f(x) = 3x² - 24x + 10 ← factor out 3 from 3x² - 24x

     = 3(x² - 8x) + 10

Using the method of completing the square

add/ subtract ( half the coefficient of the x- term )² to x² - 8x

f(x) = 3(x² + 2(- 4)x + 16 - 16) + 10

      = 3(x - 4)² - 48 + 10

      = 3(x - 4)² - 38 ← in vertex form → D

Answer:

d

Step-by-step explanation:

Answer:

volume = 33965.39

Step-by-step explanation:

Attached below is a detailed solution of the problem and the required sketch

volume of this solid is calculated integrating about the axis of : 5,3

Y = In x = x = e^y

the shaded region in the sketch represent the region where the rotating takes place.

Answer:

[tex]x\geq -30[/tex]

Step-by-step explanation:

Work to isolate x on one side of the inequality:

[tex]3-\frac{x}{2} \leq 18\\3-18\leq \frac{x}{2} \\-15\leq \frac{x}{2}\\-30 \leq x[/tex]

Therefore the answer is all x values larger than or equal to -30

[tex]x\geq -30[/tex]

Answer:

A) P_n = 1.06(P_(n-1)) - 80

B) 887 fishes

Step-by-step explanation:

A) We are told that the lake initially contains 1000 fishes.

Thus, P_o = 1000

Now, the number of fishes increases by 6% each month

Thus, after n months, we have;

P_n = P_(n-1) + 0.06P_(n-1)

P_n = 1.06P_(n-1)

Where P_(n-1) is the population of fish in the previous month.

We are told that 80 fishes are lost each month.

Thus;

P_n = 1.06(P_(n-1)) - 80

B) We want to find out how many fishes we have after 5 months.

Thus;

P_5 = 1.06(P_(5-1)) - 80

P_5 = 1.06(P_4) - 80

We don't know P_4,thus;

P_o = 1000

P_1 = 1.06(1000) - 80 = 980

P_2 = 1.06(980) - 80 = 958.8

P_3 = 1.06(958.8) - 80 = 936.328

P_4 = 1.06(936.328) - 80 = 912.50768

Thus,

P_5 = 1.06(912.50768) - 80 = 887.2581408 ≈ 887

Answer:

The height of the plank after the π/3 rotation motion is 8.464 ft

Step-by-step explanation:

The radius of the wheel = 4 ft

The elevation of the bottom of the wheel from the bottom = 1 foot

The angle to which the wheel is rolled = π/3 radians

The height of a rotating wheel is given by the following relation

f(t) = A·sin(B·t + C) + D

Where;

D = Mid line =  4 + 1 = 5 feet

B·t = π/3

C = 0

A = The amplitude = 4

Which gives;

f(t) = 4×sin(π/3) + 5 = 8.464 ft

The height of the plank after the π/3 rotation motion = 8.464 ft.

Answer:7 ft

Step-by-step explanation:

C

Answer:

the answer is going to be A. -6x - 14 x+ 6

Answer:

B and C

Step-by-step explanation:

1/5 prefer apple juice

T = prefer orange juice

9/20 prefer apple or oranger juice

First, we can subtract 1/5 from 9/20 to get 1/4 (simplified)

Equation = 9/20  - 4/20 = 5/20 = 1/4

Plug it in:

A. 9/20 + 1/4 =1/5 (Incorrect)

B. 1/5 + 1/4 = 9/20 (Correct

C. 1/4 + 1/5 = 9/20 (Correct)

D. 1/4 - 1/5 = 9/20 (Incorrect)

Answer:

1/5 + t = 9/20

t + 1/5 = 9/20

Step-by-step explanation:

1/5 are apple + unknown for orange = apple + orange

1/5  + unknown = 9/20

Let t = unknown

1/5 + t = 9/20

order doesn't matter on the left side since we are adding

t+1/5 = 9/20

Answer:

66

Step-by-step explanation:

In statistics, the formula for RANGE is given as the difference between the Highest and the Lowest value.

In the above values we are given data consisting of the 7 games that Roger bowled.

155, 165, 138, 172, 127, 193 , 142.

Step 1

We arrange from the least to the highest.

127, 138, 142, 155, 165, 172, 193

Step 2

Lowest value = 127

Highest value = 193

Step 3

Range = 193 - 127

= 66

Therefore, the range of Roger's scores is 66

Answer:

16 mi

Step-by-step explanation:

To find how many miles you could travel with one gallon, you want to multiply both sides of the equation by 64. This will make '1/64' to 1, so the answer should be 1/4 * 64 = 16.

Answer:

The mean is 7.1

The median IS NOT 1.6 (its 8)

The mode IS NOT 0 (its 8)

Step-by-step explanation:

The true statement is , The mean is 7.1.

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The median is the middle value when a data set is ordered from least to greatest.

The mode is the number that occurs most often in a data set.

here, we have,

given data, group of numbers (8, 12, 4, 8, 6, 0, 9, 11, 3, 10)

now, we get,

The mean is 7.1.

The median IS NOT 1.6 (its 8)

The mode IS NOT 0 (its 8).

hence, The true statement is , The mean is 7.1.

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Answer:

A - the arrow on the right points to the point -2. the arrow on the left moves 7 places to the left to the point -9.

this is what the expression is stating: -2 - 7 = -9

Answer:

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

[tex]\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}[/tex]

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=[tex]\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0[/tex]

[tex]-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0[/tex]

[tex]\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}[/tex]

[tex]\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}[/tex]

squaring both sides; we get

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}[/tex]

[tex]\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}[/tex]

By cross multiplying; we get

[tex]49x^2 = 25(54^2+x^2)[/tex]

[tex]49x^2 = 25 \times 54^2+ 25x^2[/tex]

[tex]49x^2-25x^2 = 25 \times 54^2[/tex]

[tex]24x^2 = 25 \times 54^2[/tex]

[tex]x^2 = \dfrac{25 \times 54^2}{24}[/tex]

[tex]x =\sqrt{ \dfrac{25 \times 54^2}{24}}[/tex]

[tex]x =\dfrac{5 \times 54}{\sqrt{24}}[/tex]

[tex]x =\dfrac{270}{\sqrt{4 \times 6}}[/tex]

[tex]x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}[/tex]

[tex]x =\dfrac{45 \sqrt{6}}{ 2}[/tex]

Answer:

- 19

Step-by-step explanation:

Let's consider the equation as ;

y = 3x + c

( 6, -1 ) satisfies the equation ;

-1 = 3( 6) + c

c = - 18 - 1

c = -19

So the slope - intercept is (- 19)

Answer:

10

Step-by-step explanation:

This expression uses the idea of exponential edition.  The basis is, when you have the same base number being multiplied, you can add the exponentials.  

Consider the case of 2 * 2.  We know this to be 4.  When writing 2 * 2, you can write this as 2^1 * 2^1 == 2^(1+1) == 2^2 == 4.  See how we added the powers to get the new exponential?

We will apply this same idea here.

10^(1/2) * 10^(1/2) == 10^(1/2 + 1/2) == 10^(1) == 10.

So, the simplified expression is 10.

Cheers.

Answer:

C. 1.01,1.01¯¯¯¯,2119

Step-by-step explanation:

1.01,1.01¯¯¯¯,2119

Is arranged from the least number to the greatest number.

It shows the numbers with decimals, and it showed the number with Dec again.

Then gave a space in between then the highest number in the least follows

So option c is the answer

Answer:

9,962

Step-by-step explanation:

3,489+8,617+1,240=13,346

564*6=3,384

13,346-3,384=9,962

Answer:

20.96 m/s is the final speed.

Step-by-step explanation:

Given that:

Initial speed of the car = 8 m/s

Acceleration of the car = 1.8 m/[tex]s ^{2}[/tex]

Time for which the car accelerates = 7.2 seconds

To find:

The speed of car after accelerating for 7.2 seconds at an acceleration of 1.8 m/[tex]s ^{2}[/tex] = ?

Solution:

First of all, let us have a look the formula given for the final velocity of an object with given initial speed, acceleration and time:

[tex]v=u+at[/tex]

Where [tex]v[/tex] is the final speed of object

[tex]u[/tex] is the initial speed of an object

[tex]a[/tex] is the acceleration of object and

[tex]t[/tex] is the time

Here, [tex]u = 8\ m/s[/tex]

[tex]a = 1.8\ m/s^{2}[/tex] and

[tex]t = 7.2\ seconds[/tex]

To find:

[tex]v = ?[/tex]

Let us put all the given values in the formula:

[tex]v =8+1.8 \times 7.2\\\Rightarrow v =8+12.96\\\Rightarrow \bold{v =20.96\ m/s}[/tex]

So, the answer is:

20.96 m/s is the final speed.

Answer: This is what i can do . i hope it helps:)

The angle between the longitude of the Galapagos Islands and that of Nauru is 90.30°+166.56°=256.86°.

We find the sum since these places have different longitude directions, but this is the major arc, and the minor arc will be 360°−256.86°=103.14°.

Angle between Galapagos Islands and 180°E/W = 180° - 90.30° = 89.70°

Angel between Nauru island and 180°E/W = 180° - 166.56° = 13.44°

Total angle between Galapagos Islands and Nauru = 89.70 ° + 13.44° = 103.14°.

Step-by-step explanation:

[tex]let \:\alpha \:be\:our\:teetah \\l = \frac{r \pi}{180 \°} \times \alpha \\\\= \frac{6400\pi}{180 \°} \times 103.14\\\\= 11520.848\\\\= 11521 km[/tex]

-17 is a rational number

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Rational numbers have finite or recurring decimal expansions. Irrational numbers are numbers that can not be expressed as the ratio or fraction of two integers. Irrational numbers have non-terminating and non-repeating decimal expansions.

Whereby -17 can be expressed as the value -17/1, based on the definition of a rational number, -17 is a rational number

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Answer:

56 different ways

Step-by-step explanation:

This is a combination question since it deals with selection. For example, if n objects is to be selected from a pool of r objects, this can be done in nCr different ways.

nCr = n!/(n-r)!r!

According to the question, If the police have 8 ​suspects, the different number of ways 5 can be selected for a line up is expressed as 8C5

8C5 = 8!/(8-5)!5!

8C5 = 8!/(3!)!5!

8C5 = 8*7*6*5!/3*2*5!

8C5 = 8*7*6/3*2

8C5 = 8*7

8C5 = 56 different ways

Hence, the selection of picking 5 for a line up out of 8 suspects can be done in 56 different ways.

Answer:

Researcher B

Step-by-step explanation:

Power of statistics is the probability that a test will correctly reject a false null hypothesis.

This probability is more accurate with greater sample size as it is better representation of the population.

Therefore researcher B has more power to detect an effect since he has nearly twice sample size (40 vs 22)

Answer:

lines CD, AE, and BD are half the length of CD

Step-by-step explanation:

All circles will have the same radius "r"

then CD = 4r

½CD = 2r

CB = AE = BD = 2r

The line CD has two circles which are equidistant from the points C and D and both meet at point B.

Point B is the midpoint of Line CD dividing line CD into two equal halves.

The line segments AE , CB and BD are line segments that are half of the length of line CD.

CB and BD form the diameters of the circles.

A diameter is a line that divides the circle into 2 equal halves. It passes through the center of the circle and joins one end point to another.

A radius is the distance from the circumference to the center of the circle.

A diameter is made up of two radius.

In the figure two equal diameters divide the line segment into two equal parts.

The third circle has the diameter AE which has radius AB and AE which are also the radius of the other two circles.

Hence the three circle are equal .

Hence the line segments AE , CB and BD are line segments that are half of the length of line CD.

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Answer:

Step-by-step explanation:

[tex] \sf{ {x}^{2} - 4x - 21}[/tex]

Here, we have to find the two numbers that subtracts to 4 and multiplies to 21

⇒[tex] \sf{ {x}^{2} - (7 - 3)x - 21}[/tex]

⇒[tex] \sf{ {x}^{2} - 7x + 3x - 21}[/tex]

Factor out X from the expression

⇒[tex] \sf{ x(x - 7) + 3x - 21}[/tex]

Factor out 3 from the expression

⇒[tex] \sf{x(x - 7) + 3(x - 7)}[/tex]

Factor out x-7 from the expression

⇒[tex] \sf{(x - 7)(x + 3)}[/tex]

Hope I helped!

Best regards!!

Answer:

[tex]\boxed{\boxed{\bold{(x - 7)(x + 3)}}}[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 4x - 21 \\ {x}^{2} - 7x + 3x - 21 \\ x(x - 7) + 3(x - 7) \\ (x - 7)(x + 3)[/tex]

Answer:

x = - 12

Step-by-step explanation:

2                5

--- x - 2 =   --- x

3                6

2x             5

---  - 2 =  ------ x

3             3 * 2

(2x) - 3 * 2          5x

----------------  =  --------

       3               2 * 3

x = - 12