Write the logarithmic expression as a single logarithm with coefficient , and simplify as much as possible. Assume that all variable expressions represent positive real numbers.

1/2ln(b^2+1)-1/2ln(b+1)

Answer:

the answer is 45

Step-by-step explanation:

the answer is 384

Step-by-step explanation:

a1 = 2, a2 = 3, a3 = 4,

an = ?

n = 44

d = a2 - a1 = 3 - 2 = 1

d = a3 - a2 = 4 - 3 = 1

Here, the common difference is the same everywhere

So,

[tex] a_{n} = a + (n - 1) \times d[/tex]

[tex]a_{44} = 2 + (44 - 1) \times 1[/tex]

[tex]a_{44} = 2 + 43[/tex]

[tex]a_{44} = 45[/tex]

Answer:

x = - 6 , x = 1

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

x² + 5x - 6 = 0

consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term ( + 5)

the factors are + 6 and - 1 , since

6 × - 1 = - 6 and 6 - 1 = + 5 , then

(x + 6)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 1 = 0 ⇒ x = 1

Answer:

2.559 × 10 to the 1st power

Step-by-step explanation:

using a SNC

Answer:

2.559 * 10^1

Step-by-step explanation:

Rules of scientific notation (that I always remember)

    - the number must be between 1 and 9

    - if number gets smaller, exponent gets bigger; if number gets bigger, exponents gets smaller

25.59 is bigger than 9 so we move the decimal one place value to the left

and the number gets smaller meaning the exponent increases

Answer:

[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]

distance = 16.2788

Step-by-step explanation:

This question is asking you to correctly apply the distance formula. This formula determines the straight line distance between two points by applying Pythagorean's Theorem ([tex]h = \sqrt{x^{2}+y^{2} }[/tex]). The distance formula can be thought of as [tex]distance=\sqrt{(x_{1}-x_{2})^{2} +(y_{1}-y_{2})^{2}}[/tex]. It doesn't matter which order you put your coordinates into the equation as long as it's the square root of the change in x-coordinates squared + change in y-coordinates squared.

Step 1: change in x-coordinates

x1 = -2

x2 = -5

x1 - x2 = -2 - (-5) = 3

Step 2: change in y-coordinates

y1 = 6

y2 = -10

y1 - y2 = 6 - (-10) = 16

Step 3: plug into distance formula

[tex]distance=\sqrt{(-2-(-5))^{2} +(6-(-10))^{2}}[/tex]

[tex]distance=\sqrt{(3)^{2} +(16)^{2}}[/tex]

[tex]distance=\sqrt{9 +256}[/tex]

[tex]distance=\sqrt{265}[/tex]

distance = 16.2788

[tex]x^3=216\\x=\sqrt[3]{216}=6[/tex]

This is a simple example. You (should) know that [tex]6^3=216[/tex].

But you can solve it like this:

[tex]\begin{array}{r|l}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}[/tex]

Therefore

[tex]\sqrt[3]{216}=\sqrt[3]{2^3\cdot3^3}=\sqrt[3]{2^3}\cdot\sqrt[3]{3^3}=2\cdot3=6[/tex]

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the value of x in the equation [tex]\pmb{x^3=216}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Is x by itself? No, it's cubed, or multiplied times itself three times.

So we need to use the opposite operation.

The opposite of cubing is taking the cube root, so we take the cube root of both sides:

[tex]\star~\large\pmb{\sqrt[3]{x^3}=\sqrt[3]{216}}[/tex]

On the left, the cube root sign and the cube cancel, because they're opposite, and we're left with x.

On the right, we take the cube root of 216, which gives us:

[tex]\star~\large\pmb{x=6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

4 x y ^2

Step-by-step explanation:

4 x y^2    would be the GFC

Answer:

9 feet, 108 inches, 274.32 cm, 2.7432 meters

Step-by-step explanation:

Not enough information is given to answer.

You didn't provide the list of "these" to choose from, but I can just list some potential answers I could see being an option.

3 yards = 9 feet [1 yard = 3 feet. 3 yards = 9 feet]

             9 feet is also 108 inches [1 foot = 12 inches. 9 feet = 108 inches]

3 yards = 108 inches

{There are 91.44 cm in a yard} (1 yard = 91.44 cm. 3 yards = 274.32 cm),

3 yards = 274.32 cm

3 yards = 2.7432 meters (1 yard = 0.9144 meters; 3 yards = 2.7432 meters)

Based on the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.

The ratio of net income to investment is known as return on investment (ROI). A high return on investment (ROI) indicates that the investment's benefits outweigh its cost.

ROI is a performance indicator that is used to assess an investment's effectiveness or to compare the efficiencies of several distinct investments.

First, find the amount earned per year:

= 850 x 12

= $10,200

The yearly expenses would be:

= (390 x 12) + (70 x 12) + (380 x 2) + 500 + (125 x 12)

= 4,680 + 840+ 760+ 500 + 1500

= $8280

The annual ROI is:

ROI= (10,200 - 8280) / 10,200 x 100%

ROI = 18.82%

Therefore the expenses involved in running the property, and the rental amount, the return on the investment would be 18.82%.

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Answer:

x=2

Step-by-step explanation:

axis of symmetry is

x-2=0

or

x=2

Answer:

Graph B. On a coordinate plane, a vertical dashed line at (2, 0) is parallel to the y-axis.

Answer:

2/5

Step-by-step explanation:

Answer:

15400 in² :)))!

Step-by-step explanation:

Input Data:

Radius = 70 in

Objective:

Find the area of the circle.

Solution:

Area = πr2

= 3.14 x (70) ^2

= 3.14 x (4900)

Area = 15400 in²

The equation connecting C,A and n is  C = 25A - [tex]\frac{49990000}{n}[/tex]

Variation is a mathematical term used to show how a quantity behaves when one quantity increases or decreases.

Analysis:

C = AK + M/n

where K and M are constants

when n = 1000, A = 5000, C = 75010

75010 = 5000K + M/1000-----------1

50004 = 10000k + M/200-------------2

solving simultaneously,  K = 25, M = -49990000

C = 25A - 49990000/n

In conclusion, the equation connecting C,A and n is C = 25A - 49990000/n

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The mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

Mean is the sum total of the number divided by number of terms

Median is the middle number when arranged in ascending or descending order.

Midrange is the average of the sum of the maximum number and the minimum number.

Given that;

First, we arrange in ascending order.

60, 62. 64, 66, 68, 70, 72

Mean = ( 60 + 62 + 64 + 66 + 68 + 70 + 72 ) / 7

Mean = 462 / 7

Mean = 66

Median = 66

66 is the middle number.

Range = ( Max + Min ) / 2

Range = ( 72 + 60 ) / 2

Range = 132 / 2

Range = 66

Therefore, the mean, median, and midrange of the given that are 66, 66 and 66 respectively.

Option D) Mean = 66, median = 66, midrange = 66 is the correct answer.

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The triangle: α = 40°, β = 35°, and a = 10. is b = 8.9, γ = 105°, c = 15.0

If A, B, and C are the measurements of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite of the corresponding angles, then the ratios of the a side’s length to the sine of the angle opposite the side must all be the same.

a/ sin A = b/ sin B = c/ sin C

Using Angle sum property in a triangle we have,

α+β+ γ = 180

40+35+ γ=180

γ= 180-75

γ= 105°

Now,

c/ sin γ= a/ sin α

c/ sin 105= 10/ sin 40

c/ 0.96592 = 10 /0.6427

c = 15

again,

b/ sin  β=  a/ sin α

b/ sin 35=  10/ sin 40

b/0.5737= 15.559

b= 8.92

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The mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

From the complete question, we have:

P(boy)= 0.5

Sample size = 950

The mean is then calculated as:

[tex]\bar x = np[/tex]

This gives

[tex]\bar x = 950 * 0.5[/tex]

Evaluate

[tex]\bar x = 475[/tex]

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

This gives

[tex]\sigma = \sqrt{950 * 0.5(1 - 0.5)[/tex]

Evaluate

[tex]\sigma = 15.41[/tex]

Hence, the mean and standard deviation for the number of boys in the 950 babies are 475 and 15.41, respectively

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The reason the "+ C" is not needed in the antiderivative when evaluating a definite integral is; The C's cancel each other out as desired.

Let us say we want to estimate the definite integral;

I = [tex]\int\limits^a_b {f'(x)} \, dx[/tex]

Now, for any C, f(x) + C is an antiderivative of f′(x).

From fundamental theorem of Calculus, we can say that;

[tex]I = \int\limits^a_b {f'(x)} \, dx = \phi(a) - \phi(b)[/tex]

where Ф(x) is any antiderivative of f'(x). Thus, Ф(x) = f(x) + C would not work because the C's will cancel each other.

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answer:

1769.344983 or 1769.34 (depends on what you’re rounding to)

explanation:

- the equation for a cylinder‘s surface area is: (2 π r h)+(2 π r^2)

so 2 just means x2

π is just pi

r is your radius and for this equation your radius is 8 cm

and h is your height so for this equation your height is 27.2 cm

- so the equation filled in is:

(2 x π x 8 x 27.2) + (2 x π8^2) = 1769.344983 or 1769.34

(2 x π x 8 x 27.2) = 1367.221123

(2 x π8^2) = 402.1238597

1367.221123 + 402.1238597 = 1769.344983

hope this helps :)

Answer:

AC ≈ 17.3 , BC ≈ 5.3

Step-by-step explanation:

using the tangent ratio in right triangle ACD

tan51° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AD}[/tex] = [tex]\frac{AC}{14}[/tex] ( multiply both sides by 14 )

14 × tan51° = AC , then

AC ≈ 17.3 ( to the nearest tenth )

using the cosine ratio in right triangle ABC

cos72° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{BC}{17.3}[/tex] ( multiply both sides by 17.3 )

17.3 × cos72° = BC , then

BC ≈ 5.3 ( to the nearest tenth )

Answer:

Step-by-step explanation:

Using it's concept, it is found that the domain of the graphed function is given as follows:

D. [tex]-4 \leq x \leq 2[/tex]

It is the set that contains all possible input values for the function. In a graph, it is given by the values of x.

In this graph, x assumes values between -4 and 2, inclusive due to the closed circle, hence the domain is given by:

D. [tex]-4 \leq x \leq 2[/tex]

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The parameters of an Exponential Distribution is D. a > 0

This refers to the distribution of probability with respects to time taken in a Poisson point process.

Hence, we can see that from the previous knowledge of exponential distributions, it is stated that λ > 0 is the parameter of the distribution, and is supported on the interval [0, ∞).

Therefore, option D is correct.

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The simplest form of the given ratios are : 10:3 , 1:3 , and 12:1

A ratio indicates how many times one number contains another.

Here, for given ratio

2 litres : 600 ml    = 2000 ml : 600 ml

                             = 20 : 6

                            = 10 : 3

8 h : 1 day       =  8 hrs : 24 hrs

                        = 8:24

                       = 1 : 3

3 km : 250 m = 3000 m : 250 m

                      = 3000 : 250

                      = 300 : 25

                     = 12 : 1

Thus, the simplest form of the given ratios are : 10:3 , 1:3 , and 12:1.

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The probability that exactly 800 chips are acceptable is less than 0.000001

The given parameters are:

The binomial probability is represented as:

[tex]P(x) = ^nC_x * p^x * (1- p)^{n - x}[/tex]

So, we have:

[tex]P(300) = ^{3000}C_{800} * (72\%)^{800} * (1- 72\%)^{3000 - 800}[/tex]

The data values are large.

So, we use a statistical calculator to evaluate the expression

Using the calculator, we have:

P(300) < 0.000001

Hence, the probability that exactly 800 chips are acceptable is very small i.e. less than 0.000001

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Answer: It will arrive at 5:55 P.M

Step-by-step explanation:

Using the together rate, it is found that it will take them 18 minutes to prepare the cards working together.

The together rate is the sum of each separate rate.

In this problem:

Hence, the time it will take for them to make the cards is given by:

[tex]\frac{1}{x} = \frac{1}{45} + \frac{1}{30}[/tex]

[tex]\frac{1}{x} = \frac{5}{90}[/tex]

5x = 90

x = 18 minutes.

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3(5x+7)-6(4-2x) - given

15x+21-24+12x - distributive property

27x-3 - combine like terms

Triangles 3 and 4 are isosceles right angles because they have same length.

It should be noted be noted that the square has all right angles equal. The largest angle of the triangle is the right angle m.

Here, the triangles are isosceles right angles as both the legs and the acute angles are congruent.

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By applying the Theorem of Intersecting Secant, the measure of angle WT is equal to 51°.

By critically observing the geometric shapes shown in the image attached below, we can deduce that they obey the Theorem of Intersecting Secants.

The Theorem of Intersecting Secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the Theorem of Intersecting Secant, angle P will be given by this formula:

m<P = ½ × (m<RS - m<WT)

Substituting the given parameters into the formula, we have;

35 = ½ × (121 - m<WT)

70 = 121 - m<WT

m<WT = 121 - 70

m<WT = 51°.

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