Add the two expressions 3z - 4 and 2z + 5

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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Answer: your mom

Step-by-step explanation:

The solution for x in the triangle is x = 51.98 units

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Using trigonometric ratio:

sin 38° = 32/x  (Sine = opposite/hypotenuse)

x = 32/sin 38°

x = 51.98 units

Therefore, the solution is x = 51.98 units

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The city that you should live in if you want a greater variability in temperature is city Y.

In order to determine the city that has the greater variability in temperature, the interquartile range has to be determined. The interquartile range is used to measure the variation in a dataset.

The interquartile range is the difference between the third quartile and the first quartile.

interquartile range = third quartile - first quartile

Interquartile range for City X = 50 - 30 = 20

Interquartile range for City Y = 50 - 25 = 25

The interquartile range for city Y is greater than that of city X. This means that city Y has a greater variation in temperature.

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Answer:

y = -1/3 x + 3

Step-by-step explanation:

To find the equation of the line that passes through the two points (-3,4) and (3,2) in slope-intercept form, we'll first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two given points.

Plugging in the given points, we get:

m = (2 - 4) / (3 - (-3)) = -2 / 6 = -1/3

Next, we'll use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points, and m is the slope of the line.

We'll use the first given point, (-3,4), so we have:

y - 4 = -1/3 (x - (-3))

Expanding the right side of the equation, we get:

y - 4 = -1/3 x + 1

Finally, we'll rearrange the equation to get it in slope-intercept form, which is:

y = -1/3 x + b

where b is the y-intercept. To find b, we'll plug in one of the given points and solve for b:

y = -1/3 x + b

4 = -1/3 * (-3) + b

4 = 1 + b

b = 4 - 1

b = 3

So the equation of the line in slope-intercept form is:

y = -1/3 x + 3

The divisor in the situation given is 14.

We can write the division algorithm as -

dividend = (divisor × quotient) + remainder

Given is that in a division the dividend is 872 the quotient is 62 and the remainder is 4

We can write -

dividend = (divisor × quotient) + remainder

872 = (d x 62) + 4

62d = 868

d = 868/62

d = 14

Therefore, the divisor in the situation given is 14.

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{Question in english -

if in a division the dividend is 872 the quotient is 62 and the remainder is 4 what is the divisor}

Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.

The second question requires the calculation of 12.5% of $100, which is equal to $12.50.

For the third question, 130 is 20% of 650.

For the fourth question, $5.40 is 120% of $4.50.

For the fifth question, $8.40 is 30% of $28.

For the sixth question, 56% of 39 is $21.84

For the seventh question, $495 is 55% of $900.

For the last question, 144 is 60% of 240.

Step-by-step explanation:

Answer:

Step-by-step explanation:

26

12.5

20%

120%

30%

12.23

900

60%

Answer:

190°

Step-by-step explanation:

Subtract 360° (this is one complete rotation)

"coterminal" is the exact same angle, but 360° bigger (or smaller)

550° - 360°

= 190°

Answer: 70˚

Step-by-step explanation:

Goal: find the other angles in the triangle and subtract them from 180 to find x:

180 - 105 = 75˚

the other angle is 35˚, (alternate interior angles).

.: x = 180 - 75 - 35 = 70˚

Step-by-step explanation:

The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.

So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

Answer:

11xy(121x²-y²)

Step-by-step explanation:

When factorizing, you should always look for what each term has in common.

First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:

1331x³y-11y³x

11(121x³y-y³x)

Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:

11(121x³y-y³x)

11x(121x²y-y³)

We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:

11x(121x²y-y³)

11xy(121x²-y²)

Since there is nothing in common left between the terms, we can say the expression is fully factorized!

The values for the sets are -

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } and n(A∪B) = 14.

A∩B = { 10 , 12 , 14 , 16 } and n(A∩B) = 4

What is sets?

A set is a precisely defined collection or aggregate of all feasible objects with predetermined qualities that are specified in accordance with a precisely defined rule. Elements of sets are the items used to compare sets.

The set S is - S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }

The set A is - A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 }

The set B is - B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

A∪B is the set of elements of S that are part of A or B, or both.

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

Count the number of elements present in set A∪B.

Therefore, n(A∪B) value is 14.

A∩B is the set of elements of S that are common to A and B.

A∩B = { 10 , 12 , 14 , 16 }

Count the number of elements present in set A∩B.

Therefore, n(A∩B) value is 4.

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The numerical value of x in the given right triangle is 20.14.

The figure in the image is right-triangle.

To find the value of x, we use trigonometric ratio.

Sine = Opposite / Hypotenuse

Plug in the values and solve for x.

sin( 32° ) = x / 38

x = sin( 32° ) × 38

x = 0.529919 × 38

x = 20.14

Therefore, the value of x is 20.14.

Option C) 20.14 is the correct answer.

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Answer:

2.016, 2.16, 2.1682, 2.2

How to put anything from least to greatest?

The decimals that you have put are the following:

2.16

2.1682

2.2

2.016

How to do it:

If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.

We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.

Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.

So now here are the decimals from least to greatest:

2.016, 2.16, 2.1682, 2.2

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Answer:

x = 32

Step-by-step explanation:

First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.

3/4x = 27-3

Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3

0.75x = 24

Now we can divide 24 by 0.75 to find x

x = 32

x = 32.

[tex]\frac{3}{4} x+3=27[/tex]

[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]

[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]

If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!

[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]

That's correct!

x = 32.

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Answer:

784 R 13

Hope this helps!

Step-by-step explanation:

The required Length of the DC is 30.47 Units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

We have;

In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.

Then, In ΔABD

Sin∅ = BD/20

Sin(54°) = BD/20

BD = 0.809(20)

BD = 16.18

in ΔBDC

tan(28°) = BD/DC

DC = BD/tan(28°)

DC = 16.18/0.531

DC = 30.47 Units.

Thus, required Length of the DC is 30.47 Units.

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The mean of the data is given by the equation M = 679.3846 and the standard deviation σ = 34.1535

The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Standard Deviation is calculated by

Each number's deviation from the mean must be determined, and then squared.

Next, add up all of these values.

Divide the result by the quantity of numbers.

Then calculate its square root.

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Given data ,

Let the data be represented as Set A

Now , the value of set A is

Set A = { 688 , 711 , 625 ,701 , 688 , 667 , 694, 630, 547, 703, 688, 697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679, 708, 699, 667, 703 }

The mean of the sample data = Sum of all the values / number of values

The mean M = 17664 / 26

The mean M = 679.3846

Now , the standard deviation is calculated by

σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²

Substituting the values in the equation , we get

The standard deviation σ = √ ( 30328.153846154 / 26 )

The standard deviation σ = √ ( 1166.4674556213 )

The standard deviation σ = 34.1535

Hence , the standard deviation is 34.1535

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Answer:

Step-by-step explanation:

To find the angle that Mrs. Becker is looking down at, we can use the tangent function. We know the height of her eyes (6 feet) and the distance from her eyes to the ladybug (100 feet), so we can use the formula:

tan(angle) = height/distance

First, we'll solve for the angle:

angle = tan^-1(height/distance)

angle = tan^-1(6/100)

Using a calculator, we can find that the angle is approximately 0.0349 radians, or approximately 2 degrees.

So, Mrs. Becker is looking down at an angle of approximately 2 degrees.

Answer:

Step-by-step explanation:

Step 1: Define each variable

Let's define some variables to make the calculations easier:

t1 = the median monthly rent in 1990, which is $447

t2 = the median monthly rent in 2002, which is $658

Δ = the change in median monthly rent, which is t2 - t1

Step 2: Calculate the change in median monthly rent

Δ = t2 - t1 = $658 - $447 = $211

This means that the median monthly rent increased by $211 from 1990 to 2002.

Step 3: Divide the change by the original amount

To find the percentage increase, we need to divide the change by the original amount and multiply by 100:

Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%

This means that the median monthly rent increased by 47.2% from 1990 to 2002.

Step 4: Round to the nearest tenth of a percent

The final answer is 47.2%, rounded to the nearest tenth of a percent.

The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.

Answer:

Step-by-step explanation:

The equation that represents the town's population after 4 years can be found using the formula:

P = P0 * (1 - r)^t

Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).

P = 4.11 x 10^4 * (1 - 0.096)^4

P = 4.11 x 10^4 * 0.6994^4

P = 4.11 x 10^4 * 0.4139

P = 1.70 x 10^4

So the town's population after 4 years is 1.70 x 10^4.

Answer:

Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:

dP/dt = -0.096P(t)

To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:

∫(dP/P) = -0.096 ∫dt

ln|P(t)| = -0.096t + C

where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:

P(t) = Ce^(-0.096t)

where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4

Substituting in t = 4, we get:

P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)

So, the equation representing the town's population after 4 years is:

P(t) = 4.11 x 10^4 e^(-0.096t)

The constant of proportionality in the equation is 0.3.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

WE are given that number of candies sold can be determined by the equation: T = 0.3c, where T is number of candies and c is the number of children.

0.3 = constant of proportionality

0.3 = p / n

which is the ratio of p to n

The constant of proportionality is the ratio between the two quantities that are directly proportional.

Therefore,

0.3 is the constant of proportionality in the equation.

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This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.

It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.

An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.

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The function type of the graph with asymptotes, x = 2, and y = 0  is a rational polynomial, where the degree of the numerator is less than the degree of the denominator, and (x - 2) is a factor of the denominator, which is a function of the form;

[tex]f(x) = \frac{1}{(x - 2)}[/tex]

An asymptote is a line to which the output value of a function approaches as the input value becomes very large approaches infinity.

The function type represented by the graph is a polynomial function that has an horizontal asymptote of y = 0, and a vertical asymptote of x = 2

A function has a vertical asymptote at the location at which the denominator approaches zero.

The vertical asymptote of x = 2 , indicates that the denominator approaches zero when x = 2, therefore, (x - 2) is a factor of the denominator

A function has an horizontal asymptote which is the value the function approaches as the input value approaches infinity.

Therefore, the horizontal asymptote of y = 0, indicates that the the degree of the numerator is less than the degree of the denominator

The function type in the question is therefore;

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Answer:

2787

Step-by-step explanation:

add them all together

Answer:

Step-by-step explanation:

Here's a step-by-step explanation of the reflections:

Point R is located at (1, 1) on the coordinate plane.

Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).

Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).

So the final location of R'' is at the ordered pair (-1, -1).

Answer:3.25

Step-by-step explanation:

Divide 325/100=3.25

Answer:

[tex]4x^{2} y^{3}[/tex]

Step-by-step explanation:

[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]

In the denominator, all the terms in the brackets or parenthesis will be squared:

= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]

Law of indices is applied:

                                                    [tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]

= [tex]4x^{4 - 2} y^{5 - 2}[/tex]

= [tex]4x^{2} y^{3}[/tex]

∴Option B

Answer:

41 inches

Step-by-step explanation:

to find the perimeter of any shape, add the length of all the sides together