Expand the logarithm fully using the properties of logs. Express the final answer in terms of \log x log x. log7x2

Answer:

7 degress celcius

Step-by-step explanation:

Answer: 6 feet long

Step-by-step explanation:

1ft. = 12 in

62 inches = 5 feet and 2 inches

Break down 62 into 60 and 2

60 divided by 12 = 5 (12x5=60)

60in. = 5ft.

2in. = 2in.

5ft. and 2in.

10in.= 10in.

Add the inches

10in. + 2 in. = 12 in.

12in.= 1ft.

5ft. + 1ft. = 6ft.

Answer: Nancy’s rope is 6ft. long

Answer:

x = 40

Step-by-step explanation:

Alternate exterior angles are congruent (equal).

2x + 16 = 96   Subtract 16 from both sides

2x + 16 -16 = 96 - 16

2x = 80  Divide both sides by 2

x = 40

Answer:

x=40

Step-by-step explanation:

What is modulus ?
In complex analysis, the modulus of a complex number z = a + bi is a measure of its distance from the origin in the complex plane. Specifically, the modulus is defined as |z| = sqrt(a^2 + b^2), where sqrt denotes the square root. Geometrically, |z| represents the length of the line segment from the origin to the point (a, b) in the complex plane.

Explanation:

The equation |x| = 2 represents the absolute value of x equals 2.

The graph of this equation will be a V-shaped graph that intersects the x-axis at x = -2 and x = 2, and the y-axis at y = 2. The vertex of the V-shaped graph is at the origin (0, 0).

Visually, the graph will look like two lines that start at the origin and extend upwards and downwards at a 45-degree angle, forming a V-shape. The two lines will be symmetric to the y-axis, meaning that the left half of the graph will be a mirror image of the right half.

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Therefore, x³ must be even. Therefore, if -z is irrational, then z must also be irrational.

In mathematics, an integer is a whole number that can be either positive, negative, or zero. It can be written without a fractional or decimal component. Some examples of integers are -3, -2, -1, 0, 1, 2, 3. Integers are used in many different areas of mathematics, including number theory, algebra, and geometry. They are a fundamental concept in mathematics and have many important properties, such as the ability to add, subtract, and multiply them.

Here,

Proof of "x³ is even if and only if x is even":

First, assume that x is even. Then x can be written as x = 2k for some integer k. Substituting this into x³, we get:

x³ = (2k)³ = 8k³ = 2(4k³)

Since 4k³ is an integer, this shows that x³ is even.

Now, assume that x³ is even. This means that x³ is divisible by 2. We can write x³ as x³ = 2m for some integer m. Taking the cube root of both sides, we get:

x = (2m)*(1/3)

If x is an integer, then (2m)*(1/3) must also be an integer. However, the only way for the cube root of an even number to be an integer is if the original number is even. Therefore, x must be even.

Proof of "z is irrational if and only if -z is irrational":

First, assume that z is irrational. By definition, this means that z cannot be expressed as the ratio of two integers. Now suppose that -z is rational. This means that -z can be expressed as the ratio of two integers, say -z = p/q, where p and q are integers and q is not equal to 0. Multiplying both sides of the equation by -1, we get:

z = -p/q

This shows that z can be expressed as the ratio of two integers, which contradicts our assumption that z is irrational. Therefore, if z is irrational, then -z must also be irrational.

Now, assume that -z is irrational. By definition, this means that -z cannot be expressed as the ratio of two integers. We can rewrite this as z = (-1)(-z), which means that z is the product of -1 and a number that is not the ratio of two integers. Multiplying a number by -1 does not change its irrationality, so z must also be irrational. Therefore, if -z is irrational, then z must also be irrational.

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a) xᵃ/xᵇ = xᵃ⁻ᵇ

b) xᵃ x xᵇ = xᵃ⁺ᵇ

c) x⁰ = 1

d) (xᵃ)ᵇ = xᵃˣᵇ

e) x⁻ᵃ = 1/xᵃ

indices are a method used in solving a variable in which the power or exponent of a number is raised to a number of variables

These questions are part of the basic theorems or rules of indices

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Answer:

27.5

Step-by-step explanation:

(x – 3)2 = 49

(x – 3) = 49/2

(x – 3) = 24.5

x = 27.5

Answer: a: To the right b: <

Step-by-step explanation: for a: Positive would be bigger than negatives always, (like -2 vs 2, 2 would be bigger.) b: that’s because 1/2 is closer to 0 than 2, 1/2 is basically 0.5 so -0.5 would be closer to 0 than -2.

Yes, The y - intercept is zero because it cannot intercept at any point on y - axis.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of your model is,

⇒ y = 0.122x

Here, The y - intercept is zero.

Since, The slope intercept form of equation of line is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

By comparing with the given equation, We get;

The y - intercept is zero.

And, By graph it cannot intercept at any point on y - axis.

Hence, The y - intercept is zero because it cannot intercept at any point on y - axis.

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The completed function to model the data is:

[tex]y = 3.1cos(\frac{2\pi }{365} (x-15.3)) + 12.2[/tex]

A periodic variable's amplitude is a gauge of its change over a single period.

A non-periodic signal's magnitude in relation to a standard value is its amplitude. There are several ways to define amplitude, and they are all dependent on how much the extreme values of the variable deviate from one another.

To find the amplitude:

max - min/2=15.3-9.1/2

= 3.1

The wavelength is 365

The midpoint is 12.2

The max position is 15.3

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Answer:

g(x) = x + 3

Step-by-step explanation:

To see how this works, we can plug g(x) into f to get:

f(g(x)) = f(x + 3) = (x + 3)^3

Then, we can simplify h(x) = (x + 9) as follows:

h(x) = (x + 9) = ((x + 3) + 6) = g(x) + 6

Finally, we can write h(x) in terms of f(g(x)) as:

h(x) = g(x) + 6 = f(g(x)) + 6 = f(x + 3) + 6 = (x + 3)^3 + 6

If a homeowner would like to spread shredded bark (mulch) over her flowerbeds. it will cost $65.07 to cover all the flowerbeds with shredded bark.

To calculate the amount of mulch needed, we need to find the volume of each flowerbed and add them together. The recommended depth for the mulch is 4 inches, which is equal to 4/12 = 1/3 feet.

For the first flowerbed, the volume of mulch needed is:

24 ft x 3.1 ft x 1/3 ft = 24.8 cubic feet

For the second flowerbed, the volume of mulch needed is:

14 ft x 4.3 ft x 1/3 ft = 20.87 cubic feet

For the third flowerbed, the volume of mulch needed is:

30 ft x 1.5 ft x 1/3 ft = 15 cubic feet

The total volume of mulch needed to cover all three flowerbeds is:

24.8 cubic feet + 20.87 cubic feet + 15 cubic feet = 60.67 cubic feet

Since there are 27 cubic feet in a cubic yard, the total amount of mulch needed is:

60.67 cubic feet / 27 cubic feet per cubic yard = 2.25 cubic yards

At a cost of $27 per cubic yard, the total cost of the mulch is:

2.25 cubic yards x $27 per cubic yard = $60.75

Therefore, it will cost $60.75 to cover all of the flowerbeds with shredded bark.

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The average rate of change of profit as x changes from 3 to 5 is $12 per item.

To find the average rate of change of profit as x changes from 3 to 5, we need to find the change in profit divided by the change in x over that interval:

Average rate of change = (P(5) - P(3)) / (5 - 3)

We can find P(5) and P(3) by plugging those values of x into the profit equation:

P(5) = 2(5)^2 - 4(5) + 6 = 36

P(3) = 2(3)^2 - 4(3) + 6 = 12

Substituting these values, we get:

Average rate of change = (36 - 12) / (5 - 3)

Average rate of change = 24 / 2

Average rate of change = 12

Hence, the average rate is $12 per item.

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The mean change in Mr.60. Connor's bank account is $6.

To find the mean change in Mr. Connor's bank account, we need to add up all the changes and divide by the total number of changes.

First, we can simplify the given list of changes by combining the positive changes and the negative changes separately:

$50.25 + $50.25 = $100.50 (total positive change)

-$22.50 + (-$22.50) + (-$22.50) = -$67.50 (total negative change)

Then, we can find the total change in Mr. Connor's account by subtracting the total negative change from the total positive change:

$100.50 - $67.50 = $33.00 (total change)

Finally, we can find the mean change by dividing the total change by the number of changes:

$33.00 ÷ 5 = $6.60 (mean change)

Therefore, the mean change in Mr.60. Connor's bank account is $6.

In mathematics, the mean is a measure of central tendency that represents the average value of a set of numbers. It is also known as the arithmetic mean or simply the average.

To find the mean of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers. For example, to find the mean of the numbers 2, 5, 7, and 10, you add them up (2 + 5 + 7 + 10 = 24) and then divide by the total number of numbers (4), which gives a mean of 6.

The mean is often used in statistics to describe the typical or average value of a data set. It is a useful measure of central tendency because it takes into account all the values in the data set, not just a few extreme values. However, the mean can be affected by outliers, or extremely high or low values in the data set that can skew the average.

There are different types of means, including the arithmetic mean, the geometric mean, and the harmonic mean, each with different methods of calculation and specific applications.

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Answer:

Yes, it is possible to determine which man has the different weight by using the seesaw three times. Here is one possible method

Divide the 12 men into three groups of four: A, B, and C.

Weigh group A against group B on the seesaw. (First use)

If the seesaw balances, then the odd man is in group C. Otherwise, he is in the heavier or lighter group (A or B).

Take two men from group C and weigh them against two men from group A or B that were balanced. (Second use)

If the seesaw balances again, then the odd man is one of the remaining two men from group C. Otherwise, he is one of the two men from group C that were weighed.

Weigh one of the suspected men against any other man. (Third use)

If the seesaw balances, then the odd man is the other one. Otherwise, he is the one that was weighed.

This method works because it eliminates half of the possible candidates at each step and identifies whether the odd man is heavier or lighter by comparing him with known balanced men.

Step-by-step explanation:

Answer:

environment .. pollution

growth if of food.... wealthy too much rain or no rain

The system of equations can be represented as a vector equation A x = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector.

Using matrices and vectors, a system of linear equations can be expressed as a vector equation. Consider a set of n variables and m linear equations. It may be written as follows:

A x = b

where A is a m x n matrix of the coefficients of the variables, x is a n x 1 column vector of the variables, and b is a m x 1 column vector of the constants on the right-hand side of each equation.

To match the rows of the system of equations to the corresponding row of the matrix A and vector b in the vector equation, we can represent the system of equations as:

a 21 x 1 + a 22 x 2 +... + a 2n x n = b 2 a 11 x 1 + a 12 x 2 +... + a 1n x n = b 1

a mn x n = b m, where a m1 x 1 = a m2 x 2 +...

The vector form of this is as follows:

Beginning with "a 11" and "a 12," adding "cdots and a 1n," going on to "a 21" and "a 22," adding "cdots and a 2n," adding "vdots and vdots and ddots and vdots," ending with "a m1" and "a m2," adding "cdots and a mn,"

With A serving as the coefficient matrix, x serving as the variable vector, and b serving as the constant vector, the system of equations can thus be expressed as a vector equation, A x = b.

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Answer:

32

Step-by-step explanation:

Please clarify OU bisects ∠XO*. Is it Z? If it is so, then the solution is below:

∠YOX = ∠XOZ (vertical angles)

5x + 21 = 9x - 55

5x - 9x = -55 - 21

-4x = -76

X = 19

=> 5x + 21 = 5(19) + 21 = 116

∠YOX + ∠XOZ = 180 (linear angles)

116 + ∠XOZ = 180

∠XOZ = 180 - 116 = 64

Since OU bisects ∠XOZ

=> ∠XOU = ∠UOZ = 64/2 = 32

Answer:

≈ 315

Step-by-step explanation:

To find the number that 105 is 33 1/3 of, we can use algebra.

Let x be the number we are looking for. Then we can write the equation:

105 = (33 1/3)% of x

To solve for x, we can first convert the percentage to a decimal by dividing by 100:

33 1/3% = 33 1/3 ÷ 100 = 0.3333

Substituting this in the equation, we get:

105 = 0.3333x

To solve for x, we can divide both sides by 0.3333:

x = 105 ÷ 0.3333

Using a calculator, we get:

x ≈ 315

Therefore, 105 is 33 1/3 of 315.

Answer:

Note that the line passes through the points (1,0) and (2,6).

Answer:

17 numbers in this range.

Step-by-step explanation:

For this function, the domain consists of all positive three-digit integers. There are 900 such integers, from 100 to 999.

The range consists of all numbers between 2 and 18, inclusive, since the smallest possible sum is 1+0+0 = 1 and the largest possible sum is 9+9+1 = 19, but the function only takes the sum of the largest and smallest digits. There are 17 numbers in this range.

Answer:

Step-by-step explanation:

The domain of this function consists of all positive three-digit integers. There are 900 three-digit integers in total, from 100 to 999 inclusive.

The range of this function consists of all integers between 2 and 18 inclusive, since the smallest and largest digits of a three-digit integer can range from 1 to 9, and their sum can range from 2 (1 + 1) to 18 (9 + 9). So the range has 17 elements in total: {2, 3, 4, ..., 18}.

Answer:

Step-by-step explanation:

To find the 90% confidence interval for the difference in proportions, we can use the following formula:

CI = (p1 - p2) ± zα/2 * √( (p1 * (1-p1) / n1) + (p2 * (1-p2) / n2) )

where:

p1 and p2 are the sample proportions from the city and rural area, respectively

n1 and n2 are the sample sizes from the city and rural area, respectively

zα/2 is the critical value from the standard normal distribution for a 90% confidence level, which is 1.645

First, we need to calculate the sample proportions:

p1 = 112 / 272 = 0.4118

p2 = 53 / 105 = 0.5048

Next, we can plug in the values and calculate the confidence interval:

CI = (0.4118 - 0.5048) ± 1.645 * √( (0.4118 * (1-0.4118) / 272) + (0.5048 * (1-0.5048) / 105) )

CI = (-0.146, -0.031)

Therefore, the 90% confidence interval for the difference in proportions is (-0.146, -0.031). This means we are 90% confident that the true difference in proportions of religious people between the city and rural areas lies between -0.146 and -0.031. Since this interval does not include zero, we can conclude that the proportion of religious people is significantly different between the two areas.

$231784 is the  to raise a child from birth to 17 years in a household with an annual income of $78,300.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Let y represents  the total cost in dollars f raising a child in the United States from birth to 17 years

x represents the households annual income

We have  y = 1.55x + 110,419

We need to find the value of y for x=78300

y=1.55(78300) + 110,419

y=231784

Hence, $231784 is the  to raise a child from birth to 17 years in a household with an annual income of $78,300.

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The expression into each letter space (a,b,c,d) to create an equation that is true for all values of x is X(x+2),X,(X+2),X^2.

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

The equation with a,b,c,d=(3/x+2)+(4/x)+(2/x^2)=(3(a)+4(b)+2(c)/d)

Now,

=(3/x+2)+(4/x)+(2/x^2)

=3/x + 2x/2 + 4/x + 2/x^2

=(3+2x)/x+4/x+2/x^2

Therefore, the answer of the expression will be X(x+2),X,(X+2),X^2.

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Hiya,

We literally just learnt about congruent shapes before the holidays.

I think it's like this-

If the shape is an SSS (Side, Side, Side) congruent or SAS (Side, Angle, Side), then you do the following:

a) Write the congruent statement... I'm not sure what the congruent statement is but it may be something you have learnt to do previously like an expression on revealing how to find the congruent shape and what type it is.

b) Sorry I'm not sure what a postulate is you may need to look back at your notes or research it.

I have attached images of the worksheet we were given in class which may or may not help!

Answer:

6. ΔANG ≅ ΔRWT by SAS Postulate.

7. The two triangles are congruent by SAS Postulate.

Step-by-step explanation:

If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, the triangles are congruent.  

The included angle is the angle between two sides of a triangle.

Therefore:

We are told that AN ≅ RW, GN ≅ TW, and ∠N ≅ ∠W.

Therefore, as two sides and the included angle in triangle ANG is congruent to the two sides and the included angle in triangle RWT, the SAS Postulate can be used to prove that the triangles are congruent.

The two given triangles have two sides of equal length, denoted by the same number of tick marks on each congruent line segment.  The included angles are also congruent (both are 90°).  Therefore, the SAS Postulate can be used to prove that the triangles are congruent.

The amount of money the organization will raise in total is $25655.17.

A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. Thus, a part per hundred is what the percentage refers to. Percent signifies for every 100.

Let us suppose the total amount raised = T.

Given that, $14,300 is 58% of the total amount we have:

T (58%) = 14300

T (58/100) = 14300

T = 14300(100)/58

T = 25655.17

Hence, the amount of money the organization will raise in total is $25655.17.

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The formula of 15% of 60kg is down below and it equals 9:

Given:

⇒ Formula = 15% of 60kg

⇒ Formula = 15 x 60

⇒ Formula = 100

⇒ Formula = 9

Check:

So, we used 15% of 60kg to find are answer:

We are going to use 100 and divide by 900:

Hence, the formula of 15% of 60kg it equals 9.

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