Expression for the quotient of twice a number, and the sum of the number and seven

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)

\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

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Answer:

6 1/12

Step-by-step explanation:

Make 1/3 and 3/4 have the same denominator.

1/3 times 4/4 is 4/12

3/4 times 3/3 is 9/12

4/12 + 9/12 = 13/12 = 1 1/12

1 1/12 +5 = 6 1/12

6.08333333333333333333333333333333333333333333

Answer:

5

Step-by-step explanation:

pemdas

Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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\(x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9\)

Using these points, the correct graph is shown in option C.

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The point satisfies the given system of inequalities is (1, -1)

A system of inequalities is a set of two or more inequalities in one or more variables.

Given is a system of inequalities y < -x+2 and -2x+y < -2,

We know that, the solution set of a system of inequalities is given by studying the graph of the system, The solution set the region covered by lines of the both inequalities.

Plotting the graphs, of the system of inequalities, we get, the set of solution is the area covered with purple shade,

In that area only, (1, -1) lies.

Therefore, the point (1, -1) is the solution of the given system of inequalities

Hence, the point satisfies the given system of inequalities is (1, -1)

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To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: 83

Step-by-step explanation:

(88+92+87+x)/4 = 90

(277+x)/4 = 90

x+ 277 = 360

x = 83

88+92+87+93 = 360 / 4 = 90

You'll probably need to get 93 on your fourth grade

Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

Hence Proved N to N is uncountable set by using a diagonalization argument

What is Diagonalization Argument?

Georg Cantor published the Cantor's diagonal argument in 1891 as a mathematical demonstration that there are infinite sets that cannot be put into one-to-one correspondence with the infinite set of natural numbers. It is also known as the diagonalization argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof.

Proof:

We write f as the sequence of value it generates

that is, say f:N-N is defined as f(x) =x then

we write f as : 1,2,3,4........

similarly if f:N-N were f(x) = 2x then we write it as :2,4,6,8.......

now assume on the contrary that the set of functions from N to N is countable

then,

\(f_{1}\)   :     \(f_{11}\)        \(f_{12}\)       \(f_{13}\) , ...........

\(f_{2}\)   :     \(f_{21}\)        \(f_{22}\)       \(f_{23}\) , ...........

\(f_{3}\)   :     \(f_{31}\)        \(f_{32}\)       \(f_{33}\) , ........... and so on

Here \(f_{ij}\) =\(f_{i}(j)\)

consider the function f as :

f : (\({f11}\) +1 ) , (\({f22}\) +1) , (\({f33}\) +1),.........

Then f wouldn't appear in the list of the function we had above since any \(f_{i}\) would disagree with f at the i th place

Therefore the set of the function from N to N is an uncountable set

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Step-by-step explanation:

There are two area of circle the dog can created

1. ¾ circle with radius 9-foot

2. ¼ circle with radius (9-6) foot.

so the exact area is

A = A1 + A2

A = π. 9² . ¾ + π . 3² . ¼ = 63π ft² ≈ 197.82 ft²

the perimeter also can be compute as

P = P1 + P2

P = ¾ . 2π . 9 + ¼ . 2π . 3

P = 15π ft ≈ 47.1 ft

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

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The system or equations can be used to find b, the number of black-and-white copies,

and c, the number of color copies that the customer paid for at the print shop is

b + c = 68

b + c = 680.08b + 0.15c = 6

Given:

Total amount paid = $6.00

Total copies = 68

cost of black-and-white copy = $0.08

cost of color copy = $0.15

let

number of black-and-white copies = b

number of color copies = c

The equation:

b + c = 68

b + c = 680.08b + 0.15c = 6

Therefore, the system or equations can be used to find b, the number of black-and-white copies,

and c, the number of color copies that the customer paid for at the print shop is

b + c = 68

b + c = 680.08b + 0.15c = 6

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Answer:

488 cm² (Option B)

Step-by-step explanation:

The figure consists of a rectangle & a right angled triangle. So,

Area of the complex figure = Area of rectangle + Area of the triangle

1) Length of the rectangle = 22 cm

Width of the rectangle = 17 cm

Area of rectangle = 22 × 17 = 374 cm²

2) Length of perpendicular of the triangle = 22 - 10 = 12 cm

Length of base of triangle = 19 cm

Area of a triangle = \(\frac{1}{2} \times 12 \times 19 = 114 cm^2\)

∴ AREA OF THE FIGURE = 378 + 114 = 488 cm²

Hey there!

For starters, you are dividing two negative numbers, so the outcome will be positive, which leaves us with A and C options. Also, we can see that C is the same as A, except C is simpler, so that rules out A because it is not the simplest version, and leaves us with C.

Hope it helps and have a great day!

Without knowing the total number of coins or the ratio between one dollar and two dollar coins in the jar, we cannot accurately determine the number of two dollar coins.

Amadi has a jar with both one dollar and two dollar coins. The question is asking how many of the coins in the jar are two dollar coins.
To determine the number of two dollar coins, we need more information. The question does not provide any details about the total number of coins or the ratio between one dollar and two dollar coins in the jar. Without this information, it is not possible to give an accurate answer.
If we assume that the jar contains a total of 100 coins, we can use algebra to solve for the number of two dollar coins.

Let's say the number of two dollar coins is x. Then, the number of one dollar coins would be 100 - x.
Since the value of the two dollar coins is double the value of the one dollar coins, we can set up the equation 2x + 1(100 - x) = total value of coins.
Simplifying the equation, we get 2x + 100 - x = total value of coins.
Combining like terms, we have x + 100 = total value of coins.
Since we don't know the total value of coins, we cannot solve for x. Therefore, we cannot determine the number of two dollar coins without additional information.

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The solution to the equation is x = 7.

What is the linear equation in one variable?

A linear equation in one variable is an equation of the form ax + b = 0, where a and b are constants and x is the variable. The general form of a linear equation in one variable is ax + b = 0, where a and b are constants and x is the variable. The graph of a linear equation in one variable is a straight line.

The first step in solving the equation 2x - 4 = 10 using algebra tiles would be to add 4 to both sides of the equation to get 2x = 14. The next step would be to divide both sides of the equation by 2 to get x = 7.

Hence, the solution to the equation is x = 7.

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Answer:15/22

Step-by-step explanation:

The blue shaded portion on the top left side is described as forming lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion W. D.

To graph the system of inequalities y ≥ 1/3x - 2 and y ≤ -4x - 2, we will plot the lines corresponding to each inequality and shade the region that satisfies both inequalities.

First, let's graph the line y = 1/3x - 2.

We can find two points on this line and connect them with a straight line:

Using (6, 0):

y = 1/3(6) - 2

y = 2 - 2

y = 0

So we have the point (6, 0).

Using (0, -2):

y = 1/3(0) - 2

y = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 1.

Next, let's graph the line y = -4x - 2 using the same process:

Using (0.5, 0):

0 = -4(0.5) - 2

0 = -2 - 2

0 = -4

So we have the point (0.5, 0).

Using (0, -2):

-2 = -4(0) - 2

-2 = -2

So we have the point (0, -2).

Plotting these two points and drawing a line through them, we get a line labeled as Line 2.

Now, we need to shade the region that satisfies both inequalities.

The shaded region will be the region where Line 1 is above Line 2.

Based on the given descriptions of the shaded portions W, X, Y and Z we can determine the correct option.

The blue shaded portion on the top left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion X.

The blue shaded portion on the left side is described as forming when lines pass through (0.5, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Y.

The blue shaded portion on the bottom left side is described as forming when lines pass through (6, 0) and (0, -2) and intersect at (0, -2).

This corresponds to the shaded portion Z.

Based on this information, we can determine the correct option:

A. X

B. Y

C. Z

D. W

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Answer:

y=8 and x =-11

Step-by-step explanation:

kinda confused by the setting of the question

but i used this form ; 3x + 2iy+ xi + 5y = 7 + 5i instead of 3x+2iy xi+5y =7+5i

Then ;

you compare

3x + 5y =7....... equation 1

2iy + xi = 5i. ( cancel out i)

u get ; 2y + x =5 .......equation2

solve simultaneously by substitution method

giving u y=8

put value of y into equation 2 and get x=-11

hope that helps

a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

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Answer: 11

Step-by-step explanation:

F(1) = 3(1) + 8

F(1) = 3 + 8

F(1) = 11

You just substitute the x in for 1 and solve from there.

y = 2/3x +6    for x < -3

y = 2/3x +1     for x > 3.

This can be solved using the concept of slope-intercept form.

The equation for a straight line is y = mx + b, where m stands for the slope and b for the y-intercept of the line. The slope-intercept formula, y = mx + b, is used when the slope of the line under study is known and the specified point also serves as the y-intercept (0, b). The y value of both the y-intercept point is represented by b in the formula.

The graph is a line for  x < -3

(-6,2) and ( -3,4)

The slope is m= ( y₂ - y₁)/(x₂-x₁)

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

m = 2/ ( -3+6)

m = 2/3

∴ The slope is 2/3

Using point slope form:

y-y₁ = m (x-x₁)  and the point ( -6,2)

y -2 = 2/3 (x - -6)

y -2 = 2/3 (x +4)

y-2 = 2/3 x + 6

y = 2/3x +6 x< -3

The graph is a line for  x > 3

(3,3) and ( 6,5)

The slope is m= ( y₂-y₁)/(x₂-x₁)

m = ( 5-3)/(6-3) = 2/ (3) = 2/3

The slope is 2/3

Using point slope form:

y-y₁ = m(x-x₁)  and the point (6,5)

y -5 = 2/3(x - 6)

y-5 = 2/3 (x -4)

y = 2/3x +1   x> 3

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