Evaluate each logarithm.
log₂1/4

Answer:

All are good ideas for a frequency chart.

But not 100% sure on A and C

Answer: 16% :)

Step-by-step explanation: 25x4=100, and 4x4=16. so 16/100, which equals 16%

Answer:

[tex] \sf {\large{16 \: \%}}[/tex]

Step-by-step explanation:

We know that

4/25 is the same as 4÷25

Then using

Long Division for 4 divided by 25 gives us

0.16

Converting our number to a percentage:

0.16×100

=16%

The coordinate of point C from the given expression is (2, 4)

The formula for calculating the midpoint of coordinates is given by the equation shown below:

Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the following parameters

Midpoint = M(5, 2)

B(8, 0)

Required

Coordinate point C

Substitute the given parameters

5 = (8+x₂)/2

5(2) = 8+x₂

10 = 8+x₂

x₂ = 2

Similarly

2 = (0+y₂)/2

2(2) = 0+x₂

4 = 0 +y₂

y₂ = 4

Hence the coordinate of point C from the given expression is (2, 4)

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Answer: Graph A represents the given inequality 3y−5x>−6. Option A is correct.

From the graphs, the graph is to choose which best describes the inequality 3y−5x>−6

Step-by-step explanation: hope this helps

Graph A represents the inequality 3y - 5x≤-6. Correct option is A. The inequality 3y - 5x ≤ -6 represents a linear inequality in two variables, y and x.

To graph this inequality, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.

Let's rearrange the given inequality:

3y - 5x ≤ -6

First, add 5x to both sides of the inequality:

3y ≤ 5x - 6

Now, divide both sides by 3 to isolate y:

y ≤ (5/3)x - 2

Now, you have the inequality in slope-intercept form:

y ≤ (5/3)x - 2

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Answer:

[tex]2ab^{(-6)}[/tex]

Step-by-step explanation:

Multiply exponents/group exponents

[tex]2ab^{(-2)} \times b^{(-4)}\\2ab^{-2 + -4}\\2ab^{-6}[/tex]

Answer: 5.94

Step-by-step explanation: In order to find the mean, you first add up all the values in the data set and then divide this number by the number of values!

Hope it helps ^^

Answer: - 2x³ - 5x² - 4x, trinomial

Step-by-step explanation:

    When writing a polynomial, the standard form is to have the terms ordered from highest power to lowest power. 3 > 2, so we will reorder them as so;

- 5x² - 2x³ - 4x ➜  - 2x³ - 5x² - 4x

    To identify the polynomial, we will look at the number of terms. This polynomial has three terms, so it is a trinomial.

- 2x³ - 5x² - 4x

[1] - 2x³

[2] - 5x²

[3] - 4x

Answer:

73° & 107°

Step-by-step explanation:

1. Those angles are supplementary, so they add up to 180 degrees.

2. (8x - 20) + (8x + 8) = 180

3. You need to add both 8x's together to make 16x. Do the same with -20 & 8. That makes -18. This is binomial addition.

4. 16x - 18 = 180

5. Add 18 to both sides

6. 16x = 198

7. Divide both sides by 16

8. x = 12.375

9. Plug in your x for both angles.

Rollercoaster Car is at 4 m above the ground by using integer concept.

As per the question statement, Rollercoaster Car that goes above and below the ground.

Before solving the question, we need to know the concept of integer operations on a number line.

Here the car is [tex]1 meter[/tex] above the ground level and then goes 4 meter down.

So the position is [tex]1-4=-3 meter[/tex] or 3 meter below the ground level.

Now it rises 13 meter above the ground. So now the position is [tex]-3+13 = 10 meter[/tex] or 10 meter above the ground.

Now it again falls by 6 meter so position is [tex]10-6 = +4 meters[/tex] or 4 meters above the ground.

Therefore the final position is 4 meters above the ground level.

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Interest accrued at the end of the month is $1.41.

Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.

Step 1: Make the initial payment of $882 ($1,032 - $150).

Step 2: $882 times 1.00938 is $890.27

Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.

Step 4. $1,041.68 - $150= $891.68

The interest for the first month is $1.41.

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The solution set for the open sentence with the given replacement set is; 6

We are given the equation as;

13 - x = 7

To solve this , let us use subtraction property of equality to subtract 13 from both sides to get;

13 - 13 - x = 7 - 13

-x = -6

Use division property of equality to divide both sides by -1 to get;

x = 6

Now, the set of possible solutions is  {4, 5, 6, 7}. Thus, our solution falls within the set.

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Given the values that we have here for the large sizes and the family size of cereal the one that has the lowest price per ounce is that of the Large size at $0.21 per ounce

For the family size

We would first have to divide 5.34 by 24

= 5.34 / 24

= 0.22 per dollar

For the large size we have

15 ounces for $3.14

= 3.14 / 15

= 0.21 dollars

Hence we can see that the size of the cereal that is the lowest price per ounce is given as Large size at $0.21 per ounce

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Answer: x=0

Step by step explanation:

1/3 (9x+3) =3x+1

=3x+1=3x+1

=3x-3x=1-1

=0x=0

So x=0

I hope this helps you! Have a nice day!!!!

Answer:

line J and line L are parallel so C.

The parallel line are j and l.

Hence the correct answer is c.

Given are four lines that have been graphed on the same coordinate grid.

We need to check which of these are parallel to each other.

To determine which lines are parallel to each other, we need to compare their slopes. Parallel lines have the same slope.

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Let's identify the slopes of the given lines:

Line j: y = (2/3)x + 1/2

Slope of j: 2/3

Line k: y = (1/2)x + 2/3

Slope of k: 1/2

Line l: y = (2/3)x + 3/2

Slope of l: 2/3

Line m: y = (3/2)x + 1/2

Slope of m: 3/2

Now, let's see which lines have the same slope:

A. k & m - The slopes are different (1/2 and 3/2). These lines are not parallel.

B. k & l - The slopes are different (1/2 and 2/3). These lines are not parallel.

C. j & l - The slopes are the same (2/3). These lines are parallel.

D. j & m - The slopes are different (2/3 and 3/2). These lines are not parallel.

So, the correct answer is:

C. j & l

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The equation solved for x gives  -0. 61

Algebraic expressions are expressions that comprise variables, terms, factors, constants and coefficients.

They are also made up of certain arithmetic operations such as addition, subtraction, multiplication, division, bracket, parenthesis, etc.

Given the expression;

-1/2 + 6/7  = x + 9.7

Find the lowest common multiple

-7 + 12/14 = x + 9. 7

Add the numerators

5/ 14 = x + 9. 7

Find the quotient

0. 36 = x + 0. 97

collect like terms

x = 0. 36 - 0. 97

x = -0. 61

Thus, the equation solved for x gives  -0. 61

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Answer: 2

UvU This might help might not

20 degrees is your angle

For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

We are given the system of equations as:

4 x+2 y = 4    … (1)

6 x+2 y = 8    … (2)

We need to solve it to find the value of x and y.

Subtracting equation (1) form equation (2), we get that:

6 x - 4 x + 2 y - 2 y = 8 - 4

Combining the like terms, we get that:

2 x = 4

x = 4 / 2

x = 2

Now put it in equation (1) to get the value of y

4 (2) + 2 y = 4

8 + 2 y = 4

2 y = - 4

y = - 2

(x, y) = (2, - 2)

Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

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The numbers are 8 and 24.

Let the smaller number be x.

Larger number = 3x

Therefore, the expression will be:

3x - 10 = x + 8

Collect like terms

3x - x = 8 + 10

2x = 18

Divide

x = 18/2

x = 9

The bigger number will be:

3x = 3 × 8 = 24

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The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Rotation is the flipping of a figure about a fixed point.

Square ABCD have vertices at A(-2, 2), B(-2, 4), C(-4, 4) and D(-4, 2). The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)

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[tex]21x + 4y = 300[/tex]

We have infinitely many numbers that make this equation hold. For example:

[tex](x,y)=(69,-287.25) \\ (x,y)=(1,69.75) \\ (x,y)=(7,38.25)[/tex]

This could go on forever, so your question does not have a right answer.

The total revenue the previous year is $20,000

This year the total revenue of the small  business is $14,200

This amount is 29% less than the total revenue in the previous year

Therefore the total revenue in the previous year can be calculated as follows

100 - 29

= 71

= 71/100

= 0.71

Total revenue= 14,200/0.71

= 20,000

Hence the total revenue the previous year is $20,000

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The answer would be 0.0078

The decimal number 0.00784 rounded off to 2 decimal places is 0.

We round off numbers to make them easier to remember and it also keeps its value approximately to the place it has been rounded off.

To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.

Given, 0.00784 and we have to round off to two significant figures means

the number will have 2 digits after the decimal place.

Now, 0.00784

= 0.00780.

= 0.0078.

= 0.0080.

= 0.008.

= 0.010.

= 0.01.

= 0.00.

= 0.

So, 0.00784 rounded off to 2 decimal places is 0.

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P(A) = 4 / 20, this is the probability that a customer has enough cash

P (B) =16 / 20, this is the probability that a customer has a credit card.

P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.

The probability that a customer has enough cash or a credit card is 0.85.

Probability is defined as the ratio of favorable outcomes to a total number of outcomes.

It is given that, 20 customers are eating dinner at a local restaurant.

The total number of customers = 20

Of the 20 customers,

4 have enough cash to pay for their meal

16 have a credit card and

3 have enough cash and a credit card.

Event A is the probability that a customer has enough cash

Event B is the probability that a customer has a credit card.

P(A) = 4 / 20 = 1 / 5, this is the probability that a customer has enough cash

P (B) =16 / 20 = 4 / 5, this is the probability that a customer has a credit card.

P (A and B) = 3 / 20, this is the probability that a customer has enough cash and a credit card.

To find the probability that a customer has enough cash or a credit card :

The formula used is P(A or B) = P(A) + P(B) - P(A∪B)

P (A or B) = P(A) + P(B) - P (A and B)

                = 4 / 20 + 16 /20 - 3 / 20

                = 17 / 20

                = 0.85

Therefore, The probability that a customer has enough cash or a credit card is 0.85.

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0 is a counterexample to Kelvin's conjecture.

Firstly rewriting the expression -

x²>x + 1

Now, we will use hit and trial method to find the counterexample to Kelvin's conjecture.

We can not use first two options, because question mentions that x is not negative. So, starting our hit and trial method from 0.

We will keep the value in expression to find the result -

0²>0 + 1

0 > 1

This contradicts or opposes Kevin's statement, as 0 is not greater than 1.

Trying the second number -

5²>5 + 1

25 > 6

This is in accordance with Kevin's conjecture or conclusion, as 25 is greater than 6.

Hence, 0 is the value which is a counterexample to Kelvin's conjecture.

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The complete question is -

Given that x is a number that is not negative, Kelvin conjectured that x^2>x+1 .

Which value is a counterexample to Kelvin's conjecture?

−12

−2

0

5

The meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.

According to the task content, it follows that the meaning and equivalent of seven-tenths of half of a century is to be determined.

On this note, since it follows from place value that seven-tenths means; 7 × (1/10) = 7/10.

Also, since half a century means; (1/2) × 100 years = 50 years.

Ultimately, the word phrase given in the task content is equivalent to;

= (7/10) × 50 years.

= 35 years.

Ultimately, the meaning and equivalent of the word phrase; seven-tenths of half a century as given in the task content is; 35 years.

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Answer:  E

Step-by-step explanation:

4 x 4 = 16

7 x 7 = 49

16 + 49 = 65

8.062 is the square root of 65.

Round 8.062 I guess you could round it to 9 but I believe the actual answer should be 8.

Answer: 0.0016

Step by step explanation:

Answer:

=1/5⁴ = 1/625

Step-by-step explanation:

(1/5)² (1/5)² = (1/5)⁴

= 1⁴ / 5⁴

= 1 / 625