Express log 161 in the form of loga + logb.

Answer:

40

Step-by-step explanation:

2x² - 5y + 7 when x = 2 and y = -5

2(2)² - 5(-5) + 7

= 2(4) -5(-5) + 7

= 8 + 25 + 7

= 40

Therefore, Kallie will need to use a total of 6 teaspoons of water conditioner for all the water in 12 fish tanks.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign, with the expression on the left being equal to the expression on the right. Equations are used to represent various relationships and situations in mathematics and other fields, and are solved to find the values of variables that make the equation true.

Here,

First, we need to determine the total amount of water in all 12 fish tanks. Since each fish tank is filled with 20 quarts of water, the total amount of water in all 12 fish tanks is:

12 fish tanks * 20 quarts per fish tank = 240 quarts of water

To convert quarts to gallons, we divide by 4 (since there are 4 quarts in a gallon):

240 quarts / 4 quarts per gallon = 60 gallons of water

Now, we can use the given conversion factor to determine how many teaspoons of water conditioner are needed for 60 gallons of water. Since for every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, for 60 gallons of water, she will use:

60 gallons / 10 gallons per teaspoon = 6 teaspoons of water conditioner

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Answer:

$43

Step-by-step explanation:

Multiply 1.75 and 8 which equals 14

2.00 times 13 is 26

.25 times 12 is 3

Add 'em all up and you get $43(before dividing them up in thirds)

If you divide them by 3 each third is 14.33 repeating.

Answer:

Does the table show evidence of an association between not taking piano lessons and not attending an Ivy League school? From the table, the joint relative frequency for people who did not take piano lessons and who did not attend an Ivy League school is the greatest

Answer:

A

Step-by-step explanation:

Answer: All I want for Christmas is you lyrics lol

I don't want a lot for Christmas

There is just one thing I need

I don't care about the presents

Underneath the Christmas tree

I just want you for my own

More than you could ever know

Make my wish come true

All I want for Christmas is you, yeah

I don't want a lot for Christmas

There is just one thing I need

And I don't care about the presents

Underneath the Christmas tree

I don't need to hang my stocking

There upon the fireplace

Santa Claus won't make me happy

With a toy on Christmas Day

I just want you for my own

More than you could ever know

Make my wish come true

All I want for Christmas is you

You, baby

Oh, I won't ask for much this Christmas

I won't even wish for snow

And I'm just gonna keep on waiting

Underneath the mistletoe

I won't make a list and send it

To the North Pole for Saint Nick

I won't even stay awake to

Hear those magic reindeer click

'Cause I just want you here tonight

Holding on to me so tight

What more can I do?

Baby, all I want for Christmas is you

You, baby

Oh, all the lights are shining so brightly everywhere

And the sound of children's laughter fills the air

And everyone is singing

I hear those sleigh bells ringing

Santa, won't you bring me the one I really need?

Won't you please bring my baby to me?

Oh, I don't want a lot for Christmas

This is all I'm asking for

I just wanna see my baby

Standing right outside my door

Oh, I just want you for my own

More than you could ever know

Make my wish come true

Baby, all I want for Christmas... is you

You, baby

All I want for Christmas is you, baby

All I want for Christmas is you, baby

All I want for Christmas is you, baby

All I want for Christmas is you, baby

All I want for Christmas is you, baby

Step-by-step explanation:

Answer:

207

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

10 plus 13 equals 23, so if it is more than that than the lines wont be able to connect. if it is 23 exactly, the triangle will be a stright line, not a triangle, so it is 22.

Answer:

22

Step-by-step explanation:

triangle inequality theorem:

10 + 13 > x

x < 23

10 + x > 13

x > 3

third side:  3 < x < 23

The point (2,-4) satisfies y < 3x - 6

Answer:

10) x= -5

Step-by-step explanation:

you want to do the opposite of the 10 to get it to the other side. in this case that would be to subtract 10 from both sides. you should get 4x= -20. then you divide 4 by both sides and you get your answer

Answer:

1. Is a continuous random variable

2. Is a discrete random variable

3. Is not a random variable

Step-by-step explanation:

1. The exact Weight of quarters in circulation in the united states is a continuous random variable. This is because a random variable such as this can take uncountable and infinite number of values.

2. The shoe sizes if humans is an example of discrete random variable. This is a discrete random variable because it has countable number of values.

3. Political party affiliation is not a random variable.

Thank you!

The solution of inequalities is  y≤\(\frac{1}{2}\)x +2 and y> 2x-1.

What is inequality?

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given inequalities is x-2y≥-4 and 2x-y<1.

=>  x-2y+4≥-4+4   and   2x-y +(-1)<1-1

=> x-2y+ 4 ≥ 0 and 2x-y-1<0

=> 2y ≤x+4 and y > 2x-1

=> y≤\(\frac{1}{2}\)x +2 and y> 2x-1

Hence the solution of the inequalities is  y≤\(\frac{1}{2}\)x +2 and y> 2x-1.

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Answer:

2/15

Step-by-step explanation:

Answer:

2/15

Step-by-step explanation:

12 & 18 can be reduced to 2 & 3

25 & 5 can be reduced to 5 & 1

2/5 × 1/3 = 2/15

Answer:

2/10 + 30/100 = 50/100

Step-by-step explanation:

First, you want to multiply 2/10 by 10, to get the same common denominator in both numbers, you would get 20/100. Then, its pretty simple from there, you just add the number that gets you to 50, which is 30, 20 + 30 =50. I Hope This Helps :)

The required missing number is 30. So, the correct answer is (a) 30.

Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division.

Here,
To find the missing number, we can use the fact that 50/100 is equivalent to 1/2.

So, we need to find a number that, when added to 2/10, gives 1/2 as the sum.

We can write this as an equation:

2/10 + x/100 = 1/2

Multiplying both sides by 100 to eliminate the denominator, we get:

20 + x = 50

Subtracting 20 from both sides, we get:

x = 30

Therefore, the missing number is 30. So, the correct answer is (a) 30.

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

The formation of the equation is odd, but I assume it's supposed to be:
4k - 10k = -8k

-6k = -8k
-6k + 8k = -8k + 8k
2k = 0
\(\frac{2k}{2}\) = \(\frac{0}{2}\)
k = 0

Answer:

The student will have 130 dollars in the bank at the end of week 11.

Step-by-step explanation:

Pattern:

The pattern given by this graphic is that:

For each passing week, the student will have $10 more in the bank than at the end of the previous week. So, following this pattern:

At the end of 6 weeks, he will have $80.

At the end of 7 weeks, he will have $90.

At the end of 8 weeks, he will have $100.

At the end of 9 weeks, he will have $110.

At the end of 10 weeks, he will have $120.

At the end of 11 weeks, he will have $130.

The student will have 130 dollars in the bank at the end of week 11.

Answer:

Step-by-step explanation:

scam . smď

Since my friend says that all multiples of 3 are also multiples of 6. My response is Yes, My friend is correct because all multiples of 3 are also multiples of 6.

For every multiple of 3, one will find the multiple of 6. The fact remains that students will need to known that all multiples of 6 can also be said to multiples of 3 due to the fact that 3 is seen and is a factor of 6.

The multiples of 3 are: 3,6,9,12,15,18,21,24,27,30.

The multiples of 6 are: 3,6,9,12,15,18,21,24,27,30.

Therefore, based on the fact that my friend says that all multiples of 3 are also multiples of 6. My response is that my friend is correct because all multiples of 3 are also multiples of 6.

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Answer:

A

Step-by-step explanation:

As 2 < a < 5, only option A suffices this condition, because 2 < 3 < 5.

Answer:

yes it is a dilation

Step-by-step explanation:

a dilation makes the size different but shape the same. as we can see the shape is the same meaning this is a non rigid motion or called a dilation.

Answer:

C.1%

Step-by-step explanation:

The probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

To find the probability that a student got an 'A' given they are male, we need to use Bayes' theorem:

P(A | Male) = P(Male | A) × P(A) / P(Male)

We can find the values of the terms in the formula using the information given in the table:

P(Male) = (25/54) = 0.46 (the proportion of all students who are male)

P(A) = (17/54) = 0.31 (the proportion of all students who got an 'A')

P(Male | A) = (3/17) = 0.18 (the proportion of all students who are male and got an 'A')

Therefore, plugging these values into the formula:

P(A | Male) = 0.18 × 0.31 / 0.46

P(A | Male) ≈ 0.12

So the probability that the student got an 'A' given they are male is approximately 0.12 or 12%.

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The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

7.18421051

Step-by-step explanation:

76 ÷ 6 = 12.6666667

91 ÷ 12.6666667 = 7.18421051

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Answer:

a9 = 42

Step-by-step explanation:

Thats the correct answer

you just have to add +7 until the 9 term for a easier way

Answer: log7 21 /  log7 5

I took one for the team and guessed, and got it right.

You are welcome future students.

The expression that correctly shows how to rewrite the logarithm \(\log_5{21}\), using a logarithm of base 7, with change of base, is given as follows:

\(\frac{\log_7{21}}{\log_7{5}}\)

To change the base of a logarithm, a new fraction is written, in which:

In this problem, the logarithm that will be calculated is:

\(\log_5{21}\)

Hence the number and the base of the logarithm are presented as follows:

With the change of the base to base 7, the numerator and the denominator of the fraction are given as follows:

Hence the simplified logarithm is presented as follows:

\(\frac{\log_7{21}}{\log_7{5}}\)

Meaning that the correct option is the second option.

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Answer:

- Discount car rentals charges less daily

- After 3 days

Step-by-step explanation:

Required

Which charges less per day

When is the total cost the same

First, calculate the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

From the table, we have:

\((x_1,y_1) = (2,185)\)

\((x_2,y_2) = (6,345)\)

So, we have:

\(m = \frac{345 - 185}{6 - 2}\)

\(m = \frac{160}{4}\)

\(m = 40\)

The equation is then calculated as:

\(y = m(x - x_1) + y_1\)

\(y = 40(x - 2) + 185\)

\(y = 40x - 80 + 185\)

\(y = 40x + 105\)

So, the equation of the table (i.e. Discount Car rental) is: \(y = 40x + 105\)

While the equation of Pay Less is: \(y = 55x + 60\)

The company that charges less per day has the smaller slope and that is: Discount car rental because the slope (40) is less than the slope (55)

For the total cost to be the same, we simply equate both expressions:

i.e.

\(y = y\)

\(55x + 60 = 40x + 105\)

\(55x - 40x = - 60 + 105\)

\(15x =45\)

\(x = 3\)

Answer:

3 costumers per minutes

Step-by-step explanation:

Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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