If AC = 13 and AB = 5 and BC = 12, calculate m angle C in degrees. Round to two decimal places.

The value of \(log_35 \times log_{25}9\) is 1.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

\(log_35 \times log_{25}9\)

\(log_ab = \frac{logb}{loga}\)

So,

= log 5 / log 3 x log 9 / log 25

= log 5 / log 3 x log 3² / log 5²

\(logm^n = n~logm\)

So,

= log 5 / log 3 x log 3² / log 5²

= (log 5 / log 3) x (2 log 3 / 2 log 5)

= (log 5 / log 3) x (log 3 / log 5)

= 1

Thus,

1 is the value.

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Answer:

A. 5:4

Step-by-step explanation:

Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.

There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.

To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.

Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):

Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.

Therefore, the probability that a randomly selected student scored A or B

in Biostatistics is:

Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.

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Based on the number of seats on the balcony, the number of seats in the theatre are 600 seats.

The balcony is said to have 120 seats and these are 1/5 of the total seats in the theatre.

The total number of seats in the theatre are:

= Number of seats on balcony / Proportion of seats this represents

Solving gives:

= 120 ÷ 1/5

= 120 ÷ 0.2

= 600 seats

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Answer:

y=-1

x=-3

Step-by-step explanation:

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Answer:

44.125 inches

Step-by-step explanation:

Given that:

Length of picture = 32 1/2 inches

Length of wall = 120 3/4 inches

Hence, to center picture horizontally ;

Distance from the edge of the wall in which the picture should be placed :

(Length of wall - length of picture) / 2

(120 3/4 - 32 1/2) / 2

(483/4 - 65/2) / 2

Take the L. C. M of 4 and 2 = 4

((483 - 130) / 4) ÷ 2

(353 / 4) ÷ 2

(353 / 4) * (1 / 2)

= 353 / 8

= 44 1/8

= 44 1/8

= 44.125 inches

The space that will be left in each side of the picture from the edge of the wall if Jon is to hang the picture at the center of the wall horizontally is: 44.125 inches.

The wall that Jon wants to hang the picture has been sketched in the diagram attached below (see attachment).

Given the following:

Therefore, the following equation can be derived as follows:

\(2x + 32.5 = 120.75\)

\(2x = 120.75 - 32.5 \\\\2x = 88.25\\\\x = \frac{88.25}{2} \\\\\mathbf{x = 44.125 $ inches}\)

Therefore, the space that will be left in each side of the picture from the edge of the wall if Jon is to hang the picture at the center of the wall horizontally is: 44.125 inches.

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Answer:

answer is D

x = -4±√4^2 - 4(3)(5)

               2(3)

Step-by-step explanation:

ax^2 + bx + c = 0

3x^2 + 4x + 5 = 0

x = -b ±√b^2 - 4ac

             2(a)

x = -4±√4^2 - 4(3)(5)

               2(3)

Answer:

The last choice is correct.

Step-by-step explanation:

Use only the coefficients and the constant, a, b & c. not the variable x.

Answer:

If a negative number is multiplied with a positive number, the result will be negative. If two positive numbers are multiplied, the result will be positive. If two negative numbers are multiplied, the result will also be positive.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

B 10x+5

Step-by-step explanation:

:)

Answer:

A parallelogram with congruent diagonals, a parallelogram with a right angle, a parallelogram with perpendicular diagonals.

Step-by-step explanation:

By definition, a rectangle is nothing but a parallelogram with one right angle. One of the properties of a rectangle is that its perpendiculars are congruent. Finally, the diagonals of a rectangle are congruent (this can be proved by finding congruent triangles split by the diagonals, using CPCTC, etc.).

Answer:

By getting head's 12 times

Step-by-step explanation:

Answer:

11C9 = 55

11! / [9!(11 - 9)!]

39916800 / (362880 * 2)

39916800 / 725760

55

Step-by-step explanation:

Answer:

the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Step-by-step explanation:

The probability of selecting a quarter or a nickel can be found by adding the probability of selecting a quarter to the probability of selecting a nickel. Since the coins are chosen randomly, the probability of selecting a coin from the jar is the number of coins of that type divided by the total number of coins in the jar.

So, the probability of selecting a quarter is:

P(quarter) = number of quarters / total number of coins

P(quarter) = 80 / (70 + 100 + 80 + 50)

P(quarter) = 0.32

Similarly, the probability of selecting a nickel is:

P(nickel) = number of nickels / total number of coins

P(nickel) = 70 / (70 + 100 + 80 + 50)

P(nickel) = 0.175

To find the probability of selecting a quarter or a nickel, we add these probabilities:

P(quarter or nickel) = P(quarter) + P(nickel)

P(quarter or nickel) = 0.32 + 0.175

P(quarter or nickel) = 0.495

Therefore, the probability of selecting a quarter or a nickel is 0.495 or 49.5%.

Answer:

I think the answer is 24

Step-by-step explanation:

Answer:

First write all the data that you have.

Then make pairs.

Step-by-step explanation:

He can make 2 more pairs and the remaining things will be 2 lips and 2 noses.

Hope This Is Useful.

Car Make and Model that i choose is Toyota RAV4

The Cost of this car as of today is about $27,000

To know the value of car after one year will be:

20% of $27,000

= $5,400.

So the car  value will be:

$27,000 - $5,400

= $21,600 after year 1

3.  Value of car after second year of ownership:

15% of $27,000

= $4,050.

So, the car  value will be:

$21,600 - $4,050

= $17,550 after year 2.

4 The Exponential Function If the car continues to decrease in value by 15% each yea will be

V(x) = 27,000 x (0.85)ˣ

V(5) = 27,000 x (0.85)⁵

= 27,000  x  0.44370

= $11979.9

Therefore, the value of the car after owning it for five years is  $11979.9

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See text below



Car Value: Exponential

1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.

Car Make and Model:

Cost of this car as of today:

2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?

Value of car after one year:

3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?

Value of car after second year of ownership:

4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.

Exponential Function:

Use your exponential function to calculate the predicted value of your car after you own it for five years.

Value after five years of ownership:

I believe it's 5! Hope this helps!

Answer:

5

Step-by-step explanation:

5 / 1 = 5

10 / 2 = 5

15 / 3 = 5

20 / 4 = 5

Answer:

A = 19

Step-by-step explanation:

A - 6 = 13

19 - 6 = 13

A = 19

I hope this helps!

Answer:

19

Step-by-step explanation:

13 + 6 = 19

19 - 6 = 13

Answer:

Pull terms out from under the radical, assuming positive real numbers.

0

Step-by-step explanation:

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$21000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}\)

\(A=21000\left(1+\frac{0.07}{12}\right)^{12\cdot 20}\implies A=21000\left( \frac{1207}{1200} \right)^{240}\implies A\approx 84813.52\)

The mean for the number of people with the genetic mutation in such groups of 600 is 18.

Given that,

About 3% of the population has a particular genetic mutation.

This means that for any group of people, 3% of the people has a particular genetic mutation.

This is a binomial distribution.

Probability that people having genetic mutation = 3% = 0.03

Random sample size = 600

Mean for a binomial distribution can be calculated as,

Mean = n × p

         = 600 × 0.03

         = 18

Hence the mean number of people having genetic mutation is 18.

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The probability that all fail on their first submissions is 27.1%.


For each student, there are only two possible outcomes. Either their first program run will fail, or it wont. The probability of the first program run of a student failing is independent of the first program run of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.


In which  is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

The expected value of the binomial distribution is

The variance of the binomial distribution is

The standard deviation of the binomial distribution is

In this question, we have that:

83% of all students taking a beginning programming course fail to get their first program to run on first submission. Sample of 7 students. This means that

All fail on their first submissions

So,

0.271 = 27.1% probability that all ail on their first submissions

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Answer:

p(x) = x^2 - 8x + 41

Step-by-step explanation:

If a polynomial with rational coefficients has a complex root, then the roots come in complex conjugate pairs. If the polynomial we need to find has the root 4 - 5i, then it must also have its complex conjugate 4 + 5i as a root.

p(x) = [x - (4 - 5i)][x - (4 + 5i)]

p(x) = [(x - 4) + 5i][(x - 4) - 5i]

Now it's a difference of two squares.

p(x) = (x - 4)^2 - (5i)^2

p(x) = x^2 - 8x + 16 + 25

p(x) = x^2 - 8x + 41

The expression for the area of frame is 4x² + 24x + 35

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.

Here, Old length of photograph = 5 inch

          Old width of photograph = 7 inch

Now, length of new photograph = (5 + 2x) inch

        width of new photograph = (7 + 2x) inch

Now, Area of frame with new dimension = Length X breadth

                                                                     = (5+2x) X (7+2x)

                                                                     = 5(7+2x) + 2x(7+2x)

                                                                    = 35 + 10x + 14x + 4x²

                                                                    = 4x² + 24x + 35

Thus, the expression for the area of frame is 4x² + 24x + 35.

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Answer: 3.6

Step-by-step explanation:

According to the graph:

The number of almonds in jaars from Brand X tends to be greater and less consistent than Brand Y