If the measure of angle A is 27 degrees, what is the measure of angle 'B'?

The correct answer is:  " [tex]\frac{16}{21}[/tex] " .

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Step-by-step explanation:

" [tex]2\frac{2}{3}[/tex]  ÷ [tex]3\frac{1}{2}[/tex] "  =  

               " [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex]   "  ;

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" [tex]2\frac{2}{3} = \frac{[(3*2)+2]}{3} = \frac{(6+2)}{3} = \frac{8}{3}[/tex]  " .

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" [tex]3\frac{1}{2} = \frac{[(2*3)+1]}{2} = \frac{(6+1)}{2} = \frac{7}{2}[/tex]  " .

_______

→  "  [tex]\frac{(2\frac{2}{3})}{(3\frac{1}{2})}[/tex]  " ;

          [tex]} = \frac{8}{3}[/tex] ÷ [tex]\frac{7}{2}[/tex]  ;

Note that "dividing by a value"  results in the same value as "multiplying by the reciprocal of that value" ;

  The reciprocal of:  " [tex]\frac{7}{2}[/tex] " ;  is:  " [tex]\frac{2}{7}[/tex] " ;

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         [tex]= \frac{8}{3} *\frac{2}{7}= \frac{(8*2)}{(3*7)} = \frac{16}{21}[/tex] ;  which cannot be further reduced as a fraction.

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The correct answer is:  " [tex]\frac{16}{21}[/tex] " .

_______

Hope this is helpful!

 Best wishes to you!

_______

Answer:

(1,-9)

Step-by-step explanation:

During rotation anytime you rotate the figures the arrangement will change and also since you are rotating to 270 counter-clockwise(anti-clockwise)your answer will be (1,-9)

Answer: The correct answer is -1,9

Step-by-step explanation:

270 rule - (x, y) ⇒ (y, -x)

(-9, -1) ⇒ (-1, 9)

Answer:

3x4=12 is the same as

4x3=12 and

12/3=4 and

12/4=3

The commutative property of multiplication is true for the expression 4 x 3 = 3 x 4 = 12.

Multiplication is one of four mathematical arithmetic operations.

It is also a process of adding the same types of expression for some number of times.

The repeated addition is multiplication.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

The commutative property of multiplication:

Let a and b are the two numbers.

And the product of a x b is n.

So,  a x b = b x a = n

Changing the numbers position does not affect the result.

Here,

3 x 4 = 4 x 3

12 = 12

This expression holds the commutative property of multiplication.

Therefore, 3 x 4 = 12 holds the commutative property.

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Answer:

-x-x-0.7

is equivalent to 1-2x-1.7

There was 4 boys and 11 girls in the class.

Let x represent the number of boys and y represent the number of girls.

Since the number of girls in the class was 1 less than 3 times the number of boys, hence:

y = 3x - 1

3x - y = 1         (1)

Also, there were 15 students in all, hence:

x + y = 15        (2)

Solving equations 1 and 2 simultaneously gives:

x = 4, y = 11

Hence, there was 4 boys and 11 girls in the class.

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Answer:

2750 pages

Step-by-step explanation:

but i am not sure how many books exactly .

Answer:

.(0,4,3,1,2,5)..............

Probabilities are used to determine the chances of an event

(a) Probability that a person is sick

From the table, we have:

[tex]\mathbf{Sick = 59+1 = 60}[/tex]

So, the probability that a person is sick is:

[tex]\mathbf{Pr = \frac{Sick}{Total}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{60}{7500}}[/tex]

[tex]\mathbf{Pr = 0.008}[/tex]

The probability that a person is sick is: 0.008

(b) Probability that a test is positive, given that the person is sick

From the table, we have:

[tex]\mathbf{Positive\ and\ Sick=59}[/tex]

So, the probability that a test is positive, given that the person is sick is:

[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{59}{60}}[/tex]

[tex]\mathbf{Pr = 0.9833}[/tex]

The probability that a test is positive, given that the person is sick is 0.9833

(c) Probability that a test is negative, given that the person is not sick

From the table, we have:

[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]

[tex]\mathbf{Not\ Sick = 75 + 7365 = 7440}[/tex]

So, the probability that a test is negative, given that the person is not sick is:

[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{7365}{7440}}[/tex]

[tex]\mathbf{Pr = 0.9899}[/tex]

The probability that a test is negative, given that the person is not sick is: 0.9899

(d) Probability that a person is sick, given that the test is positive

From the table, we have:

[tex]\mathbf{Positive\ and\ Sick=59}[/tex]

[tex]\mathbf{Positive=59 + 75 = 134}[/tex]

So, the probability that a person is sick, given that the test is positive is:

[tex]\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{59}{134}}[/tex]

[tex]\mathbf{Pr = 0.4403}[/tex]

The probability that a person is sick, given that the test is positive is: 0.4403

(e) Probability that a person is not sick, given that the test is negative

From the table, we have:

[tex]\mathbf{Negative\ and\ Not\ Sick=7365}[/tex]

[tex]\mathbf{Negative = 1+ 7365 = 7366}[/tex]

So, the probability that a person is not sick, given that the test is negative is:

[tex]\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}[/tex]

This gives

[tex]\mathbf{Pr = \frac{7365}{7366}}[/tex]

[tex]\mathbf{Pr = 0.9998}[/tex]

The probability that a person is not sick, given that the test is negative is: 0.9998

(f) When a test is 99% accurate

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.

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Answer:

12

Step-by-step explanation:

13x-21=5x+75

8x=96

x=96/8=12

Answer:

x=12

Step-by-step explanation:

Since the 2 lines are parallel we can use the rules of transversals. These 2 angels are alternate side interior. This means that they are congruent and have the same measurement. Because they have the same measurement, we can set them equal to each other and solve for x.

13x-21 = 5x+75

13x = 5x+96

8x = 96

x=12

Answer:

96Consider the arithmetic sequence with a first term of 11 and sixth term of 21. What is the

sum of these first six terms?

The required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.

Given that,
Consider the arithmetic sequence with the first term of 11 and the sixth term of 21. To determine the sum of these first six terms.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
First term a = 11
6th term = a + 5d
21 = 11 + 5d
5d = 10
d = 2
Now,
sum of the six terms, = 6 / 2{11 + 21}
                                   = 3 (32)
                                   = 96

Thus, the required sum of the first 6th term of an arithmetic progression is 96. Option D is correct.

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(t^3-t)/a=b because a t the simple of questions

Answer:

Step-by-step explanation:

The domain is the x value between - 5 and 7

The range is the y value between -2 and 6

You can find all sorts of definitions for the domain and range, but in this example it is really straight forward.  If you put - 5 into the function, you get -2. If you put 7 into the function, you get 6. Now just draw a line between the two end points.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The point at the left end of the domain is not included in the function, but the function includes the limits of its range. One such function is shown in the attachment.

Answer:

54

Step-by-step explanation:

6/100 = x/90

6×90=540

540/100=54

Answer:

Step-by-step explanation:

1 bowl holds 5 fish

x bowls hold 263 fish

1/x = 5/263                      Cross multiply

5x = 263                         Divide by 5

5x/5 = 263/5

x = 52.6

So you actually need 53 fishbowls. One of them holds only 3 fish

Answer:

0.0026

I don't know how to add the work here

Answer:

24.5 pounds

Step-by-step explanation:

0.176*139= 24.5

Answer: the answer is 19

Step-by-step explanation:okay so she already have read 119 pages and the total pages is 271 so we substract 271-119=152 so she has 152 pages left so we divide 152 pages divided by 8 because she read 8 pages per hour so 152/8=19

Answer:

1 yard = 3 feet

We can re-write this by dividing both sides by yards or feet to get

1 = 3 feet / 1 yard

or

1 yard / 3 feet = 1

Since we're solving for feet we want yards to cancel, so use the top proportion

(3 feet / 1 yard)(100 yards) = 300 feet / 1 = 300 feet

Using compound interest, it is found that it will take 11.28 years for the the account to grow to $4500.

The compound interest formula is given by:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

A(t) is the amount of money after t years.

P is the principal(the initial sum of money).

r is the interest rate(as a decimal value).

n is the number of times that interest is compounded per year.

t is the time in years for which the money is invested or borrowed.

In this problem:

We have to solve for t when [tex]A(t) = 4500[/tex], thus:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]4500 = 3000(1 + \frac{0.036}{12})^{12t}[/tex]

[tex](1.003)^{12t} = 1.5[/tex]

[tex]\log{(1.003)^{12t}} = \log{1.5}[/tex]

[tex]12t\log{1.003} = \log{1.5}[/tex]

[tex]t = \frac{\log{1.5}}{12\log{1.003}}[/tex]

[tex]t = 11.28[/tex]

It will take 11.28 years for the the account to grow to $4500.

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Answer: 33

Step-by-step explanation: Let x equal the shorter piece.

x + (x + 18) = 84

2x + 18 = 84

2x = 66

x = 33

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therefore, the Correct choice is d) 15

Answer:

y=-x-6

Step-by-step explanation:

First, you have to distribute the - that is outside the parentheses. That leaves you with -x-4. So now your equation is y+2=-x-4. You want the y by itself so you subtract two from both sides leaving you with y=-x-4-2, which adds up to y=-x-6.

Answer:

I'm not sure I'm only in middle school, but I'll put what I know.

Step-by-step explanation:

Step 1: Calculate the minor for the given matrix.

Step 2: Turn the obtained matrix into the matrix of cofactors.

Step 3: Then, the adjugate, and.

Step 4: Multiply that by reciprocal of determinant.

Answer:

B 33

Step-by-step explanation:

Answer:

85 sodas

Step-by-step explanation:

Total sold was 127

The number of sodas was 43 + the number of hotdogs

Let x represent hotdogs:

x + (43 + x) = 127                (The 43 + x is the number of sodas sold.)

2x + 43 = 127

2x = 84

x = 42

42 hotdogs were sold., Since sodas are 42 + 43, 85 sodas were sold

-Chetan K

Step-by-step explanation:

Find the sides and perimeter:

Perimeter:

Find the area using shoelace formula: