The width and length of the bulletin board are whole numbers what is the width of the bulletin board if the length is 4 feet

Answer:

2/5 thx for the points

Step-by-step explanation:

Answer:

Option A. [tex]cot\theta = -1[/tex]

Step-by-step explanation:

[tex]\frac{tan^{3}\theta -1}{tan\theta -1}-sec^{2}\theta +1=0[/tex]

we have to the value of [tex]cot\theta[/tex]

We further solve the equation

[tex]\frac{(tan\theta -1)(tan^{2}\theta +1+tan\theta )}{(tan\theta -1)}-sec^{2}\theta+1=0[/tex]         [a³- b³= (a-b)(a² + b²+ ab)]

[tex]sec^{2}\theta +tan\theta -sec^{2}\theta +1=tan\theta +1=0[/tex]

[tex]\frac{1}{cot\theta }=-1[/tex]

[tex]cot\theta = -1[/tex]

Therefore Option A. [tex]cot\theta = -1[/tex] is the answer.

(a) All the possible outcomes of the compound event are {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}

(b) Probability is 2/3.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

Given that,

At a fair, each person can spin two wheels of chance.

The first wheel has the numbers 1, 2, and 3.

The second wheel has the letters A and B.

(a) 1 can be followed by A and B, 2 can be followed by A and and B and so is 3.

Possible outcomes = {(1, A), (1, B), (2, A), (2, B), (3, A), (3, B)}

(b) Total possible outcomes = 6

Number of outcomes which has either 1 or A = 4

Probability = 4/6 = 2/3

Hence the required probability is 2/3.

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It says "No more than 8 books are in your bag". Here "Not more than" a specific number would be a set of all values that are "less than or equal" to given number.  

So let's consider 'n' represents the number of books in the bag and we know this number can not be a negative value i.e. n is "greater than or equal" to 0.

Also n is "less than or equal" to 8 as given in the question.

Hence, the inequality would be 0 ≤ n ≤ 8.

Let the dog's age be called x.

From the given statement, the following equation can be framed

Cat's age = 2*x -5

We are given to know that Cat's age is 11 years

So, we have:

11 = 2x -5

2x = 16

x = 16/2

x = 8

Dog's age = 8 years

Answer:

18 units

Step-by-step explanation:

[tex]\pi r^2=81\pi[/tex]

Solve for [tex]r[/tex]:

[tex]\pi r^2=81\pi \\r^2=81\\r=9[/tex]

Knowing diameter is 2*r, we can apply the formula to find diameter

[tex]d=2*r\\d=2*9\\d=18[/tex]

The experimental probability of Brandy rolling a strike in the first frame of the next game is 1/2.

To find the experimental probability that Brandy will roll a strike in the first frame of the next game, we need to divide the number of times Brandy rolled a strike in the first frame by the total number of frames. In this case, Brandy rolled a strike in 5 out of 10 frames, so the experimental probability is 5/10, which simplifies to 1/2.

y = 5 is the equation of the horizontal line that passes through the point (-2,5).

Mathematically, an equation is a statement that two expressions are equal. The expressions on either hand of the equals sign are termed the left-hand side and the right-hand side of the equation. The equals sign is perused as" is equal to" or" equals".

An equation comprises variables, numbers and comparison sign.

As the ordinate of the given point is 5 then y = 5 is the horizontal line that passes through (-2,5).

Thus, the equation that passes through the point (-2,5) and is the horizontal line is y = 5.

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Answer:

is greater for data set 2 ; is greater for data set 2

Step-by-step explanation:

The range is found by subtracting the highest and lowest value.  The range of the first plot would be

34-21 = 13.

The range of the second plot would be

36-12 = 24.

The mean is found by adding together all of the data points and dividing by the number of data points.  For the first plot, the sum of the data is 274 and there are 10 data points; this makes the mean 274/10 = 27.4.

For the second plot, the sum of the data is 280.5 and there are 10 data points; this makes the mean 280.5/10 = 28.05.

The range is greater for data set 2.

Then mean is greater for data set 2.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Consider the data plot for 13 to 15 years olds.

Mean = Average of the values

          = (21 + 24 + 26 + 27 + 27 + 28 + 28 + 28 + 31 + 34) / 10

          = 27.4

Range = Maximum value - Minimum value

           = 34 - 21

          = 13

Consider the data plot for 16 to 18 years olds.

Mean = Average of the values

          = (12 + 21 + 28 + 28 + 28 + 28 + 30.5 + 34 + 35 + 36) / 10

          = 28.05

Range = Maximum value - Minimum value

           = 36 - 12

          = 24

Hence the range and mean are greater for data set 2.

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The number of the times cube is rolled for getting less than three is 8.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability of getting less than three = 2 / 6 = 1 / 3

The number of the times cube rolled is,

Pn = ( 1 / 3 ) x 24 = 8

Therefore, the number of the times cube is rolled for getting less than three is 8.

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1. The probability P of an event and its complement P' are mutually exclusive and add up to 1

2.  If the probability of an event is 0.3, then the probability of its complement is 0.7.   (1 - 0.3 = 0.7)

Answer:

[tex]( \frac{36n^{2} }{25} - 1) [/tex] factors to become [tex]( \frac{6}{5}n - 1)( \frac{6}{5}n + 1) [/tex]

Explanation:
The binomial [tex]( \frac{36n^{2} }{25} - 1) [/tex] is what is called a difference of two squares which can be identified by the equation being in the form (a² - b²) where both terms can be square-rooted.

Because the equation is a difference of two squares, its factors will be in the form: (a - b)(a + b).

With a² = [tex]\frac{36n^2}{25}[/tex] and b² = 1, we can find the square root of both and plug them into the above factor form.

√(36n² / 25) = 6n/5
√1 = 1

So the factors are [tex](\frac{6}{5}n -1)(\frac{6}{5}n +1)[/tex]

Answer: 537

Step-by-step explanation:

Given: a = 640 A =70° B =52°

Whenever two angles and one side of a triangle is given, we can always use the sine formular to find the other side

Using the sine formula;

sin A / a = sin B /b

sin70° / 640 = sin 52° / b

cross multiply

bsin70° = 640sin52°

To get b, we divide bothside by

sin 70°

b = 640sin52° / sin 70°

b = 504. 327 / sin70°

b = 536. 693

b = 537 to the nearest whole number

How far are 27 and -54 apart on the number line?

Solution:

If we see on the number line , 27 is 27 units apart from 0 and it is 27 units to the right of 0

And, -54 is 54 units apart from 0 and it is 54 units to the left of 0. So, -54 is in opposite direction with respect to 27.

So, To find how far is 27 from -54 we must add 27 and 54

As, 27+54=81

So, -54 and 27 are 81 units away from each other.

Answer:81 units

Please see the number line attached.