the least positive value of x for which csc x= -1
A. π/2
B. π
D. 1
E. 3π/2
F. -1

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's solve ~

\(\qquad \sf  \dashrightarrow \: \sin(40 - x) = \cos(3x) \)

\(\qquad \sf  \dashrightarrow \: \cos\{90 - (40 - x ) \} = \cos(3x) \)

\(\qquad \sf  \dashrightarrow \:90 - (40 - x) = 3x\)

\(\qquad \sf  \dashrightarrow \:90 - 40 + x = 3x\)

\(\qquad \sf  \dashrightarrow \:3x - x = 50\)

\(\qquad \sf  \dashrightarrow \:2x = 50\)

\(\qquad \sf  \dashrightarrow \:x = 25 \degree\)

Answer:

12:20

Step-by-step explanation:

3 : 5 = 3x : 5x = 32

3x + 5x = 8x = 32

x = 32/8 = 4

3x = 3x4 = 12

5x = 5x4 = 20

so there are 12 boys and 20 girls

Answer:

i think is would be D

hope that helps if not i can change it

Step-by-step explanation:

=================================================

Explanation:

The variable n represents the term number.

Plug n = 1 into the expression to get 40-3n = 40-3*1 = 37.

Therefore, 37 is the first term.

The second term is 34 because 40-3n = 40-3*2 = 34.

This process is repeated for values n = 3, n = 4, and n = 5. You should get 31, 28, and 25 for the third, fourth, and fifth terms in that order.

--------

An alternative is to subtract 3 from each term to get the next term.

This alternative method will only be useful once you find the first term is 37.

Probability of Two people was born on Friday = 1/49

Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.

Assume that birthdays are equally distributed throughout the week.

probability of one people having birthday on Friday = 1/ 7

probability of another people has birthday on Friday = 1/7

probability of two people was born on Friday = 1/7× 1/7 = 1/ 49

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The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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Answer:

\(3\sqrt{2}+3\sqrt{7}\)

Step-by-step explanation:

looks like your question don't need a step.

<3

Red

Answer:

\(\huge\boxed{\text{1. }\$ 15}\)

\(\huge\boxed{\text{2. } \$ 1200}}\)

Step-by-step explanation:

By examining the different parts of this equation and what they mean in the context of this problem, we can use the equation to find out different pieces of information about the scenario.

An equation in the form \(y = mx+b\) is set up in the way that m = slope, and b = y-intercept.

When starting on a graph, you start at x = 0. Plugging 0 into the equation as x leaves y as 1200. This shows that the base price to make a book is

$1200.

Also, the equation shows that the slope of the line is 15. If we were to put this on to a graph, then every time x (books) increases by 1, y (cost) would increase by 15. Therefore, books cost $15 per book to publish. This makes it the total cost for every book published.

Hope this helped!

Answer:

3rd option.

Step-by-step explanation:

1. Mean: You can find the mean my adding all Values/observations and divide it by the number of value/observations(n)

2. Range: Maximum Value - Minimum Value

→ 19-11= 8

3. Midrange: The value between the biggest Value and the Lowest value i.e., 15

An easy way to find the surface area of a composite figure is to divide the composite figure up into smaller shapes whose area it is easier to find. It is best to divide a composite figure up into a figure composed of many triangles and rectangles. Then, one will find the area of each of these smaller figures and add the value up to find the total surface area of the composite figure.

Answer:

hi there user!

The answer is he needs to save $37.49 more

Step-by-step explanation:

59.99 - 22.50 = 37.49

Answer:

2 units.

Step-by-step explanation:

It is given that point M is on line segment LN. So,

\(LN=LM+MN\)         (Segment addition property)

The given values are LN=3x+3, LM=4x, and MN=2x. Substitute these values in the above formula.

\(3x+3=4x+2x\)

\(3x+3=6x\)

Subtract 3x from both sides.

\(3x+3-3x=6x-3x\)

\(3=3x\)

Divide both sides by 3.

\(1=x\)

\(x=1\)

The value of x is 1.

Now,

\(MN=2x=2(1)=2\)

Therefore, length of MN is 2 units.

Answer:

392 gallons

Step-by-step explanation:

First, you have to multiply 36 by 3. That should give you 180. After that, all you have to do is subtract 180 from 500. Your final answer is 392 gallons.

There are three major forms of linear equations:

Point slope form:

The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.

Slope intercept form:

A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.

Standard form:

An equation's conventional form is as follows:

Ax+By=C

Where A is not a negative number and B, C, and all three are whole numbers.

Hence we get the required answer.

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Answer:

Try C

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

I = Prt

I = 40  R = .10  T = 5

40 = P (.10)(5)

40 = P(.5)

Divide each side by .5

40/.5 = .5P/.5

80 = P

The interest over 5 years is $80.

The correct option is B.

Simple interest is the borrowing amount added only to the principal amount.

The Formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is the principal amount, T is the time period and R is the interest rate in a year.

We can use the formula I = Prt to solve for P. We know that I = 40, r = 0.10, and t = 5. Substituting these values, we get:

40 = P(0.10)(5)

Simplifying:

40 = 0.5P

Dividing both sides by 0.5:

P = 80

Therefore, the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years is $80.

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For the given information, the value of the test statistic is -1.724 and its associated p-value is 0.0426.

In order to calculate the p value of students with GPA of 3.00 or below, the standard score (z -score or test statistic) must be determined first. In statistics, the standard score refers to the number of standard deviations by which the scores differs from the mean value of the observed or measured data. Scores above the mean have positive standard scores, while those below the mean have negative standard scores.

In a sample of 190 graduates, 28 students have a GPA of 3.00 or below, x = 28/190 = 0.15

The standard deviation = √(p(1 – p)/n) = √(0.2(1-0.2)/190) = 0.029 (where p is the probability of success and n is the total number of data)

The z-score = (x - µ)/σ = (0.15 – 0.2)/0.029 = - 1.724

From the table,

The P (z < -1.724) = 0.0426 or 4.26%.

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The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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Answer:

The answer is 45

Step-by-step explanation:

the way to find this answer is by, first, knowing that each angle of a triangle adds up to 180. So, we must first add the 85 and 50 which will give us 135. After, you subtract it all from 180, which gives you 45.

In the triangle, the value of x is,

⇒ x = 45°

We have to given that;

In triangle;

The angles are 85 degree, 50 degree and x.

Since, We know that;

Sum of all interior angle of a triangle are 180 degree.

Hence, We get;

⇒ x + 85 + 50 = 180

⇒ x + 135 = 180

⇒ x = 180 - 135

⇒ x = 45°

Thus, the value of x is,

⇒ x = 45°

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The allowance time, if the standard time is 234.15 minutes and the basic time is 233.4 minutes is 0.75 minute

To calculate the allowance time, we can use the following formula:

Allowance time = Standard time - Basic time

Thus, Allowance time = 234.15 minutes - 233.4 minute = 0.75 minutes

Therefore, the allowance time is 0.75 minutes.

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The answer of the given linear equation 23 - 7 = 6 - 3x is -10/3.

In the question, we are asked to find the answer to the given linear equation, 23-7=6-3x.

To find the answer to the given linear equation, we do the following steps:

The given equation is:

23 - 7 = 6 - 3x.

We first simplify the equation, to get:

16 = 6 - 3x.

We add 3x to both sides of the equation, to get:

16 + 3x = 6 - 3x + 3x.

We again simplify the equation, to get:

16 + 3x = 6.

We subtract 16 from both sides of the equation, to get:

16 + 3x - 16 = 6 - 16.

We again simplify the equation, to get:

3x = -10.

We divide both sides of the equation by 3, to get:

3x/3 = -10/3.

We again simplify the equation, to get:

x = -10/3.

Thus, the answer of the given linear equation 23 - 7 = 6 - 3x is -10/3.

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The required value of y is 108° for the given diagram. The correct answer would be option (A).

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

In the diagram below, AB is parallel to CD.

Here we can see that the angles y° and 72° are supplementary angles.

So y + 72 = 180°

⇒ y = 180 - 72

Apply the subtraction operation, and we get

⇒ y = 108

Thus, the required value of y is 108°.

Hence, the correct answer would be an option (A).

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The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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Answer:

6746734

Step-by-step explanation:

first fo 45 minus 45 get 0 add then 56 plus 34

Answer:

1200

Step-by-step explanation:

1000(1+.05x4)

5%=.05

convert the months into years

The given system in matrix form is shown below:x' = Ax + fr' (t) = 9r(t) + sin tO'(t) = r(t) 50(t) + 4

We need to put this system in matrix form, thus,x' = Ax + f,where A is a matrix, f is a column vector, and x is a column vector.

The given system can be written as shown below:x' = [0 1 0; 0 0 0; 0 0 0] x + [0; 0; 4]r' (t) = [9 0 0] r(t) + [0; sin t; 0]O'(t) = [0 50 0] r(t) + [0; 0; 0]

Therefore, the matrix form of the given system is:x' = [0 1 0; 0 0 0; 0 0 0] x + [0; 0; 4]r' (t) = [9 0 0; 0 0 0; 0 0 0] r(t) + [0; sin t; 0]O'(t) = [0 50 0; 0 0 0; 0 0 0] r(t) + [0; 0; 0]

Thus, the required matrix form of the given system is shown above.

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Answer:

First option

Step-by-step explanation:

Hope this helps