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The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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8 halls would be required to accommodate 520 people in the hall.

As we know that a hall can accommodate 65 people.

To determine the number of hall required for 520 people,

first we need to find that how many halls would be required for one person,

So, we will divide the 1 by 6 to find :

The number of one person accommodate = 1/65 Hall

Then, 520 people required to accommodate = 1/65 × 520

                                                                      = 8 Halls.

[Accommodate: to have enough space for somebody/something, especially for a certain number of people]

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Answer: x=4

Step-by-step explanation:

 -8-x=x-4x

  -8-x=-3x

-x+3x=8

    2x=8

      x=4

Answer:

It will take Stephon about A: 163 seconds to run two laps when he is 192 months old.

Step-by-step explanation:

To find 163 seconds all I did was eyeball where 192 months is going to be on the x-axis and lined it up with the provided line of fit, then I ran it across the x-axis to the y-axis and I got around 163 seconds.

Given line of best fit is y = -2.1x + 565.6, where x is age in months and y is time in seconds, it take Stephon 162.4 seconds to run two laps on the track when he is 192 months old

A line of best fit is a straight line that minimizes the distance between it and some data. The line of best fit is used to express a relationship in a scatter plot of different data points.

Given in the question,

x =  age in months

y = time in seconds

Here, age of child is independent and time taken to run two laps is dependent variable.

given line of best fit :  y = -2.1x + 565.6

given y = 192 months

finding the value of y :

y = -2.1x + 565.6 = -2.1 * 192 + 565.6 = 162.4

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Answer:

Probability = number of yellow jellybeans / total number of jellybeans

=  24 / 80

=  3/10.

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

There are 80 total jelly beans, as stated in the question. Therefore, there are 80 "Total Events".

There are 12 yellow jellybeans in the bowl. Therefore, there are 12 preferred events, since the question asks the probability of pulling one yellow jellybean randomly.

\(\frac{\text{Preferred Events}}{\text {Total Events}} =\frac{12}{80}\)

I do not know what form the question prefers, so I did the probability in all forms.

Divide 12 by 80.

\(12/80 = 0.15\)

There is a 0.15 chance that Ricky would pull out a yellow bean.

Divide 12 by 80.

\(12/80=0.15\)

Convert into a percent. Multiply 0.15 by 100.

\(0.15*100=15\)

There is a 15% chance that Ricky would pull out a yellow bean.

Simplify 12/80.

\(\frac{12/2}{80/2} =\frac{6/2}{40/2} =\frac{3}{20}\)

There is a \(\frac{3}{20}\) chance that Ricky would pull out a yellow bean.

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Answer:

Step-by-step explanation:

110

Answer:

Jiri is 12 years old

Step-by-step explanation:

To start off we need to make an equation. Since we know both of their ages add up to 48 and that Pamela's age is 3 times Jiri's age we can say x(Jiri's Age) + 3x(Pamela's age) =48 --> x+3x=48

Now we have the equation x+3x=48, and we need to solve it.

First combine like terms

4x=48

Now divide both sides by 4

x=12

And now since we are using Jiri's age as x we know Jiri is 12 years old.

3 lightning bugs per minute

Unit rates are special ratios that help describe rates of time or price.

Defining Unit Rates

Unit rate is the rate per one quantity. For example, the question tells us the rate at which Alexander caught lightning bugs in 7 minutes. So, the unit rate would be the number of bugs caught in one minute. Unit rates are most commonly used for time and price. Another example of a unit rate is the price of apples per pound. Just as 21:7 is a ratio, unit rates can be written as a ratio.

Finding the Unit Rate

The easiest way to find the unit rate is through division. We want to find the rate per 1 minute. Since the current rate is given per 7 minutes, we need to divide both values by 7.

This means that the unit rate is 3 lightning bugs per 1 minute.

Answer:

The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Step-by-step explanation:

Let us denote the events as follows:

Event 1: a sunny day

Event 2: a rainy day

From the provided data we know that the transition probability matrix is:

                 \(\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right\)

\(\text{P}=\left\begin{array}{c}1&2\end{array}\right\)  \(\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\)

In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.

This implies that we need to compute the value of P₁₁².

Compute the value of P² as follows:

\(P^{2}=P\cdot P\)

     \(=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right]\)

The value of P₁₁² is 0.86.

Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.

Answer:

Step-by-step explanation:

The greatest difference possible is 0.4

The decimal 0.4 is equivalent to 410 , so 0.4 is located between 0 and 1 . On a number line, divide the interval between 0 and 1 into 10 equal parts and place marks to separate the parts.

The greatest difference possible difference of two decimals to the hundredths place that are between 0 and 1 is 0.99

For us to get the difference possible difference, we will take the difference between the highest values and the lowest values between 1 and 10

Greatest values = 0.99999999999

Possible least value = 0.0000000001

Taking the difference:

Difference = 0.99999999999 - 0.0000000001

Difference = 0.9999999998

Convert to the nearest hundredth place

0.9999999998 to the nearest hundredth is 1.00. Since the value must be between 0 and 1, the required value will be 0.99

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Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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Answer:234.6

Step-by-step explanation:

i got it right on the test

According to the z-score distribution table, we find out that the p-value is 0.0752 for the given test statistic of z = 1.438 which is accurate to four decimal places.

It is given to us that -

A study is conducted to see if the probability of catching the flu this year is significantly more than 0.23

The sample data produces the test statistic

The value of z = 1.438

We have to find out the p-value accurate to four decimal places.

We know that the p-value is known as the decimal value which can be expressed from 0 to 100%. This p-value is important in hypothesis testing in order to establish the significance of the results expected.

We are given that the test statistic, z = 1.438 and we know that this is a two-tailed test.

So, we can obtain the p-value from the z distribution table.

P-value = 2P (Z<1.438)

=> P-value = 0.0752       [Value from z-score table]

Thus, from the z-score distribution table, we find out that the p-value is 0.0752 which is accurate to four decimal places.

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The percent decrease from 15 to 12 is 20%

What is percentage ?

Percentage is a way of expressing a proportion or a ratio as a fraction of 100. It is often denoted by the symbol "%". For example, if we say that 20 out of 100 people in a room are wearing a red shirt, we can express this proportion as a percentage by multiplying it by 100:

20/100 x 100% = 20%

To calculate the percent decrease from 15 to 12, we first need to find the difference between the two values:

15 - 12 = 3

Then we divide the difference by the original value (15) and multiply by 100 to get the percent change:

(3/15) x 100 = 20%

Therefore, the percent decrease from 15 to 12 is 20%.

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Answer:

x =23

Step-by-step explanation:

ok first, the full degree of a straight line is 180°

subtract 38° out of 180°

180-38= 142

so 6x+4= 142°

subtract 4 from both sides of the equation

6x +4 -4= 142-4

6x=138

divide 6 from 6x and 138

x=23

The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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Answer:

y = 4x - 11

Step-by-step explanation:

The general equation of the slope-intercept form of a line is given by:

y = mx + b, where

We can find b, the y-intercept of the line, by plugging in 4 for m and (3, 1) for (x, y) in the slope-intercept form:

1 = 4(3) + b

1 = 12 + b

-11 = b

Thus, the y-intercept is -11.

Thus, the equation of the line with a slope of 4 passing through the point (3, 1) in slope-intercept form is y = 4x - 11

The answer is:

Work/explanation:

First, we will write the equation in point slope:

\(\sf{y-y_1=m(x-x_1)}\)

where m = slope;

(x₁,y₁) is a point on the line.

Plug in the data:

\(\sf{y-1=4(x-3)}\)

Simplify

\(\sf{y-1=4x-12}\)

Add 1 on each side

\(\sf{y=4x-12+1}\)

\(\sf{y=4x-11}\)

The price of the cost per quart of laundry detergent is A = $ 3.47

Given data ,

Let the unit cost rate be A

Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.

To find the price per quart, we can divide the total cost by the number of quarts:

Price per quart = Total cost / Number of quarts

Price per quart = $27.76 / 8 = $3.47

Hence , the price per quart of laundry detergent is $ 3.47

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Since the segments taht are shown are all tangents to the circle, we can use the property that the tanget segments of the same circle and that have an external common point have the same length. From this, we see that the pairs AV and BV, BZ and CZ, CW and AW are tangets with common eterior points, thus:

Than, we can see that that:

Also:

So, we already know AV, BV, BZ and CZ. AW and CW are the same, and the sum of all of them is the perimeter, that we know is 64, so:

Answer:

\(k(k-3)(k+5)\)

Step-by-step explanation:

\(k^2+5k=k(k+5) \\ \\ k^2 + 2k-15=(k+5)(k-3)\)

So, the least common denominator is \(k(k-3)(k+5)\).

Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters

Answer:

5cm^3

Step-by-step explanation:

The measure of angle ∠A will be 60° for the given triangle.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Given that the two angles are ∠B = ( 3y + 6 )°, ∠A = (4y)° and the exterior angle ∠C = 111°.

The measure of the angle ∠A will be,

( 3y + 6 ) +  (4y) = 111

7y = 111 - 6

7y = 105

y = 105 / 7

y = 15

The angle ∠A will be,

∠A = 4 x 15

∠A = 60°

Therefore, the angle ∠A will be 60°.

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Answer:

2x +6

Step-by-step explanation:

Multiply using the distributive property.

Answer:

2x+6

Step-by-step explanation:

2 x x= 2x

2 x 3= 6

2x+6

The probability of selecting a number greater than 8 will be \(p=\dfrac{1}{9}\).

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.

The number of outcomes = { 1,2,3,4,5,6,7,8,9 } = Counts = 9

Favourable outcomes = { 9 } = counts = 1

The probability will be given as:-

\(P = \dfrac{1}{9}\)

Therefore the probability of selecting a number greater than 8 will be \(p=\dfrac{1}{9}\).

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)

From the question, we have the following parameters that can be used in our computation:

Start = (0, -4)

Also, we have

You move left 1 unit and right 4 units

Mathematically, this can be expressed as

(x, y) = (x - 1 + 4, y)

Substitute the known values in the above equation, so, we have the following representation

Endpoint = (0 - 1 + 4, -4)

Evaluate the expression

Endpoint = (3, -4)

Hence, the endpoint is (3, -4)

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Answer:

an individual who invested in the market in 2006  has yet to regain the losses incurred in 2008

Step-by-step explanation: