1. Inte the size of angle Mae a fraction, Then we decimal rounded to the 8-20

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

-3a

Step-by-step explanation:

3(-a)

Expand brackets.

3 × -1a

-3a

The required function y = 7 cos (2π * 0.1 * x) and period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

he cosine function can be used to model periodic motion, and its general form is:

y = A cos (Bx + C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, we know that a 14 in. wave occurs every 10 s, so we can use this information to find the frequency, which is the reciprocal of the period. The period is the time it takes for one complete cycle of the wave, which in this case is 10 s.

Therefore, the frequency is:

\(f = \frac{1}{T}=\frac{1}{10} = 0.1 Hz\)

We can also see that the amplitude of the wave is 7 inches, since the wave has a height of 14 inches from its highest point to its lowest point.

Now we can write the function that models the height of the particle in inches y as it moves in seconds x:

y = 7 cos (2π * 0.1 * x)

Here, the frequency is expressed in radians per second (2π * 0.1 = 0.2π), since the cosine function takes radians as its argument. The phase shift and vertical shift are both zero in this case, since the wave starts at its highest point and has no vertical shift.

Therefore, the period of the function is 10 seconds, which is the time it takes for one complete cycle of the wave.

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Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

The probability that you collect 10 fish from this pool and half have infected gills is given as follows:

0.0047 = 0.47%.

The mass probability formula is presented as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

The parameter values for this problem are given as follows:

N = 25, k = 5, n = 10.

The probability half have infected gills is P(X = 5), hence:

P(X = 5) = C(5,5) x C(20,5)/C(25,10)

P(X = 5) = 0.0047 = 0.47%.

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Answer:

a. A two way table is presented as follows;

\(\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}\)

ii) The percentage of students in the study that have myopia are approximately 24.867%

iii) The percentage of children living in Australia with myopia are approximately 3.2258%

The percentage of children living in Singapore with myopia are approximately 29.14%

b. Children in Australia spend more time reading, writing and also outdoors than children in Singapore

c. The study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children

The study does not suggests that more time spent outdoors is associated with a greater risk of myopia

d. The advantage is to reduce associated variables the generate more accurate findings or result

Step-by-step explanation:

a. A two way table is presented as follows;

\(\begin{array}{cccc}&Had \ Myopia&Do \ not \ have \ Myopia& Totals\\Sydney \ (Australia)&4&120&128\\Singapore&183&445&628\end{array}\)

ii) The percentage of students in the study that have myopia are;

(4 + 183)/(124 + 628) × 100 ≈ 24.867%

iii) The percentage of children living in Australia with myopia is given as follows;

4/124 × 100 ≈ 3.2258%

The percentage of children living in Singapore with myopia is given as follows;

183/628 × 100 ≈ 29.14%

b. The data for the time spent reading and writing is presented as follows;

                    Number of children  \({}\)  Mean     Standard deviation

Australia        109       \({}\)                      20.8        13.9

Singapore \({}\)    611                               17.8          8.8

The data for the time spent outdoors is presented as follows;

                    Number of children  \({}\)  Mean     Standard deviation

Australia        102       \({}\)                       13.75        1.02

Singapore \({}\)    586                               3.05        0.12

From the data, more children in Australia spend more time reading and writing and also outdoors than children in Singapore

c. From the data, more children spend their time reading and writing in Australia and are also less likely to develop myopia than children in Singapore

Therefore, the study does not suggest that more time spent reading or writing is associated with a greater risk of myopia among the enrolled children

Similarly, the study does not suggests that more time spent outdoors is associated with a greater risk of myopia

d. The advantage of collecting data from children with the same ethnicity compared with selecting random samples of children from each location regardless of ethnicity is to reduce the variables or influential factors that may alter the impact on the test and the results

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

The second box plot represents the data

Step-by-step explanation:

A box and whisker plot gives you the five-number summary of the data, which includes:

the minimum (lowest value of the data)

the maximum (highest value of the data)

Q1 (25% of the data lies below this point)

Q3 (75% of the data lies below this point), and

the median (the middle of the data).

The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively.  From the data, we see that the minimum is 5 and the maximum is 10.

Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.

Answer:

Assuming that the spinner is fair (i.e., each color has an equal chance of being landed on), we can find the best prediction for the number of times the spinner will not land on yellow by using probability.

There are 6 colors on the spinner, so the probability of the spinner landing on yellow is 1/6. The probability of the spinner not landing on yellow is therefore:

1 - 1/6 = 5/6

This means that for each spin of the spinner, there is a 5/6 probability that it will not land on yellow. If we spin the spinner 55 times, we can expect the number of times it will not land on yellow to be:

55 x 5/6 = 45.83

However, since we cannot have a fractional number of spins, we need to round to the nearest whole number. The best prediction for the number of times the spinner will not land on yellow is therefore 46.

Answer:

The height of the tree is 35 meters.

Step-by-step explanation:

Let the height of the tree be x meters, then the length  of the wire is

x+2 meters.

The distance from the tree to the anchor is  x-23 meters.

So using the pythagoras theorem:

(x + 2)^2 = x^2 +(x -23) ^2

x^2 + 4x + 4 = x^2 + x^2 - 46x + 529

x^2 - 50x + 525 = 0

( x - 15)(x - 35) = 0

x = 15, 35

x cannot be 15   as this would make the distance 15-23 which is negative so x mustr be 35 meters,

Step-by-step explanation:

The equation for this function is y=2x

So 32*2=64

36/2=18

2*x=2x

y/2=y/2

2x*2=4x

(x+3)*2=2x+6

Answer:

Multiplication

Step-by-step explanation:

\(\frac{x}{3} =15\)

To get the 3 out of the denominator, you would have to multiply each side by 3:

\(3*\frac{x}{3} =3*15\\x=45\)

Answer:

X=45

Step-by-step explanation:

Multiply 3 on both sides

The probability of a prime number or a number greater than 3 coming up is given as follows:

5/6.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

When a dice is thrown, there are six possible outcomes, ranging from 1 to 6, and the desired outcomes are given as follows:

Hence the probability is given as follows:

5/6.

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Answer: 12 1/3

hope this helps.. stay safe and have a great day

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

22 because SA= 2lw+2lh+2hw

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:

y= 0.5x + 8.2

$13.6 per hour

Step-by-step explanation:

(Is it weird that I had the same exact question? Maybe not. But I also found another person with the same question as me. It was a different question though. This is probably too late. But I'm just gonna try to answer it for anyone who needs it.

"Linear regression" is just a fancy word for scatter plots. Scatter plots take place in graphs. The dots or plots are scattered and the way they are scattered means something. If it's going down, it's negative, up it's positive, and if it's scattered, it has no corrolation.

Also, you should have learned this in 9th grade. So, check your notes.

If you don't have it, WRITE IT!!!

To find it in your calculator:

1. Go to "Lists and Spreadsheets"

2. Rename the first column "x" and the second on "y"

3. Write all of your numbers in the right column

1, 5, 3, 7 under the "x"

8.67, 10.50, 9.58, 11.41 under the "y"

4. Move your cursor to an empty cell

4. Click: "MENU" #4 #1 #3

5. Rename the correct rows "x" and "y" and press enter

6. Now you can find "m" and "b"

7. Then move your cursor to an empty cell and click "doc" "insert" #7

8. Find the x-axis and find "x"

9. Find the y-axis and find "y"

10. Now press "MENU" #4 #6 #1

And you found your y=mx+b: y=0.5x+8.2

Now, how much money per hour.

So you've found your m and b but now you have to:

1. Replace y with 15 and solve it

15=0.5x+8.2

-8.2       -8.2

6.8=0.5x

Divide 0.5 on both sides

6.8/0.5=13.6

13.6=x

$13.6 per hour

The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

Based on a weather record, the probability of snowfall in a certain town in New York on January 1 is 0.230.

Now, WE get;

the probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 1 - P (snowfall)

P (no snowfall) = 1 - 0.230

P (no snowfall) = 0.770

Thus, The probability that next year there will be no snowfall in that town on January 1 is,

P (no snowfall) = 0.770

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Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

x − 43 = 90

Step-by-step explanation:

2x + 43 = 180

2x − 43 = 90

x + 43 = 180

x − 43 = 90

Answer:

Rajesh did πr2 (π × r × 2) instead of πr². The correct work would be

Area = 3.142 x 10²  so... Area = 3.142 x 100 not 3.142 x 20.

Answer:

n = 1/2 or .5

Step-by-step explanation:

4n + 3 = 10 -10n

14n = 7

n = 1/2 or .5

Hope this helps!

Answer:

n = -0.5

Step-by-step explanation:

4n + 3 = 5(2 - 2n)

First you multiply 2 and 2n by 5

4n + 3 = 10 - 10n

subtract 4n on both sides (meaning subtract 4n by itself on the left side of the equal sign and subtract 10n and 4n)

3 = 10 + 14n

Subtract 10 on both sides

-7 = 14n

Divide on both sides

Your answer should be n = -0.5 (or -0.5 = n)

Hope this helps!

The length of the bottom diagram in the final tape diagram is 5.04 units.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

The top diagram length is 60 units.

20 % of the 60 units is carried down, the length of the new section is:

20/100 * 60 = 12units.

60% of the next 12 units are carried down, the length of the new section is:

60/100 * 12 = 7.2 units

Similarly, when 70% of the section is carried down the length of the new section is:

70/100 * 7.2 = 5.04 units.

Hence the length of the bottom diagram is 5.04 units.

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Answer:

24.58 km

Step-by-step explanation:

1 km = 1000 m

1 m = 1 / 1000 km

24580 m

= 24580 / 1000

= 24.58 km

Answer:

3 m^3 - 26 m^2 + 45 m - 70

Step-by-step explanation:

Applying distributive property we get:

3 m^3 - 5 m^2 + 10 m - 21 m^2 + 35m - 70

combining like terms:

3 m^3 - 26 m^2 + 45 m - 70

Answer:

80 : n < 32

Step-by-step explanation:

100-20=80

Answer: 0

Step-by-step explanation: -8+8=0

Answer:

0

Step-by-step explanation:

So if you have -8 and 8 and you add them together they cancel out each other and make 0

Answer:

A

Step-by-step explanation:

Y

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.