In how many map squares did we spot less than 20 plant species

Answer: C(t) = -475.5*cos(t*pi/6) + 475.5

Step-by-step explanation:

We know that we have a sinusoidal relation, with a minimum at 9:00 am and at 9:00 pm.

If we define the 9:00 am as our t = 0, we have that the maximum, at 3:00pm, is at t = 6 hours.

and the other minimum, at 9:00pm, is at t = 12 hours.

Then we need to find a trigonometric function that has the minimum at t = 0, we can do this as:

-Cos(c*t)

when t = 0

-cos(0) = - 1

then we have a function:

C(t) = -A*cos(c*t) + B

where A, c and B are constants.

We know that at t = 0 we have 0 customers, and that at t = 6h we have 875 customers, that is the maximum.

then:

C(0) = 0 = -A + B

this means that A  = B, then our function is:

C(0) = -A*cos(c*t) + A.

now, at t = 6h we have a maximum, this means that -A*cos(c*6h) = A

then:

C(6h) = A + A = 875

2A = 875

A = 875/2 = 437.5

and we also have that, if -cos(c*6) = 1

then cos(c*6) = -1

and we know that cos(pi) = -1

then c*6 = pi

c = pi/6

Then our function is

C(t) = -475.5*cos(t*pi/6) + 475.5

Final answer:

On average, one customer arrives every two minutes at Somerset Mall on a Saturday, which means it takes six minutes on average for three customers to arrive. This question applies trigonometry, algebra, and statistical concepts.

Explanation:

A research firm finds that the average number of customers in Somerset Mall on a Saturday varies sinusoidally with time. The question involves understanding sinusoidal functions, their applications, and basic statistical concepts related to customer arrival rates. The sinusoidal nature of customer arrivals is a practical application of trigonometry and algebra in solving real-world problems.

Part a: Average Minutes Between Arrivals

Given that 30 customers arrive per hour, to find the average time between successive arrivals, we divide the number of minutes in an hour by the number of arrivals: 60 minutes / 30 customers = 2 minutes. Therefore, on average, one customer arrives every two minutes.

Part b: Time for Three Customers to Arrive

Since one customer arrives every two minutes on average, for three customers to arrive, it would take 3 * 2 minutes = 6 minutes on average.

The model's assumption that customers arrive one at a time and at a constant rate throughout the day simplifies the real-life complexity of customer behavior and peak shopping times. This is a critical consideration in the practical application of mathematical models in business.

Answer:

x=2

Step-by-step explanation:

x^2 + 4x - 16 = 0

I'm using the quadratic formula to solve this equation.

A = 1

B = 4

C = -16

x = -b +- [tex]\sqrt{b^2 - 4ac}[/tex]  

over 2a

Plug it in:

x= -4 +- [tex]\sqrt{4^2 -4(-16)}[/tex] over 2

x= -4 +- [tex]\sqrt{16+64[/tex] over 2

x = -4 +-[tex]\sqrt{80}[/tex] over 2

x = -4 +- 4[tex]\sqrt{5[/tex]

Divide by 2.

x = -2 +- 2[tex]\sqrt{5[/tex]

Therefore, x would be -2 + 2[tex]\sqrt{5}[/tex], -2 - 2[tex]\sqrt{5}[/tex]

Convert to decimal form: 2.47213595, -6.47213595

Round it: 2.4714595 = 2.5 and -6.47213595 = -6.5

Answer:

C.Lines r and s and lines t and u must be parallel.

Step-by-step explanation:

Line r s and t must be parallel and c is closest to that lol

The lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

If Angle 2 is congruent to angle 4 and Angle 5 is congruent to angle 7.

From the information given we can draw lines r, s, t, and u(please attached picture)

From the picture, we can clearly see: lines r and s and lines t and u must be parallel.

Thus, the lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

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Answer:

Step-by-step explanation:

Recognize that the (1/2) in  4n=1/2(2n-12)  is a coefficient, the coefficient of the (2n - 12) term.

Thus, multiply both sides of this equation 4n=1/2(2n-12) by 2, to obtain:

8n = 2n - 12

Combining like terms, we get 6n = -12, so that n = -2.  

Multiplying both sides of the equation by a constant does not in any way affect your ability to find a solution and does not change the solution.

Answer:

0.8

Step-by-step explanation:

Answer: The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. The vertex of the parabola is (2,1) . So, the axis of symmetry is the line x=2.

Step-by-step explanation:

Answer:

This does make a right triangle

Step-by-step explanation:

Because when you square 8 you get 64 and when you square 15 you get 225. Then you add those together and you should get 289 so when you find the square root of 289 is 17 which makes those number true

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle. This is because these side lengths satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have:

a² + b² = 8² + 15² = 64 + 225 = 289

c² = 17² = 289

Since a² + b² = c², these side lengths satisfy the Pythagorean theorem, and the triangle is a right triangle.

Thus,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

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Answer:

Pythagorean Theorem

SSS

C

the definition of right triangle

Step-by-step explanation:

Answer:

2.9

Step-by-step explanation:

The mean is the average of the date It is surprisingly easy to calculate: add up all the data, then divide by how many data points there are.

Becker's data added up is 28. Kayla's data added up is 30. The total amount is 58.

The amount of data points are 20.

58/20 = 2.9

Hope this helps!

The mean number of games chess team members play per day is 2.9

Becker = 5,2,4,1,1,4,5,3,2,1

= (5 + 2 + 4 + 1 + 1 + 4 + 5 + 3 + 2 + 1) / 10

Mean average = 28 / 10

= 2.8

Kayla = 2,3,1,1,4,1,5,3,5,5

= (2 + 3 + 1 + 1 + 4 + 1 + 5 + 3 + 5 + 5) / 10

= 30 / 10

= 3

Total = Becker + Kayla

= 2.8 + 3

= 5.8

Mean average = 5.8 / 2

= 2.9

Therefore, the mean number of games chess team members play per day is 2.9

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Answer:

B. 5,200

Step-by-step explanation:

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

Her total monthly living expenses = 750 + 500 + 250 = $1,500

Sarah wants an emergency fund of 5 times monthly living expenses.

1500 × 5 = $7,500

Currently she is having her emergency fund savings account is = $2,300

She needs to save more = 7,500 - 2,300 = $5,200

Sarah need to save more $5,200.

Sarah need to save $5,200 to have an adequate emergency fund.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

⇒ total monthly living expenses = 750 + 500 + 250 = $1,500

∵ Sarah wants an emergency fund of 5 times monthly living expenses.

∴ emergency fund = 1500 × 5 = $7,500

Currently she is having her emergency fund savings account = $2,300

Thus, Amount needs to be save = 7,500 - 2,300 = $5,200

Thus, Sarah need to save $5,200 to have an adequate emergency fund.

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Answer:

1) x/8+ x/16= 3/4    2) 4 miles

Step-by-step explanation:

The table is an illustration of distance, rates (speed) and time.

From the question, we have:

[tex]t =45\ mins[/tex] --- total time spent

Convert to hours

[tex]t =\frac{45}{60}hr[/tex]

Reduce fraction

[tex]t =\frac{3}{4}hr[/tex]

The times spent to school and back home are given as:

[tex]t_1 = \frac x8[/tex]

[tex]t_2 = \frac x{16}[/tex]

So, we have:

[tex]t_1 + t_2 = t[/tex]

This gives:

[tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Take LCM

[tex]\frac{2x + x}{16} = \frac 34[/tex]

[tex]\frac{3x}{16} = \frac 34[/tex]

Multiply through by 16

[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]

[tex]3x = 12[/tex]

Divide both sides by 3

[tex]x = 4[/tex]

The distance to school and back home are given as:

[tex]d_1 = d_2 = x[/tex]

So, we have:

[tex]d_1 = d_2 = 4[/tex]

This means that Gerry lives 4 miles from school

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Answer:

B. distribution skewed to the right, mean pulled to the right, median not effected

Step-by-step explanation:

When a distribution is skewed to the right, it means that the data is positively skewed or has more positive numbers than negative numbers.

An outlier can affect the mean of a distribution since a high value outlier will make the mean be much higher than the median. In this case, since the distribution is positively skewed, a high outlier will pull the mean to the right (to higher positive values).

The high outlier  in a data set affects the mean and median is

B. distribution skewed to the right, mean pulled to the right, median not effected

At the time When a distribution is skewed to the right, so it represents the data is positively skewed or it contains more positive numbers as compared to the negative numbers. An outlier can impact the mean of the distribution.

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Answer:

あなたがこれを翻訳するなら私はあなたを愛しています

Step-by-step explanation:

私は英語がわかりませんが、答えは4倍になります

To find the value of 5x + 5y, you can solve the system of equations using the elimination method, and substitute the values of x and y into the expression.

To find the value of 5x + 5y based on the system of equations:

2x + 3y = 1200

3x + 2y = 1300

we can solve the system by either substitution or elimination method. Let's use the elimination method:

The value of 5x + 5y in this system of equations is 12500.

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Answer:

= 3

Step-by-step explanation:

4 − 5 + 9 = 5 − 9

− + 9 = 5 − 9

i hope this helps<3

:)

The value of solution of expression is,

⇒ x = 3

We have to given that;

Mathematical expression is,

⇒ 4x - 5x + 9 = 5x - 9

Now, We can simplify as;

⇒ 4x - 5x + 9 = 5x - 9

⇒ - x + 9 = 5x - 9

⇒ 9 + 9 = 5x + x

⇒ 18 = 6x

⇒ 6x = 18

⇒ x = 18 / 6

⇒ x = 3

Thus, The value of solution of expression is,

⇒ x = 3

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

Explanation:

The rule is that if [tex]|a| \le k[/tex] for some positive number k, then it can be written as the compound inequality [tex]-k \le a \le k[/tex]. This is a shorthand way of writing the two inequalities [tex]a \ge -k \ \text{ and } \ a \le k[/tex] combined together.

note: [tex]-k \le a[/tex] is the same as [tex]a \ge -k[/tex]

From here, we replace k with 3

Therefore, [tex]|a| \le 3[/tex] turns into [tex]-3 \le a \le 3[/tex] which breaks down further to [tex]a \ge -3 \ \text{ and } \ a \le 3[/tex]

The keyword "and" is important as we can't pick one or the other. We must pick both [tex]a \ge -3[/tex] and also [tex]a \le 3[/tex]

Answer:

Choice 2.  

Step-by-step explanation:

Answer:

Question 1. (2.2, -1.4)

Question 2. (1.33, 1)

Step-by-step explanation:

Equations for the given lines are

-----(1)

It is given that this line passes through two points (0, 2.5) and (2.2, 1.4).

------(2)

This equation passes through (0, -3) and (2.2, -1.4).

Now we have to find a common point through which these lines pass or solution of these equations.

From equations (1) and (2),

x =

x = 2.2

From equation (2),

y = -1.4

Therefore, solution of these equations is (2.2, -1.4).

Question 2.

The given equations are y = 1.5x - 1 and y = 1

From these equations,

1 = 1.5x - 1

1.5x = 2

x =

Therefore, the solution of the system of linear equations is (1.33, 1).

The correct approximate solution of the system of linear equations[tex]\( y = 1.5x - 1 \) and \( y = 1 \) is \( (1.33, 1) \).[/tex]

To find the solution, we need to set the two equations equal to each other since they both equal \( y \). This gives us the equation:

[tex]\[ 1.5x - 1 = 1 \][/tex]

Now, we solve for [tex]\( x \)[/tex]:

[tex]\[ 1.5x = 1 + 1 \][/tex]

[tex]\[ 1.5x = 2 \][/tex]

[tex]\[ x = \frac{2}{1.5} \][/tex]

[tex]\[ x = 1.\overline{3} \][/tex]

[tex]\[ x \approx 1.33 \][/tex]

Having found [tex]\( x \)[/tex], we can now find the corresponding [tex]\( y \)[/tex] value by substituting [tex]\( x \)[/tex] into either of the original equations. Since [tex]\( y = 1 \)[/tex] is given, we already know that [tex]\( y \)[/tex] is exactly 1. Therefore, the solution to the system is approximately [tex]\( (1.33, 1) \)[/tex].

Answer:

C. The vertex of the function doesn't change.

Answer:

10/20=1/2

Step-by-step explanation:

Without additional information about the height or area of the base of the prism, it is impossible to determine the base length from the volume alone.

To determine the base length of a prism when the volume is known, one must have additional information about the prism, such as the area of the base or other dimensions. Since the question does not provide any information about the height or the area of the base, we cannot calculate the base length solely from the volume. Typically, the volume of a prism is calculated using the formula V = base area × height. Without knowing either the base area or the height of the prism in this question, we cannot find the base length. Thus, we cannot choose from the provided options (10 inches, 12 inches, 13 inches, 15 inches) without additional information about the prism.

Answer:

You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line,  square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.

Step-by-step explanation:

Answer: 397.39 cm2

Step-by-step explanation:

Hi, first we have to calculate the area of the circle:

Area of a circle = π x r^2

Replacing with the values:

A(C) =π x 12^2 = 452.39cm2

Now, we have to calculate the rectangle area:

Rectangle area = width x length = 5 x11 = 55cm2

Finally, since the shaded region is the circle and the rectangle is inside of it, we have to subtract the area of the rectangle to the area of the circle:

452.39 -55 = 397.39 cm2

Feel free to ask for more if needed or if you did not understand something.

Answer:

397.39

Step-by-step explanation:

extras...

Answer:

1/2

Step-by-step explanation:

Do  I get brainliest?

Answer:

1/2

Step-by-step explanation:

Answer:

D) 30

Step-by-step explanation:

The third quartile is the last line of the box

Hope this helps!

A box and whisker plot is a graphical representation of variance. The third quartile of the box-and-whisker plot is 30.

A box and whisker plot is a graphical representation of variance in a set of data.

The third quartile of the box-and-whisker plot is the rightmost line of the box, which means the third quartile of the box-and-whisker plot is 30.

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Step-by-step explanation:

2X alla seconda meno 3

Answer:  C) 297 in2

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Surface area of a square pyramid (S) = 2 (length of the base) slant + length of the base ^2

S = 2bs + b^2

Replacing with the values given:

S = 2 (9) 12 + 9^2

S = 216 +81 = 297 square inches

Feel free to ask for more if needed or if you did not understand something.

Answer:

856.4

Step-by-step explanation:

10% of 8564 =856.4

Answer:

0.53333333333

Step-by-step explanation:

The fraction of the class that is boys is 16/30.Therefore, the decimal equivalent the fraction of boys in Daniel's class is 0.53.

The fraction of the class that is boys is obtained by dividing the number of boys by the total number of students. In this case, there are 16 boys and 30 students in total. The fraction is therefore 16/30.

To write this fraction as a decimal, divide the numerator (16) by the denominator (30). The decimal equivalent of 16/30 is approximately 0.5333.

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