The ratio of males to females in the class is 5 to 9. If the lunchroom has the same ratio but 45 females, how many males are in the lunchroom?​

The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.

P(t) = 100 + 120t - 3t^2

This formula can be used to calculate the number of people sick with the flu at time t, where time is measured in days from the beginning of the epidemic. The initial number of people sick with the flu at time 0 is 100 and the rate of increase of the number of people sick with the flu is 120t - 3t^2 people per day.

To calculate P(t), the initial number of people sick with the flu, 100, is added to the rate of increase of the number of people sick with the flu over t days, which is 120t - 3t^2. The sum of these two values is the number of people sick with the flu at time t.

For example, at t=2 days, P(2) = 100 + 120(2) - 3(2^2) = 100 + 240 - 12 = 328 people sick with the flu.

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Answer:

(a) \(\frac{1}{13}\)

(b) \(\frac{3}{13}\)

(c) \(\frac{10}{13}\)

Step-by-step explanation:

The probability of an event B occurring is given by;

P(B) =  \(\frac{n(E)}{n(S)}\)

Where;

P(B) = probability of the event B

n(E) = number of favourable outcomes

n(S) = total number of events in the sampled space.

From the question, the card is drawn randomly from a standard 52-card deck. The probability of

(a) drawing a "king" card is analyzed as follows.

Let the event of drawing the "king" card be B.

In a standard 52-card deck, the number of cards that are of type king is 4. i.e 1 from the diamond pack, 1 from the spade pack, 1 from the heart pack and 1 from the club pack.

Therefore, the number of favourable outcomes is 4, while the total number of events in the sampled space is 52.

The probability of drawing a "king" card, P(B) is;

P(B) = \(\frac{4}{52}\)

P(B) = \(\frac{1}{13}\)

(b) drawing a "face" card is analyzed as follows.

Let the event of drawing the "face" card be B.

In a standard 52-card deck, a face card can either be a Jack, Queen or a King. There are 4 Jack cards, 4 Queen cards and 4 King cards in the deck.  The number of cards that are of type face is 12.

Therefore, the number of favourable outcomes is 12, while the total number of events in the sampled space is 52.

The probability of drawing a "face" card, P(B) is;

P(B) = \(\frac{12}{52}\)

P(B) = \(\frac{3}{13}\)

(c) drawing a card that is not a "face" is analyzed as follows;

The sum of the probability of drawing a face card and the probability of not drawing a face card is always 1.

Let the event of drawing a "face" card be B and the event of not drawing a "face" card be C.

P(B) + P(C) = 1

P(C) = 1 - P(B)

From (b) above, the P(B) = \(\frac{3}{13}\)

Therefore,

P(C) = 1 - \(\frac{3}{13}\)

P(C) = \(\frac{10}{13}\)

For a unique solution is: \(\frac{10}{a}\neq \frac{5}{b}\)

For an infinitely many solution is: \(\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}\)

An equation of the form ax+by+c=0 is called a linear equation where a, b, c∈R

We have the linear equation is:

10x + 5y = 20

Now, we have to find the unique solution and infinitely many solution:

Firstly, For a unique solution, we need an equation ax+by+c=0 such that

\(\frac{10}{a}\neq \frac{5}{b}\)

Now, For an infinitely many solutions, we need an equation ax+by+c=0 such that:

\(\frac{10}{a}= \frac{5}{b}=\frac{-20}{c}\)

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For, complete question, to see the attachment.

Using trigonometric function the length to the nearest foot of the shortest ladder that will safely reach a roof that is 23 feet high is calculated as 25 feet.

What are trigonometric functions?

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trigonometric functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the angle a ladder makes with the ground should be no greater than 67°.

So the angle θ ≤ 67°.

Let us assume the angle to be equal to 67°

The height of the roof from the ground is 23 feet.

The ladder and wall form the right triangle where the ladder works as hypotenuse and the wall as perpendicular.

With the sine function, find the length of the ladder -

sin θ = perpendicular/hypotenuse

Let the length of ladder be x.

sin 67° = 23/x

x = 23/sin 67°

x = 23/0.920

x = 25 feet

Therefore, the length of the ladder is 25 feet.

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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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a) The sum of the measures of the interior angles of the regular nonagon is given by S₉ = 1260°

b) The measure of each interior angle of the regular nonagon is a = 140°

c) The measure of each exterior angle of the regular nonagon​ is b = 40°

Given data ,

Sum of the measures of the interior angles of a regular nonagon:

The Polygon Interior Angle Sum Theorem states that the sum of the measures of the interior angles of a polygon with n sides is given by the formula:

Sum of interior angles = (n - 2) * 180°

For a nonagon, which has 9 sides, we can plug in n = 9 into the formula:

Sum of interior angles = (9 - 2) * 180

Sum of interior angles = 7 * 180

Sum of interior angles = 1260°

So, the sum of the measures of the interior angles of a regular nonagon is 1260°

Measure of each interior angle of a regular nonagon:

Since a regular nonagon has 9 sides, we can divide the sum of the interior angles (which we calculated as 1260 degrees) by the number of sides to find the measure of each interior angle:

Measure of each interior angle = Sum of interior angles / Number of sides

Measure of each interior angle = 1260 / 9

Measure of each interior angle = 140°

So, the measure of each interior angle of a regular nonagon is 140°

Measure of each exterior angle of a regular nonagon:

The Polygon Exterior Angle Sum Theorem states that the sum of the measures of the exterior angles of a polygon with n sides is always 360°

Since a regular nonagon has 9 sides, we can divide 360 degrees by the number of sides to find the measure of each exterior angle:

Measure of each exterior angle = 360 / Number of sides

Measure of each exterior angle = 360 / 9

Measure of each exterior angle = 40°

Hence , the measure of each exterior angle of a regular nonagon is 40°

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Answer:

the probability is:

P(A) 2/6 =1/3

Now let's take rolling a prime number:

A prime number is a natural number greater than 1 which can only be divided without a remainder by 1 and itself. So from the numbers on the cube prime numbers are:

2, 3 and 5. The probability of getting a prime number in a single roll is:

P(B) =3/6=1/2

Now to calculate the probability of A and B

you have to multiply both probabilities:

P(A-B)=P(A) . P(B) = 1/3 . 1/2 = 1/6

Step-by-step explanation:)

Answer:

101.6cm²

Step-by-step explanation:

1 inch = 2.54cm

that means:

40in² × 2.54 = 101.6cm²

The sixth term of the geometric sequence is 2048.

The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.

The formula for the nth term (an) of a geometric sequence is given by:

an = a1 * r^(n-1)

where a1 is the first term and r is the common ratio.

For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:

an = 2 * 4^(n-1)

To find a6, we substitute n = 6 into the formula:

a6 = 2 * 4^(6-1)

  = 2 * 4^5

  = 2 * 1024

  = 2048

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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,

Then find a6. Round to the nearest tenth if necessary.

a = 5×4 X

a1 = n-1 X

The equation of line for the given data is y = 5x -1.

According to the given question.

We have a data of points for a equaton of line.

As we know that the standard equation of line is y = mx + b.

Where, m is the slope of line and b is the y intercept.

Since, the points which are given in the data must satisfy y = mx + b.

Therefore,

Lets take the points (1, 4) and (2, 9) and substitute it in y = mx + b to find the value of m and b.

At x = 1 and y = 4

4 = m + b ..(i)

And at x = 2 and y = 9

9 = 2m + b ..(ii)

From equation i and ii

m = 5

So, b = -5 + 4 = -1

Hence, the equation of line for the given data is y = 5x -1.

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Answer:

(E) square

Step-by-step explanation:

because it's all side's are equal

A, B, C, D, E, F

A square is all of them :D

Answer:

67

Step-by-step explanation:

cause math

Answer:

It is 67

Step-by-step explanation:

Answer: \(\frac{x^{2}}{3^{2}}+\frac{y^{2}}{5^{2}}=1\)

Answer: $119

Step-by-step explanation:

     We will find the rate of dollars per hour by dividing.

$289 dollars / 17 hours = $17 dollars per hour

     Next, we will multiply this rate by 7 hours.

7 hours * $17 dollars per hour = $119

a. The image is attached below.

b. Length of the equator is 24,000 miles.

c. The image is attached below.

d. No, it is not possible for a satellite to see 50% of the Earth's equator.

Satellite B will see more of the Earth's equator than Satellite A. This is because the viewing angle of Satellite B is larger than the viewing angle of Satellite A. The viewing angle of Satellite B is 60 degrees, while the viewing angle of Satellite A is 45 degrees.

The length of the equator in view of Satellite B is 24,000 miles. This can be calculated using the following formula:

length of the equator = 2 * \(\Pi\) * radius * sin(m/2)

Use a third color to draw the viewing angle from Satellite C. Label the points of tangency J and K. If m/C=45", find the mJK and mJZK

This is because the Earth is a sphere, and a sphere has no flat surfaces. A satellite can only see a portion of the Earth's surface, and the portion that it sees will always be less than 50% of the total surface area.

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Answer:

x = -13 or 2

Step-by-step explanation:

x² + 11x + ¹²¹/₄ = ¹²⁵/₄

(x + ¹¹/₂)² = ¹²⁵/₄

x + ¹¹/₂ = ±¹⁵/₂

x = -¹¹/₂ ± ¹⁵/₂

x = -13 or 2

Answer: D is the correct answer.

Step-by-step explanation: I took the test :)

Answer:

\(1\frac{9}{12}\)

Step-by-step explanation:

Convert any whole numbers to improper fractions

\(\frac{9}{4}-\frac{3}{6}\)

Find the LCM of the denominators and use multiplication to change the denominators to the LCM

\(\frac{27}{12}-\frac{6}{12}\)

Subtract

\(\frac{21}{12}\)

Simplify

\(1\frac{3}{4}\)

\(1\frac{9}{12}\) can be simplified to \(1\frac{3}{4}\) so the answer is \(1\frac{9}{12}\)

The length of each leg of the triangle is 2 and 2√3. The result is obtained by using the trigonometric ratio formula.

See the angle of a triangle in the picture attached!

We have a triangle with a hypotenuse 4 and angles shown in the picture. Find the length of each leg of the right triangle!

Let's take

See the second picture in the attachment!

cos θ = adjacent/hypotenuse

cos 60° = x/4

1/2 = x/4

x = 2

sin 60° = opposite/hypotenuse

sin 60° = y/4

1/2 √3 = y/4

y = 2√3

Hence, the legs of the triangle have lengths of 2 and 2√3.

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Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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Answer:

2m/s^2

Step-by-step explanation:

the difference between 30 and 40 is 10. divide 10 by 5 and you get 2

Answer:

The answer is 2m/s2

Step-by-step explanation:

i got it right

Answer:      -172

Explanation: (-17.2 x2.5)=  -43x4= -172

Answer:

x^2 + y^2 = 100

Step-by-step explanation:

The equation of the circle that you are looking for is x^2 + y^2 = 100.

You can find this by using the base formula for a circle:

(x - x1)^2 + (y - y1)^2 = r^2

In which x1 is the x-coordinate of the origin, y1 is the y-coordinate of the origin, and r is the radius. So we put in the values we know and simplify.

(x -0)^2 + (y - 0)^2 = 10^2

x^2 + y^2 = 100

Answer:

false

Step-by-step explanation:

to get the area of a rectangle u need to multiple length and width.

Answer:

false

Step-by-step explanation:

the given expression describes the perimeter.

the area is

length × width (or breadth or depth or whatever word applies best for the second dimension in a certain scenario)

Answer:

-3

Step-by-step explanation:

12/-4=-3

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex..

Trigonometry is a discipline of mathematics that examines relationships between triangles' degrees and sides. Trigonometry is used frequently in geometry because every straight-sided form may be broken down into a group of triangles. Trigonometry and other areas of mathematics, particularly calculus, real or complex, infinite series, logarithms, and infinite series, have a staggering amount of interrelationships.

Here,

Angle of elevation to the balloon's peak: = 28°

When the balloon is erect, a right triangle is formed by the horizontal distance to the balloon, l, the height of the balloon, h, and the distance to the top of the balloon, d.

Aside from the hypotenuse

l = The leg next to the provided reference angle

,h = The leg perpendicular to the specified angle,

Trigonometric ratios give us;

Cosx is equal to the product of the hypotenuse and adjacent lengths.

where we obtain;

Cos x equals l/d

=>Cos 28 = 30 m /d

=> d = 30m/Cos 28 ≈ 33.977

Therefore , the solution of the given problem of solution of trigonometry d = 33.977 m is the distance from the balloon's base to its apex.

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