In a class of 26 students, 15 play an instrument and 5 play a sport. There are 3 students who play an instrument and also play a sport. What is the probability that a student chosen randomly from the class plays a sport and an instrument?

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

A rectangle that could have a perimeter of 52 feet is a 12 feet by 14 feet rectangle.

The symbols W and L are variables.

The symbol P is a constant.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + W)

52 = 2(12 + 14)

52 = 2(26)

52 feet = 52 feet.

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Answer:

Step-by-step explanation:

To calculate the area of a triangle, multiply the height by the width (this is also known as the 'base') then divide by 2.

6 * 10 : 2 =

30cm²

a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Answer:

0 > -10

True

Step-by-step explanation:

7 > -3 Starting with a true statement. This math sentence says, "7 is greater than -3"

7 > -3

-7 -7 Subtract 7.

Working vertically now (from the top, down)

7 > -3

-7 -7

_______

0 > -10

Because 7-7 is 0 on the left side. And

-3-7 is -10 on the right side. This statement is true, because zero is bigger than -10.

Answer:

x = 9°

y = 39°

Step-by-step explanation:

7x = 63

x = 9°

3y + 63 = 180

3y = 117

y = 39°

Answer:

Step-by-step explanation:

Let the distance from the point Malaya is standing to the courthouse be x and the distance to the bank is y

Then we have:

Answer:

106.3ft

Step-by-step explanation:

x= tan72=90/x

x= 90/tan 72

x= 29.2

y= tan35=54/y

y= 54/tan35

y= 77.1

x+y= answer

29.2 + 77.1 = 106.3

1) Counting the circles, we can write the following

20 = 1 x 20

20 = 4 x 5

20 = 2 x 10

2) So that's the answer

Answer:

7 + 2 = 9, so AC = 7/9 and CD = 2/9

1 + 2 = 3, so AB = 1/3 = 3/9 and

BD = 2/3 = 6/9

AB + BC = AC

3/9 + BC = 7/9, so BC = 4/9

AB:BC:CD = (3/9):(4/9):(2/9) = 3:4:2

Option E:

This graph is not a function because the value of y is the same for every value of x

Solution :

Domain:

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.

For example, when we use the function notation f:R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real number R (and its set of possible outputs or codomain is also the set of real numbers R).

relation represents y as a function of x

1) is NOT a function of if there are two or more points with the same − , but

− .

2) is a function of if each has a different

There is a technique called the vertical line test that is often used to determine if a graph represents y

as a function of x

In this question only a horizontal line is present.

Option E:

This graph is not a function because the value of y is the same for every value of x

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Answer:

your answer are c and d hope it helps .

Answer:

Step-by-step explanation:

P(-2,-1) and Q(4,3)

average of x-coordinates = (-2+4)/2 = 1

average of y-coordinates = (-1+3)/2 = 1

midpoint of PQ: (1,1)

distance between midpoint and Q = √((4-1)²+(3-1)²) = √13

(x-1)² + (y-1)² = 13

The equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

A circle is a shape consisting of all points in a plane that are at a given distance from a given point (the Centre) Equivalently .

Equation of circle

The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle.

The equation of circle represents all the points that lie on the circumference of the circle .

The standard equation of a circle with center at \((h , k )\) and radius r is

  \((x - h)^{2} + (y - k)^{2} = r^{2}\)

The distance formula in coordinate geometry is used to calculate the distance between two given points.

The formula says the distance between two points (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\))

\(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

The Midpoint Formula:

The midpoint of two ends coordinates points,  (\(x_{1} ,y_{1}\)), and (\(x_{2} , y_{2}\)) is the point M can be found by using:

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

According to the question

P = (-2,-1) and Q = (4,3) are the

endpoints of the diameter of a circle

Therefore, distance between point P and Q which is diameter of circle is

 \(Distance(D) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }\)

P(-2,-1) =  (\(x_{1} ,y_{1}\))

Q (4,3) =  (\(x_{2} , y_{2}\))

Now,

Diameter of circle = \(\sqrt{(4 - (-2) )^{2} + (3 - (-1) )^{2} }\)

                             = \(\sqrt{(6 )^{2} + (4 )^{2} }\)

                             = \(\sqrt{(36 + 16) }\)

                             = \(\sqrt{52}\)

As , radius  =  \(\frac{diameter }{2}\)

       radius (r) =  \(\frac{\sqrt{52}}{2}\)          

As we know The center of the circle separates the diameter into two equal segments called radii and radii are equal in a circle .

i.e mid point of coordinates of diameter are coordinates of circle .

\(M = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(Centre of circle (h,k) = \frac{x_{1} + x_{2}}{2}, \ \ \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{x_{1} + x_{2}}{2}, \ \ k = \frac{y_{1} + y_{2}}{2}\)

\(h = \frac{ -2 + 4}{2}, \ \ k = \frac{-1 + 3}{2}\)

\(h = 1, \ \ k = 1\)

Now , substitute the value in the equation of circle

\((x - h)^{2} + (y - k)^{2} = r^{2}\)

\((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

Hence, the equation of the circle is \((x - 1)^{2} + (y - 1)^{2} = \frac{52}{4}\)

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The differential equation dy/dt = y(3-y) smug all of the given conditions.

One possible autonomous differential equation with equilibrium solutions at y=0 and y=3, and with y' > 0 for 0 < y < 3 and y' < 0 for -∞ < y < 0 and 3 < y < ∞, is:

dy/dt = y(3-y)

We can see that y=0 and y=3 are equilibrium solutions by setting dy/dt = 0 and solving for y:

dy/dt = y(3-y) = 0

y = 0 or y = 3

To check the sign of y', we can use the derivative of y(3-y) with respect to y:  d/dy (y(3-y)) = 3 - 2y

For y < 0, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which says that y' < 0.

For 0 < y < 3, we have y(3-y) > 0, so d/dy (y(3-y)) > 0, which implies that y' > 0.

For y > 3, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which implies that y' < 0.

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Answer:

The answer is y = .22x + 17.4

Step-by-step explanation:

I got it right on a major test. just trust me

According to the information, the maximum infection rate is:  k * 2500 * (5000 - 2500) = 6250k = 40

To address this problem, we can use the law of the infection rate, which states that the infection rate is directly proportional to the product of the number of people infected and the number of people not infected. Therefore, we can write:

where "k" is a constant of proportionality. Since we want to find the number of people infected that produces the maximum infection rate, we can consider the infection rate as a function of the variable "x" representing the number of people infected. Therefore, we can write:

To find the value of "x" that maximizes the infection rate, we can derive this function and set the derivative equal to zero:

This implies that 5000 - 2x = 0, and therefore:

Therefore, the number of infected people that produces the maximum daily rate of infection is 2,500.

However, we must verify that this result is consistent with the information given in the problem. We know that when there are 1,000 people infected, the flu spreads at the rate of 40 new cases per day. Therefore, if we add 1,500 more infected people (for a total of 2,500), the infection rate would be:

If the infection rate is 40 new cases per day, we have:

which implies that:

Therefore, the maximum infection rate is:

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Answer:

25\(\pi\)

Step-by-step explanation:

\(\pi\)r^2 is the formula for a circle (in this case, a circular rug)
and we would set it equal to 84 (since we are trying to get the biggest size possible).
We would isolate r so that r^2 = 84/\(\pi\), and r would be around 5.17219.
If we were going by rounding 5 would be the largest radius possible and the radius would be 25\(\pi\) or about 78.5398 units.

Answer:

Rounded to one decimal place, the maximum area circular rug that can fit in the dining room is 38.5 square feet.

Please See the attached screenshot for the exact solutions and answer for this question

The geometric series is;

when n=1, we have

When n=2, we have,

When n = 3, we get,

when n = 4, we get,

a. So, the first four terms of the series are: - 4, -4/3, -4/9 and -4/27

The sum to infinity of the series is:

b. The series, as we can see, is CONVERGENT, because it has a definite value as its sum.

c. The sum of the series is - 6

Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

P(X>1) = 1 - P(X<1),

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

option 2, 3, and 5

Step-by-step explanation:

yuh

Answer:

456

Step-by-step explanation:

Product means an answer derived from multiplication.  Therefore, if the product is 155952, and one value is 342, then the following equation is true:

342x = 155952, or 342 * x = 155952

Divide 155952 by 342 to get: 456.

Check the work in the equation:

342(456) = 155952

155952 = 155952, which is true, so the answer is 456.

If I helped, please make this answer brainliest! ;)

9514 1404 393

Answer:

  C.  3.6

Step-by-step explanation:

AC = FA + FC = 4+6 = 10

AC is the hypotenuse of right triangle ABC, which has leg BC = 8. Then the length of AB is given by the Pythagorean theorem as ...

  AB² +BC² = AC²

  AB = √(10² -8²) = 6

The side lengths of these similar triangles are proportional, so you have ...

  FG/FC = AB/AC

  FG = FC(AB/AC) = 6(6/10)

  FG = 3.6

Answer:

43.6 has 3 significant figures.

Answer:

\(\overrightarrow{VU}\text{ and }\overrightarrow{VW}\)

Step-by-step explanation:

From the given figure it is clear that we two rays because both sides have one endpoint and goes on infinitely in only one direction.

If a ray has end point at A and goes on infinitely in only one direction towards point B, then ray is denoted as \(\overrightarrow{AB}\).

For first side, we have point V as end point and ray goes goes on infinitely in only one direction towards point U. So, first side is \(\overrightarrow{VU}\).

For second side, we have point V as end point and ray goes goes on infinitely in only one direction towards point W. So, second side is \(\overrightarrow{VW}\).

Therefore, the sides are \(\overrightarrow{VU}\text{ and }\overrightarrow{VW}\).

Answer:

$181.4

Step-by-step explanation:

Note,

Therefore, the store applied a discount price of $181.4 to the set of golf clubs.

Answer:

x = (- \(\frac{13}{2}\), 0)
y = (0,26)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer:

d.

3. 1 < d < 3

e.

1. t > 6

f.

2. -z ≤ 7

Step-by-step explanation:

To express the given statements as an inequality, we need to determine the relationship between the given quantities.

d. The statement "d is between 3 and 1" means that d is greater than 1 and less than 3. Mathematically, we can represent this as 1 < d < 3.

e. The statement "t is no less than 6" means that t is greater than or equal to 6. Mathematically, we can represent this as t > 6.

f. The statement "The negative of z is not greater than 7" means that the value of -z is less than or equal to 7. Mathematically, we can represent this as -z ≤ 7.

Answer:

d)  3. 1 < d < 3

e)  5. t ≥ 6

f)  2. -z ≤ 7

Step-by-step explanation:

If d is between 3 and 1 then d is greater than 1 and less than 3.

Therefore, the expression of this statement is:

If t is no less than 6, then t is greater than or equal to 6.

The expression of this statement as an inequality is:

If the negative of z is not greater than 7, then the negative of z must be less than or equal to 7.

The expression of this statement as an inequality is:

a.

The dilation is a reduction, this comes from the fact that the dilation factor is less than 1.

b.

A point after a dilation is given as:

where k is the dilation factor.

In this case we need to divide all the coordinates by two, then we have that:

Answer:

y = 5

Step-by-step explanation:

\(14y-7y=35\\7y=35\\y=5\)

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

The zeros with each multiplicity are given as follows:

The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

Considering the linear factors of the function in this problem, the zeros are given as follows:

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