The average rainfall of a prairie land is:

Answer:

Step-by-step explanation:

hello,

how many students ? 14 + 2 + 5 +3 = 24

how many students who had C and S ? 14 + 2 + 5 = 21

so P(C∪S)=21/24=(7*3)/(8*3)=7/8

hope this helps

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

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

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

To learn more about central tendencies,

brainly.com/question/17631693

#SPJ4

The height of the cone in terms of Y is as follows:

The cylinder and the cone have the same volume.  The cylinder has a radius of X and a height of Y.

Therefore,

volume of a cylinder = πr²h

volume of the cylinder = π × X² × Y

volume of a cylinder = X²Yπ  unit cube

The cone has radius 1/2X. The height of the cone can be found as follows:

Recall the volumes of the cylinder and cones are the same.

Therefore,

volume of a cone = 1 / 3 πr²h

X²Yπ = 1 / 3 π (1 / 2 X)²h

1 / 3 π × 1 / 4 X² h =  X²Yπ

divide both sides by π

1 / 3 × 1 / 4 X² h = X²Y

divide both sides by X²

1 / 12 h = Y

cross multiply

h = 12Y units

learn more on cone and cylinder here: https://brainly.com/question/28127632

#SPJ1

Answer:

1) 54+2x=5x−6−18x Distributive Property

2) 60=−15x Division Property of Equality

3) −4=x Division Property of Equality

Explanation:

1.) This answer is Distributive Property because the parenthesis in the original equation were removed through the process of distributing.

3(–2 – 6x) was distributed by multiplying 3 • –2 and 3 • –6x to get –6 – 18x

2.) This answer is Division Property of Equality because for all real numbers x, y, and z, if x = y and z ≠ 0, then x/z = y/z. This is true in this equation because of 60/–15 = −15x/–15.

3.) Division is used to get the value of x, which is –4.

Hope that helps! Have an amazing rest of your day! Please consider giving me the Brainliest! :)

Answer:

$36.00 markup

Step-by-step explanation:

$72 x 50% (0.50) = $36.00

The bearing the pilot should fly is approximately 70°, and the plane's groundspeed is approximately 242 knots.

To find the bearing the pilot should fly, we need to consider the effect of the wind on the plane's path. The pilot wants to maintain a flight path on a bearing of 65°30', but the wind is blowing from the south at 24.4 mph.

First, let's analyze the wind vector. Since the wind is blowing from the south, its direction is opposite to the north, which is 180°. Additionally, we can convert the wind speed from mph to knots by dividing it by 1.15 (since 1 knot is equal to 1.15 mph). Therefore, the wind vector can be represented as 180° with a magnitude of 21.2 knots (24.4 divided by 1.15).

Next, we need to consider the effect of the wind on the plane's path. The wind will cause the plane to drift off course, creating a resultant vector when combined with the plane's velocity. To determine the resultant vector, we can use vector addition.

Given that the plane's velocity is 245.1 mph, we can convert it to knots by dividing it by 1.15, resulting in approximately 213 knots. Now, using vector addition, we can add the wind vector (180°, 21.2 knots) to the plane's velocity vector (65°30', 213 knots).

Adding these vectors, we find the resultant vector, which represents the plane's groundspeed and direction. To calculate the bearing, we can use trigonometry. The angle between the resultant vector and the north direction gives us the bearing. In this case, the bearing is approximately 70°.

To determine the plane's groundspeed, we can find the magnitude of the resultant vector. Using the Pythagorean theorem, we can calculate the magnitude as follows:

groundspeed = sqrt(213² + 21.2²) = sqrt(45369.69 + 449.44) = sqrt(45819.13) ≈ 214.2 knots

Therefore, the plane's groundspeed is approximately 214.2 knots.

In summary, the pilot should fly on a bearing of approximately 70° to compensate for the wind and maintain a desired flight path of 65°30'. The plane's groundspeed will be approximately 214.2 knots.

Vector addition is a fundamental concept in mathematics and physics, commonly used to calculate the combined effect of multiple vectors. It involves breaking down vectors into their components and adding corresponding components to obtain the resultant vector.

Trigonometry is then used to determine the magnitude and direction of the resultant vector. Understanding vector addition is crucial for solving problems involving motion and forces in various fields of science and engineering.

Learn more about Bearing

brainly.com/question/30446290

#SPJ11

For any natural number N, there exists N consecutive integers none of which is a power of an integer with exponent greater than one

The question reads thus:  Prove that for any natural number N, there exists N consecutive integers none of which is a power of an integer with exponent greater than one

Now, let n and n+1 be the two integers

⇒ n(n+1)

Now two cases are possible

Case 1:

n = even number = 2k

Product: = 2k(2k +1) = 4k² + 2k

= 2(2k² + k)    ................................ even number

case two:

n= odd number = 2k - 1

Product: (2k + 1) (2k+1)

= 4k² + 6k + 2

= 2(2k² +3k + 1 ) ............................................ even

Learn more about product of natural numbers on https://brainly.com/question/15633116

#SPJ1

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

That is representative of all possible outcomes from flipping the coin

Using the Poisson distribution, it is found that:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

In this problem, the mean is of \(\mu = 16\), hence the probability of 15 patients in a day is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 15) = \frac{e^{-16}16^{15}}{(15)!} = 0.0992\)

Hence the mean number of days in a month (30 days) with 15 patients visiting is given by:

M = 30 x 0.0992 = 2.976.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530

#SPJ1

Answer:

The answer you're looking for is D! I hope this helped :)

Simplify:2yp'' + 3yp' + 24yp = 0 .This is just the homogeneous part of the equation, which we already solved, so we know that this holds.

Given the differential equation

2d²z/dx² + 3 dz/dx + 24z = 22

Propose an appropriate particular solution.

Take A, B and C to be functions of x.

dz² yp = Ar + e(B cos(√7 x) + C sin(√7 x))

We are given the differential equation:

2d²z/dx² + 3dz/dx + 24z = 22.

We can find an appropriate particular solution using the method of undetermined coefficients.

Since the right-hand side is a constant, we can propose a constant particular solution:

zp = k

Substitute into the differential equation:

2d²(k)/dx² + 3d(k)/dx + 24k = 22

The derivatives of k are zero, so we get:

24k = 22k = 11/12

Therefore, a particular solution for the differential equation is:

zp = 11/12

Since zp is a constant, we can't include any x-terms.

So let's use an exponential function for yp, then:

yp = Ae^(mx)

Differentiating:

yp' = Ame^(mx)

and:

yp'' = Am^2 e^(mx)

Substitute into the differential equation:

2A m^2 e^(mx) + 3Am e^(mx) + 24Ae^(mx) = 22e^(mx)

Divide by Ae^(mx):

2m^2 + 3m + 24 = 22e^(-mx)

We can use a sine or cosine function to satisfy the left side of the equation.

Since we don't have an imaginary number in the exponential, we can choose a cosine function.

Therefore, let's assume that:

yp = A cos(√7 x) + B sin(√7 x)

Then:

yp' = -A √7 sin(√7 x) + B √7 cos(√7 x)

and:

yp'' = -A (7 cos(√7 x)) - B (7 sin(√7 x))

Substitute into the differential equation:

2[-A (7 cos(√7 x)) - B (7 sin(√7 x))] + 3[-A √7 sin(√7 x) + B √7 cos(√7 x))] + 24[A cos(√7 x) + B sin(√7 x))] = 22 cos(√7 x)

We can collect terms:

(-49A + 3B + 24A) cos(√7 x) + (-49B - 3A + 24B) sin(√7 x) = 22 cos(√7 x)

Therefore:

A = 22/74 = 11/37 and B = 0

We can substitute this back into yp to get:

yp = 11/37 cos(√7 x)

Therefore, a particular solution for the differential equation is:

yp = 11/12 + 11/37 cos(√7 x)

Let's verify that the general solution with

yp = 11/12 + 11/37 cos(√7 x)

satisfies the differential equation:

2d²z/dx² + 3dz/dx + 24z = 22

We have:

z = yp + yc

Let's differentiate z:

z' = yp' + yc'

and:

z'' = yp'' + yc''

Substitute into the differential equation:

2(yp'' + yc'') + 3(yp' + yc') + 24(yp + yc) = 22

Simplify:2yp'' + 3yp' + 24yp = 0

to know more about differential equation visit:

https://brainly.com/question/32645495

#SPJ11

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

To know more about sequence visit:

https://brainly.com/question/21961097

#SPJ1

Answer:

0.6

Step-by-step explanation:

Given problem:

                 \(\sqrt[3]{\frac{64}{343} }\)  

if an expression is of this form, we simplify

           \(\sqrt[3]{x}\)   = \(x^{\frac{1}{3} }\)  

\(\sqrt[3]{\frac{64}{343} }\)   = \(\frac{64^{\frac{1}{3} } }{343\frac{1}{3} }\)  

            = \(\frac{4^{3x ^{\frac{1}{3} } } }{7 ^{3 ^x{\frac{1}{3} } } }\)

           = \(\frac{4}{7}\)

           = 0.57 to the nearest tenth

          = 0.6

Answer:

Hello the answer is 5x - y = 30!

Step-by-step explanation:

m = (0 (-5))/(6 - 3) = (0 + 5)/(3) = 5/3

y = mx + b

O = (5/3)(6) + b

O = (30/3) + b

O = 10 + b

-10 = b

3y = 5x - 30

3y + 30 = 5x

5x - 3y = 30

Answer:

\(x=-2\)

Step-by-step explanation:

Use the distributive property, \(a(b+c)=ab+ac\)

\((2x - 3)(2x + 1) + 35 = 4x (x-5)\\(2x - 3)(2x + 1) + 35 = (4x)(x)-(4x)(5)\\(2x - 3)(2x + 1) + 35 = 4x^2-20x\)

Use the concept of FOIL (First Outer Inner Last ), \((a+b)(c+d)=ac+ad+bc+bd\)

\((2x)(2x)+(2x)(1)-(3)(2x)-(3)(1) + 35 = 4x^2-20x\\4x^2+2x-6x-3 + 35 = 4x^2-20x\\-4x+32 = -20x\\-4x+20x=-32\\16x=-32\\x=\dfrac{-32}{16}\\x=-2\)

Answer:

15 batches of cookies

Step-by-step explanation:

We need to find out how many third cups do into 5 cups. We can do this by 5 ÷ 1/3

When dividing fractions, use KFC:

Therefore, 5 ÷ 1/3 = 5 × 3/1 which is 15 batches of cookies

Hope this helps!

Answer:

Step-by-step explanation:

no because 6 , 7 and 10 doesn't add up to 180 so it is not

A triangle has sides with lengths of 6 kilometers, 7 kilometers, and 10 kilometers is not a right triangle.

To determine if a triangle is a right triangle, you can use the Pythagorean Theorem. The Pythagorean Theorem states that "In a right-angled triangle, the sum of the square of the two shorter sides is equal to the square of the longest side." It can be written as:

a² + b² = c², where 'a' and 'b' are the lengths of the two legs of a right triangle, and 'c' is the length of the hypotenuse.

In this triangle, the two shorter sides have lengths of 6 kilometers and 7 kilometers and the longest side is 10 kilometers.

The square of 6 kilometers is 36 kilometers and the square of 7 kilometers is 49 kilometers.

The sum of 36 kilometers and 49 kilometers is 85 kilometers.

The longest side of the triangle has a length of 10 kilometers, and the square of 10 kilometers is 100 kilometers.

Since 85 kilometers is not equal to 100 kilometers, this triangle is not a right triangle.

Learn more about the Pythagorean Theorem here:

brainly.com/question/13095504

#SPJ11

Answer:

I. First number, a = 40.

II. Second number, b = 50.

III. Third number, c = 120.

Step-by-step explanation:

Let the three numbers be a, b and c respectively.

Given the following data;

Translating the word problem into an algebraic equation, we have;

a + b + c = 210

b = a + 10

c = 3a

Substituting the value of b and c into the equation, we have;

a + a + 10 + 3a = 210

5a + 10 = 210

5a = 210 - 10

5a = 200

a = 200/5

a = 40

To find the value of b;

b = a + 10

b = 40 + 10

b = 50

To find c

c = 3a

c = 3*40

c = 120

To find the intersection of A and B figure who has the bigger lower bounds and smaller upper bounds out of A and B.

The lower bound of A is -4 while the lower bound of B is (but not including) 1. So the lower bound will be (1.

The upper bound of A is 4 while the upper bound of B is 7. So the resulting upper bound will be 4].

Put these together and get (1,4].

Hope this helps :)

Answer:

46$ in total

y=2r+20

If Isabella goes on 13 rides, she would have to pay a total of $46. If she rides 'r' times, the total cost would be expressed by the mathematical equation 20 + 2r.

This question relates to a linear relationship involving a fixed cost and a variable cost. In Isabella's case, the fixed cost is the admission fee, which is $20. The variable cost is the rides, where each ride costs $2.

So, if she goes on 13 rides, she will have to pay: $20 (for admission) + ($2 * 13 (rides)) = $20 + $26 = $46.

For r rides, the total cost would be: $20 (for admission) + ($2 * r (rides)). So the total cost for r rides can be expressed in a mathematical equation as: 20 + 2r.

https://brainly.com/question/34783456

#SPJ2

The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

Learn more about social security tax here:

https://brainly.com/question/18268724

#SPJ1

An equation for C is C = 0.1t + 4.

An interpretation of the slope of the graph is that the total cost of using a computer increases by 0.1 per minute.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 4.5)/(10 - 5)

Slope (m) = 0.5/5

Slope (m) = 0.1

At data point (10, 5) and a slope of 0.1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 0.1(x - 10)

y = 0.1x + 5 - 1

y = 0.1x + 4 ≡ C = 0.1t + 4

Read more on point-slope here: brainly.com/question/24907633

#SPJ1

Answer:

9y+45

Step-by-step explanation:

9(y+5)

=9*y+9*5

=9y+45

The expression that is equivalent to 9(y+5) is 9y + 45.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

The distributive property of multiplication over addition (or subtraction) allows you to simplify an expression by distributing the multiplication over each term inside the parentheses.

In this case, you can use the distributive property to simplify 9(y + 5) by multiplying 9 by each term inside the parentheses:

9(y + 5) = 9y + 45

So the expression that is equivalent to 9(y + 5) is 9y + 45.

Learn more about algebraic Expression here:

https://brainly.com/question/953809

#SPJ3

The correct statements for comparing the effectiveness of the SAT preparation program are the 3rd, 4th, 5th, 6th statements.

The statements in order are

Since, school counselor want to compare effectiveness of SAT preparation program with response variable will be the improvement in SAT score.

We can consider this as a improvement assessment, so that the initial abilities of each student will be different. With this we can see the improvement from student with bad initial score, and for the student that has a good score in initial exam they barely to have improvement.

For example student A have initial score 600 and student B have initial score 1300 after preparation program student A have final score 1200 and student B have final score 1350. In the example, we can see 200% improvement from student A and only 4% improvement from student B.

Also, with matching pair design that based on variable, we can see the variability in improvement making it easier to know the effectiveness of SAT preparation program than the randomized design.

Thus, the correct statements is the 3rd, 4th, 5th, 6th statements.

Learn more about matched pair design here:

brainly.com/question/23413412

#SPJ4

Therefore, an automobile insurance policy can provide him with financial protection for the total loss of his Lexus and the RAV4 in the garage

David's full coverage policies for his home and automobile should provide him with financial protection for the damages caused by the accident. From his home insurance policy, he may be able to receive compensation for the damage to his garage. And from his automobile insurance policy, he should be able to receive compensation for the total loss of his Lexus and the RAV4 that was also in the garage.

With full coverage on his home and automobile, David can expect to receive financial compensation for the damages caused by the accident. From his home insurance policy, he can get compensation for the garage damage, while his automobile insurance policy can provide him with financial protection for the total loss of his Lexus and the RAV4 in the garage.

Therefore, an automobile insurance policy can provide him with financial protection for the total loss of his Lexus and the RAV4 in the garage.

To learn more about the unit price visit:

https://brainly.com/question/29023044

#SPJ11

Answer:

\(x = 2\)

Step-by-step explanation:

Given

Conjecture: \(x + 3 < x^2\) --- (Missing)

Required

Which value of x prove the conjecture otherwise

To do this , we simply substitute the values of x in the options

\(1.\ x = -\frac{1}{3}\)

This is negative;

So, there is no need to check

\(2.\ x = -3\)

This is also negative;

So, there is no need to check

\(3.\ x = 2\)

\(x + 3 < x^2\)

\(2 + 3 < 2^2\)

\(5 < 4\)

This value of x is false because 5 is not less than 4

\(4.\ x = 3\)

\(x + 3 < x^2\)

\(3 + 3 < 3^2\)

\(6 < 9\)