a satellite traveling in a circular orbit 1,000 miles above the earth passes directly over a tracking station at noon. assume that the satellite takes 2 hours to make an orbit and that the radius of the earth is 4,000 miles. find the distance between the satellite and tracking station at 12:03 p.m. draw a picture (using the idea of orbits like above), then solve.

The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

What is a quadratic equation?

Any equation of the form  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

x = [-b± (√b²-4ac )] / 2a

The quadratic equation:

x²+6x+9=20

x²+6x -11 = 0

a = 1, b = 6, c = -11

x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)

x = -3 + 2√5 , x = -3 - 2√5

Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.

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Using the Pythagorean triplet, the value of AB is 2.

In the given question we have to find the length of AB.

From the given diagram we can see that;

ED = 2, DC = 8 and BC = 6.

To solve this question we use the Pythagorean Triplet.

Pythagorean triples consist of the three positive numbers a, b, and c, where a^2+b^2 = c^2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

Since we have to find the value of AB.

So we can write it as

EC^2 = AE^2+AC^2

(ED+DC)^2 = AE^2+(AB+BC)^2

Now putting the value

(2+8)^2 = AE^2+(6+AB)^2

10^2 = AE^2+(6+AB)^2

As we know that triplet (6,8,10).

The value of EC is 10, AE = 6, the value of AC can't be 6 because one part of value of AC is already given 6. So the value of AC is 8. AS BC=6, so AB=2.

Hence, the value of AB is 2.

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The inequality is: h less than equal to 2 That is the Numbers written in order from least to greatest going across

To find:

The values that make the given inequality true.

We have,

h less than equal to 2

It means the value of h must be less than or equal to 2.

In the given options, the list of numbers which are less than or equal to 2 is

-6, -3, -1, 1, 1.9, 1.99, 1.999, 2

The list of numbers which are greater than 2 is

2.001, 2.01, 2.1, 3, 5, 7, 10

Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.

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The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

[tex]P(t) = \frac{K}{1 + Ae^{-kt} }[/tex]

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

[tex]7000 = \frac{28000}{1 + 9e^{-k(1)} }[/tex]

[tex]1 + 9e^{-k} = 4[/tex]

[tex]9e^{-k} = 3[/tex]

[tex]e^{-k} = \frac{1}{3}[/tex]

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

[tex]14600 = \frac{28000}{1 + 9e^{-1.0986t} }[/tex]

[tex]1.9178 = 1 + 9e^{-1.0986t}[/tex]

[tex]0.9178 = 9e^{-1.0986t}[/tex]

[tex]\frac{0.9178 }{9} = e^{-1.0986t}[/tex]

[tex]t = \frac{ln \: 0.10198}{-1.0986}[/tex]

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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The money he will have in this account if he keeps it for 5 years is $358.

Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest.

WE have given $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.

Given,

P = $800

Time t=5 years

Interest rate= 2.9%

Hence, the amount will have in his account is:

=[tex]P(1 + 10 / 2000)^{2t}[/tex]

Here, the interest is compounded semiannually.

[tex]800 (1 + 2.9 / 200)^{10}[/tex]

=$358

Therefore, if the interest rate is compounded semiannually then the money he will have in this account if he keeps it for 5 years is $358.

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The smallest number of pupils the class could contain is 25.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100

Since we are told that 56% of the pupils in a class are girls, the smallest number of pupils the class could contain is 25. This will be:

= 14 / 25 × 100

= 56%

This is correct as indicated above.

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Answer:

b. temperature

Step-by-step explanation:

It is the measure of average kinetic energy of motion or K.E of a single particle in a system.

Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis should not be rejected.

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

An assertion used in statistical inference experiments is known as the alternative hypothesis. It is indicated by Ha or H1 and runs counter to the null hypothesis. Another way to put it is that it is only a different option from the null. An alternative theory in hypothesis testing is a claim that the researcher is testing.

One less than the confidence level, or 0.01, is the test's level of significance. The null hypothesis is not rejected since the p-value of 0.05 exceeds the level of significance of 0.01.

Therefore, the null hypothesis should not be rejected.

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Answer:

9

Step-by-step explanation:

3p + 6 = 5p – 12

6 + 12 = 5p – 3p

18 = 2p

p = 18/2

p = 9

rate as brainliest

thank you

Answer:

The answer would be 9.

Step-by-step explanation:

If you plug in 18 for both of them, the answer would be:

60=78

If you plug in 9 for both of them, the answer would be:

33=33

If you plug in 0 for both of them, the answer would be:

6=-12

If you plug in -9 for both of them, the answer would be:

-21=-57

So, 9 would be the best choice.

Hope this helps! :D

the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective

Mean: $2,000

Standard Deviation: $741.42

The mean of the random variable X is calculated by taking the sum of the products of the probability of each outcome and the corresponding value of X. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. Thus, the mean of X is calculated as:

Mean =[tex]$\sum_{i=1}^{N} P(X = x_i)*x_i[/tex]

= 0*1000 + 0.38*2000 + 0.59*3000 + 0.03*4000

= 2000

The standard deviation of the random variable X is calculated by taking the square root of the sum of the products of the probability of each outcome and the square of the difference between the corresponding value of X and the mean. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. The mean of X is 2000. Thus, the standard deviation of X is calculated as:

Standard Deviation = [tex]$\sqrt{\sum_{i=1}^{N} P(X = x_i)(x_i - \mu)^2}[/tex]

= [tex]\sqrt{(0(1000-2000)^2[/tex] + [tex]0.38*(2000-2000)^2[/tex] + [tex]0.59*(3000-2000)^2 + 0.03*(4000-2000)^2)}[/tex]

= [tex]\sqrt{741.42} = 27.22$[/tex]

Therefore, the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective

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The students ratio expressed in fraction as 6/4 = 4/x is incorrect for the similar triangles, and the correct ratio is x : 3 = 10 : 6 expressed in fraction as x/3 = 10/6. The value for x = 5.

Since the triangles are similar, it implies that the length 3 of the smaller triangle is similar to the length x of the larger triangle,

Also the length 6 of the smaller triangle is similar to the length of the larger triangle (4 + 6 = 10).

So it will be wrong to write 6/4 = 4/x, rather the correct fraction will be;

x : 3 = 10 : 6

which when expressed as fraction, we get;

x/3 = 10/6

x = (10 × 3)/6

x = 30/6

x = 5

Therefore, the students expression 6/4 = 4/x is incorrect representation for the lengths of the similar triangles. And the correct expression is x/3 = 10/6, which gives us the value of x equal to 5.

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The domain and range of the given function is a set of al real numbers and as such;

Domain : (-∞,∞)

Range : (-∞,∞)

We are given the function as f(x)= -3x+7.

In order for us to sketch the graph of this given function, we need to make a function table

Lets assume some random number for x  and find out f(x)

x                f(x) = -3x + 7

-2                 -3(-2) + 7 = 13    

-1                 -3(-1) + 7 = 10

0                 -3(0) + 7 = 7

1                  -3(1) + 7 = 4

We now plot the points as shown in the graph attached

Domain is defined as the set of all x values for which the function is defined while Range is defined as the set of all y values for which the function is defined

In this case, there is no restriction for x  and y and as such the domain and range is a set of all real numbers

Domain : (-∞,∞)

Range : (-∞,∞)

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Complete question is;

Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7

If x and y be  i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.

Yes, x y are x y independent studysoup.

Here  x and y be i.i.d. unif(0, 1)

The i.i.d stands for independent and identically distributed

unif means that the uniformly distributed

Here x and y are i.i.d unif (0,1)

The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable

Here we have to find the covariance of x + y and x - y

According to the properties of covariance

Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0

Because Cov(x, x) = Cov (y, y)

Cov(y, x) = Cov(x, y)

Therefore, the covariance of x+y and x - y is 0.

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The area of the regular hexagon value calculated using given perimeter of the regular hexagon is equal to option C. 600√3 square meters.

As given in the question,

Perimeter of the regular hexagon is equal to 'P' = 120m

Relation between the area of the regular hexagon 'A' and the perimeter of the regular hexagon 'P is given by :

A = √3 × ( P²/24 )

  = √3 × [(120)²/ 24]

  = √3 × ( 14400 / 24 )

  = √ 3 × 600

 = 600√3 square meters

Therefore, the area of the regular hexagon using the perimeter of the regular hexagon is equal to Option C.  600√3 square meters.

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As per the 95% confidence interval for the population mean is (31.042, 42.958).

What is meant by confidence interval?

In math, A normal distribution with a mean, μ  and standard deviation, σ  is used to estimate the confidence interval for the unknown population mean.

Here we have given that the random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations.

And we need to find the 95% confidence interval for ju for each of these situations.

Here we are given the following data:

   • Sample size, n=70

   • Sample mean, ¯x=37

   • Population standard deviation, σ=20

Then the 95% confidence interval for the population mean is defined as:

=> x±z0.01/2×σ√n

Here by applying Excel function for the confidence coefficient: 

=> NORM.INV(0.01/2,0,1)

Then we get,

=> 37±2.58×20√75(31.042, 42.958)

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The length of the rectangle is 1.054 units and the width of the rectangle is 4.72 units.

Length times width equals the area of a rectangle. Let's assume that x represents length and y represents width. To determine the dimensions of the rectangle, we must apply y values to the area formula, differentiate with respect to x, and then set differentiate to zero.

Parabola: [tex]y=5-x^{2}[/tex]

The equation of parabola indicates that it opens down and the axis of symmetry is x=0. So we can take the vertices of the rectangle on the x-axis as [tex]A=(-x,0)[/tex] and [tex]D=(x,0)[/tex]). The other two vertices above the x-axis on the parabola will be [tex]B=(-x, 5-x^{2} )[/tex] and [tex]C=(x,5-x^{2} )[/tex]

Dimensions of the rectangle will be,

[tex]x-(-x)=2x[/tex] and [tex](5-x^{2} )[/tex]

Area of the rectangle (A) = [tex]2x(5-x^{2} )[/tex]

Area function when differentiated (A′) = [tex]2x(-2x)+(5-x^{2} )(2)[/tex]

A′= [tex]-4x^{2} + 10 -2x^{2}[/tex]

A′= [tex]-6x^{2} +10[/tex]

Critical points for maxima and minima ⟹ [tex]-6x^{2} +10=0[/tex]

                                                               ⟹ [tex]10=6x^{2}[/tex]

                                                               ⟹ [tex]x^{2} = \frac{10}{6}[/tex]

                                                               ⟹ [tex]x= \sqrt \frac{10}{6}[/tex]

                                                               ⟹ [tex]x=[/tex] ±[tex]0.527[/tex]

Maximum area of 2X2 rectangle(square)

A= [tex]2*0.527(5- 0.527^{2} )[/tex] = [tex]4.97[/tex] [tex]units^{2}[/tex]

Length = 2x = 1.054 units

Width = [tex](5-x^{2} )[/tex] = 4.72 units

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The 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is expressed as f(x) ≈ P3(x) = a₀ + a₁(x - 4) + a₂(x - 4)² + a₃(x - 4)³.

Here, a₀, a₁, a₂, and a₃ are the coefficients that need to be calculated. To find these coefficients, we must use the Taylor series formula and the derivatives of f(x) evaluated at 4.

The Taylor series formula is Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!) (x-a)² + (f'''(a)/3!) (x-a)³ + ... +[tex](f^(n)(a)/n!) (x-a)^n[/tex].

The derivatives of f(x) evaluated at 4 are f'(4) = 1/2, f''(4) = -1/8, f'''(4) = -1/16.

Using these values, the coefficients of the 3rd-order Taylor polynomial can be calculated as a₀ = 2, a₁ = 1/2, a₂ = -1/8, and a₃ = -1/16.

Therefore, the 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is P3(x) = 2 + (1/2)(x - 4) - (1/8)(x - 4)² - (1/16)(x - 4)³.

Using this polynomial to approximate √14.03, we have P3(14.03) = 2 + (1/2)(14.03 - 4) - (1/8)(14.03 - 4)² - (1/16)(14.03 - 4)³ ≈ 3.76401097.

Therefore, the approximation of √14.03 using the 3rd-order Taylor polynomial is 3.76401097 to 8 decimal places.

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The simplified form of an expression is the expression written in its simplest form, usually achieved by combining like terms and removing unnecessary parentheses.

On solving the question we got to know that - Answer: For every ticket sold, 52$ is made, 1 : 52

A diagram or graphical representation that organizes the depiction of data or values is known as a graph. The relationships between two or more items are frequently represented by the points on a graph.

A graph is a type of non-linear data structure that consists of nodes and links. While the vertices are often sometimes referred to as nodes, in a graph the edges are the lines or arcs that connect any two nodes. The vertices (V) and edges (E) that make up a graph are what constitute it most rigorously ( E ). The prefix "G" appears in the graph (E, V).

y = mx - rise/run  = 208/4,  m = 52

The proportion is that for every ticket sold, 52 $ is made, 1 : 52

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Answer:

<MON = 102°

Step-by-step explanation:

Alternative Interior Angles so both of those angle equal to each other.

(12x + 30) = (9x + 48)

Get x to one side by subtracting.

12x - 9x + 30 = 48

3x + 30 = 48

Subtract 30 to both side to get x by itself.

3x = 18

Divide 3 to both side to solve for x.

x = 6

Plug x = 6 into <MON = (9x + 48)

9*6 + 48 = 54 + 48 = 102°

Answer:

The answer would be 12.

The equation would be (25/5)+7

Step-by-step explanation:

To solve this problem, first divide 25 by 5.

25/5=5

Now, add 7 to 5 for your answer.

The answer would be 12.

The equation would be (25/5)+7

Hope this helps! Have a great day! :D

25÷5=5

5+7=12

12 is your answer

The cost for two stations that are 10 miles apart will be $8.21.

What is cost?

Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.

Given equation is;

y = 0.354x+4.669

Where x represents the number of miles traveled.

For measuring the cost for two stations that are 10 miles apart;

x=10

Putting in given equation

y=0.354(10)+4.669

y=3.54+4.669

y=8.209

Rounding off to nearest hundredth;

y=$8.21

The cost for two stations that are 10 miles apart will be $8.21

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a. The number of students who were in math only is 7 students.

b. The number of students who were not majoring in computer science is 15.

c. The number of students who were not math or computer science is 8

From the information given, in a class of 25 students, there were 13 math majors, 10 were computer science majors, and 6 were dual majors in both.

It should be noted that the number of math majors only will be:

= 13 - 6

= 7

The number of students not majoring in computer science will be:

= 25 - 10

= 15

Those not math or computer science majors will be:

= 25 - 6 - 7 - (10 - 6)

= 8

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Answer:

(-∞, -4)

Step-by-step explanation:

11x > 4(1+3x)

11x > 4*1+4*3x  ==> distribute 4 to 1 and 3x using the distribution property

11x > 4 + 12x  ==> simplify

11x-12x > 4 + 12x-12x  ==> isolate x by subtracting 12x on both sides

-x > 4

x < -4  ==> when dividing by a negative number, switch the inequality sign

x < -4 can also be written as -∞ < x < -4

This is because x is greater than -∞ but can never equal -∞.

-∞ < x < -4 ==> (-∞, -4)

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Answer:

21.4

Step-by-step explanation:

If the ladder originally reaches up 21 feet on the side of the house, and Elijah pulls it 4 feet farther away from the house, the distance from the base of the ladder to the side of the house will increase by 4 feet. This means that the new distance from the base of the ladder to the side of the house will be 21 feet + 4 feet = 25 feet.

Since the height of the ladder is the same, and the base of the ladder is now 25 feet from the side of the house, the ladder will still reach up 21 feet on the side of the house. Therefore, the new distance from the top of the ladder to the ground will be 25 feet - 21 feet = <<25-21=4>>4 feet.

To find the new distance from the top of the ladder to the side of the house, we can use 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 a right triangle with legs of lengths 21 feet (the height of the ladder) and 4 feet (the distance from the top of the ladder to the ground), and we want to find the length of the hypotenuse (the distance from the top of the ladder to the side of the house). We can use the formula c^2 = a^2 + b^2 to find the length of the hypotenuse:

c^2 = 21^2 + 4^2

= 441 + 16

= 457

c = sqrt(457)

= 21.37

Therefore, the distance from the top of the ladder to the side of the house is 21.37 feet, and the ladder will reach up 21.37 feet on the side of the house after Elijah pulls it 4 feet farther away. Round to the nearest tenth of a foot, the ladder will reach up 21.4 feet on the side of the house.

The answer would not be 17 feet because the height of the ladder and the distance from the base of the ladder to the side of the house are two separate and independent quantities. The height of the ladder is a fixed distance and does not change, regardless of the position of the base of the ladder. Therefore, even if Elijah pulls the ladder 4 feet farther away from the house, the height of the ladder will still be 21 feet and the ladder will still reach up 21 feet on the side of the house. The only change will be the distance from the base of the ladder to the side of the house, which will increase by 4 feet.

From the given numbers root (3/4) and root (9/4) irrational numbers.

What are irrational numbers?

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Here,

root(3/16) is a rational number

root(9/16) is a rational number.

Therefore, from the given numbers root(3/4) and root(9/4)  are the irrational numbers.

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the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees .The angle measure of the hypotenuse in this case would be 45 degrees.

In right triangles, the angles of the triangle always add up to 180 degrees. Since the base and leg side of the triangle have the same measure, the two angles opposite of them must both be 45 degrees. Thus, the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees.In right triangles, the sum of the angles is always 180 degrees. The base and leg of a right triangle have the same measure, thus the angles opposite of them must both be equal. This means that the two angles add up to 90 degrees. Subtracting 90 from 180 degrees gives us the angle measure of the hypotenuse, which is 90 degrees.

180° - (45° + 45°) = 90°

Therefore, the angle measure of the hypotenuse in this case is 90°

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Answer:

True

Step-by-step explanation:

This is true by definition.

To find the angular speed in rpm, we need to use the formula for tangential speed, which is the speed at which an object moves along a circular path. The formula for tangential speed is:

v = r * omega

where v is the tangential speed, r is the radius of the circle, and omega is the angular speed.

In this case, we are given that v = 25 mph and r = 15 feet. We can solve for omega by dividing both sides of the equation by r:

omega = v / r

Substituting the given values, we get:

omega = 25 mph / 15 feet

To convert the units of speed from mph to feet per second, we need to use the conversion factor that 1 mph is equal to 5280/3600 feet per second. We can use this conversion factor to rewrite the expression for omega in terms of feet per second:

omega = (25 mph * (5280/3600)) / 15 feet

This simplifies to:

omega = 0.7222 feet/second

Next, we need to convert the angular speed from feet per second to rpm. To do this, we need to use the formula for converting from linear speed to angular speed, which is:

omega = (v * 60) / (2 * pi * r)

where v is the linear speed, r is the radius of the circle, and omega is the angular speed in rpm.

In this case, we are given that v = 0.7222 feet/second and r = 15 feet. We can solve for omega by plugging these values into the formula and simplifying:

omega = (0.7222 feet/second * 60) / (2 * pi * 15 feet)

= 0.7222 feet/second * 60 / (2 * pi * 15 feet)

= 0.7222 * 60 / (2 * pi * 15)

= 4.3332 / (2 * pi * 15)

= 0.2821 / (pi * 15)

Therefore, the angular speed in rpm is 0.2821 / (pi * 15), or approximately 0.0046 rp