A race car drove around a circular track that was 0.3 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.

504.46 feet
252.23 feet
160.66 feet
80.34 feet

The approximate  ratio of the difference in the means to each of the mean absolute deviations is 2. The correct option is B = 2.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Theo recorded the means and mean absolute deviations of his language arts and Biology scores.

And the means scores are 98 and 90.

Mean absolute deviation is 3.5.

He found the difference in the means of the scores of the two subjects.

That means, 98 - 90 = 8

The ratio of the difference in the means to each of the mean absolute deviations : 8/3.5

= 2.28

≈ 2.

Therefore, 2 is the required value.

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Answer:

  3 -√7

Step-by-step explanation:

You want to rationalize the denominator of 2/(3 +√7).

The denominator of such an expression is turned to an integer by multiplying numerator and denominator by the conjugate of the denominator.

  [tex]\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\cdot\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-7}=\boxed{3-\sqrt{7}}[/tex]

__

Additional comment

This process takes advantage of the factorization of the difference of squares:

  a² -b² = (a +b)(a -b)

If 'b' is a value that can be made a rational real number by squaring it, then this multiplication by the conjugate can achieve that end. The conjugate of a sum is the corresponding difference.

This process is also used with complex numbers, since i² = -1, a real number.

The Pythagorean Theorem can be used to solve for the legs of the right triangle given the sum of their lengths. The equation x2 + y2 = 232 can be rearranged to x2 = 529 - y2 and y2 = 529 - x2.

Let x be the length of one leg and y be the length of the other leg.

x + y = 23 cm

Since this is a right triangle, the Pythagorean Theorem can be used to solve for x and y:

x2 + y2 = 232

x2 + y2 = 529

x2 = 529 - y2

x = √(529 - y2)

y = √(529 - x2)

Therefore, the lengths of the legs of the right triangle are x = √(529 - y2) and y = √(529 - x2).

The lengths of the legs of a right triangle can be determined if the sum of the lengths is known. The Pythagorean Theorem can be used to solve for the lengths. Let x be the length of one leg and y be the length of the other leg. Then x + y = 23 cm and x2 + y2 = 232. This can be rearranged to x2 = 529 - y2 and y2 = 529 - x2. Therefore, the lengths of the legs of the right triangle are x = √(529 - y2) and y = √(529 - x2).

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Plane X contains point C. Plane Y contains points A andB. there are three planes that pass through points A, B, and C.To find these planes, we need to draw a triangle connecting points A, B, and C.

The three planes that pass through A, B, and C are the planes that are parallel to the sides of the triangle and that contain points A, B, and C. These planes divide the space into three sections. Each plane will contain one of the points of the triangle. The three planes together form a three-dimensional space that is bounded by the three planes. This space contains all the points A, B, and C, and all the points in the triangle. Therefore, there are three planes that pass through points A, B, and C.

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4 weeks and 22 weeks after the beginning of the year does the mosquito population equal 200 thousand by solving the given equation.

What is a equation ?

An equation is a statement that shows equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

We need to solve the equation [tex]80 cos (\pi t/26) + 130 = 200[/tex]  for t.

First, we can simplify the equation by subtracting 130 from both sides:

[tex]80 cos (\pi t/26) = 70[/tex]

Then, divide both sides by 80:

[tex]cos (\pi t/26) = 7/8[/tex]

To solve for t, we need to take the inverse cosine ([tex]cos^{-1}[/tex]) of both sides.

[tex]cos^{-1} (cos (\pi t/26)) = cos^{-1} (7/8)[/tex]

[tex]\pi t/26 = 0.436[/tex]

[tex]t = 0.436*26/\pi[/tex]

t ≈ 4.19 weeks

So the mosquito population equals 200,000 approximately 4 weeks and 1 day after the beginning of the year.

We can also check the function to see if the mosquito population equals 200,000 more than once during the year.

[tex]A(t) = 80 cos (\pi t/26) + 130[/tex]

When we graph this function, we can see that it oscillates between 50,000 and 210,000.

There are two times during the year when the mosquito population equals 200,000:

Around week 4 (which we already calculated)

Around week 22 (which we can find by solving the equation again, but using [tex]\pi/2[/tex] instead of [tex]cos^{-1}(7/8)[/tex]

Therefore, the correct answers are 4 weeks and 22 weeks.

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The derivative of the given function f(x) = log₆ x is given by :

f'(x) =  1 /( xlog6).

As given in the question,

Given function is equal to:

f(x) = log₆ x

The derivative of logarithmic function log x is given by :

d (log x) / dx = 1 / x

log₆ x can be written as:

log₆ x = log x / log 6

Derivative of the given function f(x) = log₆ x with respect to x is written as:

d(f(x))/dx = d( log₆ x ) / dx

⇒ f'(x) = ( 1 / log 6 )d( log x ) / dx  

⇒ f'(x) = ( 1 / log 6 )( 1 / x )

⇒ f'(x) = ( 1 / x log 6 )

Therefore, the value of the derivative of the given function f(x) = log₆ x is equal to f'(x) = ( 1 / x log 6 ).

The above question is incomplete , the complete question is :

What is the derivative of the function f(x) = log₆ x?

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Answer:

940

Step-by-step explanation:

No. of occupied rooms= (47/100) X 2000

                                     =940

x = 8

m∠V = 89°

m∠W = 90°

m∠V = 11x + 1

m∠U = 12x + 10

m∠X = 75

The sum of all the angles in a quadrilateral is 360°

m∠W + m∠V + m∠U + m∠X = 360°

Plug what you know into the above equation in the appropriate spots

90 + (11x + 1) + (12x + 10) + 75 = 360

Combine like terms

90 + 11x + 1 + 12x + 10 + 75 = 360

176 + 11x + 12x = 360

176 + 11x + 12x = 360

176 + 23x = 360

23x = 184

Isolate x

x = 8

Given: m∠V = 11x + 1

Plug in the x you previously found into the equation above and solve

m∠V = 11(8) + 1

m∠V = 88 + 1

m∠V = 89°

Mikaela would not be able to run for the same distance as she would on her bicycle in one hour. This is because running is a much more strenuous activity than cycling, and humans generally can't maintain the same speed when running as they can when cycling. Therefore, it is not possible to determine how many kilometers Mikaela could run in one hour.

Answer:

[tex]y = \frac{3}{2} x + 2[/tex]

Step-by-step explanation:

from, y=mx+c

2y=3x+4

y=3x/2+4/2

y=3x/2+2

The equation for g(x) that matches the graph is g(x) =| -x - 3| +3

There are many tools we can use to find the information of the relation which was used to form the graph.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

We are given that function, g(x), is shown below. It is a shifted graph of y = |x|.

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged.

The equation for g(x)  is g(x) =| -x - 3| +3

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Answer: Yes it is

Also could you mark my answer as brainliest? It helps and doesnt hurt

Answer:

Yes.

Step-by-step explanation:

This line is a linear function to be exact.

Explicit formula of the sequence: T(n) = 10240(1/4)ⁿ⁻¹.

To get the nth phrase in a series, we can use an explicit formula. Exact or definite is the simplest definition of explicit. The reason the formula is explicit is because it allows for the easy determination of the nth term when used appropriately.

Each sequence in which the ratio of any term to the one before it is constant is said to be geometric. A geometric sequence can be expressed explicitly using the formula a = a₁r⁻¹, where r is the common ratio.

here T₁ = 10240

Explicit formula of the sequence:  T(n+1) = T(n)(0.25)

If a sequence is in the form of ar, ar², ar³,.....,arⁿ terms

Sequence will be the geometric sequence and the explicit formula of the sequence will be: T(n) = arⁿ⁻¹

Here,  

a = First term

r = Common ratio

n = Number of terms

From the table attached,

There is common ratio between the successive term and previous term under the column (height after the bounce) is:

T₂/T₁ = 2560/10240 = 1/4

T₂/T₃ = 064/2560 = 1/4

Therefore, height of the ball after each bounce will represent a geometric sequence.

Explicit formula of a geometric sequence will be given by the expression:

T(n) = 10240(1/4)ⁿ⁻¹

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Answer:

18

Step-by-step explanation:

You take 30% of 60 to find the number of brown beads.

Answer:

Letter recognition, Letter naming, Letter sound knowledge, Letter writing

When adding two rational numbers with different signs, you can determine the sign of the sum by comparing the magnitudes of the numbers.

•   If the absolute value of the first number is greater than the absolute value of the second number, the sum will have the same sign as the first number.

•   If the absolute value of the second number is greater than the absolute value of the first number, the sum will have the same sign as the second number.

To determine whether the sum will be positive or negative, you can also compare the signs of the numbers:

•   If one number is positive and the other is negative, the sum will be negative if the positive number is smaller than the negative number and positive if it is greater.

•   If the numbers have different signs, the sum will be positive if the numbers have opposite signs and negative if they have the same sign.

•   If the sum of the two rational numbers is zero, it means that the two numbers cancel each other out, which happens when the absolute value of the first number is equal to the absolute value of the second number with opposite signs.

It's important to note that if you are adding two rational numbers with different signs, you also have to keep in mind that the order of the numbers matters and you might get different results depending on the order.

I hope this helps :)

-25 is the  difference of outputs of any two inputs that are one value apart

A relation is a function if it has only One y-value for each x-value.

The given table of linear function

x          f(x)

-2         20

-1          -5

0           -30

1            -55

2          -80

The difference of outputs of any two inputs that are one value apart is -5-20=-25

Hence, -25 is the  difference of outputs of any two inputs that are one value apart

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The probability of getting the number 10 is 0.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a die has six faces numbered 1 to 6.

A) Getting the number 6

Probability of getting the number 6 = 1/6

B) Getting the number 10

Probability of getting the number 10 = 0/6

C) Not getting the number 6

Probability of not getting the number 6 = 1-1/6

(6-1)/6 =5/6

D) Getting one of the numbers 1,2,3,4,5 or 6

Here, P(E) = 5/6 + 1/6

= 6/6

= 1

Therefore, the probability of getting the number 10 is 0.

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Answer: To simplify the expression, you can first simplify the terms inside the parentheses.

6(3) = 18

(4)n-1(5)/(12)n = (4n-5)/(12n)

Then you can combine the like terms:

18/(4n-5)/(12n) = (18 * 12n)/(4n-5)

This is the simplified form of the original expression.

Step-by-step explanation:

In the given triangle KLM , measure of k = 4.4 cm , l = 3.1cm , ∠M = 150° then length of m is equal to 7.3 cm ( nearest tenth centimeter ).

As given in the question,

In the triangle KLM,

Length of k = 4.4 cm

Length of l = 3.1cm

Measure of ∠M = 150°

Length of m is calculated using cosine rule

m² = k² + l² - 2kl cos M

⇒ m² = ( 4.4 )² + ( 3.1 )² - 2(4.4)(3.1)cos 150°

⇒ m² = 19.36 + 9.61 - 27.28 (-0.866)

⇒ m² = 52.59

⇒ m = 7.3cm ( nearest tenth in centimeter )

Therefore, in the given triangle KLM the length of m as per the given measurements is equal to 7.3cm ( nearest tenth centimeter ).

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The term known as K-value is a constant. The proportionality constant, k, is represented in the direct variation equation y = kx. Similar to this, k is the variational constant in the equation for inverse variation, y = kx.

Which variant of K?

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After solving he question, Lin is walking the southwest direction making an obtuse angle.

In the given question, we have to find general direction did Lin walk from the gym to his house and what type of triangle did his walking path form.

To solve this question we have to thoroughly read the question. According to the given question we have to draw one by one with mentioning the distance. If we created the diagram correctly according to the question, then we can easily answer any question without any problem.

Lin walked west 651 feet.

After class, he walked northeast 910 feet to the gym.

Finally, he walked 615 feet back to his house from the gym.

So if we check the diagram that given below, we can say that Lin is walking the southwest direction making an obtuse angle.

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The complete question is:

To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym.

What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

If x−5 The value of (3)h(3) is 4.

It follows from the task content that the value of h(3) be determined from the function definition given; h(x)=3x−5.

On this note, by substituting 3 for x; we have;

h(3) = 3(3) - 5

= 9 -5

= 4.

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The perimeter of the square is 40 meters.

The complete length that a square's edge in a plane covers is known as its perimeter. The route that encircles a form is called the perimeter.

By summing all the sides of a closed geometrical object (two-dimensional), the perimeter is determined. Since a square is a polygon with four equal sides, its perimeter will be equal to the sum of those sides.

Since all the sides of a square are equal, therefore, the perimeter of the square will be 4 times its side, i.e. 4 × Side. It is measured in units, such as m, cm, in, ft, etc.

Because a square has four sides of equal length, the perimeter is 12 m+12 m+12 m+12 m=48.0m

Thus, The perimeter of the square is 40 meters.

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Answers R

Step-by-step explanation:

Answer:

Step-by-step explanation:

wait a minute

Graph and table can be made by first making a exponential equation for the given increment in cells.

What are exponential equations?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3^x = 81, 5^x - 3 = 625, 6^2y - 7 = 121, etc. are some examples of exponential equations. We may come across the use of exponential equations when we are solving the problems of algebra, compound interest, exponential growth, exponential decay etc.

Therefore,

Equation will be y=1000(2)^t

where t=no. of days

Table:-

  X=days                 Y=bacteria cells

  1                             2000

  2                             4000

  3                              8000

  4                              16000

Graph is given in image.

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Step-by-step explanation:

I take it then that all 3 lumbers (the central vertical one, and the 2 left and right slanted ones) have 1 ft in diameter.

the scenario creates 4 large right-angled triangles (left and right inner and outer ones).

and we need a few small ones on the ends of the slanted beams to get the distances there.

let's start on the right side :

inner triangle A

leg1 = 3 ft

leg2 = tbd

Hypotenuse = tbd

angle1 (opposite of leg1) = 30°

angle3 (opposite of Hypotenuse) = 90°

angle2 = 180 - 90 - 30 = 60°

remember the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

with a,b,c being the sides opposite of the corresponding angles A, B, C.

3/sin(30) = Hypotenuse/sin(90) = Hypotenuse

3/0.5 = Hypotenuse

Hypotenuse = 6 ft

Hypotenuse² = leg1² + leg2²

6² = 3² + leg2²

36 = 9 + leg2²

25 = leg2²

leg2 = 5 ft

outer triangle A

the angles are the same as the inner triangle.

the sides increase by the side lengths of small right-angled triangle at the end of the beam.

at both ends of the inner Hypotenuse we draw right-angled heights to the outer edge of the beam.

these heights are 1 ft (remember, 1 ft diameter for each beam).

the bottom right little triangle has also 30°, 60°, 90° angles, the extension of leg2 of the inner triangle A is the Hypotenuse of that small triangle, one leg is the 1 ft diameter of the beam, the other leg is the lower extension of the beam of the outer triangle A.

1/sin(30) = extension of leg2iA = 1/0.5 = 2 ft

leg2oA = 5 + 2 = 7 ft

leg1oA² = 2² - 1² = 3

leg1oA = sqrt(3) = 1.732050808... ft

now for the upper extensions with the upper right little triangle. it had also the angles 30°, 60°, 90°.

1/sin(60) = extension of leg1iA = 1.154700538... ft

leg1oA = 3 + 1.154700538... = 4.154700538... ft

lenghtA² = leg1oA² + leg2oA² =

= 4.154700538...² + 7² =

= 17.26153656... + 49 =

= 66.26153656...

lengthA = 8.140118953... ft

inner triangle B

leg1 = 3 ft

leg2 = 3 ft

(45° angle in right-angled triangle means isoceles triangle)

Hypotenuse² = 3² + 3² = 18

Hypotenuse = sqrt(18) = 4.242640687... ft

since the small triangle at both ends of length B are also isoceles triangles with 1 ft legs

lengthB = Hypotenuse + 1 + 1 = 6.242640687... ft

the extension to the bottom inner leg is

Hypotenuse² = 1² + 1² = 2

Hypotenuse = sqrt(2) = 1.414213562... ft

Dim. X = 15 - 1 - 7 - 1 - 3 - 1.414213562... = 1.585786438... ft

length A ≈ 8.14 ft

length B ≈ 6.24 ft

Dim. X ≈ 1.59 ft