There are 24 events at an indoor track and field meet. The ratio of track events to field events is 7:5. How many of the events are track event

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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Answer:

√33

Step-by-step explanation:

it is a right triangle and we use Pythagoras

x² = 7² - 4²

x² = 49 - 16

x² = 33

x = √33

The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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Answer:the answer is 319.857 and round to 320

Step-by-step explanation:

Answer:

d≤7

Step-by-step explanation:

-10d≥-70

d≤7

Answer:

9x^2 - 3x - 2,  R -7.

Step-by-step explanation:

x - 5) 9x^3 - 48x^2 + 13x + 3(9x^2 - 3x - 2 <---- Quotient.

        9x^3 - 45x^2

                  - 3x^2 + 13x

                   -3x^2 + 15x

                                -2x + 3

                                -2x + 10

                                          -7 <----- Remainder

Step-by-step explanation:

-3 times -6r= 18r

-3 times 6 =-18

18r=-18

R=-1

If the answer is wrong try just 1

Answer:

0

Step-by-step explanation:

remove r first

-3(-6+6)

-3x-6= 18 -3x6|=-18

18-18=0

or

-3(-6+6)

=-3(0)

=-3x0

=0

don't forget the r you removed which equals to one

so you got 1

-3(-6r+6)=1

wish it could help

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

Probability that she gets an outcome of tails and 2 = 1 / 12

Isabelle flips a fair coin and rells a fair six-sided dice.

Coin has two face H or T

Dice has six face hat is 1, 2, 3, 4, 5, 6  

When a six sided dice through with the coin all the possible outcomes  are as follows

H-1 H-2 H-3 H-4 H-5 H-6

T-1 T-2 T-3 T-4 T-5 T-6

So there are total 12 outcomes possible when a six sided dice through with the coin.

Probability that she gets an outcome of tails and 2 = event occur / total number of events = 1 / 12

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The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.

An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.

Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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The area of rectangle with has its vertices defined on parabola is 32 square units.

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

Square, figure, oblong, parallelogram, plane a.re terms to describe rectangle

Equation of Parabola is y = 12 - x^2 is an even function.

Therefore, its rectangle form also is even at the origin.

We know area of rectangle = length × width

Here,

length = 2x, width = y

Area, A = 2x(12 - x2)

⇒ A = 24x - 2x^3

Take derivative of A with respect to x

⇒ A' = 24 - 6x^2

The area is largest when A' = 0

⇒ 24 - 6x^2 = 0

⇒ x^2 = 4

⇒ x = 2

Put the value of x in y = 12 - x^2

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Therefore, the largest area of a rectangle is 32 square units.

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Answer: 1.82 m

Step-by-step explanation:

Ratios

0.14     n              0.14 x 13 = 1.82

 1.         13                    1.82/1 = 1.82

For the correlation between the fund returns is .0459, the reward-to-volatility ratio of the best feasible CAL is equals to 0.1621 or 16.21%.

A probability distribution is helps to determine the future what frequency distribution is to the past. Standard deviation is used in the concept of risk of portfolio of investment. Risk refer to the dispersion of a probability distribution.

Stock fund (S) Bond fund (B)

Expected Return 14% 7%

Standard Deviation 43% 37%

Risk-free returns , Rf = 5.3%

Correlation coefficient = 0.459

Covariance : 0.459 = COV(s,b)/0.43×0.37

Covariance = 0.073

Stock Fund =( (σB)²− σS× σB× correationco, SandB)/((σS)²(σB)² - 2 × σS× σB× correationco, SandB)

= ((0.37)²− 0.43× 0.37× 0.0459) /((0.43)²(0.37)² −2× 0.43× 0.37× 0.0459)

Weight of S = 42.18%

Weight of B = 1 - 42.18 = 57.82%

Expected Return of the portfolio (Rp) = WS× E(RS) + WB × E(RB) = 42.18 × 14% + 57.82 × 7%

= 5.90 + 4.05 = 9.95

Standard Deviation of the portfolio (SDp)

= (WS²SD² + WB²× lSD²+ 2WS WBCov(S,B))1/2

= 28.68

Reward to volatility = (Expected return - Rf) / SD of Portfolio

= (9.95- 5.3) / 28.68

=0.1621

Hence, the required volatility is 0.1621 or 16.21%.

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Answer:

D.

Step-by-step explanation:

Simply plug in your variables and solve (r = x + 2 and h = 3x + 8):

V = π(x + 2)²(3x + 8)

V = π(x² + 4x + 4)(3x + 8)

V = π(3x³ + 20x² + 44x + 32)

V = 3x³π + 20x²π + 44xπ + 32π

Answer:

Step-by-step explanation:

First, list the fractions in between. 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 2.49, then 2.5. When looking at the list, you can see that 2.45 is halfway between 2.4 and 2.5. One other way to find it is thinking what is between 0 to 10? The answer is 5.

The area of the painted face with vertices at (-4, 2), (-4, -11), (4, 2), and (4, -11) which represents a rectangle is 104 square inches

A rectangle is a quadrilateral with the four interior angles that are each right angles, and opposite sides that are congruent and parallel.

The specified vertices of the face of the brick are;

(-4, 2), (-4, -11), (4, 2), and (4, -11)

The graph of the above point used to draw the quadrilateral representing the shape of the face in the question, created with MS Word, is attached

From the attached graph and drawing, we get;

Shape of the face of the doorstop = A rectangle

Length of the sides of the quadrilateral (rectangle)

Length = 2 - (-11) = 13

Width = 4 - (-4) = 8

Area of a rectangle  Length × Width

Area of the painted face of the brick, A = 13 × 8 = 104

The area of the rectangular painted face of the brick = 104 square inches

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Answer:

1.05 x 10^31

Step-by-step explanation:

10 x 10 = 100

100/5 = 20

20 x 56^17

Is about 1.05 x 10^31

Answer:

Approximately 1.0476747e+31

Step-by-step explanation:

Well.... 56 to the 17th power is 5.2383735e+29 , or 523837348053896201440996622336. 10*10/5 = 20 so,

523837348053896201440996622336 * 20 = 1.0476747e+31 and I don't know how to convert that to a real number but yeah. I don't know why I wasted my time on this.

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

A function assigns the values. The (f·g)(x) equals 5x³ + 5 + 5x²+15x.

A function assigns the value of each element of one set to the other specific element of another set.

Given the value of the functions f(x)=5x³ and g(x)=x+1. Therefore, the value of (f·g)(x) is,

(f · g)(x) = f(g(x))

             = 5(x+1)³

             = 5(x³+1+3x²+3x)

             = 5x³ + 5 + 5x²+15x

Hence, the (f·g)(x) equals 5x³ + 5 + 5x²+15x.

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Answer:

what is the expressio

Step-by-step explanation:

Answer:

8(x) = 56 (x = 7)  (x) + 5 3/4 = 8 3/4 (x = 3) x/2 = 3.5 (x = 7) Neither x - 2.56 = 0.44 (x = 3)

Step-by-step explanation:

Answer:

I see no picture

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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Answer:

  745

Step-by-step explanation:

You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.

We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...

  (2x +298)/(5x +298) = 4//7

Cross multiplying gives ...

  7(2x +298) = 4(5x +298)

  3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))

  149 = x

  745 = 5x . . . . . . the original number of books in the library

There were 745 books in the library at first.

__

Additional comment

If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...

  2/5x +298 = 4/7(x +298)

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Answer:

So, first, we have to establish how much the base rent ends up costing. So to find that, we do 1,800x12=21,600. So the base rent is $21,600. Then, we add the 4% of sales which is 125,000x0.04=5,000. So, we add $21,600 with $5,000 and we get a final answer of $26,600 owed at the end of the year :)

Step-by-step explanation: