(L8) The 30°-60°-90° Triangle Theorem states that in a 30°-60°-90° triangle, the length of the hypotenuse is __________ the length of the shorter leg, and the length of the longer leg is __________ times the length of the shorter leg.

The 20 people, the committee allocated an equal amount of $18.60 to cover the cost of their costumes.

To find out the cost of each costume, we need to divide the total amount spent on costumes by the number of people. In this case, the committee spent $372 on costumes for 20 people.

Dividing the total amount spent on costumes ($372) by the number of people (20), we can calculate the cost per costume.

$372 / 20 = $18.60

Therefore, each costume cost $18.60.

This means that for each of the 20 people, the committee allocated an equal amount of $18.60 to cover the cost of their costumes. By dividing the total expenditure evenly among the individuals, the committee ensured that each person's costume was of the same value.

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Answer:

Bus 18 is more consistent than Bus 47 based on the IQR, which is smaller for Bus 18 (16) compared to Bus 47 (24), indicating less spread of data between the 25th and 75th percentiles.

Step-by-step explanation:

Answer: The correct option regarding which bus has the least spread among the travel times is given as follows:

Bus 14, with an IQR of 6.

How to obtain the measures of spread?

First, we consider the dot plot, which shows the number of times that each observation appears in the data set.

Then we consider the interquartile range, which gives the difference between the third quartile and the first quartile of the data set.

The interquartile range is a better measure of spread compared to the range of a data set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Step-by-step explanation:

The number of possible ways in which we can select 3 elements from 7 elements are  given in option d. 35.

There are a total of 7 elements and we can to select 3 elements out of them.

We have to apply the permutation and combination here in order to find the answer,

The formula is ⁿCₐ

Where, C represents combination,

n is the total number of combination,

a is the number of selections that we have to do,

ⁿCₐ = n!/(n-a)!a!

Now, putting n = 7 and a = 3,

ⁿCₐ = 7!/(4)!3!

ⁿCₐ = 35

So, the total number of ways possible are 35.

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Answer:

A. x < $20 or x > $150

B. x \(\geq\) $25

C. x \(\leq\) 35mph

D. x \(\leq\) $4

Step-by-step explanation:

Not sure of the format desired for item A but this is what I came up with.

Answer:

x=2

Step-by-step explanation:

Primero, necesitamos calcular <<a>>

Sabemos que AD=BC y AB=CD porque lados opuestos congruentes

Entonces, vamos a calcular <<a>>.

Usamos AD y BC

2a-1=4a-15

suma 15 a ambos lados

2a+14=4

añada 2 en ambos lados

14=2a

divida

7=a

Ahora, usamos esta información para calcular <<x>>

Usamos CD=AB

2a-8=4x-2

pero sabemos que <<a>> es 7

entonces:

14-8=4x-2

6=4x-2

8=4x

2=x

<<x>> es 2

(¡lo siento mi español no es perfecto!

Answer:

3.85inches

Step-by-step explanation:

7*0.55 or 3.85 inches

Hope this helps :D

Merry Christmas!

Answer:

3.85inches

Step-by-step explanation:

7*0.55 or 3.85 inches

Hope this helps ;D

Answer:

you bad

Step-by-step explanation:

ferfrfvrgb rg bg bb

Answer: y = -2x + 5

ok done. Thank to me :>

Answer:

I think you mean the prime factorization, which is (2^3)*5

Step-by-step explanation:

you can use a prime factorization tree and find that 40 is divisible by 4 which is 2^2 and 10 which is 2*5. combine the twos and you get (2^3)*5

There are 43,680 possible ways for Sally, Sam, Sue, and Simon to place in the bottom 4 spots in a race with 17 people.

There are 17 people in the race, so there are 17 ways to choose who comes in first place. After that, there are 16 people remaining, so there are 16 ways to choose who comes in second place.

Similarly, there are 15 ways to choose who comes in third place, and 14 ways to choose who comes in fourth place.

Therefore, the total number of ways that Sally, Sam, Sue, and Simon can place in the bottom 4 spots is:

16 x 15 x 14 x 13 = 43,680

So there are 43,680 possible ways for Sally, Sam, Sue, and Simon to place in the bottom 4 spots.

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You can calculate the steady-state heat transfer rate through the double-glazed window and the internal surface temperature. Make sure to use the given values for the dimensions, thermal conductivity, and convective heat transfer coefficients in the calculations.

To determine the steady-state heat transfer rate through the double-glazed window and the internal surface temperature, we can use the concept of thermal resistance. The heat transfer through the window can be divided into three parts: conduction through the glass, convection on the inner surface, and convection on the outer surface.

First, let's calculate the thermal resistance for each part. The thermal resistance for conduction through the glass can be calculated using the formula R = L / (k * A), where L is the thickness of the glass (3 mm), k is the thermal conductivity of the glass (0.78 W/mK), and A is the area of the glass (1.5 m * 2.4 m).

Next, we calculate the thermal resistance for convection on the inner surface using the formula R = 1 / (h1 * A), where h1 is the convective heat transfer coefficient on the inner surface (10 W/m^2K).

Similarly, the thermal resistance for convection on the outer surface can be calculated using the formula R = 1 / (h2 * A), where h2 is the convective heat transfer coefficient on the outer surface (25 W/m^2K).

Once we have the thermal resistances for each part, we can calculate the total thermal resistance (R_total) by summing up the individual thermal resistances.

Finally, the steady-state heat transfer rate (Q) through the double-glazed window can be calculated using the formula Q = (T1 - T2) / R_total, where T1 is the inside temperature (21°C) and T2 is the outside temperature (5°C).

The internal surface temperature can be calculated using the formula T_internal = T1 - (Q * R_inner), where R_inner is the thermal resistance for convection on the inner surface.

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The fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

Ryan grew \($\frac{1}{2}$\) feet in a year.

1. To express the fraction \($\frac{9}{12}$\) as a sum of smaller fractions, we can simplify it by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of \(9\) and \(12\) is \(3\).

So, we can rewrite \($\frac{9}{12}$\) as:

\($\frac{9}{12} = \frac{3 \times 3}{3 \times 4} = \frac{3}{4}$\)

Therefore, the fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).

2. To find how much Ryan grew in a year, we need to calculate the difference between his height this year and his height last year.

Let's convert the mixed fractions to improper fractions for easier computation:

Last year's height: \($4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}feet\)

This year's height: \($5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} feet\)

To determine the growth, we subtract last year's height from this year's height:

\($\frac{21}{4} - \frac{19}{4} = \frac{21 - 19}{4} = \frac{2}{4} = \frac{1}{2}feet\)

Therefore, Ryan grew \($\frac{1}{2}$\) feet in a year.

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If a student selects one chip at random and p(blue) = 0.58, then, p(not blue) is 0. 42

Probability is simply defined as a branch of mathematics that concerns numerical descriptions of how likely an event can occur, or how likely it is that a proposed event is true.

The probability of an event to occur is a number between 0 and 1.

Where;

If the  p(blue) = 0.58, then

p(blue and not blue) = 1

p(not blue) = 1 - 0. 58

subtract the values

p(not blue) = 0. 42

Hence, the value is 0. 42

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It will take Carlos 33 minutes to cycle from home to work along the same route at an average distance rate of 6 miles per hour.

To find out how many minutes it will take Carlos to cycle from home to work, we'll need to determine the distance of the route first, and then calculate the time it takes to cover that distance at the average cycling speed.

To solve this problem, we can use the formula:
time = distance/speed

1. Find the distance: Since Carlos drives from home to work in 9 minutes at an average rate of 22 miles per hour, we can calculate the distance using the formula: distance = rate × time.

First, convert the time from minutes to hours: 9 minutes ÷ 60 minutes/hour = 0.15 hours.

Now, calculate the distance: distance = 22 miles/hour × 0.15 hours = 3.3 miles.

2. Calculate the cycling time: Now that we know the distance is 3.3 miles, we can find out how long it will take Carlos to cycle at an average rate of 6 miles per hour.

Use the formula: time = distance ÷ rate.

time = 3.3 miles ÷ 6 miles/hour = 0.55 hours.

Now, convert the time back to minutes: 0.55 hours × 60 minutes/hour = 33 minutes.

So, it will take Carlos 33 minutes to cycle from home to work along the same route at an average rate of 6 miles per hour.

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Answer:

TBH IF YOU WANT TO ROAST I GOT NO IDEA BUT THIS IS THE THING I DO

Step-by-step explanation:

Well to be honest I think you should just treat him the same say the same things you would normallily say when you didnt know he waS

Answer:

Go back to roasting them be the cool one

Step-by-step explanation:

Principal = 9000

Interest rate = 7% = 0.07

Time = 5 years

Simple interest formula:

A = P(1 + rt)

In this case:

A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150

Interest = A - P = 12150 - 9000 = 3

Answer:

Rate of change = -12

Step-by-step explanation:

y − 3 = −12(x + 4)

Expanding, we have;

y - 3 = -12x - 48

y = -12x - 48 + 3

y = -12x - 45

Now, formula for rate of change is;

Rate of change = (y(x + h) - y)/h

y(x + h) is; y = -12(x + h) - 45

This gives;

Rate of change = (-12(x + h) - 45 + 12x + 45)/h

Rate of change = (-12x - 12h - 45 + 12x + 45)/h

Rate of change = -12h/h

Rate of change = -12

a. The angular velocity of the ball is 1.57rad/sec

b. The angular acceleration of the bicycle is 0.23 rad/sec²

angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.

angular velocity = change in angle/ time

w = 2π/t

w = 2× 3.14/4

w = 6.28/4

w = 1.57 rad/sec

angular acceleration =( final angular velocity - initial angular velocity )/time

= (4.2 - 3.5)/3

= 0.7/3

= 0.23 rad/s²

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Moving along a circle that is encircled by a square is point p. The bottom-left corner of the square is fixed at point q. Drag the point p around the circle in the applet below to investigate this issue.

As Point P moves from A to \($B \rightarrow$\)

(d) Distance, increases then decreases.

As point P moves from B to \($C \rightarrow$\)

(a) Distance Decreases

As point P moves from C to \($D \rightarrow$\)

(b) Distance tier eases then increases.

a As Point P moves from D to\($A \rightarrow$\)

(c) Distance increases.

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Did this wrong sorry I thought it was greatest to least.

Answer:

-6, -1, 0, 4, 15

Step-by-step explanation:

the higher the negative number is, the smaller it is. its like being in debt

The listed elements of the sets are as follows:

Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things.

The sets in the Venn diagram are U, X and Y.

Therefore, let's find the elements of the sets.

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Answer:

541m

Step-by-step explanation:

The scale given 1 represents the height of the model and 10000 represents the actual height,place the 5.41 in line with the one and an unknown letter in line with the 10000 inorder to calculate the actual height

1:10000

5.41:x

cross multiply and solve for x,which will be 54100cm

but since the answer has to be in meters convert the 54100cm to a meter by dividing it by 100..

Answer:

109.090909%

Step-by-step explanation:

Answer:

9.09091%

Step-by-step explanation:

From 11 friends to 12 friends find the percent

from 11 friends to 12 friends. The number of friends is increased by 1.

To get the percentage of increase:

(12 - 11) / 11 = 1 / 11 = * 100% =

The increase of 1 friend is equivalent to 9.09091% increase

11 is the basis. It is the 100%

 1 is the increase. It is the 9.09091%

12 is the total number of friends.

The decay constant of a radioactive nuclide exists its probability of decay per unit time.

The half life of i 125 is 60 days exists 0.169 ml.

The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.

The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.

The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.

Decay constant: \($& \lambda=\frac{0.693}{t_{1 / 2}}\)

Decay constant expressed in any unit of time

Such as reciprocal seconds, minutes, hours etc.

\($\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$\)

Half Life: \($\quad t_{1 / 2}=\frac{0.693}{\lambda}$\)

The half life of i 125 is 60 days exists 0.169 ml.

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Answer:

27/3=9

Step-by-step explanation:

9 books per day

Answer: 9 books per day

Step-by-step explanation:

27 books / 3 days = 9 books per day

Answer:

X intercept is 3

Step-by-step explanation:

Hope this helps also I would appreciate brainliest is possible please :)

The simplified expression of 2(5+3x)+(x+10) is 7x + 20

From the question, we have the following parameters that can be used in our computation:

2(5+3x)+(x+10)

Open the brackets

so, we have

10 + 6x + x + 10

Evaluate the like terms

7x + 20

Hence, the expression is 7x + 20

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Answer:

r =   4/(x+y)

Step-by-step explanation:

rx + ry = 4

Factor out r

r ( x+y) = 4

Divide each side by (x+y)

r ( x+y) /(x+y) = 4/(x+y)

r =   4/(x+y)

Answer: derivative of the given function y = (x^2 - 3x + 7)/(x^2 + 9) is :

              y' = (15x - 27) / (x^2 + 9)^2.

To find the derivative of the given function using the quotient rule, we need to follow these steps:

1. Identify the numerator and denominator of the function:
  Numerator: x^2 - 3x + 7
  Denominator: x^2 + 9

2. Apply the quotient rule, which states that the derivative of a quotient of two functions is equal to:
  (f'(x)g(x) - f(x)g'(x)) / (g(x))^2

3. Differentiate the numerator and denominator separately:
  The derivative of the numerator (f(x)) is:
  f'(x) = d/dx (x^2 - 3x + 7) = 2x - 3

  The derivative of the denominator (g(x)) is:
  g'(x) = d/dx (x^2 + 9) = 2x

4. Plug these values into the quotient rule formula:
  y' = ((2x - 3)(x^2 + 9) - (x^2 - 3x + 7)(2x)) / (x^2 + 9)^2

5. Simplify the expression:
  y' = (2x^3 + 18x - 3x^2 - 27 - 2x^3 + 6x^2 - 14x) / (x^2 + 9)^2

  Combining like terms:
  y' = (15x - 27) / (x^2 + 9)^2

Therefore, the derivative of the given function y = (x^2 - 3x + 7)/(x^2 + 9) is y' = (15x - 27) / (x^2 + 9)^2.

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