For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
A. 0B. 1C. 2D. 3E. 4

Answer:

3/2π and π/480

Step-by-step explanation:

The question given says that the minute hand on a clock moves through  complete circle in 1 hour, that is 360° or 2π. It also says that the hour hand moves through 1/12 of a circle, that means 30° or π/6.

To know how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m, it's necessary to calculate how many radians move them per minute.

Between 1:00 p.m. and 1:45 p.m 45 minutes have passed. With that information, the radians can be calculated using multiplication and division.

Minute hand: To know how many radians move the minute hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/60 min= π/30 rad-min

That means the minute hand move π/30 radians in a minute.

Now, multiplication can be used to calculate how many radians move the minute hand in 1h.

(π/30 rad-min)(45 minutes)= 3/2π rad

The minute hand moves 3/2π radians between 1:00 p.m. and 1:45 p.m.

Hour hand: To know how many radians move the hour hand per minute division wil be used.

Movement in an hour/ minutes in an hour

2π rad/(60 min x 12 hours)= π/360 rad-min

That means the minute hand move π/360 radians in a minute.

Now, multiplication can be used to calculate how many radians move the hour hand in 1h.

(π/360 rad-min)(45 minutes)= π/8 rad

The minute hand moves π/8 radians between 1:00 p.m. and 1:45 p.m.

Between 1:00 p.m. and 1:45 p.m., the minute hand on a clock moves 1.5π radians and the hour hand moves π/8 radians.

In clock motion, a full circle or a complete revolution equates to 2π radians. So, in 1 hour the minute hand moving through a complete circle means it moves through 2π radians. Since the time duration considered here is 45 minutes, which is 0.75 of an hour, the minute hand sweeps 2π * 0.75 = 1.5π radians.

Similarly, for the hour hand, a one-twelfth of a circle would be 2π/12 = π/6 radians. As the time frame is again 0.75 hours, the hour hand sweeps a distance of π/6 * 0.75 = π/8 radians.

https://brainly.com/question/33058879

#SPJ3

Answer:

The number of black T-shirts in 110 experiments is 20.

Step-by-step explanation:

It is given that in 55 trials of the experiment, a black T-shirt was drawn 10 times.

Formula of probability:

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Since 55 trials of the experiment, a black T-shirt was drawn 10 times, therefore the probability of getting black T-shirts in 1 experiment is

[tex]P=\frac{10}{55}[/tex]

[tex]P=\frac{2}{11}[/tex]

The number of black T-shirts that would be drawn in 110 times is

[tex]T=\frac{2}{11}\times 110=20[/tex]

Therefore the number of black T-shirts in 110 experiments is 20.

Answer:

Step-by-step explanation:

Answer:

It's C.

Step-by-step explanation:

Note. x^2 + 6x - 40 = (x + 10)(x - 4) so we have

     x - 16                    1

----------------        +  ---------

(x + 10)(x - 4)          (x + 10)

=   x - 16  + (x - 4)            2x - 20

   --------------------  =     -----------------------

    (x + 10)(x - 4)            x^2 + 4x - 40

Answer:

2

Step-by-step explanation:

Consider two functions:

[tex]y=\sin x[/tex] and [tex]y=\sin 2x[/tex]

The period of each function is

[tex]2\pi[/tex] and [tex]\pi[/tex]

This means that the graph of the function [tex]y=\sin x[/tex] (red graph) intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] twice and the graph of the function [tex]y=\sin 2x[/tex] intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] four times (blue graph) for [tex]x\in [0,2\pi ).[/tex]

So the equation [tex]\sin \theta=\dfrac{1}{2}[/tex] has 2 solutions and  the equation [tex]\sin 2\theta=\dfrac{1}{2}[/tex] has 4 solutions. Thus, the difference is 2.

Answer:

21 ways

Step-by-step explanation:

number = 7 digit

5 digit no = 52115

to find out

How many different seven-digit numbers

solution

first we need to place the two missing 3s in the number 52115

we consider here two cases

case 1  the two 3's appear separated (like 532135 or 3521135)  

case 2 the two 3's appear together (like 5332115 or 5211533)  

Case 1 we can see  that number type as _5_2_1_1_5_  

place 3's placeholders show potential locations

( type a ) for  3's  separated we will select 2 of  6 place and place 3 in every location so we do this 6C2  = (15) ways  

and (type b): again use same step as  _5_2_1_1_5_  

here 3s together for criterion and we will select 1 of the 6 place and place both 3s here and there are 6 ways.  

so that here will be 15+6=21 ways

If 3 and 3 are separate so 6C2 = 15  ways

If 3 and 3 are together so there = 6  ways

= 15 + 6 = 21 ways

Answer:

please ignore my answer

Answer:

0, 6 = x

Step-by-step explanation:

I hope you can see how and if this was alot of help to you, and as always, I am joyous to assist anyone at any time.

Answer:

y=4

Step-by-step explanation:

Slope equal 0 means you have a horizontal line. Horizontal lines are all of the form y=a where a is the constant you have to figure out. Our horizontal line goes through (2,4) and the coordinate there is 4 so the line is y=4.

The equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

It is given that the line passes through (2,4) and it has slope 0 .

Thus, general equation of straight line is y = mx + c

Slope(m) = 0

∴ y = c

The y-coordinate of the point is 4 , so c = 4

Thus, the equation of a straight line in slope-intercept form is -

  y = 0*(x) + 4

∴ y = 4 .

Therefore, the equation in slope-intercept form that describes a line through (2, 4) with slope 0 is y = 4 .

To learn more about slope-intercept form, refer -

https://brainly.com/question/22057368

#SPJ2

Answer:

  C. 615.7536 square inches

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr²

Fill in the given numbers and do the arithmetic.

  A = 3.1416×(14 in)² = 615.7536 in²

_____

Comment on the value of pi

We are interested to see that recent problems require use of a value of pi that has 5 significant digits, instead of 3 (as in 3.14). The only problem in this scenario is that the answer is now reported to 7 significant figures, so is still wrong. The correct 7-digit answer to this problem is 615.7522 in². It would be obtained by using a 7- or 8-digit value for pi: 3.141593 or 3.1415927 and rounding appropriately.

Answer:

your answer would be 4.5 cubic feet!!! HOPE I HELPED!!!!! good luck to anyone who needs this in the future

Step-by-step explanation:

The volume of the triangular prism is 44.52 cubic feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

To find the volume of a triangular prism, we need to multiply the area of the base by the height of the prism.

The base of the triangular prism is a triangle with sides of lengths 2 ft, 2.5 ft, and 18 ft.

The perimeter of the base is the sum of the lengths of these sides, which is:

2 ft + 2.5 ft + 18 ft = 22.5 ft

To find the area of the base, we can use Heron's formula, which states that for a triangle with sides of lengths a, b, and c, the area is given by:

[tex]area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]

where s is half the perimeter of the triangle:

s = (a + b + c) / 2

In this case, we have:

a = 2 ft, b = 2.5 ft, c = 18 ft

s = (2 ft + 2.5 ft + 18 ft) / 2

s = 11.25 ft

Plugging these values into the formula, we get:

[tex]area = \sqrt{11.25(11.25-2)(11.25-2.5)(11.25-18)}[/tex]

area = 14.84 ft^2

The volume of the triangular prism is:

volume = area of base x height

volume = 14.84 ft² x 3 ft

volume = 44.52 ft³

Thus,

The volume of the triangular prism is 44.52 cubic feet.

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ2

To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t).

To find the average temperature Tave during the period from 9 AM to 9 PM, we need to find the average value of the temperature function T(t). The formula for the average value of a function over an interval is given by:

Ave = (1/(b-a)) * ∫[a, b] f(x) dx

In this case, a = 0 (corresponding to 9 AM) and b = 12 (corresponding to 9 PM). Plugging in the temperature function T(t) = 52 + 17 sin(πt/12), we get:

Tave = (1/(12-0)) * ∫[0, 12] (52 + 17 sin(πt/12)) dt

Tave = (1/12) * (52t - 204cos(πt/12))

To find the definite integral ∫[0, 12] (52t - 204cos(πt/12)) dt, we evaluate the antiderivative at the upper and lower limits, and subtract the two values:

Tave = (1/12) * ((52(12) - 204cos(π(12)/12)) - (52(0) - 204cos(π(0)/12)))

https://brainly.com/question/36772575

#SPJ3

Answer:

  see below

Step-by-step explanation:

In addition to the exponent rule ...

  (a^b)^c = a^(bc)

it is helpful to know the first few powers of some small integers.

  5^3 = 125

  9^2 = 81

  4^3 = 64

  2^6 = 64

__

Answer:

Step-by-step explanation:

You know that ...

Using what you know about the relationships of these trig functions, you can find ...

  cos(θ)² = 1 - ((-√3)/2)² = 1 - 3/4 = 1/4

  cos(θ) = -1/2 . . . . . negative square root of 1/4

__

  tan(θ) = sin(θ)/cos(θ) = ((-√3)/2)/(-1/2)

  tan(θ) = √3

Answer:

KM = 10.68; angle K= 55; angle M=35  

Step-by-step explanation:

Using Law of Cosine, you can find KM. Then using Law of Sines, you can find the angle of M. Find the sum of angle M and 90. Then subtract the total of that to 180 to fine angle K.  (sidenote: your angle K should be bigger then angle M since the side measurement of K is larger than M.)

A correct option is option (b).

Given,

[tex]KL=6.2\\LM=8.7\\KM=x(let)[/tex]

Trigonometric ratios:

The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

The given triangle is right angle triangle then

[tex]KM^2=LM^2+KL^2\\KM=\sqrt{(8.7)^2+(6.2)^2}\\KM=\sqrt{114.13}\\ KM=10.68[/tex]

Now, calculate the angles.

[tex]\angle m=sinm\\=\frac{P}{H}\\ =\frac{6.2}{10.6}\\ m=35[/tex]

Again,

[tex]\angle k=sink\\=\frac{P}{H}\\ =\frac{8.7}{10.6}\\ k=55[/tex]

Learn more about trigonometric ratios:

https://brainly.com/question/24349828

Answer:

Step-by-step explanation:

[tex]4^0=1\\2^2=2\cdot2=4\\3^3=3\cdot3\cdot3=27\\\\4^0\cdot2^2\cdot3^3=1\cdot4\cdot27=108[/tex]

Answer:

108

Step-by-step explanation:

4 to the power of 0 is always 1. multiply to 2 to the power of 2 gives you 4. multiplying 4 to 3 to the power of 3 gives you 108 because 3^3 is 27 but if you multiply that by 4, you get 108

Answer:

  5/3 m/s

Step-by-step explanation:

Antonio's speed in the 400 m dash was ...

  (400 m)/(80 s) = 5 m/s

Antonio's speed in the hurdles was ...

  (400 m)/(120 s) = 3 1/3 m/s

His speed in the dash was ...

  (5 -3 1/3) m/s = 1 2/3 m/s = 5/3 m/s

faster than in the hurdles.

Answer:

Step-by-step explanation:

Let X be the pulse rates of females

X is N(72,12.5)

a) P(66<x<78) = P(|Z|<6/12.5)

= P(|Z|<0.48) = 2*.1844=0.3688

b) Each person is independent of the other

Hence P(4*66<4x<4*78) = P(|Z|<24/50) =0.3688^4

c) Because parent distribution is normal

Answer:

segment EG over segment LN equals segment FG over segment MN

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

EF and LM

EG and LN

FG and MN

The corresponding angles are

∠E≅∠L

∠F≅∠M

∠G≅∠N

therefore

EF/LM=EG/LN=FG/MN=3/1

Answer:

C: Segment EG over segment LN equals segment FG over MN.

Step-by-step explanation:

We are given that [tex]\triangle EFG \sim\traingle LMN[/tex] with ratio 3:1

We have to find the true statement about two similar triangles in given options

When two triangle are similar

Then ratios of all sides of one triangle to its  corresponding  all sides of another triangle are equal.

Therefore, Corresponding side of EF is LM

Corresponding side of FG is MN

Corresponding side of EG is LN

Ratio

[tex]\frac{EF}{LM}=\frac{FG}{MN}=\frac{EG}{LN}=\frac{3}{1}[/tex]

Hence, segment FG over segment MN equals to segment EG over segment LN.

Therefore, option C is true.

Answer : C: Segment EG over segment LN equals segment FG over MN.

Step-by-step explanation:

1 can is to 10 liters as x cans is to 35 liters.

Write a proportion:

1 / 10 = x / 35

Cross multiply:

10x = 35

Divide:

x = 3.5

It takes 3.5 cans.

Answer:

Measure of <QTS = 20°

Measure or minor arc QS = 40°

Step-by-step explanation:

From the figure we can see a circle with center U.

To find the measure of <QTS

m<QTS = m<QPS   [Angles subtended by same arc are equal]

Therefore m<QTS = 20°

To find the measure of minor arc QS

Measure or minor arc QS = 2 * m<QPS

 = 2 * 20 = 40°

Measure or minor arc QS = 40°

Answer:

A) m∠QTS = 20°

B) The degree measure of minor arc QS is 40°

C) The degree measure of arc QTS is 320°

Step-by-step explanation:

* Lets revise some facts about the circle

- The inscribed angle in a circle is the angle whose vertex lies on the

 circumference of the circle and its sides are the chords in the circle

- Each inscribed angle subtended by an opposite arc to its vertex

- The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

- The measures of the inscribed angles subtended by the same arcs

  are equal

- The measure of the circle is 360°

* Lets solve the problem

- In circle U

A)

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ ∠QTS is an inscribed angle subtended by arc QS

∴ m∠QPS = m∠QTS

∵ m∠QPS = 20°

∴ m∠QTS = 20°

B)

- Lets find the measure of the arc QS

∵ ∠QPS is an inscribed angle subtended by arc QS

∵ The measure of the arc is twice the measure of the inscribed angle

  subtended by this arc

∴ Measure of arc QS = 2 × m∠QPS

∵ m∠QPS = 20°

∴ Measure of arc QS = 2 × 20° = 40°

∴ The degree measure of minor arc QS is 40°

C)

∵ The arc QTS is an major arc

∵ The sum of the major arc QTS and the minor arc QS equals the

   measure of the circle

∵ The measure of the circle is 360°

∴ m of major arc QTS + m of minor arc QS = 360°

∵ m of minor arc QS = 40°

∴ m of major arc QTS + 40° = 360°

- Subtract 40° from both sides

∴ m of major arc QTS = 320°

∴ The degree measure of arc QTS is 320°

Answer:

Step-by-step explanation:

To maximize profit, the greatest possible number of the most profitable item should be manufactured. Remaining capacity should be used for the less-profitable item.

Up to 30 of model B, which has the highest profit, can be made each day. The remaining amount (20 sets) of the daily capacity of 50 sets should be used to make model A sets.

Answer:

accounting profit =$ 51,000

Economic profit = $ 7000

Step-by-step explanation:

In economic profit we consider opportunity cost opportunity cost is next best alternative for gone.

Economic profit =140,000 - 50,000 - 50,000 - 15,000 - 4000 - 20,000 + 6000            

                           = $ 7000

In accounting profit we do not consider opportunity cost.

hence,

accounting profit = 140,000 - 50,000 - 15,000 - 4000 - 20,000

                            = $ 51,000

Answer:

  cos(θ) = -3/5

Step-by-step explanation:

The cosine of the reference angle (in the first quadrant) is ...

  cos(θ) = √(1 -sin(θ)²) = √(1 -(4/5)²) = √(1 -16/25) = √((25-16)/25)

  = √(9/25) = 3/5 . . . . in the first quadrant

In the second quadrant, the cosine is negative, so the answer is ...

  cos(θ) = -3/5

Answer:

Step-by-step explanation:

The equation is y = 225 - 60x

y is the distance from Seattle

x is the number of driving hours.

At the start of the journey, x = 0.

y = 225 - 60*0

Therefore he has 225 miles to go.

====================

The change for every hour is the slope of the equation, which is - 60.

So the answer to the second part is - 60

Answer:

The distance was 225 miles when be began driving. The change in Milan's distance from Seattle for each hour he drives is -60.

Step-by-step explanation:

Consider the provided equation.

225 - 60x = y

Where x is the time and y is distance.

For part (A):

When she begins the drive, x = 0.

Substitute the value of x in the provided equation.

y = 225 - 60(0)

y = 225

Hence, the distance was 225 miles when be began driving.

Part (B)

The slope intercept form is: y = mx + c

Where m is the slope and c is the y intercept.

By comparing the provided equation with the slope intercept form it can be conclude that the slope is -60 or the rate of change of distance with respect to x is -60

The change for every hour is the slope of the equation, which is - 60.

Hence, the change in Milan's distance from Seattle for each hour he drives is -60.

Answer:

  nothing

Step-by-step explanation:

Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.

The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)

Answer:

 nothing

Step-by-step explanation:

Loan payments are linear in the loan amount for a given rate and period, so the payments for loans of $2000 and $1000 sum to the amount of payments for a loan of $3000.

The only possible savings (or cost) might come from rounding to the nearest cent. (In any event, the final payment on each loan should make up for any differences due to rounding.)

The given line is y = 3x - 5 after adding Y and subtracting 5 from both sides.

The slope of this given line is 3.

Therefore, the slope of the perpendicular line is -1/3, as it must be the negative reciprocal.

The general form of a line equation in slope intercept form is y = Mx+B where M is the slope and B is the intercept.

Solving for B is: B = y- Mx

So the intercept of the perpendicular line with slope M=-1/3 and passing through (x=4, y=-3) is

y M * x

B = -3 - (-1/3)*4 =

-3 + 1/3*4 = <-- subtracting the negative is the same as adding the positive; definition of subtraction

-3 + 4/3 = <-- multiplies the fractions first per order of mixed operations

-9/3 + 4/3 <-- common denominator is 3

= -5/3

So the equation of the perpendicular line is y = -1/3X + -5/3 = -1/3X-5/3

Notice when X=4, y = -1/3(4) - 5/3 = -4/3 - 5/3 = -9/3 = -3 as expected

Answer:

interest rate is 38.68 %

Step-by-step explanation:

Given data

installment = $60

time = 36 months = 36/12 = 3 years

principal = $1000

to find out

interest rate

Solution

we know student pay $60 for 36 months

so he pay total = 60 × 36 = 2160

total amount pay by student = $ 2160

so we can find interest rate by given formula

rate = (1/time)(amount/Principal - 1)

put the value time amount and principal here

rate = (1/3)(2160/1000 - 1)

rate = 0.386667

interest rate is 38.68 %

Answer:

3

Step-by-step explanation:

lim(t→∞) [t ln(1 + 3/t) ]

If we evaluate the limit, we get:

∞ ln(1 + 3/∞)

∞ ln(1 + 0)

∞ 0

This is undetermined.  To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.

lim(t→∞) [t ln(1 + 3/t) ]

lim(t→∞) [ln(1 + 3/t) / (1/t)]

This evaluates to 0/0.  We can simplify a little with u substitution:

lim(u→0) [ln(1 + 3u) / u]

Applying L'Hopital's rule:

lim(u→0) [1/(1 + 3u) × 3 / 1]

lim(u→0) [3 / (1 + 3u)]

3 / (1 + 0)

3

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. It involves differentiating the numerator and denominator separately and then taking the limit again. The process is repeated until a determinate form is obtained.

L'Hospital's Rule is a technique used to evaluate limits of indeterminate forms. An indeterminate form is an expression that does not have a unique value when evaluating the limit. To use L'Hospital's Rule, we differentiate the numerator and denominator separately and then take the limit again. If the new limit is still indeterminate, we repeat the process until we get a determinate form.

For example, let's say we have the limit lim(x → 0) (sin(x) / x). This is an indeterminate form since both the numerator and denominator approach 0. Applying L'Hospital's Rule, we differentiate sin(x) and x, giving us lim(x → 0) (cos(x) / 1). Since the new limit is determinate, we can simply evaluate it as cos(0) / 1, which equals 1.

Answer:

Reflects over the x-axis, then translate (x + 3, y + 1).

Step-by-step explanation:

Your have to flip is over the X-axis to get the short side on the bottom.

Then move is 3 places to the right, so X+3. After which it is move 1 place up, Y+1

Reflects over the x-axis, then translate (x + 3, y + 1).

The answer is:

[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]

The cost of the watch is $19.39.

To solve the problem, we can create a linear equation using the given information about the starting balance and the ending balance.

We know that the starting balance was $515.50, and then, after writing a check to buy the watch, the balance was $496.11, so, writing the function we have:

[tex]WatchCost=StartingBalance-EndingBalance\\\\WatchCost=515.50-496.11=19.39[/tex]

Hence, we have that the cost of the watch is $19.39.

Have a nice day!

Answer:

Step-by-step explanation:

Wherever you see an x in g(x) you are supposed to put f(x).

If g(x) = x

then

g(f(x)) = f(x)

g(x) = f(x)

Since g(x) has no xs, then g(f(x)) = - 2

g(x) = -2 no matter what x is in g(x)

g(2x - 1) = - 2

Answer:

[g ◦ f](x)=-2

Step-by-step explanation:

f(x) = 2x – 1

g(x) = – 2

[g ◦ f](x)

This is a composite function.  It means we take f(x) and substitute it in for x in the function g(x)

g(x) = -2

There is no x in the function, so g(x) remains the same

[g ◦ f](x)= -2