What is the equation of the line of symmetry for the parabola represented by the equation y=−2(x−3)^2+4 ? Enter your answer as the correct equation, like this: x = 42

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)))

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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:

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

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:

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:

  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:

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 .

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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:

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:

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.

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:

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:

  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.)

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:

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).

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.

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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:

0

Step-by-step explanation:

if you added anything else you would be higher than 24

Answer: The following statements are correct :

Data are typically collected from a sample because it is too difficult and expensive to collect data from an entire population.

When the results from a sample are extended to the​ population, it is called inference.

If data are not collected​ properly, the conclusions that are drawn will be meaningless.

The following statement is false: The first step in the process of statistics is to collect the data.

The first step in the process of statistics is to Plan: develop a statistical inquiry that can be answered with aggregation of data.

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:

D

Step-by-step explanation:

Consider the inequality

[tex]\dfrac{x^2+4x-12}{x}>0[/tex]

First, factor the numerator:

[tex]x^2+4x-12=x^2+6x-2x-12=x(x+6)-2(x+6)=(x+6)(x-2)[/tex]

Now, the inequality is

[tex]\dfrac{(x+6)(x-2)}{x}>0[/tex]

The equivalent inequality is

[tex]x(x+6)(x-2)>0[/tex]

On the number line plot doted points -6, 0 and 2 and put signs +, -, +, - from the right to the left. Intervals with + signs are the solution of the inequality:

[tex]x\in(-6,0)\cup(2,\infty)[/tex]

that is represented by D number line.

Answer:

D

Step-by-step explanation:

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]

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Answer:

5 seconds

Step-by-step explanation:

This follows the pattern

[tex]h(t)=-4.9t^2+v_{0}t+h_{0}[/tex]

It is parabolic and it is used to model projectile motion.  This is the model you would use.  Now for the math of it.

The v₀ is the initial velocity and the h₀ is the initial height.  The whole thing is negative because it is an upside down parabola.  Our initial velocity is 12 and the initial height is 62.5.  That means that our particular model is

[tex]h(t)=-4.9t^2+12t+62.5[/tex]

h(t) is the height of the projectile after a certain length of time, t, has gone by.  We want to know how long, t, it takes the projectile to hit the ground.  When something is laying on the ground, its height is 0.  Therefore, in order to find how long it takes for the height to be 0, we replace h(t) with 0 and then factor to find the values of t:

[tex]0=-4.9t^2+12t+62.5[/tex]

If you plug this into the quadratic formula you will get that the values of t are

t = -2.55 and t = 5

We all know that the 2 things in math that will never EVER be negative are time and distance/measures, so we can disregard the negative value of time and say that the length of time it takes for the object to hit the ground from its initial height of 62.5 m is 5 seconds.

Answer:

C.

Step-by-step explanation:

p(x)=sin(x) is an odd function since sin(-x)=-sin(x).

q(x)=cos(x) is an even function since cos(-x)=cos(x).

r(x)=tan(x) is an odd function since tan(-x)=-tan(x).

s(x)=csc(x) is an odd function since csc(-x)=-csc(x).

So the only contender seems to be C.

Let's check.  To check we have to plug in (-x) in place of (x) and see if we get the same function back since we are looking for an even function.

[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex]

Replace (x) with (-x):

[tex]f(-x)=\cos(\frac{5\pi}{4}(-x)[/tex]

[tex]f(-x)=\cos(\frac{-5\pi}{4}x)[/tex]

[tex]f(x)=\cos(\frac{5\pi}{4}x)[/tex] since cosine is even; that is cos(-u)=cos(u) where u in this case is [tex]\frac{5\pi}{4}x[/tex].

So f is even.

C. f(x) = cos(x) The cosine function is an even function. So, the correct answer is C. f(x) = cos(x).

An even function is a function that satisfies the following property:

f(x) = f(-x)

Let's examine the provided functions:

A. f(x) = sin(-31)

This is not an even function because the sine function is an odd function, and negating the angle in a sine function doesn't produce an even function.

B. f(x) = tan(3x)

The tangent function is an odd function, so this function is not even.

C. f(x) = cos(x)

The cosine function is an even function. This is the correct answer.

D. f(x) = csc(-1)

The cosecant function (csc) is the reciprocal of the sine function, and as mentioned earlier, the sine function is an odd function. So, the cosecant function is also odd, and this function is not even.

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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:

  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:

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:

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

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:

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