Answer:
(140, 37)
Step-by-step explanation:
If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same. The number of miles will also be the same at this cost. That means we need cost functions for each. x is the number of miles that is driven, our independent variable. If A-1 charges .10 per mile, the expression is .1x. If the flat fee is 23, regardless of how many miles you drive, you can expect to pay
y = .1x + 23
If EZ charges .05 per mile, the expression is .05x. If the flat fee is 30, regardless of how many miles you drive, you can expect to pay
y = .05x + 30
If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.
.1x + 23 = .05x + 30 and
.05x = 7 so
x = 140 miles.
In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.
y = .1(140) + 23
y = 14 + 23
y = 37
The coordinate pair is (140 miles, $37)
This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.
Help please?
If sin O = -sqrt3 over 2 and n < O < 3 pi over 2, what are the values of cos O and tan O?
Answer:
cos(θ) = -1/2tan(θ) = √3Step-by-step explanation:
You know that ...
cos(θ)² = 1 - sin(θ)²tan(θ) = sin(θ)/cos(θ)cosine is negative in the third quadrant (where π < θ < 3π/2)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
A. What is the degree measure of
B. What is the degree measure of minor arc QS
C. What is the degree arc qts?
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°
What is the volume of the triangular prism below?
V =________ft3
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.
What is a prism?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.
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In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1 12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p.m. and 1:45 p.m. (on the same day)?
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.
Explanation: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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Hillary starts her own business. She quits her $50,000 a year job, rents an office for $15,000 a year, pays wages and salaries of $50,000 a year, utilities of $4,000 a year, and materials of $20,000. She uses her own car for sales work rather than leasing an equivalent car for $6000 a year. If revenues are $140,000, her accounting profit and economic profit are respectively ______ and _____ .
Answer:
accounting profit =$ 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
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. HELP ASAP!!
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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This question is a Fractions as divisions and it's kinda bit harder to figure it out.
Need help!!
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.
What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?
y = –x + 33
y = –x + 36
y = 4x − 16
y = 4x + 16
The answer is:
The line that is parallel to the given line and passes through the point (4,32) is:
[tex]y=4x+16[/tex]
Why?To solve the problem, we need to remember that parallel lines have the same slope, so, we need to find a line that has the same slope that the given line and it also pass through the point (4,32).
So, we are given the line:
[tex]y-1=4(x+3)\\\\y=4x+12+1\\\\y=4x+13[/tex]
So, we have that the line has a slope which is equal to "4".
Now, we have to find which of the given lines that have a slope equal to "4", also pass through the point (4,32), so, we need to evaluate it into the equations.
Therefore, evaluating we have:
Third line:
[tex]y=4x-16\\\\32=4*4-16=0\\32=0[/tex]
We can see that the equation is not satisfied, so the line does not pass through the point.
So, evaluating the fourth line, we have:
[tex]y=4x+16\\\\32=4*4+16=16+16=32\\\\32=32[/tex]
We can see that the equation is satisfied, so the line does pass through the point (4,32)
Hence, we have that the line that is parallel to the given line and passes through the point (4,32) is:
[tex]y=4x+16[/tex]
Have a nice day!
Answer:
y=4x+16
Step-by-step explanation:
Let us first rearrange the equation of the given line to be in the form y=mx+c. M gives the gradient of the line and c gives the y intercept.
y-1=4(x+3)
y-1=4x+12
y=4x+13
The gradient of parallel lines is equal. For the second line m=4
m=Δy/Δx
(y-32)/(x-4)=4
y-32=4(x-4)
y-32=4x-16
y= 4x+16
The equation of line 2 will be y=4x+16
Need some help with this question please
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
last question... help, please
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.
!!!!DONT SKIPP!!!!! ALGEBRA 12TH GRADE
PLEASE HELP SOMEONE ASAP!!!
WILL GIVE BRAINLY POINTS!
IM RUNNING OUT OF TIME..
WRONG ANSWERS WILL BE REPORTED
SEE ATTACHED FILE FOR QUESTION
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
(easy) If ΔEFG ~ ΔLMN with a ratio of 3:1, which of the following is true?
segment EG is congruent to segment LM
segment EF is congruent to segment LM
segment EG over segment LN equals segment FG over segment MN
segment EF over segment LM equals segment EG over segment LM
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.
Please help and explain this question!
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.
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 52 + 17 sin πt 12 . Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)
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).
Explanation: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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Find the equation in slope intercept form and standard form of the line that passes through (4,-3) and is perpendicular to 3x-y=5.
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
Cookies are sold singly or in packages of 11 or 33 with this packaging how many ways can you buy 66 cookies
There are three ways to buy 66 cookies with packaging options of single cookies, or packages of 11 or 33. They are two packages of 33, six packages of 11, or sixty-six single cookies.
Explanation:To find out how many ways you can buy 66 cookies using single cookies, or packages of 11 or 33, we can set up a problem using combinations of these quantities. As we know, 66 is a multiple of both 11 and 33, so we'll want to find out how many packages of 11 and how many packages of 33 can be combined without exceeding 66.
Firstly, since 33 is exactly half of 66, we can have either two packages of 33 or zero packages of 33. If we choose two packages of 33, then we have no need for additional cookies. If we choose zero packages of 33, we can then use six packages of 11 to make up the total because 6 x 11 = 66. There's also the option of buying 66 single cookies, although that tends to be inefficient.
So, our possibilities are:
Two packages of 33 cookiesSix packages of 11 cookiesSixty-six single cookiesThus, there are three ways to buy 66 cookies given the packaging constraints.
An experiment consists of drawing different colored T-shirts from a drawer that contains an unknown number of T-shirts of different colors. In 55 trials of the experiment, a black T-shirt was drawn 10 times. If the experiment were repeated 110 times, how many times would you predict that a black T-shirt would be drawn?
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.
It's time for another financial calculator problem. A UCF student (who has not taken FIN 2100) decides that he really needs a large screen HD TV for football season. The student goes to a "rent to own" center and agrees to rent a TV for $60 per month (end of month). After 36 months, the student will own the TV. Assuming that the student could buy the same TV today for $1,000, what is the interest rate (APR) of renting the TV?
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 %
using exponent laws please answer this
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
__
125^3 = (5^3)^3 = 5^(3·3) = 5^981^7 = (9^2)^7 = 9^(2·7) = 9^14(1/64)^3 = ((1/4)^3)^3 = (1/4)^(3·3) = (1/4)^9(1/64)^3 = ((1/2)^6)^3 = (1/2)^(6·3) = (1/2)^18Find the area of a circle whose radius is 14 inches. (Use π = 3.1416.)
A. 87.9648 square inches
B. 43.9824 square inches
C. 615.7536 square inches
D. 153.9384 square inches
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.
If f(x) = 2x – 1 and g(x) = – 2, find [g ◦ f](x).
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
URGENT PLEASE ANSWER THIS MATH QUESTION WILL GIVE 20 points
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).
What is the solution to -4 | -2x +6 | = -24
Answer:
please ignore my answer
Answer:
0, 6 = x
Step-by-step explanation:
|-2x + 6| = 6 [Divided by -4]Here is where you can see how to find your two x-values [first one being 0].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.
Find the equation in slope-intercept form that describes a line through (2, 4) with slope 0
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 .
What is slope-intercept form of equation of straight line ?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.
How to form the given equation of straight line ?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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Antonio is on the track team. He ran the 400-meter dash in 1 minute and 20 seconds. The graph shows his performance on the 400-meter hurdles. How much faster was his average speed in the 400-meter dash?
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.
Use L’Hospital’s Rule to evaluate the following limit.
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.
Explanation: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.
Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts (a) through (c) below.
(a) If 1 adult female is randomly selected, find the probability that her pulse rate is between 66 beats per minute and 78 beats per minute.
The probability is?
(b) If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute
The probability is?
(c) Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
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
Sid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Sid have meant to type?
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
A manufacturer of golf clubs makes a profit of $50 per set on a model A set and $55 per set on a model B set. Daily production of the Model A clubs is between 20 and 50 sets, inclusive, and that of the model B clubs is between 10 and 30 sets, inclusive. The total daily production is not to exceed 50 sets. How many sets of each model should be manufactured per day to maximize the profit?
Answer:
30 sets of model B20 sets of model AStep-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.
write 4^0 * 2^2 * 3^3 as a single number
BRAINLIEST!!
Answer:
108Step-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