Answer:
35 cm
Step-by-step explanation:
is the correct answer
An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.
Which inequality describes all times t for which the object is traveling toward the right?
the function is given, and it's value is where the object is ("how far to the right").
so as long as it rises (going more right), this will be apply.
in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.
for the first 1.25 seconds the object goes to the left, and after that always to the right.
since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.
x(t) = 2t² – 5t – 18
x'(t) = 4t -5
x'(t) = 0
0 = 4t -5
5 = 4t
1.25 = t
plugging it into the second derivative
x''(t) = 4
x''(1.25) = 4
it's positive, so at t=1.25 there is a low point
(of course the second derivative is constant anyways.)
the object is traveling toward the right
the object is traveling toward the rightfor t > 1.25
The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have:
An object travels along the x-axis so that its position after t seconds is given by:
x(t) = 2t² – 5t – 18
x'(t) = 4t - 5
x'(t) = 0
4t -5 = 0
t = 5/4 = 1.25 seconds
x''(t) = 4
x''(1.25) = 4
x''(1.25) > 0
At t = 1.25 the object travels at a low point.
Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.
Learn more about the inequality here:
brainly.com/question/19491153
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4x-5y +7z= -14
9x + 2y +3z= 47
-y + x -5z = 11
Find x if A'B
Answer:
x = 5
Step-by-step explanation:
Here we have the system of equations:
4x - 5y +7z= -14
9x + 2y +3z= 47
-y + x -5z = 11
We want to find the value of x.
To do it, we need to isolate one variable (not x) in one of the 3 equations. We could isolate y in the third equation to get:
x - 5z - 11 = y
now we can replace this in the other two equations to get:
4x - 5*( x - 5z - 11 ) +7z = -14
9x + 2*(x - 5z - 11 ) + 3z = 47
notice that now we have only two variables, now we need to simplify these two equations so we can get:
-x + 32z = -69
11x - 7z = 69
Now we do the same thing, this time we need to isolate z in one of the two equations, let's isolate it in the second one:
7z = 11x - 69
z = (11/7)*x - (69/7)
now we can replace this in the other equation to get:
-x + 32*( (11/7)*x - (69/7) ) = -69
now we have an equation for x, that we can solve to find its value:
-x + 32*(11/7)*x - 32*(69/7) = -69
x*(32*(11/7) - 1) = -69 + 32*(69/7)
x = [-69 + 32*(69/7)]/(32*(11/7) - 1) = 5
The value of x is 5.
Average person who drives car in United States drives 15, 350 miles which is 50% more than an average driver in Europe. We assume that the number of yearly miles by U.S. drivers is approximately a normal random variable of standard deviation of 4200 miles. Calculate percent of drivers who traveled between 10,000 to 12,000 miles in a year.
Answer:
7,675
that is your answer
6 + 7* log base 2 of x = 21
6 + 7* log base 2 of x = 21
Answer:
Step-by-step explanation:
Please help me, by completing this proof!
Answer:
Step-by-step explanation:
Statement Reasons
1). Line PQ is an angle bisector of ∠MPN D). Given
2). ∠MPQ ≅ ∠NPQ A). Definition of angle bisector
3). m∠MPQ = m∠NPQ F). Definition of congruent
angles.
4). m∠MPQ + m∠NPQ = m∠MPN C). Angle addition postulate
5). m∠MPQ + m∠MPQ = m∠MPN G). Substitution property of
equality
6). 2(m∠MPQ) = m∠MPN B). Distributive property
7). m∠MPQ = [tex]\frac{1}{2}(m\angle MPN)[/tex] E). Division property of equality
If A={2,3,5,7} and B={2,4,6,8} then what is AnB?
Answer:
A∩B = {2}Step-by-step explanation:
It asks for the common set of A and B.
There only one element common to both the given sets:
A={2,3,5,7} and B={2,4,6,8} ⇒ A∩B = {2}Answer:
A ∩ B = {2}Step-by-step explanation:
∩ == this symbol stands for the common element/set
So according to this question you have to find the element which is common for both A and B sets.
A = { 2,3,5,7}B = {2,4,6,8}So now you can see that only number 2 is common for both.
So, the answer is,
A ∩ B = {2}find the LCM of 210, 280, 360 by prime factorisation
Answer:
Step-by-step explanation:
210=2x3x5x7
280=2x2x2x5x7
360=2x2x2x3x3x5
Answer:
210= 2×3×5×7
280=2×2×2×5×7
360=2×2×2×3×3×5
common factors=2×2×2×3×5×7=840
uncommon factors=3
L.C.M=Common factors× uncommon factors
L.C.M=840×3
L.C.M=2520
Step-by-step explanation:
i hope it will be helpful
plzz mark as brainliest
I need help guys thanks so much
Answer:
A. 243
Step-by-step explanation:
[tex] 81^\frac{5}{4} = (3^4)^\frac{5}{4} = 3^{4 \times \frac{5}{4}} = 3^5 = 243 [/tex]
Answer: A
I just simplified it to 3^5, and that is also 243.
what is the area of a circle if the radius is 9 m
Answer:
(approximately) 254.34 meters
Step-by-step explanation:
Concepts:
Area is the amount of space a 2D shape has.The area of a circle is the amount of space it has. The formula to find the area is πr^2, where r is the radius and π is often represented as 3.14 or 22/7. The radius of a circle is a straight line from the center to the circumference of it. The radius is 1/2 of the diameter, meaning the diameter of a circle is a straight line passing from one side to the other side of the circle.Solving:
Let's use the formula for area of a circle to solve.
1. Formula for Area of a Circle
πr^22. Exchange π for 3.14
3.14 · r^23. Plug in the value of r (radius of circle) as 9
3.14 · 9^24. Simplify
3.14 · 81254.34Therefore, the area of a circle when the radius is 9 meters is approximately 254.34 meters.
In an episode of the old school version of the game show Family Feud, 43 out of a random sample of 100 people said they pick their noses at red lights. Find a 95% confidence interval of the proportion of all people who pick their noses at red lights. Be sure to interpret your answer
Answer:
[tex]P_{95\%}=(0.333,0.527)[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=100[/tex]
Selected sample [tex]x=43[/tex]
Confidence Interval [tex]CI=95\%[/tex]
Significance Level [tex]\alpha=0.05[/tex]
Probability of picking nose is
[tex]P=\frac{x}{n}[/tex]
[tex]P=\frac{43}{100}[/tex]
[tex]P=0.43[/tex]
Generally the equation for standard error is mathematically given by
[tex]S.E=\sqrt{p*(1-p)}{n}[/tex]
[tex]S.E=\sqrt{0.4*(1-0.57)}{100}[/tex]
[tex]S.E=0.0495[/tex]
Therefore
The proportions 95\% interval is
[tex]P_{95\%}=[P-1.96x SE(P),P+1.96*SE(P)][/tex]
[tex]P_{95\%}=(0.43-1.96*0.0495,0.43+1.96*0.045)[/tex]
[tex]P_{95\%}=(0.333,0.527)[/tex]
Find the length of the missing side. If necessary, round to the nearest tenth.
A. 22
B. 15.6
C. 44
D. 484
Answer:
Option B, 15.6
Step-by-step explanation:
Using the Pythagoras theorem,
√(11²+11²)
= √(121+121)
= √(2×121)
= √121×√2
= 11√2
= 15.6
Answered by GAUTHMATH
Option B - 15.6 is Correct.
We have a figure in which a right angled triangle is shown with it base (b) = 11 and perpendicular(p) = 11.
We have to find the value of c or hypotenuse (h).
What is Pythagoras theorem?According to the Pythagoras theorem : for a right angled triangle -
[tex](h)^{2} = (b)^{2} +(p)^{2}[/tex]
According to the question -
[tex]b =11\\p =11\\h=c[/tex]
Substituting the values, we get -
[tex]c^{2} = (11)^{2} + (11)^{2} \\c^{2} = 121 + 121\\c^{2} =242\\c=15.55[/tex]
Rounding to nearest 10, we get -
c = 15.6
Hence , Option B is correct.
To solve more questions on Pythagoras theorem, visit the following link -
https://brainly.com/question/8587612
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Can someone help me with this plz
Answer:
170.7
Step-by-step explanation:
We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7
Write the sum using summation notation, assuming the suggested pattern continues.
100 + 121 + 144 + 169 + ... + n2 + ...
100 = 10², so the sum you're considering is the sum of squared integers starting with 10.
[tex]\displaystyle 100+121+144+168+\cdots+n^2+\cdots = \boxed{\sum_{k=10}^\infty k^2}[/tex]
find the value of x²-6x+13 when x=3+2i
Answer:
18
Step-by-step explanation:
x squared -6 +13
5 squared-6×3+2+13
25-20+13
5+13
=18
Write a number in which the value of the 3 is ten times as great as the value of 3 in 135,864
Answer:
Step-by-step explanation:
the 3 in 135,864 is 30,000
if you mutiply that by 10 you get 300,000
you just need to write any number with a 3 in the hundred thousands place
Juan had 5 candy bars for himself and 4 friends to share with after lunch. Then three other friends joined them. Juan divided the 5 candy bars equally with all of his friends. How much did each person get?
Answer:
5/8
Step-by-step explanation:
There are 5 people when 3 more join for a total of 8 people
5 candy bars divided by 8 people
Take the candy bars and divide by the people
5/8
What is the are of the polygon below!help please!
Answer:
Area= 525
Step-by-step explanation:
14x9=126
3x7=21
14x27=378
126+21+378=525
An electrician charges a fee of $40 plus $25 per hour. Let y be the cost in dollars of using the electrician for x hours. Choose the correct equation.
y = 40x - 25
y = 25x + 40
y = 25x - 40
y = 40x + 25
Answer:
y = 25x + 40
Step-by-step explanation:
The electrician charges $25 per hour.
The number of hours is x.
Therefore after x hours the electrician will charge $25x. (multiply the charge by the number of hours $25 * x)
Therefore fee(y) charged by the electrician = $40 + $25x
Hence y = 25x + 40
Pls if anyone knows the answer with work included/steps that will be greatly appreciated :)
Answer:
1. Option D. 15x²
2. Option C. 3
Step-by-step explanation:
1. Determination of the area of one section.
Length (L) of one section = 25x/5 = 5x
Width (W) of one section = 3x
Area (A) of one section =?
The area of one section can be obtained as follow:
Area (A) = Length (L) × Width (W)
A = L × W
A = 5x * 3x
A = 15x²
Thus, the area of one section is 15x²
2. Determination of the expressions that are equivalent to (p²)³.
We'll begin by simplifying (p²)³. This can be obtained as follow:
(p²)³ = p²*³
(p²)³ = p⁶
Next we shall compare each expression given in the question above to see which will be the same as p⁶.
p × p × p × p × p × p = p¹⁺¹⁺¹⁺¹⁺¹⁺¹
p × p × p × p × p × p = p⁶
p² × p² × p² = p²⁺²⁺²
p² × p² × p² = p⁶
p² × p³ = p²⁺³
p² × p³ = p⁵
Thus,
p² × p³ ≠ p⁶
p⁵ ≠ p⁶
p⁶ = p⁶
SUMMARY
p × p × p × p × p × p = p⁶ = (p²)³
p² × p² × p² = p⁶ = (p²)³
p⁶ = (p²)³
Therefore, 3 expressions are equivalent to (p²)³. Option C gives the correct answer to the question.
An observer, who is standing 47 m from a building, measures the angle of elevation of the top of the building as 30˚. If the observer’s eye is 167 cm from the ground, what is the exact height of the building?
9514 1404 393
Answer:
28.81 m
Step-by-step explanation:
The tangent relation can help find the height of the building above the observer's eye.
Tan = Opposite/Adjacent
Opposite = Adjacent·Tan
above eye height = (47 m)(tan 30°) ≈ 27.14 m
Adding this to the eye height gives the height of the building above the ground where the observer is standing.
27.14 m + 1.67 m = 28.81 m
The height of the building to the nearest centimeter is 28.81 meters.
which of the following is the correct graph of the solution to the inequality -18 > 5x + 2 > -48?
Answer:
good luck
.............
Answer: the third one. filled circle for 4 ,5,6,7,8,9, open circle 10
Step-by-step explanation:
At the Olympic games, many events have several rounds of competition. One of these events is the men's 100100100-meter backstroke. The upper dot plot shows the times (in seconds) of the top 888 finishers in the semifinal round at the 201220122012 Olympics. The lower dot plot shows the times of the same 888 swimmers in the final round. A dot plot is divided into 2 parts labeled, Semifinal Round and Final Round. The horizontal axis is labeled, Time, in seconds, from 52 to 54, in increments of 0.10 second. The portion of the dot plot dedicated to Final Round has dots above the following points; 52.2, 52.3, 52.8, 53.1, 53.2, 53.3, 53.5, and 53.8. The portion of the dot plot dedicated to Semifinal Round has dots above the following points; 52.7, 53, 53.3, 53.3, 53.5, 53.5, 53.5, and 53.7. Which pieces of information can be gathered from these dot plots? (Remember that lower swim times are faster.)
Answer: None of the above.
Step-by-step explanation:
I got it right on khan. I’ll explain a little though. Semifinals median=47.05. Finals median=53.05. Therefore A is not and option and B is DEFINITLEY not an option. Sorry I’m not good at explaining
Answer:
None of the above
Step-by-step explanation:
Got it right on test
I WILL GIVE BRAINLEST FAST PLEASE ANSWER THE QUESTION IN THE IMAGE
Answer:
Cannot be determined
Step-by-step explanation:
We only know one angle and we could only compare one set of sides.
We do not have enough information to determine if the triangles are similar
Sam is five years old his brother Tom is three times as old as Sam when sam is 20 how old will Tom be?
Answer:
30
Step-by-step explanation:
5 x 3 = 15
15 - 5 = 10
20 + 10 = 30
Please helpppppp i need help…
///..
ASAP!!!!
!!!,,!!!!!!
Answer:
True
Step-by-step explanation:
64 - x^2
Rewriting as
8^2 - x^2
(8-x)(8+x)
This is the difference of squares
A sample of 4 different calculators is randomly selected from a group containing 14 that are defective and 34 that have no defects. What is the probability that at least one of the 4 calculators in the sample is defective
Answer:
The answer is "0.7616".
Step-by-step explanation:
Using formula:
[tex]\text{P( at least one de-fective) = 1 - P( all calculators work )}[/tex]
[tex]= 1-(\frac{34}{48}\times \frac{33}{47}\times \frac{32}{46}\times \frac{31}{45})\\\\= 1-(\frac{34}{1}\times \frac{11}{47}\times \frac{1}{23}\times \frac{31}{45})\\\\=1-(\frac{11594}{48647})\\\\=\frac{48647-11594}{48647}\\\\=\frac{37051}{48647}\approx 0.7616[/tex]
Solve the inequality (help pls)
Answer:
B
Step-by-step explanation:
(-2/3x)-10<1/3
(-2/3x)<1/3+10
(-2/3x)<31/3
x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)
Having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old. They can afford to save $440 per month. They place the money into an annuity that pays 5.5% per year, compounded monthly. How much will they have to spend on a car after 4 years?
having just turned 16 years old, your friend has their mind set on buying a new car by the time they turn 20 years old
Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.
9514 1404 393
Answer:
14.3%
Step-by-step explanation:
We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.
The APR is about 14.3%.
_____
The amount to be repaid is calculated using the simple interest formula:
A = P(1 +rt) = $4900(1 +0.08·4) = $6468
Then the required monthly payment (for 48 months) is ...
$6468/48 = $134.75
__
The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...
A = 4900(r/12)/(1 -(1 +r/12)^-48)
In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).
_____
Additional comment
The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.
We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.
Mr. Jerome has an outstanding balance of $12000 on his credit card. The interest rate on the card is 12% he intends to pay off
the card in 2 years. Find the APR on the card.