Answer: 0.388 m
Step-by-step explanation:
Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:
h1 = (3/5)*1.8m = 1.08m
now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:
h2 = (3/5)*1.08m = 0.648m
Now, using the same method as before, the height after the third bounce will be:
h3 = (3/5)*0.648m = 0.388 m
Notice that we can write this relation as:
h(n) = 1.8m*(3/5)^n
where n is the number of bounces.
if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:
h(3) = 1.8m*(3/5)^3 = 0.388 m
Write the first five terms of the arithmetic sequence.
Answer:
a1 = 4
a2= -2
a3 = -8
a4= -14
a5= -20
Step-by-step explanation:
a12= a1 + 11d
-62 = 4 + 11d
-62-4 = 11d
-66= 11d
d = [tex]\frac{-66}{11}\\[/tex]
= -6
a1 = 4
a2 = 4 - 6 = -2
a3 = 4 - (6×2) = -8
a4 = 4 - (6×3) = -14
a5 = 4 - (6×4) = -20
When a person throws a ball into the air, it follows a parabolic path that opens downward as shown in the figure to the right. Suppose that the ball's height in feet after t seconds is given by h(t)=-16t^2+32t+2. If possible, determine the time(s) when the ball was at a height of 14 feet.
Answer:
0.5 seconds and 1.5 seconds.
Step-by-step explanation:
h(t) = -16t^2 + 32t + 2
14 = -16t^2 + 32t + 2
16t^2 - 32t - 2 + 14 = 0
16t^2 - 32t + 12 = 0
8t^2 - 16t + 6 = 0
4t^2 - 8t + 3 = 0
(2x - 3)(2x - 1) = 0
2x - 3 = 0
2x = 3
x = 3/2
x = 1.5
2x - 1 = 0
2x = 1
x = 1/2
x = 0.5
So, the ball was at 14 feet at 0.5 seconds and 1.5 seconds.
Hope this helps!
Daniel's mom deposits $80 into his savings account for the year. Daniel decides to upgrade his game account which costs $7 per month. How many months will Daniel be able to pay for his game account if his mom doesn't deposit any more money into his savings account?
Answer:
11.43
Step-by-step explanation:
80÷7= 11.428571428571428571428571428571
i hope this helps
Which of the following is a radical equation?
x+ square root 5 = 12
x² = 16
3+ square root 7 = 13
7 square root x = 14
Answer:
7 square root x = 14
Step-by-step explanation:
A radical equation will have the variable inside the radical
Answer:
D
Step-by-step explanation:
A radical equation persists when a radical includes a variable within it. In this case the x is in the radical, times 7. The rest of the answers do not have a variable in a radical.
Find the rectangular coordinates of the point with the polar coordinates ordered pair 7 comma 2 pi divided by 3.
Answer:
[tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].
Step-by-step explanation:
The given point is
[tex]\left(7,\dfrac{2\pi}{3}\right)[/tex]
We need to find the rectangular coordinates of the given point.
If a polar coordinate is [tex](r,\theta)[/tex], then
[tex]x=r\cos theta[/tex]
[tex]y=r\sin theta[/tex]
In the given point [tex]\left(7,\dfrac{2\pi}{3}\right)[/tex],
[tex]r=7,\theta=\dfrac{2\pi}{3}[/tex]
Now,
[tex]x=7\cos \dfrac{2\pi}{3}[/tex]
[tex]x=7\cos \left(\pi-\dfrac{\pi}{3}\right)[/tex]
[tex]x=-7\cos \left(\dfrac{\pi}{3}\right)[/tex]
[tex]x=-7\left(\dfrac{1}{2}\right)[/tex]
[tex]x=-\dfrac{7}{2}[/tex]
and,
[tex]y=7\sin \dfrac{2\pi}{3}[/tex]
[tex]y=7\sin \left(\pi-\dfrac{\pi}{3}\right)[/tex]
[tex]y=7\sin \left(\dfrac{\pi}{3}\right)[/tex]
[tex]y=7\left(\dfrac{\sqrt{3}}{2}\right)[/tex]
[tex]y=\dfrac{7\sqrt{3}}{2}[/tex]
Therefore, the required point is [tex]\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)[/tex].
Find the equilibrium price and quantity
from given demand and supply Funchon
Qd = 400-4p and Qs = 6p-10
Answer:
Step-by-step explanatiio:
Ep is when Qd=Qs
400-4p=6p-10
-4p-6p=-10-400
-8p=-410
P=51.25frs
EQ=400-4(51.25)
400-205
=125kg
On a recent shopping trip, you see a sale advertising 3 pairs of socks and 2 pairs of shoes for $60. Write an equation using x to represent the cost of socks and y to represent the cost of shoes.
Answer:
3x + 2y =60
Step-by-step explanation:
x = socks
y = shoes
3x + 2y =60
Answer:
3x + 2y =60
Step-by-step explanation:
Hope this Helps you !
The graph of y=sinx is transformed to y=asin(x−c)+d by a vertical compression by a factor of 14, then translated π3 units right and 5 units down. The new equation is:
Answer:
y= 1/14 sin(x-3π)-5
For functions f(x)=2x^2−4x+3 and g(x)=x^2−2x−6, find a. (f+g)(x) b. (f+g)(3).
Answer:
a) 3x^2-6x-3
b) 6
Step-by-step explanation:
f(x)=2x^2−4x+3
g(x)=x^2−2x−6
a) (f+g)(x) = (2x^2−4x+3) + (x^2−2x−6)
collect like terms
(f+g)(x) = 2x^2+x^2-4x-2x+3-6
(f+g)(x) = 3x^2-6x-3
b) (f+g)(3). This implies that x=3
recall (f+g)(3) = 3x^2-6x-3
(f+g)(3) = 3(3)^2-6(3)-3 = 27-18-3
(f+g)(3) = 27-21 =6
Get every whole number from 0−10 using exactly five 3's, and any arithmetic operations and parentheses
Answer:
Step-by-step explanation:
(3 +3 - 3 -3) / 3 = 0
3 - 3/3 - 3/3 = 1
3 + 3 - 3 - 3/3 = 2
(3*3*3/(3*3) = 3
(3 + 3+ 3+ 3) / 3 = 4
(3 * 3) - (3 + 3/3) = 5
((3*3*3)/ 3)) - 3 = 6
(3 * 3) - 3 + 3/3 = 7
(3*3*3 - 3) / 3 = 8
(3 + 3+3 + 3) - 3 = 9
3 + 3 + 3 + 3/3 = 10.
Threr are 8 children standing. There are 3 fewer children standing than sitting. How many children are sitting?
Answer:
11 children sitting
Step-by-step explanation:
3+8=11
Please help ASAP!!! Thank you so much!!! Just want confirm my answer it is y=150x-50. A concession stand at a football game took in $100 after being open for 1 hour. After 3 hours, the stand had taken in $400. Assuming a linear function, write an equation in the form y=mx+b that shows the revenue earned from being opened for x hours.
Answer: You have the correct answer. It is y = 150x-50
Nice work on getting the correct answer. For anyone curious, the explanation is below.
=============================================
x = number of hours the stand is open
y = amount earned
(1,100) is from the fact the stand is open 1 hour and earns $100
(3,400) is due to the stand earning $400 after 3 hours.
Slope Formula
m = (y2 - y1)/(x2 - x1)
m = (400-100)/(3-1)
m = 300/2
m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.
Use m = 150 and (x,y) = (1,100) to find the value of b as shown below
y = mx+b
100 = 150(1) + b
100 = 150 + b
100-150 = b
-50 = b
b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.
So we have m = 150 as the slope and b = -50 as the y intercept.
Therefore, y = mx+b turns into y = 150x-50.
-------
As a check, plugging in x = 1 should lead to y = 100
y = 150x-50
y = 150(1)-50
y = 150-50
y = 100 and indeed it does
The same should be the case with (3,400). Plug in x = 3 and we should get y = 400
y = 150x-50
y = 150(3)-50
y = 450-50
y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).
The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
$100 for 1 hour
So,
x = 1 and y = 100
And,
$400 for 3 hour
So,
x = 3 and y = 400
Now the slope of the linear equation is given by
m = difference in ys coordinate / difference in xs coordinate
m = (400 - 300)/(3-1) = 150
So equation become
y = 150x + b
Now put (3,400) to find out b
400 = 150(3) + b
b = -50
So, equation
y = 150x - 50
Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".
For more about the equation,
https://brainly.com/question/10413253
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Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer
Answer:
1 1/3 ft
Step-by-step explanation:
12 inches in a foot, so 16/12, or 1 4/12 feet, or 1 1/3 feet
What is the length of AB? (Nearest TENTH) A.34 B.105.3 C.11.8 D.24.7
Answer:
The answer is option A.
Step-by-step explanation:
To find the length of AB we use sine
sin∅ = opposite / hypotenuse
From the question
AB is the hypotenuse
AC is the opposite
sin 36 = AC / AB
sin 36 = 20/ AB
AB = 20 / sin 36
AB = 34.026
AB is 34 to the nearest tenthHope this helps you
he geometric property of any polygon feature that is represented by the ratio of the perimeter of the polygon to the circle with the same perimeter is called
Answer:
"Compactness" is the right answer.
Step-by-step explanation:
In mathematical or geometry, compactness seems to be the characteristic of some mathematical morphology or spaces which have its primary use during the analysis of parameters based upon such spaces.An accessible space protect (or set) is another series of open field sets shielding another space; i.e., every space position is throughout some series member.So that the above would be the correct answer.
A catering company is catering a large wedding reception. The host of the reception has
asked the company to spend a total of $454 on two types of meat: chicken and beef. The
chicken costs $5 per pound, and the beef costs $ 7 per pound. If the catering company
buys 25 pounds of chicken, how many pounds of beef can they buy?
The answer is 47 pounds
Explanation:
1. First, let's calculate the amount of money that was spent on chicken
$5 per pound of chicken x 25 pounds = $125
2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.
$454 (total) - $125 (chicken) = $329
3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.
$329 / $7 = 47 pounds
Select all angle measures for which sin0= -√2/2
Answer:
5π/4 & 7π/4 & 13π/4
Step-by-step explanation:
For this problem, we simply need to find the value of theta for which arcsin(-sqrt(2)/2) is true. This value is π/4 or 45 degrees if we had a positive. To make the negative true, we need the angle to be in the third or fourth quadrants (i.e., 5π/4 and 7π/4). These are two of the answer choices. And then anytime these return (i.e., by adding 8/4 to either of these) should also be selected as a correct angle. Thus we get 13π/4 as the final angle.
Answer:
Option 1
Step-by-step explanation:
[tex]Total \: value \: of \: \pi \: in \: terms \: of \: angles \: = 180 [/tex]
[tex]So \: putting \: the \: of \: \pi \: in \: \frac{3\pi}{4} gives[/tex]
[tex] \frac{3 \times 180}{4} = 3 \times 45 = 135 \: degrees [/tex]
[tex] \sin(135) = \frac{- \sqrt{2} }{2} = \frac{-1}{ \sqrt{2} } [/tex]
someone please do this like literally please
Answers:
sin a=12/15=4/5
step by step explanation:
AB=9, and BC=12
find c: hyp.=√12²+9²=c²
c=15
sin a=opp/hyp.=12/15=4/5 ( convert to degrees)
a=41.10
which of the following descriptions represent the transformation shown in the image? Part 1d
Answer:
(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.
Step-by-step explanation:
Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.
In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).
Q is right now at (-3,-4) so we can translate this.
To get from -3 to -1 in the x-axis, we go right by 2 units.
To get from -4 to -3 in the y-axis, we go up one unit.
Now, if we reflect it, the triangles will be the same.
Hope this helped!
Answer:
C.
Step-by-step explanation:
When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.
Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.
All of these conditions match the ones put forth in option C, so that is your answer.
Hope this helps!
Gabrielle's age is three times Mikhail's age. The sum of their ages is 92. What is Mikhail's age?
Answer:
Gabrielle is 69 while Mikhail is 23.
Step-by-step explanation:
Let G represent Gabrielle's age and M represent Mikhail's age.
Gabrielle is three times Mikhail's age. In other words:
[tex]G=3M[/tex]
The sum of their ages is 92. In other words:
[tex]G+M=92[/tex]
This is a system of equations. Solve. Substitute in G:
[tex]G+M=92\\(3M)+M=92\\4M=92\\M=23[/tex]
Thus, Mikhail is 23. Now, find Gabrielle's age:
[tex]G=3M\\G=3(23)\\G=69[/tex]
Gabrielle is 69.
(25 points) PLEASE HELP, I gotta get this done or my mom will beat the hell out of me
Solve
x + y = 2
4y = -4x + 8
by elimination (not Gaussian!)
Thanks!
(also, please show work!)
Answer:
x=1
y=1
Step-by-step explanation:
Please look at the image below for solutions⬇️
Answer:
Step-by-step explanation:
Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.
Point form
(x, 2-x)
HeLpPPppPpppPPPPPPPppppppPPPPpppppPPPpppppPPPPPPppppppPP AGgaGAGgagagGAGin!!!!!!!!!!!!
Answer:
Pii is equAAAaaaaallLLLL to 3.14(rounded)
Step-by-step explanation:
Here listed are some formulas which can help you with your problems:
circumference of a circle=C=2πr
however, you can also write it as dπ, since is two d times r.
area of a circle= πr^2
simply plug in your values, and solve them
you have all the materials you need to know
Further assistance/spoonfeed time:
We know the formulas for the circumference and area.
We also have the values of the circles A and B.
C=2πr
That's the formula, and now I'm gonna plug in the values given to me for A, which is 21.98 for circumference, and 7 for diameter.
(21.98)=2πr
Like I said before, the radius multiplied by 2 is the diameter, which is 7. But if you actually want the radius for some reason, just divide the diameter by 2.
let's update the equation: 21.98= 7π
now divide both sides by seven, and you'll get 3.14=π
area=π^2
now do what i just did, according to this formula
What is the center of the circle? Also, use the midpoint formula to verify it.
Answer:
center : (-2, -2.5)
Step-by-step explanation:
Midpoint point formula says that if there are two points (x1,y1) and (x2,y2) then
coordinate of midpoint is given by
midpoint (x1+x2)/2 , (y1+y2)/2
_______________________________________________
In the problem, we have to find the center of circle of by using the midpoint formula.
Since the circle is circumscribed in square. Its center will be midpoint of either of the diagonal.
To find the center we can take coordinate of any of two diagonal points of square and find midpoint for this and that will be center of circle.
_________________________________________________
1st diagonal pair(4,8) and (-8,-3)
Then midpoint is (4 + -8)/2 , (8+ -3)/2
midpoint (-2, -2.5)
Thus, center of circle is (-2,-2.5)
we can verify this by using other diagonal pair (-8,8) and (4,-3)
Midpoint in this case can be calculated as
midpoint (-8+4)/2 , (8 + -3)/2
midpoint (-2,-2.5)
Thus, we see that in both cases Midpoint is same and hence center is (-2, -2.5)
A survey of 700 non-fatal car accidents showed that 183 involved faulty equipment. Find a point estimate for the population proportion of non-fatal car accidents that involved faulty equipment.
Answer:
Point of faulty equipment car = 0.2614 (Approx)
Step-by-step explanation:
Given:
Total number of car = 700
Faulty equipment car = 183
Find:
Point of faulty equipment car
Computation:
Point of faulty equipment car = Faulty equipment car / Total number of car
Point of faulty equipment car = 183 / 700
Point of faulty equipment car = 0.261428571
Point of faulty equipment car = 0.2614 (Approx)
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2
pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per
pound of apples, and y is the cost per pound of bananas.
5x + 3y = 8.5
3x + 2y = 5.25
If you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate
the y terms when making a linear combination?
Complete the multiplication and add the equations. What is the result?
What is the price per pound of apples? $
What is the price per pound of bananas?
Answer:
price per pound of apple = $1.25
price per pound of banana = $0.75
Step-by-step explanation:
Your first question is what value should you multiply the second equation by in order to eliminate the y terms.
The number should be 3. Let us multiply the first equation by 2 and the second equation by 3 and see how y will be eliminated.
10x + 6y = 17...............(i)
9x + 6y = 15.75...........(ii)
10x - 9x = x
6y - 6y = 0
17 - 15.75 = 1.25
x = 1.25
let us find y
10x + 6y = 17...............(i)
10(1.25) + 6y = 17
12.5 + 6y = 17
6y = 17 - 12.5
6y = 4.5
divide both sides by 6
y = 4.5/6
y = 0.75
In order to eliminate y term from the system of equations we multiply equation 2 by -3.
The price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
Given equations,
[tex]5x + 3y = 8.5[/tex].........(1)
[tex]3x + 2y = 5.25[/tex].......(2)
Here x is the cost per pound of apples, and y is the cost per pound of bananas.
According to the question, multiply the first equation by 2, we get
[tex]10x+6y=17[/tex].....(3)
So, in order to eliminate y term from the system of equations we multiply equation 2 by -3, we get
[tex]-9x-6y=15.75[/tex].....(4)
Now Adding (3) and (4) equation, we get
[tex]x=1.25[/tex]
Putting the above value of x in equation 3 we get,
[tex]10\times1.25+6y=17\\12.5+6y=17\\6y=17-12.5\\6y=4.5\\y=\frac{4.5}{6} \\y=0.75[/tex]
Hence the price per pound of apple is 1.25 dollars and the price per pound of bananas is 0.75 dollars.
For more details follow the link:
https://brainly.com/question/11897796
What is the solution to this equation? w - 3 = 15
Answer:
w = 18Step-by-step explanation:
w - 3 = 15
Add 3 to both sides to make w stand alone
That's
w - 3 + 3 = 15 + 3
w = 15 + 3
We have the final answer as
w = 18
Hope this helps you
Answer: w = 18
Step-by-step explanation: To solve for w in this equation, we want to get w by itself on the left side of the equation.
Since 3 is being subtracted from w, to get w by itself,
we need to add 3 to the left side of the equation.
If we add 3 to the left side, we must also add 3 to the right side.
Notice that on the left side, -3 and +3 cancel
each other out so were simply left with w.
On the right side, 15 + 3 is 18.
So we have w = 18.
A sample of 4 different calculators is randomly selected from a group containing 42 that are defective and 20 that have no defects. What is the probability that all four of the calculators selected are defective? No replacement. Round to four decimal places.
Answer: = approx 0.2006
Step-by-step explanation:
The probability that first 1 randomly selected calculator is defective is
P(1st defect)= 42/(42+20)=42/62=21/31
If the first calculator is defective the residual number of defective calculators is 42-1=41. The residual total number number of calculators is 62-1=61
So the probability that second calculator is defected
P(2nd defective)=41/61
If both previous calculators are defective the residual number of defective calculators is 42-2=40. Total residual number of calculators is 62-2=60
So the probability that third calculator is defected
P(3rd defective)=40/60=2/3
Finally the probability that also fourth calculator is defective is 39/59
P(4th defective)=39/59
The resulted probability that all 4 calculators are defective is
P(all 4 are defective)= P(1st defect)* P(2nd defect) * P(3rd defect)* P(4th defect)=21*41*2*39/(31*61*3*59)=67158/334707=0.200647... = approx 0.2006
A distribution has a mean of 90 and a standard deviation of 15. Samples of size 25 are drawn randomly from the population. Find the probability that the sample mean is more than 85 g
Answer:
The probability is 0.04746
Step-by-step explanation:
Firstly, we calculate the z-score here
Mathematically;
z-score = x-mean/SD/√n
Where from the question;
x = 85, mean = 90 , SD = 15 and n = 25
Plugging these values into the equation, we have;
Z = (85-90)/15/√25 = -5/15/5 = -1.67
So the probability we want to calculate is ;
P(z > -1.67)
We use the standard normal distribution table for this;
P(z > -1.67) = 0.04746
Enrique is making a party mix that contains raisins and nuts. For each ounce of nuts, he uses twice the amount of raisins. How many ounces of nuts and how many ounces of raisins does he need to make 24 ounces of party mix?
Answer:
16
Step-by-step explanation:
1x to 2x ratio
total is 24 oz, aka 3x or 1x+2x
24oz=3x
do some math
x=8oz
raisins = 2x = 16 oz
Answer:
Step-by-step explanation: 2x-16 oz
 Given that UVW XYZ, what is the measure of Y?
A.
180
B.
70
C.
40
D.
90
Answer:
Y = 40
Step-by-step explanation:
First find the measure of V
The sum of the angles of a triangle equal 180
U+V+W =180
70+Y+70 =180
140+U =180
U = 180-140
U = 40
Since the triangles are similar
V = Y
40 = Y