Answer:
442.96875 ft.
Step-by-step explanation:
Original Height (h) : 150 ft
Bounce 1 (h₁) : h/2 = 150/2 = 75 ft
Bounce 2 (h₂) : h₁/2 = 75/2 = 37.5 ft
Bounce 3 (h₃) : h₂/2 = 37.5/2 = 18.75 ft
Bounce 4 (h₄) : h₃/2 = 18.75/2 = 9.375 ft
Bounce 5 (h₅) : h₄/2 = 9.375/2 = 4.6875 ft
Bounce 6 (h₆) : h₅/2 = 4.6875/2 = 2.34375 ft
Finding the sum of bounces 1 - 5 :
75 + 37.5 + 18.75 + 9.375 + 4.6875 112.5 + 18.75 + 9.375 + 4.6875131.25 + 9.375 + 4.6875140.625 + 4.6875145.3125 ftDistance traveled :
Original Height + 2 x Sum of Bounces (1 - 5) + Height of 6th bounce150 + 2 x 145.3125 + 2.34375150 + 290.625 + 2.34375440.625 + 2.34375442.96875 ft.
Answer:
442.96875 ft
Step-by-step explanation:
We can model the height of each bounce as a geometric series.
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the initial term and [tex]r[/tex] is the common ratio)
If we let n be the number of bounces, then the initial term has to be:
[tex]a_1=\dfrac12(150)=75[/tex]
since this is the height of the ball after the first bounce.
The common ratio r has already been given to us, as we have been told that the height of the bounce halves after each bounce.
[tex]\implies r=\dfrac12=0.5[/tex]
Therefore, the geometric series to model the peak height of each bounce is:
[tex]a_n=75(0.5)^{n-1}[/tex]
(where [tex]a_n[/tex] is the height and n is the number of bounces)
Therefore, to calculate the total number of feet the ball travels until it reaches the peak height of the 6th bounce:
Total = 150 + (2 × sum of 1, 2, 3, 4 & 5th bounces) + 6th bounce
To find the sum, use the geometric sum formula:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Therefore, the sum of the bounces 1 through 5 is:
[tex]\implies S_5=\dfrac{75(1-0.5^5)}{1-0.5}=145.3125[/tex]
Height of the 6th bounce:
[tex]\implies a_6=75(0.5)^{6-1}=2.34375[/tex]
[tex]\begin{aligned}\textsf{Total distance} & =150+2\left(\dfrac{75(1-0.5^5)}{1-0.5}\right)+75(0.5)^{6-1}\\ & = 150 + 2(145.3125)+2.34375\\ & = 150 + 290.625+2.34375\\ & =442.96875\: \sf ft \end{aligned}[/tex]
3. Amy Schorling is age 24 and is unmarried. She uses her vehicle
for business. Her driver-rating factor is 1.85. Her vehicle is
classified D-14. Her insurance consists of $25,000 property
damage, 25/50 bodily injury, $50-deductible comprehensive, an
no collision coverage.
a. What is her annual premium?
b. How much is her annual premium if she includes
$50-deductible collision coverage?
Based on Amy Schorling's driver rating factor, vehicle classification and bodily injury coverage, her annual premium is $576.46.
If she includes the $50-deductibel collision coverage, her insurance premium becomes $1,067.08.
How much is Amy Schorling's annual premium?At $25,000 property damage, her 25/50 bodily injury coverage premium is $206.40.
This should be added to her $50 comprehensive deductible D-14 vehicle classification of $105.20.
Annual base premium:
= 206.40 + 105.20
= $311.60
Annual premium:
= Annual base premium x Driver rating factor
= 311.60 x 1.85
= $576.46
How much is the annual premium including collision coverage?The annual base premium becomes:
= 311.60 + 265.20
= $576.80
Annual premium becomes:
= 576.80 x 1.85
= $1,067.08
Find out more on insurance coverage at https://brainly.com/question/25740123.
Construct the indicated confidence interval for the population mean using the t-distribution. Assume the population is normally distributed.
picture of question below
Using the t-distribution, it is found that the confidence interval is (14.2, 14.8).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The other parameters are given by:
[tex]\overline{x} = 14.5, s = 0.68, n = 18[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 14.5 - 2.1098\frac{0.68}{\sqrt{18}} = 14.2[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 14.5 + 2.1098\frac{0.68}{\sqrt{18}} = 14.8[/tex]
The confidence interval is (14.2, 14.8).
More can be learned about the t-distribution at https://brainly.com/question/16162795
In a class of 26 students, 14 have a cat and 7 have a dog. There are 5
students who have a cat and a dog. What is the probability that a
student chosen randomly from the class does not have a dog?
Jake scored 9 out of 12 field goals during a basketball game. Reggie scored 3 out of 5. Who has the better average for this game?
Explain.
(I will give brainliest if you show your work)
Answer: jake
Step-by-step explanation:
no need to find avarage
9 to 12 is 0.75 or 75%
3 to 5 is 0.60 or 60%
step by step
9 divided by 12 is 0.75
3 divided by 5 is 0.60
to turn in to percentage just move two decimal places to the left .
Answer:
Jake
Step-by-step explanation:
When you compare them with fractions like on a fraction line Jake has more than Reggie
A six-sided die with sides labeled 1 through 6 will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than 2? Write your answer as a fraction in simplest form.
Answer:
4/6
Step-by-step explanation:
6 is the denominator as it's the total of the entire thing.
4 is the numerator because there's 4 numbers greater than 2
Is 32,000 millimeters = 3.2 liters?
Answer:
no
Step-by-step explanation:
WHAT IS THE ANSWER TO THIS QUESTION
Solve using elimination. Write your answer as an ordered pair (x,y).
3x - 4y = -29
and
6x + 5y = -32
Answer:
x=-7,y=2
Step-by-step explanation:
3x - 4y = - 29
and 6x + 5y = - 32
3x - 4y = - 29 (1)
6x + 5y = -32 (2)
equation (1) x 2
6x-8y = -58
equation (2) × 1
6x + 5y = - 32
Substracting → - 13y = -26
13y = 26.
26/ 13 ⇒ y =
⇒ yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy = 2
Putting y = 2 in equation (1), we have
3x - 4(2) = - 20
→ 3x = -29 +8
→3x = -21
→ X = -7
x = - 7
Please help you don't have to do 11 please help
Answer:
Step-by-step explanation:
for number 8 we have to use the equation πr^2, so plugging 9 into the equation would give us π(9^2). squaring the 9 gives us 81, and 81 times π equals ~25.
for number 9 we need to use the same equation, πr^2 to find the area, but since we are given the diameter we do not need to use r^2. Instead, we can use π(106) which gives us 333.
WORTH 75 POINTS WILL MARK BRAINLYEST HELP ME PLEASE 75 75 POINTS
Your answer is [tex]\frac{d^7}{c}[/tex]
Yw :D
Answer:
d⁷/c
Step-by-step explanation:
djsjdnsjjwndjaojc
Solve for x: 3(x + 1) = 2(x - 1)
0-5
What’s the answer?
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x=−8/3
Decimal Form:
x=−2.6
Mixed Number Form:
x=−2 2/3
hope this helps
Let's Apply Solve for the surface area of the following figures.
please i need this rn
Answer:
Step-by-step explanation:
1) Surface area of a square = s*s = 12*12 = 144 in
2) Surface area of a Cone = A=πr(r+h2+r2) = 3.142*4(4+22*2+4*2) = 351.904 cm^2
3) S.A of a Cylinder =2πrh+2πr2 = 2*3.142*2*14 + 2*3.142*2*2 = 201.088 m^2
4) S.A of a square Pyramid = a^2 + 2a squareroot (a^2/4 + h^2) = 516.5m^2
5) S.A of a Sphere = 4*pie*r^2 = 4* 3.142*15^2 = 2827.8mm^2
Carly needs $149 to buy a skateboard. She already has $52. She earns money washing cars for $20 a car.
Carly says that if she washes 5 cars she will have enough money to buy the skateboard.
Use the drop-down menus to explain how to solve this problem.
First, multiply
Choose...
× $20 to find how much money Carly will earn washing cars. Then add this amount to
Choose...
to find how much money Carly has in all. Finally,
Choose...
the total to the cost of the skateboard.
Answer:
Answer:
$149 - skateboard price
$52 - carly's money
$20 × 5 cars = $100
$100 + $52 = $152
$152 - $149 = $3 left
Step-by-step explanation:
A car can travel 580 miles on a full tank of gas. With four new eco-tyres it
can travel 620 miles. Find the percentage increase in miles the tyres have
made.
f(x) = 1.1–4x when x = – √2
Answer:
f(x)=2x^2+4x+6
f(x)=2(x^2+2x)+6
f(x)+?=2(x^2+2x+?)+6
f(x)+?=2(x^2+2x+1)+6
f(x)+2x1=2(x^2+2x+?)+6
f(x)+2=2(x^2+2x+1)+6
f(x)=2(x+1)^2+6-2
f(x)=2(x+1)^2+4
Answer:
f(x)=2(x+1)^2+4
Find the least common denominator (LCD) 8/9 and 4/5
Answer:
45
Step-by-step explanation:
First we write the first 10 multiples of 9 (the first denominator) :
9,18,27,36,45,54,63,72,81,90
Now we write the first 10 multiples of 5 (the second denominator) :
5,10,15,20,25,30,35,40,45,50
As we can see 45 is the lowest number that appears in both list.
Therefore 45 is the LCD of 8/9 and 4/5
Answer:
45
Step-by-step explanation:
So since we are finding the LCD, we only look at the denominators, 9 and 5.
We can count until we find the denominator:
[tex]9,18,27,36,45\\5,10,15,20,25,30,35,40,45[/tex]
So the LCD would be 45.
Determine the finance charge on a $6,800 car loan if monthly payments were $158.50 for 48 months.
Answer:
808
Step-by-step explanation:
Plan
You make 48 payments of 158.50. That gives you the total of what you have paid back.
Equation
Total payment = months * monthly payments
Solution
Total Payment = 48 * 158.50
Total Payment = 7608
Cost of the loan
Finance charge = amount paid - amount loaned
Finance charge = ?
amount paid = 7608
amount loaned = 6800
Finance charge = 7608 - 6800
Answer: Finance charge = 808
Multiply.
12x^4 (-5/6x^3y^2)
Answer:
-10[tex]x^{7}[/tex][tex]y^{2}[/tex]
Step-by-step explanation:
12[tex]x^{4}[/tex]([tex]-\frac{5}{6} x^{3}[/tex][tex]y^{2}[/tex])
First multiply 12 * - [tex]\frac{5}{6}[/tex] , solving this you get -10
Next multiply [tex]x^{4}[/tex] by [tex]x^{3}[/tex] , solving this you get [tex]x^{7}[/tex]
Finally you have [tex]y^{2}[/tex], and nothing to multiply it by. So it stays as [tex]y^{2}[/tex]
Put is all together and you get -10[tex]x^{7}[/tex][tex]y^{2}[/tex]
-10x^7y^2
i do k12 i just took that test
In which type of circuit is the total current equal to the sum of all the branch currents?
Answer:
Parallel circuit
Hope this one helps :)
In the study of vacuum tubes, the equation y + (0.4)(y^ -1) y' y 0 is encountered. Find the Taylor polynomial of degree 4 approximating the solution with initial values y(0)= 1, y'(0) 0 P4 (x)=
Answer: let me get back with you after
Step-by-step explanation:
2. Expand the following expression: 7 (1 + f)
Hello!! I'm always here to help!!!
_____________________
7 (1+f) = 7 · 1 + 7f
= 7 · 1 + 7f
_____________________
Have a great day!!
Help me again! No one replied to my last one!
Help help help help help
Answer:
4
Step-by-step explanation:
5x/2 - 1 = 9
add 1 to each side
5x/2 = 10
multiply both sides by 2
5x = 20
divide both sides by 5
x=4
Answer:
x=4
Step-by-step explanation:
5x-2=18 (multiply 9 with 2=18)
5x=18+2 (move 2 to the other side)
5x=20 (add 18 and 2=20)
X=4 (divide 20 and 5 =4)
Solve the following equation for x. 10=2-4(ax-3)
Answer:
[tex]x=\frac{1}{a}[/tex]
Step-by-step explanation:
10 = 2 - 4 (ax - 3)
10 = 2 - 4ax + 12
10 = - 4ax + 14
-4 = -4ax
1/a = x
Angles A and C are supplementary. Find the measure of angle C.
A. List 2 pairs of angles in square CDFG that are complementary.
B. Name three angles that sum up to 180°
a. Two pairs complementary angles are: ∠DCM and ∠DMC; ∠MGF and ∠GMF
b. m∠GMF + m∠CMG + m∠DMC = 180°
What are Supplementary Angles and Complementary Angles?If the sum of two angles equal 90°, they are complementary angles.
If the sum of two angles equal 180°, they are supplementary angles.
Given square CDFG:
a. Two pairs of angles that are complementary are: ∠DCM and ∠DMC; ∠MGF and ∠GMF
b. m∠GMF + m∠CMG + m∠DMC = 180° (angles on a straight line)
Therefore, three angles that sum up to 180° are: ∠GMF, ∠CMG, and ∠DMC.
Learn more about complementary angles on:
https://brainly.com/question/16281260
15)
Common Metals
Name Melting Point Density (w/cm)
Zinc
419.53 °C 7.134
Nickel 1455°C 8.912
Copper 1084.62°C 8.96
Silver 961.78°C 10.501
Gold 1064.18°C 19.282
You are hired as a scrap metal dealer. A customer wants to sell you a piece of precious scrap metal. You know it is one of these
common metals. You slowly heat the metal and it melts at 962 °C. You also take the density of the metal and find it to be roughly
10.5 g/cm? What is the MOST LIKELY identity of the metal?
copper
A)
B
B)
gold
C)
silver
D)
zinc
The data given are
melting point density
Zinc 419.53 oC 7.134
Nickel 1455oC 8.912
Copper 1084.62oC 8.96
Silver 961.78oC 10.501
Gold 1064.18oC 19.282
density is the mass per unit volume. Melting point is determined by the intermolecular forces between particles in the solids.
We have been asked to find which cube weighs the most
density = mass/volume
when volume is constant for all the metals, then density is directly proportional to mass. Therefore metal with highest density has the highest mass.
from the given metals, metal with highest density is Gold.
correct answer is Gold.
I need help! what is this equation in factored form and how do you solve it using the X-method (or really any other method?)
y = -3x^2 - x + 2
Answer:
See below
Step-by-step explanation:
Part 1:
Factored: y = (-3x+2)(x+1)
Part 2:
Not exactly sure what the "x" method is after your explaination, so ill just use the quadratic formula.
Quadratic Formula:
[tex]x = \frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Also:
[tex]x^2=a\\x=b\\2=c[/tex]
So if you solve (not showing work):
Your x-ints are:
-1
2/3
Which expression represents a negative number? A.-4.5x-22.1 B.4.5x22.1 C.-45x2.21 D.-45x-2.21
Hey there!
-4.5 * (-22.1)
= -4.5(-22.1)
= 99.45
4.5 * 22.1
= 99.45
-45 * 2.21
= -99.45
-45(2.21)
= -99
Therefore, your answer is:
Option C.
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
C.-45 x 2.21Step-by-step explanation:
When you multiply two negative or two positive numbers you get a positive result and when you multiply one positive and one negative number you get a negative result.
Looking at answer choices, we see
A) negative x negative = positiveB) positive x positive = positiveC) negative x positive = negativeD) negative x negative = positiveSo the correct one is C
HELP my mom said if i get caught up with my school work they will take me to the beach so help me with this test pls
Answer:
If i give you the answers, it will not help you, because you need to learn these things...I will however give you something that will help you .
Step-by-step explanation:
Hope this helps! Have a good day! :)
Marlene is going on a camping trip with a group of friends. She brings 3 boxes of granola bars, plus 3 extra bars. Robyn bring 2 boxes of granola bars and Wendy brings one box. They have a total of 57 granola bars. If each box contains the same number of bars, how many bars are in each box?
Answer:
19
Step-by-step explanation: