Given:
The height of a golf ball is represented by the equation:
[tex]y=x-0.04x^2[/tex]
To find:
The maximum height of of Anna's golf ball.
Solution:
We have,
[tex]y=x-0.04x^2[/tex]
Differentiate with respect to x.
[tex]y'=1-0.04(2x)[/tex]
[tex]y'=1-0.08x[/tex]
For critical values, [tex]y'=0[/tex].
[tex]1-0.08x=0[/tex]
[tex]-0.08x=-1[/tex]
[tex]x=\dfrac{-1}{-0.08}[/tex]
[tex]x=12.5[/tex]
Differentiate y' with respect to x.
[tex]y''=(0)-0.08(1)[/tex]
[tex]y''=-0.08[/tex]
Since double derivative is negative, the function is maximum at [tex]x=12.5[/tex].
Substitute [tex]x=12.5[/tex] in the given equation to get the maximum height.
[tex]y=(12.5)-0.04(12.5)^2[/tex]
[tex]y=12.5-0.04(156.25)[/tex]
[tex]y=12.5-6.25[/tex]
[tex]y=6.25[/tex]
Therefore, the maximum height of of Anna's golf ball is 6.25 units.
Jessie has rewritten the quadratic equation x2-32x +54 -0 in the form (-p) = 202. What is the value of p in the rewritten equation?
Given:
The quadratic equation is:
[tex]x^2-32x+54=0[/tex]
It can be written as [tex]-p=202[/tex].
To find:
The value of p in the rewritten equation.
Solution:
We have,
[tex]x^2-32x+54=0[/tex]
Isolate the constant term.
We need to make 202 on the right side. So, add 256 on both sides.
[tex]x^2-32x+256=-54+256[/tex]
[tex]x^2-32x+256=202[/tex]
[tex]-(-x^2+32x-256)=202[/tex]
Let [tex]-x^2+32x-256=p[/tex], then
[tex]-p=202[/tex]
Therefore, the value of p is [tex]-x^2+32x-256[/tex].
The given equation can be written as:
[tex]54=-x^2+32x[/tex]
Adding 148 on both sides, we get
[tex]54+148=-x^2+32x+148[/tex]
[tex]202=-(x^2-32x-148)[/tex]
Let [tex]x^2-32x-148=p[/tex], then
[tex]202=-p[/tex]
Therefore, the another possible value of p is [tex]x^2-32x-148[/tex].
Tommy bought p boxes of 26 paperclips. He already had 35 paperclips. Now, he has 191 paperclips. How many boxes of paperclips did Tommy buy in all?
Answer:
Tommy bought 6 boxes
Step-by-step explanation:
subtract 35 from 191, and you get 156. 156 divided by 26 = 6. so 6 boxes
Answer choices are
A. 4
B. 6
C. 8
D .10
Answer:
c us the correct answer for this question
A team of students is designing a new game to help their class review for a science test. They will make a rolling cube with a side length of 7 cm as part of the game.
A cube has side lengths of 7 centimeters.
How much material will they need to make the rolling cube?
49 square cm
138 square cm
294 square cm
307 square cm
Answer:
C (294)Step-by-step explanation:
Took the test :)
udent
You roll a number cube two times. Which of the theoretical probabilities are accurate?
Check all that apply.
OP(1 then 0) = }
Pleven number then odd number) = 4
P(6 then 2) = 36
Pleven number then 5) = 12
ook
ons
ative
Plodd number then 2) =
HELP
Answer:
B ; C ; D
Step-by-step explanation:
Number of faces on a number cube = 6
Sample space = (1, 2, 3, 4, 5, 6)
P(1 then 0)
P(1) = 1/6 ; P(0) = 0
P(1 then 0) = 1/6 * 0 = 0
P(even number then odd number) :
P(even number) = 3/6 = 1/2
P(odd) = 3/6 = 1/2
P(even number then odd number) = 1/2 * 1/2 = 1/4
P(6 then 2) :
P(6) = 1/6 ; P(2) = 1/6 = 1/2
P(6 then 2) = 1/6 * 1/6 = 1/36
P(even number then 5) :
P(even) = 3/6 = 1/2
P(5) = 1/6
P(even number then 5) = 1/2 * 1/6 = 1/12
P(odd number then 2) :
P(odd) = 3/6 = 1/2
P(2) = 1/6
P(odd number then 2) = 1/2 * 1/6 = 1/12
Maria is saving money to buy a bike. She has $42 and is going to save an additional $ 7 each week. The bike costs $133. In how many
weeks will she have enough money to buy the bike?
Answer:
Maria will have enough money to buy the bike in 13 weeks.
Step-by-step explanation:
w = weeks
42 + 7w = 133
take away 42 frim each side
7w = 91
divide each side by 7
w = 13
Solve for x to the nearest tenth.
х
3
7
3
20 POINTS
Answer:1.7
Step-by-step explanation:
Please help for final!!
How big is
Answer:
72degrees
Step-by-step explanation:
triangle=180
C:90 B:18
180-90-18=72
hello please help i’ll give brainliest
Answer:
2nd and 3rd OptionsStep-by-step explanation:
As,
These two,
A large rock breaking down into smaller rocks, and water carving a canyon out of the ground
Are physical changes within the Earth's system
Using the Exxon data as an example pretend Pennys Pickles divide their company into 10,000 shares of stock. If you buy 200 of these shares what percent of Penny's Picklesdo you own
Penny's Pickles divide their company into 10,000 shares of stock. If you buy 200 of these shares then you will have [tex]2\[/tex] percent of Penny's Pickles.
What is percentage?Percentage a is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, [tex]\%[/tex].
Percentage [tex]=\frac{ You\ owned}{Total \ share} * 100[/tex]
We have,
Total shares of Penny's Pickles [tex]=10,000[/tex]
You owned shares [tex]= 200[/tex]
So,
Using above formula,
Percentage [tex]=\frac{ You\ owned}{Total \ share} * 100[/tex]
Percentage of shares I owned [tex]=\frac{200}{10000} * 100[/tex]
[tex]= 2 \%[/tex]
So, the shares you owned are [tex]2\ \%[/tex] of total share of the Penny's Pickles.
Hence, we can say that Penny's Pickles divide their company into 10,000 shares of stock. If you buy 200 of these shares then you will have [tex]2\[/tex] percent of Penny's Pickles.
To know more about percentage click here
https://brainly.com/question/24159063
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Drew has two cats. One cat weighs 17 pounds, and the other one weighs 1212 pounds. Audrey’s dog weighs 33 pounds.
What is the difference in ounces between Audrey’s dog and the combined weights of Drew’s cats?
Enter your answer in the box.
Answer:
48 ounces
Step-by-step explanation:
Answer:
64 ounces.
Step-by-step explanation:
combined weigh = weight of cat 1 + weight of cat 2
combined weigh = 17 + 12 = 29 pounds
The difference in weight of the Dog's weigh by the combined cat's weigh is the subtraction between the two, so we have:
Difference in weigh = 33 - 29 = 4 pounds
We now have to convert it to ounces, since 1 pound contains 16 ounces we can multiply the value of the weigh in pounds by 16 to obtain the final value:
Difference in weigh = (4 pounds)* 16 = 64 ounces
Please help me with this problem
The histogram shows the number of classes missed by students in a class during the school year. How many students are in the class?
Answer:
25
Step-by-step explanation:
9+13+3 = 25
__________
Taylor bought a watch on sale for 60% off of the original price, and another 10% off of the discounted price. If the watch originally cost $82, what was the final sale price?
Answer:
I think the answer is $4.92.
Step-by-step explanation:
Although the answer seems a little unreasonable, I think this is the answer:
$82 * 60% = $49.2
49.2 * 10% = $4.92
Please mark brainliest if correct!!!!!!!!!!!!!!! have a nice day!!
How can I find the height of a pyramid that has a base of 13m and a 13m lateral height
Answer:
Calculate the unknown defining height, slant height, surface area, side length and ... Online calculators and formulas for a pyramid and other geometry problems. ... h = height s = slant height a = side length. P = perimeter of base e = lateral .
Step-by-step explanation:
Which equation represents: three times the difference of a number and five is nine
Help me plzzz I need area and perimeter
Answer:
Area = 37.5
Perimeter = 36
Step-by-step explanation:
Have a good day! :)
Ps: I am not sure my method of finding area is correct
I will put the method in the comments
how to find the P: To find the p of Any Shape is the same formula, adding all the sides up. So to find the p of this shape all you need to do is add all the sides up. 3+12.5+7.5+13. Add these up and you get the P
[tex]p^{2} =0.81[/tex]
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
[tex]p ^{2} = 0.81 \\ p = \sqrt{0.81 } \\ p = 0.9[/tex]
•°• √81 = 9 or 9² = 81
Answer:
P = 0.9
Step-by-step explanation:
Do square root Of .81.
A variable can never Have a square root OR a negative symbol
as Final answer
I hope this helps!
Select all that apply 40% is what percent of 25
Answer:
10
Step-by-step explanation:
:)
Answer:
the answer is 10 :) I hope you do well in the rest of your test!
Send help plsssss math is difficult
Ian invested $20,000 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded continuously. Lauren invested $20,000 in an account paying an interest rate of 3\tfrac{7}{8}3 8 7 % compounded monthly. After 20 years, how much more money would Lauren have in her account than Ian, to the nearest dollar?
Answer:
$5047
Step-by-step explanation:
im smart
deltamath gang
Help, so You pick a card at random. Without putting the first card back, you pick a second card at random. There are 3 cards, a 5 a 6 and a 7 What is the probability of picking a 5 and then picking a 6?
Given:
There are 3 cards, a 5 a 6 and a 7.
You pick a card at random. Without putting the first card back, you pick a second card at random.
To find:
The probability of picking a 5 and then picking a 6.
Solution:
We have,
Total number of cards = 3
Number of card of 5 = 1
So, probability of getting a card of 5 is:
[tex]P(5)=\dfrac{\text{Number of card of 5}}{\text{Total number of cards}}[/tex]
[tex]P(5)=\dfrac{1}{3}[/tex]
After this selection, the remaining number of cards is 2. So, probability of getting a card of 6 in second draw is:
[tex]P(6)=\dfrac{\text{Number of card of 6}}{\text{Total number of remaining cards}}[/tex]
[tex]P(6)=\dfrac{1}{2}[/tex]
Now, the probability of picking a 5 and then picking a 6 is
[tex]P(\text{5 then 6})=P(5)\times P(6)[/tex]
[tex]P(\text{5 then 6})=\dfrac{1}{3}\times \dfrac{1}{2}[/tex]
[tex]P(\text{5 then 6})=\dfrac{1}{6}[/tex]
Therefore, the probability of picking a 5 and then picking a 6 is [tex]\dfrac{1}{6}[/tex].
hello please help i’ll give brainliest
Answer:
The sun and the earth's interiorStep-by-step explanation:
As,
The Earth has two basic sources of energy -
Earth's Interior- hat reaching the Earth from the Sun (Solar Energy) and that reaching the surface of the Earth the Earth itself (Internal or Geothermal Energy). Solar Energy - reaches the Earth in the form of radiant energy, and makes up 99.987% of the energy received by the Earth.please help i will give brainliest
Answer:
Step-by-step explanation:
P=3/6 ×5/26=5/52
2.for Corner
P=3/6×5/26=5/52
3. for Cecilia
P=2/6×5/26=5/78
Use the dice lattice shown below to answer the question that follows.
When Martha rolled the dice 36 times, she got a sum of 8 seven times. Explain why Martha's
experimental probability is different than a theoretical probability.
Answer:
Theoretical probability is what is expected and experimental probability is the answer.
Step-by-step explanation:
Theoretical probability is what you expected the answer to be. In reality the experimental probability is the actual answer.
Find the measure of angle b.
Which is the answer?
A.79
B.101
C.169
B.11
Can you help me, I would appreciate it very much:)
Use the following function rule to find f(-62). help plz!!
Answer: 8
Step-by-step explanation: plug in -62 as equal to x
7 times 6 pls answer this
Answer:
42
Step-by-step explanation:
7 * 6 = 42
Hope this helps!
Answer:
42
Step-by-step explanation:
6 x 7 =42
Hope this helps! Please mark brainiest!
The length of a rectangle is 5 inches more than its width. The area of the rectangle
is 150 centimeters. Find the dimensions of the rectangle.
it's good to write it out
length = 5 + width
area = 150
width = x
length = 5 + x
area = length * width
so
(5 + x) (x) = 150
5x + x^2 = 150
x^2 + 5x - 150 = 0
following you have to guess what 2 numbers when multiplied male 150 and when added make 5
and they are 15 and 10
(x +15) (x-10)
x = -15
x = 10
so the dimensions are
length = 15
and
width = 10
The radius of a cylindrical construction pipe is 3.5ft. If the pipe is 40ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
1539 ft^3
Step-by-step explanation:
3.5×3.5=12.25
12.25×3.14=38.465
38.465×40=1,538.6
1538.6 rounded to the nearest whole number is 1539.
Can you help me im stuck on this
One question
Answer:
She forgot to multiply. She wasn’t supposed to add.
Step-by-step explanation:
Jasmine made an error where the 9(9) connect. She added and got 18, but instead, you’re supposed to multiply the 9 x 9, which is 81. Now, we add the 3, and the sum is 84m.