Step-by-step explanation:
the extreme values of a function happen at the zeros of the first derivation of that function.
f(t) = -16t² + 72t
f'(t) = -2×16t + 72 = -32t + 72
0 = -32t + 72
32t = 72
t = 72/32 = 2.25 seconds
f(2.25) = -16(2.25)² + 72×2.25 = -16×5.0625 + 72×2.25 =
= -81 + 162 = 81 ft
so, the rocket reaches its maximum height of 81 ft after 2.25 seconds of flight.
Estimate by rounding ONLY the prime numbers to the nearest ten
193 + 228 + 149
i need help !
[tex]3\sqrt{5} +5\sqrt{15}[/tex]
Answer:
26
Step-by-step explanation:
SORRY IF IM WRONG
You are shooting arrows at a target with three rings: there is a circle with 4 inch radius, a ring around it with 8 inch radius, and a ring around that with a 12 inch radius. If your 3 arrows will hit the target somewhere uniformly at random, what is the probability that you land exactly one shot in each of the three rings
The probability that you land exactly one shot in each of the three rings is 0.122
How to get the probability?
The probability of hitting each section will be the quotient between the area of the section and the total area of the target.
The area of the target is:
A = 3.14*(12 in)^2 = 452.16 in^2
The area for the smallest circle is:
A₁ = 3.14*(4 in)^2 = 50.24 in^2
So the probability of hitting the smallest circle is:
p₁ = A₁/A = (50.24/452.16) = 0.11
For the first ring, the area is:
A₂ = 3.14*(8in)^2 - 50.24 in^2 = 150.72 in^2
So the probability of hitting this ring is:
p₂ = (150.72)/(452.16) = 0.33
The probability of hitting the final ring is 1 minus the probabilities of hitting the two other regions, so we have:
p₃ = 1 - 0.11 - 0.33 = 0.56
The joint probability of hitting one arrow in each region, is given by the product between the individual probabilities for each region times the permutations (the permutations for 3 arrows are 3! = 3*2*1 = 6)
So the probability is:
P = 0.11*0.33*0.56*6 = 0.122
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Your teacher writes the fact below on the board.Using only mental math, will the answer be less than or greater than 5? How do you know?.
(5 × 7/8
Answer:
Less than 5
Step-by-step explanation:
The eason behind the answer being less than 5 is because if you multiply something by a fraction that is less than a whole number, then you will get less than the original number you multiplied the fraction with.
Hope this helps :)
A spinner has 8 equal sized spaces numbered 1-8. If the spinner is spun once, find the probability that it lands on an even number or a number greater than 6.
The probability that it lands on an even number or a number greater than 6 are 1/2 and 1/4 respectively
Data;
Number of sides in the spinner = 8Number of even numbers from 1 - 8 = 4Numbers greater than 6 = 2ProbabilityThe probability of an event occurring is the ratio between number of possible outcomes to the total number of sample space.
a)
The probability of having an even number is
[tex]P = \frac{4}{8} = \frac{1}{2}[/tex]
b)
The probability of having a number greater than 6 is
[tex]P = \frac{2}{8} = \frac{1}{4}[/tex]
The probability that it lands on an even number or a number greater than 6 are 1/2 and 1/4 respectively
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The following table shows a portion of a five-year amortization schedule. A 5-year amortization schedule. Loan amount or principal: 10,900 dollars. Interest rate on loan: 10. 95 percent. A 5-column table with 6 rows. Column 1 is labeled Month with entries 15, 16, 17, 18, 19, 20. Column 2 is labeled Payment with all entries 236. 72. Column 3 is labeled Principal with entries 155. 87, 157. 29, 158. 73, 160. 18, 161. 64, 163. 11. Column 4 is labeled Interest with entries 80. 85, 79. 43, 77. 99, 76. 54, 75. 08, 73. 61. Column 5 is labeled Balance with entries 8,704. 27, 8,546. 98, 8,388. 25, 8228. 07, 08. 66. 43, 7,903. 32. What percent of the payments made were due to interest for the months shown? a. 30. 9% b. 32. 6% c. 62. 5% d. 63. 4%.
The percentage of the payments made were due to interest is 32.6 %. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
The following table shows a portion of a five-year amortization schedule.
A 5-year amortization schedule.
Loan amount or principal: 10,900 dollars.
The interest rate on loan: 10. 95 percent.
The table will be
Month Payment Principal Interest Balance
15 236.72 155.87 80.85 8704.27
16 236.72 157.29 79.43 8546.98
17 236.72 158.73 77.99 8388.25
18 236.72 160.18 76.54 8228.07
19 236.72 161.64 75.08 80.66.43
20 236.72 163.11 73.61 7903.32
Total payment = 6 × 236.72 = $ 1420.32
Total interest = 80.85 + 79.43 + 77.99 + 76.56 + 75.08 + 73.61
Total interest = $ 463.38
Then the percentage will be
[tex]\rm Percentage = \dfrac{463.38}{1420.32}*100\\\\Percentage = 32.625 \approx 32.6\ \%[/tex]
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Find Distance (4,6) (-4,-3)
Answer:
[tex]\sqrt{145}[/tex]
Step-by-step explanation:
The distance formula states that the distance between two points [tex](a,b)[/tex] and [tex](c,d)[/tex] is [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex].
The two points we have are [tex](4,6)[/tex] and [tex](-4,-3)[/tex]. Plugging these numbers into the distance formula, we have
[tex]\sqrt{(4-(-4))^2+(6-(-3))^2[/tex].
Simplifying with order of operations, first using the distributive property, gives
[tex]\sqrt{(4+4)^2+(6+3)^2[/tex].
Squaring and adding gives
[tex]\sqrt{(4+4)^2+(6+3)^2}=\sqrt{8^2+9^2}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\sqrt{64+81}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~=\boxed{\sqrt{145}},[/tex]
which is the answer in simplest form. This also rounds to about 12.04.
Help,Vector
Thanks!!
What is the recursive formula for this sequence?
14, 18, 22, 26, 30, .
Answer:
4
Solving steps:
In order to find the sequence substract the previous
=> 18 - 14
=> 4
So, 14 + 4 = 18
18 + 4 = 23
etc.
Prove that the value of the expression
(3^5-3^4)(3^3+3^2) is divisible by 24
Answer:
243
Step-by-step explanation:
(3^5 – 3^4) (3^3 + 3^2)
= (243 – 81) (27 + 9)
= (162) (36)
= 5832
24 = 8*3
because 832 can be divided by 8 and 5+8+3+2 = 18 is divisible by 3,
5832 is divisible by 24
Find the surface area of the prism.
Answer: 26
Step-by-step explanation:
I would say 26 because you multiplying 3 and 4 and then add whatever number you get for 8 and 5.
An incident ray strikes a boundary at a 72. 5-degree angle, resulting in an angle of refraction of 39. 6 degrees. The index of refraction of the first medium is 1. 3. What is medium 1? What is medium 2?.
Refractive index is the ratio of sin(i) to sin (r). Medium 2 is sodium chloride with a refractive index of 1.54.
What is Refractive Index?A material's refractive index (sometimes called refraction index or index of refraction) is a dimensionless quantity that specifies how quickly light passes through it.
As we know that the Refractive index is the ratio of sin(i) to sin (r), and it can be represented as,
[tex]\rm Refractive\ Index = \dfrac{Sin(i)}{Sin(r)}[/tex]
where
i is the incident angle and
r is the refraction angle.
Now, the refractive index can be written as for the given medium can be written as,
[tex]\rm Refractive\ Index = \dfrac{Sin(i)}{Sin(r)}\\\\[/tex]
[tex]\rm Refractive\ Index = \dfrac{Sin(79.5)}{Sin(39.6)}=1.542[/tex]
Now, if we take the ratio of the refractive index of the two mediums, then
[tex]\rm 1.542 = \dfrac{n}{1.0003}\\\\n = 1.542 \times 1.0003\\\\n= 1.5425\ \approx 1.54[/tex]
Hence, Medium 2 is sodium chloride with a refractive index of 1.54.
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Answer:
What is medium 1?
air
What is medium 2?
lucite
Step-by-step explanation:
what is this can you figure it out
First, we can see that this is a reduction because ΔXYZ is larger than its dilation, ΔX'Y'Z'.
But by how much? We can compare two sides such as XY and X'Y' to see.
-> I am going to compare sides XY and X'Y' because they are fully vertical lines that we can count without needing to use a distance formula.
-> XY is 8 units long
-> X'Y' is 4 units long
-> 8 / 4 is a scale factor of 2
Answer:This is a reduction with a scale factor of 2.
sum of all three angles of a Triangle is
Answer:
180°
Step-by-step explanation:
the angles in a triangle add up to 180°
The number of boys of grade 6 students is 220.This is 40more than number of boys grade seven students. How many grade seven boy students are enrolled
Answer:
Given
no of Grade 6 students = 220
no of Grade 7 students = 40 more than grade 6 students
Step-by-step explanation:
boys Grade 7 students = no of Grade 6 students - 40 more than grade 6 students
boys Grade 7 students = 220 - 40
boys Grade 7 students = 180 grade 7 boy students are enrolled
Therefore, 180 grade 7 boy students are enrolled.
find the missing side length
1. cross multiply
3/1 = m/5
15 = m
m = 15
The number 180 is the ?
Answer:
sorry there's no explanation IN this question
Answer:
Inconclusive.
Step-by-step explanation:
This equation is not understandable due to the lack of clarity, thank you.
the width of a rectangle is 2 units less than the length. the area of the rectangle is 63 units.what is the length, in units, of the rectangle
Answer: 9
Step-by-step explanation:
HELP ON 17!!?!?!?!?!? PLEASEEEEEEEEEEEEEp
Answer:
See Below
Step-by-step explanation:
[tex]m \angle \: 1 = m \angle \: 4 \: \: \: (1) \\ (vertical \: angles) \\ \\ m \angle \: 7 = m \angle \: 6 \: \: \: (2) \\ (vertical \: angles) \\ \\ m \angle \: 4 + m \angle \: 6 = 180 \degree \: \: \: (3) \\ (Interior\:angles \: on \: same \: side \: of \: transversal) \\ \\ from \: equations \: (1),\: (2) \: and \: (3) \\ \\ \red { \boxed{ \bold{m \angle \: 1 + m \angle \: 7 = 180 \degree}}} \\ \\ thus \: proved[/tex]
Use the map and the provided ruler to find the actual distance between cities. The actual distance between Kalamazoo and Ann Arbor is ___ miles.
The actual distance between Kalamazoo and Ann Arbor is approximately 62.5 miles.
How to estimate distances by scale factorsThe real distance is the producto of the scale factor and the in-scale distance. According to the figure, the scale factor is 50 miles per centimeters and the in-scale distance is approximately 1.25 centimeters. Then, the real distance between Kalamazoo and Ann Arbor is:
[tex]d \approx \left(50\,\frac{mi}{cm} \right)\cdot (1.25\,cm)[/tex]
[tex]d \approx 62.5\,mi[/tex]
The actual distance between Kalamazoo and Ann Arbor is approximately 62.5 miles. [tex]\blacksquare[/tex]
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You noticed that you used 3 gallons of gas to get to post falls and back. How many miles to the gallon did your car get?
4
Step-by-step explanation:
4 because it sounds close to me
Which equations represent an indirect variation relationship whit a constant of variation equal to -4? Select ALL correct answers
A) xy = -4
b) y = -4/x
c) y = x/-4
d) y = -4x
The equations that represent an indirect variation relationship with a constant of variation equal to -4 are y = -4/x and xy = -4
Direct and indirect variationAn indirect variation is also known as the inverse variation
If the variable y is indirectly proportional to x , this is expressed as:
y = k/x
where
k is the variation constant
If the variation constant is -4, then;
y = -4/x
Hence the equations that represent an indirect variation relationship with a constant of variation equal to -4 are y = -4/x and xy = -4
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Tammy learns in science class that water freezes when its temperature is
no more than 32 °F. Which number line shows all of the possible
temperatures, t, at which Tammy can set her freezer in order to make ice
cubes?
The required number line that shows all of the possible
temperatures is option A.
Inequalities and number lineFrom the given question, we have that water freezes when its temperature is no more than 32 °F
The statement no more than 32 °F shows that the temperature cannot be greater than 32 but less than or equal to 32. This is written mathematically as;
t ≤ 32.
We are to select the number line that shows all of the possible temperatures. The required number line that shows all of the possible
temperatures is option A.
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A square pyramid has a height of 12 units and a volume of 256 units3. If a square prism has the same the base area and volume as the square pyramid, what is its height? 12 units 10 units 4 units 3 units.
A square prism has the same the base area and volume as the square pyramid is 4 units.
What is the volume of square pyramid?The volume of a square pyramid is,
[tex]a^{2} *h/3[/tex]
[tex]256=a^{2} *12/3[/tex]
[tex]256=4 a^{2}[/tex]
[tex]256/4=a^{2}[/tex]
[tex]64=a^{2}[/tex]
[tex]a=8[/tex]
Now we know that the square is 8 by 8.
A square pyramid has a height of 12 units and a volume of [tex]256 units^3[/tex]
What is the volume of of a square prism?The volume of a square prism is a²h
[tex]V=a^{2} h[/tex]
[tex]256=64h[/tex]
[tex]256/64=h[/tex]
[tex]h=4[/tex]
The height is 4 unit
Also, a square pyramid is 1/3 the volume of a square prism.
[tex]\frac{12}{3}=4[/tex]
Therefore,we get a square prism has the same the base area and volume as the square pyramid is 4 units.
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Answer:
4 units
Step-by-step explanation:
I got it right on the test :)
Find the area and perimeter of the triangle. See picture for problem. Please and thank you so very much!(:
Answer:
Area = 2.28 sq km
Perimeter = 13.7 km
Step-by-step explanation:
[tex]A(\triangle)=\frac{1}{2}(1.2)(3.8)[/tex]
[tex]\implies A(\triangle)=(1.2)(1.9)[/tex]
[tex]\implies \boxed{\red{\bold{A(\triangle)=2.28\:km^2}}}[/tex]
[tex]P(\triangle)=7+1.2+5.5[/tex]
[tex]\implies \boxed{\purple{\bold{P(\triangle)=13.7\: km}}}[/tex]
Which graphs show a system of equations with infinitely many solutions?
Help asap!!
Answer:
Systems with infinitely many solutions are equations that are the same (on top of one another)
Ex:
4x=4 and 2x=2
4x=0, 5x=0
Help, will give 28 points
Answer:
you are crazy
Step-by-step explanation:
that is a whole assignment
Ricky said"he is the son of the only son of my mother. How is ricky related to the boy?
Answer:
That’s her nephew!
He could also be the father.
Step-by-step explanation:
Math, Please Help 15 points
Answer:
the second one
Step-by-step explanation:
(1.75) ^2 in expanded form
Answer:
(1.75)(1.75)
Step-by-step explanation:
[tex](1.75)^{2} =(1.75)(1.75)[/tex]
Hope this helps