Answer:
Step-by-step explanation:
a) The height of the springboard above the water should be h(0) : Read, the height at t = 0
h(0) = -5(0) + 10(0) + 3
h(0) = 0 + 0 + 3
h(0) = 3
a) 3 meters
b) The time it takes the diver to hit water should be, the positive 0 solution for t. Remember, in a quadratic equation, there are two values for t where a parabola crosses the horizontal axis, which in this case would be t. Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac) / 2a
Substitute t for x, and use the coefficients for a, b, c:
t = (-10 ± √((102 - 4(-5)(3)))/2(-5)
t = (-10 ±√(100 + 60))/-10
t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:
t = (-10 ±√(10*16))/-10
t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:
t = -2(5 ± 2√10)/-10
t = (5 ± 2√10)/5
Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):
t ≈ 2.265
b) approx. 2.265 seconds for diver to hit water.
c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).
-5tt + 10t + 3 = 3
-5t2 + 10t = 0 ; factor out t
t(-5t + 10) = 0
We know t = 0:
We also know that -5t + 10 = 0
-5t = -10
t = 2
c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.
d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).
h = -10/2(-5)
h = -10/-10
h = 1
h(1) = -5(1)2 + 10(1) + 3
h(1) = -5 + 10 + 3
h(1) = 8
d) At t = 1 second, diver will have reached peak of dive.
e) At t = 1 second, diver will have reached a maximum height of 8 meters.
|a| if a>0
Please help!
Answer:
Step-by-step explanation:
the absolute value bars mean we ignore the sign of the variable
As (a) is always positive for a>0, |a| = a
For contrast, If the range were a<0 where (a) is always negative, then |a| = -a
Answer:
1/a > 0
Step-by-step explanation:
For males in a certain town, the systolic blood pressure is normally distributed with a
mean of 125 and a standard deviation of 5. What percentage of males in the town that
have a systolic blood pressure higher than 131, to the nearest tenth?
Answer:
11.5 %
Step-by-step explanation:
mean- 125 | sd: 5
z-score: 131-125/5= 6/5= 1.2
for z= 1.2, percent: 88.49 %
100-88.49= 11.51 -> 11.5
If 14 out of 20 students in a college classroom are make, what percentage of the class is composed of men?
Answer:
70% of the class is composed of men.
Step-by-step explanation:
14: 20*100 =
(14*100): 20 =
1400: 20 = 70
33. Due to some error in a weighing scale, it shows the following reading when at rest (no weight is placed on it). Neerja measured her weight on this scale. The weight shown on the scale was 28 kg. What should she do to find out her correct weight?
(A) Add 2 kg to the weight shown. (B) Subtract 2 kg from the weight shown.
(C) Subtract 28 kg from the weight shown. (D) Add 4 kg to the weight shown
Answer:
The traditional scale consists of two plates or bowls suspended at equal distances from a fulcrum. One plate holds an object of unknown mass (or weight), while known masses are added to the other plate until static equilibrium is achieved and the plates level off, which happens when the masses on the two plates are equal. The perfect scale rests at neutral. A
Can someone help me with this problem 9(n+3)<10(n+1)
[tex]9(n+3)~<~10(n+1)\implies 9n+27~<~10n+10 \\\\\\ 27~<~n+10 \implies 17 ~<~ n[/tex]
f(x)=2x^2-3x+5 and g(x)=x-4,
find (f+g)(x)
Answer:
2x^3-2x^2+x
Step-by-step explanation:
Just trust me!
Which equation represents the statement: Three times the sum of a number and 5 is –30?
3n + 5 = -30
3(n+5) = -30
n + 15 = -30
(n + 5) ÷ 3 = -30
Answer:
3(n+5)=-30
Step-by-step explanation:
Three times the sum of a number and 5 is - 30
Vocabulary:
times = multiplication, represented with *
sum = addition, represented by +
unknown number = n
Three * the sum of a number and 5
The sum of a number and 5 is the same as saying n + 5
So we are multiplying 3 by n + 5
Because n is an unknown variable we have to separate the sum of n and 5 from being multiplied by 3 with parenthesis. We do this because if we want to multiply 3 by the sum of n and 5. If we put 3 * n + 5 we are only multiplying the unknown variable by 3 not including the 5 that is added to it.
So we get 3( n + 5 ) is -30
3(n+5)=-30 is the answer.
Answer:
[tex]3(n+5)=-30[/tex]
Step-by-step explanation:
1. Divide the problem into pieces. The sum of a number and five can be written as [tex]n+5[/tex], where n is any number.
2. Since the question tells us that this sum is multiplied by 3, we expand the expression to [tex]3(n+5)[/tex].
3. Finally, the question tells us that this expression is equal to -30. This means we can express the entire statement as the equation [tex]3(n+5)=-30[/tex].
2x-32=12
means they spent how much
Answer:
22
Step-by-step explanation:
In a school of 1,000 students, 600 study physics, 300 study Calculus, and 100 study both. What is the probability that someone who does not study calculus studies physics? Give your answer as a decimal to one decimal place.
The probability that someone who does not study calculus studies physics is 0.5
Since there are 1000 students in the school and 600 study physics, 300 study Calculus, and 100 study both, we need to find the number of students that study only physics to find the probability that someone who does not study calculus studies physics.
Let x = number of students who study both = 100, y = number of students who studies only physics and z = number of students who studies only calculus.
Given that the number of students who study physics are 600, we have
x + y = 600 (1)
Also, given that the number of students who study calculus are 300, we have
x + z = 300 (2)
From (1)
y = 600 - x
y = 600 - 100
y = 500
So, the probability of students that study only physics = probability that someone who does not study calculus studies physics is
P(physics) = number of students studying only physics/total number of students
= 500/1000
= 5/10
= 0.5
So, probability that someone who does not study calculus studies physics is 0.5
Learn more about probability here:
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Can somebody give me an answer? ill give brainiest.
Answer:
The mystery divisor is 18
Step-by-step explanation:
In the beginning, I found it by simply dividing the dividend by the quotient which gave me the divisor of 18. You can start the division equation again and add in the divisor 18 and it'll give you the exact answer.
Another way you'll know it's correct, is by dividing the dividend by that divisor and it'll give you the quotient 225 just like in the image.
if in a game of glass stepping stones. there are 18 tiles of glass. two in each row. one is tempered and will be fine if you jump on it. and the other will break. if 1 player was to play what are his/her chances of getting across?
(NO links)
(5,65) (7,71) slope
Answer:
3
Step-by-step explanation:
The slope formula is m=y2-y1/x2-x1
y2 is 71
y1 is 65
x2 is 7
x1 is 5
71-65 is 6
7-5 is 2
So the slope looks like this:
6/2
Simplify:
Which is 3
Hope this helps!
Find the number N , such that when 1 ÷3
of it's added to 8 , the results is the same as when 1÷2 of it is subtracted from 18
Answer:
Step-by-step explanation:
8 + N/3 = 18 - N/2
N/3 + N/2 = 18 - 8
2N/6 + 3N/6 = 10
5N/6 = 10
N = 10(6/5)
N = 12
Answer:
N=12
Step-by-step explanation:
Set up an equation involving N
(1/3)N+8=18-(1/2)N
We want to clear the denominator to start with by multiplying everything on both side by 6
2N+48=108-3N
Move all the N's to one side and the number to the opposite
5N=60
Divide by 5
N=12
Check:
(1/3)12+8=18-(1/2)12
4+8=18-6
12=12
Find m/_ABC if BD is an angle bisector of ABC
Answer:
im not quite sure but i think u do it like this:
Step-by-step explanation:
4x-6=x+6
(add 6 to both sides as well as subtracting x from both sides)
3x=12
(divide 3 from both sides)
x=4
–5(–2) = help me please ill give brainlist
Answer:
The answer is 10!
Step-by-step explanation:
What is the slope of the line that has a y-intercept of (0, 6) and passes through the point (2, 8)?
m= ?
Answer:
m=1
Step-by-step explanation:
[tex]m=\frac{8-6}{2-0} =\frac{2}{2} =1[/tex]
I hope this help you
A shipment of 8 computers contains 3 with defects. Find the probability that a sample of size 2, drawn from the 8, will not contain a defective computer.
What is the probability that a sample of 2 of the 8 computers will not contain a defective computer?
(Type an integer or a simplified fraction.)
Answer:
5/28
Step-by-step explanation:
First of all, probability is defined as the number of ways a certain event can happen divided by the total ways of an event happening. In this scenario, we are asked to find the number of non-defective computers divided by the total ways that a sample of two can be chosen.
The number of ways to choose 2 computers from 8 can be written as [tex]8\choose2[/tex], which is equal to [tex]\frac{8\cdot7}{2}[/tex], which is 28. Now, there are 3 defective computers, for a total of 5 non-defective computers, so the probability is 5/28.
A package contains 12 ounces of cereal .If you use 1 portion of this cereal which is 1 1/3 how much would be left in the cereal box?
To answer this question, you would need to divide the total amount of cereal in the box by the serving size.
This would be 12 2/3 divided by 1 1/3.
We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3
Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2
Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.
Hope this helps
For the function f(x) = 4x3 + 3x + 1, find f '(1).
A.
15
B.
8
C.
12
D.
13
Answer:B
Step-by-step explanation:
She calculates the percentage of applicants in her sample that are in poverty. Is this percentage a parameter or a statistic, and why
Answer:
A statistic
Step-by-step explanation:
This is because she only examined the applications that she selected.
The given percentage represents statistic.
What is percentage?
" Percentage is defined as the hundredth part of a given quantity."
According to the question,
Given,
Collection of data applicants in form of sample
Percentage calulation based on sample
Parameter : Parameter represents the data of whole population, here she collects sample.
parameter is not the correct answer.
Statistic : Statistic represents the sample of the data and she has calculated percentage of the sample.Statistic is the correct answer.
Hence, the given percentage represents statistic.
Learn more about percentage here
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Write the letter of the arrow that matches each probability word.
a)
*certain' is shown by the letter
b)
'evens' is shown by the letter
C)
'impossible' is shown by the letter
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
A. " Certain " is shown by letter E
B. " Even " is shown by letter C
C. " Impossible " is shown by letter A
How do you solve x+20<-10
Answer:
X = - 31
Step-by-step explanation:
The < always faces the largest number so do. -10-20= - 30 so any number bellow that e.g.-31, -45 will be correct I think
[tex]2 {}^{3} \times 2 - {}^{3} [/tex]
I need answers
solve pls brainliest
Answer:
Mixed number: 5(1/10)
Improper fraction: (51/10)
Step-by-step explanation:
Hope this helps!
Answer:
Mixed number: 5 1/10 and improper fraction: 52/10
Please help I do not understand thanks
To mix weed killer with water correctly, it is necessary to mix 10 teaspoons of weed killer with 2 gallons of water. Find how many gallons of water are needed to mix with the entire box if it contains 20 teaspoons of weed killer.
Answer: 4 gallons
Step-by-step explanation:
$32.00for a 14 2/9 km taxi ride. What is the cost per kilometer
[tex]\begin{array}{ccll} \$&km\\ \cline{1-2} 32&14\frac{2}{9}\\[1em] x&1 \end{array}\implies \cfrac{32}{x}=\cfrac{14\frac{2}{9}}{1}\implies \cfrac{32}{x}=14\frac{2}{9}\implies \cfrac{32}{x}=\cfrac{14\cdot 9+2}{9} \\\\\\ \cfrac{32}{x}=\cfrac{128}{9}\implies 288=128x\implies \cfrac{288}{128}=x\implies \stackrel{~\hfill \textit{2 bucks and 25 cents}}{\cfrac{9}{4}=x\implies 2\frac{1}{4}}=x[/tex]
At a sale this week, a table is being sold for $119. This is a 65% discount from the original price.
What is the original price?
Answer:
77,35
Step-by-step explanation:
6=2(y+2) what is the value of y in the equation
Answer: the value of y is 1
Step-by-step explanation: 6=2 x 1+2
what is 3/4 divided by 11/20
Answer:
11/15
Step-by-step explanation:
11/20 / 3/4
11/20*4/3
44/60
22/30
11/15
Answer:
15/11
Step-by-step explanation:
3/4 divided by 11/20?
Reduce the expression, if possible, by canceling the common factors.
Exact Form: 15/11
decimal form: 1.36
mixed number form: 1 4/11