Answers
Answer:
a) The golf ball reaches a height of 64 feet.
b) The golf ball will take 2 seconds to reach maximum height.
c) The golf ball will take 4 seconds to land after being hit.
d) The golf ball will be 48 feet above ground 1 and 3 seconds after being hit.
Step-by-step explanation:
a) The parabolic motion of the golf ball is described by a second order polynomial, that is, the equation of the parabola. To determine the maximum height of the golf ball, we need to transform the equation of the parabola given into vertex form:
[tex]h = -16\cdot (t^{2}-4\cdot t)[/tex]
[tex]h - 64 = -16\cdot (t^{2}-4\cdot t + 4)[/tex]
[tex]h - 64 = -16\cdot (t-2)^{2}[/tex]
From this form we can obtain relevant information of the maximum height of the golf ball, contained in the left side of the equation. On this approach, we conclude that the golf ball reaches a height of 64 feet.
b) The time taken by the golf ball is contained in the right side of the formula. That is, the golf ball will take 2 seconds to reach maximum height.
c) In this case, we need to factor the polynomial to find right times, that is:
[tex]h = 64\cdot t - 16\cdot t^{2}[/tex]
[tex]h = 16\cdot t \cdot (4 - t)[/tex]
The time taken by the golf ball to land is contained in the second binomial. In a nutshell, the golf ball will take 4 seconds to land after being hit.
d) If we know that [tex]h = 48[/tex], the time taken by the golf ball to be 48 feet above the ground is:
[tex]64\cdot t - 16\cdot t^{2} = 48[/tex]
[tex]16\cdot t^{2}-64\cdot t +48 = 0[/tex]
By Quadratic Formula, we have the following roots:
[tex]t_{1} = 3[/tex], [tex]t_{1} = 1[/tex]
The golf ball will be 48 feet above ground 1 and 3 seconds after being hit.
Related Questions
Find the final amount of money in an account if
$
7
,
200
is deposited at
6
%
interest compounded annually and the money is left for
6
years.
Answers
Answer:
$10,213.34
Step-by-step explanation:
Using the compound interest formula;
A = P(1+r/n)^t
Given that;
P = $7,200
rate r = 6% = 0.06
Time t = 6years
n = 1
Substitute into the formula
A = 7200(1+0.06)^6
A = 7200(1.06)^6
A = 7200(1.4185)
A = 10,213.34
Hence the final amount is $10,213.34
Can someone please help me with this
Answers
Answer:
39 sq inches
Step-by-step explanation:
You need the area of the square base
Area = side^2
A = 3 x 3 = 9
And the 4 triangle sides.
Area of a triangle = 1/2(base)(height)
a = 1/2 (3)(5) = 7.5
We have 4 of those triangles on this shape
4 x 7.5 = 30
Add the triangles to the base for goal surface area
30 + 9 = 39 square inches
Kevin
makes $78.37 per day. How much does he
make in 7 days?
Answers
Answer:
$78.37 ÷7
Step-by-step explanation
im not smart
In training, Kayden does
reps
where
he bench presses 65 kilograms. How
many reps does he have to do to
bench press a total of 1 metric ton?
Answers
Answer:
0.065 metric tons
Step-by-step explanation:
Given
65 kg
To find
Convert 65 kg to metric tons
Then, the answer is 0.065 metric tons
Mr. and mrs. Brown bought a new kitchen table for $450. It was 75% of the original price. Determine the original price of the kitchen table.
Answers
Answer:
$600
Step-by-step explanation:
To find the original price, divide the cost by 0.75
450/0.75
= 600
So, the original price was $600
Answer: $600
Step by Step explaination:
simplify 2 1/2 times 3/4
Answers
Answer:
[tex] \frac{5}{2} \times \frac{3}{4} \\ \frac{15}{8} [/tex]
Answer:
15/8
Step-by-step explanation:
2.5/2 = 1.25
1.25/2 = 0.625
2.5 - 0.625 = 1.875
1.875 = 75/40 = 15/8
PLEASE EXPLAIN YOUR FREAKING ANSWER IVE BEEN DOING THIS ALL NIGHT AND NO ONE ACTUALLY HAS HELPED ITS DUE SOON PLS IM BEGGING U
Answers
Answer:
B
Step-by-step explanation:
First we find out over how many years the growth happened, from 1985 to 2020, that's 35 years.
In 1985 the club had 23,000 members, and it grew at an ave. rate of 5% each year. So, to find out 5% of 23,000 we can divide it by 100 to find 1% and then multiply by 5.
23,000 / 100 = 230 now 230 times 5 is 1150, to check our work we can multiply 1150 by 20 because it is 5% to get 100% and it is 23000 so we are on track so far. Now over the span of 35 the club grew by 1,150 each year, so, 1150 times 35 is 40,250 and if we add that to 23,000 we get 63,250. Round to the nearest thousand which would be
B. 78,000 but I may have went about solving exponential growth wrong but if this is the answer you have been getting there you go.
4,843 divided by 44?
Answers
Answer:
110.068181818
Step-by-step explanation:
Complete the table.
Given: GHIJ is rhombus
Prove: ∠1≅∠3
Answers
Answer:
Step-by-step explanation
HELP ASAP! I REALLY NEED IT!
Answers
Answer:
[tex]46 \frac{7}{8} \: cubic \: feet[/tex]
Step-by-step explanation:
[tex]\boxed{volume \: of \: prism = base \: area \: \times height}[/tex]
Base area= length ×width
Let's convert all the mixed numbers into improper fraction for easier calculation.
Width
= 7½
[tex] = \frac{7(2)}{2} + \frac{1}{2} [/tex]
[tex] = \frac{14}{2} + \frac{1}{2} [/tex]
[tex] = \frac{15}{2} ft[/tex]
Height
= 1¼
[tex] = \frac{4}{4} + \frac{1}{4} [/tex]
[tex] = \frac{5}{4} ft[/tex]
Volume of prism
[tex] = 5 \times \frac{15}{2} \times \frac{5}{4} [/tex]
[tex] = \frac{375}{8} [/tex]
[tex] = 46 \frac{7}{8} \: ft {}^{3} [/tex]
Find the circumference of the circle and round to the nearest tenth
Answers
Answer:
circumference of circle = 2×pi×r
circumference of circle =2×3.14×2.8 mi
circumference of circle =17.584 mi
please with the mathematics
Answers
1.)1/6
2.)1 5/10
3.)2 6/7
4.)2
5.)1 7/12
6.)2 4/5
7.)1/12
with like denominators you can just add or subtract freely just the top numerators
Answer:
1.)1/6
2.)1 5/10
3.)2 6/7
4.)2
5.)1 7/12
6.)2 4/5
7.)1/12
Step-by-step explanation:
How many Perpendicular lines does an H have
Answers
Answer:
it has two line
Step-by-step explanation:
6. What is the area of he trapezoid? Help Please
Answers
Answer:
It’s G. 330 m^2
Step-by-step explanation:
The formula for a trapezoid is (a+b)/2 times h.
So a is base one and b is base two and the h is the height.
So it would be like (19+41)/2 X 11 then you would get
60/2 X 11
30 X 11 equals 330
help I will mark brainliest!
Answers
Answer: g
its g cause I solved it and got g
Answer:
The answer is G. Hope this helps!
What is $45.79 multiplied by .50 equal
Answers
Answer:
686.85
Step-by-step explanation:
Answer:
$45.79 multiplied by .50 equals 22.895
PLEASE HELP
do question 8 and 9
Answers
Answer:
x=7
x=4
x=1/9
Step-by-step explanation:
For number 9 you can either type out the work or say something like:
To solve all of the problems in Question 8 I had to move all of the terms without an (x) to the right side. After I did this I divided everything by the number attached to the (x) to find the value of (x) by itself.
Answer and Step-by-step explanation:
8a.
3x + 6 = 27
Subtract 6 from both sides.
3x = 21
Divide 3 from both sides.
x = 7
8b.
6x + 3 = 27
Subtract 3 from both sides.
6x = 24
Divide 6 from both sides.
x = 4
8c.
27x + 3 = 6
Subtract 3 from both sides.
27x = 3
Divide 27 from both sides.
x = 3/27
Simplify the fraction
x = 1/9
9.
The above steps are the reasonings for the above answers.
Kara and Steven are biking around a 105 kilometer path. They start biking from the same place, at the same time, and in the same direction. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take before Steven and Kara will be at the same place of the path next time?
It says 120 is wrong :(
Answers
9514 1404 393
Answer:
7 hours
Step-by-step explanation:
They will be at the same place when Kara completes one lap and Steven completes 2 laps. It will take Kara 7 hours to complete one lap.
(105 km)/(15 km/h) = 7 h
Answer:
7 hours
Step-by-step explanation:
They will be at the same place when Kara completes one lap and Steven completes 2 laps. It will take Kara 7 hours to complete one lap.
(105 km)/(15 km/h) = 7 h
Which equation defines the graph of y=x^2 if it is shifted vertically 3 units up, and horizontally 2 units right
Answers
A 50 foot ladder is set against the side of a house so that it reaches up 40 feet. If Aisha grabs the ladder at its base and pulls it 9 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 31 ft.) Round to the nearest tenth of a foot.
Answers
Answer: ~31.3
first use the pythagorean theorem. a^2+(40)^2=50^2.
simply. a+1600=2500. subtract 1600 from both sides. a^2=900.
square root both sides to get a= 30
then find how far the top of the ladder is from the ground once in its new position.
a^2+(39)^2=50^2.
simplify. a^2+1512=2500. subtract 1512 from both sides to get a^2=979.
square root both sides to get a=31.288975. round to the nearest tenth to get a=31.3
Answer:
Step-by-step explanation: iT'S 31.3
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 40 % salt and Solution B is 90 % salt. She wants to obtain 50 ounces of a mixture that is 80 % salt. How many ounces of each solution should she use?
Answers
Answer:
The scientist must use 10 ounces of Solution A and 40 ounces of Solution B.
Step-by-step explanation:
Since a scientist has two solutions, which she has labeled Solution A and Solution B, each containing salt, and she knows that Solution A is 40% salt and Solution B is 90% salt, and she wants to obtain 50 ounces of a mixture that is 80% salt, to determine how many ounces of each solution should she use the following calculation must be performed:
100 x 0.9 + 0 x 0.4 = 90
90 x 0.9 + 10 x 0.4 = 85
80 x 0.9 + 20 x 0.4 = 80
50 x 0.8 = 40
Therefore, the scientist must use 10 ounces of Solution A and 40 ounces of Solution B.
Will mark brainliest for area.
Answers
Answer:
c
Step-by-step explanation:
first, find the area of the rectangle thing,
A = lw
14 x 8
112
but, there is a semicircle in it so you need to subtract that from it:
A = πr^2/2
A = π(4)^2/2
A = π16/2
A = 8π
A ≈ 25.132741228718346
then subtract that area from the area of the rectangle:
112 - 25.132741228718346
86.867258771281654
or about 89.9
One hundred volunteers who have agoraphobia (fear of open and crowded space) are available for a study. Fifty are selected at random and are given the drug imipramine, which is believed to be effective in treating agoraphobia. The other 50 are given a placebo. A psychiatrist evaluates the symptoms of all volunteers after two months to determine if there has been substantial improvement in the severity of their symptoms.
What type of study is this?
A. Matched pair design
B. Observational study
C. Completely randomized block design
D. Completely randomized design
Answers
Answer:
D. Completely randomized design
Step-by-step explanation:
Based on the description given about the experiment above and the manner in which the subjects were assigned to each of the treatment groups available, we can deduce that the study was conducted using a completely randomized design. The subjects weren't matched or blocked for any variable such as sex, height, age or any other variable. They were just evenly split randomly into the two available treatment levels ( those who receive the treatment and the placebo) group. With this design, all subjects have an equal chance of being in any of the two groups and the selection bias is almost totally eliminated using this sort of design as errors are being considered as arising from experimental faults.
A government agency reports that 22% of baby boys 6-8 months old in the United States weigh less than 25 pounds. A sample of 147 babies is studied. Use the TI-84 Plus calculator as needed. Round the answer to at least four decimal places. (a) Approximate the probability that more than 40 babies weigh less than 25 pounds. (b) Approximate the probability that 34 or more babies weigh less than 25 pounds. (c) Approximate the probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive. Part 1 of 3 The probability that more than 40 babies weigh less than 25 pounds is .
Answers
Answer:
a) 0.0526 = 5.26% probability that more than 40 babies weigh less than 25 pounds.
b) 0.409 = 40.9% probability that 34 or more babies weigh less than 25 pounds.
c) 0.6249 = 62.49% probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.
Step-by-step explanation:
The binomial approximation to the normal is used to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
A government agency reports that 22% of baby boys 6-8 months old in the United States weigh less than 25 pounds.
This means that [tex]p = 0.22[/tex]
A sample of 147 babies is studied.
This means that [tex]n = 147[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 147*0.22 = 32.34[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{147*0.22*0.78} = 5.02[/tex]
(a) Approximate the probability that more than 40 babies weigh less than 25 pounds.
Using continuity correction, this is P(X > 40 + 0.5) = P(X > 40.5), which is 1 subtracted by the pvalue of Z when X = 40.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{40.5 - 32.34}{5.02}[/tex]
[tex]Z = 1.62[/tex]
[tex]Z = 1.62[/tex] has a pvalue of 0.9474
1 - 0.9474 = 0.0526
0.0526 = 5.26% probability that more than 40 babies weigh less than 25 pounds.
(b) Approximate the probability that 34 or more babies weigh less than 25 pounds.
Using continuity correction, this is [tex]P(X \geq 34 - 0.5) = P(X \geq 33.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 33.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.5 - 32.34}{5.02}[/tex]
[tex]Z = 0.23[/tex]
[tex]Z = 0.23[/tex] has a pvalue of 0.591
1 - 0.591 = 0.409
0.409 = 40.9% probability that 34 or more babies weigh less than 25 pounds.
(c) Approximate the probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.
Exclusive means that we dont count 28 and 38, so, using continuity correction, this is [tex]P(28 + 0.5 \leq X \leq 38 - 0.5) = P(28.5 \leq X \leq 37.5)[/tex], which is the pvalue of Z when X = 37.5 subtracted by the pvalue of Z when X = 28.5. So
X = 37.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{37.5 - 32.34}{5.02}[/tex]
[tex]Z = 1.03[/tex]
[tex]Z = 1.03[/tex] has a pvalue of 0.8485
X = 28.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28.5 - 32.34}{5.02}[/tex]
[tex]Z = -0.76[/tex]
[tex]Z = -0.76[/tex] has a pvalue of 0.2236
0.8485 - 0.2236 = 0.6249
0.6249 = 62.49% probability that the number of babies who weigh less than 25 pounds is between 28 and 38 exclusive.
Below, the two-way table is given for a class of students. Freshmon Sophomora fontores Seniors Male 4 6 2 2 Female 3 4 6 б 3 Total If a student is selected at random, find the probability the student is a junior. Round to the nearest whole percent.
Answers
Answer:
22% probability the student is a junior.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes:
The table says that:
There are 4 + 6 + 2 + 2 + 3 + 4 + 6 + 6 + 3 = 36 total students.
2 + 6 = 8 are juniors.
If a student is selected at random, find the probability the student is a junior.
8/36 = 0.2222 = 22.22%
Rounding to the nearest whole percent, 22% probability the student is a junior.
Answer:
27%
Step-by-step explanation:
8 (6-4x) = 12
equation with parentheses
Answers
Answer:
x=9/8
Step-by-step explanation:
Select ALL the correct answers.
Which of the following statements are true about the equation below? x^2-6x+2=0
Answers
GEOMETRY!! Will give brainliest which one is better please explain
Answers
Calculate for y given that mean of 20,2y,25,y,30 is 27
Answers
Answer:
y = 218
Step-by-step explanation:
Mean = (Sum of all numbers)/(How many numbers present)
27 = (20 + 2y + 25 + y + 30)/27
27 = (3y + 75)/27
3y + 75 = 729
3y = 729 - 75
3y = 654
y = 218
How many times greater is 8.4x10^4 than 2.1x10^2
Answers
Answer:
4 times greater
Step-by-step explanation:
[tex]8.4*10^2=840\\2.1*10^2=210\\840/210=4\\[/tex]
Answer:
C. 400 times greater
Step-by-step explanation:
8.4 · [tex]10^{4}[/tex]
84000
2.1 · 10²
210
84000 ÷ 210 = 400
C. 400 times greater