A ball is thrown from the top row of seats in a stadium. The function h(t) = −16t2 + 64t + 80 gives the height, h, in feet, of the ball t seconds after it is thrown. How long will it be before the ball hits the ground?
Answer:
Step-by-step explanation:
Given the height of the ball expressed as:
h(t) = −16t^2 + 64t + 80
The ball hits the ground the when h(t) = 0
Substitute h(t) = 0 and find t as shown:
h(t) = −16t^2 + 64t + 80
0 = −16t^2 + 64t + 80
−16t^2 + 64t + 80 = 0
Divide throigh by -16
t^2-4t-5 = 0
t^2-5t+t-5 = 0
t(t-5)+1(t-5) = 0
(t+1)(t-5)= 0
t+1 = 0 and t - 5 = 0
t = -1 and t = 5
time can not be negative:
t = 5seconds
Hence it will take 5 secs before the ball his the ground
Solving a quadratic equation, it is found that the ball hits the ground after 5 seconds.
The height of a ball after t seconds is given by:
[tex]h(t) = -16t^2 + 64t + 80[/tex]
It hits the ground at the values of t for which:
[tex]h(t) = 0[/tex]
Then
[tex]-16t^2 + 64t + 80 = 0[/tex]
Simplifying by -16:
[tex]t^2 - 4t - 5 = 0[/tex]
Which is a quadratic equation with coefficients [tex]a = 1, b = -4, c = -5[/tex].
Then:
[tex]\Delta = (-4)^2 - 4(1)(-5) = 36[/tex]
[tex]x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5[/tex]
[tex]x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1[/tex]
We want the positive value, thus, the ball hits the ground after 5 seconds.
A similar problem is given at https://brainly.com/question/24764843
PLZ HELP 42 POINTS IF U ANSWER I WILL GIVE BRAINEST PLEASE YA'LL What is the product?
Enter your answer as a fraction, in simplified form, in the box.
−14⋅(−611)
Answer:
0.14!
Step-by-step explanation:
Answer:
There is no way I can answer in fraction form, but here is what I calculated: 8554
what is the value of x
х = 0/4
Answer:
0
Step-by-step explanation:
0 divided by anything is 0
1/4(-16x+8)? simplify or expand the expression
Answer:
-4x+2
Step-by-step explanation:
Which figure represents the image of parallelogram LMNP after a reflection across the line y = x?
Answer:
Quick answer option C
Step-by-step explanation:
If f(x) = (1\7)(7x), what is f(3)?
Answer:
3
All the steps are in the picture below.
explain how you would use the communitive property of multiplication to aswer 7x3.
Answer:
since 7 times 3 is 21
Step-by-step explanation:
it would be 7+7+7 becuase you do seven times 3
hope that helped!
Jasmin's dog weighs 64 pounds . Her vet told her that a healthy weight for her dog would be less than or equal to 49 pounds . Jasmin's dog can lose an average of 4 pounds every week . Write the solution to an inequality that describes all possible number of weeks for which her dog can be at a healthy weight .
Answer:
9 > 10
Step-by-step explanation:
90 = 9
100 = 10
answer = 9.10
(3+sqrt-16)(6-sqrt-64)
Answer:
12i + 9
Step-by-step explanation:
Since sqrt of negative numbers cannot exist, they are numbers followed by the letter I.
sqrt -16=4i
sqrt -64=8i
3 and 6 cannot be grouped with them, so you would add these two
3+6=9
8i+4i=12
I believe this would be the answer:
12i + 9.
Answer:
18-32i
Step-by-step explanation:
(3+sqrt(16i)(6-sqrt(64i)
= 18-32i
At the hardware store you can buy 9 boxes of bolts for $18.81. This can be expressed by the equation 18.81=(2.09)9.
How much would it cost for 2 boxes?
Group of answer choices
$18.00
$4.18
$2.09
$9.00
3. Critique Reasoning Each side of a square patio
is 10.5 feet. The patio is made up of 1.5-foot by
1.5-foot square stones. What is the number of
stones in the patio? Look at the solution below.
Does it include all the steps needed to solve the
problem? Explain.
10.5 X 10.5 = 110.25
110.25 = 1.5 = 73.5
Answer:
Yes
Step-by-step explanation:
Find the quotient. 0.16/-0.2
- 0.8
Simple division. Shouldn’t be that hard
Given that the expression "p dollars for every q items" describes a unit price, which statement must be true? p=1 p=9 q=1 pg= 1
Answer:
p = q
Step-by-step explanation:
Answer:
the answer is q=1
Step-by-step explanation:
I did the quiz
the martin family‘s truck gets an average of 25 miles per gallon. Predict how many miles they can drive using 7 gallons of gas.
Answer:
175
Step-by-step explanation:
7 times 25=175
A doctor gives a patient a 70% chance of surviving bypass surgery after a heart attack. If the patient
Isurvives the surgery, then the patient has a 40% chance that the heart damage will heal. Find the
probability that the patient survives the surgery and the heart damage heals. The probability is nothing
Answer:
The probability the person will survive the bypass surgery and that the heart damage will heal is about 28%
Step-by-step explanation:
(7/10)*(4/10)*100=28
To solve for probability of situations like this you have to multiply the fractional values of the two percentages and multiply by 100 to get the new percentage.
Using conditional probability, it is found that there is a 0.28 = 28% probability that the patient survives the surgery and the heart damage heals.
Conditional Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Surviving.Event B: Healing.70% chance of surviving, thus [tex]P(A) = 0.7[/tex].If the patient survives, 40% chance of healing, thus [tex]P(B|A) = 0.4[/tex].The probability of both is [tex]P(A \cap B)[/tex], then:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)P(A)[/tex]
[tex]P(A \cap B) = 0.4(0.7)[/tex]
[tex]P(A \cap B) = 0.28[/tex]
0.28 = 28% probability that the patient survives the surgery and the heart damage heals.
A similar problem is given at https://brainly.com/question/24161830
help me please thank you
The accompanying table shows the probability distribution for x, the number that shows up when a loaded die is rolled. Find the mean.
1
2
3
4
5
6
P(x)
0.14
0.16
0.12
0.14
0.13
0.31
A. = 3.5
OB. u = 3.8
O C. 1 = 0.2
OD. u = 3.9
Answer:
Mean = 3.9
Step-by-step explanation:
Given
The above table
Required
Determine the mean
The mean is calculated as thus:
Mean = Summation of x * P(x)
So, we have:
Mean = 1 * 0.14 + 2 * 0.16 + 3 * 0.12 + 4 * 0.14 + 5 * 0.13 + 6 * 0.31
Mean = 0.14 + 0.32 + 0.36 + 0.56 + 0.65 + 1.86
Mean = 3.89
Mean = 3.9 (approximated)
The mean should be 3.9.
Calculation of the mean;Here the following formula should be used:
Mean = Summation of x * P(x)
So,
Mean = 1 * 0.14 + 2 * 0.16 + 3 * 0.12 + 4 * 0.14 + 5 * 0.13 + 6 * 0.31
= 0.14 + 0.32 + 0.36 + 0.56 + 0.65 + 1.86
= 3.89
= 3.9
Therefore, we can conclude that The mean should be 3.9.
Learn more about mean here: https://brainly.com/question/21678821
I will give brainliest :)
Which equation represents this tape diagram?
44
• 4x+3x=44
• 4+(3+x) = 44
• 4(3+x)=44
• 4x+3=44
Find the difference. Express the answer in scientific notation.
(9.1 × 10–6) – (8.9 × 10–6)
2.0 × 10–7
0.2 × 10–6
2.0 × 10–6
2.0 × 10–5
Answer:
2.0 * 10^-6
Step-by-step explanation:
Because both numbers have the same scientific notation, you can just subtract the 9.1 from the 8.9 and keep the scientific notation.
(9.1*10^-6) - (8.9*10^-6)
(9.1 - 8.9)*10^-6
(2)*10^-6
Now that you have the answer, you need to use scientific notation, which is
2*10^-6, or 2.0*10^-6.
If anything is unclear, please let me know!
Answer:
it’s A / 2.0 x 10^-7
Step-by-step explanation:
THIS IS THE ANSWER ON EDU
i know because i just took it
Suppose you have a $60,000 loan with an annual percentage rate of 8% for 25 years.
what are the monthly payments
Find the perimeter of the figure.
7 mi
7 mi
Answer:
28mi
Step-by-step explanation:
The perimeter of a figure is the total length of its outline, so a sum of all its lengths.
In the diagram we are given two of them, both 7, but not the other two.
Luckily these can be easily worked out.
Since this is a square figure (all angles 90-degrees), all parallel sides will be exactly equal in length. This means both of the unknown sides are 7mi long as well. This means the total perimeter is the sum of all four sides, each of which are 7mi.
7+7+7+7 (OR 4x7) = 28 mi
Hope this helped!
Answer:
The perimeter of the figure is 28 mi
Step-by-step explanation:
Perimeter of a Square
Given a square shape of side length A, the perimeter can be found using the expression below:
P = 4*A
Recall the perimeter is the sum of all the side lengths.
Since the figure shows a square with side length A=7 mi, the perimeter is:
P = 4 * 7 mi = 28 mi
The perimeter of the figure is 28 mi
Let v= 3i − 2j + k (or equivalently ). Find non zero vectors w and u such that each of v, w and u is orthogonal (another word for perpendicular) to the other two Make sure you demonstrate that they are each orthogonal to one another after you find them.
Answer:
w = 1 i + 1 j - 1 k
u = 1 i + 4 j + 5 k
Step-by-step explanation:
Two possible vectors are:
w = 1 i + 1 j - 1 k
and
u = 1 i + 4 j + 5 k
since they verify the rules for scalar product equal zero among them:
v * w = 3 - 2 - 1 = 0
v * u = 3 - 8 + 5 = 0
u * w = 1 + 4 - 5 = 0
Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view additional questions
Online Content Site 1
What are some of the ways citizens can participate in ggovernment? (Site 1) This is a change to online content
Answer:
paying taxes, voting , serving a public office, and obeying the law.
g 3. Suppose X and Y are independent, Binomial random variables, respectively, with parameters (n1, p) and (n2, p). Calculate the frequency function of X Y .
Answer and Explanation:
Solution:
Let x and y are independent, ariables.
The parameters of x and y are (n1, p) and (n2, p), respectively.
It means the sum of the independent binomial variable is itself a binomial random variable.
Consider probability of the event [ x = n1],
Denoted by: p(x=n1)
The function:
P(n1) = p(x = n1)
Over the possible value of x say, n1, n2, n3, …, is called frequency function.
The frequency function must satisfy.
∑I p (ni) = 1,
Where the sum is possible values of x.
Similarly,
Consider probability of the event [ y = n2],
Denoted by: p(y=n2)
The function:
P (n2) = p(y = n2)
Over the possible value of y say, n1, n2, n3, …, is called frequency function.
The frequency function completely describes the probabilistic nature of the random variable.
Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?
Answer: A. The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
Step-by-step explanation:
Answer: A. The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
Step-by-step explanation:
Type the integer that makes the following addition sentence true
Blank + (-8) = -2
In which of the following stores would you pay the least amount for an item that is priced $360?
Store A: Sale of 10% off and a successive discount of 10% off.
Store B: Sale of 15% with no additional discount.
Store C: Sale of $35 off and a successive discount of 10% off.
a.
All of the stores have the same discounted price.
b.
You can get the lowest price at Store A.
c.
You can get the lowest price at StoreB.
d.
You can get the lowest price at Store C.
Please select the best answer from the choices provided
A
B
C
D
''Store A'' has the least amount to pay for an item at price of 291.60.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
Price : 360
Hence,
Store A: Sale of 10% off and a successive discount of 10% off.
360 x (100-10)% = 360 x 90% = 324
324 x (100-10)% = 324 x 90% = 291.60
Store B: Sale of 15% with no additional discount
360 x (100-15)% = 360 x 85% = 306
Store C: Sale of $35 off and a successive discount of 10% off
360 - 35 = 325
325 x (100-10)% = 325 x 90% = 292.50
Hence, Store A has the least amount to pay for an item at price of 291.60
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ5
Can anyone solve this for me. Thanks
Answer:
y=-1/3x+3
Step-by-step explanation:
Help APSPPP!!!!!!!!!!!! Hurry
Answer: Linear Pair, 23 degrees
Step-by-step explanation:
So I checked all of the answers and noticed that 23 was the only valid value for X because it means both values add up to 180. This is a linear pair because both angles are separated by another line and are on a straight 180 degree line.
5. The total number of people who went to Disneyland this weekend was
6,405. If the ratio of boys to girls is 7 to 9 for those that attended, what was
the TOTAL number of boys and girls that went to Disneyland this weekend?
Show your work or explain your thinking.
Answer:
2,802 boys and 3,693 girls went to Disneyland this weekend
Step-by-step explanation:
System of Equations
Let's call:
b = Number of boys who went to Disneyland this weekend.
g = Number of girls who went to Disneyland this weekend.
The first condition states there was a total of 6,405 people who went to Disneyland this weekend, thus:
[tex]b+g=6,405\qquad\qquad [1][/tex]
The second condition states that the ratio of boys to girls is 7 to 9. This can be written as:
[tex]\displaystyle \frac{b}{g}=\frac{7}{9}\qquad\qquad [2][/tex]
To eliminate denominators, multiply [2] by 9g:
[tex]\displaystyle (9g)\frac{b}{g}=(9g)\frac{7}{9}[/tex]
Simplify:
[tex]9b=7g\qquad\qquad [3][/tex]
From [1]:
[tex]b=6,405-g[/tex]
Substituting into [3]
[tex]9(6,405-g)=7g[/tex]
Operating:
[tex]57,645-9g=7g[/tex]
Simplify:
[tex]16g=57,645[/tex]
Solve:
[tex]g=57,645 / 16 \approx 3,603[/tex]
Take the approximate value:
g=3,603
Find b:
[tex]b=6,405-3,603=2,802[/tex]
2,802 boys and 3,693 girls went to Disneyland this weekend
Note: Due to the nature of the problem, the results had to be rounded to the nearest integer. This condition makes the ratio not being exactly as required.