Answer:
3.0 seconds
Step-by-step explanation:
i took the test.
The time it takes the rock to reach 50 feet on its way down is 13.2 seconds and option B is the correct answer.
We have,
We are given the equation for the height of the rock as it travels upward and then downward:
h = -1672 + 63.2t - 4.9t²
We want to find the time it takes for the rock to reach a height of 50 feet on its way down.
This means we need to solve for t when h = 50:
50 = -1672 + 63.2t - 4.9t²
Rearrange the equation to isolate the quadratic term:
4.9t² - 63.2t + (1672 + 50) = 0
4.9t² - 63.2t + 1722 = 0
For an equation of the form "ax² + bx + c = 0", the solutions for "x" are given by:
x = (-b ± √(b² - 4ac)) / 2a
In your equation, the coefficients are:
a = 4.9
b = -63.2
c = 1722
Plugging these values into the quadratic formula:
t = (-(-63.2) ± √((-63.2)² - 4 * 4.9 * 1722)) / (2 * 4.9)
Now, let's calculate the discriminant (the value inside the square root):
Discriminant = (-63.2)² - 4 * 4.9 * 1722 ≈ 39884.96 - 33529.6 ≈ 6355.36
Since the discriminant is positive, there are two distinct real solutions for "t".
Now, plug the discriminant back into the quadratic formula and solve for "t":
t = (63.2 ± √6355.36) / 9.8
Now, calculate the square root of the discriminant:
√6355.36 ≈ 79.58
Now, plug in the values for "t":
t₁ = (63.2 + 79.58) / 9.8 ≈ 13.02
t₂ = (63.2 - 79.58) / 9.8 ≈ -1.69
So, the solutions for the equation 4.9t² - 63.2t + 1722 = 0 are approximately:
t₁ ≈ 14.61
t₂ ≈ -1.69 (rejected)
Thus,
The time it takes the rock to reach 50 feet on its way down is B. 13.2 seconds.
Learn more about equations here:
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A tennis player hits a ball hard and 0.4 s later hears the echo sound from a wall. The speed of sound in air is 330 ms. How
?far away is the player from the wall
The distance traveled by the echo is used to determine the player's distance from the wall
The player's distance from the wall is 66 m.
Reason:
Known parameter;
The time after which the tennis player hears the echo of the ball, t = 0.4 s
The speed of sound in air, v = 330 m/s
The distance of the player from the wall = Required
Solution:
Let d, represent the distance of the player from the wall
An echo is the reflection the wave of the sound of hitting the ball that
travels to the wall and back
The distance traveled by the sound to the wall, d, and back, (d again), is 2·d
[tex]Speed = \dfrac{Distance}{Time}[/tex]
Therefore;
[tex]The \ speed \ of \ the \ sound,\ v = \dfrac{2 \cdot d}{t}[/tex]Therefore;
[tex]330 = \dfrac{2 \cdot d}{0.4}[/tex]
330 × 0.4 = 2·d
[tex]d = \dfrac{330 \times 0.4}{2} = 66[/tex]
The distance of the player from the wall, d = 66 mLearn more here:
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A pipe is leaking at 1.5 cups per day. About how many gallons per week is the pipe leaking? (Hint: 1 gallon=16 cups)
Answer:
21/32 gal
Step-by-step explanation:
1 gallon equals 16 cups, so we first need to convert the rate from cups to gallons
1.5cup/1 x 1/16 gal
can be simplified to 3/32 gal
so we now multiply this rate by 7 for a week
so in total it leaks
3/32 x 7/1 = 21/32
Help me please!!!!!!!!
Answer:
10 is answer if your question.
Step-by-step explanation:
mark me as a brainlist plz.
Which is 3,200 divided by 40?
A.
6
B.
8
C.
60
D.
80
Answer:
80
Step-by-step explanation:
40 x 80 = 3200
The solution of the expression is, 80
We have to give that,
3200 divided by 40.
Now, Divide the numbers as,
⇒ 3200 ÷ 40
⇒ 3200 / 40
⇒ 320/4
⇒ 80
So, The solution after dividing is, 80
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How many tenths are there in ⅘
Answer:
8
Step-by-step explanation:
4/5 = ?/10
4/5 * (2/2) = ?/10
8/10 = ?/10
Answer:
8
Step-by-step explanation:
multiply the denominator and numerator, you get 8/10
8x − 7y = –5
–x + 4y = –15
Answer:
Answer is invalid. You cannot solve it.
Step-by-step explanation:
Answer:
y=4.8 X=34.2
Step-by-step explanation:
A satellite flies 87100 miles in 16.75 hours, How long would it take to fly 104520
miles?
Answer:
22.41
Step-by-step explanation:
Set up a proportion where x is the time to fly 174798 miles
Cross multiply and solve for x:
118404x = 2653433.64
x = 22.41
So, it would take 22.41 hours to fly 174798 miles
hey can anyone help and explain this to me
hjdjenenenwnwnwmemkwksksjsj
Plz can anyone slove 3 & 4 questions plzz
Answer:
For question 3 its definitely 5^15 and I searched 4 so I thinks its 71 or 161? sorry I don't know angles but 3 is correct
Answer:
[tex] {5}^{4 + 8 + 3} = {5}^{15} \\ \\ 90 - 19 = 71[/tex]
Can someone help me pls.....
Answer:
the first one is equivalent and the second one is not equivalent
Step-by-step explanation:
In the first one do the distributive property first by distributing the the -2.
[tex]3x - 4.6x - 5 = 1.6x - 5[/tex]
collect like terms on the left side
[tex] - 1.6x - 5 = - 1.6x - 5[/tex]
they are equivalent.
The second equation do the distributive property first by multiplying by -3.
[tex]5 + 4.8x + 6.3 = 4.8x - 1.3[/tex]
collect like terms on the left.
[tex]4.8x + 11.3 = 4.8x - 1.3[/tex]
not equivalent
The claim is that weights (grams) of quarters made after 1964 have a mean equal to 5.670 g as required by mint specifications. The sample size is n = 39 and the test
statistic is t= -3.276. Use technology to find the P-value. Based on the result what is the final conclusion? Use a significance level of 0.01.
State the null and alternative hypotheses
Hop
H.
(Type integers or decimals. Do not round)
Testing the hypothesis, we have that:
The null hypothesis is [tex]H_0: \mu = 5.67[/tex]The alternative hypothesis is: [tex]H_1: \mu \neq 5.67[/tex]The p-value of the test is of 0.002252.The p-value is 0.002252 < 0.01, which means that the final conclusion is that the mean weight of quarts made after 1960 is different than 5.67g.At the null hypothesis, we test if the mean is of 5.670g, that is:
[tex]H_0: \mu = 5.67[/tex]
At the alternative hypothesis, we test if the mean is different of 5.670g, that is:
[tex]H_1: \mu \neq 5.67[/tex]
The test statistic is t = -3.276, with the number of degrees of freedom given by:
[tex]df = n - 1 = 39 - 1 = 38[/tex]
The p-value is found using a t-distribution calculator, using a two-tailed test(as the alternative hypothesis is that the mean is different from the value), with t = -3.276 and 38 df. This p-value is of 0.002252.
The p-value is 0.002252 < 0.01, which means that the final conclusion is that the mean weight of quarts made after 1960 is different than 5.67g.
A similar problem is given at https://brainly.com/question/24146681
Evaluate the expression.
{[(20 – 32) = (-6)}? – 11} = (–7)
What is the value of the expression?
Enter your answer in the box.
please mark this answer as brainlist
The value of the numerical expression {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7) will be 1.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
The expression is given below.
⇒ {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7)
Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction are all part of the PEMDAS formula. To answer the problem properly and accurately, this rule must be followed.
⇒ {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7)
⇒ {[(–12) ÷ (–6)]² – 11} ÷ (–7)
⇒ {[2]² – 11} ÷ (–7)
⇒ {4 – 11} ÷ (–7)
⇒ (– 7) ÷ (–7)
⇒ 1
The value of the numerical expression {[(20 – 32) ÷ (–6)]² – 11} ÷ (–7) will be 1.
More about the value of the expression link is given below.
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You need $3,000 to buy a new stereo for your car. If you have $1,200 to invest at
6% compounded annually, how long will you have to wait to buy the stereo?
Answer:
15 years and 8 months
Step-by-step explanation:
I used the formula for compound interest as shown below and solved for the unknown, time.
Since our interest is compounded annually (So once a year) our m value is 1.
translate the 3 triangles below 4 units right and 3 units down
Answer:
If we translated the triangle 4 units right and 3 units down, then our new points would be J' (3,0) K' (3,-2) L' (0,-2). Hope this helped ..
Step-by-step explanation:
Write four hundred thirty-five thousand, two hundred two in standard form.
Answer:
four hundred thirty-five thousand : 435,000
two hundred two : 202
i don’t understand this i’m confused.
Players
Amount
Paid
The table above represents the number of people in a group who played laser tag and the group's total cost to play. Which of the
following represents the rate of change relative to this situation?
Answer:
C. 4.00 per person
Step-by-step explanation:
I say its 4.00 per person because in each row you mutiply the players and 4.00 you get the other side of the row. Ex 11 players multiplied by 4 dollars per person equals 44.00 dollars in total which the graph shows.
What is the sum of the 10th square number and the 2nd square number?
Answer:
104
Step-by-step explanation:
10th square number is 100, 2nd square number is 4. 100+4=104
I NEED HELP ASAP!!! (NO LINKS)
FULL EXPLANATION WILL GET BRAINLIEST!!!
#33
Answer:
35
Step-by-step explanation:
Using the definition of n[tex]C_{r}[/tex]
with n = 7 and r = 3
7[tex]C_{3}[/tex]
= [tex]\frac{7!}{(7-3)!3!}[/tex]
= [tex]\frac{7!}{4!(3!)}[/tex]
= [tex]\frac{7(6)(5)(4)(3)(2)(1)}{4(3)(2)(1)3(2)(1)\\}[/tex] ← cancel 4(3)(2)(1) on numerator/denominator
= [tex]\frac{7(6))(5)}{3)2)(1)}[/tex]
= [tex]\frac{210}{6}[/tex]
= 35
(10)/(4)<(z+8)/(2)<(22)/(4)
Answer:
-3 < z < 3
Step-by-step explanation:
×4
10 < 2z + 16 < 22. -16
-6 < 2z < 6. ÷2
-3 < z < 3
Evaluate the expression: 5 + 3 × (5 - 2x2)
32
72
36
16
Answer:
5+3*(5-2*2)
5+3*(5-4)
5+3*1
5+3
=8
Step-by-step explanation: i think
find the value of y. 7y + y - 2y =18
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
y=3
Step-by-step explanation:
if you are to put this on a graph the would be Linear
Identify the parent function.
O A. Reciprocal
OB. Square root
O C. Absolute value
O D. Cube root
Answer:
The answer is reciprocal
Answer:
Absolute value
Step-by-step explanation:
Parent function: y = |x|
please help me with this sum
Answer:
2880
1950
3960
2240
920
5220
4320
3760
6650
1080
32980 is the sum of all combined
Please allow me to know if this helped you by clicking thank you, rating or brainly!
Miss Hawaii
Answer:
1. 2880
2. 1950
3. 3960
4. 2240
5. 920
6. 5220
7. 5760
8. 3760
9. 6650
10. 1080
hi please help me here thank you very much.
ill give brainliest if able to.
Answer:
-1= -1/1
1 to 1 = 1/1
2:3 = 2/3
3 to 2 = 3/2
-2 = -2/1
Step-by-step explanation:
Help please? What do I do?
You have just bought a new Sony 55" 3D television set for $1,800. The value of the television set decreases by $210 per year. How long before the television set is worth half of its original value?
Round your answer to the nearest tenth as needed.
PLZZZ HELP!!!!!!!!!!!!!!!!!!!!!!
Harrison and Sherrie are making decisions about their bank accounts. Harrison wants to deposit $200 as a principal amount, with an interest of 2% compounded quarterly. Sherrie wants to deposit $200 as the principal amount, with an interest of 4% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Answer:
HarrisonPrincipal P = 200Interest rate r = 2% = 0.02Number of compounds n = 4Time t = 2Total amount:
[tex]A = P(1+r/n)^{nt}=200*(1+0.02/4)^{4*2} = 208.14[/tex]SherriePrincipal P = 200Interest rate r = 4% = 0.04Number of compounds n = 12Time t = 2Total amount:
[tex]A = P(1+r/n)^{nt}=200*(1+0.04/12)^{12*2} = 216.63[/tex]As we see the second method is a better choice
Answer:
SHERRIE
- Princible P= 200
- Interest rate R= 4% or 0.04
- Number of compounds N= 12
- Time T= 2
HARRISON
- Princible P= 200
- Interest rate R= 2% or 0.02
- Number of compounds N= 4
- Time T= 2
Formula: A= P(1+r/n)^nt
Now plug in values for each person:
200(1+0.02/4)^4*2= 208.14
200(1+0.04/12)^12*2= 216.63
And as you can see, the second method (Sherrie's) is the best choice.
Step-by-step explanation:
You are playing a card game. If you pull an Ace you win $26, if you pull the King of hearts you win $204, if you pull a jack or a queen you win $13, all other pulls you lose. What price should you be charged to make this a fair game?
$5
$7
$6
$8
Using the expected value, it is found that a price of $6 should be charged to make it a fair game.
--------------------------
The game is fair if the expected value is 0.The expected value is given by each outcome multiplied by it's probability.A probability is the number of desired outcomes divided by the number of total outcomes.In a standard deck, there are 52 cards.
The cost of x.
There are 4 Aces in a standard deck, thus [tex]\frac{4}{52}[/tex] probability of earning 26 - x.
There is 1 King of Hearts in a standard deck, thus [tex]\frac{1}{52}[/tex] probability of earning 204 - x.
There are 4 Jacks and 4 Queens in a standard deck, thus [tex]\frac{8}{52}[/tex] probability of winning 13 - x.
The other 39 cards you lose, thus [tex]\frac{39}{52}[/tex] probability of losing x.
Considering we want the expected value to be 0.
[tex]\frac{4}{52}(26 - x) + \frac{1}{52}(204 - x) + \frac{8}{52}(13 - x) - \frac{39}{52}x = 0[/tex]
[tex]\frac{4(26 - x) + 204 - x + 8(13 - x) - 39x}{52} = 0[/tex]
[tex]104 - 4x + 204 - x + 104 - 8x - 39x = 0[/tex]
[tex]52x = 312[/tex]
[tex]x = \frac{312}{52}[/tex]
[tex]x = 6[/tex]
$6 should be charged.
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10. The graph of linear equations in two variables is a
A. Straight line
B. curve line
D. half line
C. broken line
Which number has the greatest absolute value?
A. −7.5
B. −12
C. 5
D. 3/4
Answer:
B
Step-by-step explanation: