Answer:
45 minutes
Step-by-step explanation:
At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...
t = d/s
t = (7.5 mi)/(10 mi/h) = 0.75 h
to catch Peter.
Mitchell will catch Peter in 45 minutes.
__
Alternate Solution
Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:
3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter
_____
You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.
A rocket leaves the surface of Earth at time t=0 and travels straight up from the surface. The height, in feet, of the rocket above the surface of Earth is given by y(t), where t is measured in seconds for 0≤t≤600. Values of y(t) for selected values of t are given in the table above. Of the following values of t, at which value would the speed of the rocket most likely be greatest based on the data in the table?
(1) t=100
(2) t=200
(3)t=300
(4) t=400
Answer:
Remember that:
Speed = distance/time.
Then we can calculate the average speed in any segment,
Let's make a model where the average speed at t = t0 can be calculated as:
AS(t0) = (y(b) - y(a))/(b - a)
Where b is the next value of t0, and a is the previous value of t0. This is because t0 is the middle point in this segment.
Then:
if t0 = 100s
AS(100s) = (400ft - 0ft)/(200s - 0s) = 2ft/s
if t0 = 200s
AS(200s) = (1360ft - 50ft)/(300s - 100s) = 6.55 ft/s
if t0 = 300s
AS(300s) = (3200ft - 400ft)/(400s - 200s) = 14ft/s
if t0 = 400s
AS(400s) = (6250s - 1360s)/(500s - 300s) = 24.45 ft/s
So for the given options, t = 400s is the one where the velocity seems to be the biggest.
And this has a lot of sense, because while the distance between the values of time is constant (is always 100 seconds) we can see that the difference between consecutive values of y(t) is increasing.
Then we can conclude that the rocket is accelerating upwards, then as larger is the value of t, bigger will be the average velocity at that point.
Speed is simply the rate of change of distance over time.
The greatest speed is at [tex]t = 400[/tex]
To calculate the time of the greatest speed, we simply calculate the slope between each interval.
The slope (m) of a line is:
[tex]m = \frac{y_2 - y_1}{t_2 - t_1}[/tex]
When [tex]t = 100[/tex]
[tex](t_1,y_1) = (0,0)[/tex]
[tex](t_2,y_2) = (200,400)[/tex]
So, we have:
[tex]m = \frac{400-0}{200 -0}[/tex]
[tex]m= \frac{400}{200}[/tex]
[tex]m = 2[/tex]
When [tex]t = 200[/tex]
[tex](t_1,y_1) = (100,50)[/tex]
[tex](t_2,y_2) = (300,1360)[/tex]
So, we have:
[tex]m = \frac{1360-50}{300 -100}[/tex]
[tex]m = \frac{1310}{200}[/tex]
[tex]m = 6.55[/tex]
When [tex]t = 300[/tex]
[tex](t_1,y_1) = (200,400)[/tex]
[tex](t_2,y_2) = (400,3200)[/tex]
So, we have:
[tex]m = \frac{3200-400}{400 -200}[/tex]
[tex]m = \frac{2800}{200}[/tex]
[tex]m = 14[/tex]
When [tex]t = 400[/tex]
[tex](t_1,y_1) = (300,1360)[/tex]
[tex](t_2,y_2) = (500,6250)[/tex]
So, we have:
[tex]m = \frac{6250-1360}{500-300}[/tex]
[tex]m = \frac{4890}{200}[/tex]
[tex]m = 24.45[/tex]
From the above computation, the greatest speed (i.e. slope) is
[tex]m = 24.45[/tex]
The corresponding time at [tex]m = 24.45[/tex] is [tex]t = 400[/tex]
Hence, the greatest speed is at [tex]t = 400[/tex]
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Simplify i12. 1 −1 −i i
Answer:
The answer for the first one is 1 and the second answer is 12i.
Step-by-step explanation:
The value of the given imaginary number i¹² will be 1 thus option (A) is correct.
What is a complex number?A complex number is the sum of a real number and an imaginary number.
The idea of a complex number has come by solving a quadratic equation that has root as negative under root.
If we solve x² + 1 = 0 ⇒ x = √(-1) which is called as iota(i).
The value of iota(i) is given as i = √(-1).
By the law of indices,
i¹² = (i²)⁶
⇒ (-1)⁶
Since the even exponents of a negative number give positive output thus (-1)⁶ = 1.
Thus, i¹² = 1
Hence "The value of the given imaginary number i¹² will be 1".
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The sum of three numbers is 82 The second number is 3 times the third. The third number is 8 more than the first. What are the numbers?
Answer:
22 46 15
Step-by-step explanation:
i looked it up because i was even confused. but i think this is right. hope this helps.
There are 12 red pens, 20 blue pens and 5 black pens in a bag. What is the probability that you will pick a black pen? Round
Answer:
The probability of getting a black pen from the bag is 13.5%.
Step-by-step explanation:
To determine the percentage probability that a black pen will be obtained from the bag, the following calculation must be performed:
12 + 20 + 5 = 37
37 = 100%
5 = X
(5 x 100) / 37 = X
500/37 = X
13.5 = X
Thus, it is determined that the totality of pens is 100%, and through a cross multiplication the percentage of the 5 black pens with respect to the total of pens is obtained.
Therefore, the probability of getting a black pen from the bag is 13.5%.
6/31. There are 6 black pens left and the red pen was removed, so the original sample size of 32 is reduced to 31.
Some number added to 17
Help with this pls ?
Answer:
x = 5
x = 11/2
x = -5/2
x = 3
x = 5/2
Step-by-step explanation:
Find the daily rate if the annual interest rate is 12%.
.
a. 0.0003287671
• b. 0.03287671
.
C. 0.23076923
.
d. 0.00230769
Answer:
B.) 0.03288%
Step-by-step explanation:
I hope this helps you :)
Answer:
Periodic Interest Rate (P)
(rate per compounding period)
0.03288%
Answer is B
Step-by-step explanation:
When rounding to the nearest ten, what is is the least whole number that roundd to 840
Answer:
835
5 and up is rounded higher.
Which expression is equivalent to 25 x 1/5?
Answer:
The answer would be E.
When you solve 25 x 1/5, you get 5.
When you solve 25 ÷ 5, you get 5.
The equivalent expression is 25 ÷ 5.
Option E is the correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example.
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
25 x 1/5
= 25 x 1/5
= 5 x 5 x 1/5
= 5
Now,
1/25 x 5
= 1/5
1/25 x 1/5
= 1/125
1/25 ÷ 1/5
= 1/25 x 5
= 1/5
5 ÷ 25
= 5/25
= 1/5
25 ÷ 5
= 5
We see that,
25 x 1/5 and 25 ÷ 5 have the same value.
Thus,
The equivalent expression is 25 ÷ 5.
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CE is an angle bisector of angle ACB.
If m angle ACE = 2x - 15 and m angle ECB = x +5,
determine the value of x.
Answer:
x = 20
Step-by-step explanation:
[tex] \because \overrightarrow {CE}[/tex] is an angle bisector of[tex] \angle ACB. [/tex]
[tex]\therefore m \angle ACE = m \angle ECB\\ 2x - 15 = x + 5 \\ 2x - x = 15 + 5 \\ \huge \orange{ x = 20}[/tex]
The value of x from the angle bisector is: x = 20
How to find the value of the angle bisector?Angle bisector theorem is a theorem in geometry that states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. An angle bisector is a ray that divides a given angle into two angles of equal measures.
Thus, we can say that:
∠ECB = ∠ACE
Thus:
x + 5 = 2x - 15
2x - x = 15 + 5
x = 20
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-√121 + 5 please help fast
Answer:
-6
Step-by-step explanation:
vhbhbububjbvuvhjuvvbihjbuvi
Answer:
thanks
Step-by-step explanation:
:) hahahahahah
The equation A=1250(1.03)^7 is being used to calculate the amount of money in a savings account. What does the 1.03 represent in this equation?
Answer:
The amount of Interest
Step-by-step explanation:
I'm 98% sure. It make sense because that how much interest ^7 you would multiply by 1250. And I've had questions like this. Hope this helps!
The surface area Q of a certain shape is three times the product of u and the square of its width w.
Answer:
Q = 3uw
Step-by-step explanation:
What fraction is equivalent to 2 31/32
Answer:
95/32
Step-by-step explanation:
You can multiply 32 by two, 64, then add 31, 95
Answer:
95/32
Step-by-step explanation:
yea i checked and it is 95/32
Dr. Jane is studying the growing population of a species of jellyfish in a body of water. Each year, she records the population of jellyfish. The first year, she recorded a population of 15 jellyfish. Every following year, the population increased by four times the previous year’s population. At this rate, what will be the jellyfish population in the 9th year of her study?
Answer:
983040
Step-by-step explanation:
Second Year : 15x4=60
Third Year : 60x4=240
Fourth Year : 240x4=960
Fifth Year : 960x4=3840
Sixth Year : 3840x4=15360
Seventh Year : 15360x4 = 61440
Eighth Year: 61440x4=245760
Ninth Year : 245760x4= 983040
If h(x) = −x − 10, find h(−2). (1 point)
−20
1.6
−1
0
Answer:
-8
Step-by-step explanation:
substitute X with -2 across the equation
-(-2) - 10
minus times minus gives plus, hence positive 2 minus 10
+2 - 10
= -8
from the product of 30 and 70 take the sum of the two numbers
Huh? Is yo question finished
1 A line passes through (0, 2) and has a slope of 3. Which function's graph is parallel to this line?
A. f(x) = 2
B. f(x) = 3
C. f(x) = 2x
D f(x) = 3x
Can someone Identify the terms and coefficients;
8x-20y-10
Answer:
cooeficients are + 8,20 and 10
terms are x and y
x is less than nine
Answer:
x < 9
Step-by-step explanation:
x is less than nine
x < 9
Answer:
x<9
Step-by-step explanation:
less than symbol is this <
The question is x is less than 9
so
x<9
Hope this helps!
Solve for x.
3(-4x-1)-2x+4=43
Please help I’m crying my eyes out I hate delta math
Answer:
x = - 3Step-by-step explanation:
3 (-4 x - 1) - 2 x + 4 = 43
Expand the terms in the bracket
That's
- 12x - 3 - 2x + 4 = 43
- 14x + 1 = 43
Using the subtraction property subtract 1 from each side of the equation
- 14x + 1 - 1 = 43 - 1
- 14x = 42
Divide both sides by - 14
[tex] \frac{ - 14x}{ - 14} = - \frac{42}{14} [/tex]
We have the final answer as
x = - 3Hope this helps you
what are three ratios equivalent to 8:5
Answer:
80:50 800:500 16:10
Step-by-step explanation:
The Atlas V Rocket could go 1 full mile in just 1/10 of a second. How fast did it travel?
Answer:
10 miles per second
Step-by-step explanation:
if 1/10 seconds is equal to one mile, then 10/10 (1) second would be equal to 10 miles (per second).
The speed of Atlas V Rocket was 10 mile per second.
Here,
The distance travel by Atlas V Rocket was = 1 mile
Time taken = 1/10 second
We have to find the speed of Atlas V Rocket.
What is Speed?
Speed of an object is calculated as;
Speed = Distance/Time
Now,
The distance travel by Atlas V Rocket = 1 mile
Time taken = 1/10 second
Hence, The speed of Atlas V Rocket = [tex]\frac{1}{\frac{1}{10} }[/tex] = [tex]10[/tex]
Therefore, The speed of Atlas V Rocket was 10 mile per second.
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You are buying tickets to a Star Wars Convention. The tickets cost $10 per adult and $3 per child. Parking is a one-time fee of $5. If you
purchased two adult tickets, a, and the total cost was $109, how many child tickets, c, were purchased?
Answer:
28 children tickets
Step-by-step explanation:
$109 for the whole cost
bought 2 adult tickets that costed 10$ each and payed 5$ for parking fee
add them together 25$
109-25 =84
84/3 =28
I need some help: A survey of 120 persons was conducted at TCC, and it was found that 97 persons carried a cell phone, 12 persons carried a tablet computer, and 9 carried both a cell phone and a tablet. How many people carried a cell phone or a tablet?
Answer:
100
Step-by-step explanation:
n(u)=120 total people in survey
n(c)=97 people carrying cell phone
n(t)=12 people carrying tablet
n(c∩t)=9 people carrying both tablet and cell phone
n(c∪t)=? people carrying cell phone or tablet
now,
n(c∪t)= n(c)+n(t) - n(c∩t)
= 97+12-9
=109-9
=100
there fore the number of people carrying cell phone or tablet = 100
helpppppppppp!!!!!!
1) If a recipe that uses 12 cups of flour to make 8 cakes needs to be scaled down to make 6 cakes, how much flour will the new yield require?
○6 cups
○9 cups
○10 cups
○11 cups
2) What is the benefit of formulas?
○They require less time to cook.
○They produce the same results every time.
○Most home cooks will become familiar with formulas.
○Formulas require fewer ingredients than most recipes.
3) If a restaurant needs 10 pounds of ground beef to make 50 servings of chili, how many pounds of ground beef are required to make 65 servings?
○13 pounds
○15 pounds
○18 pounds
○20 pounds
4) How much dough can a commercial freestanding mixer make at once?
○Up to 100 pounds
○Up to 175 pounds
○Up to 350 pounds
○Up to 500 pounds
5) A blender would be the best choice when making which of the following?
○A fruit pie
○A fish entrée
○Cookie dough
○A mustard sauce
6) If a batch of cake batter is cooked in one large pan instead of two round pans, how will this change the cooking time?
○There is no change in the cooking time.
○The larger pan will take longer to cook.
○The two smaller pans will take longer to cook.
○It won’t since the amount of batter is the same.
Answer:
1)9 cups
2) they produce the same results
3)13 pounds
4)100 pounds
5) a mustard sauce
6) the larger pan would take a longer to cook
4.0 divided by 0.02=
Answer:
Step-by-step explanation:
A woman has a total of $ 12 , 000 to invest. She invests part of the money in an account that pays 7 % per year and the rest in an account that pays 9 % per year. If the interest earned in the first year is $ 920 , how much did she invest in each account?
Write the recurssive formula. Clarissa is buying a homecoming dress onlayaway. The dress costs $185. She makes a down payment of $20 to put the dress on layaway and then makes weekly payments of $15. In how many weeks will the dress be paid off?
Answer: x = 11
Step-by-step explanation:
185= 15x +20
minus 20 from both side
165 = 15x
divide 15 by both side
11 = x