The solution can be simplified to determine when the object will hit the ground is; h(t) = -9.8t² + 20t + 60
What is projectile motion?Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory
Projectile motion
We are told that the projectile motion of an object can be modeled using;
h(t) = gt² + v0*t + h0
Where;
g is the acceleration due to gravity
t is the time since launch
h(t) is the height of the projectile after time t
v0 is the initial velocity
h0 is the initial height.
Now, we are given;
The acceleration due to gravity; g = –9.8 m/s²
Initial velocity; v0 = 20 m/s
Initial height; h0 = 60 m
Hence solution can be simplified to determine when the object will hit the ground is; h(t) = -9.8t² + 20t + 60 h(t) = -9.8t² + 20t + 60
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Answer:
it's c on edge :] have a nice day
Which expression is equivalent to 6x - 24?
A. 6(x-24)
B. 6(x-18)
C. 6(x-4)
D. 24(x-6)
Answer:
C
Step-by-step explanation:
If you factorise 6x-24 you will get 6(x-4) as 6 times x equals 6x and 6 times -4 equals -24.
Kaya does homework for 2 2/3 hours. She spends 1/4 of this time doing her science
homework. How much times does she spend doing her science homework?
Answer:
2/3
Step-by-step explanation:
1/4 is the same thing as 25%
25% of 2 2/3 is 2/3
You can also divide 2 2/3 by 4.
Normal Distribution- Empirical Rule - please help
The first five terms of an arithmetic sequence are given: $4,10,16,22,28, \\ldots$ What is the sixth term in the sequence
Answer:
34
Step-by-step explanation:
to find the number to add 4 which will increase it to 10 with them subtract 10 from 4 to find the number which is increasing termly
=> 10 - 4 = 6
increasing by 6
4 + 6 = 10
10 + 6 = 16
16 + 6 = 22-
22 + 6 = 28
28 + 6 = 34
6th term = 34
Find the value of each variable. Show all the work
Answer:
x° = 45°
y° = 90°
z° = 45°
Step-by-step explanation:
Angles on a straight line add up to 180°
⇒ z° + 135° = 180°
⇒ z° = 180° - 135°
⇒ z° = 45°
The dashes on the side lengths mean that the sides are of equal length. Therefore this is an isosceles triangle. The base angles of an isosceles triangle are equal.
⇒ x° = z°
⇒ x° = 45°
The sum of the interior angles of a triangle is 180°
⇒ x° + y° + z° = 180°
⇒ 45° + y° + 45° = 180°
⇒ y° = 180° - 45° - 45°
⇒ y° = 90°
in a binomial experiemnt the probability of success is 0.16. what is the probability of two successes in seven trials
Answer:
0.2248307402
Step-by-step explanation:
Let 'success', p = 0.16,
and 'failure', q = 1 - 0.16 = 0.84
and the number of trials, n = 7
r = 2
[tex]P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} \\ P(X = 2) = \binom{7}{2} {(0.16)}^{2} {0.84}^{5 - 2} \\ = 0.2248307402[/tex]
a number, x, rounded to 1 decimal place is 3.7. write down the error interval for x
Answer:
3.65 ≤ x < 3.75
Step-by-step explanation:
We are finding the lower and upper bounds:
The lowest possible number that can be rounded to 3.7 is 3.65 as the 5 makes the 6 go next.
The maximum possible number to 2 d.p that will be 3.74 as the 4 keeps it at 3.7.
But someone can say 3.749 is a bigger number that 3.74 that will get rounded to 3.7
Someone else can argue with 3.7499.
So to solve this argumnet we put 3.75 but we don't include it.
Therefore our final answer is :
3.65 ≤ x < 3.75
Hope this helped and branliest please.
Find the surface area of the sphere if its radius is 13 inches. Round your answer to
nearest hundredth (two decimal places). Use 3.14 to approximate pi.
Solve the System of these Equations
Answer:
y=-9/2, x=7
Step-by-step explanation:
You can solve this via substitution. First solve for x in terms of y in one of the equations given. Lets use the first one:
25+4y=x
Now plug 25+4y in for x in the second equation
3(25+4y)-2y=30
75+12y-2y=30
75+10y=30
10y=-45
y=-9/2
Plug this into the first equation:
25-x=-4(-9/2)
25-x=18
x=7
Helpppppp plssss!!!!!!
Answer:
The answer is D or 180 degrees
Thank you Consider brainliest <3
Step-by-step explanation:
Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction pi over 4 endfraction)) minus 2 y = negative 3 sine (2 (x startfraction pi over 4 endfraction)) minus 2 y = 3 cosine (2 (x startfraction pi over 4 endfraction)) minus 2 y = negative 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2
The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
How to convert sine of an angle to some angle of cosine?We can use the fact that:
[tex]\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)[/tex]
to convert the sine to cosine.
Which trigonometric functions are positive in which quadrant?In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.In second quadrant(π/2 < θ < π), only sin and cosec are positive.In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)
Here, the given function is:
[tex]y= 3\cos(2(x + \pi/2)) - 2[/tex]
The options are:
[tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= -3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\cos(2(x + \pi/4)) - 2[/tex][tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]Checking all the options one by one:
Option 1: [tex]y= 3\sin(2(x + \pi/4)) - 2[/tex][tex]y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2[/tex]
(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.
This option if would be true, then from option 1 and this option, we'd get:
[tex]-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0[/tex]
which isn't true for all values of x.
Thus, this option is not same as the given function.
Option 3: [tex]y= 3\cos(2(x + \pi/4)) - 2[/tex]The given function is [tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
This option's function simplifies as:
[tex]y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2[/tex]
Thus, this option isn't true since [tex]\sin(2x) \neq \cos(2x)[/tex] always (they are equal for some values of x but not for all).
Option 4: [tex]y= -3\cos(2(x + \pi/2)) - 2[/tex]The given function simplifies to:[tex]y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2[/tex]
The given option simplifies to:
[tex]y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2[/tex]
Thus, this function is not same as the given function.
Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2
Learn more about sine to cosine conversion here:
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Answer:
a
Step-by-step explanation:
1. Mrs. Grape has 90 students. On her last test, 3/10 of these students earned an A. Of those students, 1/9 got a perfect score. How many students got a perfect score?
2. Using the information from the problem above, what fraction of the total students got a perfect score on the test?
Answer: 1/30
Step-by-step explanation:
3/10 of 90 = 27
1/9 of 27 = 3
3/90 = 1/30
Answer:
3 1/30
Step-by-step explanation:
90 * 3/10 got A
of these 1/9 = perfect
90 * 3/10 * 1/ 9 = 3
3 out of 90 = 3/90 = 1/30
need help asapppl !!!!
Answer:
After 12 days both bamboo plants were 9ft tall
How many ways are there to deal hands of five cards to each of six players from a deck containing 48 different cards
Using the combination formula, it is found that there are [tex]6.4 \times 10^{32}[/tex] ways to deal the cards to the six players.
The order in which the cards are handed to each player is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
For the first player, 5 cards are taken from a set of 48.For the second player, they are taken from a set of 43.For the third for a set of 38, for the fourth from a set of 33, for the fifth from a set of 28 and for the sixth from a set of 23, hence:[tex]T = C_{48,5} \times C_{43,5} \times C_{38,5} \tims C_{33,5} \times C_{28,5} \times C_{23,5}[/tex]
[tex]6.4 \times 10^{32}[/tex]
There are [tex]6.4 \times 10^{32}[/tex] ways to deal the cards to the six players.
More can be learned about the combination formula at https://brainly.com/question/24372153
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What are all the solutions to the equation sin 2x = 2cos x in the interval [0, 2π)?
Answer:
[tex]x=\dfrac{1}{2} \pi, \dfrac{3}{2} \pi \quad \textsf{in the interval}\:[0,2 \pi)[/tex]
Step-by-step explanation:
Rewrite the given equation so that it equals zero, using the trig identity:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
[tex]\begin{aligned}\sin(2x) & =2\cos(x)\\\sin(2x)-2\cos(x) & =0\\2\sin(x)\cos(x)-2\cos(x) & =0\\2\cos(x)[sin(x)-1] & =0\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Therefore}:\quad 2\cos(x) & =0\\\cos(x) & =0\\x & =\dfrac{1}{2} \pi \pm 2 \pi n, \dfrac{3}{2} \pi \pm 2 \pi n\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Therefore}:\quad \sin(x)-1 & =0\\\sin(x) & =1\\x & =\dfrac{1}{2} \pi \pm 2 \pi n\end{aligned}[/tex]
[tex]\implies x=\dfrac{1}{2} \pi, \dfrac{3}{2} \pi \quad \textsf{in the interval}\:[0,2 \pi)[/tex]
An equation is formed of two equal expressions. The value of x for which the sin(2x) = 2cos(x) will have solution in the interval [0, 2π) is (π/2) and (3π/2).
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation can be rewritten as,
sin(2x) = 2 cos(x)
2 sin(x) cos(x) = 2 cos(x)
2 sin(x) cos(x) - 2 cos(x) = 0
Taking 2cos(x) as common,
2 cos(x) [sin(x) - 1] = 0
Now, the two factors can be written as,
cos(x) = 0
x = (π/2)±2πn, (3π/2)±2πn
sin(x) - 1 = 0
sin(x) = 1
x = (π/2)±2πn
Hence, the value of x for which the sin(2x) = 2cos(x) will have solution in the interval [0, 2π) is (π/2) and (3π/2).
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Which equation matches the table? (I have a screenshot)
If I get this wrong I will lose my 57 streak :(
Answer:
b-2a
Step-by-step explanation:
this is beacuse when u find the slope u look in the chart and divide the numbers and will give u the sum of 2
8/4
8/12
12/16
Answer:
b=a+4
Step-by-step explanation:
Its a 58 streak now :)
According to Howard Jones, what is one historical circumstance that led to support for United States expansion overseas in the 1890s?
The context clues show that a historical circumstance that led to United States expansion overseas in the 1890s is economic dominance.
What are context clues?It should be noted that context clues are the hints that are given in a literary work to help readers understand a story.
In this case, the context clues show that a historical circumstance that led to United States expansion overseas in the 1890s is economic dominance. This was achieved through commercial penetration.
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simplifi the expresion 3^-3
Answer:
0,(037)
Step-by-step explanation:
At this question, if I understood correctly, the answer for that is 0,037037037037...
You can write it as 0,(037)
I hope that I helped :)
Determine the equation of the line with the following characteristics.
Slope=3, passing through (-1, 10)
Answer:
y = 3x + 13
Step-by-step explanation:
The equation of a line is also known as slope-intercept form.
Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.
To put an equation in slope-intercept form, we need the slop and the y-intercept.
In this case, we already have the slope which is 3.
So far, we have y = 3x + b
Now, we need to find the y-intercept.
Since you already have a point, we can plug in the x and y values from the point, into the equation.
10 = 3(-1) + b
Now, we can solve for b.
10 = -3 + b
Add three on both sides so it becomes:
13 = b
13 is the y-intercept
y = 3x + 13
Can anyone please help answer this?
A = 45 inches!
11 + 7 = 18
12 + 5 = 17
6 + 4 = 10
18 + 17 = 35
35 + 10 = 45
The perimeter of a triangle is 42 yards. The first side is 5 yards shorter than the
second side, and the third side is 2 yards shorter than the first side. What is the length
of each side?
Answer: Is your question "What is the length of each side?"
Let x = the length of the second side
Let x - 5 = the length of the first side
Let (x - 5) - 2 = the length of the third side
P = a + b + c
x + x - 5 + x - 7 = 42
3x - 12 = 42
3x = 54
x = 18 yards
x - 5 = 13 yards
x - 7 = 11 yards
Step-by-step explanation:
How to Convert 3,18km to M
Answer:
1.97596 miles
simplified
1.976 miles
3.5 divided by 470.75 with solution.
Answer:
0.00743494
Step-by-step explanation:
1.) First start by writing down your equations.
It should look like this: 3.5/470.75
2.) Next you want to move the decimal place equally on both sides.
It should look like this: .00350 divided by .47075
3.) Lastly solve by seeing how many times 47075 goes into 3.5 which results in 0.00743494
A researcher is interested in knowing whether responses to lowering the legal age for drinking alcohol varies by gender. Which statistical test would be most appropriate for this type of data
The statistical test that would be most appropriate determine the answer the researcher is interest in knowing is a chi-square test.
What is a chi-square test?A chi-square test is a statistical test used to test the relationship between categorical variables. It is used to determine the difference between the expected data and the observed data is due to chance.
Chi squared = [tex]\frac{(O_{i} - E_{i} )^{2} }{E_{i} }[/tex]
Where:
[tex]O_{i}[/tex] = observed value[tex]E_{i}[/tex] = expected value.The researcher is interested in knowing if the response to lowering the legal age for drinking alochol (observed value)) varies by gender (expected value). Thus, a chi-square test would be used.
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which number is between 8.270 and 8.280
Answer:
8.275
Step-by-step explanation:
8.280 - 8.270 = 0.010
0.010/2 = 0.005
8.270 + 0.005 = 8.275
Percent of discount is 40% sale price is 78 what’s the or
Answer:
124.8
Step-by-step explanation:
Answer: $130
Step-by-step explanation:
60% = 78
1% = 78/ 60
100% = 78/60 ×100
Discount is 40% = $52
Help Please. I'm not that smart
Answer:
8580 yards
Step-by-step explanation:
[tex]4 \frac{7}{8}miles \times 1760 \frac{yards}{mile} = 8580yards[/tex]
The total will the friend's paddle combined is 51480 yards.
What is the unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor.
The Great Adventures Canoe and Kayak company offers 3 different options as shown in the table.
This afternoon a group of 6 friends is paddling the Adventure Mid Trip in individual kayaks.
The totals will the friends paddle combined is;
[tex]\rm = 4\dfrac{7}{8} \times 6\\\\=\dfrac{4\times 8+7}{8}\times 6\\\\=\dfrac{32+7}{8} \times 6\\\\ =\dfrac{39}{8} \times 6 \\\\=\dfrac{234}{8}\\\\= 29.25[/tex]
Here 1 mile = 1760 yards
The totals will the friends paddle combined is;
[tex]= 29.25 \times 1760\\\\=51480[/tex]
Hence, The total will the friend's paddle combined is 51480 yards.
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PLS HELP ME ONLY GOT 5 MIN LEFT!!!! LOTS OF POINTS
Answer:
G is the correct answer
.
.
1. Jackie is saving money to buy a new cell phone. The cell phone costs $175, but she has
already saved $56. What percent of the cost of the cell phone has Jackie saved?
Answer:
32%
Step-by-step explanation:
Given that:Jackie is saving money to buy a new cell phone.The cell phone costs $175 she has already saved $56To find:The percent of the cost of the cell phone has Jackie savedIn order to find the percent of the cost of the cell phone has Jackie saved,
divide the cost of the cell phone by the amount of the money Jackie savedMultiply the result (1) by 100See below how it's done:
[tex] \dfrac{56}{175} \times 100[/tex]
dividing yields:
[tex] 0.32 \times 100[/tex]
multiplying yields:
[tex]32\%[/tex]
Alternative:
Instead of dividing,we can consider reducing the fraction and multiply that with 100 to get the answer.
[tex] \dfrac{56}{175} \times 100 \\ \implies \frac{8}{25} \times 100 \\ \implies 8 \times 4 \\ \implies \boxed{32\%}[/tex]
In conclusion:
Jackie has saved 32% of the cost of the cell phone
The interquartile range is
Answer:
11.
Step-by-step explanation:
Lower quartile = (12 + 8) /2 = 10
Upper quatrile = (20+22)/2 = 21
Interquartile range = 21-10 = 11,