Answer:
Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].
Step-by-step explanation:
The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.
Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].
Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].
By the power rule:
the first derivative of [tex]t[/tex] (same as the first derivative of [tex]t^2[/tex] (same as [tex]t[/tex] to the second power) with respect toTherefore:
[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].
In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.
Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].
Answer:
58.28 m/s
Step-by-step explanation:
y = 62t - 1.86t²
Speed, S = dy/dt = 62 - 2(1.86)t
S = 62 - 3.72t
When t = 1
S = 62 - 3.72 = 58.28 m/s
A checking account is
overdrawn by $5, then a
$5 fee is charged. What
is the balance on the
account?
Ty for any help!!!
minus/negative ten dollars.
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ind the missing length. The triangles are similar. similar 16 A. 27 B. 24 C. 16 D. 21
2x/9 +x/3 = 13/6, solve for x
Answer:
x = 3 9/10
Step-by-step explanation:
2x/9 +x/3 = 13/6
Get a common denominator on the left side
2x/9 + x/3 *3/3 = 13/6
2x/9 + 3x/9 = 13/6
5x/9 = 13/6
Multiply each side by 9/5 to isolate x
5x/9 *9/5 = 13/6 * 9/5
x = 117/30
Divide the top and bottom by 3
x = 39/10
x = 3 9/10
Answer:
[tex]\bold{\red{\boxed{\blue{ x = 3.9}}}}[/tex]
Step-by-step explanation:
[tex] \frac{2x}{9} + \frac{x}{3} = \frac{13}{6} \\ \frac{2x + 3x}{9} = \frac{13}{6} \\ \frac{5x}{9} = \frac{13}{6} \\ use \: \: cross \: \: multipication \\ 5x \times 6 = 9 \times 13 \\ 30x =11 7 \\ \frac{30x}{30} = \frac{117}{30} \\ x = 3.9[/tex]
X
( = [?]
DK
x Х
А AK
140°
B
HC
Angles are not drawn to scale
Answer:
40 degrees
Step-by-step explanation:
Supplementary angles are a pair of angles that add up to 180 degrees
Since ABD and DBC are supplementary, you can make the equation:
180=140+x
Simplify and you get x=40
[tex]\bf \large \implies \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\bf \large \implies \: \: x \: = \: 180 \degree - \: 140 \degree[/tex]
[tex]\bf \large \implies \: \: x \: = \: 40 \degree[/tex]
Find an expression which represents the sum of (6x + 9y) and (7x – 4y) in
simplest terms.
Answer:
Submit Answer
attempt out of 2
0
Answer:
[tex]6x + 9y + 7x - 4y \\ 6x + 7x + 9y - 4y \\ 13x + 5y \\ thank \: you[/tex]
Answer: 13x+5y
Step-by-step explanation:
is 16 a perfect cube
Answer:
No
Step-by-step explanation:
No, 16 is not a perfect cube. Perfect cubes are numbers that are the cube of an integer and can also be written in the form x³ where x is an integer. Since 16 cannot be written like that, it is not a perfect cube.
3-5n+4n=4. help please
Answer:
n = -1
Step-by-step explanation:
3-5n+4n=4
3 - n = 4
-n = 1
n = -1
27 – 4 + 2a = 4a + 10 what is the answer
Answer:
13/2 = a
Step-by-step explanation:
27 – 4 + 2a = 4a + 10
Combine like terms
23 +2a = 4a +10
Subtract 2a from each side
23+2a-2a = 4a-2a +10
23 = 2a+10
Subtract 10 from each side
23-10 = 2a+10-10
13 = 2a
Divide by 2
13/2 = a
Answer: a = 13/2
I assume you don't need a step - by - step, you're just asking for the answer. Hope this helps!
which of the following statements are true? check all that apply. check all that apply. the volume of a cube depends on the lenght of its sides. a cube with a side length of 10 feet has a volume of 1,000 cubic feet. a cube with a side length of 2 feet has a volume of 8 cubic feet.
A. volume(2)=8
B. volume (8)=2
C. volume (10)=1,000
D. volume (1,000)=10
Answer:
Option A and Option C
Step-by-step explanation:
Answer ASAP THANKKK YOUUUUU
Answer:
D. 40
Step-by-step explanation:
Interquartile range is the difference between the upper quartile value (Q3) and the lower quartile value (Q1).
In a box plot, Q1 is located at the beginning of the edge of the rectangular box from our left, while the Q3 is located at the end of the edge of the rectangular box to our right.
Interquartile range for City A = 70 - 40 = 30
Interquartile range for City B = 80 - 40
Therefore, city B has greater variability. The interquartile range is 40.
4. Find the height, x, of the building
Urgent please help
Answer:
D
Step-by-step explanation:
The function you need to use is the Tan(39).
Tan(x) = opposite / adjacent.
The opposite side does not make up the reference angle.
In this case, the opposite side = x
The adjacent side is not the hypotenuse and does make up the reference angle (which is not the right angle).
opposite = x
adjacent = 68
Tan(39) = x / 68 Multiply by 68
68*Tan(39) = x Divide by Tan(39)
Tan(39) = 0.9098
68*.9098 = x
x = 55.07
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 982 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5. It is assumed that the two tests measure the same aptitude, but use different scales.If a student gets an SAT score that is the 20-percentile, find the actual SAT score.SAT score =What would be the equivalent ACT score for this student?ACT score =If a student gets an SAT score of 1437, find the equivalent ACT score.ACT score =
Answer:
Actual SAT Score = 815.284
Equivalent ACT Score = 15.811
The equivalent ACT Score = 29.95
Step-by-step explanation:
From the given information:
Scores on the SAT test are normally distributed with :
Mean = 982
Standard deviation = 198
If a student gets an SAT score that is the 20-percentile
Then ;
P(Z ≤ z ) = 0.20
From the standard z-score for percentile distribution.
z = -0.842
Therefore, the actual SAT Score can be computed as follows:
Actual SAT score = Mean + (z score × Standard deviation)
Actual SAT score = 982 + (- 0.842 × 198)
Actual SAT score = 982 + ( - 166.716)
Actual SAT score = 982 - 166.716
Actual SAT Score = 815.284
Scores on the ACT test are normally distributed with a mean of 19.6 and a standard deviation of 4.5.
Mean = 19.6
Standard deviation = 4.5
Equivalent ACT Score = 19.6 + (- 0.842 × 4.5)
Equivalent ACT Score = 19.6 + ( - 3.789)
Equivalent ACT Score = 15.811
If a student gets an SAT score of 1437, find the equivalent ACT score.
So , if the SAT Score = 1437
Then , using the z formula , we can determine the equivalent ACT Score
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z = \dfrac{1437 - 982}{198}[/tex]
[tex]z = \dfrac{455}{198}[/tex]
z =2.30
The equivalent ACT Score = 19.6 + (2.30 × 4.5)
The equivalent ACT Score = 19.6 + 10.35
The equivalent ACT Score = 29.95
Graphically, a point is a solution to a system of two inequalities if and only if the point lies in the shaded region of the top inequality, but not in the shaded region of the bottom inequality. lies in the shaded region of the bottom inequality, but not in the shaded region of the top inequality. lies in the shaded regions of both the top and bottom inequalities. does not lie in the shaded region of the top or bottom inequalities.
Answer:
lies in the shaded regions of both the top and bottom inequalities
Step-by-step explanation:
For a point to be a solution of two inequalities, it must lie in both solution sets. It ...
lies in the shaded regions of both the top and bottom inequalities
We want to define when a point is a solution of a system of inequalities, we will see that the correct option is: "lies in the shaded regions of both the top and bottom inequalities."
Just like in a system of equations, a solution of the system is must be a solution of both equations.
Here, a solution ot the system of inequalities must be at the same time a solution of each inequality.
Remember that the solutions of the inequalities are represented by shaded regions, so the point must belong to the intersection of the two shaded regions.
So the correct option is:
"lies in the shaded regions of both the top and bottom inequalities."
If you want to learn more, you can read:
https://brainly.com/question/20067450
A study of long-distance phone calls made from General Electric Corporate Headquarters in Fairfield, Connecticut, revealed the length of the calls, in minutes, follows the normal probability distribution. The mean length of time per call was 3.5 minutes and the standard deviation was 0.70 minutes. What is the probability that calls last between 3.5 and 4.0 minutes? (Round your z value to 2 decimal places and final answer to 4 decimal places.)
Answer:
0.2611
Step-by-step explanation:
Given the following information :
Normal distribution:
Mean (m) length of time per call = 3.5 minutes
Standard deviation (sd) = 0.7 minutes
Probability that length of calls last between 3.5 and 4.0 minutes :
P(3.5 < x < 4):
Find z- score of 3.5:
z = (x - m) / sd
x = 3.5
z = (3.5 - 3.5) / 0.7 = 0
x = 4
z = (4.0 - 3.5) / 0.7 = 0.5 / 0.7 = 0.71
P(3.5 < x < 4) = P( 0 < z < 0.714)
From the z - distribution table :
0 = 0.500
0.71 = very close to 0.7611
(0.7611 - 0.5000) = 0.2611
P(3.5 < x < 4) = P( 0 < z < 0.714) = 0.2611
2x-4Y+6 take aaway 3y-11
Answer:
2x - 7y + 17
Step-by-step explanation:
Subtracting the 2 expressions
2x - 4y + 6 - (3y - 11) ← distribute parenthesis by - 1 )
= 2x - 4y + 6 - 3y + 11 ← collect like terms
= 2x - 7y + 17
Answer:
0
Step-by-step explanation:
2x_4y +6_3y_11
2x_7y=17
2x _7y+17=0
A bag contains n white tiles and five black tiles. The tiles are all equal in shape and sizes. A tile is drawn at random and is replaced. A second tile is then drawn.
Find
a) the probability that the first tile is white
b) the probability that both the first and second tiles are white
We know that our bag has n white tiles and 5 black tiles.
So, the total number of tiles in the bag is n + 5.
We know that a tile is drawn at random and is replaced, then a second tile is drawn.
a) We want to find the probability that the first tile is white.
Because all the tiles have the same probability of being randomly drawn, the probability of drawing a white tile is just the quotient between the number of white tiles and the total number of tiles in the bag.
[tex]P = n/(n + 5)[/tex]
And for the second draw, we do not have any restrictions, so the probability is the above one.
[tex]P = n/(n + 5)[/tex]
b) Now we want both tiles to be white.
For the first one we already know the probability, which is:
[tex]P = n/(n + 5)[/tex]
And because the tile is replaced, the probability of drawing a white tile again is exactly the same:
[tex]Q =n/(n + 5)[/tex]
The joint probability (the probability of both of these outcomes to happen together) is the product of the individual probabilities.
Probability = [tex]P*Q = (n/(n + 5))^2[/tex]
If you want to read more about probability, you can read:
https://brainly.com/question/24256398
Please Help me with this math question
write each number as a reduced fraction or mixed number. A. 16/24 B. 15/24. C. 4%
Answer:
A.1/3 B.5/8 C.1/25
Step-by-step explanation:
just simplify it down to the lowest
Answer:
Ä. 16/24 as reduced fraction = 2/3
B. 15/24 as reduced fraction= 5/8
How many subsets are there in {p, e, t}?
Answer:
Step-by-step explanation:
Number of subset= [tex]2^{n}[/tex]
Her, n is the number of elements in the set.
{p , e , t}
n = 3
Number of subset = 2³ = 2 * 2 *2 = 8
In your own words what is the absolute value of a number?
Answer:
see below
Step-by-step explanation:
The absolute value is the distance from zero.
It is the non-negative quantity.
Which of these is NOT an integer
A) 3 raised to the power of -5
B) -3 raised to the power of 5
C) (1/3) raised to the power of -5
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option A
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]
⸻⸻⸻⸻
[tex]\text{Option \textbf{A} does not simplify into an integer.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
9x) = 27^y and X-Y = -3/2
find the value of y
Answer:
− y ln (27) + ln (9x) = 0
Weather balloons burst at an altitude of 27.5 km. What is the altitude in meters?
Answer:
27500
Step-by-step explanation:
meters are 100 times more than kilometers hope this helps:)
what is the answer to 4x^2+2x-10
Answer:
2 (2x^2 + x - 5)
Step-by-step explanation:
Factor 2 out of 4 x^ 2
Factor 2 out of 2 x
Factor 2 out of − 10
Factor 2 out of 2 (2x^2) + 2x
Factor 2 out of 2 ( 2 x^ 2 + x ) + 2 ⋅ − 5
Hope this can help you
URGENT PLZ!! Drag the correct transformation into the box to match the definition. [BLANK]... moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding preimage and image points. Translation Rotation Reflection
Answer:
Reflection.
Step-by-step explanation:
Reflection moves points across a specified line so that the line is the perpendicular bisector of each line segment connecting corresponding pre-image and image points.
On the other hand, "Translation" moves points the same distance along lines that are parallel to each other while "Rotation" moves points along concentric circles and through the same angle of rotation.
At an angle of 90°, a line of reflection intersects the line segments connecting corresponding points of the pre-image under a reflection.
Basically, a reflection allows us to flip an object or figure across a line, point or plane without any change in its shape or size.
Hence, to reflect an object or a figure such as a triangle simply means that its mirror image would be produced with respect to a line; this line is generally referred to as the line of reflection.
Which regular polygon can be used to form a tessellation?
I need help
Answer: Option 4 (Hexagon)
Step-by-step explanation:
A equilateral triangle, square and hexagon can be used to form a tessellation.
Please click thanks and mark brainliest if you like
Need help and will mark brainlist and thank You
In a circle whose center is O, arc AB contaisn 100 degrees. Find the number of degrees in angle ABO?
Answer:
40
Step-by-step explanation:
Angles ABO, BAO, and AOB are the angles of isosceles triangle AOB. The angles at A and B are equal, so we have ...
AOB +2ABO = 180° . . . . . sum of angles in the triangle
100° +2ABO = 180° . . . . . . use the given value
50° +ABO = 90° . . . . . . . . divide by 2; next, subtract 50°
∠ABO = 40°
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about
triangles.
9 in
9 in.
Xin
6 in
Answer:
8.5
Step-by-step explanation:
Applying pythagora's theorem,
hypotenuse^2 = opposite^2 + adjacent^2
but, hypotenuse = 9
opposite = X
adjacent = 1/2(base of triangle)= 1/2(6)
adjacent = 3
9^2 = X^2 + 3^2
X^2 = 81 - 9
X^2 = 72
X = 8.5
answer these questions with Always,never it sometimes
An exterior angle of a triangle is equal to the sum of its adjacent angle and one remote interior angle
An isosceles triangle is an equilateral triangle
An equilateral triangle is an isosceles triangle
Answer:
sometimes. exterior angle of a triangle is equal to the sum two remote interior angles. But in a special case when the adjacent angle is equal to the remote interior angle, it is true
sometimes. Only when the isosceles triangle is equilateral
always. This is always true by definition.
S(t) = -105t + 945 to determine the salvage value, S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely? A. 11 years B. 8 years C. 7 years D. 9 years
Answer:
D
Step-by-step explanation:
When something depreciates completely, it will have a total value of 0 dollars. Therefore, set the equation to zero and solve for t to find the years.
[tex]S(t)=-105t+945\\0=-105t+945\\-105t=-945\\t=9[/tex]
Therefore, the table saw will completely depreciate after 9 years.
Answer:
[tex]\large \boxed{\sf \bold{D.} \ 9 \ years}[/tex]
Step-by-step explanation:
[tex]S(t) = -105t + 945[/tex]
For the value to depreciate completely, the amount has to be equal to 0 dollars.
Set S(t) to 0.
[tex]0 = -105t + 945[/tex]
Solve for the time t.
Subtract 945 from both sides.
[tex]0 -945= -105t + 945-945[/tex]
[tex]-945=-105t[/tex]
Divide both sides by -105.
[tex]\displaystyle \frac{-945}{-105}=\frac{-105t}{-105}[/tex]
[tex]9=t[/tex]
It will take 9 years for the saw to depreciate completely.