Answer:
khai niem hinh cat don gian?
A ball is thrown from an initial height of 7 feet with an initial upward velocity of 23 ft/s. The ball's height h (in feet) after 1 seconds is given by the following.
h = 7+23t-16t^2
Find all values of 1 for which the ball's height is 15 feet.
Answer:
Step-by-step explanation:
If we are looking for the time(s) that the ball is at a height of 15, we simply sub in a 15 for the height in the position equation and solve for t:
[tex]15=-16t^2+23t+7[/tex] and
[tex]0=-16t^2+23t-8[/tex]
Factor this however you factor a quadratic in class to get
t = .59 seconds and t = .85 seconds.
This means that .59 seconds after the ball was thrown into the air it was 15 feet off the ground. Then the ball reached its max height, gravity took over, and began pulling it back down to earth. The ball passes the height of 15 feet again on its way down after .85 seconds.
Ross resides in an apartment where houses are arranged horizontally. She resides at door number 3.if she want to visit her friend Martha at door number 7, how many house should she Cross?
Answer:
3 doors if we are excluding her own. 4 if we are not.
4, 5, 6. she does not pass 7, she enters 7.
3, 4, 5, 6. it could be argued she must first pass her own door.
that context changes the answer.
it takes engineer 3 hrs to drive to his brother's house at an average of 50 miles per hour. if he takes same route home, but his average speed of 60 miles per hour, what is the time, in hours, that it takes him to drive home?
Answer:
t2 = 2.5 hours.
Step-by-step explanation:
The distance is the same.
d = r * t
The rates and times are different so
t1 = 3 hours
t2 = X
r1 = 50 mph
r2 = 60 mph
r1 * t1 = r2*t2
50 * 3 = 60 * t2
150 = 60 * t2
150 / 60 = t2
t2 = 2.5
Answer:
Answer: Travel Time is 2 hours & 30 minutes
Step-by-step explanation:
Original Journey Time is 3 hours, Speed is 50 mph, Distance is 150 miles
Original Distance is 150 miles, New Speed is 60 mph.
Also Combined Distance was 300 miles, Combined Time was 5 hours & 30 minutes. therefore: Average Speed for complete round trip is 54. 54 mph
Michael invest $P at a rate of 3.8% per year compounded interest. After 30 years the value of this investment is $1,469. Calculate the value of P.
Answer:
Step-by-step explanation:
The formula for this is
[tex]A(t)=P(1+r)^t[/tex] and we have everything but the P. Filling in:
[tex]1469=P(1+.038)^{30[/tex] and
[tex]1469=P(1.038)^{30[/tex] and
1469 = P(3.061403718) so
P = 479.85
A research center conducted a telephone survey of 2,000 adults to learn about the major economic concerns for the future. The survey results showed that 1,620 of the respondents think the future health of Social Security is a major economic concern. (a) What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern
Answer:
0.81
Step-by-step explanation:
Find the point estimate by dividing the number of respondents that thought it was a major economic concern by the total number of people in the survey:
1,620/2,000
= 0.81
So, the point estimate is 0.81
I need help solving this problem
Answer:
300
Step-by-step explanation:
g Find an equation of the line with slope m that passes through the given point. Put the answer in slope-intercept form. (-4, 8), undefined slope Hint: Any line parallel to Y axis has undefined slope.
Answer:
The equation is x + 4 = 0.
Step-by-step explanation:
Point (-4 , 8)
A line parallel to the Y axis has slope is infinite.
The equation of line is
[tex]y - y' = m (x-x')\\\\y - 8 =\frac{1}{0}(x+4)\\\\x + 4 = 0[/tex]
PLEASE CORRECT BEFORE ANSWERING I AM HAVING TROUBLE GETTING THINNGS RIGHT SO PLEASE HELP
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Answer:
3
Step-by-step explanation:
AB is 1 unit long.
A'B' is 3 units long.
The scale factor is the ratio of these lengths:
scale factor = A'B'/AB = 3/1 = 3
ABC is dilated by a factor of 3 to get A'B'C'.
Find the length of XW.
Answer:
XW = 78
Step-by-step explanation:
Both triangles are similar, therefore based on triangle similarity theorem we have the following:
XW/XZ = VW/YZ
Substitute
XW/6 = 104/8
XW/6 = 13
Cross multiply
XW = 13*6
XW = 78
What is the value of Z? Z =2^3
the value of Zis 8.
Z =2^3=8
Now we have to,
find the required value of Z.
→ Z = 2^3
→ [Z = 8]
Therefore, value of Z is 8.
Find the expression that is equivalent to 7(x2 – 5x + 1).
Answer:
7x^2 -35x +7
Step-by-step explanation:
7(x^2 – 5x + 1)
Distribute
7x^2 -7*5x +7*1
7x^2 -35x +7
identify the angles relationship
Which of the following expressions are equivalent to -3x- 6/10
Choose all that apply:
A=3/6x1/10
b=- 3/10x-6
c= none of the above
Answer:
c= none of the above
Step-by-step explanation:
-3x- 6/10
This has two separate terms, a term with a variable
-3x and a term with a constant -6/10
A=3/6x1/10 This has only one term
b=- 3/10x-6 This has a different x term -3/10 which is not -3
c= none of the above
6. A boy pushes his little brother in a box with a force of 500 N for 324 m How much work is this if the force of
friction acting on the sliding box is (a) 100 N (6) 250. N?
Answer:
(a) 129600 J
(b) 81000 J
Step-by-step explanation:
The work done is given by the product of force and the displacement in the direction of force.
Force, F = 500 N
distance, d = 324 m
(a) friction force, f = 100 N
The work done is
W = (F - f) x d
W = (500 - 100) x 324
W = 129600 J
(b) Friction, f = 250 N
The work done is
W = (F - f) d
W = (500 - 250) x 324
W = 81000 J
find c.round to the nearest tenth
Answer:
we need a picture...
Step-by-step explanation:
Solve for x.
7(x+2) = 6(x+5)
O x=-44
O X=-16
O x= 44
O x= 16
Answer:
x = 16
Step-by-step explanation:
7(x + 2) = 6(x + 5)
First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.
7x + 14 = 6x + 30
Next, let's subtract "6x" from both sides of this equation!
x + 14 = 30
Now, we have to subtract "14" from both sides of the equation.
x = 16
Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.
7(16 + 2) = 6(16 + 5)
7(18) = 6(21)
126 = 126
Since our equations equal each other we know that our x-value is correct!
Hope this Helps! :)
Have any questions? Ask below in the comments and I will try my best to answer.
-SGO
Suppose an annuity pays 6% annual interest, compounded semi-annually. You invest in this annuity by contributing $4,500 semiannually for 6 years. What will the annuity be worth after 6 years?
Answer:
$3240
Step-by-step explanation:
hope it is well understood
Answer: 59300
Step-by-step explanation:
The average cost when producing x items is found by dividing the cost function, C(x), by the number of items,x. When is the average cost less than 100, given the cost function is C(x)= 20x+160?
A) ( 2, infinit)
B) (0,2)
C) (-infinit,0) U (2,infinit)
D) (- infinit,0] U [2,infinit)
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Answer:
A) (2, ∞) . . . . or C) (-∞, 0) ∪ (2, ∞) if you don't think about it
Step-by-step explanation:
We want ...
C(x)/x < 100
(20x +160)/x < 100
20 +160/x < 100 . . . . . separate the terms on the left
160/x < 80 . . . . . . . subtract 20
160/80 < x . . . . . multiply by x/80 . . . . . assumes x > 0
x > 2 . . . . . . simplify
In interval notation this is (2, ∞). matches choice A
__
Technically (mathematically), we also have ...
160/80 > x . . . . and x < 0
which simplifies to x < 0, or the interval (-∞, 0).
If we include this solution, then choice C is the correct one.
_____
Comment on the solution
Since we are using x to count physical items, we want to assume that the practical domain of C(x) is whole numbers, where x ≥ 0, so this second interval is not in the domain of C(x). That is, the average cost of a negative number of items is meaningless.
Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)
Bcoz I really need this rn :(
DUEEEE AFTERRR LUNCHH! :(:(:(:(
If your answer is NONSENSE it will be deleted as soon as possible!
But if your answer is CORRECT, HELPFUL, HAS AN EXPLANATION, I'll chose your answer as the BRAINLIEST ANSWER!
Answer:
The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.
The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2
Explanation:
Interior angles are the angles that are inside the shape. The remote interior angles would be the 2 angles away from the exterior angle.
The exterior angle is the angle, made by the side of the shape and a line drawn out from an adjacent side.
I hope this helps!
Answer:
In LDR
Exterior = d Interior = a, bIn PDR
Exterior = 4Interior = 1, 2Exterior angle of a triangle is formed when one side of the triangle is extended .
Interior remote angles the angles in the triangle that do not lie on the extended side.
What is the derivative of x^2?
Answer:
[tex]\displaystyle \frac{d}{dx}[x^2] = 2x[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = x^2[/tex]
Step 2: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = 2x^{2 - 1}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
If he is correct, what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months
Complete Question
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 91 months with a standard deviation of 10 months if he is correct. what is the probability that the mean of a sample of 68 computers would differ from the population mean by less than 2.08 months? Round your answer to four decimal places. Answer How to enter your answer Tables Keypad
Answer:
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Step-by-step explanation:
From the question we are told that:
Population mean \mu=91
Sample Mean \=x =2.08
Standard Deviation \sigma=10
Sample size n=68
Generally the Probability that The sample mean would differ from the population mean
P(|\=x-\mu|<2.08)
From Table
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
T Test
[tex]Z=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]Z=\frac{2.08}{\frac{10}{\sqrt{68} } }[/tex]
[tex]Z=1.72[/tex]
[tex]P(|\=x-\mu|<2.08)=P(|z|<1.72)[/tex]
[tex]P(-1.72<Z<1.72)[/tex]
Therefore From Table
[tex]P(-1.72<Z<1.72)=0.9146[/tex]
Can someone explain how to solve this step by step? Thank you
Answer:
x=10
Step-by-step explanation:
Using the Rational Roots Test, we can say that the potential rational roots are
± (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90).
Unfortunately, there doesn't really seem to be an easy way to figure out which numbers are actually roots outside of guess and check. Therefore, to solve this, we'll have to go through numbers until we hit something.
To make the process faster, I wrote a Python script as follows:
numbers = [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
negative_numbers = [i * (-1) for i in numbers]
numbers = numbers + negative_numbers
for i in numbers:
if (i**3 - 10*(i**2) + 9*i-90) == 0:
print(i)
The result comes out as 10, meaning that 10 is our only rational root. Using the Factor Theorem, we can say that because 10 is a root, (x-10) is a factor of the polynomial. Using synthetic division, we can divide (x-10) from the polynomial to get
10 | 1 -10 9 -90
| 10 0 90
_________________
1 0 9 0
Therefore, we can say that
(x³-10x²+9x-90)/(x-10) = (x²+0x+9), so
x³-10x²+9x-90 = (x-10)(x²+9)
As the only solution to x²+9=0 contains imaginary numbers, x=10 is the only solution to x³-10x²+9x-90 = (x-10)(x²+9) = 0
Suppose f(x)=x^2. What is the graph of g(x)=1/2f(x)?
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Answer:
see attached
Step-by-step explanation:
The graph of g(x) is a vertically scaled version of the graph of f(x). The scale factor is 1/2, so vertical height at a given value of x is 1/2 what it is for f(x). This will make the graph appear shorter and fatter than for f(x).
The graph of g(x) is attached.
I need help finding the answer to this question on edge.
Answer:
6
Step-by-step explanation:
We need to evaluate :-
[tex]\rm\implies \displaystyle\rm\sum^4_n (-1)^n (3n + 2 ) [/tex]
Here the [tex]\Sigma[/tex] is the sum operator . And here we need to find the sum from n = 1 to n = 4 . We can write it as ,
[tex]\rm\implies (-1)^1 ( 3*1 +2) + (-1)^2 ( 3*2+2) + (-1)^3(3*3+2) + (-1)^4(3*4+2) [/tex]
Now we know that for odd powers of -1 , we get -1 and for even powers we get 1 . Therefore ,
[tex]\rm\implies -1 ( 3 + 2 ) + 1 (6+2)+-1(9+2)+1(12+2)[/tex]
Now add the terms inside the brackets and then multiply it with the number outside the bracket . We will get ,
[tex]\rm\implies -1 * 5 + 1 * 8 + -1*11 + 1*14 \\\\\rm\implies -5 + 8 - 11 + 14 \\\\\rm\implies\boxed{\quad 6 \quad}[/tex]
Hence the required answer is 6.
A car travels 1/8 mile in 2/13 minutes. What is the speed in terms of miles per minute?
Answer:
13/16 miles per minute
Step-by-step explanation:
Take the miles and divide by the minutes
1/8 ÷ 2/13
Copy dot flip
1/8 * 13/2
13/16 miles per minute
A number is chosen at random from 1 to 50. What is the probability of selecting
multiples of 10.
Answer: 25
Step-by-step explanation:
Use a table of values to graph the function ƒ(x) = x−−√. Choose the correct graph from the options below.
Answer:
B
Step-by-step explanation:
The square root function's graph is graph (b). This makes logical sense, because, when taking the square root (the principal root in particular), a general rule is that both the input and the output must be positive. Moreover, if one were to create a table of values to find points on the graph of the function, each of the points can be found on graph (b).
[tex]f(x)=\sqrt{x}[/tex]
x y
1 1
4 2
9 3
16 4
Therefore graph (B) is the correct answer.
describe how you could use the point-slope formula to find the equation of a line that is perpendicular to a given line and passes through a given point
Answer:
Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.
Write each question as a single logarithm (Picture attached)
Answer:
a.
[tex] log_{5}( {u}^{3 \times {v}^{4} } ) [/tex]
b.
[tex] ln( \frac{1}{( {x}^{2} - 2x + 1 } ) [/tex]
c.
[tex] log_{2}(x { \sqrt{3x - 2} }^{4} ) [/tex]
Give the properties for the equation x2 + y2 + 8x - 2y +15 = 0
Radius √2 4 2
Answer:
ind the center and radius of the sphere: x2 + y2 +z2-8x + 2y + 62+1 0 2) Find an equation of the sphere that passes through the point (6,-2, 3) and has center (-1,2, 1). Find the curve in which the sphere from #2 intersects the yz-plane. For #4-11, u : ? + j-2k 4) 2u +3v 5) Iv 6) uv and v-3i-2j + k 8) Ivxu 9) comp,v 10) proju 11) Find the angle between u and v 12) Find the scalar triple product of a, b, and c. If a (3, 1,2), b (-1,1,0), and c (0,0,-4) 13) Find the values of x such that (3,2, x) and (2x, 4, x) are orthogonal 14) Find two unit vectors that are orthogonal to both j + 2k and i-2j+3k 15) Find the acute angle between two diagonals of a cube 16) Find a vector perpendicular to the plane through the points A(1,0,0), B(2,0,-1) and C(1,4,3) 17) Find parametric equations for the line through (4,-1, 2) and (1, 1, 5) 18) Find parametric equations for the line through (-2, 2, 4) and perpendicular to the plane 2x-y+5z 12 19) Find an equation of the plane through (2, 1,0) and parallel to x + 4y -3z 1 20) Find an equation of the plane through (3, -1, 1), (4, 0, 2), and (6, 3, 1). 21) Show that the planes x y-z 1 and 2x 3y + 4z 5 are neither parallel nor perpendicular. Find the angle between the planes.
