Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
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.
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
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
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]
someone find x for me lol
Hi there!
[tex]\large\boxed{x = 60^o}[/tex]
We know:
∠AGB ≅ ∠DGC because they are vertical angles. They both are 90°.
∠AGE ≅ FGC because they are vertical angles, equal 30°.
∠BGF ≅ ∠DGE are vertical angles, both equal x.
All angles sum up to 360°, so:
360° = 90° + 90° + 30° + 30° + x + x
Simplify:
360° = 240° + 2x
Subtract:
120° = 2x
x = 60°
A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.
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Answer:
C. h ≥ 1.9 in
Step-by-step explanation:
As the final step, divide both sides of the inequality by 5.3:
(5.3h)/5.3 ≥ 10/5.3
h ≥ 1.9
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'.
Let f(x) = 5 + 12x − x^3. Find (a) the x- coordinate of all inflection points, (b)
the open intervals on which f is concave up, (c) the open intervals on which
f is concave down.
Answer:
A) x = 0.
B) f is concave up for (-∞, 0).
C) f is concave down for (0, ∞).
Step-by-step explanation:
We are given the function:
[tex]f(x)=5+12x-x^3[/tex]
A)
We want to find the x-coordinates of all inflection points.
Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:
[tex]f'(x) = 12-3x^2[/tex]
And the second:
[tex]f''(x) = -6x[/tex]
Set the second derivative equal to zero:
[tex]0=-6x[/tex]
And solve for x. Hence:
[tex]x=0[/tex]
We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:
[tex]f''(-1) = 6>0[/tex]
And testing x = 1:
[tex]f''(1) = -6<0[/tex]
Since the signs change for x = 0, x = 0 is indeed an inflection point.
B)
Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.
From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:
[tex](-\infty, 0)[/tex]
C)
From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:
[tex](0, \infty)[/tex]
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.
identify the angles relationship
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.
The function ƒ(x) = x−−√3 is translated 3 units in the negative y-direction and 8 units in the negative x- direction. Select the correct equation for the resulting function.
Answer:
[tex]f(x)=\sqrt[3]{x}[/tex] [tex]3~units\: down[/tex]
[tex]f(x)=\sqrt[3]{x} -3[/tex] [tex]8 \: units \: left[/tex]
[tex]f(x+8)=\sqrt[3]{(x+8)} -3[/tex]
----------------------------
Hope it helps..
Have a great day!!
Answer:
its not B that what i put and i missed it
Step-by-step explanation:
13 A traffic roundabout has a circular garden
in the centre and two lanes for traffic
encircling the garden. The diameter of the
garden is 16 metres and each lane is 3 metres
wide. Each lane is to be resurfaced. Calculate
the area to be resurfaced. Answer in square
metres to the nearest whole number.
Answer:
Step-by-step explanation:
The area to be resurfaced is the area of the
whole circle including garden and lanes minus
the area of the garden.
Area of a circle is (pi)r2
radius of garden is (1/2)diameter = 8 m
Garden area: (pi)82 = 64(pi) m2
Diameter of garden plus traffic lanes is
16 + 2(6) because we add 6 m to both sides
of the diameter of the garden.
Full diameter = 16+12 = 28 m
Full radius = 28/2 = 14 m
Full area: (pi)142 = 196(pi) m2
Area to be resurfaced:
196(pi) - 64(pi) = 132(pi) m2 ≅ 415 m2
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
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.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with % confidence if (a) she uses a previous estimate of ? (b) she does not use any prior estimates?
Answer:
732 samples ;
752 samples
Step-by-step explanation:
Given :
α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42
Using the relation :
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.58 * 0.42) / 0.03²
n = 0.65918769 / 0.0009
n = 732.43076
n = 732 samples
B.)
If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.5 * 0.5) / 0.03²
n = 0.67650625 / 0.0009
n = 751.67361
n = 752 samples
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
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.
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
^please answer, thanks in advance ^
Answer:
There is not enough information to determine the mean, the median is 28.
There is not enough information to determine the mean absolute deviation, the interquartile range is 18
Step-by-step explanation:
The box plot given has a skewed distribution, this means that both the mean and median values are not the same. From a box plot, the median value Can be obtained as the point in between the box.
From the box plot given, the marked point in between the box is 28 cm
Hence, Median = 28 cm
The mean cannot be inferred from the skewed box plot.
There is also not enough information to determine the mean absolute deviation ;
The interquartile range:
(Q3 - Q1)
Q3 = upper quartile, the endpoint of the box = 40
Q1 = the starting point of the box = 22
IQR = Q3 - Q1
IQR = 40 - 22 = 18
Evaluate − x 2 −5 y 3 when x = 4 and y =−1
Answer:
-11
Step-by-step explanation:
I am going to assume that it is -x^2-5y^3.
-(4^2)-5(-1^3)
-16-5(-1)
-16+5
-11
Answer:
- 11
Step-by-step explanation:
If x = 4, y = -1
then,
- x^2 - 5y^3 = - (4)^2 - 5(-1)^3
= - 16 + 5
= - 11
write your answer in simplest radical form
Answer:
n = 2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan 30 = n / 2 sqrt(3)
2 sqrt(3) tan 30 = n
2 sqrt(3) * sqrt(3)/3 = n
2 = n
We have to find,
The required value of n.
Now we can,
Use the trigonometric functions.
→ tan(θ) = opp/adj
Let's find the required value of n,
→ tan (θ) = opp/adj
→ tan (30) = n/2√3
→ n = 2√3 × tan (30)
→ n = 2√3 × √3/3
→ n = 2√3 × 1/√3
→ [n = 2]
Thus, the value of n is 2.
Describe a rule for the transformation.
Answer: 90° counterclockwise
Step-by-step explanation:
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.
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.
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
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 35113511 grams and a variance of 253,009253,009. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 46174617 grams. Round your answer to four decimal places.
Answer:
The answer is "0.1397".
Step-by-step explanation:
[tex]\mu=3511\\\\[/tex]
variance [tex]\ S^2= 253,009\\\\[/tex]
standard deviation [tex]\sigma =\sqrt{253,009}=503\\\\[/tex]
Finding the probability in which the weight will be less than [tex]4617 \ grams\\\\[/tex]
[tex]P(X<4617)=p[z<\frac{4617-3511}{503}]\\\\[/tex]
[tex]=p[z<\frac{1106}{503}]\\\\=p[z< 2.198]\\\\= .013975\approx 0.1397[/tex]
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
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
