Answer:
2
Step-by-step explanation:
The mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of 5 cm/s. When
the length is 12 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm/s)? Write an equation for A in terms of l and w.
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
[tex]A=w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to t, where w and l are both functions of t:
[tex]\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell][/tex]
By the Product Rule:
[tex]\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w[/tex]
Since we know that dl/dt = 6 and that dw/dt = 5:
[tex]\displaystyle \frac{dA}{dt}=5\ell + 6w[/tex]
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
[tex]\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}[/tex]
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
help pls
Draw a line segment AB=8cm. Construct angle BAC=angle ABC=60 DEGREE.
Now draw the angular bisector of each angle of angle ABC.
pls help
Answer:
Step-by-step explanation:
Bisection implies dividing a given segment into equal haves by construction. So that in the given question, angle ABC would be divided into equal parts.
After drawing segment AB to given length, use a compass to construct the required angle ABC. Then use the ends of the arc for the angle to bisect the angle.
The construction to this question is herewith attached to this answer for more clarifications.
what will the time be after 1 hour 5 minutes from 8:15 am
Answer:
9:20 am
Step-by-step explanation:
So, lets go over two things.
Minutes and hours.
Minutes changes the second number.
You know how when a number goes from 9 to 10 how the ones place is set to 0, and the tens place goes up? Its the same with time, only when the number goes from 59 to 60, the hour goes up.
Hours changes the hours place, and when it hits 12, it resets to 1, and the words am go to pm, or pm goes to am.
In this case. we are moving the minutes place up by 5:
15+5=20
So the minutes place is 20, and does not change the hours place since it is below 60.
Next we have a increase in hours by 2:
8+1=9
So the hours place is 9, and does not reset or change the pm/am since its below 12.
Answer:
9:20am
Hope thias helps!
Answer:
9:20 am
Step-by-step explanation:
Add 1 hour
8:15 to 9:15
Add 5 minutes
9:15 to 9:20
(I+ tan square theta)(1-sin square theta)
Answer:
1
Step-by-step explanation:
Formulas used:
[tex]sin^2 \theta + cos^2\theta = 1 => 1-sin^2 \theta = cos^2 \theta\\\\tan^2 \theta + 1 = sec^2 \theta[/tex]
[tex]Q) \ (1 + tan^2 \theta)(1-sin^2 \theta)\\\\= \ sec^2 \theta \times cos^2 \theta\\\\=\frac{1}{cos^2 \theta} \times cos^2 \theta\\\\= 1[/tex]
Answer:
[tex](1 + \tan {}^{2} ( \alpha ) )(1 - \sin {}^{2} ( \alpha ) ) \\ = \frac{1}{ \cos {}^{2} ( \alpha ) } \times \cos {}^{2} ( \alpha ) \\ = 1[/tex]
The picture has the question
Select the correct answer.
What is the solution to this equation?
g^x-1=2
A. -1/2
B. 1/2
C. 2
D. 1
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Answer:
B. 1/2
Step-by-step explanation:
Maybe you want the solution to ...
[tex]9^x-1=2[/tex]
You can use logarithms, or your knowledge of powers of 3 to solve this.
[tex]9^x=3\qquad\text{add 1}\\\\3^{2x}=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=\dfrac{1}{2}}\qquad\text{divide by 2}[/tex]
Using logarithms, the solution looks like ...
[tex]x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}[/tex]
you spin each spinner and find the sum how many different sums are possible
Answer:
let's use a sample set.
8+8, 8+4, 8+5, 8+6, 8+7
4+8, 4+4, 4+5, 4+6, 4+7
5+8, 5+4, 5+5, 5+6, 5+7
6+8, 6+4, 6+5, 6+6, 6+7
7+8, 7+4, 7+5, 7+6, 7+7
There is 25 sums.
please answer the question first
Answer:
Yes, 2.4
Step-by-step explanation:
Y is directly dependant on x, and the constant we multiply x by to get y is 2.4.
Answer:
Yes, 2,4
Step-by-step explanation:
This explains direct proportion because it shows that y equals the 2.4x which is the direct proportion
Hopes this helps
if f(y)=y^6/6lny-y^6/36, find f'(y)
It looks like you have
[tex]f(y)=\dfrac{y^6}{6\ln(y)}-\dfrac{y^6}{36}[/tex]
Differentating gives
[tex]f'(y)=\dfrac{6y^5\times6\ln(y)-6y^6\times\frac1y}{(6\ln(y))^2}-\dfrac{6y^5}{36}= -\dfrac{y^5\left(\ln^2(y)-6\ln(y)+1\right)}{6\ln^2(y)}[/tex]
Consider a two-station production line in which no inventory is allowed between stations (i.e., the stations are tightly coupled). Station 1 consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely (i.e., potential production is determined by the roll of a single die). Station 2 consists of a single machine that has a potentialdaily production of eitther three or four units both which are equally likely (i.e. it produces three units if a fair coin comes up heads and four units if ir comes up tails).
Required:
a. Compute the capacity of each station (units per day). Is the line balanced (do both stations have the same capacity)?
b. Compute the expected throughput of the line. Does this diifer from a.?
c. Suppose a second identical machine is added to station 1 and station 2. What is the expected throughput of the line. How does this compare to previous throughput.
Answer:
a) Capacities : station 1 = 3.5 , station 2 = 3.5
Both stations have the same capacity
b) 3.5 ( it does not differ from a )
c) The value will double i.e. 3.5 * 2 = 7
Step-by-step explanation:
a) compute the capacity of each station and show if the line is balanced
for station 1
Units : 1 ,2 ,3, 4 ,5, 6
probabilities : 1/6 ( same value for all units )
for station 2
units : 3, 4
probabilities : 1/2 1/2
Capacity of station 1= ( 1/6 * 1 ) + ( 1/6 *2 ) + ( 1/6 *3) + (1/6 *4) + (1/6*5) + (1/6*6 )
= 3.5
Capacity of station 2 = ( 1/2 * 3 ) + ( 1/2 * 4 )
= 3.5
∴ both stations have the same capacity
B) Expected throughput of the line
= Min( capacity of station 1 , capacity of station 2 )
= 3.5 ( It does not differ from a )
C) When an additional identical machine is added to both stations the expected throughput of the line will be doubled
i.e. expected throughput = ( 3.5 ) * 2 = 7
the volume of a cylinder is 44cm3. find the volume of another cylinder of the same height and double the base radius
Answer:
[tex]Volume \ of \ other\ cylinder = 176 \ cm^3[/tex]
Step-by-step explanation:
Let the volume of cylinder Vₐ = 44cm³
Let radius of cylinder " a " be = rₐ
Let height of cylinder " b" be = hₐ
[tex]Volume_a = \pi r_a^2 h_a\\\\44 = \pi r_a^2 h_a[/tex]
Given cylinder " b ", Radius is twice cylinder " a " , that is [tex]r_b = 2 r_a[/tex]
Also Height of cylinder " b " is same as cylinder " a " , that is [tex]h_b = h_a[/tex]
[tex]Volume_b = \pi r_b^2 h_b[/tex]
[tex]= \pi (2r_a)^2 h_a\\\\=4 \times \pi r_a^2 h_a\\\\= 4 \times 44\\\\= 176 \ cm^3[/tex]
An aerodynamic 1,000 kg car takes about 270 newtons of force to maintain a speed of 25 m/s. how much horsepower is required from the engine to maintain this speed?
Answer:
9.05 horse power
Step-by-step explanation:
Given:
Force = 270 Newton
Speed = 25 m/s
Power = Force * velocity
Power = 270 Newton * 25 m/s
Power = 6750 watt
Recall:
1 horse power = 746 watts
Hence, required horsepower is :
6750 watt / 746 watt
9.048 hp
9.05 horse power
what is the volume of the triangular prism 13 m x 6 m x 5 m
Answer:
U R ANSWER
Step-by-step explanation:
177.26657
Answer:
[tex]V=195m^2[/tex]
Step-by-step explanation:
Volume formula of a triangular prism is [tex]V=\frac{1}{2} (b)(h)(l)[/tex]
[tex]V=\frac{1}{2}(13)(6)(5)[/tex]
[tex]V=\frac{1}{2} (390)[/tex]
[tex]V=195[/tex]
Hope this helps
f(x)=x^2+2x-4 and g(x)=3x+1 find
Answer:
Step-by-step explanation:
[tex]f(x)=x^2+2x-4\\g(x)=3x+1\\\\g\circ f(x)=g(f(x)=3(x^2+2x-4)+1=3x^2+6x-11[/tex]
Answer:
g(f(x)) = 3x^2 + 6x - 11.
Step-by-step explanation:
Replace the x in g(x) by f(x):
g(f(x)) = 3(x^2 + 2x - 4) + 1
= 3x^2 + 6x - 12 + 1
= 3x^2 + 6x - 11.
Write the equation of the line that passes through the points (6,-6)
and (7,-4) Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
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Answer:
y +6 = 2(x -6)
Step-by-step explanation:
The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-4 -(-6))/(7 -6) = 2/1 = 2
The point-slope equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Using the slope we found and the first point, the equation is ...
y +6 = 2(x -6)
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Please help me with #26-28
Answers:
26) probability = 1/427) probability = 0.058828) probability = 0.157=================================================
Work Shown:
26)
1/2 = probability of an odd number, since half of the numbers are odd
1/2 = probability of tails
(1/2)*(1/2) = 1/4 is the probability of both events happening at the same time
----------------------------
27)
13/52 = probability of pulling out one club
12/51 = probability of pulling out a second club, assuming the first one is not put back
(13/52)*(12/51) = 156/2652 = 1/17 = 0.0588 is the probability of pulling two clubs in a row (without replacement).
----------------------------
28)
11/27 = probability first person has blonde hair
10/26 = probability second person has blonde hair (cannot reselect the first person again)
(11/27)*(10/26) = 110/702 = 55/351 = 0.157 is the probability of selecting two people with blonde hair
4x - 3(2x - y) if x = and y = 4.
Help me pls
Answer:
[tex]=0[/tex]
Step-by-step explanation:
Given:
[tex]4x-3(2x-y)[/tex]
Let's substitute for y
[tex]4x-3(2x-4)=0[/tex]
Let's distribute the parenthesis
[tex]4x-6x+12=0[/tex]
Combine like terms
[tex]-2x+12=0[/tex]
Subtract 12 from both sides
[tex]-2x=-12[/tex]
divide both sides by -2
[tex]x=6[/tex]
Now let's insert 6 for the [tex]x[/tex] and 4 for the [tex]y\\[/tex]
[tex]24-3(12-4)=[/tex]
[tex]24-3(8)=[/tex]
[tex]24-24=0[/tex]
Hope this helps
Answer: The x = -1
Step-by-step explanation: I just looked it up on line.
Simplify the following expression
7-5/6 × 7-7/6
[tex]\longrightarrow{\blue{ 0 }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex]7 - ( \frac{5}{6} \times 7) - \frac{7}{6} [/tex]
[tex] = 7 - \frac{35}{6} - \frac{7}{6} [/tex]
Since the denominators are unequal, we find the L.C.M (lowest common multiple) for the denominators.
The L. C. M is 6.
Now, multiply the L.C.M. with both numerator & denominator.
[tex] = \frac{7 \times 6}{1 \times 6} - \frac{35}{6} - \frac{7}{6} [/tex]
Now that the denominators are equal, we can add/subtract them.
[tex] = \frac{42- 35 - 7}{6} [/tex]
[tex] = \frac{42 - 42}{6} [/tex]
[tex] = \frac{ 0}{6} [/tex]
[tex] = 0[/tex]
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]
The two way table shows information about preferred drinks of some people how many males drank only coffee
Answer:
73% The two-way table shows information about the preferred drinks of some people. b a How many males drank only coffee? b What is the probability that any person is male and only drinks coffee? 73% The two-way table shows information about the preferred drinks of some people
In the coming year, a vehicle manufacturer has decided to manufacture 150 vehicles per day. The function v = 150d represents the company’s production for the coming year, v, with respect to the number of days, d.
The rate of change of the function representing the number of vehicles manufactured for the coming year is , and its graph is a . So, the function is a function.
Given:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
The rate of change of the function representing the number of vehicles manufactured for the coming year is CONSTANT (150) , and its graph is a STRAIGHT LINE . So, the function is a LINEAR function.
I hope this helps!
Answer:
v = 150d
v represents company's production for the coming year
d represents the number of days
150 is the daily production
What’s the volume of the rectangular prism in cubic meters
Answer:
Volume of the prism=60m3
Step-by-step explanation:
Volume of any prism=height*width*length
Volume of the prism=3m*5m*4m=60m3
Volume of the prism=60m3
b. If you take one spin, what is your expected value?
Answer:
3/7
Step-by-step explanation:
Expected Value:
3(1/7) + 1(2/7) + 0(2/7) - 1(2/7) = 3/7
Expected value when we take one spin = 3/7
What is the expected value?It is the sum of values multiplied by their respective probabilities.
How do we calculate the expected value after one spin?We have 2 red, 2 purple, 2 yellow, and 1 blue sector.
Total number of Sectors = 7
∴Probability of landing on red sector = 2/7
∴Probability of landing on purple sector = 2/7
∴Probability of landing on yellow sector = 2/7
∴Probability of landing on blue sector = 1/7
Points on blue sector = 3, on yellow sector = 1, on purple sector = 0, and on red sector = -1.
X 3 1 0 -1
P(X) 1/7 2/7 2/7 2/7
Expected Value = ∑X.P(X)
=3.(1/7) + 1(2/7) + 0(2/7) - 1(2/7)
= 3/7
Learn more about Expected Values on
https://brainly.com/question/15858152
#SPJ2
if f(×) = [tex] \frac{1}{ \sqrt{x - 1} } [/tex]
then find [tex] \frac{f(x) - f(2)}{x - 2} [/tex]
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Answer:
(1 -x +√(x -1))/(x² -3x +2)
Step-by-step explanation:
Fill in the given function definition and simplify.
[tex]\dfrac{f(x)-f(2)}{x-2}=\dfrac{\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{2-1}}}{x-2}=\dfrac{1-\sqrt{x-1}}{(x-2)\sqrt{x-1}}\\\\=\dfrac{\sqrt{x-1}-x+1}{(x-2)(x-1)}=\boxed{\dfrac{\sqrt{x-1}-x+1}{x^2-3x+2}}[/tex]
HELP PLEASE! What is BD??
Answer:
[tex]BD=13[/tex]
Step-by-step explanation:
Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.
Hence:
[tex]\displaystyle \frac{27}{x+5}=\frac{12}{x}[/tex]
Solve for x. Cross-multiply:
[tex]12(x+5)=27(x)[/tex]
Distribute:
[tex]12x+60=27x[/tex]
Subtract 12x from both sides:
[tex]15x=60[/tex]
Divide both sides by 15. Thus:
[tex]x=4[/tex]
BD is the sum of BC and CD:
[tex]BD=BC+CD[/tex]
Substitute:
[tex]BD=x+(x+5)[/tex]
Substitute and evaluate:
[tex]BD=(4)+(4+5)=13[/tex]
Therefore, BD is 13.
At a local concert, the cost for 3 adults and 2 children was $32.00. The cost for 8 adults and 5 children
was $84.00. Find how much it costs for an individual adult and how much it costs for an individual
child.
Adult ticket price = $
Child ticket price = $
Answer:
Hence the cost of adult tickets is $8
and the cost of child ticket is $4
Step-by-step explanation:
Given data
Let the cost per adult be x
and the cost per child be y
So
3x+2y= 32------------1
8x+5y= 84------------2
Now solving 1 and 2 simultaneously, we have
3x+2y= 32------------1X 5
8x+5y= 84------------2 X 2
15x+ 10y= 160
16x+ 10y= 168
-x+0)=-8
-x= -8
x= 8
Put x= 8 in 1 to find y
3*8+2y= 32
24+2y= 32
2y= 32-24
2y= 8
y= 4
A box of golf balls contains 10 balls. Each golf ball has a diameter of 3.6 centimeters. What is the total
volume of golf balls in 3 boxes?
about 1465.74 cm
c. about 1221.45 cm
b. about 732.87 cm
d. about 81.43 cm
Answer:
C
Step-by-step explanation:
a carton of orange juice is 9 centimeters wide. 13 centimeters long and 24 centimeter is tall. if i drink one third of the fruit juice what is the volume left in the carton?
Answer: 1872cm³
Step-by-step explanation:
First and foremost, we've to calculate the volume of the carton which will be:
= Length × Width × Height
= 13cm × 9cm × 24cm
= 2808cm³
The volume that'll be left after ⅓ of the volume is drank will be:
= 2808 - (⅓ × 2808)
= 2808cm³ - 936cm³
= 1872cm³
What is the equation, in point-slope form, of the line that
is perpendicular to the given line and passes through the
point (-4,-3)?
Answer:
Step-by-step explanation:
We first need to find the slope of the line that is graphed. We can wither use the slope formula or you can use the slope triangle. From the upper point on the line (-1, 1) count down til you're on the same horizontal as the lower point on the line (0, -3). You have to count down 4 (which is -4) and over to the right 1 (which is +1). So -4/+1 = -4 and the slope is -4. That means that the perpendicular slope, the opposite reciprocal of that, is 1/4. Using that slope and the point (-4, -3), the point-slope form of the line is
[tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex] which we can simplify a bit to
[tex]y+3=\frac{1}{4}(x+4)[/tex]. That's the line in point-slope form.
If f(x) = x2 – 2x, find:
f(-3) = [?]
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Answer:
15
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
f(-3) = (-3)² -2(-3) = 9 +6
f(-3) = 15
15
Step-by-step explanation:
f(-3)=(-3)^2 - 2(-3)
= 9 + 6 = 15
please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answer:
A
Step-by-step explanation:
Because the angles must add to 180 we can see the misssing angle is 69
This means that answer is either A or C
Using SOH we can solve for side CD
sin(21)=x/18
18sin(21)=x
x=6.45
If CD= 6.45 this means that the answer is A