Answer:
52
Step-by-step explanation:
42, 45, 58, 63
The mean is the sum divided by the number of terms
(42+ 45+ 58+ 63)/4
208/4
52
Answer:
Step-by-step explanation:
42 + 45 + 58 +631 + 422 + 473 + 52 = 1723
then divide by 7 to get 246.142857
hope this helps :)
PLEASE HELP! 20 POINTS!!
(c) Analysts predict the share price of a new company, Hydrate Energy, to be modelled by the equation
V = 2.95 + 2log10 (10t + 1) where t is the number of years and V is the value in dollars.
(i) How much do they expect the share price to increase in value between the first and third years?
Show working
Answer:
The share price increased by $40
Step-by-step explanation:
In the first year: (t = 1)
=> V = [tex]2.95 +2log10(10(1)+1)[/tex]
=> [tex]V = 2.95 + 2 (10+1)\\V = 2.95+2(11)[/tex]
=> [tex]V = 2.95+22[/tex]
=> V = $ 24.95
In the 3rd Year: (t = 3)
=> [tex]V = 2.95 + 2log10(10(3)+1)[/tex]
=> [tex]V = 2.95+ 2(30+1)[/tex]
=> [tex]V = 2.95+2(31)[/tex]
=> V = 2.95 + 62
=> V = $64.95
The Share Price increased by:
=> $64.95-$24.95
=> $40
The share price increased by $40
pls help!!!! it has been a struggle 2 find this answer!
Answer:
U to V: 5/2
V to U: 2/5
Step-by-step explanation:
Simplify the ratio of the corresponding sides.
20 in to 8 in
25 in to 10 in
30 in to 12 in
Which letter of the alphabet is next in the series?
J O T Y D
(A) I (B) J (C) K (D) L
Answer:
A
i
Step-by-step explanation:
Hope it helps
WILL MARK BRAINLIEST
Answer:
A
Step-by-step explanation:
Answer this question
Answer:
1.
a) exact form: -1 /14 or decimal form: -0.0714285
b) exact form: -23/120 or decimal form: -0.1916
2.
a) 89
b)98
c) 5.7
d) 4.8
3.
i) 2*2*2*2*2*2*3*3*3
ii) 3*3*3*5*5*5
iii) 2*2*2*2*2*2*2*2*2*2*2*2
iv) 2*2*2*2*2*2*5*5*5
9.
i) x = -9
ii) x + 1/7
I hope this helps get you started :)
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
This means volume of the larger canister is 8 times more than volume of the smaller canister.
This means surface area of the larger canister is 4 times greater than volume of the smaller canister.
Step-by-step explanation:
Smaller canister
Diameter=9cm
Radius=diameter/2
=9/2=4.5cm
Height=12cm
Larger canister (double of the smaller canister)
Radius=4.5*2=9cm
Height=12*2=24cm
Volume=πr^2h
Surface area=2πrh + 2πr^2
Volume of smaller canister=πr^2h
=3.14*(4.5)^2*12
=3.14*20.25*12
=763.02
Surface area of the smaller canister=2πrh + 2πr^2
=2*3.14*4.5*12 + 2*3*14*(4.5)^2
=339.12 + 127.17
=466.29
Volume of larger canister=πr^2h
=3.14*(9)^2*24
=3.14*81*24
=6104.16
Surface area of larger canister=2πrh + 2πr^2
=2*3*14*9*24 + 2*3.14*(9)^2
=1356.48 + 508.68
=1865.16
Compare smaller and larger volume of the canister:
Volume if larger/volume of smaller
=6104.16/763.02
=8
This means volume of the larger canister is 8 times more than volume of the smaller canister
Compare surface area of larger and smaller canister:
Surface area of larger canister/surface area of smaller canister=1865.16/466.29
=4
This means surface area of the larger canister is 4 times greater than volume of the smaller canister
Answer:
Yeah, what she said above.
Step-by-step explanation:
Isosceles trapezoid ABCD is inscribed in ⊙O with radius 5. AD=6 and the median of ABCD has length 7. Find the distance from AD to BC. this was the only info given!
Answer:
The distance from AD to BC is 7
Step-by-step explanation:
The information given are;
The type of inscribed quadrilateral ABCD = Isosceles trapezoid
The radius of the circle = 5
Segment AD of ABCD = 6
The median of the trapezoid ABCD = 7
Given the trapezoid theorem, the median is equal to half the length of the two bases added together, we have;
(AD + BC)/2 = 7
Which gives;
(6 + BC)/2 = 7
BC = 7×2 - 6 = 8
Therefore the distance from AD to BC is given by the distance from BC to the median line added to the distance from AD to the median line given as follows;
The distance from BC to the median = √(Radius² - (BC/2)²) = √(5² - (8/2)²) = 3
The distance from BC to the median = 3
The distance from AD to the median = √(Radius² - (AD/2)²) = √(5² - (6/2)²) = 4
Which gives;
The distance from AD to BC = 3 + 4 = 7
Which system of equations has the solution shown in the graph? A. y = -5x + 1 and y = -x + 5 B. y = 5x + 1 and y = -x − 5 C. y = 5x − 1 and y = -x + 5 D. y = -5x − 1 and y = -x − 5
Answer:
C. y = 5x-1 and y = -x+5Step-by-step explanation:
Since there are two lines on the graph, we will find the equation of both lines. The standard form of equation of a line is y = mx+c where;
m is the slope of the line = y₂-y₁/x₂-x₁
c is the intercept (the point where the line cuts the y axis)
For the blue line;
It can be seen that the coordinate of the lines are (1,4) and (0, -1)
m = -1-4/0-1
m = -5/-1
m = 5
For this line, it can be seen that the line cuts the y-axis at -1, hence the intercept of the line is -1
The equation of the blue line will be y = 5x+(-1)
y = 5x-1
For the red line;
It can be seen that the coordinate of the lines are (0,5) and (5, 0)
m = 0-5/5-0
m = -5/5
m = -1
For this line, it can be seen that the line cuts the y-axis at 5, hence the intercept of the line is 5
The equation of the red line will be y = -x+5
Hence, the system of equations that has the solution shown in the graph are y = 5x-1 and y = -x+5
The mean height of a Clydesdale horse is 72 inches with a standard deviation of 1.2 inches. What is the probability that a Clydesdale is greater than 75 inches tall?
Answer:
0.0062
Step-by-step explanation:
Given that:
Mean (μ) = 72 inches, Standard deviation (σ) = 1.2 inches.
The z score is a measure in statistics is used to determine by how many standard deviation the raw score is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean, the z score is negative.
The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For Clydesdale is greater than 75 inches tall, x = 75 inches, the z score is:
[tex]z=\frac{x-\mu}{\sigma}=\frac{75-72}{1.2} =2.5[/tex]
The probability that a Clydesdale is greater than 75 inches tall = P(X > 75) = P(Z > 2.5) = 1 - P(Z < 2.5) = 1 - 0.9938 = 0.0062 = 0.62%
The probability that a Clydesdale is greater than 75 inches tall is 0.62%
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate the rate that the water is draining out of the pool. (Hint: remember this line is sloping down to the right) b) Calculate how much water was in the pool initially (at time 0). I think it was 80 000 c) Write an equation for this relationship. d) Use your equation to calculate how much water is in the pool at 62 minutes.
Step-by-step explanation:
At t = 20 min, V = 45,000 L.
At t = 70 min, V = 0 L.
a) The rate is the slope:
m = ΔV/Δt
m = (0 L − 45,000 L) / (70 min − 20 min)
m = -900 L/min
b) Using the slope to find V when t = 0 min:
m = ΔV/Δt
-900 L/min = (V − 0 L) / (0 min − 70 min)
V = 63,000 L
c) Use slope-intercept form to find the equation.
V = -900t + 63,000
d) At t = 62 min:
V = -900(62) + 63,000
V = 7200
Answer:
a. -900 L/min
b. Vo = 63,000 Liters
c. V ( t ) = 63,000 - 900*t
d. 7,200 Liters
Step-by-step explanation:
Solution:-
We have a swimming pool which is drained at a constant linear rate. Certain readings were taken for the volume of water remaining in the pool ( V ) at different instances time ( t ) as follows.
t = 20 mins , V = 45,000 Liters
t = 70 mins , V = 0 Liters
To determine the rate ( m ) at which water drains from the pool. We can use the linear rate formulation as follows:
[tex]m = \frac{V_2 - V_1}{t_2 - t_1} \\\\m = \frac{0 - 45000}{70 - 20} \\\\m = \frac{-45,000}{50} = - 900 \frac{L}{min}[/tex]
We can form a linear relationship between the volume ( V ) remaining in the swimming pool at time ( t ), using slope-intercept form of linear equation as follows:
[tex]V = m*t + V_o[/tex]
Where,
m: the rate at which water drains
Vo: the initial volume in the pool at time t = 0.
We can use either of the data point given to determine the initial amount of volume ( Vo ) in the pool.
[tex]0 = -900*( 70 ) + V_o\\\\V_o = 63,000 L[/tex]
We can now completely express the relationship between the amount of volume ( V ) remaining in the pool at time ( t ) as follows:
[tex]V ( t ) = 63,000 - 900*t[/tex]
We can use the above relation to determine the amount of volume left after t = 62 minutes as follows:
[tex]V ( 62 ) = 63,000 - 900*(62 )\\\\V ( 62 ) = 63,000 - 55,800\\\\V ( 62 ) = 7,200 L[/tex]
What is the slope intercept form of the equation of the line that passes through the points (7,-5) and (3,-9)?
Answer:
1
Step-by-step explanation:
y2 - y1 divided by x2 - x1
-9 + 5 = -4
3 - 7 = -4
-4/-4 = 1
To make lines m and n parallel, identify the measures of Angle 3 and angle 4.
Answer:
<3 = 112 degrees
<4 = 68 degrees
Step-by-step explanation:
<3 = 112 degrees (Alternate angles are congruent)
And,
<4+<3 = 180 (Angles on a straight line add up to 180)
=> <4 + 112 = 180
=> <4 = 180-112
=> <4 = 68 degrees
An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 300 miles per hour. The other is 200 miles from the point and has a speed of 400 miles per hour.
(a) At what rate is the distances between the planes decreasing?
(b) How much time does the air traffic controller have to get one of the planes on a different flight path?
Answer:
(a) D(t) = 250t -500 miles
(b) Controller has 2 hours, but including time for pilots to divert course or altitude.
Step-by-step explanation:
Given:
two planes at same altitude heading in a collision course.
Plane A at 400 miles from collision point at 200 mph
Plane B at 300 miles from collision point at 150 mph.
Theoretical collision happens in
t = 400/200 = 300/150 = 2 hours
Distance ya of plane A from collision point as a function of time in hours
ya(t) = 400 -200t
Distance yb of plane B from collision point as a function of time in hours
yb(t) = 300-150t
(a) Distance between two planes,
Since the two planes are on courses perpendicular to each other, will need using pythagorean theorem
D(t) = sqrt(ya(t)^2+yb(t)^2)
= sqrt((400-200t)^2+(300-150t)^2)
= 250(t-2)
D(t) = 250t -500 miles
b. time available
Time until D(t) = 0
solve D(t) = 0
D(t) = 0
250(t-2) = 0
t = 2 (two hours)
Answer:
a) -500 mph
b) 1/2 h
Step-by-step explanation:
a)[tex]\frac{ (150(-300))+(200(-400))}{\sqrt{150x^{2} +200^{2} } }[/tex]
b) [tex]\frac{\sqrt{150^{2}+200^{2} } }{500}[/tex]
Coffee is sold in two different sized canisters. The smaller canister has a diameter of 9 cm and a height of 12 cm. The larger canister is double the size of the small canister (i.e., the diameter and height are doubled). Calculate the volume and surface area of each canister and compare the results of doubling the dimensions.
Answer:
The larger canister has 8 times the volume and 4 times the volume of the smaller one.
Step-by-step explanation:
The smaller canister has a diameter of 9 cm (radius = 4.5 cm) and height of 12 cm.
The larger canister has double the diameter and height of the smaller one. The diameter of the larger canister is 18 cm (radius = 9 cm) and height of 24 cm.
The canisters are in the shape of a cylinder.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
The surface area of a cylinder is given as:
A = 2πr(r + h)
SMALLER CANISTER
Volume = π * 4.5 * 4.5 * 12 = 763.41 cubic centimetres
Area = 2 * π * 4.5(4.5 + 12) = 2 * π * 4.5 * 16.5 = 466.53 square centimetres
LARGER CANISTER
Volume = π * 9 * 9 * 24 = 6107.26 cubic centimetres
Area = 2 * π * 9(9 + 24) = 2 * π * 9 * 33 = 1866.11 square centimetres
By reason of comparison, the larger canister has 8 times the volume and 4 times the volume of the smaller one despite having double the dimensions.
Answer:
Yeah, what they said above.
Step-by-step explanation:
Find each product.
(X3+2x2)x4
PLEASE HELP!!! ASAP!!!
Answer:
4x^3+8x^2
Step-by-step explanation:
Multiply each term:
4x^3+8x^2
PLZ MARK ME BRAINLIEST
How many solutions does the nonlinear system of equations below have?
Answer:
OneStep-by-step explanation:
There is only one intercepting point, it means one solution.
There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen. How many possibilities are there?
Answer: The number of possibilities = 380
Step-by-step explanation:
Given, There are 20 players on a soccer team. From them, a captain and an alternate captain have to be chosen.
Since, captain and alternate captain comes in order.
Number of ways to choose r things out of n things (when order matters) :
[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Number of ways to choose 2 players ( for captain and alternate captain ) from 20 players :
[tex]^{20}P_2=\dfrac{20!}{18!}=20\times19=380[/tex]
Hence, the number of possibilities = 380
I need help with this!
Part A
Answer: 33.2 degrees F
Explanation: Adding on a negative is the same as subtracting. So 72.3 + (-39.1) = 72.3 - 39.1 = 33.2
================================================
Part B
Answer: 70 + 2 + 0.3 + (-30) + (-9) + ( -0.1 )
Explanation:
Think of 72 as 70+2. Furthermore, think of 72.3 as 70+2+0.3; we just break the number up into its corresponding digits (adding zeros when needed). The 7 is in the tens place, the 2 is in the units or ones place, and the 3 is in the tenths place.
Similarly, we have 39.1 break down into 30+9+0.1, in which all three terms are made negative to represent -39.1
================================================
Part C
Answer: 70 + (-30) + 2 + (-9) + 0.3 + ( -0.1 )
Explanation: Arrange the tens place value items to be next to each other. Same goes for the units place value, and also the tenths place value.
================================================
Part D
Answer: [70 + (-30)] + [ 2 + (-9) ] + [ 0.3 + ( -0.1 ) ]
Explanation: Take the result of part C and surround each pair of terms in square brackets to show how the terms pair up.
I need the answer in degrees
Answer:
x = 69°Step-by-step explanation:
Angles at a point add up to 360°
To find x add up all the angles and equate them to 360°
That's
168 + 123 + x = 360
291 + x = 360
x = 360 - 291
x = 69°
Hope this helps you
Answer:
x = 69
Step-by-step explanation:
The sum of a circle is 360 degrees
x+ 168+123 = 360
Combine like terms
x +291 = 360
Subtract 291 from each side
x+291-291 = 360-291
x =69
The area of a circle is 49\pi square units. What is the radius of the circle, in units?
Answer:
7
Step-by-step explanation:
The formula to find the area of a circle is pi*r^2.
We were given 49pi. This means that 49=r^2.
The square root of 49 is 7.
So our radius is 7.
Hope this helps! <3
PLEASE HELP!! A car manufacturer does performance tests on its cars. During one test, a car starts from rest, and accelerates at a constant rate for 20 seconds. another car starts from rest three seconds later, and accelerates at a faster constant rate. The equation that models the distance (d) in metres the first cars equation is d=1.16t^2, where t is time, in seconds, after the car starts. The equation for the second car is: d=1.74(t-3)^2. a) in context, what is a suitable domain for the graph of the system? b) at what time will both cars have driven the same distance? c) how far will they have driven at this time?
Answer:
0 ≤ t ≤ 2516.348 seconds310.0 metersStep-by-step explanation:
a) Since these are production vehicles, we don't expect their top speed to be more than about 70 m/s, so the distance functions probably lose their validity after t = 25. Of course, t < 0 has no meaning in this case, so the suitable domain is about ...
0 ≤ t ≤ 25
Note that the domain for the second car would be 3 ≤ t ≤ 25.
__
b) The graph of this system shows the cars will both have driven the same distance after 16.348 seconds.
__
c) At that time, the cars will have driven 310.0 meters.
_____
Non-graphical solution
If you like, you can solve the equation for t:
d1 = d2
1.16t^2 = 1.74(t -3)^2
0 = 0.58t^2 -10.44t +15.66
t = (10.44 +√(10.44^2 -4(0.58)(15.66)))/(2(0.58)) = (10.44+8.524)/1.16
t = 16.348 . . . . time in seconds the cars are at the same distance
That distance is found using either equation for distance:
1.16t^2 = 1.16(16.348^2) = 310.036 . . . meters
The cost of importing five dozen china dinner sets, billed at $32 per set, and paying a duty of 40%, is
Answer:
duty = 64
Total cost is 224
Step-by-step explanation:
First find the cost of the 5 sets
5 * 32 = 160
Then find the duty
160 * 40%
160 * .4 = 64
Add this to the cost of the sets
160+64 =224
What is the approximate perimeter of the figure?
Answer:
7.1 inches
Step-by-step explanation:
perimeter you go round from apointof your choice so
add 2+2=4
then apply 1/4πd for the round part
d=4 and it's quarter a circle then add them together
Answer:
7.1 inches
Step-by-step explanation:
To find the perimeter of the circle you would need to follow the formula: 2piR. Since r=2, 2*2=4. So 4 multiplied by pi (3.14 or 22/7). Since this is a quarter of a circle you would divide the answer 12.56 by four which equals 3.14. Now just add the extra two 2s left on the flat sides of the figure which ends up with your answer of 7.14 OR 7.1.
Hope this helps!! <3
Point A is at (-6,6) and point C is at (-6,-2). Find the coordinates of point B on Ac such that AB =3/4AC
Answer:
B(-6, 0)
Step-by-step explanation:
You want to find B such that ...
(B -A) = (3/4)(C -A) . . . . the required distance relation
4(B -A) = 3(C -A) . . . . . . multiply by 4
4B = 3C +A . . . . . . . . . . add 4A, simplify
Now, we can solve for B and substitute the given coordinates:
B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)
The coordinates of point B are (-6, 0).
Answer:
the answer your looking for is (-3,-3)
Step-by-step explanation:
Please answer this question now
Answer:
36°
Step-by-step explanation:
<U + < V + <W = 180° (sum of angles in a triangle)
<W = 54°
The tangent is always perpendicular to the radius drawn to the point of tangency...
therefore,
<U = 90°
90° + <V + 54° = 180°
144° + <V = 180°
<V = 180° - 144°
<V = 36°
Answer:
V=36
Step-by-step explanation:
tangent makes rigt angle with radius angle U=90
W+V+U=180
V=180-90-54
V=36
Find the equation of a line passing through the point A (14,23) and the slope 2.
Answer:
y=2x-5
Step-by-step explanation:
y=mx+c
mx=slope
In this case, the slope is already given to you which means the m=2.
y=2x+c.
The coordinates are (14, 23) and when you put -5 into c, the line goes through the coordinates (14, 23).
Hope this helps!
Solve each problem below. Show all working in the space provided.
1. A square shed measures 8m 35cm along each side. Find the perimeter of th
shed.
Answer:
Answer:
33m 40cm.
Step-by-step explanation:
One side of the shed measures 8 meters and 35 centimetres, which is 800 + 35 = 835 centimetres.
Since the shed is a square, all side lengths are 835 centimetres long. So, the perimeter is 835 * 4 = 3,340 centimetres. That means that the perimeter is 33 meters and 40 centimetres.
Hope this helps!
A triangle has sides 45, 4x and 2x−4. What is the possible range of x?
Answer: I think it's 2
Step-by-step explanation: i am not dat good at math
BRAINLEST Use the function f(x) = 2x^2 − 5x + 3 to answer the questions. Part A: Completely factor f(x). Part B: What are the x-intercepts of the graph of f(x)? Show your work.
Answer:
answer pic below :)
Step-by-step explanation:
A city survey of two neighborhoods asked residents whether they would prefer a new playground or a dog park.
Answer:
so if it is asking about the exact percentage then the answer is B but if it is the percentage in all the answer is D.
Step-by-step explanation: My reasoning behind is that 70 percent of the neighborhood wants a playground if it is 40 to 17
Percentage Hill point residence want playground is about 70% .
What is percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"
According to the question
Hill point residence want playground = 0.40
Total who want playground = 0.58
now,
Percentage Hill point residence want playground over total
[tex]\frac{0.40}{0.58} *100[/tex]
= 68.96%
≈ 70%
Hence, Percentage Hill point residence want playground is about 70% .
To know more about Percentage here:
https://brainly.com/question/16797504
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