Answer:
[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]
The maximum amount of sand that can be stored in this structure is 1675.52 m³.
Step-by-step explanation:
The volume of a conical-shaped structure is given by
[tex]V = \frac{1}{3} (\pi \cdot r^2 \cdot h)[/tex]
Where r is the radius and h is the height of the structure.
We are given that
radius = 10m
height = 16m
Substituting the above values into the formula, we get
[tex]V = \frac{1}{3} (\pi \cdot 10^2 \cdot 16) \\\\V = \frac{1}{3} (1600 \pi ) \\\\V = 1675.52 \: m^3[/tex]
Therefore, the maximum amount of sand th can be stored in this structure is 1675.52 m³.
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
A driver decends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and decends another 18 feet. At this point what is his depth in the water
Answer:
-26 ft or 26 ft below the surface
Step-by-step explanation:
Starting at the surface
0
Descending 20 ft
0 -20 = -20
Rose 12 ft
-20 +12 = -8
Descends 18 ft
-8 -18= -26 ft
1. Robert and Casey added the following values shown below. Who solved
correctly?
ROBERT
CASEY
5 1/8+ 2 1/3 = 7 1/2
-4 1/2+ 6 3/4= 2 1/4
Answer:
Casey is correct.
Step-by-step explanation:
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same. The denominator would have to be 24. That would make the fractions 3/24 and 8/24. If you added them together, it would not be able to simplify to 1/2.
Casey's -4 1/2 + 6 3/4 = 2 1/4 is correct because —4 - 6 = 2. In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator wich would equal -2/4. Now add -2/4 and 1/4 and you get 1/4. If my explaining is confusing, I'm sorry!☜(ﾟヮﾟ☜)
Casey is correct and he will get the correct solution.
We have given that,
ROBERT CASEY
5 1/8+ 2 1/3 = 7 1/2 -4 1/2+ 6 3/4= 2 1/4
Robert's 5 1/8 + 2 1/3 = 7 1/2 is wrong because if 5+2 = 7, I would have to change the denominator of both fractions so they are both the same.
What is the equation?A statement that the values of two mathematical expressions are equal.
The denominator would have to be 24.
That would make the fractions 3/24 and 8/24.
If you added them together, it would not be able to simplify to 1/2.
Casey is correct.
-4 1/2 + 6 3/4 = 2 1/4 is correct
because 4 - 6 = 2.
In order to make the fractions have the same denominator, you would have to multiply -1/2 by 2 on both numerator and denominator which would equal -2/4.
Now add -2/4 and 1/4 and you get 1/4.
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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
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
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 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
...............................
Answer:
[tex]2 \sqrt{10} [/tex]Option C is the correct option.
Step-by-step explanation:
√ 8 • √ 5
Calculate the product
[tex] = \sqrt{40} [/tex]
Simplify the radical expression
[tex] = \sqrt{2 \times 2 \times 10} [/tex]
[tex] = 2 \sqrt{10} [/tex]
Hope this helps...
Best regards!!
Twenty increased by the product of four and a number is equal to thirty-two. Find the number.
Answer:
the number would be 3 because you start at 20 and then 4 times something will make 32 so 3 times 4 equals 12 and 20 plus 12 equals 32.
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:
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
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.
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:
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!
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
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
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
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
which graph represents exponential decay
Answer:
1
Step-by-step explanation:
Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the end, Daniel had 92 more stickers than Elle. How many stickers did Daniel have at first? (please refrain from using algebra to solve this question as this is a primary 6 question thanks.)
Answer:
Daniel had 108 stickers at first
Step-by-step explanation:
Number of Daniel's stickers = d
Number of Elle's stickers = e
Since Daniel had 80 more stickers than Elle, d = 80 + e
e = d - 80
Daniel gave 1/4 of his stickers to Elle, Daniel is left with (d - d/4) = 3d/4
Elle now has e + d/4 = d - 80 + d/4 = (5d/4) - 80 = (5d - 320)/4
Elle now gave 3/5 of her remaining stickers to Daniel:
Elle now has:
[tex]e_{new} = \frac{5d -320}{4} - \frac{3}{5} * \frac{5d -320}{4}\\\\e_{new} = \frac{5d -320}{4} - \frac{15d -960}{20}\\\\e_{new} = \frac{25d - 1600 - 15d + 960}{20} \\\\ e_{new} = \frac{10d-640}{20}[/tex]
Daniel now has:
[tex]d_{new} = \frac{3d}{4} + \frac{3}{5} (\frac{5d - 320}{4} )\\d_{new} = \frac{3d}{4} + \frac{15d - 960}{20} \\d_{new} = \frac{30d - 960}{20}[/tex]
Daniel now had 92 more stickers than Elle
[tex]d_{new} = E_{new} + 92[/tex]
[tex]\frac{30d - 960}{20} = \frac{10d - 640}{20} + 92[/tex]
Multiply through by 20
30d - 960 = 10d - 640 + 1840
20d = -640 + 1840 + 960
20 d = 2160
d = 2160/20
d = 108
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]
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% .
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Which of these workers is paid less than the minimum hourly wage? Bartender Electrician Hotel Manager Plumber
Answer:
It's A, the bartender
Step-by-step explanation:
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
First solve for y in [tex]2x - 3y \le 12[/tex] to get [tex]y \ge \frac{2}{3}x-4[/tex]. The inequality sign flips because we divided both sides by a negative value.
To graph [tex]y \ge \frac{2}{3}x-4[/tex] we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).
Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in [tex]y \ge \frac{2}{3}x-4[/tex].
---------------
As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.
---------------
After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.
Answer: Choice CThe graph is image 2. (last option)
We first draw the lines 2x - 3y = 12 and y=-3. Image 1.
For 2x - 3y ≤ 12
or, 2x - 12 ≤ 3y
or, 3y ≥ 2x - 12
or, y ≥ (2x - 12)/3
we shade upwards.
For y < - 3 we shade below.
So the graph is image 2.
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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
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!
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
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
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 hours. What was the average rate of speed for the trip?
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
--------------------------------------------------------
Edit: Thanks to Chegsnut36 for calculation correction
Answer:
≅45.29
Step-by-step explanation:
Hey there!
To find the average rate speed we need to add all the same number.
188 + 197 = 385
4 + 4.5 = 8.5
Now to find the average rate we do,
385 ÷ 8.5 ≅ 45.29
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