Answer:
1/24
Step-by-step explanation:
In the above question, we are asked to solve for:
start fraction, 3, divided by, 8, end fraction, divided by, 9, equals
Mathematically, this is represented as:
(3/8) ÷ 9
= (3/8) × 1/9
= 3/72
= 1/24
Therefore, start fraction, 3, divided by, 8, end fraction, divided by, 9, equals 1/24
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:
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 :)
You have 0.895 m of ribbon to hang the “Grand Opening” sign. You need 100 cm to hang it correctly. Do you have enough ribbon? If not,how much more do you need?
Answer:
no you need 10.5cm
Step-by-step explanation:
so convert 0.895m to cm by multiplying it by 100 to get 89.5 which is less
so take the required 100-89.5
Subtraction is a mathematical operation. The ribbon is not enough. 10.5 cm of ribbon is more needed.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
It is known that 1 meter is equal to 100cm, therefore, the length of the ribbon will be equal to,
[tex]\rm 1\ m =100\ cm\\\\0.895\ m = 0.895 \times 100 = 89.5\ cm[/tex]
Now, as the ribbon needed is 100 cm, therefore, the length of ribbon that is needed more is
[tex]\rm \text{length of the ribbon needed} = 100\ cm - 89.5\ cm = 10.5\ cm[/tex]
No, the ribbon is not enough. 10.5 cm of ribbon is more needed.
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How do I solve: 2 sin (2x) - 2 sin x + 2√3 cos x - √3 = 0
Answer:
[tex]\displaystyle x = \frac{\pi}{3} +k\, \pi[/tex] or [tex]\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi[/tex], where [tex]k[/tex] is an integer.
There are three such angles between [tex]0[/tex] and [tex]2\pi[/tex]: [tex]\displaystyle \frac{\pi}{3}[/tex], [tex]\displaystyle \frac{2\, \pi}{3}[/tex], and [tex]\displaystyle \frac{4\,\pi}{3}[/tex].
Step-by-step explanation:
By the double angle identity of sines:
[tex]\sin(2\, x) = 2\, \sin x \cdot \cos x[/tex].
Rewrite the original equation with this identity:
[tex]2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0[/tex].
Note, that [tex]2\, (2\, \sin x \cdot \cos x)[/tex] and [tex](-2\, \sin x)[/tex] share the common factor [tex](2\, \sin x)[/tex]. On the other hand, [tex]2\sqrt{3}\, \cos x[/tex] and [tex](-\sqrt{3})[/tex] share the common factor [tex]\sqrt[3}[/tex]. Combine these terms pairwise using the two common factors:
[tex](2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0[/tex].
Note the new common factor [tex](2\, \cos x - 1)[/tex]. Therefore:
[tex]\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0[/tex].
This equation holds as long as either [tex]\left(2\, \sin x + \sqrt{3}\right)[/tex] or [tex](2\, \cos x - 1)[/tex] is zero. Let [tex]k[/tex] be an integer. Accordingly:
[tex]\displaystyle \sin x = -\frac{\sqrt{3}}{2}[/tex], which corresponds to [tex]\displaystyle x = -\frac{\pi}{3} + 2\, k\, \pi[/tex] and [tex]\displaystyle x = -\frac{2\, \pi}{3} + 2\, k\, \pi[/tex].[tex]\displaystyle \cos x = \frac{1}{2}[/tex], which corresponds to [tex]\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi[/tex] and [tex]\displaystyle x = -\frac{\pi}{3} + 2\, k \, \pi[/tex].Any [tex]x[/tex] that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:
[tex]\displaystyle x = \frac{\pi}{3} + k \, \pi[/tex] (from [tex]\displaystyle x = -\frac{2\,\pi}{3} + 2\, k\, \pi[/tex] and [tex]\displaystyle x = \frac{\pi}{3} + 2\, k \, \pi[/tex], combined,) as well as[tex]\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi[/tex].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.
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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A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people.
If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
a. Different sample proportions would result each time, but for sample size 100 they would be centered (have their mean) at the true population proportion, whereas for sample size 900 they would not.
b. For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be 0.
c. Different sample proportions would result each time, but for sample size 900 they would be centered (have their mean) at the true population proportion, whereas for sample size 100 they would not.
d. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
answer:
choice letter b
What the answer now fast
Answer:
45°
Step-by-step explanation:
This is right triangle with equal legs of √31
Since two sides are equal and the angle between them is 90°, other angles are equal and their value is:
(180°- 90°)/2= 45°Answer is m∠V= 45°
Mr. Johnson has $15,000 to invest. Part of it is put in the bank at 4 percent, and part he puts in a savings and loan at 7 percent. If his yearly (simple) is $951, how much did he invest at each rate?
Answer:
$3300 at 4%
$11700 at 7%
Step-by-step explanation:
Total investment = $15000
Total simple interest on investment = $951
Investment A:
Rate = 4% =0.04
Investment B:
Rate = 7% =0.07
Simple interest (S. I) = principal * rate * time
(S. I on investment A + S. I on investment B)
Let principal amount in investment A = A
principal amount in investment B = B
(A * 0.04 * 1) + (B * 0.07 * 1) = $951
0.04A + 0.07B = $951 - - - - (1)
A + B = $15000 - - - - (2)
from (2)
A = 15000 - B
Substitute A = 15000 - B into (1)
0.04(15000 - B) + 0.07B = 951
600 - 0.04B + 0.07B = 951
600 + 0.03B = 951
0.03B = 951 - 600
0.03B = 351
B = 351 / 0.03
B = $11700
From (2)
A + B = $15000
A + $11700 = $15000
A = $(15000 - 11700)
A = $3300
A rectangular tank with a square base, an open top, and a volume of 10,976 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.
Answer:
Dimensions to minimize surface are is 28 ft x 28 ft x 14 ft
Step-by-step explanation:
The Volume of a box with a square base of say;x cm by x cm and height
h cm is;
V = x²h
Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.
The formula for the surface area of the box described is given by;
A = x² + 4xh
However, we need A as a function of
only x, so we'll use the formula;
V = x²h
V = x²h = 10,976 ft³
So,
h = 10976/x²
So,
A = x² + 4x(10976/x²)
A = x² + 43904/x
So, to minimize the area, it will be at dA/dx = 0.
So,
dA/dx = 2x - 43904/x² = 0
Factorizing out, we have;
2x³ = 43904
x³ = 43904/2
x³ = 21952
x = ∛21952
x = 28 ft
since, h = 10976/x²
h = 10976/28² = 14 ft
Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft
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:
how many unique planes can be determined by four noncoplanar points?
Answer:
Four unique planes
Step-by-step explanation:
Given that the points are non co-planar, triangular planes can be formed by the joining of three points
The points will therefore appear to be at the corners of a triangular pyramid or tetrahedron such that together the four points will form a three dimensional figure bounded by triangular planes
The number of triangular planes that can therefore be formed is given by the combination of four objects taking three at a time as follows;
₄C₃ = 4!/(3!×(4-3)! = 4
Which gives four possible unique planes.
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
please heLp :’) thank you
Answer:
A
Step-by-step explanation:
Just like in the last problem, we have a right triangle but in this case, x is a leg, 10 / 2 = 5 is the other leg, and 13 is the hypotenuse. Using the 5 - 12 - 13 Pythagorean Triple, we know that x = 12.
Nine less than five times a number is three more than twice the number?
Answer:
x = 4
Step-by-step explanation:
5x-9 = 2x+3
3x = 12
x = 4
Answer:
4
Step-by-step explanation:
12 miles below sea level
Answer:
In terms of figures, up to 12 nautical miles (22 km) from the coast, the sea belongs to the coastal state. In these territorial waters, anyone who fishes, finds an object or even an offense must submit to its laws. The coastal state can even suspend the right of a foreign country to navigate there
Step-by-step explanation:
The integer 12 can be written as -12 for 12 miles below sea level the answer is -12.
What is the number?A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
An integer can be defined as a whole number it can be a negative whole number or a positive whole number for example: 2, 4, 1, -8, 0, etc.
It is given that:
The integer number is 12
Thus, the integer 12 can be written as -12 for 12 miles below sea level the answer is -12.
Write an integer for the situation: 12 miles below sea level
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[4 + (3 – 1)]3 = ? A. 12 B. 32 C. 64 D. 128 E. 216
Answer:
18
Step-by-step explanation:
Answer:
18.
Step-by-step explanation:
[4 + (3 - 1)] * 3
= (4 + 2) * 3
= 6 * 3
= 18
Hope this helps!
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
Find the missing angle measures in the given rhombus.
Answer:
1 = 4 = 38°, 2 = 3 = 90°
Step-by-step explanation:
Because the diagonals of rhombi are perpendicular, ∠2 = ∠3 = 90°. Since the sum of angles in a triangle is 180°, ∠1 = 180° - 52° - 90° = 38°. If we look at the triangle with 1 and 4 as its base angles, we notice that it's an isosceles triangle, therefore ∠1 = ∠4 = 38°.
Answer:
Step-by-step explanation:
In rhombus, diagonals are perpendicular to each other.
∠2 = ∠3 = 90°
52° + ∠1 + ∠ 2 = 180° { Angle sum property of triangle}
52 + ∠1 + 90 = 180
∠1 + 142 = 180
∠1 = 180 - 142
∠1 = 38°
∠4 = ∠1 = 38° { Isosceles triangle}
What is the coefficient of the second term in the expression 12x+xy-7y?
Answer:
1
Step-by-step explanation:
Which of the following options have the same value as 15 percent of 20?
Answer: A, C, D
(3/20)*20 = 0.15*20 = 3
0.15*20 = 3
(15/100)*20 = 0.15*20 = 3
all expressions lead to the same result of 3
another thing to notice
3/20 = 15/100 = 0.15 = 15%
which are multiple ways to say the same thing just in a different form
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:
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 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]
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
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.
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
WILL MARK BRAINLIEST
Answer:
A
Step-by-step explanation:
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds out he is off course and 160 miles from island B. What bearing should he turn to, so he is heading to island B?
CHECK THE COMPLETE QUESTION BELOW
Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?
A. 111.65
B. 119.84
C. 21.65
D. 135.53
Answer:
OPTION A IS CORRECT
A. 111.65
Step-by-step explanation:
This question can be explained using a triangle, let us say triangle ABD
and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .
We will be making use of cosines rule to calculate our angles, and we know that from cosine rule
D² = a² + b² -2abCosD
Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles
250²= 60² + 260² - 2(160*260)Cos(D)
62500= 625600+ 67600- 83200CosD
83200CosD= 25600+ 67600 - 625600
83200CosD= 30700
CosD= 30700/83200
CosD= 0.369
D= cos⁻¹ (0.369)
D=68.35
Therefore, the angle inside the triangle is 68.35°
Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )
Then the angle he would turn will be external angle of the triangle - 68.35°
= (180 - 68.35)
= 111.65°
Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.