Answer: 280 tons
Step-by-step explanation: divide all at tons/pound which accumulated to 280 tons
Answer: 10 ships
Step-by-step explanation:
Cheryl earns (p+3) dollars per hour. In 8 hour she earns ___ dollars.
Answer:
8p + 24 dollars
Step-by-step explanation:
1 hour = (p+3)
8 hours = 8 (p+3)
=> 8p + 24
In 8 hours, Cheryl earns 8p + 24 dollars.
Answer:
[tex]\boxed{8p + 24}[/tex]
Step-by-step explanation:
Hey there!
Well if Cheryl earns p + 3 per hour and it is asking us to find the amount made in 8 hours, we can make the following,
8(p + 3)
8*p = 8p
8*3 = 24
Together,
8p + 24
Hope this helps :)
A wooden jewelry box has the shape of a prism with a regular hexagonal base of 85.3 in2. The sides of the hexagonal base are all 5.73 inches. If the height of the box is 18.10 inches, what is the surface area of the wood used to make the jewelry box?
Answer:
792.9 in²
Step-by-step Explanation:
Given:
Area of the base of the regular hexagonal prism box (B) = 85.3 in²
Each side length of hexagonal base (s) = 5.73 in
Height of prism box (h) = 18.10 in
Required:
Surface area of the wood used in making the hexagonal prism box
SOLUTION:
Surface area for any given regular prism can be calculated using the following formula: (Perimeter of Base × height of prism) + 2(Base Area)
Perimeter of the hexagonal base of the prism box = 6(5.73) (Note: hexagon has 6 sides.)
Perimeter of base = 34.38 in
Height = 18.10 in
Base area is already given as 85.3 in²
Surface area of the hexagonal prism box [tex] = (34.38*18.10) + 2(85.3) [/tex]
[tex] = 622.278 + 170.6 = 792.878 in^2 [/tex]
Surface area of the wood used in making the jewelry box ≈ 792.9 in²
The width of a rectangle measures (8.3c-8.4d)(8.3c−8.4d) centimeters, and its length measures (5.3c+4.8d)(5.3c+4.8d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answer:
P = 27.2c-7.2d
Step-by-step explanation:
It is given that,
The width of a rectangle is (8.3c-8.4d)
The length of a rectangle is (5.3c+4.8d)
The perimeter of a rectangle is equal to the sum of its all sides i.e.
P = 2(l+b)
P = 2(8.3c-8.4d+5.3c+4.8d)
P = 2[(8.3c+5.3c)+(4.8d-8.4d)]
P = 2(13.6c-3.6d)
⇒P = 27.2c-7.2d
Hence, the expression that represents the perimeter of the rectangle is 27.2c-7.2d.
find the area of a sector with a central angle of 150 and a diameter of 7.8 cm
Answer:
19.9 cm²
Step-by-step explanation:
The following data were obtained from the question:
Angle at the centre (θ) = 150°
Diameter (d) = 7.8 cm
Area of sector =.?
Next, we shall determine the radius.
This can be obtained as illustrated below:
Radius (r) = Diameter (d) /2
r = d/2
Diameter (d) = 7.8 cm
Radius (r) =.?
r = d/2
r = 7.8/2
r = 3.9 cm
Finally, we shall determine the area of the sector as follow:
Angle at the centre (θ) = 150°
Radius (r) = 3.9 cm
Pi (π) = 3.14
Area of sector (A) =.?
A = θ/360 × πr²
A = 150/360 × 3.14 × 3.9²
A = 15/36 × 3.14 × 15.21
A = 19.9 cm²
Therefore, the area of the sector is 19.9 cm²
The tens digit of a two-digit number is three times greater than the ones digit. The difference between twice the original number and half the number obtained after reversing the digits is 108. What is the original number? Show your work.
Answer:
Now solve these two equations.ull get andwer
The original number will be "63".
Let,
The ten's digit be "x".One's digit be "y".The equation will be:
→ [tex]x=y+3[/tex]...(equation 1)
Original number will be:
→ [tex]10x+y[/tex]
then,
→ [tex]2 (10x+y)-\frac{(10y+x)}{2} = 108[/tex]
→ [tex]\frac{4(10x+y)}{1} -(10y+x) = 216[/tex]
→ [tex]40x+4y-10y-x = 216[/tex]
→ [tex]39x-6y=216[/tex]...(equation 2)
By using (equation 1) and (equation 2), we get
→ [tex]39(y+3)-6y=216[/tex]
→ [tex]39y+117-6y=216[/tex]
→ [tex]33y=99[/tex]
→ [tex]y = \frac{99}{33}[/tex]
→ [tex]= 3[/tex]
Now,
[tex]x = y+3[/tex]
[tex]=3+3[/tex]
[tex]=6[/tex]
hence,
The original number will be:
= [tex]10x+y[/tex]
= [tex]10\times 6+3[/tex]
= [tex]60+3[/tex]
= [tex]63[/tex]
Thus the above approach is right.
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helpppppppppppppppp
Express the following English phrase using an algebraic expression.
The product of 12 and a number y.
Represent "The product of 12 and a number y " mathematically.
Answer:
12y
Step-by-step explanation:
product means multiplycation so twelve times y is 12y
If p-1 is a factor of p^4+p^2+p-k,the value of k is ?
[tex]1^4+1^2+1-k=0\\3-k=0\\k=3[/tex]
Answer:
k=3
Step-by-step explanation:
Hello, if p-1 is a factor of
[tex]f(p)=p^4+p^2+p-k[/tex]
it means that f(1)=0, so
1+1+1-k=0
3-k=0
k=3
thank you
need help will give you a good rating us
Answer:
[tex]\boxed{2\pm \frac{\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
[tex]2x^2-8x=-7[/tex]
[tex]\sf Add \ 7 \ on \ both \ sides}.[/tex]
[tex]2x^2-8x+7=-7+7[/tex]
[tex]2x^2-8x+7=0[/tex]
[tex]ax^2 +bx+c=0[/tex]
[tex]\sf Apply \ quadratic \ formula.[/tex]
[tex]a=2 \ \ \ b=-8 \ \ \ c = 7[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-(-8)\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)}[/tex]
[tex]x=\frac{8\pm\sqrt{64-56}}{4}[/tex]
[tex]x=\frac{8\pm\sqrt{8}}{4}[/tex]
[tex]x=\frac{8\pm2\sqrt{2}}{4}[/tex]
[tex]x=2\pm \frac{\sqrt{2}}{2}[/tex]
Add or subtract. Write your answer in scientific notation.
4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5
3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8
8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3
Answer:
1. 38.3 x 10^5
2. 6.67 x 10^9
3. 4.48 x 10^4
Step-by-step explanation:
4.2 X 10 ^6 - 1.2 X 10^5 - 2.5 x 10^5
For the above question, we need to make the exponents equal
=> 42 x 10^5 - 1.2 x 10^5 - 2.5 x 10^5
SInce, all the exponents are equal, we can now add and subtract the normally.
=> (42 - 1.2 -2.5) x 10^5
=> (42 - 3.7) x 10^5
=> 38.3 x 10^5
So, the answer to the 1st question is 38.3 x 10^5
Next question:
=> 3.3 x 10^9 + 2.6 x 10^9 +7.7 x 10^8
=> we need to make the exponents equal
=> 3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9
=> All the exponents are equal, we can now add and subtract the normally.
=> (3.3 + 2.6 + .77) x 10^9
=> 6.67 x 10^9
=> So the answer to the 2nd question is 6.67 x 10^9
Next question,
=> 8 X 10^4 - 3.4 x 10^4 - 1.2 x 10^3
=> we need to make the exponents equal
=> 8 x 10^4 - 3.4 x 10^4 - .12 x 10^4
=> All the exponents are equal, we can now add and subtract the normally.
=> (8 - 3.4 - .12) x 10^4
=> 4.48 x 10^4
=> So the answer to the 3rd question is 4.48 x 10^4
The solutions to the expressions are:
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]=[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex] = [tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex] = [tex]4.48 \times 10^4[/tex]
[tex]4.2 \times 10^6 - 1.2 \times 10^5 - 2.5 \times 10^5[/tex]
Combine like terms:
[tex]4.2 \times 10^6 - (1.2+2.5) \times 10^5[/tex]
[tex]4.2 \times 10^6 - 3.7 \times 10^5[/tex]
[tex]42 \times 10^5 - 3.7 \times 10^5[/tex]
[tex](42-3.7)\times 10^5[/tex]
[tex]38.3\times 10^5[/tex]
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 7.7 \times 10^8[/tex]
Convert all terms with same power:
[tex]3.3 \times 10^9 + 2.6 \times 10^9 + 0.77 \times 10^9[/tex]
[tex](3.3+2.6+0.77) \times 10^9[/tex]
[tex]6.67\times 10^9[/tex]
[tex]8.0 \times 10^4 -3.4 \times 10^4 - 1.2 \times 10^3[/tex]
[tex]8.0 \times 10^4 - 3.4 \times 10^4 - 0.12 \times 10^4[/tex]
[tex](8.0-3.4-0.12) \times 10^4[/tex]
[tex]4.48 \times 10^4[/tex]
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Combine your expressions from part E (x+2) and part F (y+ (-4) to give the pair of coordinates of any point after a translation two yards East and four yards south.
Answer:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Step-by-step explanation:
A transformation is the movement of a point from its initial position to a final position. If an object is transformed all its points are also transformed. Types of transformation are reflection, rotation, translation and dilation.
If a point O(x, y) is translated left by h unit, the new coordinate is O'(x-h, y) while if O(x, y) is translated right by h unit the new coordinate is O'(x+h, y)
If a point O(x, y) is translated up by h unit, the new coordinate is O'(x, y+h) while if O(x, y) is translated down by h unit the new coordinate is O'(x, y-h)
The location of the shape as shown in the diagram is:
A(3, 6), B(3, 3), C(4, 3), D(4, 6)
If the points are translated two yards East and four yards south, it means it is translated 2 unit right and 4 unit down i.e. (x+2, y-4). The new coordinates are:
A'(5, 2), B'(5, -1), C'(6, -1), D'(6, 2)
Answer:
ombining the expressions from parts E and F, for any given initial point (x, y), the coordinates of the new point after a translation of two yards east and four yards south are (x + 2, y + (-4)).
Step-by-step explanation:
this is more simple
which has greater cenetic energy a car traveling 30.0 km/hr or one twice as heavy traveling at 15 km/hr?
Answer:
30 km/h car
Step-by-step explanation:
From analysis the car traveling at 30 km/h has greater kinetic energy
we can deduce it from the expression of kinetic energy which is
[tex]KE=\frac{1}{2} mv^2[/tex]
Assuming the mass m= 1 kg
For the 30 km/h
[tex]KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J[/tex]
For the 15 km/h
[tex]KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J[/tex]
Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE
There are 67 bikes in the bike rack outside a school. Out of all the bikes, 33 are silver. Half of the remaining
bikes are red.
Estimate how many bikes are red.
Answer:
17
Step-by-step explanation:
67 minus 33 leaves 34 red bikes but divided that by half gives you 17
There are approximately 17 red bikes in the bike rack outside the school.
What is Algebra?Algebra is the estimation of mathematical representations, while logic is the manipulation of those symbols.
We can solve this problem by setting up an equation to represent the relationship between the number of bikes in the bike rack, the number of silver bikes, and the number of red bikes.
Let's define a variable, r, to represent the number of red bikes. We know that 33 bikes are silver, so the number of bikes that are not silver is 67 - 33 = 34 bikes.
Half of the remaining bikes are red, so we can say that there are r = 34/2 = 17 red bikes.
Therefore, there are approximately 17 red bikes in the bike rack outside the school.
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The company will be launching a firework from the ground, but you want to increase the time it stays in the air by 2 seconds to build up the suspense. How can the company make this happen without changing the length of the fuse? How will this affect the maximum height of the firework? g(t) = -16t2 + 224t + 120
Answer: find the answer in the explanation.
Step-by-step explanation:
To increase the time the fireworks stays in the air by 2 seconds to build up the suspense, 2 should be added to the time t.
T + 2 = t
T = t - 2
Substitute T for t in the function g(t)
The company will make this happen without changing the length of the fuse by substituting T for t which will lead to
g(t) = -16(t - 2)^2 + 224(t - 2) + 120
How will this affect the maximum height of the firework?
Initially the function is:
g(t) = -16t2 + 224t + 120
Where the time at maximum height is found by using the formula
t = -b/2a
b = 224, a = -16
Substitutes both into the formula
t = -224/2(-16)
t = -224/-32
t = 7
Substitute 7 for t in the first equation
g(t) = -16(7)^2 + 224(7) + 120
g(t) = -16(49) + 224(7) + 120
g(t) = -784 + 1568 + 120
g(t) = 904 metres
But when the time is delayed by 2 seconds in the air, the maximum height will be
g(t) = -16( 7 - 2 )^2 + 224(7 - 2) + 120
g(t) = -16(5)^5 + 224(5) + 120
g(t) = -16(25) + 224(5) + 120
g(t) = -400 + 1120 + 120
g(t) = 840
The effect will surely reduce the maximum height of the fireworks.
A number “x” increased by 5 is 19?
Answer:
x+5=19
Step-by-step explanation:
i think that right let me know...:/
Answer:
x= 14
Step-by-step explanation:
a number x increased by 5, so it will be x + 5 and is in math means equals to so it becomes
x+5=19
19-5=x
14=x
This composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. 2 identical pyramids with rectangular bases are connected at their base. The height of the pyramid is 2. The lengths of the sides of the rectangle are 5 and 0.25 units. Which expression represents the volume, in cubic units, of the composite figure? One-half (One-third (5) (0.25) (2) ) One-half (One-third (5) (0.25) (4) ) 2(One-third (5) (0.25) (2) ) 2(One-third (5) (0.25) (4) )
Answer:
The total volume of the solid is 1.67 cubic units.
Step-by-step explanation:
Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.
1/3 x (area of base) x height
= 1/3 x (5 x 0.25) x 2= 0.833
Therefore, the volume of each pyramid will be
= cubic units.
So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)
Hope it helped ya!
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Tysmm
The total volume of the solid is 1.67 unit³.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Given:
Each pyramid has a height of 2 units.
and the rectangular base with dimensions of 5 units × 0.25 units.
So, the Volume of each Pyramid is
= 1/3 x (area of base) x height
= 1/3 x (5 x 0.25) x 2
= 0.833
and, the total volume of the solid
= (2 × 0.833)
= 1.67 cubic units.
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Can someone answer this please? Okay so it says that something is made 3 times than the other item. The other item uses 13 beads. So, what is 13 times 3?
Answer:
13x3= 39
Step-by-step explanation:
10x3=30
3x3=9
30+9=39
Hope it helps!
find the roots of the following equation X + 1 whole square minus x square equal to 2
Answer:
x = 1/2
Step-by-step explanation:
Let's represent this in a mathematical way,
(x+1)^2 - x^2 = 2
Ok now we expand,
x^2 + 2x + 1 -x^2 = 2
rearrange,
x^2 - x^2 + 2x + 1 = 2
subtract,
2x + 1 = 2
subtract 1 from both sides,
2x + 1 - 1 = 2 - 1
2x = 1
Now divide 2 from both sides and get your answer,
x = 1/2
Answer:
[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]
[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]
[tex]2x + 1 = 2[/tex]
[tex]x = 1 \div 2[/tex]
what are the order of operations for integers ?
Answer:
PEMDAS
Step-by-step explanation:
P - Parentheses (Brackets also!)
E - Exponents
M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).
A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.
i need help. Can u help me solve for x?
Answer:
[tex] x = \sqrt {40}[/tex]
Step-by-step explanation:
Given is an isosceles triangle, dotted line is the bisector of top angle which is also perpendicular bisector of the base of the triangle. Hence, by Pythagoras theorem:
[tex] {x}^{2} = {6}^{2} + ({ \frac{4}{2} })^{2} \\ = 36 + 4 \\ = 40 \\ \therefore \: x = \sqrt{40} \\ [/tex]
Answer:
D. x = sqrt(52).
Step-by-step explanation:
Since the line measuring 6 units bisects the top angle, there are two right angles. We can use the Pythagorean Theorem to solve for x.
a^2 + b^2 = x^2
4^2 + 6^2 = x^2
16 + 36 = x^2
52 = x^2
x = sqrt(52)
x = sqrt(2 * 2 * 13)
x = 2sqrt(13)
x = 7.211102551.
Hope this helps!
Which table represents a function?
Answer:
A
Step-by-step explanation:
it is A for every output y , there is only one input x
Answer:
A
Step-by-step explanation:
Because all the x-intercepts are different. Whereas all the other ones have repeats of numbers in the x-intercepts.
PLEASE help me with this question! No nonsense answers please. This is really urgent.
Answer:
The third option: x= [tex]\frac{8}{3} \pi[/tex]
Step-by-step explanation:
Arc length formula=[tex]\frac{Central Angle}{360} * 2\pi r[/tex]
Arc length = [tex]\frac{120}{360} *2\pi (4)[/tex]
=[tex]\frac{8}{3}\pi[/tex]
find six rational numbers between 3 and 4
Answer:
3.1
3.2
3.3
3.4
3.5
3.6
Hope this answer correct :)
can you make a triangle with 1. 2cm 3cm and 4cm 2. 2cm 3 cm 6 cm 3. 90 degrees 45 degrees 45 degrees 4. 90 degrees 60 degrees 60 degrees?
Answer:
1. 2cm 3cm and 4cm
yes, because 2+3>4
2. 2cm 3 cm 6 cm
no, 2+3<6
3. 90 degrees 45 degrees 45 degrees
yes, 90+45+45 = 180
4. 90 degrees 60 degrees 60 degrees?
no, 90+60+60=210!=180
Raj correctly determined that ray LH is the bisector of AngleGLI. A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I. Which information could he have used to determine this? AngleGLH Is-congruent-to AngleILM mAngleKLM = 5mAngleILM mAngleGLI = 2mAngleGLH mAngleGLI = mAngleGLH + mAngleHLI
Answer: C.) mAngleGLI = 2mAngleGLH
Step-by-step explanation:
Hope it helps!!!
For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.
∠GLI is bisected by LH, hence:
∠GLH = ∠HLI (definition of bisection)
∠GLI = ∠GLH + ∠HLI (angle addition)
∠GLI = 2∠GLH
The information that can be used to determine this is ∠GLI = 2∠GLH
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what are the roots of the quadratic equation below 2x^2+8x+7=0
Answer:
x = -1.29 and -2.71
Step-by-step explanation:
Use the quadratic formula, which is [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex] and [tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-8+\sqrt{8^2-4(2)(7)} }{2(2)}[/tex] and [tex]\frac{-8-\sqrt{8^2-4(2)(7)} }{2(2)}[/tex]
[tex]\frac{-8+\sqrt{8} }{4}[/tex] and [tex]\frac{-8-\sqrt{8} }{4}[/tex]
Further reduced down to:
[tex]\frac{-8+2\sqrt{2} }{4}[/tex] and [tex]\frac{-8-2\sqrt{2} }{4}[/tex]
In decimal form, to the hundredths place, both of these are:
-1.29 and -2.71
Two trains station at the same time one travels east at 8 miles per hour .The other train traveles east at 8 millas per hour the other train travels west at 11 miles per hour in how many hours will the two trains apart
(Will give brainliest to the most explained answer!) Can someone explain how to factor Polynomials. Please explain it like you’re teaching this to a 5 year old. :)
Step-by-step explanation:
Find the Greatest Common Factor (GCF) of a polynomial.
Factor out the GCF of a polynomial.
Factor a polynomial with four terms by grouping.
Factor a trinomial of the form .
Factor a trinomial of the form .
Indicate if a polynomial is a prime polynomial.
Factor a perfect square trinomial.
Factor a difference of squares.
Factor a sum or difference of cubes.
Apply the factoring strategy to factor a polynomial completely
Answer:
See explanation
Step-by-step explanation:
We can factor polynomials by breaking down the expression.
For instance, let's say we have the polynomial [tex]x^2 - 9x + 14[/tex].
We can start solving this because this polynomial is in standard form, meaning that the highest exponents go first. ([tex]ax^2 + bx + c[/tex].)
To factor a polynomial, we are looking for two numbers that:
A. When multiplied, get us [tex]c[/tex] (in this case, 14)
B. When added, get us [tex]b[/tex] (in this case, -9).
If we play around with numbers, looking at the factors of 14, we see that the numbers 7 and 2 might be useful here. They add up to 9 and multiply to be 14.
However, these numbers ADD to be -9, meaning that they both need to be negative.
[tex]-7 + -2 = -9\\-7\cdot-2=14[/tex]
Now that we know our numbers, -7 and -2, we can make these our factors (which are represented by [tex](x + y)[/tex], y being our factor.
So our factors turn out to be [tex](x-7)[/tex] and [tex](x-2)[/tex].
Let me know if you need anything explained more, and I hope this helped!
help me plsssssssssssssssss
Answer:
Step-by-step explanation:
I'm assuming you are trying to solve for x. I'm not sure, but that's what I figured out for the answer, so I'm gonna go with that. : )
We are looking for the value of x to make that statement true. It's going to take some trig manipulations, but if you are at this level of precalc, these identities should definitely NOT be new to you. We will begin by squaring both sides of that equation to get:
[tex]9sin^2(x)+3cos^2(x)=3[/tex]
From here we will factor out a 3 to get:
[tex]3(3sin^2x+cos^2x)=3[/tex] and then divide both sides by 3 to get:
[tex]3sin^2x+cos^2x=1[/tex]
Knowing the Pythagorean identity for the trig ratios, we will replace the sin-squared with what it is equal to in terms of cos-squared. If:
[tex]sin^2x+cos^2x=1[/tex], then
[tex]sin^2x=1-cos^2x[/tex]. Making that replacement gives us an equation with only one trig ratio in it, namely, cos:
[tex]3(1-cos^2x)+cos^2x=1[/tex] and distributing:
[tex]3-3cos^2x+cos^2x=1[/tex] which simplifies down to:
[tex]-2cos^2x=-2[/tex]. Divide both sides by -2 to get:
[tex]cos^2x=1[/tex]. When you take the square root of both sides you get:
[tex]cos(x)=1[/tex] and [tex]cos(x)=-1[/tex]. Here is where we will use the unit circle to see where the cos is 1 and where the cos is -1. You didn't give me an interval in which to work, so I am going to use from 0 degrees to 180. Within that interval, the cos is 1 at 0 degrees; within that interval, the cos is -1 at 180.
Now we need to plug those values into the original equation to see if they work. One of them may be extraneous. Plugging in 0 first:
3sin(0) + √3cos(0) = -√3. We need to see if this is true.
The sin of 0 is 0; the cos of 0 is 1, so
0 + (√3)(1) = -√3?
The left side is √3, not -√3, so 0 doesn't work. Let's try 180 now, shall we?
3sin(180) + √3cos(180) = -√3. We need to see if this is true.
The sin of 180 is 0; the cos of 180 is -1, so
0 + (√3)(-1) = -√3?
The left side is -√3 and so is the right side, so
x = 180°
Write and solve an equation to answer the question. How many people must attend the third show so that the average attendance per show is 3000?
Answer:
3250
Step-by-step explanation:
so for the first and 2nd show, the attendance is 2580 and 2920.
The average of both these numbers is 2750
the if the third show had 3000 people, the average attendance would only be 2875.
We need the average number to be 3000.
2750 is 250 less than 3000, so the other number must be 250 more.
3250 is how many people should go to the last show.
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Explanation:
We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance
average attendance = (sum of individual attendance values)/(number of days)
average attendance = (5500+x)/3
So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.
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We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000
(5500+x)/3 = 3000
5500+x = 3*3000
5500+x = 9000
x = 9000-5500
x = 3500
We need 3500 people to show up on day 3 so that the average of all three days is 3000.
3500 goes in the second box.
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Check:
The figures for the three days are 2580, 2920, and 3500
They add to 2580+2920+3500 = 9000
Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.
Plz ans ASAP! Tysm! Pzlllzzz!
Answer:
Step-by-step explanation:
Number of class intervals = 7
Class width = 5
Class intervals (heights) Frequency (Number of boys)
130 - 135 3
136 - 140 5
141 - 145 3
146 - 150 5
151 - 155 2
156 - 160 1
161 - 165 1
Therefore, frequency table given above will represent the distribution of the heights and number of students.
