The arc length of a 330° sector is 33π. Find the area of the sector
The area of the sector is 297π units squared.
How to find the area of a sector?The arc length of a 330° sector is 33π. Therefore, let's find the area of the sector.
Let's find the radius of the circle.
length of arc = ∅/ 360 × 2πr
where
∅= central angler = radiusTherefore,
33π = 330 / 360 × 2π × r
cross multiply
660πr = 11880π
divide both sides by 660π
r = 11880π / 660π
r = 18 units
Therefore,
area of the sector = 330 / 360 × π × 18²
area of the sector = 106920 / 360 π
area of the sector = 297π units²
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Question: 4/8
Mr. Oswald, the head of human resources, has
been in the company for 24 years, which
corresponds to three times as many as the
number of years Mrs. Bright, the finance
director, is also employed there.
Considering neither of them leaves their jobs,
how many years will Mr. Oswald have worked for
the company when that corresponds to twice as
many as Mrs. Bright's number of years there?
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.
The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.
So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.
Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.
Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.
Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.
16 more years - 24 years = -8 years.
The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.
Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.
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On January 1 2019, a company reported assets of $1500000 and liabilities of $700000. During 2019, assets decreased by $100,000 and stockholders equity decreased $200,000. What is the amount of liabilities at December 31 2019? Enter your answer to the nearest whole number
The amount of liabilities at December 31, 2019, is $900,000.
To determine the amount of liabilities at December 31, 2019, we can use the accounting equation:
Assets = Liabilities + Stockholders' Equity
Given that the company reported assets of $1,500,000 and liabilities of $700,000 on January 1, 2019, we can set up the equation as follows:
$1,500,000 = $700,000 + Stockholders' Equity
During 2019, assets decreased by $100,000, so the new value of assets at December 31, 2019, would be $1,500,000 - $100,000 = $1,400,000.
Stockholders' equity decreased by $200,000, so the new value of stockholders' equity at December 31, 2019, would be $700,000 - $200,000 = $500,000.
Now we can substitute these values into the accounting equation to solve for liabilities:
$1,400,000 = Liabilities + $500,000
Rearranging the equation, we find:
Liabilities = $1,400,000 - $500,000
Liabilities = $900,000
Therefore, the amount of liabilities at December 31, 2019, is $900,000.
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This week laptops are 25% off the original price. If the original price of a laptop was $300, what is the new sale price?
Answer:
$255
Step-by-step explanation:
25% in decimal form is 0.25
300 x 0.25 = 75
25% off means 300 - 75 = 255
answer is $255
a prime number that is between 48 and 58
Answer:
53 is prime. How are you in collage?
A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.
Rachel has discovered the perfect recipe for icing that she wants to put on top of her cinnamon buns. The recipe calls for 5 tablespoons (tbsp) of sugar for every 2 teaspoons (tsp) of milk. Rachel already made her cinnamon buns and is ready to put on the icing. She has 7 teaspoons of milk for her next batch. How many tablespoons of sugar does she need?
Answer:
Step-by-step explanation:
Rachel already has 7 teaspoons of milk.
so 7 x 5 = 35
So Racheal will need 35 teaspoons of surger.
Identify a situation that would fit into this scenario and explain how would you organize this calculation to solve it without a calculator. Assume a 5% sales tax rate. For full credit, you will need the cost of the it, an explanation of how you would calculate the sales tax and the total cost.
You would add the sales tax amount to the cost of the meal to get the total cost. In this case, the sales tax amount is $1, so the total cost would be $26.
One situation that would fit into this scenario is calculating the total cost of a meal at a restaurant that costs $25. Firstly, to calculate the sales tax, you would need to convert the percentage of sales tax into a decimal.
In this case, the sales tax rate is 5%, so you would convert it to 0.05.Next, you would multiply the cost of the meal by the sales tax rate to calculate the sales tax amount.
To do this calculation without a calculator, you can use mental math or estimation techniques.For example, you could estimate 5% of $25 by breaking the 5% into a 1% and 4% calculation.
To calculate 1%, you would simply move the decimal point two places to the left, which gives you $0.25. Then, to calculate 4%, you could multiply $0.25 by 4, which equals $1.
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Answer is option a, c, d
Ik it may seem like too easy question but how option C is answer since vector depend on both magnitude and 'direction' T-T
Won't direction will change?
The value of a scalar does not depend on the orientation.
The magnitude of a vector does not depend on the orientation of the axes.
(a) The value of a scalar does not depend on the orientation of the axes. Scalar is a quantity that has only magnitude and no direction, so it is independent of the coordinate system. Examples of scalars include temperature, mass, and time.
(b) Component of a vector depends on the orientation of the axes. If the coordinate axes are rotated or shifted, the components of a vector will change accordingly.
(c) A vector depends on the orientation of the axes. A vector has both magnitude and direction and changes when the orientation of the axes is changed.
(d) The magnitude of a vector does not depend on the orientation of the axes. The magnitude of a vector is defined as the length of the vector, which is independent of the coordinate system. For example, the magnitude of a velocity vector is the speed, which is the same regardless of the orientation of the axes.
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The vertices of △JKL are J(−3, −2), K(1, 4), and L(4, 2). Find the vertices of the image of △JKL under the dilation centered at the origin with scale factor 5.
J′ = (
,
)
K′ = (
,
)
L′ = (
,
)
The vertices of the image triangle △JKL under the dilation centered at the origin with a scale factor of 5 are:
J′ = (−15, −10)
K′ = (5, 20)
L′ = (20, 10)
To find the vertices of the image of triangle △JKL under the dilation centered at the origin with a scale factor of 5, we need to multiply the coordinates of each vertex by the scale factor.
Let's apply the dilation to each vertex:
J(−3, −2) → J′ [tex]= (5 \times -3, 5 \times -2)[/tex] = (−15, −10)
K(1, 4) → K′ [tex]= (5 \times 1, 5 \times 4)[/tex] = (5, 20)
L(4, 2) → L′ [tex]= (5 \times 4, 5 \times 2)[/tex] = (20, 10)
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Can someone answer this question
Answer: 4th one is the correct one
Step-by-step explanation:
Last year, the Ross family spent $3,336 for electricity. They are opting to use balanced billing for next year. What will their monthly payment be?
Using balanced billing, the monthly payment is $278
What will be their monthly payment?Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.
Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:
Monthly payment = Total cost / Number of months
Monthly payment = $3,336 / 12
Monthly payment = $278
Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.
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Multiply using the Vertical Method: (x+4)(2x^2−3x+5).
Using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
What is vertical multiplication?
In vertical multiplication, the numbers to be multiplied are placed vertically over one another with their least significant digits aligned.
The top number is named the multiplicand and the lower number is the multiplier. The result of the multiplication is the product.
The given expressions;
(x+4)(2x² −3x+5).
We will multiply as follows;
2x² - 3x + 5
× x + 4
_________________
2x² - 3x + 5 (Multiply by x)
+ 8x² - 12x + 20 (Multiply by 4)
_________________
10x² - 15x + 25
Thus, using vertical method, the multiplication of (2x² −3x+5). by x + 4 is determined as 10x² - 15x + 25.
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Find the slope of the line through the points (4, 8) and (5, 10).
A. -1/2
B. 2
C. 1/2
D. -2
Answer:
2, answer choice B
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1).
You are given points (4,8) and (5,10).
slope = (8-10)/(4-5)
slope = (-2)/(-1)
slope = 2
Find the inverse of y = log₂x
Answer: 2ˣ = y
Step-by-step explanation:
In order to find the inverse of any function, switch the x and the y, then solve for y.
y = log₂x >swap/switch variables and solve for y
x = log₂y >rewrite in exponential form
2ˣ = y
7. Mark wants to put a circular swimming
pool in his backyard. The base of the
pool has an area of 615.44 square feet,
and the rectangular section of the
yard where he wants to put the pool is
25 feet by 35 feet. Use this information
to answer Parts A and B.
Yes, the circular pool will fit into the rectangular section of the yard.
Part A: Given that, the base of the pool has an area of 615.44 square feet.
We know that, the area of a circle is πr².
Here, πr²=615.44
3.14r²=615.44
r²=615.44/3.14
r²=196
r=14 feet
Therefore, the diameter is 14×2=28 feet
Part B: The rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet.
Area of a rectangular section = Length×Breadth
= 25×35
= 875 square feet
Yes, the circular pool will fit into the rectangular section of the yard.
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"Your question is incomplete, probably the complete question/missing part is:"
Mark wants to put a circular swimming pool in his backyard. The base of the pool has an area of 615.44 square feet, and the rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet. Use this information to answer Parts A and B.
Part A: What is the diameter of the swimming pool?
Part B: Will the pool fit in the rectangular section of the yard?
Can I have answers for 2 a b c and d
Using the centimeter ruler:
a. 1 ÷ 1/10 and 4 ÷ 1/10 are 10 and 40b. multiplying by reciprocalc. 18 ÷ 1/10 is 180d. 4 ÷ 2/10 and 4 ÷ 8/10 are 20 and 5.For the quotients:
a. 50b. 16²/₃c. 5⁵/₉How to determine measurement?2.a. To find 1 ÷ 1/10, divide 1 by the fraction 1/10. Dividing by a fraction is the same as multiplying by its reciprocal, rewrite the problem as 1 × 10/1, which simplifies to 10. Therefore, 1 ÷ 1/10 = 10.
To find 4 ÷ 1/10, divide 4 by the fraction 1/10. Again, rewrite the problem as 4 × 10/1, which simplifies to 40. Therefore, 4 ÷ 1/10 = 40.
b. To find each quotient, we used the fact that dividing by a fraction is the same as multiplying by its reciprocal.
c. Following the same pattern, find 18 ÷ 1/10 by dividing 18 by 1/10. This is the same as multiplying 18 by the reciprocal of 1/10, which is 10/1. Therefore, 18 ÷ 1/10 = 180.
d. To find 4 ÷ 2/10, divide 4 by 2/10. Rewrite the problem as 4 × 10/2, which simplifies to 20. Therefore, 4 ÷ 2/10 = 20.
To find 4 ÷ 8/10, divide 4 by 8/10. Rewrite the problem as 4 × 10/8, which simplifies to 5. Therefore, 4 ÷ 8/10 = 5.
3. a. To divide 5 by 1/10, Rewrite the problem as 5 × 10/1, which simplifies to 50. Therefore, 5 ÷ 1/10 = 50.
b. To divide 5 by 3/10, Rewrite the problem as 5 × 10/3, which simplifies to 16 2/3. Therefore, 5 ÷ 3/10 = 16²/₃.
c. To divide 5 by 9/10, Rewrite the problem as 5 × 10/9, which simplifies to 5 5/9. Therefore, 5 ÷ 9/10 = 5⁵/₉.
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6 sinθ=5 to the nearest 0.1°
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
need help with two part edulastic question
(4,2)
I
5
(x, y)
Given that the circle to the left has a center at
point (4,2), and point (x, y) is on the
circle,write the equation for the distance (x, y)
is away from the center. Rearrange this
equation so it contains no radicals.
The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²
What is the general form of the equation of a circle?The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a
The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.
The coordinates of the center of the circle, (h, k) = (4, 2)
The radius of the circle, r = a = 5
The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;
Equation of a circle; (x - h)² + (y - k)² = a²
Equation from the center; (x - 4)² + (y - 2)² = 5²
Where;
5 = The radius, a = The distance from the center of the circle
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
The value of x will be 16.
Given ,
Parallelogram with two sides:
side 1 = 3x + 20
side 2 = 5x - 12
In parallelogram the opposite side are equal and parallel.
Thus,
side 1 and side 2 will be equal and parallel.
Equating both sides to get the value of x,
3x + 20 = 5x - 12
x = 16
Hence the value of x can be found out by property of parallelogram.
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Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One-half of the commission goes to the broker, and one-half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Answer:
Danielle Stevenson receives $2,600 from selling the $160,000 house.
Step-by-step explanation:
To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:
Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.
Commission = 0.065 * $160,000 = $10,400.
Determine the broker's share: Broker Share = 0.5 * Commission.
Broker Share = 0.5 * $10,400 = $5,200.
Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.
Remaining Amount = $10,400 - $5,200 = $5,200.
Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.
Salesperson Share = 0.5 * $5,200 = $2,600.
Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.
Amount Danielle Receives = $5,200 - $2,600 = $2,600.
Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.
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1. If an object has a mass of 12kg, it has a weight of
Answer:
weight = gxg = 12kg to g = 0.12 and then using formula we get 0.12x0.12 = 1.44 is the weight
Step-by-step explanation:
Answer:
Therefore, the weight of the object is approximately 117.72 Newtons.
Step-by-step explanation:
The weight of an object is given by the formula:
weight = mass x acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.81 m/s².
So, the weight of an object with a mass of 12 kg is:
weight = 12 kg x 9.81 m/s² = 117.72 N
Therefore, the weight of the object is approximately 117.72 Newtons.
help me solve my math
Answer:
653.3 bacteria
Step-by-step explanation:
A continuously growing population of bacteria is modeled by the function:
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
where:
[tex]P(t)[/tex] is the population after [tex]t[/tex] time periods[tex]P_0[/tex] is the initial population[tex]r[/tex] is the relative rate of growthIn this problem, we are given the following values:
[tex]P_0 = 484 \text{ bacteria}[/tex][tex]r = 15\% = 0.15[/tex][tex]t = 2[/tex]We can plug these into the function to solve for [tex]P(2)[/tex].
[tex]P(t) = P_0 \cdot e^{rt}[/tex]
[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]
[tex]P(2) = 484 \cdot e^{0.3}[/tex]
Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.
[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]
What is the volume of this
rectangular pyramid?
6 ft
8.4 ft
8.6 ft
The volume of the rectangular pyramid is 144.48 cubic feet.
What is a rectangular pyramid?A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.
The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.
The volume of a rectangular pyramid is given as:
[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]
[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]
[tex]\sf V = \dfrac{433.44 }{3}[/tex]
[tex]\sf V = 144.48 \ cubic \ feet[/tex].
Hence, the volume of the rectangular pyramid is 144.48 cubic feet.
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Two forces of 5N and 12N act at right angles to each other. Use a graph paper to determine the magnitude and direction of the resultant force graphically. State the scale you use to represent each vector. You will need a protractor to measure the angle the resultant makes with the 5N force.
The resultant of the force that acts in opposite directions is 7 N.
We have,
We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.
By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.
We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;
Let the +B force be 12 N
Let the -B force be 5N
12 N - 5 N = 7 N
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please helpppppppppppppppppppppppppppppppppppppppp
Answer:
Step-by-step explanation:
It's c
-4 1/6
Plug in the number for a and you get -2 1/3 - 11/6
make the first number into a fraction, so -7/3
-7/3 - 11/6
common denominator, so, -14/6 - 11/6, which equals -25/6
simplify: -4 1/6
Hope that helps!
Answer:
The answer is
[tex] \frac{ - 25}{6} [/tex]
-4⅙
Step-by-step explanation:
[tex]a - \frac{ - 11}{6} [/tex]
[tex]a = - 2 \times \frac{1}{3} [/tex]
[tex] \frac{ - 7}{3} - \frac{ - 11}{6} [/tex]
[tex] = \frac{ - 25}{6} [/tex]
What the surface area
Step-by-step explanation:
the surface area is the sum of all areas of the individual outside faces/sides.
so, what do we see here, what outside sides do we have here ?
of course, we have to assume that this is a regular object (left and right sides are the same).
2 right-angled triangles (left and right).
1 rectangle in the back.
1 rectangle at the bottom.
1 times rectangle in the front.
the area of a right-angled triangle is
leg1 × leg2 / 2
in our case that is
6 × 2.5 /2 = 3 × 2.5 = 7.5 mm²
we have 2 of these triangles :
2×7.5 = 15 mm²
the area of the rectangle in the back is
8 × 6 = 48 mm²
the area of the rectangle at the bottom is
8 × 2.5 = 20 mm²
the area of the rectangle in the front is
8 × 6.5 = 52 mm²
the surface of the object is the sum of all that :
15 + 48 + 20 + 52 = 135 mm²
here is my algebra 13 homework, can someone please help me fast! Quick!!
The function h(x) = (2ˣ) + 1 does not have an x intercept.
A function has an x-intercept when the value of the function is equal to zero at some point on the x-axis.
(a) f(x) = -x + 2 is a linear function with a negative slope (-1) and a y-intercept of 2.
To find the x-intercept, we set f(x) equal to zero and solve for x:
0 = -x + 2
x = 2
Therefore, the function f(x) has an x-intercept at (2, 0).
(b) g(x) = -(x²) is a quadratic function that opens downward and has a vertex at (0, 0).
To find the x-intercept, we set g(x) equal to zero and solve for x:
0 = -(x²)
x²= 0
x = 0
Therefore, the function g(x) has an x-intercept at (0, 0).
(c) h(x) = (2ˣ) + 1 is an exponential function
To find the x-intercept, we set h(x) equal to zero and solve for x:
0 = (2ˣ) + 1
-1 = 2ˣ
However, there is no real value of x that satisfies this equation.
h(x) = (2ˣ) + 1 has no x intercept.
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need help with edualastic question answer a b c or d
the amount of cubic feet(Volume) the tent can hold is 165 ft³.
What is volume?Volume is the space occupied by an object.
To caculate the amount of cubic feet(Volume), the tent can hold, we use the formula below.
Formula:
V = bhL/2..................... Equation 1Where:
V = Volume of the tenthb = Base of the triangleh = Height of the triangleL = Height of the tentFrom the question,
Given:
b = 5 fth = 6 ftL = 11 ftSubstitute these values into equation 1
V = 5×6×11/2V = 165 ft³Hence, the right option is (A) 165 ft³.
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x^2 -5x + 29 = 8x -6
Answer:
Step-by-step explanation:
x²-5x+29=8x-6
x²-13x+35=0
[tex]x=\frac{13 \pm\sqrt{(-13)^2-4(1)(35)} }{2(1)} \\x=\frac{13 \pm\sqrt{169-140} }{2} \\x=\frac{13 \pm\sqrt{29} }{2}[/tex]