The area of sector POR is approximately equal to 68.76 square centimeters, and the perimeter of sector POR is approximately equal to 34.92 centimeters.
How to calculate the length of the arc?In Mathematics, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle is given by:
Length of an arc = 2πr × θ/360
Substituting the given parameters into the formula, the radius of this circle is given by;
12 = 2 × 3.142 × r × 60/360
12 = 2 × 3.142 × r × 1/6
72 = 6.284r
Radius, r = 72/6.284
Radius, r = 11.46 centimeters.
Now, we can calculate the area of sector POR:
Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = πr² × θ/360
Where:
r represents the radius.θ represents the central angle.Substituting the given parameters into the formula, we have;
Area of sector = 3.142 × 11.46² × 60/360
Area of sector = 3.142 × 131.3316 × 1/6
Area of sector = 68.76 square centimeters.
Next, we would calculate the perimeter of sector POR:
Perimeter of sector POR = 2r + Length of an arc
Perimeter of sector POR = 2(11.46) + 12
Perimeter of sector POR = 22.92 + 12
Perimeter of sector POR = 34.92 centimeters.
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The diameter of a sphere is 16.4 mm Calculate the sphere's volume
Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume of the sphere is 2308.4 mm³
Calculating the volume of a SphereFrom the question, we are to determine the volume of the sphere
The volume of a sphere is given by the formula
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the given information,
Diameter, d, of the sphere = 16.4 mm
r = 16.4/2
r = 8.2 mm
∴ [tex]V=\frac{4}{3}\times 3.14 \times 8.2^{3}[/tex]
V = 2308.394
V ≅ 2308.4 mm³
Hence, the volume of the sphere is 2308.4 mm³
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Which expression is equivalent to the following complex fraction? 2-1/y/3+1/y
The equivalent expression to2-1/y/3+1/y is [tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]
What are equivalent expressions?Equivalent expressions are expressions does not look the same but when a value is being replaced with their variable, they end up giving the same result.
From the information given:
We have are to determine the equivalent expression to:
[tex]\mathbf{=\dfrac{(2-\dfrac{1}{y})}{(3+ \dfrac{1}{y})}}[/tex]
So if we multiply both the numerator and the denominator with 1/y, we have:
[tex]\mathbf{=\dfrac{(2y-1)}{(3y+1)}}[/tex]
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How many five digit numbers can be created? pls help will mark brainliest
There are 120 five digit numbers that can be created
How to determine the number of digits?The digits are given as:
2, 3, 5, 7 and 8
Since there are no conditions, and the digits cannot be repeated.
Then the number of digits is:
Digits = 5!
Expand
Digits = 5 * 4 * 3 * 2 * 1
Evaluate
Digits = 120
Hence, there are 120 five digit numbers that can be created
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someone help please, im FAILING summer school like an idiot
Answer:
awnser D is the only function
I need help plsssssssss
Answer:
x = 1
y = -2
Step-by-step explanation:
x = 19 + 9y
3x- 3y = 9
________
3(19+9y)-3y=9
y=-2
x=19+9(-2)
x=1
(1,-2)
Answer:
[tex] - x = - 1 - 9y \\ \frac{ - x}{ - 1} = \frac{ - 1}{ - 1} - \frac{9}{ - 1} \\ x = 1 + 9y...(3) \\ 3(1 + 9y) - 3y = 9 \\ 3 + 27y - 3y = 9 \\ 3 + 24y = 9 \\ 24y = 9 - 3 \\ 24y = 6 \\ \frac{24y}{24} = \frac{6}{24} \\ y = \frac{1}{4} \\ \\ \\ \\ x = 9( \frac{1}{4} ) + 1 \\ x = \frac{9}{4} + 1 \\ x = \frac{13}{4} [/tex]
Step-by-step explanation:
ATTACHED IS THE SOLUTION!
The volume of a cone is 1782 cm³ a cylinder has the same radius and height as the cone what is the volume of the cylinder
Answer:
A
Step-by-step explanation:
cone volume equals
V=π/3r²h
(1782=π/3r²h) multiplied by 3 to get rid of the denominator
5346=πr²h
cylinder v=πr²h by substitution the volume would be the same as cone 5346
Can y’all help this is for Plato !!!!!! PLEASEEE HELP ME
The two real values that are not in the domain of the composition are x = 2 and x = -2.
What two numbers are not in the domain of f°g?
Here we have:
f(x) = 1/x
g(x) = x^2 - 4
The composition is:
f°g = f(g(x)) = 1/(x^2 - 4)
The two values that are not in the domain are the values of x such that g(x) = 0, because we can't divide by zero.
g(x) = 0 = x^2 - 4
4 = x^2
±√4 = x
±2 = x
So g(x) = 0 when x = 2 or x = -2, so these are the two real values that are not in the domain of f°g.
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The quadratic equation 5x2 45x 24 = 0 was solved using the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a. one solution is −8.43. what is the other solution? round to the hundredths place. 8.43 0.05 −0.57 −1.14
Answer:
Please review the equation format. I made an assumption (below) for this answer.
-0.57
Step-by-step explanation:
5x2 45x 24 = 0 is not a quadratic formula,
5x^2 + 45x + 24 = 0 is, however. Also, it gives -.8.43 as one solution. The other is −0.569351, or -0.57 to the nearest hundredth.
The other solution of the given quadratic equation would be -0.57
Quadratic Equation
An algebraic equation of the second degree in x is known as a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
The given quadratic equation is,
5x² + 45x + 24 = 0
Here,
a = 5
b = 45
c = 24
Applying the Quadratic Formula
The quadratic formula for the two roots of a quadratic equation is given as,
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] ........... (1)
and [tex]x=\frac{-b+\sqrt{b^{2}+4ac } }{2a}[/tex] ............ (2)
Substituting the values of a, b, and c in equation (1), we get,
x = -8.43
Calculating the Second Root
Now, the other solution can be found by substituting the values of a, b, and c in the equation (2),
[tex]x=\frac{-45+\sqrt{45^{2}+4(5)(24) } }{2(5)}[/tex]
[tex]x=\frac{-45+\sqrt{(2505) } }{10}[/tex]
[tex]x=-0.57[/tex]
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10. The cost of manufacturing a kitchen cabinet consists of the cost of materials at $250, labour cost at $120 and warehousing cost at $60. After a change of management, the cost of materials and labour cost are increased by 10% and 8% respectively, and warehousing cost is decreased by 18%. Calculate the percentage change in the cost of manufacturing the kitchen cabinet. State whether it is an increase or a decrease.
Using proportions, the percentage change in the cost of manufacturing the kitchen cabinet was a increase of 5.5%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The standard cost is given as follows:
S = 250 + 120 + 60 = $430.
After the increases, the price will be given as follows:
S = 250 x 1.1 + 120 x 1.08 + 60 x 0.82 = $453.8.
The price increased. The percent change, given by the change divided by the initial value, is:
P = 23.8/430 x 100% = 5.5%.
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which function is increasingnon the interval (negative infinity, positive infinity)
HELP 25 POINTS WILL MARK BRAINLIEST!
Answer:
h(x) = 2^(x) - 1.
Step-by-step explanation:
Let's look at each equation:
f(x) = -3x +7, Well as x increases, since it's multiplication, there are "going to be more" -3's, so it's going to be decreasing.
g(x) = -4(2^x). While 2^x is increasing, because "there are going to be more 2's multiplied by each other" as x increases, it's being multiplied by a negative number, so it's actually going to be decrasing
h(x) = 2^(x) - 1. Here's it's going to be increases as x goes towards infinity because "there are going to be more 2's multiplied by each other", and there isn't any negative sign, while there is a negative 1, it's constant, so the overall value will be increasing
Which function has a range of fyly ≤ 5}?
O f(x) = (x-4)² +5
Of(x) = -(x-4)² +5
O f(x) = (x - 5)² + 4
O f(x) = -(x - 5)² + 4
Answer: Option 2
Step-by-step explanation:
The vertex must have a y-coordinate of 5, so eliminate options 3 and 4.
Also, since there must be a maximum, the coefficient of [tex]x^2[/tex] must be negative. So, eliminate option 1.
This leaves us with option 2.
What is the difference?
X
3
x²-16 X-4
2(x+6)
O (x+4)(x-4)
O
-2(x+6)
(x+4)(x-4)
X-3
(x+5)(x-4)
-2(x-6)
(x+4)(x-4)
Answer:
your question is wrong, it's not an expression but a quadratic equation. if so your answer will be x=8±2√7
Step-by-step explanation:
by using, completing the square method
x²-16x-4=0
x²-16x=4
x²-16x+(-16×0.5)²=4+(16×0.5)²
x²-16x-8²=4+8²
(x-8)²=68
x-8=√68
x-8=±2√7
so x=8±2√7
please next time write the correct question
Hey i need help with this problem i cant figure it out
Answer:
inverse variation: xy=20
Step-by-step explanation:
Direct Variation is when y increases as x increases and is linear
Inverse Variation is when y decreases as x increases although it's not linear and the x and y has a constant product.
By observing the table, you'll see as x increases, y decreases. You'll also notice a constant product of 20 between x and y. (2 * 10) = 20. (4 * 5) = 20. ( (8 / 1) * (5 / 2) = 40/2 = 20))... and so on. So the function can be represented as xy = 20
Apply the Distributive property:
[tex] \boxed{\sf 3(x-4)=2(-2x+1) }[/tex]
Answer:
x = 2
Step-by-step explanation:
The left side would be (3x - 12)
The right side would be (-4x+2)
In an equation, 3x - 12 = -4x+2
Combine all the letters on the left and plain numbers on the right,
3x + 4x = 12 + 2
Note: When you transfer to the other side of the equal sign, the number will change its sign.
Simplify the 3x + 4x = 12 + 2,
7x = 14
[tex]x=\frac{14}{7}[/tex]
x = 2
⊱________________________________________________________⊰
Answer:
x=2Step-by-step explanation:
[tex]\large\begin{gathered} \sf{Simplify \ using \ the \ distributive \ property:} \\ \sf{3(x-4)=2(-2x+1)} \\ \ \sf{3x-12=-4x+2} \\ \rm{Move \ 12 \ to \ the \ right, \ with \ the \ opposite \ sign} \\ \ \sf{ 3x=-4x+2+12} \\ \rm{Move \ -4x \ to \ the \ left, \ wth \ the \ opposite \ sign.} \\ \sf{3x+4x=14} \\ \rm{Collect \ the \ like \ terms} \\ \sf{7x=14} \\ \rm{Divide \ the \ entire \ equation \ by 7.} \\ \sf{\dfrac{7x}{7}=\dfrac{14}{7} \\ \sf{x=2} \ \bigstar \end{gathered}[/tex]
Done!!
⊱______________________________________________________⊰
Cαlligrαρɦγhere's a graph of a linear function. write the equation that describes that function. express it in slope intercept form. HELP!
Answer:
[tex]y=\frac{3}{4}x+2[/tex]
Step-by-step explanation:
So when you express a linear function in slope-intercept form it's given in the form of y=mx+b, where m is the slope, and b is the y-intercept. This is because as x increases by 1, the y-value will increase by m (because multiplication), and since the slope is defined as rise/run, the rise will be m, and run will be 1, giving you a slope of m/1 or m. The reason b is the y-intercept, is because whenever the linear function crosses the y-axis, the x-value will always be 0. Meaning that mx will be 0 because m * 0 will equal 0... and that leaves b by it self, so b will determine the y-intercept.
So if you look at the graph, the linear function crosses the y-axis as (0, 2) so the value of b will be 2. This gives you the equation y=mx+2.
Now to calculate the slope, we can take any two points and see how much the rise was and how much the run was. It can also be more formally defined in the equation: [tex]y=\frac{y_2-y_1}{x_2-x_1}[/tex]. So let's take the points (0, 2) and (8, 8). As you can see the x-value increases by 8 or "ran" by 8, and the y-value increased by 6. So the rise over run in this case is 6/8 which can simplified as 3/4. That is the slope. This gives you the complete equation of: [tex]y=\frac{3}{4}x+2[/tex]
Carmen is planning rail lines for a new train station. Help her find
. Explain how you found that solution.
The angle based on the information given about the rail is 163°.
How to illustrate the information?From the information given, the value of angle 2 will be:
17° + x = 180° (angle on a straight line)
Collect like terms
x = 180° - 17°
x = 163°
In this case, it should be noted that angle 1 and 2 are alternate angles. Therefore, angle 1 will be 163°.
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The quadratic $x^2 1300x 1300$ can be written in the form $(x b)^2 c$, where $b$ and $c$ are constants. What is $\frac{c}{b}$
The value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The given quadratic expression needs to be expressed using the perfect square method to be of the form (x + b)² + c.
We express the quadratic expression x² + 1300x + 1300 using the perfect square method following these steps:
x² + 1300x + 1300
= x² + 2x(1300/2) + (1300/2)² + 1300 - (1300/2)²
= x² + 2x(650) + (650)² + 1300 - (650)²
= (x + 650)² + 1300 - 422500
= (x + 650)² - 421200.
Comparing this to (x + b)² + c, we get:
b = 650, and c = -421200.
Therefore, the value of c/b = (-421200)/650 = -648.
Therefore, the value of c/b when the quadratic equation x² + 1300x + 1300 is written in the form (x + b)² + c, b and c being constants is -648.
The question seems improper. The proper question is:
" The quadratic x^2+1300x+1300 can be written in the form (x + b)^2+c, where b and c are constants. What is c/b?"
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Classify the following triangle.
Answer:
A. Scalene
E. Obtuse
Step-by-step explanation:
Obtuse are angles that are greater than 90°
Scalene is not congruent sides.
Milo's car can be driven an average of 21.6 miles on each gallon of gasoline. How far can his car be driven on 9.8 gallons of gasoline?
Answer:
211.68 miles
Step-by-step explanation:
21.6 x 9.8
solve over the set of real numbers for the equation below x-2=√2x-1
The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equation is given below.
x – 2 = √(2x – 1)
Square on both side, then we have
(x – 2)² = 2x – 1
x² – 4x + 4 = 2x – 1
x² – 6x + 5 = 0
x² – 5x – x + 5 = 0
x(x – 5) – 1(x – 5) = 0
(x – 5)(x – 1) = 0
x = 1, 5
The set of real numbers for the equation x – 2 = √(2x – 1) will be 5.
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Let X = the number of heads in 4 flips of a fair coin. Use the probability distribution of X found here to calculate the
probability of each event.
at least 2 heads
exactly 2 heads
not all heads
more than 2 heads
0.3125
0.9375
0.6875
0.375
The graph of the piecewise function f(x) is shown.
On a coordinate plane, a piecewise function has 2 lines that connect. The first line is horizontal to the y-axis at y = 4 and goes to (0, 4). The second line goes from (0, 4) through (4, 0).
What is the range of f(x)?
The range of the function is f(x) <= 4
How to determine the range?The attached graph is the missing piece in the question
The function f(x) is given as:
2 lines connectedHorizontal line y = 4 to (0, 4)Another line from (0, 4) through (4, 0)The above means that, the value of the function do not exceed y = 4
Hence, the range of the function is f(x) <= 4
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please help!!! im going to fail!!!
Using the given information, the percent error is 52%
Percentage errorFrom the question, we are to calculate the percentage error
From the given information,
Prediction = 23 people
Actual = 48 people
Using the formula,
[tex]Percent \ error = \frac{|Prediction - Actual|}{|Actual|}\times 100\%[/tex]
[tex]Percent \ error = \frac{|23 - 48|}{|48|}\times 100\%[/tex]
[tex]Percent \ error = \frac{|-25|}{|48|}\times 100\%[/tex]
[tex]Percent \ error = \frac{25}{48}\times 100\%[/tex]
Percent error = 52.083%
Percent error ≈ 52%
Hence, the percent error is 52%
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Im really bad at geometry. Can someone please help me out
Answer:
x = 4
Step-by-step explanation:
Since they are parallel, we use the formula
[tex]\frac{part}{part} = \frac{part}{part}[/tex]
[tex]\frac{14}{x} =\frac{7}{2}[/tex]
7x = 28
x = 4
10
TIME REMAINING
59:02
Which is the graph of the linear inequality 2x – 3y < 12?
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
The graph of the inequality will be B. on a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded.
How to get the graph?It can be deduced that the coordinates satisfy the equation of the line.
3y = 2x - 12
Divide through by 3.
y = 2/3x - 4.
The slope is 2/3.
In conclusion, the correct option is B.
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Answer:
b
Step-by-step explanation:
PQ¯¯¯¯¯ and PR¯¯¯¯¯ are tangent to ⊙ S. Identify PQ.
pls help 30 points
Answer:
9
Step-by-step explanation:
Because line PQ and line PR are both tangent to circle S, it would result in them being equal. So first to find PQ, you would have to find the value of variable x. To do this you would set both equations equal to each other and solve
6x - 9 = 2x + 3
-2x -2x
4x - 9 = 3
+9 +9
4x = 12
x = 3
Now you have to substitute 3 back into the equation for PQ:
6(3) - 9
18 - 9
= 9
Resulting in PQ = 9, to check your answer, take the value of x (3) and substitute it into PR and you should also get 9
2(3) + 3
6 + 3
= 9
A new washing machine is purchased for $300. it's value depreciates 20% every year for the first 6 years of its life
The value of the washing machine after 6 years with 20% depreciation every year is $78.64.
What is depreciation?Depreciation is the practice of subtracting a business asset's cost over a number of years as opposed to just one.
Depreciation is used to adjust the cost of a productive asset with a longer-than-year-long useful life to the income generated by operating the asset. The expense of the asset is typically dispersed across the years that it is utilized.
Calculation for the asset value after depreciation of 20% every year.
The purchasing cost of washing machine is $300.
The rate after 6 years is-
Rate = purchased price×[tex](1-r)^{t}[/tex]
= 300×[tex](1-0.2)^{6}[/tex]
= 300×[tex]0.8^{6}[/tex]
= 78.64
The cost of washing machine after 6 years will be $78.64.
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Which expression is equivalent to −[tex]i[/tex]?
Select one:
a. (i[tex]i^{15[/tex])
b. [tex](i^{6 ) ^ {7[/tex] [tex]-(i^{5} )^{4}[/tex]
c. [tex](1+i)(1-i)[/tex]
d. [tex]i^{12} -(i^{13}) ^{3}[/tex]
The equation which is equivalent to -i among the answer choices is; i^(15), option A
Which expression is equivalent to -i?It follows from the concept of complex numbers that the representation -i stands for √-1 and on this note, it follows that;
i² = -1
i³ = -i
i⁴ = 1
Hence, it follows that;
i^(15) = i⁴ × i⁴ × i⁴ × i³ = 1 × 1 × 1 × -i = -i.
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The cards of a standard 52-card deck are dealt out in a circle. What is the expected number of pairs of adjacent cards which are both black
The expected number of pairs of adjacent cards which are both black is 650 / 51
For each pair of cards, the probability that they are both black is 26/52 * 25/ 51 = 25 / 102,
So since there are 52 pairs in the circle, the expected number of pairs which are both black is
25 / 102 * 52 = 650 / 51
Probability is genuinely how probable something is to happen. Every time we're unsure about the final results of an occasion, we can speak approximately the chances of sure results—how probably they're.
The evaluation of occasions governed by chance is referred to as statistics.
A sequence of movements where the outcomes are constantly unsure. The tossing of a coin, deciding on a card from a deck of playing cards, throwing a cube. It's far a single final results of an experiment. Getting a Heads even as tossing a coin is an event.
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The tree diagram represents an experiment consisting of two trials P(A andC)=
The value of P(A and C) is 0.18
How to determine the probability?From the tree diagram, we have the following probability values:
P(A) = 0.6
P(C) = 0.3
The probability P(A and C) is then calculated as:
P(A and C) = 0.6 * 0.3
Evaluate
P(A and C) = 0.18
Hence, the value of P(A and C) is 0.18
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