In circle F, FG = 2 and m/GFH = 120°
Find the area of shaded sector. Express your answer as a fraction times T.
Answer:
A = [tex]\frac{4}{3}[/tex] π
Step-by-step explanation:
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{120}{360}[/tex] ( r is the radius of the circle )
here r = FG = 2 with central angle = 120° , then
A = π × 2² × [tex]\frac{1}{3}[/tex]
= [tex]\frac{4}{3}[/tex] π
Find the perimeter of the following square and the area of the shaded part if the radius of the
circle is 12 cm.
The perimeter of the square and the area of the shaded part are 48cm and 454.16cm² respectively²
How to determine the valueThe formula for calculating the area of a circle is expressed as;
Area = πr²
Now, substitute the value, we have;
Area = 3.14 × 12²
Find the square and multiply the values, we have;
Area = 3.14(144)
Multiply the values
Area = 452. 16 cm²
Perimeter of a square take the formula;
Perimeter = 4a
Substitute the value
Perimeter = 4(12) = 48 cm
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Linear sequence of 35/100,5/10,65/100
The linear rule for the sequence is f(n) = 7/20 + 3/20(n - 1)
Finding the linear rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
35/100,5/10,65/100
In the above sequence, we can see that 15/100 is added to the previous term to get the new term
This means that
First term, a = 35/100
Common difference, d = 15/100
The nth term is then represented as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(n) = 35/100 + 15/100(n - 1)
So, we have
f(n) = 7/20 + 3/20(n - 1)
Hence, the explicit rule is f(n) = 7/20 + 3/20(n - 1)
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Ms. Lee used two dozen Mud Bugs in her suit the recipe makes 20 cups of soup approximately how many Mud Bugs are in each cup of soup round off the answer to the nearest whole number
Answer:
1
Step-by-step explanation:
So, 1 dozen is 12. Two dozen is 24.
She used 24 Mud Bugs in this soup.
This soup makes 20 cups.
So, 24 Mud Bugs are in 20 cups of soup.
To find the amount of Mud Bugs in each cup of soup, you divide the amount of Mud Bugs by the number of cups.
24/20
Which equals 1.2
You asked for the nearest whole number, so there is 1 Mud Bug per sup of soup.
A dime is flipped, and a single die is rolled. Find the odds against obtaining a head.
Answer:
11 : 1
Step-by-step explanation:
The probability of obtaining a head when a dime is flipped is 1/2, since there are two possible outcomes (heads or tails) and each is equally likely.
The probability of rolling any particular number on a fair six-sided die is 1/6, since there are six equally likely outcomes (the numbers 1 through 6).
To find the odds against obtaining a head and rolling any number on the die, we need to multiply the probabilities of the two events. This gives us
(1/2) x (1/6) = 1/12
So the probability of obtaining a head and rolling any number on the die is 1/12.
To find the odds against this event, we need to compare the probability of the event happening to the probability of it not happening. The probability of the event not happening is 1 - 1/12 = 11/12.
Therefore, the odds against obtaining a head and rolling any number on the die are:
11 : 1
An import company brought into the country some amplifiers that cost sh. 3,750-each. The government imposed an import duty of 125% and a sales tax of 20 %. If the company decided to make a 10% profit on the sales, calculate the selling price of each amplifier.
Answer:
To calculate the selling price of each amplifier, we need to consider the cost, import duty, sales tax, and the desired profit margin.
Cost of each amplifier: sh. 3,750
Import duty of 125% on the cost:
Import duty = 125% of sh. 3,750
= 125/100 * sh. 3,750
= sh. (125/100 * 3,750)
= sh. 4,687.50
Cost of each amplifier including import duty:
Total cost = Cost + Import duty
= sh. 3,750 + sh. 4,687.50
= sh. 8,437.50
Sales tax of 20% on the total cost:
Sales tax = 20% of Total cost= 20/100 * sh. 8,437.50
= sh. (20/100 * 8,437.50)
= sh. 1,687.50
Total cost including sales tax:
Total cost = Total cost + Sales tax
= sh. 8,437.50 + sh. 1,687.50
= sh. 10,125
Desired profit margin of 10% on the total cost:
Profit = 10% of Total cost
= 10/100 * sh. 10,125
= sh. (10/100 * 10,125)
= sh. 1,012.50
Selling price of each amplifier:
Selling price = Total cost + Profit
= sh. 10,125 + sh. 1,012.50
= sh. 11,137.50
What is the five-number summary for the data set? 73, 62, 90, 28, 45, 90
Answer:
it's easy
Step-by-step explanation:
first take a deep breath and then search it
2. Sandra's house is located at the point (2,2). The school is located at the point (7, 10). Each
unit on the graph represents 1 mi. How far is the school from Sandra's house? Remember to
show your work.
Plot and label your points on the coordinate plane (1 point)
Use the Pythagorean Theorem to calculate the diagonal distance between the two
points, express your answer as a radical and as a decimal rounded to nearest
hundredths.
Answer:
Step-by-step explanation:
Analyzing Wages-Plus-Commission Pay
Maybelle works in the shoe department for a high-end
store. She earns $15 per hour for at least 40 hours per
week. On top of that, she earns 10% commission for each
pair of shoes she sells. She is expected to sell $2,500
worth of shoes every week.
What will Maybelle earn in wages in a typical week?
How much commission will Maybelle earn if she sells
$3,000 of shoes in one week?
v
The next week, customers return $1,000 worth of
shoes. How much money will be deducted from
Maybelle's paycheck?
With an economic downturn, sales slump. As a result,
Maybelle will likely
a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850
b) Her total earnings for the week would be: $600 + $300 = $900
c) Her paycheck will be reduced by $100.
d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.
To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:
$15 x 40 = $600
In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:
$2,500 x 0.10 = $250
b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:
$3,000 x 0.10 = $300
On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)
c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.
d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.
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What is the perimeter of a rectangle with workings
Answer:
See below
Step-by-step explanation:
The perimeter of a rectangle is [tex]P=2L+2W[/tex] where L is the length and W is the width.
Use the 2021 marginal tax rates in the table to compute the tax owed by the person with the given filing status and taxable income.
Single with a taxable income of $61,000
The tax owed is $_____.
(Type an integer or a decimal. Round to the nearest cent as needed.)
The amount of tax owed is $13,420
How to determine the amount of tax owedFrom the question, we have the following parameters that can be used in our computation:
Single with a taxable income of $61,000
Using the table of marginal tax, we have
Tax = 22%
So, we have
Tax = 22% * 61000
Evaluate
Tax = 13420
Hence, the amount of tax owed is $13,420
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What’s the temperature change in 120 to -20
Answer: 140
Step-by-step explanation: 120-(-20) to 120 + 20 goes to 140.
Cos5pi/3 =
A. 3/2
B.1/2
C. 2/2
D.-2/2
HELPP
Answer:
B) 1/2
Step-by-step explanation:
Note that pi=180.
Then we have 180/3=60 and so 5*60=300.
Thus cos 300=1/2.
Therefore, cos 5pi/3=1/2.
Answer: B
Step-by-step explanation:
50 POINTS GEOMETRY QUESTION
Answer:
first one, the one you have selected
In circle M below, diameter AC, chords AB and BC, and radius MB
are drawn.
The statement which is not true about the circle M is ∆ABM is isosceles.
The correct answer choice is option 2.
Which statement is not true?Based on the circle M;
diameter AC,
chords AB and BC,
radius MB
Isosceles triangle: This is a type of triangle which has two equal sides and angles.
Equilateral triangle is a triangle which has three equal sides and angles.
Hence, ∆ABM is equilateral triangle.
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Find the measure of KV
LEO
K
L
V
N
128°
M
202°
The measure of the arc angle KV is 54 degrees.
How to find angle measure in a circle?If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
Therefore, let's find the arc angle KV in the circle as follows:
Hence,
let
arc angle KV = x
128 = 1 / 2 (202 + x)
128 = 101 + 0.5x
128 - 101 = 0.5x
27 = 0.5x
divide both sides by 0.5
x = 27 / 0.5
x = 54 degrees.
Therefore,
arc angle KV = 54 degrees.
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Please help urgent thank you I am so confused
The speed of the boat in water without a current is 15 miles per hour
Calculating the speed of the boat in water without a current?From the question, we have the following parameters that can be used in our computation:
Current of river = 4 miles per hour
Distance travelled = 209 miles
Time = 30 hours.
Represent the speed with x
So, we have
Upstream = x - 4Downstream = x + 4Next, we have
Time = Speed/Distance
So, we have
209/(x - 4) + 209/(x + 4) = 30
When evaluated, we have
x = 15
Hence, the speed is 15 miles per hour
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"Twice the difference of M and 14 equals 64."
Answer:
2(M - 14) = 64
M - 14 = 32
M = 46
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
Answer:
$6.84
Step-by-step explanation:
This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.
Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84Which type of conic section is defined by the equation:... 100pts
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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=
Find the x and y intercepts of the graph of the equation: y= |3x-7|. Select all that
apply.
What are the coordinates of the image of vertex P
Answer:
(- 7, 4 )
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
P (- 7, - 4 ) → (- 7, - (- 4) ) → (- 7, 4 )
in a right triangle the hypotenuse is 17 and an adjacent side is 9. What is the measure of the angle opposite the adjacent sied?
★ Apply Phythagoras Theorem:-
[tex] \sf \longrightarrow \: {(adjacent \: side)}^{2} + {(opposite \: side)}^{2} = {(hypotenuse)}^{2} [/tex]
[tex] \sf \longrightarrow \: {(9)}^{2} + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = {(17)}^{2} [/tex]
[tex] \sf \longrightarrow \: 81 + {(opposite \: side)}^{2} = 289[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 289 - 81[/tex]
[tex] \sf \longrightarrow \: {(opposite \: side)}^{2} = 208[/tex]
[tex] \sf \longrightarrow \: opposite \: side= \sqrt{ 208}[/tex]
[tex] \sf \longrightarrow \: opposite \: side=14.422[/tex]
An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.
Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.
Answer:
45°
Step-by-step explanation:
An isosceles triangle has two angles both equal to x. The third angle is 45 degrees bigger than either of these. Find the value of x.Let's turn the question into an equation
180 = x + x + x + 45
180 - 45 = 3x
135 = 3x
x = 135 : 3
x = 45°
------------------
check
180 = 45 + 45 + 45 + 45
180 = 180
same value the answer is good
What is the coefficient in the expression
6-4x-8+2
Answer:
-4 is the coefficient or -4x whatever the answers are
Step-by-step explanation:
the coefficient in mathematics is basically whatever the number is infront of a variable in an expression, equation, etc.
The product of two irrational numbers is
rational. (Sometimes,Never,always)?
The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
The product of two irrational numbers can be either rational or irrational, depending on the specific irrational numbers being multiplied. It is not always rational, nor is it never rational.
Consider the square root of 2 (√2) and the square root of 3 (√3), both of which are irrational numbers. When you multiply √2 and √3, you get √6, which is also an irrational number. In this case, the product of two irrational numbers is irrational.
However, there are cases where the product of two irrational numbers can be rational. For example, consider √2 and its reciprocal (1/√2), both of which are irrational. When you multiply these two numbers, you get 1, which is a rational number. So, in this case, the product of two irrational numbers is rational.
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IfmZC = 142° and m LI = 48°, find mU B.
The minor arc UB in the circle measures 46 degrees,
What is the measure of arc UB?The external angles theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.
It is expressed as;
External angle = 1/2 × ( major arc - minor arc )
From the diagram:
External angle I = 48 degrees
Major arc ZC = 142 degrees
Minor arc UB = ?
Plug these values into the above formula and find the minor arc UB:
External angle = 1/2 × ( major arc - minor arc )
48 = 1/2 × ( 142 - minor arc )
Multiply both sides by 2:
2 × 48 = 2 × 1/2 × ( 142 - minor arc )
2 × 48 = ( 142 - minor arc )
96 = ( 142 - minor arc )
96 = 142 - Minor arc
Minor arc = 142 - 96
Minor arc = 46°
Therefore, the minor arc measures 46 degrees.
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point slope form (0,12), (-6,0)
This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).
To find the equation of a line in point-slope form, we need a point on the line and the slope of the line.
Given the points (0, 12) and (-6, 0), we can calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 12) as (x1, y1) and (-6, 0) as (x2, y2):
slope = (0 - 12) / (-6 - 0)
slope = -12 / -6
slope = 2
Now that we have the slope, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Using the point (0, 12) as (x1, y1) and the slope (m) as 2:
y - 12 = 2(x - 0)
Simplifying the equation:
y - 12 = 2x
This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).
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please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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A zoo has categorized its visitors into three categories: member, school, and general. The member category refers to visitors who pay an annual fee to support the zoo. Members
receive certain benefits such as discounts on merchandise and trips planned by the zoo. The school category includes faculty and students from day care and elementary and
secondary schools; these visitors generally receive a discounted rate. The general category includes all other visitors. The zoo has been concerned about a recent drop in
attendance. To help better understand attendance and membership, a zoo staff member has collected the following data.
Attendance
School
Visitor
Category 2011
General 154,213 159,204 163,933 169,606
Member 114,023 103,295
96,937 79,717
82,385 79,376
81,470
80,790
Total 350,621 341,875 342,340
330,113
(0) Construct a bar chart of total attendance over time. Comment on any trend in the data.
(b) Construct a side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis.
(c) Comment on what is happening to zoo attendance based on the charts from parts (a) and (b).
2012
2013
2014
(a) Based on the total attendance data provided, a bar chart can be constructed to visualize the attendance trends over time. The horizontal axis represents the years (2011, 2012, 2013, 2014), and the vertical axis represents the total attendance. The bars will correspond to the attendance numbers for each year.
(b) A side-by-side bar chart can be created to compare the attendance by visitor category with the year as the variable on the horizontal axis. The visitor categories (school, general, member) will be represented by different colors or patterns, and the bars will show the attendance for each category in each year.
(c) By analyzing the charts from parts (a) and (b), we can observe the trends in zoo attendance.
(a) The bar chart of total attendance over time shows the following trend: In 2011, the attendance was 350,621. It decreased slightly in 2012 to 341,875, remained relatively stable in 2013 at 342,340, and then decreased again in 2014 to 330,113.
(b) The side-by-side bar chart showing attendance by visitor category with year as the variable on the horizontal axis provides a visual comparison of attendance for each category over the years.
The chart reveals that the general category consistently had the highest attendance throughout the years, followed by the school category. The member category consistently had the lowest attendance.
(c) Based on the charts from parts (a) and (b), it can be observed that there has been a general decline in zoo attendance over the years, with a notable decrease from 2011 to 2014.
The drop in attendance could indicate a potential issue that the zoo needs to address in order to attract more visitors.
Additionally, the consistently lower attendance in the member category suggests that the zoo may need to reconsider its membership benefits and strategies to retain and attract more members.
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