Answer:
x=18 or x=6
Step-by-step explanation:
2x=36
x=18
if it was x^2 then
x^2=36
x=6
In a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys
whether they have a pet.
Use the binomial distribution to compute the probability that exactly 2 of the families have a pet.
Identify the following information required to find the probability of families that have a pet.
If in a large population, about 70% of families have a pet. A researcher takes a random sample of 6 families and surveys whether they have a pet. The probability of families that have a pet is: 0.0595.
How to find the probability?Number of trial= 6
Probability of success = 0.7
Probability of failure = 1 - 0.7 = 0.3
Probability that exactly 2 of the families have a pet
Let make us of binomial distribution formula to determine the probability
P(X = 2) = (6 choose 2) * 0.7² *[tex]0.3^{4}[/tex]
= 15 * 0.49 * 0.0081
= 0.0595
Therefore the probability is 0.0595.
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Which statements describe finding the limit shown?
Check all that apply.
O Multiply by √x +2+3
√x+2+3
Getx-1 in the numerator.
Get (x-7)(√x+2-3) in the denominator.
O Divide out a common factor of x- 7.
Calculate the limit as
The correct statements that apply to the given limits are:
Option A: Multiply by (√(x + 2) + 3)/(√(x + 2) + 3)
Option D: "Divide out a common factor of x - 7."
Option E: The limit of the given expression is 1/6.
How to find the limits of the function?Option: We generally multiply by the conjugate of the expression to eliminate square roots in simplification. Thus, option A applies.
Option B: Get x - 1 in the numerator:
This statement is not correct. The expression does not involve x - 1 in the numerator.
Option C: Get (x - 7)(√(x + 2) - 3) in the denominator:
This statement is not correct due to the fact that we want to simplify the expression, and not introduce a more complex denominator.
Option D: Divide out a common factor of x - 7:
This statement is correct because by factoring out (x - 7) from both the numerator and denominator, we can cancel out the common factor.
Option E: Calculate the limit as 1/6:
After canceling out the common factor of x - 7, the simplified expression becomes:
lim x -> 7 (√(x + 2) - 3)/(x - 7)
= lim x -> 7 1/(√(x + 2) + 3)
To find the limit, we substitute the value x = 7 into the simplified expression:
lim x -> 7 1/(√(7 + 2) + 3) = 1/(√(9) + 3) = 1/(3 + 3) = 1/6
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Triangle- m ∠ 2 m ∠ 3 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
The statements are true. still, grounded on the given options, three statements that are always true regarding any triangle are . The sum of the angles of a triangle is always equal to 180 degrees.
This statement is true because the total degrees of any triangle is 180 degrees.
This is known as the Triangle Sum Theorem.
2. The surface angle of a triangle is equal to the sum of its interior contrary angles. This statement is true for any triangle. The surface angle is the angle formed by extending one side of the triangle. The contrary innards angles are the two angles inside the triangle that don't partake a vertex with the surface angle.
3. The measure of each angle of an equilateral triangle is 60 degrees. This statement is true for any equilateral triangle. An equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. thus, grounded on the given options,
the three statements that are always true regarding the illustration could be
- m ∠ 3 m ∠ 4 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
- m ∠ 5 m ∠ 6 = 180 °( by the sum of the angles of a straight line)
- m ∠ 2 m ∠ 3 m ∠ 5 = 180 °( by the Triangle Sum Theorem)
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VNIHO NI es sequence. c). C 9 is 27 km from R on a bearing of 060° town T is 19km from town R on a aring of 3400 draw a diagram showing the relative position of the towns.
The description of the given bearing with the towns and a similar drawing of bearing is given below:
How to solveThe directions to draw the diagram that shows the relative position of the towns is given below:
Town R is at the center of the coordinate system.
Town C is 27km away on a bearing of 060°. Start at R, move 27km at 060° to find C towards east-southeast.
Town T is 19 km away from R on a ring of 3400.
T is on a circular path of radius of 3400 units.
To plot T, draw a circle at R with a 3400 unit radius. Put T on the circle, 19 km from R. Diagram: R center, C ESE, T on a circular path with a 3400 unit radius around R.
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Is Saturn less dense than water which has a density of 997 kg/m³? Find out by calculating the density of Saturn in kg/m³. The mass of Saturn is 5.68 x 1026 kg, and its radius is 5.6 x 107 m.
Density of Saturn:
Answer:
Sure, I can help you with that.
To calculate the density of Saturn, we can use the following formula:
Density = Mass / Volume
We know the mass of Saturn is 5.68 x 1026 kg, and we can calculate the volume of Saturn using the following formula:
Volume = (4/3)πr³
where π is approximately equal to 3.14159 and r is the radius of Saturn, which is 5.6 x 107 m.
Plugging in these values, we get the following:
Density = 5.68 x 1026 kg / (4/3)π(5.6 x 107 m)³
Density = 0.687 kg/m³
Therefore, the density of Saturn is 0.687 kg/m³, which is less than the density of water (997 kg/m³). This means that Saturn would float on water.
Step-by-step explanation:
pls calculate all of this: (one at a time)
The solution to the equations are
1/3(2x - 3/7) + 1/6x = 4/7 is x = 6/7
7/8 x + 3/4 x + 7/16 x - 1/16 = 5/8 is x = 1/3
1 1/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5 is y = 6/10
3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21) is x = 12
4/3x + 9/2y
How to solve for x1. To solve this equation, we can start by simplifying
1/3(2x - 3/7) + 1/6x = 4/7
2/3x - 1/7 + 1/6x = 4/7
Multiplying both sides by the lcm of the denominators which is 42
28x - 6 + 7x = 24
35x = 30
x = 6/7
2. 7/8x + 3/4x + 7/16x - 1/16 = 5/8
Multiplying both sides by the lcm of the denominators which is 16
14x + 12x + 7x - 1 = 10
33x = 11
x = 1/3
3.
6/5 y + 3/10 y - 1/2 y = 1/3 y + 2/5
2/3 y= 2/5
y = 2/5 * 3/2
y = 6/10
4.
3/4 * (1/6 x + 16) = 3/7 * (4 3/8 x - 21)
opening the parenthesis
1/8 x + 12 = 15/8 x - 9
1/8 x - 15/8 x= -12 - 9
-7/4 x = -21
x = 12
5.
2x - 2/3 x + 3 y + 1 1/2 y
4/3 x + 9/2 y
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Sketch BC intersecting KT at point F. F is the midpoint of BC but not KTp
The desired sketch is attached below.
To sketch the scenario where BC intersects KT at point F, with F being the midpoint of BC but not KT, you can follow these steps:
Take a blank sheet of paper or open a drawing application on your device.Draw a straight line segment BC anywhere on the paper, and label the endpoints as B and C.Draw another line segment KT, intersecting BC at some point. Make sure that KT does not pass through the midpoint of BC.Label the intersection point of BC and KT as F.Draw a small line segment perpendicular to BC from point F. This line segment represents the intersection between BC and KT.Add arrows or marks on BC and KT to indicate the directions in which the lines extend.Finally, write the labels B, C, K, and T next to their respective points on the sketch to make it clear which points correspond to each line segment.Learn more about midpoint here:
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For the function , find f' (1).
guys pls help me
The derivative of the function is solved and f' ( 1 ) = 0.183
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = sinh⁻¹ ( √ (2x + 3 )
On taking the derivative of the function , we get
f' ( x ) = 1/ ( √2x + 4 ) ( √ ( 2x + 3 ) )
On simplifying , we get
when x = 1
f ( 1 ) = 1 / ( √6 ) ( √5 )
f ( 1 ) = 1/√30
f ( 1 ) = 0.18257
f ( 1 ) = 0.183
Hence , the function is solved
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1. Power Company signed a 3-year lease for equipment and leased the equipment on September 1, 2022. The lease
agreement calls for Power to make monthly lease payments of $8,000, assuming a 8% borrowing rate. The first lease
payment begins September 30, 2022. (Worth 7 points)
Required:
A. Calculate the present value of the lease payments. Please explain how you calculated the present value and the
inputs used and why.
B. Record the journal entry for the lease on September 1, 2022.
Please no chat gpt answers
The lease payment's present value is $258,743.55.
The journal entry for the lease on September 1, 2022, are:
- Lease equipment $258,743.55
- Lease liability $258,743.55
We have,
A.
To calculate the present value of the lease payments, we can use the present value formula:
PV = PMT x [ (1 - (1 + r)^{-n} / r]
where PV is the present value, PMT is the monthly lease payment, r is the monthly interest rate
(which is 8 % / 12 = 0.67%), and n is the number of lease payments
(which is 36 since it's a 3-year lease with monthly payments).
Plugging in the values.
PV = $8,000 x [(1 - (1 + 0.0067)^{-36} / 0.0067]
= $258,743.55
B.
The journal entry for the lease is on September 1, 2022.
i.e
Lease equipment $258,743.55
Lease liability $258,743.55
This records the initial recognition of the lease liability and the right-of-use asset at the present value of the lease payments.
Thus,
The lease payment's present value is $258,743.55.
The journal entry for the lease on September 1, 2022, are:
- Lease equipment $258,743.55
- Lease liability $258,743.55
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In recent years, Sheffield Transportation purchased three used buses. Because of the frequent turnover in the accounting department, a different accountant was in charge of selecting the depreciation method for each bus, and various methods have been used. Information concerning the buses is summarized in the table below. Bus 1, Bus 2, Bus 3, For the declining-balance method, the company uses the declining method rate. For units-of-activity method, total miles are expected to be 125,000. Actual miles of use in the first 3 years were 2021, 27,000; 2022, 35,000; and 2023, 33,000.
(a1) For Bus #3, calculate depreciation expense per mile under units-of-activity method.
Under the units-of-activity method, the depreciation expense per mile for Bus #3 is $0.4616.
How is the depreciation expense per mile determined?The units-of-activity method is one of the depreciation methods in use.
Under the units-of-activity method, the depreciation expense per unit is determined by dividing the depreciable amount by the total units of activity.
The depreciation amount (the value of the asset subject to depreciation) is the net of the total cost less the salvage value.
Depreciable amount of Bus #3 = $57,700 ($66,500 - $8,800)
Expected total miles for Bus #3 = 125,000
Depreciation expense per mile for Bus #3 = $0.4616 ($57,700 ÷ 125,000)
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Question Completion:Bus Acquired Cost Salvage Useful Life Depreciation
Value in Years Method
1 1/1/12 $99,100 $7,900 4 Straight-line
2 1/1/12 128,000 11,000 4 Declining- balance
3 1/1/13 66,350 8,800 5 Unit-of-activity
There is a ratio of 5 apples to 3 pears in a basket. There are 24 pears in the basket. How many apples are in the basker?
Answer:
There are 40 apples in the basket.
This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.
I hope this helped you, have an amazing day! :)
How long would it take to pay off a $1000 balance with an interest rate of 14% APR when you only make the minimum payments of $20 each month?
3 months
1 year
3 years
6 years
To calculate how long it would take to pay off a $1000 balance with an interest rate of 14% APR when making minimum payments of $20 each month, we need to consider the monthly interest and the decreasing balance.
First, let's calculate the monthly interest. The annual interest rate is 14%, so the monthly interest rate would be 14% divided by 12 months, which is approximately 1.167%.
Now, let's determine how much of the minimum payment goes towards interest each month. The remaining amount after deducting the interest is used to decrease the balance.
In the first month, the interest on the $1000 balance would be 1.167% of $1000, which is approximately $11.67. So, after making a $20 minimum payment, $11.67 is subtracted from the balance, resulting in a new balance of $988.33.
In the subsequent months, the same process is repeated. The interest is calculated based on the new balance, and the minimum payment is made. This continues until the balance reaches zero.
Given the small minimum payment of $20 and the interest accumulating on the balance, it would take significantly longer than 3 months, 1 year, or 3 years to pay off the $1000 balance. Therefore, the correct option is 6 years.
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darges d
16. For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part
A, Part B, and Part C.
Part A: Describe how to determine if a triangle is a right triangle when given the triangle's side lengths.
Part 8: Describe how to determine if a triangle is acute or obtuse when given the triangle's side lengths.
Part C: Classify the triangle below as either right, acute, or obtuse, and show all work to explain the classification.
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(a) For right triangles, the following must be true a² = b² + c²
(b) For acute triangles, a² > b² + c² and For obtuse triangles, a² < b² + c²
(c) The triangle is an obtuse triangle because a² > b² + c²
(a) Checking for right triangleFor a triangle to be a right triangle given the triangle's side lengths.
The square of the largest side must be equal to the sum of the square of the other sides
(b) Checking for acute or obtuse triangleFor a triangle to be a acute triangle given the triangle's side lengths.
The square of the largest side must be less than the sum of the square of the other sides
For a triangle to be an obtuse triangle given the triangle's side lengths.
The square of the largest side must be greater than the sum of the square of the other sides
(c) Classifying the triangle by side lengthsWe have
Lengths = 7.2, 8.3 and 12.4
So, we have
12.4² = 7.2² + 8.3²
Evaluate
153.76 = 120.73
The correct inequality is
153.76 > 120.73
Hence, the triangle is an obtuse triangle
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Write the equation of a line that is perpendicular to y=7/5 x+6 and that passes throght the point (2,-6)
The equation of line that passes through and is perpendicular toy = (7/5)x + 6 is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
What is the equation of the perpendicular line?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line:
y = (7/5)x + 6
Using the slope intercept, slope m is 5/2
Slope m = 7/5
Note: the equation of a perpendicular line to y = (7/5)x + 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 7/5 )
Slope of perpendicular line = -5/7
Plug the slope m = -5/7 and point (2,-6) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
[tex]( y - (-6) = -\frac{5}{7}( x - 2 ) \\\\y + 6 = -\frac{5}{7}x + \frac{10}{7} \\\\y = -\frac{5}{7}x + \frac{10}{7} - 6\\\\y = -\frac{5}{7}x - \frac{32}{7}[/tex]
Therefore, the equation of the line is [tex]y = -\frac{5}{7}x - \frac{32}{7}[/tex].
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Can you expess this answers for me express 625 as a fraction of 1000 in its lowest terms
625 as a fraction of 1000 in its lowest terms is 5/8.
Express 625 as a fraction of 1000 in its lowest terms. Here's a step-by-step explanation:
1. Write the given numbers as a fraction: 625/1000
2. Find the greatest common divisor (GCD) of the numerator (625) and the denominator (1000). The GCD of 625 and 1000 is 125.
3. Divide both the numerator and the denominator by the GCD: (625 ÷ 125) / (1000 ÷ 125)
4. Simplify the fraction: 5/8
So, 625 as a fraction of 1000 in its lowest terms is 5/8.
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S
9.
Are
Is square root of -6 8 a rational numbers?
Answer:
Not rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
have a great day and thx for your inquiry :)
Two observation towers A and B are located 10 miles apart scientist at tower A spot an exotic bird at 42° and scientist at tower B spot the same bird at 64° how far away from tower A is the exotic bird
The distance of bird away from the tower is 4.04 miles.
Given that,
Distance between A and B = 10 miles
To solve this problem,
Use the law of tangents and basic trigonometry.
Let the distance from tower A to the bird = x
Then,
tan(180° - 64°) = x / (10 - d)
(where d is the distance from tower B to the bird)
tan(42°) = x / d
We can rearrange the first equation to get,
10 - d = x / tan(116°)
Substituting this into the second equation, we get:
⇒ tan(42°) = x / (x / tan(116°))
⇒ tan(42°) = tan(116°) x / x
⇒ x = 10 tan(42°) / (tan(116°) - tan(42°))
Plugging this into a calculator, we get:
x ≈ 4.04 miles
Therefore,
The exotic bird is approximately 4.04 miles away from tower A.
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Three children have an average age of 7 years 11 months. If The youngest child is not included, the average age increases to 8 years 11 months. Find the age of the youngest child.
Step-by-step explanation:
7 yr 11 mos = 95 mos
8 yr 11 mos = 107 mos
(x + y + z) / 3 = 95 mos z is youngest
(x+y)/2 = 107 or x+y = 214 <=====sub into first equation
(214 + z ) / 3 = 95 solve for 'z'
214+ z = 285
z = 71 months = 5 yrs 11 months
10. Kristen compared the y-intercept of the graph of the function f(x) = 7x - 5 to the y-intercept of the graph of the linear function that includes the points in the table below. X -5,-2,0,3 g(x) -56,-20,4,40
What is the difference when the y-intercept of g(x) is subtracted from the y-intercept of f(x)?
Use a calculator to find the trigonometric ratio. Round your answer to four decimal places
sin 98°~
Using a calculator, the trigonometric ratio of sin 98 is approximately 0.9848.
How to Find the Trigonometric Ratio?One of the trigonometric ratio we have in mathematics is the sine ratio. We can use calculator to find the sine of an angle without making use of tables. To do this on your calculator, enter the sine function followed by the degree of the angle you want to find its sine. You will get your answer.
Using a calculator, we can find the sine of 98 degrees as follows:
sin 98° ≈ 0.9848
Rounding this to four decimal places, we get:
sin 98° ≈ 0.9848
Therefore, sin 98° is approximately equal to 0.9848.
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which equation is equivalent to 4(2-5x)=6-3(1-3x)?
The equivalent equations of 4(2-5x)=6-3(1-3x) are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5
Calculating which equation is equivalent to 4(2-5x)=6-3(1-3x)?From the question, we have the following parameters that can be used in our computation:
4(2-5x)=6-3(1-3x)
Express properly
So, we have
4(2 - 5x) = 6 - 3(1 - 3x)
Open the brackets
So, we have
8 - 20x = 6 - 3 + 9x
Evaluate the like terms
This gives
29x = 5
This means that the equivalent equations are 4(2 - 5x) = 6 - 3(1 - 3x), 8 - 20x = 6 - 3 + 9x and 29x = 5
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Alex, Bill, Carl and David shared $168. David received 1/7 of the total amount of money received by Alex, Bill and Carl. Alex received 3/4 of the total amount of money received by Bill and Carl. Bill received 2/5 as much money as Carl. How much did Bill receive?
Bill's share = $56 Therefore, Bill received $56.
Let's start by setting up some equations based on the given information:
David's share = 1/7 * (Alex's share + Bill's share + Carl's share)
Alex's share = 3/4 * (Bill's share + Carl's share)
Bill's share = 2/5 * Carl's share
The sum of all four shares is $168.
We can use the fourth equation to solve for one of the shares in terms of the others:
Alex's share + Bill's share + Carl's share + David's share = $168
Alex's share + Bill's share + Carl's share = $168 - David's share
Substituting the other equations into this expression, we get:
Alex's share + (2/5 * Carl's share) + Carl's share + (1/7 * (Alex's share + (2/5 * Carl's share) + Carl's share)) = $168
Simplifying this equation, we get:
(8/7) * Alex's share + (22/35) * Carl's share = $168
Now we can use the other equations to solve for Carl's share, and then for Bill's share:
From Bill's share = 2/5 * Carl's share, we get Carl's share = (5/2) * Bill's share
From Alex's share = 3/4 * (Bill's share + Carl's share), we get Alex's share = (3/4) * ((7/2) * Bill's share) = (21/8) * Bill's share
Substituting these expressions into the equation we derived earlier, we get:
(8/7) * (21/8) * Bill's share + (22/35) * (5/2) * Bill's share = $168
3 * Bill's share = $168
Bill's share = $56
Therefore, Bill received $56.
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Heather has a combination of dimes and quarters in her piggy bank. If Heather has a total of 43 coins and the value in the piggy bank is $7.60, how many of each coin does she have?
Answer:
Step-by-step explanation:
5.6
The classroom had a 16-centimetre-long glue stick, and then Christina used 2.5 centimetres of it. How long is the stick now?
Answer:
[tex]13.5cm[/tex]
Step-by-step explanation:
You just need to subtract to find your answer!
The information we are given:
We have a 16cm glue stick.
Christina used 2.5cm of it.
Subtracting:
16 - 2.5 = 13.5
Now, dont forget your units :D
[tex]13.5 -- > 13.5cm[/tex]
I hope I helped!~~~Harsha~~~
100 Points! Algebra question. Please show as much work as possible. Thank you!
Michio answer was wrong. The correct answer for x in the expression 2(3)ˣ = 34 is 2.5789
How do i determine the correct answer?To know if Michio is correct or not, we shall determine the value of x in the algebraic expression. This is shown below:
Algebraic expression: 2(3)ˣ = 34Value of x =?2(3)ˣ = 34
Divide both sides by 2
3ˣ = 34 / 2
3ˣ = 17
Take the Log of both sides
Log 3ˣ = Log 17
Recall
Log Aⁿ = nLogA
Thus, we have
xLog 3 = Log 17
Divide both sides by Log 3
x = Log 17 / Log 3
x = 2.5789
From the above calculation, we see that Michio was wrong as the correct value of x in the expression is 2.5789
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The choir director wants to divde the choir into groups. There ar 24 Altos and 36 Tenors. Each group must have the same amount of each Alto and Tenors. What is the greates amount of groups the choir director could make?
The greatest number of groups the choir director could make is 12.
To find the greatest number of groups the choir director could make, we need to determine the highest common factor (HCF) of 24 and 36.
First, let's prime factorize both numbers:
[tex]24 = 2^3 \times 3\\36 = 2^2 \times 3^2[/tex]
Next, we identify the common factors between 24 and 36:
The factors common to both numbers are [tex]2^2[/tex]and 3.
To find the HCF, we take the smallest exponent for each common prime factor:
[tex]HCF = 2^2 \times 3 = 12[/tex]
Therefore, the greatest number of groups the choir director could make is 12.
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when the square of a natural number is multiplied by 5,the product is 125
Answer:The least number by which 125 be multiplied to make it a perfect square is 5.125 = 5 × 5 × 5
The question deals with solving an equation pertaining to natural numbers and their squares. The solution involves finding the square root of 125 divided by 5, which gives us 5. Thus, the natural number whose square multiplied by 5 equals 125 is 5.
Explanation:The subject of this question is Mathematics, specifically working with natural numbers and their squares. Here, you're given that 'when the square of a natural number is multiplied by 5, the product is 125'.
It's a simple application of the basic arithmetic operations. We have to try and find the square root of 125 divided by 5 because multiplication is inverse of division.
The calculation would be: √(125/5) = √25 = 5.
Thus, the natural number in question is 5, as 5 squared (25) times 5 is equal to 125.
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Here is a right-angled triangular tile.
3cm
Diagrams not drawn to scale
4 cm
A hollow shape is made using four of these
triangular tiles and four square tiles.
Work out the perimeter of the hollow shape.
Optional working
+
Answer:
cm
The perimeter of the hollow space is 14 cm².
We have,
From the figure,
We see that the hollow space is a rectangle.
Now,
We see that,
The length of the hollow space is the side of one square.
The width of the hollow space is also the side of another square.
So,
The rectangles dimensions:
Length = 3 cm
Width = 4 cm
The perimeter of the hollow space.
= 2 (length + width)
= 2 (3 + 4)
= 2 x 7
= 14 cm²
Thus,
The perimeter of the hollow space is 14 cm².
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Guys please help asap!!!!!!
Determine the measure of each arc.
The measure of the arc angles which subtends angles at the center are: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.
What is angle subtended by an arc at the centerThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
So;
arc angle MN = 72° {vertical angles}
arc angle NQR = 95 + 13 + 72 = 180°
arc angle NQ = 95 + 13 = 108°
arc angle MRP = 108 + 72 + 13 = 193°
arc angle QR = 72
arc angle MR = 95 + 13 = 108 {vertical angles}
arc angle QMR = 180 + 108 = 288°
arc angle PQ = 13° {sum of angles on a straight line}
arc angle PRN = 85 + 108 + 72 = 265°
arc angle MQN = 180 + 12 + 95 = 288°.
Therefore, the following are measures of the arc angles which subtends angles at the center: MN = 72°, NQR = 180°, NQ = 108°, MRP = 193°, QR = 72, MR = 108, QMR = 288°, PQ = 13°, PRN = 265°, and MQN = 288°.
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Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 85 workers can produce 136 cars in 8 hours, find the number of cars that 125 workers can produce in 7 hours.
125 workers can produce approximately 102.94 cars in 7 hours.Additionally, this assumes that the constant of Proportionality remains the same for different numbers of workers and hours worked.
We are given that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. This can be expressed as:
C = kWT
where C is the number of cars produced, W is the number of workers, T is the time they work, and k is a constant of proportionality
We can use this formula to solve the problem. We are given that 85 workers can produce 136 cars in 8 hours, so we can set up an equation using this information:
136 = k(85)(8)
Solving for k, we get:
k = 2/17
Now we can use the formula to find the number of cars that 125 workers can produce in 7 hours:
C = (2/17)(125)(7)
C = 102.94
Therefore, 125 workers can produce approximately 102.94 cars in 7 hours.
It's important to note that this is an approximation since we have rounded the answer to two decimal places. Additionally, this assumes that the constant of proportionality remains the same for different numbers of workers and hours worked.
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