Of the 38 plays attributed to a playwright, 13 are comedies, 13 are tragedies, and 12 are histories. If one play is selected at random, find the odds in favor of selecting a comedy
Answer:
13/38
Step-by-step explanation:
To find the odds in favor of selecting a comedy, we divide the number of comedies by the total number of plays. In this case, there are 13 comedies out of a total of 38 plays Therefore, the odds in favor of selecting a comedy are 13/38. I hope that helps!
14 An aeroplane leaves an airport A and to 2 decimal place. (WAEC) flies on a bearing 035° for 1 hours at 600 km/h to an airport B. It then flies on a bearing 130° for 1 hours at 400 km/h to an airport C. Calculate the correct (a) distance from C to A, correct to the nearest kilometre. (b) bearings romC from A, correct to the nearest degree. (WAEC)
Answer:
So the bearing from C to A is approximately 87° to the nearest degree.
Step-by-step explanation:
(a) To find the distance from C to A, we can use the cosine rule. Let's call the distance from A to B "d1" and the distance from B to C "d2". Then:
d1² = (600 km/h * 1 hour)² = 360,000 km²
d2² = (400 km/h * 1 hour)² = 160,000 km²
Now, let's find the angle between d1 and d2. We know that the angle between the two bearings is 130° - 35° = 95°. We also know that the angle between d1 and d2 is 180° - 95° = 85° (because the three angles in a triangle add up to 180°).
Using the cosine rule:
d² = d1² + d2² - 2d1d2cos(85°)
d² = 360,000 + 160,000 - 2(600)(400)cos(85°)
d ≈ 1,013 km
So the distance from C to A is approximately 1,013 km to the nearest kilometre.
(b) To find the bearings from C to A, we can use trigonometry. Let's call the bearing from C to A "x". Then:
cos(x) = (d2/d)
cos(x) = 160,000/1,013,000
x ≈ 87°
So the bearing from C to A is approximately 87° to the nearest degree.
4
Based on the March expense statement, what proportion of Maria's total expenses are for her car?
A. Less than one quarter.
B. More than a quarter but less than half.
O C. More than three-quarters.
D. More than half but less than three-quarters.
Auto
Check Number 87
Credit Card March)
Clothing
Marla's Expense 1
Get Card Mash
Food
Credit Card Mesh &
Sends Card March 11
Petal food
Cash Paya
Para Coch
Total
Out of Maria's total expenses, the proportion of expenses for her car would be 0. 57 .
How to find the proportion ?To find the proportion, the formula would be :
= Maria total car expenses / Maria total expenses for the month
Maria total car expenses = $ 290. 02
Maria total expenses for the month = $ 507. 59
The proportion of expenses for her car would be :
= 290. 02 / 507. 59 x 100 %
= 0. 57 x 100 %
= 57 %
In conclusion, Maria's car alone takes over 0. 57 or 57 % of her total expenses.
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1) C.M. Burns Enterprises, Inc. is considering investing in a machine to produce
computer keyboards. The price of the machine will be $400,000 and its economic life
five years. The machine will be fully depreciated by the straight-line method. The
machine will produce 10,000 units of keyboards each year. The price of each keyboard
will be $40 in the first year, and it will increase at 5% per year. The production cost per
unit of the keyboard will be $20 in the first year, and it will increase at 10% per year.
The corporate tax rate for the company is 34%. If the appropriate discount rate is 15%,
what is the NPV of the investment?
2) Kwik-E-Mart, Inc. is considering the purchase of a $500,000 computer that has an
economic life of 5 years. The computer falls into the MACRS 5-year class and will be
sold in 5 years for $100,000. The use of the computer will save five office employees
whose combined annual salaries are $120,000. It also contributes to lower net working
capital by $100,000 when they buy the computer. The net working capital will be
recovered at the end of the project. The corporate tax rate is 34%. Is it worthwhile to
buy the computer if the appropriate discount rate is 12%? Use the internal rate of return
The solution is:
Break-even point in units= 1,000 units
Here, we have,
Explanation:
Giving the following information:
The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45.
To calculate the break-even point in units, we need to use the following formula:
Break-even point in units= fixed costs/ contribution margin per unit
Break-even point in units= 20,000 / (45 - 25)
Break-even point in units= 1,000 units
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complete question:
The variable cost of a new computer keyboard is $25 per unit, and the fixed costs to produce the keyboard are $20,000 per year. If the selling price of the keyboard is $45, how many units must the company sell to break?
I NEED HELP WITH THIS!!!
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The y-intercept represents the base price of $200 for airfare from NYC.
The slope represent a cost of $0.30 cents per mile traveled.
According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.
According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this trip, a linear equation that models the situation is given by;
y = mx + c
y = 0.30x + 200
When x = 2000, the price of airfare (y) is given by;
y = 0.30(2000) + 200 = $800.
When y = 500, the distance traveled (x) is given by;
500 = 0.30x + 200
300 = 0.30x
x = 1000 miles.
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Joe works in a
cafe. He is paid a per hour. How much klage of $19.26 would 4 Joe earn for working a 35 low week
Answer:
To calculate how much Joe would earn for working a 35-hour week, you need to multiply his hourly wage by the number of hours he worked123. For example, if Joe is paid $19.26 per hour, then his weekly pay is:
$19.26 x 35 = $673.10
This is his gross pay, which means it does not include any deductions for taxes or other benefits. His net pay, or take-home pay, may be lower depending on his filing status, allowances, withholding information and voluntary deductions1. You can use an hourly paycheck calculator to estimate his net pay1.
I hope this helps you understand how to calculate hourly pay. If you have any other questions, please let me know.
A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.3 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building? (Round your answer to one decimal place.)
Answer:
decreasing 0.5 m/s
Step-by-step explanation:
You want the rate at which the height of a shadow on a wall is decreasing as a 2 m tall man walks at 1.3 m/s toward the wall. The shadow is cast by a light 12 m from the wall, and the man is 4 m from the wall at the time of interest.
Similar trianglesIn the attached diagram, triangles ABC and LMA are similar. This lets us write the proportion ...
y/x = 2/(12 -x)
y = 2x/(12 -x) . . . . . . multiply by x to get expression for y
Rate of changeTaking the derivative with respect to time gives ...
y' = (2/(12 -x) +2x/(12-x)²)x'
At x = 4, this is ...
y' = (2/8 +8/8²)x' = (3/8)x'
When x' = -1.3 m/s, the rate of change of the shadow height is ...
y' = (3/8)(-1.3 m/s) = -0.4875 m/s
The length of the shadow is decreasing at about 0.5 m/s.
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From her first husband, Mindy has a son, Jaime, who is 14 years old and twins Keisha and lesha, age 11. From her second marriage, she has a daughter, Monifah, age 7 and triplets. Mike, Ike, and Spike, age 4. Since she dumped her second husband, Mork, she has not remarried but now has a one year old baby daughter named Moesha.
#5) if a person is chosen from this family at random, what is the probability of the person being a female?
Answer:
24%
Step-by-step explanation:
how to estimate the amount of concrete, rebar, grout for garage project
We need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.
We need to determine the dimensions of the footings. Since the footings are 8 inches thick, we can convert this to feet by dividing by 12:
8 inches / 12 inches/foot = 0.67 feet
The dimensions of the footings will depend on the size of the building, but let's assume for this example that the footings are 2 feet wide and 30 feet long.
Volume = length x width x thickness
= 30 ft x 2 ft x 0.67 ft
= 40.2 cubic feet
Convert the volume to cubic yards.
Since there are 27 cubic feet in a cubic yard, we can divide the volume by 27:
40.2 cubic feet / 27 cubic feet/cubic yard = 1.49 cubic yards
Adding 10% as instructed, we get:
1.49 cubic yards + 0.149 cubic yards = 1.639 cubic yards
Therefore, we need 1.5 yards of 3000 psi air entrained concrete for the footings, dug with a 24'' bucket.
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Marco completely filled a box with 36 unit cubes with no gaps or overlap
Answer:
If Marco completely filled a box with 36 unit cubes with no gaps or overlap, then the box must have a volume of 36 cubic units.
The box could have different dimensions depending on how the cubes are arranged. For example, the box could be a cube with side length 3 units, since 3 x 3 x 3 = 27. Then, Marco could add another layer of 3 x 3 cubes on top of the first layer, giving a total of 3 x 3 x 4 = 36 cubes.
Alternatively, the box could have dimensions 6 x 1 x 6, since 6 x 1 x 6 = 36. This box would have two layers of 6 x 6 cubes stacked on top of each other.
There are many other possible dimensions for the box, but all of them must have a volume of 36 cubic units to accommodate the 36 unit cubes with no gaps or overlap.
Score: 11/20 12/20 answered
Question 7
$
A car was valued at $42,000 in the year 2009. By 2013, the car value had depreciated to $11,000. If the
car's value continues to drop by the same percentage, what will it be worth in 2019? Round to the
nearest dollar.
Question Help: VIDEO
<
Submit
Answer:
Worth in 2019 is $12423.75
Explanation:
Current worth is C=$28000
Depreciation rate is D=15%
Time in years is T=19
Worth (W) 2019: W=C(1−D100)T=2800⋅(1−15100)19=$12423.75 [Ans]
The polynomial -24x² +337x-138represents the average number of visitors (in thousands) per day to a park area, where x represents the month of the year. Use this model to predict the average daily attendance at the park for the month of April. (Hint- April is the fourth month.)
For the month of April, the park is expected to get an average of 826 thousand people every day.
To predict the average daily attendance at the park for the month of April, we need to substitute x = 4 in the given polynomial and simplify:
-24x² +337x-138 = -24(4²) + 337(4) - 138
= -24(16) + 1348 - 138
= -384 + 1210
= 826
Therefore, the predicted average daily attendance at the park for the month of April is 826 thousand visitors per day.
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This is my last chance I need this done by tomorrow if anyone can help please I'd really appreciate it. I need this explained and answered! Whoever get's this correctly get's the points and brainly.
Answer:
He made 7 black-and-white drawings and 2 color drawing
Step-by-step explanation:
10x+25y=120
x+y=9
Multiply bottom by ten,
10x+25y=120
10x+10y=90
--------------------
15y=30
y=2
Now find x
x+2=9
x=7
Answer: 7 black and white, 2 color
Step-by-step explanation:
Let b= black and white drawings 10 min
Let c= color 25 min
She make 9 total drawings
b+c=9
She takes 2 hrs = 120 min
10b + 25c =120
Now you have 2 equations. Solve the system of equations. They want you to use elimination. Take the 1st equation multiply both sides by -10 so when you add it to next it will eliminate b
-10(b+c=9) multiply -10 to both sides
-10b-10c=-90 add to other equation
-10b-10c=-90
10b+25c=120
15c=30
c=2 >substitute back into an original equation
b+c=9 c=2 >substitute
b+2=9 > subtract 2 from both sides
b=7
Find the future value of an investment if $650 is deposited at the beginning of each month for 4 years and the interest rate is 2.2% compounded monthly.
$28,600.00
$35,252.54
$32,615.54
$22,425.51
The future value of the investment is equals to $[tex]32,582.78[/tex].
What is future value of the monthly investment?The number of monthly payments over 4 years is:
= 4 years x 12 months/year
= 48 months.
We will use future value of an annuity formulae to solve which is FV = PMT x [(1 + r)^n - 1] / r
Plugging in the values, we get:
FV = 650 * [(1 + 0.022/12)^48 - 1] / (0.022/12)
FV = 650 * (0.09190014604/0.00183333333)
FV = 650 * 50.1273524766
FV = 32582.7791098
FV = $32,582.78.
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arrange 12 coins in four rows with four in each row
Answer:
3 coins each row
Step-by-step explanation:
if you put 3 coins in 4 rows it we'll be equivalent to 12
8 1/2 pounds of hamburger meat are to be divided into 17 equal packages. How many pounds of meat will each package contain
Answer:
Each package will contain 1/2 pound of meat.
Step-by-step explanation:
To divide 8 1/2 pounds of hamburger meat into 17 equal packages using fractions, you need to divide the total weight by the number of packages:
First, convert the mixed number 8 1/2 to an improper fraction:
(8 * 2) + 1 = 16 + 1 = 17
So, 8 1/2 = 17/2
Now, divide 17/2 pounds by 17 packages. Since division is the same as multiplying by the reciprocal, we'll multiply by the reciprocal of 17, which is 1/17:
(17/2) * (1/17)
Multiply the numerators together (17 * 1 = 17) and the denominators together (2 * 17 = 34):
17/34
Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (17):
17 ÷ 17 = 1
34 ÷ 17 = 2
So, the simplified fraction is 1/2.
Solve ARST.
R
S
72°
7
T
15
r
S
Answer:
r = 14.3s = 4.6S = 18°Step-by-step explanation:
You want the solution to right triangle RST with RS = 15, R = 72°, T = 90°.
Trig relationsThe mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse ⇒ r = 15·sin(72°) ≈ 14.3
Cos = Adjacent/Hypotenuse ⇒ s = 15·cos(72°) ≈ 4.6
The acute angles in a right triangle are complementary, so ...
S = 90° -R = 90° -72° = 18°
Probability Problem that I need help with
The value of probability of getting a bowl of chicken soup is,
⇒ 52.1%
Given that;
Two way frequency table is shown.
Hence, We get;
The value of probability of getting a bowl of chicken soup is,
⇒ 642/1233
⇒ 0.5206 x 100%
⇒ 52.1 %
Thus, The value of probability of getting a bowl of chicken soup is,
⇒ 52.1%
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the points on the graph show the number of miles that jing rode during the first 4hrs of a bike trip jing plans to keep the same speed for the rest of the trip which ordered pair shows an equivalent ratio of hrs in miles
The ordered pair that shows an equivalent ratio of hours to miles is (1, 12) and Jing will complete a 60-mile trip in approximately 5 hours.
To find an equivalent ratio of hours to miles, we need to divide the number of miles by the number of hours.
For example, for the first 4 hours of the bike trip, Jing rode 48 miles, which is equivalent to a rate of 12/4 = 3 miles per hour.
Since Jing rode 60 miles in the first 4 hours of the trip, we can use this rate to find the time it takes her to ride 60 miles.
We can set up a proportion:
12 miles / 1 hours = 60 miles / x hours
Cross-multiplying, we get:
12x = 60
Dividing by 12, we get:
x = 60/12
x = 5
Therefore, Jing will complete a 60-mile trip in approximately 5 hours.
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The missing figure is attached below.
Translation to the question
The curve y=2x-x^2 contains along with the x-axel an area. See figure. Calculate the triangles maximum area. Answer exactly.
[tex]1/2 * 2 * 1 = 1[/tex] square unit.
Step-by-step explanation:
To find the maximum area of the triangle, we need to locate the vertex of the parabola. This occurs when x=1. The y-coordinate at x=1 is 1. We can then use this as the height of the triangle. The base of the triangle is the distance between x=0 and x=2, which is 2. Therefore, the maximum area of the triangle is 1/2 * 2 * 1 = 1 square unit.
The box plots show the heights of tomato plants in a random sample of 20 plants from Nursery X and a random sample of 20 plants from Nursery Y. ) Why can you use the box plots to make inferences about plant heights at the two nurseries? The samples of 20 plants are both taken from the same population. The data include all of the tomato plants at each of the nurseries. The random samples are likely to be 4) representative of the population of plants at each nursery. Heights of Tomato Plants Nursery X 6 Nursery Y 57 10 12 Height (in.) 14 16
We can use the box plots to make inferences about plant heights at the two nurseries because; "The random samples are likely to be 4) representative of the population of plants at each nursery." (Option C)
What is a box plot ?A box plot, often known as a boxplot, is a method in descriptive statistics for graphically displaying the localization, spread, and skewness groups of numerical data through their quartiles.
The box plot is useful for examining the range and distribution of numerical data sets. The box plot is useful for organizing vast volumes of data and seeing outlier values.
Disadvantages: Because it deals with a summary of the data distribution, the box plot is ineffective for thorough data analysis.
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The table shows the number of turtles hatched at a zoo each year since 2003. Year. Turtles Hatched.
2003. 21
2004. 17
2005. 16
2006. 16
2007. 14
A. Find the line of the best fit.
B. Predict the number of turtles to be hatched in 2011.
need step by step
A) The equation of the line of the best fit is y = -1.5x + 3024.3
B) The number of turtles to be hatched in 2011 = 8
Let us assume that x represents the years since 2003 and y represents the number of turtles hatched each year.
From the table of data values we draw a scatter plot.
The scatter plot for the data of the number of turtles hatched each year since 2003 is shown below.
From the scatter plot, the equation of the line of the best fit is:
y = -1.5x + 3024.3
Now we need to find the number of turtles to be hatched in 2011.
i.e., we find the value of y for x = 2011
y = -1.5x + 3024.3
y = -1.5(2011) + 3024.3
y = 7.8
y ≈ 8
Thus, the number of turtles to be hatched in 2011 = 8
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Suppose g1 = 3 and g2 = 5. The rest of the terms in a recursive sequence are given by the formula gn = n·gn-1 + gn-2.
Find the 7th term of the sequence, g7.
We can use the recursive formula to find the values of the sequence:
g3 = 3·g2 + g1 = 3·5 + 3 = 18
g4 = 4·g3 + g2 = 4·18 + 5 = 77
g5 = 5·g4 + g3 = 5·77 + 18 = 395
g6 = 6·g5 + g4 = 6·395 + 77 = 2457
g7 = 7·g6 + g5 = 7·2457 + 395 = 17276
Therefore, the 7th term of the sequence is g7 = 17276.
I need help With this problem and D says (1,1) is the x- and y- intercept of the function
The statement which is true include the following: A. (0, 0) is the x- and y-intercept of the function.
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
What is the x-intercept?In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept and y-intercept are located at the origin (0, 0).
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find the unit rate. 186 words/3 min
Answer: 62 words/ 1 minute
Step-by-step explanation:
186 words/3 minutes is basically 186 divided by 3. So divide the numerator by the denominator.
Example: $35 for 5lbs of flour. 35/5 in the simplest form is 7/1; therefore it is the unit rate.
Cuál es el diámetro 8m
The diameter of the circle, given the radius of 8 m, can be found to be 16 m.
How to find the diameter ?One can discover the diameter of a circle, based on its radius, by multiplying the radius value with 2 since the length of the diameter is twice that of the former.
Comparatively, another segment of equal distance measured between the central position of the same given circle to only one point found within the border outline is called the radius. Henceforth, simply duplicating the established radius equivalent will provide conclusive knowledge of its corresponding diameter measure.
The diameter is therefore :
= 8 x 2
= 16 meters
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A sequence can be generated by using an=3an−1, where a1=7 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
The first three terms of the given sequence is 7, 21 and 63. Therefore, option D is the correct answer.
Given that, the sequence can be generated using aₙ=3aₙ₋₁ and a₁=7.
Here, n is a whole number greater than 1.
So, a₂=3a₂₋₁
a₂=3a₁
a₂=3×7
a₂=21
a₃=3a₂
a₃=3×21
a₃=63
So, the first three terms are 7, 21, 63
Therefore, option D is the correct answer.
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Given vector u=<3,-4> find magnitude and degree
The sum of magnitude of u + v is 15.99.
What is magnitude?The magnitude or size of a mathematical object is described as a property which determines whether the object is larger or smaller than other objects of the same kind.
Given that, magnitude of u = 5
Magnitude of v = 11
The angle between them i= 40°
we represent u and v in vector form,
u = 5 ( cos 40° i + sin 40° j ) = 3.83 i + 3.21 j
v = 11 ( cos 40° i + sin 40° j ) = 8.42 i + 7.07 j
The sum of two vectors is given by
u + v = 3.83 i + 3.21 j + 8.42 i + 7.07 j
u + v = 12.25 i + 10.28 j
Magnitude of u + v = √(12.25²+10.28²)
Magnitude of u + v
Magnitude of u + v = √( 150.063 + 105.678)
Magnitude of u + v = 15.99
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complete question:
Given the magnitudes of vectors u and v and the angle θ between them, find sum of . Give the magnitude to the nearest tenth when necessary and give the direction by specifying the angle that the resultant makes with u to the nearest degree. ∣ u∣ = 5, ∣ v∣ = 11, θ = 40°
The weight of an object on the moon is about 1/6 its weight on earth. How much would a 10 4/5 pound cat weigh on the moon? Express your answer as a mixed number in simplest terms.
A cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.
Given that, an object will weigh 1/6 of its weight on moon of earth,
So, a cat having a weight of 10 4/5 pound will weight =
10 4/5 × 1/6
= 54/6 × 1/6
= 54 / 36
= 9/6
= 3/2
= 1 1/2
Hence a cat weighing 10 4/5 pounds on earth will weigh 1 1/2 pounds on the moon.
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