The probability that the meeting takes place is 7/24.
What is the probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes(sample space) of the event.
It is given by
P(A) = n(A)/n(S)
Where A - event, S - sample space
Calculation:From the given data,
The probability, if the engineers arrive in the first hour and the boss arrives in the second hour is 1/8,
So, the meeting will be held i.e., p = 1.
The probability, if all the three arrive in the same hour (first or second)
= 1/8 + 1/8
= 1/4
So, the meeting will be held only if the boss (he may arrive first, second, or last) arrives last, the probability is 1/3
The probability, if one of the engineers arrives in the first hour while the other engineer and the boss arrive in the second hour is
= 1/4
So, the meeting will be held only if the second engineer arrives before the boss and before the first engineer leaves, the probability is 1/3
Thus, the final probability for the meeting to take place is
= (1/8) × 1 + (1/4) × (1/3) + (1/4) × (1/3)
= 7/24
Therefore, the required probability is 7/24.
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To solve the equation 1. 75n = 7 for n, what operation must be applied to both sides in order to isolate the variable n?
a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60 degrees, what is the length of the third side of the triangle
The length of the third side of the triangle is 4. 33
How to determine the side
We have the length of the two sides to be;
2 and 5
If the angle between them is 60 degrees, then the third side is the opposite side
To find the opposite side, we use the sin ratio, which is
sin 60 = opposite/hypotenuse
sin 60 = x/ 5
Cross multiply
sin 60 × 5 = x
x = 0. 8660 × 5
x = 4. 33
Thus, the length of the third side of the triangle is 4. 33
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The length of a rectangle is 3 less than twice the width. Determine how the area will change if the length of the rectangle is increased by 5 and the width is decreased by 2. Show your work.
The change in the area is represented by the expression ΔA = 9 · x + 4, where x is the original width of the rectangle.
What is the change in the area of the rectangle if side lengths are changed?
By geometry we know that the area of a rectangle is equal to the product of its width (x) and length (y). Based on the statement, the original rectangle is equal to:
A = x · y
A = x · (2 · x - 3)
And the change in the area is:
A + ΔA = (x + Δx) · (y + Δy)
A + ΔA = x · y + Δx · y + Δy · x + Δx · Δy
ΔA = Δx · y + Δy · x + Δx · Δy
ΔA = (2 · x - 3) · Δx + Δy · x + Δx · Δy
ΔA = 2 · (2 · x - 3) + 5 · x + 10
ΔA = 9 · x + 4
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Leigh has information on how many customers purchase bagels at her coffee shop. With the bagel sales numbers from the past four months, she wants to
To predict the bagel sales numbers for the next month, Leigh could use Predict trend.
Given that Leigh has information on how many customers purchase bagel at her coffee shop.
We are required to answer the spreadsheet Leigh could use to predict bagel sales number for the next month.
Spreadsheet is developed for windows, macOS, Android and iOS.It features calculation through functions. In this we can use mathematical functions,logical functions, etc.
Leigh could use predict trend to predict the sales number of bagels of next month.
Hence predict trend could be used by Leigh to predict the sales for the next month.
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Question is incomplete as question should include the following:
What spreadsheet could Leigh use to predict the sales of next month?
Practice with Laws of Logic
Provide the valid conclusion to the argument below.
If I am sick, then I will not come to school.
If I do not come to school, then I am sad.
Answer:
if I am sick, then I will not come to school.
Step-by-step explanation:
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
Answer:
Step-by-step explanation:
You have 35 coins. they are all quarters and nickels. if you have $3.15, how many nickels and how many quarters do you have?
(-1/2 - 1/8) + (3/4 + 5/6) A.1/12
Answer:
23/24
Step-by-step explanation:
Let's convert all the fractions to a common denominator
(-12/24 - 3/24) + (18/24 + 20/24)
Combine like terms and you get 23/24
Jaime currently pays $60 a YEAR for his Amazing Primo membership,
which allows him to rent movies for $2.25 each. However, he finds out that
with a Netflakes membership he could rent each movie for only $1.00. If
Netflakes charges $15 a MONTH for membership, how many movies
would Ricardo have to rent each month for a Netflakes account to be
cheaper overall than having Amazing Primo?
8
24
23
9
15
Answer:
9
Step-by-step explanation:
Let x = # of movies Jamie watches in a month. 5 + 2.25x represents the monthly cost of Amazing Primo, and 15 + x represents the monthly cost of Netflakes.
5 + 2.25x > 15 + x
1.25x > 10
x > 8
Jamie must watch more than 8 movies each month for the Netflakes account to be cheaper overall.
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours
The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.
The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.
Equation of cosine function:The following is a presentation of the cosine function's generic form;
y = a + cos(bx - c) + d
amplitude = a
b = cycle speed
Calculation for the model height;
The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Obtain amplitude 'a' as
[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]
The time 'T' is calculated as-
[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]
Now, calculate 'd'
[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]
Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:
h=0.5cos([tex]\pi[/tex]/6t)+9.5
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The complete question is-
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
A. h=0.5cos([tex]\pi[/tex]/12t)+9.5
B. h=0.5cos([tex]\pi[/tex]/6t)+9.5
C. h=cos([tex]\pi[/tex]/12t)+9
D. h=cos([tex]\pi[/tex]/6t)+9
The graph below represents the data from Part A. Use the data from Part A to correctly label the graph. Drag the labels to their appropriate locations on the graph.
The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.
What is a graph?A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.
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Part A:
According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.
Select the correct answer. An experiment consists of rolling a six-sided die to select a number between 1 and 6 and drawing a card at random from a set of 10 cards numbered 1, 2, 3, ... 10. Which event definition corresponds to exactly one outcome of the experiment?
Answer:
Step-by-step explanation:
Solution
You want to find the probability of one certain event happening. For example, you want the die to come up 5 and you want the 6 to be drawn from the cards.
The total number of outcomes is 6 (for the die) times 10 for the cards.
One 1 outcome is possible.
So the vent probability is 1/6*10 = 1/60. You will have to translate this to the choices you have been given. 1/60 = 0.0167 is another possibility.
Answer
1/60 or 0.0167
Can someone help me with these problems having trouble and show work please !!
Answer:
(2x-5)(2x-5), 81 meters
Step-by-step explanation:
All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)
Using this equation we can plug in 7 for x:
(2(7)-5)(2(7)-5) =
(14-5)(14-5) =
9*9 = 81
There were 150 females surveyed, evenly divided for all levels of expertise. there were 450 males surveyed. there were 80 expert players and 180 novice players.
The values which would help complete the table according to the complete part of the task content are as evaluated.
What value would help complete the table?First, the total number of average players can be evaluated by summing up the total number of players vertically as follows;
180 + average + 80 = 600
The number of average players is therefore; 600-180-80 = 340 average players.
Also, the number of female expert players can be evaluated vertically as;
50 + 50 + female expert = 150
Female expert = 150-50-50 = 50 female experts.
The number of male novice players can be evaluated horizontally as;
Male novice + 50 = 180
Male novice = 180 - 50 = 130.
The number of average male players is therefore easily evaluated vertically as;
130 + male average + 30 = 600
male average = 600-130-30 = 440.
Remarks: The table which is required to be completed is that which is in the attached image.
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Answer:
130, 290, 340, 50
Step-by-step explanation:
just do the math, I got it right on edmentum.
Triangle KLM represents a section of a park set aside for picnic tables. The picnic area will take up approximately 400 square yards in the park.
The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.
We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.
We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.
Using this in the given triangle KLM, we get:
Area = (1/2)(KL)(KM)(sin K),
or, 400 = (1/2)(KL)(45)(sin 25°),
or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.
Thus, we get KL = 42 yards.
Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.
Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.
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For the complete question, refer to the attachment.
Your ship has steamed 1651 miles at 20 knots using 580 tons of fuel oil. The distance remaining to your next port is 1790 miles. If you increase speed to 25 knots, how much fuel will be used to reach that port
The 680 tons of fuel needed to cover the next 1790 miles distance.
According to the statement
We have given that the ship covered a 1651 miles distance at 20 knots by a 580 tons of fuel oil.
And distance remaining to next port is 1790 miles and speed increases to 25 knots.
And we have to find that how much fuel used to reach that port.
So, Distance covered = 1651 mile
fuel used = 580 tons
distance covered with 1 tons fuel = 1651/580
distance covered with 1 tons fuel = 2.85 mile at a speed of 20 knots.
so, The fuel consumption for 1790 mile is = 1790/2.85
The fuel consumption for 1790 mile is = 628 tons of fuel needed.
So, The 680 tons of fuel needed to cover the next 1790 miles distance.
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true ir false .
A central angle is equal to half the measure of its intercepted arc.
Answer:
Step-by-step explanation:
Answer
False but close.
The intercept arc and the central angle are equal.
On a hike, Maria walked up a hill in 30 minutes, and then she ran back down the hill in 10 minutes. Which of the following graphs could model the total distance Maria hiked?
The graph that describes the motion of Maria is the graph in Option B.
What is displacement?Displacement is the term that is used to describe the distance covered in a specified direction.
We are told that Maria walked up a hill in 30 minutes, and then she ran back down the hill in 10 minutes. The graph that describes this motion is the graph in Option B.
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Can someone help me please
Answer:
10. 20.9°
11. 73.2°
Step-by-step explanation:
The inverse sine function is used to find the angle from its sine value.
10.In each case, the equation is of the form ...
a/sin(x) = b/c
Multiplying both sides by c/b·sin(x), we find the solution is ...
sin(x) = ac/b . . . . . find sin(x)
x = arcsin(ac/b) . . . . . find the corresponding angle
For the given values a=7.2, b=13, c=sin(40°), we have ...
x = arcsin(7.2sin(40°)/13) ≈ 20.9°
11.For the given values a=6.53, b=√40, c=sin(68°), we have ...
x = arcsin(6.53sin(68°)/√40) ≈ 73.2°
Here's a Question for you! Solve for Reasoning
Step-by-step explanation:
3) Triangle QTR is similar to triangle STP (AA)
4) RT/PT = QR/PS (corresponding sides of similar triangles are proportional)
The cost of a fan is Rs 1,600. If Mrs. Khadka purchased it with 13% VAT, how muc did she pay for it?
Answer:
Rs 1808
Step-by-step explanation:
Sp=Selling price
Mp=main price
Sp=Mp+Mp*VATSp=Rs 1600+Rs 1600*13%Sp=Rs 1600+Rs 208Sp=Rs 1808HELP ASAP THANK YOU!)
In order to hang a block of gold from a chain necklace, a jeweler drilled a hole in the center, 5 mm in diameter the original block of gold.
If the original block of gold was 27 mm long, 8 mm wide, and 12 mm high, find the volume of the remaining piece of gold to the nearest tenth cubic millimeter.
(The answer choices are below)
Answer:
2061.9[tex]mm^{3}[/tex]
Step-by-step explanation:
We can see the original shape of the gold block is a cuboid.
Volume of Cuboid = Length x Width x Height
Volume of Original Gold Block = 27mm x 8mm x 12mm = [tex]2592mm^{3}[/tex]
Next, we can see the shape of the cut-out hole is a cylinder.
Volume of Cylinder = [tex]\pi r^{2} h[/tex]
We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm
Volume of cut-out hole = [tex]\pi (2.5)^{2} (27)\\[/tex] = [tex]168.75\pi mm^{3}[/tex]
Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole
= [tex]2592mm^{3} -168.75\pi mm^{3}[/tex]
= 2061.9[tex]mm^{3}[/tex]
3. Which of the following is equivalent to (10a³b³) (5a³b²)?
Answer:
50a^6b^5
Step-by-step explanation:
I don't see answer choices, but this is the simplified version. To do this, multiply 10*5, a^3 * a^3 (which adds the exponents), and then b^3*b^2.
Convert each rate using dimensional analysis. round to the nearest tenth, if necessary. 4.5 qt / min = ____ gal / h a. 67.5 c. 56.3 b. 33.8 d. 65
Option a is correct.
What is dimension analysis?
Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed.
We can convert qt/min to gal/h as shown below:
1 qt = 0.25 gallon
1 min = 1/60 hour
4.5 qt/min = (4.5*0.25)/ (1/60) gal/h
= 4.5*0.25*60 gal/h
= 67.5 gal/h
Hence option a is correct.
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Can someone help me with this pls
Answer:
x = 1/3 or x = -2/3
Step-by-step explanation:
Let's solve your equation step-by-step.
9x2+3x−2=0
For this equation: a=9, b=3, c=-2
9x2+3x+−2=0
Step 1: Use quadratic formula with a=9, b=3, c=-2.
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(9)(-2)} }{2(9)}[/tex]
[tex]x=\frac{-3\pm\sqrt{81} }{18}[/tex]
x = 1/3 or x = -2/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the quadratic formula?}[/tex]
[tex]\rm{x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
[tex]\textsf{Or even}[/tex]
[tex]\rm{ax^2 + bx + c = 0}[/tex]
[tex]\huge\textbf{What are we looking for?}[/tex]
[tex]\rm{9x^2 + 3x - 2 = 0}[/tex]
[tex]\huge\textbf{What are the labels in the equation?}[/tex]
[tex]\mathsf{a \rightarrow 9}\\\\\mathsf{b\rightarrow 3}\\\\\mathsf{c \rightarrow -2}[/tex]
[tex]\huge\textbf{Solving for your equation:}[/tex]
[tex]\rm{x = \dfrac{-(3)\pm \sqrt{3^2 - 4(9)(-2)}}{2a}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\rm{x = \dfrac{-3\pm \sqrt{81}}{18}}[/tex]
[tex]\rm{x = \dfrac{1}{3}\ or\ x = - \dfrac{2}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\mathsf{x} = \dfrac{1}{3}\ or\ \mathsf{x} = - \dfrac{2}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
The value of a company’s stock is represented by the expression x2 – 2y and the company’s purchases are modeled by 2x 5y. the company’s goal is to maintain a stock value of at least $5,000, while keeping the purchases below $1,000. which system of inequalities represents this scenario? x2 – 2y > 5000 2x 5y < 1000 x2 – 2y > 5000 2x 5y ≤ 1000 x2 – 2y ≥ 5000 2x 5y < 1000 x2 – 2y ≤ 5000 2x 5y ≤ 1000
Answer:
answer is (c)
May it help you
Option C. The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
How to write the inequality
Stock = x² - 2y
Purchase = 2x + 5y
Stock is said to be at least 5000 dollars. We can write this as
x² - 2y ≥ 5000
Then the purchase is said to be below 1000. This is written as 2x + 5y <1000
The inequality can then be written as x² - 2y ≥ 5000 and 2x + 5y <1000
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Solve the equation. Give your simplified answer as an improper fraction.
 -(x-1)+10 = -3(x-2)
pls help me out lol
Answer:
Step-by-step explanation:
I'm not entirely sure that this is correct, but it seems so to me from what I've read.
The Coordinate system uses N,S,E,W to denote plus and minus. N (north) and E (east) are plus, and S (south) and W (west) are minus. North is + y and S is - y. E (east is plus x W is minus x)
(4,-7) = 4 east 7 south is what I would use as my answer.
Question 6 of 20
What is the common difference between consecutive terms in the following
arithmetic sequence?
51, 47, 43, 39, ...
OA. 3
B. -3
O C. -4
D. 4
Common difference formula
[tex]\boxed{\sf d=t_2-t_1}[/tex]
So
Here
[tex]\\ \tt{:}\longrightarrow d=47-51[/tex]
[tex]\\ \tt{:}\longrightarrow d=-4[/tex]
Option C
Answer:
C. -4
Step-by-step explanation:
Given sequence: 51, 47, 43, 39, ...
To find the common difference (d) between consecutive terms in an arithmetic sequence, subtract the previous term from the next term:
[tex]\implies \sf d=47-51=-4[/tex]
[tex]\implies \sf d=43-47=-4[/tex]
[tex]\implies \sf d=39-43=-4[/tex]
Therefore, the common difference for the given arithmetic sequence is -4.
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the product of 1540 and m is a square number. find the smallest possible value of m
Answer:
Step-by-step explanation:
the smallest value is 96.25 or rounded to the nearest whole number it is 96
what i did was put in my calculator 1540 divided by 4^2 because it is squared and has 4 sides
Supergran runs from her chalet to the top of the mountain. She knows that if she runs at a speed of 6 mph she will arrive at 1 pm, whereas if she leaves at the same time and runs at 10 mph, she will arrive at 11 am. At what speed should she walk if she wants to arrive at 12 noon
Using proportions, it is found that she should walk at a speed of 8 mph to arrive at noon.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, considering the speeds of arrival at 11 am and at 1 pm, we have that for each 2 km slower, she arrives one hour later.
Walking at 10 mph she arrives at 11 am, hence she should walk at a speed of 8 mph to arrive at noon.
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