Step-by-step explanation:
A U.S. dime has a thickness of 7.05 millimeters. Gary has a stack of dimes 42.3 millimeters tall. How many dimes does he have?
Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons on to the airplane. Suppose that at O’hare International Airport, an average of 10 passengers per minute arrive (interarrival times are exponential). To check passengers for weapons, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. A checkpoint can check an average of 12 passengers per minute (the time to check a passenger is exponential). Under the assumption that the airport has only one checkpoint, answer the following questions:
a. What is the probability that a passenger will have to wait before being checked for weapons?
b. On the average, how many passengers are waiting in line to enter the checkpoint?
c. On the average, how long will a passenger spend at the checkpoint?
Answer:
a
[tex]P_k = 0.83[/tex]
b
[tex]N_{\mu} \approx 4 \ passengers[/tex]
c
[tex]T_{\lambda} = 0.5 \ minutes[/tex]
Step-by-step explanation:
From the question we are told that
The average number of passengers that arrive per minute is [tex]\lambda = 10[/tex]
The average number of check that can be carried out in one minute is [tex]\mu= 12[/tex]
Generally the probability that a passenger will have to wait before being checked for weapons is mathematically represented as
[tex]P_k = \frac{\lambda }{ \mu }[/tex]
=> [tex]P_k = \frac{10 }{ 12}[/tex]
=> [tex]P_k = 0.83[/tex]
Generally the number of passengers are waiting in line to enter the checkpoint is mathematically represented as
[tex]N_{\mu} = \frac{\lambda^2}{\mu (\mu -\lambda) }[/tex]
=> [tex]N_{\mu} = \frac{10^2}{12 (12 -10) }[/tex]
=> [tex]N_{\mu} \approx 4 \ passengers[/tex]
Generally the average time a passenger spend at the checkpoint is mathematically represented as
[tex]T_{\lambda} = \frac{ \frac{\lambda}{(\mu - \lambda)} }{ \lambda}[/tex]
=> [tex]T_{\lambda} = \frac{ \frac{ 10}{(12 - 10)} }{10}[/tex]
=> [tex]T_{\lambda} = 0.5 \ minutes[/tex]
Express decimal as a fraction 8.25
Answer:
33/4
Step-by-step explanation:
if the slope is -3/5 and the y intercept is 1 what is the slope intercept form of the equation of each line given the slope and y intercept
Answer:
y = -3/5x + 1
Step-by-step explanation:
A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 400 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.46.
Required:
What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50?
Answer:
0.0544
Step-by-step explanation:
From the given information;
The population proportion of the voters that would support the ballot measures in region A = 0.46
The random sample n = 400 voters
The required probability can therefore be computed as follows:
[tex]P[p_1>0.5] = P \bigg [ \dfrac{p_1-P_1}{\sqrt{\dfrac{P_1(1-P_1)}{n_1}}}>\dfrac{0.5-0.46}{\sqrt{\dfrac{0.46(1-0.46)}{400}}} \bigg][/tex]
[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{\dfrac{0.46(0.54)}{400}}} \bigg][/tex]
[tex]P[p_1>0.5] = P \bigg [ Z>\dfrac{0.04}{\sqrt{6.21\times 10^{-4}}} \bigg][/tex]
[tex]P[p_1>0.5] = P \bigg [ Z>1.605 \bigg][/tex]
[tex]P[p_1>0.5] = 1- P [ Z<1.605 ][/tex]
Using the Excel Function =NORMDIST(1.605)
[tex]P[p_1>0.5] = 1- 0.9456[/tex]
[tex]P[p_1>0.5] =0.0544[/tex]
Therefore, the required probability = 0.0544
Last year Mr Peterson had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year but he needs to buy more fencing to go around this years garden. How many more meters of fencing is needed for this years garden than last years?
Complete Question:
Last year Mr. Petersen’s rectangular garden had a width of 5 meters and an area of 20 square meters. This year he wants to make the garden three times as long and two times as wide.
Last year, Mr. Petersen had a fence all the way around his garden. He can reuse all of the fence he had around the garden last year, but he needs to buy more fencing to go around this year’s garden.
How many more meters of fencing is needed for this year’s garden than last year’s?
Answer:
26 meters of fencing needed
Step-by-step explanation:
Given
Last Year:
[tex]Width = 5m[/tex]
[tex]Area = 20m^2[/tex]
This Year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Width = 2\ times\ wider[/tex]
Required
Determine how many more meters is needed
Represent last year's length of Fence with L and last year's width with W
First, we need to calculate L
[tex]Area = L * W[/tex]
Where
[tex]Area = 20m^2[/tex]
[tex]W = 5m[/tex]
[tex]20m^2 = L * 5m[/tex]
Divide both sides by 5m
[tex]\frac{20m^2}{5m} = \frac{L * 5m}{5m}[/tex]
[tex]\frac{20m^2}{5m} = L[/tex]
[tex]L = \frac{20m^2}{5m}[/tex]
[tex]L = 4m[/tex]
So, we have that:
For Last Year
[tex]Length = 4m[/tex] and [tex]Width = 5m[/tex]
For this year:
[tex]Length = 3\ times\ longer[/tex]
[tex]Length = 3 * 4m[/tex]
[tex]Length = 12m[/tex]
[tex]Width = 2\ times\ wider[/tex]
[tex]Width = 2 * 5m[/tex]
[tex]Width = 10m[/tex]
So, for this year, we have:
[tex]Length = 12m[/tex] and [tex]Width = 10m[/tex]
Next, we calculate perimeter of fencing in both years.
[tex]Perimeter = 2 * (Length + Width)[/tex]
Last Year:
[tex]Perimeter = 2 * (4m + 5m)[/tex]
[tex]Perimeter = 2 * 9m[/tex]
[tex]Perimeter = 18m[/tex]
This Year:
[tex]Perimeter = 2 * (12m + 10m)[/tex]
[tex]Perimeter = 2 * 22m[/tex]
[tex]Perimeter = 44m[/tex]
To get the meters of fencing needed this year, we simply calculate the difference in the calculated perimeters.
[tex]Difference = 44m - 18m[/tex]
[tex]Difference = 26m[/tex]
Hence, there are 26 meters of fencing needed
-3a-3=-2n+3p solve for a
Answer:
a=−2n3−p−1a=-2n3-p-1
Answer:
a=−2n3−p−1a=-2n3-p-1
Step-by-step explanation:
The hiking path to the top of a mountain makes, at the steepest place, an angle of 20° with the
horizontal, and it maintains this constant slope for 500 meters, as illustrated below. Which of the
following is the closest approximation to the change in elevation, in meters, over this 500-meter
section?
500 meters
20
A 20
B) 170
180
D 250
We are given:
a right angled triangle with the angle of elevation = 20 degrees
Hypotenuse of the Triangle = 500 m
Finding the change in Elevation:
We will use trigonometry in the given triangle to find the length of the perpendicular of the triangle
Using trigonometry, we found that the perpendicular = 500 * Sin 20 degrees
Perpendicular = 500 * 0.342 [sin(20 degrees) = 0.342]
Perpendicular = 171 m
The closest value to 171m in the given options is 170m
Therefore, 170m (option B) is correct
-5(2× - 4)=2(x - 8) with work please :)
Answer:
Step-by-step explanation:
−5(2)(−4)=2(x−8)
Simplify both sides of the equation.
−5(2)(−4)=2(x−8)
−5(2)(−4)=(2)(x)+(2)(−8)(Distribute)
40=2x+−16
40=2x−16
Step 2: Flip the equation.
2x−16=40
Step 3: Add 16 to both sides.
2x−16+16=40+16
2x=56
Step 4: Divide both sides by 2.
2x/2 = 56/2
x=28
ME NEEDS SOME MORE HELP FOR QUESTION 2
also whoever answers this question first I will mark them the brainliest :3
Answer:
C is answer I think 0, because
Answer:
C.
Step-by-step explanation:
100%sure
Because -5 in front will equal a positive because you have a positive 0 in back therefore it will be C brainliest please!
Choose the fraction that has not been reduced to simplest form.
[tex]\frac{1}{16} \frac{21}{34} \frac{3}{57} \frac{11}{17}\\[/tex]
Answer:
3/57
Step-by-step explanation:
3/57 because 3/3*19=1/19
What’s the constant term for 7k-8k=
Answer:
K?
Step-by-step explanation:
Solve the equation for x.
– 1/2x – 3 = 4
Answer:
x = -4
Step-by-step explanation:
Multiply both sides by 2. Move constant to the right-hand side and change the sign. Add the numbers. And change the signs on both sides of the equation.
5. My red or blue shirt club has 32 members. If the number of people wearing read shirts
is 4 less than triple the number of people wearing blue shirts, how many people are
wearing red shirts?
Answer:
(red shirt people) r - 4[tex]\sqrt[3]{b}[/tex] (blue shirt people)
Step-by-step explanation:
I don't know if you want an equation or an exact answer. I have an equation though.
I got this answer like this:
4 less is minus 4
triple is multiplication and/or times
50+100n please awnser thisssssssssssssssssssssssssssssssssssssssssssssssss
Answer:
5 ( 1 + 20 n )
Step-by-step explanation:
Answer:
Your answer will be 150
Step-by-step explanation:
your answer going to be 150
Matrix, help.
So I was instructed to use a calculator rather than solving by hand, so I did try to use my TI-84 but I'm having trouble, Is it possible to solve this by hand and if so- how do I go about it? Thank you (:
Answer:
i knew it but i forgot
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
The density D of an object is the quotient of its mass m and its volume v
Your friend and her parents are visiting colleges. They leave their home in Enid, Oklahoma, and drive to Tulsa, which is 107 mi east and 18 mi south of Enid. From Tulsa, they go to Norman, 83 mi west and 63 mi south of Tulsa. Where is Norman in relation to Enid?
What is the equation of a line that passes through the point (1. 8) and is perpendicuarto rene rose cons y=+32 Enter your answer in the box
Answer:
-12yx
Step-by-step explanation:
y=x/2+3
y-3= -6
-6y= x/2
-6 x 2= -12yx
1. A therapeutic drug has the side effect of raising a patient's heart rate. The relationship between ,
the amount of the drug in the patient's body (in milligrams), and r, the patient's heart rate (in beats
per minute) is given by r(Q) = 60+ 0.2Q. Over time the level of the drug in the patient's
bloodstream changes. The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)".
a. What is the heart rate of this patient 5 minutes after the drug was administered? 8 minutes?
10 minutes? 13 minutes?
Complete question :
A therapeutic drug has the side effect of raising a patient's heart rate. The relationship between ,
the amount of the drug in the patient's body (in milligrams), and r, the patient's heart rate (in beats
per minute) is given by r(Q) = 60+ 0.2Q. Over time the level of the drug in the patient's
bloodstream changes. The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)^t.
a. What is the heart rate of this patient 5 minutes after the drug was administered? 8 minutes?
10 minutes? 13 minutes?
Answer:
76.384 ;
68.389 ;
65.369;
62.749
Step-by-step explanation:
Given function:
r(Q) = 60+ 0.2Q ; amount of drug on patient's body, Q and heart rate (r)
The amount of drug in the patient's body, Q, (in milligrams) t minutes after
the drug has been administered is given by Q(t) = 250(0.8)^t
a. What is the heart rate of this patient
5 minutes after the drug was administered?
t = 5 ; quantity of drug on patient's body ;
Q(5) = 250(0.8)^5 = 81.92
Q = 81.92
Heart rate (r)
r(81.92) = 60+ 0.2(81.92) = 76.384
t = 8 minutes?
Q(8) = 250(0.8)^8 = 41.94304
Q = 41.94304
Heart rate (r)
r(41.94304) = 60+ 0.2(41.94304) = 68.389
t = 10 minutes
Q(10) = 250(0.8)^10 = 26.8435456
Q = 26.8435456
Heart rate (r)
r(26.8435456) = 60+ 0.2(26.8435456) = 65.369
t = 13 minutes
Q(13) = 250(0.8)^13 = 13.7438953472
Q = 13.7438953472
Heart rate (r)
r(13.7438953472) = 60+ 0.2(13.7438953472) = 62.749
Researchers are interested in assessing if there is an association between dietary cholesterol intake and high blood pressure. The following data was summarized:
Blood Pressure
Dietary Cholesterol High Low Total
High 159 91 250
Low 78 172 250
Total 237 263 500
Required:
a. Estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol.
b. Compute an estimate of the odds ratio of high blood pressure for the two groups
c. Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
Answer:
A) Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) The odds ratio shows that BP is directly proportional to Dietary cholesterol
Step-by-step explanation:
A) estimate the conditional probabilities of high and low blood pressures given the level of dietary cholesterol
Conditional probability for a high BP given that dietary cholesterol is high as well
P = 159 / 250
Conditional probability for a high BP given that dietary cholesterol is low
P = 78 / 250
Conditional probability for a low BP given that Dietary cholesterol is high
P = 91 / 250
Conditional probability for a low BP given that Dietary cholesterol is low
P = 172 / 250
B) Compute an estimate of the odds ratio of high blood pressure for the two groups
High BP for High dietary cholesterol
= 159 / 237
High BP for low dietary cholesterol
= 78 / 237
C) Interpret the odds ratio and determine if high blood pressure is related to dietary cholesterol.
The odds ratio shows that BP is directly proportional to Dietary cholesterol as seen in the the odds ratio that ratio between High BP and High Dietary cholesterol is higher than other odds ratios
Find the equation of the line. The line is parallel to y=-6/7x +1 and passes through the point (-7, -3). The equation of the line is y=
Answer:
same slope but the y- intercept would be -9
What is 48 square feet in square meters
Answer: 4.45935
Step-by-step explanation: 1 Square foot (sqft) is equal to 0.09290304 square meter (sqm). For example, to convert 100 square feet to square meters, multiply 100 by 0.09290304, that makes 9.290304 sqm is 100 sqft. Hope this helps.
Please Help ASAP
What is the equation of the line in slope-intercept form?
Line on a coordinate plane. The line runs through points begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 5 end ordered pair.
Enter your answer in the boxes.
y =
x +
$\text{Basic}$
Answer:
y=5/2x+5
Step-by-step explanation:
Slope intercept form is y=mx+b
m is the slope, and b is the y intercept
FIrst we have to find the slope which is rise/run
Since our points are (-2,0) and (0,5) the equation will be:
5-0/0-(-2)
5/2
The slope is 5/2
Next we have to plug in 5/2 for m:
y=5/2x+b
We know that the y intercept is 5 from the coordinate (0,5)
y=5/2x+5
Answer:
y is 5/2 and x is 5
Step-by-step explanation:
i just know it already x3
What is 55/99 Rounded to the nearest half
Answer: 1/2
Step-by-step explanation:
Answer: 1/2 is your answer:)
Step-by-step explanation: 50 rounded to the nearest tenth is 50
99 rounded to the nearest tenth is 100 and
50 is half of 100:)
A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 56 had a
mild allergic reaction. What percent of the people had a mild allergic reaction?
Answer:
0.8
Step-by-step explanation:
i believe it would be 56/7000 and you multiply your answer 0.008 by 100 so 0.8 had a mild reaction
Answer:
0.8%
Step-by-step explanation:
Think of it as a fraction: 56/7,000. To get a percent you want to simplify the denominator to 100. Then what you do to the denominator, you must do to the numerator, so simplify 56 by the number you simplified 7,000 to get to 100. Then you will have your answer of 0.8%.
This is very urgent please tell me if the one that is highlighted all blue is correct or not left or right question,which is correct?
Answer:
right option
Step-by-step explanation:
Find the equation of the line.
The line is perpendicular to y = 1/2x +5 and passes through the point (4,7).
The equation of the line is: y =
Answer:
y=-2x+15
Step-by-step explanation
A perpendicular line always has the opposite reciprocal slope of the line it is 90 degrees from.
Since the slope of the other line is 1/2, the slope of this line must be -2. And with the slope of a line -2 with point (4,7), you can start plugging in numbers.
y=-2x+b
7= -2(4)+b
7= -8+b
15=b
Therefore, the equation of the line is y=-2x+15
Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 2. (Input decimals only, such as 12.71, as the answer
Answer:
3.14((4^2)+(4)(2))
3.14(16+8)
3.14(24)
=75.36
You just want to plug in the values of a and b into the equation and solve using order of operations. Hope this helps!
Step-by-step explanation:
Which point is NOT part of the solution set?
A. (-1, -3)
B. (5, 1)
C. (20, -5)
D. (0, 0)
Answer:
c becues its a bigger number
Step-by-step explanation:
Answer: A. (-1, -3)
This point is on the boundary line, but the boundary line is a dashed line. So this point is not part of the solution. The dashed line is like an electric fence you can get closer to, but you cannot touch it. It's due to the fact there isn't any "or equal to" as part of the inequality sign. So that's why (-1,-3) is not in the solution set. If the boundary line was solid, then (-1,-3) would be a solution.
Points like (5,1), (20,-5) and (0,0) are solutions because they are in the pink shaded region, and they aren't on the boundary.