Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.1 minutes and a standard deviation of 2.0 minutes. For a randomly received emergency call, find the following probabilities.
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b) 0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c) 0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 8.1 minutes and a standard deviation of 2.0 minutes.
This means that [tex]\mu = 8.1, \sigma = 2[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5.
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.1}{2}[/tex]
[tex]Z = 0.95[/tex]
[tex]Z = 0.95[/tex] has a p-value of 0.8289
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.1}{2}[/tex]
[tex]Z = -1.55[/tex]
[tex]Z = -1.55[/tex] has a p-value of 0.0606
0.8289 - 0.0606 = 0.7683
0.7683 = 76.83% probability that a randomly selected emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which, found from item a, is of 0.0606
0.0606 = 6.06% probability that a randomly received emergency call is of less than 5 min.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a, is of 0.8289
1 - 0.8289 = 0.1711
0.1711 = 17.11% probability that a randomly received emergency call is of more than 10 min.
pls I have limited time left pls help
Answer:
2B+5C
Step-by-step explanation:
Multiply them out....
2B=2*(4i-j) = 8i-2j
5C=5*(2i+3j) = 10i+15j
2B+5C= 8i-2j+10i+15j =18i+13j = A
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Answer:
a) 2B +5C
Step-by-step explanation:
It is probably easiest to simply try the answer choices. You find the first one works, which means it is the one you want.
2B +5C = 2(4i -j) +5(2i +3j) . . . . choice (a)
= 8i -2j +10i +15j
= 18i +13j = A
__
In general, you can solve for the coefficients p and q that make ...
pB +qC = A
p(4i -j) +q(2i +3j) = 18i +13j
(4p+2q)i +(-p +3q)j = 18i +13j
Equating the coefficients of i and j gives us 2 equations in p and q.
4p +2q = 18
-p +3q = 13
Adding 2 times the second equation to 1/2 the first, we get ...
1/2(4p +2q) +2(-p +3q) = 1/2(18) +2(13)
7q = 35
q = 5
Using the second equation to find p, we get ...
p = 3q -13 = 3(5) -13 = 2
These coefficients tell us ...
A = 2B +5C . . . . . . . matches choice (a)
Polygon ABCD is a rectangle. What is its area? Round your answer to the
nearest tenth.
(2,4)
(4,1)
(-4,0)
4
(-2, -3)
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Answer:
26 square units
Step-by-step explanation:
Counting grid squares on the graph, we see that segment AB is the hypotenuse of a right triangle with legs 2 and 3. Its length is ...
AB = √(2²+3²) = √13
We can also see that the adjacent longer sides are twice this length, each being the hypotenuse of a triangle that is 6 wide and 4 high.
AC = √(6² +4²) = √52 = 2√13
Then the area is ...
A = LW
A = (2√13)(√13) = 2·13 = 26 . . . square units
A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Calculate the cyclist's average speed in mph.
Answer:
v = 15 mph
Step-by-step explanation:
Given that,
A cyclist travels 3 miles in 15 minutes and then a further 7 miles in 25 minutes without stopping.
Total distance, d = 3 + 7 = 10 miles
Total time, t = 15 + 25 = 40 minutes = 0.6667 hours
Average speed,
[tex]v=\dfrac{d}{t}[/tex]
Put all the value,
[tex]v=\dfrac{10}{0.6667}\\\\= $$14.99\ mph[/tex]
or
v = 15 mph
So, the required average speed is equal to 15 mph.
What is the length of each leg of the triangle below?
459
22
90°
45
O A. 11.12
B. 1
C. 15
D. 11
ET
F. 22
Answer:
option A
Step-by-step explanation:
since the given triangle is an isosceles triangle it's two remaining sides are equal
let the length of missing side be x
using pythagoras theorem
a^2 + b^2 = c^2
x^2 + x^2 = 22^2
2x^2 = 484
x^2 = 484/2
x = [tex]\sqrt{242}[/tex]
x = [tex]11\sqrt{2}[/tex]
Which graph represents the solution set of the compound inequality -4 s 3x-1 and 2x+4 518?
-10
-5
0
10
O
+
-10
-5
0
5
10
5
-10
0
5
10
+
-10
-5
0
10
Answer:
it's the first one where X is greater or equals to -1 and X is less or equals to positive 7
The compound inequality in x : -1 ≤ x ≤ 7
The correct graph is A .
Given, inequality: -4 ≤ 3x -1 and 2x + 4 ≤ 18 .
First inequality:
-4 ≤ 3x -1
Take -2 from RHS to LHS .
-4 + 1 ≤ 3x
-3 ≤ 3x
x ≥ -1
X will have values greater than equal to -1 .
Second inequality:
2x + 4 ≤ 18
take 4 from LHS to RHS.
2x ≤ 18 - 4
2x ≤ 14
x ≤ 7
x will have values less than equals to 7.
Combined result of both inequalities: -1 ≤ x ≤ 7 .Thus graph A is correct.
Know more about inequality,
https://brainly.com/question/28823603
#SPJ3
5 > Chapter 2: Modeling with Quadratic Functions > Secti
Write an equation of the parabola in intercept form.
IN AY
х
-2.
(-1,0)
(2,0)
(1, -2)
-4
4
An equation of the parabola is y=0
Answer:
the awnser is 2,0
Step-by-step explanation:
Answer:
(1,-2) is the correct answer
A jet travels 5192 miles against a jetstream in 8 hours and 6072 miles with the jetstream in the same amount of time. What
is the rate of the jet in still air and what is the rate of the jetstream?
the answer is in the picture
What is the nearest quarter hour to 10:40
[tex]\Huge \bf \over \rightarrow\mid\mathcal {\underline{ \orange{12 \: : \: 00}}} \mid[/tex]
Answer:
I think 10:45 is the nearest quarter hour.
The equation of the line passing through (2, 3) with a slope of 5 is y = [] x - []
what are the answers to []
Answer:
y = 5x - 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5, then
y = 5x + c ← is the partial equation
To find c substitute (2, 3) into the partial equation
3 = 10 + c ⇒ c = 3 - 10 = - 7
y = 5x - 7 ← equation of line
calculate the surface area and show work :) please help me no links!!
Answer:
294 in.²
Step-by-step explanation:
I believe this figure is a rectangular prism.
------------------------------------------------------------------------------------
Explain:
To find the surface area of a rectangular prism, use this formula:
[tex]SA=2lw+2lh+2wh[/tex]
or
[tex]SA=2(lw+lh+wh)[/tex]
[tex]l-length[/tex]
[tex]w-width[/tex]
[tex]h-height[/tex]
A phrase I use to help remember this formula is:
LISA WILSON LOST HER WITCH HAT TWICE (2)
------------------------------------------------------------------------------------
Solve:
The length of this rectangular prism is 9 in.
This width is 10 in.
The height is 3 in.
Now, I will plug the numbers into the first formula.
[tex]SA=(2*9*10)+(2*9*3)+(2*10*3)=294 in.^2[/tex]
------------------------------------------------------------------------------------
Conclude:
I, therefore, believe the area of this rectangular prism is 294 in.²
please help me Solve the following equations simultaneously:
solve for x and y
x+3y =6 and 2x+8y=-12
Answer:
x+3y =6
2x+8y=-12
The solutions to your equations are:
x= 42 and y= -12
lets check this
42+-36 =6
84+-96=-12
Hope This Helps!!!
Ms.James shared 5/8 of the candies she had in a bag and had 15 left.How many candies did she have before sharing?
Answer:
40
Step-by-step explanation:
If you take 15, and divide it by the 3 out of the 3/8 left, you get 5. You then multiply 5 by 8 to get the full amount of candies she had before sharing, 40.
I hope this helped!
Thanks!
Your friend in answering,
~Steve
Answer:
40.
Step-by-step explanation:
If 15 candies are the rest of 3/8, then the total candies were 40.
Solve the Inequality: [tex]\frac{b}{3} \geq -1[/tex]
[tex] \frac{b}{3} \geq - 1 \\ = 3 \times \frac{b}{3} \geq \times ( -1 ) \\ = b \geq3 \times ( - 1) \\ = b \geq - 3 \times 1 \\ \\ = b \geq - 3[/tex]
Step By Step Explanation:
Multiply both sides of the inequality by 3Reduce the numbers with the greatest common factor 3Multiplying a positive and a negative equals a negative Any expression multiplied by 1 remains the same ☆彡Hanna#CarryOnLearning
Jordan has more than 25 coins in his collection.
Which inequality shows the number of coins in Jordan's collection?
Answer:
x + 25 is an expression, not an inequality.
Jordan has more than 25 coins, so this means that the > symbol will be used.
The answer with this symbol is B. x>25.
Step-by-step explanation:
help with algebra 1 equation pls help
Answer:
b. [tex] \blue{k = \dfrac{l - 14j}{3}} [/tex]
Step-by-step explanation:
[tex] l = 14j + 3k [/tex]
Switch sides.
[tex] 14j + 3k = l [/tex]
Subtract 14j from both sides.
[tex] 3k = l - 14j [/tex]
Divide both sides by 3.
[tex] \blue{k = \dfrac{l - 14j}{3}} [/tex]
Use the Law of Sines to write an expression that represents the angle measure x.
Answer:
Step-by-step explanation:
Law of sines says that the length of sides are proportional to the sine of the opposing angle.
Using the sine rule,
sin(x)/2.5 = sin(28)/3
therefore
sin(x) = 2.5 * sin(28) / 3
or
here we have
x = asin (2.5*sin(28) / 3)
so
box 1 = 2.5
box 2 = 28°
box 3 = 3
sum of 15,-2 and 7 is
Answer:
20
Step-by-step explanation:
15+(-2)+7=13+7=20
[tex]\longrightarrow{\blue{20}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]\:15 + ( - 2) + 7[/tex]
➺ [tex] \: 15 - 2 + 7[/tex]
➺ [tex] \: 22 - 2[/tex]
➺ [tex] \: 20[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
The run scored in a cricket match by 11 players is as follows: 7, 16, 121, 51,101, 81, 1, 16, 9, 11, and 16. Find the mean of this data
How to find the account balance
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Answer:
$163,002
Step-by-step explanation:
If you're working problems of this sort, you have been shown formulas and examples. Use the appropriate formula with the numbers of this problem.
For the formula below, you have d=3000, r=0.045, k=4, N=11
P = (3000)(1 -(1 +0.045/4)^(-11·4))/(0.045/4) ≈ 163,002
The account needs to hold about $163,002 to make this possible.
What is the volume of a sphere with a radius of 20 m? 10,666.67π m3 6,000π m3 85,333.33π m3 533.33π m3
Answer:10,666,66 [tex]\pi[/tex]m^3
Step-by-step explanation:
V=[tex]\frac{4}{3} \pi r^{3}[/tex]
[tex]\frac{4}{3} \pi 20^{3} \\ V=10,666.66 \pi[/tex]
John, Jack, and Jill have 159 marbles altogether. John has 2 more marbles than Jack, and if Jill gave 5 marbles to Jack, Jack would have the same number of marbles as Jill. How many marbles does each of them have?
Answer:
someone else tell me to thank you
The box plots show the weights, in pounds, of the dogs in two different animal shelters.
Weights of Dogs in Shelter A
2 box plots. The number line goes from 6 to 30. For the weights of dogs in shelter A, the whiskers range from 8 to 30, and the box ranges from 17 to 28. A line divides the box at 21. For shelter B, the whiskers range from 10 to 28, and the box ranges from 16 to 20. A line divides the box at 18.
Weights of Dogs in Shelter B
Which is true of the data in the box plots? Select three choices.
The median weight for shelter A is greater than that for shelter B.
The median weight for shelter B is greater than that for shelter A.
The data for shelter A are a symmetric data set.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Answer:
The median weight for shelter A is greater than that for shelter B.
The data for shelter B are a symmetric data set.
The interquartile range of shelter A is greater than the interquartile range of shelter B.
Step-by-step explanation:
The median weight for shelter A is greater than that for shelter B.
The median of A = 21 and the median of B = 18 true
The median weight for shelter B is greater than that for shelter A.
The median of A = 21 and the median of B = 18 false
The data for shelter A are a symmetric data set.
False, looking at the box it is not symmetric
The data for shelter B are a symmetric data set.
true, looking at the box it is symmetric
The interquartile range of shelter A is greater than the interquartile range of shelter B.
IQR = 28 - 17 = 11 for A
IQR for B = 20 -16 = 4 True
The ratio of girls to boys in a particular classroom is 4:3. What fraction of the total number of students are boys?
The ratio of boys to the total number of students in a particular classroom is
Answer:
3:7
Step-by-step explanation:
We know that there are 4 girls and 3 boys and 4+3=7.
PLEASE HELP ME PLEASE DUE IN 30 MINUTES
Answer:
x = 82.1º
Step-by-step explanation:
tan = opp/adj
tan75 = x/22
multiply both sides by 22
22 * tan75 = x
use calculator
82.1051177665153 = x
Rounded
x = 82.1º
Find the degree measures of the next two positive and the previous two negative angles that are coterminal with the angle 75°.
The angles are:
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Answer:
435°, 795°-285°, -645°Step-by-step explanation:
Add or subtract multiples of 360° to find coterminal angles.
Positive
75° +360° = 435°
75° +2×360° = 795°
Negative
75° -360° = -285°
75° -2×360° = -645°
In the triangle below, which is equivalent to sinA?
Right triangle A B C is shown. B is the right angle and side A C is the hypotenuse.
sinC
sinB
cosA
cosC
Answer:
CosC
Step-by-step explanation:
EDG
How much is 13,200 feet in miles
Answer:
2.5 miles
Step-by-step explanation:
Solve for H.[tex]V = \pi r^{2} h[/tex]
Answer:
h = [tex]\frac{V}{\pi r^2}[/tex]
Step-by-step explanation:
Given
V = πr²h ( isolate h by dividing both sides by πr² )
[tex]\frac{V}{\pi r^2}[/tex] = h
Part 3: The Space Inside! 1. Find the volume of the shipping box using the two methods and show your work: 2. Using the volume formula
3. Explain how both methods provide the same measurement of volume for the shipping box.
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Answer:
36 9/16 cubic feet
Step-by-step explanation:
1.Volume formula
V = LWH
V = (3 3/4 ft)(3 ft)(3 1/4 ft) = (15/4)(3)(13/4) ft³ = 585/16 ft³
V = 36 9/16 ft³ . . . the volume of the shipping box
__
Packing cubes
Each cube measures 1/4 ft on a side. In terms of cubes, the dimensions of the box are ...
3 3/4 ft = 15/4 ft = 15×(1/4 ft) ⇒ 15 cubes
3 ft = 12/4 ft = 12×(1/4 ft) ⇒ 12 cubes
3 1/4 ft = 13/4 ft = 13×(1/4 ft) ⇒ 13 cubes
This means 15 cubes can be lined up along the bottom front of the box. 12 such lines can make one layer of cubes covering the bottom of the box, and 13 such layers will fill the box.
The total number of cubes in the box is ...
15 × 12× 13 = 2340 . . . . fish food cubes
Each cube has a volume of (1/4 ft)³ = 1/64 ft³, so the volume of the shipping box is ...
(2340 cubes)×(1/64 ft³/cube) = 2340/64 ft³
= 36 9/16 ft³ . . . shipping box volume
__
2.Using the volume formula, the volume is 36 9/16 ft³
Using the packing cubes method, the volume is 36 9/16 ft³
__
3.If you consider the math used in the packing cubes method, you see it looks like ...
V = (15)(12)(13) × (1/64 ft³)
= (15)(12)(13)×(1/4 ft)³ = (15×1/4 ft)(12×1/4 ft)(13×1/4 ft)
= (3 3/4 ft)(3 ft)(3 1/4 ft)
= LWH
That is, the "packing cubes method" is simply a rearrangement of the volume formula product using the commutative and associative properties of multiplication. The same numbers are used to compute the product, but in a different order. Hence the result must be the same.