Answer:
19 bags of peanuts and 31 bags of pistachios
Geo-net, a cellular phone company, has collected the following frequency distribution for the length of calls outside its normal customer roaming area: Length (min.) Frequency 0<5 260<5 75 5<10 13910<15 10515<20 3720<25 1825+ 400 The sample mean(x) for this distribution is 14.3 minutes, and the sample standard deviation is 3.7 minutes. Determine whether these data are normally distributed (a = .05).
Answer:
Reject H0 ; and conclude that call length does not follow a normal distribution.
Step-by-step explanation:
Given :
The hypothesis :
H0: Call lengths outside normal customer roaming areas follows normal distribution
H1: Call lengths outside normal customer roaming areas do not follows normal distribution
Mean, μ = 14.3
Standard deviation, σ = 3.7
From the frequencies Given :
Expected values can be calculated :
Observed values :
16, 75, 139, 105, 37, 18 ; Total = 400
P(Z < (x - μ) / σ)) * total frequency
x = frequency
For x = 5 ;
P(Z < (5 - 14.3) / 3.7)) * 400 = 2.391
For x = 10;
P(Z < (10 - 14.3) / 3.7)) * 400 = 46.644
For x = 15;
P(Z < (15 - 14.3) / 3.7)) * 400 = 180.960
For x = 20;
P(Z < (20 - 14.3) / 3.7)) * 400 = 145.32
For x = 25;
P(Z < (25 - 14.3) / 3.7)) * 400 = 23.92
For x = 30;
P(Z < (30 - 14.3) / 3.7)) * 400 = 0.766
χ² = Σ(O - E)²/E
O = observed values
E = Expected values
χ² = (26-2.391)^2 / 2.391 + (75-46.644)^2 / 46.644 + (139-180.96)^2 / 180.96 + (105-145.32)^2 / 145.32 + (37-23.92)^2 / 23.92 + (18-0.766)^2 / 0.766 = 666.17
χ² = 666.17
The critical value "; df = n - 1= 6-1 = 5
α = 0.05
χ²critical(0.05 ; 5) = 11.07
χ²statistic > χ²critical ; Reject the Null, H0 ; and conclude that call length does not follow a normal distribution.
14. Divide and write the fraction or mixed number in its simplest form:1/4÷3/8
Answer:
1/4 ÷ 3/8 = 2/3
Step-by-step explanation:
When dividing fractions, you have to take the reciprocal of the second fraction, then multiply from there. The reciprocal of a fraction is basically flipped. So then, 1/4 ÷ 3/8 becomes 1/4 x 3/8. Multiplying fractions should be pretty straight forward as you just need to multiply numerator (top number of a fraction) with numerator and vice versa for the denominators (bottom number of a fraction).
So then you get: (1 x 8)/(3 x 4) = 8/12. Then you just simplify it by dividing the numerator and denominator by their greatest possible factor, which in this case is 4. So then, (8 ÷ 4)/(12 ÷ 4) = 2/3.
A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.
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Answer:
23°
Step-by-step explanation:
The angle a vector makes relative to the +x axis is found as ...
α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°
The angle is about 23°.
__
Additional comment
This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)
find the length of side x
Answer:
x=8
Step-by-step explanation:
Select all that apply.
Given the points (5, 10) and (-4,-8), which of the following are true about the line passing through these points?
The line has a slope of 1/2
The line represents a direct variation function
The point (6.3) is also on the line
The line has a slope of 2
4) A box has dimensions of 14 inches long, 1.4 feet wide,
and 9 inches high. What is the volume of the box?
The formula for the volume is V=1.w.h.
Answer:
2116.8 in^3
Step-by-step explanation:
V = l*w*h
All the units need to be the same
Convert 1.4 ft to inches
1.4 ft * 12 inches/ ft = 16.8 inches
V = 14 * 16.8 * 9
= 2116.8 in^3
It takes Barry 912 hours to detail a car. If he worked 57 hours during the week, how many cars did he detail?
Answer:
He detailed 16 cars.
912/57=16
Step-by-step explanation:
Given limit of f(x) = -4 as x approaches c and limit of g(x) =1/5 as x approaches c. What is limit of g(x)/f(x) as x approaches c?
Answer:
-1/20
Step-by-step explanation:
As x approaches c,
g(x) 1/5
------ = ------------ = -1/20 (matches last of the four given possible answers)
f(x) -4
Answer:
[tex]\displaystyle \frac{-1}{20}[/tex]
General Formulas and Concepts:
Calculus
Limit Property [Division]: [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{ \lim_{x \to c} f(x)}{ \lim_{x \to c} g(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to c} f(x) = -4[/tex]
[tex]\displaystyle \lim_{x \to c} g(x) = \frac{1}{5}[/tex]
Step 2: Solve
Substitute in limits [Limit Property - Division]: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{ \frac{1}{5} }{ -4 }[/tex]Simplify: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{-1}{20}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
Cos(x)=0.35 all solutions
Step-by-step explanation:
you have to type shift an cos button together at one time and then write 0.35 youwill get answer
Find the 5th term (not fourth) of the given geometric sequences.
1, 8, 64,...
Answer:
GP=ar^{n-i}
a=1
r=8/1=8
GP=8^(5-1)
GP=8^4
5th term=4096
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3
Answer:
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
Step-by-step explanation:
We have the mean, which means that the poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
The auto parts department of an automotive dealership sends out a mean of 6.3 special orders daily.
This means that [tex]\mu = 6.3[/tex]
What is the probability that, for any day, the number of special orders sent out will be exactly 3?
This is P(X = 3). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-6.3}*6.3^{3}}{(3)!} = 0.0765[/tex]
0.0765 = 7.65% probability that, for any day, the number of special orders sent out will be exactly 3
please help!!!! please help!!!!!
Answer:
1. True
2. Hundreds
Step-by-step explanation:
1. Natural numbers are positive integers (whole numbers) 1, 2, 3, etc. 0 is lower than all of them.
2. 3 (ten thousands), 0 (thousands), 8 (hundreds), 4 (tens), 6 (ones). Try reading out the number.
HELP PLEASE I CANNOT FAIL PLEASE!!!!!!!
Which statement correctly compares the two functions?
A.
They have the same y-intercept and the same end behavior as x approaches ∞.
B.
They have the same x- and y-intercepts.
C.
They have the same x-intercept but different end behavior as x approaches ∞.
D.
They have different x- and y-intercepts but the same end behavior as x approaches ∞.
Answer:
B
Step-by-step explanation:
they have the same intercepts
Convert 625 to base twelve
Answer:
441
Step-by-step explanation:
Given:
HI and JK intersect at point O.
m KOH = 110
Colleen was asked to find the measure of x and explain her reasoning
Line geometry are caused from the intersection of two line. The measure of angle x from the diagram is 110degrees
Linear geometryLine geometry are caused from the intersection of two lines. From the given figures, you can see that <KOH and <IOK forms a linear pair, hence;
<KOH + <IOK = 180
110 + <IOK = 180
<IOK = 180 - 110
<IOK = 70 degrees
Similarly <x and MIOK are linear pair pair such that <x + 1<IOK = 180
<x + 70 =180
<x = 180 - 70
<x = 110degrees
Hence the measure of angle x from the diagram is 110degrees
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Answer:
<IOK = 70 degrees
<x and <IOK form a linear pair, so m<x is = 110
Step-by-step explanation:
i did it on khan and got it right, i hope your day goes well and you get all your other questions right :)
Jan gives Ted a loan at 4% effective to be repaid by 10 annual payments of 100, followed by 5 annual payments of 200. Just after Ted makes the 5th payment, Jly and Ted discover that each of the 15 payments should have been 10% higher than they were originally scheduled. They agree that Ted will make increased payments of K in the 6th through 10th years to adjust for the error. The payments of 200 in the 11th through 15th years will not change. Determine K.
a. 129
b. 113
c. 145
d. 139
e. 149
Answer:
139 ( D )
Step-by-step explanation:
Interest rate on loan = 4% = 0.04
Number of payments = 15
First 10 payments = 100 each
last 5 payments = 200 each
Calculating the value of K
K = [ ( 100 / 0.04 * ( 1-1 / 1.04^10 ) + 200/0.04 * ( 1-1 / (1 +0.04)^5)* 1 /1.04^10)
* 1.1 - 100 / 0.04 * ( 1-1 / (1+0.04)^5 ) - 200/0.04 * (1-1 /1.04^5) * 1/1.04^10)*0.04 / ( 1-1 / 1.04^5) * (1 + 0.04)^5
= 138.6051 ≈ 139
Please Help!!! Whoever helps first and gets it correct gets Brainliest!
Answer:
Step-by-step explanation:
You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):
y = 0.5x + 0.5
It takes 0.5 hour to clean up.
I really need help please
what is this?
Answer:
431.2
Step-by-step explanation:
Area of a regular polygon = # of sides * side length of 1 side * apothem
We want to find the area of a regular polygon with 7 sides, an apothem of 8 meters, and a side length with 7.7 meters
So # of sides = 7
apothem = 8
side length = 7.7
so the area would equal 7 * 8 * 7.7 = 431.2
It says to round to the nearest tenth however 431.2 is already rounded to the nearest tenth
Answer:
That answer ^ is incorrect. The correct answer ( in acellus that is ) is 2
15.6
Step-by-step explanation:
How do I graph y = -x + 4, please explain
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind. The speed of the plane in still air is
Answer:
540 miles per hour and 50 miles per hour respectively.
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
What is 5 (x-4) + 3x - 9x + 7?
Answer:
-x - 13
Step-by-step explanation:
5(x-4) + 3x - 9x + 7
First we use the distributive property to remove the parenthesis
5x -20 + 3x - 9x + 7
then we combine the like terms
-x - 13
i dont understand questions like these
Answer:
same
Step-by-step explanation:
Jason collects baseball cards. He bought one card for $25. Its current value is represented by the expression 25(1.02)t, where t is the number of years Jason has owned the card. Is Jason’s baseball card going up or down in value?
If f(x)=5(x+3)^3-2. What does f^-1(x) equal?
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Answer:
C ∛((x+2)/5) -3
Step-by-step explanation:
To find the inverse function, solve for y:
x = f(y)
x = 5(y +3)³ -2 . . . . . . substitute f(y)
x +2 = 5(y +3)³ . . . . . add 2 -- already you know C is the answer
(x +2)/5 = (y +3)³ . . . . divide by 5
∛((x +2)/5) = y +3 . . . . take the cube root
∛((x +2)/5) -3 = y . . . . subtract 3
f^-1(x) = ∛((x +2)/5) -3 . . . . matches expression C
In a certain survey, 513 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts (a) through (d) below. a. Are any of the three requirements violated? Can a test about a population proportion using the normal approximation method be used?
Answer:
The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Step-by-step explanation:
The necessary conditions are
The sample must be random and independently selected from the normally distributed population.
n*p and n*q both must be greater than 5
There must be two outcomes "success" and "failure"
The number of trials must be fixed.
From the given information 2), 3)and 4) conditions are satisfied, but not 1) because we are not given that people are selected randomly.
Answer: The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Total 427 tickets sold 73 fewer student tickets than adult tickets how many adult tickets
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Answer:
250
Step-by-step explanation:
Let 'a' represent the number of adult tickets.
a +(a -73) = 427
2a = 500 . . . . . add 73
a = 250 . . . . . . divide by 2
250 adult tickets were sold.
_____
Additional comment
I call this a "sum and difference problem" because we are given the total of two values and the difference between them. As you can see here, the larger of the two values is the average of the given numbers, their sum divided by 2. This is the generic solution to such a problem: the larger number is the average of the given sum and difference.
find the area of this unusual shape
Answer:
38 ft²
Step-by-step explanation:
The shape consists of a rectangle and two triangles.
Area of the shape = area of rectangle + area of the two triangles
✔️Area if the rectangle = L × W
L = 8 + 2 = 10 ft
W = 3 ft
Area of rectangle = 10 × 3 = 30 ft²
✔️Area of the large triangle = ½ × bh
b = 4 ft
h = 3 ft
Area of large triangle = ½ × 4 × 3 = 6 ft²
✔️Area of the small triangle = ½ × bh
b = 2 ft
h = 2 ft
Area of large triangle = ½ × 2 × 2 = 2 ft²
✅Area of the shape = 30 + 6 + 2 = 38 ft²
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
Step-by-step explanation:
Question 1 of 25
Is ARST - AXYZ? If so, name the postulate that applies.
R
S
x
Given
STYZ
2
A. Congruent - SSS
B. Congruent - SAS
C. Congruent - ASA
D. Might not be congruent
The triangles are congruent by SAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔRST
Let the second triangle be represented as ΔXYZ
Now , the measure of side RS = measure of side XY
And , the measure of side ST = measure of side YZ
The measure of angle ∠S = measure of angle ∠Y
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Therefore , the triangles ΔRST and ΔXYZ are congruent triangles by the SAS theorem
Hence , they are congruent
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Which of the following is the graph of
(x - 1)^2 + (y + 2)^2 = 4 ?
Answer:
a
Step-by-step explanation:
The correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given equation is ( x-1 )² + ( y + 2 )² = 4
The graph of the equation is attached with the answer below when we plot the graph we will get the circle that is lying in the third and the fourth quadrant.
Therefore the correct answer is option C which is the graph of the equation ( x-1 )² + ( y+ 2 )² = 4 will be the circle in the third and the fourth quadrant.
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