In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 46 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of daily phone calls numbering between 43 and 49
Answers
Answer:
P( 43 ≤ X ≤ 49) = 0.9545
Step-by-step explanation:
We are given mean of 46 and a standard deviation of 3
We want to find the percentage of daily phone calls numbering between 43 and 49. This can be written as;
P( 43 ≤ X ≤ 49)
Using the z-formula, we have;
z = (x - μ)/s
This transforms to;
P((43 - 46)/3)) ≤ Z ≤ ((49 - 46)/3))
This gives;
P(-2) ≤ Z ≤ P(2)
From z - table attached, P(-2) = 0.02275 and P(2) = 0.97725
Thus;
P( 43 ≤ X ≤ 49) = 0.97725 - 0.02275
P( 43 ≤ X ≤ 49) = 0.9545
Related Questions
Metro buses are scheduled to arrive at each stop every 30 minutes. If the time a person waits at a bus stop is uniformly distributed and the maximum possible wait time for a bus is 30 minutes, what is the probability that you will wait more than 25 minutes for a bus
Answers
Answer:
The probability is [tex]P(X > 25 ) = 1.667[/tex]
Step-by-step explanation:
From the question we are told that
The maximum wait is [tex]b = 30 \ minutes[/tex]
The minimum wait would be [tex]a = 0\ minutes[/tex]
Generally the probability that you will wait more than 25 minutes for a bus is mathematically represented as
[tex]P(X > 25 )[/tex]
Now given that the time a person waits is uniformly distributed and that the maximum is 30 then we can evaluate the above probability as
[tex]P(X > 25 ) = P(25 < X < 30 ) = \frac{30 - 25}{30 - 0}[/tex]
[tex]P(X > 25 ) = 1.667[/tex]
find the fraction below that is equivalent to 3/4
Answers
Answer:
6/8 9/12 15/20 12/16 and alot more
Step-by-step explanation:
Can't explain
Answer:
the answer is 6/8
Can someone please help me with these questions! Please explain to me how to do it as well!
Thank You!
Answers
Answer:
(2) (-2, 4), (3, 9)
(3) (-2, 4), (1, 1)
Step-by-step explanation:
My favorite way to answer questions like this is to use a graphing calculator to find the points of intersection. The attached shows the points of interest.
If you want to solve this by hand, equate the expressions for y, then solve the resulting quadratic using any of the methods you know. Once you find the x-values, put those in either equation to find the y-value.
__
(2) x^2 = y = x+6
x^2 -x -6 = 0 . . . . put in standard form
(x -3)(x +2) = 0 . . . . factor
x = 3 or -2 . . . . . find the x-values that make the factors zero
y = x^2 = 9 or 4
The points are (3, 9) and (-2, 4).
__
(3) x^2 = -x +2
x^2 +x -2 = 0 . . . . standard form
(x +2)(x -1) = 0 . . . factored
x = -2 or 1 . . . . . . .zeros
y = x^2 = 4 or 1
The points are (-2, 4) and (1, 1).
_____
Comment on factoring
When you consider the factored form and its expanded equivalent, ...
(x +a)(x +b) = x^2 +(a+b)x +ab
you see that the coefficient of the linear term (a+b) is the sum of factors of the constant term (ab). Your knowledge of multiplication tables will often help you factor equations easily. You need to pay attention to signs.
In problem 2, we want factors of -6 that have a sum of -1:
-6 = (-1)(6) = (-2)(3) = (-3)(2) = (-6)(1)
These factor pairs have sums of 5, 1, -1, -5. The pair whose sum is -1 is the one we're looking for: -3 and 2. So, the factors in problem 2 are (x-3)(x+2).
__
In problem 3, we want factors of -2 that have a sum of +1:
-2 = (-1)(2) = (-2)(1)
These factor pairs have sums of 1, -1. So, the second pair is the one of interest: -2 and 1. That makes the factors be (x-2)(x+1).
What are REAL Numbers? (definition) What is one example of a property of real numbers? What was your favorite way to learn in Algebra 1?
Answers
Answer:
a) The set of real numbers is the union of the set of Irrational numbers and the set of rational numbers.
b) Real numbers have a lot of properties, one example is that they are closed under a lot of operations, like addition or multiplication.
This means that if we have two real numbers A and B:
A + B is also a real number.
A*B is also a real number.
c) A good way to learn Algebra (or math in general) is:
First, read the textbook, have a general idea of the complete topic, if you don't understand something, keep reading, just take note of all the things you don't understand.
Second, ask the things that you do not fully understand, not shame in it, math has a lot of complex relations that sometimes can be really hard to understand, and there are a lot of cases (at least for me) where one can think that understands very well a topic, but it is wrong, so in order to avoid this, ask everything you can.
Third, do a LOT of exercises, the only way in which you can learn to use your equations and relations is applying them in math problems, and it will also help you to understand the meaning of those equations in a more profound way.
A......... divides a two-dimensional shape into two congruent shapes
Answers
Answer:
A diagonal
Step-by-step explanation:
What is the vertex of the graph of f(x) = |x - 13|+ 11
Answers
Answer:
The vertex is located at the point (13, 11)
Step-by-step explanation:
When this equation is graphed, the vertex falls on this point on the graph. Hope this helps!!!
The opposite of 11 is 11. True False
Answers
Answer:
FALSE. The opposite of 11 is -11.
Find the equation of the line that goes through (2,9) and (-1,5) in point-slope form
Answers
Answer:
y-9=4/3(x-2)
Step-by-step explanation:
First, find your slope:
The formula for finding slope is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Our coordinate point for our x₁ and y₁ values will be (2,9) and our coordinate point for our x₂ and y₂ values will be (-1,5). Now, let's plug those into our formula:
[tex]m=\frac{5-9}{-1-2}=\frac{-4}{-3}=\frac{4}{3}[/tex]
Your slope is 4/3.
Next, plug in your x₁ and y₁ values in for point-slope form. The equation in variable form is "y-y₁=m(x-x₁)". So, plugging in our point (2,9) for x₁ and y₁, we get:
y-9=4/3(x-2)
In the episode pertaining to the discovery of radium, all of the hypotheses turned out to be true.
a. true
b. false
Answers
Answer:
In the episode pertaining to the discovery of radium, it is false that all of the hypotheses turned out to be true.
There are some hypotheses in the episode thay turned out to be false.
The characteristic polynomial of a 5 × 5 matrix is given below. Find the eigenvalues and their multiplicities. 2) λ5 - 24λ4 + 189λ3 - 486λ2
Answers
The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).
The eigenvalues of the 5 x 5 matrix are represented by the roots of the characteristic polynomial. The multiplicity of a eigenvalue is the number of times that a root is repeated.
Now we proceed to determine the roots of the characteristic polynomial by algebraic means:
[tex]p = \lambda^{5}-24\cdot \lambda^{4}+189\cdot \lambda^{3}-486\cdot \lambda^{2}[/tex]
[tex]p = \lambda^{2}\cdot (\lambda^{3}-24\cdot \lambda^{2}+189\cdot \lambda -486)[/tex]
[tex]p = \lambda^{2}\cdot (\lambda -6)\cdot (\lambda - 9)\cdot (\lambda - 1)[/tex]
The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).
To learn more on eigenvalues, we kindly invite to check this verified question: https://brainly.com/question/5596684
Jayden uses the net below to design a box. A net with 4 rectangles and 2 squares. The rectangles measure 6 feet by 4 feet and the squares have side lengths of 4 feet. How much cardboard will Jayden need to make the box? A. 60 ft2 B. 96 ft2 C. 128 ft2 D. 144 ft2
Answers
Answer:
C .128 ft²
Step-by-step explanation:
net with 4 rectangles and 2 squares.
The rectangles measure 6 feet by 4
Area of the rectangle=6*4
Area of the rectangle= 24.ft²
Total area of the rectangle= 4*24.
Total area of the rectangle= 96 ft²
the squares have side lengths of 4 feet.
Area of tge square= 4²
Area of the square= 16ft²
Total area of the square= 16*2
Total area of the square= 32 ft²
Total area of the cardboard needed
= Area of square + Are of rectangle
= 32+96
= 128 ft²
[tex] {2}^{x + 2} = 9 \times ( {2}^{x} ) - 2[/tex]
How is this solved pls
Answers
Answer:
[tex]x = 1 - log_{2}(5) [/tex]Step-by-step explanation:
[tex] {2}^{x + 2} = 9 ( {2}^{x} ) - 2[/tex]Using the rules of indices
That's
[tex] {x}^{a + b} = {x}^{a} \times {x}^{b} [/tex]So we have
[tex] {2}^{x + 2} = {2}^{x} \times {2}^{2} = 4( {2}^{x} )[/tex]So we have
[tex]4( {2}^{x}) = 9( {2}^{x} ) - 2[/tex]Let
[tex] {2}^{x} = y[/tex]We have
4y = 9y - 2
4y - 9y = - 2
- 5y = - 2
Divide both sides by - 5
[tex]y = \frac{2}{5} [/tex]But
[tex] {2}^{x} = \frac{2}{5} [/tex]Take logarithm to base 2 to both sides
That's
[tex] log_{2}( {2}^{x} ) = log_{2}( \frac{2}{5} ) [/tex][tex] log_{2}(2) ^{x} = x log_{2}(2) [/tex][tex] log_{2}(2) = 1[/tex]So we have
[tex]x = log_{2}( \frac{2}{5} ) [/tex]Using the rules of logarithms
That's
[tex] log( \frac{x}{y} ) = log(x) - log(y) [/tex]Rewrite the expression
That's
[tex]x = log_{2}(2) - log_{2}(5) [/tex]But
[tex] log_{2}(2) = 1[/tex]So we have the final answer as
[tex]x = 1 - log_{2}(5) [/tex]Hope this helps you
Simplify 3m4-2+8
A.8m4
B.9m4
C.3m+244
D.3m+284
Answers
Answer:
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
Step-by-step explanation:
Given
[tex]3m^4 - 2 + 8[/tex]
Required
Simplify
[tex]3m^4 - 2 + 8[/tex]
Subtract 2 from 8
[tex]3m^4 - 2 + 8 = 3m^4 + 6[/tex]
Factorize
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
The expression cannot be further simplified;
Hence;
[tex]3m^4 - 2 + 8 = 3(m^4 + 2)[/tex]
None of the options answers the question
11
Solve the following equation when a =4 and b=7. 5a2_11b+9=
Can you help me with the answer if you know?
Answers
Answer:
12
Step-by-step explanation:
a = 4 and b = 75a² - 11b + 9 = ?-------------
Plugging in values of a and b and simplifying to get answer:
5a² - 11b + 9=5*4² - 11*7 + 9=5*16 - 77 + 9 =80 - 77 + 9 =3+ 9 = 12Answer is 12
The fourth term of an arithmetic
progression is one less than twice the
second term - If the sixth term is 7
find the first term
Answers
[tex] \huge{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]
Let the first term of the AP be a and the common difference of the AP be d
We know the formula for finding the nth term,
[tex] \large{ \boxed{ \rm{a_n = a + (n - 1)d}}}[/tex]
Here,
an = nth term of the APn = number of terms of APBy using formula,
a4 = a + 3da2 = a + da6 = a + 5dAccording to given condition,
⇛ a4 = 2a2 - 1
⇛ a + 3d = 2(a + d) - 1
⇛ a + 3d = 2a + 2d - 1
⇛ a - 2a + 3d - 2d = -1
⇛ -a + d = -1
⇛ a - d = 1
Then,
⇛ a = d + 1-----------(1)
It is given that, a6 = 7
⇛ a + 5d = 7
Putting a from eq.(1),
⇛ d + 1 + 5d = 7
⇛ 6d + 1 = 7
⇛ 6d = 6
⇛ d = 6/6 = 1
Putting value of d in eq.(1),
⇛ a = 1 + 1 = 2
⛈ First term of the AP(a) = 2
━━━━━━━━━━━━━━━━━━━━
Assume two independent random samples are available which provide sample proportions. For the first sample assume n1= 100 and x1= 39. For the second sample, assume n2= 100 and x2= 49. Test the null hypothesis that the population proportions are equal versus the alternative hypothesis that the proportions are not equal at the 90% confidence level. Frame the test statistic by subtracting the proportion for population 1 from that for population 2. Pick an appropriate z value, p-value and conclusion. Round your answer to the nearest thousandth.
a) z-value = -1.425 p-value= 0.077 statistically significant
b) z-value = 1.425 p-value= 0.077 not statistically significant
c) z-value = 1.425 p-value= 0.077 statistically significant
d) z-value = -1.425 p-value= 0.1543 not statistically significant
Answers
Answer:a) z-value = -1.425 p-value= 0.077 statistically significant
Step-by-step explanation:
Given the following :
n1 = 100; x1 = 39 ; n2 = 100 ; x2 = 49
Z value for two independent samples can be obtained using the relation :
Z = (p1 - p2) /(√p(1-p)) * (√[(1/n1) + (1/n2)]
Z = -1.425
P-value : using the online p-value calculator at a confidence level of 90% from z score
Obtained p value = 0.077079
The p value is less than 0.1 , hence result is significant at p<0.10
Write the ratio as a ratio of whole numbers using fractional notation 15 hours to 40 hours simplified fraction
Answers
Answer:
3/8
Step-by-step explanation:
Since it is 15/40 hours originally, what we need to do is just simplify this fraction.
The numerator and denominator are both divisible by 5.
3/8
HELP!!!!! What is the slope of a line with the equation 3x+7?
Answers
Explanation:
The slope is 3 or 3/1 meaning that it rise 3 and run 1.
Answer:
m=3
Step-by-step explanation:
The equation of the line is in slope-intercept form, or:
y=mx+b
where m is the slope and b is the y-intercept. The slope is multiplied by x and the y-intercept is added or subtracted from that.
The equation of the line is:
y=3x+7
3 and x are being multiplied, therefore 3 is the slope. 7 is added to 3x, therefore 7 is the y-intercept.
The slope is 3, or 3/1. Therefore, on a graph, the line will rise 3 up, then run 1 to the right.
The slope of the line is 3.
Which of the following is NOT a formula for determining complementary probability? O Ploutcome) = 1- P(-outcome) O P(outcome) - P(-outcome) = 1 O P(outcome) + P(-outcome) =1 O P(-outcome) = 1 - P(outcome)
Answers
Answer:
P(outcome) - P(-outcome) = 1
Step-by-step explanation:
Given
Let the complementary probabilities be represented with P(outcome) and P(-outcome)
Required
Determine which of the options do not show complementary probabilities
In probability, complementary probability sums up to 1
i.e.
[tex]P(outcome) + P(-outcome) = 1[/tex]
Hence option C is correct
Make P(outcome) the subject of formula
[tex]P(outcome) = 1 - P(-outcome)[/tex]
Hence, option A is correct
Make P(-outcome) the subject of formula
[tex]P(-outcome) = 1 - P(outcome)[/tex]
Hence, option D is correct
So, from the list of given options,
[tex]P(outcome) - P(-outcome) = 1[/tex] is incorrect
Evaluate the expression x+43x when x = 2
a.316
b.34
c.1
d.2
Answers
Answer:
88
Step-by-step explanation:
We are given the expression:
x+43x
and asked to evaluate when x=2. Therefore, we must substitute 2 in for x.
x + 43 x (plug 2 in for each x )
2+43(2)
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Multiply 43 and 2 first.
2+ (43*2)
2+ 86
Add 2 and 86.
88
The expression x+43x when evaluated for x=2 is 88.
Answer:
1
Step-by-step explanation:
71 x 103 in scientifc notation
Answers
Answer:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
7.313×10^3
Step-by-step explanation:
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props. How much space is inside the steps? Give an exact answer (do not round).
Answers
Answer:
0.045
Step-by-step explanation:
khan
The required amount of the space available is 0.045 cubic meter.
Space inside the steps to be determine.
What is volume?Volume, is defined as the mass of object per unit density.
The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2
= 0.06 - 0.015
= 0.045 cubic meter
Thus, the required amount of the space available is 0.045 cubic meter.
Learn more about Volume here:
https://brainly.com/question/1578538
#SPJ2
Identify the careers that match the descriptions:
Makes sure products meet safety regulations:
Operates equipment to cook meat for packaging in soup cans
Classifies eggs based on size and quality
Operates a large oven in a factory to bake bread before packaging
Operates equipment that mixes ingredients together to make candy
Options:
Agricultural Inspector
Food Baking Machine Operator
Food Batchmaker
Grader or sorter
Food cooking machine operator
Answers
Answer:
1. agricultural inspecter
2. food-cooking machine operator
3. grader or sorter
4. food-baking machine operator
5. food batchmaker
Step-by-step explanation:
i got this correct on ED2021
The correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
What is food processing?The process of turning agricultural materials into food or transforming one type of food into the next is referred to as transformation.
It is given that:
For the descriptions:
Makes sure products meet safety regulations - agricultural inspector.
Operates equipment to cook meat for packaging in soup cans - food-cooking machine operator.
Classifies eggs based on size and quality - grader or sorter.
Operates a large oven in a factory to bake bread before packaging - food-baking machine operator.
Operates equipment that mixes ingredients together to make candy - food matchmaker.
Thus, the correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.
Learn more about food processing here:
https://brainly.com/question/27044001
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how would you demonstrate the understanding of estimating a non perfect square? Estimate 388 to the nearest whole number.
Answers
Answer:
20
Step-by-step explanation:
Square root of 388=19.6977156
20
A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive-up teller service. How many spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars
Answers
This question is incomplete, the complete question is;
A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive-up teller service.
The drive-up service will have three tellers and a single waiting line. At another branch of the bank in a similar setting, the average service time for drive-up tellers is four minutes per customer, and average arrival rate is 36 customers per hour. It is expected that the new bank will have similar characteristics.
How many spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars?
Answer:
Eleven (11) spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars
Step-by-step explanation:
Given that:
the average service time for drive-up tellers is four (4) minutes per customer at each branch
Average number of customers per hour is 36
Therefore for 36 customers,
the branch can give ( 36 / 4 ) = 9, mins each customer
from the question, there is a probability of 96%
so we will calculate on the 9 as mentioned above
96% of 9 = 0.96
0.96 × 9= 8.64
If there are 3 tellers in a single line- , then
8.64 + 3 = 11.64 approximately 11
Therefore Eleven (11) spaces should be provided to have a 96 percent probability of accommodating all of the waiting cars
The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 67% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 63%. Make the decision to reject or fail to reject the null hypothesis at the 0.05 level.
Answers
Answer:
We have to reject null hypothesis
Step-by-step explanation:
n = 800
P* = sample proportion = 0.67
Alpha = 0.05
Null hypothesis h0: proportion = 63%
Alternate hypothesis h1: proportion > 64%
Test statistics:
Z = (p* - P)/√pq/n
Z = 0.67 - 0.64/√0.63x0.37/800
= 0.67 - 0.63/0.017
=0.04/0.017
= 2.352
At 0.05 the critical value of z = 1.645
We compare z calculated and z critical value.
2.352 is greater than 1.645 therefore we take the decision to reject the null hypothesis at 0.05 level of significance.
The percentage of residents that supports construction is greater than 63%
Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the P-value.
Answers
Answer:
hello your question has some missing parts below is the missing part
Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.
Identify the p-value.
Source DF SS MS F p
Factor 3 13.500 4.500 5.17 0.011
Error 16 13.925 0.870
Total 19 27.425
A) 0.011 B) 4.500 C) 5.17 D) 0.870
answer : p-value = 0.011 ( A )
Step-by-step explanation:
using this information
Source DF SS MS F P
Factor 3 13.500 4.500 5.17 0.011
Error 16 13.925 0.870
Total 19 27.425
significance level = 0.05
given that the significance level = 0.05
and
F statistics are given as : F = 5.17 , F critical = 3.25
hence the p-value = 0.011
from the analysis the p-value is less than the significance level is lower than the significance level
does anyone know this?
Answers
Answer: about 270
Step-by-step explanation:
If you look closely at 200 ml, you will see that there are 5 evenly spaced bars. This tells us that 200-300 ml is split by 20s. Counting the bars, you reach 260, but it goes almost halfway past it. Therefore, we get 270 since 270 is halfway past 260 and 280.
4. Order the numbers from least to greatest.
√5, 5, 2.5. Ja
Answers
Answer:
√5 < 2.5 < 5
Step-by-step explanation:
√5= 2.23
therefore,
√5 < 2.5 < 5
Plssssssssssss help and fast
Answers
Answer:
Graph 11, 14, and 15 are proportional
But I'm not 100% sure ;>;