Answer:
7
Step-by-step explanation:
481 + 223
approximately 481 =5
223 =2
5+2=7
Answer:
7
Step-by-step explanation:
Calls to a customer service center last on average 2.8 minutes with a standard deviation of 1.4 minutes. An operator in the call center is required to answer 75 calls each day. Assume the call times are independent. What is the expected total amount of time in minutes the operator will spend on the calls each day
Answer:
The expected total amount of time the operator will spend on the calls each day is of 210 minutes.
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.
n-values of normal variable:
Suppose we have n values from a normally distributed variable. The mean of the sum of all the instances is [tex]M = n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]
Calls to a customer service center last on average 2.8 minutes.
This means that [tex]\mu = 2.8[/tex]
75 calls each day.
This means that [tex]n = 75[/tex]
What is the expected total amount of time in minutes the operator will spend on the calls each day
This is M, so:
[tex]M = n\mu = 75*2.8 = 210[/tex]
The expected total amount of time the operator will spend on the calls each day is of 210 minutes.
Malachy rolls a fair dice 720 times.
How many times would Malachy expect to roll a five?
Answer:
120 times
Step-by-step explanation:
On a dice, there are 6 sides.
Since one of these sides is a 5, the chance of rolling a five is 1/6.
Find how many times Malachy can expect to roll a five by multiplying 720 by 1/6:
720(1/6)
= 120
So, Malachy can expect to roll a five 120 times
Is triangle XYZ = ABC ? If so, name the postulate that applies. A. Congruent - ASA B. Congruent - SAS C. Might not be congruent D. Congruent - SSS
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces.
(a)What is the standard deviation of the average fill volume of 22 bags?
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
Answer:
a) 0.0171 fluid ounces.
b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces
c) The mean should be of 6.153 fluid ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 0.08 fluid ounces.
This means that [tex]\sigma = 0.08[/tex]
(a)What is the standard deviation of the average fill volume of 22 bags?
This is s when n = 22. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.08}{\sqrt{22}}[/tex]
[tex]s = 0.0171[/tex]
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]
[tex]Z = -12.3[/tex]
[tex]Z = -12.3[/tex] has a p-value of 0.
0% probability that the average fill volume of 22 bags is below 5.95 ounces.
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]
[tex]6.1 - \mu = -3.09*0.0171[/tex]
[tex]\mu = 6.153[/tex]
The mean should be of 6.153 fluid ounces.
What translation maps ABC to A'B'C'?
A positive real number is 5 more than another. When - 10 times the smaller is added to the square of the larger, the result is 57. Find the numbers.
Answer:
4√2 and 5+4√2
Step-by-step explanation:
Let the two numbers be x ad y
Smaller = y
Bigger = x
If a positive real number is 5 more than another, then;
x = 5 + y ... 1
When - 10 times the smaller is added to the square of the larger, the result is 57, then;
-10y + x² = 57 ...2
Substitute 1 into 2;
-10y + (5+y)² = 57
-10y + 25+10y+y² = 57
y²+25 = 57
y² = 57 - 25
y² = 32
y = √32
y = 4√2
Since x = 5 + y
x = 5 + 4√2
Hence rhe numbers are 4√2 and 5+4√2
The product of three consecutive numbers is divisible by
Answer:
6
Step-by-step explanation:
The product of three consecutive numbers is divisible by 6
Let us say the numbers are x, x+1 , x+2
if x = 1,
Product of the three consecutive numbers,
(1)(2)(3)
=> 6, which is divisible by 6
if x = 2,
Product of the three consecutive numbers,
(2)(3)(4)
=> 24, which is divisible by 6
Similarly if we take any 3 consecutive numbers their product will be divisible by 6.
what are the adjectives in this sentence: the class cheered when Sonia had finished reading her funny poem.
6 Write 89.4945 correct to (a) nearest whole number, [1] (b) two decimal places.
Answer:
a)89
b)89.45
Step-by-step explanation:
Three bags contain 3 red, 7 black; 8 red, 2 black, and 4 red & 6 black balls
respectively. 1 of the bags is selected at random and a ball is drawn from it. If the ball
drawn is red, find the probability that it is drawn from the third bag.
Answer:
[tex]Probability = \frac{4}{15}[/tex]
Step-by-step explanation:
B1 = first bag
B2= second bag
B3 = third bag
Let A = ball drawn is red
Since, there are three bags.
Probability of choosing one bag= P(B1) = P(B2) = P(B3) = 1/3.
From B1: Total balls = 10
3 red + 7 black balls.
Probability of drawing 1 red ball from it , P(A) = 3/10.
From B2: Total balls = 10
8 red + 2 black
Probability of drawing 1 red ball is, P(A) = 8/10
From B3 : Total Balls = 10
4 red + 6 black
Probability of drawing 1 red ball, P(A) = 4/10 .
To find Probability given that the ball drawn is red, that the ball is drawn from the third bag by Bayes' rule.
That is , P(B3|A)
[tex]=\frac{\frac{1}{3} \times \frac{4}{10}} { \frac{1}{3} \times \frac{3}{10} + \frac{1}{3} \times\frac{8}{10} + \frac{1}{3} \times \frac{4}{10}}[/tex]
[tex]=\frac{4}{30} \times \frac{30}{15}\\\\=\frac{4}{15}[/tex]
Therefore, the probability that it is drawn from the third bag is 4/15.
Answer:
4/15
Step-by-step explanation:
Solution of conditional probability problem:
Given:
Bags (3R,7B), (8R,2B), (4R,6B)
Let
P(R,i) = probability of drawing a red AND from bag i
P(R, 1) = 3/10 * (1/3) = 3/30
P(R, 2) = 8/10 * (1/3) = 8/30
P(R, 3) = 4/10 * (1/3) = 4/30
Let
Let P(R) = probability of drawing a red from any bag
P(R) = sum P(R,i) for i = 1 to 3 using the addition rule
= 3/30 + 8/30 + 4/30
= 15/30
= 1 / 2
Conditional Probability of drawing from the third bag GIVEN that it is a red
= P(3 | R)
= P(R, 3) / P(R)
= 4/30 / (1/2)
= 8/30
= 4 / 15
(Since all bags contain 10 balls, by intuition, 4 red from third / 15 total red = 4/15)
c+12<16
what will be the answer
Answer:
[tex]c < 4[/tex]
Step-by-step explanation:
Move the constant to the right-hand side and change its signs:
[tex]c < 16 - 12[/tex]
Subtract the numbers:
[tex]c < 16 - 12 = c < 4[/tex]
Use Pythagorean Theorem to find each missing length
please help with the steps
Answer:
25 is A and 26 is B
Step-by-step explanation:
25) a²+b²=c²
missing side can be=b
to find the missing side subtract 6.7² from 12.6²
b²=12.6²-6.7²
b²=158.76-44.89
the square root of b²= the square root of 113.87
b=10.67
the missing side is equal to 10.7(1d.p)
26) a²+b²=c²
c= hypotenuse
10.8²+11²=c²
116.64+121=c²
c²=237.64
the square root of c²= the square root of 237.64
c=15.42(2d.p)
the hypotenuse is=15.4
The places that I have "the square root of" you must replace it with the square root sign. I'm using my phone so I wasn't sure how to insert a square root sign.
How tall is the table?
120cm
90cm
I
The values of variables, such as the height of the table can be found by writing equations of their relationships
The height of the table is 105 cm
The reason the above height value is correct is as follows;
Known parameters:
The diagram shows a table, a cat and a mice
Let x, represent the height of the table, let y represent the height of the cat, and let z represent the height of the mice
From the given diagram, we have;
Height of the table + Height of the cat - Height of the mice = 120 cm
∴ x + y - z = 120...(1)
Height of the table + Height of the mice - Height of the cat = 90 cm
∴ x + z - y = 90...(2)
Adding equation (1) to equation (2) gives;
x + y - z + (x + z - y) = 120 + 90 = 210
x + y - z + (x + z - y) = 210
However;
x + y - z + (x + z - y) = x + x + y - y - z + z = 2·x
∴ x + y - z + (x + z - y) = 2·x = 210
x = 210/2 = 105
Therefore;
The height of the table, x = 105 cm
Learn more about word problems leading on simultaneous equations here:
https://brainly.com/question/16513646
which elements in the following set are integers -8,3/4,-0.18,0,0.16,5,-2/7,6
Answer:
345
Step-by-step explanation:
Find the percent of decrease from 46 songs to 41 songs. Round to the nearest tenth of a percent if necessary.
percent of decrease
%
Answer:
10.9 %
Step-by-step explanation:
46 - 41 = 5
5/46 * 100% = 10.8695652174%
Rounded
10.9 %
Find the equation of the straight line that passes through the points (1, 10) and (3, 2)
ANSWER ASAP
Answer:
y = -4x+14
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
m = (2-10)/(3-1)
=-8/2
= -4
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -4x+b
Substitute a point into the equation
10 = -4(1)+b
Add 4 to each side
14 = b
y = -4x+14
What is the slope of the line that passes through the points (-6, -2) and (2, -2)?
Answer:
0
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( -2 - -2)/(2 - -6)
= (-2+2)/(2 +6)
= 0/8
= 0
Answer:
Slope is 0
Step-by-step explanation:
Slope formula is (y2-y1)/(x2-x1)
-2 - (-2)/2 - (-6)
0/8
0
Write the following equation in the general form Ax + By + C = 0.
y - x - 1 = 0
2x - 3y + 6 = 0
2x - 3y - 6 = 0
-2x + 3y - 6 = 0
Answer:
C. -2x +3y-6=0
this is the answer
PLEASE HELP!! graph the circle whose equation is (x-6)^2 + (y+2)^2 =4
Answer:
Y= -x^2+12x-36
Step-by-step explanation:
You are having a birthday party and are inviting 6 friends. You have 9 cupcakes, and you are going to share the cupcakes fairly among you and your 6 friends.
Which equation describes how many cupcakes each of you will receive?
Answer:
split the other three in half
Step-by-step explanation:
Ivan runs a cake shop. Renting the
shop costs him $1600 per month,
and he makes a profit of $16 on each
cake he sells. Ivan wants a profit of at
least $2000 a month.
Somebody please help me asap
Answer:
sum of angles in a triangle = 180°
180-(90+21)
= 69
pls am I correct
Y=x^3+x what's the domaine and range
domain is (- infinity, infinity)
range is (- infinity, infinity)
What is the inverse function of y = 2x - 8
Answer:
Step-by-step explanation:
y = 2x-8
2x = y+8
x = 0.5y+4
inverse function: y = 0.5x+4
One evening Papa John’s sold a total of 33 pizzas topped with pepperoni, sausage, or pepperoni and sausage. There were 29 pizzas that had pepperoni. Of these, 15 also had sausage. How many more pizzas had pepperoni only than had sausage only?
Answer:
10
Step-by-step explanation:
Total pizza topped with pepperoni, sausage or pepperoni and sausage = 33
Number of pizzas with pepperoni = 29
Number of pizzas with pepperoni and sausage = 15
Pizza with pepperoni only = 29 - 15 = 14
Pizza with sausage only = 33 - 29 = 4
Pepperoni only than sausage only :
14 - 4 = 10
HELP HELPPP!!!у- 3
|
у+
у- 3
3
What is the common denominator of y+
3
in the complex fraction
5 2
9* Зу
?
Зу(у – 3)
у(у – 3)
Зу
О 3
Answer:
The common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3
Step-by-step explanation:
Given
The complex fraction
Required
The common denominator
To solve this, we need not consider the whole complex fraction.
We only consider
[tex]y + \frac{y-3}{3}[/tex]
Take LCM
[tex]y + \frac{y-3}{3} = \frac{3y - (y-3)}{3}[/tex]
Single out the denominator, i.e. 3
Hence, the common denominator of [tex]y + \frac{y-3}{3}[/tex] is 3
HELP PLEASE MATH PROBLEM
Answer:
x=41
Step-by-step explanation:
LM =JM
154=4x-10
154+10=4x
164=4x
164/4=4x/4
41=x
hope this is helpful
How much is six dimes, 8 nickels, and three one-dollar bills? *
Answer:
.60 + .40 + 3.00 = 4.00
Step-by-step explanation:
Answer:
$ 4
Step-by-step explanation:
six dimes (.10 each) = .60
8 nickels (.05 each)= .40
3 dollars (1.00 each) = 3.
Add together
A jacket costs $154.85. There is a 45% discount. What is the new price of the jacket.
A.) $68.68
B.) $85.17
C.) $224.53
Answer:
B) $85,167
Step-by-step explanation:
u got discount 45% so u just have to pay 55% of it
cost = 55% x $154,85 = $85,1675
Weekly demand for a certain brand of a golf ball at The Golf Outlet is normally distributed with a mean of 35 and a standard deviation of 5. The profit per box is $5.00. Write an Excel formula that simulates the weekly profit:
= 5 * 35 * NORMSINV(RAND())
= 5* NORMINV(RAND(), 35, 5)
= 5 * RANDBETWEEN(5, 35)
= NORMINV(RAND(), 5 * 35, 5)
Answer:
= 5 * NORMINV(RAND(), 35, 5)
Step-by-step explanation:
From the given information:
The total weekly profit is achieved by the multiplication of the unit profit (5) and the weekly demand.
Here, the weekly demands obey a normal distribution where the mean = 35 and the standard deviation = 5.
Using the Excel Formula:
The weekly profit can be computed as:
= 5 * NORMINV(RAND(), 35, 5)
