The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:
0.618 = 61.8%.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for n instances of a normal variable, the mean is of [tex]\mu n[/tex] and the standard deviation is of [tex]\sigma\sqrt{500}[/tex]Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:
[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]
Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:
3600 x 18 = 64800.
The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (64800 - 65000)/670.82
Z = -0.3.
Z = -0.3 has a p-value of 0.382.
1 - 0.382 = 0.618 = 61.8% probability.
TranslationThe problem says that:
Telephone calls are normally distributed with mean of 130 seconds and standard deviation of 30 seconds.A sample of 500 calls is taken.The problem asks for the probability that the total duration of these calls is greater than 18 hours.Calls are independent.More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
4) A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
As per the unitary concept,
a) There are 5/8 cups of flour would you need for half the recipe
b) There are 6 1/4 cups of flour would you need for 5 dozen cookies.
Unitary method:
The method by which first we find the value of single unit and then the value of the required number of units is known as the Unitary Method.
Given,
Here we have given that, A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.
So, here we need to find the following:
a) Exactly how much flour would you need for half the recipe?
b) Exactly how much flour would you need to make 5 dozen cookies?
In order to find these value, we have to calculate the amount of flour need for 1 dozen.
In order to calculate that, one we need to divide the total amount by the cups of flour need.
Then we get,
=> 3/ (2 2/5)
=> 3/ (12/5)
=> 15/12
=> 1.25
So, for half dozen cookies, we need
=> 1.25/2
=> 0.625
Which is in the fraction form of,
=> 5/8
And for 5 dozen of cookie we need.
=> 5 x 1.25
=> 6.25
The fraction equivalent is
=> 6 1/4 cups.
To know more about Unitary method here.
https://brainly.com/question/28276953
#SPJ1
Please help on two geometry questions!!!
Considering the two figures the value of x is
8) x = 12degrees9) x = 8.25 degreesHow to determine the value of xThe value of x is found by the external angle theorem which states that the sum of the two opposite internal angels of a triangle gives the external angle
The value of x is calculated as below
8) 70 + 5x = 9x + 22
70 - 22 = 9x - 5x
48 = 4x
x = 12
9) 65 + 8x + 11 = 16x + 12
65 + 11 - 12 = 16x - 8x
66 = 8x
x = 8.25
Learn more on exterior angle theorem here:
https://brainly.com/question/29322749
#SPJ1
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
Answer: median = 61
Reason:
A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.
Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.
S:{11}
S:{14}
S:{30}
S:{42}
Answer:
S: {11}
Step-by-step explanation:
Hello!
Solve the inequality for n by isolating the variable.
Solve for n 6(n − 5) < 3(n + 4) 6n - 30 < 3n + 123n - 30 < 123n < 42n < 14The solution for n is all values less than 14, so 11 would work.
Calculate the eighth term in the sequence 512, 256,128, ...
Answer:
4
Step-by-step explanation:
You want the 8th term of the geometric sequence 512, 256, 128, ....
Explicit formulaThe formula for the n-th term of a geometric sequence is ...
an = a1×r^(n-1)
where a1 is the first term (512), and r is the common ratio (1/2).
Then the 8th term is ...
a8 = 512(1/2)^(8-1) = 512/128 = 4
The eighth term of the sequence is 4.
Which equation represents a line that has a slope of 1/3 and passes through point (-2, 1)?
y=1/3x-1
Y=1/3x+5/3
Y=1/3x-5/3
Y=1/3x+1
Considering the definition of a line, the equation of the line that passes through the point (-2, 1) and has a slope of 1/3 is y= 1/3x + 5/3.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Line in this caseIn this case, you know:
The line has a slope of 1/3.The line passes through the point (-2, 1).Substituting the value of the slope m, you get:
y= 1/3x + b
Replacing the value of the point in previous expression, the value of the ordinate to the origin b can be obtained:
1= 1/3× (-2) + b
1= - 2/3 + b
1 + 2/3= b
5/3= b
Finally, the equation of the line is y= 1/3x + 5/3.
Learn more about equation of a line:
brainly.com/question/20842634
#SPJ1
line m passes through the points (-4, 3) and (-4, 7) what is the slope of the line that is perpedicular to the line m
Answer:
The slope is 4 and the equation is y = 4x + 18
Step-by-step explanation:
Okay, so you start by solving for the slope. The formula for slope is
m = y1-y2 over x1-x2 (it looks lke a fraction)
then you plug in your coordinates, so it becomes:
m = 7-3 over -4 - (-4) which then you get your slope as 4, but because it has to be perpendicular, the slope becomes -1/4. this is because the slope has to be the reciprocal and the opposite sign to be perpendicular.
Then, you can continue to create the equation by using point-slope form, which is y - y1 = m (x-x1) (y1 and x1 are from the coordinates btw)
so the point-slope equation is:
y - 3 = -1/4 (x + 4)
y - 3 = -1/4x - 1
+3 +3
y = -1/4x + 2 (this is your equation in slope - intercept form)
I hope this helps!!
Solve the inequality3/2 w ≤1/2.
Solve by factoring.
6x^2 - x - 12 = 0
Answer:
x = 3/2 and -4/3
Step-by-step explanation:
[tex] \rm \implies 6 {x}^{2} - x - 12 = 0 \\ \\ \rm \implies 6 {x}^{2} - 9x + 8x - 12 = 0 \\ \\ \rm \implies 3x(2x - 3) + 4(2x - 3) = 0 \\ \\ \rm \implies (2x - 3)(3x + 4) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: \: and \: \: 3x + 4 = 0 \\ \\ \rm \implies 2x = 3\: \: and \: \: 3x = - 4 \\ \\ \rm \implies x = \frac{3}{2} \: \: and \: \: x = - \frac{4}{3} [/tex]
in a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g
The number of division that will take place when the chocolate factory a machine takes a 1 kg block of chocolate is 100.
How to calculate the value?From the information, in the chocolate factory a machine takes a 1 kg block of chocolate and then divides it into rectangles each weight 10g.
It is important to note that:
1000 grams = 1 kilograms
Therefore, since the chocolate is divided into 10g, this will be:
= Total grams / 10 gram
= 1000g / 10g
= 100
Therefore, there will be 100 division.
Learn more about rectangles on;
brainly.com/question/25292087
#SPJ1
Complete question
In a chocolate factory a machine takes a 1 kg block of chocolate. It then divides it into rectangles each weight 10g. How many division will take place?
imagine it as a degree:
We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
Given that,
We have to find the power of the expressions.
a) x⁻³.x⁵
Bases are equal so powers must be added.
x⁻³⁺⁵
x²
b) m⁻³:m⁶
It is in ratio that means
m⁻³/m⁶
We can take the m⁶ to numerator
m⁻³.m⁻⁶
Bases are equal so powers must be added.
m⁻³⁻⁶
m⁻⁹
c) a⁻⁷.a⁻²
Bases are equal so powers must be added.
a⁻⁷⁻²
a⁻⁹
d) (m⁻³)⁻²
Powers are multiplied
m⁶
Therefore, We get the expression with the powers as
a) x⁻³.x⁵= x²
b) m⁻³:m⁶= m⁻⁹
c) a⁻⁷.a⁻²= a⁻⁹
d) (m⁻³)⁻²= m⁶
To learn more about powers visit: https://brainly.com/question/10706914
#SPJ1
Can someone help please? Very much appreciated
Answer:
Coefficient is 7, variable is z
Step-by-step explanation:
Fill in blank by finding number pattern
1,2,1,1,2,3,2,1,1,2,3,4,3,__,__,1,2,__,__,__,__,__,2
The number pattern for the missing numbers is 1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,1,2,3,2,1,2,2
A pattern of numbers formed with a definite rule is called sequence
How to find a number pattern?
In every number patter, first term of this number pattern is 1; and the terms after the first term are obtained by adding, subtracting or multiply by 1 to the previous term.
1+1=2
2-1=1
1*1=1
1+1=2
2+1=3
3-1=2
2-1=1
1*1=1
.1*1=1
1*1=1
2+1=3
3+1=4
4-1=3
3-1=2
2-1=1
1*1=1
1+1=2
2+1=3
3-1=2
2-1=1
1+2=2
2*1=2
learn more about number pattern on brainly.com/question/14471389
#SPJ1
Does X have a binomial distribution? Give your reasons
Opinion polls find that 45% of teens say that their parents put at least some pressure on them to get into a good college. If you take an SRS of 980 teens, X has a distribution of the number in your sample who say they feel at least some pressure from their parents to get into a good college.
The variable X has a binomial distribution, as:
It has a fixed number of observations.The trials are independent.For each outcome, there are only two possible outcomes.What are the requirements for the binomial distribution?There are three requirements for the binomial distribution to represent a variable, as follows:
Fixed number of trials.The result of each trial is independent of the result of any other trial.Two possible outcomes for each trial, one representing a success and the other representing a failure.In the context of the variable X, these requirements are respected as follows:
Fixed number of 980 trials.For each trial, there is a 45% probability that the teen says that their parents put some pressure on him/her to get on good college, and 55% that the parents do not put pressure.For each trial, there are only two possible outcomes, either the parents put pressure, or they do not.Hence yes, the variable X has a binomial distribution.
More can be learned about the binomial distribution at https://brainly.com/question/24756209
#SPJ1
Select all symmetries that apply
Answer:
graph 1
symmetry about the x and y axes
graph 2
symmetry about the y axis
graph 3
symmetry about the y axis
Step-by-step explanation:
try to imagine that you folded the graph by the x axis or y axis. If the to side of the graph are overlapping, the graph is symmetry across the axis you folded.
Hope this helps.
Assume the $26,000 Treasury bill, 5% for 13 weeks. Calculate the effective rate of interest.
Note: Use calendar year. Round your answer to the nearest hundredth percent.
Effective rate of interest
Simple interest of $325 was accrued on a principal of $26,000.00 for a period of 0.25 years (13 weeks) at a rate of 5% per year, bringing the total amount due to $26,325.00 (principal plus interest).
What is simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay additional interest on the interest that has already accrued.
Here,
A = $26,325.00
I = A - P = $325.00
A is equal to P(1 + rt).
The first step is to convert R percent to r a decimal, which is equal to R/100 = 5%/100 = 0.05 per year.
For ease, let's convert time to years: 13 weeks / 52 weeks / year = 0.25 years.
How to resolve our equation
A = 26000(1 + (0.05 × 0.25)) = $26,325.00
Simple interest accrued on a principal of $26,000.00 at a rate of 5% per year for 0.25 years (13 weeks) totaling $26,325.00 (principal plus interest).
To know more about simple interest,
https://brainly.com/question/8100492?referrer=searchResults
#SPJ1
The first three terms of a sequence are given. Round to the nearest thousandth. 10, 5, 5/2. Find the 6th term
Answer:
0.3125
Step-by-step explanation:
10 / 2 is 5
5 / 2 is 2.5
2.5 / 2 is 1.25
1.25 / 2 is 0.625
0.625 / 2 is 0.3125
Look at this graph:
10
9
8
7
9
S
4
لیا ۔
N
L
0
1 2 3 4 5 6 7 8 9 10
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
For the given graph , slope of the line is equal to ( 1 / 2 ).
As given in the question,
Form the given graph,
Scale is given by,
On x-axis each unit of the graph represent 1 unit.
On y- axis each unit of the graph represent 1 unit.
Consider two coordinates from the line of the graph,
( x₁ , y₁ ) = ( 1, 2 )
( x₂ , y₂ ) = ( 3, 3 )
Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value in the formula of the slope we get,
Slope of the line = ( 3 - 2 ) / ( 3 - 1 )
⇒ Slope of the line = 1 / 2
Therefore, for the given graph , slope of the line is equal to ( 1 / 2 ).
Learn more about slope here
brainly.com/question/3605446
#SPJ1
Start with the graph of
f(x) = 6x.
Then write a function
g(x)
that results from the given transformation.
shift f(x) 5 units downward
g(x) =
Ashley has a $80 gift card to her favorite coffee shop. Each day, she uses her gift *
card to buy a coffee for $4.50, Aaron has a $60 gift card to the same coffee shop.
Each day, he uses his gift card to buy an iced tea for $2.50. For what number of
drinks purchased will Ashley's gift card balance be greater or equal to Aaron's?
Step-by-step explanation:
I assume this means that both purchase one item every day.
so, their number of purchases are the same (x).
80 - 4.5x >= 60 - 2.5x
20 - 4.5x >= -2.5x
20 >= 2x
10 >= x
our
x <= 10
after 10 purchased drinks their balances will be equal.
before that, Ashley's card balance will be greater than Aaron's.
after that, Aaron's card balance will be greater than Ashley's.
so, for up to 10 purchased drinks Ashley's card balance will be greater or equal to Aaron's.
4/7 of a group of children are boys, if they are 18 more boys than girls how many children are there altogether
Answer:126 children
Step-by-step explanation:
first you want to multiply 18 times 4 (72) then 18 times 3 (54) and then you add 72+54=126
your welcome :)
Then has a recipe for a marinade recipe says to mix 3/8 cup olive oil 1/4 cup soy sauce and 1/8 cup lime juice how much olive oil does he need to make 9 cups of the marinade show your work
You have to multiply 3/8 by 9 and then you get your answer which is 3.375
is the line through points P(-8, -10) and Q(-5, -12) perpendicular to the line through points R(9, -6) and S(17, -5) explain
Answer:
No, the lines are not perpendicularStep-by-step explanation:
Perpendicular lines have opposite-reciprocal slopes.
It means the product of the slopes is - 1.
Let's find the slopes of the two lines and their product.
m(PQ) = (- 12 - (-10)) / (- 5 - (-8)) = - 2/3m(RS) = (- 5 - (-6)) / (17 - 9) = 1/8Find the product of slopes:
- 2/3*1/8 = - 1/12This is not - 1, therefore the lines are NOT perpendicular.
*PRE-CALC URGENT + 100 POINTS*
A jumping spider's movement is modeled by a parabola. The spider makes a single
jump from the origin and reaches a maximum height of 20 mm halfway across a horizontal distance of 160 mm.
Part A: Write the equation of the parabola in standard form that models the spider's jump. Show your work. (4 points)
Part B: Identify the focus, directrix, and axis of symmetry of the parabola. (6 points)
Answer:
A. (x - 80)² = -320(y = 20)
B. Focus: (80, -60)
Directrix: y = 100
Axis of symmetry: x = 80
Step-by-step explanation:
Part AIf the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:
x-intercepts = (0, 0) and (160, 0)Vertex = (80, 20)Standard form of a parabola with a vertical axis of symmetry:
[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]
If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.
[tex]\textsf{Vertex}=(h, k)[/tex][tex]\textsf{Focus}=(h,k+p)[/tex][tex]\textsf{Directrix}:y=(k-p)[/tex][tex]\textsf{Axis of symmetry}:x=h[/tex]Substitute one of the x-intercepts and the vertex into the formula and solve for p:
[tex]\implies (0-80)^2=4p(0-20)[/tex]
[tex]\implies (-80)^2=4p(-20)[/tex]
[tex]\implies 6400=-80p[/tex]
[tex]\implies p=-80[/tex]
Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:
[tex]\implies (x-80)^2=4(-80)(y-20)[/tex]
[tex]\implies (x-80)^2=-320(y-20)[/tex]
Part BGiven:
h = 80k = 20p = -80[tex]\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}[/tex]
Describe how the graph of g(x)= –||x+2||+4 is related to the graph of the parent function.
The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.
Reflection over the x-axis.Shift left of 2 units.Shift up of 4 units.Which transformations were used?The parent function in this problem is defined as follows:
f(x) = |x|.
The transformed function in this problem is defined as follows:
g(x) = -|x + 2| + 4
The transformations are listed and described as follows:
The multiplication by -1 represents a reflection of the parent function over the x-axis.The addition by 2 in the domain, that is, x -> x + 2, represents a shift right of two units of the parent function.The addition by 4 in the range, that is, y -> y + 4, represents a shift up of four units of the parent function.More can be learned about transformations at https://brainly.com/question/28792248
#SPJ1
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers.
x + (x + 1) + (x + 2) = 42
x + (x + 2) + (x + 4) = 42
(x minus 1) + x + (x + 1) = 42
(x minus 2) + x + (x + 2) = 42
x + 2 x + 3 x = 42
Answer:
A and C are correct choices========================
The difference between two consecutive integers is 1.
Test it with the given choicesA) x + (x + 1) + (x + 2) = 42,
YesB) x + (x + 2) + (x + 4) = 42
No, the difference between the pairs is 2 not 1.C) (x minus 1) + x + (x + 1) = 42
YesD) (x minus 2) + x + (x + 2) = 42
No, the difference between the pairs is 2 not 1.E) x + 2 x + 3 x = 42
No, here is the multiples of integers and the difference between the pairs is x not 1.Answer:
x + (x + 1) + (x + 2) = 42
(x minus 1) + x + (x + 1) = 42
Step-by-step explanation:
Integer: A whole number that can be positive, negative, or zero.
Consecutive integer: Integers that follow each other in order.
Let x be an integer.
Consecutive integers of x are one more or one less than each other in order.
x + (x + 1) + (x + 2) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
x + (x + 2) + (x + 4) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
(x minus 1) + x + (x + 1) = 42This equation represents 3 consecutive integers as each value is one more than the previous value.
(x minus 2) + x + (x + 2) = 42This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.
x + 2 x + 3 x = 42This equation does not represent 3 consecutive integers as each value is x more than the previous value.
Enter an inequality that represents this graph
The inequality that represents the graph is y < 4
The graph is shown in the figure
The graph is the pictorial representation of the collection of data. It has 2 axis . The x axis and y axis
Consider the each block of the graph as 1 units
At y = 4 there is dotted line parallel to the x axis of the graph
The dotted line represents the inequality symbol less than, Therefore the value of y is less than 4
From the graph, the entire region of the graph that y less than 4 are shaded therefore for all the value of x the value of y is less than 4
The inequality will be
y < 4
Hence, the inequality that represents the graph is y < 4
Learn more about inequality here
brainly.com/question/20383699
#SPJ1
(y − 1)(y + 10)(y-6) < 0
Solve for y by simplifying both sides of the inequality, then isolating the variable.
Inequality Form:
y<−10 or 1<y<6
Interval Notation:
(−∞,−10)∪(1,6)
3. If, over a few months, Jane saw 92 mayflies,
how many flying insects did she see ?? Need awnsers
Graph the point on the graph.
Answer:
see below
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph
Answer:
Info down in Explaination
Step-by-step explanation:
To graph this equation, start at the origin (0,0) since there is not y-intercept.
Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.
Because the rise (up and down, numerator) is 1, we know that we will go up one unit.
The run (side to side, denominator) is 4, so we will go to the right 4 units.
This makes the first point (4, 1).
Continue doing this until you get an idea of the line and connect the points to get the graph