The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -
f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.
Also, the mean for an exponential distribution is given by u = 1/θ .
In the question it is 22 seconds.
So, the value of θ is 1/22.
Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.
P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -
P(X<x)= F(X) = 1- e^(-θ x) , where x>0.
Putting θ = 1/22 and x= 30 in F(X) , we get -
F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.
So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
To learn more about exponential distribution , visit link - brainly.com/question/22692312
#SPJ4
The probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
The problem involves exponential distribution which is a standard continuous distribution. The probability density function of this distribution is given by -
f(x) = θe^(-θx) ; where θ is a parameter and characteristic of the distribution, x is the random variable.
Also, the mean for an exponential distribution is given by u = 1/θ.
In the question, it is 22 seconds.
So, the value of θ is 1/22.
Now, we have to find P(X<30) where X is the random variable denoting the calling time in seconds.
P(X<30) is nothing but F(x) at x = 30 seconds, i.e. cumulative distribution function. For an exponential distribution , F(X) is given by -
P(X<x)= F(X) = 1- e^(-θ x) , where x>0.
Putting θ = 1/22 and x= 30 in F(X) , we get -
F(X) = 1-e[(-1/22)30] = 1- 0.2555 = 0.7445 which is P(X<x) = P(X<30) = 0.7445.
So, the probability that a randomly selected call time will be less than 30 seconds is approximately 0.7445.
To learn more about exponential distribution, visit the link - brainly.com/question/22692312
#SPJ4
The quadratic function h(t)=-16. 1t2+150 models a balls height in feet over time in seconds after it is dropped from a 15 story building
f(x) = ax2 + bx + c, where a, b, and c are real values and a = 0, is a quadratic function. A quadratic function's domain is (,). The graph of the simplest quadratic function, f(x) = x2, is shown below. Its shape, a parabola, should be recognizable from Intermediate Algebra.
To find the time at which the ball hits the ground, we need to find the value of t when h(t) = 0.
Solving -16.1t^2 + 150 = 0 gives us:
-16.1t^2 = -150
t^2 = 9.37
t = 3.05 (rounded to the nearest hundredth)
So the ball hits the ground after 3.05 seconds.
The complete question is:-
The quadratic function h(t)=-16.1t^2 + 150 models a balls height, in feet, over time, in seconds, after it is dropped from a 15 story building.
- From what height, in feet, was the ball dropped?
-After how many seconds, rounded to the nearest hundredth, did the ball hit the ground?
To learn more about quadratic function, refer:-
https://brainly.com/question/27958964
#SPJ4
The Joseph family took out a $175,000, 25-year mortgage at an APR of 4%. The assessed value of their house is $9,000. The annual property tax rate is 97.22% of assessed value. What is the annual property tax?
The annual property tax for the Joseph family is $8749.8.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
The Joseph family took out a $175,000,
25-year mortgage at an APR of 4%.
The assessed value of their house is $9,000.
The annual property tax rate is 97.22% of assessed value.
The annual property tax = 9000 x 97.22/100
The annual property tax = $8749.8
Therefore, the annual property tax = $8749.8
To learn more about the percentage;
https://brainly.com/question/24159063
#SPJ1
PLEASE HELP HURRY!!
A line passes through the points (1, 1) and (2, 8). Write its equation in slope-intercept form.
The slope-intercept equation of the line that includes the points (1, 1) and (2, 8) is y = 7x - 6.
What is the point-slope form?In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear equation representing the line which passes through the points (1, 1) and (2, 8) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 1 = (8 - 1)/(2 - 1)(x - 1)
y - 1 = 7(x - 1)
y = 7x - 7 + 1
y = 7x - 6
Read more on slope here: brainly.com/question/23086745
#SPJ1
the _____ of a square are both congruent and perpendicular.
The diagonals of a square are both congruent and perpendicular.
Because a square is a regular quadrilateral with four equal sides and four equal angles, it is a quadrilateral. A rectangle with two adjacent sides of equal length can also be used to describe it. A chess board, dice, tiles, napkins, etc. are a few examples.
The perpendicular bisectors of a square's diagonals are one another. Each diagonal is divided into two congruent parts as a result, and their intersection creates four right angles. As a result, if a diagonal is given, its length, one segment's length is equal to half of the diagonal's overall length. They are also divided at a 90-degree angle, making them perpendicular, and they are similar in length.
Read more about the square on:
https://brainly.com/question/27307830
#SPJ4
I need help geometry 1 find the angles in the pictures
Answer:
f= 68
g= 88
h= 100
i= 114
Step-by-step explanation:
In which of the rectangles are the area and the perimeter the same number of units or square units?
In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.
What are the perimeter and area?
The area is the region covered by shape or figure whereas the perimeter is the distance covered by the outer boundary of the shape. The unit of area is given by a square unit or unit2 and the unit of the perimeter is the same as the unit.
(a)
Area of a rectangle = length × breadth
=(8×6)
=48 feet²
Perimeter of the rectangle = 2(length + breadth)
=2(6+8)
=28 feet
(b)
Area of a rectangle = length × breadth
= (4×4) yards²
= 16 yards²
Perimeter of the rectangle = 2(length + breadth)
=2(4+4)
=16 inches
(c)
Area of a rectangle = length × breadth
=(9×4) inches²
= 36 inches²
Perimeter of the rectangle = 2(length + breadth)
=2(9+4)
=26 inches
(d)
Area of a rectangle = length × breadth
=(7×4) meters²
=28 meters²
Perimeter of the rectangle = 2(length + breadth)
=2(7+4)
=22 meters
Hence, In the second option (b) the rectangles have the area and the perimeter the same number of units or square units.
To learn more about the perimeter and area visit,
https://brainly.com/question/7070108
#SPJ1
if x=1y=2, what is the ratio of x4 to y4 ? A.1/16 B.1/2 C.1/1 D. 256/1
The ratio of the given expression is equal to 1:16.
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.
We have x=1 and y=2, and we have to find the ratio of x4:y4,
x=1 and y=2 (given)
[tex]x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16[/tex]
the ratio of the given expression is equal to 1:16.
learn more about ratio .
https://brainly.com/question/13419413
#SPJ4
Draw an x-y graph that show the vertical profiles of pressure, density, and temperature in the troposphere. This means the vertical y-axis, which will be height or altitude, going from 0 to 10 km. You can draw three separate graphs, or combine them into one (the axes do not need to be precisely calibrated; you are showing the general trends of each parameter, so the shapes of the plots are important).
The vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
Explain the relation of pressure, density, and temperature in the troposphere.Pressure altitude is temperature-adjusted density altitude.
In simple terms, it has a direct impact on an aircraft's performance parameters and is essentially the height at which the aircraft "thinks" it is performing. The performance of an airplane decreases with increasing density altitude and vice versa.Pressure and temperature have a direct and indirect relationship with density.
Density rises as pressure rises and temperature remains constant. Conversely, density falls as temperature rises while maintaining the same pressure. For every 10 hPa decrease in pressure or 3 °C rise in temperature, the air density will drop by around 1%.Thus, the vertical profiles for pressure, density, as well as temperature with in troposphere are displayed in an x-y graph.
To know more about the troposphere, here
https://brainly.com/question/30126542
#SPJ4
A financial manger ha $14,000 to invet for her company. She plan to invet part of the money in
tax-free bond at 6% interet rate and the reminder in taxable bond at 9%. She want to earn $1005
per year in interet from the invetment. Find the amount he hould invet at each rate
Answer:
she should charge $10 for interest or even more is she wants to make $1005 per year from investing
I need to make sure part b is correct
Answer:
no picture is added ill help you if you add it
Step-by-step explanation:
Answer:
Add a picture than I'll tell you if (b) is correct or not :)
Step-by-step explanation:
can some one help meeee please ...
The price a customer pays for a printer which the company bought for $1700 is $2125 and the price the company paid for a printer which was sold to a customer for $2500 is $2000.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a company sells its printers to customers in order to make a profit of 25%.
We have to find the price a customer pays for a printer which the company bought for $1700.
x-1700/1700=25%
x-1700=425
Add 1700 on both sides
x=$2125.
We need to find the price the company paid for a printer which was sold to a customer for $2500
2500-x/2500=25%
x=2000
Hence, the price a customer pays for a printer which the company bought for $1700 is $2125 and the price the company paid for a printer which was sold to a customer for $2500 is $2000.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Hello please please please help I really need help with this
Answer:
well if 4 is x and y is -6 but =2 then it's 8
Step-by-step explanation:
hope u have a good day
Water is poured into a clear triangular prism as shown to the left. It takes 5 cubic inches of water to fill the prism to the height of 1 inch. 15. What is the area of the BASE of this prism?
The area of the base of this prism is 2. 5 square inches
How to determine the base area of the triangular prismIt Is important to note the properties of a triangular prism, they include;
It has five facesIt has nine edgesIt has six verticesIt is a polyhedron having two triangular bases and also three rectangular sides.The base is a triangle.The sides is rectangular.The triangular bases are equalFrom the information given, we have that;
Base area = 1/2 base × height
Substitute the values, we get
Base area = 1/2 × 5 × 1
Multiply the values
Base area = 2. 5 square inches
Hence, the value is 2. 5 square inches
Learn about area on:
https://brainly.com/question/25292087
#SPJ1
The length of a ide of a triangle i in the extended ratio of 3:5:7. The perimeter of the triangle i 120cm. What are the length of the ide?
The height of the corresponding to the longest side is 25.03 cm
What is triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Use the equation area = 1/2 * base * height to determine a triangle's surface area. Decide which side will serve as the triangle's base, then calculate the triangle's height from that base. After that, enter the height and base measurements you have into the formula.Given data :
Let the sides of triangles are 3x,5x and 7x.
And perimeter of the triangle is 120cm.
So , 3x + 5x +7x =120
15x = 120
x = 8
so, the sides are triangle are 3(8) = 24cm, 5(8) = 40cm , 7(8) = 56cm
so , the longest side is 56 cm.
Area of triangle = [tex]\sqrt{s(s - a)(s -b)(s-c)}[/tex]
here , s = 64 and a = 24, b = 40c = 56
= [tex]\sqrt{64*(64-24)(64-40)(64-56)}[/tex]
= [tex]\sqrt{64*(40)(24)(8)}[/tex]
=[tex]\sqrt{491520}[/tex]
= 701.08
So, the area of triangle is 701.08 cm 2 and the height corresponding to longest side
h = 2 x 701.08 / 56 = 25.03 cm
Learn more about Triangle refer to :
https://brainly.com/question/89544
#SPJ4
The illustration shows a wheelchair ramp from the side. The support at BC binds the ramp to the floor. Are Triangles ABC and ADE similar?
Triangle ABC is similar to triangle ADE by AA test of similarity
What is similarity in triangle?Similarity is a property which says that the respective angles of two triangles are of equal measure and corresponding sides are in proportion.
here, we have,
There are different types of similarity test by which we can prove the similarity of triangles.
We are given that BC is parallel to Line DE
As the lines are parallel the respective angle are corresponding angles
hence Angle D = Angle B
And Angle E = Angle C
And both triangle have angle A as common angle
By AA test of similarity we can say that the two triangles are similar
Hence by AA test similarity the two triangles are similar
To learn more about similar triangle please refer
brainly.com/question/14285697
#SPJ1
Which value of x is a solution to this equation?
2x2+7x−30
Question 2 options:
2. 5
5
-2. 5
-3
If the equation be 2x² + 7x – 30 then the solution to this equation be 2.5.
What is meant by equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.
Let the given equation be 2x² + 7x – 30 = 0
Factorizing it as
(2x – 5) (x + 6) = 0
then we get
2x – 5 = 0 or x + 6 = 0
simplifying the equation we get
2x = 5 or x = –6
x = 5/2 or x = –6
x = 2.5 or x = –6
Therefore, the correct answer is option a) 2.5.
The complete question is:
Which value of x is a solution to this equation?
2x² + 7x – 30
a) 2. 5
b) 5
c) -2. 5
d) -3
To learn more about equation refer to:
https://brainly.com/question/2228446
#SPJ1
2x＝ 3 -5√x usind log form find x
2x＝ 3 -5√x using log form, x = log(2x + 5√x) = log(3)
How did we get the value?To convert the equation 2x = 3 - 5√x into logarithmic form, we need to isolate the radical expression on one side of the equation. We can do this by adding 5√x to both sides:
2x + 5√x = 3
Next, we'll take the square root of both sides to eliminate the radical:
√(2x + 5√x)^2 = √(3^2)
Expanding the left side and simplifying:
2x + 5√x = 3
Finally, we'll take the logarithm of both sides to get x in logarithmic form:
log(2x + 5√x) = log(3)
To solve for x, we'll need to use logarithmic properties and/or exponential functions to isolate x on one side of the equation. log(2x + 5√x) = log(3)
learn more about log form: https://brainly.com/question/25710806
#SPJ1
Simplify the expression
(Please show the work)
Pls help
Beatriz is in charge of setting up a banquet hall. She has five tables that
will seat six people each. If no more than 62 people will attend, how
many tables seating four people each will she need?
The number of tables with a seating of 4 people is 13.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Beatriz is in charge of setting up a banquet hall. She has five tables that will seat six people each. If no more than 62 people.
The number of the tables will be calculated as:-
Number = 62 / 4
Number = 13
Hence, the number of tables with a seating of 4 people is 13.
To know more about an expression follow
https://brainly.com/question/744711
#SPJ1
Which one of the following is a statistically valid reason for sampling randomly when choosing subjects for a study?Correct Response- Sampling randomly tends to reduce sampling bias or risk- Sampling randomly (with a large sample) gives a perfect reflection of the population- Sampling randomly is easier than sampling nonrandomly- Actually, there is no statistically valid reason for sampling randomly
Sampling randomly is considered a statistically valid reason for choosing subjects for a study as it reduces the risk of sampling bias. The correct option is a.
Sampling bias refers to a systematic error that occurs in the process of selecting subjects for a study, leading to a sample that is not representative of the population.
By selecting subjects randomly, researchers aim to eliminate any preconceived biases or preferences that may influence the selection process. This leads to a sample that is more representative of the population, providing a more accurate representation of the population's characteristics.
Furthermore, random sampling (with a large sample) has the potential to give a perfect reflection of the population, assuming that the sample size is large enough. This is because, as the sample size increases, the sample becomes more representative of the population and tends to exhibit the same characteristics and distributions as the population.
To learn more about Sampling refer here
https://brainly.com/question/29357010#
#SPJ11
1. Here are a few pairs of positive numbers whose sum is 50.
first number
second number
product
1
49
2
48
10
40
a Find the product of each pair of numbers.
b. Find a pair of numbers that have a sum of 50 and
will produce the largest possible product.
c. Explain how you determined which pair of
numbers have the largest product.
Activate Wir
Go to Settings to
The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40, with a product of 400. This was determined by comparing the products of each pair and determining which is the largest.
a. The product of the first pair of numbers is 1 x 49 = 49, the product of the second pair of numbers is 2 x 48 = 96, and the product of the third pair of numbers is 10 x 40 = 400.
b. The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40.
c. To determine which pair of numbers have the largest product, we need to compare the products of each pair and determine which is the largest. In this case, the pair of 10 and 40 have the largest product of 400.The pair of numbers that have a sum of 50 and will produce the largest possible product is 10 and 40, with a product of 400. This was determined by comparing the products of each pair and determining which is the largest.
The complete question is :
What are a few pairs of positive numbers whose sum is 50 and which have the largest possible product?
learn more about product here
https://brainly.com/question/29775042
#SPJ4
Gloriana has a wire 7/8 foot long. She is going to cut it into twisties 1/6 foot long. How many twisties will she make?
A. 5 twisties
B. 51/4 twisties
C. 6 twisties
D. 61/4 twisties
Answer:
The answer is B. 5 1/4 twisties
What is the solution to the system of equations?
{y=7x+11
y=−3x+1
Enter your answer as an ordered pair, like this: (42, 53)
The solution to the system of equations ordered pair is (-1, 4).
What exactly is an equation system?A simultaneous equation is any one or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.the solution to the system of equations {y=7x+1 , y=−3x+1
Given:
a collection of equations
Equation 1 is y = 7x + 11.
Equation 2: y = 3x + 1.
Equation 1's y value is changed to equation 2's value.
7x + 11 = -3x + 1
10x = -10
x = -1
And y = 4
Consequently, the answer is (-1, 4).
The solution to the system of equations ordered pair is (-1, 4).
To learn more about system of equations refer to:
https://brainly.com/question/15834407
#SPJ4
The Sugar Sweet Company is going to transport its sugar to market. It will cost $4500 to rent trucks, and it will cost an additional $250 for each ton of sugar transported.
solve both equation and Total cost to transport 13 tons of sugar
The cost of transporting 17 tons of sugar is $8750.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
here, we have,
It will cost $4500 to rent trucks,
and it will cost an additional $250 for each ton of sugar transported.
we know,
Multiplication and division do not separate the terms of an equation.
now,
The given information can be related as,
C = 250S + 4500.
Now, when tons of sugar is 17 we'll simply replace S with 17.
∴ C = 250(17) + 4500.
C = 4250 + 4500.
C = 8750.
Hence, The cost of transporting 17 tons of sugar is $8750.
learn more about equations here :
brainly.com/question/29657992
#SPJ1
Just to make sure, what is 0.4x2.5 equal?
Answer:
1
Step-by-step explanation:
You can think of this problem this way:
[tex]0.4*2.5=\frac{2}{5}*\frac{5}{2}=\frac{10}{10}=1[/tex]
Answer: 1
Step-by-step explanation:
there are two decimal places in total, keep that in mind
multiply everything by 10 to make whole numbers and multiply
4x25=100 because 4x5=20 and 4x20=4x10x2=80 and 20+80=100
remember those two decimals we counted, take that number, and move the decimal place over that many in your answer. 100 becomes 1
why not just use a calculator lol, you have internet access
Use the distributive property to rewrite 5(a+9)
Answer:
5a + 45
Step-by-step explanation:
5(a+9)
5a + 45
What Is The Answer To This Problem??
need some help with this third question
Answer:
276.46 in^3
Step-by-step explanation:
See the attached worksheet. The pencil balloon if formed by a cylinder and cone. Use the volume formulas for each of these shapes to calculate that shape's contribution to the total volume, and then add them.
The volume of the cylinder portion is 263.9 in^3.
The volume of the cone portion is 12.56 in^3
The sum is 276.46 in^3, which matches the first answer option.
Answer:
276.46 cubic inches
Step-by-step explanation:
Volume of the cylindrical part = πr²h, r= radius, h = height
Volume of a cone (1/3) πr²h, r= radius, h = height
For given dimensions
cylinder h = 21, cylinder r = 2
Volume of cylindrical part of balloon = π · 2² · 21 = 4 · 21 · π = 84π cubic inches
Volume of conical part of balloon = (1/3) π · 2² · 3 = 4π
Total volume = 84π + 4π = 88π = 276.46 cubic inches
refer to the t-account below: raw materials debit credit balance 15,000 (9) 75,000 (5) 85,000 balance 25,000 entry (5) could represent which of the following?
The amount of raw materials in Entry (5), which would raise the raw materials balance from $15,000 to $25,000, might cost $85,000.
Entry (5) can refer to a $85,000 purchase of raw materials. The raw materials balance would rise from $15,000 to $25,000 as a result. The raw materials account's balance is shown in the t-account above both before and after the entry. The raw materials balance was $15,000 prior to this entry. The raw materials balance is now $25,000, an increase of $10,000 after this input. This increase is attributable to the $85,000 purchase of raw materials. This transaction is documented in entry (5), which represents a $85,000 debit to the account for raw materials. The raw materials account now has a balance of $25,000 instead of just $15,000. This is how entry (5) may describe a $85,000 purchase of raw materials.
Learn more about amount here
https://brainly.com/question/28970975
#SPJ4
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 5.
8 over 60
10 over 60
27 over 60
42 over 60
The probability of rolling a number less than 5 is 42/60
How to find the experimental probability?It is given by the quotient between the number of times that we got a given outcome and the total times that the experiment was performed.
Here we want to find the experimental probability of landing on a number less than 5 (these are 1, 2, 3, 4)
Outcome Frequency
1 12
2 13
3 11
4 6
These are the tables, adding these we get:
12 + 13 + 11 + 6 = 42
So in 42 out of 60 tosses we got a number less than 5, then the experimental probability is:
42/60
Learn mroe about probability at:
https://brainly.com/question/25870256
#SPJ1