value of variable x and y in simultaneous equations are 3,1 and 3,-3 respectively.
What are Simultaneous Equations?Several algebraic equations that have the same unknown variables and the same answer are referred to as simultaneous equations. It suggests that there is a single solution to the simultaneous equations. Examples of concurrent equations include: 2x - 4y = 4, 5x + 8y = 3.
Given Simultaneous Equation;
Equation 1 ; y=x²-x+3
Equation 2 ; y=6-3x
Putting Equation 2 in 1 we get
6-3x=x²-x+3
x²+2x-3=0
x²+3x-x-3=0
x(x+3)-1(x-3)=0
(x-3)(x-1)=0
x=3,1
By entering x values in equation 2, we obtain
y=6-3×3
y=-3
Or y=6-3×1=3
Hence, value of x and y are 3,1 and 3,-3 respectively.
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1(1/2)= 1 1/2 draw number line and represent this
|-----|-----|-----|----|-----|-----|--│--|-----|----|-----|
-5 -4 -3 -2 -1 0 1 │ 2 3 4 5
1 1/2
On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.
To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.
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Roll a fair die three times. What is the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll?
The probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.
Probability is the study of random events. It is a measure of the likelihood of an event occurring. Probability can be expressed as a decimal, a fraction, or a percentage. There are two types of probability - empirical probability and theoretical probability.
Empirical probability is calculated by conducting experiments or collecting data. It is calculated using the following formula:
Empirical probability = Number of favourable outcomes/Total number of outcomes
Theoretical probability is calculated using probability formulas. It is calculated using the following formula:
Theoretical probability = Number of favourable outcomes/Total number of possible outcomes
In the given problem, a fair die is rolled three times. We need to find the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll. There are 2 favourable outcomes for the first roll, 2 favourable outcomes for the second roll, and 2 favourable outcomes for the third roll.
Total number of outcomes = 6×6×6 = 216
Number of favourable outcomes = 2×2×2 = 8
Probability = Number of favourable outcomes/Total number of outcomes
Probability = 8/216
Probability = 1/27
Therefore, the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.
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sunitha is 24 years older than her daughter kavita. 6 years ago, sunitha was thrice as old as kavitha. find their present ages.
Solve for x. Round to the nearest tenth, if possible.
-. If f(x) = x² + 3x-2, find f(x) when x = -2
Answer:
-4
Step-by-step explanation:
substitute -2 into the formula and solve
[tex]f(x)=(-2)^2+3(-2)-2\\f(x)=4+(-6)-2\\\boxed{f(x)=-4}[/tex]
what is the answer to this problem. solve x
Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let x= the number of free throws faith makes out of 20 shots. Calculate and interpret the standard deviation of x
If at practice, each player shoots 20 free throws, the standard deviation of x is 0.975.
To calculate the standard deviation of x, we need to first determine the variance. The variance is the average of the squared differences of each observation from the mean.
In this case, Faith is a 95% free throw shooter, so she is expected to make 19 out of 20 shots on average. The probability of making a free throw is 0.95, and the probability of missing a free throw is 0.05. Therefore, the mean of x is:
mean(x) = 20 * 0.95 = 19
To calculate the variance, we need to find the expected value of (x - mean(x))^2. Since Faith's free throw shooting is independent, we can use the binomial distribution to find the probability of making x shots out of 20.
The formula for the variance of a binomial distribution is np(1-p), where n is the number of trials and p is the probability of success. Therefore, the variance of x is:
var(x) = 20 * 0.95 * 0.05 = 0.95
Finally, the standard deviation is the square root of the variance:
sd(x) = √(var(x)) = √(0.95) = 0.975
This means that on average, Faith is expected to make 19 out of 20 free throws, but there is a standard deviation of 0.975, which indicates the degree of variability or spread around the mean. In other words, we can expect Faith to make between 18 and 20 free throws in most cases, but there is a small chance that she may make fewer or more than that.
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without calculation, find one eigenvalue and two linearly independent eigenvectors of a d 2 4 5 5 5 5 5 5 5 5 5 3 5 . justify your answer.
The eigenvalues of A are λ = 0 (with multiplicity 1) and λ = 5 (with multiplicity 2), and the corresponding eigenvectors are [1, 0, -1], [0, 1, -1], and [1, -1, 1].
The matrix A = [5 5 5; 5 5 5; 5 5 5] is a 3x3 matrix with all entries equal to 5.
First, we can calculate the determinant of A - λI, where I is the identity matrix and λ is an unknown eigenvalue:
A - λI = [5-λ 5 5; 5 5-λ 5; 5 5 5-λ]
det(A - λI) = (5-λ)[(5-λ)(5-λ)-25] - 5[5(5-λ)-25] + 5[5-25]
= (5-λ)(λ^2 - 15λ) = -λ(λ-5)^2
From this equation, we can see that the eigenvalues are λ = 0 and λ = 5 (with multiplicity 2).
To find the eigenvectors, we can substitute each eigenvalue into the equation (A - λI)x = 0 and solve for x.
For λ = 0, we have:
A - 0I = A = [5 5 5; 5 5 5; 5 5 5]
(A - 0I)x = 0x = [0 0 0]
This implies that any vector of the form [a, b, -a-b] is an eigenvector for λ = 0. For example, we can choose [1, 0, -1] and [0, 1, -1] as linearly independent eigenvectors corresponding to λ = 0.
For λ = 5, we have:
A - 5I = [0 5 5; 5 0 5; 5 5 0]
(A - 5I)x = 0
⇒ 5x2 + 5x3 = 0
⇒ 5x1 + 5x3 = 0
⇒ 5x1 + 5x2 = 0
This implies that any vector of the form [1, -1, 1] is an eigenvector for λ = 5. Therefore, we can choose [1, -1, 1] as another linearly independent eigenvector corresponding to λ = 5.
Eigenvectors are a fundamental concept in linear algebra. They are essentially special vectors that remain in the same direction when a linear transformation is applied to them, only changing in magnitude. In other words, an eigenvector of a linear transformation is a vector that when multiplied by the transformation matrix, results in a scalar multiple of itself.
Eigenvectors play a crucial role in diagonalizing matrices, which can simplify calculations involving matrix operations. They are also useful for solving differential equations and understanding the behavior of dynamic systems. In addition, eigenvectors are often used for data analysis, such as in principal component analysis (PCA), which is a technique for reducing the dimensionality of data.
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What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.
Therefore, the measure of ∠D is approximately 60.96 degrees.
What is measure?A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.
by the question.
To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:
[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]
Taking the inverse tangent of both sides, we get:
[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]
Rounding this to the nearest hundredth, we get:
[tex]angleD = 60.95 degrees =60.96 degree.[/tex]
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Classify the following linear differential equations according to whether they are time- variable or time-invariant. Indicate any time-variable terms. a. + 2y = 0 dtz d b. (t²y) = 0 dt C. (+)²+(+) y = - t+1 d²y d. + (cost)y = 0 dt² y = 0 ECO
a. Time-invariant (no time-variable terms)
b. Time-variable (t² is time-variable)
c. Time-invariant (no time-variable terms)
d. Time-invariant (no time-variable terms)
e. Time-invariant (no time-variable terms)
A linear differential equation is one that involves only linear combinations of the dependent variable and its derivatives, as well as any coefficients that are functions of the independent variable (time in this case).
In the first equation, +2y=0, there are no terms that involve the independent variable, so this is a time-invariant equation.
In the second equation, (t²y)'=0, there is a term involving the independent variable t, specifically t². Therefore, this equation is time-variable.
In the third equation, y''+y'=-t+1, there are two terms involving the independent variable, namely -t and 1. Therefore, this equation is time-variable.
In the fourth equation, (cos(t)y)'=0, there is a term involving the independent variable t, specifically cos(t). Therefore, this equation is time-variable.
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(8,-4) and (-1-2) to the nearest tenth
In 2010, the population of Belvedere was estimated to be 39,366 people with an annual rate of increase of approximately 2.8%.
Select the explicit expression that represents the population in the next 6 years.
OA. 39,366(1.0028)5
OB. 39,366(1.28)5
OC. 39,366(0.028)
OD. 39,366(1.028)
Based on exponential growth function, the explicit expression that represents the population of Belvedere, which was estimated to be 39,366 in 2020 with an annual increase of 2.8%, in the next 6 years is D. 39,366(1.028)^6.
What is an exponential growth function?An exponential growth function is one of the two exponential function, including exponential decay function.
The exponential growth function is given as y = a(1 + r)^t, where:
y is the new valuea is the current valuer is the constant ratioand t is the time in years.Population of Belvedere in 2010 = 39,366
Annual rate of increase = 2.8%
The time, t = 6 years
Exponential function expression: 39,366(1.028)^6
Thus, the population of the city in the next 6 years can be represented by the expression in Option D.
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can anyone help me please???
thank you xxxx
Using the property of a kite: the angles formed by two unequal sides of a kite are equal. The value of ∠BCD∠BCD is
∠BCD = ∠BAD ⇒ ∠BCD = 106°
6 : water pours into a fish tank at a rate of 0.3 cubic meters per minute. how fast is the water level rising if the base of the fish tank is a 2 meter by 3 meter rectangle?
Water pours into a fish tank at a rate of 0.3 cubic meters per minute, the water level is rising at a rate of 1/60 m/min
How to calculate the water level?Given
The base of the fish tank is a 2-meter by 3-meter rectangle.The area of the base of the fish tank = length x breadth= 2 m x 3 m = 6 m².Let, h is the height of the water level in the fish tank after t minutes. Then, the volume of the water in the fish tank after t minutes is given by [tex]V = Area of the base * height V = 6 * h m^3[/tex]The rate at which water pours into the fish tank is 0.3 cubic meters per minute.
Therefore, the rate of change of volume of the water in the fish tank after t minutes is [tex]dV/dt = 0.3 m^3/min[/tex]. As per the chain rule of differentiation,[tex]dV/dt = dV/dh *dh/dt[/tex] We have[tex]V = 6h^3m^3 \Rightarrow dV/dh = 18h^2\Rightarrow dV/dt = 18h^2 * dh/dt[/tex] Given that,[tex]dV/dt = 0.3 m^3/min[/tex]. Therefore,[tex]0.3 = 18h^2 * dh/dt \Rightarrow dh/dt = 0.3/18= 1/60 m/min[/tex] Hence, the water level is rising at a rate of 1/60 m/min.
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if the radius of a circle is increasing and the magnitude of a central angle is held constant, how is the length of the intercepted arc changing? explain your reasoning.
Answer:
When the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is also increasing.
To see why this is the case, let's consider the formula for the length of an arc, which is given by:
s = rθ
where s is the length of the intercepted arc, r is the radius of the circle, and θ is the central angle in radians.
If the radius is increasing but the magnitude of θ is held constant, then the length of the intercepted arc will increase as well. This is because s is directly proportional to r; as r increases, s will also increase.
To see this more concretely, imagine drawing a circle on a piece of paper with a certain radius and then drawing a central angle that intercepts a certain arc length. If we then increase the radius of the circle while keeping the central angle the same, the arc length will increase proportionally to the increase in radius. This is because the same central angle will now subtend a larger arc on the circle, since the circle is larger.
Therefore, when the radius of a circle is increasing while the magnitude of a central angle is held constant, the length of the intercepted arc is increasing as well.
Step-by-step explanation:
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class does not play an instrument?
This probability that a randomly selected student from the classroom doesn't really play an item is , which equals or .
What are the basics of probability?Probability is the possibility of something occurring to occur, to clarify. We may talk about the possibility with one result, or the likelihood of several outcomes, when we don't understand how an occurrence will turn out. Biostatistics seems to be the study of things with a probability distribution.
Is the ace a playing card?The number one is known as the ace and is denoted by the letter A in the majority of Western card games. The ace scores highest, surpassing even the king, in games predicated on the supremacy of one level over the other, such as the majority of trick-taking games.
The total of a number of masculine and female pupils involved in sports [tex]$\mathrm{20}+10=30$[/tex] represents the total amount of pupils that don't play an instrument.
The sum of the four numbers in the table, [tex]$12+20+18+10$[/tex] , corresponds to the total amount of pupils in the class, or 60 .
So, [tex]$30/60=1/2\ \mathrm{Or}\ 0.5$[/tex] or is the likelihood that a randomly selected student from of the class doesn't really play an instrument.
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Complete question:
2.3. Ntando can either walk to school at 5 km/h or ride his bicycle at 15 km/h. If he rides his bicycle, it takes him 10 minutes to get to school. 2.3.1. How long will it take him if he walks to school?
Answer:
30 minutes
Step-by-step explanation:
Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.
10 minutes * 3 = 30 minutes
Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
factorise (x-3)²-(x-3)²
Step-by-step explanation:
(x-3)²-(x-3)²
=(x2-6x+9) - (x2-6x+9)
=x2-6x+9-x2+6x-9
=0
Eva is packing for a camping trip. There are 3 sleeping bags and 2 pillows to choose from. For the tent, Eva has 6 options. In how many different ways can Eva pick a set of camping gear that includes one of each item?
Eva has 36 different combinations of camping gear to choose from.
What are combinations?Combinations are arrangements of a given set of objects, without regard to their order. Combinations are used in mathematics to describe the possible arrangements of a given set of objects.
In this case, there are 3 sleeping bags, 2 pillows, and 6 tents. In order to determine the total number of combinations, Eva would need to multiply 3x2x6 which equals 36.
If she decides to pick a sleeping bag first, then she can pick any of the 3 available sleeping bags. She would then need to pick one of the 2 pillows and one of the 6 tents. If the order in which she selects her gear does not matter, then she can use the same method to determine the number of combinations available.
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The number of ways in which Eva can pick a set of camping gear that includes one of each item is 55.
What is combination?Combination involves selecting items from a set of items without regard to the order in which they are selected. It is typically expressed using the notation C(n,r) which stands for the number of combinations of n items taken r at a time, where n is the total number of items and r is the number of items taken at a time.
This is an example of a combination problem, as Eva is looking to select a set of items from multiple categories, rather than a permutation problem, which would be selecting a set of items where the order matters.
In this case,
n= 6 (the number of tents)+ 3 (the number of sleeping bags)+ 2 (the number of pillows)= 11.
We want to choose 1 of each item, so r is 3.
Plugging 11 and 3 into the formula, we get
11C3 = 11! / (3! * 8!)
= 11 * 10 * 9 / (3 * 2 * 1)
= 11 * 5
= 55
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j by 9 and then multiply the quotient by 2
The sequence of the questions is [tex]J/9[/tex] when you multiply [tex]J[/tex] by [tex]9[/tex] and the quotient by [tex]2[/tex].
What in arithmetic is a quotient?In this example, the number being divided (15) is known as the result, and the number being divided by (3 in this instance) is known as the divisor. The quotient is the outcome of the division.
Is quotient the same as answer?The result of dividing two integers is known as the quotient. Six divided into two results in the number three. Latin's "how many times" is the meaning of the word "quotient." It makes perfect sense: by dividing two numbers, you can determine "how many time" the two digits enters the first.
[tex]2 * (J/9)[/tex]
This means you first divide [tex]J[/tex] by [tex]9[/tex] to get the quotient, and then multiply the quotient by [tex]2[/tex]. So the order of operations is:
[tex]J/9[/tex]
Multiply the quotient by [tex]2[/tex]
For example, if [tex]J = 45[/tex], then:
[tex]J/9 = 45/9 = 5[/tex]
[tex]2 * (J/9) = 2 * 5 = 10[/tex]
So the result of multiplying [tex]J[/tex] by [tex]9[/tex] and then multiplying the quotient by [tex]2[/tex], when [tex]J = 45[/tex], is [tex]10[/tex].
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What are the roots of the equation 4x^2+16x+25=0 in simplest a+bi form
Answer:
The roots are
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Step-by-step explanation:
4x² + 16x + 25 = 0
Using the quadratic formula
That's
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
From the question
a = 4 , b = 16 , c = 25
Substitute the values into the above formula and solve
We have
[tex]x=\dfrac{-16\pm\sqrt{16^2-4(4)(25)} }{2(4)}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{256-400} }{8}[/tex]
[tex]x=\dfrac{-16\pm\sqrt{-144} }{8}[/tex]
[tex]x=\dfrac{-16\pm12 \ i}{8}[/tex]
Separate the real and imaginary parts
That's
[tex]x=\dfrac{-16}{8}\pm\dfrac{12}{8} \ i[/tex]
[tex]x=-2\pm\dfrac{3}{2} \ i[/tex]
We have the final answer as
[tex]x=-2+\dfrac{3}{2} \ i \ \ or \ \ x=-2-\dfrac{3}{2} \ i[/tex]
Hope this helps you
how many legs does it take to make 109657 spiders
Assuming each spider has 8 legs, it would take 877,256 legs to make 109,657 spiders
use a random sampling distribution of means to determine the probability for different ranges of values of a mean (x-bar). please use the following information to answer questions 1-5. imagine that after graduation, you need to find an apartment to rent. the city in which you intend to live reports that the average rental payment (house or apartment) is $1225.15, with a standard deviation of $777.50. it also reported that the average cost of an apartment rental, rather than a house rental, was $1068.86. for the following questions, treat the average rental payment and standard deviation (house or apartment) as parameters (the population), and treat the average apartment rental cost as a statistic (the sample mean or x-bar) based on a sample of 100. use this information for questions 1-5. 1. what is the mean of the random sampling distribution of means? 2) What is the standard error of the random sampling distribution of means? 3) What is the z statistic for the average cost of an apartment rental? 4) What is the probability of finding an apartment rental with a average cost of $1068.86 or less?
1) The mean of the random sampling distribution of means is the same as the sample mean ($1068.86).
2) The standard error of the random sampling distribution of means is calculated by taking the population standard deviation ($777.50) divided by the square root of the sample size (100), which yields $7.78.
3) The z statistic for the average cost of an apartment rental is calculated by subtracting the population mean ($1225.15) from the sample mean ($1068.86) and dividing the difference by the standard error ($7.78), yielding -37.37.
4) The probability of finding an apartment rental with an average cost of $1068.86 or less is determined by looking up the z statistic in a z table and finding the corresponding probability, which is 0.000.
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Como le hago ayuda aaaa
When the area is constant, the proportionality constant, 48, reflects the sum of the base and height.
What does the proportionality constant mean?When two quantities grow and shrink at the same rate, they are directly proportional. The proportionality constant k is defined as k=y/x when y and x are two numbers that are directly proportional to one another.
Using the formula for the area of a rectangle, we can determine the missing data in the table:
Area = base x height
The missing values can be located as follows using the values listed in the table:
Base (b) Height (h) Area
24 2 48
3 8 24
8 3 24
4 6 24
We can apply the inverse variation formula to find the constant of proportionality:
y = k/x
This equation can be changed in order to account for k:
k = xy
Using any pair of values from the table, we can find k as follows:
k = xy = 24(2) = 48
Hence, 48 is the proportionality constant. It is possible to verify that this value applies to all of the value pairs in the table:
For the first pair (b=24, h=2), we have xy = 24 x 2 = 48, which is the constant of proportionality.
For the second pair (b=3, h=8), we have xy = 3 x 8 = 24, which is the area.
For the third pair (b=8, h=3), we have xy = 8 x 3 = 24, which is the area.
For the fourth pair (b=4, h=6), we have xy = 4 x 6 = 24, which is the area.
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Question:
The following table shows some values for the base and height of a rectangle whose area is constant. Write down the missing data.
Base (b)
Height (h)
24
2
3
8
4
4
What is the area of the rectangle?
What kind of variation do you see in this table?
What is the constant of proportionality?
How did you determine the constant of proportionality?
the cylinder has a volume of 45 cubic inches and a height of 5 inches what is the raduis of the cylinder
The radius of the cylinder is 3 inches.
What is the volume of a cylinder?
A cylinder is a three-dimensional solid with two parallel circular bases and a curved lateral surface connecting the two bases. The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius of the base, h is the height of the cylinder, and π is a constant value approximately equal to 3.14.
Calculating the value of radius :
We are given that the cylinder has a volume of 45 cubic inches and a height of 5 inches. Using the formula for the volume of a cylinder, we get:
[tex]V = \pi r^2h[/tex]
Substituting the given values, we get:
[tex]45 = \pi r^2(5)[/tex]
Simplifying the equation, we get:
[tex]9 = r^2[/tex]
Taking the square root of both sides, we get:
[tex]r = \pm 3[/tex]
Since the radius cannot be negative, we take the positive value of r, which is:
r = 3 inches
Therefore, the radius of the cylinder is 3 inches.
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I need help with these
By answering the presented question, we may conclude that Therefore, equation the cost per pound of turkey is $1.99 and the cost per pound of ham is [tex]$2.39[/tex] .
What is equation?In mathematics, an equation is an assertion that affirms the equivalence of two factors. An algebraic equation (=) separates two sides of an equation. For instance, the assertion [tex]"2x + 3 = 9"[/tex] states that the word "2x + 3" corresponds to the number "9".
The goal of solution solving is to figure out which variable(s) must still be adjusted for the equations to be true. It is possible to have simple or intricate equations, recurring or complex equations, and equations with one or more components.
For example, in the equations [tex]"x2 + 2x - 3 = 0,"[/tex] the variable x is lifted to the powercell. Lines are utilised in many areas of mathematics, include algebra, arithmetic, and geometry.
Therefore,Let's denote the cost per pound of turkey as $t, and the cost per pound of ham as $h. Then we can write the following system of linear equations.
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plss help meeeeeeeeeeeeeeeeee
DO THE MATH: Gracie is a manager at Prescribe Pharmaceutical. An employee turned in the timesheet below. Given that Prescribe Pharmaceutical uses the 7-Minute Rule daily for calculating employee hours worked, how many hours did this employee work for the week?
A. 25 hours and 0 minutes
B. 26 hours and 0 minutes
C. 25 hours and 48 minutes
D. 25 hours and 45 minutes
It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
What is a timesheet?A timesheet is a data table which an emplοyer can use tο track the time a particular emplοyee has wοrked during a certain periοd. Businesses use timesheets tο recοrd time spent οn tasks, prοjects, οr clients. There are different methοds that have been used tο recοrd timesheets, such as paper, spreadsheet sοftware, and οnline time-tracking sοftware. Paper-based timesheets have nοw given way tο the digital fοrmats.
1st Day = 12 + 4 pm - 8:45 am
= 16 - 8:45
= 7:15 hours
2nd day = 12 + 5 pm - 9:14 am
= 17 - 9:14
= 7:46 hours
3rd day = 12 + 4:02 pm - 8:30 am
= 16:02 - 8:30
= 7:32 hours
4th day = 12 + 5:00 pm - 9:08am
= 17:00 - 8:30
= 8:30 hours
5th day = 12 + 3:30 pm - 8:07 am
= 15:30 - 8:07
= 7:23 hours
Adding all the hours of work = 7:15 hours + 7:46 hours +7:32 hours + 8:30 hours + 7:23 hours = 25 hours and 48 minutes
Thus, It took 25 hours and 48 minutes employee worked for the week. Thus, option B is correct.
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A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed.
a. What is the probability that a randomly selected customer spends less than 65 minutes at the gym?
b. Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation of the sample mean of the time spent at the gym?
c. If 49 members are randomly selected, what is the probability that the average time spent at the gym exceeds 75 minutes?
a. The expected value of the sample mean is 70 and the standard deviation of the sample mean is 2.857.
b. The probability that a randomly selected customer spends less than 65 minutes at the gym is approximately 0.4013.
c. The probability that the average time spent at the gym exceeds 75 minutes is approximately 0.0070.
How do we solve?a. To answer this question, we need to standardize the value of 65 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
z = (65 - 70) / 20
z = -0.25
Using a standard normal distribution table, we find that the probability of a z-score less than -0.25 is approximately 0.4013.
b. The expected value of the sample mean can be calculated using the formula:
E(x) = μ
where μ is the population mean.
E(x) = 70
The standard deviation of the sample mean can be calculated using the formula:
σ(x) = σ / √(n)
where σ is the population standard deviation and n is the sample size.
σ(x) = 20 / √(49)
σ(x) = 2.857
c. To answer this question, we need to standardize the value of 75 using the formula:
z = (x - μ) / (σ / √(n))
where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
z = (75 - 70) / (20 / √(49))
z = 2.45
Using a standard normal distribution table, we find that the probability of a z-score greater than 2.45 is approximately 0.0070.
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