Spencer will be on the phone for 56 minutes in total if he routes 28 calls.
To solve problemUsing unit rates, we can calculate how long Spencer will spend on the phone when routing 28 calls if he spent 10 minutes on the phone while routing 5 calls.
The amount of time spent on each phone call is the unit rate. In this instance, the unit fee is 10 minutes / 5 phone calls = 2 minutes each call.
In order to determine how much time Spencer will spend on the phone when routing 28 calls, we can use this unit rate as follows:
Time on phone = unit rate times the number of calls.Time on phone = 2 minutes per phone call x 28 phone callsTime on phone = 56 minutesTherefore, Spencer will be on the phone for 56 minutes in total if he routes 28 calls.
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Please help
given vectors u and v, find (a)6u (b)6u+4v (c) v-4u
u=(4,5) v=(4,0)
(a) 6u
(b) 6u+4v
(c) v-4u
For the given vectors u and v, (a) 6u = (24, 30). (b) 6u+4v = (40, 30). (c) v-4u = (-12, -20).
Given vectors u and v.
a) To find 6u, we simply multiply each component of u by 6:
6u = 6(4, 5) = (6(4), 6(5)) = (24, 30)
Therefore, 6u = (24, 30).
b) To find 6u + 4v, we first need to find 4v by multiplying each component of v by 4:
4v = 4(4, 0) = (4(4), 4(0)) = (16, 0)
Next, we add 6u and 4v by adding the corresponding components:
6u + 4v = (24, 30) + (16, 0) = (24+16, 30+0) = (40, 30)
Therefore, 6u + 4v = (40, 30).
c) To find v - 4u, we first need to find 4u by multiplying each component of u by 4:
4u = 4(4, 5) = (4(4), 4(5)) = (16, 20)
Next, we subtract 4u from v by subtracting the corresponding components:
v - 4u = (4, 0) - (16, 20) = (4-16, 0-20) = (-12, -20)
Therefore, v - 4u = (-12, -20).
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How much must be deposited today into the following account in order to have a $110,000 college fund in 17 years? Assume no additional deposits are made.
An account with quarterly compounding and an APR of 4.9%
Therefore, an initial deposit of $37,728.66 is required to have a college fund of $110,000 in 17 years with quarterly compounding and an APR of 4.9%.
What is a deposit used for?An amount held in an account is referred to as a deposit. It might be put up in a bank as collateral for goods that are being rented out or bought. A deposit is used in many different sorts of economic transactions.
Compound interest can be calculated using the following formula to determine the required down payment:
A = P(1 + r/n)(nt)
where:
A = the future value of the account (in this case, $110,000)
P = the principal or initial deposit
r = the annual interest rate (4.9%)
n = the number of times the interest is compounded per year (4 for quarterly compounding)
t = the number of years (17)
When we enter the specified numbers into the formula, we obtain:
$110,000 = P(1 + 0.049/4)(4*17)
$110,000 = P(1.01225)⁶⁸
$110,000 = P * 2.9126
Dividing both sides by 2.9126, we get:
P = $37,728.66
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Mrs. Ramirez worked on her personal trainer to help develop a nutrition plan. The circle graph shows the recommended percentages for her daily intake. If she will be eating 1800 cal, then how many calories should be from proteins?
630 calories of total calory intake of Mrs. Ramirez should be from proteins.
From the circle graph we can see that,
percentage of calories from fruits is = 15%
percentage of calories from grains is = 15%
percentage of calories from vegetables is = 25%
percentage of calories from proteins is = 35%
percentage of calories from Dairy is = 10%
Here it is also given that Mrs. Ramirez need to eat 1800 calories.
So the calories should be from proteins
= 35% of 1800 calories
= (35/100)*1800 calories
= 35*18 calories
= 630 calories.
Hence, 630 calories should be from proteins.
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The question is incomplete. The complete question will be -
67. 8 x 9. 7 pls someone answer within the next 20 Minutes with work I'm in school lol
For each problem, determine what will happen to the first factor.
10x1/2
15 x 7/2
Answer:
52.5
Step-by-step explanation:
15×7=105÷2
=52.5 ans it means fifteen times seven divided by two
Use the definition of the laplace transform to show that if f(x) = 0 then
[tex]l[f(x)] = 0[/tex]
show that f(x)= 1 then
[tex]l[f(x)] = \frac{1}{s} [/tex]
show that f(x)= x then
[tex]l[f(x)] = \frac{1}{ {s}^{2} } [/tex]
show that f(x)= e^ax then
[tex]l[f(x)] = \frac{1}{s - a} [/tex]
provide the steps by using the definition and evaluating the integral.
Answer:
Step-by-step explanation:
the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
The definition of the Laplace transform of a function f(t) is given by:
L{f(t)} = F(s) = ∫_0^∞ e^(-st) f(t) dt
where s is a complex number.
If f(x) = 0, then we have:
L{f(x)} = L{0} = ∫_0^∞ e^(-st) 0 dt = 0
Therefore, the Laplace transform of the zero function is zero.
If f(x) = 1, then we have:
L{f(x)} = L{1} = ∫_0^∞ e^(-st) dt
Using integration by parts, we get:
L{1} = ∫_0^∞ e^(-st) dt = [-e^(-st)/s]_0^∞ = [0 - (-1/s)] = 1/s
Therefore, the Laplace transform of the constant function 1 is 1/s.
If f(x) = x, then we have:
L{f(x)} = L{x} = ∫_0^∞ e^(-st) x dt
Using integration by parts again, we get:
L{x} = ∫_0^∞ e^(-st) x dt = [(-e^(-st) x)/s]_0^∞ + (1/s) ∫_0^∞ e^(-st) dt
Since e^(-st) x approaches zero as t approaches infinity, the first term evaluates to zero. We can then simplify the second term using the result from part 2:
L{x} = (1/s) ∫_0^∞ e^(-st) dt = 1/s * (1/s) = 1/s^2
Therefore, the Laplace transform of the function f(x) = x is 1/s^2.
If f(x) = e^(ax), then we have:
L{f(x)} = L{e^(ax)} = ∫_0^∞ e^(-st) e^(ax) dt
Simplifying the integrand, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt
We can evaluate this integral using the formula:
∫_0^∞ e^(-bx) dx = 1/b
Setting b = a - s, we get:
L{e^(ax)} = ∫_0^∞ e^((a-s)t) dt = 1/(a-s)
Therefore, the Laplace transform of the function f(x) = e^(ax) is 1/(a-s).
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If the Math Olympiad Club consists of 14 students, how many different teams of 6 students can be formed for competitions?
The different teams of 6 students that can be formed for competitions is 3003
How many different teams of 6 students can be formed for competitions?From the question, we have the following parameters that can be used in our computation:
Students = 14
Students in the team = 6
Using the above as a guide, we have the following:
n = 14
r = 6
The different teams of 6 students that can be formed for competitions is calculated as
Teams = nCr
substitute the known values in the above equation, so, we have the following representation
Teams = 14C6
So, we have
Teams = 14!/(6! * 8!)
Evaluate
Teams = 3003
Hence, the different teams of 6 students that can be formed for competitions is 3003
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Select the correct answer from each drop-down menu. José and Manuel are soccer players who both play center forward for their respective teams. The table shows the total number of goals they each scored in each of the past 10 seasons. Season José Manuel 1 7 17 2 12 23 3 17 21 4 4 31 5 18 30 6 25 5 7 38 26 8 32 37 9 37 19 10 11 9 The measure of center that best represents the data is mean , and its values for José and Manuel are and , respectively. Comparing this measure of center for José’s and Manuel's data sets shows that generally scores more goals in a game
The measure of center that best represents the data is mean and its values for José and Manuel are 20.1 and 21.8, respectively. Comparing the mean values, José generally scores less goals in a game than Manuel.
What is the measure of center for the number of goals scored?To find the measure of center that best represents the data, we will use the mean.
The measure is calculated by adding up all the values and dividing by the total number of values.
The mean number of goals for José is:
= (7+12+17+4+18+25+38+32+37+11)/10
= 20.1
The mean number of goals for Manuel is:
= (17+23+21+31+30+5+26+37+19+9)/10
= 21.8.
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La probabilidad de que un vuelo se retrase es 0. 2 (=20%),¿Cuales son las probabilidades de que no haya demoras en un viaje de ida y vueta
La probabilidad de que no haya demoras en un viaje de ida y vuelta es 0.64 (64%).
How to calculate the probabilities?La probabilidad de que no haya demoras en un viaje de ida y vuelta se puede calcular utilizando la probabilidad complementaria. Si la probabilidad de que un vuelo se retrase es 0.2 (20%), entonces la probabilidad de que no haya retrasos en un vuelo individual es 1 - 0.2 = 0.8 (80%).
Para un viaje de ida y vuelta, la probabilidad de que no haya retrasos en ambos vuelos se calcula multiplicando las probabilidades de no retraso de cada vuelo.
Entonces, la probabilidad de que no haya demoras en un viaje de ida y vuelta sería 0.8 * 0.8 = 0.64 (64%), o 64 de cada 100 viajes de ida y vuelta no experimentarían retrasos.
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Find the perimeter of a square that has a side length of 4.3x + 2 inches.
The calculated perimeter of the square from the side length is 17.2x + 8
Finding the perimeter of a square from the side lengthFrom the question, we have the following parameters that can be used in our computation:
A square that has a side length of 4.3x + 2 inches.
Using the above as a guide, we have the following:
Perimeter = 4 * side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * (4.3x + 2)
When teh brackets are opened, we have
Perimeter = 17.2x + 8
Hence, the perimeter is 17.2x + 8
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ANSWER THE QUESTIONS A AND B ! 1ST ONE WHO ANSWERS WITH A CORRECT ANSWER WILL BE MARkED BRAINLIEST!
Answer:
A is -4.5,2 and B is 0,-3.5
Step-by-step explanation:
Answer:
Coordinates of A: (-4.5, 2), Coordinates of B: (0, -3.5)
Liquid a has a density of 1. 2 g/cm'
150 cm of liquid a is mixed with some of liquid b to make liquid c.
liquid c has a mass of 220 g and a density of 1. 1 g/cm
find the density of liquid b.
If Liquid a has a density of 1. 2 g/cm³, 150 cm of Liquid a is mixed with some of Liquid b to make Liquid c whose mass is 220 g and has a density of 1.1 g/cm³, then the density of liquid B is 0.8 g/cm³.
To find the density of liquid B, you can follow these steps:
1. Calculate the mass of liquid A using its density and volume:
Liquid A has a density of 1.2 g/cm³ and a volume of 150 cm³.
Mass of A = Density of A × Volume of A = 1.2 g/cm³ × 150 cm³ = 180 g
2. Calculate the mass of liquid B using the mass of liquid C and mass of liquid A:
Liquid C has a mass of 220 g.
Mass of B = Mass of C - Mass of A = 220 g - 180 g = 40 g
3. Calculate the volume of liquid C using its mass and density:
Liquid C has a density of 1.1 g/cm³.
Volume of C = Mass of C ÷ Density of C = 220 g ÷ 1.1 g/cm³ = 200 cm³
4. Calculate the volume of liquid B using the volume of liquid C and the volume of liquid A:
Volume of B = Volume of C - Volume of A = 200 cm³ - 150 cm³ = 50 cm³
5. Calculate the density of liquid B using it's mass and volume:
Density of B = Mass of B ÷ Volume of B = 40 g ÷ 50 cm³ = 0.8 g/cm³
So, the density of liquid B is 0.8 g/cm³.
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If donuts are 12 cents a dozen how much does 100 donuts cost.
The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.
This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.
1 dozen refers to a group of 12.
Cost of 1 dozen donuts or 12 donuts = 12 cents
Cost of 1 donut = [tex]\frac{12}{12}[/tex] = 1 cent
Cost of 100 donuts = 1 * 100 = 100 cents
100 cents = 1 dollar.
Thus, the cost of 100 donuts is 100 cents or 1 dollar.
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6. (07.06 LC)
Given a polynomial f(x), if (x-4) is a factor, what else must be true? (3 points)
Of(0) = 4
Of(0) = -4
Of(4) = 0
Of(-4)=0
None of the other statements necessarily follow from (x-4) being a factor of f(x). So the correct statement is Of(4) = 0
What is a statement?
A statement is a proposition that is either true or false, but not both. It may be a mathematical equation, an inequality, or a proposition that can be tested for its truth value.
What is meant by factor?
A factor refers to a number or algebraic expression that is multiplied by another number or expression to obtain a product. Factors can be either integers or polynomials.
According to the given information
If (x-4) is a factor of f(x), then f(4) = 0. This is because when you divide f(x) by (x-4), the remainder is zero when x=4.
Therefore, the correct statement is: f(4) = 0
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G(x)=5−2xg, left parenthesis, x, right parenthesis, equals, 5, minus, 2, x Determine for each x xx-value whether it is in the domain of g gg or not
The domain of function is the set of all possible values of x for which the function is defined. In this case, the function G(x) = 5 - 2x is defined for all real numbers of x.
The collection of all feasible input values (x-values) for which a function may be defined is known as the domain of function. In other words, it is the collection of all x values that may be passed into the function and provide a legitimate result (a y-value).
The function G(x) = 5 - 2x in this instance is a linear function, meaning it is defined for all real values of x. This is so that we may plug in any real value for x, and the function will output a real number for G(x) that corresponds. As an illustration, when we enter x = 0, we obtain G(0) = 5 - 2(0) = 5, and when we enter x = 2, we obtain G(2) = 5 - 2(2) = 1.
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Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation.
f(x) = 4 tan x- 6x, Xo = 1,4
After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.
To compute the first 10 iterations of Newton's method for the given function and initial approximation, follow these steps:
1. Write down the function and its derivative:
[tex]f(x) = 4 * tan(x) - 6 * x
f'(x) = 4 * sec^2(x) - 6[/tex]
2. Define the initial approximation, X₀ = 1.4.
3. Apply Newton's method formula to find the next approximation, X₁:
X₁ = X₀ - f(X₀) / f'(X₀)
4. Repeat steps 3-4 for a total of 10 iterations (X₁ to X₁₀).
Note that I'm unable to perform calculations on this platform, but I'll provide a general outline for performing the iterations:
Iteration 1 (X₁):
[tex]X₁ = 1.4 - (4 * tan(1.4) - 6 * 1.4) / (4 * sec^2(1.4) - 6)[/tex]
Iteration 2 (X₂):
[tex]X₂ = X₁ - (4 * tan(X₁) - 6 * X₁) / (4 * sec^2(X₁) - 6)[/tex]
Repeat these steps up to the 10th iteration (X₁₀).
After performing these calculations using a calculator or a program like Python, MATLAB, or Excel, you will have the values of the first 10 iterations of Newton's method for the given function and initial approximation.
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A smart phone screen measures 5 inches by 7 inches. It is surrounded by a frame of width w. Write an expression in standard form for the total area of the screen and frame
Answer:
4x² + 24x + 35
Step-by-step explanation:
Total area = (7 + 2x)(5 + 2x)
= 35 + 10x + 14x + 4x²
= 4x² + 24x + 35
In the expression πr² + πrℓ, what
part of the expression is π?
a constant
a coefficient
a variable
a term
In the expression πr² + πrℓ, the part of the expression that is π is a constant.
A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.
From a Word Problem
Jack has $10 in his lunch account. He plans to
spend $2 a week on snacks. How long until
Jack's lunch account reaches zero?
Answer:
Sure, here's the solution to the word problem:
Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.
```
$10 / $2 = 5 weeks
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Here's another way to solve the problem:
We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:
```
$10 - $2x = 0
```
Solving for x, we get:
```
x = 5
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Answer:
in 5 weeks he will have 0$ in his account
Step-by-step explanation:
Use the scatter plot to fill in the missing coordinate of the ordered pair.(,12)
Answer: Pairs (0, 14) and (10, 0
Step-by-step explanation:
Given y = 4x² + 3x, find dy/dt when x= -1 and dx/dt = 3(Simplify your answer.)
Given the function y = 4x² + 3x, we will find dy/dt by differentiating y with respect to t. Therefore, the value of dy/dt is -15.
Using the chain rule, we have:
dy/dt = (dy/dx)(dx/dt)
Differentiating y with respect to x, we get:
dy/dx = 8x + 3
Now, we are given that x = -1 and dx/dt = 3. We can substitute these values into our equation:
dy/dt = (8(-1) + 3)(3)
dy/dt = (-5)(3)
dy/dt = -15
So, when x = -1 and dx/dt = 3, the value of dy/dt is -15.
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How much would you have to deposit in
an account with a 4.75% interest rate,
compounded continuously, to have
$20,000 in your account 20 years later?
Answer:
Pe^(.0475 × 20) = $20,000
P = $7,734.82
Traffic Jam
There are 8 cans of strawberry jam, 7 raspberry jam,
and 5 cherry jam in the cellar. You're trying to sneak
some out, but don't want to attract attention or take
too many. It's dark, so you can't tell what kind of jam
you're taking.
How many cans can you sneak out of the
cellar in the dark with the certainty that there
will still be at least 4 cans of one kind of jam
and 3 cans of another left over?
Answer:
Hey!
You could obviously count how many you're taking, so that's 7 left behind. My guess is that you could taste the jam... but that's the best I've got.
The requreid we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
What is arithmetic?It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
Let's first find the minimum number of cans that need to be left in the cellar to meet the given criteria. We want at least 4 cans of one kind of jam and 3 cans of another leftover. This means we can take a maximum of:
8 - 4 = 4 cans of strawberry jam
7 - 3 = 4 cans of raspberry jam
5 - 3 = 2 cans of cherry jam
So, we can take a maximum of 4 + 4 + 2 = 10 cans in total.
To have certainty that we meet the criteria, we need to take one less than the maximum number of cans, which is 9 cans. So, we can sneak out 9 cans of jam in the dark and still be sure that there will be at least 4 cans of one kind of jam and 3 cans of another left over.
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Helppp translation and reflection
The images of points B and C are B'(x, y) = (- 2, 6) and C'(x, y) = (- 1, 7), respectively.
How to compute the image of a point by translation
In this problem we find must determine the image of two points by translation, whose formula is introduced below:
T(x, y) = P'(x, y) - P(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.First, determine the translation vector:
T(x, y) = (1, 4) - (0, 0)
T(x, y) = (1, 4)
Second, determine the images of points B and C:
B'(x, y) = (- 3, 2) + (1, 4)
B'(x, y) = (- 2, 6)
C'(x, y) = (- 2, 3) + (1, 4)
C'(x, y) = (- 1, 7)
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Hey, I'm struggling with this lately, please help!
The measure of the exterior angle of the triangle is 128°.
How to find the measure of the exterior angle?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Trigonometric functions are the functions that denote the relationship between angle and sides of a right-angled triangle.
Sin θ = Opposite Side/Hypotenuse
Cos θ = Adjacent Side/Hypotenuse
Tan θ = Opposite Side/Adjacent
Recall that the measure of the exterior angle of a triangle is the sum of the opposite interior angles. That is:
x = 38 + 90
x = 128°
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When Nabhitha goes bowling, her scores are normally distributed with a mean of 115
and a standard deviation of 11. What percentage of the games that Nabhitha bowls
does she score between 93 and 142, to the nearest tenth?
The percentage of the games that Natasha scores between 93 and 142 is given as follows:
96.9%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation 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 of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation are given as follows:
[tex]\mu = 115, \sigma = 11[/tex]
The proportion of games with scores between 93 and 142 is the p-value of Z when X = 142 subtracted by the p-value of Z when X = 93, hence:
Z = (142 - 115)/11
Z = 2.45
Z = 2.45 has a p-value of 0.992.
Z = (93 - 115)/11
Z = -2
Z = -2 has a p-value of 0.023.
0.992 - 0.023 = 0.969, hence the percentage is of 96.9%.
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Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs. If no interval is specified, use the real numbers, (-00,00). f(x) = -0.002x2 + 4.2x - 50 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. at x= O A. The absolute maximum is at x= and the absolute minimum is (Use a comma to separate answers as needed.) B. The absolute minimum is at x = and there is no absolute maximum. (Use a comma to separate answers as needed.) C. The absolute maximum is at x= and there is no absolute minimum. (Use a comma to separate answers as needed.) D. There is no absolute maximum and no absolute minimum.
The correct choice is: C. The absolute maximum is at x = 1050, and there is no absolute minimum.
To find the absolute extrema of the function f(x) = -0.002x^2 + 4.2x - 50 over the interval (-∞, ∞), we need to find the critical points and then determine if there's a maximum or minimum at each point.
Step 1: Find the derivative of the function f(x) with respect to x. f'(x) = -0.004x + 4.2
Step 2: Set the derivative equal to zero and solve for x. -0.004x + 4.2 = 0 x = 1050
Step 3: Since we have only one critical point, we need to determine if it's a maximum or a minimum. To do this, we can use the second derivative test.
Step 4: Find the second derivative of the function f(x) with respect to x. f''(x) = -0.004
Step 5: Since the second derivative is negative (f''(x) = -0.004 < 0), the critical point x = 1050 corresponds to an absolute maximum. Step 6: Calculate the value of the function f(x) at x = 1050. f(1050) = -0.002(1050)^2 + 4.2(1050) - 50 = 2150
Thus, the absolute maximum is at x = 1050, and the value is 2150. Since the function is a parabola with the "mouth" facing downwards, there is no absolute minimum.
The correct choice is: C. The absolute maximum is at x = 1050, and there is no absolute minimum.
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The null and alternate hypotheses are:
H0 : μd ≤ 0
H1 : μd > 0
The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of 4 days last month.
Day: 1, 2, 3, 4
Day Shift: 12, 16, 20, 24
Afternoon Shift: 12, 10, 16, 18
At the 0. 05 significance level, is there a difference in the mean number of citations given by the two shifts?
a. What is the p-value?
Note that where the above statistics are give, the p-value is 0.04.
What is the explanation for the above ?1st , we calculate the differences between the number of citations given in the day shift and afternoon shift for each day
Differences - 0, 6, 4, 6
The mean difference is (m) = (0 + 6 + 4 + 6) / 4 = 4
The sample standard deviation of the differences is s = √ ([((0-4)² + (6-4)² + (4-4)² + (6-4)²)/3]) = 2.31
The standard error of the mean difference is SE(m) = s / √(n) = 2.31 / √(4) = 1.155
The t-statistic is t = (m - 0) / SE(m) = 4 / 1.155 = 3.4632034632
The paired t-test has n-1=3 degrees of freedom. We calcu0late the p-value associated with a t-statistic of 3.46 using a t-table or a t-distribution calculator with three degrees of freedom.
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QuestionThe mean monthly salary of the 12 employees of a firm is Rs. 1450. If one more person joins the firm who gets Rs. 1645 per month, what will be the mean monthly salary of 13 employees?ARs. 1465BRs. 1954CRs. 2175DRs. 2569Medium
1465 will be the mean monthly salary .The answer is (A) Rs. 1465.
Let the sum of the 12 employees' salaries be S.
Then, the mean monthly salary of the 12 employees is given by:
S/12 = 1450
S = 12 * 1450
S = 17400
If one more person joins with a salary of Rs. 1645, the new sum of the 13 employees' salaries is:
S' = S + 1645
S' = 17400 + 1645
S' = 19045
The new mean monthly salary of the 13 employees is:
S'/13 = 19045/13
S'/13 = 1465
Therefore, the answer is (A) Rs. 1465.
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Lana offered to buy groceries for her roommates, Pam and Cheryl. The total bill was $74. She forgot to save the individual receipts but remembered that Pam's groceries were $0. 05 cheaper than half of her groceries, and that Cheryl's groceries were $2. 10 more than Pam's groceries. How much was each share of the groceries?
Lana paid $36, Pam paid $17.95, and Cheryl paid $20.05, by using substitution or elimination, for the groceries.
Let's start by assigning variables to the unknown quantities in the problem. Let's call the cost of Lana's groceries "L", the cost of Pam's groceries "P", and the cost of Cheryl's groceries "C". We can set up a system of equations based on the information given:
1) P = 0.5L - 0.05 (Pam's groceries were $0.05 cheaper than half of Lana's groceries)
2) C = P + 2.10 (Cheryl's groceries were $2.10 more than Pam's groceries)
3) L + P + C = 74 (the total bill was $74)
We now have three equations with three unknowns, which we can solve using substitution or elimination. Let's use substitution:
Substitute equation 1 into equation 2 for P:
C = (0.5L - 0.05) + 2.10
Simplify:
C = 0.5L + 2.05
Substitute equations 1 and 3 into the equation above:
L + P + C = 74
L + (0.5L - 0.05) + (0.5L + 2.05) = 74
Simplify:
2L + 2 = 74
2L = 72
L = 36
Now that we know the cost of Lana's groceries, we can use equation 1 to find the cost of Pam's groceries:
P = 0.5L - 0.05
P = 0.5(36) - 0.05
P = 17.95
Finally, we can use equation 2 to find the cost of Cheryl's groceries:
C = P + 2.10
C = 17.95 + 2.10
C = 20.05
Therefore, Lana paid $36, Pam paid $17.95, and Cheryl paid $20.05 for the groceries.
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