The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.
The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:
Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7
Subject to:
x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)
x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)
x1 + x4 <= 1 (3)
x2 + x4 <= 1 (4)
x3 + x4 <= 1 (5)
x4 + x5 <= 1 (6)
x4 + x6 <= 1 (7)
x4 + x7 <= 1 (8)
x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)
The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.
To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.
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a cheese merchant looks again at the data set about total cheese sales, in which the sample mean is 164.5 and the sample standard deviation is 103. find the rounded upper level of the 68% confidence interval estimate.
The rounded upper level of the 68% confidence interval estimate is
164.5 ± 3.260.
Given:
a cheese merchant looks a again at the data set about total cheese of sales, in which the sample mean is 164.5 and the sample of standard deviation is 103.
μ = x =164.5
σ = s = 103
n = 987
z score at 68 % :
= 0.9945
Confidence interval CI = x + z * s/[tex]\sqrt{n}[/tex]
= 164.5 + 0.9945 * 103 / √987
= 164.5 ± 3.260
Therefore The rounded upper level of the 68% confidence interval estimate is 164.5 ± 3.260.
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Calculate the margin of error for a ampling ditribution that ha a ize of 36 for a 93% confidence level. The population tandard deviation i known to be 12
The margin of error for a sampling distribution is found as 3.34.
Explain the term margin of error?The margin of error, sometimes known as the confidence interval, provides information on how closely your survey results will likely reflect the opinions of the general community. Keep in mind that conducting surveys requires you to strike a balance by using a smaller group (the survey respondents) to represent a much broader one.Margin of error = z × σ/√n
n = sample size (36)σ = population standard deviation (12) z = z-scoreThus, put the values;
z-score for 93% confidence level = 1.67
Margin of error = 1.67 ×12/√36
Margin of error = 3.34
Thus, the margin of error for a sampling distribution is found as 3.34.
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Someone answer this please
Answer:
Step-by-step explanation:
B because that is the letter of my first name!
Is the converse of the following conditional True or False? "If a polygon is a triangle, then it has exactly three sides."
The converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
A polygon has precisely three sides if it is a triangle. The opposite is also accurate.
Contrarily, a polygon is a triangle if it has precisely three sides. Both of the statements can be joined to create a biconditional because they are both true.
Thus, the converse of the following conditional True which is If a polygon is a triangle, then it has exactly three sides."
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Select the equation of the line that passes through (3, 4) and (-1, -4).
y= -1/2x+2
y=2x+2
y=2x-2
y=-1/2x+4
none of the above
The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
The points are (3, 4) and (-1, -4). Then the equation of the line is given as,
(y + 4) = [(4 + 4) / (3 + 1)](x + 1)
y + 4 = 2(x + 1)
y = 2x + 2 - 2
y = 2x - 2
The equation of the line that passes through (3, 4) and (-1, -4) will be y = 2x - 2. Then the correct option is C.
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two poles are connected by a wire that is also connected to the ground. the first pole is 20 ft tall and the second pole is 10 ft tall. there is a distance of 30 ft between the two poles. where should the wire be anchored to the ground (in ft, from the shorter pole) to minimize the amount of wire needed?
The wire should be anchored to the ground to minimize the amount of wire needed 20 ft from the left pole.
What is the quadratic equation?
ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Let x (ft) be the distance from the base of the left pole to the anchor point. Since 2 poles has a distance of 30 ft, the distance from the anchor point to the right pole is 30 - x.
The wire length from the top of the left pole to the anchor point is
[tex]L^{2} _{l} = 20^{2} + x^{2} = x^{2} + 400[/tex]
Similarly for the 2nd part of the wire
[tex]L^{2} _{t} = 10^{2} + (30 - x^{2})[/tex]
= 100 + 900 - 60x + x²
= x²+ 1000 - 60x
We want to minimize the length of the wires, or [tex]L^{2} _{l} + L^{2} _{r}[/tex]
[tex]\frac{x}{\sqrt{{x}^2 + 400} } + \frac{x - 30}{\sqrt{{x}^2 + 400}} = 0[/tex]
we can take the first derivative of this and set it to 0
x = 20
Hence, the wire should be anchored to the ground to minimize the amount of wire needed 20ft.
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a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere. b. on the diagram, sketch vectors to indicate the direction of the polarization density in the shell. where do positive and negative bound charges appear? explain. c. consider a point inside the polarizable shell. at this point, is the magnitude of the net electric field greater than, less than, or equal to the magnitude of the electric field before the shell was added? explain. consider a point outside the shell. at this point, how does the magnitude of the electric field with the shell compare to before the shell was added? explain. d. is the electric potential difference between the sphere and ground in this case greater than, less than, or equal to the electric potential difference before the shell was added? explain. the sphere is re-connected to the battery with the shell still attached. e. will the total amount of charge on the sphere change? explain why or why not. f. does adding this polarizable shell change the capacity of the sphere to hold charge? explain.
when the charged rod is brought closer to the sphere negative charges get induced on the sphere by gathering some electrons from the ground and the negative remain on the sphere even after disconnecting it.
here the ground acts as a reservoir of electrons.a conducting sphere of radius r is connected to ground through a battery with a voltage vo as shown. a. assuming ground is at infinity, find the net charge on the sphere. the sphere is disconnected from the battery, and a thick shell of a neutral, polarizable material is placed around the sphere.
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Bicycle Parade There was a parade of bicycles and tricycles. Jackie counted the number of wheels; there were 23 wheels. Tony counted the riders; 10 children were riding. How many bicycles were there and how many tricycles?
Which of the following Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?statements is true about the graphs of f(x)=x and g(x)=f(x+7)?
A statement which is true about the graphs of f(x) = x and g(x) = f(x + 7) is: C. g(x) is the graph of f(x) translated 7 units to the left.
What is a translation?In Mathematics, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) or g(x) = f(x + 7) simply means shifting a graph 7 units to the left as illustrated by the graph shown in the image attached below.
In this context, we can reasonably infer and logically deduce that the parent function f(x) = x was shifted by 7 units to the left.
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Complete Question:
Which of the following statements is true about the graphs of f(x)=x and g(x)=f(x+7)?
A. g(x) is the graph of f(x) translated 7 units down.
B g(x) and f(x) have the same y-intercept.
C g(x) is the graph of f(x) translated 7 units to the left.
D g(x) is the graph of f(x) translated 7 units to the right.
a sample of 17001700 computer chips revealed that 366% of the chips fail in the first 10001000 hours of their use. the company's promotional literature states that 399% of the chips fail in the first 10001000 hours of their use. the quality control manager wants to test the claim that the actual percentage that fail is less than the stated percentage. is there enough evidence at the 0.020.02 level to support the manager's claim? step 1 of 7 : state the null and alternative hypotheses. answer
After solving, the value of Test statistic z is 1.449.
In the given question,
A sample of 1700 computer chips revealed that 36% of the chips fail in the first 1000 hours of their use.
The company's promotional literature states that 39% of the chips fail in the first 1000 hours of their use.
Then we have to find the value of z statistic.
Hypothesized proportion (p) = 36%=0.36
Sample proportion (p') = 39% = 0.39
Sample size (n) = 1700
Hence,
Test statistic z
z= (0.76-0.78)/√(0.78* 0.22/900)
z= (-0.02)/√(0.78* 0.000244)
z= -0.02/√0.00019032
z= -0.02/0.0138
z = -1.449
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if you were trying to store a list of single digit numbers in your short-term memory, about how many should you be able to store on average? group of answer choices 10 2 15 7
If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.
What is short-term memory?
Short-term memory is a concept in psychology that defines the capacity for holding a small amount of information in mind for a short interval. The concept of short-term memory is given by Atkinson-Shiffrin. The information of short-term memory can be transformed into long-term memory through rehearsal.
According to several studies, short-term memory has a space limit of 7 ± 2 chunks of information. The fact is written by a cognitive psychologist of Harvard University named George A. Miller and was published in 1956 in psychological reviews.
Hence, If one tries to store a list of single-digit numbers in his or her short-term memory, then he will be able to store 7 numbers on average.
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a binomial experiment consists of 10 independent trials. the probability of success in each trial is 0.43. give the variance of the random variable associated with this experiment. a) 1.5656 b) 4.3000 c) 0.2451 d) 2.4510 e) 2.0736 f) none of the above.
Part (d) is correct.
i.e. The variance of the random variable associated with this given experiment is 2.4510.
What is Binomial experiment?
It is an experiment with a set number of independent trials, each having the same chance of success and the two outcomes of success or failure. A binominal distribution can be used to describe the likelihood of a certain number of successes.
Given that,
No. of independent trials ( n ) = 10
Probability of success in each trail ( p ) = 0.43
∴ probability of failure in each trial ( q ) = 0.57
we can find the variance of a binomial experiment by using the formula i.e. npq.
∴ Variance = npq
= 10 × 0.43 × 0.57
= 2.4510.
Hence, part (d) matches with the answer.
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a tree is 37.95 feet tall. what is its height in meter? use the following conversion: 1 meter is 3.3 feet
The height of tree in meter is 11.5 meter after the conversion from 37.95 feet to meter.
What is conversion factor?A conversion factor is measurement value in numbers that is used in converting one unit to another unit by arithmetic operations.
Given that a tree is 37.95 feet tall and 1 meter is 3.3 feet.
So to find 37.95 feet tree in meter we have to divide 37.95 by 3.3
= 37.95 / 3.3
= 11.5 meter
1 meter is 3.3 feet, then 11.5 meter is 37.95 feet.
Therefore, the height of tree in meter is 11.5 meter.
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Convert these unlike fractions to equivalent like fractions and add them. You must use the lcd to get the answer correct. If possible, reduce the final sum. 14512.
Unlike fraction 1/7 is converted to equivalent like fraction 2/14 and the sum of 2/14 + 3/14 = 5/14.
As given in the question,
Given fraction is equal to:
1/7=? + 3/14=?
Here there are two fractions
1/7 and 3/14
LCD( least common denominator) of 7 and 14 is equal to 14.
Now make them like fractions
1/7 is equivalent to
( 1/7) × ( 2/2) = 2/ 14
Now 2/14 and 3/14 are like fractions
Sum of like fractions is:
2/14 + 3/14
= ( 2+ 3) / 14
= 5/ 14
Therefore, the conversion of unlike fraction 1/7 to like fraction is 2/14. And sum of 2/14 + 3/14 = 5/14.
The complete question is:
Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If possible, reduce the final sum. 1/7=? + 3/14=?
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Math Question Attached
The slope of the straight line is 4/5
Slope of a LineThe slope of a line is a measure of the ratio between the rise and run of that line. The slope of a line is an integral quantity used to calculate the equation of a line
In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.
The slope of a line basically the change in y-coordinate with respect to change in x-coordinate.
This is easily done with a formula given as
m = y₂ - y₁ / x₂ - x₁
Taking data points from the graph attached;
A = (5, 2)B = (0, -2)Substituting the values into the slope equation;
m = -2 - 2 / 0 - 5
m = -4 / - 5
m = 4/5
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The longest side of a triangle is a cm. The second side is b cm shorter than the first side. The third side is half as long as the second side.
Write an expression, in its simplest form, for the perimeter of the triangle.
Answer:
2.5a - 1.5 b or
5/2a - 3/2b
Step-by-step explanation:
a + (a - b) + 0.5(a - b) =
a + a - b + 0.5a - 0.5b =
2a - b + 0.5a - 0.5b =
2a - 1.5 b + 0.5a =
2.5a - 1.5 b
a woman decides to purchase a $23,800 car and makes a down payment of $3,500. she arranges to borrow the remainder from a bank that will charge her 4.5% interest. she will make monthly payments for 4 years. a. find her monthly payment amount.
The monthly payment amount a woman has to pay for the car is $462.91.
Here we have to find the monthly payment amount.
The cost of car = $23,800
Down payment = $3,500
Rate(r) = 4.5%
time(t) = 4 years
Periodic interest(i) = 0.045/12
Formula to calculate monthly payment:
A = P i( 1 + i[tex])^{n}[/tex] / ( 1 + i[tex])^{n}[/tex] - 1
Loan amount = 23800 - 3500
= $ 20300
A = 20300 ( 0.045 /12 ( 1 + 0.045/12[tex])^{48}[/tex])/ (1 + 0.045/12[tex])^{48}[/tex] - 1
= 20300× 0.004488 / 0.196814
= 462.91
Therefore the monthly payment is $462.91.
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The Rodriguez family ate One-third of a pan of brownies, and they plan to divide the remaining brownies into two equal parts. They will take one part to their block party and the other part to share with co-workers. How much of the whole pan of brownies will each place get?
A model has 2 shaded parts and 1 unshaded part.
Answer:
1
Step-by-step explanation:
The equation to represent this would be (1 - (1 / 3)) / 2
1 - (1 / 3) = 2 / 3
2 / 3 / 2 = 1 / 3
a university charges students $2,300 less for tuition each year to encourage them to stay in school. the tuition for freshman year is $34,000. write a regression equation for this formula, with y
a regression equation for this formula, where x represents the number of years enrolled and y represents the tuition.
y = 34000 - 2300x
Regression is a statistical technique that connects one or more independent (explanatory) variables to a dependent variable. If there is a relationship between changes in one or more of the explanatory factors and changes in the dependent variable, it can be shown using a regression model.
The regression equation for this formula would be:
Y = 34,000 - 2,300x
where Y is the tuition cost and x is the number of years in school.
The equation states that the tuition cost for any year in school (x) is equal to the freshman year tuition cost (34,000) minus 2,300 multiplied by the number of years in school (x).For example, if x = 4 (4 years in school), then the tuition cost for that year would be 34,000 - 2,300(4) = 25,400.
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In ACDE, M/C = (x-4)°, m/D = (9x + 4)°, and m/E = (2x + 12)°.
Find m/D.
Thus, in ΔCDE the m/∠D = 130⁰, which can be calculated using angle sum property of triangle.
What is triangle?Triangle is derived from the Latin word triangulus, which means "three-cornered" or "having three angles," and is composed of the roots tri-, "three," and angulus, "angle or corner." Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.
Given that: In ΔCDE
m/∠C = (x-4)°
m/∠D = (9x + 4)°
m/∠E = (2x + 12)°
Now, to find m/∠D
So, We know that sum of internal angles of a triangle is equal to 180⁰ .Here, we are given a ΔCDE and all its three internal angles.
Putting the sum of all three equal to 180⁰:
∠C + ∠D + ∠E = 180⁰(x-4)°+ (9x + 4)°+ (2x + 12)°
= 180⁰12x +12
= 180⁰x +1 = 15⁰
x = 14⁰
Thus, Putting value of x in m/∠D = (9x + 4)°.
m/∠D = (9 × 14 +4)⁰
m/∠D = 130⁰
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The complete question is as follows:
In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D.
Eliza solves the equation (x-7)^2 = 25 and gets X = 12. Winnie solves the same equation and finds a different solution. What is the other solution to the problem?
Answer: 5^2
Step-by-step explanation:
5 x 5 = 25
and (x-7)^2 = 25
a helicopter is lifting an 800-pound unit at a rate of 200 feet per minute. how much horsepower, of work energy, is the helicopter using in the process?
4.84 HP is the amount of work energy used.
Given info,
A helicopter is lifting an 800-pound unit at a rate of 200 feet per minute.
1 horsepower = 550 foot-pounds per second
⇒ 800 x 200 = 160,000 foot-pounds per minute
= 160,000/60 foot pounds per second.
Horsepower = 160,000/60 * 550 = 428/33
= 4.848 HP
Therefore, the horsepower of work energy used is 4.84 HP
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Samuel prob please answer
The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.
What is meant by linear equation?A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.
Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.
Sodium contains in a can of soup is 300mg
Sodium contains in a can of frozen dinners is 450mg
Let the number of cans of soup purchased be x
Then, the number of frozen dinners purchased=x+5
Total sodium purchased=6000mg
So, 300x+450(x+5)=6000mg
Therefore, the system is 300x+450(x+5)=6000mg
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suppose x is a normal random variable with exam image and exam image find p(3.6 < x < 53.5). a) exam image b) exam image c) exam image d) exam image e) exam image f) none of the above.
After using the test statistic z, P(3.6<X<53.5) = 0.967.
In the given question, suppose X is a normal random variable with mean 35 and sdev 10.
We have to find P(3.6<X<53.5).
Fro the given question,
Mean x = 35
sdev s = 10
Z = X - mu / sd
P(3.6<X<53.5) = P ( 3.6-35/10 < Z < 53.5-35/10 )
P(3.6<X<53.5) = P ( -31.4/10 < Z < 18.5/10 )
P(3.6<X<53.5) = P ( -3.14 < Z < 1.85 )
P(3.6<X<53.5) = P ( Z < 1.85) - P ( Z < -3.14)
left tail of both
P(3.6<X<53.5) = 0.9678 - 0.0008
P(3.6<X<53.5) = 0.967
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The right answer is:
Suppose X is a normal random variable with mean 35 and sdev 10. Find P(3.6<X<53.5)
Help me solve this question!
The volume of foam needed for the 45 cones is
v = 16,956 cm³
How much foam is needed to make 45 cones?
We know that the volume of a cone of diameter F and height H is:
V = pi*(D/2)²*H/3
Where pi = 3.14
Here we know that:
D = 12cm
H = 10cm
And we want to find the volume of 45 of these cones, so the total volume of foam needed is:
v = 45*V = 45*(3.14*(12cm/2)²*10cm/3
v = 16,956 cm³
That is the volume of foam needed.
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Please help I’m timed
If g(n) varies inversely with n and g(n)= 10 when n=3 then find the value of n when
g(n)= 3
Round final answer to the tenths place. If answer is a whole number then put a zero
in the tenths place before entering your answer. Work must be shown for this
problem in order to receive any credit.
The value of n when the function g(n) assumes a value of 3 is of:
n = 10.
What is a proportional relationship?In the case of an inverse proportional relationship, as is the case in this problem, the output variable y is obtained as the division of the constant of proportionality k by the input variable x, as follows:
y = k/x.
Considering the variables in this problem, the equation is given as follows:
g(n) = k/n.
g(n)= 10 when n=3, hence the constant is obtained as follows:
10 = k/3
k = 3 x 10
k = 30.
Hence the equation is:
g(n) = 30/n.
When the input variable n when g(n) = 3 is obtained as follows:
3 = 30/n
3n = 30
n = 30/3
n = 10.
(we replaced the output variable g(n) by it's value and solved for the input variable)
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three regular dice are rolled simultaneously. if the probability that the sum of the faces is 7 can be represented by m n in simplest form, what is m n?
The probability that the sum of the faces is 7 = 15/216
The value of m = 15 and the value of n = 216
In this question, we have been given three regular dice are rolled simultaneously.
We need to find the probability that the sum of the faces is 7.
When three dice are rolled simultaneously, the total number of outcomes
n(S) = 6 * 6 * 6
n(S) = 216
Let event A: sum of the faces is 7
A = {(1, 2, 4), (1, 4, 2), (4, 1, 2), (4, 2, 1), (2, 1, 4), (2, 4, 1), (1, 3, 3), (3, 3, 1), (3, 1, 3), (2, 2, 3), (2, 3, 2), (3, 2, 2), (1, 5, 1), (5, 1, 1), (1, 1, 5)}
n(A) = 15
So, the probability that the sum of the faces is 7 = 15/216
Hence, if the probability that the sum of the faces is 7 can be represented by m/n in simplest form then m = 15 and n = 216
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لیا
The prism below is made of cubes which measure 1/4 of a centimeter on one side. What is the volume?
Answer:
Below
Step-by-step explanation:
You didn't include the picture......
each cube has a volume of 1/4 * 1/4 * 1/4 = 1/64 cm^3
count the total number of cubes and multiply by 1/64
to get volume in cm^3
Phone-Phriends charges $35 for a text-message plan with 250 text messages included. If the customer goes over the 250 messages, the cost is $0.14 per extra text message.
A customer sent and received 329 text messages last month. What are the total charges?
Answer:
Step-by-step explanation:
11.
Find the distance between the two points.
(3,2)
(3,0)
✓ [?]
Enter the number
that goes beneath the
radical symbol.
Enter
4
[tex] \Large{\boxed{\sf d = \sqrt{40} }} [/tex]
[tex] \\ [/tex]
Explanation:The distance between two points is given by the following formula:
[tex] \Large{\sf d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}} [/tex]
Where:
d is the distance between the points.[tex] \sf (x_A \: , \: y_A) [/tex] and [tex] \sf (x_B \: , \: y_B) [/tex] are the coordinates of the points.[tex] \\ [/tex]
First, let's identify our values:
[tex] \sf (\underbrace{\sf -3}_{\sf x_A} \: , \: \overbrace{\sf 2}^{\sf y_A}) \: \: and \: \: (\underbrace{\sf 3}_{\sf x_B} \: , \: \overbrace{\sf 0}^{\sf y_B}) [/tex]
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Now, substitute these values into our formula:
[tex] \sf d = \sqrt{\sf (3 - (-3))^2 + (0 - 2)^2} \\ \\ \sf d = \sqrt{\sf 6^2 + (-2)^2} \\ \\ \sf d = \sqrt{\sf 36 + 4 } \\ \\ \boxed{\boxed{\sf d = \sqrt{40} }} [/tex]
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▪️Learn more about finding the distance between two points here:
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