The probability will be 1/17 i.e. A.
What exactly is probability?
Probability expresses the likelihood of an event. This mathematical branch of study is concerned with the occurrence of a random event. The value ranges from zero to one. Probability is used in mathematics to anticipate the possibility that events will occur.
Probability refers to the possibility of something happening. This fundamental idea in probability theory is also used by the probability distribution. Before determining the chance of a certain event occurring, we must first determine the total number of possibilities.
The probability that an event will occur P(E) = the number of positive outcomes divided by the total number of outcomes.
Now,
Total cards =52
No. of ways to select 2 cards=52C₂
=52*51*50!/50!*2!=51*26
Now to select two cards with same values we have no. of ways =13*6
so probability that two cards are chosen at random from a deck of 52 and they have the same value=13*6/26*51=3/51=1/17
Hence,
The probability will be 1/17.
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please tell me what i need to do to solve this problem
The standard form of the equation of the sphere with center (0, -1, 3) and a radius of square root of 5 is given as follows:
x² + (y + 1)² + (z - 3)² = 5.
How to obtain the equation of a sphere?The two parameters for the equation of a sphere are given as follows:
Center (x*, y*, z*).Radius r.Then the equation for the sphere is given as follows:
(x - x*)² + (y - y*)² + (z - z*)² = r².
The parameters for this problem are given as follows:
Center (0, -1, 3).Radius: square root of 5.Hence the equation of the sphere is defined as follows:
x² + (y + 1)² + (z - 3)² = 5.
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The length of a rectangle is 2 ft longer than it’s width if the perimeter of the rectangle is 36ft find it’s area
Answer:
two of the sides are x and the other two sides are x+2
x+x+x+2+x+2 = 36
4x = 32
x = 8
the sides are 8, 8, 10, 10
area is length x width
8 x 10 = 80
answer: 80ft
Step-by-step explanation:
2.
A house that costs $200,000 will appreciate in value by 3% each year.
Write a function that models the cost of the house over time. Use x for years and y for
the value of the house, in dollars.
Find the value of the house at the end of ten years.
Answer: The function that models the cost of the house over time can be written as y = 200,000 * (1 + 0.03)^x, where x is the number of years and y is the value of the house.
To find the value of the house at the end of ten years, we need to plug in x = 10 into the function:
y = 200,000 * (1 + 0.03)^10 = 200,000 * 1.33489 = 266,978.8
So the value of the house at the end of ten years is $266,978.8.
Step-by-step explanation:
A child is flying a kite. If the kite is "h" feet above the child's hand level and the wind is blowing it on a horizontal course at "v" feet per second, the child is paying out cord at _____ feet per second when "s" feet of cord are out. Assume that the cord remains straight from hand to kite.
The child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The distance between the kite and the child's hand level "d".
By using the Pythagorean theorem, we can write:
d² + h² = s²
Simplifying and solving for d, we get:
d² = s²-h²
d = √(s²-h² )
Let's call the length of the cord "L". Then, we can write:
d² + L² = s²
Differentiating both sides with respect to time (t), we get:
2d (dd/dt) + 2L (dL/dt) = 2s (ds/dt)
We want to find (dL/dt) when L = s and d = √(s²-h² )
(dd/dt) = 0 as the height of the kite above the child's hand level is constant.
(dL/dt) = (s(ds/dt) - d (dd/dt)) / L
Substituting in the values we found for d and L, we get:
(dL/dt) = s(ds/dt)) / √(s²-h² )
Therefore, the child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.
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Alice decides to finish her trip by riding a train 700 miles to Washington D.C. The train travels at an average speed of 80mph. What are the domain and range of the function this creates?
The range of the function is 8.75.
And the domain is all the positive integers.
What is a domain?The collection of all conceivable independent values that a function or relation may take is known as its domain.
Given:
Alice decides to finish her trip by riding a train 700 miles to Washington, D.C.
The train travels at an average speed of 80mph.
Let s be the average speed.
So, speed = distance / time
s = 700/t
t = 700/80
t = 8.75 hours.
The range of the function is 8.75.
And the domain is all the positive integers.
Therefore, the time it will take is 8.75 hours.
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Consider the cubic function g(x) = −2( + 4)^3 − 5. Please describe how this function has been transformed from the cubic parent function f(x) = x^3
The cubic function g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
The cubic parent function f(x) = x³ has been transformed to the function g(x) = −2(x + 4)³ − 5 through a combination of translations, scaling, and reflection.
Translation: The parent function has been shifted 4 units to the right, resulting in x + 4 instead of x in the argument of the function.
Scaling: The parent function has been scaled vertically by a factor of -2, resulting in a coefficient of -2 in front of the argument.
Reflection: The parent function has been reflected on the x-axis, resulting in the negative sign in front of the argument.
Thus, g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.
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explain why A*B*C and (A*B)*C are not same
concerning the relationship between the chi squared test and two proportion z test with a two sided alternative hypothesis, which of the following statements is true?The x^2 test statistic is equal to the z test statistic. The x^2 test statistic is equal to the z test statistic squared. The x^2 test statistic is not equal to the z test statistic squared. The x^2 test statistic is not equal to the alternative hypotheses value squared.
The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.
The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.
The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The
Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.
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4. Write a word problem for 3/4 X 1/2! Please help me!!
A word problem for the given expression is the division of 3/4 cups of juice among two friends equally.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given is an expression [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex].
Suppose that there are 3/4 cups of juice available.
There are two friends who are in need of this.
The total amount of juice has to be divided equally among these two friends.
Amount of cups of juice each friend gets = [tex]\frac{3}{4}[/tex] ÷ 2.
[tex]\frac{3}{4}[/tex] ÷ 2 = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]
So each friend gets 3/8 cups of juice.
Hence the division of a total of 3/4 cups of juice among two friends equally is a word problem for the given expression.
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A car can be rented for $80 per week plus $0.25 per mile. How many miles can be driven if you have at most $110 to spend for weekly transportation?
Answer: Let x be the number of miles driven.
The cost of renting the car and driving x miles is 80 + 0.25x.
We want to find the maximum number of miles that can be driven given a budget of $110, so we set 80 + 0.25x = 110 and solve for x:
80 + 0.25x = 110
0.25x = 110 - 80
0.25x = 30
x = 120
So the maximum number of miles that can be driven is 120.
Step-by-step explanation:
Assume that program runs in f (n) microseconds; where f (n) is the function given on the left. Fill in how large an input can be calculated, given cach of the runtimes given along the top. have filled in two values for you: You do not need to fill in every box, but should have at least of every row filled in, and at least half of the rows complete: second minute hour day month year Ign Vnl n lgn 72 1000 2n Show some calculations, O some of your code if you use code: What row is the most sucktastic one? Why? Do you have any non-integer answers?
The row with the most sucktastic runtime is the one with[tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes.
No, we do not have any non-integer answers.
Second: 72
Minute: 1000
Hour: [tex]2^(17)[/tex]
Day: [tex]2^25[/tex]
Month: [tex]2^30[/tex]
Year: [tex]2^35[/tex]
Second: f(n) = 72 => n = 72
Minute: f(n) = 1000 => n = 1000
[tex]Hour: f(n) = 2^n = > n = 17Day: f(n) = 2^n = > n = 25 Month: f(n) = 2^n = > n = 30Year: f(n) = 2^n = > n = 35[/tex]
Seconds: The runtime for an input of size n is 72 microseconds, so the largest input that can be calculated in a second is 72.
Minutes: The runtime for an input of size n is 1000 microseconds, so the largest input that can be calculated in a minute is 1000.
Hours: The runtime for an input of size n is[tex]2^n[/tex] microseconds, so the largest input that can be calculated in an hour is [tex]2^17.[/tex]
Days: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a day is [tex]2^25[/tex]
Months: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a month is [tex]2^30.[/tex]
Years: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a year is [tex]2^35.[/tex]
The row with the most sucktastic runtime is the one with [tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes. Therefore, the longer the time period, the larger the input size that can be calculated. No, we do not have any non-integer answers as the runtimes of the inputs are in microseconds and the input size is given as an integer.
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Identify the hypothesis and the conclusion for each of the following conditional statements. (a) If n is a prime number, then n2 has three positive factors.
(b) If a is an irrational number and b is an irrational number, then a⋅b is an irrational number.
(c) If p is a prime number, then p=2 or p is an odd number.
(d) If p is a prime number and p≠2 or p is an odd number.
(e) p≠2 or p is a even number, then p is not prime.
The hypothesis and conclusion are -
(a) Hypothesis : n is a prime number.
Conclusion : n² has three positive factors.
(b) Hypothesis : a and b are irrational numbers.
Conclusion : a · b is an irrational number .
(c) Hypothesis : p is a prime number.
Conclusion : p = 2 or p is an odd number .
(d) Hypothesis : ap is a prime number and p≠2 .
Conclusion : p≠2, p is an odd number .
(e) Hypothesis : p≠2 and p is a even number.
Conclusion : p is not a prime number .
What is irrational number?
A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio.
The hypothesis of a conditional statement is the phrase immediately following the word if.
The conclusion of a conditional statement is the phrase immediately following the word then.
(a) If n is a prime number, then n² has three positive factors.
Hypothesis : n is a prime number.
Conclusion : n² has three positive factors.
(b) If a is an irrational number and b is an irrational number, then a⋅b is an irrational number.
Hypothesis : a and b are irrational numbers.
Conclusion : a · b is an irrational number .
(c) If p is a prime number, then p=2 or p is an odd number.
Hypothesis : p is a prime number.
Conclusion : p = 2 or p is an odd number .
(d) If p is a prime number and p≠2 or p is an odd number.
Hypothesis : ap is a prime number and p≠2 .
Conclusion : p≠2, p is an odd number .
(e) p≠2 or p is a even number, then p is not prime.
Hypothesis : p≠2 and p is a even number.
Conclusion : p is not a prime number .
Therefore, the hypothesis and conclusions are made.
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The area of the circle is 4pix^2+12pix+9pi what is the least possible integer value of x for the circle to exist
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The area of the circle is 4π x² + 12πx + 9π. Then the radius is given as,
A = 4π x² + 12πx + 9π
πr² = π [(2x)² + 2 · 2x · 3 + 3²]
r² = (2x + 3)²
r = 2x + 3
The value of the radius should be more than zero. Then we have
r > 0
2x + 3 > 0
x > - 3/2
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
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The complete question is given below.
The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.
The graph below shows the relationship between the number of money spent and the amount of cans bought. For the data in the graph, which of the following equations can be used to calculate c, the amount of cans, bought for m money spent ?
c = 2m
c = 5m
c = 10m
c = 1/10m
Answer:
C = 10m
Step-by-step explanation:
when c=20, m=2
when c=40, m=4
we can see that c is equals to 10 times the value of m
Therefore c = 10m
ASAP!! Please help!!
If on the scale of a map, 3/4 inch equals 72 miles, what is the actual distance between two cities that are 3 7/8 inches apart on the map?
Answer:
The actual distance between two cities that are 3 7/8 inches apart on the map is 279 miles.
Step-by-step explanation:
To find the actual distance between two cities, we need to convert the distance on the map to miles. The scale of the map is 3/4 inch equals 72 miles, which means 1 inch on the map is equal to 72/3=24 miles.
So, the actual distance between two cities on the map that are 3 7/8 inches apart is 24 * 3 7/8 = 279 miles.
Find one possible missing coordinate so that the point becomes a solution to the given inequality.
(x,9)
is a solution to 8x−7
.
Answer:
x=2Step-by-step explanation:
y=8x-7
9=8x-7
9+7=8x-7+7
16=8x
16/8=8x/8
2=x
Find the volume of a frustum of a pyramid with square base of side 22, square top of side 13 and height 20.
The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.
What is frustum of pyramid?
The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).
We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.
We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3
We are given b = 22, a = 13 and h = 20
From this, we get
⇒V = h(b^2 + a^2 + ab)/3
⇒V = 20(22^2 + 13^2 + 22*13)/3
⇒V = 20(484 + 169 + 286)/3
⇒V = 20(939)/3
⇒V = 20*313
⇒V = 6260 cubic units
Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.
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A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : [tex]\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}[/tex]
GGRRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}[/tex]
GGGRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}[/tex]
GGGGR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
GGGGG : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]
The sum is [tex]\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}[/tex]
Probability that you do not eat green candy after you eat a red candy =[tex]\frac{1}{5}[/tex]
so m = 1 and n = 5
m + n =6
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marks) There are more than 600 million bacteria in a person's body. Work out and write your answer correct to 1 significant figure the number of bacteria there would be in the people of a town with a population of 200 thousand. (Write answer in scientific notation)
Answer: The number of bacteria in the people of a town with a population of 200 thousand would be 200,000 * 600 million = 120 x 10^9 bacteria.
Step-by-step explanation:
Shayla created two patterns. Pattern X increases by 7 each time. Pattern Y increases by 5 each time. Shayla used the corresponding values in each pattern to make coordinate pairs. She graphed the coordinate pairs on a coordinate plane.
The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
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]
Then the equation of the line is given as,
(y - 5) = [(10 - 5) / (14 - 7)](x - 7)
y - 5 = (5/7)x - 1
y = (5/7)x + 4
At x = 63, the value of 'y' is given as,
y = (5/7)63 + 4
y = 45 + 4
y = 49
The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.
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c)If 2000 items sell when the price is 30 dollars and if the number of items that are sold decreases by 400 for every 1 dollar increase in price, find the rate of change of the profit when the item price is 30 dollars.
The rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let's call the number of items sold at a price of $p as x(p).
Based on the information given, we can write an equation for x(p) as:
x(p) = 2000 - 400(p - 30)
The profit from selling the items at a price of $p is given by the product of the number of items sold and the price:
Profit(p) = x(p)×p
Taking the derivative of the profit function with respect to the price, we can find the rate of change of the profit:
dProfit/dp = dx/dp×p + x(p)
= -400 p + 400 ( 30) + 2000 - 400(p - 30)
= -400 p + 12000
When p = 30, the rate of change of the profit is:
dProfit/dp = -400(30 )+ 12000
= 3600
So the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
Hence, the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.
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Can you help me in this problem algebra
Answer:
2^4*2^5=2^(4+5)=2^9
Step-by-step explanation:
When dealing with operations with exponents and multiplication, the exponent operations always come first. So while the exponent 9 is correct for the answer, 4 is incorrect.
For example, if you were to solve each operation and eliminate every exponent, you would have
2^4*2^5=16*32=512 which is the same as 2^9=512.
As you can see, the exponent operation must come before the multiplication.
round 107.06 one decimal place
Answer: 107.1
Step-by-step explanation:
4 or less down
5 or more up
In this case, we round to 1 decimal place, so we look at the hundredths column.
It is 6, so we round up.
Which of the following lists of properties contains only those that are characteristic properties of a substance? Odensity, solubility, melting point O boiling point, mass, density O volume, density, temperature O solubility, mass, volume
Of the lists of properties you provided, only the list of "identity, solubility, melting point" contains only those that are characteristic properties of a substance.
Identity refers to the name or chemical formula of the substance, which is unique to that substance and can be used to identify it.
Solubility refers to the ability of a substance to dissolve in a solvent, such as water. The solubility of a substance can also be used to identify it, as different substances have different solubility's.
Melting point refers to the temperature at which a solid substance will change into a liquid. Like solubility, the melting point of a substance is also a characteristic property that can be used to identify it.
On the other hand, boiling point, mass, and density are not always characteristic properties of a substance. While they can give us information about a substance, they are not unique to that substance and cannot be used to identify it.
Volume and temperature are not considered characteristic properties of a substance, as they are dependent on external factors, such as the pressure and the amount of the substance being measured.
In conclusion, the list of "identity, solubility, melting point" contains only those properties that are characteristic of a substance and can be used to identify it.
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Baseball The table shows the height of a baseball hit, with
x representing the time (in seconds) and y representing
the baseball's height (in feet). Use a graphing calculator
to find the best-fitting model for the data.
Time, x
2 4 6 8
0
Helght, y 3 28 40 37 26
Oy 1.553x² +15.1782 -3.37
Oy -1.553x² - 15.178x + 3.37
Oy = -1.553x² +15.178x + 3.37
Oy 1.553x² +15.178x + 3.37
Answer: The best-fitting model for the data is a parabolic equation with the form y = ax^2 + bx + c. The coefficients a, b, and c represent the parameters that best describe the relationship between the time (x) and the height (y) of the baseball.
Based on the information provided, the best-fitting model is:
y = 1.553x^2 + 15.178x + 3.37
where y is the height of the baseball (in feet), x is the time (in seconds), 1.553 is the coefficient for x^2, 15.178 is the coefficient for x, and 3.37 is the constant term. This equation represents the best fit of the data to a parabolic function.
Step-by-step explanation:
Use a table to find the solution of each equation.
38.2+-1= 11
Answer:
Here is a table that can be used to solve the equation:
Operation Result
38.2 38.2
+ (-1) 37.2
= 11 False
The equation 38.2 + (-1) = 11 is not true for any value of x. There is no solution for this equation.
Oh, hello there! Let's work on this equation together.
38.2 + -1 = 11
Let's create a table to keep track of our work.
-1 38.2 11
+1 37.2 12
As you can see, we added 1 to both sides to cancel out the negative 1.
So now, our equation is 37.2 = 12.
Let's subtract 12 from both sides.
-12 37.2 11
-12 25.2 -1
And there you have it! The solution is 25.2.
I hope this helps!
Determine if the triangle below is a right triangle. If it is not, compute what the hypotenuse would have to be for the triangle to be a right triangle. A. No, the hypotenuse should be 98 B. No, the hypotenuse should be 99 C. No, the hypotenuse should be 94 D. Yes
The triangle will by a right triangle if the sum of the squared side lengths is equals to the squared length of the hypotenuse.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Hence, a triangle will only be a right triangle if the Pythagorean Theorem is respected, hence the sum of the squared side lengths must be compared to the square of the hypotenuse length.
Missing InformationThe problem is incomplete, hence the procedure to verify whether the triangle is a right triangle was presented.
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Two ordinary fair dice are thrown. The resulting score is found as follows.
• If the two dice show different numbers, the score is the smaller of the two numbers.
• If the two dice show equal numbers, the score is 0.
(i) Draw up the probability distribution table for the score.
The probability distribution table is shown below
How to determine the probability distribution tableFrom the question, we have the following parameters that can be used in our computation:
Dice = 2
This means that
Sample size = 6 * 6
Sample size = 36
So, the number of outcomes is 36
To determine the distribution table, we need to identify that the dice are distinct.
This means that (1, 2) and (2, 1) are not the same outcomes
We can create a probability distribution table for the score by listing all possible outcomes and their probabilities, and then determining the score for each outcome based on the rules given.
So, we have
Outcomes Probability
(1, 1) 1/36
(1, 2) 1/36
(1, 3) 1/36
(1, 4) 1/36
(1, 5) 1/36
(1, 6) 1/36
........
(6, 1) 1/36
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A multimeter and an oscilloscope cost $574. The oscilloscope cost $356 more than the multimeter. Find the cost of the oscilloscope and the multimeter.
Answer:
oscilloscope: $465multimeter: $109Step-by-step explanation:
You want the costs of an oscilloscope and a multimeter when the sum of their costs is $574, and the difference of their costs is $356.
Sum and differenceLet o and m represent the costs of the oscilloscope and multimeter, respectively. Then the costs can be described by ...
o +m = 574
o -m = 356
SolutionAdding these two equations gives ...
2o = (574+356) = 930
o = 465 . . . . . . . . . . . . divide by 2
Subtracting the second equation from the first gives ...
2m = 574 -356 = 218
m = 109 . . . . . . . . . . . . divide by 2
The oscilloscope costs $465; the multimeter costs $109.
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Additional comment
This is the generic solution to a "sum and difference" problem: the higher value is half the sum of the given numbers, and the lower value is half their difference.
can someone tell me how to do this problem? please
Hi there, here's your answer:
The general formula of a circle:
[tex](x-h)^{2} +(y-k)^{2}=r^2\\[/tex]
Where the ordered pair (h, k) is the center of the circle.
Given (h, k) = (-6, -2)
We also have that the circle passes through a point (7, 12)
Which means that (7, 12) lies on the circumference of the circle.
Let this be labelled as [tex](x_{1}, y_{1})[/tex]
Since this point lies on the circumference of the circle, it must satisfy the equation when substituted in for (x, y).
Thus, we substitute [tex]x_{1}[/tex] for x and [tex]y_{1}[/tex] for y.
We get the final equation to be:
[tex](7+6)^2 + (12+2)^2 = r^2[/tex]
Or
[tex]169 + 196 = r^2[/tex]
[tex]r^2 = 365[/tex]
Thus, we get the final equation of the circle to be [tex](x+6)^2 + (y+2)^2 = 365[/tex]
Hope it helps!