The solution to the system of equations is x = 6 and y = -5, which is the same as we obtained using the elimination method.
What is the system of equations?A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:
2x + y = 7 ---(1)
x + y = 1 ---(2)
To solve this system, we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.
Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:
-2(x + y) = -2(1) --
Multiplying equation
(2) by -2-2x - 2y = -2
Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:
2x + y = 7(-2x - 2y = -2)0x - y = 5
We now have a new equation in which y is isolated.
To solve for y, we can multiply both sides by -1:
-1(-y) = -1(5)y = -5
Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6
Therefore, the solution to the system of equations is (x,y) = (6,-5).
Method 2: Substitution
In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.
From equation (2), we can solve for y in terms of x:y = 1 - x
We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6
Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5
Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.
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Solve: log2(x-1)+log2(x+5)=4
Answer: X=3
Step-by-step explanation:
what the work out 320.041 - 47.96
Working out the expression 320.041 - 47.96 gives 272.081
Work out the expression 320.041 - 47.96From the question, we have the following parameters that can be used in our computation:
320.041 - 47.96
The above expression is a difference or subtraction expression that can be done using a calculator
Using the above as a guide, we have the following:
320.041 - 47.96
Evaluate using a calculator
So, we have
320.041 - 47.96 = 272.081
Hence, teh solution of 320.041 - 47.96 is 272.081
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Find the following angles
Answer:
10. x=82 11.x=25 9. p=225
What should you know about your audience?
A) how much experience they have had doing research
B) their preferences for recreation
C) what are their astrological signs are
D) what they already know about your topic
Answer: B) their preferences for recreation
Step-by-step explanation:
In the state of Pennsylvania 12% of students submit box tops for education to their school. a large school district in western Pennsylvania runs a contest to see if they can increase participation. the superintendent takes a random sample of 210 students from the district and finds that 35 have submitted box tops this year.
(a) do these data provide convincing evidence that the contest has increased participation in the box tops for education program?
(b) interpret the p-value from part (a).
If in sample of 210 students from district and finds 35 have submitted "box-tops" this year, then
(a) Yes, data provide enough evidence regarding contest which has increased participation in "box-tops" for "education-program",
(b) the p-value is 0.0187.
Part(a) : To find if contest has increased the participation in "box-tops" for "education-program", we conduct a "hypothesis-test".
We use a "significance-level" of 0.05, which means we will accept a 5% chance of making a "Type I Error",
Let Null Hypothesis ⇒ The proportion of students submitting "box-tops" is = 12%,
Let Alternative Hypothesis ⇒ The proportion of students submitting "box-tops" for education is increased after contest,
To test above hypothesis, we use "one-sample" proportion-test.
We will use the sample proportion (p') = 35/210 = 0.1667, as estimate of population proportion (p).
So, "test-statistic" (z) is ⇒ z = (p' - p₀)/√(p₀ × (1-p₀)/n),
where n = sample size,
In "Null-Hypothesis", the "expected-value" of the test statistic is 0, and "standard-deviation" of the "test-statistic" is √(p₀×(1-p₀)/n),
Substituting, p₀ = 0.12 and n = 210,
We get,
⇒ z = (0.1667 - 0.12)/√(0.12 x 0.88/210) ≈ 2.08,
Now, we know that "right-tailed" critical value at 0.05 level is = 1.645,
Since, z (2.08) > 1.645, the Null-Hypothesis is Rejected.
So, above data provides enough evidence regarding contest has increased the participation in "box-tops" for "education-program".
Part(b) : We need to find the "p-value" for the test-statistic that we found in part(a),
So, p-value = P(z>2.08),
⇒ 1 - P(z ≤ 2.08),
⇒ 1 - 0.9813,
⇒ 0.0187,
Therefore, the required "p-value" is 0.0187.
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You bake 7 different pies for a bake sale. You sell 4 pies on the first day of the sale. Use the Fundamental Counting Principle to find the probability that your
friend correctly guesses which pies were sold on the first try. Write your answer as a fraction in simplest form.
Probability:
The probability of correctly guessing which pies were sold on the first day is near to 2/3.
What is Fundamental Counting Principle?The Fundamental Counting Principle states that if there are m number of ways to do an activity and n number of ways for a second activity, then there are m x n ways to do the two activities together.
In this case, there are 7 pies and 4 of them were sold on the first day. Therefore, the probability of correctly guessing which pies were sold on the first day is 4/7.
This can be written in simplest form as 2/3.
In conclusion, the probability of correctly guessing which pies were sold on the first day is 2/3.
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3 divided by 2/5 quotient
Answer:
3 divide 2/5 is 7.5 since 2/5 is 0.4
8. You and your friend each collect coins and stamps. Your friend collects one fifth as many coins and twice as many stamps as you. You collect a total of 70 coins and stamps. Your friend collects a total of 95 coins and stamps.
How many coins and how many stamps do you each collect?
Answer:
you: 25 coins, 45 stampsfriend: 5 coins, 90 stampsStep-by-step explanation:
Given you have collected 70 coins and stamps, and your friend has collected 1/5 as many coins and twice as many stamps, for a total of 95 coins and stamps, you want the numbers of each.
SetupWe can let x represent the number of coins you have collected. Then 70 -x is the number of stamps you have collected. The corresponding numbers for your friend are x/5 coins and 2(70-x) stamps. Your friend's collection is ...
x/5 +2(70 -x) = 95
Solution-9/5x +140 = 95 . . . . . . . . simplify
45 = 9/5x . . . . . . . . . . . . . add 9/5x -95
25 = x . . . . . . . . . . . . . . . . multiply by 5/9
70 -x = 45
1/5x = 5
2(70 -x) = 90
You collect 25 coins and 45 stamps; your friend collects 5 coins and 90 stamps.
<95141404393>
Solve for the value of x. Show your work and explain the steps you used to solve. Round your answer to the nearest
tenth.
B
D x
45
24
C
The calculated value of x from the special triangle is 17.0
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The right triangle is a special triangle that has a measure of 45 degrees
For a triangle that has a measure of 45 degrees, we have
Hypotenuse = Legs√2
In this case, we have
Leg = x
Hypotenuse = 24
So, we have
x√2 = 24
Divide by √2
x = 24/√2
Evaluate
x = 17.0
Hence, the calculated value of x is 17.0
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In 2010, the mean starting salary for college graduates who major in Statistics was $54000. An analyst for a job searching company claims that the mean starting salary has since increased. In a random sample of 40 job posting requiring knowledge of Statistics, the mean starting salary was $63500 with a standard deviation of $10540. Test the claim using a significance level of 0.05.
Our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of 1.684, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.
How can we Test the claim using a significance level of [tex]0.05[/tex]?We can use a one-sample t-test to test the claim that the mean starting salary for college graduates who major in Statistics has increased.
The null hypothesis is that the mean starting salary is still $[tex]54000[/tex], while the alternative hypothesis is that the mean starting salary is greater than $[tex]54000[/tex].
We can calculate the t-statistic as:
t = (sample mean - null hypothesis value) / (standard error of the mean)
= [tex](63500-54000)/(10540/\sqrt{40}[/tex]
= [tex]4.22[/tex]
where [tex]\sqrt{40}[/tex] is the sample size.
The degrees of freedom for the t-test is [tex](n-1) = 39[/tex], where n is the sample size.
Using a t-table or calculator with [tex]39[/tex] degrees of freedom, a one-tailed test, and a significance level of [tex]0.05[/tex], we find the critical t-value to be [tex]1.684[/tex]
Since our calculated t-value of [tex]4.22[/tex] is greater than the critical t-value of [tex]1.684[/tex], we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean starting salary for college graduates who major in Statistics has increased.
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K(10,..), L. (..,20), and M (30,.. .. are on that line too. Write their missing coordinates.
The coordinate of points K, L and M is the location of the points on a coordinate plane
Here, we have,
to determine the missing coordinates:
The given parameters are:
K = (10, )
L = ( ,10)
M = (30, )
The question has missing parameters.
So, I will assume that the line is a perfectly horizontal line.
This means that the y-coordinates of points K, L and M are equal.
The y-coordinate of point L is 10.
So, we have:
K = (10, 10)
L = ( ,10)
M = (30, 10)
Assume that point L is halfway points K and M, then we have:
K = (10, 10)
L = (20, 10)
M = (30, 10)
See attachment for the diagram of the coordinate plane showing the line
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S certain forest covers an area if 3500km^2. Supposr that each year this area decreases by 4.25%. What will the area be after 13 years? Use the calculator provided and round your answer ti the nearest square kilometer
The area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b[tex])^x[/tex], where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
Here initial area a = 3500[tex]km^2[/tex] ,
Rate of decay = 4.25%= 4.25/100 = 0.0425
Now using exponential decay formula then,
=> [tex]y=a(1-b)^x[/tex] where x=13 years .
=> y = [tex]3500(1-0.0425)^{13}[/tex]
=> y = [tex]3500(0.9575)^{13}[/tex]
=> y = 1990.08 [tex]km^2[/tex]
Hence the area of the forest after 13 years is 1990.08 [tex]km^2[/tex].
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Consider the number 3^6.
Rewrite the number as the product of two whole-number powers of 3.
We can rewrite 3^6 as the product of two whole-number powers of 3 as: [tex]3^4 . 3^2.[/tex]
How can we rewrite the number as the product?To rewrite 3^6 as the product of two whole-number powers of 3, we need to find two exponents that add up to 6.
A way to do this is to use the fact that 3^4 = 81, which is close to 3^6.
Specifically, we have:
3^6 = 3^4 * 3^2
We can check that this is true by using the rule for multiplying exponents that states that a^m * a^n = a^(m+n).
Applying this rule, we get:
= 3^4 * 3^2
= 3^(4+2)
= 3^6.
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if I bike for 180 minutes and I cover a
total distance of 47 Mi what is my
average speed
Average Speed Calculator
The average speed of the bike is calculated as: 15.67 mph
How to find the average speed?The formula for the average speed is:
Average speed = Distance/Speed
We are given the parameters as:
Time = 180 minutes = 3 hours
Distance = 47 miles
The average speed is defined as the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.
Thus:
Average speed = 47/3
= 15.67 mph
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x^2+25x+136=0 use the quadratic formula
Using the quadratic equation, the solution is x = -8 and x = -17.
What is the quadratic equation?A second-order equation of the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.
The equation is x²+25x+136=0
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
For the given equation x² + 25x + 136 = 0, we can identify a = 1, b = 25, and c = 136.
Substituting these values in the quadratic formula, we get:
x = (-25 ± √(25² - 4(1)(136))) / 2(1)
x = (-25 ± √(625 - 544)) / 2
x = (-25 ± √(81)) / 2
imply them
x = (-25 + 9) / 2 or x = (-25 - 9) / 2
x = -8 or x = -17
Therefore, the solutions to the quadratic equation x^2 + 25x + 136 = 0 are x = -8 and x = -17.
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Elsa repairs types of electronic devices in her repair shop. The number of each type that she repaired last week is shown in the bar graph below. Using this bar graph, answer the questions.
A relief worker needs to divide 2250 bottles of water and 144 cans of food into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?
The required, we can put 125 bottles of water or 8 cans of food in each box, and each box will contain the same number of items.
To find the largest number of relief supplies that can be put in each box, we need to find the greatest common factor (GCF) of 2250 and 144. We can do this by listing the prime factors of each number:
2250 = 2 * 3 * 3 * 5 * 5 * 5 * 2
144 = 2 * 2 * 2 * 2 * 3 * 3
To find the GCF, we need to find the highest power of each common prime factor that appears in both numbers. In this case, the common prime factors are 2 and 3, so we take the highest power of each:
2 * 3 * 3 = 18
So the largest number of relief supplies that can be put in each box is 18. We can check that this works by dividing each quantity by 18:
2250/18 = 125
144/18 = 8
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Mari makes bows for floral arrangements she uses 1/8 yard of ribbon for each bow .how many bows can she make from 24 yards of ribbon
First, you need to find out how much ribbon she has total. Because there are two spools, you multiply 24 x 2. The answer for that is 48. Then you have to figure out how many bows she can make. Each bow uses 1/8 of a piece of yard of ribbon, so you can divide 48 by 8. Your answer would then be 6 bows.
Here are the equations.
[tex]24\times2 = \text{X}[/tex]
[tex]\dfrac{\text{X}}{8} =\text{B}[/tex]
Where X represents the yards of ribbon available and B represents the number of bows that Mari can make.
Complete Question:
Mari makes bows for floral arrangements. She uses 1/8 of a yard ribbon for each bow. How many bows can she make from 2 spools that each has 24 yards ribbon?
1. Trish can complete 10 problems in 60 minutes. At this rate, could she complete 25 problems in 130 minutes? Write your answer as Yes or No.
2. How many minutes would it take Trish to complete 15 problems?
3. Solve the proportion. 5/27 = x/54. Write your answer as x = "_".
You have 36 liters of fuel and just added 4,000 milliliters more. How many hectoliters of fuel do you have?
Answer:
we have to first start converting the given volume to liters, since the answer is expected in hectoliters.
36 liters + 4,000 milliliters = 36 liters + 4 liters = 40 liters
1 hectoliter = 100 liters
Therefore, we have:
40 liters = 0.4 hectoliters
So, we have 0.4 hectoliters of fuel.
Answer:
0.4 hectoliters of fuel
Step-by-step explanation:
We Know
You have 36 liters of fuel and just added 4,000 milliliters more.
How many hectoliters of fuel do you have?
1000 milliliters = 1 liters
4000 milliliters = 4 liters
We Take
36 + 4 = 40 liters of fuel
We Convert 40 liters to hectoliters
1 liter = 0.01 hectoliters
40 liters = 40 x 0.01 = 0.4 hectoliters
So, you have 0.4 hectoliters of fuel.
In each of 10 consecutive weeks, 1000 college students were randomly selected and the number who applied for credit cards that that weck was determined. The results are listed below. Find the values you would use for the centerline, the upper control limit, and the lower control limit.
465 502 395 488 472 462 524 434 481 386
The centerline= 459.9
The upper control limit= 852.55.
The lower control limit = 67.25.
How do we calculate?We determine the mean to set up the standard limits:
Mean is gotten as :
(465 + 502 + 395 + 488 + 472 + 462 + 524 + 434 + 481 + 386) / 10
mean = 459.9
we then find the Standard Deviation:
Standard Deviation = √variance
variance = ((465-459.9)^2 + (502-459.9)^2 + (395-459.9)^2 + (488-459.9)^2 + (472-459.9)^2 + (462-459.9)^2 + (524-459.9)^2 + (434-459.9)^2 + (481-459.9)^2 + (386-459.9)^2) / 9
variance = 17119.1
Standard Deviation = √(17119.1)
Standard Deviation= 130.88
Hence
Centerline = 459.9
upper control limit = 459.9 + 3 x (130.88) = 852.55
lower control limit. = 459.9 - 3 x (130.88) = 67.25
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Expressions Task Card #10
What is the difference in the areas of
the polygons shown?
7/
A = x + 5
A = 4x - 6
We can see here that the difference in the areas of the polygons shown is: 3x + 1.
What is a polygon?A polygon is a two-dimensional geometric object that is made up of a finite number of sides that are connected end to end to create a closed shape.
We can find the difference in the areas of the polygons shown in the following way:
Area of Polygon 1: A = x + 5
Area of Polygon 2: A = 4x - 6
Finding their difference, we have:
(4x - 6) - (x + 5)
= 4x + 6 - x - 5
Collecting like terms, we have:
= 4x - x + 6 - 5
= 3x + 1
Thus, we see here that the difference in the areas of the polygon is =
3x + 1
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Supplementary angles
Answer: ∠EBJ
Step-by-step explanation:
Starting Angle: ∠EBH
Possible Supplement: ∠EBJ
a cube is cut into two pieces by a single slice that passes through point a,band c what shape is the cross section
If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross-section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.
What is meant by cross section?
The form we obtain by cutting a straight through an object is called a cross-section.
The shape of the cross section of a cube that is cut into two pieces by a single slice that passes through point A, B, and C depends on the location of these points on the cube.
If points A, B, and C are three nonadjacent vertices of the cube, then the cross section will be a triangle. Specifically, it will be an isosceles triangle with base equal to the length of the edge of the cube and legs equal to the distances between point A and the other two points B and C.
If points A, B, and C are three adjacent vertices of the cube, then the cross section will be a square. Specifically, it will be a square with side length equal to the length of the edge of the cube.
If points A, B, and C are not three nonadjacent vertices of the cube or three adjacent vertices of the cube, then the cross section will be a polygon with more than four sides, and its shape will depend on the location of the points A, B, and C on the cube.
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Calculate how far the village is north of O
Step-by-step explanation:
See image
Suppose that you are thinking about buying a car and have narrowed down your choices to two options.
The new-car option: The new car costs $31,000 and can be financed with a three-year loan at 7.19%.
The used-car option: A three-year old model of the same car costs $16,000 and can be financed with a four-year
loan at 5.89%.
What is the difference in monthly payments between financing the new car and financing the used car? Use
PMT=
[-(19]
The difference in monthly payments between financing the new car and financing the used car is
(Round to the nearest cent as needed.)
Answer:
To calculate the monthly payments for each option, we can use the PMT function in Excel or a financial calculator.
For the new car option:
Loan amount = $31,000
Interest rate (annual) = 7.19%
Loan term = 3 years
Number of payments = 3 x 12 = 36
Using the PMT function in Excel, we get:
PMT(7.19%/12, 36, -$31,000) = $966.59
For the used car option:
Loan amount = $16,000
Interest rate (annual) = 5.89%
Loan term = 4 years
Number of payments = 4 x 12 = 48
Using the PMT function in Excel, we get:
PMT(5.89%/12, 48, -$16,000) = $385.36
The difference in monthly payments between the two options is:
$966.59 - $385.36 = $581.23
Therefore, the difference in monthly payments between financing the new car and financing the used car is $581.23.
Step-by-step explanation:
The royal fruit company produces 2 types of drinks. The first type is 35% pure fruit juice,and the second type is 85%pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of each of the two existing type of drink must be used to make 150pints of a mixture that is 75% pure fruit juice
Answer:
We should use 30 pints of the first drink and 120 pints of the second drink
Step-by-step explanation:
Let x represent the number of pints of the first drink used
Volume of fruit juice in x pints = 35% of x = 0.35x
Let y represent the number of pints of the second drink used
Volume of fruit juice in y pints = 85% of y= 0.85y
Since the final mixture volume is 150 pints we get
x + y = 150 ..... [1]
If the final mixture has to contain 75% pure fruit juice, the volume of fruit juice in the mixture = 0.75 x 150 = 112.5 pints
Therefore
0.35x + 0.85y = 112.5 ...[2]
We will solve this set of simultaneous equations by making the coefficients of one of the variables equal and then subtracting to eliminate that variable
Multiply equation [1] by 0.35 to get the x coefficients equal
0.35 x [1]
=> 0.35(x + y) = 0.35(150)
=> 0.35x + 035y = 52.5 ... [3]
Subtract [3] from [2]:
[3] - [2] =>
0.35x + 0.85y - (0.35x + 035y) = 112.5 - 52.5
0.35x + 0.85y - 0.35x - 0.35y = 60
0x + 0.5y = 60
0.5y = 60
y = 60/0.5
y = 120
Therefore x = 150 - 120 = 30
Therefore we should use 30 pints of the first drink and 120 pints of the second drink
Write an equation for an ellipse centered at the origin, which has foci at
(
0
,
±
15
)
(0,±15)left parenthesis, 0, comma, plus minus, 15, right parenthesis and co-vertices at
(
±
8
,
0
)
(±8,0)left parenthesis, plus minus, 8, comma, 0, right parenthesis.
The equation of the ellipse is:
x²/64 + y²/289 = 1
How to determine the equation of an ellipse?The standard form of the equation of an ellipse with centered at the origin and major axis parallel to the vertical is:
x²/b² + y²/a² = 1
Coordinates of covertices are ( ±b, 0) = (±8, 0)
Coordinates of foci are (0, ±c) = (0, ±15)
Also c²= a²-b²
a² = b² + c²
a² = 8² + 15²
a² =289
a = √289
a = 17
Using x²/b² + y²/a² = 1:
x²/8² + y²/17² = 1
x²/64 + y²/289 = 1
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Complete Question
Write an equation for an ellipse centered at the origin, which has foci at (0,±15) and co-vertices at (±8,0)
Answer the following questions.
a) The number of weeks that she has been saving when she needs $277 is given as follows: 17 weeks.
b) The amount she will need after 5 weeks is given as follows: $505.
How to obtain the amounts?The function for this problem is defined as follows:
A(w) = 600 - 19w.
The output of the function is the amount remaining after w weeks.
Hence the number of weeks that she has been saving when she needs $277 is obtained as follows:
277 = 600 - 19w
19w = 600 - 277
w = (600 - 277)/19
w = 17 weeks.
The amount that she needs after 5 weeks is given as follows:
A(5) = 600 - 19 x 5
A(5) = $505.
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Find the exact value of x. (7 - 9).
Find the exact values of x and y. (10 - 12).
7. The exact values of x is 17.
8. The exact values of x is 12.
9. The exact values of x is 10.9.
10. The exact values of y is 15.
11. The exact values of y is 15.
12. The exact values of y is 6.
What is the exact value of x and y?
The exact values of x and y is calculated by applying Pythagoras theorem as follows;
7.
x² = 8² + 15²
x² = 289
x = √289
x = 17
8.
x² = 15² - 9²
x² = 144
x = √144
x = 12
9.
x² = 12² - 5²
x² = 119
x = √119
x = 10.9
The value of y is calculated as follows;
10.
y² = 12² + 9²
y² = 225
y = √(225)
y = 15
11.
y² = 17² - 8²
y² = 225
y = √(225)
y = 15
12.
y/10 = 6/10
y = 6
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