Answers
9514 1404 393
Answer:
(x, y) = (3, 12)
Step-by-step explanation:
The first step in any problem solving is to look at the problem. Here, we see that the first equation can be reduced to standard form by dividing it by 2. This would give both terms a coefficient of 1.
We see that the second equation already has a variable with a coefficient of 1.
When solving a system by substitution, it can save some effort if you start by finding a variable with a coefficient of 1 or -1. Since we see that in the second equation, we choose to solve the second equation for y:
y = 4x . . . . . . . add 4x to both sides of the second equation
Now, we have an expression for y that we can substitute into the first equation.
2x +2(4x) = 30 . . . . substitute for y
10x = 30 . . . . . . . . simplify
x = 3 . . . . . . . . . . divde by 10
y = 4(3) = 12 . . . . . find y using y=4x
The solution is (x, y) = (3, 12).
__
Additional comment
I doesn't matter what variable gets substituted. The purpose of the exercise is to reduce the number of variables in the equation. Here, we start with an equation that has 2 variables. Substituting for one of them gives an equation with only one variable, a lot easier to solve.
You don't have to find an expression for the "bare" variable. We could solve the second equation for 2x, for example: 2x = y/2, then substitute for 2x in the first equation: y/2 +2y = 30 ⇒ y = (2/5)(30) = 12. Or, we could solve the first equation for 2x and substitute into the second: 2x=30-2y, y-2(2x) = 0 ⇒ y-2(30-2y) = 0 ⇒ y = 60/5 = 12.
The substitution property of equality says you can make any substitution of equal values anywhere. "butter = margarine" means you can substitute butter for margarine, or vice versa, wherever you may wish.
Related Questions
Suppose that 100,000 men were screened for prostate cancer for the first time. Of these, 4,000 men had a positive result on the screening blood test; of those who tested positive, 800 had a biopsy indicating a diagnosis of prostate cancer. Among the remaining 96,000 men who screened negative, 100 developed prostate cancer within the following year and were assumed to be false negatives to the screen. a) set-up the two-by-two table for this data. (please provide an actual table) b) what is the prevalence of prostate cancer in this population? c) calculate and interpret the sensitivity of this screening test d) calculate and interpret the specificity of this screening test. e) Calculate and interpret the positive predictive value of this screening test.
Answers
An actual two-by-two table is a tabular representation containing two rows and two columns.
The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancerThe rows consist of the predicted positive screening and predicted negative values a)Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
b)The prevalence rate of prostate cancer in this population is:
[tex]\mathbf{ =\dfrac{900}{100000}}[/tex]
[tex]\mathbf{ =\dfrac{9}{1000}}[/tex]
= 9 per thousand.
c)
The calculation of the sensitivity of this screening is as follows:
[tex]\mathbf{=\dfrac{TP}{TP+PN_1}}[/tex]
where;
TP = True positive for cancerPN₁ = Predicted Negative for true positive cancer∴
[tex]\mathbf{=\dfrac{800}{800+100}}[/tex]
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
d)The calculation of the specificity of this screening is as follows:
[tex]\mathbf{=\dfrac{PN_2}{PN_2+TN}}[/tex]
where;
TN = True positive for cancerPN₂ = Predicted Negative for true negative cancer∴
[tex]\mathbf{=\dfrac{95900}{95900+3200}}[/tex]
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
e)
The positive predicted value of the screening test is computed as:
[tex]\mathbf{= \dfrac{TP}{TP + TN}}[/tex]
[tex]\mathbf{= \dfrac{800}{800 + 3200}}[/tex]
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
Learn more about tabular representation here:
https://brainly.com/question/8307968
An account earns simple interest. Find the annual interest rate. I = $60 P = $500 t = 2 years The annual interest rate is %. 10
Answers
Answer:
100
Step-by-step explanation:
A = P(1 + rt)
A = 500(1 + (0.1 × 2)) = 600
A = $600.00
600-500= 100
A square tile has sides of 20 cm how many tiles are needed to cover an area of 3 m by 1.8m
Answers
Answer:
135 tiles
Step-by-step explanation:
3 x 1.8 = 5.4 (m2)
20 cm = 0.2 m
0.2 x 0.2 = 0.04 (m2)
5.4 / 0.04 = 135 (tiles)
2
2
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Question 2 (1 point)
1) Listen
5
Opening an industry to international competition tends to:
O increase X-inefficiency.
O force lazy monopolists to increase efficiency.
O increase the incidence of lazy monopolists.
raise a monopolist's profit as the price is driven up.
Answers
Answer:
increse X-inefficiency is the answer
Step-by-step explanation: im here to help
is it 90 IF NOT CAN SOMEONE TELL ME please
Answers
Answer:
90Step-by-step explanation:
1000 + 500 = 1500mg (for 1 day)
1500 * 30 = 4500mg (1 month)
4500 : 500 = 90 tablets
The town of Winchester recently built an artificial body of Vater. This reservoir will store drinking water for the
town. Which of the following could cause contamination of the water and lead to human health-related problems
and loss of native species?
development of a water quality plan
B building a fence around the reservoir
C improvements to a water treatment facility
increased use of pesticides (chemicals) by farmers within the local watershed
Answers
Answer:
This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.
Step-by-step explanation:
Help. i need it ASAP
Answers
Answer:
The third choice is correct.
Step-by-step explanation:
A test has twenty questions worth 100 points. The test consists True/False questions worth 3 points each and multiple choice questions worth 11 points each. Howmany multiple choice questions are on the test?
Answers
Multiple choice questions = 5
True questions = 15
Given that:
Total number of questions = 20
Total worth of point = 100
Multiple choice questions (M) = 11 points each
True false questions (T) = 3 points each
Hence,
M + T= 20 ____(1)
11M + 3T = 100 ____(2)
M = 20 – T
Using the relation in (2)
11(20 – T) + 3T= 100
220 – 11T + 3T= 100
220 – 8T = 100
-8Tf = 100 – 220
-8T = – 120
T = 120/8
T = 15
Mc = 20 – 15
Mc = 5
Multiple choice questions = 5
True false questions = 15
The diner ordered 144 bagels. The order was for 80% plain 20% sesame bagels. An employee says that the diner should receive 43 sesame bagels. Explain whether the employee’s statement is sense (true) or nonsense (false).
Answers
Answer:
nonsense
Step-by-step explanation:
[tex]144\times0.2=28.8[/tex]
This employees statement is nonsense, as 43 sesame bagels is far more than the 29 they should expect when they order 20% of 144 bagels.
Answer:
it's nonsense. coz a person can't receive 43 sesame Bangles. it is not the actual number of sesame Bangles she should receive.
PLEASE HELP!!!!!!!!!!!!! ASAPPP
Answers
Answer:
JO !
Step-by-step explanation:
get he exponet out the way
\
that leaves you with 3+4x1
do 4x 1 that equals 4
3+ 4 = 7
Hey there!
3 + 4 × 1^2
= 3 + 4 × 1
= 3 + 4
= 7
[Jo is correct] whereas Mia is incorrect because she misunderstood the question.
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the volume of a cone
Answers
As a car ages, its value decreases. The value of a particular car with an original purchase price of $27, 200 is modeled by the following function, where
c is the value at time t, in years.
c(t) - 27, 200(1 -0.21)
a. What is the value of the car when it is 4 years old?
The value of the car after 4 years is Sl
b. What is the total depreciation amount after 5 years?
After 5 yehrs, the total depreciation amount is s[
Answers
a. The value of the car when it is 4 years old is approximately $13,645.23.
b. The car has depreciated by about $16,367.54 after 5 years.
To find the value of the car when it is 4 years old, we can substitute t = 4 into the given function:
c(4) = 27,200(1 - 0.21)^4
c(4) = 27,200(0.79)^4
c(4) ≈ 13,645.23
b. To find the total depreciation amount after 5 years, we need to find the difference between the original purchase price ($27,200) and the value of the car after 5 years. Using the function given, we can find the value of the car after 5 years by setting t = 5:
c(5) = 27,200(1 - 0.21)^5
c(5) = 27,200(0.79)^5
c(5) ≈ 10,832.46
Therefore, the total depreciation amount after 5 years is:
27,200 - 10,832.46 ≈ $16,367.54
For such more questions on value
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this can explain everything . please help
Answers
35 - 45 / 9 x 5
Divide 45 by 9 to get 5.
35 - 5 x 5
Multiply 5 and 5 to get 25.
35 - 25
Subtract 25 from 35 to get 10.
= 10
an amount ogf $3700 id deposited into an account that pays 8.25% confounded semi-annually. how much money eill you receive in 15 years
Answers
Answer: The answer is seventeen
Step-by-step explanation:
i just answered this question
an object has a mass of 24 grams and a volume of 6cm3. what is the density
Answers
Answer:
4 grams
Step-by-step explanation:
What correlations can you use when one or more of the variables are measured on an ordinal scale?
Answers
HEY
For variables at ordinal level use Spearman's correlation. However, Chi-Square is also suitable to use for test of significance with cross tabulation of ordinal level data
thank me later
carryonlearing
✨ jufaith ✨
I need help with this one. I will give someone brainliest.
Answers
I need help with this.
Answers
Answer:
check online for more information
Type the correct answer in each box.
Quadrilateral EBCD is an isosceles trapezoid with m∠EDC = 110°, m∠ABC = 133°, and m∠DEA = 114°.
m∠DEB = __°
m∠BCD= __°
m∠EAB= __°
Answers
Answer:
m∠DEB = _70_°
m∠BCD= _110_°
m∠EAB= _73_°
Step-by-step explanation:
To find ∠DEB:
Take the angle of ∠EDC, which is 110°. We know the total degree in a triangle is 180°. So, we do 180° - 110° to get 70°.
To find ∠BCD:
Because EBCD is an isosceles trapezoid, this means that ∠D and ∠C both have the congruent angles. Since we know ∠EDC is 110°, this means that ∠C is also 110°.
To find ∠EAB:
We know that m∠ABC is 133° and ∠DEA is 114°. However, both angles count both the triangle and trapezoid. Previously we figured out that ∠DEB is 70°. We'll take the angle of ∠DEA and subtract the angle of ∠DEB from it, which gets us 44°. To figure out the angle of ∠B, we take the angle of ∠ABC and subtract 70° or the angle of ∠DEB, which gets us 63°. Now we take the total degree of a triangle, 180° and minus both 44° and 63° from it, which is 73°.
- 2021 Edmentum
Allison was comparing the price of salmon at two stores. At SuperGrocery B, 0.5 pounds of salmon costs $2.77. The table below represents the total cost, in dollars and cents, yy, that it costs for xx pounds of salmon at SuperGrocery A.
Answers
Answer:
15.48
Step-by-step explanation:
When we divide 6.45 by 10, we get 0.645 so, we know that is the rate per 0.1 pound. We multiply 6.45 by 2 to get 12.9 and add 0.645 four times since it is 2.4 pounds and get 15.48.
Answer:15.48
Step-by-step explanation:
15.48
Evaluate the expression 3 x ; for x = 7
Answers
This would become 3(7) because of x = 7 in the original equation of 3x and the answer would be 21.
Answer:
3(7)= 21
Step-by-step explanation:
3 x
This means you are multiplying.
x = 7
3(7)= 21
What reaction did Pocahontas's people have to her helping the Jamestown colonists?
Answers
Answer:
They were very angry about her helping the colonists.
Step-by-step explanation:
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answers
Answer:
y = 2
Step-by-step explanation:
there is no slope but the line is at 2 so 2 is the y-intercept so y = 2.
co-efficint of (-xy²) in -5x³y²z⁴
Answers
[tex]-5x^3y^2 z^4 = 5x^2z^4(-xy^2)\\\\\text{The coefficient of}~ (-xy^2) ~\text{is }~ 5x^2 z^4.[/tex]
Can the sum of two palindromic numbers be another palindromic number?
Answers
Answer:
Every positive integer can be written as the sum of three palindromes, numbers that remain the same when their digits are reverse. For example, 389 = 11 + 55 + 323. This holds not just for base 10 but for any base b ≥ 5.
if (a+b)^2=54, and (a-b)^=46, then a^2+b^2=?
Answers
[tex](a+b)^2 =a^2 +b^2 + 2ab = 54~~~.....(i)\\\\(a-b)^2 = a^2 +b^2 -2ab = 46~~~.....(i)\\\\\\(i)+(ii):\\\\(a+b)^2 +(a-b)^2 = 54+46\\\\\implies a^2 +b^2 + 2ab + a^2 +b^2 - 2ab =100\\\\\implies 2a^2 +2b^2 =100\\\\ \\\implies 2(a^2 +b^2) =100\\\\\implies a^2 +b^2 = \dfrac{100}2 = 50[/tex]
Create your own example for each cases of multiplying
polynomials
Case 1: Distributive Property
Case 2: FOIL Method
Case 3: Binomial to Polynomial
Pls needed badly
If you have nothing to answer dont answer
Answers
Step-by-step explanation:
CASE 1:2x(3x+7) = 6x^2+14x.CASE 2:(2x + 3)(3x – 1)CASE 3:x2 + 4xGiven that f(x) = 4x V3x + 3 and g(x) = 2vx + 1, find x(*)(). х Ox3 20x +3 OxVx+3 +3 O 2x 73
Answers
Answer: The answer is the last option, Option D.
Solve.
Write an expression for the total cost (in dollars) of Sam's purchase if he buys x candies costing 39 cents each and y bars of chocolate cost $1.25 each.
a. (0.39 + x) ∙ (1.25 + y)
b. 0.39x + 1.25y
c. 1.64(x + y)
d. 39x + 1.25y
Answers
Answer:
the answer to the question is c
HELP!!!!
Solve, 4/9 - 4/10
Answers
Answer:
[tex]\frac{2}{45}[/tex]
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
4/10 times 9 = 36/90
40/90-36/90= 4/90 or 2/45 (simplified)
