The mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.
What is an insurance?
Let X be the random variable representing the amount of money the insurance company will lose on a policy. Then we can calculate the expected value (mean) of X and the standard deviation of X as follows:
Expected value:
E(X) = 30,000(1/1,000) + 10,000(1/250) + 0(1 - 1/1,000 - 1/250) = $142.00
The first term in the sum corresponds to the probability of a client dying (1/1,000) multiplied by the payout ($30,000), the second term corresponds to the probability of a client becoming disabled (1/250) multiplied by the payout ($10,000), and the third term corresponds to the probability of neither event occurring (1 - 1/1,000 - 1/250).
Standard deviation:
To calculate the standard deviation, we need to find the variance of X first:
Var(X) = [30,000 - E(X)]²(1/1,000) + [10,000 - E(X)]²(1/250) + [0 - E(X)]²(1 - 1/1,000 - 1/250)
= $1,547,797.56
The first term in the sum corresponds to the squared difference between the payout for a client dying and the expected payout, multiplied by the probability of a client dying, and so on for the second and third terms.
Then, we can take the square root of the variance to find the standard deviation:
SD(X) = √[Var(X)] = $1,243.67
Therefore, the mean amount of money the insurance company can expect to lose on each policy is $142.00 with a standard deviation of $1,243.67.
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You are sent to the local tea shop to pick up 12 drinks. You purchase 8 sweet teas and 4 unsweetened teas. Unfortunately, you forgot to label them. If you pick 3 drinks at random, find the probability of each event below. Give your answers as simplified fractions.
a) All of the 3 drinks picked are sweet teas.
b) Exactly one drink is sweetened.
a) The probability of picking a sweet tea on the first draw is 8/12. Since we did not replace the first tea, the probability of picking another sweet tea on the second draw is 7/11. Similarly, the probability of picking a sweet tea on the third draw is 6/10. Therefore, the probability of picking 3 sweet teas in a row is:
(8/12) * (7/11) * (6/10) = 0.2545 or 127/500
b) There are 3 ways to pick exactly one sweet tea: S U U, U S U, U U S, where S represents a sweet tea and U represents an unsweetened tea. The probability of picking a sweet tea on the first draw is 8/12, and the probability of picking an unsweetened tea is 4/12. Therefore, the probability of picking exactly one sweet tea is:
(8/12) * (4/11) * (3/10) + (4/12) * (8/11) * (3/10) + (4/12) * (3/11) * (8/10) = 0.4364 or 48/110
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
The first and second one
Step-by-step explanation:
Since they are one-to-one functions, the first table and the first graph (under the table) are the answers.
Be sure to mark this as brainliest and hope this helps!
Answer: The first one and second one.
Step-by-step explanation:
It's a bit cut-off but for the very first function, each x-value has a corresponding y-value so it is a function. For the second one (the graph), if we do the vertical line test, it will pass it (vertical line touches only one point of the function). The third one (the loop graph) , however, will not pass the vertical line test as there's a point on the graph where if we were to draw a vertical line, it would be touch 2 or 3 points of the function.
In October, Meg's pumpkin weighed 3 pounds and 11 ounces. In November, it weighed 8 pounds and 2 ounces. How many more ounces did it weigh in November?
Result:
The weight of the pumpkin in November = 71 ounces more than in October.
How to compare the weights?
To compare the weights, we need to convert both weights to the same unit of measurement, either pounds or ounces.
Let's convert the first weight, which is 3 pounds and 11 ounces, to ounces:
3 pounds = 3 x 16 = 48 ounces
11 ounces = 11
So the first weight is 48 + 11 = 59 ounces.
Now, let's convert the second weight, which is 8 pounds and 2 ounces, to ounces:
8 pounds = 8 x 16 = 128 ounces
2 ounces = 2
So the second weight is 128 + 2 = 130 ounces.
To find how many more ounces the pumpkin weighed in November, we subtract the October weight from the November weight:
130 - 59 = 71
Therefore, the pumpkin weighed 71 more ounces in November than it did in October.
Solve the following showing all steps. (x+6)2=8
Expanding the left-hand side of the equation, we get:
(x+6)2 = (x+6)(x+6) = x(x+6) + 6(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36
So now we have the equation:
x^2 + 12x + 36 = 8
Subtracting 8 from both sides, we get:
x^2 + 12x + 28 = 0
We can factor this quadratic equation as:
(x+2)(x+14) = 0
This gives us two possible solutions:
x+2 = 0, so x = -2
x+14 = 0, so x = -14
Therefore, the solutions to the equation (x+6)2 = 8 are x = -2 and x = -14.
Step-by-step explanation:
Here is one way :
(x+6)^2 = 8 Take the square root of both sides
x+6 = +- sqrt 8
x = -6 +- sqrt8 = -6 + 2 sqrt 2 or -6 - 2 sqrt 2 = - 3.17 or - 8.83
Just before the presidential election in November 2016, a local newspaper conducted a poll of registered voters in a large city and found that 120 out of a random sample of 250 men intended to vote for Donald Trump and 132 out of a random sample of 240 women intended to vote for Donald Trump.
(a) is there convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a=0.05 significance level?
(b) based on your conclusion in part (a), which mistake, a type i error or a type ii error, could you have made? interpret this error in context
(c) a 95% confidence interval for the difference (men - women) in the proportion of all men and the proportion of all women in this city who intended to vote for trump is (-0.158. 0.018). based upon the interval, is there convincing evidence to support the claim that a greater proportion of women than men intended to vote for trump?
(d) give one way to increase the power of the test other than increasing the sample sizes. what is a drawback of making that change?
With a p-value of 0.022, there is convincing evidence of a difference in the proportion of men and women who intended to vote for Trump in the city. Type I error could have been made. No, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump. Increasing the significance level would increase power, but would also increase the likelihood of making a Type I error.
We can use a two-sample z-test to test for the difference in proportions between men and women who intended to vote for Trump.
Let p1 be the proportion of men who intended to vote for Trump and p2 be the proportion of women who intended to vote for Trump. Then the null and alternative hypotheses are
H0: p₁ = p₂
Ha: p₁ ≠ p₂
We can calculate the pooled sample proportion
p = (x₁ + x₂) / (n₁ + n₂)
= (120 + 132) / (250 + 240)
= 0.508
where x₁ = 120, x₂ = 132, n₁ = 250, and n₂ = 240.
We can calculate the test statistic
z = (p₁ - p₂) / √(p * (1 - p) * (1/n₁ + 1/n₂))
= (0.48 - 0.55) / √(0.508 * 0.492 * (1/250 + 1/240))
= -2.29
Using a standard normal distribution table, the p-value for a two-tailed test with a test statistic of -2.29 is 0.022. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.
The mistake we could have made is a type I error, which is rejecting the null hypothesis when it is actually true. In this case, it would mean concluding that there is a difference in proportions between men and women who intended to vote for Trump when there is actually no difference.
The confidence interval for the difference in proportions is (-0.158, 0.018), which includes 0. Since 0 is in the interval, we cannot reject the null hypothesis that there is no difference in proportions between men and women who intended to vote for Trump.
Therefore, based on the interval, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump.
One way to increase the power of the test is to decrease the significance level (i.e., increase the alpha level). This would allow us to reject the null hypothesis more easily and increase the chance of detecting a true difference in proportions.
However, the drawback of making this change is that it increases the chance of making a type I error, which means rejecting the null hypothesis when it is actually true.
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For a standard normal distribution, find the approximate value of P(-0.41)<=z<=(0.73).
. Use the portions of the standard normal table below to help answer the question
a. 43%
b. 34%
c. 57%
d. 45%
For a standard normal distribution, the approximate value of
P(-0.41) ≤ z ≤ (0.73) is 43%.
Option A is the correct answer.
We have,
To find the approximate value of P(-0.41) ≤ z ≤ (0.73) for a standard normal distribution, we need to use the standard normal table.
Looking at the table,
The value of P(Z ≤ 0.73) = 0.7673.
The value of P(Z ≤ -0.41) = 0.3409.
To find the value of P(-0.41) ≤ Z ≤ (0.73),
We need to subtract P(Z ≤ -0.41) from P(Z ≤ 0.73):
P(-0.41) ≤ Z ≤ (0.73) = P(Z ≤ 0.73) - P(Z ≤ -0.41)
P(-0.41) ≤ Z ≤ (0.73) = 0.7673 - 0.3409
P(-0.41) ≤ Z ≤ (0.73) = 0.4264
Rounding this value to the nearest whole percent, we get 43%.
Therefore,
For a standard normal distribution, the approximate value of
P(-0.41) ≤ z ≤ (0.73) is 43%.
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Analyze and solve the word problem
An elephant at Emirates Park and Zoo weighs 200 pounds at birth and gains approximately 2 pounds per day. The
function w = 2d +200 represents the weight w of an elephant on a given day during his first year.
How much more does an elephant weigh on Day 60 than it does on Day 5?
An elephant weighs 110 pounds more on Day 60 than it does on Day 5
Here, function w = 2d +200 represents the weight w of an elephant on a given day during his first year.
From above function , the weight of an elephant on Day 60 would be,
w₆₀ = 2(60) + 200
w₆₀ = 120 + 200
w₆₀ = 320 pounds
and the weight of an elephant on Day 5 would be,
w₅ = 2(5) + 200
w₅ = 10 + 200
w₅ = 210
The difference between these weights is:
w = w₆₀ - w₅
w = 320 - 210
w = 110 pounds
Therefore, an elephant weighs 110 pounds more on Day 60 than on Day 5
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Use z scores to compare the given values.
<
The tallest living man at one time had a height of 222 cm. The shortest living man at that time had a height of 98.4 cm. Heights of men at that time had a mean of
171.59 cm and a standard deviation of 5.47 cm. Which of these two men had the height that was more extreme?
Since the z score for the tallest man is z- and the z score for the shortest man is z-. the
(Round to two decimal places.)
man had the height that was more extreme.
the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.
To answer this question, we need to use standardized values, and we can obtain them using the formula:
z = (x - μ)σ .. [1]
Where,
x is the raw score we want to standardize.
μ is the population's mean.
σ is the population standard deviation.
A z-score "tells us" the distance from in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.
In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.
Heights of men at that time had:
μ = 171.59 cm
σ = 5.47 cm.
Let us see the z-score for each case:
Case 1: The tallest living man at that time
The tallest man had a height of 222 cm.
Using [1], we have (without using units):
z = (x - μ)σ
z = (222 - 171.59)/5.47
z = 50.41 / 5.47
z = 9.21
That is, the tallest living man was 9.21 standard deviation units above the population's mean.
Case 2: The shortest living man at that time
The shortest man had a height of 98.4 cm.
Following the same procedure as before, we have:
z = (x - μ)σ
z = (98.4 - 171.59)/5.47
z = - 13.38
That is, the shortest living man was 13.38 standard deviation units below the population's mean (because of the negative value for the standardized value.)
The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in standard deviation units more than the tallest man.
Then, the more extreme height was the case for the shortest living man (13.38 standard deviation units below the population's mean) compare with the tallest man that was 9.21 standard deviation units above the population's mean.
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Maths
Find y using the graph
Answer:
y = 4x² -8x +10
Step-by-step explanation:
You want to write the equation y = 4(x -1)² +6 in standard form.
Distributive propertyThe distributive property is used to eliminate parentheses.
y = 4(x -1)² +6 . . . . . . given equation
y = 4(x -1)(x -1) +6 . . . . . the meaning of the exponent of 2
y = 4((x(x -1) -1(x -1)) +6 . . . . . distributive property applied once
y = 4(x² -x -x +1) +6 . . . . . . . . . . distributive property applied again
y = 4(x² -2x +1) +6 . . . . . . collect terms inside parentheses
y = 4x² -8x +4 +6 . . . . . . . distributive property applied
y = 4x² -8x +10 . . . . . . . . . collect terms
Find the slope of the line shown belowpp
Answer: the slope is 6
Step-by-step explanation: the line y=6x-3
10. Mary just bought solar panels that cost $2,000 and will reduce her electricity bills by $40 per month. How long will it take her to recoup her investment in the panels if she can earn 12% interest, compounded monthly, on her money?
* Mary's solar panels cost $2,000.
* The panels will reduce her monthly electricity bill by $40.
* She can earn 12% interest compounded monthly.
* So her monthly savings is $40
* And her 12% monthly interest rate is 12% / 12 = 1% per month.
* So each month her balance grows by 1% of the current balance.
* Let's think through this step-by-step:
* Initial balance = $2,000 (from paying for the solar panels)
* Month 1:
** Savings = $40 (from lower electric bill)
** Interest = 1% of $2,000 = $20
** Balance after Month 1 = $2,000 + $40 + $20 = $2,060
* Month 2:
** Savings = $40
** Interest = 1% of $2,060 = $20
** Balance after Month 2 = $2,060 + $40 + $20 = $2,120
* Month 3: (continue the calculations for Months 3 through 24)
** Savings = $40
** Interest = 1% of $2,121 = $21
** Balance after Month 3 = $2,121 + $40 + $21 = $2,182
* After 24 months, the balance is $3,149 (calculated step-by-step as shown above)
* The initial investment was $2,000
* So it took about 24 months to recoup her investment.
Does this help explain the steps? Let me know if you have any other questions!
In an experiment, the probability that event A occurs is 1 3 , the probability that event B occurs is 5 6 , and the probability that events A and B both occur is 1 5 . What is the probability that A occurs given that B occurs?
Note that where the above events are described, the probablity of A occurring given that B occurrs is 6/25.
How did we arriave at that?We can use Bayes' theorem to find the conditional probability
P (A| B) = P(A and B ) / P( B)
From the problem statement, we know that P(A) = 1/3,
P(B) = 5/6, and
P (A and B) = 1/5.
Substituting to get .....
P(A | B) = (1/5) / (5/6)
= 1/5 x (6 /5)
= 6/25
Hence, we are corect to state that the probability of A occurring given that B occurs is 6/25.
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Find the square root of 3 whole numbe 6 over 25
The value of the square root 3 6/25 is 1⅘
What is square root?The square root of a number is a value that can be multiplied by itself to give the original number. For example the square root of 225 is 15.
Another example is the square of 16, which can be gotten by finding the prime product of 16
16 = 2×2×2×2. we can group the 2s into two i.e (2×2) × (2×2) . We can now take one out of 2 .
= 2 × 2 = 4. Therefore the the square root of 16 is 4.
Therefore the square root of 3 6/25 can be found by converting the fraction into improper fraction.
= 81/25
therefore the √81/25 = 9/5 = 1⅘.
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please answer this question
The quadrilateral ABCD is trapezoid.
What is trapezoid?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezium. It can have congruent sides (isosceles) and right angles (a right trapezium), but neither is necessary.
Here in the given figure ,
[tex]\overline{AD}=\overline{BC}[/tex] are parallel to each other.
We can make right angle using ABC.
Hence the given quadrilateral ABCD is trapezoid.
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10 yd
17 yd
4 yd.
Find the surface area of the prism
The surface area of the rectangular prism is 502 mm²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²
The surface area is 502 mm²
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How many of each size of cube can fill a 1-inch cube: Edge= 1/4 inch
Please help and if answer please give how you solved it
The number of cubes needed with an edge length of 1/3 inches is needed to build a cube with an edge length of 1 inch is 27.
We have,
the edge length of smaller cube, a = 1/3 inches
the edge length of the cube to be built, S = 1/3 inches
Now, Volume of cube = a³
= (1/3)³
= 1/27 in³
Volume of the cube to be build = S³
= 1³
= 1 in.³
Thus, Cubes of smaller length are needed for the larger cube
= 1/ (1/27)
= 27
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Use the information in the charts to answer the questions.
Barbara- 3 3/10
Donna - 2 4/5
Cindy - Find
Nicole - 2 1/10
1. The four girls ran in a relay race as a team. Each girl ran one part of
the race. The team’s total time was
3 11 /5 minutes. What was Cindy’s
time?
2. Find the difference between the fastest girl’s time and the slowest
girl’s time.
3. To break the school’s record, the girls’ time had to be faster than
2 12/5 minutes. Did the girls break the record? If so, how much faster were
they? If not, how much slower were they?
Answer:
Step-by-step explanation:
...
...
..
..
......
Find a.the mean b.the median wage
The mean is 4746
The median wage is #4618
The wages for the five local government trainees are
#4,166, #4,618, #3,742, #5,838 and #5,366
= 4166+ 4618+ 3742+5838+5366/5
= 23,730/5
Mean = 4,746
The median wage is
Arrange the wages orderly
3,742, 4166, 4618, 5366, 5838
The median wage is #4618
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What is the volume of a cube whose edges can have a measure of 1.8 inches
The volume of the cube will be 5.832 cubic inches.
The volume of a cube is given by the formula V = s³, where s is the length of one of its edges.
In this case, the length of one edge is given as 1.8 inches.
So, substituting s = 1.8 inches in the formula, we get:
V = s³ = 1.8³ = 5.832 cubic inches
Therefore, the volume of the cube is 5.832 cubic inches.
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Please help me with this question!!!
Charlie works as a salesperson and receives a monthly salary of $2,000 plus a commission of $100 for every item that they sell. Find the model of Charlie's monthly pay, using P for pay and q for the number of items they sell in a month.
Enter your answer as a formula including "P(q)="
(do not include the dollar sign)
Step-by-step explanation:
Charlie's monthly pay, P, can be represented as a linear function of the number of items sold, q. The monthly salary of $2,000 represents the y-intercept of the line, and the commission of $100 per item sold represents the slope of the line.
Thus, the model for Charlie's monthly pay, P(q), can be expressed as:
P(q) = 100q + 2000
where q is the number of items sold in a month, and P(q) is Charlie's monthly pay in dollars.
A soft drink machine outputs a mean of 24
ounces per cup. The machine's output is normally distributed with a standard deviation of 3
ounces. What is the probability of filling a cup between 26
and 27
ounces?
2/7
Assuming I know what standard deviation is, it is there is a 3 ounce "range" that the machine can give, based on that 24 oz mean. So there can be 21,22,23,24,25,26, and 27. Out of those 7, 2 are the numbers we are looking for, so it is 2/7.
Look at image on top pls help quickly
Based ont he the function y = - 2x + 5 + 2x - 5 is given ,
if x < -2.5, y = 0
i f x > 2.5, y = 0
if -2.5 ≤ x ≤ 2.5 = 0
How did we reach this conclusion ?Without the absolute value symbols
y = -2x + 5 + 2x - 5
Where x < - 2.5
y = -2 (-2.5) + 5 + 2 (-2.5 ) - 5
y = 5 + 5 + (-5)-5
y = 0
Where x > 2.5
y = -2 (2.5) + 5 + 2(2.5) - 5
y = 0
Where -2.5 ≤ x ≤ 2.5
y = -2x + 5 + 2x -5
grouping like terms we have
-2x + 2x +5 -5
y = 0
thus, Where -2.5 ≤ x ≤ 2.5
y = 0
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Given this equation what is the value of x at the indicated point?
Answer:
x = -1
Step-by-step explanation:
You will plug in 8 for y then solve for x:
[tex]\frac{12}{3} = (x-1)^2\\4 = (x-1)^2\\\frac{+}{-}2 = x-1 \\ x= +3, and -1[/tex]
Then the answer is -1 because the graph shows the point in the 2nd quadrant meaning x is negative
Solve for the angles of the triangle described below. Express all angles in degrees and round to the nearest hundredth.
a = 9,b= 5, c = 7
The angles of the triangle are:
A = 95.7°, B = 33.6°, C = 50.7°.
What are the angles of the triangle?
The area created between two of a triangle's side lengths is known as the angle. Both internal and external angles are present in a triangle. In a triangle, there are three interior angles. When the sides of a triangle are stretched to infinity, exterior angles are created.
Here, we have
Given: a = 9, b= 5, c = 7
We have to find all angles in degrees.
Using law of cosines, a² = b²+c² - 2bc cos(A),
9² = 5²+7² - 2(5)(7) cos(A)
81 = 25 + 49 - 70 cos(A)
7 = -70 cos(A)
cos(A) = -7/70
cos(A) = -1/10
A = cos⁻¹(-1/10)
A = 95.7°
Now, using the law of sines,
[sin (A)]/(a) = [sin (C)]/(c)
[sin (95.7°)]/(9) = [sin (C)]/(7)
0.9955/9 = sin (C)/(7)
0.7742 = sinC
C = sin⁻¹(0.7742)
C = 50.7°
The sum of all the angles of a triangle= 180°
A + B + C = 180°
95.7° + B + 50.7° = 180°
B = 33.6°
Hence, the angles of the triangle are:
A = 95.7°, B = 33.6°, C = 50.7°.
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The table below shows the earnings, in thousands of dollars, for three different commissioned employees.
Employee #1
Employee #2
Employee #3
$2,000 - 3% on all
7% on all sales
5% on the first $40,000
sales
8% on anything over
$40,000
December
4.4
5.6
5.2
January
3.5
3.85
3.6
February
4.7
4.9
4.4
Which employee did not have the same dollar amount in sales for the month of February as the other two employees?
a. Employee #1.
b.
Employee #2
c. Employee #3
They each had the samè dollar amount in sales.
I am pretty sure the answer is b. emplyee 2# but im not 100% sure since your graph is really weird and hard to uunderstand
Prove that (A-B)xC=(AXC)-(BXC)
Step-by-step explanation:
supposedly
A=3
B= -2
C=2
(3-(-2)×2=(3×2)-(-2×2)
5×2=6-(-4)
10=6+4
10=10
Complete each ordered pair so that it is a solution of the given linear equation.
y=1/4×−8; (4, ), ( ,−11)
The first ordered pair is (4, )
The second ordered pair is ( ,-11)
Answer:
(4, -3)
(-28,-11)
Step-by-step explanation:
y = [tex]\frac{1}{4}[/tex] x - 4 Substitute 4 for x
y = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex] - 4 another name of 4 is [tex]\frac{4}{1}[/tex]
y = 1 - 4
y = -3
(4,-3)
y = [tex]\frac{1}{4}[/tex] x - 4 Substitute -11 for y
-11 = [tex]\frac{1}{4}[/tex] x - 4 Add 4 to both sides
-11 + 4 = [tex]\frac{1}{4}[/tex]x - 4 + 4
-7 = [tex]\frac{1}{4}[/tex]x Multiply both sides by 4
-7(4) = [tex]\frac{1}{4}[/tex][tex](\frac{4}{1})[/tex]x
-28 = x
(-28,-11)
Helping in the name of Jesus.
2x + y = 7
x + y = 1
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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I am 41 years old. I am 24 years older than double my elder son's age. How old is my elder son?
Answer:
8.5 yrs
Step-by-step explanation:
parent: 41 yrs
eldest son: x
Firstly, we will need to subtract 24 from 41 to get 2x the eldest son's age.
By doing that, we will have an equation that looks like this:
41-24=2x
This equation would basically get us through the whole problem.
Simplify the equation:
17=2x
x=8.5
The eldest son's age is 8.5.
Let's check our work!
8.5 x 2 = 17
17+24=41 (parent's age.)
Hope this helps :)
this is what I don’t know
Answer:
84 degrees for number 6
Step-by-step explanation:
the area of a circle is 360 degrees, so just subtract the other angles by 360 i think that's how you do it