The required solution to the given system of equations is (3,1) using the substitution method.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The system of given equations following as:
y = - 2x + 7 ....(i)
y = 3x - 8 ....(ii)
We have to determine the solution to the given system using substitution or elimination.
The required solution using the substitution method would be as;
Substitute the value of the equation y = 3x - 8 in equation (ii), and solve for x
3x - 8 = - 2x + 7
3x + 2x = 7 + 8
5x = 15
x = 15/5
x = 3
Substitute the value of x = 3 in equation (ii), and solve for y
y = 3(3) - 8
y = 9 - 8
y = 1
Thus, the solution to the given system of equations is (3,1).
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A farmer has found that in a typical year they earn $75000 from their harvest. In a wet year they earn $48000, and in a drought they earn $26000. If the probability of a wet year is 0.30 and the probability of a drought is 0.20 find the mean amount this farmer will make from their harvest over a long period of years. If the farmer has the option of buying insurance for $2000 a year that pays $20000 in a year of a drought, does it make sense financially to buy the insurance? Justify.
Answer:
1. The mean amount that this farmer will earn over a long period of years is:
$57,100
2. It makes sense financially for the farmer to buy the insurance. In a year of drought, he earns only $5,200. If he spends on insurance premium, his earnings are reduced by $2,000 to $3,200 but the insurance reimbursement will take his overall net earnings to $23,200 ($3,200 + $20,000). Incurring the insurance expense is highly justified.
Step-by-step explanation:
Earnings in a typical year = $75,000
Earnings in a wet year = $48,000
Earnings in a drought = $26,000
Pro
Typical Wet Drought
Earnings $75,000 $48,000 $26,000
Probability 0.50 0.30 0.20
Expected
earnings $37,500 $14,400 $5,200
Mean earnings = $57,100
Insurance expense $2,000
Net earnings after insurance expense $3,200
Insurance Reimbursement $20,000
Net earnings $23,200
According to the report by the government-lending institution, college students who have credit cards have an average credit card balance of $1,076. A random sample of 40 college students was selected, and their average credit card debt was found to be $1,436. Assume the standard deviation for student credit card debt is $276. Using α=0.10 to complete parts a and b below.
a. Does this sample provide enough evidence to challenge the findings by Sallie Mae?
b. Determine the p-value for this test.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Population mean (μ) = 1076
Sample mean (m) = 1436
Number of samples (n) = 40
Population standard deviation (sd) = 276
α=0.10
Null: μ = 1076
Alternative : μ > 1076
This is a right tailed test;
Reject null;
If z > z0.10
Z0.10 = 1.28 ( right tailed)
Test statistic (z) :
(m - μ) / (σ / √n)
(1436 - 1076) / (276 / √40)
360 / 43.639431
= 8.249
Since
8.249 > 1.28
We reject the null.
B) using the p value calculator from Zscore and alpha level
Zscore = 8.249 ; α=0.10, one tailed
P value < 0.00001
Which shoes that result is significant at 0.10
Maria fills up a tank of water at 10 gallons per hour. How many gallons of water does she fill up the tank in 15 minutes?
Answer:
2.5 gallons in 15 minutes
Step-by-step explanation:
10/60=1/6 gallon per minute
1/6*15=2.5
rafael counted a total of 40 white and yellow cars. there are 9 times as many white cars as yellow cars. how many white cars did rafael count.
Answer:
360
Step-by-step explanation:
40 times 9 = 360
there are 360 yellow cars
or we can do it like this
360 divided by 9 = 40
or 360 divided by 40 = 9
pls mark me brailest for real :,,(
Answer:
360
Step-by-step explanation:
9 x 40 = 360
If you divide 360 by 9 it will give you 40,
or if you divide 360 by 40 it will give you 9.
Question 3
1 pts
The three angles of a triangle add up to 180°. If two angles are 57and 8what is the measure of the third angle?
39
96
141°
123
Answer:
39
Step-by-step explanation:
assuming the angles are 57 & 84
141 + 57 > 180
123 + 57 = 180 (no room for an 8)
96 + 57 = 153
180 - 153 = 27 (an 8 doesn't work for this answer)
57 + 39 = 96
180 - 96 = 84 ( we have a winner!)
Arlo bought a salad for $8 and 3 hamburgers. His total was
$29. How much did each burger cost?
Answer:
Each hamburger cost 7 dollars.
Mrs. Totino makes her own spaghetti sauce. If she buys 24 cans of tomatoes, and
each can weighs 79.254 grams, what is the total weight of the cans?
Well, this is easy and rather basic in my opinion. If you open a calculator and multiply 79.924 by 24, you come out with 1,902.96 grams. If you wanted to convert it into pounds, it would be 4 pounds.
Divide X^2-14x+45 by x-9
Answer:
x + 5
Step-by-step explanation:
Answer: [tex]$x-5$[/tex]
Step-by-step explanation:
Factoring [tex]$x^2-14x+45$ gives us $(x-9)(x-5)$. Cancelling we get our desired answer, $\boxed{x-5}$.[/tex]
Tiyanna received 90 votes for class sweetheart. The amount of votes she received were 30 more than 4 times the amount that Dominique . Write and equation that demonstrates the relationship between the amounts Tiyanna and Dominique received.
Answer:
30x4
Step-by-step explanation
the answer is 120
The Powerball lottery jackpot has a winning probability of 1/189,000,000. If you only consider the options of winning the jackpot ($100,000,000) or losing, what the is the mean value of a ticket that costs $2 to buy? At what point does the mean value of a ticket become positive?
Answer:
In this case, we can write the mean value as:
MV = ∑pₙxₙ - $2
Where pₙ is the probability of event xₙ
in this case we consider only two events:
x₁ = winning $100,000,000, p₁ = 1/189,000,000
x₂ = not winning (or winning $0.0), p₂ = 1 - p₁.
Then the mean value of the ticket is:
MV = $100,000,000*1/189,000,000 + 0*(1 - 1/189,000,000) - $2 = $0.53 - $2
MV = -$1.47
b) At what point the mean value becomes positive?
Well, if the ticket costs less than $0.53, the value would become positive.
if we also consider other possible prices, we will have other positive components in the sum above, then the mean value may become positive.
Now, you may notices that it does not matter if you buy N tickets, the mean value will always be negative becuase:
MV = N*$0.56 - N*$2 = N*-$1.47
This is because yes, as more tickets you buy, the more probabilities of winning the prize you have, but if you buy N tickets, you need to pay N times $2, so the mean value actually decreases.
Miles per day if you walk 6 2/3 miles in 3 days
Answer:
2.22 miles
Step-by-step explanation:
Order these numbers from least to greatest.
9.7082, 9.8, 7.938, 9.78
Answer:
Step-by-step explanation:
7.938, 9.7082, 9.78, 9.8
a
Negative
b
Zero
c
Positive
d
Undefined
What is A−1? Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
Step-by-step explanation:
ooo matrics um if you give me a second ill solve it
Which statements describe the functions? Check all
Answer: A,b,e
A:Each successive output is the previous output divided by 3.
B:As the domain values increase, the range values decrease.
E:The range of the function is all real numbers greater than 0.
These are the answers on e2020. Hope this helps
Solve for x.
4x + 5 = 25
x=7 1/2
x = 5
x= 2 7/9
x = 2 1/2
What is the slope of the line that passes through the points(2,−3) and (2, 13) ?
Answer:
The slope would be undefined (16/0)
Step-by-step explanation:
(2, -3) and (2, 13)
13- -3 = 16
2-2 = 0
16 divided by 0 is undefined on a calculator so, undefined is the answer unless you weren't asked to simplify the answer then it would be 16/0.
The Palm Beach High Swimming Team is holding a car wash to raise money
for the team's banquet. All of the supplies for the car wash were donated by
parents of the team members. The graph below represents the situation.
SWIM TEAM CAR WASH
How much did the swim team charge for each car that it washed?
How much money did the swim team have in its account before the car wash?
If the team wants to earn $300, how many cars do they need to wash?
Answer:
Step-by-step explanation:
From the graph attached,
Relation between the amount of money raised and number of car washed is represented by a straight line.
Let the equation of the line is,
y = mx + b
where m = slope of the line = charges for each car wash
b = y-intercept = Initial amount the team have before the car wash.
Slope of the line will define the charges of car wash for each car.
Since, slope of the line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (0, 100) and (10, 150) will be,
m = [tex]\frac{150-100}{10-0}[/tex]
m = 5
Therefore, charges of each car wash will be = $5
y-intercept of the line 'b' = 100
Equation of the line will be,
y = 5x + 100
If team wants to earn $300,
300 = 5x + 100
5x = 200
x = 40
Therefore, 40 cars will be needed to wash by the swim team to earn $300.
1) The amount of money the swim team charged for each car that it washed is; $5 per car
2) The amount of money that the swim team had in its account before the car wash is; $100
3) If the team wants to earn $300, then number of cars they need to wash is; 40 cars
We know that formula for slope between two points is;
m = (y₂ - y₁)/(x₂ - x₁)
Let us take 2 coordinates from the given graph which are;
(10, 150) and (30, 250)
Thus;
m = (250 - 150)/(30 - 10)
m = 100/20
m = 5
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
From our graph, the y-intercept is 100. Thus, equation of the line of the graph is;
y = 5x + 100
A) From our equation y = 5x + 100, we can say that number of cars are x and as such amount charged per car is $5 per car.
B) The amount of money the swim team had before washing cars is when the value of x is 0. Thus;
y = 5(0) + 100
y = $100
C) The team wants to earn $300 and so we will plug 300 for y into y = 5x + 100 to get;
300 = 5x + 100
5x = 300 - 100
5x = 200
x = 200/5
x = 40 cars.
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if you toss a die (1), what is the probability of getting the number 5 NOT coming up?
Answer: .833333
Step-by-step explanation:
5/6
You could get a 1, 2, 3, 4, 6
So 5 in total over 6 options
Is 3.777777... a rational number?
Answer:
3.777777777.... is a rational number
Step-by-step explanation:
3.777777777777777.............
Try this trick: for all (something)/9 is its repeat. Example: 7/9 = 0.77777....
so 3.777777.... is 3 7/9
So technically it is a rational number
The Sun has a greater influence on Earth's tides than the Moon.
True
False
Answer:
false.
look at the image
hope this helps
Answer: False
Step-by-step explanation: The moon controls earths oceans tides. The sun only controls about 44% of the tides whilst the moon controls the other 56%. Simply just gravitational pull, the moon is closer to earth than the sun
Using the coordinate system, translate the point (-3, -5) using the rule, x->+2 and y->+2, then using the answer, describe the movement vertically and horizontally on the coordinate system.
Answer:
Step-by-step explanation:
Translated point (-1,-3). The point moved to the right 2 (horizontal) and up 2 (vertical).
The coordinate of translated point would be (-1,-3) and its movement is vertically upside and horizontally right side of the coordinate system.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
The original coordinate is (-3, -5).
Translate the point (-3, -5) using the rule, x→+2, and y→+2,
The coordinate of translated point would be (-3+2, -5+2) = (-1, -3).
Here the movement is vertically upside and horizontally right side of the coordinate system.
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I need help with this question‼️
Answer:
123
Step-by-step explanation:
Angle 1 and angle 3 are vertical angles, which are congruent.
So, if angle 1 is 123, then angle 3 is also 123.
show your work
21 = −7n
Answer:
It would equal -3
Step-by-step explanation:
you are trying to find how to get a positive 21 so you would have to divide 21 by -7
21 ÷ -7 = -3
to make sure it's correct muiltply it
-7 × -3 = 21
So therefore n = -3
h-1=5h+3h-8 i need help with this ASAP
Answer:
1 = h
Step-by-step explanation:
h-1=5h+3h-8
Combine like terms
h-1 = 8h-8
Subtract h from each side
h-1-h = 8h-8-h
-1 = 7h-8
Add 8 to each ide
-1+8 = 7h
7 =7h
Divide by 7
7/7 =7h/7
1 = h
9. The
divides a segment into two
segments.
segment, additional
midpoint, congruent
ray, equal
line, broken
Answer:
it would be the midpoint
please help me! i need the answer really quick!
Answer:
The average of the grade is 7.
Step-by-step explanation:
Add all of the grades up then divide by the number of grades there are
8+8+5=21
21÷3=7
Have a blessed day! I hope my answer was helpful!!
Answer:
The answer is 7
Step-by-step explanation:
So, we need to distribute the mean, (AKA:) average.
There is a rule when finding the average of numbers.
That rule is:
Adding all of the numbers together and dividing that sum by how many numbers there are in total that you added together.
1. First, we to add 8 and 8.
2. 8 + 8 = 16
3. Next, we need add to 5 to that 16.
4. 5 + 16 = 21
5. Since we have 3 numbers, we need to divide that 21 by 3.
6. 21 / 3 = 7
Thus showing that our answer is 7.
When trying to find the mean of numbers, always remember the rule of finding the average.
What is b/2+c=d equal to, please give me the full steps.
Answer:
ou can deduce what should (a+b+c)2 be using same reasoning..
(a+b+c)2=a2+ab+ac+ab+b2+bc+ac+bc+c2
=a2+b2+c2+2ab+2bc+2ca
Now the question is what is (a+b+c+d)2=?
Do I need to tell you ? Or you can figure it out ?
(a+b+c+d)2
Step-by-step explanation:
oops i put it all in the answer but heres your answer
What angle is this? ....
Please help
Find the slope between (2,4) and (5,8).
Answer:
Not sure what you exactly need, so I'll give a simple answer=4/3 or 1 1/3
Step-by-step explanation:
Slope is the change in y over the change in x. Substitute the numerator and denominator and you'll get the slope. Substitute the numerator for 4 and the denominator for 3. You get 4/3, or 1 1/3.
Hope this helps! :)
Answer:
(4,3)
Step-by-step explanation:
8 - 4 = 4
5 - 2 = 3
m = (y2 - y1)
< a "fraction"
(x2 - x1)