What is b in this? Y=-1/3+b
Or how do i graph it?
NEED ASAP
The equation of line passing through the points (-2, 4) & (4, 2) is :
y = -1/3 x + 6
The value of b = 6
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is any point on the line.
To find the slope of the line, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two given points.
Plugging in the values for the given points, we get:
m = (2 - 4) / (4 - (-2))
m = -2 / 6
m = -1/3
Next, we can use one of the given points to write the equation in point-slope form:
y - 4 = -1/3 (x - (-2))
y - 4 = -1/3 x + 2
y = -1/3 x + 6
This is the equation of the line passing through the two given points (-2, 4) and (4, 2).
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PSA: this question is a macroeconomics question so please don’t answer if you do not have a clear understanding of it.
In answering the question, you should emphasize the line of reasoning that generated your results; it is not enough to list the results of your analysis. Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes.
Because bagels and cream cheese are often eaten together, they are complements.
(a) We observe that both the equilibrium price of cream cheese and the equilibrium quantity of bagels have risen. What could be responsible for this pattern—a fall in the price of flour or a fall in the price of milk? Illustrate and explain your answer.
(b) Suppose instead that the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen. What could be responsible for this pattern—a rise in the price of flour or a rise in the price of milk? Illustrate and explain your answer.
The solution to the question on the equilibrium of the cheese and bagels have been given below
How to get the equilibriuma) If the equilibrium price of cream cheese and the equilibrium quantity of bagels have both risen, this could be caused by a fall in the price of flour, one of the inputs used to produce bagels.
This decrease in the cost of production would cause the supply of bagels to increase, leading to a rightward shift in the supply curve. At the same time, the demand for bagels would increase as consumers substitute away from other breakfast foods and toward bagels, leading to a rightward shift in the demand curve.
These two shifts would result in a higher equilibrium price for cream cheese, since bagels and cream cheese are complements. The increased demand for bagels would lead to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward.
The diagram below illustrates this relationship. The initial equilibrium is at point A, with a price of P1 and a quantity of Q1. After the decrease in the price of flour, the supply curve for bagels shifts rightward to S', and the demand curve for bagels shifts rightward to D'. The new equilibrium is at point B, with a higher price of P2 and a higher quantity of Q2. The increase in the demand for bagels leads to an increase in the demand for cream cheese, causing the demand curve for cream cheese to shift rightward to D'''. The new equilibrium for cream cheese is at point C, with a higher price of P3 and a higher quantity of Q3.
b) If the equilibrium price of cream cheese has risen but the equilibrium quantity of bagels has fallen, this could be caused by a rise in the price of milk, one of the inputs used to produce cream cheese.
This increase in the cost of production would cause the supply of cream cheese to decrease, leading to a leftward shift in the supply curve. At the same time, the demand for cream cheese would decrease as consumers substitute away from cream cheese and toward other breakfast foods, leading to a leftward shift in the demand curve.
These two shifts would result in a higher price for cream cheese, but a lower quantity of bagels consumed. The decreased demand for cream cheese would lead to a decrease in the demand for bagels, causing the demand curve for bagels to shift leftward.
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1
34°
2
3
4
find m angle 4?
HURRRRRRYYYYYYYYYYYYYYYYYYYYYYYY Drag numbers to show which are closest to ‐1
and ‐1/4
on the number line.
The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.
What are the closest numbers?In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.
Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.
Options;
A. -0.28
B. -0.82
C. -4/5
D. -1/5
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How long is a movie if it starts at 2:25pm and ends at 16:41 pm
Answer:
It would be a little over 2 hours or so since 16:41 is just 4:41.
2 hours and 16 minutes
Step-by-step explanation:
You're welcome.
the perimeter of this triangle is 32,
write down the equation in terms of x
The value of x in the triangle is 5 units.
How to find the perimeter of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.
Hence,
x + 2x + 3 + x + 9 = 32
4x + 12 = 32
subtract 12 from both sides of the equation
4x + 12 = 32
4x + 12 - 12 = 32 - 12
4x = 20
divide both sides of the equation by 4
x = 20 / 4
x = 5
Therefore,
x = 5
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HELP ASAP WILL GIVE BRAINLIEST
The system of linear equations 3x + 2y = -4 and y=x+1 is graphed on a coordinate plane. Approximate the solution to the system.
7
3
(-1.5, 0.25)
(-0.5, 0.75)
(1.5, 0.25)
(-2.5, 1.5)
4
3
2
-2 1 0
-1
-2
-3
-4
-5
1
.
2
32
4
5
Answer:yo no se como ablar ingles
Step-by-step explanation: perdoname
please help me with this question
Answer:
2nd answer : it is equivalent but not completely factored
Step-by-step explanation:
the "pulling out" of 3 as factor was completely correct.
but
3(x² - 4) can be further factored.
remember :
(a + b)(a - b) = (a² - b²)
therefore,
(x² - 4) = (x + 2)(x - 2)
and then
3(x + 2)(x - 2)
would be a complete factorization.
Answer: B) The expression is equivalent, but is not completely factored
Step-by-step explanation:
What would be the amount of force between two objects 10 mm away from each other
The amount of force between two objects 10 mm away from each other is G[tex]m_1m_2[/tex] / 100.
What is Gravitational Force?All physical things with mass are drawn to the gravitational force, which can be thought of as an attracting force. It is the known natural force that is by far the weakest.
Given:
Distance = 10 mm
As, the Gravitation force between two objects
F = G[tex]m_1m_2[/tex] / r²
or, F = G[tex]m_1m_2[/tex] / 10²
F = G[tex]m_1m_2[/tex] / 100
Also, the force between two objects decreases as the far they are apart from each other.
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The Question attached is Incomplete/ inappropriate, the Complete Question is
What would be the amount of force between two objects 10 mm away from each other having the [tex]m_1[/tex] and [tex]m_2[/tex]?
How many cups will you get if you mix 2 gallons, 4 quarts, and 1 pint?
You will get
cups.
Answer: 50 Cups
Step-by-step explanation:
16 cups in a gallon. so times that by 2, which equals 32. There are four cups in one quart so times 4 by 4 which is 16 and add to 32. 16 + 32 = 48
Two cups in a pint so add 2 to 48 which is 50
Answer:
You will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
Step-by-step explanation:
To convert between gallons, quarts, and pints, we need to use the following conversions:
1 gallon = 4 quarts
1 quart = 2 pints
Here's the step-by-step process to convert the given volume to cups:
Convert gallons to quarts: 2 gallons * 4 quarts/gallon = 8 quarts
Add the number of quarts from step 1 to the number of quarts given: 8 quarts + 4 quarts = 12 quarts
Convert pints to quarts: 1 pint * 1 quart/2 pints = 0.5 quarts
Add the number of quarts from step 3 to the number of quarts from step 2: 12 quarts + 0.5 quarts = 12.5 quarts
Convert quarts to cups: 12.5 quarts * 2 cups/quart = 25 cups
Therefore, you will get 25 cups if you mix 2 gallons, 4 quarts, and 1 pint.
Pls help me with this math space question
The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
Given expression,
= 3ˣ
put x = 4
= 3⁴ = 81
Now put x = -4
= 3⁻⁴
= 1/3⁴
= 1/81
Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.
Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.
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What else would need to be congruent to show that AABC= AXYZ by ASA?
A
B
A.
B. AC=XZ
C. BC=YZ
D. ZCE Z
C
X
Y
N
Given:
AC = XZ
ZAEX
Answer:
D
Step-by-step explanation:
ASA = 2 non included angles + 1 included side
by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.
The correct statements would need to be congruent to show that
Δ ABC= ΔXYZ by ASA are,
⇒ ∠ B ≅ ∠ Y
⇒ ∠ C ≅ ∠ Z
What is mean by Angle?An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.
Given that;
AC = XZ
∠ A = ∠ X
Now, To prove the triangles are congruent by ASA , we get;
AC = XZ
∠ A = ∠ X
⇒ ∠ Z = ∠ C
or, ∠ B = ∠ Y
Thus, The correct statements would need to be congruent to show that
Δ ABC= ΔXYZ by ASA are,
⇒ ∠ B ≅ ∠ Y
⇒ ∠ C ≅ ∠ Z
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ACTIVITY 2 1. Mr Nkomo lives in Three Rivers, in the Emfuleni municipality and uses prepaid electricity that is sold to customers at a VAT inclusive rate. The table below shows the cost of prepaid units of electricity. BLOCK UNITS (kWh) 2 3 4 0-50 51-350 351-600 >600 *Prepaid electricity: Paying for electricity before using it. *VAT = 15% *The municipality buys electricity from Eskom at an average VAT inclusive price of R1,33 per kWh. 1.1. State any two reasons why it is an advantage for the municipality to sell prepaid electricity. Verify, by showing ALL calculations, If his claim is VALID. You may use the formula: % Profit = (4) 1.2. Determine the number of units Mr Nkomo received when he bought prepaid electricity for R68,02. (3) 1.3. How much will Mr Nkomo pay if he wanted to buy 310 kWh of electricity? (3) 1.4. Mr Nkomo stated that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34%. RATE c/kWh (Including vat) sell price for the units-cost price for the units 144,72 186,06 261,87 308,37 ✓ 1000z IC) 2
Answer:
Step-by-step explanation:
1.1. Advantages of Selling Prepaid Electricity
Two advantages of selling prepaid electricity are:
a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.
b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.
1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02
The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:
Units = Amount / Rate
Units = R68,02 / R1,33
Units = 51.04 kWh
So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.
1.3. Cost of 310 kWh of Electricity
The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:
Cost = Units * Rate
Cost = 310 kWh * R1,33
Cost = R411,30
So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.
1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity
To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.
Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.
For 2-50 kWh:
Cost = 2-50 kWh * R1,33
Cost = 50 kWh * R1,33
Cost = R66,50
Selling price = R144,72
Profit = Selling price - Cost
Profit = R144,72 - R66,50
Profit = R78,22
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R78,22 / R66,50) * 100
Percentage profit = 17.7%
For 51-350 kWh:
Cost = 51-350 kWh * R1,33
Cost = 350 kWh * R1,33
Cost = R466,50
Selling price = R186,06
Profit = Selling price - Cost
Profit = R186,06 - R466,50
Profit = R29,56
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R29,56 / R466,50) * 100
Percentage profit = 6.3%
For 351-600 kWh:
Cost = 351-600 kWh * R1,33
Cost = 600 kWh * R1,33
Cost = R798,00
Selling price = R261,87
Profit = Selling price - Cost
Profit = R261,87 - R798,00
Profit = -536,13
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-536,13 / R798,00) * 100
Percentage profit = -67.3%
For over 600 kWh:
Cost = over 600 kWh * R1,33
Cost = R1,33 * 1000
Cost = R1330,00
Selling price = R308,37
Profit = Selling price - Cost
Profit = R308,37 - R1330,00
Profit = -1021,63
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-1021,63 / R1330,00) * 100
Percentage profit = -76.7%
The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.
For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.
For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.
For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.
For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.
The average percentage profit for the municipality for the four ranges of units is calculated as follows:
Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4
Average percentage profit = -34.05%
Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.
5x + 3y = 28
y=-1/5x+2
Answer:
x = 5, y = 1
Step-by-step explanation:
For x :
Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28
Simplify : 22/5x + 6 = 28
Isolate x : x = 5
For y :
Substitute x for 5 : y = -1/5 * 5 + 2
Solve: y = 1
The graph of g(x) is the result of translating the graph of f(x) = 3* six units to the right. What is the equation
g(x) = 3^x-6
g(x) = 3^x+6
g(x) = 3^x-6
g(x) = 3^x+ 6
Translation the graph of the function [tex]y=f(x)[/tex]a units to the right gives you the function [tex]y=f(x-a)[/tex]
If the graph of the function [tex]f(x)=3^{x}[/tex] is translated 6 units to the right, then the function becomes
[tex]g(x)=f(x-6)=3^{x-6}[/tex]
Answer: correct choice is A
If d²=3520, and you're solving for D, how do you get the form d=8√55, -8√55. I'm just genuinely confused on how you would calculate to this step.
1 = 3520/d² → d² = 3520 → d = 8√55, -8√55 → d = 59.330, D = -59.330
↑Multiply Both sides by 1 ↑ ??? ↑ ???
Does this make sense?
Answer:
Step-by-step explanation:
The square root of a number can be both positive and negative, so to find all possible values of d, we need to take both the positive and negative square root of 3520.
Starting with the positive square root:
d = √3520 = √(55^2 * 8) = 55 * √8 = 8 * √55
And for the negative square root:
d = - √3520 = - √(55^2 * 8) = - 55 * √8 = - 8 * √55
So the two possible values of d are 8√55 and -8√55.
Find the exact value of x
Step-by-step explanation:
answer, verified answer
The fish in a hatchery tank have mean length = 9.7 inches, with standard deviation = 1.2 inches. If a random sample of 40 fish is taken from the tank, what is the probability that their average length is less than 10 inches?
The probability that their average length is less than 10 inches is; 5.71%
How to find the probability from the z-score?The formula for z-score is;
z = (x' - μ)/(σ/√n)
where;
x' is sample mean
μ is population mean
σ is standard deviation
n is sample size
We are given;
x' = 10 inches
μ = 9.7 inches
σ = 1.2 inches
n = 40
Thus;
z = (10 - 9.7)/(1.2/√40)
z = 0.3/0.1897367
z = 1.58
From online p-value from z-score calculator, we have;
P(z < 1.58) = 0.0571 or 5.71%
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In these triangles, the largest angle and the
largest side have been measured. What do
you notice?
The shortest distance between two points is a straight line.
It would obviously be shorter to walk distance c than to walk
a plus b. The Triangle Inequality says that a + b > c. What
other two inequalities could you write?
In these triangles, the largest angle and the largest side have been measured. This means that the two smaller sides and the two smaller angles are proportional to each other. This is known as the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. This means that the two smaller angles and the two smaller sides of the triangle must add up to be larger than the largest angle or side.
The Triangle Inequality states that the sum of any two sides of a triangle must be greater than the third side. This means that two other inequalities can be written:
a > |c - b| and b > |c - a|,
where |x| is the absolute value of x. This means that the length of each side must be greater than the difference between the other two sides
The last time it placed an order for ingredients, Sweet Treats Bakery ordered 9,390 kilograms of sugar. This time, the bakery is ordering 7,512 kilograms. What is the percent of decrease in the size of the sugar order?
Answer:A decrease of 20%.
First we must subtract out new total from our old total.
9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.
7512/9390 is 0.8 & 1878/9390 is 0.2
As a percentage that is 80% and 20%.
This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.
I hope this helped & Good Luck <3 !!!
DIANA WORKED 5 1/3 HOURS AND GABE WORKED 1 1/4 HOURS. PAULA WORKED ON HERS 3/4 TIMES AS LONG AS DIANA.
DID DIANA WORK ON HER PROJECT LONGER THAN GABE?
DID PAULA WORK LESS ON HER PROJECT THAN DIANA?
DID GABE WORK LONGER ON HIS PROJECT THAN PAULA?
DID GABE WORK LONGER ON HIS PROJECT THAN DIANA?
Classify the following triangle. Check all that apply.
A. Right
• B. Acute
C. Scalene
• D. Obtuse
•E. Isosceles
• F. Equilateral
Answer:
Right, Isosceles
Step-by-step explanation:
The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.
The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.
PT=y, TR=3x + 1, QT=3y, TS = 4x + 13
find x and y
The values of x and y for the parallelogram PQRS are respectively, 2 & 7
What are the properties of parallelogram ?Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.
Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.
Given that,
The parallelogram PQRS has diagonals PR and SQ that intersects at T,
T is the midpoint of PR and T is the midpoint of SQ
If T is the midpoint of PR, then PT = TR
Given PT = y and TR = 3x+1
y = 3x+ 1 _____(i)
Also, If T is the midpoint of SQ, then ST = TQ
Given QT=3y and TS=4x+13
3y = 4x+ 13 ____(ii)
Substitute equation 1 into 2;
3y = 4x+ 13
3(3x+1) = 4x+ 13
open the parenthesis
9x+3 = 4x+13
club like terms
9x-4x = 13-3
5x = 10
x = 10/5
x = 2
Substitute x = 2 into equation 1
From 1; y = 3x+1
y = 3(2)+1
y = 6+1
y = 7
Hence, the values are x = 2 and y = 7
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The complete questions :
Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13
The American flag has 50 stars, 7 red stripes, and 6 white stripes. Write a ratio to represent the ratio of stars to red stripes.
Answer:
50:7
Step-by-step explanation:
You just put ":" in between the numbers requested.
Si una granja tiene chivos y canguros y hay 58 cabezas y 180 patas cuantos chivos y cuantos canguros hay en la granja
Answer:
26 kangaroos on the farm
32 goats on the farm
Step-by-step explanation:
To find the number of goats and kangaroos on the farm, we need to determine the number of legs each animal has. Let's say that there are 'g' goats and 'k' kangaroos.
Since each goat has 4 legs, the total number of legs for all the goats is 4g. Similarly, since each kangaroo has 2 legs, the total number of legs for all the kangaroos is 2k.
Adding these two quantities, we have:
4g + 2k = 180
Since each goat has 1 head, the total number of heads for all the goats is g. Similarly, since each kangaroo has 1 head, the total number of heads for all the kangaroos is k.
Adding these two quantities, we have:
g + k = 58
Now, we have two equations and two unknowns. To solve for 'g' and 'k', we can use substitution or elimination method.
Let's use substitution method:
From the second equation, we can find g:
g = 58 - k
Substituting this in the first equation, we get:
4(58 - k) + 2k = 180
Expanding and solving, we get:
232 - 4k + 2k = 180
232 - 2k = 180
-2k = -52
k = 26
So, there are 26 kangaroos on the farm. To find the number of goats, we can use the first equation:
g = 58 - k = 58 - 26 = 32
Therefore, there are 32 goats on the farm.
f(x) = 12 + 1
(f + g) (x) =
g(x) = 5 - x
Answer:
Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).
Assuming that the equation for f(x) is as follows:
f(x) = 12 + x
Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):
(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17
So, (f + g)(x) is a constant function with a value of 17 for all values of x.
And the expression for g(x) was already given:
g(x) = 5 - x
9. In a cranberry punch recipe, four cups of cranberry juice and one quart of pineapple juice make up half of the punch. How many cups of punch does the recipe make?
On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
by fraction
4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.
20/3.5=5.7 or 6
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Evaluate student loan options
Question
Alvin will be finishing his payments on his 10-year, $26,000 student loan and wants to know the amount of interest th
paid over the course of the loan. The student loan has a 4.4% fixed interest rate that is compounded monthly. Calcula
total amount of interest Alvin paid, rounding to the nearest cent.
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The total amount of interest that Alvin paid over the course, guven the value of the student loan and the interest rate is $ 6, 185
How to find the interest paid ?To find the interest paid, you need to find the total amount that Alvin paid in the 10 years that he was paying.
To do this, you first need to find the monthly payments. This will be an annuity as the amount will be the same throughout the student loan payment period.
The amount would be :
Student loan value = Amount x Present value interest factor of annuity, 120 periods, 4. 4 % / 12
The periods are :
= 10 years x 12 months
= 120 months
The amount is:
26, 000 = Amount x 96.939576551857
Amount = 26, 000 / 96.939576551857
Amount = $ 268. 21
The total paid over the 10 years is :
= 268. 21 x 120 months
= $ 32, 184. 9972
The interest is :
= 32, 184. 9972 - 26, 000 loan amount
= $ 6, 185
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In an election, 2325 votes were cast. Person A received 59 fewer votes than person B, and person C received 5 more votes than person B. How many votes did each candidate receive?
The candidates received ;
Person A = 734 votes
Person B = 793 votes
Person C = 798 votes
How to determine the valuesFrom the information given, we have that;
The total votes is 2325Person A received Person B - 59Person C received Person B + 5Now, substitute the values
Person A + Person B + Person C = 2325
Person B - 59 + Person B + Person + B = 2325
Let Person B = x
x -59 + x + x + 5 = 2325
collect like terms
3x = 2325 +54
Add the like terms
3x = 2379
Make 'x' the subject of formula
x = 2379/3
x = 793 votes
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The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.62. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. a. The desired margin of error is $.10. b. The desired margin of error is $.07. c. The desired margin of error is $.05.
The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can use the formula for the margin of error for a 95% confidence interval:
margin of error = z× (standard deviation / √n)
where z is the z-score for a 95% confidence interval, which is 1.96.
a. The desired margin of error is $0.10:
0.10 = 1.96(0.25 /√n)
√n = 1.96×0.25 / 0.10
√n= 4.9
n = 4.9^2
n = 24.01
So the appropriate sample size for a margin of error of $0.10 is at least 25.
b. The desired margin of error is $0.07:
0.07 = 1.96 (0.25 / √n)
√n = 1.96 × 0.25 / 0.07
√n= 6.97
n = 6.97²
n = 48.53
So the appropriate sample size for a margin of error of $0.07 is at least 49.
c. The desired margin of error is $0.05:
0.05 = 1.96 (0.25 / √n)
√n= 1.96 × 0.25 / 0.05
√n= 9.8
n = 9.8²
n = 96.04
So the appropriate sample size for a margin of error of $0.05 is at least 97.
Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
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