Answer: To calculate the total cost of the units in beginning inventory for each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units in beginning inventory = 0 units * $13 + $5 + $5 = $0
Year 2: Cost of units in beginning inventory = 1,000 units * ($13 + $5 + $5) = 1,000 * $23 = $23,000
To calculate the total cost of the units produced during each year, we need to multiply the number of units by the per-unit cost:
Year 1: Cost of units produced = 10,000 units * ($13 + $5 + $5) = 10,000 * $23 = $230,000
Year 2: Cost of units produced = 9,000 units * ($13 + $5 + $5) = 9,000 * $23 = $207,000
To calculate the total cost of the units sold during each year, we need to multiply the number of units sold by the per-unit cost:
Year 1: Cost of units sold = 9,000 units * ($13 + $5 + $5 + $6) = 9,000 * $29 = $261,000
Year 2: Cost of units sold = 8,000 units * ($13 + $5 + $5 + $6) = 8,000 * $29 = $232,000
To calculate the total variable manufacturing costs for each year, we need to sum the costs of the units in beginning inventory, units produced, and units sold:
Year 1: Total variable manufacturing costs = $0 + $230,000 + $261,000 = $491,000
Year 2: Total variable manufacturing costs = $23,000 + $207,000 + $232,000 = $462,000
To calculate the total fixed manufacturing overhead costs for each year, we need to add the fixed manufacturing overhead per year to the total variable manufacturing costs:
Year 1: Total manufacturing costs = $491,000 + $90,000 = $581,000
Year 2: Total manufacturing costs = $462,000 + $90,000 = $552,000
To calculate the total variable selling and administrative expenses for each year, we need to multiply the number of units sold by the variable selling and administrative expense per unit:
Year 1: Total variable selling and administrative expenses = 9,000 units * $6 = $54,000
Year 2: Total variable selling and administrative expenses = 8,000 units * $6 = $48,000
To calculate the total selling and administrative expenses for each year, we need to add the fixed selling and administrative expenses per year to the total variable selling and administrative expenses:
Year 1: Total selling and administrative expenses = $54,000 + $61,000 = $115,000
Year 2: Total selling and administrative expenses = $48,000 + $61,000 = $109,000
Step-by-step explanation:
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.
Which equation could represent a proportional relationship?
A)h = p +27
B)h=38p
C) h= 47.3/p
D)hp = 29.50
B) h = 38p
An equation represents a proportional relationship if the ratio of the dependent variable to the independent variable is constant. In this equation, h is directly proportional to p, meaning that if p increases, h increases, and if p decreases, h decreases. The constant of proportionality is 38.
In other words, the equation h = 38p can be written as h/p = 38, which shows that the ratio of h to p is always equal to 38. This means that the equation represents a proportional relationship.
The other equations listed do not represent a proportional relationship because the ratio of the dependent variable to the independent variable is not constant. For example, in equation A, h is not directly proportional to p because the constant of proportionality changes as p changes. In equation C, h and p are inversely proportional because h decreases as p increases, and h increases as p decrease. And in equation D, the equation is not in the form of a proportion because there is an additional constant term on the right-hand side.
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.
Compare to greatest or least 7/8 14/16
Answer:
The fraction 14/16 is greater than 7/8.
Step-by-step explanation:
Help me, please!!!!!!!!!
Answer: D, 3x+12
Step-by-step explanation: Distributing a number means that you have to multiply the number by all of the numbers inside the parentheses. 3*x is 3x, and 3*4 is 12. 3x+12 is 3x+12.
Which relation is also a function?
Domain Range
A
V
11
C. Domain Range
X
Domain Range
B.
X
D. Domain Range
V
P
The relation is a function only if for element x in Set X, there is only one element in Set Y so, the choice B shows the relation.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable).
When a relation will be called as a function .
Consider there be a relation R from a set X to a set Y .
Since the relation will be called a function if each element of set X is related to exactly one element in set Y.
which is, an element x in X, there is only one element in Y that x is related to.
Therefore , the correct option is B.
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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.
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
A total of 382 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 fewer student tickets than adult tickets. How many adult tickets were sold?
At the school play, 225 adult tickets were sold.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The number of adult tickets sold be 'x',
Therefore, The number of student tickets would be 'x - 68'.
Therefore, The expression can be formed as,
x + (x - 68) = 382.
2x - 68 = 382.
2x = 450.
x = 225.
So, The number of adult tickets sold is 225.
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Find the exact value of x
Step-by-step explanation:
answer, verified answer
I need help with this problem
The estimate of the number 7th grader who play in the school band will be 120.
How to calculate the valueIt is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:
= 60 / 200 × 400
= 120
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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.
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 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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Ismail tried to prove that
sin
(
�
)
=
cos
(
90
°
−
�
)
sin(θ)=cos(90°−θ)sine, left parenthesis, theta, right parenthesis, equals, cosine, left parenthesis, 90, degree, minus, theta, right parenthesis using the following diagram. His proof is not correct.
The first mistake in Ismail's proof is that (3) cos(90 - Ф) = AC/BC
How to determine Ismail's mistakeThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The two column proof
In the two column proof, we have
cos(90 - Ф) = AC/BC
This equation is incorrect because by the definition of cosine, we have
cos(90 - Ф) = AB/BC
i.e. cos(x) = adjacent/hypotenuse
Hence, the mistake in his proof is cos(90 - Ф) = AC/BC
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What is the value of f(3) in the function below?
f(x) = 1/4 • 2*
A. 4
B. 2
C. 8
D. 3/2
The value of f(3) is 2.
Option B is the correct answer.
What is a function?A function has an input and an output with a relationship between them.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 1/4 x [tex]2^x[/tex]
Substitute x = 3.
f(3) = 1/4 x 2³
f(3) = 1/4 x 8
f(3) = 2
Thus,
The value of f(3) is 2.
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Write the dual of following problems: Maximize Z = 7X1 + 5X2 Subject to: X1 + 2X2 ≤ 6 4X1 + 3X2 ≤ 12 X1 , X2 ≥ 0 brainly
The dual problem of the primal problem "Maximize Z = 7X1 + 5X2, Subject to X1 + 2X2 ≤ 6, 4X1 + 3X2 ≤ 12, X1, X2 ≥ 0" is:
What are inequalities?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Greater than (or greater than or equal to), less than (or less than or equal to), or not equal to signs are used in place of the equal sign.
Minimize Z = 6Y1 + 12Y2
Here
Y1 + 4Y2 ≥ 7
2Y1 + 3Y2 ≥ 5
Y1, Y2 ≥ 0
(b) The dual problem of the primal problem "Maximize Z = 3X1 + 4X2, Subject to 5X1 + 4X2 ≤ 200, 3X1 + 5X2 ≤ 150, 8X1 + 4X2 ≥ 80, X1, X2 ≥ 0" is:
Minimize Z = 200Y1 + 150Y2
Subject to:
4Y1 + 5Y2 ≥ 3
5Y1 + 3Y2 ≥ 4
4Y1 + 8Y2 ≤ -80
Y1, Y2 ≥ 0
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"Your question is incomplete, probably the complete question/missing part is:"
Write the dual of following problems:
(a) Maximize Z = 7X1 + 5X2
Subject to:
X1 + 2X2 ≤ 6
4X1 + 3X2 ≤ 12
X1, X2 ≥ 0
(b) Maximize Z= 3X1 + 4X2
Subject to:
5X1 + 4X2 ≤ 200
3X1 + 5X2 ≤ 150
8X1 + 4X2 ≥ 80
X1, X2 ≥ 0
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
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.
For a fishing trip, Henry is going to choose lures to put in his tackle box. He has 4 lures that are crankbaits and 9 that are Jigs. In how many ways can he choose
7 lures if more than 5 must be jigs?
The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:
372 ways.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The possible combinations are given as follows:
Six jigs from a set of 9 and one crankbait from a set of 4.Seven jigs from a set of 9.Hence the number of ways is given as follows:
n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)
n = 372 ways.
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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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Let f(x) = x2 − 2x + 1. Find the inverse function of f by identifying an appropriate restriction of its domain.
Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Step-by-step explanation:
[tex]y = x^2 - 2x + 1[/tex]
We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).
So, to find the inverse, first we'll switch the x and y and solve for y:
[tex]x = y^2 - 2y +1[/tex]
[tex]x = (y-1)^2[/tex], (factor!)
±[tex]\sqrt{x} = y - 1[/tex]
So, the inverse "function" is:
[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]
But theres an issue here!
If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!
We need to restrict the domain to only include the values that are above the x axis.
So our final inverse function is:
[tex]f^{-1} (x) = \sqrt{x} +1[/tex]
Factorise (i) 4y²-6yz+9z²
Answer please
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The identity to be used here is [ (a - b)² = a² - 2ab + b² ]
First, try to get the given expression in form of terms on the RHS of the above identity
[tex]\qquad \sf \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]
[ it's in form of a² - ab + b² now, add and deduct ab here ]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]
[ Apply the identity ]
[tex]\qquad \sf \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]
[tex]\qquad \sf \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]
[ That's probably the answer, it can't be simplified more ]
To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.
We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.
The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:
[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]
Applying this formula to our quadratic expression, we get:
[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]
Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].
[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]
✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]
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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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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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]?
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
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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area of triangle۔ab =154،bc=346،ac=349
Therefore, the area of the triangle ABC is approximately 18096.3 square units.
What is the area of the triangle?
To calculate the area of a triangle, use the formula area = 1/2 * base * height.
We can use Heron's formula to find the area of the triangle ABC when the lengths of its three sides are known:
[tex]Area = {\sqrt{(s(s-a)(s-b)(s-c))}[/tex]
where "s" is the semiperimeter of the triangle, which is half the sum of the lengths of its three sides:
s = (a + b + c)/2
In this case, we have:
a = AB = 154
b = BC = 346
c = AC = 349
So the semiperimeter is:
s = (a + b + c)/2 = (154 + 346 + 349)/2 = 424.5
Now we can use Heron's formula to find the area of the triangle
[tex]Area = \sqrt{(s(s-a)(s-b)(s-c))}\\\\Area = \sqrt{(424.5(424.5-154)(424.5-346)(424.5-349))}\\\\Area= 18096.3[/tex]
Therefore, the area of the triangle ABC is approximately 18096.3 square units.
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According to Wikipedia, the following are the lengths of terms of the US Presidents that preceded Joe Biden. There is a total of 44. You may have expected to see a total of 45, as Biden is the 46th us President, but Grover Cleveland was considered the 22nd and the 24th President, but is only counted once in this list The 2922 is the length of two full terms and the 1461 is the length of one full term FDR, the 4422 in the table, had actually started his FOURTH term before dying in office The 31 is William Henry Harrison who became ill shortly after his inauguration. His death may have been due to pneumonia Number of US Presidents 12 1 1 Term in Days 4422 2922 2865 2.840 2.728 2.041 2.027 1.886 1,654 1.503 1,461 1.460 1.430 1.419 1 1 12 1 1 1.419 1.262 1,036 969 895 881 492 199 31 TOTAL: 1 1 1 1 1 1 1 1 1 44 Determine the mean, median and mode for this set of data Give each to the nearest whole day Mean = Median = Mode = and With one of the modes being a high value as well as the term of FDR being much higher than all others, was pulled up to a higher value than another of hte measures of central tendency the
The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.
To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:
Mean:
To find the mean, we add up all of the term lengths and divide by the total number of terms:
Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44
Mean = 1743.77 days
Median:
To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:
31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422
Median = (1460 + 1461) / 2
Median = 1460.5 days
Mode:
The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.
Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.
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