plss help me for brainleist

Plss Help Me For Brainleist

Answers

Answer 1

[tex]\large \maltese \:{ \underline { \underline{ \pmb{ \sf{SolutioN }}}}} : -[/tex]

we have given ,

∠ A = 60°∠ B = 60°∠ C = ?? ( to be calculated)

★ According to Angle sum property of triangle, the sum of interior angles of a triangle is 180°.

➝ ∠ A + ∠ B + ∠ C = 180°

➝ 60° + 60° + ∠ C = 180°

➝ 120° + ∠ C = 180°

➝ ∠ C = 180° - 120°

➝ ∠ C = 60°

Now,

★ Calculating for x :-

↝ ∠ C + x = 180°

↝ 60° + x = 180°

↝ x = 180° - 60°

↝ x = 120°

Hence, The value of x will be 120°.

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Answer 2

Answer:

The major of the exterior angle is 120°

Step-by-step explanation:

In given triangle we have to find the value of exterior angle and in interior of the triangle there are two angles 60 degree and second one is also 60 degree and we have to find value of exterior angle which is x.

So, here we apply exterior angle property which is exterior angle is equal to the sum of the two interior opposite angles. Here, there are two opposite interior angles so we have to add these two and we get the value of exterior angle.

Exterior angle property :-

[tex] \implies \sf \angle60 \degree + \angle60 \degree[/tex]

[tex] \implies\angle120 \degree[/tex]

Additional information :-

Some important properties :-

Exterior angle property :- An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Angle sum property :- The total measure of the three angles of a triangle is 180°

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Related Questions

PLS HELP ASAP I WILL GIVE BRAINLIEST GEOMETRY

Answers

Answer:  A. 32

Step-by-step explanation:

Rule:  That if an angle is created on the end of circle The arc that it creates is 2 times the angle.

arc AX = 2 (<B)

arc AX = 2(56)

arc AX = 112

Rule:  The angle of 2 secants = 1/2 (outer arc - inner arc)

<C =  1/2 (arc AB - arc AX)

<C = 1/2 ( 176 - 112)

<C = 1/2 (64)

<C = 32     >A

5) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many times did Stacy run her fastest mile?

Answers

Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

Answer:

2 times

Step-by-step explanation:

According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

A point is located 5 units to the right origin along the x axis and 3 units up along the y-axis on a coordinate plane

Answers

Answer: (5, 3)

Step-by-step explanation:

this is just basic coordinate geometry. it tells you how far to go right and up.

graph 5x - 2y greater than or equal to 10​ step by step

Answers

The graph of the inequality y ≤ (5/2)x - 5 is a downward-sloping line with shading below the line.

To graph the inequality 5x - 2y ≥ 10, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's go step by step:

Step 1: Start with the original inequality:

5x - 2y ≥ 10

Step 2: Move the 5x term to the other side of the inequality by subtracting 5x from both sides:

-2y ≥ -5x + 10

Step 3: Divide the entire inequality by -2 (since we want to isolate y and have a positive coefficient for y):

y ≤ (5/2)x - 5

Now we have the inequality in the desired form. The graph of y ≤ (5/2)x - 5 represents all the points below or on the line y = (5/2)x - 5.

To graph this inequality, follow these steps:

Step 1: Plot the y-intercept, which is -5. This point is (0, -5).

Step 2: Find a second point by using the slope (5/2). The slope is the ratio of the change in y to the change in x. Starting from the y-intercept, move up 5 units (numerator of the slope) and move right 2 units (denominator of the slope). This gives us the point (2, 0).

Step 3: Draw a solid line passing through the two points (0, -5) and (2, 0). This line represents the equation y = (5/2)x - 5.

Step 4: Since the inequality is "y ≤ (5/2)x - 5," we need to shade the region below the line (including the line itself) to represent all the points that satisfy the inequality.

The graph should resemble a downward-sloping line passing through the points (0, -5) and (2, 0), with the shaded region below the line.

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Graph the line with slope -1 passing through the point (-4,-5) .

Answers

The equation of line is y = -x - 9 which passes through the point Z(-4,-5)

Given data ,

To graph the line with a slope of -1 passing through the point (-4, -5), we can use the point-slope form of a linear equation:

Now , the value of A is

Let the line passes through the point P ( -4 , -5 )

The slope which is the rate of change is is m=-1

y-y₁ = m(x-x₁)

On simplifying , we get

y-(-5) = (-1)(x+4)

Expanding the brackets:

y + 5 = -x - 4

y = -x - 9

Now we have the equation in slope-intercept form. To graph the line, we can plot the given point (-4, -5) and use the slope to find additional points.

Hence , the equation of line is y = -x + 1

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2 4/5 yards x 2 yards x 3/5 yards =

Answers

The product of [tex]2\frac{4}{5}[/tex] yards, 2 yards, and [tex]\frac{3}{5}[/tex] yards comes out to be [tex]16\frac{4}{5}[/tex] yards.

Firstly we have to convert the mixed fraction into the improper fraction.

1. We multiply the denominator and the whole number

2. To the product add the numerator to get the numerator of the fraction

3. The denominator remains the same.

[tex]2\frac{4}{5}[/tex] = 2 * 5 + 4 / 5 = 14/5

To multiply the fractions:

1. We multiply the numerators to get the numerator

2. Similarly the product of the denominator is the denominator

3. We simplify the resultant fraction

= 14/5 * 2 * 3/5 = 84/5

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summary of this shape help u will get 100 points I need it cry cyr ycr

Answers

The line of symmetry for the above figure is attached accordingly.

What is a line of symmetry?

In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.

That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.

After inserting the symmetry lines, the above resulted in a kite.

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Please help asap I need to turn this in RIGHT NOW

Answers

The requried domain and range of the given graph are a set of all real values i.e. (-∞, ∞).

Consider the given figure,
The domain is said to be the values of the set of dependent variables, in the given case the value on the x-axis, represents the domain.
The domain is given as all real value i.e. (-∞, ∞)

Similarly, the range is represented by the y-axis and given as (-∞, ∞).

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Use a graphing calculator or other technology to solve this problem. x y 0 6 1 8.5 2 12 3 14.9 4 18 Which linear regression model best fits the data in the table? Responses y=5.8x−3.04 y equals 5.8 x minus 3.04 y=3.04x+5.8 y equals 3.04 x plus 5.8 y=−5.8x+3.04 y equals negative 5.8 x plus 3.04 y=−3.04x−5.8

Answers

The linear regression equation that best fits the data is y = 3.04x + 5.8.

Using a graphing calculator, we can plot the data points and find the linear regression model that best fits the data.

The linear regression equation that best fits the data is

y = 3.04x + 5.8.

Therefore, the answer is: y=3.04x+5.8.

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A triangle has a base of 14 feet and a height of 6 feet. By how much does the base need to increase for the area to incre
by 1.2 square feet?

Answers

For the area to increase by 1. 2 square feet, the base would need to increase by 0. 4 ft.

How to find the base ?

The area of a triangle is given by the formula:

Area =  ( 1 / 2) x base x height

= 1 / 2 x 14 x 6

= 42 square feet

The new area after the increase would be :

= 42 + 1. 2

= 43. 2 square feet

The base for this to happen is:

43. 2 = 1 / 2 x base x 6

base = 14. 4 ft

The increase in base is:

= 14. 4 - 14.

= 0. 4 ft

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Peter's restaurant is bringing in money from customers, and he needs to know how much he needs to pay off the bill for the electricity to run the place. To turn the electricity on, he has to pay $25. For every hour that the electricity is on, he has to pay $4. How many hours can he have the electricity on for if she makes a $49 profit?
Please answer with step-by-step instructions. Thank you.

Answers

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

We have,

Let's start by setting up an equation to represent the situation:

Profit = Revenue - Cost

We know that Peter's profit is $49, and we can find the revenue by multiplying the number of hours by the hourly rate:

Revenue = Hourly rate x Number of hours

The hourly rate is $4, and the cost includes the initial fee of $25 plus the hourly cost:

Cost = Initial fee + Hourly rate x Number of hours

Now we can substitute these equations into the profit equation and solve for the number of hours:

$49 = ($4 x Number of hours) - ($25 + $4 x Number of hours)

$49 = $4 x Number of hours - $25 - $4 x Number of hours

$49 + $25 = $4 x Number of hours - $4 x Number of hours

$74 = $4 x Number of hours

Number of hours = $74 / $4

Number of hours = 18.5

Thus,

Peter can have the electricity on for 18.5 hours if he wants to make a $49 profit.

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The distance between home and
school is 4.5 miles.On a map it
shows the distance to be 9 cm.
What is the scale?

Answers

Answer:

1 mile : 2 cm

Step-by-step explanation:

ratio is 4.5 miles : 9

Which, if you want simplified, 1:2

Answer:

2 cm is 1 mile

or 1 cm is 1/2 mile

Step-by-step explanation:

We are going  from 9 cm to 4.5 miles

9 cm * scale factor = 4.5 miles

scale factor = 4.5 miles / 9 cm

scale factor = 1/2 mile per cm

The scale is 2 cm is 1 mile

or 1 cm is 1/2 mile

If the diameter of a circle is 22 in what is its area

Answers

Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

Please help I’m confused

Answers

If 0 < θ < [tex]360^0[/tex] and sin θ = 0.3097, then θ is approximately [tex]24^0[/tex].

Trigonometric problem

In order to find the value of θ given sin(θ) = 0.3907, we can use the inverse sine function, also known as arcsine or [tex]sin^{(-1)[/tex].

Using a scientific calculator or trigonometric tables, we can find the inverse sine of 0.3907:

θ= sin^(-1)(0.3907)

θ ≈ 23.576 degrees

Since 0 < θ < 360 degrees, we can conclude that θ is approximately 24 degrees.

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Please check the picture
Please answer 2a&b
i give you 70points!!!



For f(x) = 2x³ - 12x² + 18x
(a) (8pts) Find all local max and local min.
(c) (7pts) Make a nice sketch of the graph.
ty
X
(b) (5pts) Find all points of inflection.

Answers

Answer:

  2a. maximum: (1, 8); minimum: (3, 0)

  2b. point of inflection: (2, 4)

  3.  a = 1/4

Step-by-step explanation:

You want the extrema and the point of inflection of f(x) = 2x³ -12x² +18x, and you want the value of 'a' that makes the end behavior a horizontal asymptote at y = 1.

2. Cubic

The cubic function f(x) = 2x³ -12x² +18x has derivative ...

  f'(x) = 6x² -24x +18 = 6(x² -4x +3) = 6(x -1)(x -3)

The derivative will be zero at x = 1 and 3. These are the x-coordinates of the extrema of f(x).

The values of f(x) at those points are ...

  f(x) = 2x((x -6)x +9)

  f(1) = 2·1((1 -6)1 +9) = 2(-5 +9) = 8

  f(3) = 2·3(3 -6)·3 +9 = 6(-9 +9) = 0

The leading coefficient is positive, so the leftmost portion of the curve is increasing. The maximum will be at the leftmost turning point. The minimum is the other one (rightmost).

The maximum is (1, 8); the minimum is (3, 0).

The point of inflection is the midpoint between the extrema of a cubic:

  ((1, 8) +(3, 0))/2 = (2, 4) . . . . point of inflection

3. Limit

You want the limit as x → -∞ of ((x -2)(3x² +5) -4ax³)/(8ax³ +5x -1) to be 1.

The ratio of leading terms of the numerator and denominator is ...

  (3 -4a)x³/(8ax³) = 1

This requires ...

  3 -4a = 8a   ⇒   3 = 12a   ⇒   a = 1/4

The value of 'a' that makes the limit be 1 is 1/4.

__

Additional comments

A cubic is symmetrical about its point of inflection, so the point of inflection will be equidistant from the extrema, their midpoint. When the leading coefficient is positive, the function is increasing everywhere except between the local extrema. (The first attachment has a graph of the derivative, for reference.)

The end behavior of a rational function of equal numerator and denominator degree is the ratio of the leading coefficients.

<95141404393>

The expression P(z<2.04) represents the area under the standard normal curve below the given value of z. What is the value of P(z<2.04)?

Answers

P(z<2.04) is approximately 0.9793 or 97.93% (rounded to two decimal places).

We can use a table or a calculator that offers the cumulative distribution function (CDF) of the standard normal distribution to determine the area under the standard normal curve below a specified value of z.

The chance that a standard normal random variable is less than or equal to a specified value is provided by the CDF.

In this case, we want to find the value of P(z<2.04), which represents the probability that a standard normal random variable is less than 2.04. Using a table or a calculator, we can look up the value of the CDF at z = 2.04, which is approximately 0.9793.

Therefore, we can say that the value of P(z<2.04) is approximately 0.9793, or about 97.93% (rounded to two decimal places).

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Look at the map showing the European Union (EU) and countries with which it has free-trade agreements (FTAs). The pending agreements are
concentrated in North America
concentrated in Southeastern Asia
mostly located in South Africa
spread across several continents

Answers

Answer:

The North American Free Trade Agreement (NAFTA) among the United States, Canada and Mexico went into effect on January 1, 1994. It is the first trade agreement the United States has entered into with a geographically-close developing country and has raised concerns about its economic effect, particularly on U.S. communities and workers. Since the mid-1980s, when Mexico began reducing trade restrictions, the U.S. and Mexican economies have become more highly integrated. This is evidenced by the rapid growth in U.S. merchandise trade with Mexico, which is now 12% of all U.S. trade

Step-by-step explanation:

Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. What is the shape of distribution:
A.skewed right
B. skewed left
C. uniform
D. symmetric

Answers

B skewed left is the answer

Probability
See picture attached

Answers

Answer:

The answer is down below

Step-by-step explanation:

G={2,3,4}

W={1,5}

Total cards=1,2,3,4,5

let P(x) be G

Probability of X=G/Total

P(x)=3/5

P(not x)=2/5

X={2,3,4}

not X={1,5}

Question 3 of 10
Which expressions are equivalent to the one below? Check all that apply.
25.2x

Answers

The expressions that are equivalent to the one below  is [tex]2 ^{(5+x) }[/tex], option C.

How can the expression be known?

Based on the definition of power multiplication properties, The Product of Powers Property serves as one that stressed that in a cae wehereby we are multiplying two exponents with the same base, then the exponents  can be multiplied and keep the base.

It shoud be noted that when  want to simplify the expressions [tex]2x^4[/tex]by [tex]6x2[/tex] , the base wil will be kept whereby  we add the exponent.

The given expression is [tex]2^5.2^x[/tex], which can be simplified as;

= [tex]2^5.2^x[/tex]

=[tex]2 ^{(5+x) }[/tex]

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the radius of a circle is 8cm. find its area to he nearest whole number

Answers

Answer:

Area of circle = pi×r²

Where, pi =22/7 or 3.142

r = 8cm

Area =22/7 × 8²

=201.142

Approximately 201 to the nearest whole number

You're welcome

Given ⊙ N, what is mAB?

Answers

Answer: the answer  of mab is 72 degrees.

Answer:

146°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

73° = (1/2)m(arc)AB

Multiply both sides by 2.

2 × 73° = 2 × (1/2) × m(arc)AB

m(arc)AB = 146°

María del Carmen colecciona cremos de animales tiene más de 30 y menos de 50 los quiere organizar en un álbum de manera que en cada página

Answers

From the calculation and based on the Least common multiples, , we can tell that Maria del Carmen has a total of 36 stickers

How is this so?

The least common multiple is of a set of numbers is the least multiple that they have in common and is obtained by decomposing each number into prime factors and taking common and uncommon factors with their greatest exponent.

Then we break down each number to know how much is the minimum that Maria del Carmen has:

2 = 2

4 = 2*2 = 2²

6 = 2*3

9 = 3*3 = 3²

12 = 2*2*3 = 2²*3

18 = 2*3*3 = 2*3²

LCM = 2²*3² = 4*9 = 36

Now this number is between 30 and 50: so Maria del Carmen has 36 stickers

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Full Qustion:

Maria del carmen colecciona cromos de animales;tiene mas de 30 y menos de 50.los quiere organizar en un album de manera q en cada pagina guarde el mismo numero de cromos.si puede ubicar 2,4,6,9,12 o 18 cromos en cada pagina ¿cuantos cromos tiene maria del carmen?

Translation:
Maria del Carmen collects animal stickers; she has more than 30 and less than 50. She wants to organize them in an album so that on each page she keeps the same number of stickers. If she can locate 2,4,6,9,12 or 18 Stickers on each page. How many stickers does Maria del Carmen have?

please see attached doc

Answers

The cosine value is given as follows:

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

How to obtain the cosine value?

The tangent value is given as follows:

[tex]\tan{\theta} = -\frac{\sqrt{7}}{4}[/tex]

First we must obtain the secant value, according to the identity presented as follows:

[tex]\sec^2{\theta} = 1 + \tan^{2}{\theta}[/tex]

Replacing the tangent into the expression, we have that:

[tex]\sec^2{\theta} = 1 + \frac{7}{16}[/tex]

[tex]\sec^2{\theta} = \frac{23}{16}[/tex]

[tex]\sec{\theta} = \frac{\sqrt{23}}{4}[/tex]

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

[tex]\cos{\theta} = \frac{1}{\sec{\theta}}[/tex]

[tex]\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}[/tex]

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

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can someone please help me out?

Answers

The radius of the circle is [tex]\sqrt{59[/tex] and the coordinates are (6,8).

The given equation of the circle is:

[tex]x^2+Y^2-12x-16y+51=0[/tex]

To find the center and radius of the given circle, we need to rewrite the equation in the standard form [tex](x-a)^2 + (y-b)^2 = r^2[/tex],

where (a,b) is the center of the circle and r is the radius.

We can start by completing the square for the x and y terms. For the x terms, we add and subtract (12/2)² = 36 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y = -51 + 36 + 0[/tex]

Similarly, for the y terms, we add and subtract (16/2)² = 64 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y + 64 = -51 + 36 + 64[/tex]

Simplifying:

[tex](x - 6)^2 + (y - 8)^2 = 59[/tex]

Now we can see that the center of the circle is at (6, 8), and the radius is [tex]\sqrt{59[/tex].

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Answer the following questions.
1.) Explain the significance of r<0 in an ordered pair (r, 0) in polar coordinates.
2.) Explain why a point in the plane can be represented by infinitely many ordered
pairs in polar coordinates.
3.) How is the component form of the vector related to the graph of the
vector in standard position?
4.)
A plane travels N30°W at 450 mph and encounters a wind blowing due west at 30 mph. (See Example 9)
a. Express the velocity of the plane Vp relative to the air in terms of I and J.
b. Express the velocity of the wind V in terms of i and j.
e. Express the true velocity of the plane vr in terms of i and j and find the true speed of the plane.

Answers

Answer:

1. An ordered pair in polar coordinates (r, θ) represents a point in the plane with a distance of r from the origin and an angle of θ with respect to the positive x-axis. When r < 0, this means that the point is located on the opposite side of the origin from the positive x-axis. In other words, the angle θ is shifted by 180 degrees.

2. In polar coordinates, a point can be represented by infinitely many ordered pairs because the distance r and the angle θ are not unique. For example, the point (1, π/4) and the point (1, 9π/4) both represent the same point in the plane.

3. The component form of a vector (a, b) represents the horizontal and vertical displacement of the vector from its initial point to its terminal point. The graph of a vector in standard position is a line segment from the origin to its terminal point. The horizontal and vertical components of the vector correspond to the x- and y-coordinates of the terminal point, respectively.

4a. The velocity of the plane Vp relative to the air can be expressed as Vp = (450 cos(60°), 450 sin(60°)) - (30, 0) = (225 - 30, 389.71) = (195, 389.71) mph.

4b. The velocity of the wind V can be expressed as V = (-30, 0) mph.

4e. The true velocity of the plane vr can be expressed as vr = Vp + V = (195 - 30, 389.71) = (165, 389.71) mph. The true speed of the plane is the magnitude of the true velocity, which is approximately 414.7 mph.

Simplify each side of 4a+ 5a-2=5+3-1

Answers

Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

please help easy, area and perimeter related

Answers

The amount of paint needed to cover the walls of a room, you can use the area of the walls to estimate the amount of paint required.

The area of a two-dimensional shape is the amount of space inside its boundaries, while the perimeter is the length of its outer edge.

These concepts are often related, as the perimeter of a shape can be used to calculate its area.
For example, consider a square with sides of length 5cm.

The perimeter of the square would be 4 x 5cm = 20cm, while the area would be 5cm x 5cm = 25cm².

We can see that the area is greater than the perimeter, as there is more space inside the square than around its edges.
Another way that area and perimeter can be related is through similar shapes. Similar shapes have the same shape, but different sizes.

For example, a small square and a large square are similar shapes, but the large square has longer sides and therefore a larger area and perimeter.

The ratio of the areas of two similar shapes is equal to the square of the ratio of their corresponding side lengths.

Similarly, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Understanding the relationship between area and perimeter can be helpful in a variety of situations.

For example, if you need to calculate the amount of fencing needed to enclose a rectangular garden, you can use the perimeter of the garden to determine the length of the fencing required.
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HELP (question in image)

Answers

Answer:

C) F(n) = 10n-1

Step-by-step explanation:

C) F(n) = 10n-1

Try a few points

F(n) = 10n-1

= 10(20) - 1

= 200-1

= 199 >>> which matches the table

F(n) = 10n-1

= 10(5) - 1

= 50-1

= 49 >>> which matches the table

F(n) = 10n-1

= 10(1) - 1

= 10-1

= 9 >>> which matches the table

The answer is C


10(1)-1=9
10(2)-1=19

It’s the only answer that applies to all

Dawson Toys, Limited, produces a toy called the Maze. The company has recently created a standard cost system to help control costs and has established the following standards for the Maze toy:

Direct materials: 7 microns per toy at $0.33 per micron
Direct labor: 1.2 hours per toy at $7.10 per hour

During July, the company produced 4,700 Maze toys. The toy's production data for the month are as follows:

Direct materials: 77,000 microns were purchased at a cost of $0.30 per micron. 35,875 of these microns were still in inventory at the end of the month.
Direct labor: 6,040 direct labor-hours were worked at a cost of $45,904.

Required:
1. Compute the following variances for July: (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values. Do not round intermediate calculations. Round final answer to the nearest whole dollar amount.)
a. The materials price and quantity variances.
b. The labor rate and efficiency variances.

Answers

a. Materials price variance: U$990  and Materials quantity variance: F$198

b. Labor rate variance: F$248

Labor efficiency variance: U$752

a. Materials price and quantity variances:

Materials price variance:

The materials price variance measures the difference between the actual cost of materials purchased and the standard cost of materials.

Actual quantity purchased = 77,000 microns

Actual cost per micron = $0.30 per micron

Standard quantity allowed for production = (7 microns per toy) x (4,700 toys) = 32,900 microns

Standard cost per micron = $0.33 per micron

Materials price variance = (Actual quantity purchased x Actual cost per micron) - (Standard quantity allowed x Standard cost per micron)

Materials price variance = (77,000 x $0.30) - (32,900 x $0.33)

Materials quantity variance:

The materials quantity variance measures the difference between the actual quantity of materials used and the standard quantity allowed for production.

Actual quantity used = (77,000 microns purchased) - (35,875 microns in ending inventory)

Standard quantity allowed = (7 microns per toy) x (4,700 toys)

Materials quantity variance = (Actual quantity used - Standard quantity allowed) x Standard cost per micron

Materials quantity variance = ((77,000 - 35,875) - (7 x 4,700)) x $0.33

b. Labor rate and efficiency variances:

Labor rate variance:

The labor rate variance measures the difference between the actual labor rate paid and the standard labor rate.

Actual labor hours worked = 6,040 hours

Actual labor cost per hour = $45,904 / 6,040 hours

Standard labor hours allowed for production = (1.2 hours per toy) x (4,700 toys)

Standard labor cost per hour = $7.10 per hour

Labor rate variance = (Actual labor hours worked x Actual labor cost per hour) - (Standard labor hours allowed * Standard labor cost per hour)

Labor rate variance = (6,040 x Actual labor cost per hour) - (5,640 x $7.10)

Labor efficiency variance:

The labor efficiency variance measures the difference between the actual labor hours used and the standard labor hours allowed for production.

Labor efficiency variance = (Actual labor hours worked - Standard labor hours allowed) x Standard labor cost per hour

Labor efficiency variance = (6,040 - (1.2 x 4,700)) x $7.10

Please note that the actual labor cost per hour and the actual labor cost per micron need to be calculated before computing the variances.

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