Please answer, what is x?

The area of triangle YCX is given as follows:

G. 2 units squared.

The area of square WXYZ is 16, hence the side length is given as follows:

s² = 16

s = 4.

Considering the midpoints, we have that the sides of the right triangle are given as follows:

YC = CX = 4/2 = 2

Hence the area of the triangle is given as follows:

0.5 x 2 x 2 = 2 units squared.

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The Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

Two or more expressions with an Equal sign is called as Equation.

Predetermined overhead rate for Finishing Department = $550,000 / 500,000 direct labor hours = $1.10 per direct labor hour

Predetermined overhead rate for Production Department = $400,000 / 80,000 direct labor hours = $5.00 per direct labor hour

For one unit of table lamp, 2 hours of finishing and 1 hour of production are required, so the total direct labor hours for one unit of table lamp is 2 + 1 = 3 hours.

Finishing Department overhead cost per unit of table lamp = 2 hours * $1.10 per direct labor hour = $2.20

Production Department overhead cost per unit of table lamp = 1 hour * $5.00 per direct labor hour = $5.00

Total factory overhead cost per unit of table lamp

$2.20 + $5.00 = $7.20

Therefore, the Kaumajet Factory will allocate $7.20 of factory overhead to each unit of table lamp using the multiple production department factory overhead rate method with an allocation base of direct labor hours.

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The Kaumajet Factory produces two products-table lamps and desk lamps. It has two separate departments - Finishing and Production. The overhead budget for the Finishing Department is $550,000, using 500,000 direct labor hours. The overhead budget for the Production Department is $400,000 using 80,000 direct labor hours.

If the budget estimates that a table lamp will require 2 hours of finishing and 1 hour of production, how much factory overhead will the Kaumajet Factory allocate to each unit of table lamp using the multiple production department factory overhead rate methods with an allocation base of direct labor hours?

a. $4.91

b. $6.33

c. $7.20

d. $5.00

1/8 x 5 = 5/8

5/8 of the passengers were adults :)

The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

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Answer:

43.68

Step-by-step explanation:

28÷500=0.056

0.056×780=43.68

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a. Length of GK = \(\sqrt{34}\)  and Length of adjacent to GK = \(\sqrt{34}\)

b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. The parallelogram GHJK is Square.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)

a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)

for points G(-3, 6) and K(-6, 1)

Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)

Length of GK = \(\sqrt{34}\)

Length of adjacent side (GH, KJ) to GK =  \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)

Length of adjacent to GK = \(\sqrt{34}\)

b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)

Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)

Slope of GK = \(\frac{5}{3}\)

Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)

Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. All sides are equals to \(\sqrt{34}\)

So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)

and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)

All sides and diagonals are equal then parallelogram GHJK is Square.

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The image is attached below

Generally, To plot the numbers 4/5 and 5/6 on the real number line, we first need to determine their respective locations on the number line.

The number line is a continuous line that represents all the real numbers, with smaller numbers towards the left and larger numbers towards the right.

The number 4/5 can be plotted on the number line by finding its location relative to other known numbers.

For example, we can place the number 4/5 to the right of 1/2 and to the left of 3/4.

Similarly, the number 5/6 can be plotted on the number line by finding its location relative to other known numbers.

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Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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The area of a shape is the amount of space, the shape can occupy. The equation to calculate the value of x is: \((e)\ x^2 + 11x -42= 0\)

The space on the border is given as:

\(Top = 2\)

\(Others = 3\)

So, the dimension of the sheet of paper is:

\(Length = x + 2 + 3\)

\(Length = x + 5\)

\(Width = x + 3 + 3\)

\(Width = x + 6\)

The area of the sheet is then calculated as follows:

\(Area= Length \times Width\)

\(Area= (x + 5) \times (x + 6)\)

Open brackets

\(Area= x^2 + 5x + 6x + 30\)

\(Area= x^2 + 11x + 30\)

From the question, we understand that the area of the sheet is \(72cm^2\)

So, the equation becomes

\(x^2 + 11x + 30 = 72\)

Subtract 72 from both sides

\(x^2 + 11x + 30 -72= 0\)

\(x^2 + 11x -42= 0\)

Hence,

\((e)\ x^2 + 11x -42= 0\) can be used to calculate the value of x

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Answer:

1. isosceles 2. Scalene 3. Equilateral 4. Equilateral

Step-by-step explanation:

Answer:

mean score of class B = 1778/25 = 71.12

Step-by-step explanation:

This was your question : Class A has 12 pupils and class B has 25 pupils. Both classes sit the same maths test. The mean score for class A is 80. The mean score for both classes is 74. What is the mean score (rounded to 2 DP) in the maths test for class B?

mean of class A = Σfx/Σf

mean of class A =  80

Σfx = 80 × 12 = 960

Mean score for both classes = 74

where

b = Σfx  of class B

960 + b/37 = 74

cross multiply

960 + b = 2738

b = 2738 - 960

b = 1778

mean score of class B = Σfx/Σf

Σfx = 1778

Σf = 25

Therefore,

1778/25 = 71.12

Answer:(15,0)

Step-by-step explanation:

Ending Inventory Cost and Cost of Goods Sold using different inventory methods:

FIFO Method:

Ending Inventory Cost: $11,920

Cost of Goods Sold: $15,068

LIFO Method:

Ending Inventory Cost: $11,996

Cost of Goods Sold: $15,123

Weighted Average Cost Method:

Ending Inventory Cost: $11,974

Cost of Goods Sold: $15,087

Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.

This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.

Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.

This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.

Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.

Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.

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Answer:

we need more info

Step-by-step explanation:

The inequality that models this situation is:

l + b ≥ 12

Here we know that Sophie has two jobs, and she must work no less than 12 hours a week.

Then the inequality is of the form:

total number of hours ≥ 12 hours.

Now, we can define the variables:

b =  number of hours babysitting.

l = number of hours lifeguarding.

Then the total number of hours that she works is l + b

Then the inequality is:

l + b ≥ 12

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Step-by-step explanation:

first we use Pythagoras to get t :

c² = a² + b²

with c being the Hypotenuse.

so,

t² = r² + s² = 10² + 31² = 100 + 961 = 1061

t = sqrt(1061)

and then we use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the angles being opposite of their related sides.

so, r/sin(R) = t/sin(T) = t/sin(90) = t/1 = t

sin(R) = r/t = 10/sqrt(1061) = 0.30700278...

R = 17.8786966... ≈ 17.9°

Answer:

52

Step-by-step explanation:

56+(x+72) =180

180 because it is supplementary

Answer:

x=12

corect me im wrong paki report nalang kung mali

The angle measure of x is 115°.

A parallelogram is a four-sided shape with two sets of parallel sides, which means that opposite sides are both parallel and have equal length. Parallelograms also have opposite angles with the same measure, and their diagonals intersect at the midpoint and bisect each other. This results in the parallelogram being divided into two triangles that are congruent. Examples of parallelograms include rectangles, squares, and rhombuses, and they are commonly used in both geometry and everyday life, particularly in the design of buildings and other structures.

We can call this figure ACDEF. Let us join CB.

Now we can see that BDEF is a parallelogram. Opposite angles of a parallelogram are equal, hence ∠DBF = ∠DEF = x°

And also consider the triangle ABC,

∠BAC = 50°

∠ABC = 180 - ∠DBF = 180° - x° (linear pair)

∠ACB = 180 - ∠ACD = 180° - x° (linear pair)

We know that all the angles of a triangle adds up to 180°.

Using this we can find x°:

∠BAC + ∠ABC + ∠ACB = 180°

50° + 180° - x° + 180° - x° = 180°

-2x° + 410 = 180°

-2x° = 180° - 410° = -230°

x° = -230/ -2

x ° = 115°

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The sum of the series ∑[infinity]n=15n(n+2) is 'dne' (does not exist) as the series diverges.

To determine the sum of the series, we first need to check if the series converges or diverges.

The series is given as:
∑[infinity]n=15n(n+2)

Step 1: Identify the type of series
This is an infinite series with terms involving a polynomial in n.
Step 2: Apply the Ratio Test
The Ratio Test is used to determine the convergence or divergence of a series. Let's take the ratio of consecutive terms:
lim (n→∞) \((|a_(n+1) / a_n|)\)
where, \((|a_(n+1) / a_n|)\)
\(a_(n+1) = (n+1)((n+1)+2) = (n+1)(n+3)\)
So, we have:
lim (n→∞) (|((n+1)(n+3))/(n(n+2))|)
Step 3: Simplify the limit
To simplify the limit, divide both the numerator and the denominator by the highest power of n,

which is \(n^2:\)
lim (n→∞) (|((1+(1/n))(1+(3/n)))/((1)(1+(2/n)))|)

Step 4: Calculate the limit
As n approaches infinity, the terms with 1/n will approach 0:
lim (n→∞) (|(1)(1+0)/(1+0)|) = 1
Step 5: Interpret the result
Since the limit is 1, the Ratio Test is inconclusive, and we cannot determine if the series converges or diverges based on this test alone.
However, since the series is an infinite series with terms involving a polynomial in n, it will diverge.

This is because the terms do not approach 0 as n approaches infinity.

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Answer:

2500 grams makes 5.511557 pounds = 5.5

Answer:

it is 5.5 lbs

Step-by-step explanation:

math

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.

Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.

For example, let's say one missing value is x = 3. We can substitute this into the equation:

y = 2(3) + 4

y = 6 + 4

y = 10

So, the missing ordered pair is (3, 10).

Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:

8 = 2x + 4

4 = 2x

x = 2

So, the missing ordered pair is (2, 8).

In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).

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Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

Answer: 455

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

hope you find this helpfull

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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