Which values of a, b, and c correctly complete the division?
1/5 5/6= x b/c

O a-4,b-5,c-8
○a-1,b-8,c-5
O a-1,b-5,c-8
O a-4,b-8,c-5

Answer:

the answer is 150 degrees because it is the biggest

Answer:

Last option (4th option)

Step-by-step explanation:

Parallel lines have the same slope and the only choice that has the same slope of 3/4 is the last option

The standard deviation of the possible outcomes is approximately 3.46.

To calculate the standard deviation of the possible outcomes in a binomial trial, we use the formula:

σ = sqrt(n * p * (1 - p))

where σ is the standard deviation, n is the number of trials, and p is the probability of success.

In this case, the probability of success is 0.2, and the number of trials is 75. Plugging these values into the formula, we have:

σ = sqrt(75 * 0.2 * (1 - 0.2))

= sqrt(75 * 0.2 * 0.8)

= sqrt(12)

Evaluating the square root of 12, we find:

σ ≈ 3.464

Rounding to two decimal places, the standard deviation of the possible outcomes in this binomial trial is approximately 3.46.

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Mrs. Tan poured in approximately 31.04 liters of water.

To find the volume of water poured by Mrs. Tan, we need to calculate the difference between the initial volume of water poured by Mr. Tan and the final volume of water in the tank.

The initial volume of water poured by Mr. Tan is given as 8000 cm³.

The dimensions of the tank are given as 48 cm (length) and 24 cm (width). The depth to which Mrs. Tan poured the water is given as 20 cm.

To calculate the final volume of water, we need to consider the additional volume poured by Mrs. Tan. This additional volume can be calculated by multiplying the area of the base (length × width) by the depth.

The area of the base = 48 cm × 24 cm = 1152 cm².

The additional volume poured by Mrs. Tan = 1152 cm² × 20 cm = 23,040 cm³.

Now, to find the total volume of water in the tank after Mrs. Tan poured the water, we add the initial volume (8000 cm³) to the additional volume (23,040 cm³):

Total volume = 8000 cm³ + 23,040 cm³ = 31,040 cm³.

Finally, to convert the volume from cm³ to liters, we divide by 1000 (since 1 liter = 1000 cm³):

Total volume in liters = 31,040 cm³ / 1000 = 31.04 liters.

Therefore, Mrs. Tan poured in approximately 31.04 liters of water.

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Answer:

$12000 was invested at 11% and $6000 was invested at 10%

Step-by-step explanation:

Total invested amount is 18000

Let the amount of money invested in the account paying 11% be x

Let the amount of money invested in the account paying 10% be y

⇒ x + y = 18000

⇒ y = 18000 - x

Simple interest = PNR

where P is the amount invested, N is the number of years and R is the rate of interest

For the account paying 11%,

SI₁ = x(1)(11%) = x(11%)

For the account paying 10%,

SI₂ = y(1)(10%)

= (18000 - x)(10%)

= 18000(10%) - x(10%)

= 1800 - x(10%)

Total Interest = SI₁ + SI₂

⇒ 1920 = x(11%) + 1800 - x(10%)

⇒ 1920 - 1800 = x(11% - 10%)

⇒ 120 = x(1%)

⇒ [tex]\frac{x}{100}[/tex] = 120

⇒ x = 120*100

⇒ x = 12000

y = 18000 - x

⇒ y = 18000 - 12000

⇒ y = 6000

$12000 was invested at 11% and $6000 was invested at 10%

Answer: $12,000 at 11%, $6,000 at 10%.

Step-by-step explanation:

Firstly, you would identify the two interest rates as variables.

Assign variable X to the amount invested at 11% and variable Y to the amount invested at 10%. Using those two variables assigned to our interest rates, equate those to the principle of $18,000. After that, multiply the variables by the given interest rates and equate that to the total interest.

x + y = $18,000
0.11x + 0.1y = $1,920

Solve the first equation for Y, multiplying by 100 to even out decimals.

x + y = $18,000
y = $18,000 - x
11x + 10y = $192,000
11x + 10($18,000 - x) = $192,000
11x + $180,000 - 10x = $192,000
x + $180,000 = $192,000
x = $12,000

With that, we now know that the original principle for the 11% interest rate is $12,000, which when subtracted from the total principle of $18,000 gives us the interest rate for the 10% investment as well

$18,000 - $12,000 = $6,000

So, with a total Principle of $18,000, two accounts with interest rates of 11% and 10% respectively, and a total interest accumulation of $1,920, we can gather that the account with an 11% interest rate originally had $12,000 and the account with the 10% interest rate originally had $6,000.

A statement that best summarizes the data set is that there are outliers from age 90 - 100 years and the gap is located at the age 80 - 89 years.

In Mathematics and Statistics, a histogram simply refers to a type of graph that is used for the graphical representation of a data set into user-specified ranges, especially through the use of rectangular bars.

In Mathematics and Statistics, an outlier is a number that is either unusually too little (small) or large (big) in comparison with the overall pattern of the numbers contained in a data set.

By critically observing the histogram, we can logically deduce that the peak stage occurred at an age of 50 - 59 years while the gap is located at the age 80 - 89 years.

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Missing information:

The question is incomplete and the histogram is shown in the attached picture.

Therefore, 2 mL of the medication should be given if the patient is prescribed 500 mg.

To determine the volume of the medication to be given, we can set up a proportion using the concentration provided.

Given:

Reconstituted concentration: 250 mg/mL

Prescribed dosage: 500 mg

Let's assume the volume to be given is "x" mL.

We can set up the following proportion

250 mg/1 mL = 500 mg/x mL

To solve for "x," we can cross-multiply and solve the equation:

250x = 500 * 1

250x = 500

x = 500/250

x = 2

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Without additional information or a diagram, it is impossible to determine the altitude of the airplane. We need to know the horizontal distance between the two points of observation (A and B) in order to use trigonometry to solve for the altitude.

To find the combined rate of all the individuals working together, you must add the individual rates.

When calculating the combined rate of individuals working together, you need to add up the individual rates. Each worker contributes their own rate of work or productivity, and by adding these rates together, you can determine the combined rate at which they are working collectively.

This allows you to assess the overall efficiency and output of the team or group. By summing up the individual rates, we have better understanding of the overall productivity and performance of the group.

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Answer: Get into y=mx+b form by adding 2 to each side. Graph from there.

Step-by-step explanation:

tan = √3

STEPS:

based on 1,2,√3 triangle (30°,60°,90°)

where :

1 is opposite 30°

√3 (around 1.7) is opposite of 60

2 is opposite of 90°

smallest side is opposite of smallest angle

largest side is opposite of largest angle

cosθ = 1/2 = adjacent/hypotenuse so

adjacent = 1

hypotenuse = 2 so

opposite must be √3

tan = opposite/adjacent = √3/1 = √3

The direct write-off method recognizes bad debts when they are specifically identified, while the allowance method anticipates and estimates potential bad debts in advance.

The direct write-off method and the allowance method are two different approaches used by businesses to account for bad debts.

While both methods are used to recognize and account for potential losses from uncollectible accounts, they differ in their timing and impact on financial statements.

The direct write-off method is a simpler approach.

Under this method, bad debts are directly written off as an expense when they are deemed uncollectible.

This means that when a specific account is identified as uncollectible, it is removed from the accounts receivable and recorded as an expense on the income statement.

The direct write-off method provides a more accurate representation of the actual loss incurred but can distort the timing of expenses since bad debts are recognized only when they are identified.

On the other hand, the allowance method takes a more proactive approach to account for potential bad debts.

This method involves estimating the amount of uncollectible accounts at the end of each accounting period and creating an allowance for doubtful accounts.

The allowance is recorded as a contra-asset account on the balance sheet, offsetting the accounts receivable.

This estimation is based on historical data, industry trends, and management's judgment.

By creating an allowance, the potential bad debts are anticipated and accounted for in advance, resulting in a more accurate matching of expenses to revenues.

The key difference between the two methods lies in the timing of expense recognition.

The direct write-off method recognizes bad debts only when they are identified, which can result in delayed recognition.

In contrast, the allowance method anticipates potential bad debts and recognizes them in advance, providing a more accurate representation of the financial position.

However, the allowance method requires estimation and judgment, which may introduce subjectivity and potential errors.

In summary, the direct write-off method recognizes bad debts when they are identified, while the allowance method estimates and anticipates potential bad debts.

The direct write-off method provides accuracy in expense recognition but can lead to delayed recognition, while the allowance method allows for better matching of expenses to revenues but requires estimation and introduces subjectivity.

The choice between the two methods depends on the nature of the business and its preference for accuracy or timeliness in recognizing bad debts.

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Answer:

Step-by-step explanation:

The coordinates of the triangle after the translation are given as follows:

R'(0, 5), S'(7, 8), T'(0, -1).

The four translation rules are defined as follows:

The figure is translated 4 units right and 3 units up, hence the rule is given as follows:

(x, y) -> (x + 4, y + 3).

The original coordinates are given as follows:

R(-4,2), S(3,5) and T(-4,-4).

Hence the translated coordinates are given as follows:

R'(0, 5), S'(7, 8), T'(0, -1).

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The altitude of the triangle ΔABC, can be constructed using a compass and a straight edge, using the method of constructing the perpendicular line segment from a point to a line.

The steps to construct the altitude to a line segment AB from the point C are as follows;

The line segment CG is the altitude from C to AB

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Answer:

Step-by-step explanation:

Let 's x the length of the pyramid:

V=x²*h/3

V=1024 and h=12

So x²*12/3=1024

==>x²=1024*3/12

==>x²=256

==>x²=16²

==> x=16 for (x=-16 must be exclude <0)

......brainpower pts pls

i. The first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

ii. the first two terms of the series are 0 and 3, and the fifth term is 48.

(i) The formula for the nth term of the series is given by:

nothing term = 25(2/3[tex])^n[/tex]

first two terms,  substitute n=1 and n=2 into the formula

1st term = [tex]25(2/3)^1 = 25(2/3) = 50/3[/tex]

2nd term = [tex]25(2/3)^2 = 25(4/9) = 100/9[/tex]

To find the fifth term,  substitute n=5 into the formula

Fifth term: nothing term = 25(2/3[tex])^5[/tex] = 25(32/243) = 800/243

Hence, the first two terms of the series are 50/3 and 100/9, and the fifth term is 800/243.

(ii) The formula for the nth term of the series is given by:

nth term = [tex]3(n-1)^2[/tex]

To find the first two terms, we can substitute n=1 and n=2 into the formula

First term= [tex]3(1-1)^2 = 3(0)^2 = 0[/tex]

Second term= [tex]3(2-1)^2 = 3(1)^2 = 3[/tex]

To find the fifth term, we can substitute n=5 into the formula:

Fifth term: nth term = 3(5-[tex]1)^2[/tex] = 3(16) = 48

Thus, the first two terms of the series are 0 and 3, and the fifth term is 48.

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Answer:

(X-5)

Step-by-step explanation:

tHANKS

The solutions to the two inequalities is (-0.5, 2.5) as shown in the attached graph.

The inequalities we have are given as:

y ≤ −3x + 1

y ≤ x + 3

Step1 :  Remove the inequalities

This gives us:

y = −3x + 1

y = x + 3

Step2 :  Finding intersection points of equations

x + 3 = -3x + 1

4x = -2

x = -0.5

Plug in -0.5 for x in the second equation to get:

y = -0.5 + 3

y = 2.5

Thus, intersection point is: (-0.5, 2.5)

Step 3: Test of origin (0,0)

If inequalities holds true for origin then, shades the graph towards the origin.

For equation 1.

y = −3(0) + 1

y = 1

0 ≤ 1

True, Shade graph towards origin.

For equation 2.

y = x + 3

y = 0 + 3

y = 3

0 ≤ 3

True, Shade graph towards origin.

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Complete question is:

Choose the graph that represents the following system of inequalities:

y ≤ −3x + 1

y ≤ x + 3

In each graph, the area for f(x) is shaded and labeled A, the area for g(x) is shaded and labeled B, and the area where they have shading in common is labeled AB.

21(33)6O can be expressed as 13√(2(729)). The final answer is 13√1458.

Rewriting the expression 21(33)6 with a rational exponent as a radical expression yields 21(33)6O, which can be simplified as 21(33)2. The value of 21 is 2, while the value of 33 is 27. Hence, 21(33)2 is equivalent to 2(27)2

To rewrite the expression with a rational exponent as a radical expression, we make use of the property that any number raised to a rational exponent can be represented as a radical with an exponent equal to the denominator of the rational exponent.

In this case, the rational exponent is 6/3, which is equivalent to 2.

Hence, we can rewrite 21(33)6 as 21(33)2. Simplifying this expression yields 2(27)2, which is equal to 2(729).

To express this in radical form, we take the 13th root of 2(729), which gives us 13√(2(729)).

This can be further simplified as 13√1458.

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The expression as a radical expression is [tex]9(\sqrt{x})^3[/tex]

From the question, we have the following parameters that can be used in our computation:

[tex]9x^\frac32[/tex]

Introduce brackets

So, we have

[tex]9(x^\frac32)[/tex]

Next, we have

[tex]9(x^\frac12)^3[/tex]

Express as square roots

[tex]9(\sqrt{x})^3[/tex]

Hence, the radical expression is [tex]9(\sqrt{x})^3[/tex]

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The correct statements about the figure are:

(B) In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

(C) Vertical angles prove that Angle 3 is congruent to Angle 6.

(D) The triangles are similar because alternate interior angles are congruent.

Vertical angles are formed when two lines intersect, and they are always congruent.In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles.

Similarly, vertical angles are formed when two lines intersect, and they are always congruent. Here, vertical angles are Angle 3 and Angle 6, which means they are equal.

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Answer: y-9 = 2(x-1)

Step-by-step explanation:

Answer:

71.8962°

Step-by-step explanation:

In order to find the angle given 2 sides, you need to identify the 2 sides with the given measure.

Since we need to find X, the 2 sides are 52 (the opposite side) and 17 (the adjacent side)

The only way to find X with an opposite and adjacent side is by using tan.

In order to find the angle, you will need to use the tan^-1 (52/17)

That will give you 71.8962°

Answer:

x = 71.9°

Step-by-step explanation:

The given diagram shows a right triangle with an unknown angle, x.

We have been given the measures of the sides that are opposite and adjacent the unknown angle. Therefore, we can use the tangent trigonometric ratio to find the value of x.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]

The unknown angle is x, so θ = x.

The side opposite the angle measures 52 units, so O = 52.

The side adjacent the angle measures 17 units, so A = 17.

Substitute the values into the ratio and solve for x:

[tex]\tan x=\dfrac{52}{17}[/tex]

     [tex]x=\tan^{-1}\left(\dfrac{52}{17}\right)[/tex]

     [tex]x=71.8962369...[/tex]

     [tex]x=71.9^{\circ}\; \sf (nearest\;tenth)[/tex]

Therefore, the value of x is 71.9°.

The value of the missing leg from the triangle that has been shown is 8 mi .

The Pythagorean theorem provides a way to find the length of one side of a right-angled triangle if the lengths of the other two sides are known. It is widely used in various fields, such as engineering, architecture, physics, and trigonometry, to solve problems involving right triangles and calculate distances, angles, or other related quantities.

We know that;

[tex]c^2 = a^2 + b^2\\b^2 = 10^2 - 6^2[/tex]

b = 8 mi

The Pythagorean theorem is named after the ancient Greek mathematician Pythagoras

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Answer:

We have parallelogram ABCD, with BC as the diagonal, so alternate interior angles are congruent.

100° + 30° + x = 180°, so x = 50°

The surrounding area of this image is a called a Background. Option C

This area is also called a negative shape. Option A

From the information given, we have to determine the area of the image shown, we can see that image is made up of two horses racing.

The horses are inserted on a plane surface which is called a background.

Also, we can see that the background is a negative space.

Note that a solid piece of sculpture occupies space, and makes the space around it come to life.

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The complete question:

Which term describes the surrounding area of this image?

The surrounding area of this image is called

Surroundings

Foreground

Background

This area is also called a

Negative

Positive

Neutral

Answer:

Point A is at (0, –4).

Point B is at (–8, –7).

Step-by-step explanation:

point A is 4 units down : y = –4

Point B is 8 units to the left : x = –8

and 7 units down: y = –7

A : (0, –4)

B : ( –8, –7)

Answer:

XY = 30 units

Step-by-step explanation:

The formula for the perimeter of a rectangle is given by:

P = 2l + 2w, where

Since the opposite sides of rectangles are equal, WV = XY and VY = WX.

Thus, the length of side XY is also 3y + 3, and the length of side WX is also 2y + 2.

Note that sides VY and WX represent the width of the rectangle while sides WV and XY represent the length of the rectangle.

Step 1:  Find y:

Before we can find the length of side XY, we'll first need to know the value of the variable y in 3y + 3 and 2y + 2.

We can find y by plugging in 3y + 3 for l and 2y + 2 for w, and 100 for P in the perimeter formula:

100 = 2(3y + 3) + 2(2y + 2)

100 = (2 * 3y) + (2 * 3) + (2 * 2y) + (2 * 2)

100 = (6y + 4y) + (6 + 4)

(100 = 10y + 10) - 10

(90 = 10y) / 10

9 = y

Thus, y = 9.

Step 2:  Find the length of side XY:

Now we can find the length of side XY by plugging in 9 for y in 3y + 3 and simplifying:

XY = 3(9) + 3

XY = 27 + 3

XY = 30

Thus, the length of side XY is 30 units.