Solve the equation 13x-2x(3x+4)=22

9514 1404 393

Answer:

  6

Step-by-step explanation:

Dilation about the origin multiplies each coordinate by the scale factor. We can find the scale factor by considering the x-coordinates of A and A'.

  scale factor = Ax'/Ax = 18/3 = 6

The scale factor is 6.

Answer:

B

Step-by-step explanation:

Answer:

2 (assuming equatin you meant was -2(3g - 2) - (4g + 3))

Step-by-step explanation:

-2(39 - 2) - (48 + 3)

-78+4-48-3

= - 125

(assuming that your equation instead is -2(3g - 2) - (4g + 3)

-6g+4-4g-3

-10g+1

The ledger accounts for Concia Traders are given below:

Capital:

Opening Balance – R105,000

Drawings:

(5) R5,745

Land and Buildings:

(4) R64,065

Vehicles:

(2) R20,340

Equipment:

(2) R1,250

Trading Stock:

(4) R8,482

(5) R16,386

Cash:

(2) R450

Sales:

(4) R13,560

Cost of Sales:

A. Purchases (assume the missing value is for purchases since there is no other related account):

Rent Income:

(3) R5,000

Packing Material:

(4) R3,330

Trading License:

(4) R7,000

Stationery:

(4) R753

Water and Electricity:

(4) R414

Telephone:

(4) R577

(5) R1,334

(4) R994

Note that due to the missing transaction numbers and values in the provided data, this may have an effect on the precision of the ledger accounts. Nevertheless, I have done my best to create these ledger accounts with caution and accuracy.

To determine the selling price through applying a 50% markup on cost price, use this formula:

Selling Price = Cost Price + (Cost Price x Markup Percentage).

For example, if the cost price for an item is R100, then the selling price will be calculated as:

Selling Price = R100 + (R100 x 0.50) = R100 + R50 = R150.

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Failure to include some units, or entire portions, of the defined survey population in the actual operational sample frame represents: a noncoverage error.

One of the components of coverage error that results from a flawed sample frame that excludes a certain percentage of the population is noncoverage.

Sampling errors need to be controlled and reduced to a level at which their presence does not defeat or obliterate the usefulness of the final sample results.

The difference between the observed values of a variable and the long-run average of the observed values in repetitions of the measurement is the sampling error.

Noncoverage, another word for these frames, inadequate coverage is also known as undercoverage.

Sampling errors can be decreased by increasing the sample size.

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a) The equation that gives the amount A left of an initial amount A0 after time t can be written as A(t) = A0e^(-kt), where A(t) represents the amount of substance A remaining at time t, A0 is the initial amount of substance A, k is the rate constant, and e is the base of the natural logarithm.

b) Given that 18 lb of substance A reduces to 9 lb in 4.1 hours, we can use the equation from part (a) to solve for the value of k. Using the given information, we have 9 = 18e^(-k*4.1). Dividing both sides by 18, we get e^(-k*4.1) = 1/2. Taking the natural logarithm of both sides, we have -k*4.1 = ln(1/2). Solving for k, we find k ≈ -0.1694.

Now, we can use the equation A(t) = A0e^(-kt) and substitute A(t) = 1 lb and k ≈ -0.1694 to find the time it takes for there to be only 1 lb left. We have 1 = A0e^(-0.1694t). Dividing both sides by A0 and taking the natural logarithm, we get ln(1/A0) = -0.1694t. Solving for t, we have t ≈ -ln(1/A0) / 0.1694.

The final answer will depend on the value of A0, which is not provided in the given information. Once the initial amount A0 is known, it can be substituted into the equation to calculate the time required for there to be only 1 lb left.

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The average speed during the same time interval is approximately 2.02 km/h.

(a) To find the magnitude and direction of the woman's displacement, we can use the Pythagorean theorem and trigonometry.

Given:

Distance walked north = 3.55 km

Distance walked east = 2.00 km

To find the magnitude of the displacement, we can use the Pythagorean theorem:

Magnitude of displacement = √((Distance walked north)^2 + (Distance walked east)^2)

= √((3.55 km)^2 + (2.00 km)^2)

≈ 4.10 km

The magnitude of the displacement is approximately 4.10 km.

To find the direction of the displacement, we can use trigonometry. The direction can be represented as an angle north of east.

Direction = arctan((Distance walked north) / (Distance walked east))

= arctan(3.55 km / 2.00 km)

≈ 59.0°

Therefore, the direction of the displacement is approximately 59.0° north of east.

(b) To find the magnitude and direction of the woman's average velocity, we divide the displacement by the time taken.

Average velocity = Displacement / Time taken

= (4.10 km) / (2.80 hours)

≈ 1.46 km/h

The magnitude of the average velocity is approximately 1.46 km/h.

The direction remains the same as the displacement, which is approximately 59.0° north of east.

Therefore, the direction of the average velocity is approximately 59.0° north of east.

(c) The average speed is defined as the total distance traveled divided by the time taken.

Average speed = Total distance / Time taken

= (3.55 km + 2.00 km) / (2.80 hours)

≈ 2.02 km/h

Therefore, the average speed during the same time interval is approximately 2.02 km/h.

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The correct answer is d) To avoid a large number of classes with very small frequencies.

Unequal class intervals are sometimes used in a frequency distribution to avoid a large number of classes with very small frequencies. This can occur when the data range is very large or when there is a lot of variability in the data.

For example, if we have a dataset with values ranging from 0 to 1000, using equal class intervals of size 100 would result in 10 classes. However, if the data is skewed and most of the values fall in the lower range, many of the classes may have very small frequencies. Using unequal class intervals can help group the data in a way that results in more meaningful class frequencies.

Additionally, unequal class intervals can be used to better represent the distribution of the data. For example, if there is a cluster of values around a certain range, using a smaller class interval around that range can provide more detail and information about the data distribution.

Therefore, the correct answer is d) To avoid a large number of classes with very small frequencies.

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Answer:

Not probabillity of picking a green marble is 80%

Step-by-step explanation:

Answer:

.80 or 4/5

Step-by-step explanation:

Probability is all about figuring out what you are or not going to get.

One good trick of figuring this out is taking what you don't want, (here its green marbles) take them out, then add all the marbles (G,B,R) and divide. Here you are dividing 8 by 10 which comes out to .80

The only other thing to do is simplify if needed. .80 turns into 8/10 and the only thing that 8 and 10 are divisible by is 2 so it would turn into 4/5

Hope this info can help ;)

The relation between Mean, Median and mode is given by

Mode= 3 Median - 2Mean---- equation1

According to the given condition

Mode= 2+median ----- equation 2

Putting equation 2 in equation 1

2+median= 3 Median - 2Mean

2 Mean= 3 Median - 2- Median

2 Mean= 2 Median - 2

Mean= Median-1

Mean- Median=1--------Eq. A

According to the second condition

Median- Mode=-2-----------eq. 3

Putting eq. A in eq. 3

Mean -1 - Mode=-2

Mean- Mode=-1

or

Mode- Mean=1------equation 4

Adding equation A and equation4

Mode- Mean=1

Mean- Median=1

Mode+ Median =2------- equation5

Again Putting equation2 in equation 5

2+median + Median =2

2 Median =2-2

2 Median =0

Median=0

Mean= 0-1

Mean= 0-1=-1

Mode- Mean=1

Mode-(-1)=1

Mode=0

Putting values in the formula of mean

x bar =∑x/5

(-1)5 = 0+0+ x1+x2+0

-5=  x1+x2

So the highest value is 0.

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Answer:

Step-by-step explanation:

A repeating decimal or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely repeated portion is not zero.

For this case 4/11 are

0.36 36 36 36 36 36 36 36 36

it repeating 36  36

so 4/11 are repeating decimal

Answer:

\( \frac{4}{11} = 0.3636\)

Step-by-step explanation:

The remainders repeat in a pattern and the quotient also repeats in blocks of two. So, 4/11 = 0.3636, Which

36 repeats, In this case, 36 is the repeating pattern.

The given question is related to the kinematics equations of motion in physics.

Kinematics is the branch of mechanics that deals with the motion of objects without considering the forces that cause the motion. In this problem, we are given the acceleration of a particle moving in a straight line, as well as its initial velocity and displacement. We are asked to find the position function of the particle, which describes its position as a function of time.

To do this, we can use the kinematics equation: x = xo + vot + 1/2 at^2, where x is the final displacement, xo is the initial displacement, vo is the initial velocity, a is the acceleration, and t is the time interval. By substituting the given values into this equation, we can find the position function of the particle. The position function will help us to determine the position of the particle at any point in time, and to analyze its motion, such as its velocity and acceleration, at different points in time.

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Answer:

60

Step-by-step explanation:

40+ 20

60

this is your answer

A) If the triangle is a right triangle

The first step of an indirect proof of the phrase:

If the triangle is a right triangle. The correct statement is A.

A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.

Given:

The Conditional statement:

If one of the angles of a triangle equals 90, then the triangle is classified as a right triangle.

The first step of an indirect proof of the phrase:

If the triangle is a right triangle.

That means, the triangle have an angle equals to 90°.

Therefore, the correct statement : If the triangle is a right triangle.

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Answer:

$2837.40.

Step-by-step explanation:

To find the cost of constructing the fence, you will need to first find the perimeter of the lot. The perimeter is the distance around the outside of the lot.

To find the perimeter of the lot, add the lengths of all four sides of the lot: 90 feet + 175 feet + 90 feet + 175 feet = 430 feet.

Then, add 6 feet 6 inches to the height of the fence to convert it to feet. There are 12 inches in 1 foot, so 6 feet 6 inches is equivalent to 6 + (6/12) = 6.5 feet.

So, the total height of the fence is 6.5 feet.

To find the cost of the materials, you will need to find the total area of the fence. The area of the fence is the amount of surface that the fence covers. To find the area, multiply the height of the fence by the perimeter: 6.5 feet * 430 feet = 2795 square feet.

To find the cost of the materials, multiply the cost per square foot by the total area of the fence: $0.82/square foot * 2795 square feet = $2299.90.

To find the cost of the labor, multiply the number of linear feet of fence by the cost per linear foot: 430 feet * $1.25/foot = $537.50.

To find the total cost, add the cost of the materials to the cost of the labor: $2299.90 + $537.50 = $2837.40.

So, the total cost of constructing the fence is $2837.40.

Answer:

John should use:

4 grams of the 30% solution and 16 grams of the 60% solution

Step-by-step explanation:

Let the number of grams of the 30% solution = x

Let the number of grams of the 60% solution = y

John needs 20 grams of 54% acid solution for his science project.

Hence,

x + y = 20 grams..... Equation 1

x = 20 - y

His school's science lab has bottles of 30% solution and bottles of 60% solution.

30% × x + 60% × y = 54% × 20

0.3x + 0.6y = 10.8......Equation 2

We substitute 20 - y for x in Equation 2

0.3(20 - y) + 0.6y = 10.8

6 - 0.3y + 0.6y = 10.8

- 0.3y + 0.6y = 10.8 - 6

0.3y = 4.8

y = 4.8/3

y = 16 grams

x = 20 - y

x = 20 - 16

x = 4 grams

Therefore, John should use:

4 grams of the 30% solution and 16 grams of the 60% solution

The amount of 30% and 60% bottles he should join is; 4grams and 16grams respectively.

The total amount John needs is; 20 grams.

Therefore, we have;

\( (\frac{x}{20} \times 30) + (\frac{20 - x}{20} \times 60) = 54\)

Therefore, upon evaluation;

Therefore, The amount of 30% and 60% bottles he should join is; 4grams and 16grams respectively.

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The set of data that represents the interquartile range and the maximum, in that order, is (80 - 70, 95), which simplifies to (10, 95).

Looking at the box plot, we can see that the box spans from approximately 65 to 85, with the median at around 75. To find the values for the interquartile range and maximum, we need to determine the exact values for Q1, Q3, and any outliers.

From the box plot, we can estimate that Q1 is around 70 and Q3 is around 80.

The median of the lower half of the data is the middle value between the smallest value and the median, which is approximately 68.

The median of the upper half of the data is the middle value between the median and the largest value, which is approximately 83.

To find the maximum value, we look for the highest data point that is not an outlier. From the box plot, we can see that there are no outliers, so the maximum value is the highest value in the data set, which is approximately 95.

Therefore, the set of data that represents the interquartile range and the maximum, in that order, is (80 - 70, 95), which simplifies to (10, 95).

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Based on the given angle measurements, the opposite angles in quadrilateral CADF do not add up to 180°, indicating that CADF is not a cyclic quadrilateral

To determine whether the quadrilateral CADF is cyclic or not, we need to examine its properties and angles.

In the given diagram, we have the following angle measurements:

Angle LGCA = 78° (given)

Angle LBC = 41° (given)

Angle BIC = 48° (given)

Angle LCBD = 41° (given)

Angle CBDA = 34° (given)

To determine if CADF is cyclic, we need to examine if opposite angles add up to 180°. Let's check the opposite angles in the quadrilateral:

Angle CAD + Angle CFD = Angle CBDA (opposite angles)

From the given information, Angle CBDA is 34°, and the sum of the opposite angles CAD and CFD must also be 34° for CADF to be a cyclic quadrilateral.

To find Angle CAD and Angle CFD, we can subtract the known angles from the given angles:

Angle CAD = Angle LGCA - Angle LBC = 78° - 41° = 37°

Angle CFD = Angle BIC - Angle LCBD = 48° - 41° = 7°

Therefore, Angle CAD + Angle CFD = 37° + 7° = 44°, which is not equal to Angle CBDA (34°).

Since the sum of the opposite angles in CADF is not equal to 180°, we can conclude that CADF is not a cyclic quadrilateral.

In summary, based on the given angle measurements, the opposite angles in quadrilateral CADF do not add up to 180°, indicating that CADF is not a cyclic quadrilateral.

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Answer:

∠ ABC = 116°

Step-by-step explanation:

Since the angles are supplementary, they sum to 180° , that is

8x - 36 + 4x - 12 = 180

12x - 48 = 180 ( add 48 to both sides )

12x = 228 ( divide both sides by 12 )

x = 19

Then

∠ ABC = 8x - 36 = 8(19) - 36 = 152 - 36 = 116°

Answer:

The answer is the option A

The line is horizontal. The slope is

Step-by-step explanation:

we know that

The slope of the line parallel to the x-axis is equal to zero and is called a horizontal line

The slope of the line parallel to the y-axis is undefined and is called a vertical line

In this problem we have

This is a line parallel to the x-axis

therefore

Is a horizontal line with slope equal to zero

Step-by-step explanation:

x = number of t- shirts

the function for the incurring costs is

c = 5x + 45

the function for the accumulating sale is

s = 20x

the break even point is when both functions deliver the same result.

20x = 5x + 45

15x = 45

x = 3

c = s = 5×3 + 45 = 20×3 = $60

they need to sell 3 t-shirts to break even.

at that point they will have incurred $60 in costs and collected the same amount in sales.

The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.

In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.

The Central Limit Theorem establishes that for a proportion p in a sample of size n:

The expected value is μ=р

The standard error is s=\(\sqrt{\frac{p(1-p)}{n} }\)

In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.

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To determine the latitude and longitude of point x, we need to locate it on the given diagram. From the diagram, we can see that the latitude of point x is approximately 30 degrees, as it falls between the 20 and 40-degree marks on the latitude scale.

However, we cannot determine the exact longitude of point x as the diagram only shows measurements every 15 degrees, and point x falls between the 75 and 90-degree marks on the longitude scale. Therefore, we can only estimate that the longitude of point x is approximately 82.5 degrees.

Latitude and longitude are important geographic coordinates used to locate any place on Earth. Latitude is the angular distance measured north and south of the Equator, whereas longitude is the angular distance measured east and west of the Prime Meridian. The diagram provided in the question shows latitude measurements every 10 degrees and longitude measurements every 15 degrees. This allows us to locate any point on Earth using these coordinates. In the given diagram, we can determine the approximate latitude of point x to be 30 degrees, but the longitude cannot be determined accurately due to the limited measurements provided. It is essential to have accurate latitude and longitude measurements for navigation, mapping, and other geographic purposes. Therefore, it is crucial to use advanced technologies and techniques to measure and locate these coordinates accurately.

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Answer:

The arc length s = 44 inches

Step-by-step explanation:

We are given:

r = 4 in

Ф = 11 radians

We need to find s

The formula used is: \(s=r\theta\)

where s represents arc length, r is radius and Ф is angle in radians

Putting values and finding s

\(s=r\theta\)

Put r = 4 and Ф = 11

\(s=4\times 11\\s=44\)

So, the arc length s = 44 inches

Step-by-step explanation:

Storage Space of Shed = Volume of Shed.

Volume of Shed = Volume of Rectangular level

+ Volume of Triangular roof

Volume of Rectangular Level =

Length x Width x Height

=

\(12 \times 6 \times 8 \\ = 576 {ft}^{3} \)

Volume of Triangular Roof =

Area of Triangular side x Length

=

\( \frac{1}{2} \times base \times height \times length \\ = \frac{1}{2} \times 6 \times 4 \times 12 \\ = \frac{1}{2} \times 288 \\ = 144 {ft}^{3} \)

Volume of Shed = 576 + 144

=

\(720 {ft}^{3} \)

Answer: 10 - 30y - 5w

Step-by-step explanation:

Multiply each value of the first parenthesis to -5. Start with -2 (10), then 6y (-30y), and lastly w (-5w). Combine all the terms in order.

The greatest possible number of total points for each of the top three teams is 24.

Given;

Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.

After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.

Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).

Therefore, this case brings a total of 4 + 18 = 22 points.

Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.

This case brings a total of 18 + 6 = 24 points.

Therefore, we use case (II) since it brings the greater amount of points as 24.

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Answer:

After 3 bracelets , the money taken in and the number of bracelets sold will be the same for the girls

Step-by-step explanation:

Let the number of bracelets that makes the amount of profit made be equal be x

For Sandy, her gain will be 10x - 25

For Selena, her gain will be 26x - 73

So equating both, we can find x

10x - 25 = 26x - 73

26x-10x = 73-25

16x = 48

x = 48/16

x = 3

To get the amount, we can make a substitution for x

we have;

10(3) - 25 = 30-25 = $5

Answer:

The answer is

Step-by-step explanation:

The midpoint M of two endpoints of a line segment can be found by using the formula

\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(4,3) and (-6, 5)

The midpoint is

\(M = ( \frac{ 4 - 6}{2} \: , \: \frac{3 - 5}{2} ) \\ = ( - \frac{2}{2} \: , \: - \frac{2}{2} )\)

We have the final answer as

Hope this helps you

Answer:  (-1, 4)

Step-by-step explanation:

Midpoint is the the point that is equal distance from the given endpoints.

(x₁, y₁) = (4, 3)         (x₂, y₂) = (-6, 5)

\(M_x=\dfrac{x_1+x_2}{2}\qquad \qquad \qquad M_y=\dfrac{y_1+y_2}{2}\\\\\\M_x=\dfrac{4+(-6)}{2}\qquad \qquad \quad M_y=\dfrac{3+5}{2}\\\\\\M_x=\dfrac{-2}{2}\qquad \qquad \qquad \qquad M_y=\dfrac{8}{2}\\\\\\x=-1\qquad \qquad \qquad \qquad \qquad y=4\)      -->     (-1, 4)