What meaning of the statement this?

Answer: To find the area of a triangle, we can use the formula:

Area = (base x height) / 2

However, in this problem, we don't have the height of the triangle directly. Instead, we have the lengths of three sides of the triangle.

To find the height, we can use Heron's formula, which allows us to calculate the area of a triangle when we know the lengths of all three sides:

Area = √(s(s-a)(s-b)(s-c))

where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter (half of the perimeter) of the triangle:

s = (a + b + c) / 2

Once we have the area of the triangle, we can use the given price per square foot to calculate the cost of the lot.

So, to apply this to the problem at hand, we can first calculate the semi-perimeter of the triangle:

s = (94 + 188 + 168) / 2 = 250

Next, we can use Heron's formula to find the area of the triangle:

Area = √(250(250-94)(250-188)(250-168)) ≈ 7329.53 square feet

Finally, we can calculate the cost of the lot by multiplying the area by the price per square foot:

Cost = 7329.53 x $3 = $21,988.59

Therefore, the approximate cost of the triangular lot is $21,988.59.

Step-by-step explanation:

Martina is learning different kinds of Latin dance she went to 6 salsa lessons and 12 rumba lessons each lessons cost 4$ let t equal the total number of lesson, the total cost of the lessons is $72.

The problem gives us two pieces of information:

1. Martina attended 6 salsa lessons and 12 rumba lessons, which means she attended a total of 18 lessons in total.

2. Each lesson costs $4.

To find an equation for the total number of lessons (t), we simply add the number of salsa lessons and rumba lessons:

t = 6 + 12

t = 18

So the total number of lessons Martina attended is 18.

To find an equation for the total cost of the lessons (c), we can multiply the total number of lessons by the cost per lesson:

c = t x 4

c = 18 x 4

c = 72

So the total cost of the lessons Martina attended is $72.

Thus, the equation for the total number of lessons is t = 6 + 12 = 18 and the equation for the total cost of the lessons is c = t x 4 = 18 x 4 = 72.

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Answer:

Jamie gets £9.60

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the amount by 5 to find the value of one part of the ratio.

£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then

2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets

Ah Tee sold an average of 167 copies per day for the whole week.

The quantity of weekdays and weekends must be considered.

Assume that a week consists of 5 weekdays and 2 weekends (Saturday and Sunday).

We divide the total number of copies sold for the week by the number of days in the week to determine the average number of copies sold per day for the whole week:

Average number of copies sold per day for the whole week = 1169 / 7 = 167

Therefore, Ah Tee sold an average of 167 copies per day for the whole week.

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The procedure to simplify fractions is presented in this answer.

The steps to simplify a fraction are given as follows:

For example, let's say we want to simplify the fraction 12/24:

Another example, let's say we want to simplify the fraction 16/20:

Note that a fraction is in its simplest form when its numerator and denominator have no common factors other than 1.

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The face value of the note is $9,000.

The face value of a note is the principal value mentioned or stated on the note.

The face value is different from the maturity value or the discounted value.

The maturity value refers to the face value plus accumulated interest.

The discounted value is a value less than the maturity value received for discounting the note before its maturity date.

The face value of the note = $9,000

Note period or maturity period = 60 days

Note interest = 8%

Note issuance date = April 15

Note maturity date = June 14

Maturity value = $9,120 ($9,000 + $9,000 x 8% x 60/360)

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The equation where x represents the matrix would be A. [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

To find the matrix equation representing the given system of equations, we can write the system as AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

The system of equations is:

x + y + z = 260

x + y - z = 60

2x + y + 2z = 305

We can write this system as a matrix equation:

A = [tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right][/tex]

X = [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

So the correct matrix equation is:

AX = B

[tex]\left[\begin{array}{ccc}1&1&1\\1&1&-1\\2&1&2\end{array}\right] \left[\begin{array}{ccc}260\\60\\305\end{array}\right][/tex]

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The instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. It is typically used in inferential statistics, where we use a sample to make inferences about a larger population.

To determine the sample size required to construct a 95% confidence interval with a margin of error of 0.025 or less, we need to use the formula:

n = (Z² * p * (1 - p)) / E²

where:

n = sample size

Z = Z-score corresponding to the desired level of confidence (in this case, 95%, which corresponds to a Z-score of 1.96)

p = estimated proportion of students repeating the class (since we have no prior information, we will use 0.5 as a conservative estimate)

E = maximum allowable margin of error (in this case, 0.025)

Plugging in the values, we get:

n = (1.96² * 0.5 * (1 - 0.5)) / 0.025²

n = 384.16

Rounding up to the nearest whole number, the instructor would need to take a sample size of at least 385 students in order to construct a 95% confidence interval with a margin of error of 0.025 or less.

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1.The measure of the central angle is 90°.

2.Equation of x=12.

3.The measure of the angle that bisects the minor arc is 45°.

4.The measure of the major arc is 270°.

The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.

The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.

Radians to degrees conversion

5π * (180/π) = 90° degrees

Therefore, the measure of the central angle AOB is 90° degrees.

To find  Equation of x,

8x=96°

x=96°/8

x=12

Hence, Equation of x will be 12.

The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:

(1/2) * 90° = 45°

The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:

2πr - 5π = 15π

for major arc,

We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:

15π * (180/π) = 270°

Therefore, the measure of the major arc ACB is 270°.

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The correct statements describing the area and perimeter of the patio are:

The area of a rectangle is given by the product of its length and width. So, the area of the patio is:

Area = length x width

Area = (1 + 2x)(2 - 3x)

Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.

The perimeter of a rectangle is given by the sum of the lengths of all four sides.

So, the perimeter of the patio is:

Perimeter = 2(length + width)

Perimeter = 2(1 + 2x + 2 - 3x)

Perimeter = 2(3 - x)

Therefore, the perimeter of the patio is 2(3 - x) yards.

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Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

The approximate time, compass heading, distance, and fuel consumed during the climb of the airplane are 18 minutes, 214°, 2,430 nautical miles, and 3.9 gallons, respectively.

To determine the approximate time, compass heading, distance, and fuel consumed during the climb of the airplane, we need to use some basic principles of navigation and aviation.

First, we need to calculate the climb time. Since the airplane is climbing at a rate of 500 ft/min and the cruise altitude is 9,500 ft, the time it takes to climb to the cruise altitude can be calculated as (9,500-1,000)/500 = 18 minutes.

To calculate the compass heading, we need to account for the variation and deviation. The true course is given as 215°, and the variation is 3° W, which means we need to subtract 3° from the true course to get the magnetic course.

Therefore, the magnetic course is 215° - 3° = 212°. Next, we need to account for the deviation, which is given as -2°, meaning we need to add 2° to the magnetic course to get the compass heading. Therefore, the compass heading is 212° + 2° = 214°.

The distance traveled during the climb can be calculated using the average true airspeed and the climb time. The distance is given by the formula: distance = airspeed x time. Therefore, the distance traveled during the climb is approximately 135 kts x 18 min = 2,430 nautical miles.

Finally, we can calculate the fuel consumed during the climb using the average fuel consumption rate. The fuel consumed is given by the formula: fuel consumed = fuel consumption rate x time. Therefore, the fuel consumed during the climb is approximately 13 gal/hr x 18 min/60 min = 3.9 gallons.

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Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the entire population, which includes all 352 students. Therefore, the answer is (B) 352.

It's worth noting that the sample of 99 students could be used to estimate the population variance if certain assumptions are met and appropriate statistical methods are used. However, the question specifically asks for the population variance, which refers to the variance of the entire population, not just the sample.

Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the heights of all 352 students in the population.

Therefore, the answer is B. 352.

The equation of the line in slope-intercept form is:

y = 4x + 9

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

In this case, we know that the line passes through the point (-4, -7) and has a slope of 4. So, we can plug in the values of x, y, and m into the slope-intercept form and solve for b:

-7 = 4(-4) + b

Simplifying the right side:

-7 = -16 + b

Adding 16 to both sides:

9 = b

So the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is:

y = 4x + 9

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The question that is a statistical question is "How many miles did your family drive last week?"

A statistical question is a question that requires collecting and analyzing data to answer.

It involves investigating a specific variable or variables and determining patterns, trends, or relationships within the data.

The question "How many miles did your family drive last week?" is statistical, as it involves collecting and analyzing data related to a specific variable (miles driven) over a certain period of time (last week).

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According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.

To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.

According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).

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The book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

The straight-line method is a common method of calculating depreciation for fixed assets. It assumes that the asset will lose an equal amount of value each year over its useful life. To calculate depreciation using the straight-line method, you subtract the asset's estimated salvage value from its original cost to determine the total amount that needs to be depreciated. Then, divide that amount by the estimated number of years the asset will be in use to find the annual depreciation expense. The formula for straight-line depreciation is:

Annual depreciation expense = (Original cost - Salvage value) / Estimated useful life

The annual depreciation expense for the equipment is:

Depreciation expense = (cost - residual value) / useful life

Depreciation expense = ($212,000 - $14,000) / 15

Depreciation expense = $12,533.33 per year

The total depreciation expense for the first five years is:

Total depreciation expense = Depreciation expense x number of years

Total depreciation expense = $12,533.33 x 5

Total depreciation expense = $62,666.65

To find the book value at the end of the fifth year, we subtract the total depreciation expense from the original cost:

Book value = Cost - Total depreciation expense

Book value = $212,000 - $62,666.65

Book value = $149,333.35

Therefore, the book value of the equipment at December 31, the end of the fifth year, is $149,333.35.

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Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]

The variable d represents the number of days he spends on vacation, and the variable p represents the total number of postcards he buys Cooper will have bought a total of 18 postcards after 2 days of vacation.

If p = 9d represents the total number of postcards Cooper buys in relation to the number of days he spends on vacation, we can substitute d = 2 into the equation to find the total number of postcards he buys after 2 days of vacation:

p = 9d

p = 9(2)  [Substitute d = 2]

p = 18

Therefore, Cooper will have bought a total of 18 postcards after 2 days of vacation.

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Therefore , the solution of the given problem of unitary method comes out to be Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

Use the tried-and-true fundamental methodology, the real variables, and any useful information you learn from the general and specific questions to complete the assignment. Customers may be given another chance to taste the products in expression response. If these improvements don't happen, we'll lose out on significant advancements in programming comprehension.

Here,

Due to the idea of unit pricing, Stacy's Bake Shop sells cupcakes for less money than The Best Cake Shop.

In order to compare products with varying quantities or sizes, unit pricing, also known as price per unit, is used.

In this instance, Stacy's Bake Shop charges $21 for a dozen cupcakes, hence the price per cupcake is calculated as

=>  $21 /12, or $1.75 per cupcake.

On the other hand, The Best Cake Shop charges $12 for a half-dozen cupcakes; this indicates that each cupcake costs $2, or $12 divided by six.

As a result, Stacy's Bake Shop charges $1.75 less each cupcake than The Best Cake Shop, which charges $2.

As a result, Stacy's Bake Shop sells cupcakes for less than The Best Cake Shop does according to the idea of unit pricing.

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The area of the irregular shape is 34m²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles

The shape above can be divided into three rectangles and the sum of the area of this rectangles is the area of the shape.

Area of rectangle 1

= l× w

= 7×2 = 14 m²

Area of rectangle 2

= l× w

= 5×2 = 10 m²

Area of rectangle 3

= l×w

= 5×2 = 10m²

Therefore , the area of the irregular shape is

14+10+10 = 34m²

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Each cube has a volume of 1 cm³, and the rectangular prism contains 320 cubes, so the volume of the rectangular prism is 320 cm³.

Volume is a physical quantity that measures the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters (m³) or cubic centimeters (cm³).

Here,

Length side = 4 cubes

= 5 cm

Width side = 2 cubes

= 2 cm

Height side = 2 cubes

= 2 cm

The length of the rectangular prism is 4 cubes which are equal to 5 cm each, so the length is 4 x 5 cm = 20 cm. The width of the rectangular prism is 2 cubes which are equal to 2 cm each, so the width is 2 x 2 cm = 4 cm. The height of the rectangular prism is 2 cubes which are equal to 2 cm each, so the height is 2 x 2 cm = 4 cm.

To find the volume of the rectangular prism, we multiply the length by the width by the height:

Volume = length x width x height

Volume = 20 cm x 4 cm x 4 cm

Volume = 320 cubic cm

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Complete question:

Each cube in this rectangular prism is 1 cm³. What is the volume of the rectangular prism?

Answer:

127.5

Step-by-step explanation:

multiply 15 and 17 divide by 2 and boom

Answer:

40 plus 19/ 9-3=40

Gold costs less than platinum per ounce because the slope of the graph for gold is less steeper than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

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The equation of the reflected graph is y = -3ˣ.

To reflect a graph over the x-axis, we need to negate the y-coordinates of all the points on the original graph. In other words, if a point (x, y) is on the original graph, its reflection over the x-axis would be (x, -y).

Let's apply this concept to the exponential function f(x) = 3ˣ. The graph of this function is an upward sloping curve that passes through the point (0,1) on the y-axis. If we reflect this graph over the x-axis, the point (0,1) will be mapped to (0,-1), as the x-coordinate remains the same, but the y-coordinate changes sign.

To find the equation of the reflected graph, we need to replace y with -y in the equation of the original function f(x) = 3ˣ. This gives us:

-y = 3ˣ

To isolate y, we can multiply both sides by -1:

y = -3ˣ

This function is a downward sloping curve that passes through the point (0,-1) on the x-axis.

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Answer: The primary rectangle contains a length of 2a units (since it is labeled as "2a" within the diagram), so its zone is 2a x a = 2a^2 square units.

The moment rectangle contains a length of 3a units (since it is labeled as "3a" within the diagram), so its range is 3a x a = 3a^2 square units.

The third rectangle contains a length of 4a units (since it is labeled as "4a" within the graph), so its range is 4a x a = 4a^2 square units.

To discover the overall region of the expansive rectangle, able to include the zones of these three rectangles:

Add up to zone = 2a^2 + 3a^2 + 4a^2

Disentangling this expression, we are able combine the like terms (2a^2, 3a^2, and 4a^2) to urge:

Add up to range = (2 + 3 + 4) a^2

Step-by-step explanation: