4. Stephanie breaks on average 1.5 pencils every school day. How many pencils can she expect to break in a week (5 days)?

Having four sides, four vertices, and four angles, a closed quadrilateral is a type of polygon. It is made up of four linked non-collinear points.

A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. Four non-collinear points are joined to create it. Quadrilaterals' internal angles add up to a constant 360 degrees. A quadrilateral is a flat, two-dimensional shape with four sides that are all straight, closed (the lines come together), and have all four sides.

A quadrilateral in geometry is a four-sided polygon with four edges and four corners. The name is a combination of the Latin words quadri, which is a variation of four, and latus, which means "side."

Trapezium

A trapezoid, also referred to as a trapezium, is an open, flat object with 4 straight sides and 1 set of parallel sides. A trapezium's bases are its parallel sides, while its legs are its non-parallel sides. Parallel legs are another option for a trapezium.

Parallelogram

The opposite sides of a quadrilateral that is a parallelogram are parallel and equal to one another. It has equal internal opposing angles. Additionally, the angles on the same transverse side of the plane add up to 180 degrees or are complementary to one another.

Rectangle

All the angles of a rectangle are right angles, while only the opposing angles in a parallelogram are equal. The diagonals of a parallelogram are not equal, unlike the diagonals of a rectangle.

Rhombus

A quadrilateral with a rhombus shape has four equal sides. Rhombuses are an unique kind of parallelogram that have equal sides on all sides because opposite sides of a parallelogram are equal.

Square

A square has four equal sides and four equal angles, making it a regular quadrilateral in Euclidean geometry. It is also known as a rectangle with two neighboring sides of identical length.

Kite

A kite is a heavier-than-air (HTA) or lighter-than-air (LTA) device that is tethered and has wing surfaces that react to the air to produce lift and drag forces.

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the correct question is -

What is a quadrilateral ? Mention six types of quadrilaterals?

Answer:

24:18

Step-by-step explanation:

Let x be the constant of proportionality...

Hence,

4x+3x=42

7x=42

x=6

Hence,

24:18 is your answer

Answer:

720 ft^3

Step-by-step explanation:

6 * 10 *12

v = l * w * h

6 * 10 * 12 =  720

Volume is a three-dimensional scalar quantity. The volume of the self-storage centre room is 720 ft³.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a room or box that is the shape of a rectangular prism is calculated by multiplying the length, width, and height of the prism.

Volume = Length × Width × Height

Given that the self-storage centre room's are 6 feet wide, 10 feet deep, and 12 feet high. Therefore, the dimension of the room can be written as,

Length = 10 ft

Width = 6 ft

Height = 12 ft

Now, the volume of the room can be written as,

Volume of the room = 10ft × 6ft × 12ft

                                  = 720 ft³

Hence, the volume of the self-storage centre room is 720 ft³.

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Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

Answer:

Direct V:

y=3x

y=(2/7)x

-0.5x=y

Not direct V:

y=2.2x+7

x=-1

y=4

Step-by-step explanation:

That was the answer on edge2020 :))

Direct variation usually conform to the general formula : \(y = kx \) where k is the proportionality constant. Hence sorting the equation into tbe appropriate category :

Direct variation :

y = 3x

y = (2/7)x

y = -0.5x

Non - direct variation :

y = 2.2x + 7

y = 4 and x = - 1

Therefore, only three of the expressions exhibit direct variation while the other three do not.

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The correct comparison between two function is

Both functions are increasing, but function g increases at a faster average rate.

The Correct option is (B).

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume

f(x) = \(ab^x\)+ c

so, at x=0, f(0)=-10

a +c = -10

Similarly, by satisfying the above table in the f(x)

f(x) = -33/5 \((1/11)^x\) - 17/5

and, f'(x) > 0

Thus, f(x) is an increasing function.

Now, g(x) = -18 \((1/3)^x\) +2

g'(x) = -18 \((1/3)^x\) log(1/3)

as log 1/3 <0

So, g'(x) > 0

Thus, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).

Hence, Both functions are increasing, but function g increases at a faster average rate.

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The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

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Answer:

A

Step-by-step explanation:

Answer:

-----------------------

Substitute 12 and 24 for n into formula and calculate.

So, the 12th term is 63 and 24th term is 123.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:B

Step-by-step explanation:

Given the time, the distance that the.womn drives will be 240 miles.

From the information illustrated, the woman drives out at 40 miles per hour, return over the same road at 30 miles per hour, and spends 8 hours away from home.

It should be noted that the average speed will be illustrated as:

= (2 × r1 × r2) / +r1 + r2)

= (2 × 40 × 30) / (40 + 30)

= 240/7

Since she drive for 7 hours, the distance will be:

= 240/7 × 7

= 240 miles.

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First we need to find;

f(2)

simply substitute n = 2 into the function f(n) = 4f(n-1)

f(2) =4(2-1) = 4f(1) = 4(9) = 36

Next, we will find f(3)

f(3) =4f (3-1) = 4f(2) = 4(36) = 144

Next, is to find f(4)

f(4) = 4f(4-1) = 4f(3) = 4(144)= 576

Next, we will find f(5)

f(5) = 4f(5-1) = 4f(4) = 4(576) = 2304

Then, we will now find f(6)

f(6) = 4f(6-1) = 4f(5) = 4(2304) = 9216

Therefore, the value of f(6)= 9216

Answer:

About 11.025

Step-by-step explanation:

\(\sin{58^\circ}=\dfrac{x}{13}\\\\x=13\cdot\sin{58^\circ} \approx11.025\)

Answer: bottom leftt !

The group of people who should make up a sample that will best answer her question is the 9th graders in her school. The correct option is C.

Subjects are the different sets of information which is studied.

9th graders in her school will be perfect because the question is specifically asking about the opinions of 9th-grade students in the high school, so it makes sense to sample this group directly.

The other options may provide some insights, but they may not be as accurate or representative of the opinions of the 9th-grade students in the school.

Thus, the correct option is C, 9th graders in her school.

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Candice grows beets on 66 acres of farmland.

A ratio indicates the number of times one number contains another.

Given that, Candice has 88 acres of farmland and she grows beets on 3/4 of the land.

Candice grows beets on 3/4 of 88 acres of farmland,

3/4 of 88

= 3/4×88

= 66

Hence, Candice grows beets on 66 acres of farmland.

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The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer:

B, C

Step-by-step explanation:

A: √4 = 2, so the side lengths form an equilateral triangle, not a right triangle.

__

B: √(9²+40²) = 41 . . . . these form a right triangle

__

C: √(5² +10²) = √125 . . . . these form a right triangle

Answer:

Step-by-step explanation:

The three numbers are 50, 40, and 27.

We can solve this equation by setting up a system of equations.

Let x be the first number, y be the second number, and z be the third number.

x + y + z = 117

y = x - 10

z = (1/2)x + 2

Substituting the equation for y into the first equation, we get:

x + (x - 10) + (1/2)x + 2 = 117

2x - 8 = 117

2x = 125

x = 62.5

Substituting this value of x into the other equations, we get:

y = x - 10 = 62.5 - 10 = 52

z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5

Rounding these values, the three numbers are 50, 40, and 27.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

x ≤ 3

Step-by-step explanation:

To solve the inequality 5x ≤ 15, we need to isolate x on one side of the inequality. We can do this by dividing both sides of the inequality by 5:

5x/5 ≤ 15/5

x ≤ 3

So the solution to the inequality is x ≤ 3. This means that any value of x that is less than or equal to 3 will make the inequality true. To graph this inequality on a number line, we draw a closed circle at point 3 and shade the area to the left of the circle to represent all the possible values of x that satisfy the inequality:

<=======●----------------

      3

The circle is closed to indicate that x can be equal to 3, and the shading indicates all the values of x that are less than or equal to 3.

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:

x = 4 - 3 · y

Second, substitute x in the first two equations:

3 · (4 - 3 · y) + 2 · y - z = 8

12 - 9 · y + 2 · y - z = 8

- 7 · y - z = - 4

2 · (4 - 3 · y) + 2 · z = - 4

8 - 6 · y + 2 · z = - 4

- 6 · y + 2 · z = - 12

Third, clear z in the first equation derived in the previous step:

z = 4 - 7 · y

Fourth, substitute z in the second equation derived in the second step:

- 6 · y + 2 · (4 - 7 · y) = - 12

- 6 · y + 8 - 14 · y = - 12

- 20 · y = - 20

y = 1

Fifth, calculate y and x:

z = 4 - 7 · 1

z = - 3

x = 4 - 3 · 1

x = 1

The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).

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Answer:

He traveled 140 miles after 4 hours.

Step-by-step explanation:

Answer: 140 miles

Step-by-step explanation:

35 mph

4 hours

35 x 4 = 140 miles

Answer:

the answer is px and at ako

Answer:

  a.  1965

  b.  8 years

Step-by-step explanation:

For answers to questions like these it can work to consider the smallest possible dataset.

For our purpose, consider the 9 years/values to be averaged to be ...

  1, 2, 3, 4, 5, 6, 7, 8 ,9

a. The center value of the data set is 5. Its number is 5-1=4 more than the first one.

The first centered value is from the year 1961 +4 = 1965.

b. The 4 values at the beginning, and the 4 values at the end do not have a corresponding "average" value. That is, 4+4 = 8 values in the series are lost with respect to the number of average values.

8 years of values are lost.