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Answer:

147639

236647

336527862

4

5

6

7

8

Answer:

y = x^2 - 6x + 3

Step-by-step explanation:

let the equation of the parabola (in standard form) be y = ax^2 + bx + c

sub (3,-6), (1,-2) and (6,3):

-6 = a(3)^2 + b(3) + c

-6 = 9a + 3b + c

c = -6 - 9a - 3b --(1)

-2 = a(1)^2 + b(1) + c

-2 = a + b + c --(2)

3 = a(6)^2 + b(6) + c

3 = 36a + 6b + c --(3)

sub (1) into (2):

-2 = a + b - 6 - 9a - 3b

b = -(4a + 2) --(4)

sub (1) and (4) into (3):

3 = 36a + 6(-4a-2) - 6 - 9a - 3(-4a-2)

3 = 36a -24a - 12 - 6 - 9a + 12a + 6

15a = 15

a = 1

sub a = 1 into (4):

b = -(4(1) + 2)

b = -6

sub a = 1 and b = -6 into (1):

c = -6 - 9(1) - 3(-6)

c = 3

therefore, equation of parabola is y = x^2 - 6x + 3

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Answer:

The answer is a

Its a because 13 times 3 is 39

13 times 4 is 52

and 13 times 5 is 65

Credit to: alizahalder2007

other points:

x    y

-2  12

-1   3

0   0

1    3

2   12

Let's see

Take some cordinates

Graph attached

When Shannon filled a rectangular 10/279 cm by 10/178 dish with water, the area is B) 178/10 x 279/10 = A and A / 178/10 = 279/10

It should be noted that in order to make the paper, Shannon filled a rectangular 10/279 cm by 10/178 dish with water and then they gently swirled paint on top of the water.

Therefore, the area of the rectangular paper as illustrated will be calculated by multiplying the dimensions given. This will be:

Area = Length × Width

Area = 10/279 × 10/178

Therefore, based on the information, it should be noted that the correct option is B.

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Answer:

b and d

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

The probability that a randomly chosen test-taker will score between 470 and 530 is 0.2358 (or 23.58% when expressed as a percentage).

To solve this problem, we need to use the standard normal distribution formula:
Z = (X - μ) / σ
where Z is the standard score (z-score) of a given value X, μ is the mean, and σ is the standard deviation.
First, we need to convert the given values of 470 and 530 to z-scores:
Z1 = (470 - 500) / 100 = -0.3
Z2 = (530 - 500) / 100 = 0.3
Next, we need to find the probability that a randomly chosen test-taker will score between these two z-scores.

We can use a standard normal distribution table or a calculator to find the area under the curve between -0.3 and 0.3.
Using a calculator or an online tool, we find that the area under the curve between -0.3 and 0.3 is approximately 0.2358.

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The required critical value of the confidence interval is Tc = 2.947

Given data ,

Let the confidence interval value be = 0.99

Now , the sample size is n = 17

And , we have,

For a confidence level of c = 0.99 and a sample size of n = 17

(which is relatively small), we will use a two-tailed t-distribution.

we know that,

df = Sample Size - 1

So, we need to check the critical value column under confidence level 0.99 and across the row showing df = 16.

From the t-table this value comes out to be 2.921

Using a t-distribution table or statistical software, we get,

the critical value tₓ for a confidence level of 0.99 and a sample size of 17 is approximately 2.921.

Hence , the critical value tₓ for a confidence level c = 0.99 and sample size n = 17 is approximately 2.921

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The quartiles and outliers for the data provided are as follows:

1. Quartiles for the tire pressures of car tires at an auto clinic:

2. The outlier(s) for the tires prices is $450

3. The outlier(s) for the tires prices is $650

4. The outlier(s) for the tires prices is $540

5. Quartiles for the tire pressures of car tires at an auto clinic are:

They describe the dispersionof a set of data values.

Outliers are data points that differs significantly from other observations.

There are two outliers: lower boundary outliers and upper boundary outliers.

Q1 − 1.5(IQR)

Q3 + 1.5(IQR)

where IQR is interquartile range

Arranging in increasing order:

19, 20, 23, 27, 28, 29, 34, 34, 36.

Q2 = 28

Q4 = 36

Q1 = (20 + 23) / 2

Q1 = 21.5

Q3 = (34 + 34) /2

Q3 = 34

Arranging in increasing order:

58, 78, 87, 95, 125, 152, 158, 182, 195, 450

Q1 = (87 + 78)/2

Q1 = 62.5

Q3 = 182 + 195/2

Q3 = 188.5

IQR = 188.5 - 62.5

IQR = 126

Lower boundary outlier(s) = 62.5 - 1.5(126)

Lower boundary outliers = -126.5

Thus there are no lower outliers.

Upper boundary outliers = 188.5 + 1.5(126)

Upper boundary outliers = 377.5

Therefore, 450 is an outlier.

Arranging in increasing order:

78, 87, 98, 138, 145, 155, 159, 172, 195, 210, 240, 650

Q1 = 98

Q3 = 210

IQR = 210 - 98

IQR = 112

Lower boundary outlier(s) = 98 - 1.5(168)

Lower boundary outliers = -70

Thus there are no lower outliers.

Upper boundary outliers = 210 + 1.5(112)

Upper boundary outliers = 378

Therefore, 650 is an outlier.

Arranging in increasing order:

75, 85, 88, 135, 135, 156, 168, 192, 195, 210, 230, 245, 540

Q1 = (88 + 135)/2

Q1 = 111.5

Q3 = (210 + 230)/2

Q3 = 220

IQR = 220 - 111.5

IQR = 108.5

Lower boundary outlier(s) = 111.5 - 1.5(108.5)

Lower boundary outliers = - 51.25

Thus, there are no lower outliers.

Upper boundary outliers = 220 + 1.5(111.5)

Upper boundary outliers = 387.25

Therefore, 540 is an outlier.

Arranging in increasing order:

18, 23, 24, 24, 27, 29, 32, 34, 35.

Q2 = 27

Q4 = 35

Q1 = (23 + 24) / 2

Q1 = 23.5

Q3 = (32 + 34) /2

Q3 = 33

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\(\textbf{a)}\\\\(2b^4)^3 \\\\=2^3 \cdot (b^4)^3\\\\=8b^{4 \times 3}\\\\=8b^{12}\\\\\textbf{b)}\\\\\left( \dfrac{3}{x^2 y} \right)^2\\\\\\=\dfrac{3^2}{(x^2 y)^2}\\\\\\=\dfrac{9}{x^4 y^2}\\\\\textbf{c)}\\\\(5a^4b)^2\\\\=5^2\cdot a^{4 \times 2} \cdot b^2\\\\=25a^8b^2\\\\\textbf{d)}\\\\\left( \dfrac{m^3 }{2n^2} \right)^4\\\\\\=\dfrac{(m^3)^4}{(2n^2)^4}\\\\\\=\dfrac{m^{3 \times 4}}{2^4 \cdot n^{2 \times 4}}\\\\\\=\dfrac{m^{12}}{16n^8}\)

The orders are 1 stay the same. 2 change to 4, 3 change to 2, 4 change to 3, and 5 stays the same.

Multiple: 1/ 8 & 2/ 4  = 1 · 2/ 8 · 4  = 2/ 32  = 1 · 2/ 16 · 2  = 1/ 16   Multiply both numerators and denominators. Result fraction keep to lowest possible denominator (lowest=2). In the next intermediate step , cancel by a common factor of 2 gives 1/ 16 .  In words - one eighth multiplied by two quarters = one sixteenth.

Final result: 1/16

We used the fact that y goes to 1 as x goes to infinity to determine the value of the constant C in the equation we got from part B. This allowed us to find the equation for the curve.

C) To find the equation for the curve given the condition that as x goes to infinity, y goes to 1, we need to use the solution obtained in part B and determine the constant C. Here's how to do it:

As x approaches infinity, we have:
1 = sqrt((x^4 + 8x^2 + 16) / (2x)) + C

Since x is going to infinity, we can consider x^4 to be dominant over the other terms in the numerator, so:
1 ≈ sqrt((x^4) / (2x)) + C

Simplifying the above expression, we get:
1 ≈ sqrt(x^3 / 2) + C

As x goes to infinity, the term sqrt(x^3 / 2) also goes to infinity. For the equation to hold true, C must be equal to negative infinity. However, since C is a constant and not a variable, we cannot consider it to be equal to negative infinity.

Thus, there seems to be a mistake in the solution obtained in part B, as it does not satisfy the given condition in part C. Please double-check the solution and steps taken in part B to ensure the correctness of the answer.

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The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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Answer:

No solution (2nd graph)

Step-by-step explanation:

The absolute value of any number can't be negative, so there is no solution to this problem.

Answer:

second one (no solution)

Step-by-step explanation:

Answer:

x=152.5

Step-by-step explanation:

subtract from both sides 25 so it will be

10x=1525

then divide both by 10 so it will be

x=152.5

Therefore, for spheres of different sizes, we need to use different measuring units, unlike prisms and pyramids, where a unit cube can be used as a standard unit for all shapes with the same base and height.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the measure of the total amount of space that an object takes up. The standard unit of volume is the cubic meter (m³) in the International System of Units (SI), but other units such as cubic centimeters (cm³) and cubic inches (in³) are also commonly used. The volume of an object can be calculated using different formulas depending on its shape and dimensions.

Here,

A unit sphere is not a good unit of volume measurement for all spheres because spheres come in various sizes and diameters. The unit sphere has a radius of 1, and while it can be used to measure the volume of spheres with radii equal to 1, it cannot be used to measure the volume of spheres with different radii.

For example, if we want to find the volume of a sphere with a radius of 2, we cannot use the unit sphere as a measuring unit. Instead, we would need to use a larger sphere with a radius of 2 as our measuring unit.

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The correct answer is (c) between 0 and infinity. This can be answered by the concept from F statistic.

The F statistic, which is used in ANOVA (Analysis of Variance), is calculated as the ratio of the variance between groups to the variance within groups. Since variance is always a positive value (it measures the spread or dispersion of data), the F statistic will always be greater than or equal to 0.

Furthermore, the F statistic follows an F-distribution, which is a continuous probability distribution that ranges from 0 to infinity. The F-distribution has a skewed shape, with most of the values clustered towards 0 and decreasing as the values get larger. This means that the F statistic can take on values anywhere between 0 and infinity, but it cannot be negative.

Therefore, when conducting an ANOVA, FDATA will always fall within the range of 0 to infinity.

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Answer:

B. is correct

Step-by-step explanation:

have a nice day!!

Answer:

look it up :)

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

For commission on his sales is 7%

He makes a total sales of $ 12500

so 7 / 100 * 12500

it will be $ 875 as his total commission.

The solutions to the quadratic equation \(2x^2 + 6x - 1 = 0\), obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

To solve the quadratic equation\(2x^2 + 6x - 1 = 0\)by completing the square, follow these steps:

Ensure that the coefficient of \(x^2\) is 1. In this case, it is already 2, so we don't need to make any changes.

Move the constant term to the other side of the equation. Add 1 to both sides:

\(2x^2 + 6x = 1\)

Divide the coefficient of x by 2 and square it. In this case, (6/2)^2 = 9.

Add the result from step 3 to both sides of the equation:

\(2x^2 + 6x + 9 = 1 + 9\)

Simplifying, we get:

\(2x^2 + 6x + 9 = 10\)

Write the left side of the equation as a perfect square trinomial. In this case, it is \((x + 3)^2.\)

\((x + 3)^2 = 10\)

Take the square root of both sides:

\(√[(x + 3)^2] = ±√10\)

Simplifying:

\(x + 3 = ±√10\)

Solve for x by subtracting 3 from both sides:

x = -3 ± √10

So, the solutions to the quadratic equation \(2x^2 + 6x - 1\)= 0, obtained by completing the square, are x = -3 + √10 and x = -3 - √10.

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Answer: 648 in^2 of wrapping paper.

Step-by-step explanation:

The question is asking for the surface area of the prism. The dimensions of the prism are 16inX13inX4in.

All we need to do is find the area of all the surfaces and add them. So:

2(16x4)+2(13x4)+2(16X13) is our expression.

2(16x4)= 2x64= 128

2(13x4)= 2x52= 104

2(13x16)= 2x208= 416

Finally, we add:

128 + 104 + 416 = 648

Therefore, 648 in^2 of wrapping paper is needed to cover the box.

Sonya walks approximately 10.24 city blocks to get from her house to the dog park.

What is coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and figures using the coordinate system. It is also known as analytic geometry or Cartesian geometry.

To find the distance between two points in the coordinate plane, we can use the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

Using this formula, we can find the distance between Sonya's house and the stop sign:

d1 = √((-2 - (-2))² + (1 - 6)²) = √(5² + (-5)²) = √(50) = 5√(2)

We can then find the distance between the stop sign and the dog park:

d2 = √((1 - (-2))² + (1 - 1)²) = √(3²) = 3

Finally, we can add the two distances together to find the total distance Sonya walks:

d_total = d1 + d2 = 5√(2) + 3 ≈ 10.24

Therefore, Sonya walks approximately 10.24 city blocks to get from her house to the dog park.

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Answer:

1. C -- 22.5+36.4+110.1 = 169 A triangle has 180 degrees.
2. D -- 180-(29.1+80) = 70.9
3. 26 -- 180-(122+32) = 26
4. A -- 180-(42.7+90) = 47.3
5. 68 -- 180-(97+15) = 68

6. Last Triangle -- 108+32+76 = 216 216>180 Too big

Answer:

me im lonely

Step-by-step explanation:

Answer:

Center = (4, -5)

radius = 6

======================================================

Explanation:

The general template of any circle is

(x-h)^2 + (y-k)^2 = r^2

Rewrite the given equation into this form

(x-4)^2 + (y- (-5))^2 = 6^2

We can see that (h,k) = (4,-5) is the center and r = 6 is the radius.

Answer:

Step-by-step explanation:

y = (x + 12)(x - 15)

y = x^2 - 3x - 180

The percentage of 100 square quadrilateral grid shaded is 96%.

since there are 4 unshaded grids and rest 96 are shaded then the percentage will be

shaded percentage = 96 × 100/100 = 96%

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Therefore, the diagonal that connects the midpoints of the other two sides of the kite bisects the other diagonal.

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. A trapezoid can have two pairs of parallel sides, in which case it is called a parallelogram.

Here,

First, let's define what a trapezoid and a kite are:

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid.

A kite is a quadrilateral with two pairs of adjacent sides of equal length.

Now, let's look at some common trapezoid theorems and how to prove them:

The bases of a trapezoid are parallel.

To prove this theorem, we can use the fact that opposite angles of a parallelogram are equal. Since the bases of a trapezoid are parallel, we can draw a line segment that connects the endpoints of the non-parallel sides to form a parallelogram. The opposite angles of the parallelogram are equal, so the opposite angles of the trapezoid are also equal. Therefore, the bases of a trapezoid are parallel.

The legs of a trapezoid are congruent.

To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. Therefore, the legs of a trapezoid are congruent.

The diagonals of a trapezoid bisect each other.

To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. The diagonals of the trapezoid connect the midpoints of the non-parallel sides of the triangles, which are also the midpoints of the legs of the trapezoid. Therefore, the diagonals of a trapezoid bisect each other.

Now, let's look at some common kite theorems and how to prove them:

The diagonals of a kite are perpendicular.

To prove this theorem, we can use the fact that a kite can be divided into four right triangles. Since two pairs of adjacent sides of a kite are equal in length, the right triangles that share a common vertex have one leg that is perpendicular to the other leg. Therefore, the diagonals of a kite are perpendicular.

One diagonal of a kite bisects the other diagonal.

To prove this theorem, we can use the fact that a kite can be divided into four triangles. Since two pairs of adjacent sides of a kite are equal in length, the diagonal that connects the non-adjacent vertices of the kite divides the kite into two congruent triangles.

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Complete question:

Prove the trapezoid theorems: for Trapezoids and Kites.