How would the equation for the blade of the wind turbine change if the point starts at the π2

position?

The 90th percentile for the random sample of size 16 taken from the normal population with a mean of 100 and a variance of 4 is approximately 100.64

To find the 90th percentile of a random sample of size 16 taken from a normal population with a mean of 100 and a variance of 4, follow these steps:

1. Identify the population mean (μ) and variance (\(σ^{2}\)). In this case, μ = 100 and \(σ^{2}=4\).
2. Calculate the population standard deviation (σ) by taking the square root of the variance: σ = √4 = 2.
3. Since the sample size (n) is 16, the standard error (SE) is calculated by dividing the population standard deviation by the square root of the sample size: \(SE= \frac{σ}{\sqrt{n} } = \frac{2}{\sqrt{16} } = \frac{2}{4} = 0.5\).
4. Next, determine the z-score corresponding to the 90th percentile. You can use a z-table or an online calculator. The z-score for the 90th percentile is approximately 1.28.
5. Multiply the z-score by the standard error: 1.28 (0.5) = 0.64.
6. Finally, add this product to the population mean: 100 + 0.64 = 100.64.

The 90th percentile for the random sample of size 16 taken from the normal population with a mean of 100 and a variance of 4 is approximately 100.64.

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So the vector  form of the equation is: y = -1(x - 2)² + 3.

To convert from standard form to vertex form, we complete the square by following these steps:

Factor out the coefficient of the x-squared term:

y = -x² + 4x - 1

= -1(x² - 4x) - 1

To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:

y = -1(x² - 4x + 4 - 4) - 1

Simplify the expression inside the parentheses by factoring a perfect square:

y = -1((x - 2)² - 4) - 1

Distribute the -1 and simplify:

y = -1(x - 2)² + 3

Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.

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Answer:

3/10 pan left over

Step-by-step explanation:

Assume that the pan started out full of cookies.  After Kate's gift tto Maggie there are (1 - 1/4) of the pan left over, or 3/4 of the pan left over.  Kate gives 2/5 of this remaining 3/4 pan to Scott:  (2/5)(3/4) = 3/10 pan left over.

Answer:

\( (\frac{{m}^{2} }{4} )\pi\)

Step-by-step explanation:

we can find the radius from the diameter by dividing the diameter by 2 (radius is half the diameter)

the formula for the area of a circle is r²π (with r being radius) but since we must use diameter we have to replace r with (m/2)

this gives us our new formula of (m/2)²π, which simplifies to (m²/4)π

that is the answer

- kan academy advance

The polar coordinates of the point (2, 2√3) are (4, 1.05).

To find the polar coordinates (r, θ) of the point (2, 2√3), we first need to calculate r and θ.

r is the distance from the origin to the point, which can be found using the Pythagorean theorem:

r = √(2² + (2√3)²) = √(4 + 12) = √16 = 4

So r = 4.

To find θ, we need to use the tangent function:

tan θ = (2√3)/2 = √3

We know that θ lies in the first quadrant (since both x and y are positive), so we can use the inverse tangent function (arctan or tan^-1) to find θ:

θ = arctan(√3) ≈ 1.05 radians

Therefore, the polar coordinates of the point (2, 2√3) are (4, 1.05).

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\( \frac{x}{12} = \frac{25}{60} \\ 60x = 25 \times 12 \\ 60x = 300 \\ x = \frac{300}{60} \\ \boxed{x = 5}\)

Solution

Step 1:

The equation of an ellipse is

where (h,k) is the center, a and b are the lengths of the semi-major and the semi-minor axes.

Step 2

Thus, h = 5, k=1, a = 1.

The following equation takes into account different properties of an ellipse:

Final answer

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the value of Jeans property tax.

Jean's new home are 4. 23% of the value of the home. For a home of $238500:

x = 4.23% of $238500 = 0.0423 * $238500 = $10088.55

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

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William ran for 2 hours.

The distance of an object is the amount of speed covered with respect to time.

Mathematically:

\(\mathbf{speed = \dfrac{distance}{time}}\)

From the given information:

Elliot ran for 8 miles in x speed, the time at which he ran can be computed as:

\(\mathbf{= \dfrac{8}{x}}\) hours

William ran for 12 miles in x speed, the time at which he ran can be computed as:

\(\mathbf{= \dfrac{12}{x}}\) hours

If Elliot finished his race 40 minutes fewer than William, then we have:

\(\mathbf{=\dfrac{40}{60} \ hour= \dfrac{2}{3 } hour}\)

Therefore, the distance at which William ran for can be computed by using the relation:

\(\mathbf{\dfrac{8}{x}+\dfrac{2}{3}= \dfrac{12}{x}}\)

\(\mathbf{\dfrac{2}{3}= \dfrac{12}{x}- \dfrac{8}{x}}\)

By solving for x,

\(\mathbf{\dfrac{2}{3}= \dfrac{4}{x}}\)

By cross multiply;

2x = 12

x = 12/2

x = 6 miles per hour

Thus, William ran for:

= 12 miles/ 6 miles per hour

= 2 hours

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Answer:

1/2

Step-by-step explanation:

15/30

The GCF is 15

GCF is the greatest common factor

Divide both numbers by the GCF

15/15 = 1

and 30/15 = 2

reduced fraction is 1/2

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

588

Step-by-step explanation:

multiply length x width x height 7×6×14

Step-by-step explanation:

multiply 7,6,14

=588

therefore the answer in cubic centimeters is= 588

Answer:

Step-by-step explanation:

The standard form of a circle is

\((x-h)^2+(y-k)^2=r^2\) where h and k are the coordinates of the center of the circle, and r is the radius squared. Our center is located at (-6, -4)  and from the center to the outer edge is 2 units, so the radius is 2-squaraed, which is 4. That makes the equation for this circle

\((x-(-6))^2+(y-(-4))^2=4\) which simplifies to

\((x+6)^2+(y+4)^2=4\)

Answer:

432

Step-by-step explanation:

To find the volume of a rectangular prism  you multiply, L × W × H

    L = 6     W = 8    H =9  you plug that in  6 × 8 × 9= 432

     so the volume is 432in²

Answer:

35 seconds

Step-by-step explanation:

At negative values he is inside the volcano,  when he reaches 0 he will be at the top of the volcano

At 35 seconds, the elevation is 0, so he is at the top of the volcano

The depth of the chart is NOT impacted by changing the chart style. When changing the chart style, various elements of the chart may be affected.

The data in the chart is directly influenced by the chart style. Different chart styles can present the data in various formats, such as bar charts, line charts, or pie charts, altering how the data is visually represented.

The color of the chart area can be influenced by changing the chart style. The chart area refers to the background or border color surrounding the chart. Different chart styles may utilize different color schemes or themes, which can impact the chart area color.

Similarly, the color of the plot area, which represents the space within the chart where the data is plotted, can be influenced by changing the chart style. Different chart styles may use different color palettes for the plot area, affecting the visual representation of the data points.

However, the depth of the chart, referring to the three-dimensional perspective or layered effect of the chart, is not typically impacted by changing the chart style. The depth of a chart is usually a separate setting or option within charting software, allowing users to control the 3D effect or stacking of chart elements. Changing the chart style does not inherently alter this depth setting.

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Answer:

\(\frac{6}{23}\)

Step-by-step explanation:

simple

The solution is 6/23

The probability that a student chosen from random is a female is given by the equation A = 6/23

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of student being a female be represented as A

Now , the equation will be

The total number of students in the class = 23 students

The total number of females in the class = 6 females

Now ,

The probability of a student chosen at random being a female A = total number of females in the class / total number of students in the class

Substituting the values in the equation , we get

Probability that a student chosen from random is a female A = 6/23

Probability that a student chosen from random is a female A = 0.26

Therefore , the value of A is 6/23

Hence , the probability is 6/23

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From the given information, the amount that will be paid averagely each month will be $138.73.

From the information given, Tim Worker wants to purchase an automobile warranty costing $6,659 and he chooses to make 48 equal payments.

Therefore, the amount that will be paid each month will be calculated thus:

= $6,659 / 48

= $138.73

The amount will be $138.73.

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Answer:

720

Step-by-step explanation:

Out of 80 students the no. of students who sign up=48

So, out of 1200 students 48×1200÷80=720 students sign up.

Answer:

37.68 inches

Step-by-step explanation:

The equation for the circumference of the circle is:

\(C=2\pi r\)

We can substitute 6 in for "r" and 3.14 for "π":

\(C=2(3.14)(6\ in)\\C=12\ in(3.14)\\C=37.68\ in^\)

Answer:

-7/8 is greater

Step-by-step explanation:

-4/5=-0.8

-7/8=-0.875

To find the greater fraction, we can use the butterfly method.

\((-\frac{4}{5} )(- \frac{7}{8} )\)

\(-\frac{4\times8}{5\times7}=\frac{32}{35}\)

Therefore, \(-\frac{4}{5}\) is greater than \(-\frac{7}{8}\).

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

The graph for the reflection of quadrilateral about x-axis is attached below,

In mathematics, reflection refers to the transformation of a figure by flipping it over a line of reflection.  This line is called the "axis of reflection." The reflection of a point across the axis of reflection creates a corresponding point on the other side of the axis. Reflection can also be thought of as a type of mapping in which each point in the original figure is mapped to its corresponding point in the reflected figure. Reflection can be used to explore symmetry and congruence in geometric figures, and it is a fundamental concept in Euclidean geometry.

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Answer:

x=118

Step-by-step explanation:

Answer:

Solve by factoring.

1. 2x^2+9x+26=-4x+5

2x²+9x+4x+26-5=0

2x²+13x+21=0

doing middle term factorization

2x²+7x+6x+21=0

x(2x+7)+3(2x+7)=0

(2x+7)(x+3)=0

either

x=-7/2

or

x=-3.

2.

3x^2-6x-4=0

comparing above equation with ax²+bx+c=0

we get

a=3

b=-6

c=-4

By using quadratic equation

x=\( \frac{ - b±\sqrt{ {b}^{2} - 4ac } }{2a} \)

Substituting value

x=\( \frac{ 6±\sqrt{ {-6}^{2} - 4*3*-4 }}{2*-4} \)

x=\( \frac{ 6±\sqrt{ {84}}}{-8} \)

x=\( \frac{ 6±2\sqrt{ {21}}}{-8} \)

-8x=6±2√21

taking positive

-8x=6+2√21

x=\( \frac{6+2√21}{-8} \)

x=-\( \frac{3+√21}{4} \)

taking negative

-8x=6-2√21

x=\( \frac{6-2√21}{-8} \)

x=-\( \frac{3-√21}{4} \)

Answer:

\(y = -3x -10\)

Step-by-step explanation:

Slope-intercept formula: \(\frac{y_2-y_2}{x_2-x_1}\)

Find slope of  (−1, −7) and (1, -13)

\(\frac{y_2-y_2}{x_2-x_1}\\\\\\frac{-13-(-7)}{1-(-1)}\\\\\\frac{-6}{2}\\\\\-3\)

\(y = mx + b\)

\(y = -3x +b\)

\(y = -3x +b\\-7 = -3(-1) + b\\-7 = 3 +b\\-3 -3\\-10 = b\)

\(y = -3x -10\)

Hope this helps!

The answer to the first question is a. Nominal. The answer to the second and third questions are option a  -1.31 cm and  option a 87.5%, respectively

To compute the sum of squares, we need the mean of the data.

x: 2, 4, 6, 8, 10, 12, 18, 21

y: 3, 5, 8, 6, 8, 15, 10, 12

Mean of x = (2+4+6+8+10+12+18+21)/8 = 9.375

Mean of y = (3+5+8+6+8+15+10+12)/8 = 8.5

SSE = Σ(yi - ŷi)²

= (3 - 8.525)² + (5 - 9.002)² + (8 - 11.48)² + (6 - 10.336)²

+ (8 - 11.48)² + (15 - 19.556)² + (10 - 12.962)² + (12 - 15.898)²

= 127.98

The residual is given by:

residual = observed y value - predicted y value

= 29 - (10.9 + 0.23*73)

= -1.31 cm

The proportion of variation explained by x is:

R² = 1 - (SSE/SSTO) = 1 - (10.7/85.2) = 0.875 or 87.5% (approx.)

The answer to the first question is a, the second and third questions are option a and option a respectively.

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