X is a normally distributed random variable with mean 61 and standard deviation 8.
What is the probability that X is greater than 53?

Answer:

\(-7x+1-10x^2=0\)

\(-10x^2-7x+1=0\)

\(quadratic\:equation:-\) \(ax^2+bx+c=0\)

\(solutions:-\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(For \\A=-10\\B=-7\\C=1\)

\(x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}}{2\left(-10\right)}\)

\(\sqrt{\left(-7\right)^2-4\left(-10\right)\cdot \:1}=\sqrt{89}\)

\(x_{1,\:2}=\frac{-\left(-7\right)\pm \sqrt{89}}{2\left(-10\right)}\)

\(x_1=\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)},\:x_2=\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}\)

\(\frac{-\left(-7\right)+\sqrt{89}}{2\left(-10\right)}=-\frac{7+\sqrt{89}}{20}\)

\(\frac{-\left(-7\right)-\sqrt{89}}{2\left(-10\right)}=\frac{\sqrt{89}-7}{20}\)

\(x=\frac{\sqrt{89}-7}{20}\)

OAmalOHopeO

a) The area of the surface obtained by rotating the curve y = e^(-3x) about the x-axis cannot be determined without limits of integration. b) The value of a in the parabolic satellite dish is 0.1, and the surface area is approx. 33.51 ft².

a) To find the area of the surface obtained by rotating the curve y = e^(-3x) about the x-axis, we need to know the limits of integration. Without the specified limits, we cannot calculate the exact surface area.

b) The equation of the parabolic satellite dish is y = ax^2. We are given that the dish has a 10 ft diameter, which means the maximum x-coordinate is 5 ft (half of the diameter). Additionally, the maximum depth of 4 ft corresponds to the minimum y-coordinate (-4 ft).

To find the value of a, we substitute the coordinates (5, -4) into the equation: -4 = a(5)^2. Solving for a, we get a = -4/25 = 0.1.

The surface area (SA) of the dish can be calculated using the formula: SA = 2π∫[a, b] x * √(1 + (dy/dx)^2) dx, where [a, b] represents the limits of integration. Since the dish is symmetric, we only need to calculate the surface area for one half of the parabola.

Plugging in the values, the surface area is approximately 33.51 ft².

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Answer:

10 feet

Step-by-step explanation:

The formula for the Perimeter fo a rectangle

= P = 2L + 2W

Where:

L = Length

W = Width

From the question

P = 80 feet

W = 30 feet

Hence:

80 = 2L + 2(30)

80 - 2(30) = 2L

80 - 60 = 2L

20 = 2L

L = 20/2

L = 10 feet

Hence, the length of the fenced area = 10 feet

Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

Answer:

The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

Answer:

x = 17

Step-by-step explanation:

Since the triangle has 2 congruent legs then it is isosceles and the 2 base angles are congruent , that is

4x - 34 = x + 17 ( subtract x from both sides )

3x - 34 = 17 ( add 34 to both sides )

3x = 51 ( divide both sides by 3 )

x = 17

The function y = x^2 - 10x + 21 does not have any local maximum points.

To find the local maximum points of a function, we need to look for critical points where the derivative changes from positive to negative. For the given function y = x^2 - 10x + 21, we can find the derivative by differentiating the function with respect to x:

dy/dx = 2x - 10

To find the critical points, we set the derivative equal to zero and solve for x:

2x - 10 = 0

2x = 10

x = 5

So, the critical point is x = 5. To determine if it's a local maximum or minimum, we can examine the second derivative. Taking the derivative of the first derivative, we get:

d^2y/dx^2 = 2

The second derivative is a constant, and since it's positive (2), we conclude that the critical point x = 5 corresponds to a local minimum, not a maximum. Therefore, there are no local maximum points for the function y = x^2 - 10x + 21.

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Answer:

Step-by-step explanation:

The rectangular prism has a volume of 112.

The second rectangular prism has a volume of 81.

THe third rectangular prism has a volume of 108.

Hope it helps!

Kavitha

Answer:

\(volume \ of \ cuboid = lbh\)

\(volume \ of \ first \ prism = 112cm^3\\\\volume \ of \ second \ prism = 81cm^3 \\\\volume \ of \ third \ prism = 108cm^3\\\\volume \ of \ fourth \ prism = 125cm^3\)

Last prism with sides 5 x 5 x 5 has the greatest volume

Answer:

see explanation

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (4, - 6) and (x₂, y₂ ) = (0, 2)

m = \(\frac{2+6}{0-4}\) = \(\frac{8}{-4}\) = - 2

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

Find the midpoint using the midpoint formula

M =( \(\frac{x_{1}+x_{2} }{2}\) , \(\frac{y_{1}+y_{2} }{2}\) )

    = \(\frac{4+0}{2}\) , \(\frac{-6+2}{2}\) ) = (2, - 2 )

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

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-2}\) = \(\frac{1}{2}\)

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

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = \(\frac{1}{2}\) , thus

y = \(\frac{1}{2}\) x + c ← is the partial equation

To find c substitute (2, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 2 - 1 = - 3

y = \(\frac{1}{2}\) x - 3 ← equation of perpendicular bisector

Answer:

Step-by-step explanation:

Points given: (4, -6) and (0, 2)

Slope intercept form of the line going through the given pints:

y= mx+b

y= -2x+b ⇒ -6= -2*4+b ⇒ b= 8-6= 2 ⇒ y= -2x+2

The slope of the perpendicular bisector is the negative reciprocal of the line segment which it is dividing:

Equation of perpendicular bisector:

It passes through the mid point: (2, -2), so

So the equation of perpendicular line:

Therefore, the general form of the equation of a tangent line to the curve f(x) = 1/3x​ at a point (2,1/6) is given by 2x - 6y + 3 = 0.

The given function is:

f(x)=1/3x and the point is (2,1/6).

To write the general form of the equation of a tangent line to the curve f(x) = 1/3x​ at the point (2,1/6),

we will use the following formula of the point-slope form of the equation of the tangent line:

y - f(2) = f'(2)(x - 2)

Where,f(2) is the function value at x = 2

f'(2) is the slope of the tangent line

Substitute f(2) and f'(2) in the above formula,

we have:

y - 1/6 = (1/3)(x - 2)

Multiplying both sides by 6 to eliminate the fraction, we get:

6y - 1 = 2(x - 2)

Simplifying further, we have:2x - 6y + 3 = 0

This is the general form of the equation of the tangent line.

Therefore, the general form of the equation of a tangent line to the curve f(x) = 1/3x​ at a point (2,1/6) is given by

2x - 6y + 3 = 0.

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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

Answer:

third one in the photo

Step-by-step explanation:

.............

1. Independent random samples arise when one random sample is split into groups differing by an observed feature is incorrect.

2. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

1. Independent random samples arise when individuals in a sample are randomly assigned to experimental groups, data is recorded repeatedly on a random sample of individuals, or random samples are selected separately. The statement that one random sample is split into groups differing by an observed feature does not accurately describe independent random samples.

2. The margin of error in a confidence interval represents the range of values within which the true population parameter is likely to fall. It is calculated by taking half of the width of the confidence interval. Therefore, the correct answer is that the margin of error is equal to half the width of the confidence interval.

In summary, the incorrect statement is that independent random samples arise when one random sample is split into groups differing by an observed feature. The margin of error of a confidence interval about the difference between the means of two populations is equal to half the width of the confidence interval.

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Answer:

6/18 which simplifies to 1/3

Step-by-step explanation:

you know that there are 6 reds so you put that on the numerator of the fraction and you add everything together to get the denominator. then the final answer is 6/18 and you simplify that to 1/3

Answer:

6

Step-by-step explanation: not 6

Answer:

360°

Step-by-step explanation:

The sum of the exterior angles for all polygons is 360°

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

Given,

The mean number of days that the midge Chaoborus spends in its larval stage = 14.1 days

Standard deviation = 2.2 days

We have to find the z-score for an individual midge that spends 12. 7 days in its larval stage;

Now,

z score = (x - μ) / σ

Here,

x = 12.7

Mean, μ = 14.1

Standard deviation, σ = 2.2

Then,

z score = (x - μ) / σ = (12.7 - 14.1) / 2.2 = -0.636

That is,

The z-score for an individual midge that spends 12. 7 days in its larval stage is -0.636

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The probability that a randomly selected tire will have a life of at least 35,000 miles is 0.1587 or about 15.87%.

To solve this problem, we need to use the concept of probability and the normal distribution. We are given that the life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. We want to find the probability that a randomly selected tire will have a life of at least 35,000 miles.

We can use the standard normal distribution to find the probability. We first need to standardize the value of 35,000 using the formula:

z = (x - μ) / σ

where z is the standard score, x is the value we want to standardize (in this case, 35,000), μ is the mean, and σ is the standard deviation. Plugging in the values, we get:

z = (35,000 - 40,000) / 5,000 = -1

Now we can use a standard normal distribution table to find the probability that a randomly selected tire will have a life of at least 35,000 miles. We look up the value of -1 in the table and find that the corresponding probability is 0.1587. Therefore, the answer is:

0.1587

So the probability that a randomly selected tire will have a life of at least 35,000 miles is 0.1587 or about 15.87%.

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Answer: =268.19047cm^3 or 268.08 rounded

Step-by-step explanation: using \(\frac{4}{3} *\pi *r^{3}\) to get my answer.

Hope this helps :)

Answer:

Prime Factors of 72: 2, 3

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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Answer:

1. D

2. A

3. picture isn’t clear

4. B

5. C

Step-by-step explanation:

2. Anything to the power of 0 is = 1

1^-1 = 1/1 = 1

real answer : study hard

Answer:25%

Step-by-step explanation:60*0.25=15

To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

Answer:

A

Step-by-step explanation:

The entire frame is 42 x 23 in, but for each dimension there are two lengths of x inches that are included in the entire dimension but not that of the actual picture. Thus, the correct equation is (42 - 2x)(23 - 2x) = 700 which is choice A.

A single page from the US Census may not give a truly random sample because the data may be skewed due to the way information is presented.

For example, if the page only contains data from a certain age range or gender, then this will not be representative of the population. Furthermore, if the page only contains data from a certain geographic area, then the results could be biased.

Using a random sample of the same sample size would help to overcome the problems associated with taking a single page from the US Census because it would be more representative of the population. A random sample is created by randomly selecting individuals from the population, thus ensuring that all aspects of the population are represented. This ensures that the sample is representative of the population, and not biased in any way. Furthermore, it ensures that the sample size is representative of the population, thus providing accurate results.The formula for a random sample would be:

n = total size of population

m = desired sample size

Random Sample = n x (m/n)

Where n and m are the total size of the population and the desired sample size respectively.

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Answer:

k

Step-by-step explanation:

The condition that ensures a solution for the mentioned equation is :

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0.

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.

According to the Question:

Given that:

x₁+ 2x₂= b₁       ------------------------- (1)

2x₁ + 4x₂ = b₂  ------------------------- (2)

3x₁ + 7x₂ = b₃   ------------------------ (3)

3x₁ + 9x₂ = b₄   ------------------------ (4)

From equation (1) and (2), we get:

b₂ = 2b₁

After analysis equation (1), we have:

   6b₁-3b₃ +b₄ = 0

Using equation (1), (3) and (4), we get:

3(x₁+2x₂) -6(3x₁+7x₂) + 3x₁ + 9x₂ ≠ 0

Putting the value from equation (1),(3) and (4), we get:

6(x₁+2x₂) -3(3x₁+7x₂) + 3x₁ + 9x₂ = 0

Hence option (1) is correct.

Complete Question:

Consider the following system of linear equations:

x₁+ 2x₂= b₁

2x₁ + 4x₂ = b₂

3x₁ + 7x₂ = b₃

3x₁ + 9x₂ = b₄

which one of the following conditions ensures that a solution exists for the above system.

1. b₂ = 2b₁ and 6b₁-3b₃ +b₄ = 0

2. b₃ = 2b₁ and 6b₁-3b₃ +b₄ = 0

3. b₂ = 2b₁ and 3b₁-6b₃ +b₄ = 0

4. b₃ = 2b₁ and 3b₁-6b₃ +b₄ = 0

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Answer:

Step-by-step explanation:

Equation for the volume and solution:

Correct option is D.

Answer:

D. StartFraction 7 over 8 EndFraction x minus 8 = 216; x = 256 centimeters cubed