a probability distribution of the claim sizes for an auto insurance policy is given in the table below: claim size 20 30 40 50 60 70 80 probability 0.10 0.10 0.10 0.20 0.15 0.10 0.25 what percentage of the claims are within one standard deviation of the mean claim size?

Answer:

27 : 12

Step-by-step explanation:

You just add 15 and 12, then you add the dots and your good.

At point P (2, π/4, 2), vector A in Cartesian coordinates is A = <1, 2.5, 2>.

To express vector A in Cartesian coordinates, we can use the following conversions between cylindrical and Cartesian coordinates:

x = ρ * cos(θ)

y = ρ * sin(θ)

z = z

Given vector A = cos(θ) - ρ * sin(θ) + 2 * cos(θ) * sin(θ), we can substitute the corresponding expressions for ρ, θ, and z:

x = cos(θ) * cos(θ) - ρ * sin(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Simplifying these expressions, we get:

x = cos^2(θ) + 2 * cos(θ) * sin(θ) - ρ * sin^2(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Now, we can evaluate vector A at point P (2, π/4, 2):

x = cos^2(π/4) + 2 * cos(π/4) * sin(π/4) - 2 * sin^2(π/4)

y = cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4)

z = 2

Simplifying further, we have:

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

y = (1/2) + 1 + 1 = 2.5

z = 2

For more questions like Coordinates click the link below:

brainly.com/question/22261383

#SPJ11

Don't know the answer sorry

Answer:

1.5

Step-by-step explanation:

Answer:

\( m\angle A = 112 \degree \)

\( m\angle B=95 \degree \)

\( m\angle C =68 \degree \)

\( m \angle D = 85 \degree \)

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle. So, ABCD is a cyclic Quadrilateral.

Opposite angles of cyclic quadrilateral are supplementary.

Therefore,

\(m\angle A + m\angle C = 180\degree \\ (14z - 7) \degree + (8z) \degree = 180 \degree \\ (14z - 7 + 8z) \degree= 180 \degree \\ (22z - 7) \degree= 180 \degree \\ 22z - 7 = 180 \\ 22z= 187 \\ z = \frac{187}{22} \\ z = 8.5 \\ \\ m\angle A = (14z - 7) \degree \\ = (14 \times 8.5 - 7) \degree \\ = (119 - 7) \degree \\ m\angle A = 112 \degree \\ \\ m\angle C =180 \degree - 112 \degree \\ m\angle C =68 \degree \\ \\ m \angle D = (10 \times 8.5) \degree \\ m \angle D = 85 \degree \\ \\ m\angle B =180 \degree - 85 \degree \\ m\angle B=95 \degree \)

The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

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

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

Find out more on equation at: https://brainly.com/question/29174899

#SPJ1

8.8x\(10^{24}\) formula units of \(MgCl_2\) are equal to 4.868 moles of \(MgCl_2\).

To determine the number of moles of \(MgCl_2\) in 8.8x\(10^{24}\) formula units, you need to use Avogadro's number, which is the number of particles (atoms, molecules, or formula units) in one mole of a substance. Avogadro's number is approximately 6.022 x \(10^{23}\) particles per mole.

The formula for \(MgCl_2\) contains one Mg atom and two Cl atoms, so one formula unit of \(MgCl_2\) contains three particles.

To find the number of moles of \(MgCl_2\), we can use the following formula:

moles = number of particles / Avogadro's number

First, we need to calculate the number of formula units of MgCl2:

8.8x\(10^{24}\) formula units of \(MgCl_2\) / 3 particles per formula unit = 2.933 x \(10^{24}\) particles

Next, we can calculate the number of moles:

moles = 2.933 x \(10^{24}\) particles / 6.022 x \(10^{23}\) particles/mole

moles = 4.868 moles.

Therefore, 8.8x\(10^{24}\) formula units of \(MgCl_2\) are equal to 4.868 moles of \(MgCl_2\).

Learn more about moles at

https://brainly.com/question/20486415

#SPJ4

Answer:

Square root of 77.44 = height and length of gray squares = 8.8 cm

Since there are 3 squares that make up the height of that object 8.8 cm * 3 =

26.4 cm (the height of  3 gray squares

Square root of 4.84 = 2.2 cm

So the total height = 26.4 + 2.2 = 28.6 cm

Step-by-step explanation:

Based on the given information and relationships in the diagram, the three true relationships are:

□AACF AECF by HL

DACBF ACDF by SSS

ACFD AEFD by SSS

Given the information Geometry in the question and assuming appropriate triangle arrangements, the possible true statements based on congruence postulates might include: ∆ACF≅∆ECF by HL, ∆ACB≅∆DFC by SSS, and ∆BFA≅∆DFE by SAS.

The provided question appears to pertain to geometric proofs, specifically in relation to triangles and the principles of congruency. Without a proper diagram, it's somewhat difficult to clarify, but based on the clues given, we can touch on some general principles.

Given that ZBCD is a right angle, BC=DC, DF=BF, FA = FE, the most applicable congruence postulates could be Hypotenuse-Leg (HL), Side-Side-Side (SSS), or Side-Angle-Side (SAS). These are all used to prove that triangles are congruent.

So, if we presume the statements to be: ∆ACF≅∆ECF by HL, ∆ACB≅∆DFC by SSS, and ∆BFA≅∆DFE by SAS, these could possibly be correct given the appropriate conditions in the diagram.

Remember: HL can only be applied in right triangles whereas SSS and SAS can be applied without the right angle requirement. All require the triangles to share at least one side or angle.

Learn more about Geometry here:

https://brainly.com/question/31408211

#SPJ2

Yes, the sides 5 cm, 12 cm, and 13 cm form a right-angled triangle.

This is because of the Pythagorean Theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, 13 cm is the hypotenuse, and 5 cm and 12 cm are the other two sides.

5^2 + 12^2 = 25 + 144 = 169

13^2 = 169

Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, this means that the triangle is indeed a right-angled triangle.

To learn more about Pythagorean Theorem:

https://brainly.com/question/343682

#SPJ4

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

To learn more about Probability sample, refer:

https://brainly.com/question/29313175

#SPJ4

Answer:

  90° CCW

Step-by-step explanation:

The angle from C to the origin to C' is a right angle when measured counterclockwise (in the usual direction).

ΔA'B'C' is a rotation of ΔABC 90° CCW.

__

This is fully equivalent to a rotation of 270° CW.

Answer:

Their coefficient have the same number but with opposite sign

Step-by-step explanation:

We can tell that the two coefficient will add to zero because they have the same value but opposite signs.

  When two numbers are of the same value but with opposite sign, they add up to zero.

  The given numbers are;

             -2x²   and  2x²

Coefficient is the number before the variable. Here, the variable is x,

            -2x² = -2

               2x² = 2

    -2 + 2  = 0

Answer:

8

Step-by-step explanation:

Answer:

width = 1 ft

Step-by-step explanation:

"Similar" means same area.

Therefore area of first garden = area of second garden.

Let x be the width of the second garden.

5x4 = 20x

x = 1 ft

To prove that for quadratic Bezier curves, the slope of the line segment p0q equals the slope of the tangent line to the curve at p0, and that the slope of the line segment qp1 equals the slope of the tangent line to the curve at p1, we'll use the properties of Bezier curves and their derivatives.

A quadratic Bezier curve is defined by three control points: p0, p1, and p2. The curve is parameterized by a variable t, where t ranges from 0 to 1. The equation for the quadratic Bezier curve is:

B(t) = (1 - t)^2 * p0 + 2 * (1 - t) * t * p1 + t^2 * p2

Let's calculate the derivative of the Bezier curve with respect to t, denoted as B'(t):

B'(t) = d/dt [(1 - t)^2 * p0 + 2 * (1 - t) * t * p1 + t^2 * p2]

= -2 * (1 - t) * p0 + 2 * (1 - 2t) * p1 + 2 * t * p2

= -2 * (1 - t) * p0 + 2 * (1 - 2t) * p1 + 2 * t * p2

Now, let's find the slope of the line segment p0q, where q is any point on the curve. We'll substitute t = 0 into the equation of the Bezier curve:

q = B(0) = (1 - 0)^2 * p0 + 2 * (1 - 0) * 0 * p1 + 0^2 * p2

= p0

Therefore, q = p0.

The slope of the line segment p0q is given by the difference in y-coordinates divided by the difference in x-coordinates:

slope_p0q = (q.y - p0.y) / (q.x - p0.x)

Since q = p0, the numerator becomes 0, and the slope of the line segment p0q becomes 0.

Now, let's find the slope of the tangent line to the curve at p0. We'll substitute t = 0 into the equation for the derivative of the Bezier curve:

B'(0) = -2 * (1 - 0) * p0 + 2 * (1 - 2 * 0) * p1 + 2 * 0 * p2

= -2 * p0 + 2 * p1

The slope of the tangent line to the curve at p0 is given by the y-component divided by the x-component of the derivative at t = 0:

slope_tangent_p0 = (B'(0)).y / (B'(0)).x

= (-2 * p0 + 2 * p1).y / (-2 * p0 + 2 * p1).x

Since we have q = p0, we can simplify the expression:

slope_tangent_p0 = (-2 * q + 2 * p1).y / (-2 * q + 2 * p1).x

Now, let's find the slope of the line segment qp1. We'll substitute t = 1 into the equation of the Bezier curve:

q = B(1) = (1 - 1)^2 * p0 + 2 * (1 - 1) * 1 * p1 + 1^2 * p2

= p2

Therefore, q = p2.

The slope of the line segment qp1 is given by the difference in y-coordinates divided by the difference in x-coordinates:

slope_qp1 = (p2.y - q.y) / (p2.x - q.x)

Since q = p2, the numerator becomes 0, and the slope of the line segment qp1 becomes 0.

Now, let's find the slope of the tangent line to the curve at p1. We'll substitute t = 1 into the equation for the derivative of the Bezier curve:

B'(1) = -2 * (1 - 1) * p0 + 2 * (1 - 2 * 1) * p1 + 2 * 1 * p2

= 2 * p2 - 2 * p1

The slope of the tangent line to the curve at p1 is given by the y-component divided by the x-component of the derivative at t = 1:

slope_tangent_p1 = (B'(1)).y / (B'(1)).x

= (2 * p2 - 2 * p1).y / (2 * p2 - 2 * p1).x

Since we have q = p2, we can simplify the expression:

slope_tangent_p1 = (2 * q - 2 * p1).y / (2 * q - 2 * p1).x

As we can see, both slope_p0q and slope_tangent_p0 are equal to 0, and both slope_qp1 and slope_tangent_p1 are equal to 0.

Therefore, we have proved that for quadratic Bezier curves, the slope of the line segment p0q equals the slope of the tangent line to the curve at p0, and the slope of the line segment qp1 equals the slope of the tangent line to the curve at p1.

To know more about quadratic bezier curves refer here:

https://brainly.com/question/13944269#

#SPJ11

The probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

To calculate the probability that the sample mean of the waiting times is less than 1.5 minutes, we can use the Central Limit Theorem (CLT) since we have a large enough sample size (n = 35) and the waiting times are uniformly distributed.

According to the CLT, the sample mean of a sufficiently large sample size will follow an approximately normal distribution, regardless of the underlying distribution. In this case, the population mean is E(X) = 2 (the midpoint of the uniform distribution between 0 and 4), and the population standard deviation is σ(X) = √(4²/12) = √(16/12) = √(4/3) ≈ 1.155.

The standard deviation of the sample mean (also known as the standard error) is given by σ(X)/√(n), which in this case is approximately 1.155/sqrt(35) ≈ 0.196.

To calculate the probability that the sample mean is less than 1.5 minutes, we can standardize the value using the z-score formula:

z = (sample mean - population mean) / standard error

z = (1.5 - 2) / 0.196 ≈ -2.551

Next, we can look up the probability corresponding to this z-score in the standard normal distribution table.

From the table, we find that the probability of obtaining a z-score less than -2.551 is approximately 0.0057.

Therefore, the probability that the sample mean of the waiting times is less than 1.5 minutes is approximately 0.0057, or 0.57%.

Learn more about Central Limit Theorem click;

https://brainly.com/question/898534

#SPJ4

Answer:

x=2.25

Step-by-step explanation:

10-3x=5x-8

10+8=5x+3x

18=8x

18/8=x

2.25=x

The population of seniors who plan to attend community college is; 115.

According to the task content;

On this note, the number of seniors who want to attend community college among the 320 seniors is;

On this note, it follows that the number of seniors who want to attend community college is; 115 seniors.

Read more on proportions;

https://brainly.com/question/18437927

Answer:

7. 1583.36 cm³

8. 13,627.18 m³

Step-by-step explanation:

Volume of space consumed by the paper = volume of outer cylinder - volume of center cylinder

✔️Volume of Outer Cylinder:

Volume = πr²h

r = ½(12) = 6 cm

h = 14 cm

Volume = π*6²*14

Volume = 1583.36 cm³

✔️Volume of center cylinder:

Volume = πr²h

r = ½(4) = 2 cm

h = 14 cm

Volume = π*2²*14

Volume = 175.93 cm³

✅Volume of space of the toilet paper = 1583.36 - 175.93 = 1583.36 cm³

8. Volume of the solid = volume of the cone + volume of the cylinder

✔️Volume of the cone = ⅓πr²h:

r = 13 m

h = 14 m

V = ⅓*π*13²*14

V = 2,477.67 m³

✔️Volume of the cylinder = πr²h

r = 13 m

h = 21 m

V = π*13²*21

V = 11,149.51 m³

✅Volume of the solid = 2,477.67 + 11,149.51 = 13,627.18 m³

Answer:

See below

Step-by-step explanation:

The difference of square rules is \(a^2-b^2=(a+b)(a-b)\), but given that the expression is \((x+5)(x+5)\) and not \((x+5)(x-5)\), it doesn't follow this rule.

Answer:

By Looking at the shapes and sizes

Step-by-step explanation:

If you can try and look at the shape and size of it, if you can draw it, draw it on a piece of paper, trace them both, but in the same spot, you didn't specificize, if it was a sphere or just a regular circle or not, so thats all i can tell you.

If a matrix is diagonalizable then it is invertible is False.

A matrix can be diagonalizable but not invertible. For example, the zero matrix (a matrix where all entries are 0) is diagonalizable but not invertible.

What is diagonalizable metrix?

A diagonalizable matrix is a square matrix that can be transformed into a diagonal matrix through a similarity transformation. In other words, a matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D such that A = PDP⁻¹.

Geometrically, diagonalizable matrices represent linear transformations that stretch or shrink the space along a set of independent directions, which are called eigenvectors. The diagonal entries of the diagonal matrix D correspond to the eigenvalues of A, which represent the scaling factors along these directions.

Not all matrices are diagonalizable. A matrix is diagonalizable if and only if it has a sufficient number of linearly independent eigenvectors. In particular, symmetric matrices are always diagonalizable, and non-diagonalizable matrices are often associated with non-invertible linear transformations or defective geometric structures.

To know more about diagonalizable metrix, visit:

https://brainly.com/question/24149420

#SPJ1

Complete question is: If a matrix is diagonalizable then it is invertible is False.

The triangle with maximum area has a height of 11 cm and a base of 11 cm.

To find the dimensions for which the area of the triangle is a maximum, we can use the formula for the area of a triangle, which is A = 1/2 * b * h, where A is the area, b is the base, and h is the height.

Since we know that the sum of the base and height is 22 cm, we can express the base in terms of the height as b = 22 - h.

Substituting this expression for b into the formula for the area, we get A = 1/2 * (22 - h) * h.

To find the maximum value of A, we need to find the value of h that maximizes the expression 1/2 * (22 - h) * h. We can do this by taking the derivative of the expression with respect to h, setting it equal to zero, and solving for h.

Differentiating the expression with respect to h, we get dA/dh = 11 - h. Setting this equal to zero, we get 11 - h = 0, which implies h = 11.

Therefore, the maximum area of the triangle is achieved when the height is 11 cm and the base is also 11 cm (since the sum of the height and base is 22 cm).

For more questions like Area visit the link below:

https://brainly.com/question/29164098

#SPJ11

To compute the orthogonal projection of q onto the subspace spanned by p, we need to first find the projection vector. Let's call this projection vector v. We know that v must be orthogonal to the error vector e, where e is the difference between q and the projection of q onto the subspace spanned by p.

We can express v as a scalar multiple of p, so let's write v as v = ap, where a is a scalar. Then, using the inner product given by evaluation at −1, 0, and 1, we have:
=  =
Since we want v to be orthogonal to e, we need  to be 0. So, we have:
= 0
Expanding this out, we get:
2(6 - a) - 10/3(1 - a^2) = 0
Simplifying and solving for a, we get:
a = 3/5
So, v = 3/5p = 6/5t. Therefore, the orthogonal projection of q onto the subspace spanned by p is:
proj_p(q) = /||v||^2 * v = 9/5 - 18/5t

To know more about orthogonal visit:

https://brainly.com/question/27749918

#SPJ11

Step-by-step explanation:

so, let me retype this.

horizontal asymptote : y = 2

that means lim x going to ±infinity f(x) = 2.

vertical asymptotes :

x = 3

x = -4

that means the function must have these 2 points, where the expression leads to a division by 0 or something similar that would make the result undefined.

we got 4 functions :

A) y = x²/(x² + x - 12)

B) y = x²/(x² - x - 12)

C) y = 2x²/(x² + x - 12)

D) y = 2x²/(x² - x - 12)

so, for which ones we have y = 2 as limit when x goes against + or - infinity ?

that would be C and D.

A and B lead to x²/x² = 1 as limit for gigantic numbers.

C and D lead to 2x²/x² = 2 as limit.

remember, when x gets really, really big, the "±x - 12" part becomes irrelevant.

so, we look at C and D.

which one lead to a division by 0 at x = 3 and x = -4 ?

that would be C.

for x = 3

x² + x - 12 = 3² + 3 - 12 = 9 + 3 - 12 = 12 - 12 = 0

for x = -4

x² + x - 12 = (-4)² - 4 - 12 = 16 - 4 - 12 = 12 - 12 = 0

D with x² - x - 12 would have x = -3 and x = 4 as zeroes.

these are different asymptotes than requested.

so, C is the right answer.

Answer:

155

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

See for the answer below:

Step-by-step explanation:

The answer is A.

Answer:

Area of the composite figure = 42 in²

Step-by-step explanation:

Composite area of the given figure = Area of the rectangle + Area of the right triangle

Area of the rectangle = Length × Width

                                    = 6 × 5

                                    = 30 in²

Area of the right triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                         = \(\frac{1}{2}(4)(6)\)

                                         = 12 in²

Area of the composite figure = 30 + 12

                                                  = 42 in²