from a sample of 30 graduate students, the mean number of months of work experience prior to entering an MBA program was 35.41. The national standard dviation is known to be 20 months. What is a 90% confidence interval for the population mean

H satisfies all three subspace properties, it is a subspace of R³.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Let H be the set of all vectors of the form 4t, where t is any real number. We want to find a vector v in R³ such that H = Span{v}.

Let v = [4,0,0]. Then any scalar multiple of v will be of the form [4t,0,0], which is an element of H. Thus, H is contained in Span{v}.

Conversely, any vector in Span{v} can be written as a scalar multiple of v, which is of the form [4t,0,0] and therefore an element of H. Thus, Span{v} is contained in H.

Therefore, we have H = Span{v}.

This shows that H is a subspace of R³ because Span{v} is a subspace of R³ (since v is in R³) and H = Span{v}. To show that H is a subspace of R³, we need to verify the three subspace properties:

The zero vector of R³ is in H: The zero vector of R³ is [0,0,0], which is of the form [4t,0,0] when t = 0. Therefore, the zero vector is in H.

H is closed under vector addition: Let u and w be vectors in H. Then u = [4t₁,0,0] and w = [4t₂,0,0] for some t₁, t₂ in R. The sum u + w is [4t₁+4t₂,0,0], which is also an element of H. Therefore, H is closed under vector addition.

H is closed under scalar multiplication: Let u be a vector in H and let c be a scalar in R. Then u = [4t,0,0] for some t in R. The scalar multiple cu is [4ct,0,0], which is also an element of H. Therefore, H is closed under scalar multiplication.

Therefore H satisfies all three subspace properties, it is a subspace of R³.

To learn more about probability from the given  link : brainly.com/question/30034780

#SPJ1

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

https://brainly.com/question/31467231

Answer:

4

Step-by-step explanation:

12/4=3

8/4=2

Answer:

4

Step-by-step explanation:

Answer:

e^(1 - x)- 1  

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

Given : -

f ( x ) = 4x^2 + 6

To find : -

f ( 3 ) = ?

f ( 3 ) = 4 ( 3 )^2 + 6

= 4 x 9 + 6

= 36 + 6

f ( 3 ) = 42

Answer: F(x)=43x3+6x+C

Step-by-step explanation:

The monthly interest rate is the annual interest rate divided by 12

To calculate the monthly interest rate, we need to divide the annual interest rate by 12 (since there are 12 months in a year).

So if the annual interest rate is 8%, the monthly interest rate can be calculated as:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 8% / 12

Monthly interest rate = 0.6667%

Therefore, the monthly interest rate would be 0.6667%.

Read more about interest at

https://brainly.com/question/24924853

#SPJ1

Answer:

100meter per hour

Step-by-step explanation:

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Read more about area here:https://brainly.com/question/27440983

#SPJ1

In order to determine whether each pair of segments is congruent, we must apply congruence segment postulates which include SSS postulate, SAS postulate and ASA postulate. The given pair of segments is VW and UZ.

Step 1: Check if both segments are the same length. If they are, they are congruent. If they are not, move to the next step.

Step 2: Check if the segments are collinear and have the same orientation. If they are, they are congruent. If they are not, move to the next step.

Step 3: Measure each segment and compare their lengths. If they are the same, the segments are congruent. If they are different, the segments are not congruent. Since we do not have information about the length of these segments, we cannot say whether they are congruent or not. Therefore, the given pair of segments cannot be determined as congruent or not.

Know more about  congruent,  here:

https://brainly.com/question/30596171

#SPJ11

Answer:

The answer is D.

The amount of interest Judith will pay in the 40th month is $401. Thus, the correct answer is option A.

To calculate the amount of interest Judith will pay in the 40th month, we need to determine the remaining mortgage balance at that time. With an amortization period of 22 years (264 months), after 40 months, there will be 264 - 40 = 224 months remaining.

Using the formula for mortgage balance, we can find the remaining balance:

Remaining Balance = Principal * [((1 + r)^n) - ((1 + r)^m)] / [((1 + r)^n) - 1]

Where Principal = $175,000 (initial loan amount), r = 3.2% / 2 = 1.6% (semi-annual interest rate), n = 22 * 2 = 44 (total number of semi-annual periods), and m = 224 / 2 = 112 (remaining number of semi-annual periods).

Substituting the values into the formula, we find:

Remaining Balance = $175,000 * [((1 + 0.016)^44) - ((1 + 0.016)^112)] / [((1 + 0.016)^44) - 1] = $147,334.89

The interest paid in the 40th month is the difference between the previous month's balance and the remaining balance:

Interest = Previous Balance * Monthly Interest Rate = $175,000 - $147,334.89 = $27,665.11

Therefore, Judith will pay approximately $401 in interest in the 40th month. Thus, the correct answer is option A.

To learn more about “interest” refer to the https://brainly.com/question/25720319

#SPJ11

Answer:

No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.

Step-by-step explanation:

It is given that for a fundraiser, the ratio of tickets you sold to tickets your friend sold was 11:5.

Let us look at the ratio of tickets sold by both the persons.

Now, according to the condition given and the ratio mentioned in the question;

The number of tickets sold by me for the fundraiser be = 11x

and

The number of tickets sold by my friend for the fundraiser be = 5x

It is observed that total number of tickets sold by me and my friend are;

=> 11x + 5x

So, it is inferred that the number of tickets sold by me and my friend are not 11 and 5 respectively and can vary upon the value of x.

For instance, if the value of x = 2 than;

=> 11x + 5x

=> 11 × 2 + 5 × 2

=> 22 + 10

=> 32 tickets

Therefore,

No, for various value of x the number of tickets sold by me and my friend for the fundraiser can vary but will always remain in the ratio of 11:5.

To know more about this topic, click here:

https://brainly.com/question/2829334

#SPJ9

Answer:

3 1/4 pounds

Step-by-step explanation:

Marco starts with 8 1/2 pounds, to make things easier rewrite it as 8.5.

He uses 1/4 (or .25) of the apples. 8.5 * .25 = 2.125. Subtract this 2.125 from the 8.5 since it's what's being used. 8.5 - 2.125 = 6.375

Then he uses 3 1/8 (or 3.125) pounds. Subtract 3.125 from the 6.375 we got previously to get 3.25.

Marco has 3.25 pounds left which can be rewritten as 3 1/4 pounds.

Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

know more about universal set click here

https://brainly.com/question/8053622

#SPJ4

Step-by-step explanation:

\( \frac{4}{5} \times \frac{3}{8} \)

Reduce the numbers with the greatest common factor 4

\( \frac{1}{5} \times \frac{3}{2} \)

Just multiply, To multiply the fractions , multiply the numerators and denominators separately

\( \frac{1 \times 3}{5 \times 2} \)

\( \frac{3}{10} \)

That's the answer 3/10 or 0.3

The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

To know more about Laplace transform visit :

https://brainly.com/question/30759963

#SPJ11

There are 4 terms in the simplified equation making it a quadrinomial

The result is Quadrinomial cubic

Start by simplifying the polynomial using the FOIL method:

Multiply one by one:

First multiply the term:

\((2a-5)(a^2-1)=(2a)(a^2-1) -5(a^2-1)\)

And, split out the terms, we get

\((2a-5)(a^2-1)=(2a)(a^2)+(2a)(-1)+(-5)(a^2)+(-5)(-2)\\\\(2a-5)(a^2-1)=2a^3-2a-5a^2+5\)

Now, the degree is equivalent to the highest exponent in the polynomial. So, the degree for this polynomial is 3 meaning its a cubic.

There are 4 terms in the simplified equation making it a quadrinomial

Hence, The result is Quadrinomial cubic .

Learn more about Polynomial at:

https://brainly.com/question/11536910

#SPJ4

Answer:

EF = 18 in. & m∠F = 134 °

Step-by-step explanation:

Hi there,

In order to find the length of side EF, you should realize that this is an isosceles triangle. We know that two sides and two angles of this type of triangle are equal to each other. We also know that the lengths of the sides opposite of the congruent angles are equal to each other. Thus, we proved that length of side EF is equal to the length of side FG.

Therefore, EF is 18 inches because FG is 18 inches.

In order to find m∠F, you need to know that the sum of the angles in a triangle add up to 180°. You add all of the known angle values and subtract it by 180°.

m∠E + m∠G + m∠F = 180°

23° + 23° + m∠F =  180°

46° + m∠F = 180°

m∠F = 134°

Hope this explanation helps you understand this problem. Cheers.

-2.083333333333

Step-by-step explanation:

I got a rational number which is -2.083333333

-2x-10x=25

-12x=25

x=-2.083333

Answer:

Step-by-step explanation:

\(-x^{2} -10x-25=0 SE CAMBIA LOS SIGNOS\\x^{2} +10X+25=0 (se utiliza (a^{2} + 2 ab^{2} + b^{2}), asi factorizando la expresion).\\(x+5)^{2} =0\\x+5=0\\x= -5\)

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here is the step-by-step explanation:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression by following the order of operations:
(4)(7)-(1)(7/6)+0

3. Simplify further:
28-7/6

4. Find a common denominator and combine the terms:
168/6-7/6

5. Simplify the expression to get the final numerical value:
161/6

Therefore, the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

Learn more about algebraic expression

brainly.com/question/953809

#SPJ11

The numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

To find the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x, we need to substitute the given values of the variables into the expression and then simplify.

Here are the steps to do this:

1. Substitute the given values of the variables into the expression:
(2)²(3+4)-(1)²(1/2+2/3)+2(0)

2. Simplify the expression inside the parentheses:
(2)²(7)-(1)²(7/6)+0

3. Simplify the exponents:
4(7)-1(7/6)+0

4. Multiply the numbers:
28-7/6+0

5. Simplify the expression by finding a common denominator and combining the terms:
28-7/6 = 168/6-7/6 = 161/6

So the numerical value of the algebraic expression B²(c+d)-a²(m+n)+2x is 161/6.

Learn more about numerical

brainly.com/question/7067665

#SPJ11

Answer:

7.05 simplified rational

Answer:

irrational number

Step-by-step explanation:

Answer:

2x - 3

To find the value of "a" in the inequality P(-a < z < a) = 0.4314, where z scores are normally distributed with a mean of 0 and a standard deviation of 1, we need to determine the corresponding z-score for the given probability.

Since z scores follow a standard normal distribution with a mean of 0 and a standard deviation of 1, we can use the properties of the standard normal distribution to solve the problem.

The probability P(-a < z < a) represents the area under the standard normal curve between -a and a. Since the standard normal distribution is symmetric, this probability is equivalent to the area under the curve to the right of "a" minus the area to the left of "-a".

By looking up the cumulative probability 0.4314 in a standard normal distribution table, we find the corresponding z-score to be approximately 1.7725.

Learn more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

Learn more about correlation coefficient here:

brainly.com/question/29704223

#SPJ11

The cylinder that is similar has a radius of 2.8 inches and a height of 2.4 inches.

A cylinder is a three-dimensional geometric shape characterized by its radius and height. In this case, we are given a cylinder with a radius of 2.8 inches and a height of 2.4 inches. To identify a similar cylinder, we need to find another cylinder with the same ratio of radius to height.

To determine the similarity of cylinders, we can compare the ratios of their corresponding dimensions. The given cylinder has a radius-to-height ratio of 2.8:2.4, which simplifies to 7:6. Therefore, any cylinder with a radius-to-height ratio of 7:6 will be similar to the given cylinder.

Cylinders that share the same ratio of 7:6 between their radius and height will have proportional dimensions. This means that if we were to increase or decrease the dimensions of one cylinder while maintaining the 7:6 ratio, we would obtain a similar cylinder. It's important to note that the actual measurements of the cylinders may differ, but their relative proportions will remain the same.

Learn more about geometric shape

brainly.com/question/31707452

#SPJ11

There will be 48 blocks in 6 rows, with 8 blocks in each row.

Multiplication is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and division. A product is the outcome of a multiplication operation. In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilize every day.

Here,

number of rows=6

number of blocks in row=8

total number of blocks,

=6*8

=48

There will be 48 blocks in 6 rows with each row having 8 blocks.

To know more about multiplication,

https://brainly.com/question/25679586

#SPJ4

Answer:

3

Step-by-step explanation:

We would be eliminating -9x from the equations.

Thus, we need to make the (-3x) into (-9x) in the first equation.

-9x ÷ -3x = 3

After that, you should be able to solve the equations:

-3x - 2y = 2

Equation 1×3: -9x - 6y = 6

-9x + 3y = 24