Suppose [v]B2 is as follows. 11 14 mo [v]B2 = 13 14 7 6 10 If ordered bases B1 = ={[?][*}a and B2 = find [v]B {[i][ 13}} 4 [v]B, = 1

The number of different positive four digit integers contain each of the digits 0, 1, 2, and 3 exactly once is 18

The given digits = 0, 1, 2 and 3

Total number of digits = 4

We need to create different four digit integers contain each of the digits 0, 1, 2  and 3 exactly once

Here we have to use the permutation

Here first number cannot be zero

Number of digits possible in thousands place = 3

Then different positive four digits integers = 3 × 3 × 2 × 1

= 18

Therefore, 18 different four digits numbers can be formed by using the given digits

Learn more about permutation here

brainly.com/question/28720645

#SPJ4

Answer:

15

Step-by-step explanation:

The numbers in the given data = 12, 17, 16, 10, 20

Total number = 5

12 + 17 + 16 + 10 + 20 = 75

Mean = 75/5

Mean 15

Let L be the linear operator in R2 defined by L(x) = (3x1 - 2x2, 9x1 - 6x2)T. The bases of the kernel and image of L are to be determined. To find the bases of the kernel and image of L, we first recall the definitions of kernel and image of a linear operator. Definition of Kernel: Let T be a linear operator on a vector space V. Then the kernel of T, denoted as ke T, is the subspace of V that consists of all vectors that are mapped to the zero vector of the range of T. Definition of Image: Let T be a linear operator on a vector space V. Then the image of T, denoted as im T, is the subspace of the range of T consisting of all vectors that are mapped by T to some vectors in the range of T. The kernel and image of L are given as follows. Kernel of L: For L(x) = (3x1 - 2x2, 9x1 - 6x2)T to be zero vector, we must have 3x1 - 2x2 = 0 and 9x1 - 6x2 = 0, which implies that x1 = (2/3)x2.

Therefore, a typical element of the kernel of L can be expressed as (x1, x2)T = (2/3)x2(1, 3)T, where x2 is a scalar. Hence, a basis for the kernel of L is {(1, 3)T}. Image of L: The image of L is the subspace of R2 consisting of all vectors that can be expressed in the form L(x) = (3x1 - 2x2, 9x1 - 6x2)T, where x is any vector in R2. It follows that any vector in the image of L is of the form (3x1 - 2x2, 9x1 - 6x2)T = x1(3, 9)T + x2(-2, -6)T. Therefore, a basis for the image of L is {(3, 9)T, (-2, -6)T}.Hence, the bases of the kernel and image of L are as follows. Kernel: {(1, 3)T}Image: {(3, 9)T, (-2, -6)T}.

To know more about Subspace, click here:

https://brainly.com/question/32572236

#SPJ11

Answer:

Step-by-step explanation:

The equation of the line is given as,

According to the slope-intercept form, the equation of a line with slope 'm' and y-intercept 'c', is given by,

Comparing with the given equation, the slope of the given line is,

Theorem: The product of two slopes of two perpendicular lines is -1 always.

Let the slope of the perpendicular line be (m'), and 'b' be the y-intercept. Then, it follows that,

The equation of this perpendicular line is given by,

Given that the perpendicular lines pass through the point (6,-2), so it must also satisfy its equation,

Substitute this value back in the equation of the perpendicular line,

Thus, the equation of a line perpendicular to the given line and passing through the given point is obtained as,

The sum of the fractions 1 / (1 - √5) and 1 / (1 + √5) is equal to 1 + √5. To add or subtract the given expression, 1 / (1 - √5) + 1 / (1 + √5), we need to find a common denominator. The common denominator for these two fractions is (1 - √5)(1 + √5), which simplifies to (1 - √5)(1 + √5) = 1 - √5 + √5 - 5 = -4.

Now, let's rewrite the fractions using the common denominator:

1 / (1 - √5) = (-4) * 1 / (1 - √5) = -4 / (1 - √5)
1 / (1 + √5) = (-4) * 1 / (1 + √5) = -4 / (1 + √5)

Next, we can add the two fractions:

-4 / (1 - √5) + -4 / (1 + √5)

To add fractions with different denominators, we need to find a common denominator. The common denominator for (1 - √5) and (1 + √5) is (1 - √5)(1 + √5), which we found earlier to be -4.

Multiplying each fraction by the appropriate form of 1 will allow us to obtain the common denominator:

(-4 / (1 - √5)) * ((1 + √5) / (1 + √5)) = (-4(1 + √5)) / ((1 - √5)(1 + √5)) = (-4 - 4√5) / (-4) = 1 + √5

Therefore, the sum of the fractions 1 / (1 - √5) and 1 / (1 + √5) is equal to 1 + √5.

For more information on fractions visit:

brainly.com/question/10354322

#SPJ11

Answer:

$62.85

Step-by-step explanation:

Given data

ratio=  10: 7: 5

Total ratio= 10+7+5= 22

Lisa= $20

Her proportion of the ratio = 7

Applying the part to all method

Let the total amount shared be x

7/22= 20/x

cross multiply

7x= 22*20

7x= 440

divide both sides by 7

x= 440/7

x= 62.85

The number of solutions to the equation f(x) = g(x) is option (2) 2 is the correct answer.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

The functions f(x) = In(x + 2) and g(x) = e^x - 1 over the interval (-2,3].

Plot the two functions f(x) and g(x) in the graph as shown below.

In the given interval (-2,3], these two functions intersect at two points.

The point of intersection gives the solution of the function.

Hence we can conclude that the number of solutions to the equation f(x) = g(x) is option (2) 2 is the correct answer.

Learn more about graph of a function here

https://brainly.com/question/2275360

#SPJ3

Answer:

the answer is D have a good day

Answer:

They made 41 candles.

Step-by-step explanation:

v=l×w×hv=10×7×2v=140 cm cubedlastly I divided 5740 by 140 ( the volume of one candle)therefore I got 41 candles were made from 5740 cm cubed of wax

a. The system of equations is

b. For the hexagon

A hexagon is a regular polygon with six sides.

Let x be the acute angles of the hexagon and y be the obtuse angles of the hexagon.

Since he measures of the obtuse angles in the hexagon are 30 more than twice the measures of the acute angles, we have that

y = 2x + 30

Also, we know that the sum of  interior angles of a polygon is (n - 2)180.

Since x  is the interior angle and n = 6, we have that

6x = (n - 2)180.

x = (n - 2)180/6

x = 30(n - 2)

So, the system of equations is

y = 2x + 30 (1) and

x = 30(n - 2)  (2)

Since

y = 2x + 30 (1) and

x = 30(n - 2)  (2)

Substituting n = 6 into (2), we have

x = 30(6 - 2)

x = 30(4)

x = 120

Substituting x = 120 into (1), we have

y = 2x + 30

y = 2(120) + 30

y = 240 + 30

y = 270

So,

Lear more about hexagon here:

https://brainly.com/question/30015863

#SPJ1

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

To know more about Aggregate Demand visit :-

https://brainly.com/question/29349235

#SPJ11

Answer:

x=5 y=-5

Step-by-step explanation:

Answer:

24/182 = 12/91

Step-by-step explanation:

Answer:

Commutative Property

Step-by-step explanation:

-8+8 = 0

0 = 0

Answer:

g>2

Step-by-step explanation:

-g>13-15

-g>-2

g>2

you are welcome

Answer:

g < 2

Step-by-step

The volume of the irregular figure can be found to be 59 cm ³.

The shape is irregular which means that the best way to find the volume would be to split the shape into two shapes. The two shapes we will go with are two rectangular prisms.

The volume of Prism 1 is:

= Width x Height x Length

= 1 x 3 x 8

= 24 cm ³

The volume of prism 2 would be:

= 5 x 1 x 7

= 35 cm ³

The volume of the full irregular shape is :

= Volume of prism 1 + volume of prism 2

= 24 + 35

= 59 cm ³

Find out more on volume at https://brainly.com/question/23481617

#SPJ1

The given function is f(x) = (4-x)/29. We need to find the x-values where f is not continuous and determine whether the discontinuities are removable or nonremovable.

For this function, there are no nonremovable discontinuities. The only type of discontinuity that could occur is a removable discontinuity. This occurs when a point is undefined, but the limit exists and is finite. In other words, the function can be made continuous by redefining it at that point.

To find any possible removable discontinuities, we need to find the values of x for which the denominator becomes zero, because division by zero is undefined. The denominator is always 29, which is never zero, so there are no values of x for which the denominator is zero. Therefore, there are no removable discontinuities.

In conclusion, the function f(x) = (4-x)/29 is continuous for all values of x, and there are no removable or nonremovable discontinuities.

To learn more about denominator, click here:

brainly.com/question/15007690

#SPJ11

The correct hypothesis statement for this golfer to prove his claim would be:

\(H_{0} :u\geq 90\)

\(H_{1} :u < 90\)

The golfer claims that his average score is less than 90.

Therefore, the null hypothesis is the opposite of what he claims

Null hypothesis \(H_{0}\) is average score \(u\) is greater than or equal to 90:

\(u \geq 90\)

\(H_{0} :u\geq 90\)

Alternative hypothesis \(H_{1}\) is then the opposite of null hypothesis.

Hence alternate hypothesis \(H_{1}\) is u< 90

\(H_{1} :u < 90\)

To learn more on hypothesis statements; click here:

https://brainly.com/question/23709550

#SPJ4

Answer:

y = -2x + 3

Step-by-step explanation:

Let's just put the three points together.

(-1, 5) (-4, 11) (-7, 17)

First, let's find the slope with y2 - y1/x2 - x1

Plug in using (-1, 5) and (-4, 11)

11 - 5/-4 + 1 = 6/-3 (simplify)

-2 is the slope

Now plug in (-7, 17) in the equation to get b or the y-intercept)

y = mx + b

17 = -2(-7) + b

17 = 14 + b (subtract 14 on both sides)

3 = b

y = -2x + 3

Answer: X=50

Step-by-step explanation:

Data: 4 less than half of a number(x) is 21

Step one, make an equation

(x/2)-4=21

The reason for this is that since we know that 21 is 4 less than half the number(x) we can assume that dividing x by 2 will get half of it and by subtracting 4, we can get 21 which why it equals 21. By having it in an equation, it makes it easier to solve.

Step two, Start isolating x by adding 4 on both sides

(x/2)-4+4=21+4=(x/2)=25

The reason for this is that we have to find what x is which is done by isolating it. So if you add 4, you get rid of the -4 which helps isolate x and what you do to one side, you do to the other so you add 4 to 21 as well

Step three, multiply by 2 on both sides

(x/2)x2=25x2=X=50

The reason for this is that /2 is next to x so to isolate you have to get rid of it by multiplying by 2 and since what you do to one side you do to the other, you multiply 25 by 2 to get 50.

Answer: X=50

I hope this helps!

It seems that the formula for the distance (d) in miles that can be seen on the surface of the ocean from a certain height (h) in feet is missing. However, based on the given information, we can assume that the formula is:

d = sqrt(1.5h)

To find the height (h) in feet required to see a distance of 19.5 miles, we can rearrange the formula to solve for h:

h = (d^2 / 1.5)

Substituting d = 19.5 miles, we get:

h = (19.5^2 / 1.5) = 253.5 feet

Therefore, the platform would have to be at a height of approximately 253.5 feet to see a distance of 19.5 miles on the surface of the ocean.

To learn more about problems on height refer below:

https://brainly.com/question/24250956

#SPJ11

Answer:

24

Step-by-step explanation:

Option d. "The height of the box is between 8 and 16 inches" is not a valid conclusion.

What is volume ?

Volume is a measure of the amount of space occupied by an object or a substance. It is usually expressed in cubic units, such as cubic meters, cubic centimeters, cubic inches, etc. The volume of a three-dimensional object, such as a cube, sphere, or cylinder, is calculated by measuring the length, width, and height or radius of the object and applying the appropriate formula.

According to the question:

Option d. "The height of the box is between 8 and 16 inches" is not a valid conclusion.

From the given function V = h(16-2h)², we can see that the height of the box is represented by "h" and it can take values between 0 and 8 inches, since the height cannot be negative and must be less than or equal to the side length of the square base (which is 16-2h).

The width and length of the box are both represented by 16-2h, as the base is a square.

Therefore, option d is not valid because it contradicts the valid range of values for the height of the box.

To know more about volume visit:
https://brainly.com/question/23477586
#SPJ1

Given:

The equation is:

\((2x+3y)(2x-3y)=4x^2+6y^2\)

To find:

The error in the given equation and correct it.

Solution:

We have,

\((2x+3y)(2x-3y)=4x^2+6y^2\)

Taking left-hand side, we get

\(L.H.S.=(2x+3y)(2x-3y)\)

\(L.H.S.=(2x)^2-(3y)^2\)                 \([\because a^2-b^2=(a-b)(a+b)]\)

\(L.H.S.=(2)^2(x)^2-(3)^2(y)^2\)       \([\because (ab)^x=a^xb^x]\)

\(L.H.S.=4x^2-9y^2\)

It is not equal to right-hand side \(4x^2+6y^2\). In the right hand side, there must be a negative sign instead of positive sign.

Therefore, \((2x+3y)(2x-3y)=4x^2-6y^2\).

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

To know more about proportional savings, refer here:

https://brainly.com/question/29251832#

#SPJ11

The value οf a, b, and c are 3, 5, and 25 respectively.

There are many different ways tο define an equatiοn. The definitiοn οf an equatiοn in algebra is a mathematical declaratiοn that illustrates the equality οf twο mathematical expressiοns.

The given equatiοn is

1/(x + 5) + 2/(x -5) = (ax + b)/ (x² - c)

Sοlve the left-hand side οf the equatiοn:

L.H.S = 1/(x + 5) + 2/(x -5)

= [x-5 + 2(x+5)]/(x + 5)(x -5)

= [x-5 + 2x+ 10]/(x + 5)(x -5)

Cοmbine like terms:

= [3x + 5]/(x + 5)(x -5)

Nοw apply fοrmula (a-b)(a+b) =a² - b²:

= [3x + 5]/(x² - 5²)

= [3x + 5]/(x² - 25)

Put 1/(x + 5) + 2/(x -5) =  [3x + 5]/(x² - 25) in the given equatiοn:

[3x + 5]/(x² - 25) = (ax + b)/ (x² - c)

Nοw cοmpare bοth sides:

a = 3

b = 5

c= 25

To learn more about the equation, click on the below link:

https://brainly.com/question/30573233

#SPJ1

Answer:

hi, first question's answer B.

because if you want to draw a triangle, there is have to be some rules. like can you draw a triangle 2,2,20? that could be impossible because all the edges have to intersect. think a triangle and it has 3 edges. they are A,B,C

if you wanna write random numbers, you have to do this.

A+B>C>|A-B|

A+C>B>|A-C|

C+B>A>|C-B|

soo, 7+11= 18 and 11-7=4

second question's answer is this:

60+x+32+90=180(if you wonder where is the 90 came from, the triangle's one side has square. that mean its 90°.

182+x=180

x=-2

if you have questions about these questions, you can ask me.

good luck(: