Find the value of x. Round to the nearest tenth.

Find The Value Of X. Round To The Nearest Tenth.

Answers

Answer 1
36
i think. hope it helped sorrh if it’s wrong i’m not good at math

Related Questions

simplify 2x²y²÷m³×m²÷2xy​

Answers

x^3y^3 divided by m is the answer

HELP ASAP I WILL GIVE BRAINLIST

Convert 7π OVER 4 radians to degrees. Which quadrant does this angle lie in?
What are the sine, cosine and tangent of the angle 7π over 4? Be sure to show and explain all work.

Answers

Answer:

7π/4 radians = 315°, Quadrant IV

sin(315°) = -√2/2

cos(315°) = √2/2

tan(315°) = -1

Step-by-step explanation:

A wooden log 10 meters long is leaning against a vertical wall with its other end on the ground. The top end of the log is sliding down the wall. When the top end is 6 meters from the ground, it slides down at 2m/sec. How fast is the bottom moving away from the wall at this instant?

Answers

Answer:

Step-by-step explanation:

This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is [tex]\frac{dx}{dt}[/tex] when y = 6 and [tex]\frac{dy}{dt}=-2[/tex].

The equation for Pythagorean's Theorem is

[tex]x^2+y^2=c^2[/tex] where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:

[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and divide everything by 2 to simplify:

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Looking at that equation, it looks like we need a value for x, y, [tex]\frac{dx}{dt}[/tex] and [tex]\frac{dy}{dt}[/tex].

Since we are looking for [tex]\frac{dx}{dt}[/tex], that can be our only unknown and everything else has to have a value. So what do we know?

If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:

[tex]x^2+6^2=10^2[/tex] and

[tex]x^2+36=100[/tex] and

[tex]x^2=64[/tex] so

x = 8.

NOW we can fill in the derivative and solve for [tex]\frac{dx}{dt}[/tex].

Remember the derivative is

[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so

[tex]8\frac{dx}{dt}+6(-2)=0[/tex] and

[tex]8\frac{dx}{dt}-12=0[/tex] and

[tex]8\frac{dx}{dt}=12[/tex] so

[tex]\frac{dx}{dt}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}=1.5 m/sec[/tex]

6(5x/3 -4/3 - 2)= 6 (3 - 6x/6 +4/6)

Answers

Answer:

21/8x

Step-by-step explanation:

10x -20 = -6x+22

+6x-20 = 22

16x-20 = 22

16x +20= +20

16x/16x = 42/16x

x = 21/8x

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 100 mm

Answers

Answer:

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

How fast is the volume increasing:

To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 2 mm/s.

This means that [tex]\frac{dr}{dt} = 2[/tex]

How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?

Radius is half the diameter, so [tex]r = \frac{100}{2} = 50[/tex]

Then

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt} = 4\pi (50)^2(2) = 62832[/tex]

The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.

I need help answering this question.

Answers

Answer:

hello dude

x - 9 = - 12

x = 9 -12

x = -3

HAVE A NİCE NİGHT

Step-by-step explanation:

Greetings from Turkey

We have to,

find the required value of x.

Let's start,

→ x - 9 = -12

→ x = -12 + 9

→ x = -3

Thus, -3 is the value of x.

question:

A sequence is defined by the recursive function f(n + 1) = –10f(n).

If f(1) = 1, what is f(3)?


3

–30

100

–1,000


the answer is 100

Answers

Answer:

100

Step-by-step explanation:

f(1) = 1

f(2) = -10×f(1) = -10 × 1 = -10

f(3) = -10×f(2) = -10 × -10 × f(1) = -10 × -10 × 1 = 100

f(n) = -10 to the power of n-1

Answer:

c - 100

Step-by-step explanation:

Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 95 miles per hour. The westbound train travels at 75 miles per hour. How long will it take for the two trains to be 238 miles apart? Do not do any rounding.

Answers

Answer:

They are going away from each other.

So add up their speed.

combined speed = x+x-16

=2x-16

Time = 2 hours

Distance = 400 miles

Distance = speed * time

(2x-16)* 2

4x-32=400

4x=400+32

4x=432

/12

x=108 mph west bound

east bound = 108 -16 = 92 mph

according to byu idaho enrollment statisct there are 1200 femaile studnet here on campus during any given semester of those 3500 have serced a msion what is the probability that a radnoly selcted femal studne ton cmapus wil have served a mission g

Answers

Answer:

0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

1200 female students, out of them, 350 have served a mission. So

[tex]p = \frac{350}{1200} = 0.2917[/tex]

0.2917 = 29.17% probability that a randomly selected female student on campus will have served a mission.

Can someone pls help asap i will give Brainliest

Answers

Answer:

24/145

Step-by-step explanation:

Trigonometric identities are equalities involving trigonometric functions and remains true for entire values of the variables involved in the equation.

Some trigonometric identities are:

sin(a + b) = sinacosb + cosasinb; sin(a - b) = sinacosb - cosasinb

cos(a + b) = cosacosb - sinasinb; cos(a - b) = cosacosb + sinasinb

Given that sin a = 3/5. sin a = opposite/hypotenuse.

Hence opposite = 3, hypotenuse = 5. using Pythagoras:

hypotenuse² = opposite² + adjacent²

5² = 3² + adjacent²

adjacent² = 16

adjacent = 4

Given that sin a = 3/5. a = sin⁻¹(3/5) = 36.86

cos a = cos 36.86 = 4/5

cos b = -20/29; b = cos⁻¹(-20/29) = 133.6

sinb = sin(133.6) = 21/29

sin(a + b) = sinacosb + cosasinb = (3/5 * -20/29) + (4/5 * 21/29) = -12/29 + 84/145

sin(a + b) = 24/145

Decide which of the two given prices is the better deal and explain why.
You can buy shampoo in a ​5-ounce bottle for ​3,89$ or in a 14​-ounce bottle for 11,99$.
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.The ​-ounce bottle is the better deal because the cost per ounce is ​$
nothing per ounce while the ​-ounce bottle is ​$
nothing per ounce.
B.The ​-ounce bottle is the better deal because the cost per ounce is ​$
nothing per ounce while the ​-ounce bottle is ​$
nothing per ounce.
​(Round to the nearest cent as​ needed.)

Answers

Answer:

The 14-ounce bottle is the better deal

Step-by-step explanation:

I know this beause inorder to figure out which one is better you have to make them the same price and then see which bottle has more ounces. So I made each price 1$ so there is 1.58-ounces per dollar in the 5-ounce bottle and 1.17 -ounces per dollar in the 14-ounce bottle.

Which expression is equivalent to -9x-1y-9/-15x5y-3?

Answers

Answer: -9x-1y-9/

Step-by-step explanation:

Answer: b

Step-by-step explanation:

I really dont like edge

Problem: The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72
inches and standard deviation 3.17 inches. Compute the probability that a simple random sample of size n=
10 results in a sample mean greater than 40 inches. That is, compute P(mean >40).
Gestation period The length of human pregnancies is approximately normally distributed with mean u = 266
days and standard deviation o = 16 days.
Tagged
Math
1. What is the probability a randomly selected pregnancy lasts less than 260 days?
2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days
or less?
3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days
or less?
4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of
the mean?
Know
Learn
Booste
V See

Answers

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

[tex]\mu = 266, \sigma = 16[/tex]

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{260 -  266}{16}[/tex]

[tex]Z = -0.375[/tex]

[tex]Z = -0.375[/tex] has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 20[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 50[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]

[tex]Z = -2.65[/tex]

[tex]Z = -2.65[/tex] has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = 2.42[/tex]

[tex]Z = 2.42[/tex] has a p-value of 0.9922.

X = 256

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

I need help answering this question.

Answers

Answer:

6x

Step-by-step explanation:

If x is the length of one side, and each side is the same length, you will multiply it by 6 times (there are 6 sides in a hexagon).

So, you will add it up 6 times, but you can say 6x for short.

Estimate the student's walking pace, in steps per minute, at 3:20 p.m. by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)

Answers

This question is incomplete, the complete question is;

A student bought a smart-watch that tracks the number of steps she walks throughout the day. The table shows the number of steps recorded (t) minutes after 3:00 pm on the first day she wore the watch.

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

a) Find the slopes of the secant lines corresponding to the given intervals of t.

1) [ 0, 40 ]

11) [ 10, 20 ]

111) [ 20, 30 ]

b) Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part (a). (Round your answer to the nearest integer.)

Answer:

a)

1) for [ 0, 40 ], slope is 96

11) for [ 10, 20 ],  slope is 86.3

111) for  [ 20, 30 ], slope is 116.4

b) the student's walking pace is 101 per min

Step-by-step explanation:

Given the data in the question;

t (min)       0          10          20         30         40

Steps   3,288    4,659    5,522    6,686    7,128

SLOPE OF SECANT LINES

1) [ 0, 40 ]

slope =  ( 7,128 - 3,288 ) / ( 40 - 0

= 3840 / 40 = 96

Hence slope is 96

11)  [ 10, 20 ]

slope = ( 5,522 - 4,659 ) / ( 20 - 10 )

= 863 / 10 = 86.3

Hence slope is 86.3

111)  [ 20, 30 ]

slope = ( 6,686 - 5,522 ) / ( 30 - 20 )

= 1164 / 10 = 116.4

Hence slope is 116.4

b)

Estimate the student's walking pace, in steps per minute, at 3:20 pm by averaging the slopes of two secant lines from part .

Since this is recorded after 3:00 pm

{ 3:20 - 3:00 = 20 }

so t = 20 min

so by average;

we have ( [ 10, 20 ] + [ 20, 30 ] ) /2

⇒ ( 86.3 + 116.4 ) / 2

= 202.7 /2

= 101.35 ≈ 101

Therefore, the student's walking pace is 101 per minutes

HELP HELP HELPPPP
ILL GIVE BRAINLIEST HELPPPPPPPPP
100 POINTSSS

Answers

Answer:

C. 0.48

Step-by-step explanation:

Probability = number of required outcome

_______________________

number of possible outcome

= total volleyball game events

_______________________

total sophomore + junior

= 66/137

= 0.48

Answer: D) 0.31

Step-by-step explanation:

Let A denote the event that a person is a sophomore.

Let B denote the event that a person has attended volleyball game.

A∩B denote the event that a person is a sophomore and attend volleyball game.

Let P denote the probability of an event.

We are asked to find:

P(A∩B)

From the table provided to us we see that:

A∩B=42

Hence,

P(A∩B)=42/137=0.3065 which is approximately equal to 0.31. Therefore ur answer will be 0.31.

You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 12 customers and find that the average dollar amount spent per transaction per customer is $116.194 with a standard deviation of $11.3781. Create a 90% confidence interval for the true average spent for all customers per transaction.1) ( 114.398 , 117.99 )2) ( 112.909 , 119.479 )3) ( -110.295 , 122.093 )4) ( 110.341 , 122.047 )5) ( 110.295 , 122.093 )

Answers

Answer:

(110.295, 122.093).

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 12 - 1 = 11

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7959

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 116.194 - 5.899 = 110.295

The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093

So

(110.295, 122.093).

Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00​

Answers

Answer: 3 years

Step-by-step explanation:

Interest is calculated as:

= (P × R × T) / 100

where

P = principal = 150,000

R = rate = 2.5%.

I = interest = 11250

T = time = unknown.

I = (P × R × T) / 100

11250 = (150000 × 2.5 × T)/100

Cross multiply

1125000 = 375000T

T = 1125000/375000

T = 3

The time taken will be 3 years

Find the union {6, 11, 15} U Ø​

Answers

Answer:  {6, 11, 15}

Explanation:

The Ø​ means "empty set". It's the set with nothing inside it, not even 0.

We can write Ø​ as { } which is a pair of curly braces with nothing between them.

The rule is that if we union any set A with Ø​, then we'll get set A

A U Ø​ = A

Ø​ U A = A

In a sense, it's analogous to adding 0. So it's like saying A+0 = A and 0+A = A.

So that's why {6, 11, 15} U Ø​ = {6, 11, 15}

There's nothing to add onto the set {6, 11, 15}, so we just get the same thing back again.

Which line is parallel to the line that passes through the points (1,7) and (-3, 4)? A. y=--x-5 B. y=+*+1 y=-x-8 O c. D. 11 v==x+3 4 ​

Answers

Answer:

B

Step-by-step explanation:

because

PLEASE HELP WILL MARK BRAINLIST AND GIVE 20 POINTS

Answers

Answer:

The first one

Step-by-step explanation:

You just need to find the slope in the average of all the dots.

Answer:

the first option, y=3/7x-3

Step-by-step explanation:

the scatterplot begins around y=-3, so therefore the y-intercept is -3. The slope is obviously not higher than 1, so it is y=3/7x-3.

Identify the transformation that occurs to create the graph of m(x)
m(x)=f(5x)

Answers

Answer:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Step-by-step explanation:

The transformation is a horizontal dilation

The general transformation is defined as:

For a given function f(x), a dilation of scale factor K is written as:

g(x) = f(x/K)

If K > 1, then we have a dilation (the graph contracts)

if 0 < K < 1, then we have a contraction (the graph stretches)

Here we have m(x) = f(5*x)

Then we have a scale factor:

K = 1/5

So this is a contraction.

Then the transformation is:

m(x) is a dilation of scale factor K = 1/5 of f(x).

please help with this quadratic equations​

Answers

Answer:

I don't understand the question

hello here are the answers (pls brainly for this) ✌
1) 3(x+12)
2) 4x(x+14)
3) x^2-14x-40
4) (x-2)(x-12)
5) (x^2+4) (x+2) (x-2)
6) (9x+7) (9x-7)
7) 2(5x+6) (5x-6)
8) 2(x+1) (x-9)
9) (4x-3) (x+5)
10) 7x(5-2x)
11) (x-3) (x^2+5)
12) (s+5) (5r-3)
13) (5x-6x)
14) (5x-4) (25^2+20x+16)
15) 2(x+4y) (x^2-4xy+16y^2

:3

Factor out the greatest common factor.

Answers

Answer:

The answer to your question is given below.

Step-by-step explanation:

6x⁴ + 4x³ – 10x

The greatest common factor can be obtained as follow:

6x⁴ = 2 * 3 * x * x * x * x

4x³ = 2 * 2 * x * x * x

10x = 2 × 5 * x

Greatest common factor = 2 * x

= 2x

Thus, the expression 6x⁴ + 4x³ – 10x can be written as:

6x⁴ + 4x³ – 10x = 2x(3x³ + 2x² – 5)

Find the equation of the line passing through (3,5) with a slope of 1

WILL GIVE BRAINLIEST

Answers

Slope-intercept form:

y = x + 2

Point-slope form:

y − 5 = 1 ⋅ ( x − 3 )

I hope this is correct and helps!

Find the radius of a circle with a diameter whose endpoints are (-7,1) and (1,3).​

Answers

Answer:

r = 4.1231055

Step-by-step explanation:

So to do this, you need to find the distance between the two points:

(-7,1) and (1,3).

To do this, the distance or diameter (d) is equal to:

d = sqrt ((x2-x1)^2 + (y2-y1)^2)

In this case:

d = sqrt( (1 - (-7))^2 + (3 - 1)^2 )

d = sqrt( 8^2 + 2^2)

d = sqrt( 64 + 4)

d = sqrt( 68 )

The radius is half of the diameter, so:

r = 1/2 * d

r = 1/2 * sqrt( 68 )

r~ 4.1231055

Look at the numbers in the bon
5
9
-11
6
-21
9
-6
-10
20
1
Find four numbers whose sum is 5

Answers

20 is the answer because it is the only number that has positive and it says sum

Find m < A
Round to the nearest degree.
CA = 6
CB = 13
AB = 10

Answers

Answer:

CA=6 is 6.0
CB= 13 is 13.0
AB= 10 is 10.0

What is the value of x?

Answers

The value of x is 2 because we can compare like terms

If V= {i}, subset of V are? ​

Answers

Answer:

Defintion. A subset W of a vector space V is a subspace if

(1) W is non-empty

(2) For every v, ¯ w¯ ∈ W and a, b ∈ F, av¯ + bw¯ ∈ W.

Expressions like av¯ + bw¯, or more generally

X

k

i=1

aiv¯ + i

are called linear combinations. So a non-empty subset of V is a subspace if it is

closed under linear combinations. Much of today’s class will focus on properties of

subsets and subspaces detected by various conditions on linear combinations.

Theorem. If W is a subspace of V , then W is a vector space over F with operations

coming from those of V .

In particular, since all of those axioms are satisfied for V , then they are for W.

We only have to check closure!

Examples:

Defintion. Let F

n = {(a1, . . . , an)|ai ∈ F} with coordinate-wise addition and scalar

multiplication.

This gives us a few examples. Let W ⊂ F

n be those points which are zero except

in the first coordinate:

W = {(a, 0, . . . , 0)} ⊂ F

n

.

Then W is a subspace, since

a · (α, 0, . . . , 0) + b · (β, 0, . . . , 0) = (aα + bβ, 0, . . . , 0) ∈ W.

If F = R, then W0 = {(a1, . . . , an)|ai ≥ 0} is not a subspace. It’s closed under

addition, but not scalar multiplication.

We have a number of ways to build new subspaces from old.

Proposition. If Wi for i ∈ I is a collection of subspaces of V , then

W =

\

i∈I

Wi = {w¯ ∈ V |w¯ ∈ Wi∀i ∈ I}

is a subspace.

Proof. Let ¯v, w¯ ∈ W. Then for all i ∈ I, ¯v, w¯ ∈ Wi

, by definition. Since each Wi

is

a subspace, we then learn that for all a, b ∈ F,

av¯ + bw¯ ∈ Wi

,

and hence av¯ + bw¯ ∈ W. ¤

Thought question: Why is this never empty?

The union is a little trickier.

Proposition. W1 ∪ W2 is a subspace iff W1 ⊂ W2 or W2 ⊂ W1.

i hope this helped have a nice day/night :)

Other Questions
highest common factor of 9 and 29 easy biology question below first correct answer gets brainliest What is the image of (3, -12) after a dilation by a scale factor of centeredat the origin? Describe the main barrier to education for many children in India. Is it extremely slowly or extremely slow?I know this is dmb but I don't want to get this wrong.Sentence: The door opened extremely slow/slowly.Or does it not work? PLEASE HELP!!! geometry! Who was the first South African president? What is meant by a neutral symbioticrelationship?A. At least one organism is harmed.B. At least one organism gains.C. At least one organism is unaffected. The presidential election of 1924 revealed American voters' strong support for government regulation of industry and for other progressive principles. emphasis on an interest in consumer goods rather than an interest in politics. rejection of labor unions, government regulation of business, and the protection of civil liberties. strong support for the candidate who was more physically attractive, regardless of experience. Andrea's Sequoia gets 12 miles per gallon while driving in the city, and 20 miles per gallon while on the highway. The last time she filled up the car it took 16 gallons of gas, and she had driven 280 miles since the previous fill-up. How many miles of that 280 were city driving? (Picture) Could someone help me solve this I need to use Inverse Operations but I don't fully understand? I'll mark brainliest, 10 Points. Your company buys a computer system for $3 million and pays the vendor $200,000 to install the computer system. Your company should record: A. $3.2 million as expenses. B. $2.8 million as equipment and the rest as expenses. C. $3.2 million as equipment. D. $3 million as equipment and $200,000 as expenses. if k = p+2q/3 , find the value of p when k=7 and q=3 Why we need to learn languages? Think about the consequences Ghost faces as a result of his decision to steal a pair of running shoes. Do you think that the way that Coach punishes him is fair? What would the consequences have been if Ghost had been stopped by the police instead? What would the consequences have been if his mother had discovered the theft? What would have happened if Ghost had never been caught? Why might it have been better for him to get caught? Explain. Civil WarWhich reconstruction plan was used after the Civil War?a.The Lincoln Reconstruction Plan.b.The Initial Congressional Plan.c.The Andrew Johnson Reconstruction Plan.d.The Radical Republican Reconstruction Plan. what is reductionasim evaluate the expression. check all possible sets that the solution may belong in. 40-5^2 Which federal agency enforces regulations for product advertising and labeling? Office of the Comptroller of the Currency Federal Deposit Insurance Corporation Securities and Exchange Commission Bureau of Consumer Protection Find the surface area of a cylinder with a base diameter of 6yd and a height of 8yd.Write your answer in terms of pi, and be sure to include the correct unit.