Parallel lines /////////////

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

Answer:

L = A÷W

Step-by-step explanation:

The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If you know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W.

Answer:

Time travelled each day = 8 hours

Step-by-step explanation:

total distance of 2-day trip = 880 miles

half the distance each day = 880 ÷ 2 = 440 miles

velocity travelled each day = 55 miles per hour

time travelled each day = ???

velocity = (distance trvaelled) ÷ (Time)

55 = 440 ÷ Time

[tex]55=\frac{440}{Time} \\cross-multiplying\\55\ \times\ Time = 440\\Time = \frac{440}{55} \\Time = 8\ hours[/tex]

∴ Time travelled each day = 8 hours

Answer:

9 hours

Step-by-step explanation:

Total distance for the two days = 880 miles

If half of the distance is to be traveled each day, then;

distance each day = 440 miles

speed of the automobile = 55 miles per hour.

Now, let's calculate the number of hours that will be driven each day.

Remember that;

speed = distance / time

=> time = distance / speed           [substitute the values of distance and speed]

=> time = (440 miles) / (55 miles/hour)

=> time = 9 hours.

Therefore, the number of hours that will be driven each day is 9

Answer:

1/3

Step-by-step explanation:

√2 is irrational because radicals are irrational. π is also an irrational number. The third option, 1.3985624785461.... is obviously not a terminating decimal, hence, it is also irrational. Therefore, the answer is 1/3. We know this because 1/3 can be written in the form a / b where a and b are rational numbers, in this case, a = 1 and b = 3.

Answer:

plz mark as BRAINLIEST....

Step-by-step explanation:

60÷3[150÷2{6+3(17-14)}]

= 60÷3[150÷2{9-3}]

=60÷3[75-6]

=20-69

=49

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3,1) and (1,-4)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

A reflection over  x - axis

Step-by-step explanation:

If f(-x) = f (x), (ie all the signs are the same), then the function is even

also,  if f(-x) = -f (x), (ie all the signs are switched), then the function is odd.

Given;

h(x) = 12x + 49

Then test for h(-x);

h(-x) = 12(-x) + 49

h(-x) = -12x + 49,  

Thus h(-x)  ≠ h(x)  and also h(-x) ≠ -h(x)

The function is neither odd nor even.

Therefore, a reflection over  x - axis would result in a function that is neither even nor odd.

Answer:

1/10

Step-by-step explanation:

divide the numerator by the denominator. For example, 1/2 is equal to 1 divided by 2, which is equal to 0.5.

Answer:

1/10

Hoped I helped

Answer:

(2, 1)

Step-by-step explanation:

To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.

y = 6x - 11

-2x - 3(6x - 11) = -7 Distribute.

-2x - 18x + 33 = -7 Combine like terms.

-20x + 33 = -7 Subtract 33 from both sides of the equation.

-20x = -40 Divide by -20 on both sides of the equation.

x = 2

Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.

y = 6(2) - 11

y = 12 - 11

y = 1

Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).

The correct answer is D)  If a polygon is not a kite, then it is not a quadrilateral. FALSE

Explanation:

The statement "If a polygon is a kite, then it is a quadrilateral" as other statements is composed of two parts: the if statement or hypothesis and the conclusion. Additionally, to create the inverse of this statement it is necessary to negate both statements, this means the inverse is "If a polygon is not a kite, then it is not a quadrilateral" because this negates the hypothesis and the conclusion. Besides this, it can be concluded this inverse statement is false because the word "quadrilateral" describes all shapes with four sides, which include not only kites but squares, rectangles, trapezoids, etc. Therefore, a polygon can be quadrilateral without being a kite.

Answer:

(x² + 4)(x - 3)

or

A

Step-by-step explanation:

Step 1: Write out expression

x³ - 3x² + 4x - 12

Step 2: Factor by grouping

x³ - 3x²

x²(x - 3)

4x - 12

4(x - 3)

Step 3: Combine

(x² + 4)(x - 3)

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ \: 12.9 \: \: dollars}}}}}[/tex]

Step-by-step explanation:

Given,

Cost without tax = $ 12

Tax percent = 7.5 %

Cost including tax = ?

First, finding the tax amount :

[tex] \sf{tax \: amount \: = \: 7.5 \: \% \: of \: 12}[/tex]

⇒[tex] \sf{tax \: amount = \frac{7.5}{100} \times 12} [/tex]

⇒[tex] \sf{tax \: amount = 0.9}[/tex] dollars

Finding the total cost of the lunch including tax :

⇒[tex] \sf{total \: cost \: = \: 12 + 0.9}[/tex]

⇒[tex] \sf{total \: cost \: = \: 12.9}[/tex] dollars

Hope I helped!

Best regards ! :D

Answer:

The standard error is 0.033.

Step-by-step explanation:

We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.

Let [tex]\hat p[/tex] = proportion of employees who planned to take an extended vacation next year

[tex]\hat p[/tex] = [tex]\frac{X}{n}[/tex] = [tex]\frac{21}{125}[/tex] = 0.168

n = number of employees at her company = 125

Now, the standard error is calculated by the following formula;

       Standard error, S.E. =  [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168(1-0.168)}{125} }[/tex]

                                         =  [tex]\sqrt{\frac{0.168 \times 0.832}{125} }[/tex]  = 0.033

Hence, the standard error is 0.033.

Answer:

.10 - .23

Step-by-step explanation:

.168 +/- 1.96 ( sqrt ((.168 * .832)/125))

Answer:

R(7a, 0 )

Step-by-step explanation:

R is on the vertical line RQ so will have the same x- coordinate as Q

R is on the horizontal line OR so will have the same y- coordinate as O

Thus coordinates of R = (7a, 0 )

Answer: m∠ TUW =  38°

m∠WUV =  12°

m∠TUV =  103°

Step-by-step explanation:

Given: m∠ TUW = (5x + 3)°, m∠WUV=(10x-5)°, and m∠TUV=(17x-16)°

Since, m∠TUV = m∠ TUW  +  m∠WUV

So, 17X-16 = (5x + 3) + (10x-5)

⇒ 17X-16 = 5x + 3 + 10x-5   [open parenthesis]

⇒  17X-16 =5x +  10x +3 -5   [combine like trems]

⇒  17X-16 =15x -2

⇒   17X -15x = -2+16     [subtract 15x and add 16 on both sides]

⇒   2x = 14        

⇒  x= 7               [divide both sides by 2]

Now, m∠ TUW = (5(7) + 3)°=  38°

m∠WUV=(10(7)-5)° =  12°

m∠TUV=(17(7)-16)° =  103°

Hence,  m∠ TUW =  38°

m∠WUV =  12°

m∠TUV =  103°

Answer:

Step-by-step explanation:

[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]

[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]

Answer:

x = 0

Simplified: [tex]36^{x} = 1[/tex]

Step-by-step explanation:

How to simplify:

Answer:

2

Step-by-step explanation:

Pretend there is no decimal point. We can do this by multiplying both numbers by 10.

After that, it becomes 68/34. You then divide those two, and you get 2 as your answer.

Answer:

2

Step-by-step explanation:

its easy you can do it with calculator or paper -__-

Answer:

x > 5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

8x - 6(x + 1) < 4(2x - 9)

Step 2: Distribute parenthesis

8x - 6x - 6 < 8x - 36

Step 3: Combine like terms

2x - 6 < 8x - 36

Step 4: Subtract 2x on both sides

-6 < 6x - 36

Step 5: Add 36 on both sides

30 < 6x

Step 6: Divide both sides by 6

5 < x

Step 7: Rewrite

x > 5

Answer:

X= 60°

Y= 30°

Step-by-step explanation:

In triangle ABD, we have:

AB = BD = AD

Then triangle ABD is equilateral triangle.

Then, all its angles are equal to 60°.

=> X = 60°

____________________________________

ADC is right triangle at D.

So, X and Y are congruent angles (their sum is equal to 90°)

So, X + Y =90°

60° + Y = 90°

Y = 90 - 60

Y= 30°

[tex]hope \: this \: helps[/tex]

Answer:

-7/3

-3/4

0.5

2/3

1.2

You can get these numbers by sorting in your head. Think of a number line and that'll make things easier :)

Answer:

-7/3, -3/4, 0.5, 2/3, 1.2

Step-by-step explanation:

The larger the negative number is the smaller it's value is and its the complete opposite for positive numbers

Answer:

(1) The point estimate for the population mean is 4.925.

(2) Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

(3) Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

(4) As the level of confidence increases, the width of the interval increases.

Step-by-step explanation:

We are given that the following data represent the pH of rain for a random sample of 12 rain dates.

X = 5.20, 5.02, 4.87, 5.72, 4.57, 4.76, 4.99, 4.74, 4.56, 4.80, 5.19, 4.68.

(1) The point estimate for the population mean is given by;

Point estimate, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]

                            = [tex]\frac{5.20+5.02+ 4.87+5.72+ 4.57+ 4.76+4.99+ 4.74+ 4.56+ 4.80+5.19+ 4.68}{12}[/tex]

                            = [tex]\frac{59.1}{12}[/tex]  = 4.925

(2) Let [tex]\mu[/tex] = mean pH of rainwater

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~  [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 4.925

             s = sample standard deviation = 0.33

            n = sample of rain dates = 12

            [tex]\mu[/tex] = population mean pH of rainwater

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.201 < [tex]t_1_1[/tex] < 2.201) = 0.95  {As the critical value of t at 11 degrees of

                                               freedom are -2.201 & 2.201 with P = 2.5%}  

P(-2.201 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.201) = 0.95  

P( [tex]-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.201 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.201 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                      = [ [tex]4.925-2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+2.201 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]  

                                     = [4.715, 5.135]

Therefore, a 95% confidence interval for the population mean pH of rainwater is [4.715, 5.135] .

The interpretation of the above confidence interval is that we are 95% confident that the population mean pH of rainwater is between 4.715 & 5.135.

(3) Now, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-3.106 < [tex]t_1_1[/tex] < 3.106) = 0.99  {As the critical value of t at 11 degrees of

                                               freedom are -3.106 & 3.106 with P = 0.5%}  

P(-3.106 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 3.106) = 0.99

P( [tex]-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99

P( [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.99

99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-3.106 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+3.106 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                                     = [ [tex]4.925-3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] , [tex]4.925+3.106 \times {\frac{0.33}{\sqrt{12} } }[/tex] ]  

                                     = [4.629, 5.221]

Therefore, a 99% confidence interval for the population mean pH of rainwater is [4.629, 5.221] .

The interpretation of the above confidence interval is that we are 99% confident that the population mean pH of rainwater is between 4.629 & 5.221.

(4) As the level of confidence increases, the width of the interval increases as we can see above that the 99% confidence interval is wider as compared to the 95% confidence interval.

Answer: im pretty sure its exponential decay?

Step-by-step explanation:

Answer:

2A /h = b

Step-by-step explanation:

A=1/2bh

Multiply each side by 2

2A = 2*1/2bh

2A = bh

Divide each side by h

2A/h = bh/h

2A /h = b

Step-by-step explanation: First, get rid of the fraction by

multiplying both sides of the equation by 2.

That gives us 2A = bh.

Don't be thrown off by the capital A in this problem.

Just treat it like any other variable.

To get b by itself on the right side of the equation, we now simply

divide both side of the equation by h and our answer is 2A/h = b.

Take a look back at the formula now in the original problem.

Does it look familiar?

It's the formula for the area of a triangle.

Take a look at the image I have provided below.

I have made the "b" purple so you

can see that we are solving for it.

Answer:

m = 48

Step-by-step explanation:

Isolate the variable, m. Note the equal sign, what you do to one side, you do to the other. Multiply 8 to both sides:

6 = m/8

(6) * 8 = (m/8) * 8

6 * 8 = m

m = 6 * 8

m = 48

48 is your answer for m.

~

Answer:

24 - 16x

Step-by-step explanation:

8(3 - 2x)

Distribute

8*3 - 8*2x

24 - 16x

Answer:

Step-by-step explanation:

When you work addition and subtraction problems, it is often easier to do them if you can "make a 10" or "make a 100", because adding or subtracting 10 or 100 is easier than with non-zero digits.

__

Here, you are steered toward noticing that there are two elements of the sum that have a total of -100. Those elements are -65 and -35. With the above in mind, you can use the commutative property to rearrange the sum to ...

  -65 +(-35) +(-150) . . . . . . . last two terms were swapped

Then the first step is to add -65 and -35:

  [tex]\text{It is easier to add }\boxed{-65}\,+\,\boxed{(-35)}\text{ first to get $-100$.}[/tex]

Now, the sum reduces to ...

  -100 +(-150) = -250

So, the final sentence becomes ...

  [tex]\text{Then add }\boxed{-100+(-150)}\text{ to get }\boxed{-250}\,.[/tex]

Answer:

5000 pounds

Step-by-step explanation:

1 ton = 2000 pounds so 2.5 = 2000 + 2000 + 1000 = 5000

Answer:

5,000 pounds

Step-by-step explanation:

just subtract 2.5 by 1,000 5 times

Answer : The polynomial in standard form is [tex]1a^2+9a+20[/tex]

Step-by-step explanation :

The polynomial in standard form means that the terms are ordered from highest exponent to lowest exponent.

Given: Subtract [tex]9a^2-6a+5[/tex] from [tex]10a^2+3a+25[/tex]

The expression will be :

[tex](10a^2+3a+25)-(9a^2-6a+5)[/tex]

Now open the bracket and change the sign.

[tex]=10a^2+3a+25-9a^2+6a-5[/tex]

Now we are adding or subtracting the like terms, we get:

[tex]=1a^2+9a+20[/tex]

Thus, the polynomial in standard form is [tex]1a^2+9a+20[/tex]