If W is a subspace of a vector space V and B W is a basis for W,then there is a unique subspace U so that V = W⊕U and a basis B U for U so that BV =BW +BU is a basis for V.

Is this true or false?

The correct statement regarding the reflection rules in this problem is given as follows:

D. g(x) is a reflection of f(x) over the x-axis.

The functions f(x) and g(x) in the context of this problem are defined as follows:

The entire function was multiplied by -1, meaning that the signal of the function was exchanged, hence the function was reflected over the x-axis.

As the function was reflected over the x-axis, the correct option in the context of the problem is given by option D.

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Answer:

Step-by-step explanation:

To solve for m/MNP if m/MNO = 132° and m/PNO = 40°, we can use the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find the measure of angle MNO:

m/MNO + m/PNO + m/MNP = 180

132 + 40 + m/MNP = 180

m/MNP = 8

Copy

Therefore, m/MNP = 8 degrees.

I hope this helps! Let me know if you have any other questions.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

1. 176,500 centimeters

2. 940,000 centimeters

3.42,000,000 grams

Step-by-step explanation:

Convertion:

1.1.1

1765m to cm

1 meter = 100 centimeters

Therefore, 1765 meters =1765*100 centimeters = 176,500 centimeters

1.1.2

9.4 km to cm

1 kilometer = 1000 meters

First convert it into m.

9.4 kilometers = 9.4*1000 meters = 9400 meters

then in cm

1 meter = 100 centimeters

Therefore, 9400 meters = 9400*100 centimeters = 940,000 centimeters

1.1.3

4.2 tons to grams

1 ton = 1000 kilograms

First convert it into kilogram

1 kilogram = 1000 grams

Therefore, 4.2 tons = 4.2*1000 kilograms = 4200 kilograms

then in grams

4200 kilograms = 4200*1000 grams = 42,000,000 grams

I hope this helps! Let me know if you have any other questions.

The graph of this relation is four points on the coordinate plane (see attached diagram).

Hence option D is true.

Since we know that,

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

And a function is a special relation,

where each input x has a single output y.

This relation is not a function, because for one x (x=-1),

Here are two different possible y (y=3 or y=2).

If you consider the graph, you can see that there will be vertical line passing through the points (-1,3) and (-1,2).

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Answer:

Step-by-step explanation:

See image below

The required outputs of the given rule are 6, 10, 14, 18, 22.

Given inputs are 3, 5, 7, 9, 11 and the rule is 2x.

To find the outputs by applying the given rule to the inputs.

Let x be the input, then the output is 2x.

That implies,

x = 3 then output = 2× 3 = 6.

x = 5 then output = 2× 5 = 10.

x = 7 then output = 2× 7 = 14.

x = 9 then output = 2× 9 = 18.

x = 11 then output = 2× 11 = 22.

Hence. the required outputs of the given rule are 6, 10, 14, 18, 22.

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Answer:

Valerie's pay increased by 7.5%.

Step-by-step explanation:

The percent increase in Valerie's pay can be calculated as follows:

Percent increase = ((New pay - Old pay) / Old pay) x 100%

Substituting the given values, we get:

Percent increase = ((15.05 - 14) / 14) x 100%

Percent increase = (1.05 / 14) x 100%

Percent increase = 0.075 x 100%

Percent increase = 7.5%

Step-by-step explanation:

She now gets $1.05 per hour more .....1.05 is what percent of 14.00 ?

$ 1.05/ $ 14  x 100% = 7.5% increase

Answer:

6650 cm³

Step-by-step explanation:

area of a circle = π r², where r is the radius

area =  π (46)²

= 2116 π

= 6650 cm³ to 3 significant figures

The sale price of a pillow originally priced at 12 dollars is given as follows:

$9.

The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.

The original price is given as follows:

$12.

The markdown rate for this problem is given as follows:

25%.

Hence the sale price of a pillow originally priced at 12 dollars is given as follows:

0.75 x 12 = $9.

(markdown of 25% means that 75% of the price is paid).

The complete problem is:

"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"

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The area of a 135 slice of pizza be,

⇒ 6,782.41 inches²

We have to given that;

Recently they had a lunch special for a Personal Pie with a radius of 4 inches .

Since, WE know that;

Area of circle is,

A = πr²

Where, r is radius of circle

Here, Radius of circle = 4 inches

Hence, Area of pizza is,

⇒ A = 3.14 x 4²

⇒ A = 50.24 inches²

Hence, the area of a 135 slice of pizza be,

⇒ 50.24 × 135

⇒ 6,782.41 inches²

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Answer: Obtuse Angle

Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.

Answer:

It would be called an obtuse angle

Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!

have a wonderful Sunday!

Applying the properties of the diagonal of a rectangle, the value of x is calculated as: x = 37.

A rectangle is a quadrilateral that has two equal diagonals which bisect each other, to form equal segment. Rectangle RSTW has two diagonals RT and SW, therefore:

2(RZ) = SW

Given the following:

RZ = 2x + 7

SW = 5x - 23

Plug in the values:

2(2x + 7) = 5x - 23

4x + 14 = 5x - 23

4x - 5x = -14 - 23

x = 37

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Answer: (x+6)(x-3)

Step-by-step explanation:

y=x^2+3x-18

(x+6)(x-3 )

To calculate the rate at which the mixture is being poured, we divide the amount of mixture poured (in kilograms) by the time it takes (in minutes):

In this case, the amount of mixture poured is 50 kg, and the time taken is 8 minutes. Plugging these values into the formula, we have:

Dividing 50 kg by 8 min gives us:

Therefore, the mixture is being poured at a rate of 6.25 kilograms per minute.

Answer:

See below for answers and explanations

Step-by-step explanation:

a, b, and c are the coefficients of the quadratic, so a=1, b=6, and c=-12

(h,k) is the vertex of the parabola, so we must convert it to vertex form by completing the square:

[tex]y=x^2+6x-12\\y+21=x^2+6x-12+21\\y+21=x^2+6x+9\\y+21=(x+3)^2\\y=(x+3)^2-21[/tex]

Therefore, the vertex is (3,-21), which means h=-3 and k=-21.

The y-intercept is when x=0, or when the function passes through the x-axis:

[tex]y=x^2+6x-12\\y=0^2+6(0)-12\\y=-12[/tex]

Therefore, the y-intercept is -12 (also written as (0,-12) as an ordered pair).

The x-intercept is when y=0, or when the function passes through the y-axis:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-6\pm\sqrt{6^2-4(1)(-12)}}{2(1)}\\\\x=\frac{-6\pm\sqrt{36+48}}{2}\\\\x=\frac{-6\pm\sqrt{94}}{2}[/tex]

Therefore, the x-intercepts are (-6+√94)/2 and (-6-√94)/2.

Hope this helped!

Step-by-step explanation:

Unclear what you are asking

here is one possibility

3^2  - 4^5

9    - 1024 = - 1015

Here is another possibility

(3^(2-4) )^5    =  = (3^(-2))^5 =   3 ^-10 =    1/59049      

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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Answer: $45.31

Step-by-step explanation:

10*5*1.5=75

75/27 (formula)=2.77778

2.77778*16.31=45.31

The surface area of the prism is S = 36 feet²

Given data ,

Let the surface area of the prism be represented as S

Now , the base of the prism is B

where B = l x w

And , length of prism = l and width of prism is = w

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

S = 2 ( 1/2 ) ( 3 x 4 ) + ( 4 x 2 ) + ( 3 x 2 ) + ( 5 x 2 )

On simplifying , we get

S = 12 + 8 + 6 + 10

S = 36 feet²

Hence , the surface area is S = 36 feet²

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Given statement solution is :- The average hotel room cost in 2012 would be $199.97, none of the provided options are correct.

To calculate the average hotel room cost in 2012, we can use the formula:

y = a(1 + r)^t

where:

y = future value (cost in 2012)

a = initial value (cost in 1980)

r = annual growth rate (5.1% or 0.051)

t = number of years (2012 - 1980 = 32)

Substituting the given values into the formula, we have:

y = $48.00(1 + 0.051)^32

Calculating the value:

y ≈ $48.00(1.051)^32

y ≈ $48.00(2.718282)^0.051(32)

y ≈ $48.00(2.718282)^1.632

y ≈ $48.00 * 4.171331

y ≈ $199.97

Rounding to the nearest cent, the average hotel room cost in 2012 would be $199.97.

Therefore, none of the provided options are correct.

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The probability that event A or B takes place is 17/19

Probability is defined as the ratio of the required to the total possible outcomes of an event.

The probability of event A or B taking place can be defined as ;

P(A or B) = P(A) + P(B)

P(A) = 10/19

P(B) = 7/19

Hence,

P(A) + P(B) = 10/19 + 7/19

L.C.M of 19 and 19 = 1

P(A) + P(B) = (10 + 7)/19

P(A) + P(B) = 17/19

Therefore, the probability that event A or B takes place is 17/19

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Let's evaluate the probability based on the given information.

The number of ways to choose 6 men from 26 can be calculated as:

C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = 230,230.

The number of ways to choose 6 women from 29 can be calculated as:

C(29, 6) = 29! / (6! * (29-6)!) = 29! / (6! * 23!) = 177,100.

The total number of possible outcomes is the combination of selecting 6 men and 6 women from the given pool of 26 men and 29 women:

Total outcomes = C(26, 6) * C(29, 6) = 230,230 * 177,100 = 40,795,315,300.

Therefore, the probability of selecting exactly 6 men and 6 women from the given pool is:

Probability = 1 / Total outcomes = 1 / 40,795,315,300 ≈ 2.45 x 10^-11.

Hence, the probability is approximately 2.45 x 10^-11.

The volume of the solid generated by rotating the figure is 62.8 cubic units

From the question, we have the following parameters that can be used in our computation:

The figure

The figure is a rectangle with the following dimensions

Length = 5

Width = 2

When rotated around the given axis, we have a cylinder with the following dimensions

Height = 5

Radius = 2

So, we have

Volume = πr²h

This gives

Volume = 3.14 * 2² * 5

Evaluate

Volume = 62.8

Hence, the volume of the solid generated by rotating the figure is 62.8 cubic units

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His total earnings for a total sale of 7,000​ could be 1450sh

From the question, we have the following parameters that can be used in our computation:

Salary = 400

Commission = 15%

using the above as a guide, we have the following:

Total earnings = 400 + 15% * Total sales

So, we have

Total earnings = 400 + 15% * 7000

Evaluate

Total earnings = 1450

Hence, the total earnings is 1450

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Question

Simon earned 400sh weekly for goods sold and a commission of 15%

What could be his earnings for a total sale of 7,000​.

To determine which company has higher salaries, you can use the mean, median, or mode as measures of center. Let's calculate each of these measures for the given data:

Company A salaries: 45,000, 55,000, 53,000, 51,000, 49,000, and 42,000.

Mean (Average):

To calculate the mean, sum up all the salaries and divide by the total number of salaries.

Mean of Company A salaries = (45,000 + 55,000 + 53,000 + 51,000 + 49,000 + 42,000) / 6 = 295,000 / 6 = 49,167

Median:

To find the median, you arrange the salaries in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values.

Arranging the Company A salaries in ascending order: 42,000, 45,000, 49,000, 51,000, 53,000, 55,000

Median of Company A salaries = (49,000 + 51,000) / 2 = 50,000

Mode:

The mode represents the value(s) that appear most frequently in the dataset.

In Company A salaries, all the values occur only once, so there is no mode.

Now let's calculate the same measures for Company B salaries:

Company B salaries: 54,000, 39,000, 51,000, 52,000, 44,000, and 48,000.

Mean of Company B salaries = (54,000 + 39,000 + 51,000 + 52,000 + 44,000 + 48,000) / 6 = 288,000 / 6 = 48,000

Arranging the Company B salaries in ascending order: 39,000, 44,000, 48,000, 51,000, 52,000, 54,000

Median of Company B salaries = (48,000 + 51,000) / 2 = 49,500

Mode of Company B salaries = There are no repeating values, so there is no mode.

To summarize:

- Mean of Company A salaries: $49,167

- Median of Company A salaries: $50,000

- Mode of Company A salaries: No mode

- Mean of Company B salaries: $48,000

- Median of Company B salaries: $49,500

- Mode of Company B salaries: No mode

Based on these measures of center, we can see that the mean and median salaries of Company A are slightly higher than those of Company B. However, since there is no mode in either dataset, we cannot consider the mode as a determining factor in this case.

Answer:

The equation for a parabola that opens down, translated to the right 3, and translated down 2 can be written in the standard form as:

y = a(x - h)^2 + k

where (h,k) represents the vertex of the parabola. Since the parabola opens down, the value of 'a' must be negative. The vertex is translated to the right 3 and down 2, so we have:

h = -3 and k = -2

Substituting these values in the standard form equation, we get:

y = a(x + 3)^2 - 2

This is the equation for a parabola that opens down, translated to the right 3, and translated down 2.