Evaluate the following expression
2+(3-2x2)x1​

V is the set of polynomials of the form a + bx, V is a vector space over the field of scalars, and it satisfies all the given properties.

Let V be the set of polynomials of the form a + bx, where a and b are scalars. We can show that V is a vector space over the field of scalars using the given operations and properties.

Closure under addition: Let u and v be objects in V. Then u = a1 + b1x and v = a2 + b2x for some scalars a1, b1, a2, and b2. The sum u + v is defined as (a1 + a2) + (b1 + b2)x, which is also of the form a + bx. Therefore, u + v is in V.

Commutativity of addition: u + v = (a1 + a2) + (b1 + b2)x = (a2 + a1) + (b2 + b1)x = v + u.

Associativity of addition: u + (v + w) = (a1 + a2) + (b1 + b2)x + (a3 + b3x) = (a1 + (a2 + a3)) + (b1 + (b2 + b3))x = (u + v) + w.

Existence of a zero vector: Let 0 be the polynomial 0 + 0x. Then for any u in V, we have 0 + u = (0 + a) + (0 + b)x = a + bx = u and u + 0 = (a + 0) + (b + 0)x = a + bx = u.

Existence of additive inverses: Let u = a + bx be an object in V. Then the negative of u is -u = -a - bx. We have u + (-u) = (a + bx) + (-a - bx) = 0 + 0x = 0 and (-u) + u = (-a - bx) + (a + bx) = 0 + 0x = 0.

Closure under scalar multiplication: Let k be any scalar and u = a + bx be any object in V. Then ku = ka + kbx is also of the form a + bx. Therefore, ku is in V.

Distributivity of scalar multiplication over vector addition: k(u + v) = k((a1 + b1x) + (a2 + b2x)) = k((a1 + a2) + (b1 + b2)x) = ka1 + ka2 + kb1x + kb2x = (ka1 + kb1x) + (ka2 + kb2x) = ku + kv.

Distributivity of scalar multiplication over scalar addition: (k + m)u = ((k + m)a) + ((k + m)bx) = (ka + ma) + (kb + mb)x = (ka + kb)x + (ma + mb)x = ku + mu.

Associativity of scalar multiplication: k(mu) = k(ma + mbx) = km(a + bx) = (km)a + (km)bx = (km)u.

The identity element of scalar multiplication: 1u = 1(a + bx) = a + bx = u.

Therefore, V is a vector space over the field of scalars, and it satisfies all the given properties.

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Answer:

3,000 is the numerical increase and 15% is the percentage increase.

Step-by-step explanation:

It's quite easy to see that 3,000 more people were added to 20,000, since 23,000 - 20,000 = 3,000. To find the percentage, simply take 20,000 and divide it by the additional increase number, which is in this case 3,000. 20,000/3,000 = 0.15. Converting decimals to percentages, we take the digits behind the decimal and add the percent sign since 100 is equal to 1 or the whole. So 0.15 = 15%, which is the percent increase.

Answer:

actual amount of increase is 3000

% increase is 15%

Step-by-step explanation:

The actual amount of increase is

23,000-20,000= 3,000

To find the percent increase, take the actual amount of increase and divide by the original amount

3,000/20000=.15

Change to percent

15%

Answer:

I say its b

Step-by-step explanation:

minutes of long-distance calls in a month make plan A the better deal= 300.

you are choosing between two long-distance telephone plans. Plan A has a monthly fee of $15 with a charge of $0.08 per minute for all long-distance calls. Plan B has a monthly fee of $3 with a charge of $0.12 per minute for all long-distance calls.

f(x)=15+0.08x

g(x)=3+0.12x

The costs for the two planes be the same when f(x)=g(x),

15+0.08x=3+0.12x

12=0.04x

x=300 minut.

f(x)=15+0.08*300=15+24=39.

g(x)=3+0.12*300=3+36=39.

 minutes of long-distance calls in a month make plan A the better deal= 300.

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Answer:

228

Step-by-step explanation:

2(6x4 + 4x9 + 6x9) = 228

The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

In this question we must derive the equation of the line for a given street and look for another equation of the line parallel to the previous one. Lines are first order polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept, respectively.

Now we present the procedure in detail. First, find the equation of the first line:

5 = 4 · m₁ + b₁           (1)

2 = 3 · m₁ + b₁          (2)

(m₁, b₁) = (3, - 7)

Second, determine the equation of the line parallel to the line found in the previous step: (Please notice that two lines are parallel to each other when they share the same slope but have different y-intercepts)

- 3 = 3 · 2 + b₂

b₂ = -3 - 6

b₂ = - 9

The equation of the line parallel to the first line is y = 3 · x - 9. (Correct choice: B)

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Answer: The correct answer is B

Answer:

C. angle-side-angle

D. angle-angle-side

Step-by-step explanation:

A triangle is bounded by three sides, thus it has three angle. When two triangles are compared, the length of sides and angles could be similar or not. Thus, the triangle may be congruent or not congruent.

The relationship between congruent triangles can be expressed as regards to their sides, angles, or both.

From the given question, when the three angles of two given triangles are the same, then the two triangles are congruent. This relationship can be expressed as Angle-Angle-Angle.

Also, when two triangles have two equal sides and an included angle to be equal (i.e Side-Angle-Side), then they are congruent.

Answer:

Step-by-step explanation:

Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons

The data of the sugar solutions are;

The volume of 5% sugar solution Kate has = 3 quarts

The volume of the 12% sugar solution = X

Let 'Y' represent the volume of the 8% sugar solution, we have;

The volume of the resultant solution, Z = X + Y + 3

The concentration of the resultant solution = 10%

0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)

Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, we have;

X = (2 × 2 + 15)/2 = 9.5 Quartz

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Answer:

Yes

Step-by-step explanation:

If you substitute the x and y then you get -15 = -15

-15 = -3(4) - 3

-15 = -12 - 3

-15 = -15

Hope this helps :)

The multiplicative rate of change of a function is calculated by taking the ratio of the change in the output to the change in the input, which in this case would be 2.

The multiplicative rate of change of a function is the rate at which the output of the function changes in relation to the input. It is calculated by taking the ratio of the change in the output to the change in the input. The formula for this is:

Multiplicative Rate of Change = (Change in Output)/(Change in Input)

For example, if a function f(x) has an input of 3 and an output of 9, then the multiplicative rate of change of the function would be 2. This can be calculated by taking the difference between the output and the input, which is 9 - 3 = 6, and dividing it by the difference between the input and the output, which is 3 - 0 = 3. Thus, the multiplicative rate of change of the function is 6/3 = 2.

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complete question:

What is the multiplicative rate of change of the function f(x) = 3x?

In order to test the given hypothesis, we need to compare the test statistic (Z) with the critical value (Z alpha), where alpha is the level of significance. Since the alternative hypothesis states that mu1 - mu2 is greater than 0, we are interested in the right-tailed test.

This means that we need to find the critical value for the upper tail area under the standard normal distribution, which corresponds to the level of significance.

The null hypothesis will be rejected if the test statistic (Z) is greater than the critical value (Z alpha). Therefore, the correct option is (b) > = z alpha. This means that if the calculated value of Z is greater than or equal to the critical value of Z alpha, we can reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

It's important to note that the value of sigma is known in this case, which means that we can use the standard normal distribution to calculate the critical value and the test statistic. In summary, we reject the null hypothesis if Z is greater than or equal to the critical value Z alpha, which corresponds to the level of significance alpha for a right-tailed test.

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Given

Answer

Which is triangle 2

based on the given information, we can definitively conclude that PV- is closer to 0 than to 1. The option (b) "PV- is closer to 0 than to 1" is the correct answer.

The present value (PV) represents the current value of a future cash flow or investment. If PV is approximately 1, it means that the value of the future cash flow or investment is close to its full value in the present.

When we subtract a value from PV to get PV-, the resulting value will be smaller than PV. Since PV is approximately 1, it implies that PV- is closer to 0 than to 1. This conclusion holds because subtracting a value from 1 will always yield a smaller value.

For example, if PV is exactly 1 and we subtract 0.5 from it, the resulting PV- will be 0.5, which is closer to 0 than to 1.

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Step-by-step explanation:

Using the Intermediate Value Theorem, the following is applied:

"If f(x) is a continuous on interval [a,b] and we have two points f(a) and f(b) then there must be some value c such that f(a)<f(c)<f(b).

So here there must be a c such that

\(f(0) < f(c) < f(1)\)

Note: F(c)=0, the questions that the function have a solution between 0 and 1, so that means we must have some value, c such that f(c)=0 that exists

Next, plug in the x values into the function

\(f(0) = - 4\)

\(f(1) = {1}^{3} + 7(1) - 4 = 4\)

Since cubic functions are continuous and -4<0<4, then there is a solution c that lies between f(0) and f(1)

The area is given by f(x) = 10x² + 31x + 15.

The function is a rectangle's area function. We know that a rectangle is a flat, four-sided shape with straight sides and right-angled interior angles. Additionally, the opposing sides are parallel and of the same length.

Rectangle Area = Length * Width

The length of fabric scrap is 5x. So, the rectangular patchwork's length will be 5x + 3.

Since the width of the fabric scrap will be 2x, the rectangular patchwork's width will be 2x + 5.

Then area = f(x) = (5x + 3)(2x + 5) = 10x² + 25x + 6x + 15 = 10x² + 31x + 15

Therefore the area is given by f(x) = 10x² + 31x + 15.

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

For each additional hour of homework, the regression line predicts that a student would spend 0.1 fewer hours on independent reading.

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

y = -0.1x + 2.3

Where:

x = the number of hours they spent on homework

y = the number of hours they spent on independent reading

A linear regression equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

By comparing the equations, we have

slope = m = -0.1

y-intercept = c = 2.3

This means that as the number of hours spent on homework increases, the number of hours spent on independent reading reduces by 0.1 hour

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An integrated explanation of numerous hypotheses, supported by a large number of tests, and accepted by a majority of experts, is known as a theory .

Given,

Definition .

According to definition of theory,

A) It can be an explanation of scientific laws.

B) It is a total explanation of numerous hypothesis, each supported by a large body of results.

C) It is a summary and simplification of many data that previously appeared unrelated.

D) It is an assumption for new data suggesting new relationships among a range of natural phenomena.

Hence the definition given is of theory .

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The correlation between hours of TV and reading scores is r = -0.5. So option (C) is the correct option.

According to the information given in the question, the correlation between hours of TV and reading score must be r = -0.5.

In statistical terms, correlation is a measure of the strength and direction of a linear relationship between two variables. The strength of the relationship ranges from -1 to 1, with 0 indicating no correlation between the variables.

The correlation coefficient (r) is a measure of the strength and direction of a linear relationship between two variables. A value of -1 indicates a perfect negative relationship, while a value of 1 indicates a perfect positive relationship. A value of 0 indicates no relationship between the variables. A negative correlation coefficient indicates that as one variable increases, the other variable decreases, while a positive correlation coefficient indicates that as one variable increases, the other variable also increases.

The correlation coefficient (r) can be calculated using the following formula:

\(r = \frac{(n\Sigma XY - \Sigma X\Sigma Y) }{ \sqrt{(n\Sigma X^2 - (\Sigma X)^2)(n\Sigma Y^2 - (\Sigma Y)^2)}}\)

where

X = first data point

Y = second data point

Σ = sum of

n = total number of data points

The study report says, "Hours of television watched explains 25% of the observed variation in the reading scores of the 25 subjects."Therefore, we can assume that the correlation between hours of TV and reading scores is negative.

The correlation coefficient (r) is given by the square root of the explained variation, which is 0.25.

r = √(0.25) = 0.5, but since the variation is negative, the correlation is -0.5.

Therefore, r = -0.5 for the correlation between hours of TV and reading scores. Which is (C) option.

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Answer:

Price went up, $24.64/year for 28 years

Step-by-step explanation:

Change Year = 28

Change Price = 690

Average rate = 690/28 = 24.64

Answer:

You didn’t explain what we had to do....

Step-by-step explanation:

I’m not really sure...I’m sorry

Answer:

1050 people

Step-by-step explanation:

if there are x people at a conference

then 40% of x = 420

40% can be written as 40/100 --> 4/10 --> 2/5

2/5 * x = 420

x = 420 * 5/2

x = 1050

Answer:

it's 3.12 it's super easy it is 3.12 trust me you won't get it wrong

Answer:

11) D. 144 b/m

12) B. As exercise levels increase, heart rate increases

13) D. Transporting wastes away from cells

14) B. Capillaries

15) This is because during excercise you increase the skin blood flow in order to enable ¨heat dissipation¨. Then after the increase in blood flow to the muscles decides to have an increase which causes it to have a cardiac output which is in direct proportion to the increase in oxygen consumption.

Step-by-step explanation:

The score interval that is within one standard deviation of the mean is

(70 , 80).

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

Some of the properties of the standard deviation are:

1. It cannot be negative

2. It is only employed to calculate the spread or dispersion around a data set's mean

3. It displays the degree of deviation  from the mean value

4. The larger the spread, the more standard deviation, with data of about the same mean.

Given,

 The mean of the test μ = 75

The standard deviation σ = 5

We are asked to find the scores within one standard deviation of the mean.

This means that the scores should be in the interval ( μ - σ , μ + σ )

μ - σ = 75 - 5 =70

μ + σ = 75 + 5 = 80

Therefore the scores should be in the interval = ( 70,80), which is within one standard deviation of the mean.

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Answer:

\(Five = 31\)

Step-by-step explanation:

Given

\(Total = 142\)

\(Even = 56\)

\(One = 21\)

\(Three = 34\)

Required:

Number of times 5 were rolled

Even represents 2, 4 and 6.

So, we have:

\(Total = Even + One + Three + Five\)

\(142 = 56 + 21 + 34 + Five\)

\(142 = 111 + Five\)

Collect Like Terms

\(Five = 142 - 111\)

\(Five = 31\)

Answer:

option 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = \(\frac{0-(-2)}{4-0}\) = \(\frac{0+2}{4}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = \(\frac{1}{2}\) x - 2