If: f(x) = 4x-2
Find f(2)

Answer:

0

Step-by-step explanation:

Answer: it's C. 0

Also Happy early Christmas

Step-by-step explanation:

❀\( \underline{ \underline{ \text{Given}}} : \)

Then, Increment of the marks = 30 - 20 = 10

❀ \( \underline{ \underline{ \text{To \: find}}} : \)

❀ \( \underline{ \underline{ \text{Solution}}} : \)

\( \boxed{ \sf{Percentage \: of \: increment = \frac{Increase \: of \: marks}{Initial \: marks} \times 100\%}}\)

⇒ \( \sf{ \frac{10}{20} \times 100\%}\)

⇒ \( \boxed{ \sf{50 \: \%}}\)

\( \pink{ \boxed{ \boxed{ \bold{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{50\%}}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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The inference is that not to tile the plane means not covering a two-dimensional region with copies of the same shape.

It should be noted that tiling the plane means covering a two-dimensional region with copies of the same shape so that there are no gaps or overlaps.

In mathematics, a tiling of the plane is a collection of subsets of the plane, i.e. tiles, which cover the plane without gaps or overlaps.

Therefore, not to tile the plane means not covering a two-dimensional region with copies of the same shape.

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The function f(x) = (x-2)(x-3)^2 have a relative max at x =3 using derivative of function and critical points.

To find the relative maximum of the function f(x) = (x - 2)(x - 3)^2, we need to find the critical points of the function, which occur where the derivative of the function is zero or undefined.

First, we find the derivative of the function using the product rule,

f'(x) = (x - 3)^2 + 2(x - 2)(x - 3)

Next, we set the derivative equal to zero and solve for x:

(x - 3)^2 + 2(x - 2)(x - 3) = 0

Expanding the equation and simplifying, we get:

x^2 - 8x + 15 = 0

Using the quadratic formula, we find the solutions:

x = (8 ± √16) / 2 = 5, 3

Therefore, the critical points of the function are x = 5 and x = 3.

To determine if these critical points are relative maxima or minima, we can use the second derivative test. We find the second derivative of the function:

f''(x) = 2(x - 2) + 2(x - 3) + 4(x - 3)

Simplifying the expression, we get:

f''(x) = 6x - 20

When x = 5, f''(5) = 10, which is positive, so the critical point at x = 5 is a relative minimum.

When x = 3, f''(3) = -6, which is negative, so the critical point at x = 3 is a relative maximum.

Therefore, the function f(x) has a relative maximum at x = 3.

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Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

The constant of variation is 1/8.

The discrepancy among an ideal and real scenario is referred to as the Law of Variation. The most frequent manifestations of variation or variability are changes in the data, anticipated results, or minor changes in the quality of the output.

The types of variation are given below-

According to the question;

A quantity m varies jointly with p and r which shows that p and r in joint variation with m.

m ---> pr

m = kpr

where, k is the constant of variation.

m = 1, p = 2, r = 4.

Substitute the values in the relation,

1 = k(2)(4)

1  = 8k

k = 1/8

Therefore, the constant of variation is 1/8.

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Answer:

B: \(\frac{1}{8}\)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

n the case of errors-in-variables bias, the OLS estimator is consistent but no longer unbiased in small samples. This is the correct statement.

In statistics, the errors-in-variables bias is a form of statistical bias that occurs when an independent variable (IV) is measured with error. The presence of the errors-in-variables (EIV) bias means that the OLS estimator will be consistent but no longer unbiased. This means that the OLS estimator can still give reliable estimates, but the estimates are no longer accurate.

The errors-in-variables (EIV) bias can be corrected by using methods such as instrumental variables or two-stage least squares (2SLS) regression. In small samples, the EIV bias can have a more significant impact on the accuracy of the OLS estimator.

In such cases, other estimation methods such as maximum likelihood estimation or the generalized method of moments (GMM) may be used to improve the accuracy of the estimates

Therefore, option C: the OLS estimator is consistent but no longer unbiased in small samples, is the correct .

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Answer: $7.25

Step-by-step explanation:

Let T = taco cost

Let M = milk cost

T + M = 2.10

2T + 3M = 5.15

Multiply the first equation by (-2) and add it to the second equation

-2T - 2M = -4.20

2T + 3M = 5.15

M = 0.95

Plug this value for M in to the first equation

T + 0.95 = 2.10

T = 1.15

So a taco costs $1.15 and the milk costs $0.95

1.15 * 3 = 3.45

0.95 * 4 = 3.80

3.45 + 3.80 = 7.25

The variable b as the subject of the formula is b = √2(p -c)/a

Expressions are mathematical statements that are represented by variables, coefficients and operators

The equation is given as

p = 1/2ab^2 + c

Subtract c from both sides of the equation

So, we have

1/2ab^2 = p - c

Multiply through by 2

ab^2 = 2(p -c)

Divide by a

b^2 = 2(p -c)/a

Take the square root of both sides

b = √2(p -c)/a

Hence, b as the subject of the formula is b = √2(p -c)/a

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Answer:

B A library could have less than 12 computers.

D All libraries must have less than 35 computers.

E At least 1 library does bot have 12 computers.

Answer:

b) \(4a^{2} b^{2} c^3[\sqrt[3]{b} ]}\)

Step-by-step explanation:

The possible coordinates of point l are (7,3),(7,-13),(-5,3),(-5,-13),(9,1),(9,-11),(-7,1), and (-7,-11).

Given that:-

Coordinates of k = (1,-5)

Distance between point k and point l = 10 units.

We have to find the coordinates of point l.

Let the coordinates of point l be (x,y).

By using distance formula, we can write:-

\(\sqrt{(x-1)^2+(y+5)^2} =10\)

Squaring on both sides, we get:-

\((x-1)^2+(y+5)^2=100\)

For, integer coordinates, the possibilities are 36+ 64 or 64+36.

Hence, we can write,

\((x-1)^2+(y+5)^2 = 36 + 64 \\or\\(x-1)^2+(y+5)^2 = 64 + 36\)

Hence,

\((x-1)^2 = 36\)

x - 1 = 6 or x -1 = -6

x = 7 , -5

\((y+5)^2 =64\)

y + 5 = 8 or y + 5 = -8

y = 3,-13

or

\((x-1)^2=64\)

x - 1 = 8 or x - 1 = -8

x = 9,-7

\((y+5)^2\)

y + 5 = 6 or y + 5 = -6

y = 1,-11

Hence, the possible values of coordinates of point l are (7,3),(7,-13),(-5,3),(-5,-13),(9,1),(9,-11),(-7,1), and (-7,-11).

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There is a moderately strong positive correlation between the company's sales and industry sales.

The statistical results from the regression analysis indicate that there is a multiple R value of 0.802. This value represents the correlation coefficient, which measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient suggests a moderately strong positive correlation between the company's sales and industry sales. Additionally, the R-squared value is 0.643, which indicates that approximately 64.3% of the variability in the company's sales can be explained by the variability in industry sales. This suggests that industry sales have a significant influence on the company's sales performance. Furthermore, the adjusted R-squared value is 0.618, which takes into account the number of variables and observations in the regression analysis. It provides a more accurate measure of the model's goodness of fit. Finally, the standard error SYX is 0.9224, which represents the average distance between the actual company sales data and the predicted values based on the regression model. A lower standard error indicates a better fit of the model to the data. Overall, based on the given statistics, it can be concluded that there is a moderately strong positive correlation between the company's sales and industry sales, and industry sales significantly influence the company's sales performance.

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Step-by-step explanation:

5(3+6)2-62

(15+30)2-62

30+60-62

90-62=28

Answer:

I think that it is 1) E, F, G, H, J

The claim is false that the population means 9.2. and the required value of the t statistic is -1.02.

Given that,
Sample size (n) = 49,
Sample means (μ) = 8.5,
Standard deviation (σ) = 1.5, and the significance level of 0.01.
To determine whether the population means is equal to 9.2 and also the value of sample test statistic t.

The T - statistic is the ratio of the predictive value of a parameter from its hypothesized value to its standard disputable values.

Let to prove the claim let's assume the population means is not equal to 9.2.
Now

Z = (x - μ)/σ

Z = (8.5 - 9.2) / 1.5

  = -0.7 / 1.5

  = -0.467

The probability(P) of z of -0.467 is 0.67975.

Since the value of P is more than 0.01 so it implies that the assumption that population means is not equal to 9.2.

\(t = \frac{x - \mu}{\sigma/\sqrt{n} }\\ t = \frac{8.5 - 9.2}{1.5/\sqrt{49} } \\ t = -1.02\)

Thus, the claim is false that the population means 9.2. and the required value of the t statistic is -1.02.

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Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.

a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.

b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.

c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.

Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.

The events that would shift the factory's demand for capital are:

a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.

b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.

The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.

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Answer:

GASOLINE The table gives the cost of a

gallon of gasoline at two stations.

How much more does gasoline cost at

Gas For Less than at Cut-Rate?

Step-by-step explanation:

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}+1=0\)

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}=-1\)

\(\\ \rm\Rrightarrow 3tan(2x+10)=1\)

\(\\ \rm\Rrightarrow tan(2x+10)=1/3\)

\(\\ \rm\Rrightarrow 2x+10=18\)

\(\\ \rm\Rrightarrow 2x=8\)

\(\\ \rm\Rrightarrow x=4\)

Answer:

  £4838.11

Step-by-step explanation:

You want the amount in an account after 2 years and 5 months if interest is compounded monthly with an effective rate of 5% per year. The beginning balance is £4300.

If the amount of interest earned from monthly compounding is identical to the amount earned by annual compounding, the effective monthly multiplier is ...

  1.05^(1/12) ≈ 1.00407412

which is an effective monthly rate of 0.407412%, and an annual rate of 12 times that, about 4.88895%.

The balance after 29 months using the monthly rate of 0.407412% will be ...

  £4300·1.00407412^29 ≈ £4838.11

__

Additional comment

The key wording here is that the monthly compounding results in the same amount of interest being earned as for annual compounding at 5%. That is, the effective rate of the interest compounded monthly is 5% over a year's time.

A square-based box with an open top and volume of 4,000 cm³ has minimum surface area when its dimensions are 10√2 cm by 10√2 cm by 20√2 cm.

Let's assume that the box has a square base with side length x and height h. Then, its volume is given by:

V = x^2 * h

We are given that the volume is 4,000 cm³, so we can write:

x^2 * h = 4,000

Solving for h, we get:

h = 4000 / x^2

The amount of material used to construct the box is the sum of the areas of its five faces (four sides and the base). Since the box has an open top, we don't need to consider its area. The area of the base is x^2, and the area of each side is x times the height h. Thus, the total surface area A of the box is given by:

A = x^2 + 4xh

Substituting the expression we found for h, we get:

A = x^2 + 4x(4000 / x^2)

Simplifying and factoring out 4, we get:

A = 4(x^2 + 1000/x)

To find the dimensions of the box that minimize the amount of material used, we need to find the value of x that minimizes A. We can do this by taking the derivative of A with respect to x and setting it equal to zero:

dA/dx = 8x - 4000/x^2 = 0

Solving for x, we get:

x = 10√2

Substituting this value back into the expression we found for h, we get:

h = 20√2

Therefore, the dimensions of the box (in cm) that minimize the amount of material used are:

side length of the base: 10√2 cm

height: 20√2 cm

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Answer:

D) $115

Step-by-step explanation:

15x + 40 = y

15 (5) + 40 = 115

15 x 5 = 75

75 + 40 = 115

Answer:

D is the answer

Step-by-step explanation:

15x5=75

75+40=115

Question Should look like

determine the distance between (-4,-7) and (-8,-13)

A. \(\sqrt{10}\)

B. \(\sqrt{82}\)

C. \(\sqrt{544}\)

D. \(\sqrt{52}\)

Answer: D. \(\sqrt{52}\)

Step-by-step explanation:

\(a^{2}+b^{2}= c^{2}\)

a =(8-4)... b=(13-7)

a=4, b=6

therefore...

\(a^{2}+b^{2}= c^{2}\\4^{2}+6^{2}=c^{2}\\16+36=c^{2}\\52=c^{2}\\c=\sqrt{52}\)

The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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Given :

ATQ,

the volume of the model is thrice the height of the model

so,

the volume of the statue would be thrice it's height

hence,the height of the statue would be 13,500 cm

Answer: Let x be the width of the carpet in feet.

Then, the length of the carpet is 3 feet more than three times the width, which can be expressed as 3x + 3.

The area of a rectangle is given by the formula A = length × width. Therefore, the area of the carpet is:

A = (3x + 3) x = 3x² + 3x

We know that the area of the carpet is 216 square feet, so we can set up the equation:

3x² + 3x = 216

To solve for x, we can first divide both sides by 3:

x² + x = 72

Then, we can rearrange the equation to get it in standard quadratic form:

x² + x - 72 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -72.

Plugging these values into the formula, we get:

x = (-1 ± √(1² - 4(1)(-72))) / 2(1)

x = (-1 ± √(1 + 288)) / 2

x = (-1 ± √289) / 2

x = (-1 ± 17) / 2

This gives us two possible values for x: x = -9 or x = 8.

Since the width of the carpet can't be negative, we reject the negative solution and conclude that the width of the carpet is 8 feet.

To find the length of the carpet, we can use the expression we found earlier: 3x + 3. Plugging in x = 8, we get:

length = 3(8) + 3 = 24 + 3 = 27

Therefore, the dimensions of the carpet are 8 feet by 27 feet.

Step-by-step explanation: