If f(x) = -5x - 1, find the function value f(1).

f(1) =

➲ ( 1 + sec x )( cosec x - cot x ) = tan x

\( \implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }\)

\( \implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}\)

\( \implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}\)

\( \implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}\)

\( \implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}\)

\( \implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}\)

\( \implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }\)

\( \implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }\)

➲ ( 1+ sec x )( 1- cos x ) = sin x. tan x

\( \implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}\)

\( \implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}\)

\( \implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}\)

\( \implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }\)

\( \implies\quad \sf{\dfrac{sin^2x}{cos\:x} }\)

\( \implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }\)

\( \implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }\)

To plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

To determine what sample volume should yield a countable plate, we need to calculate the appropriate dilution factor.

The sample has a density of 7.9 x 10^9 CFU/mL, and we want to plate 1 mL of a 10^-8 original dilution, which means we need to dilute the sample by a factor of 10^8 to obtain a countable plate.

We can calculate the required dilution factor using the following formula:

Dilution factor = (Volume of sample plated) / (Total volume of diluted sample)

To dilute the sample by a factor of 10^8, we can calculate the total volume of diluted sample as follows:

Total volume of diluted sample = (Volume of sample plated) x (Dilution factor)

Substituting the values, we get:

10^8 = 1 mL / (Total volume of diluted sample)

Total volume of diluted sample = 1 mL / 10^8

Total volume of diluted sample = 0.00000001 mL

Therefore, to obtain a countable plate, we need to plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

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The quantity that maximizes revenue is 1450.

The price of each item at this production level is $14.50.

The total revenue at this price is $21,025.

The revenue as a function of q can be found by multiplying the price (p) by the quantity (q):

R(q) = pq = q(29 - 0.01q) = 29q - 0.01q^2

To find the quantity that maximizes revenue, we take the derivative of R(q) with respect to q and set it equal to zero:

R'(q) = 29 - 0.02q = 0

0.02q = 29

q = 1450

Therefore, the quantity that maximizes revenue is 1450.

To find the price at this production level, we substitute q = 1450 into the demand equation:

p = 29 - 0.01(1450) = $14.50

So the price of each item at this production level is $14.50.

The total revenue at this price can be found by substituting q = 1450 and p = $14.50 into the revenue equation:

R(1450) = 1450(14.50) = $21,025

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Answer:

13/2, 6.549, 6 6/11, 6.77

Answer:

\(\huge\boxed{\sf 14\ times}\)

Step-by-step explanation:

\(\displaystyle Probability = \frac{Possible \ no. \ of\ events}{Total \ number\ of \ events}\)

If we roll a die 1 time, the probability of obtaining a 3 is:

= 1 / 6

Because a die has total 6 faces, out of which 3 is only 1.

But, if we roll it 84 times, it becomes:

= \(\displaystyle \frac{1}{6} \times 84\)

= 84/6

\(\rule[225]{225}{2}\)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions. Option c is correct.

An equation will have infinite solutions if both sides of the equal sign are the exact same thing, for instance . (You can test this with any value of x and find that they all work!)

So to find the equations that have infinite solutions, we need to see which have the same exact sides.

(Choice A)

-6x+35 = -6x-35 have the different thing on each side: , so this has no solution.

(Choice B)

6x+35  = -6x-35 does not have the same thing on each side, so it doesn’t have infinite solutions (it has 1).

(Choice C)

-6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

(Choice D)

6x+35=-6x+35 And finally,  has the different thing on each side: , so it has one solution.

Hence , -6x+35 = -6x+35 has the same thing on each side: , so this has infinite solutions.

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Answer:

See below ~

Step-by-step explanation:

1.

2.

3.

Answer:

Only A, the first equation is true.

Step-by-step explanation:

A. (y + 6)(y – 7) + 42 = y² + 6y –7y – 42 + 42 = y² – y. This means A is true

B. (x + 3)(X – 8) = x² + 3x – 8x – 24 = x² – 5x – 24. This means B is false.

Answer:

10 would be the answer :)

Question:

Andrew owns 3 fewer DVDs than Paul. Let K represent the number of Paul's DVDs. Write the expression that can be used to find the number of DVDs that Andrew owns.

Answer:

\(Andrew = k - 3\)

Step-by-step explanation:

Given

\(Paul = k\)

\(Andrew = 3\ fewer\)

Required

Write an expression for Andrew

3 fewer means that we subtract 3 from Paul's number of DVDs.

i.e.

\(Andrew = Paul - 3\)

Substitute k for Paul

\(Andrew = k - 3\)

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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The test used to determine whether or not first-order autocorrelation is present is the Durbin-Watson test.

1. Fit a regression model to the data.

2. Obtain the residuals, which represent the differences between the observed values and the predicted values from the regression model.

3. Calculate the Durbin-Watson statistic, which is a ratio of the sum of squared differences between adjacent residuals to the sum of squared residuals.

4. Compare the calculated Durbin-Watson statistic to critical values from a Durbin-Watson table or use statistical software to determine if there is significant autocorrelation.

5. The Durbin-Watson statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, a value below 2 indicates positive autocorrelation, and a value above 2 indicates negative autocorrelation.

6. By analyzing the Durbin-Watson statistic, researchers can make conclusions about the presence or absence of first-order autocorrelation in the regression model.

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Answer:

36a^10

Step-by-step explanation:

A:

4 seconds per centimer:

30cms               15 cms

----------------       -------------

2 minutes           1 minute

1 minute= 60 seconds

15 cms                       1cm

-----------------     =     ----------------

60 seconds              4seconds

B: 15 cms per minute

30cms/2minutes

(divide by 2 to get speed for one minute)

15cm/1 minute

EXPLANATION:

To solve the exercise we must make a rule of three.

The exercise is as follows:

Answer:

The answer is in the picture

Step-by-step explanation:

hope it helps!

Answer:25th Percentile: 5

50th Percentile: 30

75th Percentile: 34

Interquartile Range: 29

Step-by-step explanation:

Answer:

it is 5

Step-by-step explanation:

i looked it up

Answer:

40 minutes is your answer

Answer: It will take a 1/2 hour or 30min to paint one full wall.

The centroid of a triangle is the point where the three medians of the triangle intersect. In this case, the triangle has vertices at (0, 0), (5, 0), and (0, 7).

First, let's calculate the average x-coordinate:
¯x = (0 + 5 + 0) / 3 = 5/3 ≈ 1.67

Next, let's calculate the average y-coordinate:
¯y = (0 + 0 + 7) / 3 = 7/3 ≈ 2.33, the centroid of the triangle with vertices at (0, 0), (5, 0), and (0, 7) is approximately (1.67, 2.33).
In summary, the centroid of the triangle with verticesvertices at (0, 0), (5, 0), and (0, 7) is located at approximately (1.67, 2.33). This point represents the average position of the three vertices and is the intersection point of the medians of the triangle.

The centroid coordinates are found by taking the average of the x-coordinates and the average of the y-coordinates of the three vertices. In this case, we add up the x-coordinates (0 + 5 + 0 = 5) and divide by 3 to get an average of 5/3, which is approximately 1.67. Similarly, we add up the y-coordinates (0 + 0 + 7 = 7) and divide by 3 to get an average of 7/3, which is approximately 2.33. These values represent the x-coordinate (¯x) and the y-coordinate (¯y) of the centroid, respectively. Therefore, the centroid of the triangle is located at approximately (1.67, 2.33).

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Answer: f(x) and g(x) both represent y of the equations

Step-by-step explanation: f(x) and  g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.

Therefore, the correct option is "Cannot be determined with the given information." when the least squares regression line for a data set is y=2.3−0.1x and the standard deviation of the residuals is 0.13.

To determine if a case with the values x = 4.1, y = 2.34 qualifies as an outlier, we need to compare the observed value of y (2.34) with the predicted value of y based on the regression line (Y).

For this case, the predicted value of y (Y) can be calculated using the equation of the least squares regression line:

Y = 2.3 - 0.1x

Y = 2.3 - 0.1 * 4.1

Y = 2.3 - 0.41

Y = 1.89

Now, we can compare the observed value of y (2.34) with the predicted value of y (1.89). If the observed value significantly deviates from the predicted value, it can be considered an outlier.

In this case, the observed value (2.34) is greater than the predicted value (1.89), suggesting that it is above the regression line. However, without knowing the specific criteria or threshold for defining an outlier, it cannot be conclusively determined if this case qualifies as an outlier based solely on the information given.

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Answer: what

Step-by-step explanation:

Answer:

m=24

Step-by-step explanation:

The given Expression simplifies to -8.1069556e+27

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. A mathematical expression's order of execution is explained using the BODMAS.

Given an equation to solve,

6234653928 + 294292342 - 424624642 x 16515615615165161 x 1156 + 6466456

Let us consider this Expression as A + B - C * D * E + F, with the corresponding terms being equal

By, the BODMAS rule,

First step: Multiply C, D, E. Let this be G

Now, the equation will look like this: A + B - G + F

Second step: We can add and subtract according to the signs now

On solving, the expression simplifies to -8.1069556e+27

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Answer:

y-intercept is 0, x-intercept is 0 and 1

Step-by-step explanation:

For y-intercept, x=0 :

\({ \tt{y = {(0)}^{2} - 2(0) }} \\ { \tt{y = 0}}\)

For x-intercept, y=0 :

\({ \tt{0 = {2x}^{2} - 2x }} \\ { \tt{2x(x - 1) = 0}} \\ { \tt{x = 0 \: \: and \: \: 1}}\)

The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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Answer:

470 is your awnser

Step-by-step explanation:

Answer:

50 + 30 * 14 = 470

Step-by-step explanation:

  50 + 30 * 14

= 50 + 420

= 470

Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is expressed as y = mx+b

m is the slope

b is the intercept

Get the slope

m = -5-1/2-(-2)

m = -6/4

m = -3/2

Get the intercept

Substitute m = -3/2 and (-2, 1) into y = mx+c

1 = -3/2(-2) + c

1 = 3 + c

c = 1-3

c =-2

Get the required equation

y = mx+c

y = -3/2 x + (-2)

y  = -3/2 x -2

Hence the required equation is  y  = -3/2 x -2

Given:

Given a graph of the function

Required:

To graph the function

Explanation:

The graph of the function h(x) is,

The blue graph is the graph of the function h(x).

Final Answer: