FIND THE COTANGENT! Help me pls.

The maximum area of rectangle is 24, that can be calculated using the derivatives.

The area of rectangle = length * breadth,

The length of the rectangle is 2x units and the breadth is 3x+12 units,

So, A(x)=2x*(-3x+12)

=2x(-3x+12)

=-6x^2+24x

The derivative A'(x)=0

-12x+24=0

x=+2

Therefore, x=+2 is the critical point.

The second derivative.

The 2d derivative measures the immediately rate of alternate of the 1st derivative. The signal of the second derivative tells us whether or not the slope of the tangent line to is growing or decreasing.

A"(x)=-12<0

By the second derivative test, A(x) has maximum value at x=+2

Thus, the maximum are is

A(x)=2x(-3x+12)

A(2)=2(2)(-3(2)+12)

=4(6)

=2

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Out of the given choices, we choose 'not enough information given to answer this question'.

Since, we are given a p-value associated with a test of the slope coefficient equal to 0.028 which leads to 3% level of significance, it means that there is 3% chance of finding difference which is larger than the one given in our study given that the null hypothesis is true. Since, it is less than 5% level of significance, the null hypothesis is rejected and accept an alternative hypothesis. As this hypothesis is not given, we conclude that there is not enough information to give an answer to the question.

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Answer:

Step-by-step explanation:

the figure is a parallelogram, therefore the sum of angle A and angle B is 180°, we solve with an equation

180 = 5x + 5 + 4x - 5

180 = 9x

x = 180 : 9

x = 20

------------------------

check

180 = 5x + 5 + 4x - 5

180 = 5 × 20 + 5 + 4 × 20 - 5  (remember PEMDAS)

180 = 180

the answer is good

Answer:

The angle x is equal to 20 degrees

Answer:

√3√ab

Step-by-step explanation:

Please look in the attachment! Hope this helps! :D

Answer: The answer should be 31.42 in

the tension in each wire will be equal. The tension in each wire, T ,the tension in each wire is 85.36 N with its weight.

Assuming that the tool has negligible mass so that its weight does not contribute to the tension in the wires, the tension in each wire will be equal. The tension in each wire, T, can be calculated using the equation:

T = (W/2) + (L/2)*sin(θ),

where W is the weight of the shelf and L is the length of the shelf. The angle θ is the angle between the ceiling and the shelf.

In this case, W = 50 N, L = 50 cm and θ = 45°. Therefore, T = (50/2) + (50/2)*sin(45) = 50 + 35.36 = 85.36 N.

So, the tension in each wire is 85.36 N.

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After 5 week the savings of both Kaylee and Jack will be same.

The equation for Kaylee's savings, in terms of t, is K = 60 + 12t.

The equation for Jack's savings, in terms of t, is J = 95 + 5t.

To determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved, we set K equal to J and solve for t.

K = J

60 + 12t = 95 + 5t

7t = 35

t = 5

Kaylee and Jack have the same amount of money saved after 5 weeks.

What are savings?

The funds one has saved, particularly through a bank or government programme is known as savings.

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The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.

The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.

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Answer:

Step-by-step explanation:

Perimeter = 400

Diagonal= 120

Each Side= 400/4 = 100

Then, find the length of a straight line:

                                   400= 120(2)+2x

                                   400= 240+ 2x

                                   400-240=2x

                                   160=2x

                                    x=80

Area of Triangle= 1/2(b)(h)

       = 1/2(80)(120)

       = 1/2(9600)

       = 4800

The exponential function Q=Q0 (1+r) t can be used to describe exponential growth or decay depending on the value of r. If r is less than 0, the function can be used to describe exponential growth, whereas if r is greater than 0, the function can be used to describe exponential decay.

The exponential function Q=Q0 (1+r) t can be used to describe exponential growth or decay. The function is determined by three variables: Q0, which is the starting value of the function; r, which is the growth or decay rate of the function; and t, which is the time when the function occurs. If r is less than 0, then the function can be used to describe exponential growth, meaning that the output of the function will increase over time. On the other hand, if r is greater than 0, then the function can be used to describe exponential decay, meaning that the output of the function will decrease over time. The exponential function can be used to describe a variety of different processes, such as population growth, compound interest, and radioactive decay. It can also be used to predict future values based on past values by using the growth or decay rate. Thus, the exponential function is a powerful tool for describing and predicting exponential growth and decay.

Q=Q0 (1+r) t

For example, if Q0 = 10, r = 0.5, and t = 5, then

Q=10 (1+0.5)5

Q= 10 x 1.53

Q= 15.3

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Answer:

1/6

Step-by-step explanation:

ia fair dice only has 6 numbers so you can't get 7 so there is two 5 since its two fair dice it's out of 12,2/12 divide both by 2 because that the highest common factor and you get 1/6 that your answer

Refer to the photo taken.

The weighted average of the average weights of each individual subgroup, where the weights represent the population proportions in each subgroup, provides the average weight of the population's constituents.

This can be mathematically represented as: average population weight = _(i=1) r P i * w i, where P i is the population's share of subgroup I and w i is the weight of the subgroup's average members.

For instance, if the population is divided into three subgroups with proportions of P1 = 0.2, P2 = 0.5, and P3 = 0.3, and the subgroups' average weights are P1 = 150 lbs, P2 = 200 lbs, and P3 = 175 lbs, respectively, then the population's average weight is P1 * 150 lbs 180 lbs is equal to +0.5 * 200 lbs + 0.3 * 175 lbs.

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Answer:

75%

Step-by-step explanation:

42/56 * 100% = 0.75 * 100

= 75%

There is a 32.81% chance (0.3182) that there will be between 32647 and 43559 ants on a randomly chosen acre.

The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. We may calculate the likelihood that the value of the measure exceeds X by subtracting 1 from the pvalue.

The zscore of a measure X in a set with mean and standard deviation may be calculated as follows:

Z= X-μ/σ

μ = 42000   σ= 12275

The pvalue of Z when X = 32647 is deducted from the pvalue of Z when X = 43559 to get this value. So

X = 43559

z= 0.13 has a pvalue of 0.5517

X = 32647

z=  -0.76 has a pvalue of 0.2236

0.5517 - 0.2236 = 0.3281

0.3182 = 32.81% probability that a randomly selected acre has between 32647 and 43559 ants.

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Step-by-step explanation:

There is not sufficient evidence to conclude that the population mean battery life is less than 20 hours, based on the sample data.

To test the null hypothesis, Javier can use a one-sample t-test. In this test, the null hypothesis is that the population mean is equal to the claimed value of 20 hours, and the alternative hypothesis is that the population mean is less than 20 hours. To determine whether to reject or fail to reject the null hypothesis, Javier can compare the t-statistic, calculated from the sample data, to the critical t-value at a significance level of 0.05. The critical t-value is the value beyond which the null hypothesis can be rejected.

In this case, the t-statistic is given as -1.51. To find the critical t-value, Javier can use a t-table or a statistical software package. At a significance level of 0.05 and a sample size of 33, the critical t-value is approximately -1.68. Since the t-statistic (-1.51) is less than the critical t-value (-1.68), Javier should fail to reject the null hypothesis.

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a. The computed regression equation's regression coefficients, which hold the other independent variable constant, show the impact of each independent variable on the dependent variable. Y will grow by 0.5906 units for every unit increase in x1 and by 0.498 units for every unit increase in x2, respectively.

b. The regression equation can be changed to predict y for the cases when x1 and x2 are 180 and 310, respectively: y = 29.1270 + 0.5906 * 180 + 0.4980 * 310 = 29.1270 + 105.208 + 156.38 = 290.82

c. The sum of squares resulting from regression (SSR) is denoted by the formula: SSR = _(i=1)n (y i - y)2.

SSR = 6,216.375.

d. R2 = SSR / SST is how it is calculated.

R2 = 6,216.375 / 6,724.125 = 0.924 e is the result of substituting the supplied values. A measurement of the overall significance of the link between the variables is the F statistic. The calculation is:

f. The following equation yields the mean square due to regression (MSR):

MSR is calculated as SSR / (r - 1), where r is the total number of independent variables. MSR = 6,216.375 / (2 - 1) = 6,216.375 / 1 = 6,216.375 is the result of substituting the provided numbers.

g. MSE = SSE / (n - r - 1), where n is the number of observations and r is the number of independent variables, is the formula for the mean square due to error (MSE).

MSE = 507.75 / (10 - 2 - 1) = 507.75 / 7 = 72.53. With (r - 1) and (n - r - 1) degrees of freedom, we must compare the derived F statistic to the crucial value of F at alpha = 0.05 in order to utilize the F test to assess the overall significance of the association between the variables at a significance level of alpha = 0.05.

The crucial value can be found via of F, we can employ a critical value table or a statistical software program. The critical value of F is roughly 3.35 when alpha = 0.05 and the degrees of freedom are (r - 1) = (2 - 1) = 1 in the numerator and (n - r - 1) = (10 - 2 - 1) = 7 in the denominator.

The numbers for MSR and MSE can be substituted to get the following result: F = MSR/MSE = 6,216.375 / 72.53 = 85.24

The estimated F statistic (85.24) is higher than the threshold value of 3.35, which allows us to reject the null hypothesis that there is no association between the variables at alpha = 0.05. This shows a meaningful relationship between the dependent variable and at least one of the independent variables.

i. We must compare the t statistic for x1 to the crucial value of t at alpha = 0.05 with (n - r - 1) degrees of freedom in order to conduct a t test for the significance of x1 at an alpha = 0.05 significance level. As stated by the formula: t = b1 / sb1

where b1 is the regression coefficient for x1 and sb1 is the coefficient's standard error. T = 0.5906 / 0.0813 = 7.26 is the result of substituting the supplied values.

Statistical software or a table of critical values can both be used to determine the critical value of t. The critical value of t at alpha = 0.05 with (n - r - 1) = (10 - 2 - 1) = 7 degrees of freedom is roughly 2.365.

The estimated t statistic (7.26) exceeds the critical value of 2.365, hence the null hypothesis that the coefficient for x1 is not substantially different from zero at alpha = 0.05 can be rejected.

j. To run a t test to determine whether x2 is significant atWith (n - r - 1) degrees of freedom and a significance level of alpha = 0.05, we must compare the t statistic for x2 to the critical value of t. The formula for the t statistic for x2 is: t = b2 / sb2, where b2 is the x2 regression coefficient and sb2 is the coefficient's standard error. When the specified values are substituted, the following results are produced:

t = 0.4980 / 0.0567 = 8.79

Statistical software or a table of critical values can both be used to determine the critical value of t. The critical value of t at alpha = 0.05 with (n - r - 1) = (10 - 2 - 1) = 7 degrees of freedom is roughly 2.365.

As a result of the calculated t statistic (8.79) exceeding the crucial value of 2.365, we

can disprove the null hypothesis that the coefficient for x2 at alpha = 0.05 is not statistically different from zero.

k. The t statistic and the coefficient's standard error can be used to create a 95% confidence interval for the coefficient of x2. B2 +/- t * sb2 yields the confidence interval.

The values are replaced to yield: 0.4980 +/- 2.365 * 0.0567 = (0.3778, 0.6182)

This suggests that we have a 95% confidence that the true value of the x2 coefficient falls inside the given range (0.3778, 0.6182).

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The continental slope of the ocean is given as follows:

-67.9.

The slope of an object or a situation is calculated by the division of the vertical change by the horizontal change.

The parameters for this problem are obtained as follows:

Then the slope of the ocean floor connecting the edge of the continental shelf in the beginning of the oceanic crust is calculated as follows:

m = -2715/40 = -67.9.

(division of the vertical change by the horizontal change obtained previously on this problem).

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The number of push ups done by each girl from the given parameters is; 72 push ups

We are given;

Rate of Push ups for Talhah = 6 push ups per set

Rate of Push ups for Rosina = 8 push ups per set

Let the number of sets of push ups done by each girl be denoted as x

Thus, since after they finished, they realized that while they did the same total number of push ups, Rosina needed 3 fewer sets to finish hers, then the equation here is;

6x = 8(x - 3)

Expanding the bracket gives;

6x = 8x - 24

8x - 6x = 24

2x = 24

x = 12 sets

Thus, number of push ups done by each = 6 * 12 = 72

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Answer:

x is 8

And each side is 27

Step-by-step explanation:

check out the photo

hope it will help

The sequence of transformations to change figure PQRS to figure P′Q′R′S′ will be;

⇒ Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

Sequence of transformations will change figure PQRS to figure P′Q′R′S′.

Now,

Since, Sequence of transformations will change figure PQRS to figure P′Q′R′S′.

And, The coordinates of figure PQRS are,

P = (1,  2)

Q = (2, 1)

R = (3, 2)

S = (3, 3)

And, The coordinates of figure P'Q'R'S' are,

P' = (1,  -2)

Q' = (2, -1)

R' = (3, -2)

S' = (3, -3)

We know that,

The transformation rule for Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis will be,

⇒ (x , y) → (x, - y)

Thus, We get;

The sequence of transformations to change figure PQRS to figure P′Q′R′S′ is,

''Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.''

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Answer:

Step-by-step explanation:

23

Answer:$2400 invested at $9% $3000 invested at $11%

Step-by-step explanation:

The equation in x and y for the line tangent to the curve is x - √3y - √3 = 0

A given curve can be defined by both its cartesian coordinates that is in x-y  form or in polar coordinates that is in terms of r and θ there exists a relationship between two sets of coordinates

x = r cosθ

y = r sinθ

The tangent to any curve f(x) is defined by f'(x) . In order to find tangent to a given terms of r and θ , we can calculate from the above to expressions f'(x)

f'(x) = dy/dx = dx/dθ ÷ dy/dθ

It is given in the question that

r = 2 sinθ

Replacing the value of r to the standard equation,

x = (2 sinθ )cosθ = sin2θ

At θ = π/3 , x = √3 / 2

y = (2 sinθ)sinθ = 2sin²θ

At θ = π/3 , y = 3/2

Differentiating both w.r.t θ

=> dx / dθ = 2cosθ

=> dy/dθ = 4sinθcosθ

So, dy/dx = 2cosθ / 4sinθcosθ

=> 1 / 2sinθ

Therefore , slope of tangent : m = 1/2sinθ ( θ = π/3)

=> m = 1 / 2sin(π/3)

=> m = 2 / 2√3

=> m = 1 /√3

Hence , the equation of line is

( y - 3/2 ) = 1 /√3 (x -  √3 / 2)

=> √3y - 3√3/2 = x - √3/2

=> x - √3y - √3 = 0

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Answer:

$3.6 saved

Step-by-step explanation:

Shop A: -

7 cookies    ---->   $5.60

24 cookies   ----->  $x

x = (24 x 5.60) / 7

x = $19.2

Shop B: -

5 cookies  ---->  $4.75

24 cookies  ---- > $y

y = (24 x 4.75) / 7

y = $22.8

Saved = Shop B - Shop A

Saved = 22.8 - 19.2

Saved = $3.6

I hope my answer helps you.

Justin paid a tip that was 26% of his bill.

[tex]\frac{44.10-35}{35}[/tex]

[tex]\frac{44.10-35}{35}=0.26[/tex]

Justin paid a tip that was 26% of his bill.

A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .

Given :

a positive and a negative co - terminal angle for each given angle

1 )  

= -5π / 2

To find positive and negative co - terminal angle we need to add and subtract by 2π .

= -5π / 2 + 2π

= -5π + 4π / 2

= -π/2

= -5π / 2 - 2π

= -5π - 2 * 2π / 2

= -5π - 4π / 2

= -9π / 2

or =

2 )

= 3π / 2

= 3π / 2 + 2π

= 3π + 2 * 2π / 2

= 3π + 4π / 2

= 7π / 2

= 3π / 2 - 2π

= 3π - 4π / 2

= -π / 2

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P = 1 / n (Celia is first and Felicity is last in line) (n - 1)

P (in the line, Celia and Felicity are next to one another) = 2/n

A class consists of n kids.

These n kids line up for recess.

Out of n kids, there are two kids named Celia and Felicity.

(b) There are n positions and n! ways for n youngsters to stand in a line.

Consequently, n is the entire number of possible situations!

Felicity is standing in the last position while Celia is in the first (fixed position)

The remaining (n - 2) children can stand in the remaining 8 (n - 2) positions! ways

As a result, Celia is first in line and Felicity is last in line for the number of favorable situations, which is (n - 2)!

P (Celia is first in line and Felicity is last in line) = [(n - 2)! / n!]

P = (n - 2)! / [n(n - 1)(n - 2)!]

P = 1 / n(n - 1)

The likelihood that Celia and Felicity are on the same row as one another.

Consider Celia and Felicity as a single student, then multiply by the number of pupils (n - 1)

One can arrange (n - 1) pupils in (n - 1) positions! ways

However, there are two methods to organize Celia and Felicity among themselves.

There are therefore 2 good reasons to put Celia and Felicity adjacent to each other (n - 1)!

P(Celia and Felicity in the line are next to one another) = 2! * (n - 1)! / n!

P = 2 * (n - 1)! / n (n - 1)

P = 2/n

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