A rectangular field is 30 yards in length and 81 feet in width.

What is the area of the field in square feet?

Simplify the integrand

[tex]\dfrac{1-\sin^2(t)}{\sin^2(t)} = \dfrac{\cos^2(t)}{\sin^2(t)} = \cot^2(t)[/tex]

Recall the derivative of csc(t),

[tex]\dfrac d{dt} \csc(t) = -\cot^2(t)[/tex]

It follows that

[tex]\displaystyle \int \frac{1-\sin^2(t)}{\sin^2(t)} \, dt = \int \cot^2(t) \, dt = \boxed{-\csc(t) + C}[/tex]

Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

looked up on Quizlet so yeah

Answer:

Step-by-step explanation:

The end solution has same volume as initial volumes of mixture.

The concentration of solution is calculated as below

Answer:

35 grams

Step-by-step explanation:

25+10=30 grams of the mixture

The answers are:

Second option, evaluating x=-1

[tex]g(-1)=-2[/tex]

Fifth option, evaluating x=6

[tex]g(6)=\frac{3}{2}[/tex]

We are given a table that shows the values for the given function (f(x), and we are asked to find the solution of an equivalent function (g(x)).

We have that:

[tex]g(x)=\frac{1}{2}f(x)[/tex]

Now, evaluating we have:

For x=-3

[tex]g(-3)=\frac{1}{2}f(-3)=\frac{1}{2}*5=2.5[/tex]

We have the values (-3,2.5) so, it's not part of the solutions to the  function g(x).

For x=-1

[tex]g(-1)=\frac{1}{2}f(-3)=\frac{1}{2}*-4=-2[/tex]

We have the values (-1,-2) so,  it's part of the solutions to the function g(x).

For x=0

[tex]g(0)=\frac{1}{2}f(0)=\frac{1}{2}*2=1[/tex]

We have the values (0,1) so, it's not part of the solutions to the function g(x).

For x=5

[tex]g(5)=\frac{1}{2}f(5)=\frac{1}{2}*-8=-4[/tex]

We have the values (5,-8) so, it's not part of the solutions to the function g(x).

For x=6

[tex]g(6)=\frac{1}{2}f(6)=\frac{1}{2} *3=\frac{3}{2}[/tex]

We have the values [tex](6,\frac{3}{2})[/tex] so, it's part of the solutions to the function g(x).

Hence, we have that the answers are:

Second option, evaluating x=-1

[tex]g(-1)=-2[/tex]

Fifth option, evaluating x=6

[tex]g(6)=\frac{3}{2}[/tex]

Have a nice day!

Answer: the answer is c which is 61 ¾ inches .

Step-by-step explanation: what I did that I made 62 ½ minus ¾ and it gave 61 ¾ inches, to know how many inches did she grew at the beginning of the year . I hope my answer is correct . Please give brainliest . Thanks .

Step-by-step explanation:

10 x + 6 y = -14 yes

21 x - 6 y = 39 yes

add those two

31 x + 0 = 25

so

x = -25/31 yes

Now go back and use -25/31 in either of the original equations to get y

5 (-25/31) + 3 y = -7

3 y = 125/31 -7

3 y = (125-217)/31

y = - 92/3

Answer:

Step-by-step explanation:

5 Digit Lock - Level One

*

242

Answer:g(x) = f(x) + 1.5g(

Step-by-step explanation:g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5g(x) = f(x) + 1.5

The equations which define y as a function of x are; −12x−85y=0 and 3x−4y=−2.

Any number that one can think of, except complex numbers, is a real number. Real numbers therefore include rational numbers like positive and negative integers, fractions, and irrational numbers.

On this note, the equations as displayed in the answers provided above define y as a function of x.

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Answer:

The correct answer is C.56.

Hope this helps you czn!!!!

Please Mark me as Brainleast!!!!!!!!

Given:

In Δ[tex]WXY,m < Y=90^o,WY=3,XW=5[/tex] and [tex]YX=4[/tex].

To find:

The ratio represents the cosine of ∠[tex]W[/tex].

Solution:

In Δ[tex]WXY,m < Y=90^o[/tex]. It means the opposite side of angle Y, i.e., XW is the hypotenuse of the triangle.

In a right angle triangle,

[tex]cos0=\frac{Base}{Hypotenuse}[/tex]

In the given triangle,

[tex]cosW=\frac{XY}{YW}[/tex]

[tex]cosW=\frac{3}{5}[/tex]

Therefore, the required cosine ratio is [tex]\frac{3}{5}[/tex].

Answer:

i believe the answer is 13,250

Step-by-step explanation:

all i did was divide the 5400/0.40 because i thiink its correct, maybe not

The employer contribute to her retirement plan is $2120.

Many American firms provide 401(k) plans, which are retirement savings plans with favourable tax treatment for the saver. It bears a section number from the United States Internal Revenue Code (IRC).

When a worker enrols in a 401(k), they consent to have a portion of each paycheck put directly into an investing account. A portion or the entire contribution may be matched by the employer. The employee has a variety of investing alternatives, most often mutual funds.

Given:

Jayne contributes $5,300

Now, the contribution of $0.40 for each dollar

So, employer contribute to her retirement plan

= 5300 x 0.40

= $2120

Hence, The employer contribute to her retirement plan is $2120.

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Answer:

0.0833... inches longer or 1/12

Step-by-step explanation:

7/12=0.583

1/2 but multiplied by 6 is 6/12

so 7/12-6/12=1/12 longer or 0.0833-

Answer:

14cm²

Step-by-step explanation:

Add up all the squares and the other bits to get the answer.

Answer:

No Solutions

Step-by-step explanation:

First to complete the square, it will need to look something like

a^2+2ab+b^2

so in order to get that we can see that 4n^2+8n seems to be missing a piece.

a is the square root of 4n^2 which is 2n.

8n/2n=4

4/2=2

b=2

so now add 2 to both sides of the equation so now it's

4n^2+8n+4=-13

rewrite as (2n+2)^2=-13

Now you see a negative number as the result of a exponent.

A number squared will never be negative.

Therefore the answer is

No Solutions

Answer:

Step-by-step explanation:

4

Answer:

. 0625

Step-by-step explanation:

1/2^4

or

1/16

just doing half life

Answer:

12

Step-by-step explanation:

this question asked us to find the given data points. Given this data set, what we know that the minimum is the smallest value, which is simply gonna be five. We know the media is gonna be the middle about you. We have to middle values seven and nine. Therefore, we couldn't find the average of the sum plus nine divided by two is eight. Now, we're looking for the first quarter mile. We know that we're gonna be averaging the middle values similarly to what we did for the media. So we have 10 plus 11 divide by two, which is 10.5, and then the maximum is simply the largest value, which is 12.

Answer:

  x+3 is not a factor

Step-by-step explanation:

A graphing calculator shows the expression has a zero at x=3 and no other real zeros. If x+3 were a factor, there would be a zero at x = -3.

  x+3 is not a factor of the expression.

_____

You can check to see if x+3 is a factor by evaluating the expression for x=-3. If (x+3) is a factor, x=-3 will make the function be zero.

  3(-x³ +2x² +2x +3) = 3(((-x +2)x +2)x +3) = 3(((-(-3)+2)(-3) +2)(-3) +3)

  = 3((-15+2)(-3) +3) = 3(39 +3) = 126 ≠ 0

The expression evaluates to 126 at x=-3, so x+3 is NOT a factor.

Factor x^5 - x to get x(x^4 - 1) = x(x^2-1)(x^2+1) = x(x-1)(x+1)(x^2+1)

We see that x = 0, x = 1 and  x = -1 are the real number roots or x intercepts. Ignore the complex or imaginary roots. Unfortunately, the graph shows the x intercepts as -2, 0 and 2 which don't match up.

So there's no way that the given graph matches with f(x) = x^5-x.

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

As more proof, let's consider the end behavior.

As x gets really large toward positive infinity, x^5 will do the same and so will x^5-x. Overall, f(x) will head off to positive infinity. Visually, moving to the right will have the graph move upward forever. This is the complete opposite of what is shown on the graph.

Likewise, the left endpoint should be aimed down instead of up. This is because x^5-x will approach negative infinity as x heads to the left.

In short, the graph shows a "rises to the left, falls to the right" end behavior. It should show a "falls to the left, rises to the right" pattern if we wanted to have a chance at matching it with x^5-x. Keep in mind that matching end behavior isn't enough to get a 100% match; however, having this contradictory end behavior is proof we can rule out a match.

I recommend using Desmos, GeoGebra, or whatever graphing program you prefer to plot out y = x^5-x. You'll get a bettter idea of what's happening.

Answer:

The answer it attached below :)

Sorry it took so long!

The diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

The two-sample t-test is used to determine if two population means are equal.

A nutritionist has developed a diet that she claims will help people lose weight. In this,

Here are the original weights, in pounds, with the weight after 6 months in parentheses.

The mean of the weights before 6 moths is,

[tex]\overline X_1=\dfrac{192+ 212 +171 +215 +180 +207 +165 +168 +190 +184 +200 +196 }{12}\\\overline X_1=190[/tex]

The mean of the weights after 6 months is,

[tex]\overline X_2=\dfrac{ 183 +196 +174 +211 +160 +191 +162 +175 +190 +179 +189 +195 }{12}\\\overline X_1=183.75[/tex]

Standard deviation of both the data is 16.9 and 14.7.

1. Null and Alternative Hypotheses.

The following null and alternative hypotheses need to be tested:

[tex]\begin{array}{ccl} H_0: \mu_1 & = & \mu_2 \\\\ \\\\ H_a: \mu_1 & > & \mu_2 \end{array}[/tex]

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Based on the information provided, the significance level is α=0.05 and the degrees of freedom are df = 22. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

[tex]df_{Total} = df_1 + df_2 = 11 + 11 = 22[/tex]

Hence, it is found that the critical value for this right-tailed test is

[tex]t_c=1.717[/tex], for α=0.05 and df=22

The rejection region for this right-tailed test is,

[tex]R = \{t: t > 1.717\}[/tex]

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

[tex]t = \displaystyle \frac{\bar X_1 - \bar X_2}{\sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}(\frac{1}{n_1}+\frac{1}{n_2}) } }[/tex]

[tex]\displaystyle \frac{ 190 - 183.75}{\sqrt{ \frac{(12-1)16.9^2 + (12-1)14.7^2}{ 12+12-2}(\frac{1}{ 12}+\frac{1}{ 12}) } } = 0.967[/tex]

Since it is observed that t=0.967≤tc=1.717 it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1721 and since p=0.1721≥0.05p = 0.1721  it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis H₀ is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is greater than μ2​, at the α=0.05 significance level.

Confidence Interval

The 95% confidence interval is −7.16<μ<19.66

Thus, the diet which is developed by the nutritionist is effective at the 0.05 level of significance. Claim is agreed.

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The power set P(X) of a finite set X is the set of all possible subsets of X. If X has n elements, then it has a total of 2ⁿ subsets.

For the set S = {1, 2, 3, 4, 5}, we have

• subsets with cardinality 0:

{ } (the empty set)

• subsets with cardinality 1:

{1}, {2}, {3}, {4}, {5}

• subsets with card. 2:

{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}, {3, 4}, {3, 4}, {4, 5}

• subsets with card. 3:

{1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 3, 4}, {1, 3, 5}, {1, 4, 5}, {2, 3, 4}, {2, 3, 5}, {2, 4, 5}, {3, 4, 5}

• subsets with card. 4:

{1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}

• subsets with card. 5:

{1, 2, 3, 4, 5}

Then P(S) is the set containing all of these sets,

{{}, {1}, {2}, {3}, …, {1, 2, 3, 4, 5}}

The scale factor of the dilation is 2.5.

A scale factor is a number that is used to change the size of shapes in geometry. It is the ratio of the length of a new shape to the length of the original shape.

Given that, a triangle with vertices, A(0, 0), B(0, 4), and C(6, 0) is dilated to yield a triangle with vertices at A(0, 0), B(0, 10), and C(15, 0).

We need to find the scale factor,

Taking the coordinates of B,

B(0, 4) → B(0, 10)

Scale factor = 10/4 = 2.5

Hence, the scale factor of the dilation is 2.5.

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Answer:

94

Step-by-step explanation:

7*78 + x = 8*80

x = 94

Or, think that he was short 2 points on each of 7 tests, so he has to make them all (14) up on the last test.

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Explanation:

If the money is compounded semiannually at a rate of 8%, then this means the multiplier (common ratio) is b = 1+r/n = 1+0.08/2 = 1.04

In short, b = 1.04 is our growth multiplier. It says that the money is growing by 4% each 6 month period. Each time x goes up by 1, y increases by 4%. The starting amount is a = 2100 dollars.

We go from the template of [tex]y = ab^x[/tex] to [tex]y = 2100(1.04)^x[/tex]

Use that equation to fill out the table. For instance, if x = 2 then,

[tex]y = 2100(1.04)^x\\\\y = 2100(1.04)^2\\\\y = 2100(1.0816)\\\\y = 2271.36\\\\[/tex]

Meaning that after 2 semiannual periods (aka 2*6 = 12 months = 1 year), we'd have $2,271.36 in the account.

Repeat this for the other x values mentioned to get the table shown below. To fill out the final column of the first row, you'll look at the very bottom of the table in the previous column. Four semiannual periods is equal to 2 years.

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

These steps are repeated for the second row of the table.

This time the growth multiplier is b = 1 + r/n = 1 + 0.14/12 = 1.0116667 approximately. The starting amount is a = 700

So that's how we go from [tex]y = ab^x[/tex] to [tex]y = 700(1.0116667)^x[/tex]

Like before, you'd plug in the various x values to find their paired y counterparts.

Example:

Plug in x = 18

[tex]y = 700(1.0116667)^x\\\\y = 700(1.0116667)^{18}\\\\y = 700(1.2321801)\\\\y = 862.52607\\\\y = 862.53\\\\[/tex]

The values are approximate. After 18 months, aka 18/12 = 1.5 years = 1 yr + 6 months, we'd have about $862.53 in the account.