if sin(x) = 0 and cos(x) = 1, what is cot(x)?

Hundredths as fractions and decimals is given below.

Step-by-step explanation:

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Answer:

In a sequence of 5 numbers, the 3rd number is the middle number. So in your problem the third number is the average of the 5 numbers -- which is the sum of the numbers, divided by how many there are: 505/5 = 101.

Explanation:

The 5 numbers will be: 97, 99, 101, 103 and 105

Let the 5 consecutive numbers be x-4, x-2, x, x+2 and x+4.

Now it is given that the sum of the 5 numbers is 505. This can be represented mathematically as follows:

[tex](x-4)+(x-2)+x+(x+2)+(x+4) = 505\\\\5x = 505\\\\x= 101[/tex]

So, x - 4 = 97

x - 2 = 99

x + 2 = 101

x + 4 = 103

Thus, the 5 numbers will be: 97, 99, 101, 103 and 105

Answer:

20 plus 4

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Step-by-step explanation:

20 plus 4 is the expression shows partial quotients of 96 divided by 4.

Here, we have,

given that,

Which expression shows partial quotients of 96 divided by 4.

now, we get,

96 divided by 4

i.e. 96/4

=24

as we know that,

24 = 20 + 4

so, we get,

24 equals 20 plus 4

i.e. 96 divided by 4 equals 20 plus 4.

Hence, 20 plus 4 is the expression shows partial quotients of 96 divided by 4.

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Answer:

None of the above

Step-by-step explanation:

None of the above polynomials are in standard form.

Answer:

For #1, the slope is [tex]\frac{2}{2}[/tex], which could also be written as 1

For #2, the slope is [tex]\frac{1}{4}[/tex]

For #3, the slope is [tex]-\frac{2}{1}[/tex], which could also be written as -2

Step-by-step explanation:

Remember, [tex]\frac{rise}{run}[/tex]

Given:

The top of the lid to a small container is in the shape of a square with a side length of 6 centimeters.

We need to determine the area of the top of the lid.

Area of the top of the lid:

The area of the top of the lid can be determined using the formula,

[tex]A=s^2[/tex]

where s is the side length of the square

Substituting [tex]s=6[/tex] in the above formula, we get;

[tex]A=6^2[/tex]

[tex]A=36[/tex]

Therefore, the area of the top of the lid is 36 cm²

Hence, Option C is the correct answer.

Answer:

Step-by-step explanation:

Answer: -(pi)/10 radians or D on Edge

Step-by-step explanation: correct answer on edge

Answer:

y=(1/4)x-3

Step-by-step explanation:

To find the equation of a line, use the following equation:

y=mx+b where m is the slope (rise/run) and b is the y-intercept.

The slope of the line is 1/4 and the y-intercept is -3. Just fill it into the problem to get the answer y=(1/4)x-3. Hope this helps! :)

Answer:

1. No.

2. No.

3. No.

4. Yes.

Step-by-step explanation:

You just need to sub in the numbers for x and y. For the first one, it is -21 - 8 > 18 which is equal to  -29 > 18, so the answer is no. For the second one, it is -21 > 18, so the answer is no. For the third one, it is -14 + 32 > 18 which is equal to 18 > 18, so the answer is no. For the fourth one, it is 56 - 36 > 18 which is equal to 20, so the answer is yes. I hope this helps, please mark me brainliest!

Answer:

Round pizza

Step-by-step explanation:

Area of the Round Pizza =[tex]49 \pi[/tex] square inches.

Area of the Square Pizza = 49  square inches.

Recall that: [tex]\pi =\frac{22}{7}[/tex]

Therefore:

Area of the Round Pizza =[tex]49 \pi=49X\frac{22}{7}=154 \:Square \:Inches[/tex]

Since 154 is greater than 49(154>49)

If Steve wants to eat more crust, he will buy the round pizza.

Answer:

C

Step-by-step explanation:

for every value of x we put in the option the only function which satisfies the table of data is C

Answer:

A

Step-by-step explanation:

bruh

Answer:

C

Step-by-step explanation:

just my guess-

Answer:

The answer is B.

Step-by-step explanation:

The picture shows a right-angle triangle which is 90°. So you have to add up the expressions, in order to solve for x :

35° + 5x° = 90

Answer:

collinear points

Step-by-step explanation:

A set of points that form a linear are called collinear points

Answer:

                    principal     interest              total money in account

                                                                         at the end of year

Year one       $100             $4.5                              $104.5

year two        $200          $ 9 +$4.5                         $ 213.5

year three      $300          $ 9 +$4.5 + $13.5           $ 327

Step-by-step explanation:

Simple interest for any principal is given by

I = p* r* t/100

I = interest rate accrued on principle amount

p is the amount deposited

r is the rate of interest

t is the time period of saving

_______________________________________________

For year one

p = $100

r = 4.5%

t=1

I = 100*4.5*1/100 = 4.5

_______________________________________________

For year two $100 more is added to already existing $100 in account.

p = 100 +100 = $200

r = 4.5%

t=1

I = 200*4.5*1/100 = 9

_______________________________________________

For year two $100 more is added to already existing $200 in account after two years.

p = 100 +100 +100 = $300

r = 4.5%

t=1

I = 300*4.5*1/100 = 13.5

_______________________________________________

There fore total  money in Margo account is

$300 saving deposited by her

$4.5 + $9 + $13.5 = $27 (interest accrued in three time)

Formulating the results in tabular form

                     principal     interest    total money in account

                                                            at the end of year

Year one       100               4.5                      104.5

year two        200           9 +4.5                     213.5

year three      300           9 +4.5 + 13.5           327

Answer:

x = -6         x=-3

Step-by-step explanation:

To find the roots, we set it equal to zero

(x + 6)(x + 3) =0

Using the zero product  property

x+6 =0        x+3 =0

x = -6         x=-3

Answer:

x=-6,x=-3

Step-by-step explanation:

To solve this question we will have to solve one after another

(X+6)(x+3)

Let equate the equation to zero

So

(X+6)(x+3)=0

X+6=0

Substrate 6 from both sides

X=-6

X+3=0

Substrate 3 from both sides

x=-3

Therefore x=-6,x=-3

The student's question involves creating an exponential decay function to determine the fish population in Lake Collins after five years, given a starting population in 2001 and a 5% annual decrease. The function is N(t) = 1200e^-rt, with r being 0.05 and t being 5. The estimated fish population for the year 2006 is approximately 935.

The student is asking for an exponential decay function to model the decrease in the fish population at Lake Collins. We are given that in 2001, there were about 1,200 fish, and the fish population is decreasing at a rate of 5% per year. To model this situation, we use the exponential decay formula:

N(t) = N0e-rt

Where:

For this problem, the initial population N0 is 1,200, the decay rate r is 0.05 (since 5% is 0.05 as a decimal), and the time t we are interested in is 2006 - 2001 = 5 years. Plugging these values into the formula, we get:

N(5) = 1200e-0.05 * 5

Calculating N(5), the fish population in 2006, using the above formula:

N(5) = 1200e-0.25 ≈ 1200 * 0.7788 ≈ 935

Therefore, the estimated fish population in Lake Collins in 2006 would be approximately 935 fish.

The statements which correctly describes a cross section of the right-rectangular prism if the base is a rectangle measuring 15 in. by 8 in. are: B, D and F.

Mathematically, the surface area of a right-rectangular prism is calculated by using this formula:

A = 2(wl + hl + hw)

Where:

Based on the surface area of this right-rectangular prism, we can deduce the following points:

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Answer:

3 =x

Step-by-step explanation:

f(x) = -10x + 45

f(x) = 15

15 = -10x +45

Subtract 45 from each side

15-45 = -10x+45-45

-30 = -10x

Divide each side by -10

-30/-10 = -10x/-10

3 =x

Final answer:

there were 7 horses and 8 chickens in the barn.

Explanation:

To represent the situation with a system of equations, let's assume that the number of horses is represented by 'h' and the number of chickens is represented by 'c'.

We know that there are a total of 15 animals, so we can write the equation: h + c = 15.

We also know that the total number of legs is 44, and since each horse has 4 legs and each chicken has 2 legs, we can write the equation: 4h + 2c = 44.

To solve this system of equations, we can use the method of substitution or elimination. Substituting h = 15 - c into the second equation, we get 4(15 - c) + 2c = 44. Simplify and solve for c to find the number of chickens, then substitute the value of c back into the first equation to find the number of horses.

Let's solve this system of equations:

h + c = 15

4h + 2c = 44

We can solve this using the method of substitution:

h = 15 - c

Substituting this into the second equation:

4(15 - c) + 2c = 44

60 - 4c + 2c = 44

-2c = 44 - 60

-2c = -16

c = -16/-2

c = 8

Substituting the value of c back into the first equation:

h + 8 = 15

h = 15 - 8

h = 7

So, there were 7 horses and 8 chickens in the barn.

The probability of drawing a girl's name from a hat with 24 students of which 12 are boys is 1/2 or 50%.

The question is regarding the probability that a randomly drawn name is a girl's if there are 24 students in a class with 12 boys. Since the number of girls must be 24 total students minus 12 boys, which leaves us with 12 girls, the probability of drawing a girl's name is the number of girls over the total number of students. Therefore, the probability is 12 girls divided by 24 students, which simplifies to 1/2.

Answer:

The 90% confidence interval for the proportion of married couples with three personality preferences in common compared  with the proportion of couples with two preferences in common is (-0.081, 0.025).

Step-by-step explanation:

The (1 - α)% confidence interval for difference in proportion formula is,

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

The given information is:

n₁ = 375,

n₂ = 571,

X₁ = 132,

X₂ = 217.

Compute the sample proportion as follows:

[tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{132}{375}=0.352\\\\\hat p_{2}=\frac{X_{2}}{n_{2}}=\frac{217}{571}=0.38\\[/tex]

For the 90% confidence level, the z-value is,

z₀.₀₅ = 1.645

*Use a z-table.

Compute the 90% confidence interval for the difference in proportion as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}[/tex]

     [tex]=(0.352-0.38)\pm 1.645\sqrt{\frac{0.352(1-0.352)}{375}+\frac{0.38(1-0.38)}{571}}\\=-0.028\pm 0.05256\\=(-0.08056, 0.02456)\\\approx (-0.081, 0.025)[/tex]

The 90% confidence interval for the proportion of married couples with three personality preferences in common compared  with the proportion of couples with two preferences in common is (-0.081, 0.025).

This confidence interval implies that the true difference between the proportions lies in this interval with probability 0.90.

The 90% confidence interval for the difference in proportions of married couples with two and three personality preferences in common is (0.027, 0.089). This indicates that with 90% confidence, the proportion of couples with two preferences in common is significantly higher.

Firstly, we need to find the proportions for both samples. The proportion for three personality preferences in common is 132/375 = 0.352 and for two personality preferences in common is 217/571 = 0.380.

Next, to compute the standard error, we use the formula √[ P(1 - P) / n ]. For three personality preferences we get √[ 0.352(1 - 0.352) / 375] = 0.026. And for two personality preferences we obtain √[ 0.380(1 - 0.380) / 571] = 0.021.

From these, the difference in the two sample proportions can be calculated, which is 0.380 - 0.352 = 0.028. The standard error of the difference can then be calculated as √( 0.026 ^ 2 + 0.021 ^ 2) = 0.033. At the 90% confidence level, the z-score is 1.645.

To calculate the confidence interval, note that 0.028 ± 1.645 * 0.033 is the equation we are trying to solve. This produces a range from 0.027 to 0.089.

So, the 90% confidence interval for difference in proportions is (0.027, 0.089), meaning that with 90% confidence, the proportion of couples with two preferences in common is significantly higher than those couples with three personality preferences in common.

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April correctly transformed the quadratic function into vertex form, and the resulting vertex is (3, 15), as determined by the completion of the square method.

April is indeed correct about the vertex of the function h(x). The vertex form of a quadratic function is h(x) = a(x - h)^2 + k, where the point (h, k) is the vertex of the parabola. April has rewritten the quadratic function h(x) = 5x^2 - 30x + 30 into vertex form as h(x) = 5(x - 3)^2 + 15, indicating that the vertex is at (3, 15). This can be verified through the completion of the square method, where a perfect square trinomial is created by adding and subtracting the appropriate constant term. April added and subtracted 9 inside the parentheses, which is (6/2)^2, to keep the equation equivalent. Finally, she factored out the coefficient of the quadratic term (5) before completing the square, which is correct.

Answer and Step-by-step explanation:

samuel---> 1pc+3dr=36.75

sebastian--->3pc+12dr=138

1pc+4dr=46

1pc+4dr=46

1pc+3dr=36.75

so 1 dr=46-36.75=$9.25

4dr is 9.25×4=37

so 1 pc=46-37=$9.00

Answer:

$9.25

Step-by-step explanation:

Cost of popcorn: x

Cost of drink: y

x + 3y = 36.75

x = 36.75 - 3y

3x + 12y = 138

x + 4y = 46

36.75 - 3y + 4y = 46

y = 46 - 36.75

y = 9.25

Answer:

240%

Step-by-step explanation:

240 / 100 Answer: 240%

Answer:

240%

Step-by-step explanation:

Answer:

0.22

Step-by-step explanation:

Looking at the Venn Diagram,

the intersection "0.43" means coming via bus and having after-school activity.

"0.12" means students who does not come by bus and who does not have after-school activity.

Now, we want probability of "having after-school" activity (the area A) but NOT COMING VIA BUS (area outside B).

We want the area outside B but within A.

That area is labeled 0.22

Hence,

The probability that the student has an after-school activity and does NOT come to school by bus is 0.22

Answer:

432π cm² or 1356.48 cm²

Step-by-step explanation:

The area of a circle is πr²

The area of the disks are 144π and 576π.

576π-144π = 432π

432π ≈ 1356.48 cm²

To find the difference in areas of two circles, calculate the area of each circle using the formula πr² and then subtract the smaller area from the larger one. For Alice's discs with diameters 12 cm and 24 cm, the areas are 36π and 144π square cm respectively, and their difference is 108π square cm.

To find the difference in the areas of Alice's two flying disks, first we need to calculate the area of each disk. The formula for the area of a circle (or disk) is πr², where r is the radius of the circle. The radius is half of the diameter, so for the first disk, the radius is 6 cm and for the second disk, the radius is 12 cm.

The area of the first disk is π*(6 cm)² = 36π square cm. The area of the second disk is π*(12 cm)² = 144π square cm. The difference between these two areas is 144π - 36π = 108π square cm.

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