How do I find sin θ and tan θ given cos θ=9/10

The integral: S1 0 (-x³ - 2x² - x + 3)dx is -1/12

An integral is a mathematical operation that calculates the area under a curve or the value of a function at a specific point. It is denoted by the symbol ∫ and is used in calculus to find the total amount of change over an interval.

To evaluate the integral:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx $\)

We can integrate each term of the polynomial separately using the power rule of integration, which states that:

\($ \int x^n dx = \frac{x^{n+1}}{n+1} + C $\)

where C is the constant of integration.

So, we have:

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = \left[-\frac{x^4}{4} - \frac{2x^3}{3} - \frac{x^2}{2} + 3x\right]_0^1 $\)

Now we can substitute the upper limit of integration (1) into the expression, and then subtract the result of substituting the lower limit of integration (0):

\($ \left[-\frac{1^4}{4} - \frac{2(1^3)}{3} - \frac{1^2}{2} + 3(1)\right] - \left[-\frac{0^4}{4} - \frac{2(0^3)}{3} - \frac{0^2}{2} + 3(0)\right] $\)

Simplifying:

\($ = \left[-\frac{1}{4} - \frac{2}{3} - \frac{1}{2} + 3\right] - \left[0\right] $\)

\($ = -\frac{1}{12} $\)

Therefore,

\($ \int_0^1 (-x^3 - 2x^2 - x + 3)dx = -\frac{1}{12} $\)

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Answer:(4,-25)

Step-by-step explanation:

Answer:

15h² -  4h

Step-by-step explanation:

-3(2h + -5h²) + 2h

-3(2h - 5h²) + 2h

(-3*2h -3*-5h²) + 2h

-6h + 15h² + 2h

-4h + 15h²

-6h

We have to solve the following inequality:

Answer:

The answer is D) f(x) = 1/3 x^2 -1

Step-by-step explanation:

the key is at the end, the minus 1

Answer:

The answer is D!

Step-by-step explanation:

Answer:

7% of $33.00 is $2.31

total $35.31

18% of $35.31 is $6.35

The total with tax and tip is $41.66

Brainly plz :))

The total cost of the meal after tax and tip will be $41.67.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

This feast costs $33.00. A 7% deals charge is applied, trailed by a programmed tip of 18%.

The cost after tax is given as,

⇒ $33 x 1.07

⇒ $35.31

The cost after the tip is given as,

⇒ $35.31 x 1.18

⇒ $41.67

The total cost of the meal after tax and tip will be $41.67.

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False. To calculate a percent increase, the portion is not the missing element. The portion refers to the initial or original value, while the missing element is the final or increased value.

The formula for calculating a percent increase is:

Percent Increase = (Final Value - Initial Value) / Initial Value * 100

In this formula, the initial value is the portion that represents the starting or original value. The final value is the missing element, as it represents the increased or final value after the increase.

By subtracting the initial value from the final value, we obtain the difference between the two. Dividing this difference by the initial value gives us the relative increase as a decimal or fraction. Multiplying by 100 converts it into a percentage, representing the percent increase.

Therefore, the portion in calculating a percent increase is the known value or initial value, while the missing element is the final value that we are trying to determine or find.

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The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.

The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.

Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.

Given that ΔAED ≈ΔBEC & AC = BD.

as  ΔAED ≈ΔBEC, AD = BC     .................(1)

Now in  ΔABD and ΔBAC,

     AD = BC        

(corresponding sides of similar triangles) [from (1)]

     AB = AB        

(common side)

     AC = BD      

   (given)

∴     ΔABD ≈ΔBAC  (By SSS criteria)    

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The ratio of the area of triangle BDC to the area of triangle ADC is

(√3 -1) : 2.

Angle ABC  = 60°

Angle DBC  = 45°

So, the measure of <ABD is

Angle ABD = ABC  - DBC

                   = 60 - 45

                   = 15°

Now, the area of triangle CDB is

= (1/2) * S * BD * sin 45

and, the area of triangle ADB

= (1/2) * S * BD * sin 15

So, the area of triangle ADB to the area of triangle CDB  =

= (1/2) * S * BD * sin 15 / (1/2 * S * BD  * sin 45  

= sin 15 / sin 45

Since, sin 15 = sin (45 -30)

                    =  sin45 cos30 - sin 30 cos 45

                    = √2/2 √3/2 -  (1/2)(√2/2)

                    = [√6 -√2] /4

                    = √2/2

So, sin 15  / sin 45 = [√6  -√2 ] / 4*2 /√2

                              =  [ √6  - √2 ]  / [ 2√2 ]

                               = √6 / [ 2√2 ]  - √2 / [ 2√2]

                               = √3 / 2  -  1/ 2

                               = (√3  - 1 ) / 2

Thus, the ratio is (√3 -1) : 2.

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The question attached here seems to be incomplete, the complete question is:

Point D lies on side AC of equilateral triangle ABC such that the measure of angle DBC is 45 degrees. What is the ratio of the area of triangle ADB to the area of triangle CDB? Express your answer as a common fraction in simplest radical form.

The answer to the question is: D. Its parameters are the mean and standard deviation.

The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is widely used in statistics and probability theory. When the normal distribution is in its standardized form, the mean is zero and the standard deviation is one. This standardized form allows for easier comparison and analysis of data across different normal distributions.

The main characteristics of the normal distribution in its standardized form are as follows:

The parameters of the normal distribution, whether in its standardized form or not, are the mean (μ) and the standard deviation (σ). The mean represents the central location of the distribution, while the standard deviation measures the spread or variability of the data around the mean.

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The statement that is true about the normal distribution in its standardized form is that its parameters are the mean and standard deviation.What is the normal distribution?A normal distribution is a bell-shaped probability distribution, where the frequency of data is highest at the center and decreases as the distribution's tails stretch towards either end. In a normal distribution, the mean and median are the same, and the data is distributed symmetrically.The standardized form of a normal distribution is obtained by subtracting the mean from each value and dividing by the standard deviation. By doing this, the standardized distribution has a mean of 0 and a standard deviation of 1. This process is called standardization, and the result is known as a Z-score. Hence, the standardized form of a normal distribution is also called a Z-distribution.The parameters of a normal distribution in its standardized form are the mean and standard deviation. Therefore, the correct option is option D. Its parameters are the mean, and standard deviation.

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The domain is the set of all the x-values used by those points.

  { -1, 0, 3, -5, -3 }

The order does not matter.

Answer:

C)  2808

Step-by-step explanation:

Volume of Triangular Prism = 1/2 x height x length x base

= 1/2 * 9 * 24 * 26

= 2808 mm^3

I hope my answer helps you.

The first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3. (Option C)

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by

(1+x)^m=1+mx+  m(m-1)/2! x^2+  m(m-1)(m-2)/3! x^3+⋯.

For the given function (1+ x/4)^(-2)

m = -2

x = x/4

Hence, using the above expansion formula

The first term = 1

The second term = mx = (-2)(x/4) = -x/2

The third term =m(m-1)/2! (x/4)^2=  (-2(-2-1))/(2*1*16) x^2=3/16 x^2

The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3

Hence, the first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3.

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9514 1404 393

Answer:

  is no extraneous solution

Step-by-step explanation:

An absolute value equation typically does not have extraneous solutions. The solutions to this one are ...

  x ∈ {-5, 1}

__

Unless there is some domain restriction, this equation has no extraneous solutions.

_____

For -2x-4 < 0

  -2(2x +4) = -12

  x +2 = 3

  x = 1 . . . . . . -2(1)-4 = -6 < 0. Not an extraneous solution

__

For -2x-4 > 0

  -2(-2x -4) = -12

  4x +8 = -12

  4x = -20

  x = -5 . . . . . . -2(-5) -4 = 6 > 0. Not an extraneous solution

Let's denote the unknown number as 'x'. The equation can be set up as x + (1/2)x = 45. Solving this equation, we find that the number is 30.

The problem states that the sum of a number and its half is equal to 45. To find the number, we can set up an equation and solve for it.

Let's represent the number as "x". The problem states that the sum of the number and its half is equal to 45. Mathematically, this can be written as:

x + (1/2)x = 45

To simplify the equation, we can combine the like terms:

(3/2)x = 45

To isolate the variable x, we can multiply both sides of the equation by the reciprocal of (3/2), which is (2/3):

x = 45 * (2/3)

Simplifying the right side of the equation:

x = 30

Therefore, the number is 30.

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The answer should be .7

Answer:

0.7

Step-by-step explanation:

Step 1:

21÷30= 7÷10

Step 2:

7÷10= 0.7

In a test of significance, if the test z-value is in the tail region or the low probability region, it does not necessarily mean that we have strong evidence against the null hypothesis.

This statement is false.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

87th term is 497

Step-by-step explanation:

first, you have to find the nth term:

figure out the difference between your set of numbers (in our case +6)

that means that is 6n. next, the nth term is basically the 0th term so you have to find the 0th term. all you have to do is do the inverse of 6n (-6n or -6), which gives us -25.

nth term= 6n-25

now replace n with 87.

final step:

87*6 (6n and n=87) and that gives you 522. then, you have to do 522-25, due to the equation. 522-25=497

497 is your 87th term.

Answer:

Step-by-step explanation:

\(a = -19\\d = T_{2} -T_{1} \\d = -19-(-13)\\d = -19+13\\d = -6\\T_{n}= a+(n-1)d \\\\T_{87} = -19+(87-1)-6\\T_{87} = -19+(86)*-6\\T_{87} = -19-516\\T_{87} = -535\)

Answer:

look up percentage calculator on google

Step-by-step explanation:

33.33%

The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.

The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.

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Answer:

The last one.Because the experimental probability is 11 ÷ 50, which is 22%, and the theoretical probability is 1 ÷ 8, which is 12.5%

Answer:

\(x=±\sqrt[]{4}+9\)

The correct option is: The null should NOT be rejected. There is NOT a significant difference in the average salaries.

The test statistic is given by the formula below:\(t = (x1 − x2 − (μ1 − μ2)) / (sqrt ((s1^2 / n1) + (s2^2 / n2)))\)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1, and n2 are the sample sizes, μ1 and μ2 are the population means, and σ1 and σ2 are the population standard deviations.

Substituting the given values we get\(,t = (51 - 47 - 0) / (sqrt ((12^2 / 72) + (10^2 / 55)))≈ 1.0235\)

The p-value is the probability of getting a test statistic as extreme or more extreme than the one calculated from the sample data.

This is a two-tailed test, so we need to find the area in both tails under the t-distribution curve with 125 degrees of freedom.

Using a t-distribution table or calculator, we get a p-value of approximately 0.3074.

At the 5% level of significance, the critical value is given by:\(t = ± 1.9800\)

Since the calculated test statistic (1.0235) falls within the acceptance region \((-1.9800 < t < 1.9800)\), we fail to reject the null hypothesis.

Therefore, we can conclude that there is NOT a significant difference in the average salaries.

So, the correct option is:

The null should NOT be rejected. There is NOT a significant difference in the average salaries.

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Given that, Katie has four grape candies and 3 cherry candies.

Thus, the total number of candies is 7.

Calculate the ratio of grape candies to total number of candies.

Therefore, ratio is 4:7.

Twenty-four thousand six hundred ninety-seven in standard form is 2.4697 × 10^4

For the purposes of representing big or small numbers in mathematics, a standard form of a number is essentially specified. To represent such numbers in standard form, we employ exponents. It would be easier to understand the right definition of the standard form if you used decimal numbers and adhered to specific restrictions. As is well known, fractions are expressed more simply as decimal numbers.

Certain fractions result in decimal values with additional digits at the thousandth, hundredth, or tenth places. Yet, there are some fractions that result in a large decimal value. We employ simpler forms, which are commonly referred to as scientific notation, to represent such large numbers

Hence, Twenty-four thousand six hundred ninety-seven in standard form is 2.4697 × 10^4

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Part A: The expression for the total number of minutes Mario volunteers each year at the animal shelter  =  (405/y)   x  365

Part B: The simplified form of the expression for the total number of minutes Mario volunteers each year at the animal shelter = (147825/y) minutes

Number of days Mario volunteers each month at the animal shelter = 1

Number of hours Mario cleans for y days = 5.5 hours

Number of hours Mario each day = 5.5/y

Number of minutes Mario uses to walk dogs for y days = 75 minutes

Number of hours Mario uses to walk dogs for y days=  75/60

Number of hours Mario uses to walk dogs for y days=  1.25 hours

Number of hours Mario uses to walk dogs each day= 1.25/y

Total number of hours Mario volunteers in a day = Number of hours Mario cleans each day + Number of hours Mario uses to walk dogs

Total number of hours Mario volunteers in a day = 5.5/y + 1.25/y

Total number of hours Mario volunteers in a day = 6.75/y

Convert the number of hours to minutes

1 hour   =  60 minutes

Total number of minutes Mario volunteers in a day = (6.75/y) x 60

Total number of minutes Mario volunteers in a day = (405/y) minutes

Number of days in 1 year = 365

The expression for the total number of minutes Mario volunteers each year at the animal shelter  =  (405/y)   x  365

The simplified form of the expression for the total number of minutes Mario volunteers each year at the animal shelter = (147825/y) minutes

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The monthly cost of the cellular phone for the given anytime minutes is:

For 250 minutes: $39.99

For 420 minutes: $52.49

For 351 minutes: $52.24

To compute the monthly cost of the cellular phone for different numbers of anytime minutes, we can use the given function:

C(x) = 39.99 if 0 < x ≤ 350

C(x) = 0.25x - 47.51 if x > 350

Let's calculate the monthly cost for the following anytime minutes:

For 250 anytime minutes:

Since 250 is less than or equal to 350, we use the first part of the function:

C(250) = $39.99

For 420 anytime minutes:

Since 420 is greater than 350, we use the second part of the function:

C(420) = 0.25(420) - 47.51

C(420) = $52.49

For 351 anytime minutes:

Since 351 is greater than 350, we use the second part of the function:

C(351) = 0.25(351) - 47.51

C(351) = $52.24

Therefore, the monthly cost of the cellular phone for the given anytime minutes is:

For 250 minutes: $39.99

For 420 minutes: $52.49

For 351 minutes: $52.24

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