Help me help me help me

Answer:

5. x = 25.6

6. x = 11.0

7. x = 41.8°

8. x = 64.2°

9. x = 12.8°

10. x = 51.3°

Step-by-step explanation:

Let's find the x value for each triangle.

For point 5      

We have:

x: is the opposite cathetus to 52°  

20: is the adjacent cathetus to 52°  

52°: is the angle

We can find "x" with the following trigonometric function:

\( tan(52) = \frac{x}{20} \)

\( x = tan(52)*20 = 25.6 \)

For point 6      

We have:

x: is the hypotenuse  

5: is the opposite cathetus to the given angle  

27°: is the angle

To find "x" we need to use the trigonometric function:

\( sin(27) = \frac{5}{x} \)

\(x = \frac{5}{sin(27)} = 11.0\)

For point 7

We know:

x°: is the angle

6: is the hypotenuse

4: is the opposite cathetus to x°

Hence, x is:

\( sin(x) = \frac{4}{6} \)

\( x = sin^{-1}(\frac{4}{6}) = 41.8 \)

For point 8    

We have:

x°: is the angle

14: is the adjacent cathetus to x°

29: is the opposite cathetus to x°

To calculate "x" we need to use the trigonometric function tan(x):

\( tan(x) = \frac{29}{14} \)

\( x = tan^{-1}(\frac{29}{14}) = 64.2 \)

For point 9    

We have:

x°: is the angle

54: is the hypotenuse

12: is the opposite cathetus to x°

We can use sin(x) to solve for x:

\( sin(x) = \frac{12}{54} \)

\( x = sin^{-1}(\frac{12}{54}) = 12.8 \)

For point 10  

We have:

x°: is the angle

40: is the hypotenuse

25: is the adjacent cathetus to x°

We need to use cos(x) to solve for x:

\( cos(x) = \frac{25}{40} \)  

\( x = cos^{-1}(\frac{25}{40}) = 51.3 \)

I hope it helps you!

To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:

5. x = 25.60

6. x = 11.00

7. x = \(41.8^{o}\)

8. x = \(64.2^{o}\)

9. x = \(12.8^{o}\)

10. x = \(51.3^{o}\)

The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be \(90^{o}\).

So, each of the questions can be solved as follows:

5. Tan θ = \(\frac{opposite}{adjacent}\)

Tan 52 = \(\frac{x}{20}\)

⇒  x = Tan 52 * 20

       = 25.5988

x = 25.60

6. Sin θ = \(\frac{opposite}{hypotenuse}\)

Sin 27 = \(\frac{5}{x}\)

⇒ x = \(\frac{5}{Sin 27}\)

       = 11.0134

x = 11.00

7. Sin θ = \(\frac{opposite}{hypotenuse}\)

Sin x = \(\frac{4}{6}\)

        = 0.66667

x = \(Sin^{-1}\) 0.66667

  = \(41.8^{o}\)

x = \(41.8^{o}\)

8. Tan θ = \(\frac{opposite}{adjacent}\)

Tan x = \(\frac{29}{14}\)

          = 2.0714

x = \(Tan^{-1}\) 2.0714

  = \(64.2^{o}\)

x = \(64.2^{o}\)

9. Sin θ = \(\frac{opposite}{hypotenuse}\)

Sin x = \(\frac{12}{54}\)

        = 0.22222

x = \(Sin^{-1}\) 0.22222

  = \(12.8^{o}\)

x = \(12.8^{o}\)

10. Cos θ = \(\frac{adjacent}{hypotenuse}\)

Cos x = \(\frac{25}{40}\)

         = 0.625

x = \(Cos^{-1}\) 0.625

  = \(51.3^{o}\)

x = \(51.3^{o}\)

Visit: https://brainly.com/question/20926900

The limit can be expressed as the definite integral ∫2⁸ [3(x*)³ - 8x*] dx on the interval [2,8].

To express the limit as a definite integral on the given interval [2,8], we need to use the definition of the definite integral.

First, we can rewrite the expression inside the limit using the definition of xi* (the sample point):

3(xi*)³ - 8xi* = 3[(2 + iΔx)*]³ - 8(2 + iΔx)*

Next, we can rewrite the limit as the definite integral of this expression:

lim n→[infinity] n i = 1 [3(xi*)³ - 8xi*]Δx = ∫2⁸ [3(x*)³ - 8x*] dx

where x* is the sample point in each subinterval.

Therefore, the limit can be expressed as the definite integral ∫2⁸ [3(x*)³ - 8x*] dx on the interval [2,8].

Learn more about interval here,

https://brainly.com/question/31529768

#SPJ11

Answer:

3.24x10^-5,    5.48x10^-2,    1.2x10^1,      4.68x10^6,         8.34x10^6

Step-by-step explanation:

3.24 x 10^-5 = 0.0000324

5.48 x 10^-2 = 0.0548

1.2 x 10^1 = 12

4.68 x 10^6 = 4680000

8.34 x 10^6 = 8340000

If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

To learn more about area refer here

https://brainly.com/question/23945265

#SPJ4

The probability of getting a heart on the fourth card but not before that is 0.2278

The probability of getting a heart on the fourth card can be calculated by multiplying the probability of not getting a heart in the first three cards by the probability of getting a heart on the fourth card.

The probability of not getting a heart in the first three cards can be calculated as follows:

(39/52) * (38/51) * (37/50) = 0.862

where 39/52 is the probability of not getting a heart on the first card, 38/51 is the probability of not getting a heart on the second card (given that no heart was drawn in the first card), and 37/50 is the probability of not getting a heart on the third card (given that no heart was drawn in the first two cards).

The probability of getting a heart on the fourth card can be calculated as follows:

13/49 = 0.265

where 13/49 is the probability of getting a heart on the fourth card (given that no heart was drawn in the first three cards).

So, the probability of getting a heart on the fourth card, but not before, can be calculated as:

0.862 * 0.265 = 0.2278

So, the chance of getting a heart on the fourth card, but not before, is approximately 22.78%.

Learn more about probability here brainly.com/question/29381779

#SPJ4

Answer:

-6k - 5

Step-by-step explanation:

I hope this helps!

Answer:

The answer would be $12. You would need to change the 30% to 0.3 then multiply by $20. Then take the -$6 and subtract it by $20.

Answer:

B. Kevin is correct. Amy did not line up the decimals correctly.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

    B- kevin is correct because amy did not line up the decimals correctly

The no. of miles driven for the cost of using Taxi A to be $2 greater than the cost of using Taxi B is; 10 miles.

For taxi A;

For taxi B;

According to the question;

I.e; When m = m; C(a) = C(b) + 2.

Therefore;

The no of miles driven can then be evaluated by solving the equation simultaneously;

Substraction of eqn(2) from (1) ; we have;

Read more;

https://brainly.com/question/15165519

If 150 is the 15%, to find which number is the 100% we use the rule of 3

and the rule say that:

Main Answer:The approximate probability is 0.033

Supporting Question and Answer:

How do we calculate the expected average and standard deviation for a sample?

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

Body of the Solution:

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Final Answer:Therefore, the approximate probability is 0.033, accurate to three decimal places.

To learn more about the expected average and standard deviation for a sample  from the given link

https://brainly.com/question/31319458

#SPJ4

The approximate probability is 0.033

To calculate the expected average and standard deviation for a sample, we need to consider the characteristics of the population and the sample size.

a) To find the expected average amount of the waiter's tips, we can use the fact that the mean of the sample means is equal to the population mean. Since the mean of the tips is given as 7 dollars, the expected average amount of his tips is also 7 dollars.

b) The standard deviation for the average amount of the waiter's tips, also known as the standard error of the mean, can be calculated using the formula:

Standard deviation of the sample means

= (Standard deviation of the population) / sqrt(sample size)

In this case, the standard deviation of the population is given as 2 dollars, and the sample size is 30. Plugging these values into the formula, we have:

Standard deviation of the sample means = 2 / sqrt(30) ≈ 0.365

Therefore, the standard deviation for the average amount of the waiter's tips is approximately 0.365 dollars.

c) To find the approximate probability that the average amount of the waiter's tips is less than 6 dollars, we can use the Central Limit Theorem, which states that for a large sample size, the distribution of sample means will be approximately normal regardless of the shape of the population distribution.

Since the sample size is 30, which is considered relatively large, we can approximate the distribution of the sample means to be normal.

To calculate the probability, we need to standardize the value 6 using the formula:

Z = (X - μ) / (σ / sqrt(n))

where X is the value we want to standardize, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we have:

Z = (6 - 7) / (2 / sqrt(30)) ≈ -1825

Using a standard normal distribution table or a calculator, we can find the probability associated with this z-score. The approximate probability that the average amount of the waiter's tips is less than 6 dollars is approximately 0.033.

Therefore, the approximate probability is 0.033, accurate to three decimal places.

To learn more about the expected average

brainly.com/question/31319458

#SPJ4

Answer:

(-5, 1)

Step-by-step explanation:

Eliminate the equal sides of each equation and combine.

\( - x - 4 = \frac{3}{5} x + 4\)

Solve − x −4 =35x + 4 for x.

\(x = - 5\)

Evaluate y when x = −5.

\(y = 1\)

hence, the system of this equation is (-5, 1).

The expression for step n is n² squares

To write an expression for step n of the given pattern, we can observe that the number of squares in each step is increasing as the square of the step number.

The expression for step n can be written as n², where n represents the step number.

In step 2, n = 2, and the expression n² becomes 2² = 4 squares.

In step 3, n = 3, and the expression n² becomes 3²= 9 squares.

In step 4, n = 4, and the expression n² becomes 4² = 16 squares.

Therefore, the expression for step n is n² squares

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Answer

Y<5+3x

Step-by-step explanation:

you add 3x to both  side of 5 and it will end up being 5+3x

then y will be left then your done

Answer: 4√2

The sides of a 45-45-90 triangle are in the ratio 1 : 1 : √2. In this case, the ratio is 4 : 4 : 4√2.

i hope this helped! :D

We are supposed to evaluate the integral:∫_0^1▒dx/(1+x^2 ).Using Romberg's method, we have to obtain an approximate value of x. The formula to calculate the integral by Romberg method is:

T_00 = h/2(f_0 + f_n)for i = 1, 2, …T_i0 = 1/2[T_{i-1,0} + h_i sum_(k=1)^(2^(i-1)-1) f(a + kh_i)]R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1)where h = (b-a)/n, h_i = h/2^(i-1).

The calculation is tabulated below: Thus, the approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is:R(4,4) = 0.7854 ± 0.0007.

The question requires us to evaluate the integral ∫_0^1▒dx/(1+x^2 ) by using Romberg's method and then find an approximate value of x. Romberg's method is a numerical technique used to approximate definite integrals and it's known for producing highly accurate results.

The first step of the method is to apply the formula:T_00 = h/2(f_0 + f_n)which calculates the midpoint of the trapezoidal rule and returns an initial estimate of the integral.

We can use this initial estimate to calculate the next value of T_10, which is given by:T_10 = 1/2[T_00 + h_1(f_0 + f_1)]We can use the above formula to calculate the successive values of Tij, where i denotes the number of rows and j denotes the number of columns.

In the end, we can obtain the value of the integral by using the formula:

R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1)where i and j are the row and column indices, respectively.

After applying the above formula, we get R(4,4) = 0.7854 ± 0.0007Thus, the approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is 0.7854 and the error is ± 0.0007. Hence, we can conclude that the value of x is 0.7854.

Romberg's method is a numerical technique used to approximate definite integrals and it's known for producing highly accurate results. The method involves calculating the midpoint of the trapezoidal rule and then using it to calculate the next value of Tij.

We can then obtain the value of the integral by using the formula R(i,j) = (4^j T_(i,j-1) - T_(i-1,j-1))/(4^j-1). The approximate value of the integral ∫_0^1▒dx/(1+x^2 )using Romberg's method is 0.7854 and the error is ± 0.0007.

To know more about Romberg method :

brainly.com/question/32552896

#SPJ11

Answer:

X=45

Step-by-step explanation:

45+3x=180

180-45=135

135/3=45

x has to be 45

x=45

The equation of the line that is parallel to y = -3x + 6 is: y = -3x - 20.

The equation of the line that is perpendicular to y = -3x + 6 is: y = 1/3x + 20/3.

Recall the following facts:

Given the equation of a line as y = -3x + 6, the slope of the line is m = -3. This implies that, the line that is parallel to y = -3x + 6 will have the same slope of m = -3, and the slope of the line that is perpendicular to y = -3x + 6 will be m = 1/3.

To write the equation of the perpendicular line, substitute m = 1/3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = 1/3(x - (-8))

y - 4 = 1/3x + 8/3

y = 1/3x + 8/3 + 4

y = 1/3x + 20/3

To write the equation of the parallel line, substitute m = -3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = -3(x - (-8))

y - 4 = -3x - 24

y = -3x - 24 + 4

y = -3x - 20

Learn more about the equation of parallel and perpendicular lines on:

https://brainly.com/question/14005330

#SPJ1

The number of lines of symmetry does the picture has 3. (option b)

Symmetry is a fascinating concept in mathematics and art that deals with the balance and proportion of an object or image.

Now, coming to the question of how many lines of symmetry a picture has, we need to analyze the image closely and identify if any lines divide it into two identical parts.

Option B says that the picture has three lines of symmetry, which is a bit tricky. Generally, an object or shape can have one, two, or more lines of symmetry. However, in this case, if we observe the picture closely, we can see that there are no three lines that divide it into two identical parts.

To summarize, the correct answer is B, which means that the picture has three lines of symmetry.

To know more about line of symmetry here

https://brainly.com/question/30963765

#SPJ4

Answer:

DG

Step-by-step explanation:

This is a rectangular prism.  BE & AH are also parallel to CF. but they r not in the answers.

Answer:

Hi! The correct answer is 7x=-3!

Step-by-step explanation:

~Write in standard form~

Answer:

ughhh i think c im not so sure though

Step-by-step explanation:

Answer:

The answer is 6

Step-by-step explanation:

The absolute value of x is x and (-x) is also x

So, |-6| = 6

Thus, The answer is 6

-TheUnknownScientist 72

The value of the test statistic for this hypothesis test = 1%

Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.

When a discovery in statistical hypothesis testing is highly improbable to have occurred given the null hypothesis, it is said to have statistical significance.

\(H_{O}\) : Mean of mean = mean of women

\(H_{a}\) : means of men < mean of women

(Left tailed test)

Since population standard deviation is known but sample sizes are small t test is used.

The mean of Men minus Women equals = -5.00

standard error of difference = 2.201

t = 2.2721

\(df\)= 53

p value = 0.0136

since p >0.01 at 1% significance level we fail to reject \(H_{O}\) .

Both means are approximately equal at 1% level of significance.

Therefore,

The value of the test statistic for this hypothesis test = 1%

To learn more about Standard deviation hypothesis test visit :

brainly.com/question/29804367

#SPJ4

Answer: the large jar is cheaper

Step-by-step explanation:

If you divide the £1.54 by 440g and £1.26 by 340g, you'll find which one is cheaper per gram :

1.54/440 = 0.0035

1.26/340 = 0.0037

So, by comparing both prices/gram, you've found that the large jar is cheaper.

The 95% confidence interval estimate for the population proportion of red candies is [0.192, 0.248]. This means that we can be 95% confident that the true proportion of red candies in the population lies within this interval.

To calculate the confidence interval, we used a sample size of 500 candies, out of which 110 were red. Using statistical methods, we determined the range within which the population proportion of red candies is likely to fall. The interval [0.192, 0.248] suggests that between 19.2% and 24.8% of the entire population of candies are red. This estimation is made with a 95% level of confidence, indicating that in 95 out of 100 samples, the true proportion will be captured within this interval.

Learn more about confidence intervals here: brainly.com/question/32546207

#SPJ11

1. The probability of making a Type I error is 0.1118.

To calculate the probability of Type I error, we need to assume that the null hypothesis is true.

In this case, the null hypothesis is that the proportion of people visiting Grant Park is 0.44.

Therefore, we can use a binomial distribution with n = 15 and p = 0.44 to calculate the probability of observing a sample proportion outside of the acceptance region (6 to 9).

The probability of observing 0 to 5 people visiting the area is:

P(X ≤ 5) = Σ P(X = k), k=0 to 5

= binom.cdf(5, 15, 0.44)

= 0.0566

The probability of observing 10 to 15 people visiting the area is:

P(X ≥ 10) = Σ P(X = k), k=10 to 15

= 1 - binom.cdf(9, 15, 0.44)

= 0.0552

The probability of observing a sample proportion outside of the acceptance region is:

a = P(Type I Error) = P(X ≤ 5 or X ≥ 10)

= P(X ≤ 5) + P(X ≥ 10)

= 0.0566 + 0.0552

= 0.1118

Therefore, the probability of making a Type I error is 0.1118.

2.The probability of making a Type II error is 0.5144.

To calculate the probability of Type II error, we need to assume that the alternative hypothesis is true. In this case, the alternative hypothesis is that the proportion of people visiting Grant Park is 0.31.

Therefore, we can use a binomial distribution with n = 15 and p = 0.31 to calculate the probability of observing a sample proportion within the acceptance region (6 to 9).

The probability of observing 6 to 9 people visiting the area is:

P(6 ≤ X ≤ 9) = Σ P(X = k), k=6 to 9

= binom.cdf(9, 15, 0.31) - binom.cdf(5, 15, 0.31)

= 0.5144

The probability of observing a sample proportion within the acceptance region is:

B = P(Type II Error) = P(6 ≤ X ≤ 9)

= 0.5144

Therefore, the probability of making a Type II error is 0.5144.

3. The power of the test is 0.4856.

The power of the test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is that the proportion of people visiting Grant Park is 0.31.

Therefore, we can use a binomial distribution with n = 15 and p = 0.31 to calculate the probability of observing a sample proportion outside of the acceptance region (6 to 9).

The probability of observing 0 to 5 people or 10 to 15 people visiting the area is:

P(X ≤ 5 or X ≥ 10) = P(X ≤ 5) + P(X ≥ 10)

= binom.cdf(5, 15, 0.31) + (1 - binom.cdf(9, 15, 0.31))

= 0.0201

The power of the test is:

Power = 1 - P(Type II Error)

= 1 - P(6 ≤ X ≤ 9)

= 1 - 0.5144

= 0.4856

Therefore, the power of the test is 0.4856.

To know more about binomial distribution refer here:

https://brainly.com/question/29163389?#

#SPJ11

Answer:

he distributed -5 incorrectly

Answer:

D one Edge 2021 ;))

Step-by-step explanation:

Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.

Absolute Value Function:

An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values ​​of x and find some ordered pairs.

In mathematics, the absolute value or modulus of the real number x, represented as.

|x| is the non-negative value of x, regardless of sign.

x is positive and |xI =-x}.  For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.

Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.

Learn more about Slope:

https://brainly.com/question/19131126

#SPJ4