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The value of inverse trigonometric function  θ = sin-1(-.5) is 30°

What is an inverse trigonometric function?

The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle.

Here, the given inverse trigonometric function is  θ = sin⁻¹(0.5)  

Now solving the given inverse trigonometric function by consider 0.5 value in terms of sine that is :

0.5 = sine (30°)

Now, substituting back this value in place of 0.5 and solve for θ :

θ = sin⁻¹(0.5)  

θ = sin⁻¹(sin(30°))  

Now the inverse of sinθ is θ itself

θ = 30°

Therefore, The value of inverse trigonometric function  θ = sin-1(-.5) is 30°.

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Answer:

133º

Step-by-step explanation:

Given that,

The measure of angle 1 = (4x + 8)º

The measure of angle 2 = (2x +17)°

The measure of angle 3 =  (7x + 7)º

We need to find the measure of angle 3. We know that, the sum of interior angle is equal to the exterior angle.

\(\angle 1+\angle 2=\angle 3\)

Put all the values,

(4x + 8)+(2x +17) = (7x + 7)

x = 18

Angle 3 = (7(18) + 7)º

= 133º

So, the measure of angle 3 is equal to 133º.

Answer:

40

Step-by-step explanation:

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Lets find f(n) formula

\(\boxed{\sf f(n)=\dfrac{1680}{n}}\)

Now

\(\\ \sf\longmapsto f(10)=\dfrac{1680}{10}=168\)

\(\\ \sf\longmapsto f(12)=\dfrac{1680}{12}=140\)

\(\\ \sf\longmapsto f(16)=\dfrac{1680}{16}=105\)

\(\\ \sf\longmapsto f(14)=\dfrac{1680}{14}=120\)

Answer:

a) Null hypothesis: \( \mu \geq 863\)

Alternative hypothesis: \( \mu >863\)

b) For this case using the significance level of \(\alpha=0.05\) we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

\( z_{\alpha}=-1.64\)

And the rejection zone would be:

\( z<-1.64\)

c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

d) \( p_v = P(z<-2.17) =0.015\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Step-by-step explanation:

Part a

We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:

Null hypothesis: \( \mu \geq 863\)

Alternative hypothesis: \( \mu >863\)

Part b

For this case using the significance level of \(\alpha=0.05\) we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

\( z_{\alpha}=-1.64\)

And the rejection zone would be:

\( z<-1.64\)

Part c

For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part d

For this case the p value would be given by:

\( p_v = P(z<-2.17) =0.015\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Answer:

530

Step-by-step explanation:

870-340 = 530

___________

Answer:

Simplify 3log3(-5) = undefined?

Step-by-step explanation:

The graph of the function y = 5|x - 4| is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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Answer:

120 x 4 = 480

Step-by-step explanation:

The equation would be 120 x 4 because it's 1/4 out of the whole sum. So 120 x 4 = 480.

Proportional and linear functions are very similar. The only difference is the addition of the “​b​” constant to the linear function. A proportional relationship is just a linear relationship where ​B​ = 0, or where the line passes through the origin (0, 0).

Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...

Step-by-step explanation:

deduct one whole number from the other number

Answer:

A. AAS

Step-by-step explanation:

In both triangles, the line mn and jh are congruent, the angles k and g are congruent, and h and m are congruent.

The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

The option d is correct for the given problem.

What is test statistic?

A statistic used in statistical hypothesis testing is known as a test statistic. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.

Given:

The data from an independent-measures research study produce a sample mean difference of 12 points and an estimated standard error of 4 points.

Test statistics = (x bar - μ) / (σ / √n)

                      = 12 / 4

Test statistics = 3

Here the test statistics is 3.

Hence, the option d is correct for the given problem.

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Complete question:

The data from an independent-measures research study produce a sample mean difference of 12 points and an estimated standard error of 4 points. If there are n = 10 scores in each sample, then the value for the t statistic is ____.​

Select one:

a. 2

b. 4

c. 1.63

d. 3

The BR is the perpendicular bisector of AC by CPCTC (corresponding parts of congruent triangles are congruent).

Based on the given information that angles ABR and ACR are right angles, and AB = AC, we can conclude that triangles ABR and ACR are right triangles.

Using the shared hypotenuse AR and the reflexive property, we can determine that side AB is congruent to side AC.

With this information, the transitive property allows us to conclude that angle BAR is congruent to angle CAR. Next, using the HL congruence postulate, we can prove that triangle ABR is congruent to triangle ACR.

This means that side BR is congruent to side CR, and angle BAC is bisected by line segment BR by the definition of bisector.

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The calculated output value for an input value of 5 is (c) 10

From the question, we have the following parameters that can be used in our computation:

Kerrin is making an input-output table for the rule "add 5."

This means that

Output = input + 5

In this case, we have

input = 5

substitute the known values in the above equation, so, we have the following representation

Output = 5 + 5

Evaluate

Output =10

Hence, the output is 10

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The function represented by the graph with the given transformations is |–x| + 2.

The function represented by the given transformations is |–x| + 2.

Let's analyze the transformations step by step:

Reflection across the x-axis:

Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.

Translation right 2 units:

Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.

Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.

Thus, the function represented by the graph with the given transformations is |–x| + 2.

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Answer: -lx-2l

Step-by-step explanation:

"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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the final result of the double integral is `(4/3)*a. we have to Integrate the inner integral with respect to z.

what is inner integral ?

An inner integral is a mathematical term that refers to the integral function that is evaluated first in a double integral.

In the given question,

To solve this double integral, we will use the following steps:

Integrate the inner integral with respect to z.

Evaluate the result of the inner integral at  upper and lower limits of z.

Substitute the result of the inner integral into the outer integral and integrate with respect to y.

Evaluate the result of the outer integral at the upper and lower limits of y.

Simplify the expression.

Now, let's apply these steps to solve the given double integral:

Integrate the inner integral with respect to z:

∫(x²*z + y²*z + z³) dz = x²/2*z² + y²/2*z² + z^4/4 + C

where C is the constant of integration.

Evaluate the result of the inner integral at the upper and lower limits of z:

(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)

Substitute the result of the inner integral into the outer integral and integrate with respect to y:

markdown

∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)

- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

Evaluate the result of the outer integral at the upper and lower limits of y:

= ∫[(x²/2*(a²-x²-y²)¹⁵ + y²/2*(a²-x²-y²)¹⁵ + (a²-x²-y²)²/4)- (x²/2*(-a²+x²+y²)¹⁵ + y²/2*(-a²+x²+y²)¹⁵ + (-a²+x²+y²)²/4)] dy

from y = -sqrt(a²-x²) to y = sqrt(a²-x²)

= (2/3)*x²*(a²-x²)¹⁵ + (2/3)*(a²-x²)²⁵

- (2/3)*x²*(-a²+x²)¹⁵ + (2/3)*(-a²+x²)²⁵

Simplify the expression:

= (4/3)*a³ - (4/3)*a*x²

Therefore, the final result of the double integral is `(4/3)*a

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The exponential model for the data is: \(y = 693(1.5)^x\)

When the cost is of $6000, the weight is of approximately 5.3 carats.

An exponential function is modeled by:

\(y = ab^x\)

In which:

From the table, the rate of change is given by:

b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.

When x = 1, y = 1040, hence the initial value is found as follows:

1.5a = 1040.

a = 1040/1.5

a = 693.

So the model is:

\(y = 693(1.5)^x\)

When the cost is of $6000, the weight is found as follows:

\(693(1.5)^x = 6000\)

\((1.5)^x = \frac{6000}{693}\)

\(1.5^x = 8.658\)

\(\log{1.5^x} = \log{8.658}\)

x log(1.5) = log(8.658)

x = log(8.658)/log(1.5)

x = 5.3

When the cost is of $6000, the weight is of approximately 5.3 carats.

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Answer:

B. Linear

Step-by-step explanation:

Answer:

\(thank \: you\)

Answer:

Take 2x- 3y= 6 as equation 1

And

x+ 3y= 3 as equation 2

Now add both equation

2x - 3y = 6

x + 3y = 3

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

3x 0 = 9

We can also write 3x 0= 9 as 3x = 9

Now we have to solve 3x =9

3x = 9

x = 9/3

x= 3

I hope this will help you