(a) The measure of the radius, r, is 5√5. (b) The measure of angle θ is approximately -63.43 degrees or approximately 296.57 degrees.
(c) A positive angle coterminal with θ is approximately 656.57 degrees.
(d) A negative angle coterminal with θ is approximately -63.43 degrees.
(e) An angle with the same value of cos θ but not coterminal with θ can be found using arccos(cos θ) + 360 degrees.
(a) To find the measure of the radius (r), we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula [tex]\sqrt{((x2 - x1)^2 + (y2 - y1)^2)}[/tex]. In this case, the coordinates of the point P(-5, 10) represent the values (x1, y1), and the origin (0, 0) represents the values (x2, y2). Plugging in the values, we get [tex]\sqrt{((-5 - 0)^2 + (10 - 0)^2) }[/tex]= sqrt(25 + 100) = sqrt(125) = 5*sqrt(5). So, the measure of the radius is 5*√(5).
(b) To find the measure of angle 0, we can use inverse trigonometric functions. Since the coordinates of the point P(-5, 10) correspond to the values of x and y, we can use the arctan function to find the angle. The formula for finding the angle in standard position is given by arctan(y/x). Plugging in the values, we get arctan(10/-5) = arctan(-2). Using a calculator, we find that the measure of angle 0 is approximately -63.43 degrees or approximately 296.57 degrees (since the angle is in the second quadrant, we add 360 degrees to get a positive coterminal angle).
(c) To find a positive angle coterminal with 0, we can add multiples of 360 degrees to the angle. In this case, adding 360 degrees to the angle of approximately 296.57 degrees, we get a positive coterminal angle of approximately 656.57 degrees.
(d) To find a negative angle coterminal with 0, we can subtract multiples of 360 degrees from the angle. In this case, subtracting 360 degrees from the angle of approximately 296.57 degrees, we get a negative coterminal angle of approximately -63.43 degrees.
(e) To find an angle with the same value of cos 0 but not coterminal with 0, we can use the inverse cosine function. The formula for finding the angle is given by arccos(cos 0). Since cosine is a periodic function, angles with the same value of cosine repeat every 360 degrees. Therefore, we can find an angle by using arccos(cos 0) + 360 degrees.
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Can someone help me please?
Answer:
81
Step-by-step explanation:
81
Answer:
6+3=9x9=81 final answer 81.
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!
Answer:
F(x)=h(x)-8
I think
Step-by-step explanation:
on the graph of f(x)=sinx and the interval [0,2π), for what value of x does f(x) achieve a maximum? choose all answers that apply.
On the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
The function f(x) = sin(x) is a periodic function with a period of 2π. Within one period, the function oscillates between the values of -1 and 1. The maximum value of sin(x) is 1, and it occurs when the angle x is π/2.
In the given interval [0, 2π), the function f(x) = sin(x) completes one full period. Starting from x = 0, the function increases and reaches its maximum value of 1 at x = π/2. After that, it starts decreasing and goes through one complete cycle by the time it reaches x = 2π.
Therefore, on the graph of f(x) = sin(x) on the interval [0, 2π), the function achieves a maximum value at x = π/2.
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can someone check my answer make sure it's right, if it's wrong can you please explain thanks ❤️❤️
Answer:
it is wrong
Step-by-step explanation:
the reason it is wrong is because I said so
Answer:
I am going to say no BECAUSE there are two y values, on the same point. For it to be linear it should only have one point per value. I think... good luck.
please help asapppppp
Answer:
45 degree
Step-by-step explanation:
The center of a circle is located at (4, 2). A point on the circle is located at (1, 2). What is the approximate area of the circle?
Answer: 9π≈28.26 squared units
Step-by-step explanation: The distance between the two points, 3 units, is the radius. And then we use that to find the area by squaring and multiplying by pi.
Please Help!!! Unit 8: Right Triangles & Trigonometry Homework 6: Trigonometry Review
The value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
Triangles and AnglesFrom the given diagram, we have the following
Adjacent = 14Hypotenuse = 13The required angle is x
Using the SOH CAH TOA identity
[tex]cos \theta =\frac{adj}{hyp}\\ cos \theta =\frac{14}{13}\\ \theta = arccos(\frac{14}{13} )[/tex]
Hence the value of x from the figure is [tex]cos^-1(\frac{14}{13} )[/tex]
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A video store has 6 new comedies, 4 new action movies, and 2 new dramas available to rent. If you choose 1 of each type of movie, how many combinations are there?
Answer:
48
Step-by-step explanation:
Number of comedy = 6
Number of action = 4
Number of drama = 2
Selecting one of each ; total Number of possible combinations ;
nCr
Comedy = 6C1
Action = 4C1
Drama = 2C1
6C1 * 4C1 * 2C1 = 6 * 4 * 2 = 48
I need this done today please help!
Answer:
1.
2. 4:7
3.
4.10:4
5.
id k the rest sorry :/
helpppppp pleaseeeeee
Answer:
50°
Step-by-step explanation:
We are to find m ∠2
And lines A and B are parallel
m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°
Hence,
m ∠2 = 50°
Therefore, m ∠2 = 50°
Can someone plzzz helpppp!!!!
Answer:
[tex] m\angle SXW =113\degree [/tex]
Step-by-step explanation:
In circle with center X, VS is diameter.
So [tex] \widehat {SWV} [/tex] is a semicircular arc.
[tex] \therefore m\widehat{SWV} = 180\degree [/tex]
[tex] \therefore (12x+7)\degree + (21x +8)\degree = 180\degree [/tex]
[tex] \therefore (33x+15)\degree = 180\degree [/tex]
[tex] \therefore 33x+15 = 180 [/tex]
[tex] \therefore 33x = 180-15 [/tex]
[tex] \therefore 33x = 165 [/tex]
[tex] \therefore x =\frac{165}{33} [/tex]
[tex] \therefore x =5 [/tex]
[tex] m\angle SXW =m\widehat{SW} [/tex]
(Measure of central angle is equal to the measure of its corresponding minor arc)
[tex] m\angle SXW =(21x + 8)\degree [/tex]
[tex] m\angle SXW =(21\times 5+ 8)\degree [/tex]
[tex] m\angle SXW =(105+ 8)\degree [/tex]
[tex] m\angle SXW =113\degree [/tex]
Children's recall of TV ads. Marketing professors at Robert Morris and Kent State Universities examined children's recall and recognition of television advertisements. (Journal of Advertising, Spring 2006.) Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rockn-Roll Shapes. One group (the AN group) was shown the ad with both audio and video; the second group (the video only group) was shown only the video portion of the commercial. Following the viewing, the children were asked to recall 10 specific items from the ad. The number of items recalled correctly by each child is summarized in the accompanying table. The researchers theorized that "children who receive an audiovisual presentation will have the same level of mean recall of ad information as those who receive only the visual aspects of the ad."
Video-Only Group
n1= 20
x1_bar = 3.70
s1 = 1.98
A/V Group
n2 = 20
x2-bar = 3.30
s2 = 2.13
a. Set up the appropriate null and alternative hypotheses to test the researchers' theory.
b. Find the value of the test statistic.
c. Give the rejection region for ? = 0.10
d. Make the appropriate inference. What can you say about the researchers' theory?
e. The researchers' reported the p-value of the test as p-value = 0.62. Interpret this result.
f. What conditions are required for the inference to be valid?
a. The null hypothesis (H0) would state that the mean recall of ad information for children who receive an audiovisual presentation is equal to the mean recall.
a.The alternative hypothesis (Ha) would state that the mean recall of ad information differs between the two groups.
b. To find the test statistic, we can use the two-sample t-test formula:
t = (x1_bar - x2_bar) / sqrt((s1^2/n1) + (s2^2/n2))
Substituting the given values:
t = (3.70 - 3.30) / sqrt((1.98^2/20) + (2.13^2/20))
c. The rejection region for a significance level of α = 0.10 in a two-tailed test can be determined using a t-table or a t-distribution calculator. Since the alternative hypothesis is two-tailed, we need to split α equally between the two tails. In this case, the rejection region would be t < -1.734 or t > 1.734.
d. Based on the test statistic value calculated in part (b), we can compare it to the rejection region. If the test statistic falls within the rejection region, we reject the null hypothesis. If it falls outside the rejection region, we fail to reject the null hypothesis. In this case, we would fail to reject the null hypothesis since the test statistic does not fall within the rejection region. Therefore, we cannot conclude that the mean recall of ad information differs between the two groups, supporting the researchers' theory.
e. The p-value is a measure of the strength of evidence against the null hypothesis. In this case, the researchers reported a p-value of 0.62. Since this p-value is greater than the significance level of α = 0.10, it indicates that the observed data is likely to occur by chance alone assuming the null hypothesis is true. Therefore, we fail to reject the null hypothesis and cannot conclude that there is a significant difference in the mean recall of ad information between the two groups.
f. For the inference to be valid, certain conditions must be met. These conditions include random sampling, independence between observations, approximately normal distributions of the populations or large sample sizes, and equal variances between the groups. Without information about the sampling method and data characteristics, we cannot determine if these conditions were met. It is important to note that if the conditions for inference are not met, the validity and reliability of the test results may be compromised.
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a single die is rolled one time. Find the probability of rolling a number greater than 4 or less than 3.
Andrea reads 36 pages each night. How many pages does Andrea read in 42 nights?
A 1,502pages
B 1,512pages
C 1,552pages
D 1,582pages
Answer:
1,512
Step-by-step explanation:
36x42
PLEASE SHOW YOUR WORK!!! WILL MARK BRAINLIEST!!!
On a youth soccer team 3 out of 12 team members have played in previous years. Based on this information, if 180 kids are in the youth soccer league, then how many could be expected to have played the year before?
Answer:
45
Step-by-step explanation:
3 out of 12 is 1/4, or 0.25, so if you divide 180 by 4, then using the same logic, you can expect 45 kids to have played last year.
3 = 1/4 OR .25 of 12, 12 divided by 4 = 3
180 divided by 4 = 45
Answer:
yes its 45 i did the test and i got an 100
Step-by-step explanation:
heres proof
PLEASE MARK BRAINLIEST!!!!!!A photo of a beetle in a science book is increased to 655% as large as the actual size. In the
beetle is 16 millimeters, what is the size of the beetle in the photo?
The size of the beede in the photo
Answer:
104.8
Step-by-step explanation:
16 x 6.55 = 104.8
Answer:
104.8 millimeters
Step-by-step explanation:
16 x 6.55 = 104.8
An object is acted upon by the forces F1=(10,6,3), and F2=(0,4,9). Find forces F3 that must act on the object so that the sum of the forces is zero.
The forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
To find the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero, we need to find a vector [tex]F_3[/tex] that satisfies the equation
[tex]F_1 + F_2 + F_3 = 0.[/tex]
Given the forces:
[tex]F_1[/tex] = (10, 6, 3)
[tex]F_2[/tex] = (0, 4, 9)
We can rearrange the equation to solve for [tex]F_3[/tex]:
[tex]F_3 = -F_1 - F_2[/tex]
Now, let's calculate [tex]F_3[/tex]:
[tex]F_3[/tex] = -(10, 6, 3) - (0, 4, 9)
= (-10, -6, -3) - (0, 4, 9)
= (-10-0, -6-4, -3-9)
= (-10, -10, -12)
Therefore, the forces [tex]F_3[/tex] that must act on the object so that the sum of the forces is zero are [tex]F_3[/tex] = (-10, -10, -12).
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The following set of data is from a sample of n = 6. 4 9 10 4 3 12 a, Compute the mean, median, and mode. b. Compute the range, variance, and standard deviation. a. Compute the mean, median, and mode. Mean=(Type an integer or decimal rounded to four decimal places as needed.) Compute the median Median-(Type an integer or a decimal. Do not round.) What is the mode? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The mode(s) is/are (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode for this data set 5. Compute the range, Range-(Type an integer or a decimal. Do not round.) ompute the variance.
a. The mean of the data set is 6.3333, the median is 4.5, and there is no mode. b. The range of the data set is 9, and the variance is 11.8667.
a. To compute the mean, we sum up all the values in the data set and divide it by the number of data points. In this case, the sum is 4 + 9 + 10 + 4 + 3 + 12 = 42. Dividing this by 6 (the number of data points), we get a mean of 42/6 = 6.3333.
To compute the median, we arrange the data set in ascending order: 3, 4, 4, 9, 10, 12. Since the number of data points is even, we take the average of the middle two values, which are 4 and 9. The median is (4 + 9) / 2 = 4.5.
The mode is the value(s) that appear most frequently in the data set. In this case, none of the values are repeated, so there is no mode.
b. The range is the difference between the largest and smallest values in the data set. In this case, the largest value is 12 and the smallest value is 3, so the range is 12 - 3 = 9.
The variance measures the variability of the data set. It is calculated by taking the average of the squared differences between each data point and the mean. Using the formula for sample variance, the calculations are as follows:
[tex](4 - 6.3333)^2 + (9 - 6.3333)^2 + (10 - 6.3333)^2 + (4 - 6.3333)^2 + (3 - 6.3333)^2 + (12 - 6.3333)^2 = 71.2[/tex]
Dividing this sum by n-1 (where n is the number of data points) gives us the sample variance: 71.2 / 5 = 14.24.
Therefore, the variance is 14.24.
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What’s the answer????
Answer:
I believe its 10 but forgive me if I'm wrong
Determine in each case for the linear system X′ = AX whether the
equilibrium point is a sink, a source, a saddle, or a nodal source
(centre), and draw the respective phase diagram.
Equilibrium point is a sink, a source, a saddle, or a nodal source (centre).
The equilibrium point is a sink in a phase diagram. A sink is a point towards which any system that begins near it will converge. This is a stable point that attracts nearby systems towards it. When the system comes close to the sink, it will slow down as it approaches, then stop at the sink. A sink is a stable equilibrium point. This is also known as an attractor that attracts nearby points. The phase diagram is a visual representation of the equilibrium point's behavior in the system. The arrows that come into or go out of the sink are pointing towards it, and they represent the direction of the flow of the system. Thus, the sink's shape is inward, indicating that any system near it will converge towards it.
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Confidence intervals based on pivotal quantities. Let Y1, Y2, . . . , Yn follow an Exponential distribution with parameter β. Note that βYn ∼ Gamma(n, n) and 2nβYn ∼ χ 2 df=2n are both pivotal quantities. (a) Explain why both statistics are indeed pivotal quantities. (b) Construct a 95% confidence interval for β using each pivot and provide interpretations. (c) Compare both intervals. Which one would you recommend using? Explain why
In the context of the Exponential distribution with parameter β, the statistics βYn and 2nβYn are both pivotal quantities. They can be used to construct confidence intervals for β.
A pivotal quantity is a function of the data and a parameter that has a known distribution regardless of the parameter's true value. In this case, both βYn and 2nβYn are pivotal quantities because their distributions (Gamma and chi-squared, respectively) do not depend on the unknown parameter β.
To construct a 95% confidence interval for β using the first pivot, βYn, we can utilize the properties of the Gamma distribution. The interval will be of the form [a, b], where a and b are the lower and upper bounds determined based on the cumulative distribution function of the Gamma distribution. This interval represents a range of plausible values for the parameter β.
Similarly, to construct a 95% confidence interval using the second pivot, 2nβYn, we can employ the chi-squared distribution. The interval will have the form [c, d], where c and d are the lower and upper bounds determined based on the cumulative distribution function of the chi-squared distribution. This interval also represents a range of plausible values for β.
When comparing both intervals, considerations such as width, interpretability, and efficiency are important. The recommended interval would be the one that is narrower (smaller width) and easier to interpret. Additionally, the efficiency of the estimators used in constructing the intervals should be taken into account.
In conclusion, both pivotal quantities, βYn and 2nβYn, can be used to construct 95% confidence intervals for β. The choice between them depends on factors such as width, interpretability, and efficiency. A comprehensive analysis considering these factors will determine the most suitable interval to use.
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Help meeeeeeeeeeeeeee pls
Answer:
-3.5
all u have to do is get the 2 and the 7 and just subtract and the 8 and 10
NEED HELP ASAP!!!!
A rectangular billboard for a high school is 10 feet high and 20 feet long. In a scale model of the school, the billboard is 3.5 inches long. How many inches tall is the scale model?
-i got 1.75
Answer:
I got 1.75 too
Step-by-step explanation:
20/3.5 is 5.7
10/5.7 is 1.75
The rectangular billboard is 1.75 inches tall in the scale model.
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the ratio between the dimensions of the new and old shapes.
Given that, a rectangular billboard for a high school is 10 feet high and 20 feet long.
In a scale model of the school, the billboard is 3.5 inches long.
So, the scale factor = 3.5/20
= 0.175 inches
Thus, the height is 10×0.175
= 1.75 inches
Therefore, the rectangular billboard is 1.75 inches tall in the scale model.
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Complete the statement. Round to the nearest hundredth if necessary.
6 lb =
oz
Answer: 96 oz
Step-by-step explanation:
4.
Which properties of equality justify steps c and f?
A. Multiplication Property of Equality; Division Property of Equality
B. Addition Property of Equality; Division Property of Equality
C. Subtraction Property of Equality; Multiplication Property of Equality
D. Addition Property of Equality; Subtraction Property of Equality
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
The answer is D, because in step c. you add to both sides to get rid of the on the right hand, so you use the fact that you can add the same number to both sides of an equation.
Likewise, in step f. you divided both sides by to get rid of the coefficient, so you use the fact that you can divide both sides of an equation by the same number.
...............................................................................................................................................
Answer:
Option C and B
Step-by-step explanation:
In the question step C is 23 + 11 = -11 +(-4x) + 11
which is in the form of a + b = c + a
In step C we have added 11 on both the sides to eliminate 11 from right side of the equation.
property which signifies this step is
Addition property of equality :
In step 'f' expression is
In this step equation has been divided by -4 on both the sides to eliminate 4 from the numerator.
In this step division property of equality has been applied.
Therefore Option C and B are the correct options.
Answer:
B. Addition Property of Equality; Division Property of Equality
Step-by-step explanation:
hope it helps...
help plzzzzzzzzzzzzz
Answer:
Building new bike paths.
Step-by-step explanation:
The reason I choose this answer was because the other ones would all use more gas when bike paths would limit the amount of driving and add to the amount of biking done.
Find the profit function if cost and revenue are given by C(x)=150+5.8x and R(x)=9x-0.01x² The profit function is P(x)
The profit function if the cost and revenue is given P(x) = -0.01x² + 3.2x - 150.
To find the profit function P(x), we subtract the cost function C(x) from the revenue function R(x). This gives us the expression for P(x) as P(x) = R(x) - C(x).
The profit function P(x) represents the difference between the revenue R(x) and the cost C(x). To find P(x), we subtract C(x) from R(x):
P(x) = R(x) - C(x)
Substituting the given expressions for R(x) and C(x), we have:
P(x) = (9x - 0.01x²) - (150 + 5.8x)
Simplifying this expression, we get:
P(x) = 9x - 0.01x² - 150 - 5.8x
Combining like terms, we have:
P(x) = -0.01x² + 3.2x - 150
Thus, the profit function is given by P(x) = -0.01x² + 3.2x - 150. This function represents the profit made as a function of the quantity of goods sold, x. It allows us to analyze the relationship between revenue, cost, and profit for different values of x.
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Please help I will give brainliest!
Answer:
Step-by-step explanation:
Distributive Property
commutative property of addition.
assosciative property of addition
Answer:
distrubutive property
Step-by-step explanation:
identify the values of coefficient a,b,and c in the quadrant equation
5x² = 4x + 7
a =
b =
C=
Answer:
a = 5, b = -4, c = - 7-----------------------
Standard form of a quadratic equation:
ax² + bx + c = 0Convert the given into standard form:
5x² = 4x + 7 5x² - 4x - 7 = 0Compare the equations to find coefficients
a = 5, b = -4, c = - 7Gary buys a 3 and 1/2 - pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food each
day. Which expression can Gary use to determine the number of pounds of cat food his cat eats each
year? (1 year = 52 weeks)
Answer:
546
Step-by-step explanation:
3 1/2 times 3 equals 10 1/2. 10 1/2 times 52 equals 546.