Answers
Answer:
13. (a) 120°, 120°, (b) 8.94 cm14. (a) 17.9 cm, (b) 22.4 cmStep-by-step explanation:
Refer to the attached sketch (not to scale)Question 13(a) The center of the circle is also the circumcenter of the triangle PQR.
Since ΔPQR is equilateral, all sides are equal, therefore opposite angles are also congruent:
∠POQ ≅ ∠QOR ≅ PORSum of the three angles is 360° as cover the full circle.
Each angle measure is:
∠POQ = ∠QOR = ∠POR = 360°/3 = 120°(b) Each side is 16 cm and the radius is 12 cm.
The distance of the midpoint M of PQ from the center O is perpendicular bisector of ΔPOQ.
The segment MO is:
MO² = PO² - PM² = PO² - (PQ/2)²MO² = 12² - (16/2)² = 80MO = √80 = 8.94 cm (rounded)Question 14ΔXYZ is isosceles with:
XY = XZ = 20 cmYZ = 18 cm(a) The altitude of ΔXYZ is a perpendicular bisector of YZ. h = XM is the altitude
Find h:
h² = XZ² - ZM² = XZ² - (ZY/2)²h² = 20² - (18/2)² = 319h = √319h = 17.9 cm (rounded)(b) Note the ∠ZXM is half of the ∠ZOM as both the angles intercept half of the arc ZY and ∠ZOM is a central angle.
Find ∠ZXM:
sin ∠ZXM = ZM/ZX = 9 / 20m∠ZXM = arcsin (9/20) = 26.7° (rounded)Find ∠ZOM:
m∠ZOM = 2*m∠ZXM = 2*26.7 = 53.4°Find the measure of the radius:
sin ∠ZOM = ZM/rsin 53.4° = 9/rr = 9 / sin 53.4°r = 11.2 cm (rounded)Find the measure of the diameter:
d = 2r = 2*11.2 cm = 22.4 cm
Related Questions
what is the area of a semicircle that has a radius of 30 feet
Answers
Answer:
1413 sq ft.
Step-by-step explanation:
Area of a semicircle=(1/2)*πr²
Radius=30ft
A=(1/2)*3.14*30²=1413 sq ft.
Convert 3.1415 x 10^-2 to standard notation.
Answers
Help me for more points right answer only
Answers
Answer:
slope- intercept form
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
In a sample of 40 people 40% are black. Test the null hypothesis that the population proportion of black 0.2 against the altemative hypothesis that proportion is not equal to 0.2. Find the p value. DA 0.5186 O 0.0015 OC 0.0528 OD 0,1967
Answers
In this case, the p-value is not provided in the question, so the actual value needs to be calculated using the appropriate statistical test.
What is the correlation coefficient between two variables when their covariance is 120 and their standard deviations are 15 and 10, respectively?In hypothesis testing, the p-value represents the probability of obtaining the observed sample data, or more extreme data, assuming that the null hypothesis is true.
It measures the strength of evidence against the null hypothesis.
In this case, the null hypothesis is that the population proportion of black people is 0.2.
The alternative hypothesis is that the proportion is not equal to 0.2, indicating that there may be a difference in the population proportion.
To find the p-value, a statistical test (such as a proportion test) is performed using the sample data.
Based on the given information, the p-value is the probability associated with the test statistic obtained from the test.
The p-value indicates the likelihood of observing a proportion as extreme or more extreme than the one observed in the sample, assuming the null hypothesis is true.
A smaller p-value suggests stronger evidence against the null hypothesis.
Learn more about appropriate statistical
brainly.com/question/30747709
#SPJ11
Determine the extreme point (x*, y*) and its nature of the following function: z = 25x + 16y - 4xy - 2x² - y² + 30
Answers
The extreme point (x*, y*) of the function z = 25x + 16y - 4xy - 2x² - y² + 30 is (-1.75, 8) and it is a maximum point.
To find the extreme point and its nature, we need to take the partial derivatives of the function with respect to x and y and set them equal to zero. The extreme point occurs when both partial derivatives are zero.
Taking the partial derivatives, we have:
∂z/∂x = 25 - 4y - 4x
∂z/∂y = 16 - 2y
Setting these derivatives equal to zero and solving the system of equations, we find:
25 - 4y - 4x = 0 ...(1)
16 - 2y = 0 ...(2)
From equation (2), we can solve for y:
2y = 16
y = 8
Substituting this value of y into equation (1), we can solve for x:
25 - 4(8) - 4x = 0
25 - 32 - 4x = 0
-4x = 7
x = -7/4 = -1.75
Therefore, the extreme point (x*, y*) is (-1.75, 8).
Since the second derivative test confirms that the point is a maximum, we can conclude that the extreme point (x*, y*) = (-1.75, 8) is a maximum point.
To know more about maximum point, refer here:
https://brainly.com/question/22562190#
#SPJ11
help with this question pleaseee !!
Answers
the quotient property of radicals requires the indices of the radicals to be the same. does this mean that it is not possible to write as a single radical? explain.
Answers
The quotient property of radicals requires the indices of the radicals to be the same. Thus, it is not possible to write the expression (5√3 + 2√2) as a single radical.What is the quotient property of radicals?
The quotient property of radicals states that for any non-negative numbers x and y with y ≠ 0, if n is an integer greater than 1, then the following property holds:√(x/y) = √x/√yNow let's take a look at the question at hand. We can see that the two radicals have different indices. Therefore, the quotient property of radicals does not apply. As a result, it is not possible to simplify the expression as a single radical. Therefore, the expression (5√3 + 2√2) cannot be written as a single radical.
The quotient property of radicals states that when dividing radicals, the indices (or roots) of the radicals involved must be the same. In other words, for the quotient property to be applicable, the radicals being divided must have the same root.
If the radicals have different indices, it is generally not possible to simplify the expression into a single radical. This is because the rules of radical arithmetic require the indices to be the same in order to combine or simplify radicals.
For example, let's consider the expression √2 / √3. Here, the radicals have different indices (square root and cube root), so we cannot combine them into a single radical using the quotient property. The expression √2 / √3 cannot be simplified further because the indices do not match.
However, it's important to note that even though the quotient property does not apply in such cases, it does not mean that the expression is mathematically invalid or cannot be manipulated further. It simply means that the expression cannot be simplified into a single radical using the quotient property. Other algebraic techniques or operations may be necessary to further simplify or manipulate the expression if desired.
To know more about indices, visit:
https://brainly.com/question/10339517
#SPJ11
The given information is the quotient property of radicals requires the indices of the radicals to be same.
Yes, it is not possible to write [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] as a single radical because the quotient property of radicals requires the indices of the radicals to be the same.
The quotient property of radicals is a mathematical concept that explains how to divide two radicals with the same index. If r is a non-negative number and s is a non-negative number, then:
[tex](\frac{r}{s})^{n}=\frac{r^{n}}{s^{n}}[/tex]
The property of quotient states that the quotient of the same degree radicals is equal to the same degree root of the quotient of the radicands. If a and b are non-negative numbers and n is an integer greater than 1:
[tex](\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}\sqrt[n]{\frac{a}{b}}[/tex]
[tex]=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]
If you look at the terms [tex]$8\sqrt{2}$ and $5\sqrt{3}$[/tex], you can tell that their indices are not the same. The term [tex]$8\sqrt{2}$[/tex] has an index of 2 while the term [tex]$5\sqrt{3}$[/tex] has an index of 3. The quotient property of radicals requires the indices of the radicals to be the same. Therefore, you cannot add or subtract two radicals that do not have the same index.
Example: [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] can be rearranged as [tex]$8\sqrt{2}+0\sqrt{3}+5\sqrt{3}$[/tex]. Then using distributive property, it can be written as [tex]$(8+0)\sqrt{2}+5\sqrt{3}$[/tex]. In conclusion, it is not possible to write [tex]$8\sqrt{2}+5\sqrt{3}$[/tex] as a single radical.
To know more about non-negative visit
https://brainly.com/question/20484693
#SPJ11
Which numbers are integers?Check all that apply.
15
-9
Two-thirds
6 and StartFraction 1 Over 9 EndFraction
0
-3,128
4.76
Answers
Answer:
the intergers include all negative whole numbers,zero,positive whole numbers
Answer:
the answer is 15. -9. 0. -3,128
Step-by-step explanation:
Suppose there are 8 boys and 7 girls in a classroom. If one student is chosen at random to run a errand. What is the probability that the student will be a girl?
Answers
Answer:
47%
Step-by-step explanation:
There are 15 total students, so find the percentage of girls out of the total students: 7/15= .466, which is about 47%. To double check, you can do the boys and make sure it adds to 100%. 8/15= .533, which is about 53%. 47+53=100. So girls are 47% and boys are 53%
Compute the z-score if X = 60, p = 10, and a = 30. Report your answer to the third decimal place. Answer: Question 17 Not yet answered Points out of 0.80 Flag question 17. In a normal distribution, what proportion of people have a score above 50 when : -30, and o-15? Report your answer to the fourth decimal place.
Answers
Approximately 0.0668 or 6.68% of people have a score above 50 in the given normal distribution.
To compute the z-score, we can use the formula:
z = (X - μ) / σ
Where:
X = observed value
μ = mean of the distribution
σ = standard deviation of the distribution
Given:
X = 60
μ = 10
σ = 30
Substituting these values into the formula:
z = (60 - 10) / 30
z = 50 / 30
z = 1.667 (rounded to three decimal places)
Therefore, the z-score is approximately 1.667.
Moving on to the second question, we need to find the proportion of people with a score above 50 in a normal distribution with a mean of -30 and a standard deviation of 15.
To calculate this proportion, we can use a standard normal distribution table or a statistical calculator. From the standard normal distribution table, we can find the area to the left of 50, which is 0.9332 (rounded to four decimal places).
Since we want the proportion above 50, we subtract this value from 1:
Proportion = 1 - 0.9332 = 0.0668 (rounded to four decimal places)
Therefore, approximately 0.0668 or 6.68% of people have a score above 50 in the given normal distribution.
Learn more about z-score:
https://brainly.com/question/30765368
#SPJ11
Please see picture. Which statement must be true?
Answers
Choose C.
x^2 = a/b must be true.
What type of triangle is this ?
Answers
Answer:
triangle bby
Step-by-step explanation:
Step-by-step explanation:
Right because there's an angle of 90
8/10=6/5 what is this
Answers
Answer:
Hi! You're uspposed to check the equality, and it is false. 8/10 is not equal to 6/5.
However, If you add the two together by making the common denominator 10, you will get 20/10 or 2.
Answer:
4/5=6/5 :3
Step-by-step explanation:
Consider this diagram of quadrilateral ABCD, which is not drawn to scale.
Which two statements must be true based on the information indicated by the diagram?
A. AC=~ BD
B. Triangle ABC =~ Triangle CDA
C.AB =~ DC
D. Angle ABD =~ Angle DBC
Answers
Option A,Option B and Option C is correct
What is parallelogram?
Parallelogram is 4 sided closed figure with opposites parallel and equal
Given,AB=CD
AD=BC
Since, its opposite sides are equal, it is a parallelogram.
∴ΔABD≅ΔBCD
AC= BD(By CPCTC)
B. Triangle ABC =~ Triangle CDA ( Since its a parallelogram)
C.AB =DC(Given)
D. Angle ABD =~ Angle DBC(wrong)
Therefore,Option A,Option B and Option C is correct
Learn more about quadrilaterals
https://brainly.com/question/16691874
#SPJ2
Answer:
( B ) △ABC ≅ △CDA
( C ) AB ≅ DC
Step-by-step explanation:
Khan Academy;
ABC = CDA, but ≅ means approximately which is also true.
AB = DC, because the distance matches.
Simplify w x 12 x 3
Helppp
Answers
Answer:-x • (w2 - 12)
——————————————
3w
If I have a two-way between subjects ANOVA with two groups per factor, how many factors do I have and how many groups do I have overall in my study? (Hint: the first number should be the number of factors that you have and the second number should be the number of groups that you have) 4; cannot be determined O 2; cannot be determined O 4: 2 O 2:4 Question 14 2 pts When doing a two-way between subjects ANOVA, can I concurrently have both a main effect and an interaction? No Yes Question 15 2 pts I do a two-way between-subjects ANOVA and find that my interaction F-test is significant. What do I do next? I would do a post-hoc Tukey test o I would look at my b-weights to see which variables are significant o I would do a post-hoc Bonferroni test I would do a simple main effects analysis Question 16 2 pts True or false: when I have an interaction in a two-way between-subjects ANOVA, the means across the levels for one factor significantly varies depending on which level of the second factor a person is looking at. True False Question 17 2 pts What type of correlation would I use if I have two factors that are both on an ordinal (or rank) scale? Spearman Phi (or a chi-square) Pearson O Point-biseral (or a t-test) D Question 18 2 pts When doing a multiple regression, how many outcome variables would I normally have in my model or analyses? As many as I think is relevant for my study 0 1 02 Question 19 2 pts What does b refer to in a regression analysis? Constant Unstandardized weight of a predictor variable Outcome variable Standardized weight of a predictor variable Question 20 2 pts a I do a multiple regression and find that my overall regression model is significant What do I do next? I would do a post-hoc Tukey test I would do a post-hoc Bonferroni test I would do a simple main effects analysis I would look at my b-weights to see which variables are significant D Question 21 2 pts Which of the following shows the largest positive standardized regression weight? ob' = -0.30 ob -0.15 Ob* -0.35 Ob -0.38
Answers
To answer your questions:
14. In a two-way between-subjects ANOVA with two groups per factor, you have 2 factors and a total of 4 groups in your study.
15. If the interaction F-test in a two-way between-subjects ANOVA is significant, the next step would be to conduct a post-hoc analysis to explore the specific group differences and determine the nature of the interaction effect. The choice of post-hoc test (e.g., Tukey, Bonferroni) would depend on the specific research question and the number of comparisons being made.
16. True. When there is an interaction in a two-way between-subjects ANOVA, it means that the means across the levels of one factor significantly vary depending on which level of the second factor is being considered.
17. If you have two factors that are both on an ordinal (or rank) scale, you would use the Spearman correlation coefficient to measure the relationship between these factors.
18. In a multiple regression analysis, you can have multiple outcome variables, but typically you would have only one outcome variable that you are trying to predict.
19. In a regression analysis, the "b" refers to the unstandardized weight (also known as the regression coefficient) of a predictor variable. It represents the change in the outcome variable for a one-unit change in the predictor, holding other predictors constant.
20. If the overall regression model is significant, the next step would be to examine the individual predictor variables (b-weights) to determine which variables are significant in predicting the outcome variable.
21. The largest positive standardized regression weight is represented by ob* = -0.35.
To learn more about regression
https://brainly.com/question/28178214
#SPJ11
HEEEELLLLPPPPPPPPP !!!!
Answers
Answer:
Step-by-step explanation:
Common difference = 5
a₁ = 24
a₆ = a₁ + (6-1)5 = 49
Mark the focus of the parabola you are going to create at F(6, 4). Draw a horizontal line that is 6 units below the focus. This line will be the directrix of your parabola. What is the equation of the line?
Answers
Answer: y=-2
Step-by-step explanation:
Based on the location of the line and the focus of the parabola, the equation of the line will be y = -2.
What is the equation of the line?The line is a horizontal line which means that the primary focus will be on the y axis.
The focus of the parabola is at F(6, 4) and the line is to be 6 units below this focus which means that the line on the y axis will be at:
= 4 - 6
= -2
This leaves the formula of the line as y = -2.
Find out more on parabolas at https://brainly.com/question/4148030.
ASAP‼️ DUE TONIGHT❕‼️
Answers
Answer:
99.95 yd
Step-by-step explanation:
Used the formulas
C=2πr
d=2r
Write the expression using a positive exponent. Leave in fraction form and do not expand numbers, leave in exponential form.
For example, 2^-7 write as 1/2^7, do NOT write as 1/128 or 0.0078125. NO SPACES!
-8k^-4/k^6
Answers
Answer:
i have to see the assigment
Step-by-step explanation:
Which is the graph of g(x)>2√3x+2?
Answers
Answer:
3rd one im pretty sure
Step-by-step explanation:
Find the confidence interval specified. The mean score, X, on an aptitude test for a random sample of 9 students was 75. Assuming that o= 10, construct a 95.44% confidence interval for the mean score, u, of all students taking the test. Select one: O 55 to 95 O 68.3 to 81.7 0 72.8 to 77.2 O 70.0 to 80.0
Answers
The 95.44% confidence interval for the mean score is approximately 68.47 to 81.53. Among the given options, the closest match is 68.3 to 81.7. Option b is correct.
To construct a confidence interval for the mean score, we can use the formula:
CI = X ± Z × (σ / √n)
where X is the sample mean, Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
In this case, the sample mean X is 75, the population standard deviation σ is 10, and the sample size n is 9. The desired confidence level is 95.44%, which corresponds to a z-score of approximately 1.96.
Plugging in these values, we get:
CI = 75 ± 1.96 × (10 / √9)
= 75 ± 1.96 × (10 / 3)
≈ 75 ± 6.53
Therefore, the 95.44% confidence interval for the mean score is approximately 68.47 to 81.53.
Among the given options, the closest match is 68.3 to 81.7, so the correct answer is b.
Learn more about confidence interval https://brainly.com/question/32546207
#SPJ11
Which variable of time could cause a student’s GPA to increase?
a) sleeping
b) working
c) eating
d) studying
Answers
The correct answer is D.
The variable of time that could cause a student’s GPA to increase is studying.
A student’s grade point average (GPA) is a reflection of their academic performance, which is determined by their cumulative grades in classes and academic subjects over a period of time.GPA can be influenced by various factors, including how much time students dedicate to studying, the amount of effort they put in, and how effectively they utilize their study time. Therefore, if students dedicate more time to studying, their grades may improve, resulting in a higher GPA.For such more questions on GPA
https://brainly.com/question/19426550
#SPJ8
Find the exact value of sin 105º.
Answers
Answer:
sin 105 = sin (45 + 60) = sin 45 cos 60 + cos 45 sin 60, or
= (1 / √2)(1 / 2) + (1 / √2)(√3 / 2)
1 + √3
= -------------
2√2
Step-by-step explanation:
(according to my calculator)
Please help due today:///
Answers
Then 600-520= 80
D. The cost to play the game is $2. The winner gets $6 for making purple. How much profit would the school make from 18 people playing the game?
Answers
Answer:
$30
Step-by-step explanation:
1 person = $ 2
18 person = 2 × 18 = $36
winner = $6
profit = 36 - 6 = $30
If x and y are two rational numbers such that x < y , then ______ is a rational number in between x and y.
Answers
Answer:
[tex]\dfrac{x+y}{2}[/tex]
Step-by-step explanation:
Let first number be x and another number is y.
A rational number is a fraction that can be expressed in the form of x/y.
A rational number between x and y is given by :
[tex]R=\dfrac{x+y}{2}[/tex]
So,
If x and y are two rational numbers such that x < y , then [tex]\dfrac{x+y}{2}[/tex] is a rational number in between x and y.
1-Pearson Publishing expects to sell $2 million of its new edition of "Foundation of Finance." However, $200,000 of this amount would have been spent on its existing past edition of the textbook. The $2 million is the appropriate cash inflow for the new edition of the book
true or false
2-Companies should use accounting profits, not cash flows, to make capital budgeting decisions.
true or false
Answers
(1) The statement that, "The $2 million is appropriate cash-inflow for the new edition of the book" is False because the cash-inflow is $1.8 million.
(2) The statement that, "Companies should use accounting profits, not cash flows, to make capital budgeting decisions" is False because, companies should focus on cash flows.
Part (1) The $2 million is not appropriate "cash-inflow" for "new-edition" of book. The $2 million represents "expected-sales" revenue from the new edition of "Foundation of Finance," but it does not take into account any costs or expenses associated with producing or marketing the book.
It is mentioned that $200,000 would have been spent on existing past edition of textbook. This expense needs to be deducted from expected sales revenue to determine the appropriate cash inflow.
So, appropriate cash-inflow for the new edition would be $2 million minus $200,000, which equals $1.8 million.
So, the statement is False.
Part (2) : Companies should use cash flows, not accounting-profits, to make capital budgeting decisions. Accounting-profits, also known as net income or earnings, are calculated based on accrual accounting principles and include non-cash items such as depreciation and amortization.
When making capital budgeting decisions, it is essential to consider the actual "cash-flows" generated by an investment project. Cash flows represent the cash inflows and outflows that occur over a specific period, and they are crucial for evaluating the feasibility and profitability of an investment.
Therefore, the statement is False.
Learn more about Budgeting here
https://brainly.com/question/32396014
#SPJ4
Guided Practice
Which property justifies the first step in solving this equation ?
[tex]\frac{x}{5}[/tex]+9=11
[tex]\frac{x}{5}[/tex]+9−9=11−9
A.
Substitution Property of Equality
B.
Addition Property of Equality
C.
Subtraction Property of Equality
Answers
Answer:
a subtraction
Step-by-step explanation:
C.
Subtraction Property of Equality
The radius r of a sphere is increasing at a rate of 5 inches per minute. (a) Find the rate of change of the volume when r = 12 inches.
Answers
To find the rate of change of the volume when the radius is 12 inches, we can use the formula for the volume of a sphere:
V = (4/3) * π * [tex]r^3[/tex]
To find the rate of change of the volume, we need to take the derivative of the volume function with respect to time (t) using the chain rule. The derivative of the volume function with respect to time will give us the rate of change of the volume.
dV/dt = (dV/dr) * (dr/dt)
where dV/dt is the rate of change of the volume, dV/dr is the derivative of the volume with respect to the radius, and dr/dt is the rate of change of the radius.
Given that the radius is increasing at a rate of 5 inches per minute (dr/dt = 5), we can substitute this value into the formula.
Now, let's calculate the derivative of the volume with respect to the radius (dV/dr):
dV/dr = d/dt [(4/3) * π[tex]* r^3[/tex]] = (4/3) * π * [tex]3r^2[/tex]= 4π[tex]r^2[/tex]
Substituting the values into the formula for the rate of change of the volume:
dV/dt = (dV/dr) * (dr/dt) = 4π[tex]r^2[/tex]* 5 = 20π[tex]r^2[/tex]
When the radius is 12 inches (r = 12), we can plug this value into the formula to find the rate of change of the volume:
dV/dt = 20π[tex]r^2[/tex] = 20π(1[tex]2^2[/tex]) = 20π * 144 = 2880π
Therefore, when the radius is 12 inches, the rate of change of the volume is 2880π cubic inches per minute.
Learn more about maxima and minima here:
https://brainly.com/question/31398169
#SPJ11