The measure of the two vertical angles is 15°
The two vertical angles have measures (4x-21)° and (x+6)°
Note that:
The measure of two vertical angles are equal
Therefore, equate (4x-21)° and (x+6)° and solve for x
(4x-21)° = (x+6)°
4x - 21 = x + 6
Collect like terms
4x - x = 6 + 21
3x = 27
x = 27/3
x = 9
Substitute x = 9 into 4x - 21
4x - 21 = 4(9) - 21
4x - 21 = 15°
Substitute x = 9 into x + 6
x + 6 = 9 + 6
x + 6 = 15°
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day. A sample of 69 stocks traded on the NYSE that day showed that 31 went up. You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of α = 0.05 α = 0.05 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α α greater than α α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3. There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3. The sample data support the claim that the proportion of stocks that went up is more than 0.3. There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is more than 0.3.
Testing the hypothesis, it is found that:
The test statistic is 2.71.The p-value is 0.0034.The p-value is less than [tex]\alpha[/tex]The test statistic leads to a decision to reject the null hypothesis.The sample data support the claim that the proportion of stocks that went up is more than 0.3.At the null hypothesis, we test if the proportion of stocks that went up is of 0.3, that is:
[tex]H_0: p = 0.3[/tex]
At the alternative hypothesis, we test if the proportion is significantly more than 0.3, that is:
[tex]H_1: p > 0.3[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are:
[tex]p = 0.3, n = 69, \overline{p} = \frac{31}{69} = 0.4493[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.4493 - 0.3}{\sqrt{\frac{0.3(0.7)}{69}}}[/tex]
[tex]z = 2.71[/tex]
The test statistic is 2.71.
The p-value is the probability of finding a sample proportion of 0.4493 or above, hence, it is 1 subtracted by the p-value of z = 2.71.
Looking at the z-table, z = 2.71 has a p-value of 0.9966.
1 - 0.9966 = 0.0034
The p-value is 0.0034.
Which is less than [tex]\alpha[/tex], and then the test statistic leads to a decision to reject the null hypothesis, and thus:
The sample data support the claim that the proportion of stocks that went up is more than 0.3.
A similar problem is given at https://brainly.com/question/25413788
Please can you help me x
Answer:
PX : XQ = 2 : 5
Step-by-step explanation:
Since RX is perpendicular to PQ , then
Δ RPX and Δ RQX are right triangle
Calculate PX and XQ using Pythagoras' identity in the right triangles
PX² = 20² - 16² = 400 - 256 = 144 ( take square root of both sides )
PX = [tex]\sqrt{144}[/tex] = 12
Similarly
XQ² = 34² - 16² = 1156 - 256 = 900 ( take square root of both sides )
XQ = [tex]\sqrt{900}[/tex] = 30
Then
PX : XQ = 12 : 30 = 2 : 5 ( in simplest form )
C(x)= 500000 +80x+0.003x^2 me ayudan hallar por favor
Answer:
It's a parabola with a minimum.
C(x)= 500,000 + 80x + 0.003x^2
C'(x) = 80 + 0.006x = 0
x = 80/0/006 = 13,333 units
Step-by-step explanation:
A company that produces chemicals used in manufacturing sells a certain product for $200 per unit. The total production cost for the product is
C(x)= 500,000 + 80x + 0.003x^2
The company can produce no more than 30,000 units during a given time period. How
many units of the chemical product should be manufactured and sold to maximize profit?
The second term of an arithmetic sequence is –5, and the third term is –20. What is the first term?
Answer:
a₁ = 10
Step-by-step explanation:
The common difference d is calculated as
d = a₃ - a₂ = - 20 - (- 5) = - 20 + 5 = - 15
Then
a₂ - a₁ = d , that is
- 5 - a₁ = - 15 ( add 5 to both sides )
- a₁ = - 10 ( multiply both sides by - 1 )
a₁ = 10
Find the perimeter. Simplify your answer.
Answer:
Perimeter = 24p + 17
Step-by-step explanation:
Perimeter = the sum of the sides of the figure.
Perimeter = (7p + 9) + (10p - 1) + (7p + 9)
Perimeter = (7p + 10p + 7p) + (9 - 1 + 9)
Perimeter = 24p + 17
Answer:
24p+17
Step-by-step explanation:
Perimeter of triangle = 2(7p+9)+(10p-1)
= 14p+18+10p-1
= 24p+17
can someone help me on this and tell me how you did it you will get 30 points
[tex] \frac{2}{3} \div 3 \frac{1}{3} \\ \frac{2}{3} \times \frac{3}{10} \\ = \frac{2}{10} = \frac{1}{5} [/tex]
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Which expression is an equivalent expression for 2(6y – 4)?
A. 8x – 2
B. 12y – 8
C. 8y
D. 12y + 4
Answer:
B. 12y-8
Step-by-step explanation:
by multiplying the 2 through the equation
How many factors of 2 are there in 2³? answers> 1 2 3 5
Answer:
2
Step-by-step explanation:
2^3= 2*2*2
factors of 8= 1,2,4,8
factors of 2= 1,2
What is the surface area of the cylinder with height 7 cm and radius 5 cm? Round
your answer to the nearest thousandth.
Answer:
376.991 cm²
Step-by-step explanation:
[tex]SA_{cylinder} = 2\pi r^{2} + 2\pi rh[/tex]
Surface Area = 2π(5²) + 2π(5)(7)
= 50π + 70π
= 120π
= 376.9911184... ≈ 376.991
Derive Surface Area of A CylinderIf you take a look at a net of a cylinder, you can see it is composed of two circles(bases) and a rectangular strip with the length of the diameter of the circle
The formula for the area of a circle = πr², and since there are 2, it is 2πr²
The formula for circumference of a circle = 2πr, and since we are multiplying that by the height by the height of the cylinder, it is 2πrh
∴ 2πr² + 2πrh
If RS=x+5 and HJ + Lk = 4x+6, find RS
What is the midpoint of KL?
Answer:
Find the midpoint between the two points.
(4,4),(-1,2)
please help asap…………
Answer:
not linear
Step-by-step explanation:
a linear function contains x and y only with the exponent 1.
this allows the function to be a line (hence the term "linear"), a constant ratio of y changes to x changes for any values of x which defines linear relation between x and y.
but this equation contains a term with x², which changes the size of change of y for every value of x.
e.g. when x changes by 1 from 1 to 2, y changes by 3 from 1² to 2² (1 to 4). but if x changes again by 1 from 2 to 3, y changes by 5 from 2² to 3² (4 to 9).
this is clearly not constant.
7th grade math help...
Answer:
a= 11/30
Step-by-step explanation:
Divide the 5 1/2 miles by the 15 minutes
5.5/15= .36
.36 = 11/30
In the diagram below segment AC is congruent to segment CE and segment BC is congruent to segment DC.
Why is triangle BCA congruent to triangle DCE?
See picture for full problem. Please and thank you!
Step-by-step explanation:
By reflection
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(c) Ada is x years old and Bill is y years old.
Last
year,
Bill was 6 times as old as Ada.
(1) Form an equation in x and y and show that it simplifies to y = 6x - 5.
Using a system of equations, it is found that the simplified equation is y = 6x - 5.
Ada is x years old.Bill is y years old.Last year, Ada was x - 1 years old and Bill was y - 1 years old.
Bill was 6 times as old as Ada, hence:
[tex]y - 1 = 6(x - 1)[/tex]
[tex]y - 1 = 6x - 6[/tex]
[tex]y = 6x - 6 + 1[/tex]
[tex]y = 6x - 5[/tex]
The simplified equation is y = 6x - 5.
For a similar problem, also involving a system of equations, you can check https://brainly.com/question/13773803
Which expression is equivalent to 7/8
A: 5/8 + 2/8 + 1/8
B: 3/8 + 3/8 + 1/8 +1/8
C: 4/8 + 2/8 + 1/8
D: 4/8 + 2/8 + 2/8
C:4/8+2/8+1/8
brainlist me please
Please help me with this homework homework
Answer:
Its A=2.38
Step-by-step explanation:
6cup=558 gram
1cup=558/6
1cup=93 gram
13gram*17kg=221gram
221/93=2.38
if i make 6000 dollars per 5.6 hours how much will I make in total in 24 hours
Answer:
About $25,714.29
Step-by-step explanation:
Divide 6000 by 5.6 to get dollar per hour rate:
6000/5.6 = 1071.43 dollars per hour
Multiply by 24:
1071.42857 * 24 = 25714.29 dollars
About $25,714.29
What are Multiple Representations
Answer:
Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity
Answer:
Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties.
cahahahahhddbsbshshsjs 98 +_=366
Answer:
268
Step-by-step explanation:
366 minus 98= 268
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The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.
Answer:
30, 60, and 90
Step-by-step explanation:
Let x be the Angle 1
2x is Angle 2
3x is Angle 3
x + 2x + 3x = 180
6x = 180
x = 30 degrees
2x = 60 degrees
3x = 90 degrees
A bakery can make 4 cheesecakes for every 5 blocks of cream cheese. Which table represents the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses?
Answer:
where is the picture of the tables?
Step-by-step explanation:
To form a hyperbola what is the relationship between the base of the cone and the angle of the plane that intersects the cone
A. The plane is a parallel to the base of the cone
B. The plane may be perpendicular to the base of the cone
C. the plane must be at a 45 degree angle to the base of the cone
D. The plane is at an angle that is neither parallel nor perpendicular to the base of the cone
Tim earns spending money by doing odd jobs for his neighbors. The table shows how much he is paid
for each job. Tim gets $12 for mowing lawns, $9 for washing cars, and $7 for walking dogs. Mr. Jeffries has not paid his bill in 3 weeks. If Tim performed each job for Mr. Jeffries
once, how much does Mr. Jeffries owe Tim? Write an addition equation using integers to represent the
situation. Represent Mr. Jeffries' balance as an integer.
Select the correct choice below and fill in the answer boxes to complete your choice.
Answer:
D ($28)
Step-by-step explanation:
-12 + -9 + -7 = -28
Enter the number in scientific notation. 86,792 =
Answer:
8.6792 × 10 4 (I don't know how to make the four smaller but its 10 to the power of 4).
Step-by-step explanation:
8.6792 × 10 4. is the scientific notation
5p + 3 = 15 Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
Expressions can be represented as equations, and vice versa.
A possible situation is as follows:
John is 15 years old, and his age is 3 more than 5 times his brother's age
The equation is given as:
[tex]\mathbf{5p + 3 = 15}[/tex]
This means that:
15 represents John's ageP represents his brother's age5 and 3 are the constants that relate their agesRead more about word equations at:
https://brainly.com/question/20518082
The equation 5p + 3 = 15 can be used to find Mgbafor's age when Okeke's age is five times Mgbafor's age and in three years time, Okeke will be 15 years old.
The equation 5p + 3 = 15 is a linear equation. The equation must represent a variable which when multiplied by 5 and 3 is added yields 15.
Lets assume that Okeke's age is five times Mgbafor's age In three years time, Okeke will be 15 years old. If i am asked to find Mgbafor's age, the equation to use is 5p + 3 = 15, where p = Mgbafor's age.
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find the value of x and y
Answer:
x = 60
y = 30
Step-by-step explanation:
We know that all triangles' interior angles combined must have a sum of 180.
Since the triangle on the left is a equilateral triangle, we know that each angle is equal to 60.
Since we already know that the sum of the two angles in the top right is 90 (shown by the right angle symbol) and we know that the angle that isn't y is equal to 60, we must do the following step:
90 - 60 = y
90 - 60 = 30
y = 30
Now that we know the value of y, it's time to find the value of x.
We know that y = 30 and that the angle in the bottom right is equal to 90 (shown by right angle symbol).
Since all triangles' interior angles combined must have a sum of 180 and we already know that one angle is equal to 30 and the other is equal to 90, we must do the following:
180 - (90 + y) = x
180 - (90 + 30) = x
180 - 120 = x
180 - 120 = 60
x = 60
This gives us the answers y = 30 and x = 60
How to find derivative of a curved graph.
The quotient of a number, divided by 3, equals-8
Answer:
x / 3 = -8
Step-by-step explanation:
Multiply.
[−8⋅4/11]⋅[(−0.1)⋅22]
Answer:
6.4
Step-by-step explanation:
Hope this helps :D