Answer:
d. 30
Step-by-step explanation:
The computation of the 35th percentile of this data set is shown below:
Before that first we have to series the number in ascending number
S. No Numbers
1 26
2 29
3 30
4 30
5 31
6 32
7 34
8 35
9 36
Now use the formula
Here n = 9
Percentile = 100
[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]
= 3.5th
= 3th + 0.5 (4th - 3th)
= 3th + 0.5 (30 - 30)
= 3th + 0
= 30
Please answer this correctly without making mistakes
Answer:
Put 1/10 in the box.
Step-by-step explanation:
Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.
Best Regards!
Answer:
To Oakdale to Milford:
2/5 mi
Step-by-step explanation:
1/10 + 3/20 + 3/20
1/10 = 2/20
then;
2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20
8/20 = 2/5
An urn contains 9 red marbles, 6 white marbles, and 8 blue marbles marbles. A child randomly selects three (without replacement) from the urn. Find the probability all three marbles are the same color
Answer:
P(identical colours) = 160/1771 (0.0903 to four decimals)
Step-by-step explanation:
Given 9R, 6W and 8B marbles (total = 9+6+8 = 23)
Choose three without replacement.
Need probability three identical colours.
Use the multiplication rule.
P(RRR) = 9/23 * 8*22 * 7*21 = 12 / 253
P(WWW) = 6/23 * 5/22 * 4/21 = 20/1771
P(BBB) = 8/23 * 7/22 * 6/21 = 8/153
Probability of getting identical colours
= P(RRR)+P(WWW)+P(BBB)
= 160/1771 (0.0903 to four decimals)
Using the probability concept, it is found that there is a 0.0903 = 9.03% probability all three marbles are the same color.
-----------------
A probability is the number of desired outcomes divided by the number of total outcomes.The order in which the marbles are chosen is not important, and they are also chosen without replacement, which means that the combination formula is used to find the number of outcomes.-----------------
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
-----------------
The desired outcomes can be:
3 from a set of 9(all red).3 from a set of 6(all white).3 from a set of 8(all blue).Thus:
[tex]D = C_{9,3} + C_{6,3} + C_{8,3} = \frac{9!}{3!6!} + \frac{6!}{3!3!} + \frac{8!}{3!5!} = 160[/tex]
-----------------
The total outcomes are 3 from a set of 9 + 6 + 8 = 23. Thus:
[tex]T = C_{23,3} = \frac{23!}{3!20!} = 1771[/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{160}{1771} = 0.0903[/tex]
0.0903 = 9.03% probability all three marbles are the same color.
A similar problem is given at https://brainly.com/question/10896842
what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?
Answer:
[tex]71,100[/tex]
Step-by-step explanation:
If you are trying to find a number that is written in word form, we can just use place values to find what goes where.
A number is broken down into this:
Ten thousands, thousands, hundreds, tens, ones.
If they have 7 ten thousands, the first digit will be a 7.
If they have 1 thousand, the second digit will be a 1.
If they have 1 hundred, the third digit will be a 1.
Since nothing is stated about tens, we assume it's value is 0.
And since there are no ones, it's value is 0.
So:
71,100.
Hope this helped!
Solve 5(2x + 4) = 15. Round to the nearest thousandth.
[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]
Answer:
[tex]\huge\boxed{x=-0.5}[/tex]
Step-by-step explanation:
[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation:
Find the intersection point for the following liner function f(x)= 2x+3 g(x)=-4x-27
Answer:
( -5,-7)
Step-by-step explanation:
f(x)= 2x+3 g(x)=-4x-27
Set the two functions equal
2x+3 = -4x-27
Add 4x to each side
2x+3+4x = -4x-27+4x
6x+3 = -27
Subtract 3
6x+3 - 3 = -27-3
6x = -30
Divide each side by 6
6x/6 = -30/6
x =-5
Now we need to find the output
f(-5) = 2(-5) +3 = -10+3 = -7
Answer:
Step-by-step explanation:
big burgewr
Using the insurance company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 14-year period. Round your answer to four decimal places.
Answer: 19.2222
Step-by-step explanation:
given data;
no of tornadoes = 2,1,0 because it’s fewer than 3.
period = 14 years
probability of a tornado in a calendar year = 0.12
solution:
probability of exactly 2 tornadoes
= ( 0.12 )^2 * ( 0.88 )^11 * ( 14! / 2! * 11! )
= 0.0144 * 0.2451 * 1092
= 3.8541
probability of exac one tornado
= ( 0.12 )^1 * ( 0.88 )^12 * ( 14! / 1! * 12! )
= 0.12 * 0.2157 * 182
= 12.7109
probability of exactly 0 tornado
= ( 0.12 )^0 * ( 0.88 )^13 * ( 14! / 0! * 13! )
= 1 * 0.1898 * 14
= 2.6572
probability if fewer than 3 tornadoes
= 3.8541 + 12.7109 +2.6572
= 19.2222
A projectile is fired vertically upward from a height of 300
300
feet above the ground, with an initial velocity of 900
900
ft/sec. Recall that projectiles are modeled by the function h(t)=−16t2+v0t+y0
h
(
t
)
=
−
16
t
2
+
v
0
t
+
y
0
. Write a quadratic equation to model the projectile's height h(t)
h
(
t
)
in feet above the ground after t seconds.
Step-by-step explanation:
It is given that, a projectile is fired vertically upward from a height of 300 feet above the ground, with an initial velocity of 900 ft/s.
The general equation with which a projectile are modled by the function is given by :
[tex]h(t)=-16t^2+v_ot+y_o[/tex]
y₀ is the initial height above the ground
v₀ = initial velocity
So,
[tex]h(t)=-16t^2+900t+300[/tex]
This is the quadratic equation that models the projectile height in feet above the ground after t seconds.
Find the value of x. A: 15 B: 12 C: 10 D: 8
Answer:
[tex]\boxed{\sf C. \ 10}[/tex]
Step-by-step explanation:
[tex]\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products[/tex]
[tex]\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.[/tex]
[tex]NH \times HT = MH \times HY[/tex]
[tex](x+20) \times 8=12 \times 20[/tex]
[tex]\sf Expand \ brackets \ and \ multiply.[/tex]
[tex]8x+160=240[/tex]
[tex]\sf Subtract \ 160 \ from \ both \ sides.[/tex]
[tex]8x+160-160=240-160[/tex]
[tex]8x=80[/tex]
[tex]\sf Divide \ both \ sides \ by \ 8.[/tex]
[tex]\displaystyle \frac{8x}{8} =\frac{80}{8}[/tex]
[tex]x=10[/tex]
The value of x is 10.
We have a circle and inside it two chords MY and NT intersect at point H.
We have to find the value of x in the figure.
What is intersecting chord theorem?According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then
AO x OB = CO x OD
Applying the chord intersecting theorem to the figure in the question, we get -
MH x HY = NH x HT
12 x 20 = (x+20) x 8
240 = 8x + 160
8x = 80
x = 10
Hence the value of x is 10.
To solve more questions on Circles and chords, visit the link below -
https://brainly.com/question/15568573
#SPJ5
Find the missing side or angle.
Round to the nearest tenth.
Answer:
b=2.7
Step-by-step explanation:
using sine rule,,,
Step-by-step explanation:
So for this problem, we need the missing angle A. From there, we can use the law of sines to compute length of b.
So the sum of the interior angles of a triangle is 180. With that in mind, we can make an equation to fine the measure of angle A.
53 + 80 + A = 180
133 + A = 180
A = 47
Now that we have the angle of A, we can use the law of sines to fine the length of b.
b / sin(B) = a / sin(A)
b = sin(B) * a / sin(A)
b = sin(80) * 2 / sin(47)
b = 2.693
Now round that to the nearest tenth to get
b = 2.7
Cheers.
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.
Answer:
D. The z scores are numbers without units of measurement.
Step-by-step explanation:
Z-scores are without units, or are pure numbers.
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?
Answer:
125π ft²
Step-by-step explanation:
1/4π(30)² - 1/4π(20)² = 125π
A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?
a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:
The interval for 95% will be given as,
Pr(X) = μ ± 2σ
Pr(X) = 200 ± 2(40)
Pr(X) = 200 ± 80
Pr(X) = (200 - 80, 200 + 80)
Pr(X) = (120, 280)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
#SPJ5
The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes
Answer5
Step-by-step explanation:
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
a) What is the cost of a chicken shawarma wrap?
$10.99
b) What is the cost of one order of spiced potatoes?
$4.99
c) If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
Step-by-step explanation:
Let x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes,
Cost of a chicken sharwarma wrap = x
Cost of an order of spiced potatoes = y
Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95.
3x + 2y = $42.95 .............Equation 1
Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91.
5x + 4y = $74.91 ................Equation 2
Hence, the Equations needed to solve the question is:
3x + 2y = $42.95 .............Equation 1
5x + 4y = $74.91 ................Equation 2
We use Elimination method to solve for this.
Multiply Equation 1 by coefficient of x in Equation 2
Equation 2 by coefficient of x in Equation 1
3x + 2y = $42.95 .............Equation 1 × 5
5x + 4y = $74.91 ................Equation 2 × 3
15x + 10y = 214.75..............Equation 3
15x + 12y = 224.73..............Equation 4
Subtract Equation 3 from Equation 4
2y = 9.98
y = 9.98/2
y = 4.99
Therefore, y = Cost of an order of spiced potatoes = $4.99
Subtitute 4.99 for y in Equation 1
3x + 2y = $42.95 .............Equation 1
3x +2(4.99) = 42.95
3x + 9.98 = 42.95
3x = 42.95 - 9.98
3x = 32.97
x = 32.97/3
x = 10.99
x = Cost of a chicken sharwarma wrap = $10.99
Therefore,
The cost of a chicken sharwarma wrap = $10.99
The cost of an order of spiced potatoes = $4.99
Which of the following is equivalent to –2i(6 – 7i)?
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
the temp fell 3 degrees every hour for 5 hours what's the change in temperature
Answer:
-15
Step-by-step explanation:
If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees
what number must be added to the sequence of 7,13 and 10 to get an average of 13
Answer:
22
Step-by-step explanation:
We can write an equation:
(7+13+10+x)/4=13
x represents the number that needs to be added to get an average of
(7+13+10+x)/4=13
(30+x)/4=13
30+x=52
x=22
The number is 22
Hope this helps! Have a wonderful day :)
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804
ASAP Which graph has a correlation coefficient, r, closest to 0.75?
Answer:
C. Graph C
Step-by-step explanation:
In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.
Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.
Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.
Graph C has a correlation coefficient, r, that is closer to 0.75.
Answer: graph A ‼️
Step-by-step explanation:
In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are
Answer:
In the error term.
Step-by-step explanation:
A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).
Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.
Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?
Answer:
rose. is. 18/2=9 years old
Answer:
Stephanie is 18years old and she is twice older than her sister
so rosa is 18÷2(since stephanie is twice older than rosa
so rosa is 9 years old
If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. A straight line is shown and is marked with three angles. The first angle measures 50 degrees. The second angle measures 60 degrees. The third angle is labeled x. The line between the 40 degree angle and angle x extends below the straight line. The angle formed is labeled angle y. Write and solve an equation to determine the measure of angle y.
Step-by-step explanation:
sorry but u should provide with a diagram for better understanding of ur question
A box is filled with 8 blue cards, 6 red cards, and 6 yellow cards. A card is chosen at a random from the box. What is the probability that the card is not red ? Write your answer as a fraction.
Answer:
14/20 or .7 or 70%
Step-by-step explanation:
Total Number of cards: 20
Number of Red cards: 6
The leftover cards: 20 -6 = 14
The probability of not getting a red = 14/20
14/20 as a decimal = 14/20 = 70/100 = .7
14/20 as a percent = 14/20 = 70/100 = 70%
Five more than the square of a number Five more than twice a number Five less than the product of 3 and a number Five less the product of 3 and a number Twice the sum of a number and 5 The sum of twice a number and 5 The product of the cube of a number and 5 The cube of the product of 5 and a number. 5 + x2 5 + 2x 5 - 3x 3x - 5 2x + 5 2(x + 5) 5x3 (5x)3 WILL MARK BRAINLIEST AND DON'T PUT A FAKE ANSWER TO GET POINTS EITHER CUS I NEED HELP
Answer:
BelowStep-by-step explanation: Let all unknown no be x
Five more than the square of a number
= [tex]5 + x^2[/tex]
Five more than twice a number ;
[tex]5+2x\\= 2x+5[/tex]
Five less than the product of 3 and a number ;
[tex]5- 3x\\= 3x-5[/tex]
Twice the sum of a number and 5 ;
[tex]2(x+5)\\[/tex]
The sum of twice a number and 5 ;
[tex]2x+5[/tex]
The product of the cube of a number and 5;
[tex]x^3 \times 5\\=5x^3[/tex]
The cube of the product of 5 and a number ;
[tex](5\times x)^3\\(5x)^3[/tex]
In triangle ABC, ∠ABC=70° and ∠ACB=50°. Points M and N lie on sides AB and AC respectively such that ∠MCB=40° and ∠NBC=50°. Find m∠NMC.
Answer:
∠NMC = 50°
Step-by-step explanation:
The interpretation of the information given in the question can be seen in the attached images below.
In ΔABC;
∠ A + ∠ B + ∠ C = 180° (sum of angles in a triangle)
∠ A + 70° + 50° = 180°
∠ A = 180° - 70° - 50°
∠ A = 180° - 120°
∠ A = 60°
In ΔAMN ; the base angle are equal , let the base angles be x and y
So; x = y (base angle of an equilateral triangle)
Then;
x + x + 60° = 180°
2x + 60° = 180°
2x = 180° - 60°
2x = 120°
x = 120°/2
x = 60°
∴ x = 60° , y = 60°
In ΔBQC
∠a + ∠e + ∠b = 180°
50° + ∠e + 40° = 180°
∠e = 180° - 50° - 40°
∠e = 180° - 90°
∠e = 90°
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
∠i = 50° - 40° = 10°
In ΔNQC
∠f + ∠i + ∠j = 180°
90° + 10° + ∠j = 180°
∠j = 180° - 90°-10°
∠j = 180° - 100°
∠j = 80°
From line AC , at point N , ∠y + ∠c + ∠j = 180° (sum of angles on a straight line)
60° + ∠c + ∠80° = 180°
∠c = 180° - 60°-80°
∠c = 180° - 140°
∠c = 40°
Recall that :
At point Q , ∠e = ∠f = ∠g = ∠h = 90° (angles at a point)
Then In Δ NMC ;
∠d + ∠h + ∠c = 180° (sum of angles in a triangle)
∠d + 90° + 40° = 180°
∠d = 180° - 90° -40°
∠d = 180° - 130°
∠d = 50°
Therefore, ∠NMC = ∠d = 50°
wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of
Answer:
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
Step-by-step explanation:
A test for the difference between two population means is to be performed.
As the population variances are known, the z-test will be used.
The hypothesis can be defined as follows:
H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ₂
Assume that the significance level of the test is, α = 0.05.
The critical region can be defined as follows:
The critical value of z for α = 0.05 is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]
Use a z-table.
[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]
