Answer:
[tex] \boxed{ \sf{ \bold{ \huge{ \boxed{x - 2}}}}}[/tex]Step-by-step explanation:
[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]
To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F
Let's solve
First expression = x - 2
Second expression = x + x - 6
Here, we have to find the two numbers which subtracts to 1 and multiplies to 6
= x + ( 3 - 2 ) x + 6
Distribute x through the parentheses
= x + 3x - 2x + 6
Factor out x from the expression
= x ( x + 3 ) - 2x + 6
Factor out -2 from the expression
= x ( x + 3 ) - 2 ( x + 3 )
Factor out x+3 from the expression
= ( x + 3 ) ( x - 2 )
Here, x - 2 is common in both expression.
Thus, H.C.F = x - 2
Hope I helped!
Best regards!!!
Answer:
x - 2
Step-by-step explanation:
by factorization method
1) x - 2
2) x^2 + x - 6
by splitting method
x^2 + 3x - 2x - 6
taking separate common from the first two terms and last two terms
x(x + 3) - 2(x + 3)
now writing x+3 once and the other term to get the right answer
(x + 3)(x - 2)
in both parts just see the similar term and write it as HCF
HCF= x - 2
and the second method by which you can get this answer is division method
Determine the value of x in the figure. Question 1 options: A) x = 90 B) x = 85 C) x = 45 D) x = 135
Answer:
A.) x=90°
Step-by-step explanation:
Note:
The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.
We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:
[tex]180=135+y[/tex]
y is the unknown angle. Solve for y:
[tex]180-135=y\\\\y=45[/tex]
y is 45°. Since this and the other angle are congruent, add:
[tex]45+45=90[/tex]
Note:
Triangles angles will always add up to a total of 180°.
To find the missing angle x°, use:
[tex]180=a+b+c[/tex]
These are the angles in a triangle. Substitute any known values and solve:
[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]
The missing angle x° is 90°.
:Done
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis?
Answer:
f(x) = -0.5x
Step-by-step explanation:
.25*8 = 2 which is really a slope of 2/1
place a negative in front flips it over the y axis and flipping the slope flips it over the x axis.
In a study of treatments for very painful "cluster" headaches, 140 patients were treated with oxygen and 158 other patients were given a placebo consisting of ordinary air. Among the 140 patients in the oxygen treatment group, 113 were free from headaches 15 minutes after treatment. Among the 158 patients given the placebo, 35 were free from headaches 15 minutes after treatment. Use a significance level to test the claim that the oxygen treatment is effective. A) Find test statistic z B) Find the P-value C) Construct the appropriate confidence interval D) determine if the oxygen treatment is effective
Answer:
A
[tex]t = 10.1[/tex]
B
[tex]p-value = p(t > 10.1)= 0.000[/tex]
C
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
D
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 140[/tex]
The number of patient which the oxygen cured is k = 113
The second sample size is [tex]n_2 = 158[/tex]
The number of patient that placebo cured is l = 35
The first sample proportion is
[tex]\r p_1 = \frac{ 113}{140 }[/tex]
[tex]\r p_1 = 0.8071[/tex]
The second sample proportion is
[tex]\r p_2 = \frac{ 35}{ 158 }[/tex]
[tex]\r p_2 = 0.222[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 > p_2[/tex]
Let assume the level of significance be[tex]\alpha = 0.05[/tex]
Generally the pooled proportion is mathematically evaluated as
[tex]p = \frac{p1 * n1 + p2 * n2}{n1 + n2}[/tex]
substituting values
[tex]p = \frac{0.8071 * 140 + 0.222 * 158}{140 + 158}[/tex]
[tex]p = 0.4969[/tex]
Generally the standard error is mathematically represented
[tex]SE = \sqrt{ p(1- p ) * [ \frac{1}{n_1} + \frac{1}{n_1}] }[/tex]
substituting values
[tex]SE = \sqrt{ 0.4969(1- 0.4969 ) * [ \frac{1}{140} + \frac{1}{158}] }[/tex]
[tex]SE = 0.0580[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p_1 - \r p_2}{ SE}[/tex]
[tex]t = \frac{ 0.8071 -0.222}{ 0.0580}[/tex]
[tex]t = 10.1[/tex]
The p-value is from the normal distribution table as
[tex]p-value = p(t > 10.1)= 0.000[/tex]
given that [tex]t< \alpha[/tex] the null hypothesis is rejected
From the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically the represented as
[tex]E = Z_{\frac{\alpha }{2} } * SE[/tex]
[tex]E = 1.96 * 0.0580[/tex]
[tex]E = 0.1137[/tex]
The 95% confidence interval is mathematically represented as
[tex](\r p_1 - \r p_2) - E < p_1 - p_2 < (\r p_1 - \r p_2) + E[/tex]
substituting value
[tex](0.8071 - 0.222) - 0.1137 < p_1 - p_2 < (0.8071 - 0.222) + 0.1137[/tex]
[tex]0.4714 < p_1 - p_2 <0.6988[/tex]
The oxygen treatment is effective because
1 the is no 0 in the interval telling us that the treatments are different
2 the upper and the lower limit are positive tell us that the proportion of those treated by the oxygen treatment is greater
g natasha is in a class of 30 students that selects 4 leaders. How many ways are there to select the 4 leaders so that natasha is one of the leaders
Answer:
3,654 different ways.Step-by-step explanation:
If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).
Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.
29C3 = 29!/(29-3)!3!
29C3 = 29!/(26!)!3!
29C3 = 29*28*27*26!/26!3*2
29C3 = 29*28*27/6
29C3 = 3,654 different ways.
This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55, then P( A| B) is:_________.
a. .19
b. 1.57
c. .64
d. .91
Answer:
P( A| B)= 0.35. None of the options are correctStep-by-step explanation:
Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A)P(B)
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,
then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.
From the condition above for independent events, P(A|B) = P(A) and since P(A) = 0.35, hence P(A|B) =0.35
Use A = -h(a + b) to find the area A of a
2
be trapezium when a = 15, b = 9 and h = 7
Step-by-step explanation:
Putting values
A = - 7(15 + 9)
A = - 7(24)
A = - 168
I need help please, m bda =
And m bca =
Step-by-step explanation:
Exterior angle BOA = 250°
Interior angle BOA = 360°- 250° = 110°
Now,
(A) BDA = interior angle BOA / 2 = 55°( Property of circles)
(B) From the figure, we observe that AOBC is a cyclic quadrilateral (i.e. sum of opposite angles is 180°).
Therefore, BCA + BOA = 180°
BCA = 180° - 110° = 70°
g Refer to the Number of Motorcycles Narrative} Are these probabilities true or false? ?a. P(X > 1)=0.35 b. P(X ≤ 2)=0.85 c. P(1 ≤ X ≤ 2)=.6 d. P(0 < X < 1)=0 e. P(1 ≤ X < 3)=.6 True False
Answer:
False.
Step-by-step explanation:
Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The variance distribution is the squared value of each the difference by the mean. values of probability are squared and then their sum is taken to calculate variance deviation. The number of motorcycles greater than 1 has probability of 0.35 so the probability of x = 1 must also be 0.35.
I cannot find the answer to my question
Answer:
14M
Step-by-step explanation:
7*2*M
14*M
14M
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Please help me solve for the median !!!
Answer:
50.93
Step-by-step explanation:
Add up the frequencies:
2 + 5 + 14 + 15 + 21 + 18 + 15 + 9 + 2 = 101
Divide by 2: 101/2 = 50.5
So the median is the 51st number, with 50 below and 50 above.
Add up the frequencies until you find the interval that contains the 51st number.
2 + 5 + 14 + 15 = 36
2 + 5 + 14 + 15 + 21 = 57
So the median is in the group 49.5 − 51.5. To estimate the median, we use interpolation. Find the slope of the line from (36, 49.5) to (57, 51.5).
m = (51.5 − 49.5) / (57 − 36)
m = 2/21
So at x = 51:
2/21 = (y − 49.5) / (51 − 36)
y = 50.93
What is the domain of f?
Answer:
-5 ≤x ≤6
Step-by-step explanation:
The domain is the values that x can take
X goes from -5 and includes -5 to x =6 and includes 6
-5 ≤x ≤6
Answer:
See attached!
Step-by-step explanation:
Calculate the nominal rate of interest convertible once every four years that is equivalent to a nominal rate of discount convertible quarterly. Let d^(4) be the nominal rate of discount convertible quarterly.
Answer:
i am having issues using the math editor and my time is almost running out. i added an attachment.
Step-by-step explanation:
which expression is equivalent to(x²y)³?
Answer:
x^6 y^3
Step-by-step explanation:
(x²y)³
We know that (ab) ^c = a^c * b^c
(x²y)³ = x^2 ^3 * y^3
We know that a^b^c = a^(b*c)
(x²y)³ = x^2 ^3 * y^3 = x^( 2*3) y^3 = x^6 y^3
The mathematics teacher proposes to his students that whoever determines their years of Experience as a teacher will have an extra point, for this they will have to solve the following expression
-5 + {4 * 6 + 3 + 1 + (3- (4-8) + (3-2)]}
How many years of experience does the teacher have?
Answer:
29 years of experience.
Step-by-step explanation:
So let's take the expression step by step. Remember that you need to follow the order of precedence here for the operations. Parentheses, exponentials, multiplication, and addition.
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( 4 - 8 ) + ( 3 - 2 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 - ( -4 ) + ( 1 ) ] }
-5 + { 4 * 6 + 3 + 1 + [ 3 + 4 + 1 ] }
-5 + { 4 * 6 + 3 + 1 + [ 8 ] }
-5 + { 24 + 3 + 1 + 8 }
-5 + { 36 }
29
So the teacher has 29 years of experience.
Cheers.
simplify theta(sin theta) ²/2tan theta
Step-by-step explanation:
When θ is very small, θ ≈ sin θ ≈ tan θ.
θ (sin θ)² / (2 tan θ)
θ³ / (2θ)
θ² / 2
The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly.Monthly Sales Salesperson After Before1 94 902 87 853 90 844 86 815 80 806 85 80
Answer:
it is clear that at 95% confidence that the bonus plan has increased the sales significantly, because if we observe you will notice that sales after is greater than sales before in all six cases.
Step-by-step explanation:
A 95% confidence interval as we have above is the range of values that we can say with utmost certainty and confidence that 95% chance it contains the true mean of the population. in other words we can say that a 95% confidence interval defines a range of values that you can be 95% certain contains the population mean.
A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
Diameter of wheel in millimetres is 660.4
Step-by-step explanation:
Diameter of wheel in inches = 26
given
1 inch = 25.4 millimeters
multiplying RHS and LHS by 26
26*1 inch = 26*25.4 millimeters
=>26 inch = 660.4 mm.
Thus, diameter of wheel in millimetres is 660.4
If 2 = 5, what is 2 3 − 4?
Answer:
27.5
Step-by-step explanation:
3 = 7.5
4 = 10
5*7.5=37.5-10=27.5
Seriously. 2=5 contradicts.
Given the polynomial, identify the coefficients and degree of each term:
Answer:
See below.
Step-by-step explanation:
The degree is simply the number of the exponent (or the sum) and the coefficient is simply the number in front of the term.
First Term: -7; Deg=0, Co=-7.
-7 is the same as saying -7x^0. Thus, the degree is 0.
Second Term: -x^4; Deg=4, Co=-1
-x^4 is the same as saying -1(x^4). Thus, the degree is 4 while the coefficient is -1.
Third Term: -5x^3; Deg=3, Co=-5
Again, this is the same as saying -5(x^3). Thus, the degree is 3 while the coefficient is -1.
Fourth Term: 7x; Deg=1, Co=7
7x is the same as saying 7x^1. Thus, the degree is 1 while the coefficient is 7.
Fifth Term: x^2; Deg=2, Co=2
x^2 is the same as 1(x^2). Thus, the degree is 2 while the coefficient is 1.
The leading coefficient is the first coefficient when the polynomial is placed in descending order based on degree number. First, arrange the polynomial into descending order based on the degree:
[tex]-x^4-5x^3+x^2+7x-7[/tex]
Thus, the leading coefficient is -1 (belonging to the x^4).
The degree of the leading term will always be the highest. In this case, it is 4.
The degree of the polynomial is the highest degree. In this case, it is 4.
Fine the surface area
Answer:
88 if a rectangular prism, 64 based on the net.
Step-by-step explanation:
A = 4 * 2
B = 6 * 2
C = 4 * 2
D = 6 * 2
E = 6 * 4
A/C= 8
B/D= 12
E = 24
2(8) + 2(12) + 24 = 64
Surface Area: 64
However, a rectangular prism must have 6 faces, so unless this is a box, the answer would be 88, and E = F, the last face.
The base of a right rectangular prism has an area of 173.6 square centimeters and a height of 9 centimeters. What is the volume, in cubic centimeters, of the right rectangular prism?
Answer:
D) 1562.4 cubic centimeters
Step-by-step explanation:
volume = area of the base × height
volume = 173.6cm² × 9 cm
volume = 1562.4 cm³
PLEASE HELP ME I DONT HAVE THAT MANY POINTS AND ITS DUE TODAY I NEED HELP ASAP
The table contains the data for your first weeks sales. Complete the table by calculating your commission and earnings for each day of the week
Answer with explanation:
Sales Commission(10% of sales)
$2,200 0.1×$2,200= $220
$2,000 0.1× $2,000= $200
$3,134 0.1×$3,134=$313.4
$2,417 0.1×$2,417=$241.7
$2,579 0.1×$2,579 =$257.9
The completed table is given as follows
Day Sales Commission Non-Sales pay Earning
(10% of sales) (Commission +Non Sales pay)
Mon $2,200 $220 $9.50 $220+ $9.50=$229.50
Tue $2,000 $200 $9.50 $200 +$9.50=$209.50
Thurs $3,134 $313.4 $9.50 $313.4+ $9.50=$322.9
Fri $2,417 $241.7 $9.50 $241.7+$9.50= $251.2
Sat $2,579 $257.9 $9.50 $257.9+$9.50=$267.4
What is the measure of FEG?
A. 30 degrees
B. 40 degrees
C. 50 degrees
D. 70 degrees
Please include ALL work!! <3
Answer:
C. 50 degrees
Step-by-step explanation:
Because 6x + 5x = 110° and x = 10
5×10 = FEG 50°
Find the product of the roots of the equation
xl-5x - 36 = 0
Answer:
Step-by-step explanation:
Hello, I assume that you mean
[tex]x^2-5x-36[/tex]
The product is -36.
[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
So in this example, it means that the sum is 5 and the product is -36.
Thank you
A probability experiment is conducted in which the sample space of the experiment is S={1,2,3,4,5,6,7,8,9,10,11,12}. Let event E={3,4,5,6,7,8}. Assume each outcome is equally likely. List the outcomes in Ec. Find P(Ec).The outcomes of Ec are {_____}P(Ec)=
Answer:
This list of all the outcome of [tex]E^c[/tex] is [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
[tex]P(E^c ) = 0.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample sample space is [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]
The number of elements in the sample space is [tex]n = 12[/tex]
The event is [tex]E = \{ 3,4,5,6,7,8 \}[/tex]
The number of outcomes in the Event is [tex]n_e = 6[/tex]
The objective in to obtain [tex]P(E^c)[/tex]
Now [tex]E^c[/tex] is the compliment of E and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as
[tex]nE^c = n - n_e[/tex]
substituting values
[tex]E^c = 12-6[/tex]
[tex]E^c = 6[/tex]
This list of all the outcomes of [tex]E^c[/tex] is
[tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]
Generally [tex]P(E^c )[/tex] which is the probability of [tex]E^c[/tex] is mathematically evaluated as
[tex]P(E^c ) = \frac{nE^c}{n}[/tex]
substituting values
[tex]P(E^c ) = \frac{6}{12}[/tex]
[tex]P(E^c ) = 0.5[/tex]
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99% confidence if (a) he uses a previous estimate of 22%?
Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is underfilling the bags. A 20 bag sample had a mean of 397 grams with a standard deviation of 13. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.
Answer:
Null hypothesis: μ = 407
Alternative hypothesis: μ < 407.
Step-by-step explanation:
In this case, the machine is SUPPOSED to fill the bag so that the bag weighs 407 grams. So, the null hypothesis will be that the machine is doing what it is supposed to be doing. And so, μ = 407 grams would be the null.
The worker thinks the machine is filling the bags to LESS THAN what it is supposed to. So, the alternative hypothesis is that the machine is NOT doing what it is supposed to and μ < 407 grams.
Hope this helps!
(3) In a group of 60 seldiers have enough food for
20 days - How many soldiers should leave the group
so that the food is enough for 100 days ? Find it.
Answer:
48 soldiers
Step-by-step explanation:
60 soldiers 20 days
x soldiers 100 days
60 x 20 = 1200 = 100x
Therefore x = 1200/100 = 12
60 - 12 = 48
Hope that helped!!! k
Answer:
30 Soldiers
Step-by-step explanation:
Given:
1) No of soldiers=60
No of days=20
2) No of days=100
No of soldiers=?
No of soldiers to leave=?
Solution:
Let us use the cross multiplication method.
Let x be the no of soldiers.
No of days No of soldiers
1) 20 60
2) 100 x
by cross multiplying,
20x=100 x 60
20x=600
x=600/20
x=30 soldiers
Therefore, No of soldiers to leave =60-30=30 soldiers
Suppose you do not know the population mean fee charged to H&R Block customers last year. Instead, suppose you take a sample of size n-8 and find a sample mean of 350. Assume that the distribution for fees is normally distributed with a sample standard deviation of $100.
i. Before conducting the survey, suppose you believed based on your previous observations, your best guess for population standard deviation of fee charged to H&R Block is $50. With this assumption in mind, What should your sample size n approximately be if you want:
Margin-of-Error of to be 2 % and confidence level to be 95 %?
Margin-of-Error of to be 4% and confidence level to be 95%?
Margin-of-Error of to be 4 % and confidence level to be 99%?
ii. 90% confidence interval for the population mean of fees H&R Block.
a. Calculate the margin of error (MOE) of x using a 10% significance level.
b. Calculate the 90 % confidence interval.
c. Suppose an analyst belief that the population mean fee is equal to $185. Using a 90% confidence level. can we conclude the analyst is right? Why or why not?
Answer:
i [tex]\to[/tex] a
[tex]n = 96040000[/tex]
i [tex]\to[/tex] b
[tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
[tex]n_2 =41602500[/tex]
ii[tex]\to[/tex]a
[tex]E = 58.16[/tex]
ii[tex]\to[/tex]b
[tex]291.84 < \mu < 408.16[/tex]\
ii[tex]\to[/tex]c
There is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 8[/tex]
The sample mean is [tex]\= x = \$ 350[/tex]
The sample standard deviation is [tex]\$ 100[/tex]
Considering question i
i [tex]\to[/tex] a
At [tex]E = 0.02[/tex]
given that the confidence level is 95% = 0.95
the level of significance would be [tex]\alpha =1-0.95 = 0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
So the sample size is mathematically evaluated as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2[/tex]
=> [tex]n =[ \frac{ 1.96 * 100}{ 0.02} ]^2[/tex]
=> [tex]n = 96040000[/tex]
i [tex]\to[/tex] b
At [tex]E_1 = 0.04[/tex] and confidence level = 95% => [tex]\alpha_1 = 0.05[/tex] => [tex]Z_{\frac{\alpha_1 }{2} } = 1.96[/tex]
[tex]n_1 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_1} ]^2[/tex]
=> [tex]n_1 =[ \frac{ 1.96 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_1 =24010000[/tex]
i [tex]\to[/tex] c
At [tex]E_2 = 0.04[/tex] confidence level = 99% => [tex]\alpha_2 = 0.01[/tex]
The critical value of [tex]\frac{\alpha_2 }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha_2 }{2} } = 2.58[/tex]
=> [tex]n_2 = [ \frac{Z_{\frac{\alpha_2 }{2} } * \sigma }{E_2} ]^2[/tex]
=> [tex]n_2 =[ \frac{ 2.58 * 100}{ 0.04} ]^2[/tex]
=> [tex]n_2 =41602500[/tex]
Considering ii
Given that the level of significance is [tex]\alpha = 0.10[/tex]
Then the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{100 }{\sqrt{8} }[/tex]
[tex]E = 58.16[/tex]
Generally the 90% confidence interval is mathematically evaluated as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]350 - 58.16 < \mu < 350 + 58.16[/tex]
=> [tex]291.84 < \mu < 408.16[/tex]
So the interpretation is that there is 90% confidence that the mean fee charged to H&R Block customers last year is in the interval .So there is insufficient evidence to conclude that the analyst is right because the population mean fee by the analyst does not fall within the confidence interval.
Find the length of AB¯¯¯¯¯¯¯¯ A. 19.56 B. 51.86 C. 42.99 D. 34.98
Answer:
Apllying cos on the triangle
cos(angle)= Base/ Hyp
cos(34)= 29/ AB
AB= 29/0.8290
AB=34.98
Step-by-step explanation:
The length of AB is 34.98 units which the correct answer would be an option (D).
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
Given that ΔABC
∠C = 90°
Here base = BC = 29 units and hypotenuse = AB
To determine the length of AB
Apply the cosine on the given right triangle
⇒ cos(θ) = Base/hypotenuse
⇒ cos(34) = 29/ AB
∴ cos(34°) = 0.8290
⇒ 0.8290 = 29/ AB
⇒ AB= 29/0.8290
⇒ AB = 34.98 units
Hence, the length of AB is 34.98 units
Learn more about Trigonometric functions here:
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