Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
A researcher is interested in determining the mean energy consumption of a new
compact florescent light bulb. She takes a random sample of 41 bulbs and determines
that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7.
When constructing a 97% confidence interval, which would be the most appropriate
value of the critical value?
A) 1.936
B) 2.072
C) 2.250
D) 2.704
E) 2.807
Answer:
The most appropriate value of the critical value is 2.289.
Step-by-step explanation:
We are given that a researcher takes a random sample of 41 bulbs and determines that the mean consumption is 1.3 watts per hour with a standard deviation of 0.7.
We have to find that when constructing a 97% confidence interval, which would be the most appropriate value of the critical value.
Firstly, as we know that the test statistics that would be used here is t-test statistics because we don't know about the population standard deviation.
So, for finding the critical value we will look for t table at (41 - 1 = 40) degrees of freedom at the level of significance will be [tex]\frac{1 - 0.97}{2} = 0.015[/tex] .
Now, as we can see that in the t table the critical values for P = 1.5% are not given, so we will interpolate between P = 2.5% and P = 1%, i.e;
[tex]\frac{0.015 - 0.025}{0.025-0.01}= \frac{\text{Critcal value}-2.021}{2.021-2.423}[/tex]
So, the critical value at a 1.5% significance level is 2.289.
Scores made on a certain aptitude test by nursing students are approximately normally distributed with a mean of 500 and a variance of 10,000. If a person is about to take the test what is the probability that he or she will make a score of 650 or more?
Answer:
0.0668 or 6.68%
Step-by-step explanation:
Variance (V) = 10,000
Standard deviation (σ) = √V= 100
Mean score (μ) = 500
The z-score for any test score X is:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = 650:
[tex]z=\frac{650-500}{100}\\z=1.5[/tex]
A z-score of 1.5 is equivalent to the 93.32nd percentile of a normal distribution. Therefore, the probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)=1-P(X\leq 650)\\P(X\geq 650)=1-0.9332\\P(X\geq 650)=0.0668=6.68\%[/tex]
The probability is 0.0668 or 6.68%
The probability that he or she will make a score of 650 or more is 0.0668.
Let X = Scores made on a certain aptitude test by nursing students
X follows normal distribution with mean = 500 and variance of 10,000.
So, standard deviation = [tex]\sqrt{10000}=100[/tex].
z score of 650 is = [tex]\frac{\left(650-500\right)}{100}=1.5[/tex].
The probability that he or she will make a score of 650 or more is:
[tex]P(X\geq 650)\\=P(z\geq 1.5)\\=1-P(z<1.5)\\=1-0.9332\\=0.0668[/tex]
Learn more: https://brainly.com/question/14109853
Find the amount of money in savings account if $3200 was deposited for 3 years at 40% interest compounded annually. Find the interest
Step-by-step explanation:
Formula for compound interest is given by
[tex]A = P(1 + R) ^{n} [/tex]
Where
A is the amount at the end of the period
P is the principal
R is the rate
n is the period
The interest = A - P
From the question
P = $ 3200
n = 3 years
R = 40%
So we have
[tex]A = 3200 \times 2.744[/tex]
A = $ 8780.80
The amount is $ 8780.80The interest is
$ 8780.80 - $3200
= $ 5580.80Hope this helps you
Question 20 of 21
In the triangle shown below, what is the approximate value of X?
12
O A. 20.78 units
O B. 26.83 units
O c. 12 units
D. 18 units
Answer:
O A. 20.78 units
Step-by-step explanation:
APEXX
The five numbers summary for a data set is shown below. What is the range of the data set? 3, 7, 11, 14, 16
Answer:
13
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
So, in order to find the range, you first order the data from least to greatest. Which it is already.
3, 7, 11, 14, 16
Then subtract the smallest value from the largest value in the set.
16 - 3 = 13
Hope this helps you out! : )
A manufacturer claims that the mean tensile strength of thread A exceeds the average tensile strength of thread B. To test his claim, 16 sample pieces of each type of thread are tested under similar conditions. Type A thread had a sample average tensile strength of 185 kg with a standard deviation of 6 kg, while type B thread had a sample average tensile strength of 178 kg with a standard of 9 kg. Assume that both populations are normally distributed and the variances are equal. Test the manufacturers claim using a = 0.05 level of significance.
The complete part of the first sentence is;
A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms.
Answer:
we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12
Step-by-step explanation:
We are given;
n_A = 16
n_B = 16
x'_A = 185 kg
x'_B = 178 kg
s_A = 6 kg
s_B = 9 kg
Let μ_A denote the population average tensile strength of thread A
Also, Let μ_B represent the population average tensile strength of thread B
Thus;
Null Hypothesis; H0;μ_A - μ_B ≤ 12
Alternative hypothesis;H1; μ_A - μ_B > 12
From the image attached, with a significance level of 0.05, the critical value for right tailed is 1.645. So we will reject the hypothesis is z > 1.645
Formula for z is;
z = (x'_A - x'_B - d_o)/√((s_A²/n_A) + (s_B²/n_B))
Plugging in the relevant values, we have;
z = (185 - 178 - 12)/√((6²/16) + (9²/16))
z = -5/2.7041634566
z = - 1.849
Since the z-value is less than 1.645,we fail to reject the null hypothesis and conclude that the difference of the average tensile strength of thread A and thread B is less than 12
Assume that IQ scores are normally distributed, with a standard deviation of 16 points and a mean of 100 points. If 60 people are chosen at random, what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points
Answer:
The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67
Step-by-step explanation:
Please check attachment for complete solution and step by step explanation
The marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation. C'(x)=x^-3/4 Find the cost of printing 142 more posters when 18 have already been printed.
The cost of printing 142 more posters when 18 have already been printed is $________.
(Round to the nearest cent as needed.)
Answer:
The cost of printing 142 more posters when 18 has already been printed is $5.57.
Step-by-step explanation:
We are given that the marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation C'(x)=x^-3/4.
The given equation is: [tex]C'(x) = x^{\frac{-3}{4} }[/tex]
The cost of printing 142 more posters when 18 have already been printed is given by;
Integrating both sides of the equation and using the limits we get;
[tex]\int_{a}^{b} C'(x) dx=\int_{18}^{142} x^{\frac{-3}{4}}dx[/tex]
As we know that [tex]\int\limits {x}^{n} \, dx = \frac{x^{n+1} }{n+1}[/tex] , so;
= [tex]\frac{x^{\frac{-3}{4}+1 } }{\frac{-3}{4}+1 } ]^{142} __1_8[/tex]
= [tex]\frac{x^{\frac{1}{4} } }{\frac{1}{4} } ]^{142} __1_8[/tex]
= [tex]4[x^{\frac{1}{4} } } ]^{142} __1_8[/tex]
= [tex]4[(142)^{\frac{1}{4} }- (18)^{\frac{1}{4} }} ][/tex]
= $5.57
Hence, the cost of printing 142 more posters when 18 has already been printed is $5.57.
Students in management science class have just received their grades on the first test. The instructor has provided information about the first test grades in some previous classes as well as the final average for the same students. Some of these grades have been sampled and are as follow:
1st test Grade 98 77 88 80 96 61 64 95 79
Final average 93 78 84 75 84 64 66 95 86
Develop a regression model that could be used to predict the final average in the course based on the first test grade.
Predict the final average of a students who made an 83 on the first test.
Give the value of r and r2 for this model.
Interpret the value of r2 in the context of this problem.
Answer:
The regression model is:
y = 20.29 + 0.73·x
Step-by-step explanation:
In this case a regression model is to be formed to predict the final average in the course based on the first test grade.
Use Excel to form the regression model.
The output is attached below.
The regression model is:
y = 20.29 + 0.73·x
Predict the final average of a students who made an 83 on the first test as follows:
y = 20.29 + 0.73·x
= 20.29 + 0.73 × 83
= 80.88
The final average of a students who made an 83 on the first test would be 80.88.
From the output:
R² = 0.839
Then the correlation coefficient will be:
[tex]r=\sqrt{R^{2}}=\sqrt{0.839}=0.91597\approx 0.92[/tex]
The value of r is 0.92.
The coefficient of determination R² specifies the percentage of the variance in the dependent-variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
In this case, the R² value of 0.839 implies that 83.9% of the variation in the final average can be explained by the grades in the first test.
Letters a, b, c, and d are angles measures. Lines m and n are cut by transversal p. At the intersection of lines p and m, labeled clockwise, from uppercase left, the angles are: a, b, c, blank. At the intersection of lines p and n, labeled clockwise, from uppercase left, the angles are: blank, blank, d, blank. Which equation is enough information to prove that lines m and n are parallel lines cut by transversal p? Select three options. a = c a = d c = d b + c = 180° b + d = 180°
Answer:
b, c, e
Step-by-step explanation:
the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right
Answer:
B. a=d
C. c=d
E. b + d=180°
Step-by-step explanation:
Got Correct On MyPath.
Lengths of pregnancies (in humans) have a mean of 267.6 days and a standard deviation of 15.4 days. A woman tracked her pregnancy and found it to be 309 days. Find the z score for 309 days. Is such a length unusual?
Answer:
The z-score is [tex]z = 2.65[/tex]
The length of days is not unusual
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 267.6 \ days[/tex]
The standard deviation is [tex]\sigma = 15.4 \ days[/tex]
The value considered is [tex]x = 309 \ days[/tex]
The z-score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma }[/tex]
[tex]z = \frac{309 - 267.6}{15.6 }[/tex]
[tex]z = 2.65[/tex]
Now given that the z-score is not greater than 3 then we can say that the length of days is not unusual
(reference khan academy)
Which of the following functions best describes this graph ?
Answer:
answer D
Step-by-step explanation:
Lets have a look to the graph and to the each of given functions.
As we can see in graph it intersects X in points (-3;0) and (-6;0) that means the function has the roots x1=-3 and x2=-6
Function A has the roots x1=+3 and x2=+6 => doesn' t fit
Function B has only 1 root x=2 , so can be factorized y=(x-2)^2 => doesn' t fit
Function C has 2 roots x1=4 and x2=-5 => doesn' t fit
Function D can be factotized as y=(x+6)*(x+3) so has 2 roots x1=-6 x2=-3 => exactly what we need!!!
We can also notice that the coefficient near x² is equal to 1 and is positive.
That means the legs of the graph directed up,- this is exactly like in our graph. It gives us extra argument why we choose D.
A college administrator predicts that the proportion of students that are nursing majors is greater than 40%. To test this, a group of 400 students are randomly selected and it's determined that 190 are nursing majors. The following is the setup for this hypothesis test:
H0:p=0.40
Ha:p>0.40
In this example, the p-value was determined to be 0.001. Find the conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Answer:
Step-by-step explanation:
Using the following data:
H0:p=0.40 (null hypothesis)
Ha:p>0.40 (alternative hypothesis)
The p-value was determined to be 0.001.
a significance level of 5%
Since the p value (0.001) is less than the significance level (0.05), we will reject the null hypothesis and then we would conclude that the proportion of students that are nursing majors is greater than 0.4.
Answer:
p value= 0.131
Step-by-step explanation:
Since we have calculated the test statistic, we can now proceed to find the p-value for this hypothesis test.Using the test statistic and since the hypothesis test is a left tailed test, the p-value will then be the area under the standard normal curve to the left of the test statistic of -1.12.Using the Standard Normal table given above, the area under the standard normal curve to the left of the test statistic of -1.12 is 0.131 (rounded to 3 decimal places.Thus the p-value = 0.131.
2 (3z-4) <16 Which one of the following values of z is a solution for the inequality
Answer:
z < 4
Step-by-step explanation:
2(3z-4) < 16
Divide by 2 on both sides
3z-4 < 8
Add 4 to both sides
3z < 12
Divide by 3 on both sides
z < 4
Which statement is true about the function f(x)= -x?
O The domain of the graph is all real numbers.
The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
The range of the graph is all real numbers less than or equal to 0.
Answer:
The domain of the graph is all real numbers less than or equal to 0.
Step-by-step explanation:
Hello,
We know that we cannot take square root of negative numbers, so we must have
[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]
So the domain of the graph is all real numbers less than or equal to 0.
For information, I attached the graph so that we can verify it.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The coldest temperature ever recorded in New York City was -15F on Feb 9, 1934. The next day, the temperature rose
Write an expression for the temperature on Feb 10
Answer:
x = -15 + y
Step-by-step explanation:
Let next days temperature be x and the temperature rise be y
=> x = -15 + y
The next day's temperature will be more since it "rose".
Answer:
[tex]\boxed{x=-15+y}[/tex]
Step-by-step explanation:
Let the temperature on Feb 10, 1934 be x.
Let the temperature increase be y.
On Feb 9, the temperature was -15F.
On Feb 10, the temperature increased.
[tex]x=-15+y[/tex]
What is the slope of the line described by the equation y-1=3x
Answer:
Hey there!
The line can be expressed into y intercept form, y=3x+1.
Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.
Let me know if this helps :)
Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $21.51 and a 95% confidence interval of [$20.52, $22.48]. Which of the following statements is a valid interpretation of the confidence interval?
a. 95% of all taxi fares are between $20.52 and $22.48.
b. We are 95% confident that a randomly selected taxi fare will be between $20.52 and $22.48.
c. We can report that the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.
d. With 95% confidence
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x =[/tex]$21.51
The 95% confidence level interval is [$ 20.52 , $22.48]
Generally the 95% confidence level interval is mathematically represented as
[tex]\= x - MOE < \mu < \= x + MOE[/tex]
Where MOE is the margin of error which defines in percentage the amount by which the sample mean taxi fare(for the 7 taxi ) will differ from the average taxi fare between Logan Airport and downtown Boston will fall between
Also [tex]\mu[/tex] is the average taxi fare between Logan Airport and downtown Boston
So we see that the this 95% confidence level interval tells us that the average taxi fare between Logan Airport and downtown Boston will fall between $20.52 and $22.48.
boxes of raisins are labled as containing 22 ounces. Following are the weights, in the ounces, of a sample of 12 boxes. It is reasonable to assume that the population is approximatly normal.
21.88 21.76 22.14 21.63 21.81 22.12 21.97 21.57 21.75 21.96 22.20 21.80
Required:
Construct a 99% confidence interval for the mean weight.
Answer:
The 99 % confidence interval on the basis of mean is ( 21.7393 ; 22.0257)
Step-by-step explanation:
Mean = Sum of observations / Number of observations
Mean = 21.88 +21.76 +22.14 +21.63+ 21.81 +22.12+ 21.97+ 21.57+ 21.75+ 21.96 +22.20 +21.80/ 12
Mean =x`= 262.59/12= 21.8825
Standard Deviation = s= ∑x²/n - ( ∑x/n)²
∑x²/n= 478.7344 +473.4976 + 490.1796+467.8569+ 475.6761 + 489.2944+ 482.6809+ 465.2649+ 473.0625+ 482.2416 +492.84 + 475.24/ 12
∑x²/n= 5746.5689/12= 478.8807 = 478.881
Standard Deviation = s= ∑x²/n - ( ∑x/n)²
s= 478.881- (21.8825)²= 478.881-478.843= 0.037
The confidence limit 99% for the mean will be determined by
x` ± α(100-1) √s/n
Putting the values in the above equation
= 21.8825 ± 2.58 √0.037/12
Solving the square root
= 21.8825 ± 2.58 (0.05549)
Multiplying the square root with 2.58
=21.8825 ± 0.1432
Adding and subtracting would give
21.7393 ; 22.0257,
Hence the 99 % confidence interval on the basis of mean is ( 21.7393 ; 22.0257)
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
Junk Bonds. 130%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answer:
(T, C, J) = (in dollars)
(10000, 10000, 0),
(15000, 4915.97, 84.03),
(18181.82, 1680.67, 137.51)
Step-by-step explanation:
There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.
__
For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...
proportion at I1 = (I2 -I)/(I2 -I1)
Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:
proportion at I2 = (I -I1)/(I2 -I1)
__
We want an overall interest rate of $2000/$20000 = 10%.
Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.
If we use only the options for 9% and 11% (no junk bonds), then we can compute ...
proportion at 9% = (11 -10)/(11 -9) = 1/2
proportion at 11% = (10 -9)/(11 -9) = 1/2
1st Option:
$10,000 in treasury bills; $10,000 in corporate bonds
__
Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:
proportion at 9% = (13 -10)/(13 -9) = 3/4
Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:
proportion at 11% = (130 -13)/(130 -11) = 117/119
proportion at 130% = (13 -11)/(130 -11) = 2/119
2nd option:
$20,000 × 3/4 = $15,000 in treasury bills
$5000 × 117/119 = $4,915.97 in corporate bonds
The remaining amount, $84.03 in junk bonds
__
Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...
proportion at 9% = (20 -10)/(20 -9) = 10/11
And the proportion at 11% will be ...
proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)
3rd option:
$20,000 × 10/11 = $18,181.82 in treasury bills
$1,818.18 × 110/119 = $1,680.67 in corporate bonds
The remaining amount, $137.51 in junk bonds
_____
Additional comment
The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)
If we assume that asset X has an expected return of 10 and a variance of 10, then its coefficient of variation is:
Answer: Its coefficient of variation = 0.316
Step-by-step explanation:
The formula to find the coefficient of variations:
Coefficient of variation: [tex](\dfrac{\sqrt{\text{variance}}}{\text{return}})[/tex]
Given: Asset X has
Variance = 10
Expected return = 10
then, coefficient of variation [tex]=\dfrac{\sqrt{10}}{10}=\dfrac{1}{\sqrt{10}}\approx0.316[/tex]
Hence, its coefficient of variation = 0.316
Y+15<3 what is the solution
Answer:
y < -12
Step-by-step explanation:
Step 1: Subtract 15 on both sides
y + 15 - 15 < 3 - 15
y < -12
This inequality means the any number smaller than -12 would work. So:
-123415235 would work
-1234 would work
-46527 would work
2 would NOT work
6 would NOT work
Answer:
[tex]y < - 12[/tex]Step-by-step explanation:
[tex]y + 15 < 3[/tex]
Move constant to RHS and change its sign:
[tex]y < 3 - 15[/tex]
Calculate the difference
[tex]y < - 12[/tex]
Hope this helps..
Good luck on your assignment..
What is the focus of the parabola? y=−1/4x2−x+3
Answer: Focus = (-2, 3)
Step-by-step explanation:
[tex]y=-\dfrac{1}{4}x^2-x+3\\\\\rightarrow a=-\dfrac{1}{4},\ b=-1[/tex]
First let's find the vertex. We do that by finding the Axis-Of-Symmetry:
[tex]AOS: x=\dfrac{-b}{2a}\quad =\dfrac{-(-1)}{2(\frac{-1}{4})}=\dfrac{1}{-\frac{1}{2}}=-2[/tex]
Then finding the maximum by inputting x = -2 into the given equation:
[tex]y=-\dfrac{1}{4}(-2)^2-(-2)+3\\\\y=-1+2+3\\\\y=4[/tex]
The vertex is: (-2, 4)
Now let's find p, which is the distance from the vertex to the focus:
[tex]a=\dfrac{1}{4p}\\\\\\-\dfrac{1}{4}=\dfrac{1}{4p}\\\\\\p=-1[/tex]
The vertex is (-2, 4) and p = -1
The focus is (-2, 4 + p) = (-2, 4 - 1) = (-2, 3)
Which of the following is an exterior angle of triangle BHE? Yes or no
Answer:
Im not 100% sure, but I think it is:
No
No
No
Yes
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. A double-blind experiment is used to increase the placebo effect. Choose the correct answer below. A. The statement is false. Double blinding has no effect on the placebo effect. B. The statement is false. Double blinding is used to increase the randomization. C. The statement is true. D. The statement is false. Double blinding is used to decrease the placebo effect.
Answer:
D. The statement is false. Double blinding is used to decrease the placebo effect.
Step-by-step explanation:
In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.
Therefore, a double-blind experiment is used to decrease the placebo effect.
In the following problem, the expression is the right side of the formula for cos (alpha - beta) with particular values for alpha and beta. cos (79 degree) cos (19 degree) + sin (79 degree) sin (19 degree)
Identify alpha and beta in each expression.
The value for alpha: degree
The value for beta: degree
Write the expression as the cosine of an angle. cos degree
Find the exact value of the expression. (Type an exact answer, using fraction, radicals and a rationalized denominator.)
Answer:
1. [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
2. [tex]cos(60)[/tex]
3. [tex]cos(60) = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]cos(\alpha - \beta )[/tex]
[tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
Solving for [tex]\alpha[/tex] and [tex]\beta[/tex]
In trigonometry;
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
Equate the above expression to [tex]cos(79)cos(19) + sin(79)sin(19)[/tex]
[tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex] and [tex]cos(\alpha - \beta ) = cos(79)cos(19) + sin(79)sin(19)[/tex]
By comparison
[tex]cos\alpha\ cos\beta + sin\alpha\ sin\beta = cos(79)cos(19) + sin(79)sin(19)[/tex]
Compare expression on the right hand side to the left hand side
[tex]cos\alpha\ cos\beta = cos(79)cos(19) \\\\ sin\alpha\ sin\beta = sin(79)sin(19)[/tex]
This implies that
[tex]cos\alpha\ = cos(79)\\cos\beta = cos(19) \\\\ and\\\\sin\alpha\ = sin(79)\\sin\beta = sin(19)[/tex]
By further comparison
[tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex]
Substitute [tex]\alpha = 79[/tex] and [tex]\beta = 19[/tex] in [tex]cos(\alpha - \beta )[/tex]
[tex]cos(\alpha - \beta ) = cos(79 - 19)[/tex]
[tex]cos(\alpha - \beta ) = cos(60)[/tex]
Hence, the expression is [tex]cos(60)[/tex]
Solving for the exact values;
Express [tex]cos(60)[/tex] as a difference of angles
[tex]cos(60) = cos(90 - 30)[/tex]
Recall that [tex]cos(\alpha - \beta ) = cos\alpha\ cos\beta + sin\alpha\ sin\beta[/tex]
So;
[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex]
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In trigonometry;
[tex]cos(90) = 0[/tex]; [tex]cos(30) = \frac{\sqrt{3}}{{2}}[/tex]; [tex]sin(90) = 1[/tex]; [tex]sin(30) = \frac{1}{2}[/tex];
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[tex]cos(90- 30 ) = cos(90) cos(30) + sin(90) sin(30)[/tex] becomes
[tex]cos(90- 30 ) = 0 * \frac{\sqrt{3}}{2} + 1 * \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = 0 + \frac{1}{2}[/tex]
[tex]cos(90- 30 ) = \frac{1}{2}[/tex]
Hence;
[tex]cos(60) = \frac{1}{2}[/tex]
Can two events with nonzero probabilities be both independent and mutually exclusive? Choose the correct answer below. A. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities add up to one. B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero. C. Yes, two events with nonzero probabilities can be both independent and mutually exclusive when their probabilities are equal. D. No, two events with nonzero probabilities cannot be independent and mutually exclusive because independence is the complement of being mutually exclusive.
Answer:
Step-by-step explanation:
B. No, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
For two mutually exclusive events , with non- zero probabilities , when one occurs , the other can not happen . In this way they become dependent events . In this way , for two events to be both independent and mutually exclusive , at least one of the two events must have zero probability .
It should be noted that two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
Mutually exclusive events simply means the events that cannot take place at the same time. The occurrence of one of the events will prevent the other event from occuring.
Therefore, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually exclusive, then when one of them occurs, the probability of the other must be zero.
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The population density, D, in people/square mile (p/mi²), for the large city Westport is related to the distance x (in miles) from the city’s center by the equation:________.
D=4300x /x^2 + 40.
a. Describe what happens to West-port's population density as the distance from the city’s center changes from one mile to six miles. What may explain this phenomenon?
b. Describe what happens to West-port's population density as the distance from the city’s center changes from ten miles to thirty miles.
c. Describe the end-behavior of this function? What may explain this phenomenon?
d. In what areas of the city is the population density below 200 p/mi²?
Answer:
Step-by-step explanation:
D=4300x /x² + 40.
x = 1
D = 4300 / 41 = 104.88 p / mi²
x = 6
D = 25800 / 76
= 339.47 p / mi²
Population density increases as we go away from city's centre .
b )
x = 10
D=4300x /x² + 40.
D = 307.14 p/ mi²
x = 30
D = 137.23 p / mi²
Population decreases .
c )
when x is very high , density will decrease due to squared denominator whose value increases very fast .
d )
D < 200
4300x /x² + 40 < 200
4300 x < 200 x² + 8000
43 x < 2 x² + 80
2 x² - 43 x + 80 > 0
( x - 19.44 ) ( x - 2.05 ) > 0
Range x < 2.05
x > 19.44
7x-x combine the like terms to create an equivelent expression
Answer:
6x
Step-by-step explanation:
7x - x
Factor out x
x( 7-1)
6x
Answer:
6x
Step-by-step explanation:
7x - x
Apply rule : a = 1a
x = 1x
7x - 1x
Factor out x.
(7 - 1)x
(6)x
67.805 what is the value of the 0 help please asap!
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)