First pair of equations :
[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]x+2y=30\ ..(iii)[/tex]
By Elimination Method, Add (i) and (ii) (term with x eliminate), we get
[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]
put y= 14.4 in (iii), we get
[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]
hence, x=1.2 and y =14.4
Second pair of equations :
[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]
Elimination Method, Add (i) and (ii) (term with y eliminate) , we get
[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]
put [tex]x=\dfrac{18}{13}[/tex] in (i), we get
[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]
hence, [tex]x=\dfrac{18}{13}[/tex] and [tex]y=\dfrac{-45}{13}[/tex] .
I am performing a before and after evaluation on 30 students who have taken a keyboarding class. I want to see if the course improved their words per minute keyed.
Required:
a. State the Null and Alternate Hypothesis.
b. The statistic that I would use is:_________
c. What would my t critical be for this calculation at a 0.10 level of significance?
d. If my t calculated = 1.62, would I reject or fail to reject the null hypothesis?
Answer:
a)
H₀ : µd = 0
H₁ : µd < 0
b)
The test statistic is
tₙ₋₁ = α / s√n
c)
at 0.10 level of significance,
tₙ₋₁ , ₐ
t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311
d)
given that T(critical) = 1.62
∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311
at 10% level of significance,
REJECT H₀
Since 1.62 > 1.311, we can reject the null hypothesis.
Which rule describes this transformation? (Zoom in to see it clearly)
Answer:
(x,y) -> (x+6, y-3)
Step-by-step explanation:
I followed c and it translated like the last ans choice.
Log 1/10 how do you convert this without a calculator
Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
22)
Subtract (4 - 21) - (3 - 51)
A)
1+3i
B)
1-71
7+3i
D)
7-7i
Answer:
1 +3i
Step-by-step explanation:
(4 - 2i) - (3 - 5i)
Subtract the reals
4 - 3 =1
Subtract the imaginary
-2i - -5i
-2i + 5i = 3i
1 +3i
Answer:
A
Step-by-step explanation:
Subtract all real numbers
4 - 3 = 1
Subtract all imaginary numbers
-2i - (-5i) = 3i
Put back together
1 + 3i
Best of Luck!
Factor 13ab3 + 39a2b5.
[tex]13ab^3+39a^2b^5\\\\\boxed{\boxed{\boxed{13ab^3(1+3ab^2)}}}\\\\[/tex]
Brazil number one.
Answer:
there's no answer for that equation
how do you figure out ratios? the problem is 12 quarters to 34 dollars. thanks
Step-by-step explanation:
When you have a ratio, you put one number as the numerator and than one number as the denominator.
so it would be (12/34)=(x/68)
In this example I made the ratio you are comparing it to have 68 dollars, so when you solve for the amount of quarters you need it should be 24, since all of the numbers in this example are just being doubled.
To solve for x, you multiply 68 on both sides of the equation, 68×(12/34)=x
24=x
So this proves that this is how ratios, are used. It also does not matter what number you place on the numerator or denominator.
Question 1 (5 points)
The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale
factor 2/3 about the origin. Find the endpoints of the dilated line segment.
OA) (-2, 4), (6,8)
B) (2, 4). (6,8)
OC) (4, -2), (6,8)
OD) (-2,4), (8,6)
Answer: A) (-2, 4), (6,8)
Step-by-step explanation:
When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).
Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.
Let A' and B' b the endpoints of the dilated line segment.
Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]
[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]
Hence, the correct option is A) (-2, 4), (6,8)
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
which rate can you set 7 miles over 1 hour equal to in order to find the distance traveled in 49 hours at 7 miles per hour
Answer:
Step-by-step explanation:
time = 49 hours
speed = 7 miles/hour
speed = distance / time
∴ distance = speed × time
= 7 × 49
= 343 miles
If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?
Answer:
252
Step-by-step explanation:
Divide 7812 by 31 and we get the average daily answer... Hope this helps!!
Which polynomial is prime? x2 + 9 x2 – 25 3x2 – 27 2x2 – 8
This is a sum of squares, which cannot be factored over the real numbers. You'll need to involve complex numbers to be able to factor, though its likely your teacher hasn't covered that topic yet (though I could be mistaken and your teacher has mentioned it).
Choice B can be factored through the difference of squares rule. Therefore, choice B is not prime.
Choice C and D can be factored by pulling out the GCF and then use the difference of squares rule afterward. So we can rule out C and D as well.
Answer:
A
Step-by-step explanation:
because it has a + sign
Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?
Answer:
4/5
Step-by-step explanation:
237/1185 = .2 = 1/5
meaning there's 4/5 left
A household survey of 10 families was conducted by students of 4th year MBBS. In the collected data, the ages of heads of families were: 32, 34, 35, 36, 36, 42, 44, 46, 48, and 52. The mean age of heads of families is
a. 36
b. 38.5
c. 40
d. 40.5
e. 42
Answer:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14
Step-by-step explanation:
Which polynomial is prime?
7x2 – 35x + 2x – 10
9x3 + 11x2 + 3x – 33
10x3 – 15x2 + 8x – 12
12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT
Simple math! What is the issue with my work? I got it wrong.
Answer:
x = 6
Step-by-step explanation:
In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.
The final value of x will be 6.
[tex] PQ^2 + QO^2 = PO^2 \\
x^2 + 8^2 = (4+x)^2 \\
x^2 + 64 = 16 + 8x + x^2 \\
64 = 16 + 8x \\
64 - 16 = 8x \\
48 = 8x \\
6 = x\\[/tex]
A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing (Simplify your answer.) nothing (Type an integer or decimal rounded to three decimal places as needed.)
Complete Question
A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26
Answer:
The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]
The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is
[tex]\sigma _{\= x} = 2.746[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 77[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
The sample size is [tex]n = 26[/tex]
Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is mathematically represented as
[tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]
[tex]\sigma _{\= x} = 2.746[/tex]
Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is equivalent to the population mean i.e
[tex]\mu_{\= x } = \mu[/tex]
[tex]\mu_{\= x } = 77[/tex]
The solution system to 3y-2x=-9 and y=-2x+5
Answer:
[tex]\boxed{(3,-1)}[/tex]
Step-by-step explanation:
Hey there!
Well to find the solution the the given system,
3y - 2x = -9
y = -2x + 5
So to find x lets plug in -2x + 5 for y in 3y - 2x = -9.
3(-2x + 5) - 2x = -9
Distribute
-6x + 15 - 2x = -9
-8x + 15 = -9
-15 to both sides
-8x = -24
Divide -8 to both sides
x = 3
Now that we have x which is 3, we can plug in 3 for x in y = -2x + 5.
y = -2(3) + 5
y = -6 + 5
y = -1
So the solution is (3,-1).
Hope this helps :)
In recent years, the interest rates on home mortgages have declined to less than 6%. However, a
recent study shows that the rate charged on credit card debt is more than 14%. A sample of 10 credit
cards showed that the mean rate charged is 15.64% with a standard deviation of 1.561%. At 1% level
of significance, is it reasonable to conclude the mean rate charged is greater than 14%?
Answer:
Yes it is reasonable to conclude the mean rate charged is greater than 14%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 0.14[/tex]
The sample size is [tex]n = 10[/tex]
The sample mean is [tex]\= x = 0.1564[/tex]
The standard deviation is [tex]\sigma = 0.01561[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o: \mu = 0.14[/tex]
The alternative hypothesis is [tex]H_a : \mu > 0.14[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.1564 - 0.14 }{ \frac{0.01561 }{\sqrt{10} } }[/tex]
[tex]t = 3.322[/tex]
Now the p-value obtained from the z-table is
[tex]p-value = P(t > 3.322) = 0.00044687[/tex]
Since the [tex]p-value < \alpha[/tex] then we reject the null hypothesis, hence we can conclude that the mean rate charged is greater than 14%
PLS HELP:Find all the missing elements:
Answer:
b = 9.5 , c = 15Step-by-step explanation:
For b
To find side b we use the sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |b| }{ \sin(B) } [/tex]a = 7
A = 23°
B = 32°
b = ?
Substitute the values into the above formula
That's
[tex] \frac{7}{ \sin(23) } = \frac{ |b| }{ \sin(32) } [/tex][tex] |b| \sin(23) = 7 \sin(32) [/tex]Divide both sides by sin 23°
[tex] |b| = \frac{7 \sin(32) }{ \sin(23) } [/tex]b = 9.493573
b = 9.5 to the nearest tenthFor cTo find side c we use sine rule
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]C = 125°
So we have
[tex] \frac{7}{ \sin(23) } = \frac{ |c| }{ \sin(125) } [/tex][tex] |c| \sin(23) = 7 \sin(125) [/tex]Divide both sides by sin 23°
[tex] |c| = \frac{7 \sin(125) }{ \sin(23) } [/tex]c = 14.67521
c = 15.0 to the nearest tenthHope this helps you
The scores for all the Algebra 1 students at Miller High on a test are normally distributed with a mean of 82 and a standard deviation of 7. What percent of students made scores above 89?
Answer:
15.7% of students made above an 89.
Step-by-step explanation:
If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%
please help! algebra 2 work
A bike wheel. A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?
Answer:
its multiple choice
A. 26inches (1inch/25.4mm)
B. 26inches (25.4mm/1inch)
C. 25.4inches (1mm/26inch)
D. 26inches (1mm/25.4inch)
and its b
According to a report in USA Today, more and more parents are helping their young adult children purchase their first home. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion
Answer:
the margin of error
= 1.96 x 0.0632
= 0.124
Step-by-step explanation:
this question has the sample size, n = 40
8 people have received help from their parents from this sample.
8/40 = 0.2
which is the sample proportion
z = 1 - 0.2
= 0.8
to calculate standard error
√pz/n
= √0.2 x 0.8/40
= √0.16/40
= 0.0632
at 95% confidence level
z(alpha/2) = 1.96
therefore the margin of error
= 1.96 x 0.0632
= 0.124
Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Part II: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.
#1: Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.
(a) lower bound: ______ (please round to four decimal places)
(b) upper bound: _____ (please round to four decimal places)
#2: Interpret the confidence interval in context:
(A) We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it
(B) 90% of Americans choose not to go to college because they cannot afford it
(C) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
#3: Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
(a) A survey should include at least ________ people.
Answer:
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval
(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
Step-by-step explanation:
We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans who decide to not go to college = 48%
n = sample of American adults = 331
p = population proportion of Americans who decide to not go to
college because they cannot afford it
Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.
So, 90% confidence interval for the population proportion, p is ;
P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level
of significance are -1.645 & 1.645}
P(-1.645 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.645) = 0.90
P( [tex]-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\hat p-p[/tex] < [tex]1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
P( [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.90
90% confidence interval for p = [ [tex]\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] , [tex]0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }[/tex] ]
= [0.4348, 0.5252]
(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].
(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.
3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }[/tex]
[tex]\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}[/tex]
[tex]\sqrt{n}[/tex] = 54.79
n = [tex]54.79^{2}[/tex]
n = 3001.88 ≈ 3002
Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.
. One sample has M = 18 and a second sample has M = 14. If the pooled variance for the two samples is 16, what is the value of Cohen’s d?
Answer:
Cohen's d : 1.00
Step-by-step explanation:
We know that M₁ = 18, and M₂ = 14. Given that the pooled variance for the these two samples are 16, S²Pooled = 16, and therefore S - pooled = 4.
The formula to solve for the value of Cohen's d is as follows,
d = M₁ - M₂ / S - pooled,
d = 18 - 14 / 4 = 4 / 4 = 1
Therefore the value of Cohen's d = 1
Determine whether each equation has one solution, no solution or infinitely many solutions. 4x + 10 = 2(2x + 5) 4x - 5 = 4x + 10 4x - 5 = -5
Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
My town has two cell phone providers. The provider Don’tTalkMuch charge is $80 per month plus 1 dollar per hour the provider TalkLots charges $20 per month plus 4 dollars per hour how much do you have to use your phone in a month in order for Don’tTalkMuch’s much is a deal to be better for you?
Answer:
The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Step-by-step explanation:
Call X is the number of hours that the author uses on monthly basis.
Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.
Total bill value if the author uses TalkLots service is $20 + $4X
The total fees between 2 providers equal as:
$80 + $1 X = $20 + $4X => 3X = $60 => X = 20
Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Given a dataset with the following properties:
mean = 50
median = 40
standard deviation = 5
What is the shape of the distribution?
Answer:
The distribution is positively skewed.
Step-by-step explanation:
A measure of skewness is defined in such a way that the measure should always be zero when the distribution is symmetric and measure should be a pure number i.e independent of origin and units of measurement.
The shape of the distribution can be found by finding the coefficient of skewness.
The coefficient of skewness can be found by
Sk= 3(Mean-Median)/ Standard Deviation
Sk= 3( 50-40)5= 30/5=6
The shape will be positively skewed.
In a positively skewed distribution the mean > median > mode. It has a long right tail.
Using the skewness formula, it is found that the distribution is right-skewed.
------------------
The skewness of a data-set with mean M, median [tex]M_e[/tex] and standard deviation s is given by:[tex]S = \frac{3(M - M_e)}{s}[/tex]
If |S| < 0.5, the distribution is said to be symmetric.If S <-0.5, the distribution is left-skewed.If S > 0.5, the distribution is right-skewed.------------------
Mean of 50, thus, [tex]M = 50[/tex]Median of 40, thus [tex]M_e = 40[/tex]Standard deviation of 5, thus, [tex]s = 5[/tex]The coefficient is:
[tex]S = \frac{3(M - M_e)}{s} = \frac{3(50 - 40)}{5} = \frac{30}{5} = 6[/tex]
Thus, the distribution is right-skewed.
A similar problem is given at https://brainly.com/question/24415645
What is the value of the mean from the following set of data: 12,10, 11, 8, 6, 5, 3, 7, 9. Round to the nearest hundredth.
Answer:
7.88 or 7.9
Step-by-step explanation:
To find the mean, we need to do:
=> (12 + 10 + 11 + 8 + 6 + 5 + 3 + 7 + 9) / 9
=> 71/9
=> 7.88 or 7.9
I divided the sum of all numbers by 9 because we added 9 numbers.
Multiple-Choice Questions
1. In 1995, Diana read 10 English books and 7 French books. In 1996, she read twice as many French books as English books. If 60% of the books that she read during the 2 years were French, how many English and French books did she read in 1996?
(A) 16
(B) 26
(0) 32
(D) 48
Answer:
(D) 48
Step-by-step explanation:
Let English book = x
Let french book = y
In 1995 x= 10
Y= 7
In 1996
Y = 2x
Total book read in the two years
0.6(Total) = y
0.4(total) = x
We don't know the exact amount of books read in 1996.
Total = 10 + 7 +x +2x
Total = 17+3x
0.6(total) = 7+2x
0.6(17+3x) = 7+2x
10.2 +1.8x= 7+2x
10.2-7= 2x-1.8x
3.2= 0.2x
3.2/0.2= x
16= x
So she read 16 English book
And 16*2 = 32 french book Making it a total of 16+32= 48 books in 1996
How many petals are on the graph? Find the trigonometric form of a given function.
Answer:
Attachment 1 : Option A,
Attachment 2 : Option C
Step-by-step explanation:
( 1 ) Here we know that " n " is 6. Now remember if n is odd, the number of petals on the graph will be n. However if n is even, the number of petals on the graph will be 2n.
6 is even, and hence the number of petals will be 2(6) = 12 petals. Solution : 12 petals
( 2 ) To solve such problems we tend to use the equation [tex]z = x + y * i = r(cos\theta +isin\theta)[/tex] where [tex]r = \sqrt{x^2+y^2}[/tex] etc. Here I find it simpler to see each option, and convert each into it's standard complex form. It might seem hard, but it is easy if you know the value of (cos(5π / 3)) etc...
The answer here will be option c, but let's prove it,
cos(5π / 3) = 1 / 2,
sin(5π / 3) = [tex]-\frac{\sqrt{3}}{2}[/tex]
Plugging those values in for " [tex]8\left(\cos \left(\frac{5\pi }{3}\right)+i\sin \left(\frac{5\pi }{3}\right)\right)[/tex] "
[tex]8\left(-\frac{\sqrt{3}i}{2}+\frac{1}{2}\right)[/tex]
= [tex]8\cdot \frac{1}{2}-8\cdot \frac{\sqrt{3}i}{2}[/tex] = [tex]4-4\sqrt{3}i[/tex]
Hence proved that your solution is option c.
