Answer and Step-by-step explanation:
This is a complete question
Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time. Identify the nullhypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.
The computation is shown below:
The null and alternative hypothesis is
[tex]H_0 : p = 0.80[/tex]
[tex]Ha : p < 0.80[/tex]
[tex]\hat p = \frac{x}{ n} \\\\= \frac{74}{97}[/tex]
= 0.7629
Now Test statistic = z
[tex]= \hat p - P0 / [\sqrtP0 \times (1 - P0 ) / n][/tex]
[tex]= 0.7629 - 0.80 / [\sqrt(0.80 \times 0.20) / 97][/tex]
= -0.91
Now
P-value = 0.1804
[tex]\alpha = 0.01[/tex]
[tex]P-value > \alpha[/tex]
So, it is Fail to reject the null hypothesis.
There is ample evidence to demonstrate that less than 80 percent of the time reports that these polygraph findings are accurate.
A normal population has a mean of 65 and a standard deviation of 13. You select a random sample of 25. Compute the probability that the sample mean is: (Round your z values to 2 decimal places and final answers to 4 decimal places): Greater than 69.
Answer:
0.0618
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 69
μ is the sample mean = population mean = 65
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 25
σ = 13/√25
σ = 13/5 = 2.6
Sample standard deviation = 2.6
z = (69 - 65) / 2.6
z = 4/2.6
z = 1.53846
Approximately to 2 decimal places = 1.54
Using the z score table to determine the probability,
P(x = 69) = P(z = 1.54)
= 0.93822.
The probability that the sample mean is greater than 69 is
P(x>Z) = 1 - 0.93822
P(x>Z) = 0.06178
Approximately to 4 decimal places = 0.0618
What is the value of this expression when x = -6 and y = — 1/2? 4(x^2+3) -2y A. -131 B. -35 C. 57 1/2 D. 157
Answer:
D
Step-by-step explanation:
[tex]4(x^2+3)-2y\\\\=4((-6)^2+3)-2(\frac{-1}{2} )\\\\=4(36+3)+1\\\\=4(39)+1\\\\=156+1\\\\=157[/tex]
The value of the expression 4(x² + 3) - 2y is 157, when x = -6 and y = -1/2.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
4(x² + 3) - 2y
Substitute x = -6 and y = -1/2 to find the value of expression,
= 4 ((-6)² + 3) - 2(-1/2)
= 4 (36 + 3) + 1
= 4 x 39 + 1
= 156 + 1
= 157
The required value of the expression is 157.
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A box is 90 cm long. Which of these is closest to the length of this box in feet?{1 inch= 2.54cm} (1 point)
Answer:
2.952755906 ft
Step-by-step explanation:
We need to convert 90 cm to inches
90 cm * 1 inch / 2.54 cm =35.43307087 inches
Now convert inches to ft
12 inches = 1ft
35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft
Factor 4x^2-22x+30.
Answer:
4x^2-22x+30
=2(2x^2 - 11x + 15)
=2(2x^2 -6x -5x +15)
= 2 { 2x(x-3) - 5(x-3) }
= 2 (x-3) (2x - 5)
Step-by-step explanation:
Hey, there!!!
The answer is option B
here, we have;
=4x^2-22x+30
=4x^2-(10+12)x+30
= 4x^2-10x-12x+30
now, taking common,
=2x(2x-5) -6(2x-5)
= 2(x-3)(2x-5).
Hope it helps
(a^8)3/2 in simplest form
Answer:
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Step-by-step explanation:
([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]
Remove the parenthesis by multiplying
[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]
This expression cannot be simplified further
[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]
Hope this helps :)
Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600
Answer:
A. 1,162.5
Step-by-step explanation:
Write the next two terms and add them up:
S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A
================================================
Explanation:
{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5
Sn = a*(1-r^n)/(1-r)
S5 = 600*(1-0.5^5)/(1-0.5)
S5 = 1,162.5
-----------
Check:
first five terms = {600, 300, 150, 75, 37.5}
S5 = sum of the first five terms
S5 = 600+300+150+75+37.5
S5 = 1,162.5
Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.
29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.
options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞
B. As x → –∞, y → –∞, and as x → +∞, y → –∞
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
D. As x → –∞, y → –∞, and as x → +∞, y → +∞
Answer:
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
Step-by-step explanation:
The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.
_____
When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.
When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.
4.9x10^_8 In decimal notation
Answer:
490000000
Step-by-step explanation:
For every exponent of 10, move the decimal point one place to the right.
Find the interest on a Principal Balance of $10,000 over the course of eight years with an interest rate of 5.5%. Do this for: Simple Interest.
Answer:
Simple Interest : $ 4400
Step-by-step explanation:
We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.
We can use the simple interest formula here, or :
I = P × r × t,
Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.
Simple Interest : 10000 × 0.055 × 8 = $4400.00
Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.
The simple interest earned on the amount is $4,400
Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.
Simple Interest = principal x time x interest rate
principal = amount borrowed = $10,000
time = 8 years
Interest rate = 5.5%
10,000 x 0.055 x 8 = $4,400
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Need Help
Please Show Work
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
consider the functions f(x)=-2x+4 and g(x)=8x-2 calculate the coordinates of the x and y interceptes of f(x)
Answer:
It more complex .Try to take help toggely
The difference of two numbers is 9. The sum of the two numbers is 15. What are the two numbers?
Let numbers be a and b
a+b=15--(1)a-b=9---(2)Adding both
[tex]\\ \qquad\quad\sf\longmapsto 2a=24[/tex]
[tex]\\ \qquad\quad\sf\longmapsto a=\dfrac{24}{2}[/tex]
[tex]\\ \qquad\quad\sf\longmapsto a=12[/tex]
Put value in eq(2)[tex]\\ \qquad\quad\sf\longmapsto 12-b=9[/tex]
[tex]\\ \qquad\quad\sf\longmapsto b=12-9[/tex]
[tex]\\ \qquad\quad\sf\longmapsto b=3[/tex]
I need help will rate you brainliest
Answer:
Yes you can
Step-by-step explanation:
To eliminate the denominator
Answer:
No
Step-by-step explanation:
We cannot be certain that x + 3 > 0
If it was negative then the sign of the inequality would change.
To solve find the critical values of the numerator/ denominator, that is
x = 2 and x = - 3
The domain is the split into 3 intervals
(- ∞, - 3 ), (- 3, 2), (2, + ∞ )
Use test points from each interval to determine valid solution
find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
24.8
Step-by-step explanation:
sin75 = 24/x
x = 24 / sin75 = 24.846628...
Set up a linear system and solve
A $2,000 principal is invested in two accounts, one earning 4% interest and another
earning 7% interest. If the total interest for the year is $101, then how much is invested
in each account
Answer:
1300 and 700 respectively.
Step-by-step explanation:
Let x be invested in first account and y be invested in second account.
ATQ, x+y=2000 and 101=(4)*x/100+7*y/100. Solving it will give us x=1300 and y=700
how many cubic meters of gravel are in the back of a full dump truck that measures 7m wide by 4m tall by 16m long
Answer:
Step-by-step explanation:
Assuming the gravel reaches the top of the walls and no higher, the volume is 7×4×16 = 448 m³
Answer:
hello thereee
now vol of truck = l b h = 7 * 4 * 16 = 448 m^3
( 448m^3 is final ans...
glad for brainliest.... hope that helps <3
n a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of inches and a standard deviation of inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between and inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
Answer:
(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.
(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.
(d) The event in part (c) is an unusual event.
Step-by-step explanation:
The complete question is: In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
We are given that the heights in the 20-29 age group were normally distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.
Let X = the heights of men in the 20-29 age group
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean height = 67.5 inches
[tex]\sigma[/tex] = standard deviation = 2 inches
So, X ~ Normal([tex]\mu=67.5, \sigma^{2}=2^{2}[/tex])
(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)
P(X < 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{67-67.5}{2}[/tex] ) = P(Z < -0.25) = 1 - P(Z [tex]\leq[/tex] 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.
(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)
P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X [tex]\leq[/tex] 67 inches)
P(X < 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{71-67.5}{2}[/tex] ) = P(Z < 1.75) = 0.9599
P(X [tex]\leq[/tex] 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{67-67.5}{2}[/tex] ) = P(Z [tex]\leq[/tex] -0.25) = 1 - P(Z < 0.25)
= 1 - 0.5987 = 0.4013
The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.
Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.
(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)
P(X > 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{71-67.5}{2}[/tex] ) = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)
= 1 - 0.9599 = 0.0401
The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.
(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.
Solve 45 - [4 - 2y - 4(y + 7)] = -4(1 + 3y) - [4 - 3(y + 2) - 2(2y -5)] (make sure to type the number only - rounded to the tenth)
Answer:
Rounded: -5.5
Step-by-step explanation:
Work above :)
Can you wiggle your ears? Use the students in your statistics class (or a group of friends) to estimate the percentage of people who can wiggle their ears. How can your result be thought of as an estimate for the probability that a person chosen at random can wiggle his or her ears? Comment: National statistics indicate that about 13% of Americans can wiggle their ears (Source: Bernice Kanner, Are You Normal?, St. Martin's Press, New York). The resulting relative frequency can be used as an estimate of the true probability of all Americans who can wiggle their ears. The resulting relative frequency can be used as an estimate of the true probability of all Americans who cannot wiggle their ears. The resulting relative frequency is the true probability of all Americans who can wiggle their ears. The resulting relative frequency cannot be used as an estimate of the true probability of all Americans who can wiggle their ears.
Answer:36
Step-by-step explanation:
Write true or false.
(I) Two intersecting lines can also be parallel.
(ii) Unlimited number of lines can be drawn through a point.
(iii) through two distinct points we can draw only one straight line.
(i) False. If two lines are parallel, then they never intersect.
(ii) True. We can draw infinitely many different lines through a single point. We can think of rotating a line around a single point to form a circular fan of lines.
(iii) True. Any line is defined uniquely by two distinct points.
find the greatest common factor of 108d^2 and 216d
Answer:
Below
Step-by-step explanation:
If d is a positive number then the greatest common factor is 108d.
To get it isolate d and d^2 from the numbers.
108 divides 216. (216 = 2×108)
Then the greatest common factor of 216 and 108 is 108.
For d^2 and d we will follow the same strategy
d divides d^2 (d^2 = d*d)
Then the greatest common factor of them is d.
So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer
Answer:
[tex]\boxed{108d}[/tex]
Step-by-step explanation:
Part 1: Find GCF of variables
The equation gives d ² and d as variables. The GCF rules for variables are:
The variables must have the same base.If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.The GCF for the variables is d.
Part 2: Find GCF of bases (Method #1)
The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.
Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!
Prime Factorization of 108
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.
Prime Factorization of 216
216 ⇒ 108 & 2
108 ⇒ 54 & 2
54 ⇒ 27 & 2
27 ⇒ 9 & 3
9 ⇒ 3 & 3
Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.
After completing the prime factorization trees, check for the common factors in between the two values.
The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.
Therefore, the greatest common factor (combining both the coefficient and the variable) is [tex]\boxed{108d}[/tex].
Part 3: Find GCF of bases (Method #2)
This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.
[tex]\frac{216}{108}=2[/tex]
Therefore, the coefficient of the GCF will be 108.
Then, follow the process described for variables to determine that the GCF of the variables is d.
Therefore, the GCF is [tex]\boxed{108d}[/tex].
Paula drives 130 miles in 2.5 hours. How far would she drive in 4.5 at the same speed?
*Please answer
I will award the Brainliest answer
Answer:
Paula will travel 234 miles in 4.5 hours
Step-by-step explanation:
Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour
Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles
Therefore Paula will travel 234 miles in 4.5 hours
Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?15x – 15 = 15x – 2415x – 5 = 15x – 2439x – 45 = 15x – 2439x – 15 = 15x – 24?
Answer:
3[x + 3(4x – 5)] = (39x-15)
Step-by-step explanation:
The given expression is : 3[x + 3(4x – 5)]
We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,
[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]
Again open the brackets,
[tex]3[x+12x-15]=3x+36x-45[/tex]
Now adding numbers having variables together. So,
[tex]3[x + 3(4x - 5)]=39x-15[/tex]
So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).
Find the Correlation of the following two variables X: 2, 3, 5, 6 Y: 1, 2, 4, 5
Answer:
The correlation of X and Y is 1.006
Step-by-step explanation:
Given
X: 2, 3, 5, 6
Y: 1, 2, 4, 5
n = 4
Required
Determine the correlation of x and y
Start by calculating the mean of x and y
For x
[tex]M_x = \frac{\sum x}{n}[/tex]
[tex]M_x = \frac{2 + 3+5+6}{4}[/tex]
[tex]M_x = \frac{16}{4}[/tex]
[tex]M_x = 4[/tex]
For y
[tex]M_y = \frac{\sum y}{n}[/tex]
[tex]M_y = \frac{1+2+4+5}{4}[/tex]
[tex]M_y = \frac{12}{4}[/tex]
[tex]M_y = 3[/tex]
Next, we determine the standard deviation of both
[tex]S = \sqrt{\frac{\sum (x - Mean)^2}{n - 1}}[/tex]
For x
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{n -1}}[/tex]
[tex]S_x = \sqrt{\frac{(2-4)^2 + (3-4)^2 + (5-4)^2 + (6-4)^2}{4 - 1}}[/tex]
[tex]S_x = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_x = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_x = \sqrt{\frac{10}{3}}[/tex]
[tex]S_x = \sqrt{3.33}[/tex]
[tex]S_x = 1.82[/tex]
For y
[tex]S_y = \sqrt{\frac{\sum (y_i - My)^2}{n - 1}}[/tex]
[tex]S_y = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (4-3)^2 + (5-3)^2}{4 - 1}}[/tex]
[tex]S_y = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]
[tex]S_y = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]
[tex]S_y = \sqrt{\frac{10}{3}}[/tex]
[tex]S_y = \sqrt{3.33}[/tex]
[tex]S_y = 1.82[/tex]
Find the N pairs as [tex](x-M_x)*(y-M_y)[/tex]
[tex](2 - 4)(1 - 3) = (-2)(-2) = 4[/tex]
[tex](3 - 4)(2 - 3) = (-1)(-1) = 1[/tex]
[tex](5 - 4)(4 - 3) = (1)(1) = 1[/tex]
[tex](6-4)(5-3) = (2)(2) = 4[/tex]
Add up these results;
[tex]N = 4 + 1 + 1 + 4[/tex]
[tex]N = 10[/tex]
Next; Evaluate the following
[tex]\frac{N}{S_x * S_y} * \frac{1}{n-1}[/tex]
[tex]\frac{10}{1.82* 1.82} * \frac{1}{4-1}[/tex]
[tex]\frac{10}{3.3124} * \frac{1}{3}[/tex]
[tex]\frac{10}{9.9372}[/tex]
[tex]1.006[/tex]
Hence, The correlation of X and Y is 1.006
Ram and his sister Kalpana win a prize of Rs 2000. They decide to share the prize in the ratio of their ages. Ram is 15 years old and Kalpana is 10 years old. How much do each of them receive
9514 1404 393
Answer:
Ram -- ₹1200Kalpana -- ₹800Step-by-step explanation:
Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.
Ram receives 0.6 × ₹2000 = ₹1200
Kalpana receives 0.4 × ₹2000 = ₹800
Angles 1 and 2 form a linear pair and the measure of angle two is 22 more than 4 times of the measure of angle 1. What degrees is angle 2
Answer:
m<2= 148.4
Step-by-step explanation:
A linear pair means that both angles add to 180.
m<2 = 4*m<1 +22
Together
m1 + m2 = 180
Put the value for m<2 into the above equation
m<1 + 4*m<1 + 22 = 180 Combine like terms\
5m<1 + 22 = 180 Subtract 22
5m<1 = 180 - 22
5m<1 = 158 Divide by 5
m<1 = 158/5
m<1 = 31.6
m<2 = 4*31.6 + 22
m<2 = 138.4
find the length of the arc. round your answer to nearest tenth
41.9 mi
Step-by-step explanation:
First, we convert the angle from degree measure to radian measure:
[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]
Using the definition of an arc length [tex]s[/tex]
[tex]s = r\theta[/tex]
[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]
[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]
Solve for y.
-1 = 8+3y
Simplify you answer as much as possible.
Answer:
-3
Step-by-step explanation:
[tex]8+3y = -1\\3y = -9\\y = -3[/tex]
Answer:
y = -3
Step-by-step explanation:
-1=3y+8
3y+8=-1
3y=-9
y=-3
Is 55/22 a rational
Answer:
The fraction [tex]\displaystyle \frac{55}{22}[/tex] is indeed a rational number.
Step-by-step explanation:
A number [tex]x[/tex] is rational if and only if there exist two integers [tex]p[/tex] and [tex]q[/tex] (where [tex]q \ne 0[/tex]) such that [tex]x = \displaystyle \frac{p}{q}[/tex].
[tex]\displaystyle \frac{55}{22}[/tex], the number in question here is already written in the form of a fraction. The two integers [tex]p = 55[/tex] and [tex]q = 22[/tex] ([tex]q \ne 0[/tex]) meet the requirement that [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]. Therefore, [tex]\displaystyle \frac{55}{22}\![/tex] is indeed a rational number.
Side note: the [tex]p[/tex] and [tex]q[/tex] here ([tex]q \ne 0[/tex]) don't have to be unique. For example:
because [tex]\displaystyle \frac{55}{22} = \frac{5 \times 11 }{2 \times 11} = \fraac{5}{2}[/tex], both of the following pairs could satisfy [tex]\displaystyle \frac{55}{22} = \frac{p}{q}[/tex]:
[tex]p = 55[/tex] and [tex]q = 22[/tex];[tex]p = 5[/tex] and [tex]q = 2[/tex].Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores.Use α=0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0 Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Their new scores are listed below. Test the claim that the book had no effect on their scores. Use α = 0.05. Assume that the distribution is normally distributed. Student 1 2 3 4 5 6 7 8 9 Scores before reading book 72 0 86 0 850 88 0 86 0 710 85 0 1200 95 0 Scores after reading book 74 0 86 0 840 92 0 89 0 720 84 0 1240 97 0
Answer:
t= 0.4933
t ≥ t ( 0.025 ,8 ) = 2.306
Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.
Step-by-step explanation:
We state our null and alternative hypotheses as
H0: ud= 0 Ha: ud≠0
The significance level is set at ∝= 0.05
The test statistic under H0 is
t= d`/ sd/√n
which has t distribution with n-1 degrees of freedom
The critical region is t ≥ t ( 0.025 ,8 ) = 2.306
Computations
Student Scores before Scores after Difference d²
reading book ( after minus before)
1 720 740 20 400
2 860 860 0 0
3 850 840 -10 100
4 880 920 40 1600
5 860 890 30 900
6 710 720 10 100
7 850 840 -10 100
8 1200 1240 40 1600
9 950 970 20 40
∑ 6930 8020 140 4840
d`= ∑d/n= 140/9= 15.566
sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775
sd= 18.2422
t= 3/ 18.2422/ √9
t= 0.4933
Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.