Step-by-step explanation:
Given that n! = n(n - 1)(n - 2)(n - 3)...2×1
We want to show that 2n - 1 ≤ n!
Since
n! = n(n - 1)(n - 2)(n - 3)...2×1
= n(n - 1)!
n! = n(n - 1)(n - 2)!
n! = (n² - n)(n - 2)!
From here obviously,
n! ≥ n
n! ≥ 2n
And
n! ≥ 2n - 1
Which implies
2n - 1 ≤ n!
What is the best interpretation of V(4)=64
I assume the normal function is V(x)=y
So if we plug it in, we know that at x=4, the y value of the function is 64.
Factor completely x3 + 9x2 + 27x+ 27
Answer:
(x + 3)^3
Step-by-step explanation:
I don't exactly know how to break this down into small steps. I can tell you that it is something like (x + a)^3
It turns out that a = 3 because all the signs in the given equation are +
Answer
(x + a) = (x + 3)^3
How many fluid ounces are there in 3 pints and 4 fluid ounces?
Answer:
52 US fluid ounces
Step-by-step explanation:
6 fluid ounces
How many fluid ounces in a pint? There are 16 fluid ounces in a pint.
Answer: 52 fluid ounces
A tent is an example of a____a0____a1.
Answer:
triangular prism
Step-by-step explanation:
A triangular prism has 3 rectangular sides and 2 triangles as the base
The answer is : Triangular, Prism
Have a great day!
God bless you!
Jose constructed Triangle DCE, where m∠D = 103° and m∠C = 22°. Remy constructed triangle PQT, where m∠Q = 22°, and m∠T = 55°. Are the two triangles similar to one another? *
Yes, because two pairs of corresponding angles in the triangles are congruent.
No, because none of the corresponding pairs of angles in the triangles are congruent.
No, because 103 + 22 ≠ 22 + 55.
There is not enough information to determine if the two triangles are similar to one another.
Answer:
The missing angle in Jose's triangle is 180 - 103 - 22 = 55° and since both triangles have two congruent pairs of corresponding angles the answer is yes.
Answer:
Yes
Step-by-step explanation:
They are similar by angle-angle similarly theorem
In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar . (Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)
The wattle thickness (in millimeters) of 15 randomly selected chickens was measured before and after treatment with phytohemagglutinin (PHA). Does treatment with PHA increase wattle thickness
Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
The wattle thickness (in milimeters) of 15 randomly selected chickens was measured before and after treatment with PHA. Does treatment wih PHA increase wattle thickness?
Chicken Number // Pretreatment // Posttreatment
1 // 1.05 // 3.48
2 // 1.01 // 5.02
3 // 0.78 // 5.37
4 // 0.98 // 5.45
5 // 0.81 // 5.37
6 // 0.95 // 3.92
7 // 1.00 // 6.54
8 // 0.83 // 3.42
9 // 0.78 // 3.72
10 // 1.05 // 3.25
11 // 1.04 // 3.66
12 // 1.03 // 3.12
13 // 0.95 // 4.22
14 // 1.46 // 2.53
15 // 0.78 // 4.39
Solution:
Corresponding wattle thickness before and after treatment form matched pairs.
The data for the test are the differences between the wattle thickness at pretreatment and posttreatment.
μd = wattle thickness at pretreatment minus wattle thickness at posttreatment
Pretreatment. Posttreatment diff
1.05 3.48 -2.43
1.01 5.02 -4.01
0.78 5.37 -4.59
0.98 5.45 -4.47
0.81 5.37 -4.56
0.95 3.92 -2.97
1 6.54 -5.54
0.83 3.42 -2.59
0.78 3.72 -2.94
1.05 3.25 -2.2
1.04 3.66 -2.62
1.03 3.12 -2.09
0.95 4.22 -3.27
1.46 2.53 -1.07
0.78 4.39 -3.61
Sample mean, xd
= (-2.43 - 4.01 - 4.59 - 4.47 - 4.56 - 2.97 - 5.54 - 2.59 - 2.94 - 2.2 - 2.62 - 2.09 - 3.27 - 1.07 - 3.61)/15 = - 3.264
xd = - 3.264
Standard deviation = √(summation(x - mean)²/n
n = 15
Summation(x - mean)² = (- 2.43 + 3.264)^2 + (-4.01 - 3.264)^2 + (-4.59 - 3.264)^2+ (-4.47 - 3.264)^2 + (-4.56 - 3.264)^2 + (-2.97 - 3.264)^2 + (-5.54 - 3.264)^2 + (-2.59 - 3.264)^2 + (-2.94 - 3.264)^2 + (-2.2 - 3.264)^2 + (-2.62 - 3.264)^2 + (-2.09 - 3.264)^2 + (-3.27 - 3.264)^2 + (-1.07 - 3.264)^2 + (-3.61 - 3.264)^2 = 627.32444
Standard deviation = √(627.32444/15
sd = 6.47
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
1) The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 15 - 1 = 14
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (- 3.264 - 0)/(6.47/√15)
t = - 1.95
We would determine the probability value by using the t test calculator.
p = 0.036
Assume alpha = 0.05
Since alpha, 0.05 > than the p value, 0.036, then we would reject the null hypothesis. Therefore, we can conclude that at a significance level of 5%, treatment with PHA increase wattle thickness
list 5 rational numbers between -4/7 and 1/2
Answer:
0, 1/10, 2/10, 3/10, 4/10, or
Step-by-step explanation:
-4/7 is about -0.57 in decimal form,
1/2 is 0.5
So we need to find 5 rational numbers between -0.58 and 0.5
A rational number is a number which can be expressed as a fraction.
0 can be expressed as 0/10
0.1 can be expressed as 1/10
0.2 can be expressed as 2/10
0.3 can be expressed as 3/10
0.4 can be expressed as 4/10
So just use those.
Solve each system by elimination
-9x -4y=2
7x +4y = -6
Answer:
cộng vế theo vế ta đc :
-2x=-4<=>x=2
thay x=2 vào 1 trong 2 ptrình ta đc: y=-5
Please answer this correctly
Answer:
0
Step-by-step explanation:
Since the original: 6 is not either the largest or the smallest, it wouldn't affect the range
The only numbers that can affect the range when replaced are the greatest and the least values: 5 and 9
What decimal part of one dollar is three quarters?
Answer:
0.75
Step-by-step explanation:
One dollar/four quarters-1.00
three quarters-0.75
two quarters-0.50
one quarter-0.25
Hope this helps
An engineer wants to obtain a random sample of the output from a process manufacturing digital cameras. The process operates 16 hours per day, five days per week. She selects five cameras on Monday, Tuesday and Wednesday at random between 3pm and 4pm each day. This is an example of
Answer:
Non-Random Sample
Step-by-step explanation:
A sample in which each element has an equal chance of being selected is known as a random sample. Otherwise, a sample is said to be a non - random sample.
An engineer selects five cameras on Monday, Tuesday, and Wednesday at random between 3 pm and 4 pm each day. So, the cameras that are not in the process of production between 3 pm and 4 pm have no chances of being selected.
So, each camera does not have an equal chance of being selected.
This is an example of a non - random sample.
Which is the vertex of x^2 + 10x = - 17?
Answer:
(-5, -8)
Step-by-step explanation:
Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the "vertex". If the quadratic is written in the form y = a(x – h)2 + k, then the vertex is the point (h, k).
x^2 + 10x = - 17
x^2+10x+17=0
x^2+2*5x+25 - 8=0
(x+5)^2-8=0
h=-5, k= -8
vertex is (-5, -8)
A bag has 8 red tiles and 2 green tiles. In a charity carnival game, you pay $5 to randomly pull a tile from the bag. The payout for pulling a red tile is $1 and the payout for pulling a green tile is $10. Which of the followig are true or false.
a. The expected payoff per game for the charity is $2.20.
b. In 20 games, the charity can expect to make $44.
c. In 30 games, the charity can expect to make $120.
d. In 5 games, the player can expect to lose $11.
Answer:
B:True
Step-by-step explanation:
B is true as a bag of 8 red tiles and 2 green tiles you pay 5 per tile meaning in twenty games you pay $100(50 per bag) and the total amount you win back is $56(28 per bag) so the equation would be $100 - $56= $44 profit to the charity
Hence only statement 1 is correct,∴The expected payoff per game for the charity is $2.20.
What is payoff?Money provided to someone as a bribe, reward, or when they leave a position. As a result, a mathematical function representing the award awarded to a single player at the game's conclusion has been developed.
How to Solve?Given a bag of tiles containing 8 red tiles, 2 green tiles.
Probability of drawing a red tile =1/8
Probability of drawing a green tile =1/2
If red tile is pulled payout is $1 else $10
Payout=
payout for 1 game= $1*8/10+$10*2/10-$5=2.20
payout in 20 games =$1*10*8/10+$10*10*2/10-$5*20=-72
payout for 30 games=$1*15*8/10+$10*15*2/10-$5*30=0
payout in 5 games=$1*5*8/10+10*5*2/10-$5*5=$25
Hence only statement 1 is correct, ∴The expected payoff per game for the charity is $2.20.
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complete this sentence in a triangle the angle with the greatest measure is always opposite the
Answer:
longest side
Step-by-step explanation:
In a triangle the angle with the greatest measure is always opposite the longest side.
A hose can fill a swimming pool in 12 hours. Another hose needs 6 more hours to fill the pool than the two hoses combined. How long would it take the second hose to fill the pool?
Answer:
I believe it is 12, but I'm not sure.
Step-by-step explanation:
If there is 2 of the first hose, then it can fill the pool twice as fast, so thats 6 hours. (12 divided by 2 = 6).
If the second hose takes 6 hours more than that, then that would be 12 hours.(6+6=12)
A classroom contains 13 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group
Answer:
16.39%
Step-by-step explanation:
We have a total number of forms, which are as follows:
-Harry Potter will serve as President AND Ron will serve as Vice President AND anyone will serve as Treasurer:
p1 = 1P11 = 11! / (11-1)! = 11
-Harry Potter will serve as President AND Hermione will serve as Vice President AND anyone who serves as Treasurer is:
p2 = 1P11 = 11! / (11-1)! = 11
- Harry Potter will not serve as President means that no one except Harry Potter (12 remaining students) serve in three locations:
p3 = 12P3 = 12! / (12-3)! = 1320
in total it would be:
11 + 11 + 1320 = 1342
Now the favorable cases are:
- Hermione becomes the president of this group, which means that anyone except Hermione and Harry Potter (11 remaining students) serve in the remaining two places:
p1 = 11P2 = 11! / (11-2)! = 110
- Ron becoming the president of this group means that anyone except Ron and Harry Potter (remaining 8 students) serve in the remaining two places:
p2 = 11P2 = 11! / (11-2)! = 110
adding it would be: 110 + 110 = 220
now then the final probability is the favorable cases among the totals:
220/1342 = 0.1639
Which means that the probability is 16.39%
Answer:
33% probability
1/3
Step-by-step explanation:
100% Hermione though.
The city of Raleigh has 9,200 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 200 randomly selected registered voters was conducted. 65 said they'd vote for Brown, 121 said they'd vote for Feliz, and 14 were undecided.
A. what is the population of this survey?B. What is the size of populationC. What is the size of the sampleD. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.E. Based on the sample, we might expect how many of th 9500 voters to vote for Brown
Answer:
A) The population of this survey is the registered voters in the city of Raleigh.
B) 9500
C) 200
D) 0.325
E) 3088
Step-by-step explanation:
A) The population of this survey is the registered voters in the city of Raleigh.
B) Population size can be defined as the total number of individuals in a population. Here the total number of individuals are the registered voters in the city. Therefore the size of the population is 9500.
c) Sample size is defined as the number of individual samples in a statistical test. Here the sample size is the 200 randomly selected registered voters. It is denoted as "n".
d) The sample statistic for the proportion of voters surveyed who said they'd vote for Brown would be:
p' = voters for brown / sample size
[tex] p' = \frac{65}{200} = 0.325 [/tex]
The sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.325
E) The expected number of voters for Brown based on the sample:
0.325 * 9500 = 3087.5
Approximately 3088
The expected number of voters for Brown based on the sample might be 3088 voters.
Two cyclists, 55 miles apart, start riding toward each other at the same time. One cycles 5 miles per hour faster than the other, and they meet after 5 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists?
Answer:
r = 6 mph and f = 11 mph
Step-by-step explanation:
Representations:
1) speed of faster cyclist: f = r + 5
2) speed of slower cyclist: r
Distances covered:
(r + 5)(5 hr) + r(5) = 55 mi (total distance covered)
Then 5r + 25 + 5r = 55, or, after reducing this equation:
r + 5 + r = 11, or
2r = 6
Then r = 6 mph and f = 11 mph
On her way to work, a commuter encounters four traffic signals. Assume that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection. The first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute.What is the probability that the commuter has to stop at least three times?
Answer:
7 in 36 or 0.1944
Step-by-step explanation:
The probability of having to stop at least three times is the probability of getting 3 or 4 red lights.
For the first two lights, the probability of getting them red is 20 in 60 (1/3).
For the last two lights, the probability of getting them red is 30 in 60 (1/2).
The probability of all of them being red is:
[tex]P(R=4) = \frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}\\P(R=4) =\frac{1}{36}=\frac{1}{36}[/tex]
The probability of three of them being red (3 red + 1 green) is:
[tex]P(R=3) = {(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}}*\frac{1}{2}+(1-\frac{1}{3})*\frac{1}{3}*\frac{1}{2}*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}+\frac{1}{3}*\frac{1}{3}*(1-\frac{1}{2})*\frac{1}{2}\\P(R=3) =2*(\frac{2}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})+2*(\frac{1}{3}*\frac{1}{3}*\frac{1}{2}*\frac{1}{2})\\ P(R=3) =\frac{4}{36}+\frac{2}{36}\\ P(R=3) =\frac{6}{36}[/tex]
Therefore, the probability of at least three red lights is:
[tex]P=\frac{1}{36}+\frac{6}{36}=\frac{7}{36}\\ P=0.1944[/tex]
The probability is 7 in 36 or 0.1944.
The probability that the commuter has to stop at least three times is at least 5.55%.
Since on her way to work, a commuter encounters four traffic signals, assuming that the distance between each of the four is sufficiently great that her probability of getting a green light at any intersection is independent of what happened at any previous intersection, and the first two lights are green for forty seconds of each minute; the last two, for thirty seconds of each minute, to determine what is the probability that the commuter has to stop at least three times the following calculation must be performed:
4/6 = 2/3 = 0.66666 0.5 x 0.5 x 0.333 = 0.083333 0.5 x 0.333 x 0.333 = 0.055555
Therefore, the probability that the commuter has to stop at least three times is at least 5.55%.
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Which of the following is the result of the operation below?
Answer:
The result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Step-by-step explanation:
The matrix provided is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right][/tex]
The operation to be performed is:
[tex]-R_{1}+R_{2}[/tex] → [tex]R_{2}[/tex]
The operation implies that, we need to replace the values in row 2 by the result of the expression ([tex]-R_{1}+R_{2}[/tex]).
Complete the operation as follows:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\1&1&1&-2\\0&2&1&5\end{array}\right]\rightarrow \ \left[\begin{array}{ccc|c}1&2&3&6\\(-1+1)&(-2+1)&(-3+1)&(-6-2)\\0&2&1&5\end{array}\right][/tex]
[tex]\rightarrow\ \left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Thus, the result of the operation is:
[tex]\left[\begin{array}{ccc|c}1&2&3&6\\0&-1&-2&-8\\0&2&1&5\end{array}\right][/tex]
Answer:
A
Step-by-step explanation:
edge 2021
Please help me thanks
Answer:
-75 and 75
Step-by-step explanation:
The two numbers chosen or plotted by them are:
-75 and 75
Step-by-step explanation:
It is given that Bernita and Derek each plot a number on a number line with the properties:
1. The two numbers they have plotted are unique or different.
2. Also there absolute value is same.
3. The sum of the absolute values of the numbers is 150.
We know that Absolute value of a positive number is a number itself and absolute value of a negative number is it's inverse.
So the two numbers that satisfy the above three properties are:
-75 and 75.
Identify the type of claim in each research question below.
For many years "working full-time" was 40 hours per week. A business researcher gathers data on the hours that corporate employees work each week. She wants to determine if corporations now require a longer work week.
Group of answer choices
a.Testing a claim about a single population proportion.
b.Testing a claim about a single population mean.
c.Testing a claim about two population proportions.
dTesting a claim about two population means.
Answer:
b.Testing a claim about a single population mean.
Step-by-step explanation:
Hello!
The researcher wants to test the claim that corporation employees work more than 40 hours per week.
The variable of interest is "The number of hours a corporate employee works per week"
The parameter of study, for her to make a valid conclusion about the weekly working hours of the population of corporation employees is the population mean μ.
If the claim is correct, she would expect the population mean of weekly hours the corporate employees work to be greater than 40.
This is an example of a single population mean test.
Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 230 yards on average. A random sample of 177 golfers show that their mean driving distance is 230.7 yards, with a standard deviation of 41.8.
1. Set up the null and alternative hypotheses to test for the designers belief.
a. H0 : µ ≥ 230 versus Ha : µ < 230
b. H0 : µ = 230.7 versus Ha : µ ≠ 230.7
c. H0 : µ ≥ 230.7 versus Ha : µ < 230.7
d. H0 : µ ≤ 230.7 versus Ha : µ > 230.7
e. H0 : µ ≤ 230 versus Ha : µ > 230
2. Find the value of the standardized test statistic.
a. 0.125
b. -0.125
c. 0.223
d. -0.7
e. 0.7
3. Find the P-value for the above mentioned test.
a. 0.8237
b. 0.0228
c. 0.5871
d. 0.4118
e. 0.0871
Answer:
a) e) H0 : µ ≤ 230 versus Ha : µ > 230
b) [tex]t=\frac{230.7-230}{\frac{41.8}{\sqrt{177}}}=0.223[/tex]
c. 0.223
c) [tex]p_v =P(t_{(176)}>0.223)=0.4118[/tex]
d. 0.4118
Step-by-step explanation:
Information given
[tex]\bar X=230.7[/tex] represent the sample mean
[tex]s=41.8[/tex] represent the sample standard deviation
[tex]n=177[/tex] sample size
[tex]\mu_o =230[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
Part a
We want to verify if the true mean is higher than 230 yards, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 230[/tex]
Alternative hypothesis:[tex]\mu > 230[/tex]
The best option would be:
H0 : µ ≤ 230 versus Ha : µ > 230
Part b
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{230.7-230}{\frac{41.8}{\sqrt{177}}}=0.223[/tex]
Part c
The degrees of freedom are:
[tex]df=n-1=177-1=176[/tex]
The p value would be given by:
[tex]p_v =P(t_{(176)}>0.223)=0.4118[/tex]
d. 0.4118
Simplify: StartRoot 64 r Superscript 8 Baseline EndRoot
Answer:
8r^4
Step-by-step explanation:
[tex]\sqrt{64r^8} =\sqrt{(8r^4)^2}=\boxed{8r^4}[/tex]
Answer:
8r^4
Step-by-step explanation:
Please answer this correctly
Answer:
V =113.04 cm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
V = 3.14 (3)^2 4
V = 3.14 *9*4
V =113.04 cm^3
Answer:
Step-by-step explanation:
3*3.14
9.42*9.42
88.7364*4
354.9456 rounded to
355
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is a=0.05, then the correct conclusion is to
Answer:
[tex] p_v = 0.027[/tex]
And for this case we have a significance level [tex] \alpha=0.05[/tex] and then:
[tex] p_v <\alpha[/tex]
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
Step-by-step explanation:
For this case we have the following hypothesis:
[tex]Null hypothesis: p =p_o[/tex]
[tex]Alternative hypothesis: p \neq p_o[/tex]
And for this case we got the following hypothesis:
[tex] p_v = 0.027[/tex]
And for this case we have a significance level [tex] \alpha=0.05[/tex] and then:
[tex] p_v <\alpha[/tex]
So then we have enough evidence to reject the null hypothesis. And we can conclude in favor the alternative hypothesis.
Fill in missing information to make the equality true:
(... +2a)2 = … +12ab2+4a2.
Answer:
I suppose it should be
6b² and (6b²)²
or
6b² and 36[tex]b^{4}[/tex]
Step-by-step explanation:
(a+b)² = a² + 2ab + b²
therefore
(6b²+2a)² = (6b²)² + 12ab² + 4a²
The missing information to make the equality true are 3b² and (3b²)². This can be obtained by using the algebraic identity (x+y)² =x² + 2xy + y².
Find the missing information:Let the missing information be p and p²
Then the given equation will be: (p+2a)² =p² + 12ab² + 4a²
The algebraic identities is (x+y)² =x² +2xy+y²
Comparing the given equation with the algebra formula we get
y=2a
2xy =12ab² ⇒2x(2a) = 12 ab² ⇒ x = 3b²
Therefore the given equation will be
(3b²+2a)² = (3b²)²+12ab²+4a²
Hence the missing information to make the equality true are 3b² and (3b²)².
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In the chi-square test of association, as the difference between the observed and expected proportions increases... a. the chi-square test statistic increases b. the chi-square critical value increases c. the likelihood of rejecting the null hypothesis increases d. the likelihood of rejecting the null hypothesis decreases e. the chi-square critical value decreases f. the chi-square test statistic decreases
Answer:
Opton A
Step-by-step explanation:
In the chi-square test of association, as the difference between the observed and expected proportions increases, the chi-square test statistic also increases. This is because if the claim made in the null hypothesis is true: the claim that frequency of the observed is equal to that of the expected (Oi = Ei) then, the observed and the expected values are close to each other and the difference Oi − Ei is small for each category and the chisquare test statistic is small.
But when the observed data does not fit to what is expected as of the null hypothesis, the difference between the observed and expected values, Oi − Ei is large producing a large chi square statistic.
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
PG = GO
2(4x-3)-8=4+2x
8x-6-8=4+2x
8x-14=4+2x
8x-2x=4+14
6x=18
Dividing both sides by 6
x = 3
Answer:
x = 3
Step-by-step explanation:
Since the chords are congruent then they are equidistant from the centre, thus
PG = GO , substitute values
2(4x - 3) - 8 = 4 + 2x ← distribute and simplify left side
8x - 6 - 8 = 4 + 2x
8x - 14 = 4 + 2x ( subtract 2x from both sides )
6x - 14 = 4 ( add 14 to both sides )
6x = 18 ( divide both sides by 6 )
x = 3
In 1970, the average length of a major league baseball game was 150 minutes compared to 180 minutes in 2018. Calculate the absolute and relative change in major league baseball game times from 1970 to 2018. Round your answer for relative change to the nearest whole percent.
Answer:
30 min20%Step-by-step explanation:
The absolute change in game length is ...
(180 min) -(150 min) = 30 min . . . . change in game length
__
The relative change is expressed as a fraction of the original game length:
(30 min)/(150 min) × 100% = 20% . . . . relative change in game length
