Answer:
38.11% probability that the mean of her sample will be between 2700 and 2800 calories
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 2760, \sigma = 500, n = 25, s = \frac{500}{\sqrt{25}} = 100[/tex]
Find the probability that the mean of her sample will be between 2700 and 2800 calories
This is the pvalue of Z when X = 2800 subtracted by the pvalue of Z when X = 2700.
X = 2800
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2800 - 2760}{100}[/tex]
[tex]Z = 0.4[/tex]
[tex]Z = 0.4[/tex] has a pvalue of 0.6554
X = 2700
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2700 - 2760}{100}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a pvalue of 0.2743
0.6554 - 0.2743 = 0.3811
38.11% probability that the mean of her sample will be between 2700 and 2800 calories
Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.
1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.
4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.
Answer:
Step-by-step explanation:
Hello!
Full Text:
As part of its "It Can Wait" campaign to discourage texting while driving, AT&T recently released the results of separate surveys concerning the extent of texting while driving among adults twd_commutor_survey and among teens att_teen_survey_executive . In the survey of the adults, 496 of n1 = 1,011 adult drivers (49.06%) said they text while driving. In the survey of the teens, 516 of n2 = 1,200 (43%) said they text while driving.
Question 1. Calculate a 98% confidence interval for the difference padult - pteen in the proportions of adults that text while driving and the proportion of teens that text while driving. (use 4 decimal places in your answers) lower bound upper bound
Be:
X₁: Number of adult drivers that text while driving, out of 1011.
n₁= 1011
x₁= 496
p₁'= 496/1011= 0.4906
X₂: Number of teen drivers that text while driving, out of 1200.
n₂= 1200
x₂= 516
p₂'= 516/1200= 0.43
For the 98% CI for p₁-p₂
[tex]Z_{1-\alpha /2}= Z_{0.99}= 2.326[/tex]
(p₁'-p₂')±[tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }[/tex]
(0.4906-0.43)±2.326*[tex]\sqrt{\frac{0.4906(1-0.4906)}{1011} +\frac{0.43(1-0.43)}{1200} }[/tex]
0.0606±2.326*0.0212
[0.011; 0.11]
Using a 98% confidence level, you'd expect that the interval [0.011; 0.11] contains the difference between the population proportion of adults that text while driving and the population proportion of teens that ext while driving.
Question 2. Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.
To decide over a hypothesis test using a confidence interval there are several conditions that should be met:
1) The hypotheses should be two-tailed:
H₀: p₁ - p₂= 0
H₁: p₁ - p₂≠ 0
2) The confidence level of the interval and the significance level of the test should be complementary, this means that if the interval was constructed with a level 1 - α: 0.98 then the test should be made using α: 0.02.
Naturally, the hypotheses and the CI should be made for the same parameters.
If all conditions are met, the decision criteria is as follows:
If the CI contains the value stated in the null hypothesis, the decision is to not reject the null hypothesis.
If the CI doesn't contain the value stated in the null hypothesis, the decision is to reject the null hypothesis.
In this case, the value stated in the null hypothesis is "zero" and is not included in the interval, so the decision is to reject the null hypothesis. You can conclude that the population proportions of adults and teens that text while driving are different.
Considering that the CI is positive, we can think that the proportion of adults that text while driving is grater than the proportion of teens that text while driving.
Options:
1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.
4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.
The correct option is: "3"
I hope this helps!
∆LMN ∼ ∆PON. What is the value of x? Select one: a. 28 1/3 b. 36 c. 20 d. 25
Answer:
b. 36
Step-by-step explanation:
x/12=42/14x=12*3x=36Last month, Carla's neighbors paid her to take care of their cat when they went on
vacation. She spent $4 of her earnings on an afternoon snack and $12 on a new book. Afterward,
she had at least $5 left. How can you best describe how much Carla's neighbors paid her?
Select the correct choice below and fill in the answer box to complete your choice.
OA. They paid her exactly $
OB. They paid her at least $
. C. They paid her at most $
Answer:
She had at least 21
Step-by-step explanation:
She had at least 4+ 12 +5
She had at least 21
She spent 4 and 12 so she had 16 dollars
She had at least 5 left
so at the very least she had 16+5 which is 21, she may have had more
Answer:
21
Step-by-step explanation:
she spent 4 and 12 so she had 16 dollars so she have at least she have $5 left
A light bulb consumes 15300 watt-hours in 4 days and 6 hours . How many watt-hours does it consume per day?
Answer:
3600 per 24 hour period or 1 day.
Step-by-step explanation:
24 x 15300/(4 x 24+6)=3600
Answer:
3600
Step-by-step explanation:
It consumes 3600 watt hours per day. Steps are included below.
We know that there is 24 hours in a day so we times 24 by the consumes watt hours that is 15300. So 24 times 15300. After that we need to time 4 times 24+6 = the answer that is 3600. That how you get the answer.
Steps:
1: 24*15300/(4*24+6)=3600
Answer: 3600 watt hours per day
Hope this helps.
A town has a population of 18000 and grows at 2% every year. What will be the population after 12 years, to the nearest whole number?
Answer:
Step-by-step explanation:
A=18000(1+0.02)^11
A=22,380.74
Answer:
y≈22828
Step-by-step explanation:
(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume the "worst case" scenario for the value of both sample proportions. We want a 98% confidence level and for the error to be smaller than 0.02.
b) Again find the sample size required, as in part (a), but with the knowledge that a similar student last year found that the proportion of boys afraid of spiders is 0.45 and the proportion of girls afraid of spiders was 0.58.
Answer:
(a) The sample sizes are 6787.
(b) The sample sizes are 6666.
Step-by-step explanation:
(a)
The information provided is:
Confidence level = 98%
MOE = 0.02
n₁ = n₂ = n
[tex]\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})[/tex]
Compute the sample sizes as follows:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}[/tex]
[tex]n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}[/tex]
[tex]=\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787[/tex]
Thus, the sample sizes are 6787.
(b)
Now it is provided that:
[tex]\hat p_{1}=0.45\\\hat p_{2}=0.58[/tex]
Compute the sample size as follows:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}[/tex]
[tex]n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}[/tex]
[tex]=\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666[/tex]
Thus, the sample sizes are 6666.
A rectangle on a coordinate plane has vertices L(0.6), M3, 6), N80), and O(0, 0) What are the dimensions of the
rectangle?
O
• The base is 6 and the height is 8
• The base is 8 and the height is 6
• The base is 6 and the height is 6
• The base is 8 and the height is 8
Answer:
• The base is 8 and the height is 6
Step-by-step explanation:
A rectangle has two dimensions:
The base, which is the distance between the points who have the same value of y.
The height, which is the distance between the points who have the same value of x.
Distance between 2 points:
Points (a,b) and (c,d).
[tex]D = \sqrt{(c-a)^{2} + (d-b)^{2}}[/tex]
I suppose there was a small typing mistake, as these points do not make a rectangle.
I will say that we have these following points:
L(0,6), M(8,6), N(8,0), O(0,0).
Base:
Same value of y.
L(0,6), M(8,6), or N(8,0) and O(0,0).
They will have the same result, will use the second.
[tex]D = \sqrt{(8-0)^{2} + (0-0)^{2}} = \sqrt{64} = 8[/tex]
The base is 8.
Height:
Same value of x.
L(0,6), O(0,0) or M(8,6) and N(8,0).
[tex]D = \sqrt{(8-8)^{2} + (6-0)^{2}} = \sqrt{36} = 6[/tex]
The height is 6.
So the correct answer is:
• The base is 8 and the height is 6
A hyperbola in the form (x ^ 2)/(a ^ 2) - (y ^ 2)/(b ^ 2) = 1 has a center, vertices, and foci that fall along a horizontal. Please select the best answer from the choices provided. True or false
Answer:
True
Step-by-step explanation:
Explanation:-
The equation of the standard hyperbola is
[tex]\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} } =1[/tex]
Center is (0,0) Hyperbola is symmetric with respective to both the axes, since if (x, y) is a point on the hyperbola, then (-x, y), (-x,-y), (x,-y) are also lie on the parabola. The relation of between focus and transverse and conjugate axes c²=a²+b² The transverse axis is along x-axis The conjugate axis is along y-axis The length of transverse axis is 2 a The length of conjugate axis is 2 b The foci is (±c,0) and the equation of foci is x=±a e) The length of Latus rectum is [tex]\frac{2b^{2} }{a}[/tex]Answer:
It is True!
Step-by-step explanation:
If AD= 2 and DC= 8, find BD 8 6 4
Answer:
[tex]BD= 4[/tex]
Answer:
BD would equal 4
Step-by-step explanation:
A researcher uses a matched-samples design to investigate whether single people who own pets are generally happier than single people without pets. A mood inventory questionnaire is administered to a group of 20- to 29-year old non-pet owners and a similar age group of pet owners. The pet owners are matched one-to-one with the non-pet owners for income, number of close friendships and general health. The data are as follows. Matched-Pair Non-pet Pet A 11 13 B 9 8 C 11 14 D 13 13 E 6 12 F 9 11 Calculate and report below the value of the appropriate test statistic to determine if there is evidence for this researcher's hypothesis.
Answer:
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets. (P-value=0.0509).
Step-by-step explanation:
We have to calculate the difference for every pair, and applied the hypothesis test to this sample of differences.
Non-pet Pet --> Difference (d)
A 11 13 --> 2
B 9 8 --> -1
C 11 14 --> 3
D 13 13 --> 0
E 6 12 --> 6
F 9 11 --> 2
The claim is that single people who own pets are generally happier than single people without pets. In the context of the sample, it means that the difference between the metric of happiness between the pet and the non-pet subjects is bigger than 0.
The mean and standard deviation of the sample of differences is:
[tex]M=\dfrac{1}{6}\sum_{i=1}^{6}(2+(-1)+3+0+6+2)\\\\\\ M=\dfrac{12}{6}=2[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{6}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{5}\cdot [(2-(2))^2+(-1-(2))^2+(3-(2))^2+(0-(2))^2+(6-(2))^2+(2-(2))^2]}\\\\\\ s=\sqrt{\dfrac{1}{5}\cdot [(0)+(9)+(1)+(4)+(16)+(0)]}\\\\\\ s=\sqrt{\dfrac{30}{5}}=\sqrt{6}\\\\\\s=2.449[/tex]
Then we perform an hypothesis test for the population mean.
The claim is that single people who own pets are generally happier than single people without pets.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_d=0\\\\H_a:\mu_d> 0[/tex]
The significance level is 0.05.
The sample has a size n=6.
The sample mean is M=2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.449.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.449}{\sqrt{6}}=0.9998[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2-0}{0.9998}=\dfrac{2}{0.9998}=2.0004[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=6-1=5[/tex]
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets.
Answer:
Step-by-step explanation:
Null hypothesis : [tex]H_0:\mu_d=0[/tex]
Alternative hypothesis: [tex]H_0:\mu_d>0[/tex]
Level pf significance [tex]\alpha =0.05[/tex]
Test statistic [tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
Mean of difference
[tex]\bar d = \frac{\sum d_i}{n} = 12/6 = 2[/tex]
Standard deviation of difference
[tex]s_d=\sqrt{\frac{\sum (d_i- \bar d)}{n-1} } \\\\=\sqrt{\frac{30}{6.1} } \\\\=2.441[/tex]
Test statistic
[tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
[tex]=\frac{2-0}{2.449/\sqrt{6} } \\\\=2.00[/tex]
Degree of freedom
df = n - 1
6-1 = 5
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets.
Please answer this correctly without making mistakes
Answer:
140.4 yards squared
Step-by-step explanation:
A jewelry store marks up the price of its jewelry up 50%. What will be the selling price of an item that the store purchased for $95?
Answer: $142.5
Step-by-step explanation: If the price is being marked up by 50%, you take 50% or half of the original price of $95, which is 47.5, and add it to your original price.
95 + 47.5 = 142.5
Answer:
$142.5
Step-by-step explanation:
If the price is being marked up by 50%, you take 50% or half of the original price of $95, which is 47.5, and add it to your original price.
95 + 47.5 = 142.5
A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years. Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2 years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will be $700 for the first year, increasing by 2% per year thereafter. Page 2 of 3 Examiners: Dr. A. Afful-Dadzie, and Dr. A. Karimu A German car will cost $45,000 and have fuel usage of 21mpg for the first 5 years, and decrease by 1% thereafter to year 8. Repair cost will start at $1000 in year 1 and increase by 4% per year. It will have a salvage value of $7000 at the end of year 8. Insurance cost will be $850 the first year, increasing by 2% per year thereafter. The American car will cost $35,000 and have fuel usage of 20mpg for the first 3 years, and will decrease by 3% per year thereafter. Repair cost will be $800 in year 1, increasing by 4% per year thereafter. Being an American, the graduate will price the pride of owning an American car at $0.4 for every 20 miles driven, increasing by 2% per year. Insurance cost will be $800 per year increasing by 2.2% per year. The car can be sold for $5500 at the end of year 8. If the graduate anticipates driving 150000 miles by the end of year 8 and the average interest rate is expected to remain at 5% per year, which car is economically affordable based on present worth analysis? Assume fuel cost will be $3 per gallon in year 1 and increase by an average of 2% per year. Show all your workings. (20 marks)
Answer:
The best option is to buy Japanese Car.
Step-by-step explanation:
Fuel usage per year is 150000/ 8 = 18750 miles per year
Fuel cost (year 1 -8) = $3.0, $3.06, $3.12, $3.18, $3.25, $3.312, $3.38, $3.5
Japanese Car:
Fuel usage 18750 / 23 = 815 * $3 = $2446
Fuel charges (year 1 -8) = $2445, $2494, $2623, $2758. $2900, $3050, $3207, $3372
Repair Cost (year 1 - 8) = $700, $721, $742, $764, $787, $811, $835, $860
Insurance cost (Year 1 - 8) = $700, $714, $728, $742, $757, $772, $788, $804
Present value of cost at 5% = 24674.07
Cost of car is $30,000
Total cost = $54674.07
Amercian Car:
Cost $35,000
Fuel usage 18750/20 = 937.5 * $3 per gallon = $2812.5.
Fuel charges (year 1 -8) = $2812, $2913, $2986, $3011. $3098, $3124, $3176, $3208
Repair Cost (year 1 - 8) = $800, $894, $921, $978, $1109, $1176, $1207, $1301
Insurance cost (Year 1 - 8) = $800, $827, $876, $898, $908, $932, $954, $934
Present value of cost at 5% = 25302.18
Cost of car is $35,000
Total cost = $60302.
German Car:
Cost = $45,000
Fuel usage 18750 / 21 = 892 * $3 = $2678
Fuel charges (year 1 -8) = $2679, $2732, $2786, $2842. $2899, $2987, $3077, $3171
Repair Cost (year 1 - 8) = $1000, $1040, $1081, $1124, $1169, $1216, $1265, $1316
Insurance cost (Year 1 - 8) = $850, $867, $884, $902, $920, $938, $957, $976
Present value of cost at 5% = 27105.73
Cost of car is $45,000
Total cost = $72105.
Help me please !!
In the spring you decide to start cleaning your room on a weekly basis. The first cleaning takes you 135 minutes. You notice for watch cleaning after that, you decrease the time it takes from the week before by 20%. After 4 weeks, how long will it take you to clean your room? Round your answer to the nearest minute.
Answer:
69
Step-by-step explanation:
first 135
second 135 - 20% = 135 - 27 = 108
third 108 - 20% = 108 - 21.6 = 86.4
fourth 86.4 -20% = 86.4 -17.28= 69.12
rounded 69
What’s the correct answer for this?
Step-by-step explanation:
Second option is the correct answer
Answer:
B
Step-by-step explanation:
Area of sector = m/360(πr²)
What is the median of the following set of data? 21, 4, 18, 9, 25, 16, 27, 30,
33, 15, 31
The median is the middle number in the data set when
the data set is written from least to greatest.
So let's write our data set from least to greatest.
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
Now, we identify the middle number.
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
Notice that 21 appears in the middle.
So the median of the data set is 21.
Answer:
Median: 21
Step-by-step explanation:
arrange all the numbers from least to greatest:
4, 9, 15, 16, 18, 21, 25, 27, 30, 31, 33
median = is the middle number in the data set/listed numbers.
Since there are eleven numbers in the set of data, we divide it equally, to find the median.
{4, 9, 15, 16, 18} 21 {25, 27, 30, 31, 33}
A farmer needs to put in a fence in their rectangular field. If we look at the field from above, the cost of the west and east sides are $10/ft, the cost of the south side is $2/ft and the cost of the north side is $7/ft. If we have $700, use optimization to determine the dimensions of the field that will maximize the enclosed area.
Answer:
north and south sides are 38 8/9 ft longeast and west sides are 17.5 ft longStep-by-step explanation:
Short answer: area is maximized when half the cost is spent in each of the orthogonal directions. This means the east and west sides will total $350 at $20 per foot, so will be 17.5 feet. The north and south sides will total $350 at $9 per foot, so will be 38 8/9 feet.
The dimensions that maximize the area are 17.5 ft in the north-south direction by 38 8/9 ft in the east-west direction.
__
Long answer: If x represents the length of the north and south sides, and y represents the length of the east and west sides, then the total cost is ...
10y +10y +2x +7x = 700
9x +20y = 700
y = (700 -9x)/20
We want to maximize the area:
A = xy = x(700 -9x)/20
We can do this by differentiating and setting the derivative to zero:
dA/dx = 700/20 -9x/10 = 0
350 -9x = 0 . . . . multiply by 10
x = 350/9 = 38 8/9
y = (700 -9(350/9))/20 = 350/20 = 17.5
The north and south sides are 38 8/9 ft long; the east and west sides are 17.5 ft long to maximize the area for the given cost.
Puji paid $7.50 for three pounds of gummy candy.
Part A
Assuming the cost per pound of gummy candy is proportional, complete the table of values representing the cost of gummy candy in pounds.
(Please look at the graph uptop)
Answer:
1: 2.5, 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5
Step-by-step explanation:
asumming it is proportional, you divide 7.5 by 3 which will give you the cost per pound which is $2.5, then you multiply this number by the amount of pounds you want
Answer:
1: 2.5 , 2: 5.0 , 3:7.5 , 4:10 , 5: 12.5
Step-by-step explanation:
Use the following information for questions 8-10: A professional basketball player has an 81% success rate when shooting free throws. Let the random variable X represent the number of free throws he makes in a random sample of 10 free throws (assume this experiment meets all binomial requirements). What is the expected number of free throws he will make
Answer:
The expected number of free throws he will make is 8.1.
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either he makes it, or he misses each. Each free throw is independent of other free throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
A professional basketball player has an 81% success rate when shooting free throws.
This means that [tex]p = 0.81[/tex]
Sample of 10 free throws
This means that [tex]n = 10[/tex]
What is the expected number of free throws he will make
[tex]E(X) = np = 10*0.81 = 8.1[/tex]
The expected number of free throws he will make is 8.1.
Use the quadratic formula to solve the equation.
4x^2−10x+5=0
Quadratic formula:
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
What do we have:
a=4
b=-10
c=5
Substitude:
[tex]x=\frac{10±\sqrt{b^{2}-4(4)(5)}}{2(a)}[/tex]
Solve:
[tex]x=\frac{10±\sqrt{(-10)^{2}-4(4)(5)}}{2(4)}\\\\x=\frac{10±\sqrt{100-4(20)}}{8}\\\\x=\frac{10±\sqrt{100-4(20)}}{8}\\\\x=\frac{10±\sqrt{100-80}}{8}\\\\x=\frac{10±\sqrt{20}}{8}\\\\x=\frac{10±2\sqrt{5 }}{8}\\\\x=\frac{2(±5\sqrt{5) }}{2(4)}[/tex]
Cancel the common terms:
[tex]x=\frac{5±\sqrt{5} }{4}[/tex]
1.Colin walked a distance of 15 miles in 6 hours.
Work out Colins average speed.
Give your answer in miles per hour.
2.Tim drives at an average speed of 80km per hour for 3 hours 45 minutes.
Work out how many kilometres Tim drives.
i will mark you the brainiest
Answer:
1. 2.5 miles
2. 21.33 km
Step-by-step explanation:
15miles/6hours=2.5 miles
80km/3.75min=21.33km
Hope this helped!!!
Franco made a dozen muffins for his party. Upon taking them out of the oven he noticed that 2 of the muffins were badly burnt. Franco served 7/10 of the remaining muffins. Which equation shows the fraction of the non burned muffins that remains?
Answer:
(B)[tex]\frac{10}{10}-\frac{7}{10}=\frac{3}{10}[/tex]
Step-by-step explanation:
The question is Incomplete. Find the complete question in the attachment.
Number of muffins made by Franco =12
Number of Badly Burnt Muffins =2
Number of non burned muffins =12-2=10
Franco served [tex]\frac{7}{10} $ of the non burned muffins = $ \frac{7}{10}*10=7$ muffins[/tex]
Therefore, the number of non burned muffins that remains =10-7 =3
We can then say the fraction of the non-burned muffins that remains[tex]=\frac{3}{10}[/tex]
Therefore, the correct equation is in Option B:
[tex]\frac{10}{10}-\frac{7}{10}=\frac{3}{10}[/tex]
find the value of x in 3x=3
Answer:
the value of x is x=1
Step-by-step explanation:
3x=3
x=3÷3
x=1
1.
Step-by-step explanation:
find the 4th term (x-y)^12
Answer:
The fourth term of the expansion is -220 * x^9 * y^3
Step-by-step explanation:
Question:
Find the fourth term in (x-y)^12
Solution:
Notation: "n choose k", or combination of k objects from n objects,
C(n,k) = n! / ( k! (n-k)! )
For example, C(12,4) = 12! / (4! 8!) = 495
Using the binomial expansion formula
(a+b)^n
= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n
For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is
C(n,3)a^(n-3)b^3
=C(12,3) * x^(12-3) * (-y)^(3)
= 220*x^9*(-y)^3
= -220 * x^9 * y^3
The fourth term in the binomial expansion of ( x - y )¹² is given by the equation A₄ = -220 x⁹y³
What is Binomial Expansion?The general term of the binomial expansion is Tr+1 = nCr x^n-r y^r . Here the coefficient values are found from the pascals triangle or using the combinations formula, and the sum of the exponents of both the terms in the general term is equal to n.
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Given data ,
Let the binomial expansion be represented as A
Now , the value of A is
A = ( x - y )¹² be equation (1)
On simplifying the equation , we get
The fourth term of the binomial expansion is calculated by
A₄ = ⁿC₃ a⁽ⁿ⁻³⁾ b³
Substituting the values in the equation , we get
A₄ = ¹²C₃ x⁽¹²⁻³⁾ ( -y )³
On further simplification , we get
A₄ = ( 12 )! / ( 9 )! 3! x⁹ ( -y )³
A₄ = 12 x 11 x 10 / 2 x 3 x⁹ ( -y) ³
A₄ = -220 x⁹y³
Hence , the fourth term of binomial expansion is -220 x⁹y³
To learn more about binomial expansion click :
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Math Problem, Please Help.....
Brainliest to whoever gets this correct The graph of g(x), shown below, resembles the graph of f(x) = x4 - x2, but it has been changed somewhat. Which of the following could be the equation of g(x)?
Why is this?
We start with x^4 - x^2, which is the original f(x) function. Adding some number to this result will increase the y coordinate of any point on the f(x) function. This is because y = f(x). The only thing that matches is choice C, where we shift the graph up 0.5 units. We say that g(x) = f(x) + 0.5
Choice D goes in the opposite direction, and shifts the graph down 0.5 units.
Choices A and B shift the graph horizontally to the right 0.5 units and to the left 0.5 units respectively.
The statement the sum of x and 7% of x is at least 30"
Answer:
x + 0.07x ≥ 30
Step-by-step explanation:
A sum is terms separated by a plus sign.
"Is at least" means "is greater than or equal to."
7% as a decimal fraction is 0.07.
"Of" means "times."
__
In consideration of the above, you have ...
x plus 7% of x is at least 30
x + 0.07x ≥ 30 . . . . . using math symbols
Roberto finishes a triathlon in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among allwomen in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better inrelation to their gender?
Answer:
Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever had the lower z-score was faster, that is, did better in relation to their gender.
Roberto:
63.2 minutes. Mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. So [tex]X = 63.2, \mu = 69.4, \sigma = 8.9[/tex]
Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{63.2 - 69.4}{8.9}[/tex]
[tex]Z = -0.7[/tex]
Zandra:
79.3 minutes. Mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. So [tex]X = 79.3, \mu = 84.7, \sigma = 7.4[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{79.3 - 84.7}{7.4}[/tex]
[tex]Z = -0.73[/tex]
Due to the lower z-score of the finishing time, Zandra was faster, that is, doing better in relation to her gender.
A restaurant offers a $12 dinner special that has 5 choice for an appetizer, 13 choices for an entree and 4 choice for a dessert how many different meals are available when you select an appetizer an entree and dessert?
To find total choices, multiply the quantity of each part by each other:
5 x 13 x 4 = 260
Answer: 260 different meals.
Given the sequence rn defined recursively below, find r4.
r1=2
rn=4rn−1−3
Answer:
[tex]r_4 = 65[/tex]
Step-by-step explanation:
Given
[tex]r_1 = 2[/tex]
[tex]r_n = 4r_{n-1} - 3[/tex]
Required
Find [tex]r_4[/tex]
Calculating the value of [tex]r_4[/tex]
This means n = 4;
Hence,
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_4 = 4r_{4-1} - 3[/tex]
[tex]r_4 = 4r_3 - 3[/tex]
At this point, we need to solve for [tex]r_3[/tex];
Taking n as 3
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_3 = 4r_{3-1} - 3[/tex]
[tex]r_3 = 4r_2 - 3[/tex]
At this point, we need to solve for [tex]r_2[/tex];
Taking n as 2
[tex]r_n = 4r_{n-1} - 3[/tex]
[tex]r_2 = 4r_{2-1} - 3[/tex]
[tex]r_2 = 4r_1 - 3[/tex]
Substitute 2 for [tex]r_1[/tex]
[tex]r_2 = 4 * 2 - 3[/tex]
[tex]r_2 = 8 - 3[/tex]
[tex]r_2 = 5[/tex]
Solving for [tex]r_3[/tex]
Substitute 5 for [tex]r_2[/tex]
[tex]r_3 = 4 * 5 - 3[/tex]
[tex]r_3 = 20 - 3[/tex]
[tex]r_3 = 17[/tex]
Solving for [tex]r_4[/tex]
Substitute 17 for [tex]r_3[/tex]
[tex]r_4 = 4 * 17 - 3[/tex]
[tex]r_4 = 68 - 3[/tex]
[tex]r_4 = 65[/tex]
Hence, [tex]r_4 = 65[/tex]
