Answer:
6.68% probability that the mean weight is below 68.5g.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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:
[tex]\mu = 70, \sigma = 2, n = 4, s = \frac{2}{\sqrt{4}} = 1[/tex]
Probability that the mean weight is below 68.5g:
This is 1 subtracted by the pvalue of Z when X = 68.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{68.5 - 70}{1}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
6.68% probability that the mean weight is below 68.5g.
Answer:
P(x ∠ 68.5) = 0.07
Step-by-step explanation:
Got it right on khan.
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Density = Mass / Volume
2.7 = 54 / V
V = 54 / 2.7
V = 20 cubic cm
A shop has 4 types of sweets (chocolate, taffy, gummies, and cookies), 2 types of snacks (chips and crackers), and 3 types of drinks (sodas, juice, and sports drinks).
Mystery boxes are put together that randomly combine 1 sweet, 1 snack, and 1 drink.
What is the probability that a mystery box contains chocolate, chips, and juice?
Answer:
1/24
Step-by-step explanation:
1/4*1/2*1/3 = 1/24
Solve the following equation for x.
|x/4+3|<6
Answer:
x<12
Step-by-step explanation:
subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12
What is the purchase price of the land
Answer:
Answer:B. $100,000
Step-by-step explanation:
x is the number of years since the purchase of the land.
That means that when 0 years have passed by, it is when the land was purchased.
At x = 0, the price of the land was $100,000.
That means that the purchase price of the land is $100,000.
1. An LG Dishwasher, which costs $800, has a 20% chance of needing to be replaced in the first 2 years of purchase. A two-year extended warrantee costs $112.10 on a dishwasher. What is the expected value of the extended warranty assuming it is replaced in the first 2 years?
2. Approximately 10% of all people are left-handed. Consider a grouping of fifteen (15) people.
a. State the random variable.
b. Write the probability distribution.
c. Draw a histogram.
d. Describe the shape of the histogram.
e. Find the mean.
f. Find the variance.
g. Find the standard deviation.
Step-by-step explanation:
The expected value of the extended warrant is calculated as follow.
Value of Waranty
= 800 x 20% − 112.10
= 800 x 20/100 − 112.10
= 47.9
The expected value of the extended warranty assuming it is replaced in the first 2 years is given as follow.
Expected value=800-112.10=>687.90
Therefore, required expected value of extended warranty is 687.90
2.
Given information:
Number of Trials (n) = 15
Probability of Success (p) = 0.10
a) Let X represents the number of left-handed people.
b) The probability distribution follows binomial distribution.
X ∼ Binomial distribution
The probability distribution is given as follow.
P(X = x) = ^nCx(p)^x(1 − p)^n − x
c)The histogram is given as follow. (See attachment)
d) The shape of histogram is skewed right.
e) The mean is calculated as follow.
Mean
=n x p
= 15 x 0.10
= 1.5
f) The variance is calculated as follow.
Variance
= n x p x q
= 15 x 0.10 x 0.90
= 1.35
g) The standard deviation is calculated as follow.
Standard deviation
=√n x p x q
=√15 x 0.10 x 0.90
= 1.162
Dorothy Kaatz, a computer programmer, earns a regular hourly rate of
$15.25 and earns double that when she works overtime. Kaatz usually works
40 regular hours and 12 hours overtime while she's trying to update the
company's systems before the month's end. What is her straight-time pay?
What is her overtime pay? What is her total pay?
Answer:
$976
Step-by-step explanation:
Straight time pay= $15.25(hourly rate) × 40(hours worked)= $610
Overtime Rate = 15.25×2= $30.50
Overtime Pay= $30.5 × 12 (Hours worked overtime)= $366
Total Pay= Basic wage + Overtime Wage = $976
What are the factors of 2x + 3x 54? Select two options
2x - 9
2x6
2x + 6
X-6
x+6
Answer:
(2x -9)(x +6)Step-by-step explanation:
Perhaps you're factoring ...
2x² +3x -54
= 2x² +12x -9x -54 . . . . rewrite 3x appropriately
= 2x(x +6) -9(x +6) . . . . factor pairs of terms
= (2x -9)(x +6) . . . . . . . . finish the factoring
The factors are (2x -9) and (x +6).
A research company desires to know the mean consumption of meat per week among people over age 27. A sample of 1179 people over age 27 was drawn and the mean meat consumption was 1.5 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 99% confidence interval for the mean consumption of meat among people over age 27. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{1.2}{\sqrt{1179}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 0.1 = 1.4 pounds
The upper end of the interval is the sample mean added to M. So it is 1.5 + 0.1 = 1.6 pounds
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Simplify the quotient shown 3480 divided by 29
Answer:
120
Step-by-step explanation:
3480/29=120
120
Simplify ———
1
final result is 120
What is the solution set up 7x^2+3X=0
Answer:
X=0,X=-3/7
Step-by-step explanation:
7x^2+3x=0
x(7x+3)=0
x=0
7x+3=0
7x=-3
x=-3/7.
Answer:-3/7
Step-by-step explanation:
Firstly add -3x to both sides of equation. 7x^2+3x-3x=0+-3x
7x^2=-3x
Divid both sides by X
7x^2/X=-3/X
7x=-3
Divid both sides by 7
7x/7=-3/7
X=-3/7
1/x=1/2 / 4/5
Solve for x.
X =
Answer:
1/x = 1/2÷4/5
1/x=1/2 x 5/4
1/x=5/8
5x=8
x=1.6
Bob is a travel agent. He receives 7% commission when he books a cruise for a customer. How much commission will he receive for booking a $3,900 cruise?
Answer:
$273
Step-by-step explanation:
$3900= 100%
$39 = 1%
39(1%)*7= $273 (7%)
The commission will he received should be $273
Given that,
He receives 7% commission when he books a cruise for a customercalculation:= 7% of $3,900
= $273
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What is the product of 4.672 and 8?
Answer:
12.672
Step-by-step explanation:
Answer: 37.376
Step-by-step explanation: Because 4.672 x 8 is 37.376
Simplify the following:
(4x^3+2x) + (8x^3 -5x + 4)
Answer:
12x^3 - 3x + 4
Im 100% percent sure and if you are kind enough, I’d love a BRAINLIEST :)
an amount was invested at r% per quarter. what value of r will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Answer:
[tex]r=25.7\%[/tex] will ensure that accumulated amount at the end of one year is 1.5 times more than amount invested
Step-by-step explanation:
Given: An amount was invested at r% per quarter.
To find: value of r such that accumulated amount at the end of one year is 1.5 times more than amount invested
Solution:
Let P denotes amount invested and n denotes time
As an amount (A) was invested at r% per quarter,
[tex]A=P\left ( 1+\frac{r}{400} \right )^{4n}[/tex]
According to question, accumulated amount at the end of one year is 1.5 times more than amount invested.
So,
[tex]A=1.5P+P=2.5P\\A=2.5P\\P\left ( 1+\frac{r}{400} \right )^{4n}=2.5P[/tex]
Put n = 1
[tex]P\left ( 1+\frac{r}{400} \right )^{4}=2.5P\\\left ( 1+\frac{r}{400} \right )^{4}=2.5\\1+\frac{r}{400} =(2.5)^{\frac{1}{4}}\\\frac{r}{100}=(2.5)^{\frac{1}{4}}-1\\r=100\left [ (2.5)^{\frac{1}{4}}-1 \right ]\\=25.7\%[/tex]
Is the function given by f(x)equalsleft brace Start 2 By 2 Matrix 1st Row 1st Column one fourth x plus 1 comma 2nd Column for x less than or equals 4 comma 2nd Row 1st Column 4 x minus 11 comma 2nd Column for x greater than 4 comma EndMatrix continuous at xequals4? Why or why not? Choose the correct answer below. A. The given function is continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist. B. The given function is not continuous at xequals4 because f(4) does not exist. C. The given function is continuous at xequals4 because the limit is 2. D. The given function is not continuous at xequals4 because ModifyingBelow lim With x right arrow 4 f (x )does not exist.
Answer:
C. The given function is continuous at x=4 because the limit is 2.
Step-by-step explanation:
Given the function:
[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]
We are to determine if the function is continuous at x=4.
For a function to be continuous at some value c in its domain:
f(c) must be defined.[tex]Lim_{x \to c}$ f(x)[/tex] must exist. [tex]f(c)=Lim_{x \to c}$ f(x)[/tex]Now: at x=4
[tex]f(4)=\dfrac{1}{4}*4+1=2[/tex][tex]Lim_{x \to 4}f(x)=2[/tex]Since the two values are the same, we say that f(x) is continuous at x=4.
The correct option is C.
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
A cylinder is formed when rotating the 3-D figure around y-axis
In right triangle $ABC,$ $\angle C = 90^\circ.$ Median $\overline{AM}$ has a length of $19,$ and median $\overline{BN}$ has a length of $13.$ What is the length of the hypotenuse of the triangle?
Answer:
AB = 2√106 ≈ 20.591
Step-by-step explanation:
The Pythagorean theorem says the square of the hypotenuse is equal to the sum of the squares of the legs.
For median AM, we have ...
AM² = CM² +AC² = (BC/2)² +AC²
For median BN, we have ...
BN² = CN² +BC² = (AC/2)² +BC²
The sum of these two equations is ...
AM² +BN² = BC²/4 +AC² +AC²/4 +BC² = (5/4)(AC² +BC²)
AM² +BN² = (5/4)(AB²)
The hypotenuse of triangle ABC is then ...
AB = √(4/5(AM² +BN²))
AB = 2√((19² +13²)/5)
AB = 2√106 ≈ 20.591
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry
What is the slope of the line that passes through the points (-3, -3) and
(-18, -23)? Write your answer in simplest form.
Answer:
work is shown and pictured
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
Required:
a. Create a valid probability table.
b. How much should the trader expect to gain or lose?
c. Should the trader buy the stock? Explain.
Answer:
Step-by-step explanation:
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will close in the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below 20.
a) Let X represent the price of the option
x P(X=x)
$1000 20/100 = 0.2
$200 50/100 = 0.5
$0 30/100 = 0.3
b) Expected option price
[tex]= \sum x.P(X=x)\\\\ = 1000 * 0.2 + 200 * 0.5 + 0 = \$ 300[/tex]
Therefore expected gain = $300 - $150 = $150
c) The trader should buy the stock. Since there is an positive expected gain($150) in trading that stock option.
Question 1 of 20 :
Select the best answer for the question.
1. Divide7/15 by 3/5
OA%
O B./25
O c. 75/21
O D.21/75
Answer:
7/9
Step-by-step explanation:
7/15 ÷ 3/5
Copy dot flip
7/15 * 5/3
7/3 * 5/15
7/3 * 1/3
7/9
The first term in the sequence 5, 7, −7, ... is 5. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is (−1) times the previous term. For example, the second term is 5+2 and the third term is (−1)×7. What is the 255th term of the sequence?
Answer:
Step-by-step explanation:
According to the condition, your terms are arranged as
5, 7 , -7 ,-5, 5, 7, -7, 5, -5,...................
So one loop will have 4 terms: 5, 7, -7. -5
Hence after 63 loops, the new loop has only 3 terms. That means the last loop will be 5, 7 ,-7. In other words, the 255th term will be -7
I need help with this one
Answer:
-12
Step-by-step explanation:
Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation of 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Answer:
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 45 - 1 = 44
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0141
The margin of error is:
M = T*s = 2.0141*170.5 = 343.4
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 390.47 - 343.40 = 47.07 units per month
The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month
The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87
A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were:
y = a + bx
a = -0.762
b = 0.119
r2 = 0.8649
r = 0.93
A) Write the equation of the Least Squares Regression line of the form y = + x
B) If a country increases its life expectancy, the happiness index will increase or decrease?
C) If the life expectancy is increased by 3.5 years in a certain country, how much will the happiness index change?
D) Use the regression line to predict the happiness index of a country with a life expectancy of 67 years.
Answer:
(A) [tex]y=-0.762+0.119x[/tex]
(B) If a country increases its life expectancy, the happiness index will increase.
(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
Step-by-step explanation:
A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).
The output of the regression analysis are as follows:
a = -0.762
b = 0.119
r² = 0.8649
r = 0.93
(A)
The equation of the Least Squares Regression line of the form y = _ + _ x is:
[tex]y=-0.762+0.119x[/tex]
(B)
The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.
The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.
Thus, if a country increases its life expectancy, the happiness index will increase.
(C)
Compute the value of y for x = x + 3.5 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]
Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.
(D)
Compute the value of y for x = 67 as follows:
[tex]y=-0.762+0.119x[/tex]
[tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]
Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.
Graph the line that represents this equation. 3x - 4y =8
Answer:
See attachment
Step-by-step explanation:
The solution is given in the image.
Which graph is the graph of the function?The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.
What does the axis of a graph constitute?An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. (f + g)(x) = x - 7
Step-by-step explanation:
→Set it up, like so:
-3x - 5 + 4x - 2
→Add like terms (-3x and 4x, -5 and -2):
x - 7
Accident rate data y1, ...., y12 were collected over 12 consecutive years t=1,2,...12. At over 12 consecutive years t = 1,2,..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.
a. The accident rate y is a linear function of t with the new safety regulations having no effect.
b. The accident rate y is a quadratic function of t with the new regulations having no effect.
c. The accident rate y is a linear function of t. The slope for t>= 7 is the same as for t<7. However there is a discrete jump for t=7.
d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.
Answer:
The correct option is;
The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7
Step-by-step explanation:
The given parameters are;
Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂
Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂
Accident rate equation is a linear model given as follows;
y = X·B + E
Where:
y = Accident rate
X = Slope of linear model
B = Year
E = y intercept of model
At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;
Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁
After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂
Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)
Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
Which expressions represent a perfect square monomial and its square root? Check all that apply. 121; 11 4x2; 2x 9x2 – 1; 3x - 1 25x; 5x 49x4; 7x2
Answer:
its 1,2,and 5
Step-by-step explanation:
Answer:
A, B, E
Step-by-step explanation:
Edge
