Answer:
The candle burns for 244 minutes.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 249, \sigma = 20[/tex]
Find the number of minutes a scented candle burns if it burns for a shorter time than 60% of all scented candles.
This is the 100-60 = 40th percentile, which is X when Z has a pvalue of 0.4. So X when Z = -0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.253 = \frac{X - 249}{20}[/tex]
[tex]X - 249 = -0.253*20[/tex]
[tex]X = 244[/tex]
The candle burns for 244 minutes.
f(x) = (x + 2)(x + 2)
[tex]\displaystyle f(x) = (x + 2)(x + 2)[/tex]
[tex]\displaystyle f(x) = (x + 2)^2[/tex]
Answer:
[tex]f(x) = {(x + 2)}^{2} [/tex]
Step-by-step explanation:
[tex]f(x) = (x + 2)(x + 2) \\ f(x) = {(x + 2)}^{2} [/tex]
hope this helps you.
if the vertex of a parabola is negative for 6 and the other point of the curve is (-3,14) what is the coefficient of the squared expression in Parabola equation?
A. 6
B. 4
C. 8
D. 2
Answer:
coefficient of the square is a.6
Information about five planets is shown in the table below.
Planet Diameter (km) Mass (kg)
Mercury 4.88 x 10 3.3 x 1023
Jupiter 1.43 x 10 1.898 x 1027
Earth
1.28 104 5.97 x 1024
Mars
6.78 x 103 6.42 x 1023
Saturn
1.21 10% 5.68 x 1026
a) Write down the name of the planet with the greatest mass.
b) Work out the radius of Mercury giving your answer as an ordinary number.
c) Work out the difference between the masses of Jupiter and Saturn.
Give your answer in standard form.
Answer:
(a)Jupiter
(b)24.4 km
(c)[tex]1.33 \times 10^{27}$ kg[/tex]
Step-by-step explanation:
Part A
The planet with the greatest ma.ss is Jupiter.
It has a ma.ss of [tex]1.898 X 10^{27}$ kg[/tex]
Part B
The diameter of Mercury = 4.88 X 10
Radius = Diameter/2
Therefore:
Radius of Mercury
[tex]=\dfrac{4.88 X 10}{2}\\ =2.44 X 10\\=24.4$ km[/tex]
Part C
[tex]M$a.ss of Saturn = 5.68 X 10^{26}\\$Mass of Jupiter = 1.898 X 10^{27}\\$Difference in their ma.ss =(1.898 X 10^{27})-(5.68 X 10^{26})\\=1.33 \times 10^{27}$ kg[/tex]
Find the interquartile range (IQR) of the data in the dot plot below. luis lacrosse scoring each season pls helpppppppppppppppp
Answer:
3.5
Step-by-step Explanation:
To find the IQR of the given data in the dot plot shown in the attachment below, follow the steps below:
==>Step 1: write out each data point represented on the dot plot in an ordered manner. A dot represents each value of number of goals scored by Luis each season.
Thus, we would have:
43 (1 dot)
44, 44, 44 (3 dots)
45, 45(2 dots)
47 (1 dot)
48, 48 (2 dots)
Our data set from the least to the highest is: 43, 44, 44, 44, 45, 45, 47, 48, 48
==>Step 2: Find the median
Our median value is the middle value of our data set. Thus:
43, 44, 44, 44, | 45, | 45, 47, 48, 48
Our median would be 45.
==>Step 3: Find the upper and lower median (Q3 & Q1):
Our upper median (Q3) would be the middle value of the upper portion of our data set, while our lower median would be the middle value portion of our data set.
Upper portion of our data set are the values we have from our median point upwards towards our right, while the lower portion are values downwards to our left. Thus, our upper and lower median values are shown below which would be the mean of the 2 middle values shown in the brackets below:
43, (44, 44,) 44, | 45, | 45, (47, 48,) 48
Upper median (Q3) = (47+48) ÷ 2 = 47.5
Lower median (Q1) = (44+44) ÷ 2 = 44
==>Step 4: Subtract the lower median from the upper median to get the IQR.
IQR = Upper median (Q3) - Lower median (Q1)
IQR = 47.5 - 44
IQR = 3.5
Answer:
3.5
Step-by-step Explanation:
To find the IQR of the given data in the dot plot shown in the attachment below, follow the steps below:
==>Step 1: write out each data point represented on the dot plot in an ordered manner. A dot represents each value of number of goals scored by Luis each season.
Thus, we would have:
43 (1 dot)
44, 44, 44 (3 dots)
45, 45(2 dots)
47 (1 dot)
48, 48 (2 dots)
Our data set from the least to the highest is: 43, 44, 44, 44, 45, 45, 47, 48, 48
==>Step 2: Find the median
Our median value is the middle value of our data set. Thus:
43, 44, 44, 44, | 45, | 45, 47, 48, 48
Our median would be 45.
==>Step 3: Find the upper and lower median (Q3 & Q1):
Our upper median (Q3) would be the middle value of the upper portion of our data set, while our lower median would be the middle value portion of our data set.
Upper portion of our data set are the values we have from our median point upwards towards our right, while the lower portion are values downwards to our left. Thus, our upper and lower median values are shown below which would be the mean of the 2 middle values shown in the brackets below:
43, (44, 44,) 44, | 45, | 45, (47, 48,) 48
Upper median (Q3) = (47+48) ÷ 2 = 47.5
Lower median (Q1) = (44+44) ÷ 2 = 44
==>Step 4: Subtract the lower median from the upper median to get the IQR.
IQR = Upper median (Q3) - Lower median (Q1)
IQR = 47.5 - 44
IQR = 3.5
A rectangular bin is going to be made with a volume of 492 in3. The base of the bin will be a square and the top will be open. The cost of the material for the base is 0.8 cents per square inch, and the cost of the material for the sides is 0.6 cents per square inch. Determine the dimensions of the bin that will minimize the cost of manufacturing it. What is the minimum cost
Answer:
base side = 9.037 inches
height = 6.024 inches
Minimum cost = 196 cents
Step-by-step explanation:
The volume of the bin is given by:
[tex]Volume = side^2 * height[/tex]
and the surface area of the bin is given by:
[tex]Surface\ area = side^2 + 4*side*height[/tex]
The cost of the bin will be:
[tex]Cost = 0.8*side^2 + 0.6*4*side*height[/tex]
[tex]Cost = 0.8*side^2 + 2.4*side*height[/tex]
From the volume equation, we have:
[tex]height = 492 / side^2[/tex]
Now the cost will be:
[tex]Cost = 0.8*side^2 + 2.4*side*492/side^2[/tex]
[tex]Cost = 0.8*side^2 + 1180.8/side[/tex]
To find the side that gives the minimum cost, we can find the derivative of Cost in relation to side and then make it equal zero:
Abbreviating Cost as C and side as s, we have:
[tex]dC/ds = 0.8*2*s - 1180.8/s^2[/tex]
[tex]1.6s - 1180.8/s^2 = 0[/tex]
[tex]1.6s = 1180.8/s^2[/tex]
[tex]1.6s^3 = 1180.8[/tex]
[tex]s^3 = 738[/tex]
[tex]s = 9.037\ in[/tex]
Finding the height of the bin, we have:
[tex]height = 492 / 9.037^2[/tex]
[tex]height = 6.024\ in[/tex]
The minimum cost is:
[tex]Cost = 0.8*9.037^2 + 1180.8/9.037 = 196\ cents[/tex]
Factor 5x4 - 30x2 - 135.
Answer:
20 - 60 - 135
95
Step-by-step explanation:
All you have to do is add/subtract the factors together
Answer:
5(x - 3)(x + 3)(x^2 + 3)
Step-by-step explanation:
First take out the GCF of the 3 numbers (5):-
= 5(x^4 - 6x^2 - 27)
= 5(x^2 - 9)(x^2 + 3)
= 5(x - 3)(x + 3)(x^2 + 3).
Fraud detection has become an indispensable tool for banks and credit card companies to combat fraudulent credit card transactions. A fraud detection firm has detected some form of fraudulent activities in 2%, and serious fraudulent activities in 0.75% of transactions. Assume that fraudulent transactions remain stable.
a. What is the probability that fewer than 2 out of 110 transactions are fraudulent?
b. What is the probability that fewer than 2 out of 105 transactions are seriously fraudulent?
Answer:
a) 35.17% probability that fewer than 2 out of 110 transactions are fraudulent
b) 81.35% probability that fewer than 2 out of 105 transactions are seriously fraudulent
Step-by-step explanation:
For each transaction, there are only two possible outcomes. Either they are fradulent(or seriously fraudulent), or they are not. Transactions are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
a. What is the probability that fewer than 2 out of 110 transactions are fraudulent?
2% are fraudulent, so [tex]p = 0.02[/tex]
110 transactions, so [tex]n = 110[/tex]
This is
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{110,0}.(0.02)^{0}.(0.98)^{110} = 0.1084[/tex]
[tex]P(X = 1) = C_{110,1}.(0.02)^{1}.(0.98)^{109} = 0.2433[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.1084 + 0.2433 = 0.3517[/tex]
35.17% probability that fewer than 2 out of 110 transactions are fraudulent.
b. What is the probability that fewer than 2 out of 105 transactions are seriously fraudulent?
0.75% are seriously fraudulent, so [tex]p = 0.0075[/tex]
105 transactions, so [tex]n = 105[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = 0) = C_{105,0}.(0.0075)^{0}.(0.9925)^{105} = 0.4536[/tex]
[tex]P(X = 1) = C_{105,1}.(0.0075)^{1}.(0.9925)^{104} = 0.3599[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.4536 + 0.3599 = 0.8135[/tex]
81.35% probability that fewer than 2 out of 105 transactions are seriously fraudulent
what is the value of y
Answer:
y=54 degrees
Step-by-step explanation:
2y+72=180
2y=108
y=54
Answer:
B
Step-by-step explanation:
72 + y + y = 180
72 + 2y = 180
2y = 108
2y/2 = 108/2
y = 54
Hope this helps ^-^
What is the product -3 1/3of -8 7/10 and ?
Answer:
Brainliest!!!
Step-by-step explanation:
See picture!!
Answer:
29
Step-by-step explanation:
Annapolis Company's bank statement indicated an ending cash balance of $9,340. Alpha's accountant discovered that outstanding checks amounted to $865 and deposits in transit were $840. Additionally, the bank statement showed service charges of $25. What is the correct adjusted ending cash balance
Answer:
The correct answer is $9,315
Step-by-step explanation:
Solution
Given that:
The ending cash balance = $9340
Checks outstanding amounted to = $865
The deposit in transit = $840
Bank statement service charges = $25
Now,
We will find the correct adjusted ending cash balance which is given below:
Correct adjusted ending cash balance = Unadjusted Balance - Outstanding Check + Deposit in transit
= $9,340 - $865 + $840
=$8,475 + $840
=$9,315
Hence,
The correct adjusted ending cash balance is $9,315
If f(x) = x^2 is reflected over the x-axis and the shifted 4 units down, what is the equation of the new function, g(x)?
Answer:
g(x) = -x² - 4
Step-by-step explanation:
In this case, we are only changing a (reflection and vertical shrink/stretch) and k (vertical movement)
k = -4 because we are moving 4 units down
a = -1 because we are just reflecting over the x-axis
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 442 gram setting. It is believed that the machine is underfilling the bags. A 44 bag sample had a mean of 438 grams. Assume the population variance is known to be 576. A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
p value is 0.1343
Step-by-step explanation:
Null: u>= 442
Alternative: u < 442
Using the formula for z score:
(x - u)/sd/√n
Where x is 438, u = 442 sd can be determined from the variance = √variance =√576 = 24 and n = 44
z score = 438-442 / (24/√44)
z score = -4/(24/6.6332)
z = -4/3.6182
z =-1.1055
Now let's find the p value at 0.1 significance level using a z score of -1.1055, using a p value calculator, p value is 0.1343 which greatest than 0.1 meaning the day is not sufficient enough to conclude that the machine is underfilling the bags.
Discuss what some of those rules are, and how they get applied in your analysis. If an engineering challenge includes "more than one reasonable estimator," (Devore, p. 249, Example 6.1 in Section 6.1) how do engineers know which to pick, and what issues arise statistically and in engineering management when making those choices?
Answer:
The engineer must verify and verify through a statistical inference that estimates and possible parameters may emerge, as well as determine what hypothesis tests should be performed to draw the most accurate conclusion.
Step-by-step explanation:
The engineer must assume that there may be more than one reasonable estimator for a different event or experiment; Something that could help you would be to perform an estimation of parameters, in that estimation it is required to know the properties of the estimators; that is to say that the closer the value of an estimator is to the real value of the parameter, it could be said that it is the most efficient or exact extimator.
What is the sampling method used in the following scenario? The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
Answer:
Step-by-step explanation:
The method applied in this scenario is called simple random sampling. A sample of 100 customers is chosen from a larger population of customers and each customer has the same chance of being selected for the survey at any given time. Also, the chance of selecting 100 customers from each store is the same during the sampling process. The order of sampling at each store does not follow a certain order, thus, It is different from systematic random sampling.
Write an equation for a polynomial function that has the given roots
-2. 3i , and 5
Answer:
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
Step-by-step explanation:
If 3i is one root then another is -3i.
In factor form we have:
(x + 2)(x - 5)(x - 3i)(x + 3i) = 0
(x^2 - 3x - 10)(x^2 -9i^2) = 0
(x^2 - 3x - 10)(x^2 + 9) = 0
x^4 + 9x^2 - 3x^3 - 27x - 10x^2 - 90 = 0
x^4 - 3x^3 - x^2 - 27x - 90 = 0.
Please help mehhh please!!
Answer:
It says your picture failed to load
Step-by-step explanation:
did it only happen to me or other people
Answer:
fraction: 70/100
decimal: 0.7
percent: 70%
Step-by-step explanation:
hope dis helps u! mark as brainlest if possible!
Google I would like to purchase 10 bags of chicken wings the store is selling three bags for $51.00 what is the cost of 10 bags of chicken wings
a. 61.00
b. 71.00
c. 170.00
d. 130.00
Answer:
A 61.00
Step-by-step explanation:
51 Added to 10 Equals 61.00 which is the Cost of 10 Bags of chicken Wings. Your Welcome.
what polynomial has roots of -5, - 4 and 1
Answer:
[tex]\boxed{\sf \ \ \ x^3+8x^2+11x-20 \ \ \ }[/tex]
Step-by-step explanation:
hello,
(x+5)(x+4)(x-1) is one example of polynomial which has roots of -5,-4 and 1
[tex](x+5)(x+4)(x-1) = (x+5)(x^2-x+4x-4)=(x+5)(x^2+3x-4)\\= x^3+3x^2-4x+5x^2+15x-20=x^3+8x^2+11x-20[/tex]
hope this helps
A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have:__________. a) 18 degrees of freedom b) 200 degrees of freedom c) 199 degrees of freedom d) 181 degrees of freedom
Answer:
The correct answer to the following question will be Option d (181 degrees of freedom).
Step-by-step explanation:
The given values are:
Regression model,
n = 200
Observations,
p = 18
Now,
⇒ [tex]n-p-1[/tex]
On putting the estimated values, we get
⇒ [tex]200-18-1[/tex]
⇒ [tex]181[/tex]
So that the correct choice will be "181 degrees of freedom".
Jamie is investing $47,000 in an account paying 9.26% interest compounded continuously. What will Jamie's account balance be in 17 years?
9514 1404 393
Answer:
$226,863.29
Step-by-step explanation:
The amount is given by ...
A = Pe^(rt)
where principal P is invested at annual rate r for t years.
A = $47,000×e^(0.0926×17) ≈ $226,863.29
Answer:
the answer is $226,863.29
Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides. The area of EFGH is 35 square units. What is the value of x? 4 units 5 units 6 units 7 units
*see attachment for the figure described
Answer:
5 units
Step-by-step explanation:
==>Given the figure attached below, let where FH and EG intercepted be K.
Since FH are midpoints of parallel lines, KE = KG = x.
Given that the area of the kite EFGH = 35 square units, and we know the length of one of the diagonals = HF = KF + KH = 2 + 5 = 7, we can solve for x using the formula for the area of a kite.
Area of kite = ½ × d1 × d2
Where d1 = KH = 7
d2 = EG = KE + KG = x + x = 2x
Area of kite EFGH = 35
THUS:
35 = ½ × 7 × 2x
35 = 1 × 7 × x
35 = 7x
Divide both sides by 7
35/7 = x
x = 5
Answer:
5 units
Step-by-step explanation:
The area of a rectangle is 352in2. If the width of the rectangle is x inches, write a function for the perimeter, P(x)
Answer:2x2
Step-by-step explanation:
At a cell phone assembly plant, 75% of the cell phone keypads pass inspection. A random sample of 110 keypads is analyzed. Find the probability that more than 78% of the sample keypads pass inspection. Use at least five decimal places for the denominator.
Answer:
23.27%
Step-by-step explanation:
From the statement we know that random sample n is 110 and that p is 75% and x the percentage to evaluate is 78%
We have that the probability would be equal:
P (x > 0.78) = [tex]P(z <\frac{x-p}{\sqrt{\frac{p*(1-p)}{n} }})[/tex]
Replacing we have:
[tex]P(z <\frac{0.78-0.75}{\sqrt{\frac{0.75*(1-0.75)}{110} }})[/tex]
P ( z < 0.73) = 1 - P ( z => 0.73)
= 1 - 0.7673
= 0.2327
Therefore the probability is 23.27%
Which would be appropriate compatible numbers to use to estimate ( 19 4 5 ) ( 4 6 ) ? Using this compatible number, what is the estimated product?
Answer: first box is 20 (1/2)
Second box is 10
Answer:
Answer: first box is 20 (1/2)
Second box is 10
Step-by-step explanation:
What is simplified expression for the expression below
Answer:
9x +17
Step-by-step explanation:
distrubute the numbers outside of the parenthesis to the inside. You would then be left with 4x +32 + 5x -15 from there you would combine like terms leaving you with 9x + 17
Please answer this correctly
problem decoded dude
thank and follow meh
Answer:
50%
Step-by-step explanation:
There are 6 sides on a die, three Of Which are even and 3 odd.
the even ones are 2,4 and 6 and the odds are 1, 3 and 5
since there are 3 evens, u divide it by the total number of outcomes 6 which is 1/2 or 50percent
The valve was tested on 270 engines and the mean pressure was 6.6 lbs/square inch. Assume the variance is known to be 0.49. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications
Answer:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
Step-by-step explanation:
Information given
[tex]\bar X=6.6[/tex] represent the sample mean
[tex]s=\sqrt{0.49}= 0.7[/tex] represent the population deviation
[tex]n=270[/tex] sample size
[tex]\mu_o =6.5[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to verify
We want to verify if the true mean for this case is equal to 6.5 lbs/square inch or not , the system of hypothesis would be:
Null hypothesis:[tex]\mu= 6.5[/tex]
Alternative hypothesis:[tex]\mu \neq 6.5[/tex]
The statistic for this case is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{6.6-6.5}{\frac{0.7}{\sqrt{270}}}=2.347[/tex]
The p value for this case would be given by"
[tex]p_v =2*P(z>2.347)=0.0189[/tex]
For this case since the p value is higher than the significance level we don't have enough evidence to conclude that the true mean is significantly different from 6.5 lbs/square inch at 10% of significance. So then there is not enough evidence to conclude that the valve does not perform to the specifications
Please answer this correctly
Answer:
33.3%
Step-by-step explanation:
The numbers greater than 6 from the spinner are 7 and 8.
2 numbers out of total 6 numbers.
2/6 = 1/3
= 0.333
= 33.3%
prove that (81/16)^-3/4 ×[(25/9)^-3/2 ÷ (5/2)^-3]=1
Answer:
First write them in positive exponent form
(16/81)¾ × [ (9/25)^3/2 ÷ (2/5)³ ]
(2⁴×¾)/ (3⁴×¾) × [ (3² × ^3/2) / (5² ×^3/2) ÷ 2³/5³)
Simplify the terms
2³/3³ × ( 3³ / 5³ ÷ 2³/5³)
Solve the terms in the bracket
2³/3³ × (3³/5³×5³/2³)
You will get
2³/3³ × 3³/2³ = 1
They will cancel each other so the answer will be 1
Hope this helps.
Mr. Taylor filled out a bracket for the NCAA National Tournament. Based on his knowledge of college basketball, he has a 0.54 probability of guessing any one game correctly. (a) What is the probability Mr. Taylor will pick all 32 of the first round games correctly
Answer:
The probability is [tex]2.7327 \times 10^{-9}[/tex]
Step-by-step explanation:
The probability of guessing correctly, P = 0.54
Probability of not guessing correctly, q = 1 – P
q = 1 – 0.54 = 0.46
Number of trials, n = 32
Now calculate the probability that Mr. Taylor will pick 32 correctly in first round of the game.
Below is the calculation using binomial distribution.
[tex]Probability = \left ( _{k}^{n}\textrm{} \right )P^{k}(1-P)^{(n-k)} \\= \left ( _{32}^{32}\textrm{} \right )0.54^{32}(0.46)^{(32-32)} \\= 0.54^{32} \\= 2.7327 \times 10^{-9}[/tex]