Answer:
a) P(0.05 < p < 0.06) = 0.1332
b) P(p > 0.07) = 0.0011.
c) P(p < 0.03) = 0.1539
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose that past records indicate that the probability that a new car will need a warranty repair in the first 90 days of use is 0.04.
This means that [tex]p = 0.04[/tex]
Sample of 400.
This means that [tex]n = 400, s = \sqrt{\frac{0.04*0.96}{400}} = 0.0098[/tex]
a. between 0.05 and 0.06?
This is the p-value of Z when X = 0.05 subtracted by the p-value of Z when X = 0.05. So
X = 0.06
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.04}{0.0098}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
X = 0.05
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.05 - 0.04}{0.0098}[/tex]
[tex]Z = 1.02[/tex]
[tex]Z = 1.02[/tex] has a p-value of 0.8461.
0.9793 - 0.8461 = 0.1332
So
P(0.05 < p < 0.06) = 0.1332
b. above 0.07?
This is 1 subtracted by the p-value of Z when X = 0.07. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.07 - 0.04}{0.0098}[/tex]
[tex]Z = 3.06[/tex]
[tex]Z = 3.06[/tex] has a p-value of 0.9989.
1 - 0.9989 = 0.0011. So
P(p > 0.07) = 0.0011.
c. below 0.03?
This is the p-value of Z when X = 0.03. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.03 - 0.04}{0.0098}[/tex]
[tex]Z = -1.02[/tex]
[tex]Z = -1.02[/tex] has a p-value of 0.1539. So
P(p < 0.03) = 0.1539
A sequence is defined by the recursive function f(n + 1) = f(n). It f(3) = 9, what is f{1) ?
Answer:
because f(n) = f(n + 1)
=> f(3) = f(2) = f(1) = 9
can someone help please with thi I only have a 1 minute left PELASE
Answer: The Last Choice- D. 2/3 x 2/5
Step-by-step explanation:
I guessed the answer............ JK
1/3 x 1/5 = 1/15
1/3 x 2/5 = 2/15
2/3 x 1/5 = 2/15
2/3 x 2/5 = 4/15
So, the last choice is correct.
Given a total-revenue function R(x) = 700/x? - 0.2x and a total-cost function 1 3 C(x) = 1400(x² + 2) +600, both in thousands of dollars, find the rate at which total profit is changing when x items have been produced and sold. P'(x) =
Answer:
Step-by-step explanation:
abcdefghijklmnopqrstuvwxyz
Aldo has been given a list of 3 bands and asked to place a vote. His vote must have the names of his favorite and second favorite bands from the list. How many different votes are possible?
Answer:
6
Step-by-step explanation:
1) A B C
2) B A C
3) C A B
4) A C B
5) B C A
6) C B A
(I probably understood it incorrectly)
Find the Surface Area and the Volume.
Answer:
volume = 1,000
surface area = 930
Step-by-step explanation:
the volume = (½×(14+6) ×4) × 25
= 1,000 cm³
the surface area =
(2×½×(14+6) ×4) + ((14+7+7+6) ×25)
= 80+850
= 930 cm²
2 times the difference between 49.5 and 37.5
Answer:
24
Step-by-step explanation:
diff is 12
12x2 is 24
1. Cheryl Douglas works 43 hours in a week for an exempt salary of $1,827 per week. What are Cheryl's gross weekly earnings?
Answer:
$1827
Step-by-step explanation:
Since Cheryl is said to be paid an exempt salary. Then it can be said that Cheyk does not qualify for minimum wage or overtime pay, Hence, exempt payment is in terms or salary rather than wage. Similarly. Gross earning refers the amount a worker receives as income over a certain period of time. The gross income has not been subjected to tax charges or any form of deduction. Hence, it could be said to be the outright earning paid to an employee before any deduction is made.
Hence, Cheryl's gross weekly earning is $1827 per week.
The following data relate to direct materials costs for February: Materials cost per yard: standard, $1.90; actual, $2.05 Standard yards per unit: standard, 4.65 yards; actual, 5.08 yards Units of production: 9,500 Calculate the direct materials quantity variance. a.$7,761.50 unfavorable b.$8,374.25 favorable c.$8,374.25 unfavorable d.$7,761.50 favorable
Answer:
The correct answer is "7,239".
Step-by-step explanation:
Given values:
Standard price,
SP = $1.90
Actual quantity purchased,
AQP = [tex]5.08\times 9500[/tex]
= [tex]48,260 \ Yards[/tex]
Actual price,
AP = $2.05
Now,
The material price variance will be:
= [tex](AQP\times AP)-(AQP\times SP)[/tex]
By substituting the values, we get
= [tex](48260\times 2.05)-(48260\times 1.90)[/tex]
= [tex]98933-91694[/tex]
= [tex]7,239[/tex]
Twice a number added to another number is –8. The difference of the two numbers is 2. Find
the numbers
Answer:
-2 and -4
Step-by-step explanation:
→ Make variable's for each number
x is the first variable and y is the second
→ Form equations
2x + y = -8
x - y = 2
→ Solve
3x = -6
→ Divide both sides by 3
x = -2
→ Resubstitute that into one of the equations
-2 - y = 2
→ Add 2 on both sides
-y = 4 therefore y = -4
can someone help me plzzz fastt
Answer:
3) 7square+11square=xsquare
49+121=x square
170=x square
x=13.038
5)9square+40square=x square
81+1600=x square
1681=x square
x=41
6)4square+6square=x square
16+36=x square
x square=52
x=7.211
i do not answer the fourth question.sorry if i can i will try
In order for the data in the table to represent a linear
function with a rate of change of +5, what must be the
value of a?
Answer:
Step-by-step explanation:
Answer: C) a=18
Step-by-step explanation: Hope i helped :)
Which of the following represents a function?
What is the value ofWhat is the value of the missing angle?
A
20
B
90
C
120
D
100 the missing angle? A 20 B 90 C 120 D 100
Answer:
The missing angle is 120
Step-by-step explanation:
Given
See attachment
Required
The missing angle (?)
Let the missing angle be x
So:
[tex]x + 60 = 180[/tex] --- angle on a straight line
Collect like terms
[tex]x = 180-60[/tex]
[tex]x = 120[/tex]
After reading the directions to paint, on the paint drum, the information
indicated two coats of paint is required when using the 5 litre paint
and one coat with the 20 litre drum. With both paints 1 litre of paint
covers 9 m2
1.3.1 There are 28 rooms to be painted. Show with calculations which
will be the cheaper paint to buy.
(1
Step-by-step explanation:
jnx-avkj-uup p.l.z join
Question 4-6. Earth is 93 million miles from the Sun. Pluto is 4.67 billion miles from the Earth.Calculate the ratio of the distance from Pluto to Earth to the distance from Earth to the Sun. Use scientific notation to calculate the ratio and express your answer in standard notation. (round to the hundredths place)
Answer:
PE/SE = 5.02×10¹
Step-by-step explanation:
Sun-Earth (SE) = 93×10⁶ miles
Pluto-Earth (PE) = 4.67×10⁹ miles
so, PE/SE = (4.67×10⁹) / (93×10⁶) = (4.67×10³)/93 =
= 50.215053763440860215... =
= 5.02×10¹ / 1 or simply 5.02×10¹
in other words, Pluto is a little bit more than 50 times farther away from Earth, than Earth is from the Sun.
Which statement is true? Q A) |13| = – 13 B) – |–13| = 13 C) |–13| = 13 D) – |13| = 13
Answer:
C
Step-by-step explanation:
The absolute value of |13| and |-13| is always 13. It never goes negative unless there is a minus sign outside the absolute value | | symbol. A is wrong
B: Not correct. Read the explanation for A. The answer to B is - 13
C: Correct. See the remark the was made about A
D: Incorrect as well. The minus is outside the absolute value symbol. The answer is - 13
Answer:
C .////.
Step-by-step explanation:
When you have /13/ its always positive even if there's a negative in there. If there was the negative symbol on the outside its a negative number :)
how many oranges and mangoes are in the basket altogether if the ratio of mangoes and oranges in the basket is 2/5if there are 40 oranges in the basket
9514 1404 393
Answer:
56
Step-by-step explanation:
We are given ...
mangoes : oranges = 2 : 5
Then the ratio we want is ...
(mangoes +oranges) : oranges = (2 +5) : 5 = 7 : 5
The total number of fruits in the basket is ...
(7/5)(40) = 56 . . . mangoes + oranges in the basket
A positive real number is 5 more than another. When - 10 times the smaller is added to the square of the larger, the result is 57. Find the numbers.
Answer:
4√2 and 5+4√2
Step-by-step explanation:
Let the two numbers be x ad y
Smaller = y
Bigger = x
If a positive real number is 5 more than another, then;
x = 5 + y ... 1
When - 10 times the smaller is added to the square of the larger, the result is 57, then;
-10y + x² = 57 ...2
Substitute 1 into 2;
-10y + (5+y)² = 57
-10y + 25+10y+y² = 57
y²+25 = 57
y² = 57 - 25
y² = 32
y = √32
y = 4√2
Since x = 5 + y
x = 5 + 4√2
Hence rhe numbers are 4√2 and 5+4√2
(d) An insurance company will only sell its Select policy to people for whom the probability of a stroke in the next 10 years is less than 0.01. If a smoker with a systolic blood pressure of 200 applies for a Select policy, under what condition will the company sell him the policy if it adheres to this standard
Answer: Hello your question has some missing data that I was able to find and attach below
A recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.
answer :
The condition : Client age ≤ 31.26 years
Step-by-step explanation:
First step : perform a regression analysis via excel ( result attached below )
P-value = 2.06E-07
Next determine the condition on which the company will sell its policy
Y = - 91.7595 + 1.0767x1 + 0.2518x2 + 8.7399x3
1 < -91.7595 + 1.0767x1 + 0.2518*200 + 8.7399*1
make X1 subject of equation above
X1 < 31.26
The filling variance for boxes of cereal is designed to be .02 or less. A sample of 41 boxes of cereal shows a sample standard deviation of 0.16 ounces.
a. Use α= 0.05 to determine whether the variance in the cereal box fillings is exceeding the design specification.
b. State the null and alternative hypotheses.
c. Calculate the value of the test statistic (to 2 decimals).
d. The p-value is:_______
e. What is your conclusion?
Answer:
-
Null hypothesis H₀ : σ² ≤ 0.02
Alternative hypothesis Hₐ : σ² > 0.02
- Chi Square = 51.2
- p-value = 0.1104
- since the calculated p-value ( 0.1104 ) is greater than the level of significance ( 0.05 ).
We fail to reject null hypothesis.
- So at, 5% level of significance, there is no evidence to support that the variance in the cereal box fillings is designed to be 0.02 or less.
Step-by-step explanation:
Given the data in the question;
filling variance for boxes of cereal is designed to be .02 or less
sample size n = 41 boxes
standard deviation S = 0.16 ounces
level of significance = 0.05
Hypothesis;
Null hypothesis H₀ : σ² ≤ 0.02
Alternative hypothesis Hₐ : σ² > 0.02
{ Upper tail test }
Test statistics;
Chi Square = [ ( n-1 ) × S² ] / σ²
Chi Square = [ ( 41-1 ) × (0.16)² ] / 0.02
Chi Square = [ 40 × 0.0256 ] / 0.02
Chi Square = 1.024/ 0.02
Chi Square = 51.2
Degree of freedom df = n - 1 = 41 - 1 = 40
Chi square value at 0.05 and df of 40 = 55.7585
p-value = 0.1104
since the calculated p-value ( 0.1104 ) is greater than the level of significance ( 0.05 ).
We fail to reject null hypothesis.
So at, 5% level of significance, there is no evidence to support that the variance in the cereal box fillings is designed to be 0.02 or less.
please help with the steps thx:)
Answer:
The answer for the first is $350,325.378, I think
Step-by-step explanation:
I hope this helps, if im wrong im sorry
Answer:
interest: 945, FV: 6345
FV= 323711.4, Interest: 226211.4
25.21 years
Step-by-step explanation:
question 1:
simple interest formula
PV(1+it)
30 months is equal to 30/12 years or 2.5 (so t= 2.5)
5400(1+.07*2.5)= 6345
This is the future value, to find the interst subtract the present value
6345-5400= 945
2.)
future value of continously compounding interst:
PV(e^(it))
97500*e^(.06*20)= 323711.4
finding the interest is the same as the last one
323711.4-97500=226211.4
3.)
same formula
let x= time in years
[tex]30000=7500e^{.055x}\\4=e^{.055x}\\\ln(4)=.055x\\x=25.20535202[/tex]
i guess we can round this to 25.21
Mr watson rives 82 miles round trip each day how many miles does mr waton travel in 23 dys?
Answer:
1886 miles
Step-by-step explanation:
82 x 23 is 1886, 82 miles each day times 23 days.
Solve for x.Round to the nearest tenth of a degree, if necessary. MKL,14,7.4
Answer:
m(∠LMK) = 27.9°
Step-by-step explanation:
We have to calculate the measure of angle LMK.
Measure of opposite side (KL) = 7.4
Measure of adjacent side (ML) = 14
By applying tangent rule in the given triangle,
tan(∠LMK) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{KL}{ML}[/tex]
= [tex]\frac{7.4}{14}[/tex]
= 0.52857
m(∠LMK) = [tex]\text{tan}^{-1}(0.52857)[/tex]
= 27.9°
What are the zeros of P(m) = (m2 – 4)(m2 + 1)?
Answer:
m=4, -1
Step-by-step explanation:
if i am interpreting this correctly, you are wanting to find at what value of m would the solution be zero.
so, there are two expressions that can cause an answer of 0.
1) if 0=m2-4
so solve for m2, and you get 4=m2
2) if 0=m2+1
solve for m2, and you get -1=m2
you can check your work by plugging the values back into the equation.
P(m)=(4-4)(4+1)
=(0)(5)
=0
and
P(m)=(-1-4)(-1+1)
=(5)(0)
=0
Which rational functions have an oblique asymptote? Check all that apply.
x2 + 1
(x) =
X
o
f(x) =
4x2 - 6
x + 1
O
f(x) =
*5
f(x) =
x3 + 1
x3 +2
f(x) =
x² + 3x
Answer:
A, B, E
Step-by-step explanation:
In the list of rational functions, 1st, 2nd, 4th, and 5th are the rational functions those have an oblique asymptote.
What is a function?"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."
The given rational functions are:
1. [tex]f(x) = \frac{x^{2}+1}{x}[/tex]
As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.
2. [tex]f(x) = \frac{4x^{2}-6}{x+1}[/tex]
As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.
3. [tex]f(x) = \frac{-x}{x^{2} }[/tex]
As the degree of numerator(1) is less than the degree of denominator(2), This function does not have an oblique asymptote.
4. [tex]f(x) = \frac{x^{5}}{x^{3}+1}[/tex]
As the degree of numerator(5) is greater than the degree of denominator(3), This function has an oblique asymptote.
5. [tex]f(x)= \frac{x^{3}+2}{x^{2}+3x}[/tex]
As the degree of numerator(3) is greater than the highest degree of denominator(2), This function has an oblique asymptote.
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A bill originally amounting Rs 1550, now amounts to Rs 1736 after adding VAT. Find the VAT rate.kaabil original amounting
Answer: 12%
Step-by-step explanation:
Original amount = Rs 1550
VAT = Rs 1736 - Rs 1550 = Rs 186
VAT rate = VAT/Original amount × 100
= 186/1550 × 100
= 18600/1550
= 12%
Therefore, the VAT rate is 12%.
Check:
= Rs 1550 + (12% × Rs 1550)
= Rs 1550 + $186
= Rs 1736
please solve in the next 10 minutes pleaseeee
Answer:
43.82 mph
266.67 feet
Step-by-step explanation:
Given :
S = √30fl
S = speed of car
f = drag Coefficient
l = Length of skid mark
If f = 0.8 ; l = 80 feets
s = √30fl
s = √(30*0.8*80)
s = √1920
s = 43.817
s = 43.82 mph
B.)
s = 80 mph
f = 0.8
s = √30fl
80 = √30*0.8*l
80 = √24l
Square both sides
80² = 24l
6400 = 24l
l = 6400/24
l = 266.67 feets
1. Round 0.007492 to the nearest hundredth.
Answer:
The answer is 0.01
Step-by-step explanation:
so in order to round it you have to know after the decimal it goes: tenths, hundreds, thousands (0 tenths, 0 hundreds, 0 thousands)
So 0.007492, take the first 3 numbers after the decimal, 0.007, since it will be in the hundreds place, lets see if we can round the 0 up. If the number behind 0 is greater then or equal to 5 round up, if the number is less then 5 then it stays the same. Since 7>5 it rounds up, so the 0 becomes 1. So your new number will be 0.01
Hoped this helped :D
By rounding 0.007492 to the nearest hundredth, we get 0.01.
What is the method of rounding a number?The number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Example: 0.3879 rounded to the nearest hundredth is 0.39.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Example: 0.3823 rounded to the nearest hundredth is 0.38.
Given number is 0.007492.
Rounding to nearest hundredth, we get:
0.00749 ⇒ 0.01.
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Sonia took a loan of $10 000 from ABC bank tob pay for a renovation at home. The bank offered her a period of 30 months at a rate of 10.5%. to repay the loan:
a) Calculate the Simple Interest she would pay in 30 months.
b) Calculate the Total amount Sonia would have to repay the bank.
Answer:
a. Simple interest, S.I = $2,625
b. Total amount = $12,625
Step-by-step explanation:
Given the following data;
Principal = $10,000
Interest rate = 10.5%
Time = 30 months to years = 2.5 years
a. To find the simple interest;
Mathematically, simple interest is calculated using this formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is simple interest. P is the principal. R is the interest rate. T is the time.Substituting into the formula, we have;
[tex] S.I = \frac {10000*10.5*2.5}{100} [/tex]
[tex] S.I = \frac {262500}{100} [/tex]
Simple interest, S.I = $2,625
b. To calculate the total amount Sonia would have to repay the bank;
Total amount = simple interest + principal
Total amount = 2625 + 10000
Total amount = $12,625
A man is changing the oil in his car. The instruction manual indicates that the car hold pints of oil. The man only has a cup measure. How many cups equal three pints?
The volume contained in a cup of oil is a fraction of the volume
contained in a pint of oil.
Correct response:
6 cupsMethod used for the above unit conversionThe measure of the volume of oil the car holds = Pints of oil
The measurement the man has for use = Cups of oil
Required:
The number of cups equal to three pints.
Solution;
1 pint of oil = 2 cups of oil
Therefore;
3 pints of oil = 3 × 2 cups of oil = 6 cups of oil
The number of cups of oil equal to 3 pints of oil is 6 cups of oilLearn more about units conversion here:
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