Using the normal distribution, it is found that:
A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.
B. 0.96 = 96% of packages that will be accepted.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]
Item A:
The proportion is the p-value of Z when X = 158, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.0071 = 0.71% of packages will be rejected because the average weight is too low.
Item B:
The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:
X = 179:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{179 - 170}{4.9}[/tex]
Z = 1.84
Z = 1.84 has a p-value of 0.9671.
X = 158:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.
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Find a polynomial function of degree 7 with -1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, and 1 as a zero
of multiplicity 1.
The polynomial function is P(x) = x^3(x + 1)^3(x -1)
How to determine the polynomial function?The zeros of the polynomial and the multiplicities are given as:
-1 as a zero of multiplicity 3, 0 as a zero of multiplicity 3, 1 as a zero of multiplicity 1The degree is given as
Degree = 7
The polynomial is represented as:
P(x) = (x - zero)^multiplicity
Using the above format, we have
P(x) = (x + 1)^3(x - 0)^3(x -1)
This gives
P(x) = x^3(x + 1)^3(x -1)
Hence, the polynomial function is P(x) = x^3(x + 1)^3(x -1)
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−6 + 3 = −21 pls can uhelp me with this
Answer:
No Solution
Step-by-step explanation:
1) Simplify -6 - 3 to -3.
-3 = -21
2) Since -3 = -21 is false, there is no solution.
No solution
suppose that g is a continuous function, 3_integral^5
g(x)dx=18, and 3_integral^10 g(x)dx =36. Find
5_ integral^10 g(x)dx
those are intergral symbols with numbers on
top and bottom. please show work. thanks
The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
The question has to do with definite integrals
What are definite integrals?Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.
Given that
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex] and also [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex] and we require [tex]\int\limits^{10}_5 {g(x)} \, dx[/tex]For any integral [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]
So, [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
Since
[tex]\int\limits^5_3 {g(x)} \, dx = 18[/tex]and [tex]\int\limits^{10}_3 {g(x)} \, dx = 36[/tex]Substituting the values of the variables into the equation, we have
[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]
[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]
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You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable preliminary estimation for the population proportion. You would like to be 98% confident that you estimate is within 2% of the true population proportion. How large of a sample size is required?
Using the z-distribution, it is found that a sample size of 3,385 is required.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.
We have no prior estimate, hence [tex]\pi = 0.5[/tex] is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327 \times 0.5[/tex]
[tex]\sqrt{n} = \left(\frac{2.327 \times 0.5}{0.02}\right)[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.327 \times 0.5}{0.02}\right)^2[/tex]
n = 3,385.
A sample size of 3,385 is required.
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what is the ration between 28000 and 14?
The ratio between 28,000 and 14 is 2000 : 1
How to determine the ratio?The numbers are given as:
28,000 and 14
Express as ratio
Ratio = 28000 : 14
Divide each number by 14
Ratio = 2000 : 1
Hence, the ratio between 28,000 and 14 is 2000 : 1
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Combine like terms to simplify the following polynomial.
5a²b+7ab² +9c+ 11a²b-3ab² - 9c
Answer:
5a²b + 7ab² + 9c + 11a²b - 3ab² - 9c
= (5a²b + 11a²b) + (7ab² - 3ab²) + (9c - 9c)
= 16a²b + 4ab²
two candles of the same height are lighted at the same time. the first is consumed in 4 hrs and the second in 3 hrs. assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?
The height of candle 4 is twice that of candle B after 2.4 hours.
How many hours after being lighted was the first candle twice the height of the second?For candle, A time is taken for 100% bearning=4hour.
For 1 hour, it burns for 25%(100/4)
After 1 hr.[tex]\frac{25}{100}[/tex]
After x hours, the amount burnt[tex]=\frac{x}{4}[/tex]
Amount left[tex]=1-\frac{x}{4} =\frac{4-x}{4}[/tex]
Let's not presume that candle B's height will be half that of candle A after x hours.
After x hours, part vemacing [tex]=1-\frac{x}{3} =\frac{3-x}{3}[/tex]
[tex]\frac{4-x}{4} =1\frac{3-x}{3}[/tex]
Height of candle A[tex]=2[/tex]×Height of candle B.
[tex]12-3x=24-8x[/tex]
⇒[tex]5x=12[/tex]
[tex]x=\frac{12}{5}[/tex]
[tex]=2.4[/tex]
The height of candle 4 is twice that of candle B after 2.4 hours.
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A train travels 600 kilometers in 1 hour. What is the train's velocity in meters/second?
lunch Then more students joined Jaden's
Answer:
166 2/3 meters/sec.
Step-by-step explanation:
1/1 =1 12 inches/1 foot =1 you are looking for equivalents that will cancel out the unit until you can get to meters and seconds. See work in the picture.
Which of the following estimates at 895% confidence level most likely comes from a small sample?
A. 67% (+-7%)
B. 59 % (+-21%)
C. 53 % (+-3%)
D. 48 % (+-5%)
Option B. The estimate that would most likey come from the small sample is going to be B. 59 % (+-21%).
How to find the sample
The sample space can be gotten rom the margin of error. A smaller sample space would be gotten by dividing with a larger number.
This would give a margin of error that is large. In the second option, we can see that the largest margin of error is ± 21%.
Hence this is the answer to the question.
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Find t and the terminal point determined by t for each point in the figure, where t is increasing in increments of /4.
The missing coordinates are listed below:
(x₁, y₁) = (0, 1)(x₂, y₂) = (- √2 /2, √2 /2)(x₃, y₃) = (- 1, 0)(x₄, y₄) = (- √2 /2, - √2 /2)(x₅, y₅) = (0, - 1)(x₆, y₆) = (- √2 /2, √2 /2)(x₇, y₇) = (1, 0)How to determine the location a terminal point in a unit circleAccording to the polar coordinate system, a vector in standard position is defined by this parametric formula:
(x, y) = (r · cos t, r · sin t), where t is in radians.
If we assume that r = 1, then we proceed to determine the location of the seven points remaining:
(x₁, y₁) = (cos π/2, sin π/2)
(x₁, y₁) = (0, 1)
(x₂, y₂) = (cos 3π/4, sin 3π/4)
(x₂, y₂) = (- √2 /2, √2 /2)
(x₃, y₃) = (cos π, sin π)
(x₃, y₃) = (- 1, 0)
(x₄, y₄) = (cos 5π/4, sin 5π/4)
(x₄, y₄) = (- √2 /2, - √2 /2)
(x₅, y₅) = (cos 3π/2, sin 3π/2)
(x₅, y₅) = (0, - 1)
(x₆, y₆) = (cos 7π/4, sin 7π/4)
(x₆, y₆) = (- √2 /2, √2 /2)
(x₇, y₇) = (cos 2π, sin 2π)
(x₇, y₇) = (1, 0)
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Evaluate 2x − 2 for x = 0, x = 1, and x = 2. Question 1 options: A) −1, 0, 2 B) −1, 1, 2 C) 0, 1, 2 D) 1, 2, 4
The value of x in 2^x - 2 when x = 0, x = 1 and x = 2 are -1, 0 and 2 respectively. option A
Algebra2^x - 2
when x = 0
2^x - 2
= 2^0 - 2
= 1 - 2
= -1
when x = 1
2^x - 2
=2^1 - 2
= 2 - 2
= 0
when x = 2
2^x - 2
= 2^2 - 2
= 4 - 2
= 2
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A house purchased last year for $160,000 is now worth $192,000. Assuming that the house's value continues to appreciate at the same rate each year, what is the value of the house 2 years from now?
A. $265,888
B. $238,240
C. $276,480
D. $230,400
The value of the house 2 years from now is $276,480.
Option (C) is correct.
According to the question,
Cost of house last year = $ 160000
Cost of house at present = $ 192000
The increase in the price of the house is calculated by finding the difference between the prices in two consecutive years.
Increment in cost = $ (192000-160000) =$ 32000
The rate of increment can be calculated by dividing the increment by the original price and then multiplying it by 100%.
Rate of increment = 32000/160000 * 100 =20%
Thus, the value of the house 2 years from now is calculated as:
=192000(1+20/100)(1+20/100)
=192000*120/100*120/100
= $ 276480
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Need help with defining this question.
Answer: 19
Step-by-step explanation:
[tex]F(5)=5^2 - 2(5)+4=19[/tex]
If a 17-foot ladder makes a 71° angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth.
Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.
How many feet up the wall will the ladder reach?Given that;
Angle with the ground θ = 71°Length of the ladder / hypotenuse = 17ftLength of wall = xTo determine the length wall from the tip of the ladder to the ground level, we use trigonometric ratio since the scenario forms a right angle triangle.
Sinθ = Opposite / Hypotenuse
Sin( 71° ) = x / 17ft
x = Sin( 71° ) × 17ft
x = 0.9455 × 17ft
x = 16.1 ft
Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.
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Someone please help with this math problem.
Find the solution of
a(-12 + a) = 0
Answer:
a=0, 12
Step-by-step explanation:
a=0 and –12+a=0===> a=12
Type 4 points found on the circumference of the following equation. Exact points only, no approximations.
(x-3)^2 +(y+2)^2+49
The points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24))
How to determine the points on the circumference of the circle?The circle equation is given as:
(x-3)^2 +(y+2)^2= 49
Rewrite as:
(y+2)^2= 49 -(x-3)^2
Take the square root of both sides
y+2= ±√[49 -(x-3)^2]
Subtract 2 from both sides
y = -2 ± √[49 -(x-3)^2]
Next, we determine the points
Set x = 3
y = -2 ± √[49 -(3-3)^2]
Evaluate
y = -2 ± 7
Solve
y = 5 and y = -9
So, we have
(x, y) = (3, 5) and (3, -9)
Set x = 8
y = -2 ± √[49 -(8-3)^2]
Evaluate
y = -2 ± √24
Solve
y = -2 - √24 and y = -2 + √24
So, we have
(x, y) = (8, -2 + √24) and (8, -2 - √24)
Hence, the points on the circumference are (3, 5), (3, -9), (8, -2 + √24) and (8, -2 - √24)
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A focus group study has always been the primary way for ABC Toys Company to gather customers' opinions for marketing strategy. In the past, when a new product was popular in the market, a focus group study had incorrectly indicated that it would be unpopular with a probability of 0.275. When a new product was unpopular, a focus group had incorrectly indicated that it would be popular with a probability of 0.175. Assume that the probability of a new product being popular in the market is 0.60. What is the probability that a new product will be unpopular if a focus group study indicates that it will be unpopular?
Using conditional probability, there is a 0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.For this problem, the events are given as follows:
Event A: Study indicates that the product is unpopular.Event B: Product is unpopular.The parameters are given as follows:
P(A) = 0.6 x 0.275 + 0.4 x 0.825 = 0.495.[tex]P(A \cap B) = 0.4 \times 0.825 = 0.33[/tex]Hence the conditional probability is:
[tex]P(B|A) = \frac{0.33}{0.495} = 0.6667[/tex]
0.6667 = 66.67% probability that a new product will be unpopular if a focus group study indicates that it will be unpopular.
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Select the symbol = (equal to) or ≠ (not equal to) to make the expression true.
{0} ? { }
Answer:
=
Step-by-step explanation:
{0}={} because 0 means that there is nothing and in null set too, there is no elements.
15) Mr. and Mrs. Rupe and their 4 sons are taking a 2500 mile camping trip across country. They plan to spend $120 for campsites per
day. The camper rental fee is $65 a day. While pulling the camper their car has a fuel economy of 8 miles per gallon. They estimate $85
per day for food for the 5-day trip. If gasoline is $1.92 per gallon how much will their trip cost?
O a.) $1950
Ob.) $1850
Oc.) $2950
Od.) $1750
Answer:
A $1950
Step-by-step explanation:
Food, camper rental and camp site will cost 1350
(120 + 65 + 85)5 = 1350
The trip is 2500 and the car gets 8 miles per gallon 2500/8 = 31.5. The will need to buy 31.5 gallons of gas at 1.92 a gallon or $600 (31.5 x 1.92).
When we add the cost of gas to the other costs, we get a total of 1950 (1350 + 600)
Identify all rays and lines in the picture below.
The rays and lines in the picture are as follows;
rays: BD, AC and AB
lines: AC
What are rays and lines?A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.
A ray is named using its endpoint first, and then any other point on the ray
A line segment has two endpoints.
Therefore, the rays and lines are as follows:
rays: BD, AC and AB
lines: AC
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In △ OPQ, OP ≅ QO and m∠O=65∘. Find m∠Q
Answer:
65°
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so both angle Q and angle P are congruent.
Since angles in a triangle add to 180°, angle Q measures (180-50)/2 = 65°
Solve 15.9 = 11.3 + b for b
Answer:
subtract 11.3 from 15.9 and b is 4.6
Step-by-step explanation:
A town planner is interested in getting some demographic data about the households in the city. The city has ten wards that vary in size. Which sampling method is most appropriate?
The best sampling method that Is most appropriate for the town planner is called Stratified Sampling.
What is the Sampling Method used?The best sampling method that I would recommend for the town planner is called Stratified Sampling.
The reason for using stratified sampling is because it is a method of sampling that involves dividing a population into smaller groups–called strata and in this case, the rows of houses can be used as a strata.
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In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic
between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut
through a small piece of Canada’s beautiful Rocky Mountains. A group of friends decide to cycle
the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston
Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind
adds or subtracts 5 km/h from their speed. If the group of friends wants to complete the round trip
in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete
the distance speed time chart to help solve the question. Round your answer to the nearest
hundredth of a km/h.
The average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
What is the average speed of travel?The average speed (S) of travel is the distance (D) traveled divided by the time taken(T).
What is an algebraic equation?An algebraic equation is a statement of the equality of two expressions that have variables, using algebraic operations, known as addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Data and Calculations:Distance to Castle Junction and from Banff = 50 km (25 x 2)
Time required to cycle = 3 hours
Effect of wind on cyclists = -+5 km/h
The algebraic equation for speed, S, is D/T
Where:
D = Total distance
T = Total time
Therefore, S = D/T = 50/3
S = 16.6667 km/h
Thus, the average speed with no wind that the group needs to cycle between Banff and Castle Junction is 16.67 km/h.
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divide 7.39 divide 0.72 rounded quotient of the nearest hundredth
Answer:
10.26 I believe you wanted me to divide 7.39/0.72. If so, you get 10.2638 that rounds to 10.26
Step-by-step explanation:
Can u give me brainliest please
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
We have,
Expression:
7.39 ÷ 0.72
Now,
The expression can be written as,
= 7.39 / 0.72 ______(1)
Simplify the numerator and denominator.
Numerator = 7.39 = 739/100 _____(2)
Denominator = 0.72 = 72/100 ______(3)
Now,
From (1), (2), and (3).
7.39 / 0.72
= (739/100) / (72/100)
= 739/100 x 100/72
100 is the common factor so it gets canceled.
= 739/72
= 10.2638888.....
Rounding to the nearest hundredths.
= 10.26
Thus.
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
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Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.
Answer:
31√2 feet
Step-by-step explanation:
The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.
SetupLet h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...
h² +(17√2)² = 50²
SolutionSubtracting the constant on the left gives ...
h² = 2500 -578 = 1992
h = √1992 = 31√2
The height of the square pyramid is exactly 31√2 feet.
__
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Dan & Alex measure themselves against a tree in their backyard. The tree is 80% taller than Dan and 20% taller than Alex. Which of the following statements is true?
A. Alex is 50% taller than Dan.
B. Dan is 60% taller than Alex.
C. Dan is 40% taller than Alex.
D. Alex is 40% taller than Dan.
The true statement is that Alex is 50% taller than Dan.
How to solve percentage questions?They both measured themselves against a tree in their backyard.
Therefore, the tree is 80% taller than Dan and 20% taller than Alex.
Hence,
let
Dan height = x
Tree's height = x + 0.8x
Tree's height = 1.8x
let
Alex height = y
Tree's height = y + 0.2y
Tree's height = 1.2y
Therefore, if we use Dan height as 100, the height of the tree will be 180.
Then,
180 = 1.2y
y = 150
This means Alex is 50 percent taller than Dan.
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questions 5 and 6 please!
will give brainliest to whoever answers
90 points
Answer:
5)
rise over run so
5/5 = 1
6)
-2/4 = -0.5
Write out the sum. Do not evaluate.
∑∑k=1 (k^2-5k-3)[tex]4\\E(K^2-5k-3)\\k=1[/tex]
Series are sum of a given sequence.. The sum of the given expression is -33
Sequence and seriesSeries are sum of a given sequence. According to the given expression
∑∑k=1 (k^2-5k-3)
Taking the sum from k = 1 to k = 4
Sum = (1-5-3) + (4-10-3) +(9-15-3)+(15-20-3)
Sum = (-7) + (-9) + (-9) + (-8)
Sum = -33
Hence the sum of the given expression is -33
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