By definition, direct variation takes the following form:
y=kx
Where k is the proportionality constant.
You can find k given the information in the problem:
7=3k
k=3/7
You can now find y when x=7 as follows:
y=(7*3)
Values can be substituted. Then:
y=(7*7)/3
y=49/3
If y varies directly from x, then the value of y = 49/3 when x = 7.
If y varies directly from x, we can write its relationship in the form of the equation below :
y = m*x
Where m is the slope of the line on the graph.
From the given data:
y=7
x=3,
We can substitute these values in the above equation and find m :
7 = m*3
m = 7/3
So, the equation can also be written as follow:
y = 7/3 x
Finding y when x=7, then substituting the x value in the above equation we get:
y = (7/3)*(7)
y = 49/3
Therefore the value of the y = 49/3.
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a german shepherd puppy weighed 25 pounds at 4 months old and 31 pounds at 5 months old. what is the percent increase or decrease of its weight? show hints
Answer:
24% increase
Step-by-step explanation:
percent change = (new value - old value)/(old value) × 100%
A positive percent change is a percent increase.
A negative percent change is a percent decrease.
In this problem:
new value = 31
old value = 25
percent change = (31 - 25)/(25) × 100%
percent change = 24%
Since the percent change is positive, the percent change is a
24% increase
The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.
The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.
To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.
To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.
In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.
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Produce an equivalent equation for f(x)=7(x-60)-28 to reveal the y-intercept for the function. What is the y-intercept?
The equivalent equation to f(x) = 7(x - 60) - 28 is f(x) = 7x - 448 and the y-intercept is -448
How to determine the equivalent equationGiven that
f(x) = 7(x - 60) - 28
To produce an equivalent equation that reveals the y-intercept of the function f(x) = 7(x-60) - 28, we need to simplify the expression by evaluating it when x = 0, since this will give us the y-intercept.
When the brackets are expanded, we have the following
f(x) = 7x - 420 - 28
Evaluate the like terms
So, we have
f(x) = 7x - 448
So, substituting x = 0 into f(x) gives:
f(0) = 7(0) - 448
Evaluate the expression
f(0) = -448
Therefore, the y-intercept is -448.
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Vectors u and v are shown on the graph. vector u with initial point at the origin and terminal point at 0 comma negative 5, vector v with initial point at the origin and terminal point at negative 7 comma 0 Which of the following vectors represents u + v? a vector that points to the right 7 units and up 5 units b vector that points to the left 7 units and up 5 units c vector that points to the left 7 units and down 5 units d vector that points to the right 7 units and down 5 units
The resultant vector is 7 units to the left and 5 units down. As a result, graphs option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle
We can add vectors geometrically by setting the starting point of the second vector at the terminal point of the first vector and drawing a vector from the first vector's initial point to the second vector's terminal point.
Next we align the starting point of vector v with the terminal point of vector u and draw a vector from the initial point of vector u to the terminal point of vector v:
The resultant vector is 7 units to the left and 5 units down. As a result, option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.
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Select the correct answer. Solve the following equation for x. x2 - 9x + 18 = 0 A. x = -3; x = 6 B. x = 3; x = 6 C. x = -3; x = -6 D. x = 3; x = -6
Answer:B
Step-by-step explanation: x=3;x=6
a frozen food company uses a machine that packages okra in six ounce portions. a sample of 54 54 packages of okra has a variance of 0.44 0.44 . construct the 98% 98 % confidence interval to estimate the variance of the weights of the packages prepared by the machine. round your answers to two decimal places.
The confidence interval for variance is (0.29,0.58)
A family of continuous probability distributions is known as the chi-square (X2) distribution. They are frequently employed in hypothesis tests, such as the chi-square test of independence and the goodness of fit test.
The parameter k, which stands for the degrees of freedom, determines the shape of a chi-square distribution.
The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for testing hypotheses rather than for modeling actual distributions.
Since we have given that the sample size n= 54,
variance = 0.44
we need to find a 98% confidence interval to estimate the variance.
So, we will use Chi-square distribution,
For this, we will find
df=n-1 = 54-1 = 53,
the interval would be,
[tex]\frac{(n-1)s^2}{X^2_{\alpha/2}} < \sigma^2 < \frac{(n-1)s^2}{X^2_{1-\alpha/2}}\\\\\alpha=1-0.98=0.02\\\\\alpha/2=0.02/2=0.01\\X^2_{0.01,53}=79.84\\Similarly\\\\1-\alpha/2=0.99\\\\X_{1-\alpha/2}^2,df=X^2_{0.99,53}=40.308\\\\So,\\\frac{53*0.44}{79.84} < \sigma^2 < \frac{53*0.44}{40.308}\\\\0.29 < \sigma^2 < 0.58[/tex]
Hence the confidence interval is (0.29,0.58)
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if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect:
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. A 95% confidence interval means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 95% of the time.
If we change the confidence level from 95% to 99%, we are increasing the degree of confidence. This means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 99% of the time.
But, to achieve this higher degree of confidence, we need to widen the interval. This is because as the degree of confidence increases, the interval needs to become wider to capture more possible values of the population parameter.
Therefore, if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
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what is the volume of the large pyramid? (rounded to the nearest cubic meter) group of answer choices 20,833 41,666 10,417 16,817 375
The volume of the pyramid is 600 cubic centimeters (cm³).
The formula for the volume of a pyramid is given by
V = (1/3) × base area × height
Since the base of the pyramid is a square with sides of 10 cm, the base area can be calculated as
base area = side length × side length = 10 cm × 10 cm = 100 cm²
Substituting the given values into the formula for the volume of a pyramid, we get
V = (1/3) × base area × height
Substitute the values in the equation
= (1/3) × 100 cm² × 18 cm
Multiply the numbers
= 600 cm³
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I have solved the question in general as the given question is incomplete.
The complete question is:
What is the volume of a pyramid whose base is square? The sides of the base are 10 cm each and the height of the pyramid is 18 cm.
Which system of inequalities has the solution shown in the graph?
in a batch of 100 cell phones, there are, on average, 6 defective ones. if a random sample of 25 is selected, find the probability of 4 defective ones
The probability of 4 defective cell phones in a sample of 25 can be found using the binomial probability formula and is equal to 0.0263.
What is probability?Probability is a branch of mathematics that deals with calculating the likelihood of a given event occurring. In probability, we calculate the number of ways an event can happen and divide it by the total number of possible outcomes.
Probability ranges from 0 to 1, with 0 indicating no chance of occurrence and 1 indicating that the event will definitely occur.
What is the binomial probability formula?If there are only two possible outcomes in a given event, the binomial probability formula is used to calculate the probability of the event happening.
The binomial probability formula is given by: P(X = x) = (nCx)px(1 - p)n - x
Where, P(X = x) is the probability of x successes in n trials
nCx is the number of ways x successes can occur in n trials
px is the probability of a single success in a given trial(1 - p)n - x is the probability of the remaining trials being failures.
How to solve the problem?The probability of 4 defective cell phones in a sample of 25 can be calculated using the binomial probability formula.
P(X = 4) = (25C4)(0.06)4(0.94)21 = 0.0263.
Therefore, the probability of 4 defective cell phones in a sample of 25 is 0.0263.
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Solve for x (please help me with this I’m willing to give 20 points)
Answer:
75°
Step-by-step explanation:
The angle in the given figure is 90°.
x + 15 = 90
x = 90 - 15
x = 75°
What is the measure of <7?
Answer:
120
Step-by-step explanation:
Ava sells pottery at a market. Each piece of pottery costs $4.50 to make. Ava marks up the pottery by 250%. She then decides to have a sale of 30% off the retail price. What is the discounted price of each piece of pottery?
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
Explain about the discounted price?The interest rate that is adjusted to the projected cash flows of either an investment to determine its present value is referred to as the discount rate. The expected rate of return on investment that businesses or investors anticipate. The viability of an investment can be determined by computing the net present value via discounting.
Cost price = $4.50
Percentage increase = 250%.
Marked price = 4.50 + 2.5*4.50
Marked price = $15.75
Discount = 30%
Discounted price = 15.75 - 0.30*15.75
Discounted price = $11.025
Thus, the discounted price on the retail price of each piece of pottery is found to be: Discounted price = $11.025.
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If you flipped a coin 550 times, how many times would you expect it to land on heads?
Answer:
275
Step-by-step explanation:
You have a 1 in 2 chance
550/2
275 times
Find the area of each of the regular polygon below.
Round non-terminating decimals to the nearest hundredth.
nonagon (9 sided figure)
apothem = 16.5
side = 12
Rοunding tο the nearest hundredth, the area οf the nοnagοn is 891.00 square units.
What is the regular pοlygοn?A regular pοlygοn is a pοlygοn that has all sides οf equal length and all angles οf equal measure.
Tο find the area οf a regular pοlygοn, we use the fοrmula:
Area = (1/2) × Perimeter × Apοthem
The perimeter οf a nοnagοn (9-sided figure) with a side length οf 12 is:
Perimeter = 9 × 12 = 108
Therefοre, the area οf the nοnagοn is:
Area = (1/2) × 108 × 16.5
Area = 891
Hence, Rοunding tο the nearest hundredth, the area οf the nοnagοn is 891.00 square units.
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a rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 412cm. the prism is filled with cubes that have edge lengths of 12 cm. how many cubes are needed to fill the rectangular prism?
The dimensions of a rectangular prism are 6 cm long, 3 cm wide, and 4 ½ cm tall. 648 cubes are required to completely fill the rectangular prism.
The formula for calculating the rectangular prism's volume is:
Volume = Length x Width x Height
Substituting the given values, we get:
Volume = 6 cm x 3 cm x 4 ½ cm
Volume = 81 cm³
Since the cubes have an edge length of ½ cm, their volume is:
Volume of one cube = (1/2 cm)³ = 1/8 cm³
To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of one cube:
Number of cubes = Volume of prism / Volume of one cube
Substituting the values, we get:
Number of cubes = 81 cm³ / (1/8 cm³)
Number of cubes = 81 cm³ x 8
Number of cubes = 648
Therefore, 648 cubes are needed to fill the rectangular prism.
The complete Question is:-
A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 1/2cm. the prism is filled with cubes that have edge lengths of ½ cm. how many cubes are needed to fill the rectangular prism?
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of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize?
Answer:
Step-by-step explanation:
big cheeze
Answer: 3/8
The given information is as follows: Out of the last 16 people, 6 people won a prize. We need to calculate the experimental probability of the next person winning the prize. To calculate experimental probability, we use the formula of experimental probability is given as: Experimental probability = Number of favorable outcomes / Total number of outcomes.
The given information tells us that out of the last 16 people, 6 people won a prize. It means that the number of favorable outcomes is 6. So, the experimental probability of winning a prize = Number of favorable outcomes / Total number of outcomes. Total number of outcomes is 16.
Therefore, Experimental probability = 6 / 16. Let's simplify this fraction. We can divide the numerator and denominator by 2.6/16 = 3/8Therefore, the experimental probability of the next person winning a prize is 3/8.
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C O Porte
zeam.org/towers/603
Zmen
MTIL30 Minutes and Miles
Karen needed to put 5 gallons 3 quarts of gas into her boat on Monday and twice as much on
Saturday. If she had an 18 gallon jug of gas available, did she have enough gas for both
days?
How much gas did Karen need to put in the boat?
Solve on paper. Then, check your work on Zearn. Use the largest units possible. 4
1 gal = 4 gt
Karen needed to put a total of
7
gal qt of gas into her boat.
The amount of gas Karen has and the amount Karen needed to put into her boat obtained using basic arithmetic operations are;
Yes, Karen had enough gas available for both daysKaren needed to put a total of 69 quarts of gas into her boatWhat are basic arithmetic operations?Basic arithmetic operations include addition, subtraction, division and multiplication operations.
The amount of gas Karen has can be found using basic arithmetic operations as follows;
On Monday, Karen needed to put 5 gallons 3 quarts of gas into her boat. Since 1 gallon is equal to 4 quarts, this is equivalent to (5 × 4 + 3) = 23 quarts of gas
On Saturday, she needed to put twice as much gas into her boat as she did on Monday. So on Saturday she needed to put (2 × 23) = 46 quarts of gas into her boat.
In total, Karen needed to put (23 + 43) = 69 quarts of gas into her boat over both days.Since, Karen had 18 gallon jug of gas available and 1 gallon is equal to 4 quarts, this mean she had (18 × 4) = 72 quarts of gas available.
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What is 8z + 3;z = 8 but evaluate it.
Answer:
Step-by-step explanation:
the answer is
z=0.625
I need help with this geometry problem
Step-by-step explanation:
Volume of a sphere is given by 4/3 pi r^3
if radius = 3 inches
4/3 pi (3^3) = 36 pi in^3
it is a HEMI- sphere so 1/2 of this would be 18 pi in^3
Find the value of x.
In the figure of circle provided. the value of x is
161 degreesHow to find the value of xIn a circle, equal chords subtends equal arc length.
In the problem it was given that:
chord SU is equal to chord ST hence we have that
x + x + 38 = 360 (angle in a circle)
collecting like terms
2x + 38 = 360
2x = 360 - 38
2x = 322
Isolating x by dividing both sides by 2
2x / 2 = 322 / 2
x = 161
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Philippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could lPhilippe knows there is a $20\%$ chance that it will rain tomorrow and an $80\%$ chance that it will not rain tomorrow. Part A Philippe considers making a spinner to simulate the probability of it raining tomorrow. Describe what the spinner could look like and the steps he should take to perform the simulation. Ook like and the steps he should take to perform the simulation
Philippe can perform a simulation of rain or no rain for tomorrow by spinning a spinner with two sections labeled "Rain" and "No rain."
The spinner could be divided into two sections, one labeled "Rain" and the other labeled "No rain." To perform the simulation, Philippe would need to give the spinner a spin and observe which section it lands on. If it lands on the "Rain" section, he would consider that as an outcome of rain for tomorrow, and if it lands on the "No rain" section, he would consider that as an outcome of no rain for tomorrow. To make the simulation more accurate, he could repeat the process multiple times and record the number of times the spinner lands on each section.
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WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
given the arithmetic sequence what is the domain for N?
The domain for n in the arithmetic sequence is the one in the first option:
all integers where n ≥1
What is the domain of N?We have a arithmetic sequence defined by the general formula:
aₙ = 4 - 3*(n - 1)
And we want to find the domain for the possible values of n that we can use in that formula.
Remember that the terms of a sequence are defined as:
a₁, a₂, a₃,...
So the values of n are positive whole numbers, in this case the first one is n = 1.
a₁ = 4 + 3*(1 - 1)
a₁ = 4
And then we can keep using any positive integer, then the correct option is:
all integers where n ≥1
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you believe that most american men under the age of 25 prefer pizza over tacos. you design an experiment with 50 men to test this hypothesis. what is the sample in your experiment?
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
what is null hypothesis ?The null hypothesis is a claim made in statistical hypothesis testing that presupposes there is no correlation between groups or any meaningful difference between a set of variables. It is commonly denoted by "H0," and the alternative hypothesis is compared with it ("H1"). The null hypothesis is typically assumed to be true, and in order to determine whether it can be rejected or not, it must be statistically tested. The alternative hypothesis is accepted if there is enough data to refute the null hypothesis. In contrast, the null hypothesis is maintained if there is not sufficient evidence to support it.
given
The group of 50 males who are chosen to take part in the study serves as the sample for the experiment.
They represent a more focused sample of people the researcher is interested in examining in order to draw conclusions about the larger community of American men under 25.
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A juice can is in the shape of a cylinder with a diameter of 4 inches. It has a volume of 125 cubic inches. What is the height of the can? leave answers in terms of π.
The height οf the juice can is apprοximately 9.98 inches.
What is cylinder?A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο cοngruent and parallel circular bases, and a curved lateral surface that cοnnects the twο bases. The twο bases are usually circular, but they can be any οther shape as well. The lateral surface οf a cylinder is curved, and it has the same crοss-sectiοn alοng its entire length.
The volume of a cylinder is given by the formula [tex]\rm V = \pi r^{2}h[/tex], where V is the volume, r is the radius, and h is the height.
Since the diameter of the juice can is 4 inches, the radius is half of that, or 2 inches.
We are given that the volume of the can is 125 cubic inches, so we can set up the equation:
[tex]\rm 125 = \pi (2)^{2}h[/tex]
Simplifying this equation, we get:
125 = 4πh
Dividing both sides by 4π, we get:
h = 125 / (4π)
So the height of the juice can is approximately 9.98 inches when rounded to two decimal places.
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-5x - 3y + 7x + 21y Simplify
Answer:
2x + 18y
Step-by-step explanation:
-5x - 3y + 7x + 21y ----> (combine like terms)
2x - 3y + 21 y ---> (combine like terms)
2x + 18y
Answer:
[tex]\huge\boxed{\sf 2(x + 9y)}[/tex]
Step-by-step explanation:
Given expression:= -5x - 3y + 7x + 21y
Combine like terms= -5x + 7x - 3y + 21y
= 2x + 18y
Common factor = 2So, take 2 as a common factor
= 2(x + 9y)[tex]\rule[225]{225}{2}[/tex]
LMNO id a parallelogram. If NM =c+30 and OL=4x +9, find the value of X NM AND OL
The value of x is 7, and NM and OL are both equal to 37.
Since LMNO is a parallelogram, its opposite sides must be parallel and equal in length. Therefore, we have,
NM = OL
We also have the following information:
NM = x + 30
OL = 4x + 9
Substituting the first equation into the second equation, we get:
x + 30 = 4x + 9
Simplifying this equation, we get:
3x = 21
Therefore, x = 7.
Substituting this value back into the original equations, we get:
NM = x + 30 = 7 + 30 = 37
OL = 4x + 9 = 4(7) + 9 = 37
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An arithmetic series of A has first term a and common difference d.
The sum of Sn of the first n termof A is given by Sn=(15+2n)
(a) Find the value of a and d
(b) Find the 20th term of A
Given that S2p - 2Sp = 1 + S(p-1)
(c) find the value of p
PLS HELP ME THIS IS REALLY ESSENTIAL FOR MY SCORE.
Answer:
(a) To find the value of a and d, we use the formula for the sum of first n terms of the arithmetic series A which is given by:Sn = n/2[2a + (n-1)d]We are also given that Sn = 15 + 2n. So we can equate these two expressions to get:15 + 2n = n/2[2a + (n-1)d]Multiplying both sides by 2 and simplifying, we get:30 + 4n = n[2a + (n-1)d]Expanding the brackets and simplifying, we get:2an + nd - d + 30 = 2n^2Rearranging terms, we get:2a = 2n^2 - nd + d - 30Now we also know that the first term of the series A is a. So we can substitute this value of a in the formula above to get:a = (2n^2 - nd + d - 30)/2Simplifying, we get:a = n^2 - (n-1)d - 15Therefore, we have found the values of a and d in terms of n. (b) To find the 20th term of A, we use the formula for the nth term of an arithmetic series which is given by:an = a + (n-1)dSubstituting the value of a and d that we found in part (a) we get:a20 = (20^2 - 19d - 15) + 19dSimplifying, we get:a20 = 391 - dTherefore, the 20th term of A is given by a20 = 391 - d.(c) Given that S2p - 2Sp = 1 + S(p-1), we can use the formula for the sum of first n terms of an arithmetic series which we used in part (a) to get:2p/2[2a + (2p-1)d] - 2p/2[2a + (p-1)d] = 1 + p/2[2a + (p-2)d]Simplifying, we get:2apd = d(p^2 - 3p + 2)Dividing both sides by d and simplifying, we get:2ap = p^2 - 3p + 2Rearranging terms, we get:p^2 - 3p + (2-2ap) = 0This is a quadratic equation with coefficients a=1, b=-3, and c=2-2ap. We can use the quadratic formula to solve for p:p = [3 ± sqrt(9 - 4(1)(2-2ap))]/2Simplifying, we get:p = [3 ± sqrt(4ap + 1)]/2Therefore, we have found the value of p in terms of a.
A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
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Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
Write a rule for g that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of f(x)=5^x
Answer:
Assuming that g(x) represents the transformed function, the rule for g can be obtained by applying the translation and reflection operations in the correct order.
To translate the graph of f(x) down by 2 units, we need to subtract 2 from the function. This gives us:
h(x) = f(x) - 2 = 5^x - 2
Next, we need to reflect the graph of h(x) in the y-axis. To do this, we replace x with -x in the function. This gives us:
g(x) = h(-x) = 5^(-x) - 2
Therefore, the rule for g(x) that represents a translation 2 units down, followed by a reflection in the y-axis of the graph of
f(x) = 5^x is:g(x) = 5^(-x) - 2
