Answer:
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
The number of students enrolled in 2014 is 1162.
Step-by-step explanation:
The number of students in the school in t years after 2002 can be modeled by the following function:
[tex]N(t) = N(0)(1+r)^{t}[/tex]
In which N(0) is the number of students in 2002 and r is the rate of change.
If 1+r>1, the function is a growth function.
If 1-r<1, the function is a decay function.
In 2002, there were 972 students enrolled at Oakview High School.
This means that [tex]N(0) = 972[/tex]
Since then, the number of students has increased by 1.5% each year.
Increase, so r is positive. This means that [tex]r = 0.015[/tex]
Then
[tex]N(t) = N(0)(1+r)^{t}[/tex]
[tex]N(t) = 972(1+0.015)^{t}[/tex]
[tex]N(t) = 972(1.015)^{t}[/tex]
Growth function.
Find the number of students enrolled in 2014.
2014 is 2014-2002 = 12 years after 2002, so this is N(12).
[tex]N(t) = 972(1.015)^{t}[/tex]
[tex]N(12) = 972(1.015)^{12}[/tex]
[tex]N(12) = 1162[/tex]
The number of students enrolled in 2014 is 1162.
The exponential function that models the given situation is [tex]P(t) = 972 \times (1.015)^{t}[/tex]. By 2014, the number of students is approximately 1162, demonstrating growth.
To model the enrollment of students at Oakview High School using an exponential function, we start with the given data:
The initial number of students (P₀) in 2002: 972.
Annual growth rate: 1.5% or 0.015 as a decimal.
The exponential formula is:
[tex]P(t) = P_0 (1 + r)^t[/tex]
where:
P(t) is the population at time t.P₀ is the initial population.r is the growth rate.t is the number of years since the initial year.In our case, the exponential formula will be:
[tex]P(t) = 972 \times (1 + 0.015)^{t}\\P(t) = 972 \times (1.015)^{t}[/tex]
To find the number of students in 2014, calculate t as follows:
t = 2014 - 2002 = 12
[tex]P(12) = 972 \times (1.015)^{12}[/tex]
Compute the result:
P(12) ≈ 972 × 1.195618
P(12) ≈ 1162 students
This is an example of 'growth', as the number of students increases over time.
A potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy. To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy. What is the probability that the potential candidate will obtain a p^ ≥ 0.30 (and run for President)? Round your answer to four decimal places.
Answer:
Probability that the potential candidate will run for President election is 0.0096.
Step-by-step explanation:
We are given that a potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy.
To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy.
Let p = % of Americans voice support for her candidacy
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans support her candidacy = 35%
n = sample of Americans = 500
Now, probability that the potential candidate will obtain a p^ ≥ 0.30 and run for President is given by = P( [tex]\hat p[/tex] ≥ 0.30)
P( [tex]\hat p[/tex] ≥ 0.30) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ≥ [tex]\frac{0.35-0.30}{\sqrt{\frac{0.35(1-0.35)}{500}} }[/tex] ) = P(Z ≥ 2.34) = 1 - P(Z [tex]\leq[/tex] 2.34)
= 1 - 0.9904 = 0.0096
The above probability is calculated by looking at the value of x = 2.34 in the z table which has an area of 0.9904.
Hence, the required probability is 0.0096.
oliver deposits $6500 in an ira. what will be the value of his investment in 8 years if the investment is earning 4% per year and is compounded continuously
Answer:
A = $ 8,951.33
Step-by-step explanation:
A = $ 8,951.33
A = P + I where
P (principal) = $ 6,500.00
I (interest) = $ 2,451.33
Formula:
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pe^rt
Calculate Principal Amount, solve for P
P = A / e^rt
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Compound Interest Equation
A = P(1 + r/n)^nt
.In the Star Wars franchise, Yoda stands at only 66 centimeters tall. Suppose you want to see whether or not hobbits from the Lord Of The Rings are taller than Yoda, on average. From prior research you know that the distribution of hobbit heights are approximately Normally distributed. From a sample of 7 hobbits, you find their mean height ¯ x = 80cm with standard deviation s = 10.8cm. Does sample evidence suggest at the α = 0.01 level of significance that the average hobbit is taller than Yoda? Use steps A through F to test the appropriate hypotheses.
Answer:
We conclude that the average height of hobbit is taller than Yoda.
Step-by-step explanation:
We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.
From a sample of 7 hobbits, you find their mean height [tex]\bar X[/tex] = 80 cm with standard deviation s = 10.8 cm.
Let [tex]\mu[/tex] = average height of hobbit.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 66 cm {means that the average height of hobbit is shorter than or equal to Yoda}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 66 cm {means that the average height of hobbit is taller than Yoda}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean height = 80 cm
s = sample standard deviation = 10.8 cm
n = sample of hobbits = 7
So, test statistics = [tex]\frac{80-66}{\frac{10.8}{\sqrt{7}}}[/tex] ~ [tex]t_6[/tex]
= 3.429
The value of t test statistics is 3.429.
Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the average height of hobbit is taller than Yoda.
Juan and Rob Are selling cookie dough for a school fundraiser Juan Has t Cookie dough Orders Rob has 40 cookie dough orders they have a total of 75 cookie dough orders all together
Answer:
Juan has 35 orders
Step-by-step explanation:
you subtract 40 from 75 to get 35
Juan has 35 cookie dough orders for the school fundraiser
The question involves solving a simple algebra problem related to a school fundraiser involving cookie dough orders. Juan and Rob have a total of 75 cookie dough orders together. Juan has t orders and Rob has 40 orders. The problem can be represented by the equation t + 40 = 75. To find out how many cookie dough orders Juan has, we subtract 40 from both sides of the equation, which gives us t = 35. So, Juan has 35 cookie dough orders.
A disease is spreading throughout a community of 3,000 people at a rate (measured in number infected per day) proportional to the product of number of people infected and the number of people not yet infected, with constant of proportionality k = 0.004. Initially, 500 people are infected. Write an initial value problem.
Answer:
[tex]I'(t)=12I-0.004I^2, I_o=500[/tex]
Step-by-step explanation:
Population of the Community=3000
Let the number of infected=I
The number of uninfected=3000-I
The rate at which disease is spreading is proportional to the product of number of people infected and the number of people not yet infected.
[tex]\frac{dI}{dt}\propto I(3000-I) \\\frac{dI}{dt}=k I(3000-I)\\\frac{dI}{dt}=0.004 I(3000-I)\\$Let I_o$=Initial Number of Infected=500\\Therefore, the initial value problem is given as:\\I'(t)=12I-0.004I^2, I_o=500[/tex]
In the morning an iceberg weighed 380,000 pounds. If it lost 0.3% of its weight during the day, what is its new weight at the end of the day?
We have been given that in the morning an iceberg weighed 380,000 pounds. It lost 0.3% of its weight during the day. We are asked to find the weight of the ice-berg at the end of the day.
The weight of the ice-berg at the end of the day would be original weight of ice-berg minus 0.3% of original weight.
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-380,000\times \frac{0.3}{100}[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-3800\times 0.3[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-1140[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=378,860[/tex]
Therefore, the weight of the ice-berg at the end of the day would be 378,860 pounds.
Answer:
378860 pounds
Step-by-step explanation:
bill drove 315 miles in 7 hours, Alisha drove 235 mile sin 5 hours, and Joanna drove 414 miles in 9 hours. which person drove at an average speed of 47 miles per hour? (and can u explain what mph each person has thx :3) if u has roblox my username is zaw1031
Answer:
Alisha
Step-by-step explanation:
Speeds:
Bill:
315/7 = 45 mph
Alisha:
235/5 = 47 mph
Joanna:
414/9 = 46 mph
Answer:
The answer is Alisha.
Step-by-step explanation:
235 mph divided by 5 is equal to 47 mph.
What’s the correct answer for this?
Answer:
RT ≈ 7.82
Step-by-step explanation:
tan θ = opposite / adjacent
tan 41 = RT / 8
RT = tan 41 × 8
RT = 0.869 × 8
RT = 7.821
RT ≈ 7.82
Help plz and thanks will mark you as BRAINLIEST
Answer: 36 cubic inches
Step-by-step explanation:
help me please;(idk how ot do this e.e
Answer:
10 cups c. 1 : 5Step-by-step explanation:
1. The basic recipe for Kool Aid makes 2 quarts. The desired amount is 20 quarts (2 multiplied by 10). The basic recipe uses 1 cup of sugar, so the desired amount of Kool Aid will use 1 cup multiplied by 10.
10 cups of sugar are needed
__
2. The problem tells us there are 8 parts pretzels and 40 total parts, so the ratio is ...
pretzels : total = 8 : 40
8 is a factor of both these numbers, so we can reduce this to the "basic ratio" by dividing both numbers by 8:
8 : 40 = 1 : 5
The basic ratio is 1 : 5.
What does the dashed part of the figure represent
9514 1404 393
Answer:
ray
Step-by-step explanation:
The dashed part of the figure is a "half-line", a line that extends in one direction from a point. Such a line is called a "ray."
A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble back in the bag. This process is repeated until you pick either two consecutive blue or two consecutive red marbles. Given that the process stopped because you picked two consecutive blue marbles, what is the probability that the first marbled you picked was blue
Answer:
(mn+n²)/(m+n)
Step-by-step explanation:
probability of blue marble= n/(n+m)
probability of red marble= m/(n+m)
probability that process stops = Probability of both blue + probability of both red= n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)
= (n²+m²)/(n+m)²
P(1st marbel is blue)= P(blue and red) + P(blue and blue)
= mn/(n+m) + n²/(n+m)
= (mn+n²)/(m+n)
P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)
= (mn+n²)/(m+n)
Jordan is a single taxpayer with taxable income of $35,000. Use this tax bracket table to compute Jordan’s total tax due. Single Taxpayers: Income Brackets Tax Rate Income Bracket 10% 0 to 9,525 12% 9,526 to 38,700 22% 38,701 to 82,500 24% 82,501 to 157,500 32% 157,501 to 200,000 35% 200,001 to 500,000 37% > 500,000 Jordan must pay a total tax due of using the marginal rates of .
Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.
To compute Jordan's total tax due, we need to apply the marginal tax rates to each income bracket. Here's the breakdown for Jordan's taxable income of $35,000:
1. Income up to $9,525: Tax rate 10%
Tax on this bracket = $9,525 * 0.10 = $952.50
2. Income from $9,526 to $38,700: Tax rate 12%
Taxable income in this bracket = $35,000 - $9,525 = $25,475
Tax on this bracket = $25,475 * 0.12 = $3,057
Now, add the taxes from each bracket to find the total tax due:
Total tax due = Tax on the first bracket + Tax on the second bracket
= $952.50 + $3,057
= $4,009.50
Therefore, Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.
The probable question may be:
"Jordan is a single taxpayer with a taxable income of $35,000. Using the provided tax bracket table for single taxpayers, where different tax rates apply to specific income brackets, compute Jordan's total tax due. The tax rates for the respective income brackets are as follows: 10% for income up to $9,525, 12% for income between $9,526 and $38,700. Please calculate Jordan's total tax due using the marginal tax rates."
Jordan's total tax due is $4,009.48. To calculate this, we determine the tax for each income bracket Jordan falls into and add them together. Jordan's taxable income of $35,000 falls into the 12% tax bracket, so we use the 12% tax rate to calculate the tax due in that bracket. We also calculate the tax due in the 10% tax bracket for the remaining income.
Explanation:To find Jordan's total tax due, we need to determine which income bracket he falls into and calculate the tax for each bracket using the corresponding tax rate. Jordan has a taxable income of $35,000, which falls into the 12% tax bracket. So, we will use the tax rate of 12% to calculate his tax due.
Step 1: Calculate the tax on the income that falls in the 12% tax bracket:
Calculate the taxable income in the 12% tax bracket: $35,000 - $9,526 = $25,474Calculate the tax on the taxable income: $25,474 x 12% = $3,056.88So, Jordan's tax due for the 12% tax bracket is $3,056.88.
Step 2: Calculate the tax on the income that falls in the 10% tax bracket:
Calculate the taxable income in the 10% tax bracket: $9,526Calculate the tax on the taxable income: $9,526 x 10% = $952.60So, Jordan's tax due for the 10% tax bracket is $952.60.
Step 3: Add the tax due for each bracket to get Jordan's total tax due:
Total tax due = $3,056.88 + $952.60 = $4,009.48.
Can someone help me?
Answer:
1. x-2y
2. 2(13a-5)
Step-by-step explanation:
1. it's asking to expand the equation, so you should distribute the -1/2. -1/2*-2x becomes 1x or just x and -1/2*4y becomes -2y, so the answer is x-2y.
2. it's asking to factor, so you should find the greatest common factor of 26a and 10, which is 2. (a isn't on both terms, but if it was, then you would factor out the a also.) 26a/2 is 13a and -10/2 is -5, so the answer is 2(13a-5).
hope this helped!
It is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number greater than 5.
Answer:
Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
Step-by-step explanation:
We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.
And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.
Let the Probability that pointer will stop on an odd number = P(A)
Probability that pointer will stop on a number greater than 5 = P(B)
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]P(A\bigcap B)[/tex]
Probability that pointer will stop on an odd number or on a number greater than 5 = [tex]P(A\bigcup B)[/tex]
Here, Odd numbers = {1, 3, 5, 7} = 4
Numbers greater than 5 = {6, 7, 8} = 3
Also, Number which is odd and also greater than 5 = {7} = 1
Total numbers = 8
Now, Probability that pointer will stop on an odd number = [tex]\frac{4}{8}[/tex] = 0.5
Probability that pointer will stop on a number greater than 5 = [tex]\frac{3}{8}[/tex] = 0.375
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]\frac{1}{8}[/tex] = 0.125
Now, [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]
= 0.5 + 0.375 - 0.125
= 0.75
Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
The probability that the pointer will stop on an odd number or a number greater than 5 is 3/4
The sample space is:
[tex]\mathbf{S = \{1,2,3,4,5,6,7,8\}}[/tex]
Count = 8
The odd numbers are:
[tex]\mathbf{Odd = \{1,3,5,7\}}[/tex]
Count = 4
The probability of odd is:
[tex]\mathbf{P(odd) = \frac{4}{8} }[/tex]
The numbers greater than 5 are:
[tex]\mathbf{Greater= \{6,7,8\}}[/tex]
Count = 3
The probability of numbers greater than 5 is:
[tex]\mathbf{P(Greater) = \frac{3}{8}}[/tex]
Odd numbers greater than 5 are:
[tex]\mathbf{OddGreater= \{7\}}[/tex]
Count =1
The probability of odd numbers greater than 5 is:
[tex]\mathbf{P(OddGreater) = \frac{1}{8}}[/tex]
So, the probability that the pointer will stop on an odd number or a number greater than 5 is:
[tex]\mathbf{Pr = P(Odd) + P(Greater) - P(OddGreater)}[/tex]
This gives
[tex]\mathbf{Pr = \frac 48 + \frac 38 - \frac 18}[/tex]
[tex]\mathbf{Pr = \frac 68}[/tex]
Simplify
[tex]\mathbf{Pr = \frac 34}[/tex]
Hence, the required probability is 3/4
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Simplify the expression please.
Answer:
tanx·secx
Step-by-step explanation:
To simply this, you can begin by factoring sin x out of the numerator to become:
[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]
Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:
[tex]\frac{sinx}{cos^{2}x }[/tex]
First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.
Finally, we get our answer as tanx·secx.
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years. (a) Predict the educational level of a woman whose husband has completed 18 years of schooling. (b) Predict the educational level of a man whose wife has completed 15 years of schooling. (c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible
Answer:
a) Predicted value =0.5×18+6= 15
b) Predicted value =0.5×15+6= 13.5
c) Since least square equation has the tendency to regress the outcome toward mean value , as both the explanatory variable (in part a and b) are above mean value , the response variable are smaller then them.
Step-by-step explanation:
[ Find the attachments for explanation]
Final answer:
Explaining how to predict the educational level of a spouse based on correlation, and discussing why well-educated individuals may marry partners with different education levels.
Explanation:
The questions can be answered as -
(a) Predicting the educational level of a woman whose husband has completed 18 years of schooling:
Given that the correlation between the educational levels of husbands and wives is 0.50, we can use this correlation to predict the wife's educational level.
Educational level of wife = correlation * (wife's SD / husband's SD) * husband's years of schooling + wife's average years of schooling.
(b) Predicting the educational level of a man whose wife has completed 15 years of schooling:
Apply the same formula as in (a) but with the wife's years of schooling given as 15 years.
(c) Explanation of why well-educated men marry women less educated than themselves:
This can occur due to various factors such as social dynamics, career aspirations, or personal preferences.
8^1/6 x2^x=32^1/2 work out the exact value of x
Answer:
i hope that helps......
For the given equation, the value of [tex]x[/tex] is [tex]2[/tex].
[tex]8^{\frac{1}{6}} \times 2^{x} = 32^{\frac{1}{2}}[/tex]
[tex](2^{3})^{\frac{1}{6}} \times 2^{x} = (2^{5})^{\frac{1}{2}}[/tex]
[tex]2^{\frac{1}{2}} \times 2^{x} = 2^{\frac{5}{2}}[/tex]
[tex]2^{\frac{1}{2}+x}=2^{\frac{5}{2}}[/tex]
Since, the bases are equal, we can compare the powers.
[tex]\frac{1}{2}+x=\frac{5}{2}[/tex]
[tex]x=\frac{5}{2}-\frac{1}{2}[/tex]
[tex]x=\frac{5-1}{2}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So, the value of [tex]x[/tex] is [tex]2[/tex].
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An organism which must obtain its food from other organisms is called a:
parasite
spore
fern
moss
Answer:
Parasite
Step-by-step explanation:
It feeds off of other organisms by living on or in the animal.
A sports drinks contains 8% fruit juice.How is the percent written as a decimal.
Answer:
.08
Step-by-step explanation:
Divide the percentage by 100.
8 / 100 = .08
Answer: 8% = .08
Step-by-step explanation: simple. if you use d2p. meaning decimal two percent. you take your decimal like .36 and move the dot two places forward making it 36%. same from percent to decimal by reversing it.
The equation of the piecewise function f(x) is below. What is the value of f(–2)
Answer: f(-2)=3
Step-by-step explanation:
Answer: D. f(–2) = 3
Step-by-step explanation: EDGE 2022
a bag is full of poker chips . the probability of randomly selecting a red chip from the bag is 1/8. the probability of selecting a blue chip from the bag is 13/24. find the probability hint there are other colors in the bag too
Answer:
1/3
Step-by-step explanation:
Let the probability of selecting all coloured chips in the bag be 1.
If the probability of randomly selecting a red chip from the bag is 1/8 and the probability of selecting a blue chip from the bag is 13/24, then the probability of selecting both will be 1/8+13/24
1/8+13/24
= (3+13)/24
= 16/24
= 2/3
If the probability of selecting both ted and blue chip is 2/3, then the probability that there are other colors in the bag too will be expressed as 1-2/3 which is equivalent to 1/3
Final answer:
To find the probability of picking a chip that is neither red nor blue from the bag, we subtract the probabilities of picking a red or blue chip from 1. The calculation shows that the probability of selecting a different color chip is 1/3.
Explanation:
The student's question pertains to the calculation of probabilities when selecting poker chips of different colors from a bag. We are given that the probability of selecting a red chip is 1/8, and the probability of selecting a blue chip is 13/24. The aim here is to find the probability of selecting a chip of a different color. Since probabilities sum up to 1 for all possible outcomes, we would subtract the given probabilities from 1 to find the probability of selecting a chip that's neither red nor blue.
The total probability for all colors in the bag is always 1 (or 100%), which can be mathematically expressed as:
P(red) + P(blue) + P(other colors) = 1
Given P(red) = 1/8 and P(blue) = 13/24, we can substitute to find P(other colors):
P(other colors) = 1 - (P(red) + P(blue))
P(other colors) = 1 - (1/8 + 13/24)
First, we need to find a common denominator to combine the fractions:
P(other colors) = 1 - (3/24 + 13/24)
P(other colors) = 1 - 16/24
P(other colors) = 1 - 2/3
P(other colors) = 1/3
Therefore, the probability of selecting a chip that is neither red nor blue is 1/3.
At a certain store, four cans of soup cost $5. What is the cost per can and the correct equation to find the total cost for any amount of cans of soup?
Let A = {t, u, v, w}, and let S1 be the set of all subsets of A that do not contain w, and S2 the set of all subsets of A that contain w. (a) Find S1. (Enter your answer in set-roster notation. Enter EMPTY or ∅ for the empty set.)
Answer:
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
Step-by-step explanation:
Given:
A = {t, u, v, w}
S1 = set of all subsets of A that do not contain w.
S2 = set of all subsets of A that contains w.
Therefore S1 & S2 in set roster notation will be given as:
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
S2 = { {w}, {t,w}, {u,w}, {v,w}, {t,u,w}, {t,v,w}, {u,v,w}, {t,u,v,w} }
a) We can see that,
S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }
The problem involves finding subsets of a given set. The set S1, which includes subsets of the original set A that do not contain the element 'w', includes eight such subsets.
Explanation:The given set A contains the elements {t, u, v, w}. The set S1 consists of all the subsets of A that do not contain the element 'w'. Similarly, the set S2 consists of all the subsets of A that do contain the element 'w'.
To find S1, we can start by listing out each possible subset of A without the element 'w'. These include {}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, and {t, u, v}. So, S1 = {{}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, {t, u, v}}.
We ignore S2 as it's not relevant to the question asked.
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A rectangle has a length of 4 inches and a width of x inches. The value of the perimeter of the rectangle is equal to the value of the area of the rectangle. Graph a system of linear equations to find x.
Answer:
see below for a graph
x = 4
Step-by-step explanation:
The perimeter is given by the formula ...
P = 2(L +W)
The area is given by the formula ...
A = LW
We want these two values to be equal. Using "y" for both perimeter and area, and substituting the given values for L and W, we have the equations ...
y = 2(4 +x)
y = 4x
The graph of these equations (below) shows the value of x is 4.
What is the mean of this sample, which consists of 10
values randomly selected from the table?
7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
Mean =
10
100
The mean of the third sample is
Answer:
The mean of the samples is 21
Step-by-step explanation:
Mean is defined as the average sum of numbers i.e total sum of given numbers divided by the total number.
Given the randomly selected numbers as shown;
7, 100, 1, 3, 7, 10, 15, 12, 17, 38
Total sum of numbers = 7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
= 210
Total numbers given = 10
Mean = 210/10
Mean = 21
Answer:mean is 21 i did it on edge 2023
Step-by-step explanation:
A table titled Text messages sent has entries 7, 100, 1, 3, 17, 10, 15, 12, 7, 38.
What is the mean of this sample, which consists of 10 values randomly selected from the table?
Mean = 7 + 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38
10
The mean of the third sample is
21
.
Which of the following expressions has a value of 3? Select all that apply.
Answer:
-6 ÷ -2 and (-1)(-3)
Step-by-step explanation:
To find which expressions have a value of 3, set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply.
Explanation:To find which expressions have a value of 3, we can set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply. Let's go through each expression:
2x - 1 = 3So, the only expression that has a value of 3 is 2x - 1 = 3 when x = 2.
Learn more about Expressions with a value of 3 here:https://brainly.com/question/13283719
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4 - 0.25(10) +0.5(5)
Answer:
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4-0.25(10)+0.5(5)
Multiply -0.25 by 10 and you get -2.5
4-2.5+0.5(5)
Multiply 0.5 by 5 and you get 2.5
4-2.5+2.5
Subtract 4 minus 2.5 and you get 1.5
1.5+2.5
Add 1.5 plus 2.5 and you get 4
4
Which shows how to determine the volume of the pyramid?
10 cm
-5.
8 cm
12 cm
V=3(1278(10)
(12)(10)
V - (12)()(10)
Answer:
V=lwh /3
Step-by-step explanation:
Answer:
a. V=1/3(12)(8)(10)
Step-by-step explanation:
observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
The value of x any y are "-5.29 and 0.79" and "3.79 and -2.29"
Step-by-step explanation:
Given values:
[tex]2xy =6.....(a)\\\\x-y= 3.....(b)\\\\[/tex]
After solve equation (a) we get
[tex]\ equation: \\\\2xy= 6\\\\xy =\frac{6}{2} \\\\xy = 3.....(x)\\\\[/tex]
After solve equation (b) we get
[tex]\ equation: \\\\x-y =3\\\\x= 3+y....(x1)\\[/tex]
put the value of x in to equation (x)
[tex](3+y)y = 3\\[/tex]
[tex]y^2+3y-3=0\\\\\ compare \ the \ value \ with \ ay^2+by+c=0\\a= 1\\b=3\\c=-3\\\ Formula: \\y= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\y= \frac{-3\pm \sqrt{9+12}}{2}\\y= \frac{-3\pm \sqrt{21}}{2}\\[/tex]
The value of y is = -5.29 and 0.79, put the value of y in x1 equation so, we get: 3.79 and -2.29