Answer:
B. 0.132
Step-by-step explanation:
For each time the dice is thrown, there are only two possible outcomes. Either it lands on a five, or it does not. The probability of a throw landing on a five is independent of other throws. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Timothy creates a game in which the player rolls 4 dice.
This means that [tex]n = 4[/tex]
The dice can land in 6 numbers, one of which is 5.
This means that [tex]p = \frac{1}{6}[/tex]
What is the probability in this game of having exactly two dice or more land on a five?
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(\frac{1}{6})^{2}.(\frac{5}{6})^{2} = 0.116[/tex]
[tex]P(X = 3) = C_{4,2}.(\frac{1}{6})^{3}.(\frac{5}{6})^{1} = 0.015[/tex]
[tex]P(X = 4) = C_{4,4}.(\frac{1}{6})^{4}.(\frac{5}{6})^{0} = 0.001[/tex]
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.116 + 0.015 + 0.001 = 0.132[/tex]
So the correct answer is:
B. 0.132
The probability of having exactly two dice or more land on a five is: 0.132.
To determine the probability of having exactly two dice or more land on a five when rolling four dice, we first need to calculate the probabilities of each possible outcome involving getting at least two fives.
1: Define the basic probabilities
Each die has 6 faces, so the probability ( p ) of rolling a five on a single die is:
[tex]\[ p = \frac{1}{6} \]The probability \( q \) of not rolling a five on a single die is:\[ q = 1 - p = \frac{5}{6} \][/tex]
2: Define the number of dice rolls
We are rolling 4 dice.
3: Calculate probabilities for 0, 1, 2, 3, and 4 fives
We use the binomial distribution formula:
[tex]\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]where \( n = 4 \), \( p = \frac{1}{6} \), and \( k \)[/tex] is the number of fives rolled.
Probability of rolling exactly 0 fives (\( k = 0 \)):
[tex]\[ P(X = 0) = \binom{4}{0} \left(\frac{1}{6}\right)^0 \left(\frac{5}{6}\right)^4 = 1 \times 1 \times \left(\frac{5}{6}\right)^4 = \left(\frac{5}{6}\right)^4 \][/tex]
Probability of rolling exactly 1 five (\( k = 1 \)):
[tex]\[ P(X = 1) = \binom{4}{1} \left(\frac{1}{6}\right)^1 \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 \]Probability of rolling exactly 2 fives (\( k = 2 \)):\[ P(X = 2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2 = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 \][/tex]
[tex]Probability of rolling exactly 3 fives (\( k = 3 \)):\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \])^1 \]Probability of rolling exactly 4 fives (\( k = 4 \)):[/tex]
[tex]\[ P(X = 4) = \binom{4}{4} \left(\frac{1}{6}\right)^4 \left(\frac{5}{6}\right)^0 = 1 \times \left(\frac{1}{6}\right)^4 \times 1 \][/tex]
4: Sum probabilities for \( k \geq 2 \)
We need to find \( P(X \geq 2) \), which is:
[tex]\[ P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \][/tex]
5: Perform calculations
[tex]\[P(X = 0) = \left(\frac{5}{6}\right)^4 \approx 0.4823\]\[P(X = 1) = 4 \times \frac{1}{6} \times \left(\frac{5}{6}\right)^3 = 4 \times \frac{1}{6} \times \left(\frac{125}{216}\right) \approx 0.3858\]\[P(X = 2) = 6 \times \left(\frac{1}{6}\right)^2 \times \left(\frac{5}{6}\right)^2 = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} \approx 0.1157\][/tex]
[tex]\[P(X = 3) = 4 \times \left(\frac{1}{6}\right)^3 \times \frac{5}{6} = 4 \times \frac{1}{216} \times \frac{5}{6} = \frac{20}{1296} \approx 0.0154\]\[P(X = 4) = \left(\frac{1}{6}\right)^4 = \frac{1}{1296} \approx 0.0008\][/tex]
6: Summing up [tex]\( P(X \geq 2) \)[/tex]
[tex]\[P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) \approx 0.1157 + 0.0154 + 0.0008 = 0.1319\][/tex]
Rounding this to three decimal places, we get 0.132.
Thus, the probability of having exactly two dice or more land on a five is:
[tex]\[ \boxed{0.132} \][/tex].
9.what is 24/32 reduced
Solve the following equation algebraically: x^2 = 180
Answer:
x = ± 6sqrt(5)
Step-by-step explanation:
x^2 = 180
Take the square root of each side
sqrt(x^2) = ±sqrt(180)
x =±sqrt(36)sqrt(5)
x = ± 6sqrt(5)
Answer:
Edge 2020
A
-13.42, 13.42
Step-by-step explanation:
La profesora de matemáticas solicita a dos estudiantes que describan las cosas que les han parecido interesantes de los números primos y de los números compuestos, a lo que dos estudiantes responden: Paola: he descubierto que cualquier número compuesto par se puede escribir como la multiplicación de factores primos. Edwin: he descubierto que cualquier número compuesto impar se puede escribir como la suma de dos números primos. La profesora pide a los estudiantes que examinen las ideas expuestas por Paola y Edwin y verifiquen si son verdaderas o falsas. De acuerdo con las afirmaciones hechas por Paola y Edwin es CORRECTO afirmar que A. ambas afirmaciones son falsas. B. ambas afirmaciones son verdaderas. C. la afirmación de Paola es falsa y la de Edwin es verdadera. D. la afirmación de Paola es verdadera y la de Edwin es falsa. The math teacher asks two students to describe the things they found interesting about the prime and composite numbers, to which two students respond:
Paola: I have discovered that any even compound number can be written as the multiplication of prime factors.
Edwin: I have discovered that any odd compound number can be written as the sum of two prime numbers.
The teacher asks students to examine the ideas put forth by Paola and Edwin and check to see if they are true or false.
According to the statements made by Paola and Edwin, it is CORRECT to affirm that
TO.
both statements are false.
B.
both statements are true.
C.
Paola's statement is false and Edwin's is true.
D.
Paola's statement is true and Edwin's is false.
Answer:
Respuesta D
Step-by-step explanation:
Paola afirma: Todo número compuesto par, se puede escribir como la multiplicación de factores primos.
Esta afirmación es cierta, pues es un caso de la afirmación de que todo número natural mayor que uno se puede escribir como multiplicación de números primos. A este proceso se le llama descomposición en factores primos.
Edwin afirma: Todo número compuesto impar se puede escribir como la suma de dos números primos.
Esta afirmación es falsa. Note que al sumar dos números impares de la forma 2k+1 y 2m+1 para k distinto de m, se obtiene
[tex] 2k+1+2m+1 = 2(km+1)[/tex]
Es decir, la suma de dos números impares es siempre par.
Note que a excepción de 2, todo número primo es impar. Para que esta afirmación fuera cierta, necesariamente tendría que pasar que cualquier número impar k se escriba de la forma p+2 donde p es un número primo. Esto es equivalente que para cualquier número impar k, el número k-2 sea primo.
Basta con dar un ejemplo para ver que esto no pasa. Tomemos k=11. En este caso, k-2 = 9, el cuál no es un número primo. Entonces 11 no se puede descomponer como la suma de dos números primos.
In ideal conditions, 200 colony-forming units (cfu) of E. coli can grow to 400 cfu in 20 minutes, to 800 cfu in 40 minutes, and to 1600 cfu in an hour.
Part A: Jenny says that the E. coli growth can be modeled with an exponential function. Do you agree? Justify your answer.
Part B: Write the equation that models the function.Immersive Reader
Answer:
(a)Yes, it is an exponential function.
(b)[tex]P(t)=200\cdot 2^{t/20}[/tex]
Step-by-step explanation:
(a)A population grows exponentially if it increases by a common ratio(called the growth ratio). We can see from the given information that the population of E.coli doubles every 20 minutes, therefore it is an exponential growth with a growth ratio of 2.
(b)The population, P(t) at any time t of an initial population, [tex]P_o[/tex] with a growth ratio of r over a period k can be modeled using the function:
[tex]P(t)=P_o\cdot r^{t/k}[/tex]
In this Case:
[tex]P_o[/tex]=200
Growth rate,r=2
Growth Period,k=20 minutes
Therefore, the equation that models the function is:
[tex]P(t)=200\cdot 2^{t/20}[/tex] , t is in minutes
Jenny is correct that E. coli growth can be modeled with an exponential function, characterized by doubling in population size at regular time intervals. An equation representing this growth is N(t) = N0 x 2^(t/20), where N0 is the initial amount of E. coli and t is time in minutes.
I agree with Jenny, the E. coli growth can indeed be modeled with an exponential function. This is supported by the fact that the E. coli population doubles after each consistent time period (20 minutes). In an exponential growth model, the rate of increase of a population is proportional to the current population size, which means as the population gets larger, it grows at an even faster rate.
Part B: Equation of Exponential Growth:
The exponential growth model for a population starting with N0 individuals and a growth rate r can be described by the equation N(t) = N0ert, where N(t) is the population at time t, N0 is the initial population size, e is the base of the natural logarithm, and r is the growth rate per unit time. For E. coli, with a doubling time of 20 minutes, the growth rate can be calculated using the doubling formula: Td = ln(2)/r, solving for r gives r = ln(2) / 20 minutes. The continuous exponential growth equation can be simplified to a discrete model for this case: N(t) = N0 * 2(t/20), where t is given in minutes.
I need help on the rounding tto try to get the right answer. Maybe mark branliest?
Answer:
3238.37571429
Step-by-step explanation:
or 3238.4
How does using a check register help you manage money?
Answer:
Inside a checkbook is the register. This is where you record events in your checking account such as checks you've written, cash withdrawals, and deposits. It's very important to write down every transaction so you know exactly how much money you have in the bank.
Step-by-step explanation:
Answer:
You can store your money in an organized fashion, separating them by type (penny, dime, $1, $5, etc.).
You have decided to set a new goal of saving at least $4,500 over the
course of the next year.
You already have $900 saved.
By how much would you need to increase your monthly net savings in
order to meet this goal?
$100
$150
$200
$250
Answer: $200
Step-by-step explanation:
Answer:
The answer is C.
A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they conclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable.
Determine the mean and the standard deviation of the random variable X, assuming that 60 percent of city henudng proosal to create a new city park.
Answer:
The mean of the the random variable X is 1200.
The standard deviation of the random variable X is 21.91.
Step-by-step explanation:
The random variable X is defined as the number of city residents in the sample who support the proposal.
The random variable X follows a Binomial distribution with parameters n = 2000 and p = 0.60.
But the sample selected is too large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
np ≥ 10 n(1 - p) ≥ 10Check the conditions as follows:
[tex]np=2000\times 0.60=1200>10\\\\n(1-p)=2000\times (1-0.60)=800>10[/tex]
Thus, a Normal approximation to binomial can be applied.
So, the random variable X can be approximate by the Normal distribution .
Compute the mean of X as follows:
[tex]\mu=np[/tex]
[tex]=2000\times 0.60\\=1200[/tex]
The mean of the the random variable X is 1200.
Compute the standard deviation of X as follows:
[tex]\sigma=\sqrt{np(1-p)}[/tex]
[tex]=\sqrt{2000\times 0.60\times (1-0.60)}\\=\sqrt{480}\\=21.9089\\\approx 21.91[/tex]
The standard deviation of the random variable X is 21.91.
An entrepreneur is having a design group produce at least eight samples of a new kind of fastener that he wants to market. It costs $6.00 to produce each metal fastener and $10.00 to produce each plastic fastener. He wants to have at least two of each version of the fastener and needs to have all the samples 58 hours from now. It takes 5 hours to produce each metal sample and 4 hours to produce each plastic sample. To minimize the cost of the samples, how many of each kind should the entrepreneur order? What will be the cost of the samples? To minimize the cost of the samples, how many of each type of sample should the entrepreneur order? The entrepreneur should order ___ metal samples and ___ plastic samples.
Answer:
b
Step-by-step explanation:
Find the volume of the composite solid. ft3 pls help!! ::)))):):):):):):)
Answer:
54
Step-by-step explanation:
because it is
Answer: The volume of the composite solid is about 589.5 cubic feet.
Step-by-step explanation:
1. The face of a brick is 3 1/2 inches by 8 inches. Suppose you want to create a
brick pathway that is 56 inches wide by 20 inches long. How many 3 1/2 inch by 8
inch bricks would you need?
Answer:
40 bricks
Step-by-step explanation:
3 1/2×8
=28
56×20
=1,120
1,120÷28
=40 bricks
he United States Marine Corps is reviewing its orders for uniforms because it has a surplus of uniforms for tall men recruits and a shortage for shorter men recruits. Its review involves data for 772 men recruits between the ages of 18 to 24. That sample group has a mean height of 69.7 inches with a population standard deviation of 2.8 inches. Construct a 99% confidence interval for the mean height of all men recruits between the ages 18 and 24.
Answer:
The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{2.8}{\sqrt{772}} = 0.26[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 69.7 - 0.26 = 69.44 inches
The upper end of the interval is the sample mean added to M. So it is 69.7 + 0.26 = 69.96 inches
The 99% confidence interval for the mean height of all men recruits between the ages 18 and 24 is between 69.44 inches and 69.96 inches.
A company has 270 employees.60% are men and 40% are women.how many more men work then women?
Answer:
that is the solution to the question
The U.S. Census Bureau conducts annual surveys to obtain information on the percentage of the voting-age population that is registered to vote. Suppose that 513513 employed persons and 604604 unemployed persons are independently and randomly selected, and that 287287 of the employed persons and 280280 of the unemployed persons have registered to vote. Can we conclude that the percentage of employed workers ( p1p1 ), who have registered to vote, exceeds the percentage of unemployed workers ( p2p2 ), who have registered to vote? Use a significance level of α=0.05α=0.05 for the test.
Answer:
We conclude that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.
Step-by-step explanation:
We are given that 513 employed persons and 604 unemployed persons are independently and randomly selected, and that 287 of the employed persons and 280 of the unemployed persons have registered to vote.
Let [tex]p_1[/tex] = percentage of employed workers who have registered to vote.
[tex]p_2[/tex] = percentage of unemployed workers who have registered to vote.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the percentage of employed workers who have registered to vote does not exceeds the percentage of unemployed workers who have registered to vote}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1>p_2[/tex] {means that the percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote}
The test statistics that would be used here Two-sample z test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of employed workers who have registered to vote = [tex]\frac{287}{513}[/tex] = 0.56
[tex]\hat p_2[/tex] = sample proportion of unemployed workers who have registered to vote = [tex]\frac{280}{604}[/tex] = 0.46
[tex]n_1[/tex] = sample of employed persons = 513
[tex]n_2[/tex] = sample of unemployed persons = 604
So, the test statistics = [tex]\frac{(0.56-0.46)-(0)}{\sqrt{\frac{0.56(1-0.56)}{513}+\frac{0.46(1-0.46)}{604} } }[/tex]
= 3.349
The value of z test statistics is 3.349.
Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.
Since our test statistic is more than the critical value of z as 3.349 > 1.645, 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 percentage of employed workers who have registered to vote exceeds the percentage of unemployed workers who have registered to vote.
1. Add and write in standard form.
(2x2 - 6x3 + 4) + (2x3 + 3x2 + 4)
Answer:
because I said one is the best number
Step-by-step explanation:
[tex](2x^2-6x^3+4)+(2x^3+3x^2+4)[/tex]
Since this is addition, you can just easily combine the terms.
[tex](2x^2+3x^2)+(-6x^3+2x^3)+(4+4)[/tex]
[tex]5x^2 -4x^3+8[/tex]
Now, all we have to do is put it in standard form meaning the exponents have to go in descending order. Largest exponent to smallest exponent.
[tex]-4x^3+5x^2+8[/tex]
So, this is your answer in standard form.
in a sample of people on the school board, 2 out of 5 were in favor of a new high school being built. If 3,500 people vote in the next local election approximately how many would vote against the new high school being built?
Answer:
2,100 people.
Step-by-step explanation:
If 2 out of 5 people were in favor of a new high school being built, we know that 3 out of 5 people are against the decision. We can simply use this as a fraction to find the amount of people against:
[tex]3500 * \frac{3}{5}= 2100[/tex]
Therefore, 2,100 people are against the decision.
Giving brainliest for CORRECT awnser. Am I correct?
Step-by-step explanation:
-13 > x - 43
-13 + 43 > x
30 > x
Leona has a bag containing letter tiles. Which describes dependent events?
Answer:
a) removing a vowel, not replacing it, and then removing another vowel
Step-by-step explanation:
This question is from the topic Probability. In Probability, a dependent event is one in which the outcome of one event alters or changes the outcome of another event. A classic example of this is seen when sampling without replacement is done. When sampling without replacement is done, the outcome of another event within the same set changes. When sampling with replacement is done, the outcome of the events are independent because every item in the population still has an equal chance of being chosen. However, in the case of sampling without replacement, once an item has been selected from a population, the outcome of every other event after it is altered based on the item that was initially chosen.
Let's assume that the bag has 26 tiles (one for each alphabet from a - z)
Population = 26, consonant = 21, vowel = 5
If a vowel or consonant is removed & is replaced, we have:
Pr (choosing "a") = number of item ÷ population
Pr = 1 ÷ 26 = 1/26
Pr (choosing "y") = 1 ÷ 26 = 1/26
Doing this for over & over again, produces the same probability
However, if an item was selected without replacement, we have:
Pr (choosing "a") = 1 ÷ 26 = 1/26
Without replacement implies that if I choose tile letter "a", tile letter "a" will not be included in subsequent events, hence:
Population = 25
Pr (choosing "u") = 1 ÷ 25 = 1/25
Without replacement, population = 24
Pr (choosing "y") = 1 ÷ 24 = 1/24
So, we see the dependent nature of the events in how that the outcome of the next event is being altered. As such, option a describes a dependent event & is the correct answer
Answer:
A. removing a vowel, not replacing it, and then removing another vowel
simple answer ^^
Step-by-step explanation:
EDGE 2021 : )
The graph on the right shows two angles that
share the same terminal side: 45° and -315º.
Together, the angles form a circle.
What if you subtract the angle measures?
45°-(-3159) =
-315º – 45º =
Answer:
45°-(315°) = 360°
-315°-45°=-360°
Second part: WOULD
Step-by-step explanation:
Trust me I gotchu
Subtracting angles involves accounting for the directions implied by their positive or negative signs. The subtraction of 45°-(-315°) equates to an addition, giving a resultant angle of 360°. Conversely, -315° – 45° provides a resultant angle of -360°.
Explanation:The question involves the mathematical concept of angles, specifically, subtracting them. Here, we are dealing with angles of 45° and -315°. When subtracting angles, consider the directions indicated by the positive and negative signs. A positive angle is measured counterclockwise from the initial side to the terminal side, while a negative angle is measured clockwise.
So, for 45°-(-315°), you're essentially adding 45 and 315 because subtracting a negative number becomes the addition of the positive equivalent. This gives you a resultant angle of 360°.
And in the case of -315° – 45°, you're subtracting 45 from -315 which gives you a resultant angle of -360°.
Learn more about Subtracting Angles here:https://brainly.com/question/27546559
#SPJ2
A random sample is selected from a normally distributed population. The following sample statistics are obtained: n = 20, = 30, and s = 10. Based on this information, and using a 95% confidence level, which of the following statements is true? a. The margin of error is approximately 4.68. b. The margin of error is approximately 3.24. c. The standard deviation of the sampling distribution of is .50. d. The critical value is 1.96. e. The critical value is 1.7921.
Answer:
b) The margin of error is approximately 3.24
e) The critical value is 1.7921.
Step-by-step explanation:
Step(i):-
Given sample size 'n' =20
Given sample standard deviation 's' = 10
Margin of error
The margin of error is determined by
[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]
The level of significance ∝ =0.95
The degrees of freedom = n-1 = 20-1=19
t₀.₉₅ = 1.729
[tex]M.E = \frac{1.729 X10 }{\sqrt{20} }[/tex]
Margin of error = 3.866
Step(ii):-
Margin of error
The margin of error is determined by
[tex]M.E = \frac{t_{\alpha } S.D }{\sqrt{n} }[/tex]
Given another sample size n =30
The level of significance ∝ =0.95
The degrees of freedom = n-1 = 30-1=29
t₀.₉₅ = 1.70
[tex]M.E = \frac{1.7021 X10 }{\sqrt{30} } =3.24[/tex]
Margin of error = 3.24
One number is six less than a second number. Six times the first is 8 more than 4 times the second. Find the numbers.
To find the values of the two numbers, we can set up a system of equations based on the given information and then solve for x and y. The first number is 16 and the second number is 22.
Explanation:Let's represent the first number as x and the second number as y.
We can set up two equations based on the given information.
The first equation is: x = y - 6
The second equation is: 6x = 4y + 8
Now we can solve this system of equations to find the values of x and y.
Substituting the first equation into the second equation, we get: 6(y - 6) = 4y + 8
Simplifying, we get: 6y - 36 = 4y + 8
Bringing like terms together, we have: 6y - 4y = 8 + 36
Combining like terms, we get: 2y = 44
Dividing both sides by 2, we have: y = 22
Now substitute y = 22 back into the first equation: x = 22 - 6
Simplifying, we get: x = 16
Therefore, the first number is 16 and the second number is 22.
Learn more about Solving a system of equations here:https://brainly.com/question/32115090
#SPJ2
In 1929 Edwin Hubble investigated the claim that distance (explanatory) and radial velocity (response) of extragalactic nebulae are positively linearly related. Hubble's data is plotted below along with the relevant diagnostic plots. These are the plots and charts needed to analyze data are given below. (Assume all observations are independent) Reference: Hubble, E. (1929) "A Relationship Between Distance and Radial Velocity among Extra-Galactic Nebulae," Proceedings of the National Academy of Science, 168.The explanatory variable is distance (in megaparsecs) and the response is radial velocity (velocity away or towards the earth). Use 3 decimal places for the following questions.(a) What is the regression equation?(b) What is the estimated mean velocity of objects that are 1.9 megaparsecs from Earth?(c) If you were to test the claim that there is a positive linear relationship between the explanatory and response variable, what would your null and alternative hypotheses be?H0: a = 0 and Ha: a < 0H0: a = 0 and Ha: a ? 0 H0: a = 0 and Ha: a > 0H0: b = 0 and Ha: b < 0H0: b = 0 and Ha: b ? 0H0: b = 0 and Ha: b > 0
Answer:
honestly this is very confusing could you send a graph?
Step-by-step explanation:
What is 5.3809 rounded to the nearest thousandth?
Enter your answer
The answer is 5.381!
The number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.
What is rounding off number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
We have a number:
= 5.3809
The thousandth(3 decimals) place is:
Rounded to the nearest 0.001 or the Thousandths Place.
The number becomes:
= 5.381
Thus, the number 5.3809 rounded to the nearest thousandth is 5.381 because the thousandth is 3 decimals.
Learn more about the rounding off number here:
https://brainly.com/question/13391706
#SPJ2
Need help on these two!!
Answer:
The first one is false and the second is vertex
Step-by-step explanation:
In 2015 college students at a large state university completed a survey about their academic and
personal life. Questions ranged from "How many credits are you registered for this semester?" to
"Would you define yourself as a vegetarian?"
The researcher randomly selected 325 students from the university: 312 responded to the survey.
Prompt
The cell-phone datafile is available in the Data section below.
Here is the research question for this lab.
Based on a recent study, roughly 80% of college students in the U.S. own a smartphone. Is
the proportion of smartphone owners lower at this university?
Respond to each of the following in your initial post. Be sure to number each answer to which
question it answers.
1. State your hypotheses in symbolic form and in words. (The following should be clear in your
answer: the population of interest and the meaning of the proportion pin terms of the variable
Cell.) You do not need to write the notation, you can just write:
o Null:
o Alternate:
Answer:
The null hypothesis is represemted as
Null: p ≥ 0.80
The alternative hypothesis is given as
Alternative: p < 0.80
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
For this question, the survey that involved comparison was the proportion of US students at the university that owned a smartphone and the proportion of college students in the US that own a smartphone (80%).
Specifically, we want to check if the proportionof smartphone owners at the university is lower than the overall proportion of smartphone owners amongst US college students (80%).
Hence,
The null hypothesis would be that there isn't significant evidence to conclude that the proportion of smartphone owners is lower at this university than the general proportion of smartphone owners amongst college students.
That is, the proportion of smartphone users at this university isn't lower than the proportion of college students in the U.S. that own a smartphone or the proportion of smartphone owners at this university is higher than or equal to the proportion of college students in the U.S. that own a smartphone.
The alternative hypothesis is then that there is significant evidence to conclude that the proportion of smartphone users at this university is lower than the proportion of college students in the U.S. that own a smartphone.
Mathematically,
The null hypothesis is represemted as
Null: p ≥ 0.80
The alternative hypothesis is given as
Alternative: p < 0.80
Hope this Helps!!!
The null hypothesis states that the proportion of smartphone owners at the university is not lower than 80%, while the alternative hypothesis states that the proportion is lower. A hypothesis test can be conducted using the data from the survey to determine if the proportion is significantly lower.
Explanation:The research question is whether the proportion of smartphone owners at this university is lower than the national average of 80%. We can state the hypotheses as:
Null Hypothesis (H0): The proportion of smartphone owners at this university is not lower than 80%.
Alternative Hypothesis (Ha): The proportion of smartphone owners at this university is lower than 80%.
To test these hypotheses, we need to analyze the data from the survey and perform a hypothesis test. We can use statistical software to calculate the proportion of smartphone owners at the university and conduct the test.
A person recently read that 84% of cat owners are women. How large a sample should the researcher take if she wishes to be 90% confident that her proportion is within 3% of the true population proportion?
Answer:
405
Step-by-step explanation:
To find sample size, use the following equation, where n = sample size, za/2 = the critical value, p = probability of success, q = probability of failure, and E = margin of error.
[tex]n=\frac{(z_{\frac{\alpha }{2} })^{2} *p*q }{E^2}[/tex]
The values that are given are p = 0.84 and E = 0.03.
You can solve for the critical value which is equal to the z-score of (1 - confidence level)/2. Use the calculator function of invNorm to find the z-score. The value will given with a negative sign, but you can ignore that.
(1 - 0.9) = 0.1/2 = 0.05
invNorm(0.05, 0, 1) = 1.645
You can also solve for q which is 1 - p. For this problem q = 1 - 0.84 = 0.16
Plug the values into the equation and solve for n.
[tex]n =\frac{(1.645)^2*0.84*0.16}{(0.03)^2}\\n= 404.0997333[/tex]
Round up to the next number, giving you 405.
graph the following line f(x)=-2/3x+4
Answer:
Ermm here I graphed it :)
Sorry for dark mode..
A) 77°
C) 109°
B) 167°
D) 150°
Answer:
Wat is the question?
Step-by-step explanation:
Mason and Christian go to the movie theater and purchase refreshments for their friends. Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.
Answer:
A bag of popcorn costs $10.25One drink costs $2,5Step-by-step explanation:
Let the cost of a bag of popcorn=p
Let the cost of a drink=d
Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks.
Therefore: 3p+6d=45.75Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks.
Therefore: 6p+4d=71.50The required system of equations is:
3p+6d=45.756p+4d=71.50Multiply the first equation by 2 to eliminate p
6p+12d=91.5
6p+4d=71.50
Subtract
8d=20
d=20/8=$2.5
Substitute d=2.5 into any of the equations to obtain p.
6p+12d=91.5
6p+12(2.5)=91.5
6p=91.5-12(2.5)
6p=91.5-30
6p=61.5
Divide both sides by 6
p=$10.25
Therefore:
A bag of popcorn costs $10.25One drink costs $2,5One year, the mean age of an inmate on death row was 39.2 years. A sociologist wondered whether the mean age of a death-row inmate has changed since then. She randomly selects 32 death-row inmates and finds that their mean age is 37.6, with a standard deviation of 9.89.8. Construct a 95% confidence interval about the mean age. What does the interval imply?
Answer:
The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.
This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a death-row inmate has not changed since then.
Step-by-step explanation:
We have the sample standard deviation, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 32 - 1 = 31
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 31 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0395
The margin of error is:
M = T*s = 2.0395*9.8 = 20
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 37.6 - 20 = 17.6 years
The upper end of the interval is the sample mean added to M. So it is 37.6 + 20 = 57.6 years.
The 95% confidence interval about the mean age is between 17.6 years and 57.6 years.
This means that we are 95% sure that the mean age of an inmate in the death row is in this interval. 39.2 is part of this interval, which implies that the mean age of a death-row inmate has not changed since then.
Final answer:
To construct a 95% confidence interval about the mean age of death-row inmates, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size). In this case, the 95% confidence interval is approximately 35.8 to 39.4 years old.
Explanation:
To construct a 95% confidence interval about the mean age, we can use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).
In this case, the sample mean is 37.6, the standard deviation is 9.8, and the sample size is 32. To find the critical value, we look up the z-score for a 95% confidence level, which is approximately 1.96.
Substituting these values into the formula, we have:
37.6 ± 1.96 * (9.8 / √32)
Simplifying the equation gives us the 95% confidence interval of approximately 35.8 to 39.4. This means that we are 95% confident that the true mean age of death-row inmates falls within this interval.