In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?

True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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Answer:

1. 52.63% 2. 47.36%

Step-by-step explanation:

20 + 18 = 38 total people

20 divided by 38 = 0.5263 to 52.63%

18 divided by 38 = 0.4736 to 47.36%

Hope this helps!

Answer:

6log 2

Step-by-step explanation:

log 16 + log 4 = log 2⁴ + log 2² = 4log 2 + 2log 2 = 6log 2

(a) The probability mass function for the number of children with Tay-Sachs disease is: P(X = k) = C(4, k) * 0.25^k * 0.75^(4-k) (b) The probability mass function for the number of emails  is seen is: P(Y = y) = (1 – 0.02)^(y – 2) * 0.02 * 0.98, where y ≥ 2.


(a) Probability mass function for the number of children with Tay-Sachs disease:
Let X be the random variable representing the number of children with Tay-Sachs disease. The possible values of X are 0, 1, 2, 3, and 4, as there can be 0, 1, 2, 3, or 4 children affected by the disease.
Assuming independence and a probability of 0.25 for a child to have the disease, the probability mass function is given by:
P(X = k) = C(4, k) * 0.25^k * 0.75^(4-k)
Where C(4, k) is the number of combinations (binomial coefficient) of choosing k out of 4 children.
The assumption made here is that the occurrence of Tay-Sachs disease in each child is independent of the others.
The probability mass function for the number of children with Tay-Sachs disease is:
P(X = 0) = C(4, 0) * 0.25^0 * 0.75^4 = 1 * 1 * 0.75^4 = 0.3164
P(X = 1) = C(4, 1) * 0.25^1 * 0.75^3 = 4 * 0.25 * 0.75^3 = 0.4219
P(X = 2) = C(4, 2) * 0.25^2 * 0.75^2 = 6 * 0.25^2 * 0.75^2 = 0.2109
P(X = 3) = C(4, 3) * 0.25^3 * 0.75^1 = 4 * 0.25^3 * 0.75^1 = 0.0469
P(X = 4) = C(4, 4) * 0.25^4 * 0.75^0 = 1 * 0.25^4 * 0.75^0 = 0.0039
Therefore, the probability mass function for the number of children with Tay-Sachs disease is:
P(X = 0) = 0.3164
P(X = 1) = 0.4219
P(X = 2) = 0.2109
P(X = 3) = 0.0469
P(X = 4) = 0.0039

(b) Probability mass function for the number of emails until the second spam message:
Let Y be the random variable representing the number of emails received until the second spam message is seen, including the second spam message. The possible values of Y are 2, 3, 4, …
To find the probability mass function, we observe the pattern:
P(Y = 2) = 0.02 * 0.98 = 0.0196
P(Y = 3) = (1 – 0.02) * 0.02 * 0.98 = 0.0192
P(Y = 4) = (1 – 0.02)^2 * 0.02 * 0.98 = 0.0188
From the pattern, we can guess that the probability mass function for Y can be represented by:
P(Y = y) = (1 – 0.02)^(y – 2) * 0.02 * 0.98
Where y ≥ 2.
Therefore, the probability mass function for the number of emails until the second spam message is seen is:
P(Y = y) = (1 – 0.02)^(y – 2) * 0.02 * 0.98, where y ≥ 2.

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A sample with r = 0.823, n = 10, and α = 0.05, determine the critical values t0 required to test the claim rho = 0. The  r and n are required to determine the critical values t0. The critical value of tα/2 with 8 degrees of freedom is ±2.306, and the answer is D. ±2.306.

The formula to calculate the critical value is given below: Critical Value t0 = 0.823 * sqrt(10 - 2)/ sqrt(1 - 0.823^2)Critical Value t0 = 2.306Since the alternative hypothesis is two-tailed, the critical values are +2.306 and -2.306. Therefore, option D. ±2.306 is the correct answer.

A critical value is a numeric value that allows statisticians to decide whether or not to decline a null hypothesis. The critical value corresponds to the significance level of the hypothesis test, which determines how much of a chance the researcher is willing to take of making an error.

The level of significance, α is 0.05, and the degree of freedom for r is df = n - 2 = 10 - 2 = 8. Using the t-distribution table, we can find the critical value of t with 8 degrees of freedom and 0.05 significance level. The critical value of tα/2 with 8 degrees of freedom is ±2.306, and the answer is D. ±2.306.

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The probability that the second traffic light is red, given that the first light is red is approximately 0.729 or 72.9%.

To find the probability that the second light is red, given that the first light is red, we can use the concept of conditional probability. The conditional probability of an event B happening, given that event A has already occurred, is denoted as P(B|A).

In this scenario, event A represents the first traffic light being red, and event B represents the second traffic light being red. We are given that the probability of event A, P(A), is 0.48, and the probability of both events A and B occurring, P(A and B), is 0.35.

The formula to calculate conditional probability is:

P(B|A) = P(A and B) / P(A)

Plugging in the values we have, P(B|A) = 0.35 / 0.48.

Dividing 0.35 by 0.48, we find that the probability of the second traffic light being red, given that the first light is red, is approximately 0.729.

Therefore, the probability that the second light is red, given that the first light is red, is approximately 0.729 or 72.9%.

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The final cost be $27.

Given that,

Based on the above information, the calculation is as follows:

\(= \$60 \times (1-0.40) \times (1-0.25)\)

= $27

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Generally, using a protractor we see x to be an angle 32 degrees

Hence, we solve

since the angle in point is given by 360 and x=35

Therefore

y=360-x

y=360-32

y=328 degrees

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The measure of angle x would be 35° and the measure of angle y would be 325°

From the question, we are to determine the measures of angle x and angle y.

The measure of angle x can be determined with the aid of a protractor.

From the given diagram, we can observe that angle x is an acute angle. That is, the measure of angle x is less than 90°.

After determining the measure of angle x by using a protractor, for example, let us say the measure of angle x is 35°.

We can determine the measure of angle y by using the sum of angles at a point theorem.

Sum of angles at a point is 360°.

Thus, we can write that

x + y = 360°

Then,

35° + y = 360°

y = 360° - 35°

y = 325°

Hence, the measure of x = 35° and the y = 325°

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Answer:

4^6 / 5^6

Step-by-step explanation:

We know that (a/b) ^c = a^c / b^c

(4/5) ^6 = 4^6 / 5^6

=======================================================

Explanation:

The rule is

\(\left(\frac{a}{b}\right)^c = \frac{a^c}{b^c}\)

Basically we raise each part of the fraction to the outer exponent. In this case, a = 4, b = 5 and c = 6.

---------------------------------

The outer exponent c = 6 tells us how many copies of (a/b) we are multiplying together. So we are multiplying 6 copies of (4/5) together like so

\(\left(\frac{4}{5}\right)^6 = \left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)*\left(\frac{4}{5}\right)\\\\\left(\frac{4}{5}\right)^6 = \frac{4*4*4*4*4*4}{5*5*5*5*5}\\\\\left(\frac{4}{5}\right)^6 = \frac{4^6}{5^6}\\\)

For larger values of c, it's easiest to use the formula directly instead of expand things out like what is shown above. I recommend trying out small values of c such as c = 2 or c = 3.

Answer:

9 and 13

Step-by-step explanation:

Answer:

13 and 9

Step-by-step explanation:

sum of num: 13+9 = 22

sum of square: 13²+9² = 250

169+81 = 250

Answer:

c. the typical value is greater in set b. the spread is greater in set a

Step-by-step explanation:

The typical value is greater in set A. The spread is greater in set B.

The correct answer is an option (B)

"It is the average value (mean) of the data"

"It is the difference between maximum and minimum value."

For given example,

We can observe that the typical value for set A is between 7 and 8

and the typical value for the set is in between 4 to 5.

So, the typical value is greater in set A

The range of the set A is :

R = 9 - 6

R = 3

The range of the set B:

R = 7 - 0

R = 7

So, the spread is greater in set B.

Therefore, the typical value is greater in set A. The spread is greater in set B.

The correct answer is an option (B)

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The number of terms that the expression 5xy 9yz 3zx 5x 4y has is 5 terms.

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

How to determine terms?

To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.

5xy 9yz 3zx 5x 4y has 4 spaces

4 + 1 = 5 terms.

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Therefore , the solution of the given problem of unitary method comes out to be the annual rate of decline is £348.11.

The goal may be achieved by using extant variables, this usual convenience, or all crucial elements from the original Diocesan malleable study that followed a particular methodology. Both crucial elements will surely miss the statement if the term expression confirmation result fails to occur, but if it does, it then turns into possible to contact the entity again.

Here,

To calculate the rate of decline, we can use the following formula:

=> (Initial value - Final value) / the number of years = depreciation per year.

This situation has a starting value of E4900, a final value of E3464.76 after 4 years, and there are 4 years involved. With these numbers entered into the formula, we obtain:

The annual depreciation rate is

=>(4900 - 3464.76) / 4.

=> Depreciation = 348.31 per year.

As a result, the annual rate of decline is £348.11.

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Algebraic expressions are mathematical statements made up of variables, constants, and operations, which can be simplified to -17x²+4x+5.

Given expression: -10x²+4x-7x²+5.A mathematical statement made up of variables, constants, and mathematical operations is known as an algebraic expression. It stands for a mixture of numbers and letters, where the letters are called variables and they can have various values. In algebra, relationships are represented and calculations are done using algebraic expressions.

The given expression can be simplified as:

Adding the like terms together,

we get,-10x²-7x²+4x+5

= -17x²+4x+5

Thus, the simplified expression is -17x²+4x+5.

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Answer:

B

Step-by-step explanation:

The  probability space and that e1 and e2 are events satisfying e1 ∪ e2 = s, p(e1) = 1/5, and p(e1 ∩ e2) = 1/30.The  p(e2) is 0.8333.

In chance principle, a probability space or a probability triple. is a mathematical construct that offers a formal model of a random manner or "test". for example, you can still outline an opportunity area that fashions the throwing of a die.

A chance area fashions random occasions and is made of three parts: pattern space: the set of all possible results. as an example, in case you toss a coin twice, the pattern space is {HH, HT, TH, TT}. The sample space is every so often denoted by way of the Greek letter omega (Ω).07-Jan-2017

A finite probability space is a fixed S and a feature p: S → R ≥zero such that p(s) > 0 (∀s ∈ S) and ∑ p(s) = 1. We re. page 1. A finite probability area is a set S and a characteristic p: S → R≥0 such that p(s) > 0. (∀s ∈ S) and ∑

Given E1 and E2 events S is the probability space

And given E1∪ E2 =S

P(E1)=1/5 and P(E1 ∩ E2 )=1/30

From given P(E1∪ E2)=P(S)

From probability axioms P(S)=1

Therefore P(E1∪E2) =1

      P(E1)+ P(E2)- P(E1 ∩E2)= 1

      (1/5) + P(E2) - (1/30) = 1

   P(E2 )= 1-(1/5) +(1/30)= 0.8333

Therefore P(E2)= 0.8333

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The open interval(s) where the following function is increasing and decreasing are respectively;  (-∞, 3) and (3, ∞)

From the graph, we can say that the function is increasing if as x increases, the value of y also increases. However, if the value of y decreases as x increases, then we can say that the function is decreasing.

Now, from the graph, we see that for values of x from negative infinity to 3, the value of y keeps increasing to zero.

Now, from the graph we see that for values of x from 3 to positive infinity, the values of y keep decreasing to negative infinity.

Thus, we can say the function is increasing on the interval (-∞, 3) and decreasing on the interval (3, ∞)

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Check the picture below.

The solution to the problem is the simplified expression: 5x³ - x² - 3x + 13.

To solve the given problem, you need to simplify and combine like terms. Start by adding the coefficients of the same degree terms.

(3x³ - x² + 4) + (2x³ - 3x + 9)

Combine the like terms:

(3x³ + 2x³) + (-x²) + (-3x) + (4 + 9)

Simplify further:

5x³ - x² - 3x + 13

In this expression, the highest power of x is ³, and the corresponding coefficient is 5. The term -x² represents the square term, -3x represents the linear term, and 13 is the constant term. The simplified expression does not have any like terms left to combine, so this is the final solution.

Remember to check for any specific instructions or constraints given in the problem, such as factoring or finding the roots, to ensure you address all requirements.

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The simplify value of numeric expression, 3 + 2, after adding 3456 then subtracting 45 and then dividing by 20 is equals the 17.8.

We have an expression of numbers, 3 + 2 we have to apply some arithematic operations on it and determine the final simplfy value. Let the expression be x = 3 + 2, add 3456 in it

=> x = 3 + 2 + 3456

Substracts 45 from above expression

=> x = 3 + 2 + 3456 - 45

Dividing the above expression of x by 20

=>

\(\frac{ x } {20} = \frac{ 3 + 2 + 3456 - 45}{20}\)

\(= \frac{3416}{20}\)

= 17.8

Hence, required simplify value is 17.8.

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The electric potential energy of the charged particles can be ranked from highest to lowest as follows: 4, 2, 3, 1.

Given four point charges, each with a charge of +Q, placed at the corners of a square with sides of length d, we need to rank the electric potential energy of the charged particles from highest to lowest.

Let's consider the different charged particles:

Particle 1 is at one corner of the square.

Particle 2 and Particle 3 are at adjacent corners of the square.

Particle 4 is at the corner opposite Particle 1.

The electric potential energy (PE) of a pair of charges can be calculated using the formula:

\(\[PE = k \left(\frac{|q_1q_2|}{r}\right)\]\)

where k is Coulomb's constant \((9 \times 10^9 N m^2 / C^2)\), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.

The electric potential energy of the four pairs of charges can be calculated as follows:

Particle 1 and Particle 2:

The distance between Particle 1 and Particle 2 is d. Therefore,

\(\[PE_{1-2} = k \left(\frac{|+Q \times +Q|}{d}\right) = k \left(\frac{Q^2}{d}\right)\]\)

Particle 1 and Particle 3:

The distance between Particle 1 and Particle 3 is √2d. Therefore,

\(\[PE_{1-3} = k \left(\frac{|+Q \times +Q|}{\sqrt{2}d}\right) = k \left(\frac{Q^2}{2d}\right)\]\)

Particle 1 and Particle 4:

The distance between Particle 1 and Particle 4 is d√2. Therefore,

\(\[PE_{1-4} = k \left(\frac{|+Q \times +Q|}{d\sqrt{2}}\right) = k \left(\frac{Q^2}{2d}\right)\]\)

Particle 2 and Particle 3:

The distance between Particle 2 and Particle 3 is d. Therefore,

\(\[PE_{2-3} = k \left(\frac{|+Q \times +Q|}{d}\right) = k \left(\frac{Q^2}{d}\right)\]\)

Particle 2 and Particle 4:

The distance between Particle 2 and Particle 4 is √2d. Therefore,

\(\[PE_{2-4} = k \left(\frac{|+Q \times +Q|}{\sqrt{2}d}\right) = k \left(\frac{Q^2}{2d}\right)\]\)

Particle 3 and Particle 4:

The distance between Particle 3 and Particle 4 is d. Therefore,

\(\[PE_{3-4} = k \left(\frac{|+Q \times +Q|}{d}\right) = k \left(\frac{Q^2}{d}\right)\]\)

Therefore, the electric potential energy of the four pairs of charges can be ranked from highest to lowest as follows:

Particle 4 and Particle 2

Particle 1 and Particle 3

Particle 2 and Particle 3

Particle 1 and Particle 2

Particle 1 and Particle 4

Particle 3 and Particle 4

Thus, the electric potential energy of the charged particles can be ranked from highest to lowest as follows: 4, 2, 3, 1.

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There is no question, just some graphs, I can not explain if I don't know the question

ok

y = 2x

This is a positive line that increases from left to right, because the number 2 of the equation is positive.

So from the graphs that you send me, the right answer is the second one, it is an increasing line.

A graph increases from left to rigth if it goes up

A graph decreases from left to right if it goes down

Answer:

21 days

Step-by-step explanation:

February has 28 days

28/4=7

1 quarter of 28 is 7

Since one quarter was above freezing, 3 were below freezing

3x7=21

21 days is the final answer

Answer:

21 days

Step-by-step explanation:

There are 28 days in February.

If one quarter of the days had a temperature above freezing, that means that three quarters of the days had a temperature below freezing.

Find how many days were below freezing by multiplying 28 by 3/4

28(3/4)

= 21

So, 21 days in February were below freezing.

The distribution of the number of business majors you choose is not binomial. The correct option is c) not binomial.

The distribution of the number of business majors you choose is not binomial because the conditions for a binomial distribution are not met:

1. There must be a fixed number of trials: In this case, we are choosing 3 students out of 10, which means the number of trials is not fixed.

2. The trials must be independent: This assumption is reasonable, as choosing one student does not affect the probability of choosing another student.

3. The probability of success must be the same for each trial: The probability of choosing a business major is 0.4 for the first trial, but it will change for the second and third trials depending on the results of the previous trials. Therefore, the probability of success is not the same for each trial.

Therefore, the correct option is c) not binomial.

The complete question is:

In a group of 10 college students, 4 are business majors. You choose 3 of the 10 students at random and ask their major. The distribution of the number of business majors you choose is

(a) Binomial with n = 10 and p = 0.4

(b) Binomial with n = 3 and p = 0.4

(c) Not binomial

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The optimal order quantity is 1256 units and the minimum total cost is S3150.04. The soft goods department of a large department store sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is S2.50 and the cost of placing an order is S375.

In this problem, the order quantity (Q) will be calculated using the economic order quantity (EOQ) formula as follows:

EOQ = √[(2DS)/H] Where: D = Annual Demand, S = Cost of placing an order, H = Carrying cost per unit per year, Carrying cost per unit per year can be computed using the following formula: H = iC

Where: i = Annual carrying charge rate, C = Unit cost of a towel to the store

Hence, H = 0.12 x S2.50H

= S0.30D is already given as 175 units per month, so the annual demand (D) will be:

D = 175 x 12D

= 2100 units per year

Substitute all values into the EOQ formula:

EOQ = √[(2 x 2100 x 375)/0.30]EOQ

= √[1,575,000]EOQ

= 1255.13 units

Rounding up, the optimal order quantity is 1256 units.

The minimum total cost will be calculated using the following formula:

TC = DH + (Q/2)S + (D/Q) x HC  

Where: TC = Total cost H = Carrying cost per unit per year, S = Cost of placing an order, Q = Order quantity, D = Annual demand.

HC = Holding cost per unit per year

TC = (2100 x S2.50 x 0.3) + (1256/2 x S2.50) + (2100/1256 x 0.12 x S2.50)TC

= S 1575 + S1570 + S5.04TC

= S3150.04

Therefore, the optimal order quantity is 1256 units and the minimum total cost is S3150.04.

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To see which amount of tickets is the best deal, look at the unit price of each.

To do this, divide the cost of the tickets by the number of tickets to see how much money a single ticket costs in each of the deals.

A) Buying 25 tickets for $10.00 offers the best deal because each ticket is only worth $.40, compared to the other deals where each ticket is worth $.50 or $.42.

B) Usually, businesses offer a better discount the more of a good someone buys due to marketing purposes. I would suggest that the students make the discount higher as the number of tickets increases. Therefore, more people would be willing to buy more tickets and both the consumer and seller will be happy because more discounts (consumer = happy) and more profit (more ticket sales -> business = happy).

The points where the tangent line is horizontal on the curve \(x^2 + xy + y^2 = 1\) are (√(1/3), -2√(1/3)) and (-√(1/3), 2√(1/3)).

First, let's differentiate the equation implicitly with respect to x:

\(d/dx (x^2 + xy + y^2) = d/dx\) (1)

Using the product rule and chain rule:

2x + x(dy/dx) + y + 2y(dy/dx) = 0

Rearranging the equation and factoring out dy/dx:

(dy/dx)(x + 2y) = -2x - y

To find the points where the tangent line is horizontal, we set dy/dx equal to zero:

dy/dx = 0

This leads to the equation:

0(x + 2y) = -2x - y

0 = -2x - y

y = -2x

Now we substitute this expression for y back into the original equation to find the corresponding x-values:

\(x^2 + x(-2x) + (-2x)^2 = 1\\x^2 - 2x^2 + 4x^2 = 1\\3x^2 = 1\\x^2 = 1/3\)

Taking the square root of both sides:

x = ± √(1/3)

Therefore, the x-values where the tangent line is horizontal are x = √(1/3) and x = -√(1/3).

Substituting these x-values back into the equation y = -2x, we find the corresponding y-values:

For x = √(1/3), y = -2√(1/3)

For x = -√(1/3), y = 2√(1/3)

So, the points where the tangent line is horizontal are (√(1/3), -2√(1/3)) and (-√(1/3), 2√(1/3)).

Complete Question:

Find all points where the tangent line is horizontal: \(x^2 + xy + y^2 = 1\).

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Answer:

1.1万

Step-by-step explanation: