32 divided by 10 - 8 divided by 2 - 3 The answer you should get is 5. I need an explanation of how I got it.

Answer:

6

Step-by-step explanation:

If X = 2 then you do 2+4 which equals 6

x + 4x and - 2 maybe i think its the answer

Null and alternative hypothesis are statements about the sample statistics.

The null hypothesis of both a test typically forecasts no effect or no association between variables, even while the alternative hypothesis expresses their research's prediction of an effect or relationship.

Because Student's t distribution will be less leptokurtic as both degrees of freedom increase, the likelihood of extreme values decreases. Gradually, the distribution resembles a standard normal distribution.

The two primary forms of probability distributions are discrete probability distributions and continuous probability distributions. Each category includes a variety of probability distribution types.

The average relative frequency over all potential trials is known as probability.

For instance, the probability of a coin falling on heads is such that if you flip a coin an infinite number of times, it will land on heads 50% of the time.

Hence we can say that the Null and alternative hypothesis are statements about the sample statistics.

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The horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

To determine the horizontal asymptote of a function, we need to examine the behavior of the function as x approaches positive or negative infinity. In this case, as x becomes very large or very small, the terms involving x-2 and x-3 become insignificant compared to the higher power of (x-3) squared in the denominator.

As x approaches positive or negative infinity, the (x - 2) term in the numerator does not affect the overall behavior of the function. However, the (x - 3)^2 term in the denominator becomes dominant.

Since (x - 3)^2 will always be positive, the function is always positive or zero. Therefore, as x approaches positive or negative infinity, the function approaches zero or a positive value but never crosses the horizontal line y = 0. Hence, the horizontal asymptote of the function f(x) = (x - 2)/(x - 3)^2 is y = 0.

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Complete question :

Six jurors are to be selected from a pool of 20 potential candidates to hear a civil case involving a lawsuit between two families. Unknown to the judge or any of the attorneys, 2 of the 20 prospective jurors are potentially prejudiced by being acquainted with one or more of the litigants. They will not disclose this during the jury selection process. If 6 jurors are selected at random from this group of 20, find the probability that the number of potentially prejudiced jurors among the 6 selected jurors is ;

a. exactly 1

b. none

c. at most 2

Answer:

0.442 ; 0.479 ; 1

Step-by-step explanation:

Given:.

Total number of candidates = 20

Number of jurors to be selected = 6

Number of prejudiced jurors = 2

Required outcome / Total possible outcomes :

Using the combination formula :

nCr = n! ÷ (n-r)!r!

1.)

P(number of prejudiced jurors is exactly 1) :

[2C1 * 18C5] ÷ 20C6

(2*8568)÷ 38760

= 0.442

B.)

P(None of the jurors is prejudiced) :

[2C0 * 18C6] ÷ 20C6

(1 * 18564) ÷ 38760

= 0.479

C.)

P(at most 2 of the jurors are prejudiced)

P(x =0) + p(x = 1) + p(x = 2)

P(x = 2) :

[2C2 * 18C4] ÷ 20C6

(1 * 3060) ÷ 38760

= 0.079

P(x =0) + p(x = 1) + p(x = 2)

(0.479 + 0.442 + 0.079)

= 1

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

9. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c) and P(d)=P(e)=P(f)=0.1, find P(a).

Since P(a), P(b), and P(c) are equal, we can let P(a) = P(b) = P(c) = x.

Then, we know that P(d) = P(e) = P(f) = 0.1.

The total probability of the sample space S is equal to 1. So, we can write the equation:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

Substituting the given values, we get:
3x + 0.1 + 0.1 + 0.1 = 1
3x + 0.3 = 1
3x = 1 - 0.3
3x = 0.7

Dividing both sides by 3, we find:
x = 0.7/3
So, P(a) = 0.233.

10. If S={a,b,c,d,e,f} with P(a)=P(b)=P(c), P(d)=P(e)=P(f), and P(d)=2P(a), find P(a).

Let P(a) = P(b) = P(c) = x. And let P(d) = P(e) = P(f) = y.

We also know that P(d) = 2P(a).

Using the equation for the total probability:
P(a) + P(b) + P(c) + P(d) + P(e) + P(f) = 1

We can substitute the given values:
3x + 3y = 1
We also know that P(d) = 2P(a):
y = 2x

Substituting this into the previous equation:
3x + 3(2x) = 1
3x + 6x = 1
9x = 1

Dividing both sides by 9, we find:
x = 1/9
So, P(a) = P(b) = P(c) = 1/9.

11. If E and F are two disjoint events in S with P(E)=0.2 and P(F)=0.4, find P(E∪F), P(Ec), and P(E∩F).

Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.2 + 0.4 = 0.6

The complement of E, Ec, is the event that consists of all outcomes in S that are not in E.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Ec) = 1 - P(E) = 1 - 0.2 = 0.8

Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

12. It is not possible for E and F to be two disjoint events in S with P(E)=0.5 and P(F)=0.7 because the sum of their probabilities would exceed 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for two events with probabilities that add up to more than 1 to be disjoint.

13. If E and F are two disjoint events in S with P(E)=0.4 and P(F)=0.3, find P(E∪F), P(Fc), P(E∩F), P((E∪F)c), and P((E∩F)c).
Since E and F are disjoint, their intersection, E∩F, is empty.

The probability of the union of two disjoint events is the sum of their individual probabilities:
P(E∪F) = P(E) + P(F) = 0.4 + 0.3 = 0.7

The complement of F, Fc, is the event that consists of all outcomes in S that are not in F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P(Fc) = 1 - P(F)

= 1 - 0.3

= 0.7
Since E and F are disjoint, their intersection, E∩F, is empty, so its probability is 0:
P(E∩F) = 0

The complement of the union of two events, (E∪F)c, is the event that consists of all outcomes in S that are not in the union of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:

P((E∪F)c) = 1 - P(E∪F) = 1 - 0.7 = 0.3
The complement of the intersection of two events, (E∩F)c, is the event that consists of all outcomes in S that are not in the intersection of E and F.

The complement of an event has a probability equal to 1 minus the probability of the event:
P((E∩F)c) = 1 - P(E∩F) = 1 - 0 = 1

14. It is not possible for S={a,b,c} with P(a)=0.3, P(b)=0.4, and P(c)=0.5 because the sum of their probabilities exceeds 1.

Since the total probability of the sample space S must be equal to 1, it is not possible for three events with probabilities that add up to more than 1 to form the sample space.

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Answer:

100⁰

because this is a quadrilateral inscribed in the circle

=> x + 80 = 180

<=> x = 180 - 80 = 100⁰

The probability of Hank pulling out a piece of chocolate candy from the jar without looking is 0.1 or 10%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The number of chocolate candies in the jar = 20

The total number of candies in the jar.

= 20 + 90 + 40 + 50

= 200

Now,

The probability of Hank pulling out a piece of chocolate candy.

= number of chocolate candies / total candies

= 20 / 200

= 0.1

= 0.1 x 100

= 10%

Thus,

The probability of Hank pulling out a piece of chocolate candy from the jar without looking is 0.1 or 10%.

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Answer:

x=6 and x=5.1

Step-by-step explanation:

We can see that there is no element which is common Hence, they are mutually exclusive events.

Let A be the event of getting a sum of 7 on dice.

Let B be the events of getting a sum of 6 on dice.

A={ (1,6), (2,5), (3,4), (4,3), (5,2) }

B = { (1,5) , (2,4), (3,3),  (4,2), (5,1), }

Mutaullty exclusive events are those when there is no common event between two events.

Where there is empty set of intersection.

But we can see that there is no element which is common

So, n(A∩B) = ∅

Hence, they are mutually exclusive events.

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a typical neighborhood, which consists of two blocks east-west and three blocks north-south, covers an area of 75,000 square meters or 300,000 square meters.

The size of each street block is given as 50 meters north-south by 250 meters east-west. Therefore, the area of each block can be calculated as 50 meters * 250 meters = 12,500 square meters.To find the area covered by a typical neighborhood, which consists of two blocks east-west and three blocks north-south, we multiply the number of blocks in each direction. The neighborhood covers 2 blocks east-west * 3 blocks north-south = 6 blocks in total.

The total area covered by the neighborhood can be calculated by multiplying the number of blocks by the area of each block. Thus, 6 blocks * 12,500 square meters/block = 75,000 square meters.

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Answer:

+9

Step-by-step explanation:

all plus signs stay the same inside and out the parenthesis

Answer:

Step-by-step explanation:

56.1,12.1,23.6

The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Answer:

12

Step-by-step explanation:

If you multiply .15 times 80, you get 12. therefore the tip was 12 dollars

\(\text{Given that,}\\\\s_1 = 5.95,\\\\s_2 = 5.42\\\\\\F= \dfrac{(s_1)^2}{(s_2)^2} = \dfrac{(5.95)^2}{(5.42)^2} = 1.21\)

the angle between 0 and 2π that is coterminal with 17π/4 is π/4.

To find the angle between 0 and 2π that is coterminal with 17π/4, we need to find an equivalent angle within that range.

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of 2π.

To determine the coterminal angle with 17π/4, we can subtract or add multiples of 2π until we obtain an angle within the range of 0 to 2π.

Starting with 17π/4, we can subtract 4π to bring it within the range:

17π/4 - 4π = π/4

The angle π/4 is between 0 and 2π and is coterminal with 17π/4.

what is equivalent'?

In mathematics, the term "equivalent" is used to describe two things that have the same value, meaning, or effect. When two mathematical expressions, equations, or statements are equivalent, it means that they are interchangeable and represent the same mathematical concept or relationship.

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Answer:

17.50 per ticket

Step-by-step explanation:

If Hector paid $105 for 6 tickets, each ticket cost $105/6 = $<<105/6=17.50>>17.50.

Answer:

awsome

Step-by-step explanation:

Answer:

Well..

Step-by-step explanation: Za Warudo

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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A jug holds 10 pints of milk. If each child gets one cup of milk, it can serve 20 children. To determine how many children can be served with the 10 pints of milk, we need to convert pints to cups and divide the total amount of milk by the amount each child will receive.

1. Convert 10 pints to cups:
Since there are 2 cups in a pint, we can multiply 10 pints by 2 to get the total number of cups.
10 pints x 2 cups/pint = 20 cups of milk.
2. Divide the total cups of milk by the amount each child will receive:
Since each child gets one cup of milk, we can divide the total cups of milk by 1 to find the number of children that can be served.
20 cups ÷ 1 cup/child = 20 children.
Therefore, the jug of milk can serve 20 children if each child receives one cup of milk.

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Answer:

30% gain

Step-by-step explanation:

$30 for 10 = $3 each

$46.80 for 12 = $3.9 each

percentage change = (final price- initial price)/inital price  *100

3.9-3 = 0.9

0.9/3 = 0.3

0.3 x 100 = 30

so gain of 30%

If your polynomial is \(P(x) = 3x^5 +x -1\) then it has the order of \(5\).

C. \(5\)

The polynomial P(x) = \(3x^{5} + x - 1\) has order Option(C) 5.

The order of a polynomial expression is defined as the value of the highest power of dependent variable in the polynomial expression given. If there are more than one dependent variable then we have the orders for separate variables in the same polynomial expression.

Given polynomial P(x) = \(3x^{5} + x - 1\) .

Thus the dependent variable here is x in the given expression.

The highest power of x in the polynomial is 5 and its order is also then 5.

Therefore, the polynomial P(x) = \(3x^{5} + x - 1\) has order of Option(C) 5.

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The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

\(-34\)

Step-by-step explanation:

\(-4^{2} +(5-2)(-6)=\)

\(-16+(3)(-6)=\)

\(-16+(-18)=\)

\(=-34\)

Hope this helps and pls do mark me brainliest if you can:)

Answer:

-34

Step-by-step explanation:

Follow PEMDAS by starting with what's in the parentheses. 5-2=3. Next, multiply 3 by -6 and you'll get -18. Then next in PEMDAS is E for Exponent. Square -4 and you'll get -16. Then you'll add those two together and get -34 as your answer.

The percentage of the reservations were for Friday or Saturday is 67%

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following data values for reservation

The total number of reservations in the bar chart is then calculated as

Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9

Evaluate the sum

So, we have the following representation

Total number of reservations = 84

The total number of reservations for Friday or Saturday is then calculated as

Total number for Friday or Saturday = 26 + 30

Evaluate the sum

So, we have the following representation

Total number for Friday or Saturday = 56

The percentage of the reservations were for Friday or Saturday is then calculated as

Percentage = Total number for Friday or Saturday/Total number of reservations

This gives

Percentage = 56/84

Evaluate

Percentage = 67%

Hence, the percentage is 67%

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Answer:

292.75mL

Step-by-step explanation:

From the ideal gas equation

PV= nRT

With each symbols having standard meaning

For pressure remaining constant the equation for two states can be written as

\(\frac{V_1}{T_1}=\frac{V_2}{T_2}\)

Given V_1 = 300mL, T_1 = 17° C = 290K and T_2 = 10°C or 283K

Now plugging values in above equation to find V_2

\(\frac{300}{290} =\frac{V_2}{283}\\V_2 =\frac{300}{290}\times283 = 292.75mL\)

Therefore, the volume at 10 degrees Celsius = 292.75mL

Answer:

1.7 × 10⁻⁴

Step-by-step explanation:

The question relates to a two sample z-test for the comparison between the means of the two samples  

The null hypothesis is H₀:  μ₁ ≤ μ₂

The alternative hypothesis is Hₐ: μ₁ > μ₂

\(z=\dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

Where;

\(\bar {x}_1\) = 13.5

\(\bar {x}_2\) = 12

σ₁ = 2.5

σ₂ = 1.5

We set our α level at 0.05

Therefore, our critical z = ± 1.96

For n₁ = n₂ = 23, we have;

\(z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^{2} }{23}-\dfrac{1.5^{2}}{23}}} = 3.5969\)

We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96

Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983

Therefore;

The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.

Refer the below solution for better understanding.

Step-by-step explanation:

Given :

Standard Deviation, \(\rm \sigma_1 = 2.5\; and\;\sigma_2= 1.5\)

Calculation :

The null Hypothesis is \(\rm H_0: \mu_1\leq\mu_2\)

The alternative Hypothesis is \(\rm H_a: \mu_1>\mu_2\)

Now,

\(z = \dfrac{(\bar{x_1}-\bar{x_2})-(\mu_1-\mu_2)}{\sqrt{\dfrac{\sigma_1^2}{n_1}-\dfrac{\sigma_2^2}{n_2}} }\)  --------------- (1)

putting the values of

\(\bar{x_1}=13.5,\;\bar{x_2}=12,\;\sigma_1=2.5,\;\sigma_2=1.5\)

in equation (1)

\(z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^2}{23}-\dfrac{1.5^2}{23}} }\)

z = 3.5969

We reject the null hypothesis at

\(\alpha =0.05\)

z-value is larger than the critical z.

3.5969 > 1.96

Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day.

The probability that Alyse has a larger time than Jocelyn is 0.99983

Therefore, the probability that Alyse has a smaller time than Jocelyn is

\(1-0.99983 = 0.00017 = 1.7\times10^-^4\)

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Answer:.

Answer:1.we have dividend =divisor*quotient+remainder=

(x²+2x-1)(x²-2x+1)+(-4x+1)

=x²(x²-2x+1)+2x(x²-2x+1)-1(x²-2x+1)-4x+1

=x⁴-2x³+x²+2x³-4x²+2x-x²+2x-1-4x+1

=x⁴-4x²

Dividend is x⁴-4x².

2.

Multiplier is a-a²+1.

Answer:

\(i \: hope \: the \: above \: picture \\ helps\)

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Answer:

mean

Step-by-step explanation:

mean of six packages = (29+19+69+24+64+59)/6 = 44 ounces

Median of these six packages (19,24,29,59,64,69) = (29+59)/2 = 88/2= 44 ounces

Now, if we includes a package that weighs 219 ounces

The new mean = (29+19+69+24+64+59+219)/7 = 69

New median (19,24,29,59,64,69, 219) = 59

Hence, we say that the mean increases more than the median

The expression represents the second partial sum for 2(0. 4) + 2(0. 4)2 2(0. 4)2 + 2(0. 4)3 2 + 2(0. 4) 0 + 2(0. 4)1 is 0.8.

The second partial sum of a sequence refers to the sum of the first two terms of the sequence.

The given sequence is: 2(0.4) + 2(0.4)^2 + 2(0.4)^2 + 2(0.4)^3 + 2(0.4)^0 + 2(0.4)^1

To find the second partial sum, we simply add the first two terms of the sequence:

2(0.4) + 2(0.4)^2 = 0.8

Therefore, the expression that represents the second partial sum for the given sequence 2(0. 4) + 2(0. 4)2 2(0. 4)2 + 2(0. 4)3 2 + 2(0. 4) 0 + 2(0. 4)1 is 0.8.

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