Assume the weights of adult males are normally distributed 150 pounds and 8=20 pounds. a) Find the prodailing that a man pleked at random will weigh less than 163 yound, (b) suppose Pl<

Step-by-step explanation:

I think 6 ways is the correct answer

Answer:

72

Step-by-step explanation:

For now, let's just distinguish between boys and girls.

Boy = X

Girl = x

There are 6 ways of placing the boys and girls so that the girls are not next to each other.

XXxXx

XxXXx

xXXXx

XxXxX

xXXxX

xXxXX

Now let's look at one of those patterns while distinguishing between the  individual boys and girls by having a different symbol for each.

Boys: A, B, C

Girls: a, b

Let's use just the first pattern above, XXxXx.

ABaCb

ACaBb

BAaCb

BCaAb

CAaBb

CBaAb

ABbCa

ACbBa

BAbCa

BCbAa

CAbBa

CBbAa

For the first pattern of the 6 different patterns on top, there are 12 ways of placing the boys ad girls. Since there are 6 of the patterns on top, the total number of ways is

6 * 12 = 72

Answer: 72

Given:

A medical researcher needs 7 people to test.

15 people have volunteered for the test.

To find:

We need to find a number of ways to select 7 from 15 people.

Explanation:

The number of ways to select 7 from 15 people can be found by the given formula.

Substitute n=1`5 and r=7 in the formula.

Final answer:

The number of ways = 6435 ways.

We get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.

We are given an equation:

4 x² - 7 x = 3 x + 24

We need to solve it for x.

4 x² - 7 x - 3 x = 24

4 x ² - 10 x = 24

4 x ² - 10 x - 24 = 0

4 x² - 16 x + 6 x - 24 = 0

4 x( x - 4) + 6( x - 4) = 0

(x - 4)(4 x + 6) = 0

Solving for x, we get that:

x = 4 or x = 6 / 4 = 3 / 2.

Therefore, we get that the solution for the equation 4 x² - 7 x = 3 x + 24 as 4 or 3 / 2.

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Answer:

hope this helps :)

Answer:

A=-4

Step-by-step explanation:

Add 3 to both sides of the equation:

7a-3 = -31

7a -3 +3 = -31 +3

Simplify:

7a = -28

Divide both sides of the equation by the same term:

7a = -28

7a/7 = -28/7

Simplify again:

A= -4

Answer:

A = -4

Given that 3/5 of the people who attended the concert live closer than 50 miles from the venue, we can find the total number of people who live closer than 50 miles by multiplying 3/5 with the total number of people who attended the concert:

Total number of people who live closer than 50 miles = 3/5 x 4800 = 2880

We are also given that 0.3 of the people who live closer than 50 miles from the venue spent more than $560 per ticket. To find the number of people who attended the concert and live closer than 50 miles from the venue and spent more than $560 per ticket, we can multiply the total number of people who live closer than 50 miles by 0.3:

Number of people who attended the concert and live closer than 50 miles from the venue and spent more than $560 per ticket = 0.3 x 2880 = 864

Therefore, 864 people who attended the concert live closer than 50 miles from the venue and spent more than $560 per ticket.

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Answer:

1/3

Step-by-step explanation:

She has 18 ribbons in total and she has 6 pink ribbons so she has a 6/18 chance or 1/3 chance of pulling a pink ribbon

To find the integer value of n that results in exactly 560 lattice points strictly in the interior of the triangle, use the equation: n = (560 + 2)/8.

This equation is derived by counting the lattice points on each side of the triangle, starting with the side between points (1,1) and (9,1). This side has a length of 8, so it contains 8 lattice points, including the two endpoints. The remaining sides have lengths of 8 + n and 8 + n, which combined have 8 + 2n lattice points. The total number of lattice points in the triangle is then 8 + 8 + 2n = 16 + 2n.  

Solving for n when the total number of lattice points is 560 gives us n = (560 + 2)/8. Therefore, the integer value of n is 70.

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Answer:

The correct option is c.

Step-by-step explanation:

Given that,

u = 7i+4j and v = 2i-3j

We need to find the product of u and v. The dot product of two vectors is given by :

\(u{\cdot}v=(7i+4j){\cdot} (2i-3j)\\\\=(7i)(2i)+(4j)(-3j)\\\\=14-12\\\\=2\)

So, the dot product of u and v is equal to 2.

Answer:

31.4

Step-by-step explanation:

Your current monthly income, before the effect of inflation, is approximately $2,129.63.

To determine your current monthly income, we need to account for the effect of inflation on the purchasing power of your income. Given that the inflation rate is eight percent, we can calculate the original income before the inflation adjustment.

Let's denote your current monthly income as "X."

The purchasing power after accounting for eight percent inflation is $2,300. This means that your original income, before the inflation adjustment, would have had a higher value. We need to find this original income.

Inflation reduces the purchasing power of your income, so we need to increase the current purchasing power by the inflation rate to find the original income. In this case, we'll increase $2,300 by eight percent:

Original Income = $2,300 / (1 + 0.08)

Original Income = $2,300 / 1.08

Original Income ≈ $2,129.63

Therefore, your current monthly income, before the effect of inflation, is approximately $2,129.63.

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Step-by-step explanation:

Subtract the largest value from the smallest in one set and that is the range of that set.

A)

B)

The equivalent form of a conditional statement, it is false that if gerald ate lunch, then he got enough nutrition, is equals to "if gerald ate lunch, then he did not got enough nutrition."

A statement formed by joining two events together based on a condition is called a conditional statement. It is also known as “If-Then” statements and can be written in the form, If p then q. If the truth table for two statement are identical then they are logically equivalent . We have a logical statement, "it is false that if gerald ate lunch, then he got enough nutrition."

This is a conditional logical statement. We can use the fact that ∼(p→q) is equivalent to p∧∼q write the equivalent form of statement. Here first write the propositions, p : gerald ate lunch

q : he got enough nutrition

So, here , negation of P implications q is equivalent to p conjunction of negation q. Then, negation of q, ∼q = he did not got enough nutrition. So, required statement is "if gerald ate lunch, then he did not got enough nutrition."

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Answer:

KL = 16

Step-by-step explanation:

For this problem, JL is the sum of KL and JK.  So we can say this:

JK + KL = JL

( 3x + 6 ) + ( 5x + 6 ) = 28

8x + 12 = 28

8x = 16

x = 2

So, now we can find KL:

5x + 6 = ?

5(2) + 6 = ?

10 + 6 = ?

16 = ?

So the length of KL is 16.

Cheers.

Therefore , the solution to the given problem of equation comes out to be the cost of carpet is $2072.

An equation is referred to as linear when all of the highest powers of the variables are equal to one. The components are interconnected. This kind of issue is also known as a one-degree equation. Learn how to solve a linear equation in one or two variables using the standard form, formula, graph, and instructions in the following paragraphs.

Here,

Given :

floor area of a square feet is 50a + 12h,

where h is the number of hours

Thus.

At t =6 and a =40

So ,

the cost of carpet

=> Cost =  50a + 12h

=> Cost =  50*40 + 12*6

=> Cost = 2000 + 72

=> Cost = 2072

Therefore , the solution to the given problem of equation comes out to be the cost of carpet is $2072.

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The ladder makes 78 degrees with the house

the ladder (c) is 20 feet long, and the height of the house (a) is 19.5 feet

find distance

19.5^2 + b^2 = 20^2 this is using the pythagorean law

b^2 = 400 - 380.25 = 19.75

b ≈ √19.75 ≈ 4.44 feet

sin(θ) = opposite side (a) / hypotenuse (c)

sin(θ) = 19.5 / 20

take the inverse sine

θ = arcsin(19.5 / 20)

≈ 78.46 degrees

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Answer:

see explanation

Step-by-step explanation:

The \(\sqrt{-1}\) = i

Answer:

The answer is I / Option B

Step-by-step explanation:

Answer:b

Step-by-step explanation:

Using a trigonometric relation we can see that x = 51°

Here we have a right triangle, and we know the length of the two legs of it.

To find the value of x, we need to use the trigonometric relation:

tan(x) = (opposite cathetus)/(adjacent cathetus)

Here we have:

opposite cathetus = 28

adjacent cathetus = 23

Then:

tan(x) = 28/23

x = Atan(28/23)

x = 50.59° = 51°

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There is no significant evidence to reject the claim that the mean rainfall from seeded clouds is 28.5 acre-feet at the 95% confidence level.

To test the claim that the mean rainfall from seeded clouds is 28.5 acre-feet, we can use a one-sample t-test.

First, we calculate the sample mean and standard deviation of the rainfall data:

Sample mean, \($\bar{x} = (18.0 + 30.7 + \ldots + 31.6)/20 = 26.545$\)

Sample standard deviation, s = 4.682

Using these values and the sample size, n = 20, we can calculate the t-statistic:

\(t = \frac{\bar{x} - \mu}{s/\sqrt{n}} = \frac{26.545 - 28.5}{4.682/\sqrt{20}} = -1.872\)

The degrees of freedom for the test are df = n - 1 = 19. Using a two-tailed t-table with α = 0.05 and df = 19, we find the critical values to be ±2.093. Since |t| = 1.872 < 2.093, we fail to reject the null hypothesis that the mean rainfall is 28.5 acre-feet.

To construct a confidence interval on the mean rainfall, we can use the formula:

\(\begin{equation*}CI = \bar{x} \pm t_{\alpha/2} \frac{s}{\sqrt{n}}\end{equation*}\)

where \(\bar{x}\), s, and n are the same as in part (a), and \(t_{\alpha/2}\) is the t-score for the desired level of confidence and degrees of freedom.

For a 95% confidence interval, α/2 = 0.025, and using df = 19, we find \(t_{0.025} = 2.093\).

Substituting the values into the formula, we get:

\($CI = 26.545 \pm 2.093 \times \frac{4.682}{\sqrt{20}} = (23.389, 29.701)$\)

Since 28.5 is within the confidence interval, we can say that there is no significant evidence to reject the claim that the mean rainfall from seeded clouds is 28.5 acre-feet at the 95% confidence level.

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The modification to a research study that will result in a narrower confidence interval is option D is correct choice

The modification to a research study that will result in a narrower confidence interval is option D: decreasing the confidence level and increasing the sample size. By decreasing the confidence level, we are willing to accept a lower level of certainty in our results, which can lead to a narrower interval. Increasing the sample size also leads to a narrower interval as it reduces the variability in our data and increases the precision of our estimates.

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Gradual, long-term movement in time-series values is called temporal variation. Therefore, the correct option is (a) temporal variation.

Temporal variation is one of the components of a time series, along with seasonal variation, cyclical movement, and irregular or random variation. Temporal variation refers to the long-term trend or pattern of movement in the time series, which can be increasing, decreasing, or remaining constant over time. It is often caused by underlying factors such as population growth, economic changes, or technological advancements.

Cyclical movement refers to the regular, repeating up and down patterns in the time series, which are usually longer than a year and can be caused by factors such as business cycles or political cycles. Exponential smoothing and linear regression are statistical methods used to forecast or model time series data, but they do not describe the components of the time series themselves.

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(-36 ÷ -4) + 9

The expression equals 18.

Answer: - 11/3

Step-by-step explanation:

-4 5/9 + 8/9

= 8/9 - 41/9

=   -33/9

simplest form=  -11/3

Answer:

Slope = -1

Step-by-step explanation:

We will use 2 points from the graph.\

(0 , 2) and (2 , 0)

formula for slope = y2 - y1/x2 - x1

0 - 2/2 - 0

=-2/2

=-1

Answer:

70 degrees

Step-by-step explanation:

Angle HMK = 50 degrees

Angles LMK, MLK and MKL are equal to 60 degrees, being in a perfectly congruent triangle which they all add up to 180 degrees.

Add 60 to 50 = 110

180 - 110 = 70 degrees, equal to angle HMG.

This is because the line that angles LMK, HMK and HMG are on is supplementary.

The Rank Theorem and the Rank-Nullity Theorem are fundamental theorems in Linear Algebra that can be used to solve problems related to matrices and to find the rank, nullity, and dimensions of the row space, column space, and null space of a matrix.

a) If a 6x8 matrix A has rank 5, then dim(null(A)) = 3.

Nullity of A is the number of free variables in the echelon form of A. Since,

row(A) = rank(A) and nullity(A) = dim(null(A)), adding them will give the number of columns of A.

Hence, dim(A) = row(A) + nullity(A) = 8.

b) If A is a 5x7 matrix and dim(null(A)) = 3, then dim(row(A)) = 4.

By the Rank-Nullity Theorem, row(A) = rank(A) and since rank(A) + nullity(A) = number of columns,

we have rank(A) = 4.

c) If A is a 6x7 matrix and dim(null(A)) = 3, then dim(col(A)) = 4. In this case, by the Rank-Nullity Theorem, col(A) = rank(A) and since

rank(A) + nullity(A) = number of columns,

we have rank(A) = 3.

Hence, dim(col(A)) = 7 - 3 = 4.

d) If A is a 3x5 matrix and dim(row(A)) = 1, then dim(null(A)) = 4.

Here, by the Rank-Nullity Theorem, rank(A) + nullity(A) = number of columns of A, i.e., 5.

Since, dim(row(A)) = rank(A) = 1, nullity(A) = 4.

e) If A is a 4x5 matrix, the smallest value of dim(null(A)) could be 0. This is possible if and only if A is a full rank matrix or a one-one matrix with no nontrivial solutions. A one-one matrix has nontrivial solutions only if it has a non-zero null space.

If dim(null(A)) = 0, then A is one-one and hence, it is full rank.

The Rank Theorem and the Rank-Nullity Theorem are fundamental theorems in Linear Algebra that can be used to solve problems related to matrices. We can use these theorems to find the rank, nullity, and dimensions of the row space, column space, and null space of a matrix. These theorems are based on the concept of linear independence and the properties of matrices. By using these theorems, we can solve a wide range of problems related to matrices, such as finding the rank and nullity of a matrix, finding the dimensions of its row space and column space, and so on.

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The probability that at least one will have a defect if if 10 items are chosen at random is  0.65132.

binomial distribution is given as :

\(P(X=x) = (_{x} ^{n}) p^{x}q^{n-x} ; x = 0,1,2,3,........n\\q = 1 - p ;\)

where

x = number of times for a specific outcome within n trials

{n  x}=      number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Let D be a random variable represents the number of defected items out of 10.

i.e., D(0,1,2,3,4,5,6,7,8,9,10)

probability that given items is defected is :

p = 0.1

q = 1 - p

q = 1 - 0.1 = 0.9

where

p = probability of defected items

q = probability of non-defective

then

D- bin(10,0.1)

P(D=0) = \(^{10} C_{0}{(0.1)^0}{(0.9)^{10}}\)

\(= \frac{10!}{0!(10-0)!} * (0.9)^{10}\)

= 0.3486784401

\(P(D\geq 1) = 1-P\)

1 - = 0.3486784401

= 0.65132

The probability that at least one will have a defect if if 10 items are chosen at random is  0.65132.

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