MATHEMATICS COLLEGE

Need help please badly

Answers

Answer 1

Answer:

Answer:

CED is a right angle, CEB=AEB

hopw that helps

Answer 2

Answer:

Answer:

1st, 2nd, 5th

Step-by-step explanation:

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Some parts of California are particularly earthquake- prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance. a. Find the probability distribution of X. [Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS, with proba bility (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.] b. Draw the corresponding probability histogram. c. What is the most likely value for X

Answers

Answer:

a. Binomial random variable (n=4, p=0.25)

b. Attached.

c. X=1

Step-by-step explanation:

This can be modeled as a binomial random variable, with parameters n=4 (size of the sample) and p=0.25 (proportion of homeowners that are insured against earthquake damage).

a. The probability that X=k homeowners, from the sample of 4, have eartquake insurance is:

$P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\n\n\nP(x=k) = \dbinom{4}{k} 0.25^(0)\cdot0.75^(4)$

The sample space for X is {0,1,2,3,4}

The associated probabilties are:

$P(x=0) = \dbinom{4}{0} p^(0)(1-p)^(4)=1*1*0.3164=0.3164\n\n\nP(x=1) = \dbinom{4}{1} p^(1)(1-p)^(3)=4*0.25*0.4219=0.4219\n\n\nP(x=2) = \dbinom{4}{2} p^(2)(1-p)^(2)=6*0.0625*0.5625=0.2109\n\n\nP(x=3) = \dbinom{4}{3} p^(3)(1-p)^(1)=4*0.0156*0.75=0.0469\n\n\nP(x=4) = \dbinom{4}{4} p^(4)(1-p)^(0)=1*0.0039*1=0.0039\n\n\n$

b. The histogram is attached.

c. The most likely value for X is the expected value for X (E(X)).

Is calculated as:

$E(X)=np=4\cdot0.25=1$

. Solve for x.
10xy=W

Answers

Answer:

x=W/10y

Step-by-step explanation:

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 25 33 34 45 48
Number of Bids 2 3 4 5 7

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.
Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.Step 3 of 6: Find the estimated value of y when x = 34. Round your answer to three decimal places.Step 4 of 6: Determine the value of the dependent variable yˆ at x = 0.Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.Step 6 of 6: Find the value of the coefficient of determination.

Answers

Answer:

1) b1=5.831

2) b0=12.510

3) y(34)=210.764

4) y(0)=12.510

5) y=12.510+5.831x

6) R^2=0.85

Step-by-step explanation:

We have the linear regression model $y=b_0+b_1 x$ .

We start by calculating the all the parameters needed to define the model:

- Mean of x:

$\bar x=(1)/(5)\sum_(i=1)^(5)(2+3+4+5+7)=(21)/(5)=4.2$

- Uncorrected standard deviation of x:

$s_x=\sqrt{(1)/(n)\sum_(i=1)^(5)(x_i-\bar x)^2}\n\n\ns_x=\sqrt{(1)/(5)\cdot [(2-4.2)^2+(3-4.2)^2+(4-4.2)^2+(5-4.2)^2+(7-4.2)^2]}\n\n\n s_x=\sqrt{(1)/(5)\cdot [(4.84)+(1.44)+(0.04)+(0.64)+(7.84)]}\n\n\n s_x=\sqrt{(14.8)/(5)}=√(2.96)\n\n\ns_x=1.72$

- Mean of y:

$\bar y=(1)/(5)\sum_(i=1)^(5)(25+33+34+45+48)=(185)/(5)=37$

- Standard deviation of y:

$s_y=\sqrt{(1)/(n)\sum_(i=1)^(5)(y_i-\bar y)^2}\n\n\ns_y=\sqrt{(1)/(5)\cdot [(25-37)^2+(33-37)^2+(34-37)^2+(45-37)^2+(48-37)^2]}\n\n\n s_y=\sqrt{(1)/(5)\cdot [(144)+(16)+(9)+(64)+(121)]}\n\n\n s_y=\sqrt{(354)/(5)}=√(70.8)\n\n\ns_y=8.414$

- Sample correlation coefficient

$r_(xy)=\sum_(i=1)^5((x_i-\bar x)(y_i-\bar y))/((n-1)s_xs_y)\n\n\nr_(xy)=((2-4.2)(25-37)+(3-4.2)(33-37)+...+(7-4.2)(48-37))/(4\cdot 1.72\cdot 8.414)\n\n\nr_(xy)=(69)/(57.888)=1.192$

Step 1

The slope b1 can be calculated as:

$b_1=r_(xy)(s_y)/(s_x)=1.192\cdot(8.414)/(1.72)=5.831$

Step 2

The y-intercept b0 can now be calculated as:

$b_o=\bar y-b_1\bar x=37-5.831\cdot 4.2=37-24.490=12.510$

Step 3

The estimated value of y when x=34 is:

$y(34)=12.510+5.831\cdot(34)=12.510+198.254=210.764$

Step 4

At x=0, the estimated y takes the value of the y-intercept, by definition.

$y(0)=12.510+5.831\cdot(0)=12.510+0=12.510$

Step 5

The linear model becomes

$y=12.510+5.831x$

Step 6

The coefficient of determination can be calculated as:

$R^2=1-(SS_(res))/(SS_(tot))=1-(\sum(y_i-f_i))/(ns_y^2)\n\n\n\sum(y_i-f_i)=(25-24.17)^2+(33-30)^2+(34-35.83)^2+(45-41.67)^2+(48-53.33)^2\n\n\sum(y_i-f_i)=0.69+ 8.98+ 3.36+ 11.12+ 28.38=52.53\n\n\n ns_y^2=5\cdot 8.414^2=353.98\n\n\nR^2=1-(52.53)/(353.98)=1-0.15=0.85$

A(2,9), B(4,k), and C(9, -12) are 3 collinear points.
Find the value of k.

Answers

Answer is 3

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

Explanation:

We're going to be using the slope formula a bunch of times.

Find the slope of the line through points A and C

m = (y2 - y1)/(x2 - x1)

m = (-12-9)/(9-2)

m = -21/7

m = -3

The slope of line AC is -3. The slopes of line AB and line BC must also be the same for points A,B,C to be collinear. The term collinear means all three points fall on the same straight line.

-------

Let's find the expression for the slope of line AB in terms of k

m = (y2 - y1)/(x2 - x1)

m = (k-9)/(4-2)

m = (k-9)/2

Set this equal to the desired slope -3 and solve for k

(k-9)/2 = -3

k-9 = 2*(-3) ..... multiply both sides by 2

k-9 = -6

k = -6+9 .... add 9 to both sides

k = 3

If k = 3, then B(4,k) updates to B(4,3)

-------

Let's find the slope of the line through A(2,9) and B(4,3)

m = (y2 - y1)/(x2 - x1)

m = (3-9)/(4-2)

m = -6/2

m = -3 we get the proper slope value

Finally let's check to see if line BC also has slope -3

m = (y2 - y1)/(x2 - x1)

m = (-12-3)/(9-4)

m = -15/5

m = -3 we get the same value as well

Since we have found lines AB, BC and AC all have slope -3, we have proven that A,B,C fall on the same straight line. Therefore, this shows A,B,C are collinear.

Add the numbers in the series 3+11+19+27+.....+395+403.

Answers

Answer:

10353

Step-by-step explanation:

The given series is in arithmetic progression since the common difference is same which is 8.

To find the sum of series we can simply apply the formula'

S= n/2( first term + last term)

S is the sum and n is the number of terms

we also need to find the number of terms n

n = (last term- first term)/2 + 1

$n= (403-3)/(8) + 1$

n= 51

$s= (51)/(2)(3+403)$

s= 10353

Please help

determine all the unknown values of the figure below.

Answers

Answer:

F=12.76

S=27.18

X=62 degrees

Step-by-step explanation:

hope this helps

mark brianliest ;)

Based on the right-angled triangle shown above, all the unknown values are;

S = 27.18 units

F = 12.76 units

x = 62°.

How to determine the measure of the missing side lengths and angle?

In order to determine the measure of the missing side length, we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side (24) of a right-angled triangle;

cos(θ) = Adj/Hyp

Where:

Adj represent the adjacent side of a right-angled triangle.
Hyp represent the hypotenuse of a right-angled triangle.
θ represent the angle.

For the cosine trigonometric function ratio, we have the following:

cos(28) = 24/S

S = 24/cos(28)

S = 27.18 units

From tangent trigonometric function ratio, we have the following:

tan(28) = F/24

F = 24tan(28)

F = 12.76 units

Since the angles formed by a right-angled triangle are acute complementary angles;

x + 28 = 90

x = 90 - 28

x = 62°.

Read more on trigonometric function here: brainly.com/question/24349828

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