Suppose that X; Y have constant joint density on the triangle with corners at (4; 0), (0; 4), and the origin. a) Find P(X < 3; Y < 3). b) Are X and Y independent

(2x+1)(x-3)

y(x-3) .... let y = 2x+1

y*x+y(-3) .... distribute

xy - 3y

x( y ) - 3( y )

x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1

2x^2 + x - 6x - 3 ..... distribute

2x^2 - 5x - 3

Answer is choice A

Answer:

B = 6

Step-by-step explanation:

2x^2 + 4xy − 48y^2

Factor out 2

2(x^2 + 2xy − 24y^2)

What 2 numbers multiply to -24 and add to 2

-4 *6 = -24

-4+6 = 2

2 ( x+6y)( x-4y)

Answer:

[tex]\huge\boxed{B=6}[/tex]

Step-by-step explanation:

They are two way to solution.

Factor the polynomial on the left side of the equation:

[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]

Therefore:

[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]

Multiply everything on the right side of the equation using the distributive property and FOIL:

[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]

Compare polynomials:

[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]

From here we have two equations:

[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]

[tex]1)\\2B-8=4[/tex]        add 8 to both sides

[tex]2B=12[/tex]         divide both sides by 2

[tex]B=6[/tex]

[tex]2)\\-8B=-48[/tex]          divide both sides by (-8)

[tex]B=6[/tex]

The results are the same. Therefore B = 6.

Answer:

true

Step-by-step explanation:

type 1 and type 2 are not independent of each other - as one increases, the other decreases

Answer:

51.

Step-by-step explanation:

f(x) = x^2 + 2x + 3 and g(x) = x + 4.

f(g(x)) = (x + 4)^2 + 2(x + 4) + 3

= x^2 + 4x + 4x + 16 + 2x + 8 + 3

= x^2 + 8x + 16 + 2x + 11

= x^2 + 10x + 27.

x = 2.

f(g(2)) = 2^2 + 10 * 2 + 27

= 4 + 20 + 27

= 31 + 20

= 51.

Hope this helps!

Answer:

1. elements it contains =  (1,3)

2.  elements it contains = 35

3.  elements it contains = 8

4.  elements it contains = 17

Step-by-step explanation:

A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.

The red die shows 1 and the numbers add to 4.

How many elements does it contain?

B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]

The numbers do not add to 2.

How many elements does it contain?

C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 11 or the red die shows a 1.

How many elements does it contain?

D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 5, or they add to 9, or at least one of them is 1.

How many elements does it contain?

NB. Attached is the solution to the problems stated above

Answer:

Step-by-step explanation:

[tex]27^{\frac{2}{3}}\\\mathrm{Factor\:the\:number:\:}\:27=3^3\\=\left(3^3\right)^{\frac{2}{3}}\\\mathrm{Apply\:exponent\:rule}:\\\\\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\\\left(3^3\right)^{\frac{2}{3}}=3^{3}\times \frac{2}{3}}\\\\3\=times \frac{2}{3}=2\\\\=3^2 \\\\=9[/tex]

[tex]27^{2/3}=(3^3)^{2/3}=3^2=9[/tex]

Answer:

a) ∠X = 67.4°

ii) ∠Y = 22.6°

b) Hypotenuse = 13 miles

ii) Length of each congruent = 4.33 miles

c) Distance of mall from point A = 5.21 miles

d) Distance os mall from point B = 8.17 miles

e) Difference = 2.96 miles

ii) Amount it will cost = $1,628,000

Step-by-step explanation:

Because of the length of the solution, I sent it as an attachment to this answer.

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▹ Answer

80

▹ Step-by-Step Explanation

(2²)³ + (2³)² ÷ 4

Rewrite:

2⁶ + 2⁶ ÷ 2²

Divide:

2⁶ + 2⁴

Factor:

(2² + 1) * 2⁴

Evaluate:

(4 + 1) * 2⁴

Calculate:

5 * 16

= 80

Hope this helps!

CloutAnswers ❁

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Answer:

  [tex]\dfrac{b^3}{8a^{18}}[/tex]   matches the first choice

Step-by-step explanation:

[tex]\left(\dfrac{2 a b}{a^{-5}b^2}\right)^{-3}=(2a^{1-(-5)}b^{1-2})^{-3}=(2a^6b^{-1})^{-3}\\\\=2^{-3}a^{6(-3)}b^{-1(-3)}=8^{-1}a^{-18}b^3=\boxed{\dfrac{b^3}{8a^{18}}}[/tex]

__

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

  a^-b = 1/a^b

Answer:

A

Step-by-step explanation:

just took the pretest! good luck!

Answer:

105.12 ft²

Step-by-step explanation:

Let's first find the area of the rectangle.

[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².

To find the area of the semi-circle, we find the area of a whole circle and divide by two.

The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.

[tex]3.14\cdot4^2[/tex]

[tex]3.14\cdot16[/tex]

[tex]50.24\div2=25.12[/tex]

Add 80 and 25.12:

[tex]80+25.12=105.12[/tex]

Hope this helped!

Answer:

48

Step-by-step explanation:

Do 60*.80

60 represent the total points the test was worth

.80 represents the % number

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

100% = 60

80% = 48

The points Salema earned are 48 points.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Salema's score = 80%

Total score in the test = 60 points

Salema's score.

= 80% of 60 points

= 80/100 x 60

= 48

Thus,

The points Salema earned are 48 points.

Learn more about percentages here:

https://brainly.com/question/11403063

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Answer:

$3 per pineapple

Step-by-step explanation:

Hey there!

If 2 pineapples are $6,

6 / 2 = 3

So 1 pineapple is $3.

Hope this helps :)

Answer:

3 dollars for 1 pineapple

Step-by-step explanation:

well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.

Answer: 7

Step-by-step explanation:

f(0) means that x is equal to zero and so you substitute all the x's for zeros which means -3 times 0 plus 7 is equal to 7

Answer:

[tex]x=\frac{7}{3}[/tex]

Step-by-step explanation:

Since any number multiplied by zero equals zero, our equation is really:

0 = -3x+7

First, we'd have to subtract the 7 from both sides:

-7 = -3x

Now we need to divide the negative three from both sides to isolate the x.

7/3 = x

So, our answer is x=7/3

Hope this helps!! <3 :)

Answer:

3.75

Step-by-step explanation:

[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]

The volume of the rectangular prism will be 3.75 cubic meters.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A box is 1 m high, 2.5 m long, and 1.5 m wide.

Then the volume of the rectangular prism will be

V = L x W x H

V = 1 x 2.5 x 1.5

V = 3.75 cubic meters

Thus, the volume of the rectangular prism will be 3.75 cubic meters.

More about the volume of the rectangular prism link is given below.

https://brainly.com/question/21334693

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Answer:

False

Step-by-step explanation:

Here, we want to check the validity of the given statement. The statement is false.

Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.

Please check attachment for diagrammatic representation of the empirical rule.

Answer:

One - way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Step-by-step explanation:

ANOVA is a statistical technique designed to test mean of one or more quantitative populations.  In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA. It is a statistical technique designed to test mean of one or more quantitative populations. In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA.

One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

It should be the statistical technique that are made for testing the mean for one or more than one quantitative population. In two-way ANOVA it should be equivalent to the block mean. Here the column block represent the square be the three-way ANOVA.

Therefore, One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Learn more about evidence here: https://brainly.com/question/6764645?referrer=searchResults

Answer:

0.065617 ft

Step-by-step explanation:

Answer:

0.0656168 feet.

Step-by-step explanation:

Answer:

8 pounds of cheaper candy,

17.5 pounds of expensive candy

Step-by-step explanation:

Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!

x + y = 25.5

[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]

We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:

y = 17.5

Plugging this in, we find that:

x = 8.

Answer:

The answer is A.

Step-by-step explanation:

Local maximums are whenever the graph reaches it's highest y value.

Local minimums are whenever the graph reaches it's lowest y value.

From the graph, we can see that the maximum y-value the graph reaches is y=1. And this happens when x=0.

This only happens once (from the graph shown). Thus, the local maximum would be:

[tex](0,1)[/tex]

The minimum values we can see from the graph is at y=-1. This happens twice from the graph, once at -π and again at 3π/2.

Thus, the local minimums are:

[tex](-\pi,-1), (3\pi/2,-1)[/tex]

Answer:

see below

Step-by-step explanation:

We want where  both inequalities are true

y > -3

-2 >-3  this is true

y ≥ 2/3x -4

-2≥ 2/3*3 -4

-2 ≥ 2 -4

-2≥ -2

This is true

This is is the graph

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]

[tex]x = 3\\y = -2[/tex]

[tex]y>-3\\-2>-3\\ \sf True[/tex]

[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]

Answer:

13/6

Step-by-step explanation:

We can use the slope formula

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

   = (6 - -7)/(1 - -5)

   = ( 6+7)/ (1+ 5)

   = 13/6

Answer:

8 M&Ms and 9 Candy Bars

Step-by-step explanation:

$15 dollars could buy 15 candy bars, and there are 17 pieces of candy total.

Prioritizing the number of bars:

0.75 * 2 = 1.50

1.50 * 2 = 3

At least $3 were spend on M&Ms, meaning 4 M&Ms and 12 candy bars, which is only 16 candy pieces...

8 M&Ms and 9 candy bars is equivalent to 17 total candy pieces.

Answer:

y = x-4

Step-by-step explanation:

The y intercept is -4

We have 2 points so we can find the slope

( 0,-4) and(4,0)

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

    = ( 0- -4)/ (4-0)

    = 4/4

   =1

The slope intercept form is

y = mx+b

y = 1x-4

y = x-4

Answer: 0%

Step-by-step explanation:

There's 40 students, and 40 students read physics. That means that every student reads physics. So, no student could read only chemistry.

Answer:

(3x+2)^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:

x = 2cost,

t = (1/2)arccosx

y = 2sint

dy/dx = dy/dt . dt/dx

dy/dt = 2cost

dt/dx = -1/√(1 - x²)

dy/dx = -2cost/√(1 - x²)

Differentiate again to obtain d²y/dx²

d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)

At t = π/4, we have

(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)

Answer:

  (B) Step 2

Step-by-step explanation:

In step 2, Raul should have had one of these results:

  8 -7 . . . . according to the order of operations

or

  3 -2 . . . . properly adding 5 -7

Raul's step 2 is not either of these (or 5-4), so is incorrect.

Answer:

step 2 i did it on khan yall

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \sf{x - 2} \: and \: { {x}^{2} + x - 6}[/tex]

To find the H.C.F of the algebraic expressions, they are to be factorised and a common factor or the product of common factors is obtained as their H.C.F

Let's solve

First expression = x - 2

Second expression = x + x - 6

Here, we have to find the two numbers which subtracts to 1 and multiplies to 6

= x + ( 3 - 2 ) x + 6

Distribute x through the parentheses

= x + 3x - 2x + 6

Factor out x from the expression

= x ( x + 3 ) - 2x + 6

Factor out -2 from the expression

= x ( x + 3 ) - 2 ( x + 3 )

Factor out x+3 from the expression

= ( x + 3 ) ( x - 2 )

Here, x - 2 is common in both expression.

Thus, H.C.F = x - 2

Hope I helped!

Best regards!!!

Answer:

x - 2

Step-by-step explanation:

by factorization method

1) x - 2

2) x^2 + x - 6

by splitting method

x^2 + 3x - 2x - 6

taking separate common from the first two terms and last two terms

x(x + 3) - 2(x + 3)

now writing x+3 once and the other term to get the right answer

(x + 3)(x - 2)

in both parts just see the similar term and write it as HCF

HCF= x - 2

and the second method by which you can get this answer is division method

Weight of man and paint = 160 + 5 = 165 total pounds.

Gravitational force is independent of the path taken so we can ignore the radius of the silo.

Work done = total weight x height

The problem says he climbs to the top so overall height is 90 feet

Work = 165 lbs x 90 ft = 14,850 ft-lbs