3.18 A continuous random variable X, which can all
mar values between x = 2 and x = 5, has a function of
density given by f (x) = 2(1 + x)/27. Calculate
to)
b)
P(X < 4);
P(3 ≤X < 4).
3.20 For the density function of exercise 3.18
compute F(x) and use it to evaluate P(3 ≤ X < 4).

Answer: I believe 864 because 24 times 18 equals 432 and that doubled is 864

Step-by-step explanation:

The expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

As per the question, we can write the expression as:

(t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9)

Using product notation, we can write this as:

Π⁷k =1 \((t^k - 9)\)

where Π represents the product of terms, k is the index of the product, and the subscript 7 indicates that the product runs from k = 1 to k = 7.

Therefore, the expression ((t − 9) · (t² − 9) · (t³ − 9) · (t⁴ − 9) · (t⁵ − 9) · (t⁶ − 9) · (t⁷ − 9) can be written in terms of product notation as Π⁷k=1 \((t^k - 9)\).

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Answer:

(x – 4)^2 + (y +10)^2 = 64

Step-by-step explanation:

Recall that the formula for a circle is:  (x – h)^2 + (y – k)^2 = r^2

1. Find the Radius (r): Luckily, we can count the distance since the coordinates have the same y-value. 12 - 4 = 8. So, r^2 = 8^2 = 64

2.  Find h and k. These are the x and y coordinates of the center of the circle. So, h = 4, k = -10

3. Substitute the values in the equation:

(x – 4)^2 + (y – (-10))^2 = 8^2

(x – 4)^2 + (y +10)^2 = 64

Answer:

  (x -4)² +(y +10)² = 64

Step-by-step explanation:

Given a circle through point (12, -10) with center (4, -10), you want its equation.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

You are given the center (h, k) = (4, -10). You only need to know the radius to finish the equation. That will be the value of r that makes the equation true at the given point:

  (x -4)² + (y +10)² = r²

  (12 -4) + (-10 +10)² = r² . . . . . . with (x, y) = (12, -10), the point on the circle

  8² + 0 = r²

The equation of the circle is (x -4)² +(y +10)² = 64.

__

Additional comment

The equation of a circle is essentially a statement of the distance formula. It is telling you that the circle consists of all points that are distance r from the center.

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True. The pessimistic approach assumes that the worst-case scenario for each alternative will occur and chooses the best of these.

An optimistic approach indicates that the decision-makers believe the outcomes will benefit the organisation. A pessimistic approach, on the other hand, indicates that the decision-makers are convinced that the outcomes will be detrimental to them. The pessimistic approach allows decision-makers to plan for the worst-case scenario. In the optimistic approach, decision-makers believe that the alternatives chosen will produce the best results. In other words, the decision-makers are confident that their options are the best for the circumstances. The pessimistic approach is characterised by decision-makers assuming that the choices they make will have the most negative outcomes.

Thus, the pessimistic approach is the approach which is used to assume the worst possible outcomes for each alternative will occur.

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Step-by-step explanation:

1. x²/4=16

x²=16×4

x= √64

x= 8 Answer

2. 2x²/3-4=2

2x²-12/3 =2. (LCM is 3)

2x²-12=2×3

2x²= 6+12

x²= 18/2

X=√9

X= 3 Answer.......

Answer: D

Step-by-step explanation:

The solution of the equation (x + 20) / 2 = 3x will be 4. Then the correct option is B.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equation the quantity of x plus 20 over 2 = 3x represents when two tutoring services with different rate plans charge the same fees for a session of x hours.

(x + 20) / 2 = 3x

Simplify the equation, then the value of x will be

x + 20 = 6x

5x = 20

x = 4

The solution of the equation (x + 20) / 2 = 3x will be 4. Then the correct option is B.

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Answer:

35

Step-by-step explanation:

a=√ c^2−b^2

a=√12^2−35^2

a=√ 144−1225

a=√  −1081

a= 35

Answer:

x= 9.8

Step-by-step explanation:

Just did it said it was correct

Answer: 64°

Step-by-step explanation:

Answer:

x = 64°

Step-by-step explanation:

Since the triangle is isosceles, the base angles are congruent, that is

∠ R = ∠ Q = 32° , then

vertex angle = 180° - (32 + 32)° = 180° - 64° = 116°

∠ NSR = 116° ( vertically opposite angle )

∠ MNS and ∠ NSR are same- side interior angles and sum to 180° , then

x = 180° - 116° = 64°

Answer:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) x( x+4)=a

    (x+1)(x+3)= a+3  

Step-by-step explanation:

(i)  X+2 and x+3;

(ii) x( x+4)= X^2 +4x;

(iii) (x+1)(x+3)=x^2+3X+X+3=x^2+4x+3;

x(x+4)=a

(x+1)(x+3)= a+3

Step-by-step explanation:

x is followed by x+1 so each time we add one

our sequence goes like this:

the first number is x and the fourth one is x+3

the second number is x+1 and the third one is x+2

the first product is x²+3x and the second one is x²+3x+2

Let P be x²+3x and P' be x²+3x+2

You have $2.30 and would like to buy some rice flour buy 9.2 ounces of rice flour with $2.30.

To arrive at this answer, we need to first convert the price per pound to price per ounce. There are 16 ounces in a pound, so the price per ounce is $4/16 = $0.25 per ounce.

Next, we divide the amount of money you have ($2.30) by the price per ounce ($0.25).

$2.30/$0.25 = 9.2 ounces.

Therefore, the conclusion is that you can buy 9.2 ounces of rice flour with $2.30.
Hi! I'm happy to help you with your question.


You can buy 9.2 ounces of rice flour.


1. First, we need to find out how many dollars you have per ounce of rice flour: $4 per pound / 16 ounces per pound = $0.25 per ounce.
2. Next, we'll determine how many ounces of rice flour you can buy with $2.30: $2.30 / $0.25 per ounce = 9.2 ounces.


With $2.30, you can buy 9.2 ounces of rice flour at the given price of $4 per pound.

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The insurance policy covers each person up to $50,000, and the insurance company must pay out $6,000 for the five people in Jose's car.

The total medical expenses for the five people in Jose's car are:

Medical expenses for person 1: $3,000

Medical expenses for person 2: $500

Medical expenses for person 3: $500

Medical expenses for person 4: $500

Medical expenses for person 5: $500

Total medical expenses: $4,500 + $500 + $500 + $500 + $500 = $6,000

Since the insurance policy covers each person up to $50,000, the insurance company must pay out $6,000 for the five people in Jose's car. Jose's personal medical expenses of $62,000 are not covered by the policy because they exceed the maximum coverage per person.

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Using proportions, it is found that her satellite bill before the switch was of $240.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, she can pay a total of $180 per 300 channels, hence her price per channel will be of:

p = 180/300 = $0.6.

She currently pays $0.2 more, that is, $0.8, hence:

B = 300 x 0.8 = 240.

Her satellite bill before the switch was of $240.

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Answer:

VX

Step-by-step explanation:

V=5

X=10

We cannot write 5 before 10

Answer:

y = 3x + 40

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (- 12, 4 ) into the partial equation

4 = - 36 + c ⇒ c = 4 + 36 = 40

y = 3x + 40 ← equation of line

Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

The correct statement about the given negative numbers is none of these

Negative numbers

A number whose value is always less than zero and it has a minus (-) sign before it is known as negative number.

Given,

Four numbers are listed.

-√50,- 36/5, - 7.05, - 2.3n

Here we need to find the correct statement that describes given numbers.

In order to find the correct statement we have to convert all the number into the same decimal form.

So, first number is written as,

-√50 = -7.07

Then the decimal form of the second number is

-36/5 = -7.2

The value is

=> -2.3n here we have to place any value for n but we have take the value of 1, then we get

=> -2.3(1) = -2.3

So, this one is rapidly decreasing based on the value of n.

Now, we have the decimal equivalent for all the four numbers.

Then we looking into the given statements we have identified that the statement none of these

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Answer:

she hiked 3.75 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

Onion Rings.

3 out of every 5 ordered onion rings and she took 585 orders.

Onion ring orders = 3/5 * 585

= 351 orders

Fries

2 out of every 5 ordered fries

Fries orders = 2/5 * 585

= 234 orders

Answer:

-3a-4b+5

Step-by-step explanation:

(3a-6b+12)-(6a-2b+7)

3a-6b+12-6a+2b-7

3a-6a-6b+2b+12-7

-3a-4b+5

Ground-state electron configuration of gas-phase Co²+ is [Ar] 3d⁷. Answer: (E) [Ar] 3d⁷.Explanation: First of all, we need to find the electron configuration of Cobalt (Co).

The electron configuration of Cobalt (Co) is 1s²2s²2p⁶3s²3p⁶4s²3d⁷.Now, we can remove the electrons to get the electron configuration of gas-phase Co²+ .Co: 1s²2s²2p⁶3s²3p⁶4s²3d⁷Co²+: 1s²2s²2p⁶3s²3p⁶3d⁷The full electron configuration of Co²+ will be [Ar] 3d⁷. Therefore, the answer is (E) [Ar] 3d⁷.

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The probability of forming a bow-tie quadrilateral from four randomly chosen chords is approximately 6.25%.

This is because there are exactly 28 possible quadrilaterals that can be formed from the seven given points, and only one of those 28 quadrilaterals is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/28, which is equal to 0.0357, or 3.57%.

To explain further, when we draw all of the chords from the seven given points, we have 21 distinct chords. Out of these, 10 chords form triangles, leaving us with 11 chords that form quadrilaterals.

Since four of these chords are randomly chosen, the number of possible combinations of quadrilaterals that can be formed is equal to 11C4, or 495. Out of these 495 combinations, only one is a bow-tie quadrilateral. This means that the probability of forming a bow-tie quadrilateral is 1/495, or 0.002041, or 0.2041%.

Since 0.2041% is too small to be expressed as a whole number, it is rounded up to 6.25.

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The next Answers are x > 0, and all real numbers

The correct function shown in graph is,

⇒ f (x) = log₁₀ x

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of the function is shown in figure.

Now, Points on the graph are (1, 0) , (5, 1) and (0.2, -1)

Hence, From the option 4;

⇒ f (x) = log₁₀ x

Put x = 1;

⇒ f (x) = log₁₀ 1

⇒ f (x) = 0

Thus, The correct function shown in graph is,

⇒ f (x) = log₁₀ x

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Answer:

x = -6f

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

Answer:

6.6/100 or 3.3/5

Step-by-step explanation:

6.6% or 6 3/5% now since those are all out of 100 (since percentages) you just put #/100 and get your fraction

Answer:

10

Step-by-step explanation:

For movie mania:

Sign-up fee = $ 20

Rent for 1 DVD = $ 4.00

For Hurricane video:

Sign-up fee = 0

Rent of 1 DVD = $ 6.

Let \(n\) be the number of DVDs to rent in order for both stores to charge the same.

For movie mania, charge to rent \(n\) DVDs = Sign-up fee + rent of \(n\) DVDs

=20+4n

For Hurricane movie, charge to rent \(n\) DVDs = Sign-up fee + rent of \(n\) DVDs

=0+6n=6n

Now, for both stores to charge the same, both the charges must be equal, we have

6n=20+4n

\(\Rightarrow 6n-4n=20\)

\(\Righatarroe 2n=20\)

\(\Rightarrow n =20/2=10\)

Hence, the required number of DVDs to rent is 10 in order for both stores to charge the same.

To find the volume of the second cylinder, we need to use the fact that the two cylinders are similar. When two objects are similar, their corresponding dimensions are propotional.

In this case, the height of the first cylinder is 23 cm, and the height of the second cylinder is 8 in. We know that 2.54 cm is equal to 1 inch, so we can convert the height of the second cylinder to centimeters:

8 in * 2.54 cm/in = 20.32 cm

Now, we can set up a proportion to find the scale factor between the two cylinders' volumes:

Volume of first cylinder / Volume of second cylinder = (Height of first cylinder / Height of second cylinder)³

552π cm³ / Volume of second cylinder = (23 cm / 20.32 cm)³

Simplifying the equation:

Volume of second cylinder = 552π cm³ / [(23 / 20.32)³]

Volume of second cylinder ≈ 552π cm³ / (1.1312)³

Volume of second cylinder ≈ 552π cm³ / 1.4386

Volume of second cylinder ≈ 383.38π cm³

Therefore, the volume of the second cylinder is approximately 383.38π cm³.

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The null hypothesis to test the significance of the slope on a regression equation is that the slope is equal to zero.

Given that we have to test the significance of slope in a regression equation.

Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c. It may be a linear equation, quadratic equation, cubic equation or many more depending on the powers of the variable present in that equation.

Slope is basically a number which indicates the direction of the line.

Null hypothesis is a statement which is tested for its validity and it is nothing but opposite of the result we want.

The standard regression equation be y=mx+c and in this m is slope of the equation.

The line depends on the slope because if it is zero then the value of y becomes zero. So, the null hypothesiss is that the slope is equal to zero.

Hence the null hypothesis to test the significance of the slope on a regression equation is that the slope is equal to zero.

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Answer:

10

Step-by-step explanation:

The volume of the composite figure is 129.85 cm³.

The volume of the composite figure is made up of volume of cylinder plus volume of cone.

height of the cylinder = 8 cm

height of the cone = 15 cm - 8 cm = 7 cm

Volume of the cylinder is calculated as follows;

V = πr²h

V = π (2 cm)² (8 cm )

V = 100.53 cm³

The volume of the cone is calculated as follows;

V = ¹/₃πr²h

V = ¹/₃π(2 cm)²(7 cm)

V = 29.32 cm³

Total volume = 100.53 cm³ + 29.32 cm³ = 129.85 cm³

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