3] If the p.d.f., of the random variable X is given byf(x)= K/sqrt x &0 1)(c) P(|X| < 3)(d) E(2X - 2)(e) V(3X)

Answer:

13a + 9b + 11

Step-by-step explanation:

I hope this helps!

Answer:

13a+ 9b+ 11

Step-by-step explanation:

9a+4a= 13a

4b+ 5b= 9b

4+7=11

Answer: s is \(> 118 \frac{2}{3}.\)

Step-by-step explanation:

The air balloon will have to fall more than 890 feet for it to reach an elevation below 300 feet. It falls at a rate of 7.5, so 890/7.5=118.6666666666, which is 118 and 2/3. The answer is positive because time can never be negative.

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

To find the function n(t) that models the population of bacteria after t hours, we can use the exponential growth formula:

n(t) = n0 * e^(kt)

Where:

n(t) is the population after t hours,

n0 is the initial population size,

e is the base of the natural logarithm (approximately 2.71828),

k is the growth rate constant.

We can determine the value of k using the given information. After 1 hour, the bacteria count is 9500, which is the population at time t = 1. Plugging these values into the equation:

\(9500 = 1100 * e^(k*1)\)

To find k, we can divide both sides by 1100:

9500/1100 = e^k

Now, we can solve for k by taking the natural logarithm (ln) of both sides:

ln(9500/1100) = ln(e^k)

ln(9500/1100) = k

Now we have the value of k. We can plug it back into the exponential growth formula to obtain the function n(t):

\(n(t) = 1100 * e^(ln(9500/1100) * t)\)

To find the population after 1.5 hours, we can substitute t = 1.5 into the equation:

\(n(1.5) = 1100 * e^(ln(9500/1100) * 1.5)\)

To find the number of hours when the number of bacteria will reach 20,000, we can set n(t) equal to 20,000 and solve for t:

\(20,000 = 1100 * e^(ln(9500/1100) * t)\)

Finally, to sketch the graph of the population function, plot the values of t on the x-axis and the corresponding values of n(t) on the y-axis using the equation n(t) = 1100 * e^(ln(9500/1100) * t). The resulting graph will show the exponential growth of the bacteria population over time.

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The length of CG is 5cm when In the picture we can see a triangle EFD and the ABC are the points middle of the Sides of the triangle.

Given that,

In the picture we can see a triangle EFD and the ABC are the points middle of the Sides of the triangle.

G is the middle of the triangle.

GD is 10cm

We have to find CG.

We know that,

The intersection of the triangle's three medians is shown in the diagram at point G.

The triangle's centre is where the three medians converge, and we refer to it as the centroid.

One characteristic of the centroid is that it splits the ratio's medians.

2:1

The medians are the lines that connect the triangle's vertices to the midpoints of its other side.

We get,

DG:CG=2:1

10:CG=2:1

10/CG=2/1

2CG=10

CG=10/2

CG=5

Therefore, The length of CG is 5cm when In the picture we can see a triangle EFD and the ABC are the points middle of the Sides of the triangle.

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Answer:

D) they gave the world an example of ideal beauty.

Step-by-step explanation:

In the passage, it talks about the Parthenon being made out of beautiful marble, with the first light of morning. However, the first light of morning is not the answer, as that is just a detail in the passage.

Answer:

$31.36

Step-by-step explanation:

If she has $38.36 and you subtract 7 you would get the answer $31.36. I hope I helpped (◡ ω ◡)

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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Answer:

w=-4

Step-by-step explanation:

multiply by number in front of the bracket and group like terms ,divide both side by - and the answer was -4

Answer:

B

Step-by-step explanation:

A vertex is where two lines intersect

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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Answer:

-------------------------

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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Answer:

Wrong

Step-by-step explanation:

Any number times one equals that number

3x1=3 not 5

The fabric  has a cost per yard of $6 per yard

From the question, the given parameters are:

Yards of fabric = 2 1/2 yards

Cost of the fabric = $15

The cost per yard of the fabric is then calculated as

Cost per yard = Cost of the fabric/Yards of fabric

Substitute the known values in the above equation

So, we have

Cost per yard = 15/(2 1/2)

Evaluate the quotient

So, we have

Cost per yard = 6

Hence, the cost per yard is $6 per yard

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Check the picture below.

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

Yes, the correct answer is $6.50..

Step-by-step explanation:

Stacy earns $6.5 per hour.

Multiplication is the process of adding a number up to a given number.

Given that Stacy worked 6 hours each day for 6 days

The total number of hours Stacy worked is 6×6=36 hours

Therefore, Stacy earned $234 for 36 hours

$234 = 36 hours

$234/36 = 1 hour

$6.5 = 1 hour

Hence, Stacy earns $6.5 per hour.

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Answer:

460 1/3

Step-by-step explanation:

175 2/3 + 456 2/3

First convert to improper fraction,

527/3 + 854/3

=> 1381/3

Then After adding convert back to mixed fraction,

=> 460 1/3

Answer:

C) A = \(3w^{2} - 4w\)

Step-by-step explanation:

First, read through what the question is asking.

Now, read it again, but slowly and take in everything it is saying (Don't read into it too slowly, or else you will over-complicate the problem and get frustrated - told from experience :) )

Alright, 4 less than 3 times the width. So, lets rearrange this and give width a variable (w).

So, the length is equal to:

l = 3w - 4

and the width is equal to:

w = w

The area of a rectangle is A = l * w

Let's plug in the values.

A = (3w - 4) * w

Now, simplify:

A = \(3w^{2} - 4w\)

A = \(3w^{2} - 4w\) is your final answer.

I hope this helps!

Answer:

The length of 'x' is 4

Step-by-step explanation:

We can use the pythagorean theorem to solve this.

The pythagorean theorem is:

\(a ^{2} + b^{2} = {c}^{2} \)

\(a ^{2} + b^{2} = c^{2} \\ {3}^{2} + {b}^{2} = 5^{2} \\ 9 + {b}^{2} = 25 \\ \frac{ - 9 \: \: \: \: \: \: \: \: = - 9}{b ^{2} = \sqrt{16} } \\ b = 4\)

Therefore x = 4

Answer:

the solution to the trigonometric inequality cos(0.65x) > 0.44 over the interval 0 ≤ x < 4.834.

Step-by-step explanation:

The given inequality is:

cos(0.65x) > 0.44

To solve this inequality, we need to isolate the variable x.

First, let's take the inverse cosine (arccos) of both sides to remove the cosine function:

arccos(cos(0.65x)) > arccos(0.44)

Since the range of the inverse cosine function is limited to [0, π], we can rewrite the inequality as:

0 ≤ 0.65x < π

Now, let's solve for x by dividing each part of the inequality by 0.65:

0/0.65 ≤ x < π/0.65

Simplifying, we have:

0 ≤ x < π/0.65

Now, let's calculate the approximate value of π/0.65 to determine the interval for x:

π/0.65 ≈ 4.834

i hope i helped!

Answer:

1 7/20

Step-by-step explanation:

I think that's the answer.

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Answer:

.5

Step-by-step explanation:

Step-by-step explanation:

\(\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{4 + 5}}}\]=\)

\(\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{9}}}\]=\)

\(\[2 + \cfrac{2}{2 + \cfrac{3}{\cfrac{31}{9}}}\]=\)

\(\[2 + \cfrac{2}{2 + \cfrac{27}{31} }}}\]=\)

\(\[2 + \cfrac{2}{ \cfrac{62+27}{31} }}}\]=\)

\(\[2 + \cfrac{2}{ \cfrac{89}{31} }}}\]=\)

\(\[2 + \cfrac{62}{{89} }}}\]=\)

\(\[2 \cfrac{62}{{89} }}}\]\)

Answer:

2 62/89

Step-by-step explanation:

reduce its not super hard lmk if u need help

9514 1404 393

Answer:

  (a) 90°, 90°

  (b) 5, 1

  (c) 10°, 20°

  (d) 10°, 20°, 150°

Step-by-step explanation:

You need to consider ways in which each statement might not apply.

(a) An obtuse angle is greater than 90°. If both angles are 90°, then neither is obtuse.

  counterexample: m∠1 = 90°, m∠2 = 90°

__

(b) If the perimeter is 12, the sum of the side lengths must be 6. There are many ways to get two numbers that have a sum of 6. Here's one:

  counterexample: length = 5, width = 1

__

(c) All that is required is that the sum of angles be 30°. They don't have to be equal.

  counterexample: m∠ABC = 10°, m∠CBD = 20°

__

(d) We know the three angles of a triangle have a sum of 180°, but that does not require it to be an acute triangle. A triangle can also be right or obtuse.

  counterexample: m∠P = 10°, m∠Q = 20°, m∠R = 150°

Answer:

width is 4 inches

length is 6 inches

Step-by-step explanation:

the length is 6 inches less than three times the width

l = 3w - 6

a = l * w

a = (3w - 6)w

a = 3w^2 - 6w

area of the rectangle is 24 square inches

3w^2 - 6w = 24

subtract 24 from both sides

3w^2 - 6w - 24 = 0

Divide both sides by 3

w^2  - 2w - 8 = 0

Factor

(w - 4)(w + 2) = 0

w = {-2, 4}

disregard the negative root since measurement must be positive

w = 4

l = 3w - 6

l = 3(4) - 6

l = 6