The area under the standard normal curve where P(Z >. - 0.5) is: 0.6479 0.3085 0.3521 0.3681 0.6915

The water level is rising at a rate of 135/64 cm per second when the water level is 6 cm.

Let's call the height of the water in the pyramid "h" and the volume of water in the pyramid "V". We know that the rate of change of volume with respect to time is constant and equal to 45 cubic centimeters per second.

We can use similar triangles to find a relationship between the height of the water and the height of the pyramid. Since the pyramid has a square base, all four triangular faces are congruent. Therefore, we can use the fact that the ratio of corresponding sides of similar triangles is constant to find:

h / (13 - h) = 6 / 8

Simplifying this equation, we get:

h = 39 / 7

Now we can find the volume of water in the pyramid when the water level is 6 cm:

V = (1/3) * 8^2 * 6 = 128 cubic cm

To find the rate at which the water level is rising when the water level is 6 cm, we can differentiate the equation for the volume of the pyramid with respect to time:

V = (1/3) * 8^2 * h

dV/dt = (1/3) * 8^2 * dh/dt

We know that dV/dt = 45, so we can plug in the values we know and solve for dh/dt:

45 = (1/3) * 8^2 * dh/dt

dh/dt = 135 / 64

Therefore, the water level is rising at a rate of 135/64 cm per second when the water level is 6 cm.

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Answer:

The common difference of the sequence 5,8,11,14 is 3.

Answer:

the answer is 3

Step-by-step explanation:

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14, therefore the common difference of the arithmetic sequence is three.

The difference between a number and 9 is written as;

⇒ 9 - x = 34

And, The number is - 25.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The algebraic expression is;

'' The difference between a number and 9 is 34. ''

Now,

Let a number = x

So, We can formulate;

⇒ 9 - x = 34

Solve for x as;

⇒ 9 - 34 = x

⇒ - 25 = x

⇒ x = - 25

Therefore, The difference between a number and 9 is written as;

⇒ 9 - x = 34

And, The number is - 25.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

numerator and denominator

Two or more angles are said to be supplementary if and only if they add up to \(180^{o}\).

Thus the required statements and appropriate reasons are stated below:

Two lines are said to be perpendicular when the measure of the angle between them is a right angle. Thus all right angle is congruent.

Angles are said to be congruent if and only if they have equal measure.

Thus in the given question, it can be deduced that:

                     STATEMENT                             REASONS

1. AC ⊥ BD, <1 ≅ <4                                  Given

2. <BCA = \(90^{o}\), <DCA = \(90^{o}\)                       Definition of perpendicular lines

3. <BCA ≅ <DCA                                      Right angles are congruent

4. <BCA = <1 + <2                                     Angle addition property

5. <DCA = <3 + <4                                    Angle addition property

6. <1 + <2 = <3 + <4                                   Distributive property

7. <1 + <2 = <4 + <3                                    Substitution property

8. <2 ≅ <3                                                 Reflexive property

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Answer:

Step-by-step explanation:

Angles x and z are supplementary, meaning that they add up to 180.  From the markings on the diagram, angle z and the angle measuring 20 are complementary, meaning they add up to 90. So the game plan is to find out the measure of angle z first, then use that to find the measure of angle x.

angle z = 90 - 20 so

angle z = 70 degrees. And

angle z + angle x = 180.  Subbing in our value for z:

70 + angle x = 180 and

angle x = 180 - 70 so

angle x = 110 degrees

The value of the trigonometric ratio sin C of the given right angle triangle is; A: a/b

We know that the three trigonometric ratios of a right angle triangle are given as;

sin θ = opposite/hypotenuse

cos θ = Adjacent/hypotenuse

tan θ = Opposite/Adjacent

Now, from the right angle triangle given to us, if we want to consider the angle C, then we will have the trigonometric ratios as;

sin C = a/b

cos C = c/b

tan C = a/c

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The best sports that need more flexibility of our body are:

Because your muscles will be strong enough to support your daily activities if they are under the proper level of strain, you will feel less aches and pains. Its advantages for the mind must also be mentioned. Stretching releases tension, which reduces stress. Overall, flexibility enhances posture, mobility, coordination, and risk of muscular discomfort. Spending time on increasing flexibility is worthwhile. Which sports are the best to achieve it knowing this?

Now that we've cleared everything up, what exactly is flexibility? The range of motion in a joint or collection of joints is referred to as flexibility. Flexibility in one joint doesn't always translate to flexibility in another.

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Answer:

7

Step-by-step explanation:

To find the maximum number of turning points of any polynomial function, subtract one from the degree.

Since the degree is 8, subtract 1 from this:

8 - 1

= 7

So, the maximum number of turning points is 7.

Answer: y=2x-3

Step-by-step explanation: I looked it up.

The dimensions of the rectangular dog park are 75 feet by 150/2 = 75 feet.

Let the length of the rectangular dog park be L, and let the width be W. We want to split the park into two pens of equal size, so we can divide the length by 2 to get the length of each pen. Therefore, the total length of fencing used will be:

L + 2W + 2L/2 = L + 2W + L = 2L + 2W

Since we are given that the total length of fencing is 300 feet, we have:

2L + 2W = 300

Simplifying this equation, we get:

L + W = 150

We want to maximize the enclosed area of the dog park, which is given by:

A = LW

Since we want to split the park into two pens of equal size, we have:

L/2 × W = A/2

Solving for L in terms of W, we get:

L = 2A/W

Substituting this expression for L into the equation L + W = 150, we get:

2A/W + W = 150

Multiplying both sides by W, we get a quadratic equation in W:

2A + \(W^{2}\) = 150W

To maximize A, we want to find the value of W that maximizes this equation. To do this, we can complete the square:

\(W^{2}\) - 150W + 2A = 0

\((W - 75)^{2}\) = 2A + 5625

Since \((W - 75)^{2}\) is always non-negative, the maximum value of the expression on the left-hand side occurs when \((W - 75)^{2}\) is as small as possible, which occurs when W = 75. Therefore, to maximize the enclosed area of the dog park, we should split it into two pens of equal size with width 75 feet. Substituting this value of W into the equation L + W = 150, we get:

L + 75 = 150

L = 75

Therefore, the dimensions of the rectangular dog park are 75 feet by 150/2 = 75 feet.

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Using Standard deviation, approximately, 95% of the area under the normal curve falls between 2 standard deviations.

The area under a normal curve represents the total probability of an event occurring for a normally distributed random variable.

A normal distribution is a bell-shaped curve that describes a continuous probability distribution of a variable, where most values cluster around the mean, and the curve tapers off symmetrically on both sides.

The total area under the normal curve is equal to 1 or 100%, which means that the probability of all possible outcomes adds up to 1 or 100%.

The Empirical Rule states that:

Hence,

Approximately, 95% of the area under the normal curve falls between 2 standard deviations.

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Answer:

Step-by-step explanation:

13

Answer:

y = -3

Step-by-step explanation:

In order to answer this, we are going to have to do some division and multiplication. First, we will have to divide -42 by 14 to see how many times 14 can fit into -42:

-42 / 14 = -3

Then, we will replace y with -3 to make sure that this is correct:

14 (-3) = -42

-42 = -42

So, y = -3 is the answer.

Hope this helps! :)

Internal validity explains the association between binge-watching tv and irritability.

In the context of a specific study, internal validity refers to how strongly a piece of evidence supports a claim regarding cause and effect. It is one of the most crucial characteristics of scientific research and a crucial idea when considering evidence more generally.

The extent to which alternative explanations for a study's findings (often, sources of systematic error or "bias") can be ruled out is a measure of its internal validity. In contrast, external validity measures how well data support judgments made regarding other situations (that is, the extent to which results can be generalized).

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To calculate the final concentration of a solution when water is added, you need to know the initial concentration of the solution and the volume of water added.

The final concentration of a solution can be determined using the formula:

Final Concentration = (Initial Concentration * Initial Volume) / (Initial Volume + Volume of Water Added)

By plugging in the values for the initial concentration and the volume of water added, you can calculate the final concentration of the solution.

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Given:

ABCD is a parallelogram.

To prove:

Proof:

Hence proved.

Answer:

0.35

Step-by-step explanation:

Answer:

7/20

Step-by-step explanation:

hope this helps :3

Answer:

11

Step-by-step explanation:

P

e

md

as

6+15/3

6+5

11

Answer:

11

Step-by-step explanation:

When doing an equation like this we want to follow the rules of PEMDAS

(parenthesis, exponents, multiplication, division, addition, subtraction)

So first we start in the parenthesis,

( 2 + 4 ) + 15 / ( 9 - 6 )

6 + 15 / 3

Now that we solved the parenthesis lets see what our next step is in PEMDAS, there aren't any exponents, there isn't any multiplication, so our next step must be division.

15/3 = 5

6 + 5

So now all we have in our equation is addition which is 6 plus 5 this is obviously 11,

Hope this helps :)

The part (percentage) of the whole trip Tigran travels during the (first) two hours of driving is 90%

A percentage is a representation of a part of a quantity as a fraction with a denominator of a 100.

The fraction of the whole trip Tigran travels in the first hour = 2/5

The distance Tigran drove in the first hour of driving = (2/5) × 150-mile = 60-miles

The distance Tigran travels in the second hour = (5/6) × (150 - 60) = 75

The distance he drove in the second hour = 75 miles

The distance, d, Tigran travels during these two hours is therefore;

d = 60 miles + 75 miles = 135 miles

The part of the whole trip traveled in the two hours is therefore;

Part of trip = 135/150 = 9/10 = 90%

The part of the whole trip Tigran travels in these two hours is therefore, 90% of the trip

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a) PX43.Y=2) = P(X=3 | Y=2) = 4/11.

b) P(X>3, Y≥3) = 0.13.

c) P(X=1, Y=4) = f(1,4) = 0.04

d) P(X+Y = k) = Σxi

(a) We need to find P(X=3, Y=2).

From the given joint probability distribution, we have:

f(3,2) = 0.16

The marginal probability distribution of X is given by:

P(X=x) = Σy f(x,y)

So, we have:

P(X=3) = Σy f(3,y) = f(3,2) + f(3,3) + f(3,4) = 0.16 + 0.12 + 0.08 = 0.36

Now, using the conditional probability formula, we get:

P(X=3 | Y=2) = P(X=3, Y=2) / P(Y=2) = f(3,2) / Σx f(x,2) = 0.16 / (0.16 + 0.12 + 0.04) = 4/11

Therefore, PX43.Y=2) = P(X=3 | Y=2) = 4/11.

(b) We need to find P(X>3, Y≥3).

Using the marginal probability distribution of X and Y as found in part (a), we get:

P(X>3, Y≥3) = P(X=4, Y=3) + P(X=4, Y=4) = f(4,3) + f(4,4) = 0.09 + 0.04 = 0.13

Therefore, P(X>3, Y≥3) = 0.13.

(c) The conditional probability distribution of X given Y=y is given by:

f(x | y) = f(x,y) / Σxf(x,y)

Using the joint probability distribution given in the problem, we get:

Σxf(x,y) = f(1,y) + f(2,y) + f(3,y) + f(4,y) = 0.04 + 0.12 + 0.28 + 0.56 = 1

In light of Y=2, the following is the conditional probability distribution of X:

f(x | 2) = f(x,2) / Σxf(x,2) = 0.16/ (0.16 + 0.12 + 0.08 + 0.04) = 4/10 = 2/5

Similarly, the conditional probability distribution of X given Y=3 and Y=4 are:

f(x | 3) = f(x,3) / Σxf(x,3) = 0.12 / (0.04 + 0.12 + 0.36 + 0.72) = 1/5

f(x | 4) = f(x,4) / Σxf(x,4) = 0.08 / (0.04 + 0.08 + 0.24 + 0.32) = 2/7

Therefore, P(X=1, Y=4) = f(1,4) = 0.04

P(X=2, Y=2) = f(2,2) = 0.12

P(X=3, Y=3) = f(3,3) = 0.28

P(X=4, Y=3) = f(4,3) = 0.09

P(X=4, Y=4) = f(4,4) = 0.04

(d) The marginal probability distribution of X+Y can be found as follows:

P(X+Y = k) = Σxi

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a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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The value of x in sequence of number is 10.

Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.

What is geometric series?

Geometric series is an infinite series of the form:

\(a+ar+a r^{2} +ar^{3} +..........\)

where r is known as common ratio.

Now, first term is x and each term there after is twice the previous term.

So the series will be;

x , 2x , 4x , 8x, ..........

Clearly this series is geometric series with common ratio 2.

And the nth term of geometric series is \(ar^{n-1}\)

⇒ fifth term is 160

\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)

Here, first term is x.

The value of x in sequence of number is 10.

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The probability that Fido and Rover (two dogs) are in adjacent cages is

\frac{17}{\binom{18}2}=\frac19,

because there are \binom{18}2 choices for the (unordered) pair of cages to put them in, and 17 pairs of adjacent cages.

To get the expected value, multiply this probability of a random  number of same-species pairs of animals:

\frac19\cdot3\cdot\binom62=5.

The expected value is 5.

Randomness has many uses in fields such as science, art, statistics, cryptography, games, and gambling. For example, random assignment in randomized controlled trials helps scientists test hypotheses, and random or pseudo-random numbers are useful in video games like video poker.

In computing, a hardware random number generator (HRNG) or true random number generator (TRNG) is a device that generates random numbers through a physical process rather than an algorithm.

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Answer:

x+y=4

Step-by-step explanation:

hello :

note :  by identity  you have   x²-y² = (x-y)(x+y)

in this exercice : 2x²-2y² = 2(x²-y²) = 2 (x-y)(x+y)

means :   2 (x-y)(x+y) = 40

but x-y = 5

so : 2(5)(x+y) =40

x+y=40/10

x+y=4

Step-by-step explanation:

The question is not properly structured but we can as well find the sum of 5/7 and 10 as shown;

\(\frac{5}{7}+ \frac{10}{1} \\The \ LCM \ is \ 7\\\\= \frac{5(1)+10(7)}{7}\\\\= \frac{5+70}{7}\\\\= \frac{75}{7} \\\\= 10 \frac{5}{7}\)

Hence the expression written in equivalent form of common denominator is \(\frac{5 + 70}{7}\)

The sum is \(10 \frac{5}{7}\)

The z score for a per - day expense of $400 is 0.65 while about 84.13% of the hotels is greater than $268

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma} \\\\\mu=mean,x=raw\ score,\sigma=standard \ deviation\\\\Given\ that:\\\\\mu=348,\sigma=80\)

a) For an expense of $400:

\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{400-348}{80}\\\\z=0.65\)

The z score for a per - day expense of $400 is 0.65

b) For an expense greater than $268:

\(z=\frac{x-\mu}{\sigma}\\\\z=\frac{268-348}{80}\\\\z=-1\)

P(x > 268) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413 = 84.13%

About 84.13% of the hotels is greater than $268

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Therefore , the solution of the given problem of expressions comes out to be the expression's value at x = -4 and y = 64 is 0.

Instead of using approximations produced at random, it is better to use shifting integers that may prove increasing, reducing, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, components, or mathematical remarks for techniques like additional disapproval, production, and mixture may be included in a statement of truth equation.

Here,

The phrase is entrusted to us:

=> -4∛y + x²

Additionally, we are told that x = -4 and y = 64. When these numbers are inserted into the expression, we obtain:

=> -4∛y + x² = -4∛(64) + (-4)²

=> -4∛4³ + 16

=> -4(4) + 16

=> 0

Consequently, the expression's value at x = -4 and y = 64 is 0.

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Answer:

114

Step-by-step explanation:

19x6=114