Find the length of WT if W (-3,0) and T (3,-1). If a decimal round to the
hundredth place.

In this scenario, Young's modulus of metal sheets follows a normal distribution with a mean of 70 GPa and a standard deviation of 1.9 GPa. We are given two probability calculations based on this distribution.

(a) To calculate the probability P(69 < X < 71) when n = 16, we are looking for the probability that the sample mean falls between 69 and 71. Since the sample mean follows a normal distribution with the same mean as the population and a standard deviation equal to the population standard deviation divided by the square root of the sample size, we can use the normal distribution to find the probability. Using the given mean and standard deviation, along with the formula for the standard deviation of the sample mean, we can calculate this probability. (b) To calculate the probability of the sample mean diameter exceeding 71 when n = 25, we are looking for the probability that the sample mean is greater than 71. Again, we can use the normal distribution with the given mean and standard deviation to calculate this probability. By performing the necessary calculations, we find the probabilities to be 0.9876 and 0.0009, respectively, rounded to four decimal places. In summary, the first probability calculation determines the likelihood of the sample mean falling between 69 and 71 when the sample size is 16. The second probability calculation determines the likelihood of the sample mean exceeding 71 when the sample size is 25.

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Answer:jac ganko

Step-by-step explanation:

Answer:

w= 27.47 degree

x=9.99 cm

y=12.02 cm

Step-by-step explanation:

The value of w:

In a right-angled triangle \(\tan \theta = \frac {\text{Perpendicular}}{\text{Base}}\)

\(\tan w = \frac {\text{Perpendicular}}{25+9}\;and \; \tan 63 = \frac {\text{Perpendicular}}{9}\)

So, \(34 \tan w = 9\tan (63)\)

\(\tan w = (9/34)\tan(63)=0.52 \\\\w=\tan^{-1}(0.52) \\\\\)

w= 27.47 degree

The value of x:

In a right-angled triangle \(\sin \theta = \frac {\text{Perpendicular}}{\text{Hypotaneous}}\)

sin (27) =x/22

x= 22sin(27)

x=9.99 cm

The value of y:

By using Pythagoras theorem,

\(y^2+y^2=17^2 \\\\2y^2 = 289 \\\\y^2 =289/2= 144.5 \\\\y=\sqrt {144.5} \\\\\)

y=12.02 cm

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:

Number 1. Hope you can read that

Step-by-step explanation:

Answer:

Hey there!

Area=1/2bh

Area=1/2(120)(90)

Area=60(90)

Area=5400

Let me know if this helps :)

Answer:

Last one

Step-by-step explanation:

The slope intercept form is: y=mx +b

m=the slope and b is the y intercept

so it would be the last one

Answer:

y=41/3 and x = -14

Step-by-step explanation:

system of the linear equation :

-3y-4x=15       eq[i]

9y+7x=25      eq[ii]

multiplying eq[i] by -7 and eq[ii] by 4,we get

21y+28x= -105    eq[iii]

36y+28x= 100     eq[iv]

subtracting eq[iii] from eq[iv],we get

15y=205

y=205/15=41/3

and x= -14

The probability of selecting exactly three clubs from a standard deck is 0.088. Where n = 5; p = 0.25; q = 0.75; and x = 3 . It is calculated by using binomial probability.

The binomial probability formula is

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾ = \(\frac{n!}{(n-x)!x!} p^xq^{(n-x)}\)

Where n is the number of trials, p i is the probability of success, and q is the probability of failure.

And q = 1 - p

It is given that, a card is selected from a standard deck and replaced.

This experiment has repeated a total of five times. i.e., trials n = 5

So, the probability of success is p = 1/4 = 0.25

(Since one card is to be selected from the five trials where each time the card is replaced)

Then, the probability of failure is q = 1 - 0.25 = 0.75

And it is given that we need to find the probability of selecting exactly three clubs. So, the required random variable is x = 3.

Then, using the binomial probability formula, we get

P(X = x) = ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾

⇒ P(X = 3) = ⁵C₃ p³q⁽⁵⁻³⁾ = ⁵C₃(0.25)³(0.75)² = 0.0878

On rounding off, we get the required probability as 0.088.

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ANSWER

STEP-BY-STEP EXPLANATION

Given information

To graph the above function, we need to find the y-intercept and x-intercept

Step 1: Make y = 0 to find the x-intercept

Step 2: Make x= 0 to find y-intercept

Step 3: Graph the solution

The correct answer is option 3. \(4x^2 + 17\) expressions represent the total perimeter of her sandwich, and if x = 1.2, the approximate length of the crust is 21.8 centimeters.

The first expression, \(4x^2 + 17\) , represents the total perimeter of the sandwich. When x = 1.2, the expression evaluates to\(4 * 1.2^2 + 17 = 21.8\).

So the total perimeter of the sandwich is 21.8 cm. However, this length is not the length of the crust, since the length of the crust would only be a portion of the total perimeter.

The expression \(4x^2 + 17\) represents a mathematical formula for the total perimeter of the sandwich. The variable x represents the thickness of each slice of bread. The expression \(4x^2\) represents the total length of the four edges of the bread slices, and the 17 represents the total length of the filling. When x = 1.2, the expression evaluates to 21.8, which represents the total perimeter of the sandwich.

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The function is increasing on the intervals (-4, 2) and (8, ∞) for the derivative of a function is f'(x) = (x - 2) (x + 4) (x - 8).

The derivative of a function represents its rate of change or slope. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing. If the derivative is zero, the function has a critical point.

In this case, the derivative of the function is:

f'(x) = (x - 2) (x + 4) (x - 8)

This function is a polynomial, and its roots are:

x = 2, x = -4, and x = 8

These are the critical points of the function. We can use these points to determine the intervals where the function is increasing or decreasing.

We can create a sign chart for the derivative:

x -4 2 8

f'(x) -ve 0 +ve

From the sign chart, we see that the function is increasing on the intervals (-4, 2) and (8, ∞).

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Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

To calculate the distance traveled, we can multiply the speed by the time traveled.

Speed = 1000 miles per hour

Time = 7.5 * 10⁵ hours

Distance = Speed * Time

Distance = 1000 miles/hour * 7.5 * 10⁵ hours

To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:

Distance = 1000 * 7.5 * 10⁵ miles

Distance = 7.5 * 10⁸ miles

Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.

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Obtaining data with a small p-value would be strong evidence against the null hypothesis. Correct option is 3).

In hypothesis testing, the null hypothesis assumes that there is no significant difference or relationship between variables, while the alternative hypothesis suggests otherwise. To determine whether to reject the null hypothesis, we calculate a p-value, which represents the probability of observing the data or more extreme results if the null hypothesis were true.

A small p-value indicates that the observed data is unlikely to occur under the null hypothesis, providing strong evidence against it. Therefore, obtaining data with a small p-value (option 3) would be considered strong evidence against the null hypothesis.

On the other hand, a large p-value (option 4) would suggest that the observed data is likely to occur even if the null hypothesis were true. This would not provide strong evidence against the null hypothesis, as it suggests that the data is consistent with the null hypothesis.

Using a small level of significance (option 1) or a large level of significance (option 2) refers to the predetermined threshold at which we decide to reject or fail to reject the null hypothesis. While the choice of significance level affects the decision-making process, it does not directly indicate evidence against the null hypothesis like the p-value does.

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Answer: 0.2 square meters.

Step-by-step explanation:

We are given the equation:

3600b² = hw

We need to find the value of b, given that h = 168 cm and w = 60 kg.

First, we need to convert the height from centimeters to meters:

h = 168 cm = 1.68 m

Substituting the given values:

3600b² = (1.68)(60)

3600b² = 100.8

b² = 100.8/3600

b² = 0.028

Taking the square root of both sides:

b = √0.028

b ≈ 0.167

Rounding to the nearest tenth:

b ≈ 0.2

Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.

Answer:

50° degrees

CARRYONLEARNIG

Generate quadratic model: \(\(y = x + x^2 + e\)\) with \(\(x\) and \(e\)\) as normal variables. Perform train-test split and fit linear, quadratic, and 7th-degree polynomial models.

To generate a quadratic model with \(\(y = x + x^2 + e\)\), where \(\(x\) and \(e\)\) are both vectors following a normal distribution with mean 0 and variance 1, and to generate a Monte Carlo sample with a length of \(\(m = 20\)\), we can follow these steps:

1. Generate the vectors \(\(x\) and \(e\)\) using the normal distribution:

\(\[x \sim \mathcal{N}(0, 1), \quad e \sim \mathcal{N}(0, 1)\]\)

2. Calculate the dependent variable \(\(y\)\) using the quadratic model:

\(\[y = x + x^2 + e\]\)

3. Generate a Monte Carlo sample of length \(\(m = 20\)\) by repeating steps 1 and 2 \(\(m\)\) times.

Now, using the `train_test_split()` function, we can split the Monte Carlo sample into a training set and a test set. The test set will be half the size of the full sample \((\(m/2\)).\)

Next, we can fit three different models: a linear model, a quadratic model, and a 7th-degree polynomial. Let's denote the input variable as \(\(x\)\) and the dependent variable as \(\(y\).\)

1. Linear Model:

The linear model can be expressed as:

\(\[y = \beta_0 + \beta_1x\]\)

2. Quadratic Model:

The quadratic model can be expressed as:

\(\[y = \beta_0 + \beta_1x + \beta_2x^2\]\)

3. 7th-Degree Polynomial Model:

The 7th-degree polynomial model can be expressed as:

\(\[y = \beta_0 + \beta_1x + \beta_2x^2 + \beta_3x^3 + \beta_4x^4 + \beta_5x^5 + \beta_6x^6 + \beta_7x^7\]\)

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Answer:

Step-by-step explanation:

When two chords intersect inside the circle, the product of their segments are equal.

BE * ED = AE * EC

x *3x = 4 *3

3x²   = 12 {Divide both sides by 3}

  x² = 12/3

  x² = 4

  x = √4

  x = 2

Answer:

The value of x is 2.

Step-by-step explanation:

We know that , when the two chords are intersect inside the circle, the product of their segment are equal.

So, BE × ED = AE × EC

putting the values

x × 3x = 4 × 3

multiply the values

3 x ² = 12

divide 12 by 3

x ² = 12 / 3

x ² = 4

Taking the square root of 4

x = √4

x = 2

The value of x is 2.

The interval equivalent to \(2 < x \leq 5\) or \(x > 7\) is \((2, 5] \cup (7, \infty)\).The symbol \(\infty\) represents positive infinity, indicating that the interval continues indefinitely in the positive direction.

The interval equivalent to the given inequality, \(2 < x \leq 5\) or \(x > 7\), can be expressed as the union of two separate intervals. Let's break it down:

1. \(2 < x \leq 5\):

This inequality represents an open interval, where \(x\) is greater than 2 but less than or equal to 5. We can express this interval as \(2 < x \leq 5\).

2. \(x > 7\):

This inequality represents an open interval, where \(x\) is greater than 7. We can express this interval as \(x > 7\).

To combine these two intervals, we take the union of the two intervals:

\(2 < x \leq 5\) or \(x > 7\)

This can be written in interval notation as:

\((2, 5] \cup (7, \infty)\)

In this notation, the parentheses indicate that the endpoints are excluded (open interval), and the square bracket indicates that the endpoint is included (closed interval). The symbol \(\infty\) represents positive infinity, indicating that the interval continues indefinitely in the positive direction.

Thus, the interval equivalent to \(2 < x \leq 5\) or \(x > 7\) is \((2, 5] \cup (7, \infty)\).

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Answer:

30:120

Step-by-step explanation:

1 + 4 = 5

150 div 5 = 30

30 times 1 = 30

30 times 4 = 120

Answer:

Step-by-step explanation:

\(1 : 4 \\ 1 + 4 = 5\)

\( \frac{150}{5} = 30\)

\( \: \: \: \: \: \: \: \: \: \: 1\: \: \: \: \: \: \: \: \: \: \: : \: \: \: \: \: \: \: \: 4 \\ 30 \times 1 \: \: \: \: \: \: \: : \: 4 \times 30 \\ \: \: \: \: \: 30 \: \: \: \: \: \: \: \: \: \: \: \: \: : 120\)

hope this helps

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good luck! have a nice day!

Answer:

Rowing speed: 10.6 miles per hour
speed of the current: 3.8 miles per hour.

Step-by-step explanation:

Let the team's rowing speed in still water be "x" and the speed of the current be "c".

x + c = 14.4

x - c = 6.8

(x + c) + (x - c) = 14.4 + 6.8

2x = 21.2

x = \(\frac{21.2}{2}\)

x = 10.6

10.6 + c = 14.4

c = 14.4 - 10.6

c = 3.8

The team's rowing speed in still water is 10.6 miles per hour, and the speed of the current is 3.8 miles per hour.

When a converging lens with a focal length of 10.6 cm is held 8.10 cm in front of a newspaper with a print size of 2.06 mm, the image formed by the lens is virtual, upright, and magnified. The height of the image is 8.32 mm.

The characteristics of the image formed by a lens can be determined by using the thin lens equation and the magnification equation. The thin lens equation relates the object distance, image distance, and focal length of the lens. The magnification equation relates the size of the object and the size of the image.

In this problem, the lens is held 8.10 cm in front of the newspaper, which is the object. The focal length of the lens is 10.6 cm. Using the thin lens equation, we can find the image distance, which is 0.322 m. The negative sign of the magnification value indicates that the image is inverted with respect to the object. The magnification value of -3.98 indicates that the image is magnified, which means that it appears larger than the object.

To find the height of the image, we use the magnification equation. The height of the object (the print size of the newspaper) is given as 2.06 mm. Using the magnification value of -3.98, we can find the height of the image, which is 8.32 mm.

Therefore, the image appears much larger than the object, and is located on the same side of the lens as the object. The image is virtual and upright, which means that it appears to be behind the lens and is not a real image that can be projected onto a screen.

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Answer:

Q is not a function

Step-by-step explanation:

Answer:

12 adults and 4 kids were there that the fair

Step-by-step explanation:

Part A: Sherise jogs for 157/10 miles each week.

Part B: Reggie jogs for 123/10 miles each week.

What is meant by week?

A period of seven days, typically starting on Monday and ending on Sunday, is commonly used as a unit of time in calendars and schedules.

What is meant by miles?

A unit of distance used in the United States and some other countries is equal to 5,280 feet or 1.609 kilometres.

According to the given information

Part A: Sherise jogs 53/10 + 41/10 + 63/10 = 157/10 miles each week.

Part B: Reggie jogs 157/10 - 34/10 = 123/10 miles each week.

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Answer:

39 quarters, or 9.75 dollars.

Step-by-step explanation:

We can turn this into an algebra equation.

23 + 4x           If x = 4

x stands for the number of weeks.

After solving that, we get 39 quarters.

To turn it into dollars, we divide it by 4 (because 4 quarters is equal to one dollar) and then we get 9 3/4. 3/4 dollars is just .75 cents, so the answer is 9.75 dollars.

Garry will have 39 quarters or $9.75 in his bank as per linear equation in 4 weeks.

A linear equation is an equation where the variable has the highest power of one.

Give, Garry has 23 quarters.

He saves 4 quarters each week for the next weeks.

Therefore, after 4 weeks Garry will save a total of (4 × 4) quarters = 16 quarters.

Hence, after 4 weeks Garry will have in his bank account is (23 + 16) quarters = 39 quarters = $9.75.

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The number line shows the value of 5 - (-8) = 13.

Addition:

Subtraction:

Here the given operation is subtraction. Where a subtrahend is a negative number i.e., -8.

Step1: Start from '5' on the number line.

Step2: Since the subtrahend is a negative number, move to the right side on the number line from '5'.

Step3: Thus, the number obtained on the line is 13.

Step4: Algebraically the result is 5 - (-8) = 5 + 8 = 13.

The number line for this operation is shown below.

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Answer:

Step-by-step explanation:

You have to use the distance formula to find that distance.  The formula is:

\(d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}\)

Let's call the first point x1, y1 (4, -1) and the second point x2, y2 (0, -2). Plugging into our formula then gives us this:

\(d=\sqrt{ (0-4)^2+(-2-(-1))^2}\)

which simplifies to

\(d=\sqrt{(-4)^2+(-1)^2}\) which is

\(d=\sqrt{17}\) ≈ 4.123 units