Does anyone know the answer to both of these questions????

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

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Answer:

(x,y)——>(-8x, 5y)

Step-by-step explanation:

Answer:

The y-intercept of the line is at the point with coordinates (0,-5)

Step-by-step explanation:

Answer:

\(-3\frac{1}{2}<-3\frac{1}{3}\)

Step-by-step explanation:

-3.5 means -(3 + \(\frac{1}{2}\))

In other words, -3.5 = \(-3\frac{1}{2}\)

When we draw two numbers \(-3\frac{1}{3}\) and \(-3\frac{1}{2}\) on a number line, \(-3\frac{1}{2}\) comes first from left to right.

We know that all the numbers on a number line from left to right are in increasing order.

Therefore, \(-3\frac{1}{2}\) is smaller than \(-3\frac{1}{3}\).

\(-3\frac{1}{2}<-3\frac{1}{3}\)

Lauren is not correct.

The shape of the probability distribution for the random walk problem depends on the values of p and q. When p = q, the distribution is symmetric, while if p and q have different values, the distribution becomes asymmetric.

The shape of the probability distribution for the problem of the random walk can be determined by considering the values of p and q, where p represents the probability of moving in one direction and q represents the probability of moving in the opposite direction.
(a) In this case, we are given that p = q = 1/2, which means that there is an equal probability of moving in either direction.
When p = q = 1/2, the probability distribution for the random walk problem will have a symmetric shape. This means that the probabilities of moving to the left and the right are the same. For example, if we start at position 0 and take 20 steps, the probability of ending up at position +10 will be the same as the probability of ending up at position -10.
It is important to note that the specific values of p and q do not affect the shape of the distribution. As long as p = q, the distribution will be symmetric.

(b) Now, let's consider a different scenario where p = 0.6 and q = 0.4. In this case, the probability of moving in one direction is greater than the probability of moving in the opposite direction. This will result in an asymmetric probability distribution.
For example, if we start at position 0 and take 20 steps, the probability of ending up in a positive position will be higher than the probability of ending up in a negative position. The distribution will be skewed towards the positive position.

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Answer:

Step-by-step explanation:

A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.

≧◉◡◉≦

when x is 0.5 then y value is 3, x is 1.5 then y is 9 and x is 4.5 then y is 27.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

A proportion is an equation in which two ratios are set equal to each other

In the given table the value of x is 0.5 and value of y is 3

y/x=3/0.5=6

In the second row the value of x is 1.5 we need to find value of y.

3/0.5=y/1.5

4.5=0.5y

Divide both sides by 0.5

y=9

In third row the value of x is 4.5 and y is 27

Hence, when x is 0.5 then y is 3, x is 1.5 then y value is 9 and x is 4.5 then y is 27.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The function that satisfies the property of having its first derivative being a constant multiple k of itself is the exponential function, specifically the function f(x) = e^(kx).

The exponential function e^(kx) has the property that its first derivative is a constant multiple of itself. Taking the derivative of f(x) = e^(kx) with respect to x, we get:

f'(x) = ke^(kx)

As we can see, the first derivative of the exponential function is a constant multiple k of itself. This property holds for all values of k.

The exponential function is widely used in various fields, including calculus, physics, and finance, due to its remarkable properties and applications. Its constant rate of change allows it to model exponential growth and decay processes, making it a fundamental function in calculus and mathematical modeling.

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Answer:

Equal to 1

Step-by-step explanation:

By using the exponential delta we can infer that the orthogonal is correct because the high order bits multivariate and are asymptomatic.

Answer:

                   .

Step-by-step explanation:

                    ..          

Answer:

36 / 4 = 9 half-lives

2^9 = 512

Therefore after 36 hrs 512 / 512 = 1 mg remains

Answer:

1 mg

Step-by-step explanation:

Power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x=1.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three.

The given equation: \(\left(x^2-2 x+26\right) y^{\prime \prime}+x y^{\prime}-4 y=0\)

It is necessary to determine the power series solutions' minimal radius of convergence R around the typical points x = 0 and x = 1.

The separation between the ordinary point and the differential equation's singularity is now the minimal radius of convergence.

The polynomial's root, which is connected to the second derivative, is the singularity point.

The singularity points will be determined as follows:

\(\begin{aligned}& x^2-2 x+26=0 \\& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\& x=\frac{2 \pm \sqrt{(-2)^2-4 \times 1 \times 26}}{2} \\& x=1 \pm \sqrt{-100} \\& x=1 \pm 10 i\end{aligned}\)

In this case, x1 = 1+10i and x2 = 1-10i are the singularity sites.

The ordinary points at this time are z1 = 0+01 and z2 = 1+0i.

One can compute the minimum radius of convergence using the formula:

\(\begin{aligned}& r_1=\left|z_1-x_1\right| \\& =|0+0 i-1-10 i| \\& =\sqrt{101} \\& =10.0498 \\& r_2=\left|z_2-x_1\right| \\& =\sqrt{100} \\& =10\end{aligned}\)

Therefore, power series solutions have a minimum radius of convergence of R of 10.0498 around the normal point x = 0 and 10 units around the normal point x = 1.

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Answer:

3.8 in

Step-by-step explanation:

Answer:

3 4/5 (three and four-fifths)

Step-by-step explanation:

convert the mixed number to improper fractions, find the LCD and combine

19/5  --   3 4/5

Answer:

hi,

Step-by-step explanation:

Let say P=(x,y) a point of the locus

\(Distance\ from\ P\ to\ (2,1)= \sqrt{(x-2)^2+(y-1)^2} \\Distance\ from\ P\ to\ (1,2)= \sqrt{(x-1)^2+(y-2)^2} \\\\\sqrt{(x-2)^2+(y-1)^2} =2*\sqrt{(x-1)^2+(y-2)^2} \\\\(x-2)^2+(y-1)^2=4*((x-1)^2+(y-2)^2)\\\\3x^2-4x+3y^2-14y+15=0\\\\\)

\(3x^2-4x+3y^2-14y+15=0\\3(x^2-2*\dfrac{2}{3} x)+3(y^2-2*\dfrac{7}{3}*y) +15=0\\3(x^2-2*\dfrac{2}{3}*x+\dfrac{4}{9})+3(y^2-2*\dfrac{7}{3}*y+\dfrac{49}{9} ) +15-\dfrac{4}{3}-\dfrac{49}{3}=0\\\\3(x-\dfrac{2}{3})^2+3(y-\dfrac{7}{3})^2-\dfrac{8}{3}=0\\\\\\\boxed{(x-\dfrac{2}{3})^2+(y-\dfrac{7}{3})^2=\dfrac{8}{9}}\\\\\)

Locus is the circle of center (2/3,7/3) and radius =2√2  /3.

Answer:

Step-by-step explanation:

We know that perpendicular lines have opposite-reciprocal slopes.

Given line:

Its slope is 2 and the perpendicular line has a slope of - 1/2.

Let's find the line with the slope of - 1/2:

Answer:

c

Step-by-step explanation:

When conducting a t-test for independent means, the best way to reduce variance is to use a control group.

When conducting a t-test for independent means, the best way to reduce variance is to use a control group. Control groups can help reduce variance by ensuring that both groups are exposed to the same conditions, except for the variable being tested. By controlling for all other factors, researchers can isolate the impact of the variable under investigation, which in turn can reduce the variance in the results.

When conducting a t-test for independent means, a control group is typically used to test the effect of a particular treatment or intervention. The control group is exposed to the same conditions as the experimental group, except for the variable being tested. By ensuring that both groups are exposed to the same conditions, researchers can control for other factors that could affect the results of the test.

In conclusion, when conducting a t-test for independent means, the best way to reduce variance is to use a control group. The control group can help control for all other factors except for the variable being tested, which in turn can reduce variance in the results.

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The area of the paperboard that remains is 613.92 square inches.

To find the area of the paperboard that remains after a semicircle is cut out, we need to calculate the area of the rectangular paperboard and subtract the area of the semicircle.

The rectangular paperboard has dimensions of 35 inches long and 24 inches wide. Therefore, the area of the rectangular paperboard is:

Area_rectangular = length * width = 35 in * 24 in = 840 in²

Now, let's calculate the area of the semicircle. The semicircle is cut out of the rectangular paperboard, and the diameter of the semicircle is equal to the width of the rectangular paperboard (24 inches).

The formula to calculate the area of a semicircle is:

Area semicircle = (π * r²) / 2

where r is the radius of the semicircle.

Since the diameter of the semicircle is 24 inches, the radius is half of that, which is 12 inches.

Plugging in the values into the formula, we get:

Area_semicircle = (3.14 * 12²) / 2 = (3.14 * 144) / 2 = 226.08 in²

Finally, to find the area of the paperboard that remains, we subtract the area of the semicircle from the area of the rectangular paperboard:

Area remaining = Area rectangular - Area semicircle = 840 in² - 226.08 in² = 613.92 in²

Therefore, the area of the paperboard that remains is 613.92 square inches.

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Answer:

in explanation

Step-by-step explanation:

Input to output so for the input when it is 1=6 because it starts at 5 and then 8 what I mean is when the input comes out the output is going to be 3 more greater than last time.

So 1=6 so 6 is 5 more then

2 to 10=8 so 5 more went to 8 more.

Next is 3 and 14 so 3 more again because 8 + 3=11 so in that case that next number is 4 it will be 14 more

So 14 more than 4=18 and that is the output.

Also for the output it adds 4 for the numbers 6 + 4=10 + 4=14+ another 4=18.

And input is just plus 1.

Hope it helps have a great day:)

La base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente.

Por geometría sabemos que el área de un rectángulo (\(A\)), en centímetros cuadrados, es igual al producto de la base (\(b\)) y la altura (\(h\)), ambas en centímetros.

Mediante álgebra tenemos la siguiente expresión:

\(x\cdot (x+ 6) = 91\)

\(x^{2}+6\cdot x - 91 = 0\) (1)

Las raíces de este polinomio se determinan mediante la fórmula cuadrática:

\(x_{1} = 7\), \(x_{2} = 13\)

En consecuencia, la base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente. \(\blacksquare\)

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Answer:

hi

Step-by-step explanation:

Answer: 2.95x+39.95(12)

Step-by-step explanation:

Hi, to answer this question we have t write an expression with the information given:

The yearly cost for x movie rentals is equal to : the product of the cost of each movie (2.95) and the number of movies (x) ;plus the product of the monthly fee (39.95) and the number of months in a year (12)

Mathematically speaking:

2.95x+39.95(12)

Answer:

D-295x+39.95(12)​

Step-by-step explanation:

EDG2021

Step-by-step explanation:

95%= 95/100×180/1

0 will cancel 0

2 can divide so 10 ÷2 = 5 and 18÷2= 9

5 can divide 95 =19

19×9= 171

Answer:

x^2+12x-8

Step-by-step explanation:

(x-8)(x+1) = x^2-7x-8

x^2+9x-7x+10x-8

simplify:
x^2+12x-8

Answer: -x^2+26x-8

Step-by-step explanation:

1. Multiply

9x-(x-8)(x+1)+10x

9x-x^2-x+8x-8+10x

2. Combine Like Terms

-x^2+26x-8

Answer: -x^2+26x-8

Answer:

a is greater than -2

Step-by-step explanation:

Solving a comparison like this is the same as solving an equation, except you need to watch out for the signs of numbers.

Given:

-2a - 12 < -8

The first thing we need to do here is to add 12 to both sides:

-2a - 12 + 12 < -8 + 12

-2a < 4

You'll notice we're just increasing both sides, so the relationship stays the same.

Now we divide both sides by -2.  Because the number is negative, it changes whether the result is greater or less.

-2a < 4

-2a ÷ -2 > 4 ÷ -2

a > -2

Giving us our final answer.

Answer:

9/14

Step-by-step explanation:

add them

Answer:

2.67

Step-by-step explanation:

The probability that a poisonous mushroom in the forest is red is 50%.

To find the probability that a poisonous mushroom in the forest is red, we need to consider the probabilities of a mushroom being red and poisonous, and compare it to the overall probability of a mushroom being poisonous.

Let's denote the events as follows:

R: Mushroom is red

P: Mushroom is poisonous

P(R) = 20% = 0.20 (probability of a mushroom being red)

P(P|R) = 20% = 0.20 (probability of a red mushroom being poisonous)

P(P|not R) = 5% = 0.05 (probability of a non-red mushroom being poisonous)

We want to calculate:

P(R|P) = ? (probability that a poisonous mushroom is red)

We can use Bayes' theorem to calculate this probability:

P(R|P) = (P(P|R) * P(R)) / P(P)

To calculate P(P), the overall probability of a mushroom being poisonous, we can use the law of total probability:

P(P) = P(P|R) * P(R) + P(P|not R) * P(not R)

P(not R) = 1 - P(R) = 1 - 0.20 = 0.80 (probability of a mushroom not being red)

Now, we can calculate P(P):

P(P) = P(P|R) * P(R) + P(P|not R) * P(not R)

      = 0.20 * 0.20 + 0.05 * 0.80

      = 0.04 + 0.04

      = 0.08

Finally, we can calculate P(R|P) using Bayes' theorem:

P(R|P) = (P(P|R) * P(R)) / P(P)

      = (0.20 * 0.20) / 0.08

      = 0.04 / 0.08

      = 0.50

Therefore, the probability that a poisonous mushroom in the forest is red is 50%.

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