The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . The solution to the inequality is . Sal's mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.

Answer:

#1 is A #2 is A

Step-by-step explanation:

The identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime.

To prove the identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime, we can use Fermat's Little Theorem, which states that if p is prime and a is relatively prime to p, then a^(p-1) ≡ 1 (mod p).

Using this theorem, we can rewrite the left side of the given identity as a^p * a^(-1) ≡ 1 (mod p). Since a is relatively prime to p, we know that a^(-1) exists and is also relatively prime to p.

Now, we can apply Fermat's Little Theorem to the first term, a^p, to get a^p ≡ a (mod p). Substituting this into our rewritten expression, we get:

a * a^(-1) ≡ a * a^(p-1) (mod p)

Simplifying, we get:

1 ≡ a^(p-1) (mod p)

Finally, we can apply Fermat's Little Theorem one more time to obtain:

1 ≡ a^(p-1) ≡ a^(p-1) mod p^2

Therefore, we have proven the identity a p(p−1) ≡ 1 (mod p 2 ), where a is relatively prime to p and p is prime.

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The focal length of the glass lens in Figure 1 assuming the refractive index of the glass lens material is 1.5. is approximately 187 cm.

To find the focal length of the glass lens in Figure 1, we need to use the lensmaker's formula, which relates the focal length of a lens to the radii of curvature of its two surfaces.

The lensmaker's formula is given by:

1/f = (n - 1) * ((1/R₁) - (1/R₂))

where: f is the focal length of the lens,

n is the refractive index of the lens material,

R₁ is the radius of curvature of the first surface,

R₂ is the radius of curvature of the second surface.

In this case, let's assume the refractive index of the glass lens material is 1.5.

Given: R₁ = 29 cm

R₂ = 42 cm

n = 1.5

Using the lensmaker's formula:

1/f = (1.5 - 1) * ((1/29) - (1/42))

Simplifying the equation:

1/f = 0.5 * (0.0345 - 0.0238)

1/f = 0.5 * 0.0107

1/f = 0.00535

Taking the reciprocal of both sides:

f = 1 / 0.00535

f ≈ 187 cm

Therefore, the focal length of the glass lens in Figure 1 is approximately 187 cm.

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The complete question is:

Find the focal length of the glass lens in the figure (Figure 1). Take R1 = 29 cm and R2 = 42 cm Express your answer to two significant figures and include the appropriate units.

Answer:

in this form the first one next to the x is the slope and the added value is the y intercept

if something is parrell that means the same slop so

3/4

Hope This Helps!!!

Answer:

j

Step-by-step explanation:

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

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The probability that a red ace is drawn first and then a black ace is mathematically given as

x=1/4

Where

Sample mean=(x,y)\, x, y \in \{h,d,c,s\}

If we want a player to draw two cards of the same color from their deck, the following combinations of cards are appropriate choices:

\((h,h),\ (h,d),\ (d,h),\ (d,d),\ (c,c),\ (c,s),\ (s,c),\ (s,s)\)

Generally, 8 possible pairings above 16. This indicates that the likelihood of a player drawing two cards of the same color is 8/16, which is equivalent to a probability of half.

In conclusion, In a similar vein, the following pairs of cards illustrate the likelihood of obtaining a black ace after having drawn a red ace in the previous round:

\((h,c),\ (h,s),\ (d,c),\ (d,s)\)

Giving

x=4/16

x=1/4

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Answer:

1/4

Step-by-step explanation:

Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

Answer:

yₙ₊₁ = yₙ + 15

Step-by-step explanation:

→ Identify the common difference between each term

15

→ Write the nth term

yn + 15

Answer:

Hey there!

p(x)=7x+25

7x+25=60

7x=35

x=5

Let me know if this helps :)

The correlation between the two variables of interest is 0.81, which is significant at the 0.0337 level. This means that there is a strong positive relationship between the variables, and the likelihood of obtaining a correlation of 0.81 or higher due to chance alone is less than 3.37%.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient of 0.81 indicates a strong positive relationship between the variables. The significance level of 0.0337 suggests that the observed correlation is unlikely to occur by chance alone.

It implies that there is evidence to support the conclusion that the correlation is statistically significant and not just a result of random variation. Therefore, the correlation of 0.81 is considered meaningful and reliable in representing the relationship between the variables.


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The height of the cup is approximately 7.64 cm.

Let's begin with some basic geometry. The circumference of a circle is the distance around its edge, and is given by the formula C = 2πr, where r is the radius of the circle.

C = 2πr

17.2 = 2πr

r = 17.2 / 2π

r ≈ 2.74

Now that we know the radius of the cup, we can use the formula for the volume of a cylinder to find its height. The volume of a cylinder is given by the formula V = πr²h, where h is the height of the cylinder.

V = πr²h

210 = π(2.74)²h

h ≈ 7.64

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Answerh

Step-by-step explanation:

huh

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope, b is the y-intercept (when x=0).

so, the solution is already fully defined for us :

y = -9x/5 - 4 or (-9/5)x - 4

The spherical coordinate system is the most suitable system of coordinates to describe the spherical shell between two concentric spheres centered at (4,1,2).

A system of coordinates is a set of numbers used to describe the position of a point in space. There are different types of coordinate systems, each with its own advantages and disadvantages.

The spherical shell is the region of space between two spheres with the same center, but different radii. In this case, the center of both spheres is at (4,1,2) and the inner sphere has a radius of 7 while the outer sphere has a radius of 13.

One of the most commonly used coordinate systems for describing spheres is the spherical coordinate system.

To use this system of coordinates to describe the spherical shell, we first need to determine the radial distance for each point in the shell. This distance is between 7 and 13, since the shell lies between the inner and outer spheres.

Therefore, to describe a point in the spherical shell using spherical coordinates, we use the radial distance, polar angle, and azimuthal angle. These coordinates can then be used to plot the spherical shell and understand its geometry and properties.

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the control limits for the x-bar chart are 9.7439 minutes (LCL) and 11.0561 minutes (UCL), and the control limits for the R chart are 0 minutes (LCL) and 2.0529 minutes (UCL).

To compute the control limits for the x-bar (mean) and R (range) charts, we'll use the following formulas:

For the x-bar chart:

Upper Control Limit (UCL) for x-bar = x-double-bar + A2 * R-bar

Lower Control Limit (LCL) for x-bar = x-double-bar - A2 * R-bar

For the R chart:

Upper Control Limit (UCL) for R = D4 * R-bar

Lower Control Limit (LCL) for R = D3 * R-bar

Where:

x-double-bar = Overall mean of the sample means

R-bar = Overall mean of the sample ranges

A2 = Constant from the control chart constants table

D4 = Constant from the control chart constants table

D3 = Constant from the control chart constants table

For sample sizes of 4, the control chart constants are as follows:

A2 = 0.729

D4 = 2.281

D3 = 0

Given the information you provided:

Overall mean (x-double-bar) = 10.4 minutes

Average range (R-bar) = 0.9 minutes

Let's calculate the control limits:

For the x-bar chart:

UCL for x-bar = 10.4 + 0.729 * 0.9

             = 10.4 + 0.6561

             = 11.0561 minutes

LCL for x-bar = 10.4 - 0.729 * 0.9

             = 10.4 - 0.6561

             = 9.7439 minutes

For the R chart:

UCL for R = 2.281 * 0.9

         = 2.0529 minutes

LCL for R = 0

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Answer:

2j-20

Step-by-step explanation:

Multiply 2 into the parenthesis. So 2(j) -2(10).

This equals 2j-20.

To use the upper and lower sums to approximate the area of a region, we need to first divide the region into subintervals of equal width. Let's say we have n subintervals.

The lower sum is the sum of the areas of rectangles whose heights are the minimum value of y in each subinterval. The upper sum is the sum of the areas of rectangles whose heights are the maximum value of y in each subinterval.

To approximate the area using the lower sum, we would calculate:

lower sum = (width of subinterval) x (minimum y value in subinterval) for each subinterval
area = sum of lower sums for all subintervals

To approximate the area using the upper sum, we would calculate:

upper sum = (width of subinterval) x (maximum y value in subinterval) for each subinterval
area = sum of upper sums for all subintervals

It's important to note that as the number of subintervals increases, the accuracy of our approximation improves. However, it also increases the amount of calculation needed. Therefore, we must find a balance between accuracy and efficiency in our calculations.

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Answer:

x=16

y=18

i took it :)

The value of x and y are x = 18 and y = 16.

The complete ratio is 18/a = a/16.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

Given:

In ΔABC and ΔBDC,

∠ABC ≅ ∠BDC (right angle)

BC ≅ BC = a (reflexivity)

∠ACB ≅ ∠BCD (same angle)

ΔABC ≅ ΔBDC.

Hence, ΔABC ~ ΔBDC

The ratio of the corresponding sides is constant.

AC/BC = BC/CD

Substituting all the given values, we get,

18/a = a/16.

Comparing the above ratio with the given ratio x/a = a/y,

we get,

x = 18 and y = 16.

Therefore, x = 18 and y = 16.

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Answer: -3.

Step-by-step explanation: To solve this problem, we need to find the value of w, which is the y-coordinate of the point (–4, w) on the line with a slope of 6. We can do this by using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line, x and y are the coordinates of a point on the line, and b is the y-intercept (the point where the line intersects the y-axis).

In this case, we are given that the slope of the line is 6 and that the line passes through the point (–4, w). We can use this information to write the equation for the line as: y = 6x + b

Substituting the coordinates of the point (–4, w) into the equation, we get: w = 6 * (-4) + b

Solving for b, we get: b = w - 24

Next, we are given that the line also passes through the point (–3, 9). Substituting the coordinates of this point into the equation for the line, we get: 9 = 6 * (-3) + b

Substituting the value of b that we found earlier, we get: 9 = 6 * (-3) + w - 24

Solving for w, we get: w = -3

Therefore, the value of w is -3.

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The expected cost of accepting or rejecting a person in fingerprint verification is defined using the cost matrix. The threshold for accepting a person is K = ca/(ca+cr). This is computed for the Supermarket and CIA applications.

The expected cost of accepting the person is the probability that the person is an intruder (i.e., g(x) ≤ 0.5) multiplied by the cost of accepting an intruder (ca), plus the probability that the person is the correct person (i.e., g(x) > 0.5) multiplied by the cost of accepting the correct person (0). Thus,

cost(accept) = P(y=-1 | x)ca + P(y=+1 | x)0

= (1 - g(x))ca

Similarly, the expected cost of rejecting the person is the probability that the person is the correct person (i.e., g(x) > 0.5) multiplied by the cost of rejecting the correct person (cr), plus the probability that the person is an intruder (i.e., g(x) ≤ 0.5) multiplied by the cost of rejecting an intruder (0). Thus,

cost(reject) = P(y=+1 | x)cr + P(y=-1 | x)0

= g(x)cr

To minimize the expected cost, we should accept the person if the cost of accepting is less than or equal to the cost of rejecting. Thus, we should accept the person if:

(1 - g(x))ca ≤ g(x)cr

Simplifying this inequality, we get:

g(x) ≥ ca / (ca + cr)

Thus, the threshold K should be set to K = ca / (ca + cr).

For the Supermarket application, we have ca = 1 (i.e., it costs $1 to investigate a customer who is actually innocent) and cr = 100 (i.e., it costs $100 to miss a thief who is actually stealing). Therefore, the threshold should be set to:

K = 1 / (1 + 100) = 0.0098

This means that the Supermarket should accept a customer only if the estimated probability that they are innocent is greater than 0.0098.

For the CIA application, we have ca = 0 (i.e., it is free to investigate a person who is actually an intruder) and cr = 1 (i.e., it costs $1 to reject a correct person). Therefore, the threshold should be set to:

K = 0 / (0 + 1) = 0

This means that the CIA should accept a person if the estimated probability that they are the correct person is greater than 0 (i.e., always accept).

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By identifying the vertex of the function, we conclude that it is decreasing for:

\(x < -3\)

Here we have an absolute value function:

\(f(x) = -|x + 3| - 4\)

This absolute value function has a positive coefficient, which means that the function opens downwards, so it looks like a regular "down" letter.

The function is decreasing when, reading from right to left, we see that the line goes downwards. And for functions like this, this happens for values of x smaller than the vertex x-value.

For:

\(f(x) = -|x + 3| - 4\)

The vertex is at (-3, -4)

Then the function is decreasing for \(x < -3\)

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the integrand in terms of u becomes e^u.To rewrite the integrand (12x - 1)e^(6x^2 - x) in terms of u, we substitute u = 6x^2 - x.

First, we find the derivative of u with respect to x:

du/dx = 12x - 1

Rearranging the equation, we have dx = (1 / (12x - 1)) du.

Substituting dx and u into the original integrand:

(12x - 1)e^(6x^2 - x) dx = (12x - 1)e^u (1 / (12x - 1)) du.

Simplifying further:

= e^u du.

Therefore, the integrand in terms of u becomes e^u.

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The advantage of using the range as a measure of variability is that it provides an account of the dataset's most extreme values.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. By considering the minimum and maximum values, the range gives us an idea of the spread or dispersion of the data.

It provides information about the dataset's most extreme values, allowing us to understand the range over which the data values vary.

However, it's important to note that the range has limitations as a measure of variability. It only considers the minimum and maximum values and does not take into account the distribution or the values in between.

It does not provide a comprehensive summary of the patterns with which values cluster within the distribution, and it does not capture the shape of the distribution.

Therefore, while the range is a simple and straightforward measure of variability, it may not fully represent the overall characteristics of the dataset.

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Answer:

90 i think :)

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

By reasoning, we can say 50% of 200 is 100

We can say 10% of 200 is 20

We divide 20 by 2 to get 5%

20/2

= 10

Subtract 100 by 10

100 - 10

= 90

45% of 200 is 90

Answer:

C. y=x

Step-by-step explanation:

If you use a graphing calculator and plot the points (-3,5) & (5,-3) and then graph y=x you can see it is the line of reflection.

Also when reflecting over the line y=x, we switch our x and y.

The approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent is 4.7%

The percentage of light remaining is calculated from the percentage of light remaining after a depth of one foot each.

Percentage of light remaining after 1 feet = 100 - 40% = 60%.

Percentage of light remaining after 6 feet = 60% × 60% × 60% × 60% × 60% × 60% = 4.7%

Therefore, the approximate percentage of light remaining after passing through 6 feet of water, to the nearest tenth of a percent is 4.7%.

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Answer and Step-by-step explanation:

Okay, we are given a number, n, which is then added to 15 less than 3 times itself.

Let's break this apart.

n will be added to (+) 15 less (-) than 3 times itself (x)

3 times itself would be 3n, and 15 less than 3 times itself (3n) would be 3n - 15.

n is added to this value: n + 3n - 15 = 4n - 15

Now we need to put this into an equation, where the expression we created will be equal to a number, which is given to be 101.

4n - 15 = 101  <-- This is the equation that would be used to find the value of n.

I hope this helps!
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