Explain in a minimum of 2 sentences how to graph the equation of the absolute value function given a vertex of (-1,3) and a value of “a” equal to ½.

I believe the parts are:

A. What is the probability that Upper X greater than 95X>95​?

B. What is the probability that Upper X less than 75X<75?

C.What is the probability that Upper X less than 85X<85 and Upper X greater than 125X>125?

D. 95​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)?

Solution:

We use the equation for z score:

z = (X – μ) / σ

Then use the standard normal probability tables to locate for the value of P at indicated z score value.

A. Z = (95 – 100) / 10 = - 0.5

Using the tables, the probability at z = -0.5 using right tailed test is:

P = 0.6915

B. Z = (75 – 100) / 10 = - 2.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0062

C. Z = (85 – 100) / 10 = - 1.5

Using the tables, the probability at z = -2.5 using left tailed test is:

P = 0.0668

Z = (125 – 100) / 10 = 2.5

Using the tables, the probability at z = 2.5 using right tailed test is:

P = 0.0062

So the probability that 85<X and X>125 is:

P(total) = 0.0668 + 0.0062

P(total) = 0.073

D. P(left) = 0.025, Z = -1.96

P(right) = 0.975, Z = 1.96

The X’s are calculated using the formula:

X = σz + μ

At Z = -1.96

X = 10 (-1.96) + 100 = 80.4

At Z = 1.96

X = 10 (1.96) + 100 = 119.6

So 95% of the values are between 80.4 and 119.6 (80.4< X <119.6).

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability that a warning would be given is 0.97.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

A hospital has three independent fire alarm systems, with reliabilities of 0.95, 0.97, and 0.99.

This means,

The probability that one alarm will give a warning = 0.95

The probability that one alarm will give a warning = 0.97

The probability that one alarm will give a warning = 0.99

Combining each of them we get,

0.95 + 0.97 + 0.99 = 2.91

Divide by 3.

= 2.91 / 3

= 0.97

This means,

The probability that a warning would be given is 0.97.

Thus,

The probability that a warning would be given is 0.97.

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Answer:

F(1) is not defined

Step-by-step explanation:

we know that

The equation in vertex form of a vertical parabola is of the form

[tex]y=a(x-h)^{2}+k[/tex]

where

[tex](h,k)[/tex] is the vertex of the parabola

and

[tex]x=h[/tex] is the axis of symmetry

if [tex]a > 0[/tex] -----> open upward

if [tex]a < 0[/tex] -----> open downward

In this problem we have

[tex]y=3(x+2)^{2}-3[/tex]

[tex]a=3[/tex]

This is a vertical parabola open upward

The vertex is a minimum

therefore

the answer is

the vertex is the point [tex](-2,-3)[/tex]

the axis of symmetry is [tex]x=-2[/tex]

see the attached figure to better understand the problem

The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].

Further Explanation:

The standard form of the parabola is shown below.

[tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]

Here, the parabola has vertex at [tex]\left({h,k}\right)[/tex] and has the symmetry parallel to x-axis and it opens left.

Given:

The quadratic function is [tex]y=3{\left({x+2}\right)^2}-3[/tex].

Calculation:

Compare the [tex]y=3{\left({x+2}\right)^2}-3[/tex] with the general equation of the parabola [tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]

.

The value [tex]a[/tex] is [tex]3[/tex], the value of [tex]h[/tex] is [tex]-2[/tex] and the value of [tex]k[/tex] is [tex]-3[/tex].

Therefore, the vertex of the parabola is [tex]\left({-2,-3}\right)[/tex].

The function is symmetric about [tex]x=-2[/tex].

The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Conic sections

Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola,

The average number of pairs of adjacent cards in a well-shuffled 52-card deck that are both red is about 12 or 13 pairs. This is calculated based on the probability of drawing red cards.

In a well-shuffled 52-card deck, there are 26 red cards out of the total 52 cards. Thus, the probability of drawing a red card is 26/52 = 0.5.

Now, let's consider two neighboring cards as an ordered pair. There are 51 such pairs in a 52-card deck. We are looking for pairs where both cards are red. The probability that the first card of any given pair is red is 0.5, as already noted. The probability that the next card (in that pair) is also red, assuming the first one is red, is now 25/51 (since one red card is assumed as taken already).

Thus, the probability that a given pair of adjacent cards are both red is 0.5 * (25/51) = 25/102 ≈ 0.245.

Given that we have 51 possible pairs, the expected number of red pairs is 51 * (probability of red pair) which equals about 12.48.

Therefore, on average, you can expect about 12 or 13 pairs of adjacent cards to be both red.

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The number of the fraction 3/8 that we can get in 6, is: 16.

We are asked to find how many of the fraction, 3/8, we will have in 6.

This implies that, what number would we need to multiply with 3/8 to get 6?

To determine this, all we need to do is to divide 6 by the fraction, 3/8.

[tex]6 \div \frac{3}{8}[/tex]

[tex]6 \times \frac{8}{3} \\\\= \frac{6 \times 8}{3} \\\\= \frac{48}{3} \\\\\mathbf{= 16}[/tex]

Therefore, the number of the fraction 3/8 that we can get in 6 is: 16.

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No Euclidean triangles can have angles that sum to more than 180°, so there are zero triangles with the given measures in Euclidean space; however, exactly one right-angled spherical triangle with these angles exists on a curved surface like a sphere.

The question asks how many triangles exist with the given angle measures of 55°, 45°, and 90°. In Euclidean geometry, the sum of the interior angles of a triangle must equal exactly 180°. Since 55° + 45° + 90° = 190°, which is greater than 180°, no Euclidean triangle can have those angle measures. Therefore, there are zero triangles that can exist with the given angle measures in a flat, two-dimensional Euclidean space.

However, in the context of spherical geometry, triangles can have angles that sum to more than 180°. The provided angles actually describe a right-angled spherical triangle, of which exactly one exists with these measures. This is because on a spherical surface, the sum of the angles of a triangle can be greater than 180° due to the curvature of the space.

Answer:

The numbers are 5 and 20.

Step-by-step explanation:

To find : What are the numbers?

Solution :

Let the one number be 'x'.

The reciprocal is [tex]\frac{1}{x}[/tex]

The another number be 'y'.

The reciprocal is [tex]\frac{1}{y}[/tex]

One number is four times another number.

i.e. [tex]x=4y[/tex] .....(1)

The sum of their reciprocals is [tex]\frac{1}{4}[/tex].

i.e. [tex]\frac{1}{x}+\frac{1}{y}=\frac{1}{4}[/tex] ....(2)

Substitute (1) in (2),

[tex]\frac{1}{4y}+\frac{1}{y}=\frac{1}{4}[/tex]

[tex]\frac{1+4}{4y}=\frac{1}{4}[/tex]

[tex]4y=20[/tex]

[tex]y=5[/tex]

One number is 4y=4(5)=20.

Therefore, the numbers are 5 and 20.

The number -0.5 divided by itself equals to 1. In general, any number (except zero) divided by itself will always equal to 1.

To find the answer to the given number −0.5/-0.5, you should simply divide the negative number -0.5 by itself (-0.5). Here, a negative number divided by another negative number results in a positive result. Therefore, -0.5/-0.5 equals 1.

In general terms, any non-zero number divided by itself will always equal 1. This is because the division operation is asking 'how many times does this number fit into itself?', and the answer is invariably 'once'.

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Answer:

A) UY

Step-by-step explanation:

From the given figure, TUYX is one of the side of the rectangular prism and UVYZ  is another side of the rectangular prism.

The both sides are intersecting perpendicular in one edge, that is the line segment UY.

You can see it on the figure.

Therefore, the intersecting line is UY.

The answer is this method is not secure but a frequency attack can be applied. Knowing the public key in this case is, nonetheless, adequate for an attacker to calculate a table, on behalf of one-to-one communication between the plaintext and the cipher text. Computed table allows him/her to decrypt any ciphertext, encoded using RSA Cryptosystem in such a means.

Encrypting each character separately in RSA is insecure due to the limited set of characters and can be compromised by frequency analysis. RSA's security typically relies on the difficulty of factorizing large numbers, but with only 26 character possibilities, patterns can emerge that allow decryption.

When Alice sends a message to Bob using the RSA cryptosystem, each alphabetic character is represented as an integer between 0 and 25 and then encrypted using RSA with a large exponent e and a large modulus n. Although this method uses a robust encryption algorithm, encrypting each character separately can be insecure due to the limited number of possible characters (26 in this case). An efficient attack against this method is a frequency analysis attack, where the attacker could exploit the fact that some letters appear more frequently in a language than others. The attacker could potentially guess the encrypted values of these common characters and use patterns to decrypt the rest of the message.

RSA encryption is one of the oldest and widely used public key encryption algorithms and relies on the difficulty of factoring very large numbers. This difficulty provides the security in RSA; however, when the encryption is done on a small set of possibilities—as is the case with single alphabetic characters—the security can be compromised, making RSA vulnerable in such a scenario.

Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place.

Hundreds place

Answer:

Step-by-step explanation:Actually we can directly check if the quotient has equal or one less amount of places than the given number. This can be checked by looking at the number on the biggest place of the dividend, if it is less than the divisor, the answer will have one less digits place. So in this case since the divisor is 4 and the greatest place of the dividend is thousands and the number is 2, so the quotient will be in the hundreds place. 

A relation that passes through the y-axis twice is not considered a function. A function, by definition, can only output one 'y' value for each unique 'x' value. This relation fails the 'vertical line test' which checks that each 'x' value only connects to a single 'y' value.

In mathematical terms, a relation is a set of ordered pairs, where each first element is related to the second element. A function, on the other hand, is a special type of relation where every input (or 'x' value) corresponds to exactly one output (or 'y' value).

Now, if a relation passes through the y-axis twice, it means that there are two 'y' values for a single 'x' value (which in this case, is zero). This violates the definition of a function. Hence, a relation that passes through the y-axis twice is not a function. It is simply a relation because it doesn't pass the 'vertical line test' (a vertical line passing through more than one point on the graph of a relation means that the relation is not a function).

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