P(T≥ 1) = P(T = 1) + P(T= 2) = 2/4+1/4

\(8(6x-7)<5(9x-4)\\\\\implies 48x- 56<45x -20\\\\\implies 48x-45x -56<-20\\\\\implies 3x < -20 +56\\\\\implies 3x<36\\\\\implies x < \dfrac{36}3\\\\\implies x<12\\\\\text{Interval,}~ (-\infty,12)\)

Step-by-step explanation:

If I'm not wrong it should be 27.93

The proof demonstrates that given a well-ordered set W, an isomorphic ordinal can be found using the function F. The uniqueness of this ordinal is established using the Replacement Axioms. The set F(W) is shown to exist for each x in W, and if the least F(W) exists, it serves as an isomorphism of VV onto -y.

Lemma 2.7: This is a previously stated lemma that is referenced in the proof. Unfortunately, without the specific details of Lemma 2.7, it's difficult to provide further explanation for its role in the proof.

Well-ordered set W: A well-ordered set is a set where every non-empty subset has a least element. In this proof, W is assumed to be a well-ordered set.

Isomorphic ordinal: An ordinal is a mathematical concept that extends the notion of natural numbers to represent order and magnitude. An isomorphic ordinal refers to an ordinal that has a one-to-one correspondence or mapping with another ordinal, preserving their order and magnitude properties.

Function F: The function F is defined to assign an ordinal o to each element x in W. This means that for every x in W, there is a corresponding ordinal o.

Existence and uniqueness: The proof asserts that if there exists an ordinal o that is isomorphic to a specific initial segment of the ordinal VV (the set of all ordinals), then this ordinal o is unique. In other words, there is only one ordinal that can be mapped to the initial segment of VV given by x.

Replacement Axioms: The Replacement Axioms are principles in set theory that allow the construction of new sets based on existing ones. In this case, the Replacement Axioms are used to assert that the set F(W) exists, which is the collection of all ordinals that can be assigned to elements of W.

For each x in W: The proof states that for every x in W, there exists an ordinal o that can be assigned to it. If there is no such ordinal, the proof suggests considering the least x for which such an ordinal does not exist.

The least F(W): The proof introduces the concept of the least element in the set F(W), denoted as the least F(W). If this least element exists, it serves as an isomorphism (a one-to-one mapping) of the set of all ordinals VV onto the ordinal -y.

Overall, the proof outlines the existence and uniqueness of an isomorphic ordinal that can be obtained from a well-ordered set W using the function F, and it relies on the Replacement Axioms and the concept of least element to establish this result.

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Answer:

The answer would be "j"

Step-by-step explanation:

First, you would want to find the value of the original equation:

5(y + 2) + 4

Use order of operations and distribute the five.

5y + 10 + 4

5y +14

This is the value of the original equation

Now we can work through the other options, but because we already know the answer, lets see about that one.

5 x y + 5 x 2 + 4

Again, use order of operations.

Multiply first

5y + 10 + 4

and complete the equation

5y + 14, which equals our original equation.

\( \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4\)

Answer:

Im pretty sure its C.

Step-by-step explanation:

because 8/2 could be 8 to the power of 2

sorry if wrong :(

Answer:

That would be 1

Step-by-step explanation:

To get 13 out of 14 you must add 1.

Let's see the sketch:

The function is differentiable at x = 0 as you can see from the graph. It doesn't have any cusp or discontinuity.

Now, to find the derivate, we use the bottom function (as x = 0 falls in this).

So,

The derivative is -1

Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

Answer:

It's option B, (f • g)(x) = 3x^3 + 6x^2 - 5x - 10

Step-by-step explanation:

In this problem, we are dealing with a branch of functions called composite functions. What the difference is between normal and composite functions is that we instead of defining a value for f(x), take two functions, f(x) and g(x), in the form of f and g. For instance, h(x) = g.

• Take the products of both functions.

f(x)g(x) = 3x²+5 • x-2

• Next, expand the functions. We expand by combining like terms.

= 3x^3 - 6x^2 + 5x - 10

Since the function cannot be simplified further, this leads to option B being our answer.

Hope this helps!

Answer:

c=-9

Step-by-step explanation:

Hello,

\((ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9\)

We can identify the like terms so:

a = 4

b-3a = c

3b = 9 <=> b = 3

So c = 3 - 3*4 = 3-12 = -9

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Answer:

D. H_0: μ > = 3 vs. H_1: μ < 3

Step-by-step explanation:

A professor of statistics at NCSU refutes the claim that the average student spends 3 hours studying for the midterm exam.

The claim is that the average student spends 3 hours studying, so the null hypothesis is that the mean is at least 3, that is:

\(H_0: \mu \geq 3\)

At the alternative hypothesis, we test if the mean is less than 3, so:

\(H_1: \mu < 3\)

This means that the correct answer is given by option D.

Answer:

b

Step-by-step explanation:

Answer: D:  y = 0

Step-by-step explanation: Hope that helped

Answer: 3 stickers

Step-by-step explanation:

From the question, we know that Pippa's 8 friends have an equal amount of stickers, meaning that the number of stickers that Pippa gave out is a multiple of 8.

Also, we are able to know that Pippa gave as much as she can, meaning that she gave out the stickers until the number is the maximum multiple of 8.

First Five Multiple of 8 = 8, 16, 24, 32, 40

As we can see from the list, 8, 16, and 24 are all multiples of 8, but they are not the maximum number that could fit under 35 stickers. Similarly, 40 exceeds the number of stickers Pippa has. Thus, we are left with 32.

This means, Pippa gave out 32 stickers in total, and each friend got 4 stickers.

Also, this means Pippa would keep 3 stickers for herself.

Hope this helps!! :)

Please let me know if you have any questions

Answer: Line perpendicular to  y = 2x - 5 is  y = (-1/2)x.

Step-by-step explanation:

The inverse of matrix A, if it exists, is:

A^(-1) = [7/43, 2/43; 10/43, 9/43]

To find the inverse of a matrix A, we need to determine if the matrix is invertible by calculating its determinant. If the determinant is non-zero, then the matrix has an inverse.

Given the matrix A = [9, -2; -10, 7], we can calculate its determinant as follows:

det(A) = (9 * 7) - (-2 * -10)

= 63 - 20

= 43

Since the determinant is non-zero (43 ≠ 0), we can proceed to find the inverse of matrix A.

The formula to calculate the inverse of a 2x2 matrix is:

A^(-1) = (1/det(A)) * [d, -b; -c, a]

Plugging in the values from matrix A and the determinant, we have:

A^(-1) = (1/43) * [7, 2; 10, 9]

Simplifying further, we get:

A^(-1) = [7/43, 2/43; 10/43, 9/43].

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The value of x in 7-3(2x-1)= 2x+26 is -4

Linear equation is is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line. The solutions of linear equations will generate values, which when substituted for the unknown values, make the equation true. In the case of one variable, there is only one solution. For example, the equation x + 3= 0 has only one solution as x = -3.

To find x in 7-3(2x-1)= 2x+26 ,we solve the parentheses first which will give

7- 6x+3= 2x+26

collect the like terms

-6x-2x=26-3-7

-8x= 16

divide both side by -8

-8x/-8= 16/-8

therefore x= -2

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Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

Answer:

11.993

Step-by-step explanation:

Trust

Answer:

plz help me too

Step-by-step explanation:

Answer:

The answer would be 32

Step-by-step explanation:

Hope this helps! :)

The round-off from the number 31.693 to the nearest whole number will be  32.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.

Given that the number is 31.693. After decimal, the value is between 5 to 9 so the round-off to the number will be 32.

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You're missing symbols in both of your expressions, but considering the first limit has a value of 10, I suspect you meant to write

\(\displaystyle \lim_{x\to2}(3x+4) = 10\)

(which is true) but unfortunately I am nowhere near as confident about what the second one is supposed to say. So one proof will have to do, unless you come around to editing your question.

The claim,

\(\displaystyle \lim_{x\to2}(3x+4) = 10\)

is to say that, for any given ε > 0, we can find δ (a number that depends on ε) such that whenever |x - 2| < δ, this ensures that |(3x + 4) - 10| < ε.

Roughly speaking: if x is close enough to 2, this translates to f(x) = 3x + 4 being close enough to 10. It's our job to figure out how close x needs to be to 2 in order that f(x) is close enough to 10, where the closeness to 10 is some given threshold.

We want to arrive at the inequality,

|(3x + 4) - 10| < ε

so suppose we work backwards. With some simplification and rewriting, we have

|3x - 6| = |3 (x - 2)| = |3| |x - 2| = 3 |x - 2| < ε

and so

|x - 2| < ε/3

which suggests that we should pick δ = ε/3.

Now for the proof itself:

Let ε > 0 be given, and let δ = ε/3. Then

|x - 2| < δ = ε/3

3 |x - 2| < ε

|3x - 6| < ε

|(3x + 4) - 10| < ε

and this completes the proof of the limit. QED

Answer:

the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}

please give me heart

The formula used to calculate the nth term of a geometric sequence is given to be:

From the question, we are given the following parameters:

Therefore, we can calculate the first 5 terms as follows:

First Term: 34

Second Term: -17

Third Term: 8.5

Fourth Term: -4.25

Fifth Term:

The first five terms are 34, -17, 8.5, -4.25, and 2.125.

Answer:

Step-by-step explanation:

Given:

Equation:

Each bag of onions costs $6.5

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

n=14

Step-by-step explanation:

since we need to isolate n to figure out what it equals to, what we do to one side of the equation must be done to the other side as well

therefore, we can subtract 2 from both sides of the equation to get:

n=14

I hope this helped, and if my answer was right, please mark this answer as brainliest! Thank you!

The measure of ER given by the equation ER = 21

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The measure of QE = 8x + 3   be equation (1)

The measure of ER = 4x + 1   be equation (2)

The measure of QR = 64

Now , QR = QE + ER   be equation (3)

Substituting the values of QE and ER in the equation (3) , we get

8x + 3 + 4x + 1 = 64

On simplifying the equation , we get

12x + 4 = 64

Subtracting 4 on both sides of the equation , we get

12x = 60

Divide by 12 on both sides of the equation , we get

x = 5

Substitute the value of x in equation (2) , we get

The measure of ER = 4 ( 5 ) + 1

The measure of ER = 21

Hence , the equation is ER = 21

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