Which conditional and its converse form a true biconditional?

A) If x>0, then lxl >0
B) If x=3, then x2^2=9
C) If x^2 =4, Then x=2
D) If x=19, then 2x-3=35

The correct option is option C that is the solution of the inequality is 2.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that an inequality is given y > 1.9. Here , y is a number which can be anything greater than 1.9.

Let's check which of the given options is a solution for the given inequality.

A)

-9 is a negative number whereas 1.9 is a positive number , so - 9 is not a solution to given inequality.

B)

-2 is also less than 1.9 , so this also not a solution to given inequality.

C)

2 is greater than 1.9 and it is a suitable solution to the given inequality. So , 2 is a solution of given inequality.

D)

As per the question value of y should be greater than 1.9 and not equal to 1.9 . So , this is also not a solution to given inequality.

Therefore , the correct option is option C that is the solution of the inequality is 2.

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The number 112,300 written in word form is 'one hundred twelve thousand three hundred'.

To write the number 112,300 in word form, you would write it as one hundred twelve thousand three hundred.

When writing numbers in word form, it's important to break them down into their place values and then use conjunctions such as 'and' where appropriate, typically between the hundreds and smaller units. In this case, there are no smaller units, so 'and' isn't used. Instead, we clearly express each place value starting from the highest, which is the hundred thousands, followed by the thousands, then hundreds, tens, and ones, though here the tens and ones places are zero and do not need to be included in the word form.

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Answer:

C- x=y^2-7

Step-by-step explanation:

To find the inverse of the function you can just exchange the name of the variables, change x for y and y for x..

original (direct) function: y = x^2 - 7

inverse function x = y^2 - 7

Then, the answer is the option c.

To find the z-score that satisfies the condition of 20% of the total area being to the left of z, use the z-table to locate the closest area to 0.20 and its corresponding z-score.

To find the z-score that satisfies the condition of 20% of the total area being to the left of z, you can use the z-table. First, locate the area in the table that is closest to 0.20, which is 0.1995.

The corresponding z-score is approximately -0.85.

Therefore, the z-score that best satisfies the condition is -0.85.

Answer:

A rectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. What are the dimensions of the rectangle?

length =  

22

centimeters

width =  

15

centimeters

Answer:

5

Step-by-step explanation:

Answer:

(C) Triangles BPA and DPC are congruent.

Step-by-step explanation:

It is given that In quadrilateral ABCD, diagonals AC and BD bisect one another.

We have to prove that quadrilateral ABCD is a parallelogram.

(A) The given statement is:

Angles ABC and BCD are congruent

The above statement is not correct because these angles forms the corresponding angle pair and thus are not congruent.

Hence, this option is not correct.

(B) The given statement is:

Sides AB and BC are congruent.

The above statement is not correct because the given sides are formed by the same vertex and thus cannot be equal.

Hence, this option is not correct.

(C) The given statement is:

Triangles BPA and DPC are congruent.

The above statement is correct because the given triangles are congruent by the SAS rule of congruency.

Hence, this option is correct.

(D) The given statement is:

Triangles BCP and CDP are congruent.

the above statement is  not correct because the given triangles cannot be congruent using any rule of congruency,

Hence, this option is not correct.

To calculate the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean, one must find the corresponding z-scores and use a standard normal distribution table. The probability is approximately 39.58%.

To find the probability that a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime of three years, we can use the properties of the normal distribution. We are given a mean (μ) of 3 years and a standard deviation (σ) of 2 years. We are interested in the probability that a wiper lasts less than 1.3 years (3 - 1.7) or more than 4.7 years (3 + 1.7).

First, we need to calculate the z-scores for 1.3 and 4.7 years:

Z1 = (1.3 - 3) / 2 = -0.85

Z2 = (4.7 - 3) / 2 = 0.85

Using a standard normal distribution table or a calculator, we find the probabilities corresponding to these z-scores. The probability of a wiper lasting less than 1.3 years is P(Z < -0.85), and the probability of lasting more than 4.7 years is P(Z > 0.85).

Since the normal distribution is symmetric, P(Z < -0.85) is equal to P(Z > 0.85). Thus, we only need to calculate one of these probabilities and double it to find the total probability. Let's say P(Z > 0.85) = p, then the total probability is 2p.

Assuming P(Z > 0.85) = 0.1979 (from standard normal distribution tables), the total probability is:

Probability = 2 * 0.1979 = 0.3958

Therefore, the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean lifetime is approximately 0.3958 or 39.58%.

Final answer:

By standardizing the values and using a standard normal distribution table, we can find the probability to be approximately 0.7422 or 74.22%.

Explanation:

To solve this problem, we can use the normal distribution. Given that the mean lifetime of the windscreen wipers is 3 years with a standard deviation of 2 years, we want to find the probability that the wiper lasts for a time that is not within 1.7 years of the mean lifetime.

First, we need to standardize the values by calculating the z-scores.

The z-score formula is (x - mean) / standard deviation. In this case, we have x = 1.7, mean = 3, and standard deviation = 2.

Plugging in these values, we get a z-score of -0.65.

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.65.

The area under the curve to the left of -0.65 is approximately 0.2578. Since we want the probability that the wiper lasts for a time that is not within 1.7 years of the mean, we subtract this probability from 1.

Therefore, the probability is approximately 1 - 0.2578 = 0.7422, or 74.22%.

Answer:

[tex]3(k+d)[/tex]

Step-by-step explanation:

We have been given a sentence. We are supposed to represent our given statement as an expression.

Sentence:

3 times the sum of k and d.

We know that we can find sum of k and d by adding them as shown:

[tex]k+d[/tex]

Since 3 is multiplied to sum of k and d, so sum of k and d will be inside parenthesis.

[tex]3(k+d)[/tex]

Therefore, our required algebraic expression would be [tex]3(k+d)[/tex].

Final answer:

The sequence ln(2n² +1) - ln(n² +1) simplifies to ln[(2n² + 1)/(n² + 1)]. As n approaches infinity, the sequence converges and the limit is ln(2).

Explanation:

To determine whether the sequence ln(2n² +1) - ln(n² +1) converges or diverges, we can use the properties of logarithms and limits.

First, we rewrite the expression using the property of logarithms that ln(a) - ln(b) = ln(a/b).

Our sequence then becomes ln[(2n² + 1)/(n² + 1)]

As n approaches infinity, the terms 2n² and n² dominate the behavior of the sequence.

Thus, the sequence can be approximated by ln(2n²/n²), which simplifies to ln(2).

Since ln(2) is a constant, we can conclude that the sequence converges and the limit is ln(2).

Robbin needs a GPA of at least 2.5 to be unconditionally accepted into the graduate program.

To determine the undergraduate grade point average (GPA) Robbin must have to be unconditionally accepted into the program, we can set up an equation based on the information given. The criterion for acceptance is that the GMAT score plus 400 times the GPA must be at least 1800. Robbin's GMAT score is 800, so we can use the following equation:

800 + 400(GPA) ≥ 1800

We can then isolate the GPA:

400(GPA) ≥ 1800 - 800
400(GPA) ≥ 1000
GPA ≥ 1000 / 400
GPA ≥ 2.5

Using the exponential decay function for Pacific halibut, it is calculated that approximately 24.7% of the original cohort is still alive after 7 years.

To approximate the percentage of the original number of Pacific halibut still alive after 7 years, we use the exponential decay model provided, N(t) = N0e^-0.2t. Plugging in t = 7 years into the equation gives us:

N(7) = N0e^-0.2(7) = N0e^-1.4.

To find this percentage, we can multiply the value of e^-1.4 by 100%. First, we calculate e^-1.4 approximately using a calculator:

e^-1.4 ≈ 0.24660

Multiplying by 100 to get the percentage: 0.24660 × 100% ≈ 24.7%.

Therefore, approximately 24.7% of the original Pacific halibut cohort is still alive after 7 years.

Answer:

3/5

Step-by-step explanation:

i am doing the same thing right now and got it right

we have

[tex] y=\frac{2}{3} x+1 [/tex] ----------> equation [tex] 1 [/tex]

[tex] y=-\frac{2}{3} x-1 [/tex] ----------> equation [tex] 2 [/tex]

using a graph tool

we know that

the intersection point of both lines is the solution of the system

so

the solution is the point [tex] (-1.5,0) [/tex]

see the attached figure

therefore

the answer is

The solution of the system is the point [tex] (-1.5,0) [/tex]

The graph in the attached figure

The limit does not exist for this expression.

To evaluate the limit as h approaches 0 of (sin(pi/6 + h) - sin(pi/6))/h, we can use the limit definition of the derivative of sin(x).

The derivative of sin(x) is cos(x), so we can rewrite the expression as:

lim h->0 (cos(pi/6 + h) - cos(pi/6))/h

Now, we can use the limit definition of the derivative to evaluate this limit. The derivative of cos(x) is -sin(x), so we have:

lim h->0 (-sin(pi/6 + h))/h

Now, let's substitute h = 0 into the expression:

(-sin(pi/6 + 0))/0

Since sin(pi/6) = 1/2, we have:

(-1/2)/0

However, division by zero is undefined. Therefore, the limit does not exist for this expression.