Which inequality is equivalent to -x < -1

Answers

Answer 1

Answer:

Answer:

x > 1

Step-by-step explanation:

To find an equivalent inequality for -x < -1, you can multiply both sides of the inequality by -1. When you multiply or divide both sides of an inequality by a negative number, you need to reverse the direction of the inequality sign. Here's how it works:

Starting inequality: -x < -1

Now, multiply both sides by -1 (remember to reverse the inequality sign):

-x * (-1) > -1 * (-1)

This simplifies to:

x > 1

So, the equivalent inequality is:

x > 1

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I need help as soon as possible with the problem bellowSimplify each of the following with justifications for your answer:
a. 290 mod 26
b. 9^{-1} mod 26
c. -15 mod 26

Answers

a) 290 mod 26

We subtract the largest multiple of 26 which is less than 290. The answer we get after the subtraction is the answer.

Largest multiple of 26 is 286, because 26 * 11 = 286

290 - 286 = 4.

290 mod 26 = 4.

b). 9^(-1) mod 26 = 0.111 mod 26.

0 * 26 = 0.
The largest multiple of 26 which is less than 0.111 is 0.
We subtract this from 0.111

0.111 - 0 = 0.111

9^(-1) mod 26 = 9^(-1) = 0.111

c). -15 mod 26.

Take note this is negative numbers. But same rules applies here.

The largest multiple of 26 which is less than -15 is -26.

We subtract this from -15

-15 - (-26) = -15 + 26 = 11

-15 mod 26 = 11

Final answer:

The results of the modulo operations are: 290 mod 26 results in 2; 9^{-1} mod 26 is equivalent to 3; and -15 mod 26 equals 11.

Explanation:

To simplify each of the following with justifications:

290 mod 26: When you divide 290 by 26, the remainder is 2. Therefore, 290 mod 26 = 2.
9^{-1} mod 26: First, you need to find the multiplicative inverse of 9 in mod 26. The multiplicative inverse of an integer a modulo m is an integer b such that (ab) mod m = 1. For 9, the multiplicative inverse is 3, since (9*3) mod 26 = 27 mod 26 = 1. Therefore, 9^{-1} mod 26 = 3.
-15 mod 26: In modular arithmetic, if you end up with a negative number, you add the modulus until you get a positive result. Here, adding 26 once to -15 gives you 11. Therefore, "-15 mod 26 = 11".

Learn more about Modulo Operations here:

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a car is designed to last an average of 12 years with a standard deviation of 0.8 years. what is the probability that a car will last less than 10 years?

Answers

The probability that the car will last less than 10 years would be .0062. With the given data (M = 12, SD = .8), i computed the z-score and looked it up on the z table. The answer yields .0062 or 0.62%. Thus, the probability is very little.

Answer: 0.621%

Step-by-step explanation:

A student is offered two different summer jobs. Job A lasts 16 weeks and pays $350.00 per week. Job B lasts 4 months and pays $1,500.00 per month, with monthly raises of 10% of the previous month's salary. How much more does the student earn by accepting Job B (rounded to the nearest cent)?

Answers

The required, by accepting job B a student can earn $1361.5 more than Job A.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
Job B lasts 4 months and pays $1,500.00 per month, with monthly raises of 10% of the previous month's salary.
Total earnings in 4 months,
= 1500 + 1.1×1500 + 1.1 [1.1×1500] + 1.1×[ 1.1 [1.1×1500] ].
= $6961.5

Job A lasts 16 weeks and pays $350.00 per week.
Total earnings in 16 weeks,
= 16 × 350 = $5600

The difference in earning = Job B - Job A
= 6961.5 - 5600
= 1361.5

Thus, the required, by accepting job B a student can earn $1361.5 more than Job A.

Learn more about arithmetic here:

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Both last 4 months.

Job B = $412.50per/week

Job A = $1600per/month

1650*1.1 = 1815 Month 2's paycheck

1815*1.1 = 1996.5 Month's 3 Paycheck

1996.5*1.1 = 2196.15 Month 4's paycheck

1600*4 = $6400 Job A total

1650+1815+1996.5+2196.15 = $7657.65 Job B total

7657.65-6400 = 1257.65

$1257.65 more thant Job A

Parker is planning for a school picnic. He would like to have 2 hot dogs per person and 15 extra on hand. How many hot dogs does he need if there are 116 students and 8 teachers?

Answers

Answer: There are 263 hot dogs he needs.

Step-by-step explanation:

Since we have given that

Number of students = 116

Number of teachers = 8

Total number of persons = 116+8=124

Number of hot dogs per person = 2

Number of hot dogs extra on hand = 15

So, Total number of hot dogs will be

$124* 2+15\n\n=248+15\n\n=263$

Hence, there are 263 hot dogs he needs.

Number of person = 116+8 = 124

Now, hot dogs would be = 124*2 +15 = 248 +15 = 263

So, 263 is your answer!!!

Write an equation for the line parallel to y = –2x – 5 that contains P(–8, 4).

Answers

$k:y=-2x-5\n\nl:y=mx+b\n\nk\ ||\ l\iff m=-2\n\nl:y=-2x+b;\ P(-8;\ 4)\n\n-2\cdot(-8)+b=4\n16+b=4\nb=4-16\nb=-12\n\nAnswer:y=-2x-12$

$k:\ y = -2x -5 \ \ \ and\ \ \ l:\ y=mx+b\n\nk\ ||\ l\ \ \ \Leftrightarrow\ \ \ m=-2\ \ \ l:\ y=-2x+b\n\n P(-8, 4)\ \in\ l\ \ \ \Leftrightarrow\ \ \ 4=-2\cdot(-8)+b\n\n\ \ \ \Leftrightarrow\ \ \ 4=16+b\ \ \ \Leftrightarrow\ \ \ b=-12\ \ \ \Rightarrow\ \ \ l:\ y=-2x-12$

Two lines are perpendicular, and neither line is horizontal. Which of the following is not necessarily true of the lines?A.
The slopes of the two lines are opposite reciprocals.
B.
One line must have a positive slope.
C.
The y-intercepts are the same.
D.
One line must have a negative slope.

Answers

I think the correct answer from the choices listed above is option C. Two lines are perpendicular, and neither line is horizontal so it must be that the slopes of the lines are opposite reciprocals, one slope is positive and the other has a negative slope. Having different slopes so they should intersect the y-axis at different values.

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