MATHEMATICS COLLEGE

How to solve -2x-10x12=18

Answers

Answer 1

Answer:

Answer:

x = −69

Step-by-step explanation:

1: Simplify

−2x−(10)(12)=18

−2x+−120=18

−2x−120=18

2: Add 120 to both sides.

−2x−120+120=18+120

−2x = 138

3: Divide both sides by -2.

-2x ÷ -2 = 138 ÷ -2

x = −69

Answer 2

Answer:

Answer:

x=-69

Step-by-step explanation:

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Geometry Question Number 16

Find the length of the indicated segments of each trapezoid.

Answers

Answer:

BC = 16

EF = 23

AD = 30

Step-by-step explanation:

Determine the validity of the following argument: For students to do well in a discrete mathematics course, it is necessary that they study hard. Students who do well in courses do not skip classes. Students who study hard do well in courses. Therefore students who do well in a discrete mathematics course do not skip class.

Answers

Answer: True

Step-by-step explanation:

Let p= Students who do well in course do not skip class

q= Student who study hard do well in course

So p^q= Student who study hard and who do well in course do not skip class.

If p= true and q=true then p^q= true by discrete maths.

The argument is valid because the conclusion is logically derived from the provided premises. However, it is important to note that the validity of an argument does not guarantee the truth of its premises. The argument may be valid, but its premises could still be false.

The argument provided is valid.

The reasoning follows a valid logicalstructure, specifically a form of argument called a syllogism, where conclusions are drawn from two or more premises. Let's break it down:

"For students to do well in a discrete mathematics course, it is necessary that they study hard." This is a premise, stating that studying hard is a necessary condition for success in a discrete mathematics course.

"Students who do well in courses do not skip classes." This is another premise, suggesting that students who perform well in their courses do not miss classes.

"Students who study hard do well in courses." This is also a premise, indicating that diligent study leads to success in courses.

The conclusion drawn is: "Therefore students who do well in a discrete mathematics course do not skip class." This conclusion logically follows from the given premises. If we accept the truth of the premises, we must also accept the truth of the conclusion.

To learn more about argument

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A statistic is a characteristic of a sample while a parameter is usually an unknown population parameter?True

False

Answers

This should be Correct-

Answer:

True

Explanation:

A statistic is a characteristic of a sample, a portion of the target population. A parameter is a fixed, unknown numerical value, while the statistic is a known number and a variable which depends on the portion of the population.

Parameter Definition: a quantity or statistical measure that, for a given population, is fixed and that is used as the value of a variable in some general distribution or frequency function to make it descriptive of that.

Population: The mean and variance of a population are population parameters.

Statistic Definiton: A statistic or sample statistic is any quantity computed from values in a sample that is used for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average of sample values is a statistic.

The answer is: true

Hope this helps! Happy holidays;)

The probabilities of poor print quality given no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0, 0.3, 0.4, and 0.6, respectively. The probabilities of no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0.8, 0.02, 0.08, and 0.1, respectively. a. Determine the probability of high ink viscosity given poor print quality.
b. Given poor print quality, what problem is most likely?

Answers

Answer and explanation:

Given : The probabilities of poor print quality given no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0, 0.3, 0.4, and 0.6, respectively.

The probabilities of no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0.8, 0.02, 0.08, and 0.1, respectively.

Let the event E denote the poor print quality.

Let the event A be the no printer problem i.e. P(A)=0.8

Let the event B be the misaligned paper i.e. P(B)=0.02

Let the event C be the high ink viscosity i.e. P(C)=0.08

Let the event D be the printer-head debris i.e. P(D)=0.1

and the probabilities of poor print quality given printers are

$P(E|A)=0,\ P(E|B)=0.3,\ P(E|C)=0.4,\ P(E|D)=0.6$

First we calculate the probability that print quality is poor,

$P(E)=P(A)P(E|A)+P(B)P(E|B)+P(C)P(E|C)+P(D)P(E|D)$

$P(E)=(0)(0.8)+(0.3)(0.02)+(0.4)(0.08)+(0.6)(0.1)$

$P(E)=0+0.006+0.032+0.06$

$P(E)=0.098$

a. Determine the probability of high ink viscosity given poor print quality.

$P(C|E)=(P(E|C)P(C))/(P(E))$

$P(C|E)=(0.4* 0.08)/(0.098)$

$P(C|E)=(0.032)/(0.098)$

$P(C|E)=0.3265$

b. Given poor print quality, what problem is most likely?

Probability of no printer problem given poor quality is

$P(A|E)=(P(E|A)P(A))/(P(E))$

$P(A|E)=(0* 0.8)/(0.098)$

$P(A|E)=(0)/(0.098)$

$P(A|E)=0$

Probability of misaligned paper given poor quality is

$P(B|E)=(P(E|B)P(B))/(P(E))$

$P(B|E)=(0.3* 0.02)/(0.098)$

$P(B|E)=(0.006)/(0.098)$

$P(B|E)=0.0612$

Probability of printer-head debris given poor quality is

$P(D|E)=(P(E|D)P(D))/(P(E))$

$P(D|E)=(0.6* 0.1)/(0.098)$

$P(D|E)=(0.06)/(0.098)$

$P(D|E)=0.6122$

From the above conditional probabilities,

The printer-head debris problem is most likely given that print quality is poor.

Answer:

Answer of Part(a) is 16/49

and Answer of Part(b) is Printer-head debris

Step-by-step explanation:

Answer is in the following attachment

This Venn diagram represents the science subjects studied by students what is the probability chosen at random that that child does not study chemistry

Answers

Answer:

Step-by-step explanation:

Looking at the Venn diagram,

The total number of students surveyed is 7 + 5 + 8 + 6 + 2 + 4 + 3 + 6 = 41

The number of children that studies none of the subjects is 6

The number of children that study only biology is 7

The number of children that study only physics is 5

The number of children that study only physics and biology is 2

Therefore, the number of students that do not study chemistry is 6 + 7 + 2 + 5 = 20

Probability = number of favorable outcomes/total number of outcomes

Therefore, the probability that a child chosen at random does not study chemistry is 20/41 = 0.49

Suppose that P dollars in principal is invested for t years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period.=P$10,000, =t112 yr

(a) 1% interest

(b) 4% interest

(c) 4.5% interest

Answers

Answer: (a )$30648.54 (b)$882,346.73 (c) $1,544,700.15

Step-by-step explanation:

Formula: $A=Pe^(rt)$ , where P= principal , r=rate of interest, t= time

Given : P= $10,000, t = 112 years

(a) r = 1% = 0.01

$A=(10000)e^(0.01*112)$

$A=(10000)e^(1.12)=10000(3.06485420)\approx 30648.54$

Hence, Amount = $30,648.54

(b) r = 4% = 0.04

$A=(10000)e^(0.04*112)$

$A=(10000)e^(4.48)=10000(88.2346726757)\approx 882346.73$

Hence, Amount = $882,346.73

(c) r = 4.5% = 0.045

$A=(10000)e^(0.045*112)$

$A=(10000)e^(5.04)=10000(154.470015026)\approx 1544700.15$

Hence, Amount = $1,544,700.15

Final answer:

For 1% interest, the investment will be worth $10100.50. For 4% interest, it will be worth $10420.96, and for 4.5% interest, it will be worth $10451.65.

Explanation:

To determine the amount that an investment is worth at the end of a given time period with continuous compounding, we can use the formula A = P * e^(rt), where A is the final amount, P is the principal, r is the interest rate, and t is the time in years.

(a) For 1% interest:

A = 10000 * e^(0.01 * 1) = $10100.50

(b) For 4% interest:

A = 10000 * e^(0.04 * 1) = $10420.96

A = 10000 * e^(0.045 * 1) = $10451.65

Learn more about Continuous compounding here:

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