Two old RSM students were standing ten feet apart when they ran in opposite directions with speeds of 180 feet per minute and 160 feet per minute respectively, how many minutes would pass before they were 1870 feet apart?

Mathematics is a discipline that has a long and rich history. It has evolved over time from simple counting and measuring to a broad and complex subject that is used in many fields. The development of mathematics has been driven by the need to solve practical problems, as well as the desire to understand the underlying patterns and structures of the world around us.

Early forms of mathematics, such as counting and measuring, were developed by ancient civilizations to solve practical problems such as trade, construction, and agriculture. These early forms of mathematics were based on empirical observations and were often tied to the physical world.

As mathematics developed, it began to include more abstract concepts such as numbers, geometry, and algebra. These abstract concepts allowed for the development of more complex mathematical techniques and the ability to solve a wider range of problems.

Today, mathematics is used in a wide range of fields including science, engineering, economics, and even art. It is an essential tool for understanding and solving problems in the world around us.

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"s" can be concluded from the premises

To use the rules of inference to show that "s" is a conclusion, we can use modus ponens,

This is a rule that allows us to infer a conclusion from a premise and its conditional statement.

Thus, "s" can be concluded from the premises "p → q", "q → r", "(q → r) → s", and "p".

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Answer:

Domain { -1,3}

Range { 2,5,6}

Step-by-step explanation:

The domain is the inputs or the x values

Domain { -1,3}

we dont list repeated values  more than once

The range is the output values

Range { 2,5,6}

Answer:

Step-by-step explanation:

domain:{-1, 3}

range:{2, 5, 6}

A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.

a) The sample space is given as:

Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.

b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.

{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}

c) find the set b corresponding to the event number of dots in the first toss is 6.

{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

e) a does not imply b or does b imply a.

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Answer:

B. A payday loan for $1500 that is due in 10 days with a fee of $90, since it has the shorter period

The higher effective interest rate is for  A payday loan for $1500 that is due in 10 days with a fee of $90, since it has the shorter period, the correct option is B.

Interest Rate is the rate at which a person either takes loan, or a person lends money to somebody.

The interest rate is different for different types of loans, some interest are simply calculated on the principal, called as Simple Interest while some are calculated on both the principal and the interest, called as Compound Interest.

A payday loan has principal of $1500

It is due in 12 days, so time period is 12 days.

The interest amount is $90

I = P * R *T / 100

90 = 1500 *12 *R /100

R = 0.5 %

A payday loan has principal of $1500

It is due in 10 days, so time period is 10 days.

The interest amount is $90

90 = 1500 *10 *R /100

R = 0.6 %

The rate of interest  is more for a payday loan for $1500 that is due in

10 days with a fee of $90.

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Answer:

$0.90 per pen

2.70/3=.90

Answer:

Answer:

its 3/10

Step-by-step explanation:

V = 3/10

3

--

10

Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.

The mean refers to the average value.

The average is the quotient of the total value divided by the number of items in the data set.

The number of boys in the class = 26

The number of girls in the class = 20

The total number of boys and girls in the class = 46

The mean number of counters that the boys have = 28

The total number of counters that the boys have = 728 (28 x 26)

The mean number of counters that the girls have =19

The total number of counters that the girls have = 380 (19 x 20)

The total number of counters that the class has = 1,108 (728 + 380)

The average or mean number of counters in the class = 24 (1,108 ÷ 46)

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Answer:

P(A∩B) = 0

P(A) = 0.1667

P(B) = 0.8333

=================================================

Explanation:

The events

are mutually exclusive. There isn't any overlap. This is because event B involves "at least 2 rolls", meaning we cannot get 5 on the first roll. Either event A happens, or B does, but not both at the same time.

This allows us to say P(A∩B) = 0

In a venn diagram, the overlapped region between circles A and B would have probability 0 marked inside.

-----------------------

P(A) = 1/6 since there is exactly one side labeled "5" out of 6 sides total. This converts to the approximate decimal form 1/6 = 0.1667 when rounding to four decimal places. The 6's go on forever, but of course we have to round at some point.

------------------------

We found that P(A) = 1/6. The complement to this is 1-(1/6) = 5/6, which is the probability of rolling anything but a "5". This fraction represents the scenario "at least 2 rolls are needed for the 1st '5' to show up" since we forced the first roll to be anything but 5.

Put another way, we have two options:

The two probabilities 1/6 and 5/6 add to 6/6, aka 1, to represent 100% of all possible cases. This means P(A)+P(B) = 1 for this scenario.

The fraction 5/6 converts to the approximate decimal form of 5/6 = 0.8333; use a calculator or long division to determine this value.

Answer:

60

Step-by-step explanation:

base times height

Answer:

the quotient is 2

Step-by-step explanation:

4/1=4

4/2=2

Answer:

$305.25 divided by $9.25 equals 33, so he worked 33 hours... hope this helped.

Step-by-step explanation:

Answer:

33 is the answer

Step-by-step explanation:

The calculated volume of the prism is 702 cubic cm

From the question, we have the following parameters that can be used in our computation

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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The upper bound of a 99% confidence interval is found as 57.07.

A random sample of size 18.

Normal population gives 36.5.

Explain the term upper confidence bound (UCB)?

Whenever a machine is often used frequently than other machines, the border shrinks.

For the stated question-

sample size n = 18

normal population mean x = 36.5

variance  s² = 1148; s = 33.88

z(α/2) for 99% confidence interval = 2.576

Thus, upper confidence bound (UCB) is estimated as;

UCB = \(x + z(\frac{\alpha}{2} )*\frac{s}{\sqrt{n} }\)

UCB = 36.5 + 2.576×33.88/√18

UCB = 36.5 + 20.57

UCB = 57.07

Therefore, the upper bound of a 99% confidence interval is found as 57.07.

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A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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The matching expressions are:

\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)

i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.

ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.

iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.

To understand the matching expressions, let's break down each one:

i) 3a x 4:

This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).

ii) a^2 x a:

This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).

iii) 6 × 1/2 a^2:

This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).

Therefore, the matching expressions are:

i) 3a x 4 = C (12a)

ii) a^2 x a = A (a^3)

iii) 6 × 1/2 a^2 = D (3a^2)

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\((-20, -4)\) and are all of the ordered pairings that fulfil this equation \(F = 9/5C + 32. (-10, 14)\).

Lines come in two varieties: identities and dependent equations. All possible values of the parameters result in an identity. Only certain combinations of the variables' values render a conditional equation true. Two expressions joined by the equals symbol ("=") form an equations.

Ax+By=C is the classic pattern for two-variable linear equations. A typical form linear equation is, for instance, 2x+3y=5. Finding all intercepts of a solution in this format is not too difficult. The approach additionally proves useful when trying to solve solutions combining two linear systems.

To find the missing y values, we need to substitute the given \(x\) values into the equation \(F = 9/5C + 32\) and solve for \(F\).

For the first ordered pair (-20, F1):

\(F1 = 9/5(-20) + 32\)

\(F1 = -36 + 32\)

\(F1 = -4\)

So the missing y value is \(-4\), and the complete ordered pair is \((-20, -4)\).

For the second ordered pair (-10, F2):

\(F2 = 9/5(-10) + 32\)

\(F2 = -18 + 32\)

\(F2 = 14\)

So the missing y value is \(14\), and the complete ordered pair is \((-10, 14)\).

Therefore, the complete set of ordered pairs that satisfy the equation \(F = 9/5C + 32\) is:

\((-20, -4)\) and \((-10, 14)\).

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The complete question is:

Given the equation

F=9,5

C+32

F=95C+32

where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:

(−20,F1)

(−20,F1),(−10,F2)(−10,F2)

Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equation.

Answer:

y = 78

Step-by-step explanation:

66 + 4 = 70 + 4 = 74 + 4 = 78

-12 + 3 = -9 + 3 = -6 + 3 = -3

x = -3

y = 78

Answer:

The answer is 50.

Step-by-step explanation:

Use MDAS

Multiplication, Division, Addition and Subtraction

2 + 6 * 8 =

Multiply first then add

2 + 6*8 = ?

= 2 + 48

= 50

Answer:

-4

Step-by-step explanation:

Answer:

\( \frac{2}{3} \)

Step-by-step explanation:

(9x+3)=9

9x+3=9

9x. =9-3

9x=6

\( \frac{9x}{9} = \frac{6}{9} \)

\(x = \frac{6}{9} \)

\(x = \frac{2}{3} \)

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Apply the exponent rules for each one:

When a number is raised by negative value, it changes to a fraction with the denominator raised to the power:

A number raised by 0 always = 1

1. 7^-2 = 1/7^2 = 1/49

2. 15^0 = 1

3. 10^-3 = 1/10^3 = 1/1000

4. 2^-5 = 1/2^5 = 1/32

5. 5^-3 = 1/5^3 = 1/125

6. 7^3 = 7x7x7 = 343

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

The mean and variance of X are 2.82 and 0.1692  respectively

Step-by-step explanation:

The binomial distribution is a discrete probability distribution that tells the percentage in which a result is likely to be obtained between two possibilities when performing n number of tests. In other words, a binomial distribution is a discrete probability distribution that describes the number of successes when conducting n independent experiments on a random variable.

In a binomial distribution, the mean indicates the mean value of a random phenomenon. It is calculated by:

μ=n*p

Where:

This case is a binomial distribution, where n = 3 and p = 0.94. Then:

μ=3*0.94

μ=2.82

The mean of X is 2.82.

Variance is a measure of dispersion that represents the variability of a data series with respect to its mean. It is calculated by:

Var[X]= n*p*q

Where:

Remembering that the random variable X expresses the number of successes obtained when performing "n" independent Bernouilli tests or tests with probability "p" of success and "(1-p)" of failure, then q = 1-p.

So:

Var[X]= n*p*(1-p)

In this case:

Var[X]=3*0.94*(1-0.94)

Var[X]=3*0.94*0.06

Var[X]=0.1692

The variance of X is 0.1692