Let a graph have vertices {L, M, N, O, P, Q, R, S} and edge set {{L,R}, {M,P}, {M,Q}, {N,Q}, {P,R}, {Q,S}, {R,S}} .

a. What is the degree of vertex P?

b.What is the degree of vertex O?

c.How many components does the graph have?

Final answer:

To calculate the difference in earnings between the two investments, we can use the compound interest formula to find the future value of each investment. The first investment would earn $2,353,121.65 more than the second investment.

Explanation:

To calculate the difference in earnings between the two investments, we need to calculate the future value of each investment. For the first investment, we have $22,000 invested for 40 years at an annual interest rate of 14%. Using the compound interest formula:

FV = PV * (1 + r)^n

FV = $22,000 * (1 + 0.14)^40 = $2,889,032.39

For the second investment, we have $22,000 invested for 40 years at an annual interest rate of 7%. Using the compound interest formula:

FV = PV * (1 + r)^n

FV = $22,000 * (1 + 0.07)^40 = $535,910.74

The difference in earnings between the two investments is:

$2,889,032.39 - $535,910.74 = $2,353,121.65

Answer:

1/6

Step-by-step explanation:

Slope is [tex]\frac{\text{rise}}{\text{run}}=\frac{1}{6}[/tex].

Answer:

[tex]\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}[/tex]

Step-by-step explanation:

The Cartesian product between two discrete sets, is given by all possible ordered pairs originated with the combinations of the elements of the two sets, thus the requested Cartesian product is:

[tex]\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}[/tex]

[tex]A = (11, 1)\\B = (11, 1.5)\\C = (11, 2)\\D = (21, 1)\\E = (21, 1.5)\\F = (21, 2)\\[/tex]

You can see the attached file

The diameter of 4.3 cm equals 1.677 inches and 43 millimeters. This is calculated by using the conversion factors of 0.39 for inches and 10 for millimeters.

To convert diameter from centimeters to inches and millimeters, we use the conversion factors that 1 cm equals 0.39 inches and 1 cm equals 10 millimeters.

First, let's convert into inches. Multiply the given diameter (4.3 cm) by the conversion factor (0.39). 4.3 cm * 0.39 = 1.677 inches.

Next, let's convert into millimeters. Multiply the given diameter (4.3 cm) by the conversion factor (10) for millimeters. 4.3 cm * 10 = 43 millimeters.

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Answer:

[tex]x\ =\ \dfrac{21}{5}[/tex]

[tex]y\ =\ \dfrac{3}{5}[/tex]

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

[tex]\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right][/tex]

[tex]R_2=>R_2-R_1\ and\ R_3=>R_3+R_1[/tex]

[tex]=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right][/tex]

[tex]R_2=>\dfrac{R_2}{5}[/tex]

[tex]=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right][/tex]

[tex]R_1=>R_1+2.R_2[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right][/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right][/tex]

[tex]R_3=>\dfrac{R_3}{2}[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right][/tex]

[tex]R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3[/tex]

[tex]=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right][/tex]

So, from the above augmented matrix, we can write

[tex]x\ =\ \dfrac{21}{5}[/tex]

[tex]y\ =\ \dfrac{3}{5}[/tex]

z = 2

To find the value of n, we can use the concept of combinations. By setting up and solving an equation using the combination formula, we find that the value of n is 6.

To find the value of n, we can use the concept of combinations. Since Columba has 2 dozen (24) each of n different colored beads, the total number of beads she has is 24n. If she can select 20 beads with repetitions allowed in 230,230 ways, we can set up the equation:

24n choose 20 = 230,230

To solve this equation, we need to use the concept of combinations. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items, r is the number of items being selected, and ! represents the factorial function.

Plugging in the values, we have:

24n! / (20!(24n-20)!) = 230,230

Simplifying the equation, we get:

n! / (20!(n-20)!) = 10

To find the value of n, we can try different values of n and calculate the factorial on both sides of the equation. Starting with n = 2, we have:

2! / (20!(2-20)!) = 1 / (20!(18)!) = 1 / (20!(18!)) = 1 / (20 * 19) = 1 / 380 = 0.00263

Since this value is smaller than 10, we need to try a larger value of n. By trying different values, we find that when n = 6, the equation holds:

6! / (20!(6-20)!) = 6! / (20!(14)!) = 720 / (20 * 19 * 18 * 17 * 16 * 15 * 14!) = 720 / (20 * 19 * 9 * 17 * 16 * 15) = 720 / 9909000 = 0.00007

Therefore, the value of n is 6.

Answer:

(a) 0.48, (b) 0.625, (c) 0.1923

Step-by-step explanation:

First define

Probability a person is a democrat: P(D) = 0.4

Probability a person is a republican: P(R) = 0.6

Probability a person support the measure given that the person is a democrat: P(SM | D) = 0.75

Probability a person support the measure given that the person is a republican: P(SM | R) = 0.3

Now for the Theorem of total probabilities we have

(a) P(SM) = P(SM | D)P(D)+P(SM | R)P(R) = (0.75)(0.4)+(0.3)(0.6) = 0.48

and for the Bayes' Formula we have

(b) P(D | SM) = P(SM | D)P(D)/[P(SM | D)P(D)+P(SM | R)P(R)] = (0.75)(0.4)/0.48 = 0.625

Now let SMc be the complement of support the measure, i.e.,

P(SMc | D) = 0.25 : Probability a person does not support the measure given that the person is a democrat

P(SMc | R) = 0.7: Probability a person does not support the measure given that the person is a republican,

and also for the Bayes' Formula we have

(c) P(D | SMc) = P(SMc | D)P(D)/[P(SMc | D)P(D)+P(SMc | R)P(R)] = (0.25)(0.4)/[(0.25)(0.4)+(0.7)(0.6)] = 0.1/(0.52)=0.1923

Final answer:

This detailed answer covers the calculation of probabilities regarding support for gun control based on political affiliation in a certain town in the United States.

Explanation:

a) To find the probability that a randomly selected resident supports the measure, we calculate as follows: P(support) = P(support|Democrat) ∗ P(Democrat) + P(support|Republican) ∗ P(Republican) = 0.75 ∗ 0.40 + 0.30 ∗ 0.60 = 0.45 + 0.18 = 0.63.

b) The probability that a supporter is a Democrat can be found using Bayes' theorem: P(Democrat|support) = P(support|Democrat) ∗ P(Democrat) / P(support) = 0.75 ∗ 0.40 / 0.63 = 0.4762.

c) To find the probability that a non-supporter is a Democrat: P(Democrat|non-support) = P(non-support|Democrat) ∗ P(Democrat) / P(non-support) = 0.25 ∗ 0.40 / (1 - 0.63) = 0.1.

Answer:

The set of solutions is [tex]\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}[/tex]

Step-by-step explanation:

The augmented matrix of the system is [tex]\left[\begin{array}{ccccc}3&6&6&-9\\-2&-3&-3&3\end{array}\right][/tex].

We will use rows operations for find the echelon form of the matrix.

Now we solve for the unknown variables:

The system has a free variable, the the system has infinite solutions and the set of solutions is [tex]\{\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}12\\-7-r\\r\end{array}\right]: \text{r is a real number}  \}[/tex]

Answer:

Number of members having previous work experience = 18

Step-by-step explanation:

As given in question,

Total number of new members hired = 27

Since, two-thirds had previous retail work experience

So,

[tex]the\ fraction\ of\ members\ having\ previous\ work\ experience\ =\ \dfrac{2}{3}[/tex]

[tex]So,\ the\ number\ of\ members\ having\ previous\ work\ experience\ =\ \dfrac{2}{3}\times\ total\ number\ of\ members\ hired[/tex]

                                              [tex]=\ \dfrac{2}{3}\times 27[/tex]

                                                = 18

So, the number of new members hired having work experience = 18

Final answer:

Two-thirds of the 27 new executive training program members had previous retail work experience, which equals to 18 members.

Explanation:

To calculate how many of the new executive training program members have previous retail work experience, we can use simple multiplication.

As two-thirds of the 27 new members had previous retail experience, we would calculate this as follows:

Number with experience =
2/3 of 27
Number with experience = 27 × (2/3)
Number with experience = 18

Therefore, out of the 27 new members, 18 have previous retail work experience.

Shown in the explanation

A Rhombus is a quadrilateral having four sides of equal length each. Here, we know that the vertices of this shape are:

[tex]W(7,2) \\ \\ X(5,-1) \\ \\ Y(3,2) \\ \\ Z(5,5)[/tex]

So the rhombus is named as WXYZ. To find its perimeter (P), we just need to find the length of one side and multiply that value by 4. By using the distance formula, we know that:

[tex]\overline{WX}=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2} \\ \\ W(7,2)=W(x_{1},y_{1}) \\ \\ X(5,-1)=X(x_{2},y_{2}) \\ \\ \\ \overline{WX}=\sqrt{(7-5)^2+(2-(-1))^2} \\ \\  \overline{WX}=\sqrt{(2)^2+(3)^2} \\ \\ \overline{WX}=\sqrt{4+9} \\ \\ \overline{WX}=\sqrt{13}[/tex]

Finally, the Perimeter (P) is:

[tex]P=4(\sqrt{13}) \\ \\ \boxed{P=4\sqrt{13}\ units}[/tex]

Answer:

4 13

Step-by-step explanation:

Answer:

[tex]\sin x + \sqrt{1-\sin^2x}[/tex]

Step-by-step explanation:

Given: sin x + cos x

To change the given trigonometry expression in term of sine only.

Trigonometry identity:-

Expression: [tex]\sin x+\cos x[/tex]

We get rid of cos x from expression and write as sine form.

Expression: [tex]\sin x + \sqrt{1-\sin^2x}[/tex]        [tex]\because \cos x=\sqrt{1-\sin^2x}[/tex]

Hence, The final expression is only sine function.

Step-by-step explanation:

Consider the provided information.

Division by zero is not defined in our number system.

You can understand this if you think about how division and multiplication are related.

For example:

4 divided by 2 is 2 because  2 times 2 is 4

Now 4 divided by 0 is x would mean that  0 times x = 4

But there is no value for x so that 0 times x =4. Because 0 times a number is 0.  

Or

4/0 means Into how many groups of zero could you separate  four blocks?

It doesn't matter how many zero groups you have, as they'd never add up to four.

0+0+0+0=0.

You can add zero billions time still add up to zero.

That the reason behind "division by zero is not allowed in our number system."

Answer:

It is a straight horizontal line where the line is only on 0.5.

Step-by-step explanation:

By the binomial theorem we know that

[tex]1 = (.4 + .6)^8 \\ = {8 \choose 0} (.4)^{8} (.6)^{0} + {8 \choose 1} (.4)^{7} (.6)^{1} +{8 \choose 2} (.4)^{6} (.6)^{2} + {8 \choose 3} (.4)^{5} (.6)^{3} + {8 \choose 4} (.4)^{4} (.6)^{4} \\ + \quad {8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}[/tex]

The probability that exactly 5 of 8 support the incumbent is the term

 [tex]{8 \choose 5} (.4)^{3} (.6)^{5}[/tex]

So at least five of eight support is the sum of this term and beyond,

[tex]p={8 \choose 5} (.4)^{3} (.6)^{5} + {8 \choose 6} (.4)^{2} (.6)^{6} + {8 \choose 7} (.4)^{1} (.6)^{7} + {8 \choose 8} (.4)^{0} (.6)^{8}[/tex]

No particularly easy way of calculating that except popping it into Wolfram Alpha which reports

[tex]p = \dfrac{ 46413}{78125}[/tex]

Shouldn't half the terms work out to .6 ?  Interestingly it's not exactly .6 but pretty close at .594.

The total probability of at least five residents supporting the candidate, denoted as P(X≥5), is calculated by summing the probabilities of exactly five, six, seven, and eight residents supporting the candidate.

To find the probability of at least five out of eight randomly selected residents supporting the incumbent candidate when 60% of the community supports them, calculate and sum the binomial probabilities for exactly five to eight residents supporting the candidate.

The student is asking for the probability of at least five out of eight randomly selected community members supporting the incumbent candidate, given that 60% of the eligible voting residents support the candidate. This is a binomial probability problem because each selection is a Bernoulli trial with only two possible outcomes (support or do not support) and the probability of a resident supporting the candidate is constant (60%).

To calculate this probability, we will sum the probabilities of exactly five, six, seven, and eight residents supporting the candidate:

Calculate the probability of exactly 5 residents supporting the candidate using the binomial probability formula: P(X = 5) = (8 choose 5) * (0.6)^5 * (0.4)^3.

Repeat the process for P(X = 6), P(X = 7), and P(X = 8).

Finally, sum these probabilities to get the total probability of at least five residents supporting the candidate: P(X \\u2265 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8).

This sum provides the required probability.

Answer:

  c(x) = 1000 +40x

Step-by-step explanation:

The total cost c will be the sum of the fixed cost and the product of the variable cost per pair and the number of pairs.

  c(x) = 1000 +40x

The mathematical model for total cost of production at the O'Neill Shoe Manufacturing Company is determined by both fixed and variable costs and can be represented as C = 1000 + 40x, where x is the number of pairs of shoes produced.

The total cost of producing a certain number of shoes includes both fixed costs and variable costs. In the case of the O'Neill Shoe Manufacturing Company, the fixed cost, which is incurred regardless of the number of shoes produced, is $1,000. This pertains to the production setup cost. The variable cost, on the other hand, depends on the quantity of shoes produced. It's given as $40 per pair of shoes. Therefore, the total cost (C) for producing x pairs of shoes can be presented as: C = 1000 + 40x. In this equation, 1000 represents the fixed cost while 40x corresponds to the variable cost of producing x number shoes.

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Linear pair makes a straight line.

A. are vertical angles.

B. are vertical angles

C. make a right angle

D. makes a straight line of TR

The answer is D.

Answer and Step-by-step explanation:

The U.S. Drug Enforcement Administration (DEA) has divided the sustances into five categories schedules, which they are:

Schedule 1 (I) drugs: substances with no accepted medical use so far and a high potential for abuse. This is the most dangerous schedule because they are considered to have a very high potential of severe psychological and physical dependence. Examples: Heroin, LSD, Methylenedioxymethamphetamine (ecstasy)

Schedule 2 (II)  drugs: substances with very controlled medical use with a abuse potential very high but less than Schedule 1 drugs. They are considered very dangerous, because they can lead to a severe psychological and physical dependence. Examples: Cocaine

Methamphetamine, Ritalin.

Schedule 3 (III) drugs: substances that are defined as drugs with a moderate to low potential for physical and psychological dependence. Their abuse potential is less than Schedule 1 and 2, but higher than Schedule 4. Examples: Vicodin, Anabolic steroids, Testosterone.

Schedule 4 (IV) drugs: substances with a abuse potential low and their risk of dependence is also low. Examples: Xanax, Valium , Ativan.

Schedule 5 (V) drugs: substances abuse potential lower potential than Schedule 4 (IV) and they are made with limited amounts of some narcotics. They are used for analgesic purposes, antidiarrheal and less serious conditions. Examples: Lomotil, Robitussin

There are 11,238,513 ways Powerball tickets can be purchased.

There are 292, 201, 338 ways to win Powerball tickets.

Given

Number of white balls = 69

Number of white balls drawn = 5

Number of red balls = 26

Number of red balls drawn = 1

The combination is the way to select the number of objects from a group.

The formula is used to select the number of the object is;

[tex]\rm = \ ^nC_r \\\\\rm = \dfrac{n!}{(n-r)!r!}[/tex]

Where n is the total number of objects and r is the number of selected objects.

1. How many possible different Powerball tickets can be purchased?

The number of ways Powerball tickets can be purchased is;

[tex]\rm = \ ^{69}C_5\\\\= \dfrac{69!}{(69-5)!. 5!}\\\\= \dfrac{69!}{64!.5!}\\\\= 11238513[/tex]

There are 11,238,513 ways Powerball tickets can be purchased.

2.  How many possible different winning Powerball tickets are there?

A number of ways to win Powerball tickets are there is;

[tex]\rm = \ ^{69}C_5 \times ^{26}C_1\\\\= \dfrac{69!}{(69-5)!. 5!} \times \dfrac{26!}{(26-1)!\times 1!}\\\\= \dfrac{69!}{64!.5!} \times \dfrac{26!}{25!.1!}\\\\= 11238513 \times 26\\\\= 292, 201, 338 ways[/tex]

There are 292, 201, 338 ways to win Powerball tickets.

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The total number of possible different Powerball tickets is 292,201,338, calculated by multiplying 11,238,513 combinations of white balls with the 26 possible red balls. There is only one winning combination for the Powerball jackpot, so there is only one possible winning Powerball ticket.

To calculate the total number of possible different Powerball tickets, we must consider the combination of white balls and the selection of the red Powerball. There are 5 white balls drawn from a set of 69, and this is a combination because the order does not matter. Therefore, the number of combinations of white balls is calculated using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of balls to choose from and k is the number of balls chosen. So, the calculation is C(69, 5) = 69! / (5!(69-5)!) = 11,238,513 combinations of white balls.

For the red Powerball, there is 1 ball drawn from a set of 26, and since there is only one ball, there are 26 possible outcomes. To find the total number of possible Powerball tickets, multiply the number of white ball combinations by the number of possible red balls: 11,238,513 × 26 = 292,201,338 possible Powerball tickets.

For part b, considering that there is only one winning combination, there is just one possible winning Powerball ticket.

Answer:

See below.

Step-by-step explanation:

2−4÷2+23 =

= 2 - 2 + 23

= 0 + 23

= 23

This is the answer of the problem you posted, where 23 is the number twenty-three. 23 is not an answer choice, so perhaps 23 is not the number twenty-three, but rather 2 to the 3rd power, 2^3.

2−4÷2+2^3 =

= 2 - 2 + 8

= 0 + 8

= 8

8 is one of the choices.

Answer:

Answer:

a) 0.2

b) 0.2

c) 0.5

Step-by-step explanation:

Let [tex]S[/tex] be the event "the car stops at the signal.

In the attached figure you can see a tree describing all possible scenarios.

For the first question the red path describes stopping at the first light but not stopping at the second. We can determine the probability of this path happening by multiplying the probabilities on the branches of the tree, thus

[tex]P(a)=0.4\times0.5=0.2[/tex]

For the second one the blue path describes the situation

[tex]P(b)=0.4\times 0.5=0.2[/tex]

For the las situation the sum of the two green path will give us the answer

[tex]P(c)=0.6\times 0.5 + 0.4\times 0.5=0.3+0.2=0.5[/tex]

Answer:

a) 0.3

b) 0.1

c) 0.3

Step-by-step explanation:

Lets call:

a = stop at first signal,  b = stop at second signal

The data we are given is P(a) = 0.4, and P(b)=0.5

Stoping at least at one is the event (a or b) = a ∪ b

P(a U b) = 0.6 is the other data we are given

a) Stoping at both signals is the event (a and b = a ∩ b)

The laws of probability say that:

P(a ∪ b)= P(a) + P(b) - P( a ∩ b) = 0.4 + 0.5  - P( a ∩ b) = 0.6

Then we get P( a ∩ b) = 0.3

b) The event is (a and not b) = a ∩(¬b).

P( a ∩(¬b) ) = P(a) - P( a ∩ b) = 0.1

c) The event is (a or b) without the cases in which (a and b)

P(a ∪ b) - P( a ∩ b) = 0.3

The Venn diagram can help you understand how the events are related to each other

Answer:

3.33 milliliters.

Step-by-step explanation:

We have been given that a 125-mL container of amoxicillin contains 600 mg/5 mL.

First of all, we will find amount of mg's of amoxicillin per ml as:

[tex]\text{Concentration of amoxicillin per ml}=\frac{\text{600 mg}}{\text{5 ml}}[/tex]

[tex]\text{Concentration of amoxicillin per ml}=\frac{\text{120 mg}}{\text{ml}}[/tex]

Now, we will use proportions as:

[tex]\frac{\text{1 ml}}{\text{120 mg}}=\frac{x}{\text{400 mg}}[/tex]

[tex]\frac{\text{1 ml}}{\text{120 mg}}\times \text{400 mg}=\frac{x}{\text{400 mg}}\times \text{400 mg}[/tex]

[tex]\frac{\text{400 ml}}{120 }=x[/tex]

[tex]\text{3.33 ml}=x[/tex]

Therefore, 3.33 milliliters would be used to administer 400 mg of amoxicillin.

To administer a 400mg dose of amoxicillin, using a solution where 5 mL contains 600 mg, approximately 3.33 mL of the solution would be needed. This was determined by setting up a proportion based on the known ratio of 600 mg of amoxicillin to 5 mL of solution.

First, we need to set up a ratio to find out how many milligrams (mg) of amoxicillin are in one milliliter (mL). We know that there are 600 mg in 5 mL, so the ratio is 600 mg:5 mL, which simplifies to 120 mg:1 mL. This tells us there are 120 mg of amoxicillin in each mL of solution.

To calculate how many mL are needed to administer 400 mg of amoxicillin, we can set up a proportion, using the known ratio of 120 mg:1 mL and the unknown value of 400 mg:x mL. The proportion would be set up as follows: 120/1 = 400/x. Solving for x, we find that x equals approximately 3.33 mL.

So, if you need to give a dose of 400mg of amoxicillin, you would need to administer about 3.33 mL of the amoxicillin solution.

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Answer:

slope = -5 ÷ 4

Step-by-step explanation:

The equation of line can be written as,

y = mx + c

where, m is slope

and c is intercept of line.

So, transforming the given equation in above standard equation.

5x + 4y - 1 = 0

⇒ 4y = -5x + 1

⇒ [tex]y = \frac{-5}{4}x +\frac{1}{4}[/tex]

Now comparing this equation with standard equation. We get,

[tex]m =\frac{-5}{4}[/tex]

and [tex]c = \frac{1}{4}[/tex]

Hence, Slope =  [tex]m =\frac{-5}{4}[/tex]

Answer:

The rate is 4.9%.

Step-by-step explanation:

The compound interest formula is :

[tex]A=p(1+\frac{r}{n})^{nt}[/tex]

A = 73677.48

p = 73377.34

r = ?

n = 12

t = 1/12

Putting the values in formula we get;

[tex]73677.48=73377.34(1+\frac{r}{12})^{12*1/12}[/tex]

=> [tex]73677.48=73377.34(1+\frac{r}{12})^{1}[/tex]

=> [tex]\frac{73677.48}{73377.34} =(1+\frac{r}{12})[/tex]

=> [tex]1.004090=(\frac{12+r}{12})[/tex]

=> [tex]12.04908=12+r[/tex]

=> [tex]r = 12.04908-12[/tex]

r = 0.04908

or r = 4.9%

Therefore, the interest rate is 4.9%.

Final answer:

Explaining how to calculate the interest rate for an investment question.

Explanation:

To find the interest rate, subtract the initial amount from the final amount: $73,677.48 - $73,377.34 = $300.14. This represents the interest earned in one month.

Next, calculate the interest rate using the formula we get the :

Interest Rate = (Interest Earned / Initial Amount) x 100%.

Plugging in the values: Interest Rate = ($300.14 / $73,377.34) x 100% ≈ 0.409% or 0.4% to the nearest tenth.

Answer:

The correct definition of statistics is D.

Step-by-step explanation:

The field of statistics is divided into descriptive and inferential statistics. This description "Statistics is the science of​ collecting, organizing,​ summarizing, and analyzing information to draw a conclusion and answer questions." corresponds to the description of Descriptive statistics and this part "In​ addition, statistics is about providing a measure of confidence in any conclusions."  is the description of Inferential statistics.

Answer:

1. 405000: Number of significant digits 3. 405

2. 0.0098: Number of significant digits 2. 98

3. 39.999999: Number of significant digits 8. 39999999

4. 13.00: Number of significant digits 4. 1300

5. 80,000,089: Number of significant digits 8. 80000089

6. 55430.00: Number of significant digits 7. 5543000

7. 0.000033: Number of significant digits 2. 33

8. 620.03080: Number of significant digits 8. 62003080

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]

Step-by-step explanation:

The significant digits in a real number refer to the digits that are held in the gutter to determine their accuracy. That is, those relative values that could be determined with certainty. Therefore, the answers are:

1. 405000: Number of significant digits 3. 405

2. 0.0098: Number of significant digits 2. 98

3. 39.999999: Number of significant digits 8. 39999999

4. 13.00: Number of significant digits 4. 1300

5. 80,000,089: Number of significant digits 8. 80000089

6. 55430.00: Number of significant digits 7. 5543000

7. 0.000033: Number of significant digits 2. 33

8. 620.03080: Number of significant digits 8. 62003080

[tex]1. \hspace{3} 70000000000 = 7\times10^{10}\\2. \hspace{3} 0.000000048 = 4.8\times10 ^{-8}\\3. \hspace{3} 67890000 = 6.789\times10^7\\4. \hspace{3} 70500 = 7.05\times10^4\\5. \hspace{3} 450900800 = 4.509008\times10^8\\6. \hspace{3} 0.009045 = 9.045\times10^{-3}\\[/tex]

The question asks to find the significant digits in several numbers and to convert different sets of numbers into scientific notation. The answers provide the number of significant digits for each number and the respective numbers in scientific notation. Significant digits provide precision in measurements, and scientific notation is useful for representing very large or very small numbers.

Part 1: Significant digits are crucial in science because they tell us how accurate a measurement is. Zeros can sometimes not be significant, as they might just be placeholders.

Part 2: Converting these numbers into scientific notation gives us:

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Answer: D. 2.5

Step-by-step explanation:

Given : Line segment DF is dilated from the origin to create line segment D’F’ at D' (0, 10) and F' (7.5, 5).

The original coordinates for line segment DF are D(0, 4) and F(3, 2).

We know that the scale factor(k) is the ratio of the coordinates of the image points and the original points.

Then, [tex]k=\dfrac{\text{ y-coordinate of D'}}{\text{y-coordinate of D}}\\\\=\dfrac{10}{4}=\dfrac{5}{2}=2.5[/tex]

Hence, the scale factor was line segment DF dilated by = 2.5

Answer:

The answer to this is 2.5

Step-by-step explanation:

Well 1 i took the test and 2 if you mulitply the otginial coordinates by 2.5 then you will get the new cordiates

Final answer:

The expected value of the winnings on a $8 bet placed on a red number in European roulette is -$1.945, indicating an average loss.

Explanation:

The question concerns the expected value of winnings on a $8 bet placed on red in European roulette. In European roulette, there are 18 red numbers, 18 black numbers, and 1 green number (0), totaling 37 numbers. A bet on red will win if the ball lands on any of the red numbers. When betting $8 on red, the player will either win $8 or lose $8, since the payoff for winning is 1:1.

To calculate the expected value, we consider the probability of winning, P(Win), and the probability of losing, P(Lose). The probability of landing on red (and wining) is 18/37, and the probability of not landing on red (and losing) is 19/37 (which includes the 18 black and 1 green).

The expected value is calculated as follows:

EV = (amount won × P(Win)) + (amount lost × P(Lose))

EV = ($8 × 18/37) + (-$8 × 19/37)

EV = $2.16 + (-$4.11)

EV = -$1.95

Rounded to three decimal places, the expected value is -$1.945.

Thus, if you were to place a $8 bet on red in European roulette, you would expect to lose, on average, $1.945 per game, as the expected value is negative.

Answer:

1) [tex]7 x 10^{15} J[/tex]

2) [tex]40.5[/tex] days

Step-by-step explanation:

1) First of all we use [tex]1MJ=1x10^{6}J[/tex] so the total energy will be [tex]7x10^{9} kg * 1x10^{6} \frac{J}{kg} =7x10^{15}J[/tex].

2)Then we use [tex]1W=1\frac{J}{s}[/tex] and [tex]Time=\frac{7 x 10^{15} J }{2x10^{9}J/s} =3.5x10^{6}s[/tex] or [tex]3.5x10^{6}s*\frac{1h}{3600s}*\frac{1day}{24h} =40.5 days[/tex]

Convert 55% to a decimal by moving the decimal point two places to the left:

55% = 0.55

Now multiply:

3650.00 x 0.55 = 2,007.50

Answer: she must walk for 72.8 s

Hi!

Lets say that with the cart she rides a time T1 (28 s) for a distance D1, then the average speed in the cart is V1 = D1 / T1 =  3.10 m/s. We can calculate D1 = (28 s )* (3.10 m/s) = 86.8 m

She then walks a time T2 for a distance D2, with average speed

V2 = D2 / T2 = 1.30 m/s

For the entire trip, we have average speed:

V3 = (D1 + D2) / (T1 + T2) = 1.80 m/s

We can solve for T2:

(1.8 m/s) *( 28s + T2) = 86.8 m  +  D2 = 86.8 m + (1.3 ms) * T2

Doing the algebra we get: T2 = 72,8 m/s

This question involves an application of the concept of average speed. Knowing that the average speed for the entire trip was 1.80 m/s, we first determined the distance covered while riding the golf cart. Using this, we set up an equation that allowed us to solve for the time spent walking to maintain the given average speed.

In order to solve this problem, we'll have to apply the formula for average speed, which is total distance covered (d) divided by the total time (t) taken.

Firstly, let's determine the distance covered while riding the golf cart. The golfer rides at an average speed of 3.10 m/s for 28.0 s. Therefore, she covers a distance of (average speed)x(time) = (3.1 m/s)(28.0 s) = 86.8 m.

Let's denote the time she walks as 't2'. The total time of the trip equals the sum of the time spent in the cart and the time spent walking: 28.0 s + t2.

Similarly, the total distance covered equals distance covered with the cart plus distance covered walking, which is 86.8 m + 1.30 m/s * t2.

Given the average speed for the entire trip is 1.80 m/s, we can write:

1.80 m/s = (total distance) / (total time)

1.80 m/s = (86.8 m + 1.30 m/s * t2) / (28.0 s + t2).

This equation could be solved for t2 to calculate how long the golfer needs to walk.

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