A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle asks the reader to match each president with his vice president.
(1) If you make the matches randomly, how many matches are possible?
Number of possible matches
(2) What is the probability all 10 of your matches are correct? (Round your answer to 8 decimal places.)

To find the square footage of the letter S on the parade float, the students can divide it into rectangles and calculate the area of each rectangle.

The students can divide the shape of the letter S on the parade float into rectangles and then calculate the area of each rectangle to determine the total area of the letter. To do this, they can measure the length and width of each rectangle and multiply them together to find the area. Once they have the area of each rectangle, they can add them all together to get the total square footage of the letter S on the float.

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Answer:

The answer to your question is -27/20

Step-by-step explanation:

Divide         3/5  ÷  - 4/9

Process

1.- Just multiply the numerator of the first fraction by the denominator of the second fraction.                                      

                    3 x - 9 = -27

2.- Multiply the denominator of the first fraction by the numerator of the second fraction.

                    5 x 4 = 20

3.- Join both results

                               -27/20

Answer: the inequality that bests represents how many tickets she can buy is 1.5x ≤ 8

Step-by-step explanation:

Let x represent the number if tickets that she wants to buy at the school fair.

Each ticket cost one dollar and 50 Cent. This means that the total cost of x tickets would be

1.5 × x = $1.5x

Michaela has eight dollars to buy tickets at the school fair. Therefore, the inequality that bests represents how many tickets she can buy is

1.5x ≤ 8

Answer:

Answer in explanation

Step-by-step explanation:

In this question, we would be examining the validity of some statements on the number π(pi)

π Is a whole number?

This is wrong, π is a fraction of 22 to 7 parts I.e 22/7

π Is double the radius?

This is wrong. It is the diameter that is double the radius

π Is approximately 3.14?

This is correct to an extent. The actual value in decimal is around 3.142857142857143 which makes the 3.14 somehow correct

π represents the ratio of the circumference of the circle to the diameter?

This is correct.

Mathematically, circumference C = π * diameter D

Hence C/D = π

π Is approximately 22/7?

This is correct. This is the ratio used for π

Answer:

• Pi is approximately 3.14.

• Pi represents the ratio of the circumference to the diameter

• Pi is approximately 22/7

Step-by-step explanation:

From the options given:

A. Pi is a whole number:

Pi is equivalent to 3.141592654. Therefore, pi is not a whole number.

B. Pi is double the radius

Pi is not double the radius of a circle. Pi is a constant.

C. Pi is approximately 3.14.

In some cases, pi can be approximated as 3.14 instead of 3.141592654.

D. Pi represents the ratio of the circumference to the diameter.

Circumference of a circle, C = 2 × pi × radius

= 2 × pi × D/2 = pi × Diameter

Pi = circumference/Diameter

E. Pi is approximately 22/7

22/7 = 3.142857143

This is also a correct approximation.

Answer:

Probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

Step-by-step explanation:

We are given that one year, professional sports players salaries averaged $1.5 million with a standard deviation of $0.9 million.

Suppose a sample of 400 major league players was taken.

Let [tex]\bar X[/tex] = sample average salary

The z-score probability distribution for sample mean is given by;

                 Z = [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean salary = $1.5 million

            [tex]\sigma[/tex] = standard deviation = $0.9 million

             n = sample of players = 400

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the average salary of the 400 players exceeded $1.1 million is given by = P([tex]\bar X[/tex] > $1.1 million)

    P([tex]\bar X[/tex] > $1.1 million) = P( [tex]\frac{ \bar X -\mu}{{\frac{\sigma}{\sqrt{n} } }} }[/tex] >  [tex]\frac{ 1.1-1.5}{{\frac{0.9}{\sqrt{400} } }} }[/tex] ) = P(Z > -8.89) = P(Z < 8.89)

Now, in the z table the maximum value of which probability area is given is for critical value of x = 4.40 as 0.99999. So, we can assume that the above probability also has an area of 0.99999 or nearly close to 1.

Therefore, probability that the average salary of the 400 players exceeded $1.1 million is 0.99999.

The approximate probability that the average salary of the 400 players exceeded $1.1 million will be "1".

According to the question,

Standard deviation, σ = 0.9

Mean, μ = 1.5  

Let,

The salaries for professional sports player be "x".

Now,

The probability will be:

= P ([tex]\bar x[/tex] > 1.1)

= P ([tex]\frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{1.1 - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex])

By substituting the values,

= P (Z > [tex]\frac{1.1 -1.5}{\frac{0.9}{\sqrt{400} } }[/tex])

= P (Z > -8.89)

By using the table,

= 1

Thus the above answer is correct.

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Answer:

517,262

Step-by-step explanation:

A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?

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

Ans: (1.5)^18 * 350 = 517,262

Answer: there will be 517262 butterflies by the 19th generation.

Step-by-step explanation:

The population of butterflies grows in such a way that each generation is simply 1.5 times the previous generation. This means that the population is increasing in geometric progression. We would apply the formula for determining the nth term of a geometric progression which is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 350

r = 1.5

n = 19

Therefore, the 19th term or generation, T19 would be

T19 = 350 × 1.5^(19 - 1)

T19 = 350 × 1.5^18

T19 = 517262

Answer:

The answer to your question is a = 4.81

Step-by-step explanation:

Process

1.- The angle B and 43° are supplementary

            B + 43° = 180°

            B = 180 - 43

            B = 137°

2.- Calculate angle C

The sum of the internal angles in a triangle equals 180°

     A + B + C = 180°

      29 + 137 + C = 180

- Solve for C

     C = 180 - 29 - 137

     C = 14°

3.- Use the law of signs to find a

            a / sin A = c / sin C

           a / sin 29 = 2.4 / sin 14

- Solve for a

           a = 2.4 sin 29 / sin 14

- Simplification

           a = 2.4 (0.485) / 0.242

- Result

           a = 4.809      

Barbarino's Rentals offers the better deal for a 432-mile trip at $117.30 compared to Mr. Kotters Rentals at $135.52. To spend the same amount at either company, Glenna would have to drive 600 additional miles over the free miles provided by the rentals.

To determine which car rental company offers the better deal for Glenna's trip to Key West, we need to calculate the total cost from both companies for a 432-mile trip. Let's start with Mr. Kotters Rentals. The cost for one week is a flat $99, plus $0.11 per mile for each mile over 100.

Therefore, Glenna would pay for 332 extra miles at a rate of $0.11 per mile. This calculation is (432 miles - 100 miles) * $0.11/mile = 332 * $0.11 = $36.52 in additional mileage charges. The total cost from Mr. Kotters Rentals would be $99 + $36.52 = $135.52.

Next, we calculate the cost with Barbarino's Rentals. They charge $75 for the week plus $0.15 per mile over 150 miles. The calculation for mileage is (432 miles - 150 miles) * $0.15/mile = 282 * $0.15 = $42.30. The total cost from Barbarino's Rentals would come out to $75 + $42.30 = $117.30.

Comparing the two totals, Barbarino's Rentals is the better deal at $117.30 compared to Mr. Kotters Rentals, which would cost $135.52.

Now, to find out how many miles Glenna would have to drive for the costs to be the same at either company, we set up the equation:
99 + 0.11x = 75 + 0.15x, where x represents the additional miles driven over the respective free miles. Solving this equation:

0.04x = 24
x = 600 miles
So, Glenna would need to drive 600 additional miles for the total costs from both rental companies to be equal.

Answer:

e) , f)

Step-by-step explanation:

42+15= 57

If the available options are:

a) 5(8+2)+5(3)=(5x10)+15=50+15=65

b) (3 x 14) + (3 x 5)= 42+15=57

c) (3 x 39) + (3 x 5)=117+15=132

d) 3(39 + 12)=3x51=153

e) 3(14 x 5)=3x70=210

f) 3(14 + 5)=3x19=57

Answer:

Step-by-step explanation:

Answer:  1/4

Step-by-step explanation:

so if 1/2 of 1/2 of cookies are with choclate chips therefore saying 1/2 cookies is the same as 2/4 cookies and since half of the cookies are with choclate chips so there are 1/4 cookies with choclate chips nd are peanut butter please mark brainliest.

Answer:1/4

Step-by-step explanation: Half of the cookies baked were peanut butter cookies. 1/2 of the peanut butter cookies have chocolate chips. 1/2 divided by 1/2 is 1/4. 1/4 of the total cookies baked are peanut butter chocolate chip cookies.

Answer:

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

Step-by-step explanation:

First one can be any of the six outcomes

Final answer:

The event that the second toss shows a two is represented as a subset of the sample space and includes all possible outcomes of the first toss with a two as the second element, written as {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which is option d.

Explanation:

The question asks to represent a specific event from a probability experiment in set notation. The experiment involves tossing a die twice, and the event of interest is that the second toss results in a two. The sample space for two tosses of a six-sided die consists of all ordered pairs where the first element is the result of the first toss, and the second element is the result of the second toss. Since the die has six sides, the first element can be any number from 1 to 6, and the same applies to the second element.

The event that the second toss shows a two can be represented by the subset of the sample space where the second element of each ordered pair is a 2. Therefore, the correct set notation for this event would be {(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)} which corresponds to option d. This subset includes all possible outcomes of the first toss combined with the fixed outcome of the second toss being a two.

Answer:

An experiment

Step-by-step explanation:

An observational study is a study in which the researchers collect data related to what is visible or heard. In this type of study the researchers do not have any control on the variables used for the research work .The researcher do not bring any changes in the behavior of the variables that is they are accepted the way they are.

An experiment is a method used in which the researchers pick up a sample from a group and test them to get a proof or knowledge about something.

Both Observational study as well as an experiment are used in statistics social sciences and psychology etc.

Thus the case given here is an experiment because there is no alterations done with the variables.

The scenario given is an experiment because it deliberately manipulates conditions (music or no music) to test its effect on students' ability to memorize words. By comparing outcomes, this study seeks to establish a causal relationship.

The study described in the student's question is an experiment because it involves a deliberate manipulation of conditions to test a hypothesis. The manipulation in this case is the presence or absence of music while memorizing words. Since there are two groups and each group is subjected to different conditions (one with music and one without), this defines a controlled experiment. Experiments involve comparing the outcomes of different treatments, in this case, music or silence, which enables researchers to make causal inferences about the effect of the independent variable (music) on the dependent variable (ability to remember words).

Now, looking at the studies referenced, the effects of music on different cognitive tasks, like memorization and reading comprehension, have been explored in various ways. While some experiments, like the one comparing the memorization of words with and without music, show that silence may be more conducive for memorization, other studies have found positive effects of music on tasks such as reading comprehension or overall task behavior.

Answer:

Option C is Correct

Step-by-step explanation:

Given System is

3x + 5y =  1

2x + 4y  = −4

Multiply the first equation by −2, and multiply the second equation by 3

we get

-6x-10y = -2 ----------(i)

6x+12y = -12 ---------(ii)

then we add both equations we get

2y = -14

y = -7

now put y = -7 in euation one we get

-6x-10(-7) =14

-6x+70=14

subtracting 70 from both sides we get

-6x=-56

dividing (-6) both sides we get

x=56/6 or x =28/3

so here is our solution

(x,y)=(28/3 , -7)

answer.

Answer:  D. a1=15.75,an = an -1 -1.5

Step-by-step explanation:

Sorry about the no explanation, but the answer is correct.

The correct recursive formula for the arithmetic sequence 15.75, 14.25, 12.75, … is a1 = 15.75, an = an-1 - 1.5. This means the first term is 15.75 and each following term is 1.5 less than the previous term.

The question asks for a recursive formula for the arithmetic sequence provided. An arithmetic sequence is a sequence of numbers wherein the difference between any two consecutive terms is constant. In this case, the common difference (d) is -1.5, because each term decreases by 1.5 from the previous term. Every term in the sequence follows the pattern of the first term, plus the common difference (d) multiplied by (n-1), where n is the term number.

To write a recursive formula for the sequence, we express the nth term (an) as the sum of the (n-1)th term and the common difference. Thus, the recursive formula for the sequence is: a1 = 15.75, an = an-1 - 1.5. This tells us that the first term a1 equals 15.75, and any term an (after the first term) is 1.5 less than the term before it(an - 1).

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Answer:

The customer's total cost for the DVD is $19.26

Step-by-step explanation:

Store buy the dvd for $12.00.

The store price is $12.00+50% more

The store price= $12.00 *(1+0.5)= $18.00

Final price (tax added)= $18.00 + 7%

Final price= $18.00 * (1 + 0.07)= $19.26

Answer:

The total cost of the DVD for the consumer was 19.26 $

Step-by-step explanation:

The sales price for the DVD was the price paid by the store plus 50%. To discover this value we will transform the percentage in a real number, by dividing it by 100, like following:

50/100 = 0.5

We then multiply this value by the price paid by the store (12) to find out how much is 50% of that. Then we add this value to the price paid by the store and we obtain the price of the DVD before taxes. So we do as following:

Price before taxes = price paid by the store + (price paid by the store)*0.5

Price before taxes = 12 + 12*0.5 = 18 $

On top of that there was 7% of tax for the consumer. We must repeat the same steps as before but using 7 instead of 50. So we have:

Final price = Price before taxes + (Price before taxes)*(7/100)

Final price = 18 + 18*0.07 = 19.26 $

The total cost of the DVD for the consumer was 19.26 $

Answer:

Option B) $940

Step-by-step explanation:

We are given the following in the question:

[tex]y = 0.94x + 12.5[/tex]

The equation represents the company sales in thousand dollars and x is time in months.

Comparing to general form of linear equation.

[tex]y = mx + c[/tex]

Comparing, we get,

Slope, m = 0.94

y-intercept, c = 12.5

Interpretation:

Thus, the slope tells us the increase in sales of company with one unit increase in x that is it tells the increase in company's sale per month.

[tex]0.94\times 1000 = 940[/tex]

$940 is the increase in company's sale per month.

Option B) $940

Answer:

B 940

Step-by-step explanation:

Answer:

[tex]1 \frac{48}{121} [/tex]

Step-by-step explanation:

divide 169/121 and that equals the answer above

Answer:

13 : 11

Step-by-step explanation:

If the ratio of radii = a : b, then

ratio of areas = a² : b²

Given

ratio of areas = 169 : 121, then

ratio of radii = [tex]\sqrt{169}[/tex] : [tex]\sqrt{121}[/tex] = 13 : 11

Option C: [tex](7 g-6 h)(5 g+4 h)[/tex] is the correct answer.

Explanation:

The given expression is [tex]35 g^{2}-2 g h-24 h^{2}[/tex]

We need to determine the factor of the expression.

Now, let us break the given expression into two groups.

Hence, we get,

[tex]35 g^{2}+28 g h-30 g h-24 h^{2}[/tex]

Simplifying, we get,

[tex]\left(35 g^{2}+28 g h\right)+\left(-30 g h-24 h^{2}\right)[/tex]

Let us factor out 7g from the term [tex]\left(35 g^{2}+28 g h\right)[/tex]

Hence, we have,

[tex]7 g(5 g+4 h)+\left(-30 g h-24 h^{2}\right)[/tex]

Similarly, let us factor out -6h from the term [tex]\left(-30 g h-24 h^{2}\right)[/tex]

Thus, we have,

[tex]7 g(5 g+4 h)-6 h(5 g+4 h)[/tex]

Now, we shall factor out the term [tex]5g+4h[/tex] , we get,

[tex](7 g-6 h)(5 g+4 h)[/tex]

Thus, the factorization of the given expression is [tex](7 g-6 h)(5 g+4 h)[/tex]

Therefore, Option C is the correct answer.

Answer:

Option C is the correct answer.

Step-by-step explanation:

Answer:

$50 is the value of interest earned in the first installment on a single bond

Step-by-step explanation:

Applying Interest earned in the first installment on a single bond ;

= PRT/100

P = $1.000

R = 5%

T = 1

Plugging the values in the equation ;

Interest = 1000 x 5 x 1 /100

= $50, hence option A is the correct one.

Answer: No, Ned will never catch up to Karen.

Step-by-step explanation:

Karen started walking at 1 mile per hour.

Time = distance/speed

If she walks 2.5 miles, it means that the time she spent walking is

2.5/1 = 2.5 hours.

After she walked 2.5 miles, her friend Ned started walking along the same route at a speed of 1 mile per hour. Since Ned is walking at 1 mile per hour which is even slower than Karen's speed, it means that for every 1 mile that Ned walks, Karen walks 2.5 miles. Therefore, if

they continue to walk at the same rate, Ned will never catch up to Karen.

Answer:

P(defective) = 126/3000 = 0.042

P(not defective) = 1 - P(defective)

= 1 - 0.042 = 0.958

Answer:

A bar graph, because if you want to compare categories, you would want to categorize the results you get from a survey. If you were to use any other chart or graph, you would have to base it off of QUANTITATIVE data. Since this is QUALITATIVE data, it wouldn't make any sense to use any other chart or graph.

A bar graph is the best way to display categorical data such as the favorite kind of pizza.

A bar graph (also known as a bar chart) is a graphical representation of data that uses bars of different sizes. It is an excellent way of displaying relative sizes.

As per the question, a bar graph is the best way to display categorical data such as the favorite kind of pizza.

Each category (i.e., pepperoni, cheese, vegetarian, etc.) can be represented by a bar, with the height of the bar indicating the number or percentage of students who chose that category.

This allows for an easy visual comparison of the popularity of each kind of pizza.

Also, labels can be added to the x-axis and y-axis to provide additional information and context to the graph.

Therefore, a bar graph is an exact and effective way to present the data from the survey on students' favorite kinds of pizza.

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Answer:

31

Step-by-step explanation:

Y = 6x+1

When x is 5

y = 6(5)+1 = 30 +1 =31

Answer:

The cost of mixture is

[tex]\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]

Step-by-step explanation:

We are given the following in the question:

Cost of white per gallon = $12 a gallon

Amount of white paint in the mixture = m gallons

Total cost of white paint =

[tex]12\times m = 12m\$[/tex]

Cost of blue per gallon = $30 a gallon

Amount of blue paint in the mixture = n gallons

Total cost of blue paint =

[tex]30\times n = 30n\$[/tex]

Total cost of mixture =

Total cost of white paint  + Total cost of blue paint

[tex](12m + 30n)\text{ dollars}[/tex]

Total amount of mixture =

Amount of white paint in the mixture + Amount of blue paint in the mixture

[tex]=(m+n)\text{ gallons}[/tex]

Cost of mixture per gallon =

[tex]=\dfrac{\text{Total cost}}{\text{Total amount}}\\\\=\dfrac{12m + 30n}{m+n}\text{ dollars per gallon}[/tex]

is the required cost of mixture.

The two zoo tours start at 8:00 am, one leaves every 30 minutes and the other every 45 minutes. The next time they will coincide, or leave at the same time, is at 9:30 am.

The tours in the zoo that are mentioned in your question represent two different intervals, 30 minutes and 45 minutes. To figure out when these tours will coincide again, we actually need to find a common multiple of the two intervals. The smallest common multiple of 30 and 45 minutes is 90 minutes or 1 hour and 30 minutes.

So, if both tours start at 8:00 am, they will sync again 90 minutes later, which is 9:30 am. Therefore, the two tours will depart together again at 9:30 am.

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Step-by-step explanation:

1. The first is a tabulation of the data, in an organized, clear and concise way for each event.

2. After tabulation, for a better understanding of the data, statistical data, such as the mean, median, and standard deviation of each event, should be collected.

3. Finally, graph the data obtained to see the trend of both cases and thus have a very precise way to make the comparison of both events

Answer:

(a) 40 milligrams

(b)  1.21 milligrams

Step-by-step explanation:

Exponential Function

It's commonly used to model real situations in life, like this one proposed in the question where the number of milligrams of a drug D(h) in a patient's bloodstream h hours after the drug is injected is modeled by the following function.

[tex]D(h) =40e^{-0.5h}[/tex]

(a) The initial amount injected to the patient can be found when h=0

[tex]D(0) =40e^{-0.5(0)}=40e^{0}=40[/tex]

Initial amount: 40 milligrams

(b) Let's plug h=7

D(7) =40e^{-0.5(7)}=40e^{-3.5}=1.21

The amount in the bloodstream after 7 hours is 1.21 milligrams

Answer:

Equation= X = 660÷22, Number of boxes is 30

Step-by-step explanation:

Since each box contains 22 cans, hence 22x is equivalent to 660 cans.

Equation = 22X = 660

Number of boxes X = 660÷22 = 30

Answer:

Step-by-step explanation:

Given:

Number of cans in a box, N = 22 cans

Total number of cans, Tc = 660 cans

Let the Number of boxes be x.

Therefore,

Tc = N × x

B.

660 = 22 × x

x = 660/22

= 30 boxes.

Answer:

The answer to your question is the letter B. x = 30

Step-by-step explanation:

Data

Find x

Process

To solve this problem use proportions. Compare the small triangle and the large triangle.

1) For the small triangle

                         x/ (24 - 4) = x/20

2) For the large triangle

                         (x + 6) / 24

3.- Equal both expressions

                         x/20 = (x + 6)/24

-Solve for x

                        24x = 20(x + 6)

-Expand

                        24x = 20x + 120

-Simplify like terms

                        24x - 20x = 120

                          4x = 120

-Result

                            x = 120/4

                            x = 30

Answer:

Option D

86

Step-by-step explanation:

When your expectation is average of 81 for a total of 10 questions, your total score is 10*81=810

Currently, for 5 questions with an average of 76, your total score is 5*76=380

Difference between total expected score and current score is 810-380=430

Average of difference with 5 questions is 430/5= 86