A researcher wishes to estimate the average amount spent per person by visitors to a theme park. He takes a random sample of forty visitors and obtains an average of $28 per person.

a.What is the population of interest?
b.What is the parameter of interest?
c.Based on this sample, do we know the average amount spent per person byvisitors to the park? Explain fully

Answer:

D.  Function 2 has a greater rate of change by  

3

2

Step-by-step explanation:

Function 2 has a greater rate of change by  

3

2

m =  

y2 − y1

x2 − x1

Function 1 has a slope of  

1

2

.

x-int = (−4, 0)

y-int = (0, 2)

m =  

2 − 0

0 − (−4)

=  

2

4

=  

1

2

Function 2 has a slope of 2.

m =  

5 − 3

3 − 2

=  

2

1

= 2

thus,

2 −  

1

2

=  

4

2

−  

1

2

=  

3

2

Answer:

Step-by-step explanation:

1)

[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]

____

2)

[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]

Answer:

The simplified expression is:

⇒ [tex]13x-8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x + \frac{1}{2})+(4x-8\frac{1}{2})[/tex]

To simplify the given expression.

Solution:

In order to simplify, we will combine the like terms by removing the parenthesis.

We have:

⇒  [tex]9x + \frac{1}{2}+4x-8\frac{1}{2}[/tex]

Combining like terms.

⇒  [tex]9x+4x+\frac{1}{2}-8\frac{1}{2}[/tex]

⇒  [tex]13x+\frac{1}{2}-8\frac{1}{2}[/tex]

In order to combine fractions, we will combine the whole number and the fraction separately.

⇒  [tex]13x-8+(\frac{1}{2}-\frac{1}{2})[/tex]

⇒  [tex]13x-8+0[/tex]

Thus, the simplified expression is:

⇒ [tex]13x-8[/tex]

Answer:

500 feet by 250 feet.

Step-by-step explanation:

Let the length be x and the width y feet.

As we have 1000 feet of wire:

x + 2y = 1000

2y = 1000 - x

y = 500 - 0.5x

So the area =   x(500 - 0.5x)

A =  500x - 0.5x^2

For a maximum  area the derivative

A' =  500 -x = 0

x = 500 feet.

2y = 1000 - 500

y = 250 feet.

Answer:

a=7.2*1.5=10.8 cm

b=6.3/1.5=4.2 cm

[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]

Step-by-step explanation:

Proportional Geometric Shapes

A) We are given two similar shapes of a logo. They are to be proportional. We only need to find the proportion ratio of two of them to find the rest of the lengths.

The upper sides have 7.5 cm and 5 cm respectively. This gives us the ratio

[tex]\displaystyle r=\frac{7.5}{5}=1.5[/tex]

Which means all the measures of the smaller logo are 1.5 smaller than those of the larger. This means  

b=6.3/1.5=4.2 cm

a=7.2*1.5=10.8 cm

B) To paint the logos, we need to cover its surface, so the ratio of the surface is 1.5*1.5=2.25

This means the cost to paint the larger logo is  

[tex]\pounds 4.48*2.25=\pounds 10.08[/tex]

Answer:

A) a = 10.8, b = 4.2

B) £10.08

Step-by-step explanation:

A) 7.5/5 = 1.5

a = 7.2 x 1.5 = 10.8

5/7.5 = 2/3

b = 6.3 x 2/3 = 4.2

B) 1.5 x 1.5 = 2.25

£4.48 x 2.25 = £10.08

Answer:

Option B. Range of the given sample data is 113.

Step-by-step explanation:

The given question is incomplete; here is the complete question.

Find the range for the given sample data.

The amounts below represent the last twelve transactions made to Juan's checking account.  Positive numbers represent deposits and negative numbers represent debits from his account.

$28   -$20   $67   -$22   -$15   $17  -$38  $41   $53   -$13   $30   $75

Option A. $75

Option B. $113

Option C. $37

Option D. -$113

Transaction done by Juan can be arrange from lowest to highest

-38   -22   -20    - 15    -13    17   28    30   41   53    67    75    

Now we know rage of the sample data = Highest value - Lowest value

= 75 - (-38)

= 113

Therefore, range of the given sample data is 113.

Option B is the answer.

Answer:yes, the lawn can be watered completely by 4 installed sprinklers.

Step-by-step explanation:

The lawn is rectangular and its area is 32 square yards. Sprinklers are to be installed and each sprinkler waters in a circle. The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

If each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards., the the maximum area that can be watered by each sprinkler would be

Area = 3.14 × 2² = 12.56 yards²

If 4 sprinklers are completely installed, then the total area that they can water would be

12.56 × 4 = 50.24 yards²

Therefore, the lawn can be watered completely by 4 installed sprinklers.

Answer:

1215 minutes are the possible numbers he has used his phone in a month.

Step-by-step explanation:

He has a monthly fee of 14$ then to the least that he has been charged we need to substract the monthly fee as follows:

Monthly charged = 74,75-14

Monthly charged= 60,75$

Then he pays an additional 0,05 $/minute of use, to know the consume:

Minutes= [tex]\frac{60,75}{0,05}[/tex]

Minutes= 1215 possible numbers of minutes he has used his phone.

Answer:

1750 + 35x ≥ 3250

Step-by-step explanation:

Average speed = 35 words

He has already typed 1500 words on his final paper

The paper must be more than 3250 words.

To find at least how many more words he has to type, we will subtract 1500 from 3250

3250 - 1500 = 1750 words

The equation will be 35x ≥ 1750

x is the number of minutes

The equation could be

1750 + 35x ≥ 3250

Answer:

Megan has left with $24.

Step-by-step explanation:

Let the total money she has be 'y'.

Given:

Megan spent two out of five of her money on a doll.

So we can say that;

Money spent on doll = [tex]\frac{2}{5}y[/tex]

Also Given:

half of the remainder on a musical box.

Money spent on musical box = [tex](y-\frac{2}{5}y)\frac{1}2[/tex]

Now we will make the denominator common using LCM we get;

Money spent on musical box =[tex](\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}[/tex]

Now Given:

she spent eight dollars more on the doll than on a musical box.

[tex]\frac{2y}{5} = \frac{3y}{10}+8[/tex]

Combining like terms we get;

[tex]\frac{2y}{5}-\frac{3y}{10}=8[/tex]

Now we will make the denominator common using LCM we get;

[tex]\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\$80[/tex]

Money spent on doll = [tex]\frac{2}{5}y=\frac{2}{5}\times 80 = \$32[/tex]

she spent eight dollars more on the doll than on a musical box.

So we can say that;

Money spent on musical box = Money spent on doll -8 = [tex]32-8 = \$24[/tex]

Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.

framing in equation form we get;

remaining money left = [tex]80-32-24= \$24[/tex]

Hence Megan has left with $24.

Answer:

proud of you keep ya head up

Step-by-step explanation:

Answer:the number of lacrosse sticks that were sold in November is 52

Step-by-step explanation:

The number of lacrosse sticks sold at a sporting goods store in November decreases by 35% from the number sold in October. If the number of lacrosse sticks sold in October is 80, then the amount by which it decreased would be

35/100 × 80 = 0.35 × 80 = 28

Therefore, the number of lacrosse sticks that were sold in November would be

80 - 28 = 52

Answer:

They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.

Step-by-step explanation:

Given:

Amount of flour Javon has = [tex]\frac{3}{2}\ cup[/tex]

Amount of flour Sam has = [tex]4\frac{1}{3}\ cups[/tex]

[tex]4\frac{1}{3}\ cups[/tex] can be Rewritten as [tex]\frac{13}{3}\ cups[/tex]

Amount of flour Sam has = [tex]\frac{13}{3}\ cups[/tex]

Amount of flour Antoine has = [tex]3\frac{4}{6}\ cups[/tex]

[tex]3\frac{4}{6}\ cups[/tex] can Rewritten as [tex]\frac{22}{6}\ cups[/tex]

Amount of flour Antoine has = [tex]\frac{22}{6}\ cups[/tex]

We need to find the amount of cups of flour they have altogether.

Solution:

Now we can say that;

the amount of cups of flour they have altogether can be calculated by sum of Amount of flour Javon has and Amount of flour Sam has and Amount of flour Antoine has.

framing in equation form we get;

amount of cups of flour they have altogether = [tex]\frac{3}{2}+\frac{13}{3}+\frac{22}{6}[/tex]

Now to solve we need to make the denominator common by using L.C.M we get;

amount of cups of flour they have altogether = [tex]\frac{3\times3}{2\times3}+\frac{13\times2}{3\times2}+\frac{22\times1}{6\times1}=\frac{9}{6}+\frac{26}{6}+\frac{22}{6}[/tex]

Now Denominators are common so we will add the numerators we get;

amount of cups of flour they have altogether = [tex]\frac{9+26+22}{6}= \frac{57}{6}\ cups\ \ OR \ \ 9\frac{3}{6}\ cups[/tex]

Hence They have [tex]9\frac{3}{6}\ cups[/tex] of flour altogether.

Answer:

56

Step-by-step explanation:

z varies jointly with x and y:

z = kxy

When x = 2 and y = 2, z = 7.

7 = k(2)(2)

k = 7/4

z = 7/4 xy

When x = 4 and y = 8:

z = 7/4 (4)(8)

z = 56

Answer:

48.6625 before rounding, I'm sure the instruction told you where it preferred you to round.

Step-by-step explanation:

1. Convert percent value to a decimal.

The way to do this is by moving the period at 15.00 two places to the left.

2. Now that you have the decimal .15, multiply it by Mrs. King's subtotal (57.25).

you should get 8.5875.

3. Subtract the discount amnt. (8.5875) from the subtotal (57.25).

You should get 48.6625.

Answer: +$45

Step-by-step explanation: if his actual pay for the week was $100 then from the question he incorrectly calculated it as {$100 + $45} = $145 which is $45 above his actual pay.

Error = measured value - actual

value.

= $145 -$100 =$45.

NOTE: since the value he assumed{$145} is greater than his actual pay{$100}, we have to include a positive sign to the error{$45}.

Therefore, Error = +$45.

Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay.

The error Ray made when calculating his overtime pay was incorrectly calculating the additional pay. To find the correct overtime pay, we need to determine how many hours Ray worked in excess of his regular hours and the rate at which he receives overtime pay. Let's assume that Ray receives time-and-a-half for overtime work.

Therefore, Ray's error was incorrectly calculating his additional pay as $45 instead of the correct amount of $90.

https://brainly.com/question/33181476

#SPJ11

Answer:

Step-by-step explanation:

The sum of the interior angles = 180 (n-2)

where n is the number of sides of the polygon.

1) if the sum of the interior angles of a polygon equals 1980,

180(n - 2) = 1980

180n - 360 = 1980

180n = 1980 + 360 = 2340

n = 2340/180 = 13

2) if n = 9, the number of degrees would be

180(n - 2) = 180(9 - 2)

= 180 × 7 = 1260 degrees

3) 180(n - 2) = 1620

n - 2 = 1620/180 = 9

n = 9 + 2 = 11

4) n = 18

The number of degrees would be

180(n - 2) = 180(18 - 2) = 2880 degrees.

5) n = 17

The number of degrees would be

180(n - 2) = 180(17 - 2) = 2700 degrees.

6) the sum of the interior angles of a quadrilateral is 360 degrees.

Answer:

[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]    

[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=32.5[/tex] represent the sample mean  

[tex]s=30[/tex] represent the sample standard deviation

[tex]n=225[/tex] sample size  

[tex]\mu_o =30[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 30[/tex]  

Alternative hypothesis:[tex]\mu > 30[/tex]  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=225-1=224[/tex]  

Since is a one side rigth tailed test the p value would be:  

[tex]p_v =P(t_{(224)}>1.25)=0.106[/tex]  

Conclusion  

If we compare the p value and the significance level given [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.  

Answer:

The probability of selecting a red car off the lot is 0.231.

Step-by-step explanation:

Given:

Number of white cars = 25

Number of blue cars = 15

Number of red cars = 21

Number of black cars = 30

We need to find the probability of selecting a red car off the lot.

Solution:

First we will find the Total number of cars in the lot.

Now we can say that;

Total number of cars in the lot is equal to sum of Number of white cars and Number of blue cars and Number of red cars and Number of black cars.

framing in equation form we get;

Total number of cars in the lot = [tex]25+15+21+30 = 91[/tex]

Now to find the probability of selecting a red car off the lot we will divide Number of red cars by Total number of cars in the lot.

framing in equation form we get;

P(red) = [tex]\frac{21}{91}=0.2307[/tex]

Rounding to three decimals we get;

P(red) = 0.231

Hence The probability of selecting a red car off the lot is 0.231.

The probability of selecting a red car off the lot, rounded to three decimals, is 0.231.

First, we need to find the total number of cars on the lot by adding up the number of cars of each color:

 Total number of cars = Number of white cars + Number of blue cars + Number of red cars + Number of black cars

Total number of cars = 25 + 15 + 21 + 30

Total number of cars = 91

 Next, we find the probability of selecting a red car by dividing the number of red cars by the total number of cars:

Probability of selecting a red car = Number of red cars / Total number of cars

Probability of selecting a red car = 21 / 91

To round to three decimals, we perform the division:

 Probability of selecting a red car = 0.2308

Rounded to three decimals, the probability is 0.231.

Answer:

88

Step-by-step explanation:

9 pages

Each holds 9

He has 7 more

81+7=88

Answer:

Lia needs [tex]7\frac{2}{4}\ cups[/tex] of flour and corn meal.

Step-by-step explanation:

Given:

Amount of flour needed = [tex]2\frac{3}{4} \ cups[/tex]

[tex]2\frac{3}{4} \ cups[/tex] can be Rewritten as [tex]\frac{11}{4}\ cups[/tex]

Amount of flour needed =  [tex]\frac{11}{4}\ cups[/tex]

Amount of Corn meal needed = [tex]4\frac{3}{4}\ cups[/tex]

[tex]4\frac{3}{4}\ cups[/tex] can be Rewritten as [tex]\frac{19}{4}\ cups[/tex]

Amount of Corn meal needed =  [tex]\frac{19}{4}\ cups[/tex]

We need to find the total amount of of flour and cornmeal she needs.

Solution:

Now we can say that;

the total amount of of flour and cornmeal she needs is equal to sum of Amount of flour needed and Amount of Corn meal needed.

framing in equation form we get;

the total amount of of flour and cornmeal she needs = [tex]\frac{11}{4}+\frac{19}{4}=\frac{11+19}{4}=\frac{30}{4}\ cups\ \ OR\ \ 7\frac{2}{4}\ cups[/tex]

Since Answers are not given:

Kindly chose the answer which contains below data.

Hence Lia needs [tex]7\frac{2}{4}\ cups[/tex] of flour and corn meal.

Answer:

Tap A 3hrs

Tap B 6hrs

Step-by-step explanation:

Let the volume of the swimming pool be Xm^3.

Now, to get the appropriate volume, we know we need to multiply the rate by the time. Let the rate of the taps be R1 and R2 respectively, while the time taken to fill the swimming pool be Ta and Tb respectively.

x/Ta= Ra

x/Tb= Rb

X/(Ra + Rb)= 2

Ta = Tb - 3

From equation 2:

X = 2( Ra + Rb)

Substituting the values of Ra and Rb Using the first set of equations

X = 2( x/Ta + x/Tb)

But Ta = Tb - 3

1/2 = 1/(Tb - 3)+ 1/Tb

0.5 = (Tb + Tb-3)/Tb(Tb - 3)

At this juncture let’s say Tb = y

0.5 = (2y - 3)/y(y - 3)

y(y-3 ) = 4y - 6

y^2 -3y - 4y + 6 = 0

y^2 -7y + 6= 0

Solving the quadratic equation, we get y =

y = Tb = 6hrs or 1hr

We remove one hour as we know that Tap A takes 3hrs left than tap B and there is nothing like negative hours

Now, we get Ta by Tb -3 = 6 - 3 = 3hrs

Frank is incorrect because both fractions are not same.

Step-by-step explanation:

We have to compare both fractions in their simplest forms to compare them

Given

Baseball cards in Missy's Collection:    [tex]\frac{3}{4}[/tex]

Baseball cards in Frank's Collection:  [tex]\frac{8}{12}[/tex]

Converting the fraction in simplest form will give us:

[tex]\frac{2}{3}[/tex]

Both the fractions are not same as one is 3/4 and one is 2/3.

Hence,

Frank is incorrect

Keywords: Fractions, decimals

Learn more about fractions at:

#LearnwithBrainly

Question is Incomplete,Complete Question is given below;

Joaquin can send 250 text each month so far this month he has sent 141 text message let T represent the number of text messages Joaquin can send during the rest of the month. Write an inequality to model the situation. Solve the inequality for t.

Answer:

The Inequality modelling the situation is [tex]141+t\leq 250[/tex].

Joaquin can send at the most 109 messages for the remaining of the month.

Step-by-step explanation:

Given:

Number of messages already sent = 141

Total number of messages he can send = 250

We need to write the inequality to model the situation and solve for the same.

Solution:

Let remaining number of messages he can send be 't'.

Now we know that;

Number of messages already sent plus remaining number of messages he can send should be less than or equal to Total number of messages he can send.

framing in equation form we get;

[tex]141+t\leq 250[/tex]

Hence The Inequality modelling the situation is [tex]141+t\leq 250[/tex].

On Solving the above equality we will find the value of 't'.

Now we will subtract both side by 141 using subtraction property of inequality we get;

[tex]141+t-141\leq 250-141\\\\t\leq 109[/tex]

Hence Joaquin can send at the most 109 messages for the remaining of the month.

In a universe of numbers 1 to 10, sets A, B, and C hold specific values. We explore intersections, differences, and unions. A's complement intersects C to give {2, 6, 8}, while B minus C's complement reveals {2, 4}. Their union boasts {1, 2, 3, 4, 5, 7, 10}, while B's complement meets A minus C in {7, 10}. Finally, (A minus B) and (B minus C) share no elements, resulting in an empty set.

Set Operations in U

Here's the breakdown of each set operation and the resulting sets:

(a) \overline{A} ∩ C:

\overline{A}: The complement of A, which includes all elements in U that are not in A. In this case, U \ A = {2, 3, 5, 6, 8, 9}.

\overline{A} ∩ C: The intersection of U \ A and C. This gives us {2, 6, 8}.

|\overline{A} ∩ C|: The cardinality (number of elements) of the intersection. Therefore, |\overline{A} ∩ C| = 3.

(b) B - \overline{C}:

\overline{C}: The complement of C, which includes all elements in U that are not in C. In this case, U \ C = {1, 3, 5, 7, 9, 10}.

B - \overline{C}: The difference between B and U \ C. This removes elements from B that are also in U \ C. Therefore, B - \overline{C} = {2, 4}.

|B - \overline{C}|: The cardinality of the difference. Hence, |B - \overline{C}| = 2.

(c) B ∪ A:

B ∪ A: The union of B and A, which includes all elements that are in either B or A or both. In this case, B ∪ A = {1, 2, 3, 4, 5, 7, 10}.

|B ∪ A|: The cardinality of the union. Therefore, |B ∪ A| = 7.

(d) \overline{B} ∩ (A - C):

\overline{B}: The complement of B, which includes all elements in U that are not in B. In this case, U \ B = {6, 7, 8, 9, 10}.

A - C: The difference between A and C. This removes elements from A that are also in C. Therefore, A - C = {1, 7, 10}.

\overline{B} ∩ (A - C): The intersection of U \ B and A - C. This gives us {7, 10}.

|\overline{B} ∩ (A - C)|: The cardinality of the intersection. Hence, |\overline{B} ∩ (A - C)| = 2.

(e) (A - B) ∩ (B - C):

A - B: The difference between A and B. This removes elements from A that are also in B. Therefore, A - B = {7, 10}.

B - C: The difference between B and C. As mentioned earlier, B - C = {2, 4}.

(A - B) ∩ (B - C)**: The intersection of A - B and B - C. Since no elements are shared between these sets, the intersection is empty.

|(A - B) ∩ (B - C)|**: The cardinality of the empty set is 0. Therefore, |(A - B) ∩ (B - C)| = 0.

Answer:

The number of bagels is 11 and the cups of coffee is 12.

Step-by-step explanation:

Given:

Keisha bought cups of coffee and bagels for the people in her office. Each bagel cost $2 and each cup of coffee cost $1.50.

Keisha spent a total of $40 to buy 23 items.

Now, to find the number of cups of bagels and coffee.

As given in question:

Let [tex]x[/tex] represent the number of bagels.

And [tex]y[/tex] represent the number of cups of coffee.

So, the total number of items:

[tex]x+y=23[/tex]

[tex]x=23-y[/tex]    ......(1)

Now, the total money spent on items:

[tex]2x+1.50y=40[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex]2(23-y)+1.50y=40[/tex]

[tex]46-2y+1.50y=40[/tex]

[tex]46-0.50y=40[/tex]

Subtracting both sides by 46 we get:

[tex]-0.50y=-6[/tex]

Dividing both sides by -0.50 we get:

[tex]y=12.[/tex]

The number of cups of coffee = 12.

Now, to get the number of bagel we substitute the value of [tex]y[/tex] in equation (1):

[tex]x=23-y[/tex]

[tex]x=23-12[/tex]

[tex]x=11.[/tex]

The number of bagels = 11.

Therefore, the number of bagels is 11 and the cups of coffee is 12.

Answer:

Speed of first train = 36 mph

Speed of second train =  60 mph

Step-by-step explanation:

Given:

First train leaves Cincinnati at 2:00 PM

Second train leaves same station at 4:00 PM

Speed of second train is 24 mph faster than first train.

The second train overtakes the first at 7:00 PM

To find the speeds of each train.

Solution:

First train:

Let speed of first train be = [tex]x\ mph[/tex]

Time of travel between 2:00 PM to 7:00 PM = [tex]7-2=5\ h[/tex]

Distance traveled by 1st train in 5 hours in miles = [tex]Speed\times time = x\times 5 = 5x[/tex]

Second train:

Then, speed of second train will be = [tex](x+24)\ mph[/tex]

Time of travel between 4:00 PM to 7:00 PM =[tex]7-4 = 3\ h[/tex]

Distance traveled by second train in 3 hours in miles = [tex]Speed\times time = (x+24)\times 3=3x+72[/tex]

At 7:00 PM both trains meet as the second train overtakes the first. This means the distance traveled by both the trains is same at 7:00 PM as they both leave from same stations.

Thus, we have:

[tex]5x=3x+72[/tex]

Solving for [tex]x[/tex]

Subtracting both sides by [tex]3x[/tex]

[tex]5x-3x=3x-3x+72[/tex]

[tex]2x=72[/tex]

Dividing both sides by 2.

[tex]\frac{2x}{2}=\frac{72}{2}[/tex]

∴ [tex]x=36[/tex]

Speed of first train = 36 mph

Speed of second train = [tex]36+24=[/tex] 60 mph

Final answer:

The speed of the first train is 36 mph and the speed of the second train, which is 24 mph faster, is 60 mph. This was determined by setting up an equation based on the equal distances covered by both trains when the second overtakes the first.

Explanation:

The question involves solving a rate, time, and distance problem typically found in algebra or kinematics. To find the speeds of the two trains, we can set up an equation based on the fact that the distance covered by both trains is the same at the point where the second train overtakes the first. Let's define the speed of the first train as s (in mph). Therefore, the speed of the second train will be s + 24 mph. Since the first train leaves at 2:00 pm and is overtaken at 7:00 pm, it travels for 5 hours. The second train, leaving two hours later at 4:00 pm, travels for 3 hours.

The distance covered by each train can be expressed as their speed multiplied by the time traveled. For the first train, it's s 5 hours, and for the second train, it's (s + 24) 3 hours. Setting these two distances equal gives us:

s 5 = (s + 24)  imes 3

Solving for s gives:

s  imes 5 = 3s + 72
5s - 3s = 72
2s = 72
s = 36

So, the speed of the first train is 36 mph, and the speed of the second train is 60 mph (36 + 24).

Final answer:

To find the possible values of b in the equation 2a + b = 15.7 in an isosceles triangle, we can assume different values for a and solve for b. Two lengths that make sense for possible values of b are 5.7 and 3.7.

Explanation:

To determine which lengths make sense for possible values of b in the equation 2a + b = 15.7, we need to consider the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Since the triangle is isosceles, two sides have the same length, which is represented by a. Let's assume that a = 5 (one possible value) and substitute it into the equation: 2(5) + b = 15.7. Solving for b, we get b = 5.7. This means that a possible value for b is 5.7. Another option is when a = 6, which gives us b = 3.7. Therefore, the two lengths that make sense for possible values of b are 5.7 and 3.7.

Answer:

a) [tex] P(A|B) = \frac{15/83}{44/83} =\frac{15}{44}=0.341[/tex]

b) [tex] P(B|A) = \frac{29/83}{44/83} =\frac{29}{44}=0.659[/tex]

c)  A. A student given a $1 bill is more likely to have kept the money.

Because the probability 0.659 is atmoslt two times greater than 0.341

Step-by-step explanation:

Assuming the following table:

                                                     Purchased Gum      Kept the Money   Total

Students Given 4 Quarters              25                              14                      39

Students Given $1 Bill                       15                               29                    44

Total                                                   40                              43                     83

a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.

For this case let's define the following events

B= "student was given $1 Bill"

A="The student spent the money"

For this case we want this conditional probability:

[tex] P(A|B) =\frac{P(A and B)}{P(B)}[/tex]

We have that [tex] P(A)= \frac{40}{83} , P(B)= \frac{44}{83}, P(A and B)= \frac{15}{83}[/tex]

And if we replace we got:

[tex] P(A|B) = \frac{15/83}{44/83} =\frac{15}{44}=0.341[/tex]

b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.

For this case let's define the following events

B= "student was given $1 Bill"

A="The student kept the money"

For this case we want this conditional probability:

[tex] P(A|B) =\frac{P(A and B)}{P(B)}[/tex]

We have that [tex] P(A)= \frac{43}{83} , P(B)= \frac{44}{83}, P(A and B)= \frac{29}{83}[/tex]

And if we replace we got:

[tex] P(B|A) = \frac{29/83}{44/83} =\frac{29}{44}=0.659[/tex]

c. what do the preceding results suggest?

For this case the best solution is:

A. A student given a $1 bill is more likely to have kept the money.

Because the probability 0.659 is atmoslt two times greater than 0.341

Using the principles of conditional probability, we find that a student given a $1 bill is more likely to spend the money (probability approximately 0.641) than keep it (probability approximately 0.359). Therefore, option B is the correct interpretation of these results.

To answer this question, we should first understand that this problem is fundamentally about conditional probability, the probability of an event given that another event has occurred. Let's take this step by step.

Part a: Here, we want to find the probability of selecting a student who spent the money, given that the student was given a $1 bill. This number would be the number of $1 bill students who bought gum divided by the total number of $1 bill students. This equates to 25/(25+14) = 0.641. So, the probability is approximately 0.641.

Part b: In this situation, we're looking for the probability of selecting a student who kept the money, given that the student was given a $1 bill. This would be the number of $1 bill students who kept the money divided by the total number of $1 bill students, or 14/(25+14) = 0.359. The probability is approximately 0.359.

Part c: These results suggest that the appropriate solution is B: 'A student given a $1 bill is more likely to have spent the money than a student given four quarters.'

https://brainly.com/question/32171649

#SPJ11

Answer:

x = 27.2.

Step-by-step explanation:

As BD || CE   the triangles ABD and ACE are similar.

AB = 25 - 8 = 17.

AB / AC = AD / AE     ( similar triangles)

17 / 25 = x / 40

x = 17*40 / 25

= 27.2.