The Stem-and-Leaf Plot and Box-and-Whisker Plot here show the average monthly temperatures for a city over the course of a year. What is the median number in this set of data?


A. 58
B. 56
C. 57
D. 59

We need to replace each letter with the required numbers (a with 2 and b with 4) in the expression they gave us,and then apply the orders for operation that are critical in math evaluation.

So first we write:

whre we have repkaced each letter by its value, making sure we use a parentheses to call the attention on the new values we are using.

Now we proceed using the order of operations that are simplified in the following pnemonics: PEMDAS.

P stands for "parenthesis" so we understand that first we need to solve whatever is in parenthesis in the original expression

E stands for "exponents", so they should ge next

MD stands for multiplications and divisions, which should go next

and finally AS which stands for "additions and subtractions" that go the very last in using operations between numbers.

So let's start by trying to address what is withing parenthesis in the first expression:

Here we have used that inside the parenthesis we had a product 3 times (4) that needs to be addressed first before doing the subtraction. So we did 3 (4) = 12 and then subtracted 12 from the number 2, obtaining a negative number "-10"

now proceed with the rest:

so iwe need now to

Answer:

The question isn't clear. Can you provide more information or context? What is A? Is it a set or a number? Without this information, I can't provide a meaningful answer.

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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3x−2y=12;−3x+8y=−6

Step: Solve3x−2y=12for x:

3x−2y=12

3x−2y+2y=12+2y(Add 2y to both sides)

3x=2y+12

3x

3

=

2y+12

3

(Divide both sides by 3)

x=

2

3

y+4

Step: Substitute

2

3

y+4forxin−3x+8y=−6:

−3x+8y=−6

−3(

2

3

y+4)+8y=−6

6y−12=−6(Simplify both sides of the equation)

6y−12+12=−6+12(Add 12 to both sides)

6y=6

6y

6

=

6

6

(Divide both sides by 6)

y=1

Step: Substitute1foryinx=

2

3

y+4:

x=

2

3

y+4

x=

2

3

(1)+4

x=

14

3

(Simplify both sides of the equation)

Answer:

x=

14

3

and y=1

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer:-16

Step-by-step explanation:

Answer:

Let x represent the number from the sentence.

Step-by-step explanation:

2(x) + 2(1/x) = 20/3

2x + 2/x = 20/3

multiply both sides of the equation by 3x

6x + 6 = 20x

6x - 20x + 6 = 0

6x - 18x - 2x + 6 = 0

6x(x-3 -2(x-3) = 0

(6x-2 = 0 or x-3 = 0

6x = 2 or x = 3

x = 2/6

x = 1/3

Since x represented the number

Therefore x = 1/3 or 3

Answer: Hello attached below is the complete question

answer :

It is convergent ,  sum = 7/12

Step-by-step explanation:

Sn = 1/3 + 1/4 - 1/n - 1/n+1

It is convergent  and the sum = 7/12

attached below is the remaining part of the solution

Answer: 54

Step-by-step explanation:

Let the nubmer = x.

Setting up the equation, we get

x+ 17 = 2x-37

17+37 = 2x-x

x = 54

\(\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ n=7\\ r=3 \end{cases} \\\\\\ S_7=a_1\left( \cfrac{1-r^7}{1-r} \right)\implies 5465=a_1\left( \cfrac{1-3^7}{1-3}\right)\implies 5465=a_1(1093) \\\\\\ \cfrac{5465}{1093}=a_1\implies \boxed{5=a_1}\)

The length KL is 8 units

The value of x is undefined

The length KL is 12 units

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

The rhombus

Also, we have

DK = 8

A rhombus is a quadrilateral with all sides equal.

So, we have

KL = 8

Here, we have

SKAL = 2x - 8

There is no point S on the rhombus

This means that

x = undefined

Here, we have

DM = 5y + 2 and DK = 3y + 6

A rhombus is a quadrilateral with all sides equal.

So, we have

5y + 2 = 3y + 6

Evaluate

2y = 4

Divide

y = 2

So, we have

KL = 5 * 2 + 2

KL = 12

Hence, the length KL is 12 units

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Answer:

E. 4/6 = 18/x

Step-by-step explanation:

4 hour using 6 logs

18 hours using x logs

The quotient of a number x and two tenths is 5x

Quotient is defined as the quantity derived from the division of two numbers.

From the information given, we are to find the the quotient of;

The quotient is written thus;

= x/ 2/ 10

Take the inverse of the denominator and multiply

= x × 10/ 2

= 10x/ 2

find common divisor

= 5x

Thus, the quotient of a number x and two tenths is 5x

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The end behavior of the function f(n) = 3(n + 2)²(n - 3)(n - 2) is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function for this problem is given as follows:

f(n) = 3(n + 2)²(n - 3)(n - 2).

Considering the degree, the function can be interpreted as follows:

\(3n^4\)

(for the limit when the input goes to infinity we consider only the term with the highest degree).

The leading coefficient is positive and the exponent is even, hence the end behavior is given as follows:

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I do not understand what do you mean

The denominator of the fraction at point Y is equal to 24.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Let the variable d represent the denominator of the fraction at point Y and since point Y is the same distance from 0 as point X, which is at 2/3 on a number line, this can be modeled by this mathematical expression:

8/d = 1 - 2/3

8/d = 1/3

Cross-multiplying, we have:

d = 8 × 3

d = 24.

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The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

The equation that represent each situation, in terms of x, is

The number of monthly movies watched, x, that would make the two plans have an equal monthly cost is 6 movies.

Let

Plan A:

A = 19 + 0.50x

Plan B:

B = 13 + 1.50x

Equate A and B

19 + 0.50x = 13 + 1.50x

collect like terms

19 - 13 = 1.50x - 0.50x

6 = x

Hence,

x = 6 movies

In conclusion, the number of monthly movies watched to have an equal amount is 6 movies.

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For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer: 2

FG is equal to 2 times FM

The value of a is 2.

A line segment is defined as a measured path between two places. Line segments can make up any polygon's sides because they have a set length.

The figure given below shows a line segment FG, where the length of line segment FG refers to the distance between its endpoints, F and G.

Given that M is the midpoint of FG

FG = 14a + 1 and  FM = 14.5

F______________M______________G

⇒ FG = FM + MG

Since M is the midpoint of FG, So FM = MG

⇒ FG = FM + FM

⇒ FG = 2FM

Substitute the values of FG = 14a + 1 and  FM = 14.5,

⇒ 14a + 1 = 2(14.5)

⇒ 14a + 1 = 29

⇒ 14a = 28

⇒ a = 28/14

⇒ a = 2

Hence, the value of a is 2.

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Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Answer: is A

Step-by-step explanation: