the ratio of the measures of three angles of a triangle is 3:6:1. Find the measurements of each angle

Answers

Answer 1

Gabe, you are doing great. Now you need to solve for x:

3x + 6x + x = 180

10x = 180

dividing by 10 at both sides:

10x/10 = 180/10

x = 18 That is the answer you have.

Finally, you need to multiply the ratio for the value of x, you just calculated:

Side 1 = 3 * 18

Side 2 = 6 * 18

Side 3 = 1 * 18


Related Questions

-4x + 0.4y = -0.8 6x + 0.4y = 4.2 The solution to the system is ( , ).

Answers

An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.

Explain about the solution?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Take into account the formula 7x - 35 = 0. If we solve, we get either x = 5 or 7x = 35. The following linear equation only has one solution, x = 5, because the above linear equation is only true if x = 5.

The solution to this system (x=0.5 y=3)

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use the ratio to solve , how can the table help me to solve ? how do I find part? please assist me

Answers

We have to determine te 30 percent of 50.

[tex]\frac{30}{100}\times50=15[/tex]

Hence the answer is 15.

please help
A bird flying over water drops a crab from a height of 10 feet. The distance

the crab is from the water as it falls can be represented by d in the equation

d equals negative t to the power of 2 end exponent plus 10, where t is time in seconds. To catch the crab as it falls, a different

bird flies along a path represented by the equation d equals 5 t plus 5. In how many

seconds will the second bird catch the crab before it hits the water?

Answers

Solving a quadratic equation we can see that the second bird catches the crab after 0.85 seconds.

In how many seconds the second bird catches the crab?

The equation that describes the height of the crab is:

d = -t^2 + 10

The equation that represents the path of the second bird is:

d' = 5t + 5

The bird will be able to catch the crab when both are at the same height, this happens when:

-t^2 + 10 = 5t + 5

We need to solve this for t.

-t^2 + 10 - 5t - 5 = 0

-t^2 - 5t + 5 = 0

Using the quadratic formula we will get:

t = (5 ± √( (-5)^2 - 4*(-1)*5))/(2*-1)

t =  (5 ± 6.7)/(-2)

We only care for the positive solution, which is:

t = (5 - 6.7)/(-2)  = 0.85

So the bird catches the crab after 0.85 seconds.

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Calculate each value requested for the following set of scores.a. ΣΧ=b. ΣΧ2=c. (ΣΧ)2=d. SS=Scores: 2, 3, 0,5Round to the hundredths place.

Answers

a.

[tex]\Sigma x=2+3+0+5=5+5=10[/tex]

b.

[tex]\Sigma x^2=2^2+3^2+0^2+5^2=4+9+25=38[/tex]

c.

[tex](\Sigma x)^2=(2+3+0+5)^2=10^2=100[/tex]

d.

[tex]\begin{gathered} SS=\Sigma(x-\bar{x})^2 \\ where: \\ \bar{x}=\frac{2+3+0+5}{4}=\frac{10}{4}=2.5 \\ so: \\ SS=(2-2.5)^2+(3-2.5)^2+(0-2.5)^2+(5-2.5)^2 \\ SS=(-0.5)^2+(0.5)^2+(-2.5)^2+(2.5)^2 \\ SS=13 \end{gathered}[/tex]

clasificar el siguiente polinomio2xy +9b -4z + 9

Answers

Los polinomios se clasifican según el número de términos que lo componen.

Los términos de una expresión están separados entre sí por los signos "+" y "-"

Se conoce como "monomio" a un polinomio con un solo término.

Son ejemplos de monomios:

6x²

2x

z

Un "binomio" es un polinomio de dos terminos.

Por ejemplo:

2x-3y

4x²+1

5y⁴z-2x²

Un "trinomio" es un polinomio con tres términos.

Por ejemplo:

2x+3y+z

y²-z+7

Un "cuadrimonio" es un polinomio de cuatro términos

Por ejemplo

xy+5y-9z+4

Los polinomios también pueden clasificarse según su grado. El grado del polinomio está dado por el valor del mayor exponente.

Un polinomio de grado cero es aquel que tiene coefficientes igual a cero.

Por ejemplo

0x²+0x

Un polinomio de primmer grado es aquel en el que la variable está elevada a la uno. En general este exponente no se escribe por lo que en un polinomio grado uno las variables no van a tener exponente.

Por ejemplo

x+2

x+y+4

Un polinomio de segundo grado es aquel cuyo mayor exponente es dos, es decir, tiene un termino elevado al cuadrado.

Por ejemplo:

x+y²+3

x-9y+5z²-7

Un polinomio de tercer grado es aquel cuyo mayor exponente es tres, es decir, al menos una variable está elevada al cubo.

Por ejemplo:

x

x³+y²

2x-y³+25

Teniendo estas definiciones en cuenta, puedes clasificar el polinomio:

[tex]2xy+9b-4x+9[/tex]

Este polinomio tiene 4 términos, "2xy", "9b", "4x" y "9" por lo que se lo puede clasificar como un cuadrimonio.

Como puedes ver, ninguna de las variables tiene exponente, es decir que, el exponente de mayor valor es 1, por lo que se puede clasificar como un polinomio de primer grado.

Entonces esta expresión es un cuadrimonio de primer grado

Solve the inequality and express your answer in intervalvenation use decimal form for numeric values

Answers

Given:

[tex]\frac{20}{4}<\frac{z+7}{2}<\frac{25}{4}[/tex]

Required :

To solve this

Explanation:

[tex]\begin{gathered} first\text{ of all separate compound inequalities into system of inequalities} \\ \\ \frac{z+7}{2}>\frac{20}{4}\text{ }\frac{z+7}{2}<\frac{25}{4} \\ \\ reduce\text{ the fraction} \\ \\ \frac{z+7}{2}>5\text{ or z+7>2}\times5 \\ \\ z+7>10 \\ \\ z>10-7 \\ \\ z>3 \end{gathered}[/tex][tex]\begin{gathered} \frac{z+7}{2}<\frac{25}{4} \\ \\ multiply\text{ both sides of the inequality by the least common denominator} \\ \\ 4\times\frac{z+7}{2}<4\times\frac{25}{4} \\ \\ reduce\text{ the expression to the lowest term} \\ \\ 2(z+7)<25 \\ \\ 2z+14<25 \\ \\ 2z<25-14 \\ \\ z<\frac{11}{2} \end{gathered}[/tex][tex]\begin{gathered} z>3\text{ and z <}\frac{11}{2} \\ \\ 3Required answer:

3

A line passes through (5,-4) and (-1,-4). Write the equation of the line in slope-intercept form.

Answers

Explanation:

The formula of the slope of a line that passes through points (x1, y1) and (x2, y2) is:

[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]

For this problem the slope is:

[tex]m=\frac{-4-(-4)}{5-(-1)}=\frac{-4+4}{5+1}=\frac{0}{6}=0[/tex]

A slope of zero indicates that the line is horizontal. Therefore it is a constant.

The slope-intercept form of the equation of a line is:

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

Where m is the slope and b is the y-intercept. In this case, the slope is zero so we just have:

[tex]y=b[/tex]

b is the y-coordinate of the given points: b = -4

Answer:

y = -4

identify which value is not in the domain of the piecewise function

Answers

From the graph we notice that the only value of x for which the fuction generating the graph it not defined is x=-3.

Answer: A).

Lisa received a 70 gift card for a coffee store. She used it in buying some coffee that cost 8.49 per pound. After buying the coffee, she had 36.04 left on her card. How many pounds of coffee did she buy?

Answers

Initially she had 70 pounds in her gift card.

After buying her coffee she was left with 36.04 pounds.

Amount she spent on coffee is 70-36.04=34.96

One pound of coffee costs 8.49

To calculate how many pounds of coffee Lisa bought ->

34.96/8.49= 4

So in total she bought 4 pounds of coffee.

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Graph the image of the figure on the right under the given translation.T(3,2)(x,y)

Answers

To translate the triangle we will translate each vertex using the rule of translation given

The vertice of the triangle are

(-1, 4), (-5, -2), (-8, 2)

The translation rule is T (3, 2)

That means we will add the x-coordinate of each point by 3,

and the y-coordinates by 2

The image of point (-1, 4) = (-1 + 3, 4 + 2) = (2, 6)

The image of point (-5, -2) = (-5 + 3, -2 + 2) = (-2, 0)

The image of point (-8, 2) = (-8 + 3, 2 + 2) = (-5, 4)

That means the triangle will move 3 units right and 2 units up

The images of the vertices are (2, 6), (-2, 0), (-5, 4)

Graph the image of the figure on the right under the given translation.T(3,2)(x,y)

a1.Find the equation for a polynomial f(x) that satisfies the following:Degree 5Root of multiplicity 1 at x = 3• Root of multiplicity 2 at x = 2• Root of multiplicity 2 at x = -3y-intercept of (0, -216)f(x) =

Answers

we have that

the polynomial is of the form

f(x)=a(x-3)(x-2)^2(x+3)^2

where

a is the leading coefficient

y-intercept -----> (0,-216)

For x=0

substitute and solve for a

-216=a(0-3)(0-2)^2)(0+3)^2

-216=a(-3)(-2)^2(3)^2

-216=a(-3)(4)(9)

-216=-108a

a=2

therefore

[tex]f(x)=2(x-3)(x-2)^2(x+3)^2[/tex]

Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.

Answers

The linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Spencer bought 17 tickets for the rides and spent a total of $30.75 at a county fair.

Let x be the number of tickets and y be the total cost:

Total ticket cost = 17×1.25 = $21.25

Admission fari = 30.75 - 21.25 = $9.5

The linear equation is:

y = 1.25x + 9.5

Here 9.5 represents the fixed admission fair.

Thus, the linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.

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Urgent!!! Long division

Answers

So, we know the bus can hold 20 people in 15 minutes, so the rate per hour is:

20/15m

60m/15m
4

20/15 x 4/4m
80/60m (80 per hour)

4/1 = 4

80/60m x 4/4
320/240m
320/4h

320 people could ride the bus in 4 hours.

Opens down with compression coefficient of 0.2. Shifted right 1 unit and down 6 unitshow do I right this as a parabola equation?

Answers

In this case, we'll have to carry out several steps to find the solution.

Step 01:

opens down

compression coefficient = 0.2

translated:

right 1

down 6

parabola equation = ?

Step 02:

opens down

(x - h)² = -4p (y - k)

compression coefficient = 0.2

0.2 (x - h)² = -4p (y - k)

translated:

right 1

down 6

0.2 (x - 1)² = -4p (y + 6)

The answer is:

0.2 (x - 1)² = -4p (y + 6)

Your company fireworks show is getting bigger, The boss has requested that the viewing area (which is 4 ft x 6 ft) be doubled; the parking area (which is 540 ft x 75 ft) be doubled; and the city ordinance requires the fireworks to be in the air less than 4 seconds and not go any higher than 600 feet.

Answer the following questions:

1. Determine the dimensions of the new viewing area. The existing area is 6 ft long by 4 ft wide.

2. Determine the dimensions of the new parking area. The existing area is 540 ft long by 75 feet wide.

3. Determine the height of the fireworks and how long they are in the air using the following equation:

ℎ= −500/9 t^2 + 1000/3 t + 10

Answers

The solution to the questions are

New viewing area dimension: 8 ft by 12 ftNew parking area dimension: 1080 ft by 150 ftHeight of fireworks: 510 units

The dimension of the new viewing area

From the question, we have the following parameters:

Initial dimension of the viewing area:

4 ft by 6 ft

The scale of dilation is given as

Scale = 2 (i.e. doubled)

Using the above as a guide, the new dimensions are calculated using

New = Old * Scale

So, we have

New = (4 ft by 6 ft) x 2

Evaluate

New = 8 ft by 12 ft

The dimension of the new parking area

The given parameters are

Initial dimension of the parking area:

540 ft by 75 ft

We use the same scale factor as (a) i.e.

Scale = 2 (i.e. doubled)

Using the above as a guide, the new dimensions are calculated using

New = Old * Scale

So, we have

New = (540 ft by 75 ft) x 2

Evaluate

New = 1080 ft by 150 ft

The height of fireworks

The function is given as

ℎ= −500/9 t^2 + 1000/3 t + 10

Differentiate the function

So, we have

ℎ'= −1000/9 t + 1000/3

Set the differentiated function to 0

So, we have

−1000/9 t + 1000/3 = 0

This gives

1000/9 t = 1000/3

Multiply  both sides by 9/1000

t = 3

Substitute 3 for t in ℎ= −500/9 t^2 + 1000/3 t + 10

ℎ = −500/9 x 3^2 + 1000/3 x 3 + 10

Evaluate

ℎ = 510

Hence, the height is 510 units

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Find the minimum and maximum values of the function on the interval [11,27].

Answers

Ok I will figure this out for you.

what is 5.37 with 15% discount

Answers

Answer

5.37 with 15% discount = 4.5645

Explanation

5.37 with 15% discount

= 5.37 - (15% of 5.37)

= 5.37 - 0.15(5.37)

= 5.37 - 0.8055

= 4.5645

Hope this Helps!!!

Answer:

Step-by-step explanation:

15% off 5.37 is 4.56.

The difference is 0.81

I would like to this math sentence question that I will send a picture of

Answers

Let

x -----> number of hours

we have that

the inequality that represents this situation is

[tex]45-12t\ge9[/tex]

solve for t

[tex]\begin{gathered} -12t\ge9-45 \\ -12t\ge-36 \\ t\leq3 \end{gathered}[/tex]

that means

the bakery can sell bread for a timeless than or equal to 3 hours

I need help with Slopes!

Answers

we know that

To find out the slope of the line, we use the formula

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we need two points

Looking at the graph

we take the points

(1,3 ) and (2,5)

substitute in the formula above

[tex]\begin{gathered} m=\frac{5-3}{2-1} \\ m=\frac{2}{1} \\ m=2 \end{gathered}[/tex]

therefore

the slope of the line is 2

Question 2 of 5
Which of the following is not an expression?
A. + 1 = 4
B. 3 - 2x
C. 4x+7
D. x/3 - 1​

Answers

Answer:

A.

Step-by-step explanation:

The answer is A, because an expression does not have an equal sign.

Going to store for Quetion‘s 9X -7 equals -7

Answers

The polynomial 9x-7=-7. The value is x=0.

Given that,

The polynomial 9x-7=-7

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. We are able to perform mathematical operations on polynomial expressions such addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The terms Poly (meaning "many") and Nominal (meaning "terms") make form the word polynomial.

The highest exponent of a monomial contained within a polynomial is referred to as the polynomial's degree. So-called polynomial degrees are polynomial equations with one variable having the largest exponent.

9x-7=-7

9x=-7+7

9x=0

x=0

Therefore, The value is x=0

Complete question: The polynomial 9X -7 = -7. Find the value of x.

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Part A: At a fair, Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times. Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times. Let x represent the number of tickets it takes to ride a roller coaster. Let y represent the number of tickets it takes to ride the bumper cars. Model Derrick and Javier's trip to the fair by creating linear equations to represent how Derrick and Javier each used their ride tickets. 4 X + y = Derrick: Javier: X + Blank 1: 4 Blank 2: Blank 3: Blank 4:

Answers

x: number of tickets it takes to ride a roller coaster

y: number of tickets it takes to ride the bumper cars

Derrick used a total of 16 tickets to ride the roller coaster 4 times and the bumper cars 2 times, that is,

4x + 2y = 16

Javier used a total of 12 tickets to ride the roller coaster 2 times and the bumper cars 3 times, that is,

2x + 3y = 12

Which of the following inequalities is false?
A: 10 < 9 incorrect answer
B: 9 < 10 incorrect answer
C: 10 > 9 incorrect answer
D: 9 (is less than or equal to)

Answers

The inequalities 9 < 10 incorrect answer and 10 > 9 incorrect answer are false. Option (B) and Option (C) are false.

Before we determine the false statement, we must understand that all negative values are less than positive values and all positive values are greater than negative values,

For the inequality 10 < 9 incorrect answer

Since, it is given that 10 is less than 9 is incorrect answer and we know that 10 is greater than 9 . Therefore, this inequality is true.

For the inequality 9 < 10 incorrect answer

Since, it is given that 9 is less than 10 is incorrect answer but we know that 9 is less than 10. Therefore, this inequality is false.

For the inequality 10 > 9 incorrect answer

Since, it is given that 10 is greater than 9 is incorrect answer but we know  that 10 is greater than 9 . Therefore, this inequality is false.

For the inequality 9 (is less than or equal to) 10 incorrect answer

Since, it is given that 9 (is less than or equal to) 10 is incorrect answer and we know that 9 is less than 10. Therefore, this inequality is true.

Therefore, Option (B) and Option (C) are false.

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Can someone give examples of negative exponents in the world
Eg : seize of bacteria 1*10^-4

Answers

The example of negative exponent in the real world is the world's smallest bat, the bumblebee bat weighs of 7 × 10^-2 ounces

How to illustrate the information?

An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite.

The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. The bat has a negative exponent.

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Rick and Chumlee buy and sell sports collectibles. Rick bought 14 rookie cards and 13 autographed baseballs
for a total of 263 dollars. Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars. Let c be the cost
of each card and let b be the cost of an autographed baseball.
a) Write an equation relating the items bought by Rick:
b) Write an equation relating the items bought by Chumlee:
c) Solve the system above using substitution and interpret in context:
The cost of a card is
dollars.
dollars and the cost of a baseball is

Answers

a) equation relating the items bought by Rick is

14c + 13 b = 263

b)equation relating the items bought by Chumlee

17c +  4b = 284

C) The cost of a card is 16

The cost of a baseball is 3

What is basic algebra ?

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical truths. It takes variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. All branches of mathematics, including coordinate geometry, calculus, and trigonometry, employ algebra. A fundamental algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations like addition, subtraction, multiplication, division, etc. are done on variables and constants.

Rick and Chumlee buy and sell sports collectibles.

Let c be the cost of each card and let b be the cost of an autographed baseball.

Rick bought 14 rookie cards and 13 autographed baseballs

for a total of 263 dollars.

a)  equation relating the items bought by Rick is

14c + 13 b = 263

Chumlee bought 17 cards and 4 baseballs for a total of 284 dollars.

b)equation relating the items bought by Chumlee

17c +  4b = 284

C)

14c + 13 b = 263 .....(i)

17c +  4b = 284......(ii)

[tex]b = \frac{284-17c}{4}[/tex]

put the value of b in equation 1 you will get

14c +13([tex]\frac{284 - 17c}{4}[/tex])=263

56c + 3692 - 221c = 1052

175c = 2640

c = 16

[tex]b = \frac{284-17c}{4}[/tex].....(iii)

put the value of c in equation 3

b = [tex]\frac{284 - 17(16)}{4}\\ = \frac{12}{4}[/tex]

= 3

The cost of a card is 16

The cost of a baseball is 3

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While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet

Answers

The line sketch of the movement and positioning of Joe and the hill are shown below.

Brief description of the sketch made.

From the sketch, point A is where Joe started from heading towards the hill.

The hill is represented by BC and the height is h

25 degrees was the initial angle of elevation.

After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.

From triangle BCD,

Using the trigonometric function of tan,

[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]

From triangle ABC,

Using the trigonometric function of tan,

[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]

Therefore, the height of the hill is 385 feet

The correct answer is option B.

Jackie had 2 part time jobs at Shoney's Restaurant. One week she earned a total $306, working 12 hours as a cashier and 10 hours as a cook. The next week, sheworked 14 hours as a cashier and 22 hours as a cook, earning $512. How much doesshe earn per hour as a cashier?

Answers

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Represent the terms with a variable

Let x be the amount she earns per hour as a cashier

Let y be the amount she earns per hour as a cook

STEP 2: Interpret the statements in the question as seen below:

[tex]\begin{gathered} 12x+10y=306 \\ 14x+22y=512 \end{gathered}[/tex]

STEP 3: Solve the simultaneous equation using elimination to get x and y

[tex]\begin{gathered} 12x+10y=306---(1) \\ 14x+22y=512----(2) \\ \\ \text{ Multiply equation 1 by 14 and equation 2 by 12} \\ 14\lbrack12x+10y=306\rbrack\Rightarrow168x+140y=4284----(3) \\ 12\lbrack14x+22y=512\Rightarrow168x+264y=6144----(4) \\ \\ \text{Subtract equation 4 from equation 3} \\ 168x\text{ cancels 168x, we have;} \\ 140y-264y=4284-6144 \\ -124y=-1860 \\ \text{Divide both sides by -124} \\ \frac{-124y}{-124}=\frac{-18600}{-124} \\ y=15 \end{gathered}[/tex]

STEP 4: Solve any of equation to get the value of x

[tex]\begin{gathered} \text{From equation 1} \\ 12x+10y=306 \\ y=15\text{, By substitution;} \\ 12x+10(15)=306 \\ 12x+150=306 \\ \text{Subtract 150 from both sides} \\ 12x+150-150=306-150 \\ 12x=156 \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{156}{12} \\ x=13 \end{gathered}[/tex]

Since x represents the amount she earns as a cashier, hence She earns $13 per hour as a cashier

find the difference between the mode and median of the distribution of data

Answers

Step 1: Rewrite the dot plot in tabular form

Step : Compute the mode

From the table, we can see that the numer appears most ( that is the number with the highest frequence, f) is 4.

Therefore,

mode = 4

Step 3: Find the median

First arrange the data in ascending order. In this case, the data is already in ascending order.

If ∑f is odd, the median is the middle value which is at position

[tex]\frac{\sum f+1}{2}[/tex]

If ∑f is even, the median is the average of the two values at positions

[tex]\frac{\sum f}{2}\text{ and }\frac{\sum f}{2}+1[/tex]

In this case, ∑f = 12 is even.

Therefore, the median is the average of the numbers at position 6 and 7

number at position 6 is 3

number at position 7 is 4

Hence, the median is given by

[tex]\frac{3+4}{2}=\frac{7}{2}=3.5[/tex]

median = 3.5

Step 4: Find the difference between the median and mode

The difference is given by

[tex]4-3.5=0.5[/tex]

Hence the difference is 0.5

Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)

Answers

Given:

The expression is,

[tex]e^{6-8\ln (x)+\ln (y)}[/tex]

Explanation:

Simplify the expression by using logathimic properties.

[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]

Simplify further.

[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]

So answer is,

[tex]\frac{e^6y}{x^8}[/tex]

I need to show you a pic of the question

Answers

The y-intercept and the x-intercept are the various points on the y and x axes where the graph cuts through.

In this our graph, there are interceptions at y = 0.4 and x = 0.3.

Thus, y-intercept exists at (0, 0.4) and x intercept at (0.3, 0)

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