Complete the ratio table below to show ratios equivalent to 4:18.

Givens

The numbers are n and n + 1

Average = Av = 105

Equation

Av = (n)(n + 1)/2

Solution

Av = 105

n(n +1)/2 = 105    Multiply both sides by 2

n(n + 1) = 105 * 2

n(n + 1) = 210      Remove the brackets.

n^2 + n = 210     Subtract 210 from both sides

n^2 + n - 210 = 0

factor

(n+15)(n - 14)

n + 15 = 0

n = - 15

n = - 15 which is the smallest of the two answers.

n + 1 = - 14

Check

(-15)*(-14)/2 =

210/2

105        It does check.

Answer:

The numbers are n and n + 1

Average = Av = 105

Step-by-step explanation:

Answer:

5x + (-6) = -2

Step-by-step explanation:

Times is used in multiplication

Sum is used in addition

Answer:

Option 3 is right

z37 is between 2 and 3 standard deviations of the mean.

Step-by-step explanation:

Let X be a random variable which represents the mean number of miles that the employees in a department live from work

X is normal (N(29,3.6)

WE have to find Z score for X

Z =[tex]\frac{x-29}{3.6}[/tex]

=2.22

i.e. 37 is 2.22 std deviations from the mean.

In other words, z37 is between 2 and 3 standard deviations of the mean.

The z-score for z37 is approximately 2.22. This indicates that it lies between 2 and 3 standard deviations of the mean. Hence, the correct statement is: z37 is between 2 and 3 standard deviations of the mean.

To determine which statement is true regarding the z-score for the value z37, we need to calculate the z-score using the given mean and standard deviation.

This means that z37 is approximately 2.22 standard deviations away from the mean. Therefore, the correct statement is:

z37 is between 2 and 3 standard deviations of the mean.

In a normal distribution, about 95 percent of the x values lie within two standard deviations, and about 99.7 percent lie within three standard deviations of the mean.

Respuesta: x/2,5=y/5=4/5=0,8

x/2,5=y/5

Multiplicando ambos lados de la ecuación por 5:

5(x/2,5)=5(y/5)→2x=y→y=2x

Sustituyendo y por 2x en la ecuación x+y=6:

x+2x=6

Resolviendo para x: Sumando términos semejantes:

3x=6

Dividiendo ambos lados de la ecuación entre 3:

3x/3=6/3

x=2

Sustituyendo x por 2 en la formula y=2x

y=2(2)→y=4

Determinando la proporción:

x/2,5. Sustituyendo x por 2:

2/2,5

Multiplicando numerador y denominador por 2:

2*2/(2,5*2)=4/5

La proporción es 4/5=0,8

Si lo hacemos con y:

y/5

Reemplazando y por 4:

4/5=0,8 (la misma proporción)

To solve this problem yo must apply the proccedure shown below:

1. You must use the formula applied to calculate the area of the garden.

[tex]A=bh[/tex]

2. You know the value of the area ([tex]127^{\frac{1}{2}}ft^{2}=127.5ft^{2}[/tex] and the value of the heigth ([tex]8^{\frac{1}{2}}ft=8.5ft[/tex] , therefore, you only need to solve for the base:

[tex]b=\frac{A}{h}\\b=\frac{127.5ft}{8.5ft}\\b=15ft[/tex]

The answer is: 15 feet.

Answer:

7/4 < x < 11/2

Step-by-step explanation:

PLATO

Inequality which ensure triangle exists is 22 > 4x > 7.

" Inequality is defined as the relation between two quantities with the sign of inequality that is >, <, ≤ , ≥ ."

Theorem used

In ΔABC,

AB + BC >AC

AC+ BC >AB

AC + AB > BC

According to the question,

In triangle ABC.

AC = 18units

BC = 6x units,

AB = 2x + 4 units

Substitute the value in the inequality to ensure triangle exists we get,

  [tex]AB + BC > AC[/tex]

⇒[tex]2x + 4 + 6x > 18[/tex]

⇒[tex]8x > 18 - 4[/tex]

⇒ [tex]8x > 14[/tex]

⇒ [tex]4x > 7[/tex]                                    ___(1)

[tex]AC + AB > BC[/tex]

⇒ [tex]18 + 2x + 4 > 6x[/tex]

⇒ [tex]22 > 6x-2x[/tex]

⇒[tex]22 > 4x[/tex]                                   ____(2)

From (1) and (2) inequality of triangle we get,

[tex]22 > 4x > 7[/tex]

Hence, Inequality which ensure triangle exists is 22 > 4x > 7.

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The numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.

The scale factors are given which are 5, 0.9, -6, 8/5, 3/8

We have to find which one has a contraction or expansion.

What do you mean by contraction and expansion on a scale ?

If the scale factor is larger than 1 then it would be an expansion whereas the scale factor between 0 and 1 would be a contraction.

As per the question ;

The scale factors given are ;

5, 0.9, -6, 8/5, 3/8

We can also write it as ;

5 , 0.9 , -6 , 1.6 , 0.375

We know that ;

If the scale factor is larger than 1 , it would be an expansion.  

So ;

The factors we have listed that are larger than 1 are 8/5 and 5.

Also ;

If the scale factor is between 0 and 1 , it would be a contraction.  

So ;

The factors we have listed that are between 0 and 1 are 0.9 and 3/8.

Also ;

A negative scale factor will result in a larger, inverted value.  

So ;

The scale factor of -6 will also be an expansion.

Thus , the numbers 8/5 , 5 and -6 will have an expansion and numbers 0.9 and 3/8 will have contraction.

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5.1=s. Use the distributive property and add like terms

A

The domain is -∞ < x < ∞

B

The range is -∞ < x ≤ 3

C

The graph is increasing from -∞ < y < 3

D

The graph is decreasing from 3 > y > -∞

E

The local maximum is at ( - 2, 3 )

F

There are no local minimums

The graph of an absolute value function is a V or inverted V. The x-coordinate of the V's vertex provides the function's line of symmetry, and the y-coordinate of the V's vertex shows the minimum or maximum value of the function.

An absolute value function is a function that contains an algebraic expression within absolute value symbols. The graph of an absolute value function is a symmetrical V or inverted V, depending on the direction of the opening. The vertex of the V, which is the minimum or maximum point of the graph, provides two important pieces of information: the x-coordinate of the vertex gives us the equation's line of symmetry, and the y-coordinate represents the minimum or maximum value of the function, depending on the opening direction.

Let's say, for example, we have the graph of the function |x - 3| + 2. The vertex of this function is at the point (3, 2). Therefore, the line of symmetry is x = 3, and the minimum value of the function is 2.

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The correct solution is shown in the graph (D)

Given that the budget is $24 and the minimum is 7 tubs, the fourth graph shows the area in which both constraints are satisfied: triangular area between the points

7 small tubs

8 small tubs

3 large and 4 small tubs

Lets x = # of small tub of popcorn and y = # of large tub of popcorn

She needs to buy at least 7 tubs of popcorn: x + y >= 7

Each small tub of popcorn costs $3 and each large tub of popcorn costs $4 but she only has $24 in her wallet.

3x + 4y <= 24

So now you have the system of inequalities

x + y >= 7

3x + 4y <= 24

Find x and y intercepts of blue line

x + y = 7

x = 0 then y = 7

y = 0 then x = 7

The inequality sign is >= so it's above.

The blue line,  B and D are matching the results

Find x and y intercepts of red line

3x + 4y = 24

x = 0 then 4y = 24; y = 6

y = 0 then 3x = 24;   x = 8

The inequality sign is <= so it's below.

The red line,  Only B is matching

Answer

D is the solution of the system of inequalities.

To determine the time needed to layout a full magazine issue, multiply the time taken to layout 1/16 of an issue (3 days) by 16, resulting in 48 days total.

If a magazine can layout 1/16 of an issue in 3 days, then to calculate how many days it takes to layout one entire issue, we simply multiply the number of days it takes to layout 1/16 of the issue by 16.

This is because if 1/16 takes 3 days, then 1/8 (which is twice the amount of 1/16) would take twice as long

(3 days * 2 = 6 days),

and similarly, we can scale up to the full issue (1/1) by multiplying 3 days by 16.

The calculation would be:

Identify the portion of the issue completed: 1/16.

Identify the time taken for this portion: 3 days.

Calculate the time for the whole issue: 3 days * 16 = 48 days.

So, it would take 48 days to layout one full issue.

First of all this is a very poor question, and you should question it a bit. What are these figures? Are they regular? (first 2). Is the last one a parallelogram. I'm going to assume that the yellow one is a rectangle and the middle one is a pentagon and the last one is a parallelogram.

Yellow

A has 4 right angles (That's the property of a rectangle).

Green

B has 5 angles that are equal to 108 degrees. If you draw a 2 lines from any vertex you get 3 triangles. The size of the interior angles totals 3 triangles * 180 degrees = 540 degrees.

540/3 = 108.

Each angle in the interior is 108 degrees.

B has 5 angles all equal 108 degrees. All 5 are obtuse.

Red

Just by sight and assumption C has 2 obtuse angles, and 2 acute angles.

Step-by-step explanation:

The Fall Festival charges $0.75 per ticket for the rides. Kendall bought 18 tickets for rides and spent a total of $33.50 at the festival

0.75 per ticket. So cost of 18 tickets= 0.75 * 18 = $13.5

Kendall spent $13.50 for tickets . Total spent = $33.50

Total spent = ticket cost + admission cost

33.50 = 13.50 + admission

Admission cost = 33.50 - 13.50 = $20

(a)  y to represent the total cost , x to represent the number of ride tickets.

'b' represents the admission cost

(b)  General form of linear equation is y=mx+b

m = 0.75 and b = admission cost = 20

So equation becomes y = 0.75x + 20

(c) Initially, she has to pay the admission price $20. then 0.75 per ticket.

The value of x changes depends on the number of tickets she wants to buy.

y is the total cost she has to pay for x tickets with admission price

3 x 6 is the simplest way of saying it

Answer: 3x6 because there are 6 3's so it's 3x6

c > -13/10

The > should have _ under it.

Answer:

Her speed driving in nice weather is 50 mph and in thunderstorm is 32 mph.

Step-by-step explanation:

Barbara drives 50 miles in clear weather and then encounters a thunderstorm for the last 16 miles.

Suppose, her speed in nice weather is  [tex]x[/tex] mph.

As she drives 18 mph slower through the thunderstorm than she does in clear weather, so her speed in thunderstorm will be: [tex](x-18) mph[/tex]

We know that,  [tex]Time = \frac{Distance}{Speed}[/tex]

So, the time of driving in clear weather [tex]=\frac{50}{x}[/tex] hours

and the time of driving in thunderstorm [tex]=\frac{16}{x-18}[/tex] hours.

Given that, the total time for the trip is 1.5 hours. So, the equation will be......

[tex]\frac{50}{x}+ \frac{16}{x-18}=1.5 \\ \\ \frac{50x-900+16x}{x(x-18)}=1.5\\ \\ \frac{66x-900}{x(x-18)}=1.5 \\ \\ 1.5x(x-18)=66x-900\\ \\ 1.5x^2-27x=66x-900\\ \\ 1.5x^2-93x+900=0\\ \\ 1.5(x^2 -62x+600)=0\\ \\ x^2 -62x+600=0\\ \\ (x-50)(x-12)=0[/tex]

Using zero-product property.........

[tex]x-50=0\\ x=50\\ \\ and\\ \\ x-12=0\\ x=12[/tex]

We need to ignore [tex]x=12[/tex] here, otherwise the speed in thunderstorm will become negative.

So, her speed driving in nice weather is 50 mph and her speed driving in thunderstorm is (50-18) = 32 mph

Answer:

Drive Faster!

Step-by-step explanation:

Answer:

NO. |-6| = 6 - a positive integer

Step-by-step explanation:

|a| = a for a ≥ 0

examples

|2| = 2, |0| = 0, |0.56| = 0.56

|a| = -a for a < 0

examples

|-2| = -(-2) = 2, |-100| = -(-100) = 100, |-0.25| = 0.25

Therefore your answer:

|-6| = 6 > 0

Let x = a number

3(6 - x) = -9

Divide both sides of equation by 3.

6 - x = -3

Subtract 6 on both sides of equation.

-x = -9

Divide both sides of equation by -1.

x = 9

The number is 9.

The difference between a number and six is [tex] x-6 [/tex]. Twice this difference is [tex] 2(x-6) [/tex]. If you want this difference to be negative, six, you have

[tex] 2(x-6)=-6 [/tex]

Divide both sides by 2:

[tex] x-6 = -3 [/tex]

Add 6 to both sides:

[tex] x = 3 [/tex]

Least common denominator is 24

Answer:

easy 5 ,0 c the x axis is run 5 then you rise on the positive y axis 0 and theres your awnser

Step-by-step explanation:

The set of coordinates satisfies the equations 3x − 2y = 15 and 4x − y = 20 is (5, 0).

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

3x - 2y = 15 _____(1)

4x - y = 20 _____(2)

The point of intersection of (1) and (2).

3x - 2y = 15

3x = 15 + 2y

x = (15 + 2y) / 3 _____(3)

4x - y = 20

4x = 20 + y

x = (20 + y) / 4 ______(4)

From (3) and (4) we get,

(15 + 2y) / 3 = (20 + y) / 4

4(15 + 2y) = 3(20 + y)

60 + 8y = 60 + 3y

8y - 3y = 0

5y = 0

y = 0

Now,

y = 0 in (1) or (2) we get,

3x = 15

x = 5

(5, 0)

4x = 20

x = 5

(5, 0)

Thus,

The coordinates (5, 0) satisfy the equations.

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Answer:

The slope is 3 (answer choice A).

Step-by-step explanation:

Take a look at the two given points, (2, -5) and (4, 1).  As we move from the first point to the second, x increases by 2 and y increases by 6, so that the slope is m = 6/2, or 3.

M= change in y /change in x

(−10, 4), (2, −5)

M= -5-4/2-(-10)

M= -9/12

M- 3/4

Slope is - 3/4

answer:  [tex]m = -\frac{3}{4}[/tex]

work:

slope formula ==> [tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

plug the points in according to the formula

[tex]m = \frac{-5-4 }{2-(-10)}[/tex]

[tex]m = -\frac{9}{12}[/tex]

[tex]m = -\frac{3}{4}[/tex]  <== simplified, and final answer :)

hope this helps! ❤ from peachimin

A translation moves the image up, down and/or right, left.  It does not change its size or shape.

Try this: Move your pencil up and to the right.  Did its size or shape change? no

Answer: D

-92.34 is the answer

Final answer:

After Nicole's check for her electric bill was processed, her account was overdrawn. She then made a deposit equal to the overdraft amount, bringing her end-of-day balance to $0.00.

Explanation:

To determine the bank balance that Nicole had at the end of the day, we need to consider the transactions that affected her account. She started with $63.44. After her electric bill check of $186.56 was processed, her account would have been overdrawn by $186.56 - $63.44 = $123.12. To cover this overdraft, Nicole made a deposit equal to the amount her account was overdrawn. Therefore, she deposited $123.12, which brought her balance back to $0.

At the end of the day, Nicole's bank balance was $0.00.

y=10x+5 because x=3 so 10*3=30 and 30+5=35 which would mean that $35 is the lowest amount you can spend.

To stay within a $50 daily budget for activities, equations are created to determine the number of tubes (t) and canoes (c) that can be rented. With tube rentals at $5 and canoe rentals at $10, the group of ten can only rent tubes (t = 10), as renting canoes would exceed the budget (c = 0).

The question involves creating and solving a budget constraint problem similar to the examples provided for Janet Bain and Mr. Higgins. To accommodate the group of 10 people with a budget of $50 per day for activities, we need to write equations to determine how many tubes (t) and canoes (c) can be rented. We know that tube rentals cost $5 and canoe rentals cost $10. Each canoe holds up to three people.

First, we write an equation that represents the number of tubes and canoes needed:

Everyone needs a tube: t = 10

Canoes can hold three people: 3c ≥ 10 (since not everyone needs to be in a canoe at the same time)

Next, we write an equation for the total cost to remain within the budget: 5t + 10c ≤ 50 (cost of tubes plus canoes must be less than or equal to $50)

Using t = 10, we can substitute t in the cost equation: 5(10) + 10c ≤ 50

50 + 10c ≤ 50

10c ≤ 0

From the final inequality, c = 0; meaning you cannot rent any canoes if you're buying a tube for each person and staying within a $50 budget. Therefore, the group can only rent tubes, with 0 canoes.