2x + 2 < 2(3x - 1)
I don’t understand this I have to solve the inequality

In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.

A. Cats who failed

The smallest positive integer which when divided by 5 leaves a remainder of 3 is 8

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

Divisor = 5

Remainder = 3

Using the above as a guide, we have the following:

Smallest integer = Divisor + Remainder

So, we have

Smallest integer = 5 + 3

Evaluate

Smallest integer = 8

Hence, the smallest is 8

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1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x

1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x

2) The equation will be; y = ²/₃ +¹/₄x

1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;

The addition of both gives to the book thickness of;

1/4 + 1/4 = 1/2 inch, despite how many pages the book  has.

We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:

y = ¹/₂ + ¹/₄x

where;

y is the width of the book in inches.

x is every hundred pages printed on bond paper.

1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;

y = ¹/₂ + ²/₅x

2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;

y = 2(1/3) +¹/₄x

y = ²/₃ +¹/₄x

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Answer:

the answer would be true

Answer:

FALSE

Step-by-step explanation:

The answer is false because the length between DC is 6 and the length between EB is 8. If the lines were parallel, both lines would have the same length.

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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Answer:16x16

Step-by-step explanation:

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

48 ft

Step-by-step explanation:

this is because the perimeter of the room is its sides so first you 9x2=18

then 14x 2= 28 and then 28 + 18 and you get 48 ft

The discriminant is positive since there are two solutions of f (x) = 0

Which can be seen in the graph as it has two intersections with the x-axis.

f(x)=0 when x=-4 or x=2, because the points (-4,0) and (2,0) belong to the function.

Then:

a) The discriminant is positive.

b) There are 2 real solutions to f(x)=0

c)The coordinate of a point belonging to the f(x) function is (x, f (x)), and that second part of the point is what we need to be 0, in other words we must find the intersections of the graph with y = 0, the x-axis.

The points (-4,0) and (2,0) belong to the given function and intercept the x-axis, then

x= - 4 and x = 2 are the solutions for f(x)=0

Answer: A best friend listens to you. ... It doesn't matter how many times you've said the same asinine thing – a true best friend never tires of hearing your ridiculous stories. Your best friend is one who listens to your work gossip, even if he or she doesn't understand it.

Step-by-step explanation:

Answer:

a = 14 m/min²

Step-by-step explanation:

The displacement of bike is given by :

\(s(t)=t^3-2t^2+3\)

Velocity, \(v=\dfrac{ds(t)}{dt}\)

Finding velocity of the bike.

\(v=\dfrac{d}{dt}(t^3-2t^2+3)\\\\=3t^2-4t\)

Acceleration, \(a=\dfrac{dv(t)}{dt}\)

\(a=\dfrac{d}{dt}(3t^2-4t)\\\\=6t-4\)

At t = 3 minutes,

a = 6(3) - 4

= 18-4

= 14 m/min²

So, the bike's acceleration after 3 minutes is 14 m/min².

Answer:

No

Step-by-step explanation:

3/5 or 3 ÷ 5 = 0.60

6/7 or 6 ÷ 7 = about 0.8571

these two numbers/decimals are obviously not the same, making them inequivalent

Answer:

0.42

Step-by-step explanation:

To solve the problem, we need to add the probability of picking a club to the probability of picking a face card, and then subtract the probability of picking a club that is also a face card (because we would have counted it twice).

There are 13 clubs in a standard deck, so the probability of picking a club is 13/52 or 0.25.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) in a standard deck, so the probability of picking a face card is 12/52 or 0.23.

However, there are 3 cards that are both clubs and face cards (the jack of clubs, queen of clubs, and king of clubs), so we need to subtract the probability of picking one of those cards. There are 3 of them out of 52 total cards, so the probability of picking a club that is also a face card is 3/52 or 0.06.

Therefore, the probability of picking a club OR a face card is:

0.25 + 0.23 - 0.06 = 0.42 (rounded to two decimal places).

So the answer is 0.42.

To find the x-intercepts, equal the equation to 0 and solve for x:

-4.9 x^2 + 19.8x + 58

ax^2 + bx + c

a = -4.9

b= 19.8

c= 58

Apply the quadratic formula:

positive : -1.97

negative : 6.01

• 1- x intercepts

x = -1.97 , x = 6.01

• 2.y-intercept

To find it replace x = 0 and solve for y:

y = -4.9x^2 + 19.8x + 58

y= -4.9 (0)^2 + 19.8 (0) + 58

y= 58

• 3. Vertex

First, find the axis of symmetry:

x = -b / 2*a = -19.8 / 2*-4.9 = 2.02

Replace x=2.02 on the equation:

y = -4.9 (2.02)^2 + 19.8 (2.02) + 58

y = -19.99 + 39.996 + 58

y = 78

Vertex = (2.02 , 78 )

4.

Since on x-intercept is at x=-1.97, replace x=-3 and see if the y value is positive or negative:

f(-3) = -4.9(-3)^2 + 19.8 (-3) + 58

f(-3)= -44.1 -59.4 +58

f(-3)= -45.5

Since the value is negative it opens downwards, so the vertex is a maximum.

Answers:

1- the x-intercepts

x = -1.97 , x = 6.01



2- the y-intercept

y= 58



3- the vertex

Vertex = (2.02 , 78 )



4- is the vertex a maximum/minimum​

The vertex is a maximum

(A) The rate of making coffee by coffee maker  is 6 mL/second.

(B) The rate of making juice by juice maker is 8 mL/second.

(C) Juice is being made at a faster rate.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

The rate of coffee made by coffee maker is represented by,

y = 6x       (1)

Here, y represents the amount of coffee in mL and x represents the time passed in seconds.

Also, The rate of juice made by juice make can be represented by the given table as,

k = 8h     (2)

Here, k represents the amount of juice in mL and h represents the time passed in seconds.

(A)

To find the rate of making coffee, solve the equation (1),

y = 6x

⇒ y/x = 6 mL/second

The rate of making coffee by coffee maker  is 6 mL/second.

(B)

To find the rate of making juice, solve the equation (2),

k = 8h

⇒ k/h = 8 mL/second

The rate of making juice by juice maker is 8 mL/second.

(C)

Since, the juice is made at the rate of 8 mL/second and the coffee is made at the rate of 6 mL/second.

Therefore, juice is being made at a faster rate.

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Answer:

Step-by-step explanation:

X would be adults Y would be children

3x+3y=35

2x+4y=25

One of the variables have to be equal to each other. So multiply all the terms in the bottom equation by 1.5

You get 3x+6y=37.5

Subtract one equation from another

3x+3y=35

3x+6y=37.5

You get 3y=2.5

Divide both sides by 3
y = 5/6

Now do the same but for X

Multiply the equation by 4/3

4x+4y=46 2/3

Minus the other equation

2x=21 2/3

Divide by 2

x = 10 5/6

Plug numbers in to double check, and they check out

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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Answer:

A (5)

Step-by-step explanation:

        c represents the slope and a and b represent the two shorter sides of the right angled triangle ( x,y)

       \(c^{2}\) = \(-4^{2} + 3^{2}\)

            = 16 + 9

             = 25,

therefore \(\sqrt{c^{2} }\) = \(\sqrt{25}\)

                   c = 5

The approximate number of guests that were children are 172 and adults are 278

From the complete question, we have the following system of equations

25x + 12y = 9014

x + y = 450

Make y the subject in x + y = 450

y = 450 -x

Substitute y = 450 - x in 25x + 12y = 9014

25x + 12(450 - x) = 9014

Expand the expression

25x + 5400 - 12x = 9014

Evaluate the like terms

13x = 3614

Divide both sides by 12

x = 278

Substitute x = 278 in y = 450 -x

y = 450 - 278

Evaluate

y = 172

Hence, the approximate number of guests that were children are 172 and adults are 278

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Answer:

supplementary angles because they add 180 degrees

Step-by-step explanation:

hope this helped

Answer: Supplemetary Angels,  Adjacent Angels

B,C

Step-by-step explanation: The other person is wrong

Answer:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

Answer: 3, 160 || 4, 320 || 5, 640 || 6, 1280

Step-by-step explanation:

The exponential function to model this situation is \(P(t) = 20\times 2^t\)

An exponential function is a mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given that, a scientist studying bacteria begins with 20 cells.

The bacteria population doubles every hour.

Let P(t) determines the population of the bacteria in 't' hours.

Hence, by the given information our function P(t) is modeled as:

\(P(t) = 20\times 2^t\)

To find the population of the bacteria after 11 hours, put t = 11,

\(P(11) = 20\times 2^{11\)

= 40,960

Hence the population of the bacteria after 11 hours will be 40,960.

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The required equation that following the pattern is n = 4s+1. So the option c is correct.

In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.

The given options are:

a) n = s+4

b) n = 4s

c) n = 4s+1

d) s = 4n

We find the pattern we firstly observe the given diagram closely.

As we can see that in first diagram have 5 blocks.

In second diagram have 9 blocks.

In third diagram have 13 blocks.

So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Step-by-step explanation:

In this case, the unit rate would be:

Unit rate = 180 miles / 3 hours

Unit rate = 60 miles/hour

Answer:

60 miles per hour

Step-by-step explanation:

Given is 180 miles in 3 hours.

We know that unit rate is written as x miles per hour or we can say x miles in one hour. So in order to find the unit rate for the above rate we can express the data in fraction form as,

180miles3hours

Now to make the denominator 1 and not change the given ratio we will divide both the numerator and denominator by 3.

=180miles÷33hours÷3

On dividing we get,

=60miles1hour

Thus we get 1 in denominator or this is the only unit rate.

Thus our answer is 60 miles per hour.

The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.

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Answer: the first option is correct

Y+ 11> -9 this answer is most likely right.

Step-by-step explanation: -25 + 11 = 14 so that makes it bigger that -9 and that it has -25 in the solution set. Let me know if this is for Edmonton.

Answer:

It was D

Step-by-step explanation:

Answer: \(20x^2 + 47x+24\)

Step-by-step explanation:

We just multiply the values on the edges like we are finding the area of a square, L * L = area.

4x * 5x = 20x^2

4x * 8 = 32x

3 * 8 = 24

3 * 5x = 15x

Next add the answers together

20x^2 + 47x + 24

Answer:

option 3

Step-by-step explanation:

you need to times (4x+3) by (5x+8)

so you basically need to expand the brackets and collect like terms