Indira finds that on a typical day, 4 out of every 5 students at her school eat a
cafeteria lunch. The rest of the students bring their lunch from home. Indira's
school has 495 students. On a typical day, how many students at her school bring
their lunch from home? Show your work.

The solution of the given inequality for the value of x, x ≥ 1/2.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than. Both mathematical phrases, equations, and inequalities are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,<,≥,≤,≠ or indicate that the two expressions in inequality are not always equal.

Given Data

Equation

[tex]\frac{4x -7}{2}[/tex] ≥ 4.5

4x - 7 ≥ 9

4x≥2

x ≥ [tex]\frac{1}{2}[/tex]

For the value of x, x ≥ [tex]\frac{1}{2}[/tex]

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The set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11},  (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.

It is defined as a diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

The universal set will be:

U = {1, 2, 3, 4, 5, 7, 9, 11}

Let:

A = {1, 2, 3, 4, 5}

B = {2, 3, 5, 7, 11},

C= {3, 5, 7, 9}

1) A ∪ B ∪ C = {1, 2, 3, 4, 5, 7, 9, 11}

3) (A – B) ∩ C = {1, 4} ∩ C= {3, 5, 7, 9}

(A – B) ∩ C = ∅

5) A' ∪ B = {7, 9, 11} ∪ {2, 3, 5, 7, 11}

A' ∪ B = {2, 3, 5, 7, 9, 11}

Thus, the set A ∪ B ∪ C will be {1, 2, 3, 4, 5, 7, 9, 11},  (A – B) ∩ C is ∅, and A' ∪ B is {2, 3, 5, 7, 9, 11}.

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The true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

Rational Numbers can be defined as the  numbers that can be expressed in the form of p/q , where p and q are integers and q not equal to 0 .

For Example : 2/3 , 2, 8/3 are all Rational Numbers.

Irrational Numbers can be defined as the  numbers that cannot be expressed in the form of p/q where , p and q are integers and q not equal to 0 .

For Example : √2 , √37 are irrational as they cannot be expressed in the form of p/q.

In the question ,

two numbers √15 and √0.001 are given .

the first number √15 is not a perfect square , hence not an integer ,

So, √15 is an irrational number .

the second number

√0.001 = √(1/1000) = 1/√1000 = [tex]\frac{1}{10\sqrt{10} }[/tex]

we see that √10 is not an integer , hence √0.001 is an irrational number .

Therefore , the true statement  is that both √15 and √0.001 are irrational , the correct option is (c).

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2pi/3 radians=120 degrees

F is 90 degree.

j is 180 degree

midpoint of F and J is 150 degree.

H is 150 degree

Hence,

G is 120 degree

The correct statement for the rational number is the opposite of the opposite of -12 is -12.

What is rational number?

Rational numbers are those numbers which include natural numbers, whole numbers as well as integers. And it is written in the form of a/b where a and b are integers. Sometimes, the values of the denominator is one then the given number is not fraction.

According to the question, rational number are those numbers which takes positive integers, negative integers as well as zero.

Therefore, on a number line, the opposite of (-12) is 12. And again the opposite of 12 is (-12). Therefore the first statement is correct.

Hence, the correct statement for the rational number is the opposite of the opposite of -12 is -12.

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x = 2

f(x) = -2x² + 8x - 9

Comparing this function with f(x) = ax² + bx + c

a = -2, b = 8, c = -9

The axis of symmetry is given by the formula:

x = -b/2a

Substitute a = -2 and b = 8 into the formula:

x = 2

The time taken to fill the bathtub by cold water is 14.4 minutes.

Given,

Time taken to fill a bathtub by both cold and hot water = 8 minutes

Time taken to fill the bathtub by hot water = 18 minutes

Time taken to fill the bathtub by cold water = t minutes

We have to find t.

We can take the full bath tub as 1.

Now,

We can equate the given data:

We get,

(8/18) + (8/t) = 1

Now, solve the equation:

((8 × t) + (8 × 18) ) ÷ (18 × t) = 1

(8t + 144) ÷ 18t = 1

8t + 144 = 18t

18t - 8t = 144

10t = 144

t = 144/10

t = 14.4

That is,

The time taken to fill the bathtub by cold water is 14.4 minutes.

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Answer:

2/17, 8/17, and 11/17
7/21, 7/18, 7/14, 7/12, and 7/8
2/12, 2/10, 2/8, 2/6, and 2/4.

Step-by-step explanation:

the order would be 2/17, 8/17, and 11/17 since the bottom number (denominator) stays the same while the numerator (top number) increases.

the order for the 2nd one would be:
7/21, 7/18, 7/14, 7/12, and 7/8. The reason for this is that when the numerator stays the same and the denominator increases, the value of the fraction decreases. For example, 1/2 is greater than 1/4, and 1/4 is more than 1/5 because 5 is greater than 4. This only works when the numerator (top number) stays the same.
The order for the 3rd one would be:
2/12, 2/10, 2/8, 2/6, and 2/4. Again, the numerator stays the same while the denominator changes. As the denominator goes down, the value of the fraction goes up.
Also if possible label your question the correct difficulty this is like middle school not college

Answer:

A

Step-by-step explanation:

See that the slope of the parabola changes at x=4

And left of x=4, the slope is positive, meaning the value is increasing (you can also see it directly from the graph)

Right of x=4, the slope is negative, meaning the value of the graph is decreasing. Thus the answer is A

Time taken to cover path around the park if he runs at speed 5miles/hour is 15.96min

What is Speed ?

Speed indicates how quickly something or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance x time.

Given that,

Time taken when Bob runs 4miles/hour = 20min

Time taken when Bob runs 5miles/hour = ?

First we have to find the distance of the path around the circle

Distance = speed x time

               = 4 x 20/60

               = 4/3 miles

               = 1.33 miles

Now to calculate the time when he ran 5 miles/hours:

Time = distance / speed

         = 1.33 / 5

         = 0.266hours

0r

         = 0.266 x 60 min

         = 15.96 min

Hence, its will take 15.96min to cover the path around the park

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A graph of a proportional relationship can be used to find any ratio in the proportional relationship when the graph passes through the origin.

A connection is proportional if its graph is a line that goes through the origin. The ratio is not proportionate if it is not a line or ray that doesn't accomplish this. K = y/x is the equation for the proportionality constant. The equation for the slope of a straight line with respect to the origin is the same as this.

A relationship is proportionate if its graph is a line or ray that passes through the origin. It is not proportionate if the line or ray does not go through the origin. Additionally, something is not proportionate if it is not linear.

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The given coordinate of the vertices of triangle XYZ is X(-2,2), Y(4,2) and Z(1,-5).

a). When rotates 180 degrees clockwise the new coordinate of the triangle can be determined as,

b). The original and the new coordinates of the triangle can be drawn as,

The original and the new triangles can be drawn as,

Answer:

g(-1)=2, g(0)=1, g(1)=1/2, g(2)=1/4, g(3)=1/8

Step-by-step explanation:

In order to find the x-intercept we need to make y=0

Then we isolate the x

x y Ordered Pair type of intercept

0 0 (0,0) x-intercept

Now for the y-intercept we need to make x=0

we isolate the y

0 0 (0,0) y-intercept

ANSWER

0 0 (0,0) x-intercept

D. moving red blood cells around the body

Integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.

As given in the question,

Number of free clues =3

Total number of clues used to escape from a room = 5clues

Out of these 5 clues, 3 clues are free to use. Hence these 3 clues do not result in any time change.

Hence total time elapsed after usage of 3 clues = 0

Each removes 5 minutes from your remaining time

Integer represents the total change in the time for the usage of 4th and 5th clue = 10 minutes

So overall change in timeline after consuming 5 clues = 10 minutes since each of the 4th and 5th clue results in decrease of 5 minutes each; thus effecting 10 minutes total time change (reduction)

Therefore, integer represents the total change in the time when you use 5 clues with the condition of using 3 free clues is equal to 10 minutes.

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When he spends $52 in total, the number of bottles of water and protein bars that he buys will be 40 and 20 respectively.

It should be noted that an equation is used to show the relationship between the variables.

In this case, Kawan buys some protein bars at $0.80 each and bottled water at $0.90 each for a group hike and he buys twice as many bottles of water as protein bars.

Let x = the number of protein bars

Table waters = 2x

Therefore, the equation will be:

0.8x + 0.9(2x) = 52

0.8x + 1.8x = 52

2.6x = 52

Divide

x = 52/2.6

x = 20

The number of proteins bars is 20.

The number of water will be:

= 2x.

= 2 × 20 = 40

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The required probability that exactly  6 insects will die is 60%.

Given that,
A certain insecticide kills 70% of all insects in laboratory experiments. A sample of 10 insects is exposed to the insecticide in a particular experiment. The probability that exactly 6 insects will die is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total number of sample spaces = 10
Total number of favorable outcomes = 6
probability can be given as,
= 6 / 10
= 0.6 or 60%

Thus, the required probability that exactly  6 insects will die is 60%.

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Answer: $2.75

Step-by-step explanation:

2) Judy spent 3*5.25 = 15.75 on popcorn bags, 13.60 on a jumbo bag of chips and 7.90 for a dip. This means that overall she spent $37.25. If she had $40, this means that she have left $40 - $37.25 = $2.75.

1) Your answer is right.

Based on the given ordered pairs, yes, the relation is a function.

A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable to an output variable.

Based on the ordered pairs shown above, we can reasonably infer and logically deduce that these ordered pairs represent a function because the elements of the set of "x" are uniquely mapped to the elements of the set of "y" as shown below:

x              y__

-2    ↔     4

-1      ↔    7

0     ↔     -6

5     ↔      3

7      ↔     5

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The line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).

As given,

Equation of the line passes through two points (1, 0, 1) and (4, −4, 4) is:

[tex]\frac{x-4}{4-1}=\frac{y+4}{-4-0}=\frac{z-4}{4-1}[/tex]

From the above equation we have

(x-4)/3 =(y+4)/-4

⇒-4x+16= 3y+12

⇒y=(-4x +4)/3  __(1)

And

(x-4)/3=(z-4)/3

⇒z=x __(2)

Substitute the value of y and z in the plane x +y+ z=6 to get point of intersection of line and plane

x+ [(-4x +4)/3] +x=6

⇒3x-4x+4 +3x =18

⇒2x=14

⇒x=7

Substitute value of x in (1) and (2)

y=-8 and z=7

Therefore, the line through (1, 0, 1) and (4, −4, 4) intersect the plane x + y + z = 6 at point (7,-8,7).

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The cost of the jalapeno poppers is $11.09    .

In the question ,

it is given that

Cost of the nachos = $18.85

amount paid by each friend = $9.98

amount paid by three friends = 9.98*3 = $29.94

let the cost of jalapeno poppers = $x

So according to the question

the total amount paid by three friends = cost of nachos + cost of jalapeno poppers

Substituting the values from above , in the equation we get

29.94 = 18.85 + x

simplifying further , we get

x = 29.94 - 18.85

x = 11.09

Therefore , the cost of the jalapeno poppers is $11.09  .

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The continents that have a lower elevation than North America are Africa and Asia.

It should be noted that elevation simply had to do with the height above sea level of a particular thing. Any of numerous huge landmasses is referred to as a continent. Up to seven geographical regions are usually regarded as continents, based on convention rather than precise requirements.

A continent is one of the seven major land divisions on Earth. Asia, Africa, North America, South America, Antarctica, Europe, and Australia are the continents, in order of size.

In this case, the table shows negative integers to represent the lowest elevations below sea level on each of the 7 continents.

In the table, Africa has -512 and Asia had -1312. It should be noted that these are lower than in North America.

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Given:

There is a graph given in the question

Required:

We want to find the solution of the given graph

Explanation:

As we can see that, both lines are parallel so there is no chance for intersection

now if there is no intersection point means there is no solution

Final answer:

No solution

Answer:

$48

Step-by-step explanation:

Simple interest (I) = PRT/100

Where P = principal

R= rate

T = time

.: Simple Interest = 120 × 8 × 5

---------------

100

S. I = $48

.: the approximate value of the investment at the end of 5 years will be = $48

Step-by-step explanation:

red feeder is smarter

Answer:Explanation:

• T

• 0.320

The player's on-base percentage = 0.320

This is equally the relative frequency of the player being on base.

Thus, the appropriate method is the relative frequency method.

Thus, the probability that the player will get on base in his next appearance is 0.320.

well, your family really ate "x" for breakfast, was pretty good with cereal and strawberries btw.

let's keep in mind that the LCD of the denominators 4 and 12 is "12", so we'll use that to do away with the denominators.

[tex]\stackrel{\textit{before breakfast}}{\cfrac{3}{4}}~~ - ~~\stackrel{for~breakfast}{x}~~ = ~~\stackrel{leftover}{\cfrac{1}{12}} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{3}{4}-x \right)~~ = ~~12\left( \cfrac{1}{12} \right)}\implies 9-12x=1 \\\\\\ 9=12x+1\implies 8=12x\implies \cfrac{8}{12}=x\implies {\Large \begin{array}{llll} \cfrac{2}{3}=x \end{array}}[/tex]

Step-by-step explanation:

Simplifying

8x + -10 + 10 + 4x = -10 + 6x + 6x + 10

Reorder the terms:

-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10

Combine like terms: -10 + 10 = 0

0 + 8x + 4x = -10 + 6x + 6x + 10

8x + 4x = -10 + 6x + 6x + 10

Combine like terms: 8x + 4x = 12x

12x = -10 + 6x + 6x + 10

Reorder the terms:

12x = -10 + 10 + 6x + 6x

Combine like terms: -10 + 10 = 0

12x = 0 + 6x + 6x

12x = 6x + 6x

Combine like terms: 6x + 6x = 12x

12x = 12x

Add '-12x' to each side of the equation.

12x + -12x = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Simplifying

8x + -10 + 10 + 4x = -10 + 6x + 6x + 10

Reorder the terms:

-10 + 10 + 8x + 4x = -10 + 6x + 6x + 10

Combine like terms: -10 + 10 = 0

0 + 8x + 4x = -10 + 6x + 6x + 10

8x + 4x = -10 + 6x + 6x + 10

Combine like terms: 8x + 4x = 12x

12x = -10 + 6x + 6x + 10

Reorder the terms:

12x = -10 + 10 + 6x + 6x

Combine like terms: -10 + 10 = 0

12x = 0 + 6x + 6x

12x = 6x + 6x

Combine like terms: 6x + 6x = 12x

12x = 12x

Add '-12x' to each side of the equation.

12x + -12x = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 12x + -12x

Combine like terms: 12x + -12x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

ANSWER:

8 square meters

STEP-BY-STEP EXPLANATION:

To calculate the area of the sector, we must first calculate the area of the entire circle and then by means of a proportion, knowing that the entire area is 360° and the sector is 45°, we could determine the area we need.

Just like this:

The area of the sector is 8 square meters