The square on the right is a scaled copy of the square on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
8
8
4

a) The greatest number of students who will get the refreshment is 210.

b) Each student will get 0.5 hot dogs.

c) Each student will get 0.6 cans of fruit juice.

a) To find the greatest number of students who will get the refreshment , we need to find the least common multiple of hot dogs and fruit juice.

The least common multiple is 210, which is the multiple of 105, and 126 is the least.

So the greatest number of students who will get the refreshment is 210.

b) To find the number of hot dogs each student will receive, we need to divide the total number of hot dogs (105) by the greatest number of students who will get the refreshment (210)

105/210 = 0.5

So each student will get 0.5 hot dogs.

c) To find the number of fruit juices each student will receive, we need to divide the total number of fruit juice (126) by the greatest number of students who will get the refreshment (210)

126/210 = 0.6

So each student will get 0.6 cans of fruit juice.

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The probability is 0.4444.

Probability is a measure of the likelihood of a particular outcome occurring in a given situation. It is the chance that something will happen or is true. Probability is expressed as a number between 0 (impossible) and 1 (certain). Probability is a mathematical way of predicting what will happen in the future based on a given set of data. It is used to analyze the likelihood of various outcomes in a range of scenarios, such as gambling, finance, insurance, and weather forecasting.

The probability of a randomly selected tester from the group of college-bound seniors having a score between 1497 and 1507 can be calculated using the standard normal distribution. First, we need to convert the scores to standard scores, or z-scores. Subtract the mean from the scores and divide by the standard deviation to get z-scores.

For XXX = 1497, z = (1497 - 1497) / 322 = 0.
For XXX = 1507, z = (1507 - 1497) / 322 = 0.31.

Using a standard normal table, we can calculate the area under the normal curve between 0 and 0.31. The probability of randomly selecting a tester with a score between 1497 and 1507 is 0.4444. The probability is therefore P(1497 ≤ XXX ≤ 1507) = 0.4444.

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Complete questions as follows-
The distribution of SAT scores of all college-bound seniors taking the SAT in 2014 was approximately normal with a mean of 149714971497 and standard deviation of 322322322. Let XXX represent the score of a randomly selected tester from this group. Find P(1497 ≤ XXX ≤ 1507).

By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).

Here we have the following system of equations:

y = x + 8

y = -(1/2)x+5

And we want to solve it graphically.

To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.

The graph of the system of equations can be seen in the image below:

There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.

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The domain of x=4 is (−∞,∞) and range is {y|y=4} .

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

(−∞,∞)

{x|x ∈ R}

y=4

is a straight line perpendicular to the y-axis, which means that the range is a set of one value  {y|y =4}

Set-Builder Notation:{y|y =4}.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

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Proportionately, the quantity of milligrams of vitamin c in 1 orange is 33.75 mg.

Proportion refers to the part of a whole contained in another value.

Proportion is a ratio representation, which is fractional in value.'

We depict proportions using decimals, fractions, or percentages.

The daily recommended allowance of vitamin c for a sixth grader = 45 mg

The content of 1 orange to the daily recommended allowance = 75%

75% of 45 mg = 33.75 mg.

Thus, 1 orange will proportionately contain 33.75 mg, which is 75% of 45 mg.

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Answer:

13/25

I hope this is the correct answer.

The equation on how to find the volume is πr²h = 24

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

Volume = 24 cubic feet

The volume of a cylinder can be calculated as

Volume = πr²h

Where

r = radius

h = height

Substitute the known values in the above equation, so, we have the following representation

πr²h = 24

Hence, the equation is πr²h = 24

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Answer:

a) 400% b) 1/4 c) 64

Step-by-step explanation:

Answer:

a. 400%

b. 25

c. 64

Step-by-step explanation:

a. 160 ÷ 40/100

160 × 100 / 40

4 × 100 = 400%

b. 40 ÷ 160%

40 ÷ 160/100

40 × 100/160 = 25

c. 40% × 160

40/100 × 160

4 × 16 = 64

If the population grows by 15 people. The original number of people was 50, hence the new share of each person was Rs. (which is refused).

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Let no. of persons = x

Each person get

= 6500/x

If there 15 persons were added more

= 6500/(x + 15)

(6500/x) - 6500/(x + 15) = 30

[tex]\Rightarrow 6500\left[\frac{(\mathrm{x}+15)-(\mathrm{x})}{\mathrm{x}(\mathrm{x}+15)}\right]=30[/tex]

[tex]\Rightarrow 6500\left[\frac{x+15-x}{x^2+15 x}\right]=30[/tex]

[tex]& \Rightarrow 1625\left[\frac{15}{x^2+15 x}\right]=3 \\[/tex]

Then,

[tex]& \Rightarrow \frac{24375}{x^2+15 x}=3 \\[/tex]

Simplifying the above equation,

[tex]& \Rightarrow 3 x^2+45 x=24375 \\[/tex]

[tex]& \Rightarrow 3 x^2+45 x-24375=0 \\[/tex]

[tex]& \Rightarrow x^2+15 n-3250=0 \\[/tex]

[tex]& \Rightarrow x^2+(65 n-50 n)-3250=0 \\[/tex]

Then we get,

[tex]& \Rightarrow x^2+65 n-50 n-3250=0 \\[/tex]

[tex]& \Rightarrow x+65)-50(x+65)=0[/tex]

[tex]\Rightarrow(\mathrm{x}-50)(\mathrm{x}+64)=0[/tex]

x = 50, x = -65

Since the number of people cannot be zero,

the number of people is 50.

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After combine they hold 115.84 ounces.

A process of combining or adding two or more numbers is called addition.

We have to given that;

One bottle holds 67.34 ounces and another bottle holds 48.5 ounces.

So, After combine, we get;

Both bottle hold = 67.34 ounces + 48.5 ounces

                         = 115.84 ounces

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We calculated   volume of pyramid = 160 cubic inches and surface area = 214.59 square inches.

A three-dimensional geometrical figure having flat polygon base along with a number of lateral triangular shaped faces.

The given pyramid is a rectangular pyramid having length 10 inch and width 8 inch. The height of pyramid is 6 inches.

length, l = 10 inch

width, w = 8 inch

height, h = 6 inch

Now the volume will be, V = 1/3 × l × w ×h

                                       V = 1/3 × 10 × 8× 6

hence, the volume = 160 cubic inches

We calculate the surface area of the given pyramid,

formula for surface area, SA = l × w + 1/2 × w ×√(4h²+l²) + 1/2 × l ×√(4h²+w²)

SA = 10 × 8 + 1/2 × 8 ×√(4×6²+10²) + 1/2 ×10×√(4×16²+8²)

Surface area = 214.593 square inches

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Answer:1000000

Step-by-step explanation:

The description for the problem involving the linear function is given as follows:

The time it will take to make a total of 20 parts is of 6 minutes.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

In this problem, the function is defined as follows:

y = 2x + 8.

In which the variables are given as follows:

Hence the time needed to make 20 pieces is given as follows:

20 = 2x + 8

2x = 12

x = 12/2

x = 6 minutes.

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The equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

Given that,

Three of a parallelogram's vertices have the coordinates (-3, 4), (-2, 1), and (2, 6).

We have to find what is the equation for the side of the line that contains the first two vertices' opposite side.

We know that,

The equation of the line is

y=mx+b

Here, we find m and d

Take the points (-3,4) (-2,1)

m = y₂-y₁ / x₂-x₁

m = 1 - 4 / -2-(-3)

m = -3 / 1

m = -3

Now take point (2,6)

6 = -3(2) + b

6 = -6 + b

6 + 6 = b

12 = b

We get m =-3 and b=12

The equation will be y=-3x+12

3x+y=12

Therefore, the equation for the side of the line that contains the first two vertices' opposite side is 3x+y=12

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A 9-sided shape is called a nonagon.

Therefore the answer is nonagon.

A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.

Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.

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Answer:

[tex]\boxed{22}.[/tex]

Step-by-step explanation:

Since Elliott drove for a total of 10 hours, and he drove for 120 miles while it was raining and 300 miles after the rain stopped, we know that he drove for a total of 120 + 300 = <<120+300=420>>420 miles.

If he drove for a total of 10 hours and covered a distance of 420 miles, then his average speed was 420 miles / 10 hours = <<420/10=42>>42 mph.

Since Elliott drove 20 mph faster after the rain stopped than he did while it was raining, then we know that his speed while it was raining was 20 mph slower than his average speed of 42 mph. That means his speed while it was raining was 42 mph - 20 mph = <<42-20=22>>22 mph.

6.022× [tex]10^2^3.[/tex]particles are in one mole.

The correct option is 6.022× [tex]10^2^3.[/tex]

Now, According to the question:

Avogadro's number

Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × [tex]10^2^3.[/tex] The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.

Now, According to Avogadro's law, one mole of any substance contains a fixed number of particles i.e.,6.022× [tex]10^2^3.[/tex]particles (atoms, molecules or ions) which is also known by the name Avogadro's number.

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Answer:

8.2 × 10⁻³

Step-by-step explanation:

1.64 × 10⁰      1.64 × 1         1.64

-------------- = -------------- = ---------- = 0.0082

2.0 × 10²        2 × 100        200

Scientific notation: 8.2 × 10⁻³

I hope this helps!

x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this statement  best describes the end behavior.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

First, we need to analyze the plotting of the graph. When it is on the negative axis of x, as the values of x increase (x values increasing in the negative axis means it's decreasing in value), the y values also increase. So as x decreases, y increases.

On the positive axis of x, as the x values increase, the corresponding values of y also increase with x. So as x increases, y values also increase with it.

Hence, x->∞,y->∞ and as x-> - ∞ , y-> - ∞ this  statement  best describes the end behavior.

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The smallest positive integer that is both a multiple of 7 and a multiple of 4, is 28 .

To find the smallest positive integer that is both a multiple of 7 and a multiple of 4, first find the multiples of both 4 and 7 to see which multiples are common between them and which are the lowest.

The multiples of 4 and 7 are:

Multiples of 4 :

4, 8, 12, 26, 20, 24, 28, 32, 36, 40,

Multiples of 7 :

7 , 14 , 21 , 28 , 35 , 42 , 49

The smallest positive integer that is both a multiple of 7 and a multiple of 4 is therefore 28.

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The best answer from the choices provided is a = plus-or-minus 16 . Option C

A quadratic equation can be defined as an equation that can be rearranged in a standard form

Such that;

These quadratic equation are also described as polynomial equation having its highest degree as 2.

From the information given, we have that;

3a² - 21 = 27

collect like terms

3a² = 27 + 21

Add the values

3a² = 48

Divide both sides by 3

a² = 48/3

a² = 16

Hence, the value is a² = 16

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In a rhombus, all sides are equal and the diagonals intersect each other at a 90 degree angle and bisect each other.  

Diagonal of a rhombus bisects the angles of the rhombus at the vertex.

So as m∠MNL is 120°,

∠MNO = ∠LNO = 120/2 = 60°

The diagonals intersect each other at a 90 degree angle, therefore

m∠MON = 90°

Considering ΔMNO, right angled at O.

cos(∠MNO) = NO/ MN

cos(60) = NO/ 8

NO = 0.5×8 = 4

NP = NO + OP

NP = 2NO

NP = 2×4

NP = 8 in

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Answer:

Step-by-step explanation:

Days in may = 31

Days in a year = 365

therefore, expected ratio = 31/365

When given expression 2x (x + 3y) +5 (2x - 2) simplified completely then it would have 4 terms.

Consider given expression.

2x (x + 3y) +5 (2x - 2)

We simplify above expression.

2x (x + 3y) +5 (2x - 2)

= [(2x × x) + (2x × 3y)] + [(5 × 2x) - (5 × 2)]       ......(distributive property)

= [2x² + (2 × 3)xy] + [(5×2)x - 10]               ............(commutative property)

= (2x² + 6xy) + (10x - 10)

= 2x² + 6xy + 10x - 10

= 2x² + 10x + 6xy - 10     ...........(by commutative property of addition)

when given expression simplified completely then it would be,

2x (x + 3y) +5 (2x - 2) = 2x² + 10x + 6xy - 10    

The number of terms in an expression 2x² + 10x + 6xy - 10 are 4

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Answer:

x² + 7x + 5

Step-by-step explanation:

(- 3x² + 2x - 4) + (4x² + 5x + 9)

since both parenthesis are being multiplies by 1 , remove parenthesis

= - 3x² + 2x - 4 + 4x² + 5x + 9 ← collect like terms

= (- 3x² + 4x²) + (2x + 5x) + (- 4 + 9)

= x² + 7x + 5

In 35 differnt ways (Combination) the 4 players can be selected from a team of 7.

Combinations are decisions that are made by choosing some or all of a group of things, regardless of how they are arranged.

Utilizing the combinations formula, it is simple to determine how many distinct groups of r items each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.

A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. In order to determine the number of configurations for seating 3 people in 5 seats, we thus multiply the alternatives at our disposal.

Permutations are several ways to arrange things in a certain sequence. It may alternatively be stated as the linear reordering of elements in an already ordered collection.

Here we have to select 4 people from a team of 7, so its a combination

So the number of ways are = [tex]\x^{7}C\x_{4} = \frac{7!}{4!\ 3!} = 35[/tex].

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The experimental group is given the experimental treatment, and the comparison group is statistically significant.

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The constant of proportionality is 9 and equation of the proportion.

is y= 10x.

If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.

Given:

As, we know using the Constant of Proportionality

y = kx

or,  k = y/x  where k is Constant of Proportionality.

Then, from the table we have

k = 90/9

k= 10

Thus, y = kx

or, y= 10x

Hence, the equation of the proportion is y= 10x.

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The four consecutive odd integers = 15, 17, 19, 21

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

x + x + 6 = -(x + 4) + 55

x + x+6 = (-x - 4) + 55

2x + 6 = -x + 51

Collect like terms

2x + x = 51 - 6

3x = 45

x = 15

Second integer = x + 2 = 15 + 2 = 17

Third integer = x + 4 = 15 + 4 = 19

Fourth integer = x + 6 = 15 + 6 = 21

The four consecutive odd integers = 15, 17, 19, 21

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Answer:

11 pounds

Step-by-step explanation:

The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds

Answer:11

Step-by-step explanation:

11 times 3 equals 33(for the clothing)

so 11 is left