(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50

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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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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You can rearrange terms in an expression using the commutative and associative qualities to arrange compatible numbers next to one another and in groups.

According to the associative property, numbers can be added to or multiplied while still maintaining the same result. According to the commutative property, even if the numbers are added or multiplied, the solution will remain the same.

Explain:

[tex]\frac{4}{5}[/tex] ×(20×17/8)

20×17/8

340÷8

[tex]\frac{4}{5}[/tex]×[tex]\frac{340}{8}[/tex]

= [tex]\frac{64}{2}[/tex]

= 32

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Answer:

13/25

I hope this is the correct answer.

Like terms for the given data are: 17x² and 3x²; -3xy and -2xy. Combining the like terms we get: 20x² and -5xy

In algebra, the term "equal terms" refers to words with the same variable to the same power.

Similar variables and powers are called similar words in algebra. Matching coefficients is not required. When two or more words do not share the same variable or power, they are called inequal terms. The order of both variables is irrelevant unless there is a power. All of these have the same terminology.

17x² and 3x²

-3xy and -2xy

Combine the same terms obtained.

17x² + 3x² = 20x²

-3xy + (-2xy)

= -3xy -2xy

= -5xy

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Answer:

Step-by-step explanation:

Days in may = 31

Days in a year = 365

therefore, expected ratio = 31/365

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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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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After 156.25 miles will the cost be the same to rent a car. This can be solved by the concept of cross-multiplication.

Fractions are multiplied by multiplying the numerator of the first fraction by the denominator of the second fraction, and the numerator of the second fraction by the denominator of the first fraction.

In order to get the second fraction's numerator, multiply the first fraction's denominator by it. Cross multiply is another name for the butterfly technique of multiplication. The cross-multiply technique is used to find one or more variables in a fraction.

Let, assume miles be m.

and, Let the total cost be x.

According to the question,

0.25m + 50 = x ........(i)

0.41m + 25 = x ........ (ii)

By solving equation (ii) by (i) we get -

0.16 m - 25 = 0

or, 0.16m = 25

or, m = 25 /0.16

or, m = 156.25

Thus, number of miles = 156.25 miles.

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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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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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Your answer should be B. Each time, t, is associated with precisely one car value, y.

Answer:

To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:

56/7 = 8

Donna reads 8 pages per hour.

Step-by-step explanation:

Hope it helps! =D

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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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

Answer:

Step-by-step explanation:6

Therefore , the solution of the given problem of combination comes out to be  there were 182 games played in all.

Combinations are operations in mathematics that count the number of possible combinations that can be created from a set of items, where the selection's direction is immaterial. You are free to select any arrangement of the parts. Permutations and combinations can be mixed up.

Here,

There still are 14 teams in all, but each team plays the other twice.

Every team plays almost every team twice, hence the total amount of games played is simply the permutations of 2 out of 14, which is determined by:

₁₄P₂

=14!/((14-2)!)

= (14×13×12!)/ 12!

= 14×13

=182

Consequently, there were 182 games played in all.

Therefore , the solution of the given problem of combination comes out to be  there were 182 games played in all.

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When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be 48 times.

The times he should expect the coin to land on tail based on the table will be 27 times.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

When Donovan flips a coin a total of 96 times, the number of times he should expect the coin to land on heads will be:

= 1/2 × 96

= 48

The number of times he should expect the coin to land on tail based on the table will be:

= 18/50 × 75

= 27 times

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Based on the information given, the number of students from Florida will be; 9000 students.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1

The Total number of students = 12000

Fraction from Florida = 3/4

Fraction of students not from Florida = 1/4

Therefore, the students from Florida will be:

= 3/4 × 12000

= 9000

Hence, the number of students from Florida is 9000.

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In "Gilgamesh: A New English Version," several pieces of evidence support the conclusion that Gilgamesh is an epic hero.

Gilgamesh is the king of Uruk: He is the main character of the story, and his actions and deeds are the focus of the epic. As a king, he holds a position of power and authority and is responsible for the well-being of his people.

Gilgamesh undertakes a quest: He embarks on a journey to find immortality after the death of his dear friend Enkidu. His quest takes him to the ends of the earth and shows his determination and courage.

Gilgamesh faces challenges and monsters: During his journey, Gilgamesh faces several challenges and monsters, such as the giant Humbaba and the Bull of Heaven. His bravery in overcoming these obstacles demonstrates his heroic qualities.

Gilgamesh has supernatural strength and abilities: He is two-thirds god and one-third man, which means he is gifted with supernatural strength, speed and endurance. He is able to perform deeds that would be impossible for a mortal.

Gilgamesh demonstrates wisdom and self-awareness: Throughout his journey, Gilgamesh comes to understand the limitations of human life and the importance of living a meaningful existence. He demonstrates wisdom and self-awareness which are the hallmark of a true epic hero.

These examples of Gilgamesh's character and actions support the conclusion that he is an epic hero and his story is an epic.

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The 4 ways to solve a problem are understanding the problem, devising a plan, carrying out the plan, look back.

A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.

Polya created his famous four-step process for problem-solving, which is used all over to aid people in problem-solving:

Step 1. Understand the problem.

x = a number

Step 2. Devise a plan (translate).

Twice the difference between a number and 1 is equal to 4 more than that number

Step 3. Carry out the plan (solve).

2(x - 1) = (x + 4)

2x - 2 = x + 4

2x - 2 - x = x + 4 - x

x - 2 + 2 = 4 + 2

x = 6

Step 4. Look back (check and interpret).

If we take twice the difference of 6 and 1, that is the same as 4 more than 6. Thus the final answer is 6.

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The required value of k is 7 for a line that includes the points (k,–4) and (5,–2).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

As per the question, the slope of the line is -1, and the given points are (k, -4) and (5, -2).

So we can substitute these values into the formula:

-1 = (-2 - (-4)) / (5 - k)

-1 = 2 / (5 - k)

-1 × (5 - k) = 2

-5 + k = 2

k = 2 + 5

k = 7

Therefore, the value of k is 7.

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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

Answer:

The cost of 1 child is £ 3.40 and the cost of 1 parent is £ 4.10. To determine this, we can use the following equation:

Cost of 1 child = (13.20 - 5.10) / (5 parents + 3 children)

Cost of 1 parent = (13.20 - 5.10) / (2 parents + 1 child)

Hope this helps!

Step-by-step explanation:

The value of cos 149 degree as calculated from the calculator is found out to be -0.857167301.

Which on round off is , -0.85.

The formula to calculate the angle of depression is , θ = tan-1 (Opposite Side/Adjacent Side) .

Therefore, the AOD for cos149 degree is found out to be as ,

α = arctan(vertical distance / horizontal distance)

α = arctan(10 / 11.998)

α = arctan(0.83347224537423)

α = 0.69482025147278 ° ≈ 0.69 °

The angle of depression is defined as the point of meeting of a horizontal line with the line between the item and the observer's eye. This angle is determined by two factors , which are their height and distance.  If the item is below the observer's level, the angle produced between the horizontal line and the observer's line of sight is known as the angle of depression.

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Answer:

c is the independent variable and f is the dependent variable

Step-by-step explanation:

To represent "infinity" or the notion that an interval lacks an ending, we use the symbol.

The endpoints of infinity and negative infinity can be seen in two different ways. One the one hand, we can never get to infinity because it is a concept and not a real quantity.

In this sense, the interval is said to be open because it excludes the endpoints infinity and negative infinity. The infinity symbol is placed on the right side since there is no higher endpoint (all values must be larger than or equal to -3). An interval is closed if its boxed end is on -3. Because there is no endpoint on that side, infinity always has a curved end.

To represent "infinity" or the notion that an interval lacks an ending, we use the symbol. The symbol shouldn't be used with a square bracket because it's not a number. Visit this tutorial on set-builder and interval notation for a more thorough discussion of set notation and interval notation.

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Answer:

d. 3^108

Step-by-step explanation:

Just multiply 6 and 18.