In 2010, the population of a city was 193,000. From 2010 to 2015, the population grew by 6%. From 2015 to 2020, it fell by 3%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?

The length of a 30° arc of a circle with a diameter of 6 meters can be calculated using the formula L = θ/360 * π * d, where L is the length of the arc, θ is the angle of the arc in degrees, d is the diameter of the circle, and π is the mathematical constant approximately equal to 3.14. Plugging in the values given in the question, we get L = 30/360 * 3.14 * 6 = 3.14 meters. So, the length of the 30° arc is approximately 3.14 meters.

The jail's function is to hold inmates (A) for terms that are shorter than a year.

A prison sometimes referred to as a jail, jail, penitentiary, detention center, correction center, correctional institution, lock-up, hoosegow, or remand center, is a place where people are imprisoned against their choice and typically denied a range of freedoms as retribution for various offenses.

The only purpose of a jail is to house inmates for a period of time shorter than a year.

With very few exceptions, modern jails are municipal or county-level detention centers run by local police departments or correctional facilities.

Like their historical forebears, they are employed to hold those who pose a flight risk or a threat to public safety while they await trial.

Therefore, the jail's function is to hold inmates (A) for terms that are shorter than a year.

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1) Quadrilateral [tex]ABCD[/tex] with diagonal [tex]\overline{AEC}[/tex] bisecting [tex]\angle DAB[/tex], [tex]\overline{BE}[/tex], [tex]\overline{DE}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle BAE \cong \angle EAD[/tex] (definition of an angle bisector)

3) [tex]\overline{AE} \cong \overline{AE}[/tex] (reflexive property)

4) [tex]\triangle BAE \cong \triangle DAE[/tex] (AAS)

5) [tex]\overline{AB} \cong \overline{AD}[/tex] (CPCTC)

6) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

7) [tex]\triangle BAC \cong \triangle DAC[/tex] (SAS)

8) [tex]\overline{BC} \cong \overline{DC}[/tex] (CPCTC)

To prove AAS congruence, we need to show that the angles and included sides of the two triangles are equal.

For example, consider two triangles ABC and DEF. If we know that ∠A = ∠D, ∠B = ∠E, and BC = DE, we can use the AAS theorem to conclude that triangle ABC is congruent to triangle DEF. To prove this congruence, we can set up the following system of equations:

Solving this system of equations will show that all of the angles and included sides of the two triangles are equal, thereby proving that the triangles are congruent.

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Answer:

age of father is 40 and son is 10

Step-by-step explanation:

let age of father be x

and age of son is y

At present,

x+y=50 eq 1

After 5 years,

Ages are,

Father = x+5

Son = y+5

As age of father is thrice so,

x+5 = 3(y+5)

x+5 = 3y+15

x-3y= 10 eq 2

Multiply eq 1 by 3

3x + 3y = 150 eq 3

Now, Add eq 2 and 3

4x = 160

x = 40 .................... ....... Age of father

Put x in eq 1

40 + y = 50

y = 10 ......................... Age of Son

Answer:

d) 5 miles

Step-by-step explanation:

Minutes for jogging 1 mile is,

→ 36/3

→ 12 minutes

Formula we use,

→ Total time ÷ Time needed for 1 mile

Then the distance she cross in 60 min,

→ 60 ÷ 12

→ 5 miles

Hence, she will cross 5 miles.

The number of beads if A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads, is 18.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.

Given:

A bag contains n beads. 6 of the beads are red, and the rest are blue. Ravi is going to take random 2 beads,

The probability of same color beads = 9 / 17

Calculate the probability as shown below,

ⁿ⁻⁶C₂ / ⁿC₂ + ⁶C² / ⁿC₂ = 9 / 17

(n - 6) (n - 7) / 2 / n(n - 1) / 2 + 15 / n(n - 1) / 2  =  9 / 17

8n² - 212n + 1224 = 0

Solve for the value of x as shown below,

x = 18

Thus, the number of beads is 18.

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Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.    

Given that,

A recipe calls for [tex]1\frac{1}{2}[/tex] teaspoons of cinnamon to make 2 dozen oatmeal cookies.

A fraction is numerical value that is a part of a whole. It is evaluated by dividing a whole into number of parts. For example, ½ represents half of a whole number or a thing.

Then,

We will find number of teaspoons needed to make one oatmeal cookies.

1 dozen = 12

2 dozens = 24

So,

We can write,

[tex]1\frac{1}{2}[/tex] divide by 24,

Convert mixed fraction into improper fraction:

[tex]\frac{3}{2}[/tex] divide by 24

Convert to division problem by flipping the second fraction as:

= [tex]\frac{3}{2}[/tex] * [tex]\frac{24}{1}[/tex]

= [tex]\frac{3}{48}[/tex]

= [tex]\frac{1}{16}[/tex]

Now, we will multiply amount needed for one cookie by 60 to find amount needed to make 60 cookies as:

= [tex]\frac{1}{16}[/tex] * 60

= [tex]\frac{15*4}{4*4}[/tex]

= [tex]\frac{15}{4}[/tex]

= [tex]3 \frac{3}{4}[/tex]

Therefore,  

Fraction [tex]3 \frac{3}{4}[/tex] teaspoons of cinnamon are needed to make 60 oatmeal cookies.

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6 cans are needed to paint an area of 2200 units square.

The cans of paints and areas are illustrations of equivalent ratios.

The quantity of paint required for a certain area of house can be found out using the area of the house.

As the area is given in this problem, it is easier to calculate the amount of paint.

The given parameter is,

Cans: area = 1: 400

Putting it in the form of fraction,

Cans/area = 1/400

Cross multiplying, we have,

Cans = 1/400 × 2200 = 5.5 ≈ 6

Thus, 6 cans are needed to paint a 2200 square feet.

The question is incomplete. The complete question is 'How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units.'

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Answer:

1 5/6

Step-by-step explanation:

Take 11 divided by 6; we can have 1 number 6 and 5/6 left. So, the answer is  1 5/6

Let's test:

1 5/6 = 11/6

So, my answer is correct!

The financial tool that is most important is creating a budget.

The ideal financial instrument for long-term planning objectives is You'll be able to set away money each week or month with the use of a budget.

You may track where your money is going and determine how much you have to spend on items besides expenses by utilizing a budget.

A budget can help you prioritize your spending and saving, and ensure that you have enough money set aside to reach your goals. Here is a step-by-step explanation of how to create a budget:

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Answer:

y=32

Step-by-step explanation:

substitute x for (-4)

(2 x -4)^2= 32

The mean and the standard deviation of the data of the purchase are 4.5 and 1.8 respectively.

According to the question we can interpret that either the candy will be blue or it will not be blue. We use the method of Binomial distribution because the probability of getting a blue candy is not dependent on any other candy. The formula for expected value of the distribution will be

Expected value = E(X) = np

The standard deviation will be

SD = √(np(1 - p))

Now, from the question, n = 15 and the value of p = 30% = 0.3

putting these values we get

Expected value = E(X) = 15×0.3 = 4.5

SD = √(15×0.3(1 - 0.3))

SD = √4.5×0.7

SD = 1.8

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Complete Question:

A candy machine contains over 1,000 pieces of candy, 30% of which are blue. Customers get an SRS of 15 candies in a purchase. Let X= the number of blue candies that a random customer gets in a purchase. Find the mean and standard deviation of X. You may round your answers to the nearest tenth.

Answer:

Step-by-step explanation:

To solve this problem, we need to divide the total amount of money Lamonte earned ($269.10) by the number of hours he worked (13 hours).

We can write this as an equation as follows:

earnings per hour = $269.10 / 13 hours

To solve for earnings per hour, we can divide both sides of the equation by 13:

earnings per hour = $269.10 / 13 hours / 13 = $269.10 / 13^2 = $269.10 / 169 = $1.60

Therefore, Lamonte earned $1.60 per hour.

The allowable set of values makes up a function's domain. The set of authorized values is the domain of a function.

The set of authorized values is the domain of a function. The x values of a function, like f, are included in this collection (x). The collection of such values serves as a representation of the range of values that can be used as input for a function. The function returns this set of values when we enter an x value.

here ,

Consider the function represented by y = f(x), where x and y are independent variables. If a function f provides a method of efficiently generating a single value y while employing a value for x to that end, the selected x-value is said to fall inside the domain of f.

The range of values that a function can accept is referred to as the domain.

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Yes, it is hard but with a lot of practice and putting effort one cam also find it easy.

Physics requires the ability to solve problems, which can only be acquired via practice. In addition to these difficult ideas, there are theoretical concepts, mathematical calculations, and laboratory experiments.

It is better to comprehend the derivations than to memorize the formulas. Making a mess of several formulas will just increase your anxiety over the topic. Instead, if you strive to comprehend where they originate, you will begin to appreciate physics and its applications.

Physics is a difficult topic since it combines science and arithmetic, which may be challenging for the best of us. Nevertheless, despite how difficult it is, you can achieve if you follow a few simple guidelines and put yourself through some practice.

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Answer:

Step-by-step explanation:

first you do 4 x 2x=8x

next you do 4 x 5=20

then you get 8x + 20  :)

We solve log2 value by following logarithm laws.

Logarithm is the alternating way of expressing an exponent. The power at which a number is needed to raise so as to obtain the other values is called logarithm.

log2 is termed as log base 2 or binary logarithm. It is called the inverse of the power of two function.

As stated earlier that Log base 2 is an inverse expression of the power 2.

Suppose N is a real positive number and x is the number of exponents.

Now, logarithm form of this exponent is written

as log2 N = x

2∧x = N

Besides, we can directly get the log2 value by using calculator.

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The correct answer is A) -12t.

To evaluate this expression, we need to use the order of operations. The order of operations is a set of rules that specifies the sequence in which operations should be performed in a math expression to get the correct result. The order of operations is typically abbreviated as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Following the order of operations, we first need to evaluate the expression inside the parentheses, which is 2+(-4t). This gives us 2-4t. Next, we need to perform the multiplication, which gives us 3(2-4t) = 6-12t. Finally, we need to perform the addition, which gives us -6+6-12t = -12t. Therefore, the expression -6+3(2+(-4t)) is equivalent to -12t.

Option B) 12t-12 is incorrect because the multiplication and addition operations are not performed in the correct order.

Option C) none of the above is incorrect because the correct answer is A) -12t.

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Answer:

3. n = 2

4. t = -13/4

Step-by-step explanation:

3)

. . . . (3a) Distribute (multiply) +5 into the expression (n-1)

. . . . . . . . [tex]n + 5n - 5 = 7[/tex]

. . . .  (3b) Add like terms (terms with the same variable)

. . . . . . . . [tex]6n - 5 = 7[/tex]

. . . . (3c) Add 5 on both sides of the equation to "get rid" of the -5

. . . . . . . . [tex]6n -5 +5 = 7 +5[/tex]

. . . . . . . . [tex]6n = 12[/tex]

. . . . (3d) Divide both sides by 6 to isolate the variable

. . . . . . . . [tex]6n/6 = 12/6[/tex]

. . . . . . . . [tex]n = 2[/tex]

4)

. . . . (4a) Distribute (multiply) -2 into the expression (2t-1)

. . . . . . . . [tex]15 = -4t + 2[/tex]

. . . . (4b) Subtract 2 on both sides of the equation to "get rid" of  the +2

. . . . . . . . [tex]15 -2 = -4t +2 -2[/tex]

. . . . . . . . [tex]13 = -4t[/tex]

. . . . (4c) Divide both sides by -4 to isolate the variable

. . . . . . . . [tex]13/-4 = -4t/-4[/tex]

. . . . . . . . [tex]-13/4 = t[/tex]

Answer:

40 tickets

Step-by-step explanation:

2800 = 70x

x is the number of tickets. You have to solve for x

Divide each side by 70

2800/70 = 70x/70

40 = x

Answer: 0.34 cubic feet

Both men and women have duties to their families and duties to the state.

According to Wollstonecraft, women are important to the country because they educate their children and because they have the potential to be "companions" to their husbands rather than merely spouses. She also contends that women should have an education appropriate to their status in society.

She asserts that in God's view, men and women are on an equal footing. But these affirmations of equality conflict with her assertions that the strength and bravery of males are superior. It is now challenging to label Wollstonecraft as a modern feminist due to her equivocal views on gender equality.

Wollstonecraft differs from the majority of her male Enlightenment contemporaries because of her emphasis on the rights of women.

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According to her, men and women are treated equally in God's eyes. However, these claims of equality run counter to her claims that men are stronger and bolder than women. Due to Wollstonecraft's conflicted opinions on gender equality, it is currently difficult to categorize her as a modern feminist.

Wollstonecraft's emphasis on women's rights sets her apart from the rest of her male Enlightenment peers.

The value of 994 to the power 1/3 is 9.97.

The binomial theorem involves the method of expanding an expression which is raised to a finite power. A binomial theorem has its application in probability, algebra, etc.

A binomial expression is said to have two dissimilar terms.

The total number of terms in (x + y)ⁿ are n+1.

The expansion of (1 + x)ⁿ can be written as,

(1 + x)ⁿ = 1 + nx + [n*(n-1)]/2! x² + [n*(n-1)*(n-2)]/3! x³ + ....

Let us find the value of 994 to the power 1/3,

⇒ (993 + 1)¹/³

⇒ 1 + 993/3 + 993* 993* [1/3* (-2/3)]/2! + 993* 993* 993* [1/3* (-2/3)* (-5/3)]/3! + ...

⇒ 1 + 331 - 54780.5 + 60441151.67 - ...

⇒ 9.97

Thus, the required value is 9.97.

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The number of terms that the expression 4xy  +5 has is 2 terms.

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

How to determine terms?

To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.

4xy +5 has 2 spaces

1 + 1 = 2 terms.

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The factor for (x³ + y³) is (x+ y) (x² + y²  - xy).

and,  factor for (x³ - y³) is (x - y) (x² + y² + xy)

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

Given:

(x³ + y³) or (x³ - y³)

Now using Algebraic identities we have

(x³ + y³)

Using (x+ y)³ = x³ + y³ + 3xy(x+ y)

(x+ y)³ -  3xy(x+ y)= x³ + y³

x³ + y³= (x+y)[ (x+y)² - 3xy]

x³ + y³ = (x+ y) [ x² + y² + 2xy - 3xy]

x³ + y³ = (x+ y) (x² + y²  - xy)

and, (x³ - y³)

Using (x- y)³ = x³ - y³ - 3xy(x+ y)

(x - y)³ +  3xy(x- y)= x³ - y³

x³ - y³= (x-y)[ (x-y)² + 3xy]

x³ - y³ = (x - y) [ x² + y² - 2xy + 3xy]

x³ - y³ = (x - y) (x² + y² + xy)

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Answer:

For the equation 2 = 2, it is not possible to make this equation false by using the Properties of Equality. This is because the equation is already true, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has one solution.

For the equation 2 ≠ 3, it is not possible to make both sides equal by using the Properties of Equality. This is because the equation is stating that the two sides are not equal, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has no solutions.

The Value of a for which (x - 5) is a factor of x³ -3x² +ax -10 is a = -8   .

The Equation is given as x³ -3x² +ax -10 ;

the factor of the above equation is given as (x - 5) ;

Since (x - 5) is given to be a factor ,

we have , x - 5 [tex]=[/tex] 0 ;

On solving  ,

we have , x = 5 .

For (x - 5) to be a factor of x³ -3x² +ax -10 ,

x = 5 should satisfy the given equation .

that means ; (5)³ -3(5)² +a(5) -10 = 0 ;

⇒ 125 - 3×25 + 5a - 10 = 0 ;

⇒ 125 - 75 + 5a - 10 = 0 ;

⇒ 50 + 5a - 10 = 0 ;

⇒ 40 + 5a = 0 ;

⇒ 5a = -40 ;

dividing both sides by 5 ,

we get ;

a = -40/5 = -8 .

Therefore , the value of a is  "-8" .

The given question is incomplete , the complete question is

For what value of a is (x - 5) a factor of x³ -3x² +ax -10 ?

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Answer:

Step-by-step explanation:

To convert from liters per day to gallons per week, we need to use the conversion factors for these units. One gallon is equivalent to 3.785 liters, and one week is equivalent to 7 days.

We can use these conversion factors to write the following conversion equation:

1 gallon/week = (3.785 liters/gallon) / (7 days/week)

We can then use this equation to convert 400 liters per day to gallons per week by multiplying the number of liters per day by the conversion factor. This gives us:

400 liters/day * (1 gallon/week) / (3.785 liters/gallon) / (7 days/week)

We can simplify this expression by canceling out the units that appear on both the numerator and denominator. This gives us:

400 / 3.785 / 7 = 105.66

Therefore, 400 liters per day is equivalent to 105.66 gallons per week