pew research center reported that among months, familt size is shrinking. suppose we are to randomly select one mother and record the number of children

Rounded to the whole number: 6

After 8 years the balance of the account would be $9600.

What is simple interest?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Simple Interest =(P×r×t)/100

where:

P =Principal

r = interest rate

t = time

​

​Given:

Principal, P = $8400

Rate of  interest, r = 1.8%

Final amount, A = $9600

Simple  interest, S.I = Final amount - Principal = 9600 - 8400 = $ 1200

Now, 1.8% of 8400 = (1.8/100) × 8400 = 151.2

⇒ Interest of 1 year = $151.2

Interest after x years = $1200

x = 1200/151.2 = 7.94 ≈ 8 years

Therefore, after 8 years the balance of the account would be $9600.

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After one hour, there would be 337,500 bacteria in the hamburger.

This problem involves exponential growth relation, which is as below:

[tex]P(t)=P_{o}*e^{rt}[/tex]

where, [tex]P_{o}[/tex] is the initial value (i.e. at t=0), P(t) is the value at time 't' and r is the growth rate.

Usually, one perceives growth as linear, which might seem logical in unspecified cases. But, when specified exponential growth, the scenario changes. The difference between linear and exponential growth is like the difference between velocity and acceleration.

In case of above stated problem; [tex]P_{o}[/tex]=100,000 and P(20)=150,000

For calculating r, we substitute values:

[tex]150,000=100,000*e^{r*20}\\e^{20r}=1.5\\20r=ln(1.5)\\r=0.0202733[/tex]

Now we have our growth rate. Using the same formula for t=60, we have:

[tex]P(60)=100,000*e^{0.0202733*60}\\P(60)=100,000*3.375\\P(60)=337,500[/tex]

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The greatest average rate is. x^2+1

What is ROC?

acc toour question-

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The value of x + y is -12i.

What are complex numbers?

Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex math, including algebra. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.

Here, we have

Given x = 4 - 5i and

y = -4 - 7i

Now we have to find the value of x+y.

We will add both complex numbers and we get

x + y = 4 - 5i + (-4 -7i)

x + y = - 12i

Hence, the value of x + y is 12i.

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The perimeter of the parallelogram is 35 cm.

The length of the continuous line that a parallelogram's boundary forms are considered to be its perimeter. The same unit applies to it as it does to its sides. A closed shape made up of four line segments is referred to as a quadrilateral. If the opposing sides of a quadrilateral are parallel and the same length, the shape is referred to as a parallelogram.

Given, the area of the parallelogram = 62 cm²

We know the area of the parallelogram = base × height

62 = b × 6.2 cm

b = 62/6.2

b = 10 cm

So, the perimeter of the parallelogram is given by

P = 7.5 + 10 + 7.5 + 10 cm

P =  35 cm

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Answer:

a. -13

b. 14

c. -6

Step-by-step explanation:

a.

Substitute x = -3 into the equation.

f(-3) = 2(-3) - 7

= - 6 - 7

= -13

b.

Substitute f(x) = 21 into the equation.

2x - 7 = 21

2x = 28

x = 14

c.

Substitute x = 1/2 into the equation.

f(1/2) = 2(1/2) - 7

= 1 - 7

= -6

Left Blue Dot (5,9)

Right Blue Dot (7,0)

m = (y2 - y1)/(x2-x1)

= (9-0)/(5-7)

=9/-2

m = -9/2

Don't know the y-intercept so use the formula below to calculate equation of line

y-b = m(x-a)

y-9 = -9/2(x-5)

y-9 = -9x/2 + 45/2

y = = -9x/2 + 45/2 + 18/2

y = -9x/2 + 63/2

A line segment that connects a circle, sphere, or other shape's center to its perimeter or border. Radius: 12 units

According to the Pythagorean Theorem, a right triangle's hypotenuse (the side opposite the right angle) or, using conventional algebraic notation,[tex]a^{2} + b^{2} = c^{2}[/tex]

The Greeks established the existence of numbers that could not be expressed as rational numbers thanks to Pythagoras' theorem. For instance, if we assume that the two shorter sides of a right triangle are 1 and 1, we are left with a length hypotenuse that is not a rational number.

By Pythagoras theorem-

[tex]adjacent side^{2} + opposite side^{2} = hypotenuse^{2}[/tex]

35= opposite side

r= adjacent side

25+r= hypotenuse

[tex](25+r)^{2} = 35^{2} + r^{2}\\ 665 + r^{2} + 50r = 1225 + r^{2} \\50r = 600\\r=12 units[/tex]

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30 boxes of popcorn and 20 free DVD rentals were given away.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...

 2p +(50 -p) = 80

 p = 80 -50 = 30 . . . . . . . boxes of popcorn

50-p= (50 -30) = 20 . . . DVD rentals

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Based on Mark's and Gigi's expenditure, a pound of ham costs $3.67.

Let us represent 1 pound of ham by x and 1 pound of turkey by y. Forming equation based on Mark's ham and turkey

2x + 4y = 40 : Equation 1

Forming equation based on Gigi's ham and turkey

5x + 4y = 51 : Equation 2

Subtracting Equation 1 from equation 2

5x + 4y = 51

(-) 2x (-) + 4y = (-) 40

The result we get on subtraction -

3x = 11

x = 11/3

Performing division on Right Hand Side of the equation

x = 3.67

Thus, one pound of ham cost $3.67.

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The measure of m∠5 is 31 degrees.

What are alternate angles?

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal

Given that,

The AB is perpendicular to CD.

And, the m∠2=31°.

Based on the above information, the following information should be considered:

The alternate angles should be equal i.e. ∠2 = ∠5 and ∠1 and ∠6.

So, ∠5 = ∠2 = 31 degrees.

Therefore we can conclude that the measure of m∠5 is 31 degrees.

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The number of miles it takes the snail to move for an hour is 25/4 miles

how far, in miles, does it move in one hour?

Equate the ratio of number of miles to number of hours

7/50 : 7/8 = x : 1

7/50 ÷ 7/8 = x / 1

7/50 × 8/7 = x / 1

50/8 = x / 1

50 × 1 = 8 × x

50 = 8x

divide both sides by 8

x = 50/8

x = 25/4 miles

In conclusion, the snail moves 25/4 miles when traveling for an hour.

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The congruency relationship which hold true after transformation is

YZ ≅ AB

What is congruent ?

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

Explanation:

A translation is known as a rigid transformation.  This is because it preserves congruence.  Since CAB is created from XYZ, this tells us that:

X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.

Since the triangles are congruent, the corresponding pieces are congruent as well.

Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.

Hence the answer is YZ≅AB.

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The list of minerals that is grouped based on color is B. chalcopyrite, pyrrhotite, and pyrite.

Chalcopyrite is a mineral that has a high concentration of copper ore. As a result, it has a golden yellow color due to the copper in it. It also has crystals of a tetragonal form.

Pyrrhotite is a mineral with iron in it. It has the color of bronze yellow which means that it is similar in color to Chalcopyrite. We also have Pyrite which is brass yellow in color and looks golden. This puts it in the same color group as Chalcopyrite.

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Answer:

241.9026

Step-by-step explanation:

2*pi*r

Answer:

241.9 cm

Step-by-step explanation:

circumference= [tex]\pi[/tex]d

circumference= [tex]\pi[/tex](77)

circumference= 241.9 cm

The value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.

According to the question,

We have the following information:

The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land can be shown by x and its width can be shown by (2x + 6).

We know that the perimeter of rectangle is given by the following formula:

2(length+width)

2(x+2x+6) = 228

2(3x+6) = 228

Dividing by 2 on both the sides:

3x+6 = 228/2

3x+6 = 114

Subtracting 6 from both the sides:

3x = 114-6

3x = 108

x = 108/3

x = 36 feet

Now, the length of the rectangle = 36 feet

Width = 2x+6

Width = 2*36+6

Width = 72+6

Width = 78 feet

Hence, the value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.

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A teacher buys pencils= 100

the equation is y=8x/100.

total number of pencils = 100

average number of pencil lost in months = 8

number of pencil lost in one month = 8/100

pencil left = y

months = x

so the equation would be:

y = 8x/100.

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When an English-language survey questionnaire is converted into a Korean version for usage in south Korea and then translated back into English to ensure accuracy.

Given statement;

When a survey questionnaire in English is translated into Korean for use in south Korea and then translated back into English to check its accuracy.

It can be described as back translation,

Back Translation:

Back translation, also known as reverse translation, is the process of literally translating text back into the source language from the target language. Translations from English to Swedish not affect would also include a reverse translation into English so that the meaning of the translated option could be clearly understood. Back translations have no effect on the translator's translation memory or other tools, such as glossaries.

It is described as a back translation.

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The exponential decay of the function shows it will take approximately 81 years for the population to decrease to 200

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. This could also be an exponential growth or exponential decay which depends on the situation.

The exponential function is an important mathematical function which is of the form f(x) = ax

The details given in this question are;

The exponential function to represent this will be given as

200 = 525(1 + 0.012)⁻ˣ

x = number of years

This can be simplified as

200 = 525(1.012)⁻ˣ

x = 80.9 years

It will take approximately 81 years

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Answer:

If two triangles are congruent, then by the definition of congruent triangles, 3 pairs of sides are congruent and 3 pairs of angles are congruent. In all, this is 6 statements of congruence.

There are ways of proving triangles congruent that require only 3 statements of congruence of corresponding parts, such as ASA, SAS, AAS, etc.

Sometimes in order to prove two segments or two angles congruent, since these segment and angles are parts of triangles, you prove the triangles congruent using some other statements of congruence, not involving these parts, and then you get 6 statements of congruence that includes the parts you wanted to prove congruent. That is where you use "corresponding parts of congruent triangles are congruent", or CPCTC for short.

The distribution of the number of fair coin tosses before one observed three heads in a row is 14.

We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".

p = 1/2

n = 3

Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.

A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]

We need to find the value of A(3).

A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]

A(3) = [1 - 0.125]/[(0.5)*(0.125)]

A(3) = 0.875/0.0625

A(3) = 14

Hence, the number of fair coin tosses before one observes three heads in a row is 14.

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The graph of the proportional relationship is

(c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.

which shows that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

So, The graph is a proportional graph which means that line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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Answer:

$4.21

Step-by-step explanation:

6*70+1=421

Answer:

b) 6

Step-by-step explanation:

Given information,

→ P = (5x + 30)°

→ S = 80°

Forming the equation,

→ P + S = 140°

→ (5x + 30)° + 80° = 140°

Now the value of x will be,

→ (5x + 30)° + 80° = 140°

→ 5x + 110° = 140°

→ 5x = 140° - 110°

→ x = 30°/5

→ [ x = 6° ]

Hence, the value of x is 6.

The absolute value of +4 will be 4 units as it is the distance from (0,0) to (4,0) in coordinate plane.

Without taking into account direction, absolute value defines how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A number's absolute value is determined by how far it is from zero on the number line. For instance, the absolute value of -7 would be 7, as it is 7 units away from zero. Additionally, since 0 is 7 units distant, the value of 7 would likewise be 7.

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The transformation from the parent function is a translation by 1 unit right and 3 units up

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

f(x) = x²

f(x) = (x − 1)² + 3

First, we have the transformation to be:

From f(x) = x² to f(x) = (x − 1)²

This means the function is translated right by 1 unit

Next, we have:

From f(x) = (x − 1)² to f(x) = (x − 1)² + 3

This means the function is translated up by 3 units

Hence, the transformation is 1 unit right and 3 units up

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Answer:

-9/4  Negative As a Fraction

How I got the answer:

2 (x+3) = (1/8) (x+2)

x+ 3 = -3 (x+ 2)

x = -9/4

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In the expression 1.5x + 18 = 36.5 - 8 x is 7, hence 4x is 28.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An expression 18 + 1.5x is 8 less than 36.5.

∴ 1.5x + 18 = 36.5 - 8.

1.5x = 36.5 - 8 - 18.

1.5x = 10.5.

x = 10.5/1.5.

x = 7.

Therefore 4x is equal to 4(7) = 28.

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