Diane deposits $400 into an account that pays simple interest at a rate of 5% per year. How much interest will she be paid in the first 2 years

(7th grade math)

Answer: An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. We can call this constant difference "d".

In this sequence, we can see that the difference between consecutive terms is -6x - 5.

The 9th term of an arithmetic sequence can be found by using the formula:

a_n = a_1 + (n-1)d

Where a_n is the nth term of the sequence, a_1 is the first term of the sequence and d is the common difference.

Given the sequence -5x + 2, -11x - 3, -17x -8, ...

The 9th term is:

-5x + 2 + (9-1) (-6x-5) = -5x + 2 - 48x - 40 = -53x -38

Therefore the 9th term of the arithmetic sequence is -53x -38.

Step-by-step explanation:

The packages of paintbrushes, p, that Mr. Grant needs to buy in order to have at least 55 paintbrushes will be at least 5 packages.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

In this case, Grant has 25 paintbrushes already and will buy more paintbrushes in packages of 6.

The inequality to illustrate this will be:

25 + 6p ≥ 55

where P = packages of paintbrushes

Collect the like terms

6p ≥ 55 - 25

6p ≥ 30.

Divide

p ≥ 30 / 6

p ≥ 5

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According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).

To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.

We must add all the values of the group that wears glasses

According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.

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Lila finds out the decimal equivalent of 3 divided by 16 is equal to 0.1875.

Lila knows that 3/16 means "3 divided by 16."

To find the decimal equivalent for 3/16, she would divide 3 by 16 using a calculator or long division. This would give her a decimal answer of 0.1875.

It's important to note that 3/16 is a fraction, which represents a ratio of two numbers, the numerator, and the denominator. The decimal equivalent is simply another way to represent the same value but in decimal form.

Lila understands that to convert fractions to decimals, she can divide the numerator by the denominator. And to convert decimals to fractions, she can write the decimal as a fraction with the denominator as a power of 10.

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Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.

Perimeter = 2*6(1/2x + 5)

Perimeter = 12(1/2x + 5)

To simplify the expression, we can distribute the 12:

Perimeter = 121/2x + 125

Perimeter = 6x + 60

So the perimeter of 6(1/2x + 5) is 6x + 60.

Step-by-step explanation:

The monthly payment during the initial period is  about $1,682.94

The type of loan Jackie obtains is an Adjustable Rate Mortgage, ARM, loan, which is a 4/2 ARM

The introductory interest rate of 5% is fixed for the first 4 years, and will be adjusted every 2 years after the first four years.

Let us assume that m represents the initial monthly payment.

[tex]M=\frac{P.(\frac{r}{12} ).(1+\frac{r}{12} )^n}{(1+\frac{r}{12} )^n - 1}[/tex]

where, M is the monthly payment during the initial period

P is the amount on loan

r is the interest rate = 5% = 0.05

n is period = 30 × 12 = 360

Here, P = $313,500

r = 5%

r = 0.05

n =  30 × 12

n = 360

Substituting these values in the above formula we get,

[tex]M=\frac{313500\times (\frac{0.05}{12} ).(1+\frac{0.05}{12} )^{360}}{(1+\frac{0.05}{12} )^{360} - 1}[/tex]

M  ≈ 1,682.94

Therefore, the monthly payment is about $1,682.94

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Step-by-step explanation:

1. MN || LO - ( PARALLEL LINES ) .

2. <NMO = <LOM - ( GIVEN ) .

3. <MLO = <ONM - ( REFLEXIVE PROPERTY ) .

4. ..... - ( AAA S-C ) .

The possible minutes Ali will run today can be represented by the inequality x ≥ 66.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Minutes taken to complete one lap = 6 minutes

Also, he will run at least 11 laps today.

This means that Ali will run laps greater than or equal to 11 laps.

Let x be the number of minutes taken by Ali today.

x ≥ 6 × 11

x ≥ 66

Hence Ali runs 11 laps in at least 66 minutes.

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The complete question is as follows :

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?

If the rate of walking is 1. 4 meters per second, then 357.14 sec would take you to walk 500 meters.

We can calculate speed, distance or time using the formula s = d/t, distance equals speed times time. The Speed Distance Time formula can solve for the unknown sdt value given two known values.

Time can be entered or solved in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh: mm: ss).

We have,

The rate of walking is 1. 4 meters per second.

The distance to cover is 500 meters.

Now, we know the formula

Speed = Distance/Time

⇒Time = Distance/Speed

⇒Time = 500/1.4

⇒Time = 357.14 sec

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Answer: 54% of youths surveyed prefer reading electronic books.

Step-by-step explanation: 74 divided by 100 = 0.74. Divide 40 by 0.74 and you get 54.05%. Round that to 54% and you have your answer.

The equation of the circle with center (-7, -15) and area π is

(x + 7)² + (y + 15)² = 1.

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Centre of the circle = (-7, -15)

The equation of a circle is r² = (x - h)² + (y - k)²

Where (h, k) is the center of the circle.

Now,

h = -7

k = -15

The equation of a circle.

r² = (x + 7)² + (y + 15)² _____(1)

Now,

Area = πr²

πr² = π

r² = 1 _____(2)

Now,

From (1) and (2),

(x + 7)² + (y + 15)² = 1

Thus,

The equation of the circle is (x + 7)² + (y + 15)² = 1.

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OC (x+1)(x-8)(4)=56 indicates that the volume of the box is 56 in³ because it takes into account the length of the sides after the four corners were cut off, and the height of the box which is 4 in. The equation can be written as (length of sides)(width of sides)(height) = volume.

A volume is a three-dimensional space that contains a specific amount of material, which is commonly measured in liters, cubic meters, or gallons. It is frequently used to calculate the capacity of containers like tanks, bottles, and barrels. Volume may also refer to the quantity of space occupied by an item, such as the volume of a room or the volume of a sphere.

In the given question, OC is the correct answer: (x+1)(x-8)(4)=56. This equation reveals that the volume of the box is 56 [tex]in^{3}[/tex] because it considers the length of the sides after the four corners were taken off, which are (x+1) and (x-8), as well as the height of the box, which is 4 in. The formula is (length of sides)(width of sides)(height) Equals volume. As a result, the equation (x+1)(x-8)(4) = 56 reveals that the box's volume is 56 [tex]in^{3}[/tex].

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Answer: $3.22 tax

Step-by-step explanation:

7/100 x 46 = $3.22

Answer:3.22$

Step-by-step explanation:3.22$ in the USA

The measure of the indicated angle is 33 degrees

It is important to note the properties of a triangle

The properties of a triangle are given as;

From the diagram shown, we have;

57° + K + 90° = 180°

Collect like terms, we get;

K = 180° - 147°

Subtract the numbers

K = 33°

Hence, the value is 33°

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Answer:

{1, 2, 3, 4, 5, 6, 7, 8}

Step-by-step explanation:

In this problem, we use the variable c to represent the independent quantity.  This means that the domain is all possible values for c. Since the store only has 8 cases of water, the domain cannot be any number larger than 8. Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number. This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=8 \end{cases}\implies V=\cfrac{\pi (3)^2(8)}{3}\implies V=24\pi ~cm^3[/tex]

I bought 30 gifts costing $2 each and 10 gifts costing $4 each for my family.

An equation is an expression showing the relationship between numbers and variables.

Let x represent the number of gifts costing $2 and y represent those costing $4

You spend $100 on gifts for your family and friends. Hence:

2x + 4y = 100    (1)

You buy 40 gifts altogether, hence:

x + y = 40     (2)

From both equations:

x = 30, y = 10

A total of 40 gifts was bought

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$7700\\ r=rate\to 3.9\%\to \frac{3.9}{100}\dotfill &0.039\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 7700\left(1+\frac{0.039}{12}\right)^{12\cdot 4}\implies A=7700(1.00325)^{48} \implies A \approx 8997.69[/tex]

By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% , 4.56, and 9/1

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We have to use each of the numbers 0 - 7 exactly once.

Hence, The percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% = 0.203

⇒ 4.56

⇒ 9/1 = 9

Thus, By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% , 4.56, and 9/1

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According to the given formula, the value of a is:

60

If b=30 then 1/2a+2/3b=50

First, replace the 30 in b.

1/2a+2/3(30)=50

According to the order of operations, we must first multiply 2/3 by 30. yes:

2/3 times 30 is equal to 20.

2/3 times 30/1. 3 is 10 times 30, so 2 times 10 = 20. Now it looks like this:

1/2a+20=50

20 and 50 are similar terms, so I'll put those two together. Move the positive 20 to the other side where the 50 is. 20 has moved to the other side, so it changes sign and becomes negative.

yes:

1/2a=50-20

50-20 = 30

1/2a=30

Multiply each side by 2, because only 2 makes the variable 1a.

1/2a × 2 = 1a

30 times 2 = 60, so:

1a=60, which is also a=60. So a perfect simplification is a= 60

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[tex]4y-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies 4\stackrel{y}{\left( -\cfrac{1}{2} \right)}-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2}\implies -2-\cfrac{1}{2}=\cfrac{x}{3}-\cfrac{5}{2} \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{6}}{6\left( -2-\cfrac{1}{2} \right)=6\left( \cfrac{x}{3}-\cfrac{5}{2} \right)}\implies -12-3=2x-15 \\\\\\ -12-3+15=2x\implies 0=2x\implies \cfrac{0}{2}=x\implies \boxed{0=x}[/tex]

The quotient for the given expression is 8x^2-8x+14 and the remainder is -19.  The solution has been obtained using the method of long division of polynomial.

What is polynomial long division?

A formula for dividing one polynomial by another of the same degree or lower is known as a long division polynomial. Like with long division of numbers, the components of long division of polynomials include the divisor, quotient, dividend, and remainder.

Using Polynomial Long Division,

Dividing :  8x^3 + 6x - 5 ("Dividend")

By         :    x+1   ("Divisor")

Dividend              8x^3  +  0x^2  +  6x  -  5

- divisor  * 8x^2   8x^3  +  8x^2        

Remainder                     -  8x^2   +  6x  -  5

- divisor  * (-8x)               -  8x^2   -  8x    

Remainder                                       14x  -  5

- divisor  * 14                                     14x +  14

Remainder                                               - 19

Quotient :  8x^2-8x+14

Remainder:  -19

Hence, the quotient for the given expression is 8x^2-8x+14 and the remainder is -19.

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Answer:

  97.5% decrease

Step-by-step explanation:

You want the percentage change in noise intensity when it is reduced from 88 to 72 dB.

The intensity can be found by solving the given equation for I:

  [tex]\beta_1=10\log\left(\dfrac{I_1}{I_0}\right)\\\\10^{\beta_1/10}=\dfrac{I_1}{I_0}\\\\I_1=I_0\cdot10^{\beta_1/10}[/tex]

Similarly, the reduced intensity is ...

  [tex]I_2=I_0\cdot10^{\beta_2/10}[/tex]

The percentage change is found from ...

  percentage change = (I₂/I₁ -1) × 100%

Using the above expressions for I₁ and I₂, this becomes ...

  [tex]\text{\% change}=\left(\dfrac{I_0\cdot10^{\beta_2/10}}{I_0\cdot10^{\beta_1/10}}-1\right)\times100\%\\\\=(10^{(\beta_2-\beta_1)/10}-1)\times100\%=(10^{(72-88)/10}-1)\times100\%\\\\=(10^{-1.6}-1)\times100\% \approx -0.975\times100\% =\boxed{ -97.5\%}[/tex]

The noise intensity decreased by about 97.5%.

__

Additional comment

It can be useful to remember that log(2) ≈ 0.30103. That is, a reduction of 3 dB is a reduction by a factor of 2. Hence 16 db is a factor of about 40.

Answer:

97.49% (2 d.p.)

Step-by-step explanation:

Given equation:

[tex]\beta=10 \log\left(\dfrac{I}{I_0}\right)[/tex]

Divide both sides by 10:

[tex]\implies \dfrac{\beta}{10}= \log\left(\dfrac{I}{I_0}\right)[/tex]

Switch sides:

[tex]\implies \log\left(\dfrac{I}{I_0}\right)=\dfrac{\beta}{10}[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies 10^{\frac{\beta}{10}}=\dfrac{I}{I_0}[/tex]

Multiply both sides by I₀:

[tex]\implies I=I_010^{\frac{\beta}{10}}\\[/tex]

Substitute the given value of I₀:

[tex]\implies I=10^{-12} \cdot 10^{\frac{\beta}{10}}\\[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies I=10^{\left(\frac{\beta}{10}-12\right)}\\[/tex]

Therefore, the value of I when β = 88 dB is:

[tex]\implies I=10^{\left(\frac{88}{10}-12\right)}\\[/tex]

[tex]\implies I=10^{-3.2}[/tex]

And the value of I when β = 72 dB is:

[tex]\implies I=10^{\left(\frac{72}{10}-12\right)}\\[/tex]

[tex]\implies I=10^{-4.8}[/tex]

Percent Decrease formula

[tex]\sf Percent\:decrease=\dfrac{original\:value-new\:value}{original\:value} \times 100[/tex]

Therefore, the percent decrease is:

[tex]\implies \dfrac{10^{-3.2}-10^{-4.8}}{10^{-3.2}} \times 100[/tex]

[tex]\implies 97.4881135...\%[/tex]

[tex]\implies 97.49\%\; \sf (2\; d.p.)[/tex]

Answer: I think its .012

hope this helps

Answer:

0.012

Step-by-step explanation:

Answer:

That is correct. The probability of rolling a 2 and a 5 when rolling two dice is 1 in 36, which is considered likely.

Answer:

not enough information

Step-by-step explanation:

The tire is shaped like a cylinder. The tread of a tire is the lateral surface of a cylinder. We know the diameter of the cylinder, 32 inches, but we are not given the width of the tire which is the height of the cylinder, so we cannot calculate the area.

Answer: not enough information

Jessica gets more rocks to skip across the surface of the pond than Henry.

To determine who gets more rocks to skip across the surface of the pond, we will take the ratio of rocks that skip to rocks that are thrown for each person.

For Henry, the ratio is 5 rocks that skip to 9 rocks thrown i.e 5/9.

For Jessica, the ratio is 7 rocks that skip to 12 rocks thrown i.e 7/12.

Now to compare the ratios, we need to convert them into like fractions. We will do this by making the denominations of both the fractions same.

We will multiply the numerator and denominator of Henry's ratio by 12 to get -

5/9 x 12/12 = 60/108

Also, we will multiply the numerator and denominator of Jessica's ratio by 9 to get -

7/12 x 9/9 = 63/108

Comparing the numerators we get 60<63.

This implies that 60/108 < 63/108.

Therefore, Jessica gets more rocks to skip across the surface of the pond.

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The complete question is -

Henry and Jessica skipping rocks across the surface of a pond. For every nine rocks Henry throws he got five of them to skip across the pond. For every twelve rocks

Jessica throws she got seven of them to skip across the pond. Who gets more rocks to skip across the surface of the pond​?

Here is the stem and leaf plot:

Stem      Leaf

0            2, 3, 5, 9

1              2, 7, 7,, 8, 8

2

3                 0, 8

A stem-and-leaf plot is a table that is used to display a dataset.  A stem-and-leaf plot divides a number into a stem and a leaf.

The stem is the first number in the digit. In this question, the stem is the tens digit.  The leaf is the last number. In this question, the leaf is the units digit.  For example in the number 18, 1 would be the stem and 8 would be the leaf.

Here is the complete question:

Create a stem and plot diagram using the dataset provided: 3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12

Key: 30 = 30

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