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The savings account balance after six months with an 8% annual percentage rate and $200 monthly contributions is $202.6.

Savings Plan Formula

The future worth of a savings or investment account in which you make regular deposits can be calculated using the formula below.

EXAMPLE 1 Assume you put $100 into a savings account each month that pays 7.3% interest that is compounded monthly.

To determine the saving plan balance after 6 month

First of all we have to calculate the growth factor

Growth factor =(1+(0.08/6)) per month

Growth factor= 1.013

Now let calculate the savings plan balance after 6 month

Saving plan balance after 6

Months =$200.00x1.0133

             = $202.6

From conclusion the saving plan balance after 6 month is=$202.6

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The set of letters in the word 'woodpecker' using the most concise method is {c, d, e, k, o, p, r, w}

From the question, we are to write the set of letters of the given word.

The word is 'woodpecker'

We are to write the set using the listing (roster) method or the set builder notation.

The roster method or listing method is a way to show the elements of a set by listing the elements inside of brackets

Set builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy

The set builder notation is not a suitable method to list the elements of the given word.

The most concise method to list the elements of the given word, 'woodpecker', is the listing (roster) method.

Thus,

Using the listing (roster) method,

The set of letters of the given word is {c, d, e, k, o, p, r, w}

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Answer: if you're asking how tall it will stand at 3 years of age it would be 6.

Step-by-step explanation: 2 times 3 equals 6.

Answer:

Part 1 is B, Part 2 is D

If you want an explanation I can give one :)

We have the next operation

the result of this operation rounded to nearest hundredths place is 57.86

Answer:y=21°

x=8°

Step-by-step explanation:

3y+27=90

3y=63

y=21°

x+90°+8x+18°=180°

9x+108°=180°

9x=72°

x=8°

Given the expressions:

You need to remember that the Distributive Property states that:

• In order to simplify the first expression, you only need to apply the Distributive Property, because there is a number multiplying a Sum. Therefore, get:

• In order to simplify the second expression, you need to follow these steps:

1. Apply the Distributive Property:

2. Solve the Addition:

Hence, the answers are:

• The first problem requires to use only the Distributive Property to simplify it. It is required because there is a number multiplying a Sum:

Notice that the second expression can be simplified using the Distributive Property as the first step.

• The second problem can be simplified by applying the Distributive Property and then adding the numbers.

The dragon would take 2.16 seconds to eat a human weighing 90 kilograms.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Let x seconds it would take to eat a human weighing 90kilograms

500 kg →  12 seconds

90 kg →  x

500/90 = 12/x

x = (90×12)/500

x = 2.16 seconds

Thus, the dragon would take 2.16 seconds to eat a human weighing 90 kilograms.

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Answer:

I think it's D because it can't be factorized

Based on the percentage of fencers who said they used foil as their main weapon when surveyed, the number of fencers out of 28 fencers who would not use foil as their main weapon is 11 fencers

The random survey showed that in a given sample, there would be 60% of fencers who would prefer to use foil as their main weapon. This means that the percentage of fencers who would not use foil as their main weapon is:

= 1 - percentage who use foil as main weapon

= 1 - 60%
= 40%

If 28 fencers are randomly surveyed, the percentage of them who would not use foil as their main weapon would be expected to be:

= Number of fencers x Percentage who don't use foil as main weapon:

= 28 x 40%

= 11.2 fencers

= 11 fencers to the nearest whole number

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The coordinates of the point Y at the other endpoint is 41

From the question, the given parameters are

Because there is not y coordinates in the coordinates, we can make use of only the x coordinate

So, we have the following equation

Point = Proportion * (Y - X)

Substitute the known values in the above equation

So, we have the following equation

12 = 1/3 * (Y - 5)

Multiply through the equation by 3

So, we have the following equation

36 = Y - 5

Add 5 to both sides of the equation

So, we have the following equation

Y = 41

This means that the conclusion is the coordinate of the point Y is 41

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Shiloh can run 04 laps per minute if in 25 minutes Shiloh can run in 10 laps around the track and it is Laps per minute is simply division.

The ratio that is connecting two given numbers is what is known as the exact proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names that can be given for the constant of proportionality.

To represent the equation in laps per min,

L/m = 10/25

= 2/5

= 0.4 laps per minute

The constant of proportionality in this situation

10/25 = 0.4

The equation to represent the relationship.

y = 0.4x

Identifying the same x and y variables is the first step in determining the proportionality constant. X will be the weight and Y will be the number of butter sticks in order to calculate the exact weight to stick ratio.

Then to determine the proportionality constant, we can use the constant equation k = y x.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

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Answer:

Step-by-step explanation:

...

Answer:

2x+9=7

Step-by-step explanation:

"Sum" means addition

"2 times a number" since the number is unknown we use a letter, since its a letter we usually don't need parentheses

"and" is usually used ror addition so another clue

"is" just means equals

Using the binomial distribution, there is a 0.8784 = 87.84% probability that at least 1 of them arrives late.

The probability mass function, giving the the probability of x successes is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the distribution are given as follows:

In the context of this problem, of 20% shipments with 90% on time, the parameters are:

p = 0.9, n = 20.

The probability that all arrive on time is:

P(X = 20) = (0.9)^20 = 0.1216.

All on time and least one late are complementary events, hence the probability of at least one package arriving late is given as follows:

P(X < 20) = 1 - P(X = 10) = 1 - 0.1216 = 0.8784.

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Answer:

x=20 and x=4

Step-by-step explanation:

Answer:

The equation is W = 1600 + .03S

Answer:

  8 < x

  see attached for the graph

Step-by-step explanation:

You want the compound inequality and the graph that represents the solution to the system ...

  2x-5>3 and -4x+7<-25

The first inequality has the solution ...

  2x -5 > 3 . . . . . given

  2x > 8 . . . . . . . add 5

  x > 4 . . . . . . . divide by 2

The second inequality has the solution ...

  -4x +7 < -25

  -4x < -32 . . . . . . subtract 7

  x > 8 . . . . . . . . divide by -4

The solution is the intersection of these solution spaces:

  4 < x    and   8 < x

The intersection is ...

  8 < x . . . . . solution to the compound inequality

The graph is attached.

By interpreting the vertex form of the equation of parabola, the focus of the curve is equal to F(x, y) = (2, 0). (Correct choice: D)

In this problem we find the equation of a parabola in standard form, which has to be rearranged into its vertex form in order to determine the coordinates of its focus.

The focus of a parabola is a point outside the curve such that the least distance from any point of the parabola and the least distance between that the point on the parabola and directrix are the same.

First, rearrange the polynomial into its vertex form by algebraic handling:

y = (1 / 8) · (x² - 4 · x - 12)

y + (1 / 8) · 16 = (1 / 8) · (x² - 4 · x - 12) + (1 / 8) · 16

y + 2 = (1 / 8) · (x² - 4 · x + 4)

y + 2 = (1 / 8) · (x - 2)²

y + 2 = [1 / (4 · 2)] · (x - 2)²

Second, determine the vertex and the distance between the vertex and the focus:

The parabola has a vertex of (h, k) = (2, - 2) and vertex-to-focus distance of 2.

Third, determine the coordinates of the focus:

F(x, y) = (h, k) + (0, p)

F(x, y) = (2, - 2) + (0, 2)

F(x, y) = (2, 0)

The focus of the parabola is equal to F(x, y) = (2, 0).

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Answer:

please provide options

Step-by-step explanation:

Answer: [tex]f(-2)=13, g(-6)=-8[/tex]

Step-by-step explanation:

[tex]f(-2)=-2(-2)^3 -3=13\\\\g(-6)=2(-6)+4=-8[/tex]

The values of functions f(-2) and g(-6) are 13 and -8 respectively.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

It is given in the question  that:-

[tex]f (x) = -2x^3 - 3[/tex]

g(x) = 2x + 4

We have to find the values of f(-2) and g(-6).

Putting x = -2 in f(x), we get,

f(-2) = [tex]-2(-2)^3 - 3[/tex] = -2*(-8) - 3 = 16 - 3 = 13

Putting x = -6 in g(x), we get,

g(-6) = 2(-6) + 4 = -12 + 4 = -8

Hence, the values of functions f(-2) and g(-6) are 13 and -8 respectively.

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On simplifying the given equation, the answer is [tex]\frac{5}{6}[/tex]

The fundamental guidelines and procedures to simplify any statement are as follows:

By multiplying factors, remove any grouping symbols like brackets and parenthesis.

If the words contain exponents, use the exponent rule to eliminate grouping.

Add or subtract like terms to combine them.

Add the constants together.

Given,

1 8/11 x 5/12 + 5/12 x 3/11

[tex]\frac{19}{11}[/tex]  ×  [tex]\frac{5}{12}[/tex]    +  [tex]\frac{5}{12}[/tex]   × [tex]\frac{3}{11}[/tex]

Taking [tex]\frac{5}{11 * 12}[/tex] as a common factor,

⇒ [tex]\frac{5}{11 * 12}[/tex] ( [tex]19 + 3[/tex])

⇒ [tex]\frac{5}{11 * 12}[/tex] × 22

On simplifying,

⇒ [tex]\frac{5}{6}[/tex]

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Answer: The Brown family ate 1.85 pies in all

Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6  and then get 1.85 so they ate 1.85 pies in all

Hope this helped!!!!

Answer: $16081.60

Step-by-step explanation:

1)

FV=3000(1.03)=$3090

2)

240*1.04=$249.60

3)

FV=14000(1.02)^7

FV=14000(1.1487)

FV=$16081.60

If the child uses the marbles at random what is the chance that the child gets less than six red marbles is given as   0.9561. See the calculation below.

Note that we are given the following:

p = 20% = 0.20

1 - p = 1 - 0.20 = 0.80

n = 14

Utilizing the binomial formula, we have:

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

P(X < 6) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)+  P(x = 4) + P(x = 5)  

Plugging in the value of n, we have:

=  ((14! / 0! (14)!) * 0.200 * (0.80)14 + ((14! / 1! (13)!) * 0.201 * (0.80)13 + ((14! / 2! (12)!) * 0.202 * (0.80)12 + ((14! / 3! (11)!) * 0.203 * (0.80)11 + ((14! / 4! (10)!) * 0.204 * (0.80)10 + ((14! / 5! (9)!) * 0.205 * (0.80)9

=  0.9561

As a result, the probability that the youngster would receive less than six red marbles is provided as 0.9561 if the marbles are used at random.

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Answer:

c

Step-by-step explanation:

2-2/5=12/5

12/5=

2-2/5 is the mixed fraction for the number 12/5

well, the key and you are absolutely correct, so you're golden

[tex]\stackrel{reciprocals}{\cfrac{3}{2}\cdot \cfrac{8}{1}\cdot \cfrac{1}{5}}\implies \cfrac{3}{5}\cdot \cfrac{8}{2}\cdot \cfrac{1}{1}\implies \cfrac{3}{5}\cdot \cfrac{4}{1}\cdot \cfrac{1}{1}\implies \cfrac{12}{5}\implies \cfrac{10+2}{5} \\\\\\ \cfrac{10}{5}+\cfrac{2}{5}\implies 2+\cfrac{2}{5}\implies 2\frac{2}{5} ~~ \checkmark[/tex]

1/4(n-6)=1/4n-3/2. We can say left side is equal to right side.

Given that,

1/4(n-6)=1/4n-3/2

We have to find the n value.

We have to 1st prove left side is equal to right side

We can split an equation into two parts, the left hand side and the right hand side. We refer to the LHS and RHS of the equation in abbreviated form. If the LHS and RHS are equal, then the equation is true; otherwise, the equation does not hold for at least some real number values.

First take the left side which is

1/4(n-6)

We multiply 1/4 to n-6

1/4n-1/4(6)

Now we divide 6/4

1/4n-3/2

See the right side

1/4n-3/2

Therefore,

left side is equal to right side.

1/4(n-6)=1/4n-3/2

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The  three equivalent ratios are given below .

What are equivalent ratios?

Ratios that can be streamlined or decreased to the same value are said to be equivalent. In other words, if one ratio can be written as a multiple of the other, then they are said to be equivalent. The ratios 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, and others are some examples of analogous ratios. To put it another way, two ratios are said to be equivalent if one of them can be written as the multiple of the other. Therefore, we must multiply the two values (antecedent and consequent) by the same number in order to obtain the equivalent ratio of another ratio. This approach is comparable to the approach for determining equivalent fractions.

1:9 , 99:11 , 9:11 , 1:99

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the answers is a. bones to bones

The maximum dimensions is a square of sides 36 ft by 36 ft;

The maximum area is 1,296 ft^2

Here, we want to know the diemensions of the largest area the farmer can enclose within the perimeter

Mathematically, the greatest dimension that can maximize the area of the plot is the shape being a square

In other words, we need the diemnsions of both sides to be equal so as to get the area

If the dimensions are equal, we can say the length and width are represented by x

The length is thus as follows;

The greatest possible or the maximum area is thus;

The value of  k = -0.079

The Fahrenheit temperature of the turkey, to the nearest degree, after 5.5 hours =  T(5.5) = 159.865

What is Temperature?

Temperature is a numerical expression of how hot a substance or radiation is. There are three different types of temperature scales: those that are defined in terms of the average, like the SI scale;

Newton's law of cooling states that T=Ta + (To-Ta)e-kt

T = Ta + (To-Ta)e-kt

Ta is the object's ambient temperature.

To equal the starting temperature.

t = the number of hours.

after t hours, temperature equals T.

decay constant is k.

According to the formula,

To = 70 and

Ta = 325,

therefore

(To -Ta) = 70 - 325.

(To -Ta)           = -255

T = 325 + (-255 e^kt) or

325 -255e^kt.

After 2.5 hours, the turkey reaches a temperature of 116°F.

In other words,

T(2.5) = 116 F.

Consequently,

116 = 325 - 255e^k2.5

Following that,

116 - 325 = - 255e^2.5k

Now,

-209 = -255e^2.5k

e^2.5k = -209/-255

Using the function 'ln,'

now

ln(e2.5k) = ln(209 / 255)

Then, 2.5k = -0.198929

The value of k is now given by k = -0.198929 / 2.5, which is -0.079571.

The result is k = -0.079.

After 5.5 hours, the temperature is

T(5.5) = 325 - 255e^(-0.079 x 5.5)

Then, = 325 - 255e^(-0.4345)

Now,

         = 325 - (165.1350) (165.1350)

T(5.5) = 159.865 is the result.

Consequently, T(5.5) = 159.865 degrees Fahrenheit is the turkey's exact temperature after 5.5 hours.

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