What is the quotient (6x^4-15x^3+10x^2-10x+4)/(3x^2+2)

The cost of the basic portrait package = $55

The cost of the deluxe portrait package = $97

What is a system of equations?

Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

Here, we let

x = the cost of the basic portrait package

y = the cost of the deluxe portrait package

Eighth graders from Dover Elementary School ordered 82 basic portrait packages and 73 deluxe portrait packages, for a total of $11,591:

82x + 73y = 11591

The seniors at Clarksville High ordered 85 basic portrait packages and 70 deluxe portrait packages, for a total of $11,465:

85x + 70y = 11465

by solving the system of equations:

82x + 73y = 11591

85x + 70y = 11465

We get

x = $55

y = $97

Hence, the cost of the basic portrait package = $55

the cost of the deluxe portrait package = $97

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If lying with the wind the same plane travels 5820 km in six hours. The  rate of the plane and still air  is 770 mph and the rate of wind is 200 mph.

Let J represent the rate of jet in still air

Let W represent the  rate of wind

Distance:

d = rt

r = d/t

Against the wind the Jet flies at a rate of  J - W

= 2850 mi/ 5hrs = 570 mph

With the wind the Jet flies at a rate of:

J+W = 5820 mi/6hrs = 970 mph

The average rate for Jet

J = (570+970)/2

J = 770 mph

So,

W = 770 - 570 = 200 mph

The rate of the plane and still air is 770 mph

The rate of wind is  200 mph.

Therefore 770 mph and 200 mph are the rate.

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The greatest possible whole number perimeter of the triangle is  29 meters .

The two sides of the triangle are 8.1 m and 6.5 m.

Now , from the properties of triangles , we can say that the third side will be less than the sum of the other two sides.

if third side is x , then we can write the inequality

x < 8.1+6.5

or, x < 14.6 m

Takin x =14.6 m. The perimeter of the triangle will be

8.1 m +6.5 m+14.6 = 29.2

Hence the greatest possible side will be 29m.

Any two-dimensional figure's perimeter is dependent on the space surrounding it. Practically any closed shape's perimeter may be calculated simply summing the lengths of its sides.

The formula used to determine the perimeter of a closed shape figure is often proportionate to the length of the figure's outside line. A triangle's perimeter is determined by multiplying its three sides together.

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The green family will double their investment in 34 years after the principal is subject to compound interest continuously.

The principal invested = $2500

Rate of interest annually = 2.75%

Time = t years

Amount  = double of principal = 2500 × 2 = $ 5000

Interest is compounded continuously

Formula to calculate the amount is given by:

[tex]A=Pe^{rt}[/tex]

Now we will use the values to find the exact value of t

or, [tex]5000 = 2500 e^{0.0275t}[/tex]

or, ln 2 = 0.0275t

or, t = 25.205 years

or, t ≈ 25 years

Compound interest allows interest to accumulate over time as opposed to simple interest, which does not compound because prior interest is simply not added to the principal for the current period.

The simple annual interest rate is obtained by multiplying the interest per period by the total number of periods in a year.

Hence the Green family will have doubled the investment in approximately 25 years.

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Answer:

Step-by-step explanation:

18 times 9 then -9

Answer:

135

Step-by-step explanation:

First, Times 18 x 8. which gives you 144. Then, subtract 9, giving you 135.

Answer:

-400.50

Step-by-step explanation:

The way to calculate confidence interval for difference in means is given below:

A range of values that, with a certain degree of confidence, are likely to represent the genuine difference between two population means is known as a confidence interval (C.I.) for a difference between means.

They will go out and take a random sample from each population, compute the mean for each sample, and use that information to estimate the difference. The difference between the two means can then be compared.

Hence, Confidence interval = (x1–x2) +/- t*√((sp2/n1) + (sp2/n2))

Example:

Let's say our goal is to determine the variation in mean weight between two turtle species, so we go out and randomly select 15 turtles from each population. The summaries for each sample are as follows:

Sample 1:

x1 = 310

s1 = 18.5

n1 = 15

Sample 1:

x2 = 300

s2 = 16.4

n2 = 15

For 90% Confidence Interval will be"

(310-300) +/- 1.70*√((305.61/15) + (305.61/15))

=  [-0.8589, 20.8589]

For 95% Confidence Interval will be:

(310-300) +/- 2.05*√((305.61/15) + (305.61/15))

=  [-3.0757, 23.0757]

For 99% Confidence Interval will be:

(310-300) +/- 2.76*√((305.61/15) + (305.61/15))

=   [-7.6389, 27.6389]

Hence, for the Difference Between Means interpretation will be: The confidence interval [-3.0757, 23.0757] has a 95% probability of containing the actual difference in mean weight between the two turtle populations.

It's possible that there is no difference in the mean weight of the turtles in these two populations because this interval contains the value "0," which indicates that it's possible.

With regard to the mean weight of the turtles in these two populations, we cannot, therefore, say with 95% confidence that there is a difference.

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Angie' s grandma drive 376 miles in each day.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The two cities are 752 travel miles apart.

And, It take 12 hours to drive that far.

Now,

Since, Angie' s grandma want to do the drive in two day.

So, The distance cover by Angie' s grandma in each day is,

= 752 / 2

= 376 miles

Thus, Angie' s grandma drive 376 miles in each day.

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Answer:

Step-by-step explanation:

it’s 5.5

The preceding quadratic equation can be factored as follows: (X + 2 ) (X - 49) (X - 49).

acc to our question,

Hence,The preceding quadratic equation can be factored as follows: (X + 2 ) (X - 49) (X - 49).

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The fraction of 3.88888 will be [tex]3\frac{11111}{12500}[/tex]

What is Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts.

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator

How to solve this problem?

The steps are as follow:

Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).

Step 2: Remove the decimal places by multiplication. First, count how many places are to the right of the decimal. Next, given that you have x decimal places, multiply numerator and denominator by 10x.

Step 3: Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

So the 3.88888 can be written as in fraction as following:

3.88888 = 388888/100000

dividing both num. and denominator ny 8

=(388888/8)/(100000/8)

=[tex]3\frac{11111}{12500}[/tex]

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Let's x be equal to 3.88888...

Multiplying both sides of the equation by 10, we get 10x = 38.88888...

Subtracting the left sides of these equations, we get:

10x - x = 38.88888... - 3.88888...

9x = 35

Dividing both sides of this equation by 9, we get:

x = 35/9

Therefore, the decimal 3.88888... is equal to the fraction 35/9. Answer: A) 38/9 (reduced form of 35/9).

(B) 1/2,1/4,1/10,6/3 are considered benchmark fractions.

Benchmark fractions are regular fractions that we can use to compare or judge other fractions when measuring, comparing, or ranking them. Benchmark fractions are simple to see and recognize, making it easier to estimate the components. We can either make the denominators of two fractions with distinct numerators and denominators the same, or we can compare them to a benchmark fraction like 1/2. The best way to use benchmark fractions is to plot the fractions to be compared on a number line next to the benchmarks.

A ruler is a tool most frequently used for number lines. As reference points, it uses half, fourth, and eighth.

Only option (B) satisfies the meaning of the benchmark fraction.

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By using the transformations of congruent triangles, the congruence statement is true for triangle ABC and triangle EFG and it is false for triangle DEF and triangle JKL.

The transformations of congruent triangles include translations, reflections and rotations.

a) Triangle ABC is a translation of triangle EFG. This is said as all the sides of the triangle ABC are proportional to that of triangle EFG. The side AB is proportional to that of side EF. The side AC is proportional to that of side EG. The side BC is proportional to that of side FG. So, triangle ABC and triangle EFG are congruent to each other.

b) In triangle DEF and triangle JKL, neither the sides nor the angles are proportionate. The side JK is neither proportional to DE, EF nor DF. Angles are also not proportional to each other as well. So, triangle DEF and triangle JKL are not congruent to each other.

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Answer:

f(1)=6

Step-by-step explanation:

f(x)=x+5

f(1)=1+5

f(1)=6

Hopes this helps please mark brainliest

Jessica's journey in total is a distance of 4.31 Kilometers.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

Given that

The distance traveled by horse = 3.31 km

The distance traveled by motorcycle = 1 km

To determine the total distance of Jessica's journey

The total distance of Jessica's journey = distance traveled by horse + distance traveled by motorcycle

The total distance of Jessica's journey = 3.31 + 1  

Apply the addition operation,

The total distance of Jessica's journey = 4.31

Therefore, Jessica's journey in total is the distance of 4.31 Kilometers.

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The equation, 4x-6y = -24, after simplification is 2x-3y = -12.

According to the question,

We have the following equation:

4x-6y = -24

Now, this equation can easily simplified by following the given steps.

First, we will divide both sides of the equation by 2. Now, we have the following expression:

2x-3y = -24/2

2x-3y = -12

Now, this equation can not be further simplified. What we can do in this equation is to only change the sides of the terms from right hand side to the left hand side or left hand side to the right hand side.

Hence, the equation, 4x-6y = -24, after simplification is 2x-3y = -12.

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Answer:

4x25/100=1

Step-by-step explanation:

How I came up with it

4÷100=25

25÷25=1

Julie will only get a 1% discount

Hope it helps

Answer:

y=3/5x+3

Step-by-step explanation:

Im sorry if this is wrong your picture is a little blurry or something but

for the +3 part you go up 3 then find a pretty spot on the graph(when the line goes through a point) and  [tex]\frac{rise}{run}[/tex]  would be 3 over five since you go down 3 and to the left 5 which would both be negative but two negatives make a positive.

Hope this makes sense.:)

Answer:9

Step-by-step explanation:

Unit conversion is the conversion of one unit to another unit with its standard conversion.

The number of dimes is 5.

The number of quarters is 11.

Unit conversion is the conversion of one unit to another unit with its standard conversion.

Example:

1 minute = 60 second

1 hour = 60 minutes

1 km = 1000 m

We have,

0.1 dollar = 1 dimes

0.25 dollar = 1 quarter

Now,

D + Q = 16 _____(1)

0.1D + 0.25Q = 3.25 ______(2)

From (1) we get,

D = 16 - Q ____(3)

Putting in (2) we get,

0.1D + 0.25Q = 3.25

0.1 (16 - Q) + 0.25Q = 3.25

1.6 - 0.1Q + 0.25Q = 3.25

1.6 + 0.15Q = 3.25

0.15Q = 1.65

Q = 11

Now,

D = 16 - Q

D = 16 - 11 = 5

D = 5

Thus,

The number of dimes is 5.

The number of quarters is 11.

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Answer:

2

Step-by-step explanation:

(-11, -16) and (-13, -20)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-20 - (-16)) / (-13 - (-11))

Simplify the parentheses.

= (-20 + 16) / (-13 + 11)

= (-4) / (-2)

Simplify the fraction.

-4/-2

4/2

= 2

This is your slope.

Equation of the line - Slope

The points of the slope are, we also apply the formula:

  [tex]\huge \boxed{\boldsymbol{\sf{\left \{ {{x_1,y_1} \atop {x_2,y_2}} \right. \iff \ m=\frac{y_2-y_1}{x_2-x_1} }}}[/tex]

The points are:

     [tex]\boldsymbol{\sf{\underbrace{x_1=-11} \ \ \ \ \ \ \ \ \ \ \overbrace{y_1=-16} \ \ \ \ \ \ \ \ \ \ \underbrace{x_2=-13} \ \ \ \ \ \ \ \ \ \ \overbrace{y_{2}=-20} }}[/tex]

Substitute data into the formula:

[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff \ m=\dfrac{y_2-y_1}{x_2-x_1} }}[/tex]

                          [tex]\boldsymbol{\sf{m=\dfrac{-20-(-16)}{-13-(-11)} }} \\ \\ \\ \boldsymbol{\sf{m=\dfrac{-4}{-2} }}\\ \\ \\ \boxed{\boxed{\boldsymbol{\sf{m=2}}}}[/tex]

The slope through the points (-11,-16) and (-13, -20) is 2.

The ratio of green balloons to the total number of balloons is 3 to 8.

What is Ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.

Given, the number of red balloons = 22

the number of blue balloons = 18

the number of green balloons = 24

Total number of balloons = 22 + 18 + 24 = 64

Now,

the ratio of green balloons to the total number of balloons =

= (the number of green balloons)/(Total number of balloons)

= 24/64

= 3/8

= 3:8

Hence, the required ratio is 3 to 8.

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Answer:

16 [tex]\pi[/tex] cm

Step-by-step explanation:

C = 8 * 2 * pi = 16 [tex]\pi[/tex] cm

Answer:C≈50.27cm

Step-by-step explanation:

C=2πr=2·π·8≈50.26548cm

The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

The function is given as

h(t) = -16t² + 72t + 7

Differentiate the above function

So, we have the following representation

h'(t) = -32t + 72

Set to 0

-32t + 72 = 0

So, we have

32t = 72

Divide by 32

t = 2.25

Hence, the time is 2.25 seconds

In (a), we have

t = 2.25

Substitute t = 2.25 in h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

Evaluate

h(2.25) = 88

Hence, the maximum height is 88 feet

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Answer:

Step-by-step explanation:

No, buying small bag and medium bag of rubber bands will not give him more rubber bands than a large bag.

Combining things and counting them as one big group is done through addition. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation. The combination of at least two numbers constitutes basic addition. Once a student has mastered counting, they can begin to study basic addition. By locating the addend at the top of the chart and tracing down to the row of the second addend, they can utilize an addition chart as a learning tool.

Given,

Small = 25

Medium = 45

Large = 70

Juan wants to buy small bag and medium bag of rubber bands.

So, adding:

Small + Medium

25 + 45

70

No, buying small bag and medium bag of rubber bands will not give him more rubber bands than a large bag.

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The values obtained from the data in the table are as follows;

a) The percentage of boys that regularly drink Water is 32.8%

b) The proportion of students that were Girls ≈ 0.43

c) The marginal frequency for Lemonade ≈ 74

d) The joint frequency for Girls  who regularly drink Lemonade = 32

e) The joint relative frequency for Boys who regularly drink Soda ≈ 0.21

f) The marginal relative frequency for Girls ≈ 0.43

A two-way table provides the values of the frequencies for two variables, such that one category of variables are presented using the rows and the other category of variables are presented along the columns.

a) The total number of boys = 45 + 50 + 42 = 137

The number of boys that regularly drink water = 45

The percentage of boys that regularly drink water is therefore;

[tex]Percentage = \dfrac{45}{137} \times 100 \approx 32.8\%[/tex]

b) The total number of students = 77 + 88 + 74 = 239

The number of girls = 32 + 38 + 32 = 102

The proportion of students that were girls is therefore;

[tex]\dfrac{102}{239} \approx 0.43[/tex]

c) The marginal frequency for Lemonade which is the row total for Lemonade is 74

d) The joint frequency for Girls who regularly drink Lemonade from the table is 32

e) The joint relative frequency for the Boys who regularly drink Soda is found using the equation;

[tex]JRF = \dfrac{50}{239} \approx 0.21[/tex]

f) The marginal relative frequency for the girls is given by the equation;

[tex]MRF = \dfrac{102}{239} \approx 0.43[/tex]

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The inverse funciton is:

g(x) =  ∛(x/0.25)

And the graph of the two functions can be seen in the image at the end.

We want to find the inverse of the function:

f(x) = 0.25*x^3

Two functions f(x) and g(x) are inverses if and only if:

f( g(x)) = x

g(f(x)) = x

So, let's say that g(x) is the inverse of f(x), then we can write:

f(g(x)) = 0.25*(g(x))^3

And that must be equal to x, then we can solve:

0.25*(g(x))^3 = x

(g(x))^3 = x/0.25

g(x) = ∛(x/0.25)

That is the inverse fuction, the graph of the two functions can be sen below.

Where the red one is g(x) and the black one is f(x).

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1 km = 1000 m and 1m = 100cm

1 km is the same as 1000 m = 1000 x 100 = 100000 cm

There are 862 kilometres so there is 862 x 100000 = 86200000 cm in 862 km.

Answer:

86200000

Step-by-step explanation:

Answer:

880 mango trees and 440 star apple strees

Step-by-step explanation:

when for every 8 mango trees there are 4 star apple trees, then there is a 2:1 ratio of mango : star apple trees.
1320 divided by 3 = 440
and 2*440 = 880 mango trees, 1*440 = 440 star apple trees