A mixture of paint calls for 1/3 cups of red paint and 3/4 cups of yellow paint. How many cups of red paint would be needed for every 1 cup of yellow paint?

The inverse function is [tex]f^-^1(x) = \frac{Inx}{In10}[/tex] and Domain (0, infinity) and Range is (-infinity , infinity).

Given,

In the question:

The inverse function f(x) = [tex]10^x[/tex]

To find the inverse function:

Now, According to the question;

f(x) = [tex]10^x[/tex]

Rewrite the function using y

y = [tex]10^x[/tex]

Interchange the position of x and y in the function

x = [tex]10^y[/tex]

Isolate the dependent variable

y = [tex]\frac{Inx}{In10}[/tex]

Find the inverse function

[tex]f^-^1(x) = \frac{Inx}{In10}[/tex]

Hence, The inverse function is [tex]f^-^1(x) = \frac{Inx}{In10}[/tex] and Domain (0, infinity) and Range is (-infinity , infinity).

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Answer:

x = - 1

Step-by-step explanation:

given a parabola in standard form

ax² + bx + c ( a ≠ 0 )

then the vertical axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

x² + 2x - 8 ← is in standard form

with a = 1, b = 2 , then

x = - [tex]\frac{2}{2}[/tex] = - 1

equation of axis of symmetry is x = - 1

Answer:

-400.50

Step-by-step explanation:

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 value of angle x is 113 degrees and y is 67 degrees.

What is angle?

In euclidean geometry, an angle is that the figure shaped by 2 rays, referred to as the perimeters of the angle, sharing a typical end point, referred to as the vertex of the angle. Angles shaped by 2 rays exist the plane that contains the rays.

Main body:

Given ;

∠C = 62°

∠A =51°

according to triangle sum property: Sum of angles of triangle is 180°

Using it,

62° +51° +∠y = 180°

113°+ ∠y =180°

∠y = 67°

∠x is equal to the sum of interior opposite angle ,so using it we get:

∠x = 61°+52°

∠x = 113°

Hence the value of ∠x is 113 degrees and y is 67 degrees.

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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).

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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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.:)

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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Answer:

2x + 3y = 5 >>>> 1st equation

2x + 4y = 6 >>>> 2nd equation

2nd equation - 1st equation

2x+4y-2x-3y=6-5

y=1

2x+3×1=5

2x=2

x=1

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 required sale for the year is given as $833,333.34.

Given that,
A real estate agent makes an annual salary of $25,000 plus 3% commission on sales. She wants to make at least $50,000 per year.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the sales be x,
according to the question,
25000 + 0.03x = 50000
0.03x = 25000
x = 25000/0.03
x = $833,333.34

Thus, the required sale for the year is given as $833,333.34.

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Answer:

See the explanation below.

Step-by-step explanation:

Whether the answer is positive or negative depends on the number of positive and negative values in the question. The rules are exactly the same as to whether an answer is positive or negative. In the case of fractions, the rules for multiplying fractions apply as well (the numerators in the expression multiply to produce the product's numerator; the denominators in the expression multiply to produce the product's denominator) and the answer should be reduced to lowest terms.If there is an odd number of negative terms, the answer will be negative.If there is an even number of negative terms, the answer will be positive.

I would appreciate it if you mark my answer as brainliest.

The linear equation in general form to represent the given statement will be 5A + 3B = 553600.

How to form general equation?

Jose invested money in fund A at interest = 6%

Interest = (A * 5 * 1) / 100

Interest on fund A = A/20

Jose invested money in fund B at interest = 5%

Interest = (B * 6 * 1) / 100

Interest = 3B/100

Total interest he get = $5536

Interest on fund A + Interest on fund B = 5536

A/20 + 3B/100 = 5536

(5A + 3B)/100 = 5536

5A + 3B = 553600

Therefore, the linear equation in general form to represent the given statement will be 5A + 3B = 553600.

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Answer:

Step-by-step explanation:

it’s 5.5

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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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:

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: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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The 21-centimeter radiation easily passes through the interstellar dust clouds that prevent optical measurements from being made deep inside the galactic center, enabling the charting of the galaxy's spiral structure.

Hydrogen line:

A change in the energy state of neutral hydrogen atoms results in the formation of the hydrogen line, also known as the 21 centimeter line, H I line, or H I line. Its frequency is exactly 1420 in this electromagnetic radiation.

The charting of the galaxy's spiral structure is made possible by the 21-centimeter radiation's ability to easily pass through the clouds of interstellar dust that prevent optical investigations deep inside the galactic center.

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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 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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1. The x-intercept of the line is: 16

2. The y-intercept of the line is: 20

The x-intercept of a line is the value of x when the corresponding value of its y-coordinate is equal to 0.

On the other hand, y-intercept of a line is the value of x when its corresponding x-value is equal to zero.

Given the equation, 5x + 4y = 80, to find the x-intercept, substitute y = 0:

5x + 4(0) = 80

5x + 0 = 80

5x = 80

x = 80/5

x = 16

x-intercept is: 16

To find the y-intercept, substitute x = 0:

5(0) + 4y = 80

0 + 4y = 80

y = 20.

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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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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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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:

f(1)=6

Step-by-step explanation:

f(x)=x+5

f(1)=1+5

f(1)=6

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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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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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