A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Step-by-step explanation:

Let x = number of ounces of 63% solution.

Let y = number of ounces of 33% solution.

The total solution to be made is 100 oz.

x + y = 100

x ounces of 63% solution is 0.63x ounces of acid.

y ounces of 33% solution is 0.33y ounces of acid.

100 ounces of 39% solution is 39 ounces of acid

0.63x + 0.33y = 39

The system of equations is

x + y = 100

0.63x + 0.33y = 39

Multiply the both sides of the first equation by -0.33. Then add it to the second equation.

         -0.33x - 0.33y = -33

    +    0.63x + 0.33y = 39

   ---------------------------------

             0.3x             = 6

x = 6/0.3

x = 20

x + y = 100

20 + y = 100

y = 80

Answer:

20 ounces of the 63% solution and 80 ounces of the 33% solution.

Answer:

Step-by-step explanation:

70%=0.7

90 X 0.7 = 63

ANSWER IS 63

Answer:

Based on the given equation, the function g is an exponential function with base 2. The y-intercept of the function g is at (0, 4).

The graph of function f is not described, so it is not possible to accurately compare the two functions. In order to accurately compare the two functions, it would be helpful to have more information about the graph of function f, such as the vertex and any other points that the graph passes through.

In math, a pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object.

A pattern has a rule that identifies the items that are part of the pattern and those that are not. A pattern in mathematics is a series of recurring figures, shapes, or numbers.

Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. A specific set of rules must be taken into account in order to create a full pattern.

We must first comprehend the nature of the sequence and the distinction between the two successive numbers provided in the pattern in order to apply these rules. 

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Answer:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

Step-by-step explanation:

•Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.

•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.

• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.

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An equation may have more than one solution.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations. A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The variable's value for which the equation holds true is referred to as the equation's solution. If the LHS and RHS are switched, an equation doesn't change. The solution is discovered after isolating the variable for which the value must be determined. Depending on the kind of equation we are dealing with, we can solve it. There are various types of equations, including linear, quadratic, rational, and radical ones.

Steps to solve a linear equation:

1. If necessary, remove the parentheses and use the distributive property.

2. By merging like terms, make both sides of the equation simpler.

3. The LCD (least common denominator) of all the fractions should be multiplied by both sides of the equation if there are any fractions.

4. If the equation contains decimals, multiply both sides by the lowest power of 10 to make the result a whole number.

5. Using the addition and subtraction properties of equality, move the constant terms to the other side of the equation and the variable terms to the other.

6. Using the equality properties of multiplication or division, set the variable's coefficient to 1.

7. Get the answer by isolating the variable.

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Answer:

y = -3/4x + 52

y + 6 = -3/4(x-8)

Step-by-step explanation:

y = mx + c

as long as the number is -3/4x , it represents slope -3/

Answer:

B. y = -3/4x + 52, C. y + 6 = -3/4(x - 8), and F. 3x + 4y = 9

Step-by-step explanation:

A. -3x + 4y = -34

y = 3/4x - 17/2

Slope = 3/4

INCORRECT

B. y = -3/4x + 52

Slope = -3/4

CORRECT

C. y + 6 = -3/4(x - 8)

y = -3/4x

Slope = -3/4

CORRECT

D. 4x + 3y = -22

y = -4/3x - 22/3

Slope = -4/3

INCORRECT

E. 4x - 3y = 48

y = 4/3x - 16

Slope = 4/3

INCORRECT

F. 3x + 4y = 9

y = -3/4x + 9/4

Slope = -3/4

CORRECT

G. y - 6 = 3/4(x - 8)

y = 3/4x

Slope = 3/4

INCORRECT

Answer:

1/12

Step-by-step explanation:

3/4 - 2/3 = 9/12 - 8/12 = 1/12

Answer:

The answer is 1/12 good luck with the rest

By altering schedules without giving adequate notice, terminating employees without giving adequate notice, and making false claims about its products, company x is not adhering to best practises.

These include bar codes, ISBNs, ASCII codes, postal codes, and bank account numbers; many of these contemporary codes use a checking mechanism, also known as a check digit. The ISBN system, now used uniformly on all new books, is one illustration of this.

Adopting sensible company procedures and policies with reference to apparently contentious issues is referred to as practicing business ethics. Corporate governance, market manipulation, bribery, racism, social duty, and fiduciary responsibilities are a few of the topics that come up in an ethical discussion.

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Answer:

The first one is right...

Step-by-step explanation:

Answer:

Step-by-step explanation:

6

Answer:

Step-by-step explanation:

9.0 × 10-10 I think.....

Answer: To solve this problem, we can use the information provided to set up and solve an equation. Let x be the number of countries that participated in the 1896 Olympic games.

According to the problem, we know that the number of countries in the 2004 Olympic games was more than 14 times the number of countries in the 1896 games. So we can write the following equation:

x * 14 < 202

To solve for x, we can divide both sides of the inequality by 14:

x < 202/14

x < 14.43

x is the number of countries, it must be an integer.

so x = 14

Therefore, 14 countries participated in the 1896 Olympic games.

Step-by-step explanation:

When Nancy wanted to find the volume of a cuboid, the volume is 352cm³.

Word problem simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

Since Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm.

The volume will be:

= Length × Width × Height

= 11cm × 8cm × 4cm

= 352cm³

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Complete question

Nancy wanted to find the volume of a cubiod she measured the length of the cubiod as 11 cm and width as 8cm and the height as 4cm. Find the. volume

On solving the provided question, we can say that - the linear equation

y=mx+b = [tex]y=6.4(82)+1900= > y=524.8+1900= > y=2424.8[/tex]

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

y=mx+b

x=gallons of fuel

y=total weight of plane including fuel

m=slope=6.4

b=weight of plane, no fuel....a constant to be calc'd

[tex]y=mx+b\\2245.6=6.4(54)+b\\2245.6=345.6+b\\ b=1900\\ y=6.4x+1900\\ y=6.4x+1900\\ y=6.4(82)+1900\\ y=524.8+1900\\ y=2424.8[/tex]

82gallons fuel is 2424.80 lbs

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The first equation will be multiplied by 3 and that of the second by 4.

An elimination method is a process of solving a system of linear equation, in this we make coefficients of the one variable equal and subtract the equations.

Given that are two equations to be solved by using elimination method,

-4x+4y = 32.....(i)

3x-y = 12......(ii)

To eliminate x, we will multiply eq(i) by 3 and eq(ii) by 4

-12x+12y = 96.....(iii)

12x-4y = 48....(iv)

Solving the equations, we get,

8y = 144

y = 18

Put y = 18 in eq (ii)

3x-18 = 12

3x = 30

x = 10

Hence, the first equation will be multiplied by 3 and that of the second by 4.

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Answer:

The fourth graph since it passes the vertical line test.

Each input has one output.

Hope this helps :)

the equation in the form of slope interpretation is y = 1/3x -4.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation has the conventional form y = mx + c.

Given data in a table such as it makes a linear equation slope-intercept form of the given equation is y = mx +c

Where m is the slope

c is constant

The slope for the given data

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 + 6 )/ (-3 + 6)

m = 1/3

Hence, the equation would be

y = 1/3x + c

for constant we would satisfy the equation with other coordinates of the line.

Substituting ( 0, -4) in the above equation

-4 = 0 + c

c = -4

thus, the equation of the line is  y = 1/3x  -4

therefore, the linear equation of the given data is y = 1/3x -4.

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Answer:

Discrete

Step-by-step explanation:

Discrete means it has ends, and continuous means it continues on forever.

Answer:

(-∞, 1] or {x|x<=1}

Step-by-step explanation:

1) The equation of a line of best fit is; y = -1.15x + 102.8

2) The predicted monthly cost for an average temperature of 25°F is $74.05

The equation of a line of best fit is represented by the equation;

y = mx + c

where;

m is the slope

c is the y-intercept

1. To calculate the slope here, we will use the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

Using two coordinate points on the scatter plot, (72, 20) and (20, 80), we have the slope as;

Slope (m) = (80 - 20)/(20 - 72)

Slope = 60/-52

Slope = -1.15.

Plug in -1.15 for m and (a, b) = (72, 20) into the formula; y = mx + c to get;

20 = -1.15(72) + c

c = 20 + 82.8

c = 102.8

The equation  will now be;

y = -1.15x + 102.8

2. Monthly heating cost, y, for a month with an average temperature of 25°F (x) will be calculated by plugging in 25 for x in the equation of line of best fit gotten earlier to get;

y = -1.15(25) + 102.8

y = 102.8 - 28.75

y = $74.05

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The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.

The rate of change of a function is the rate at which the output value changes per unit change in the input value.

The possible data and table obtained from a similar question on the website are presented as follows;

Student A

Number of minutes;         [tex]{}[/tex]1              2             3              4

Number of words read; 150        [tex]{}[/tex]300          450          600

Student B

y = 158·x

Where;

x = The time duration in minutes

y = The number of words read by the student

Student C

The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)

The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;

Reading rate for Student A = (300 - 150)/(2 - 1) = 150

The reading rate for Student A is 150 words per minute

The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute

The of the straight ling graph for the reading rate of Student C is found as follows;

Slope = (420 - 280)/(3 - 2) = 140

The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute

The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute

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Answer:

Step-by-step explanation:

sin40°=[tex]\frac{AC}{12}[/tex]
⇒AC=sin40°×12

⇒AC=7.713≈7.7
cos40°=[tex]\frac{AB}{12}[/tex]
⇒AB=cos40°×12

⇒AB=9.192≈9.2

as A=90°,B=40°

from A+B+C=180°

we can write C=180°-90°-40°

⇒C=50°

Answer:

[tex] \sf \: b) \: 45[/tex]

Step-by-step explanation:

The values given are,

→ u = 7

→ d = 10

→ e = 3.2

Now the expression is,

→ 15(d - u)

Evaluating the expression,

→ 15(d - u)

→ 15(10 - 7)

→ 15 × 3

→ 45

Hence, option (b) is correct.

Answer:45

Step-by-step explanation:

15(10-7)

15(3)

multiply and get 45

The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.

Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.

Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)

For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,

144 − 9x² − 16y² − z² > 0

9x² + 16y² + z² < 144

x²/ 4² + y²/ 3² + z²/ 12² < 1

Therefore, the domain is an ellipsoid.

Therefore x ∈ (-4, 4)

y ∈ (-3, 3)

z ∈ (-12, 12)

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The 5 life examples are:

In all these life examples that are listed above, the number 100 is divided by 20 giving 5 as the result. which is said to be:

100/20

= 5.

Therefore, reason behind this is that the number 20, in these life examples, is a representative of a whole value and the number 5 represents the number of parts it is being divided into, so when you multiply 20 by 5, you get 100, which represents the total of these five parts. So, 100 is related to 20 in this context as the multiple of 20 and 5.

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On solving the provided question, we can say that - he re the slope value is using the formula y/x = k => [tex]k = 2/3[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

Use the point (3, 2) and divide y by x using the formula y/x = k.

[tex]k = 2/3[/tex]

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Therefore ,As a result, y = 5x + 35 is the equation that gives the answer to the given algebra issue.

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols. The PEMDAS rule stands for the following operations: parenthesis, exponent, multiplication, division, addition, and subtraction. This rule is applied to solve the equation properly and accurately.

Here,

In this case, the equation for y in terms of x will be as follows:

y = 5(x + 7)

If you make the equation simpler, you get

y = 5(x + 7)

y = 5x + 35

y will have the linear equation y = 5x + 35 in terms of x.

Therefore , As a result, y = 5x + 35 is the equation that gives the answer to the given algebraic issue.

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Answer:

D+Q = 31

10D + 25Q = 595

10D + 10Q = 310

subtract to get

15Q = 285 Q = 285/15 = 19 quarters D = 31-19 = 12 dimes

The  slope of the table below? 3/8 15/12 9/10 0/7 is 23.8

Slope is defined as the rate of change of y with respect to x.  Invariably, it it the rise in y over the run  in x. put differently, slope is increase over increase in x

The slope of a line is defined

S= (increase in y)/(Increase in x) = Δy/Δx

Slope = (0/7 - 18/12) ÷ (9/10 -3/8)

Slope = 15/12 ÷ 42/80

Simplify the fractions to have

Slope = 15/12 * 80/42

The slope = 1200/504

Slope of the table is given as 23.4

Conclusively, the table gives us a slope approximately 23

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Prime numbers of the form p and p+2, where p is a prime number, are known as twin prime numbers.

A twin prime is a prime number that is either 2 less or 2 more than another prime number. For example, the number 3 and 5 are twin primes, because they are both prime and the number 5 is 2 more than 3. Similarly, the number 5 and 7 are also twin primes, because they are both prime and the number 7 is 2 more than 5.

Therefore, Twin primes are considered as interesting numbers in number theory because of their relative rarity, rare in nature and because they are the building blocks for certain types of primes such as Sophie Germain primes and safe primes.

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