13. Which situation can be represented bya true proportion?
A car used 3 gallons of gas to drive 72 miles on a highway and used 4 gallons of gas to drive 72 mileš town.
A store charged $20 for 2 shirts and charged $25 for 3 shirts.
A signal light flashed yellow 7 times in 28 seconds and flashed red 5 times in 35 seconds.
An alarm on a clock beeped 7 times in 6 seconds and beeped 14 times in 12 seconds.​

Since the two equations are identical, they intersect in an infinite number of places. They are consistent and reliant as a result.

a value or set of values that, when used as a stand-in for one or more equation's variables, cause the equation to be true. a strategy or approach for resolving a problem, such as the solutions to the equation x2 = 4 being 2 and -2. a description of a resolution. to be more precise: a group of variable values that satisfy an equation.  The equation 3(2)+5=11 states that 6+5=11 is accurate. So, the solution is 2.

given

y = 3x + 1

y = 3x + 1

The two equations are independent and consistent since they cross at a single precise location.

y = 3x + 1

y = x + 3

The two equations are independent and consistent since they cross at a single precise location.

y = x + 3

These two equations are incompatible because they do not intersect.

y = x + 3

To identify which line it is, rearrange the first equation into slope-intercept form.

Since the two equations are identical, they intersect in an infinite number of places. They are consistent and reliant as a result.

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Answer: So the positive solution is:

ANSWER:    X = 5

(x = 5 ),  (x = - 2 )

Step-by-step explanation:

when 10 is subtracted from the square of a number the result is 3 times the number.

Find the positive solution.

Let:   x = number

Let x^2 = square of a number.

x^2 - 10x = 3x transpose

x^2  -  3x - 10 = 0

Apply Factoring: Fractions of  10  are   5  and 2

( - 5)(2)  =   - 10

- 5  + 2  =  - 3

( x - 5 )(x + 2) = 0

x - 5 = 0      x + 2 = 0

x = 5             x   =  - 2

So the positive solution is:

ANSWER:    X = 5

I hope that helps!!!!

Answer:

x1=-4 x2=10

Step-by-step explanation:

step 1: x-3 = +/- 7 <--- take the square roots of both sides of the equation and use both positive and negative roots

step 2: x-3 = -7

            x-3=7

step 3: x-3=-7--> x=-4

           x-3=7--> x=10

step 4:x1=-4, x2=10 is the answer

Answer:

1. ( 1,7)

2. (17, 39)

Step-by-step explanation:

1.  Replace all occurrences of y with 6x+1, and we get

9x + 1 = 10

x = 1

y = 6x + 1

y = 7

So, the answer for number 1 is (1,7)

2. 6x - y = -15x + 2y = 17

We subtract 2y and get

6x - 3y = 15x = 17

Replace all occurrences of x with 17, and we get

102 −3y = −15

x = 17

y = 39

So, the answer for number 2 is (17, 39)

The slope of the line is 20.

The slope represents the rate of change in the price per hour is $20.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Two coordinates from the graph.

(1, 60) and (3, 100)

Slope.

= (100 - 60) / (3 - 1)

= 40 / 2

= 20

The slope represents the rate of change in the price per hour.

Thus,

The value of the slope is 20.

The slope denotes that the rate of charge per hour is $20.

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The answer to the table is given below.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given:

Learn more about ratios here: Jerome’s brother told him to add one cup of water for every cup of drink mix he added to keep the ratio of water to drink mix the same and still increase the total amount of energy drink. We get the following table using the constraints given in the question

Drink mix     3     4     5      6    7

water cups   8     9     10     11   12

Hence, The complete table is shown above.

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Answer:

7.0

Step-by-step explanation:

from the first figure which is not a 0

7.3-7.0(1 significant figure)

As a mixed number, 4.2 can be written as 4 + 2/10.

As an improper fraction, 4.2 can be written as 21/5.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

Since 4 + 2/10=4.2  so as a mixed number, 4.2 can be written as 4 + 2/10.

Also, 21/5=4.2 so, as an improper fraction, 4.2 can be written as 21/5.

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Answer:

610.75

Step-by-step explanation:

48.86 divided by 0.08

Answer:

-30

Step-by-step explanation:

-1x/5 = 6

-x/5 = 6

-x = 30

x = -30

Darnell's constant speed, as determined by the solution, is 20 miles per hour.

It covers linear transformations more broadly as well as vectors, matrices, and vector spaces. One area of mathematics is linear algebra. In comparison to other areas of mathematics that are frequently driven by innovative ideas and unresolved problems, linear algebra is a discipline that is very well understood.

Distance=8 miles

Time taken is=32 minutes

speed=distance/time

speed=15 miles/hour

Darnel has travelled a distance of 1.5x5/60=0.125 miles in under five minutes.

Hector bicycle speed = distance/time

hector speed of bike=  20 miles/hour

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B: (0, -1) , ( -4,0) , ( -2, -1) , (7, -7)

Image result for ordered pair definition

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order. It aids visual comprehension by locating a point on the Cartesian plane. An ordered pair’s numeric values can be integers or fractions.

The origin is the place where both axes cross. Every point on the coordinate plane is represented by an ordered pair (x, y), with the first element x referred to as the x-coordinate and the second element y referred to as the y-coordinate.

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The valuation of the notes in a years is given as follows:

y = 200(0.00000006)^a.

The yearly inflation rate is of:

1,666,666,667%

The valuation changed by a percentage in a period of time, hence an exponential function is used to model the situation.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial valuation is of $200, hence the parameter a is given as follows:

a = 200.

Thus the function should be modeled as follows:

[tex]y = 200(b)^a[/tex]

In which a is the time in years.

In one month, the amount decayed to $50. One month is 1/12 of a year, as one year is composed by 12 months, hence the parameter b is obtained as follows:

[tex]50 = 200(b)^{\frac{1}{12}}[/tex]

[tex](b)^{\frac{1}{12}} = \frac{50}{200}[/tex]

[tex](b)^{\frac{1}{12}} = \frac{1}{4}[/tex]

Elevating both sides to 12, we have that:

b = (0.25)^12

b = 0.00000006.

Hence the function is:

y = 200(0.00000006)^a.

The inflation rate is given as follows:

1/0.00000006 x 100% = 1,666,666,667%

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Answer:

no

Step-by-step explanation:

the one equation has variables and numbers go in for the variable and the other equation just equals 11

Growth that is slower than the Nuttall Oak growth rate is h=5t.

An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.

This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.

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The probability that Andre, Olivia, and zack all win gift cards that are at least $25 is 1/4. Hence option C is the correct option.

What is an event?

An event is a collection of experiment results (a subset of the sample space) to which a probability is ascribed in probability theory.

The wheel consists of 8 equal sections. Each section contains the price of a gift card. 4 sections contain a $5 gift card, 2 sections contain a $5 gift card, one section contains a $25 gift card, one section contains a $50 gift card.

To win at least $5, they have to get either $25 or $50.

Thus the number of outcomes of favorable event is 2.

Total number of outcomes is 8.

The probability to win at least $25 is 2/8

Divide denominator and numerator by 2:

2/8 = 1/4

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When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.

given

The grocery store is 31.92 wide overall, with 10 equally wide parking spaces.

If you assume that the width of these 10 parking spaces is equal to the width of the grocery store as a whole, you will have:

10x=31.92

on both sides of the equation, multiply by 10.

10x/10 = 31.92/10

x = 3.192

When there are 10 identically sized parking spaces in each row of the grocery store parking lot, the solution is 3.192 width.

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Answer:

Step-by-step explanation:

a.4 hours drive 240 miles, so the speed is 240÷4=60 miles per hour

b.1 days have 24 hours, then, it will go 60 ×24 = 1440 miles in 1 days

Answer:

1440

Step-by-step explanation:

240+4= 60

distance = rt

r= rate

t = time

IN ONE DAY

60 times 24= 1440

(24 for 24 hours)

The solution to the geometric progression are

a) The geometric progression converges , r = 0.1

b) The geometric progression converges , r = 0.2

c) The geometric progression diverges , r = 5

d) The geometric progression converges , r = 0.2

e) The geometric progression diverges , r = 5

f) The geometric progression converges , r = 0.2

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A geometric progression is said to converge if the common ratio r lies between -1 < r < 1

So , If -1 < r < 1, the geometric sequence converges

a)

The geometric progression is A = 0.3 + 0.03 + 0.003 + ...

The common ratio r = second term / first term

The common ratio r = 0.03 / 0.3

The common ratio r = 0.1

So , -1 < r < 1 and the GP converges

b)

The geometric progression is A = 0.25 + 0.05 + 0.01 + ...

The common ratio r = second term / first term

The common ratio r = 0.05 / 0.25

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

c)

The geometric progression is A = 0.23 + 1.15 + 5.75 + ...

The common ratio r = second term / first term

The common ratio r = 1.15 / 0.23

The common ratio r = 5

So , r > 1 and the GP diverges

d)

The geometric progression is A = 0.75 + 0.15 + 0.03 + ...

The common ratio r = second term / first term

The common ratio r = 0.15 / 0.75

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

e)

The geometric progression is A = 0.00025 + 0.00125 + 0.00625 + ...

The common ratio r = second term / first term

The common ratio r = 0.00125 / 0.00025

The common ratio r = 5

So , r > 1 and the GP diverges

f)

The geometric progression is A = 128,750 + 25,750 + 5,150 + ...

The common ratio r = second term / first term

The common ratio r = 25,750 / 128,750

The common ratio r = 0.2

So , -1 < r < 1 and the GP converges

Hence , the geometric progression is solved

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We spent a total of 40.2 + 24.5+ 37.8 = $102.50

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.

Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.

We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.

You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.

Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.

You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

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The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

[tex]r = 0.3[/tex]

The explained variance is found using the following formula:

[tex]R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9[/tex]

Thus, 81% of the variance remains unexplained by variations in the independent variable.

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He needs to make 1 and a half trips to the well to fill the barrel which has a height of 15 inches and  radius 10 inches.

A cuboid is a three-dimensional geometric shape that has six rectangular faces, three of which meet at each corner. A cuboid has three dimensions: length, width, and height. It is also commonly referred to as a rectangular prism. The formula for the volume of cuboid is [tex]V = l *w * h[/tex], where l is the length, w is the width, and h is the height. The formula for the surface area of a cuboid is [tex]2lw + 2lh + 2wh[/tex]. Cuboids are used in everyday life such as building blocks and package boxes.

The cylindrical barrel has a volume of [tex]\pi * r^2 * h = \pi * 10^2 * 15 = 1500\pi[/tex] cubic inches.

The hemisphere has a volume of [tex](2/3) * \pi * r^3 = (2/3) * \pi * 10^3 = (2000/3)\pi[/tex] cubic inches.

So, to fill the barrel, Brad must make [tex]1500\pi / (2000/3)\pi = 3/2 = 1.5[/tex] trips to the well.

In other words, he needs to make 1 and a half trips to the well to fill the barrel.

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The value of cos 149 degree as calculated from the calculator is found out to be -0.857167301.

Which on round off is , -0.85.

The formula to calculate the angle of depression is , θ = tan-1 (Opposite Side/Adjacent Side) .

Therefore, the AOD for cos149 degree is found out to be as ,

α = arctan(vertical distance / horizontal distance)

α = arctan(10 / 11.998)

α = arctan(0.83347224537423)

α = 0.69482025147278 ° ≈ 0.69 °

The angle of depression is defined as the point of meeting of a horizontal line with the line between the item and the observer's eye. This angle is determined by two factors , which are their height and distance.  If the item is below the observer's level, the angle produced between the horizontal line and the observer's line of sight is known as the angle of depression.

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In the case of Typical behavior of the sales prices of houses median is the best term. In the case of Ages of 1st graders mean is the best way of central tendency and for Heights of women mode is the best measure.

First of all we have to know the Mean, median and mode. The mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

In the case of typical behavior of the variable sales price of houses, the Median will be the best measure of central tendency because the median will not get affected by the higher/lower prices of houses.

The age of each kid will be almost the same.  In order to represent the typical behavior of the variable Age of 1st graders, the mean will be the best measure of central tendency.

Incase of Heights of women, the mode will be the best measure of central tendency as it will describe the height that most of the females have. 

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Answer:

No

Step-by-step explanation:

Since [tex]2^2+3^2 \neq 5^2[/tex], the side lengths do not satisfy the Pythagorean theorem.

Answer:

11 pounds

Step-by-step explanation:

The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds

Answer:11

Step-by-step explanation:

11 times 3 equals 33(for the clothing)

so 11 is left

The population of Cuba in 10 years will be 1.9243 million.

A process called exponential growth sees a rise in quantity over time. It happens when a quantity changes at an instantaneous rate that is proportionate to the quantity itself with respect to time.

Data patterns that exhibit exponential growth exhibit quicker rate of expansion over time. Compounding produces exponential returns in the financial world. Savings accounts with a compound interest rate have the potential to expand exponentially.

The population growth will be modeled using exponential growth:

f(x) = a(b[tex])^t[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04[tex])^t[/tex]

The population after 10 years will be:

f(x) = 1.3(1.04[tex])^{10[/tex]

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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The population of Cuba in 10 years will be 1.9243 million, if the population is expected to grow at a rate of 4% each year.

Quantities increase over time through a process known as exponential growth. It occurs when a quantity shifts at a pace that is proportional to the quantity's own rate of change with regard to time.

Data patterns that show exponential growth expand more quickly over time. In the world of finance, compounding generates exponential profits. Compound interest savings accounts have the potential to grow tremendously.

The population growth will be modeled using exponential growth:

f(x) = a(b)[tex]^{t}[/tex]

where:

a be the initial value

b be the growth rate

Substitute the values in the above equation, we get

f(x) = 1.3(1.04

The population after 10 years will be:

f(x) = 1.3(1.04

simplifying the equation, we get

f(x) = 1.9243

Therefore, the population in 10 years will be 1.9243 million.

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The given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the expression as follows -

8.5x + 0.5 + 3.5x - 2x

The given expression is -

8.5x + 0.5 + 3.5x - 2x

(8.5x + 3.5x - 2x) + 0.5

12x - 2x + 0.5

10x + 0.5

Therefore, the given expression {8.5x + 0.5 + 3.5x - 2x} is equivalent to

10x + 0.5.

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We can use the sin (), and cos () functions in C programming to find the sine and cosine values of any problem.

sin( ), cos( ) and tan( ) functions in C are used to find sine, cosine and tangent values.

sinh( ), cosh( ) and tanh( ) functions are used to find hyperbolic sine, cosine and tangent values.

exp( ) function is used to find the exponential “e” to the xth power. log( ) function is used to find the natural logarithm and the log10( ) function is used to find the base 10 logarithms.

The” math.h” header file supports all these functions in the C language.

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