Original equation:
3(a-2) + 14 =8-6a
Solution: 3a-2+14-8-6a
3a +12=8-6a
9a + 12 = 8
9a = -4
a = -4/9

1.5 kilograms of eggs is equivalent to approximately 3.31 pounds. Both kilograms and pounds are weight measuring units.

To convert kilograms to pounds, we can use the conversion factor that 1 kilogram is equal to 2.20462 pounds.

So to convert 1.5 kilograms of eggs to pounds, we can multiply 1.5 by 2.20462:

1.5 kilograms x 2.20462 pounds/kilogram = 3.30693 pounds

Therefore, 1.5 kilograms of eggs is equivalent to approximately 3.31 pounds. Both kilograms and pounds are weight measuring units. Kilograms are the primary unit of measurement for weight in the International System of Units (SI), while pounds are the primary unit of measurement for weight in the United States and other countries that use the imperial system of units. A kilogram is roughly equivalent to 2.20462 pounds. Kilograms are often used for scientific or medical purposes, while pounds are more commonly used for everyday weight measurements, such as for people's body weight or for weighing food in recipes.

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The value of 80 as fraction is 80/1.

To make 80 as a fraction, we need to place it over a denominator. The denominator can be any number as long as it is not equal to zero.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 10 in this case.

Therefore, the fraction 80 can be written as 80/1 or simplified as 8/1. This means that 80 is equivalent to 8 wholes or 8 times the unit.

In summary, 80 as a fraction is 80/1 or 8/1 when simplified.

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Answer:

A. –8.6, –5.0, –1.4, 2.2, 5.8, …

C. 5, 1, –3, –7, –11, …

D. –3, 3, 9, 15, 21, …

Step-by-step explanation:

If a sequence is an arithmetic sequence, the difference between any two terms must be the same for all terms.

This is known as the common difference

The correct choices are:
A : Common Difference = 3.6

C. Common difference = -4

D. Common difference = 6

To convert 80 kilograms (kg) to pounds (lb), Use the conversion factor that represents the relationship between kilograms and pounds, which is 1 kg = 2.20462 lb.

Now, to convert 80 kg to lb, multiply 80 by the conversion factor:

80 kg x (2.20462 lb / 1 kg) = 176.3696 lb

Therefore, 80 kilograms is equal to 176.3696 pounds (rounded to four decimal places). The complete mathematical expression for this conversion is:

80 kg x (2.20462 lb / 1 kg) = 176.3696 lb

A conversion factor is a mathematical expression that expresses the relationship between two units of measurement. It is used to convert measurements between units.

Conversion factors are commonly used to convert measurements between different units of measurement in math, science, and engineering. They are a useful tool for performing calculations and comparing data in various units.

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I'm positive the answer is 1, 7, 13, and 91

Answer:

We can use the following logarithmic identities to simplify the expression:

log a + log b = log (ab)

log a - log b = log (a/b)

n log a = log (a^n)

Using these identities, we can simplify the expression as follows:

1/2(log₂x + log₂y) - 5 log₂(x+6)

= 1/2 log₂(xy) - log₂(x+6)^5 (using the first two identities)

= log₂[(xy)^(1/2)/(x+6)^5] (using the third identity to combine the logarithms)

Therefore, the simplified expression is:

log₂[(xy)^(1/2)/(x+6)^5]

Step-by-step explanation:

Randomization in an experiment is important because it ensures that the results achieved are accurate .

Randomization in an experiment refers to a random assignment of participants to the treatment in an experiment .

Randomizing the experiments can help you get the best cause-effect relationships among the variables. It helps in controlling the lurking variables . These variables can affect the results to be different from what they are supposed to be . Randomization prevents biases and makes the results fair.

For ensuring that the information obtained from the experiment is correct, A randomized experiment is perfect to help us .

Researchers control values of the explanatory variable with a randomization procedure. So, if we see a relationship between the explanatory variable and response variables, we can say that it is a causal one.

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Answer:

5

Step-by-step explanation:

The interest for the given principal , time and rate is $ 51.06 . The Amount after interest is $ 976.06.

Simple interest is the amount of borrowing-related interest that is calculated using only the original principal and a constant interest rate. Compounding, in which borrowers end up paying interest on principal and interest that increases over a few of payment periods, is not a part of it.

Simple Interest = [tex]\frac{P*R*T}{100}[/tex]

where, P = principal, R = Rate of interest, T = Time.

Now in the given question,

Principal = $925

Rate= 2.3 %

Time = 2.4 years

Then,

Simple Interest,

                           [tex]=\frac{P*R*T}{100} \\\\=\frac{925*2.3*2.4}{100} \\\\=$51.06[/tex]

Hence the interest is $ 51.06 .

Amount after interest = P + I = 925 + 51.06 = $ 976.06.

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Answer:

Step-by-step explanation:

x is one blanket

y in one sheet

3x+y=190

2y+x=100

y=190-3x

2y+x=100

replace the y in the second equation with the first one

2(190-3x)+x=100

380-6x+x=100

380-5x=100

-5x=100-380

-5x=-280

x= -280/-5

x=56

replace the x with 56 so you can find the y

2y+56=100

2y=100-56

2y=44

y=44/2

y=22

so one blanket is 56 and a sheet is 22

Answer:

C

Step-by-step explanation:

To make it easy, if there are 3 yellow, 2 green, and 8 total, just find the equation that has the fraction result of 5/8.

The probability that a continuous random variable will be equal to any specific value is zero. This is because the probability of an individual value for a continuous random variable is represented by the area under the probability density function (PDF) at that particular value, and the area of a single point is zero.

We can convert fps to mph by using the relation, one mph = 1.18 fps.

One fps means one foot per second and one mph means one mile per hour. Foot and mile are the units of distance and second and hour are the units or time.

We have to convert fps to mph.

As per the standard unit conversion rates, we know,

One mile = 5280 foot.

Also, one hour = 3600 seconds.

So, if we want to convert, we should write,

= mph

= 4280/3600

= 1.18 fps.

So, now we have a standard relation that says, one mph is equal to 1.18 fps.

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The number of dimples per square centimeter are on the surface of a golf ball is 0.17, the correct option is A.

Suppose that radius of the considered sphere is of 'r' units.

Then, its surface area S would be:

[tex]S = 4\pi r^2 \: \rm unit^2[/tex]

We are given that;

The circumference= 13.408cm

Number of dimples = 336

Now,

2pi*r= 13.408

r= 13.408/2*3.14

r=2.13

Surface area= 4*pi*r^2

=4*3.14*2.13*2.13

=56.98

336dimple=56.98cm^2

1dimple=56.39/336

=0.167

Therefore, by the area of sphere the answer will be 0.170.

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The domain of the equation y = -16x^2 + 1700 is the set of all real numbers.

To find the domain of the equation y = -16x^2 + 1700, we need to determine the set of all real numbers for which the equation is defined.

Since the equation is a quadratic equation, it is defined for all real values of x. There are no restrictions on the values of x that can be plugged into the equation.

Therefore, the domain of the equation y = -16x^2 + 1700 is the set of all the real numbers.

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The expected value of the game is $16.50.

First we need to multiply the amount you can win by the probability of winning it, then add up all the products.

Let's call the expected value "E":

E = (0.20 x $60) + (0.15 x $30) + (0.25 x $0) + (0.40 x $0)

E = $12 + $4.50 + $0 + $0

E = $16.50

Therefore, the expected value of the game is $16.50.

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Answer:

B and E

Step-by-step explanation:

Information we need to know:

Like terms - a set of number which variables are the same

In the question we can see that there are two numbers that have the variable y and two numbers that have the variable of 0 (meaning that they are regular numbers)

Hence our options would be B and E

Hope this helps, have a lovely day! :)

the equation of the line will be 5y = 7x -7. Option c is correct.

A linear equation is an algebraic equation of the form y = mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a linear equation that passes through the points (5,0) and (0, -7)

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

slope = (-7 -0)/(0-5)

slope = 7/5

b = -7

thus,

the equation of the line will be:

y = 7/5x -7

multiply by 5 on both sides

5y = 7x -7

Therefore, the equation of the line will be 5y = 7x -7.

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Answer:

unit rate = $ 10 per km.

y = 10x

Step-by-step explanation:

Unit rate:

    Cost of travelling 1 km is $ 10. So, unit rate is $10

Equation:

       If 'x' km distance is travelled, then cost 'y',

              y = x * unit rate

               y = x * 10

               y = 10x

When you create a dot plot, the operations that you have to do are:

c. Place a dot along a horizontal scale for each observation.

d. "Pile up" dots that are too close to show separately

A dot plot is a simple way of representing numerical data. It consists of a horizontal axis and a series of dots that are placed along it to represent the values of individual observations. Each dot corresponds to one observation, and its position along the axis represents its value.

Option (a) is not correct because a dot plot typically does not have a vertical axis showing frequency of observations. Option (b) is not correct because connecting adjacent dots to create a polygon is not a common practice in dot plots. Instead, each dot represents a single observation, and dots are placed along a horizontal scale to show their value. If multiple observations have the same value, they are "piled up" on top of each other to avoid overcrowding the plot.

Therefore, the correct options are (c) Place a dot along a horizontal scale for each observation and d. "Pile up" dots that are too close to show separately

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Answer:

The step which is used is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step-by-step explanation:

Given point d is is the center of inscribed circle.

To construct the inscribed circle of abc we have several steps of construction

Step 1: First step is to construct the incenter with the help of angle bisectors of two base vertices.

Here given d center of inscribed circle that means the incenter given.

Step 2: After incenter, draw a line perpendicular to one side of triangle that passes through incenter and the label the point of intersection.

This is very important step because after labelling measure the radius(same as the distance between the incenter and labelled point) and draw the circle.  

Hence, after incenter The next step is to construct the altitude from the incentre  to a side of triangle and label the intersection point.

Step 2 is used draw inscribed circle when incenter already given.

The expression f - 5(2f – 3) is equivalent to two other expressions, option (a) -11f-3 and option (b) -11f + 15.

In mathematics, an expression is a combination of symbols, operated on by certain mathematical operations to create a numerical value or a function.

To understand why this is the case, let's break down the expression.

The first part of the expression is just the variable f, so that is unchanged. The second part involves the multiplication of -5 and (2f – 3).

To evaluate this part, we need to use the order of operations. First, we multiply -5 and 2f and get -10f.

Then, we subtract 3 from this result and get -11f.

Therefore, the expression f - 5(2f – 3) is equivalent to -11f-3 and -11f + 15.

Therefore, the correct options are both (a) and (b).

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Complete Question:

Which expressions are equivalent to - f - 5(2f – 3)?

Choose all answers that apply:

a) -11f-3

b)-11f + 15

c) None of the above​

One acre is equal to 43,560 square feet. To convert acres to square feet, you can multiply the number of acres by 43,560.

For example, if you want to convert 6 acres to square feet, you can multiply 6 by 43,560:

6 acres x 43,560 square feet/acre = 261,360square feet

So, 6 acres is equal to 261,360square feet.

Acres and feet are area and length measurement units, respectively. There is no direct conversion between acres and feet because they measure different things. However, you can convert acres to square feet using a conversion factor.

Please keep in mind that this conversion only applies to area measurements. If you need to convert linear measurements from acres to feet, you'll need more information about the area's shape and dimensions.

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The correlation coefficient ranges from -1 to +1. (option b)

Correlation is a measure that is used in statistics to measure the relationship that exists between two variables. Correlation can either be positive, negative or zero.

Positive correlation exists when two variables move in the same direction. The correlation coefficient usually ranges from 0 to 1. Negative correlation exists when the two variables move in different direction. The correlation coefficient usually ranges from  -1 to 0. Zero correlation is when there is no relationship between the variables.

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The greatest common factor of 30y⁸ +10y⁴ is 10y⁴

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4. GCF is often used to find common denominators.

The common factors of 30 are: 1,2,3,5,6,10,15,30

The common factors of 10 are : 1,2,5,10

therefore the greatest common factor is 10

The greatest common factor between y⁴ and y⁸;is y⁴

Therefore the greatest common factor of 30y⁸ +10y⁴ is 10y⁴ i.e 10y⁴(3y⁴+1)

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The solution for the given system of equations as required to be determined is such that; it has infinitely many solutions.

It follows from the task content that;

y = (2/3)x + 5 and -2x + 3y = 15.

Also, by substitution, we have that;

-2x + 3 ( (2/3)x + 5 ) = 15

-2x + 2x + 15 = 15

15 = 15.

Consequently; it follows that the system of equations given has infinitely many solutions as the equations are coinciding equations and form coinciding lines when graphed.

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The function is given as 6 < x < 15

Assuming that Pass members pay $8 each movie for the first five films, the equation y = 8x will be used to express this. Also, it is stated that after five films, additional films are free up to fifteen films. Thus, y = 40 will be the function used to represent this.

X represents the total number of films, while Y represents the monetary cost.

the function would be:

y = 8x{0 < x < 5}

y = 8 x 5

y = 40 {6 < x < 15}

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The value of conversion from Celsius to Fahrenheit for the value 31 Celsius is equal to 87.8 Fahrenheit.

Standard measuring  units for the temperature is known as Celsius and  Fahrenheit.

Formula used to convert the temperature from Celsius to Fahrenheit is written as

°F = 9 /5 ( ° C ) + 32.

Convert 31 Celsius  to Fahrenheit by substituting the given value in the above formula :

= 9 /5 ( 31° ) + 32

= (1/5) (279° ) + 32

= 55.8°  + 32

= 87.8°F

Therefore, the values after conversion for the 31Celsius to Fahrenheit is given by 87.8 Fahrenheit.

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