Bill’s spelling list is 3 words long at the start of the school year. Each month, his teacher adds 8 words to the list.

Let m represent the number of months since school began and w represent the total number of spelling words.

This relationship can also be shown in a table. Complete the equation that represents between m and w.

Answer:

Step-by-step explanation:

2(4x-3)≥-3(3x)+5x

8x-6≥-9x+5x

8x≥-4x+6

8x+4x≥6

12x≥6

x≥6/12

or

x≥1/2

Using exponent properties, the equivalent expression is given as follows:

[tex]\left(\frac{2}{3}\right)^14[/tex]

Two thirds to the fourth power is given by:

[tex]\left(\frac{2}{3}\right)^4[/tex]

Two thirds to the third power is given by:

[tex]\left(\frac{2}{3}\right)^3[/tex]

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

[tex]\left(\frac{2}{3}\right)^4 \times \left(\frac{2}{3}\right)^3 \left(\frac{2}{3}\right)^{4 + 3} = \left(\frac{2}{3}\right)^7[/tex]

Then, this entire expression is raised to the second power, meaning that:

[tex]\left[\left(\frac{2}{3}\right)^7\right]^2 = \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^7 = \left(\frac{2}{3}\right)^{7+7} = \left(\frac{2}{3}\right)^14[/tex]

[tex]\left(\frac{2}{3}\right)^14[/tex] is the equivalent expression.

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58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.

As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.

To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.

Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.

That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,

[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]

That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.

Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and

[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.

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Answer:

+ 1.45

Step-by-step explanation:

the end result is 16.55, therefore you add 1.45 to get $18 again.

Answer:

width = 6 ft

length = 21 ft

Step-by-step explanation:

Forming algebraic expressions and finding the dimensions of a rectangle:

 Width = w ft

 length =  3*w + 3 = (3w + 3) ft

              2l +2w = P

 2(3w + 3) + 2w = 54

Use distributive property to open the brackets,

 2*3w + 2*3 + 2w = 54

        6w + 6 + 2w = 54

Combine like terms,

          6w + 2w + 6 = 54

               8w   + 6   = 54

Subtract 6 from both sides,

                      8w    = 54 - 6

                         8w = 48

Divide both sides by 8

                           w = 48 ÷ 8

                           [tex]\sf \boxed{\bf w = 6 \ ft}[/tex]

l = 3w + 3

 = 3*6 + 3

 = 18 + 3

l = 21 ft

Answer: -8

Step-by-step explanation:

First, you plug -1 in for x

[tex]f(x)=f(-1)=(-1)^2 -9[/tex]

[tex]=1-9=-8[/tex]

Answer:

193,153.72460551

Step-by-step explanation:

Multiply 4 times pi or 3.14 if you are rounding. Then multiply that number by 4.6

Lastly once you done all of put it to the po wer of 3

There is no solution for the given equation i.e.10[x] =2.5

Equation:

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Greatest integer function:

The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function. Thus, the equation to determine the largest integer is fairly straightforward. It is symbolised by [x]  where x can take on any value.

⇒10[x] =2.5

⇒[x] =[tex]\frac{2.5}{10}[/tex]

⇒[x] =0.25

⇒[x] will be always a interger.As a result there is no solution for the given equation.

Therefore,There is no solution for the given equation i.e.10[x] =2.5

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The expression that best compares the minimum temperature of the two planets is -195 > -275

From the question, we are to determine which of the given options best compares the minimum temperature of the two planets

From the given information,

"The minimum temperature of mercury is approximately -275 F"

and

"The minimum temperature of Mars is approximately -195 F"

NOTE: The number -195 is greater than the number -275

Thus,

The minimum temperature of Mars is greater than the minimum temperature of Mercury

Hence, the expression that best compares the minimum temperature of the two planets is -195 > -275

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The weight of the fruits in ounces is 40 ounces

The pints of water dispensed after 50 seconds is 56 pints

The mathematical operations that would be used to determine the answer is multiplication. Multiplication is the process of determining the product of two or more numbers. Multiplication is represented with the sign - x.

A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed fraction is 2 1/2.

Weight of the fruits in ounces = 2 1/2 x 16

5/2 x 16 = 40 ounces

Pints of water dispensed after 50 seconds = gallon per second x 50 x 4 x 2

0.14 x 50 x 4 x 2 = 56 pints

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The value of d is 18.

Given, the slope of the line is 3.

Slope equals a height change (Change in width) You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y: Slope is equal to (y-change)/ (Change in x)

Two points which lie are N(₋2 , 3) and D(3,d)

slope of the line = y₂ ₋ y₁/x₂ ₋ x₁

let the points N(₋2 , 3) be (x₁ , y₁)

and D(3,d) be (x₂ , y₂)

therefore, 3 = d ₋ 3/3 ₋ (₋2)

3 = d ₋ 3/3 ₊ 2

3 = d ₋ 3 / 5

15 = d ₋ 3

d = 15₊3

d = 18

Hence we get the value of d as 18.

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The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.

When you know the slope of something like the line to be investigated and the point given also contains the y-intercept, you can utilize the slope-intercept formula y = MX + b. (0, b). The y value of the y-intercept  point is represented by b in the formula.

A line's slope is the ratio of how much y grows as x increases by a certain amount. The slope of a line indicates how steep it is, or how much y grows as x increases.

The slope of the line = -6  = m

The points (−9,−6). x = -9 , y = -6

Find the y-intercept.

y=mx+b

Substituting the value we get:

-6 = (-6 x -9) + b

-6 = -54 x b

b = 54/6

b = 9.

The equation in slope intercept form as:

y=mx+b

y = (-6)x + 9

y = -6x + 9

The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.

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The first integer is 16 and the next two integers are 17 and 18. The largest one is 18

What in math is an integer?

The first integer will be called x. Consequently, the second integer is x+1 and the third is x+2 (this is because they are consecutive integers). The total of these three numbers is 51, so build up the following equation and answer it.

x+(x+1)+(x+2)=51

3x+3=51

3x=48

x=16

Therefore, the first integer is 16 and the next two integers are 17 and 18. The largest one is 18 and this is the answer.

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The equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is  y = 4x ₋ 2.

The slope of the preceding equation is 4 because it is in slope intercept form. The slope of an equation is always equal for parallel lines, hence the slope of the equation we are requested to create is also 4.  We are given that this line passes through (2,6).

In the absence of intersection, two lines are said to be parallel. Each line has the same slope. In the event where m₁=m₂, f(x)=m₁x+b₁ and g(x)=m₂x+b₂ are. parallel

In order to write in y = mx +b form, we need to solve for b (the y-intercept).  

Given, x=2, y=6, and m = 4.

6 = (4) (2) ₊ b

simplify

6 = 8 ₊ b

solve for b.

b = 6 ₋ 8

b = ₋2

So the equation of the parallel line is   y = 4x ₋ 2

Hence we get the equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is y = 4x ₋ 2

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Answer:

6.7

Step-by-step explanation:

√45 = 6.7

.................

Answer:

0.139

Step-by-step explanation:

total = 43 + 56 + 16 = 115

country songs = 16

p(country song) = 16/115 = 0.139

Answer:

1.3 is the correct answer

Step-by-step explanation:

The simplified rational number that represents this scenario is 1/4

The given parameters are:

14 programming errors for every 56 programmers

The above means:

Error : Actual = 14 : 56

Express as fraction

Error/Actual = 14/56

Simplify the ratio

Error/Actual = 1/4

Hence, the simplified rational number that represents this scenario is 1/4

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Answer: 6.7% 0.67 6
                                 -
                                9

Step-by-step explanation:

Answer:

[tex]\sf 6.7\% < 6/9 < 0.67[/tex]

Explanation:

You would think 6.7% is a lot bigger than both, but it is not. Remember 6.7 is a percentage out of 100, thus, 6.7% actually is 0.067.

Answer: 32604

Step-by-step explanation:

The approximate location of the dolphin is 155 feet as it moves at the rate of 6.2 feet per second.

Rate in defined as the speed or the distance travelled by the dolphin in unit time.

Given the rate of the dolphin is  feet per second .

Time taken by the dolphin is 25 seconds.

∴ distance travelled is given by rate × time

Hence distance travelled is 6.2 × 25 = 155 feet

Therefore the approximate location is given by 155 feet from the starting point.

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The original logo is a triangle and measures

1.5in x 1.5in

Magnification is

Original shirt = 1:8

Shirt logo area

A = 1/2bh

A = 1 / 2 * (1.5 * 8) (1.5 * 8) = 72 square inches

The area is a quantity that describes the extent of an area on a plane or curved surface. Planar region or planar region area refers to the area of ​​a shape or planar layer, and surface area refers to the open surface or boundary area of ​​a three-dimensional object.

The area is defined as the total space occupied by a planar (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. A two-dimensional character. The space a shape occupies on paper is called its area. Now imagine that the square is made up of smaller unit squares.

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The raw score from the given table that corresponds with the 20th and 30th percentiles are;

First distribution;

Second distribution;

The Z–Score percentile normal distribution table can be used to find the Z–Score that gives the percentile value of a raw score.

The Z–Score, also known as the standard score, gives the number of standard deviations, a raw score is far from the mean.

The mathematical equation for the Z–Score is as following; [tex]Z = \frac{x - \mu}{ \sigma} [/tex]

Therefore, a positive value of Z is obtained when the raw score, x, is larger than the mean, [tex] \mu[/tex]

and negative Z value is given by raw scores lower than the mean.

Using the standard normal distribution table, raw score corresponds to the 1th percentile when the Z–Score = -2.326, while the Z–Score for the 99th percentile is 2.326.

The Z–Score of the 20th percentile is -0.842, while for the 30th percentile it is -0.524

Comparing the standard values with the values in the given table, we have;

First distribution;

-0.91960-(-0.842) = -0.0776

-0.71082 -(-0.842) = 0.13118

The smaller difference is given by -0.91960.

Similarly;

Second distribution;

While;

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The interval(s) for which f(x) ≥ 0. is x ≥ 2

The function is given as:

f(x) = x - 2

Also, we have:

f(x) ≥ 0

This means that

x − 2 ≥ 0

Add 2 to both sides of the inequality

x ≥ 2

Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2

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Answer:

non

Step-by-step explanation:

bc its not a straight line

Answer: Non-linear

Step-by-step explanation:

It’s not a straight line and there is no pattern.