s 0.4544555444........ Rational or Irrational? Why

Answer:

1. 46/35 or 1 11/35

2. 5/4 or 1 1/4

3. 5/4 or 1 1/4

4. 7/3 or 2 1/3

Step-by-step explanation:

Answer: the rectangle is 23 x 41

Step-by-step explanation:

x = length

2x - 5 =  width

A = length x width = (x)(2x-5) = 943

2\(x^{2}\) - 5x - 943 = 0

use quadratic equation to solve for x:

a = 2, b = -5, c = -943

roots are 23, -20.5

x = 23 (length)

2x - 5 = 2(23) - 5 = 46 - 5 = 41 (width)

The statements that are true about the given algorithms are: I. Algorithm 1 does not work on lists where the smallest value is at the start of the list or the largest value is at the end of the list.  II. Algorithm 2 does not work on lists that contain all negative numbers or all numbers over 1000.

Algorithm 1's reliance on initializing minVal to the first value and maxVal to the last value can lead to incorrect results if the smallest or largest value is not properly updated during the iteration. Similarly, Algorithm 2's fixed initial values for minVal and maxVal can result in incorrect differences when dealing with lists containing all negative numbers or all numbers over 1000.

It is important to consider these limitations and potential failure cases when choosing and implementing an algorithm for calculating the difference between the smallest and largest values in a list.

Learn more about Algorithm here:

https://brainly.com/question/30753708

#SPJ11

Answer: 19

Step-by-step explanation:

4x in this equation is equal to 4(4), which equal sixteen, adding the three will then get you 19

Answer: 19

Step-by-step explanation:

Insert 4 into the x in the equation.

3+ 4 × 4

Multiply.

4 × 4 = 16

Add.

3 + 16= 19

Hope this helps!

Answer:

1. Mean : 85.6

2. Median : 90

3. Mode : 95

4. Range : 35

Step-by-step explanation:

1. For Mean, you add up all the terms and divide the resulting sum by the number of terms. In this case there were 9 terms that added up to 770, and when you divided that result by 9, the answer was 85.555 repeating. Since the question asks to round to the nearest tenth 85.6 represents the correct mean or average of the class.

2. To find the median, line up all the numbers in order from least to greatest. Like so :

60,75,75,90,90,95,95,95,95

In order to find the median, find the middle term. Since there are 9 terms, the middle term will be the fifth one. In this case, the answer was 90.

3. Mode represents the number that appears the most in a data set. Look at the 9 terms and find the one that appears the most. In this case it is 90.

4. Lastly, to find the range, subtract the lowest value in the data set from the highest one. 95 is the highest and 60 is the lowest. Do \(95-60\) and you will get an answer of 35.

Hope this helps!

Answer:

Mean: 85.6

Median: 90

Mode: 95

Range: 35

Step-by-step explanation:

Mean: Add up all the value and divide by the number of values you have.

75 + 95 + 90 + 95 + 60 + 95 + 75 + 95 + 90 = 770

770 / 9 = 85.6

Median: Rearrange in increasing order + look at middle number

60, 75, 75, 90, 90, 95, 95, 95, 95

Mode: Number that shows up the most.

95 shows up 4 times.

Range: Maximum - Minimum.

95 - 60 = 35.

If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The  height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

To know more about scale visit:

https://brainly.com/question/4261493

#SPJ4

The measure of interior angle at vertex F is equal to 72 degrees, the correct option is D.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

4x+4x+4x+4x+2x+2x = 720

20x = 720

x = 36

2x = 72 degree

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

To know more about Hexagon

https://brainly.com/question/3295271

#SPJ2

The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

To know more about musical chords, visit,

https://brainly.com/question/14936810

#SPJ4

Solving the question asked, we can say: If you win tonight, your odds of winning the next game are \($58.33\%$\). After that, if you lose, you have a \($38.88 \%$\) chance of winning the game.

Probability theory is a branch of mathematics that measures the probability that an event or statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating that the event is unlikely and 1 indicating that it is certain. Probability is a numerical representation of the disease that a particular event will occur. Another way to express probability is as a percentage from 0% to 100% or 0 to 1. Proportion of occurrences in the complete set of equally likely possibilities leading to a particular occurrence compared to the total number of outcomes.

\($$\begin{aligned}& (2 / 3+1 / 2) / 2=X \\& 1,666 / 2=X \\& 0.58333=X \\& ((2 / 3+1 / 2 / 2) x 2 / 3=X \\& 0.58333 x 0.666=X .3888=X\end{aligned}$$\)

To know more about probability visit:

brainly.com/question/11234923

#SPJ4

Answer:

B) \(\$8395.80\)

Step-by-step explanation:

\(A=P(1+rt)\\A=7996(1+0.06\cdot\frac{10}{12})\\A=7996(1+0.05)\\A=7996(1.05)\\A=\$8395.80\)

This is all assuming that r=6% is an annual rate, making t=10/12 years

Answer: total cost of the stuff she buys ≤ 18 since she only has 18 dollars to buy stuff

Step-by-step explanation:

let's add up the cost of the stuff she buys:

- a flat cost of $6.50

- a savings of $5.75 (she's technically not spending money but we can count this as part of her expenses since it's taking away from the 18 dollars)

- some number (x) candy bars. if each candy bar costs $1.15 then the money she spends on candy bars is $1.15

with that being said:

6.50 + 5.75 + 1.15x ≤ 18

solve for x

since we are talking about whole # candy bars, if you get a decimal from this, round down to the nearest whole #

Answer:

Andrea can buy 5 candy bars.

Step-by-step explanation:

First to solve this we will subtract 6.50 from 18 because Andrea already spent that money. Then we must subtract 5.75 from 18 because Andrea can't spend that money. All the subtracting equals 5.75. After that we can divide the remaining money by 1.15 to see how many candy bars we can buy which equals 5. Finally the answer is that Andrea can buy 5 candy bars.

Answer:

10

Step-by-step explanation:

2kg and 500g is 2.5kg. 25kg÷2.5 is 10

⇨ By prime factorization method:

\(\begin{array}{r | l}{\sf{2 & {\sf14,28,31} \\\cline{2-2} {\sf2 & {\sf7,14,31 \\\cline{2-2} {\sf7 & {\sf7,7,31 \\\cline{2-2} {\sf31 & {\sf1,1,31 \\\cline{2-2} & {\sf1,1,1\end{array}\)

\({\sf{LCM\: = \:2 \:x\: 2 \:x\: 7 \:x\: 31}}\\\\{\sf{LCM \:= \:868}}\\}\\{\sf{Therefore,}}\\\\{\sf{LCM\:(14,\: 28,\: 31)\: = \:868\)

\({\boxed{\sf{LCM\:=\:868}}\)

Step 1

Given;

Required; To write in standard form.

Step 2

The answer will be;

Recall that the interior angles of a triangle add up to 180 degrees, then:

Now, recall that a right angle measures 90 degrees.

Then we can set the following equation:

Adding like terms we get:

Subtracting 105 degrees from the above equation we get:

Answer:

9514 1404 393

Answer:

  $81

Step-by-step explanation:

The garden is 4 yards = 12 feet by 3 yards = 9 feet. The area of it is the product of these dimensions, ...

  (12 ft)(9 ft) = 108 ft²

The cost of fertilizer for that area will be ...

  ($0.75/ft²)(108 ft²) = $81.00

They will spend $81.00 to fertilize the garden.

Answer: She payed 16 dollars for them both.

Answer:

$16.00

Step-by-step explanation:

10% of $10.00 is $1.00. 1x6= 6

10+6 = 16

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

To know more about standard deviation here.

brainly.com/question/16555520

#SPJ1

Answer:

A

Step-by-step explanation:

The diameter is 2πr or 4032π in this. The arc from B to C counterclockwise is 130° out of 360°. 130/360 multiplied by 4032 is 1456

If the radius of the circular ground be 2016 feet and angle between the radius given is 130 degrees then race car travelled 1456π feet which is option a.

Sector is basically length of that area of circle's arc which is formed by two radius of the circle. The length of sector is Θr where r is radius and Θ is angle made by both radius but in radian form.

We have been given radius equal to 2016 feet and angle 130°. We have to find the distance that race car had travelled by racing from point B to point A. It can be equal to the length of sector of the circular ground.

Sector BAC =130π/180* 2016

=262080π/180

=1456 feet.

Hence if the radius of the circular ground be 2016 feet and angle between the radius given is 130 degrees then race car travelled 1456π which is option a.

Learn more about sector at https://brainly.com/question/22972014

#SPJ2

Answer:

y=65x

Step-by-step explanation:

x represents the # of hours

Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer: (2,4) They bought 2 sodas and 4 coffees.

Step-by-step explanation:

A. c + s=6  where c is the number of coffee and s is the number of sodas

B. 1.50c + 1.20s =8.40

C. -1.50 (c    +  s) =6(-1.50)   we will multiply the first equation by -1.50 to eliminate the c

 New equation;  -1.50 - 1.50s = -9         -0.3s/-0.3=-0.6/-0.3  s=2  

                            -150 +  1.20s = 8.40          

So we know they bought 2 sodas.   so we will plot 2 into the equation.

1.50c  + 1.20(2)=8.40   c= 4  

In conclusion, 12x -3x+1, 2x-2x^2+21, 5x^2-6x-3 is a basis for P2

(a) To find the dimension of the subspace H, we need to find the number of linearly independent vectors in H. We can do this by putting the three given vectors into a matrix and reducing it to echelon form:

| 2 3 1 |

| 2 -2 1 |

| 5 0 -6 |

R2 <- R2 - R1

R3 <- R3 - (5/2)R1

| 2 3 1 |

| 0 -6 0 |

| 0 -15 -11/2 |

R3 <- R3 - (5/2)R2

| 2 3 1 |

| 0 -6 0 |

| 0 0 -121/12 |

So the matrix has rank 3 and there are no zero rows, which means the three vectors are linearly independent. Therefore, the dimension of H is 3.

(b) To check if 12x -3x+1, 2x-2x^2+21, 5x^2-6x-3 is a basis for P2, we need to check if they are linearly independent and span P2.

To check linear independence, we can set up the following equation:

a(12x -3x+1) + b(2x-2x^2+1) + c(5x^2-6x-3) = 0

Simplifying, we get:

(12a + 2b + 5c)x^2 + (-3a - 2b - 6c)x + (a + b - 3c) = 0

Since this equation must hold for all values of x, the coefficients must be zero. So we have the system of equations:

12a + 2b + 5c = 0

-3a - 2b - 6c = 0

a + b - 3c = 0

Solving this system, we get:

a = -5/14, b = 1/2, c = 9/14

Since not all coefficients are zero, the three vectors are linearly independent and therefore form a basis for P2.

To check if they span P2, we can take an arbitrary polynomial in P2, say ax^2 + bx + c, and try to write it as a linear combination of the three basis vectors:

ax^2 + bx + c = A(12x -3x+1) + B(2x-2x^2+1) + C(5x^2-6x-3)

Simplifying, we get:

(5C - 2B + 12A)x^2 + (-6C - 3A + 2B)x + (C + B + A)

For this equation to hold for all values of x, we must have:

5C - 2B + 12A = a

-6C - 3A + 2B = b

C + B + A = c

Solving this system, we get:

A = (c + (2a - b)/14)

B = (b - 5a/14 - c/2)

C = (9a/14 + 5b/14 + c/2)

Therefore, any polynomial in P2 can be written as a linear combination of the three basis vectors, and so they span P2.

In conclusion, 12x -3x+1, 2x-2x^2+21, 5x^2-6x-3 is a basis for P2

To learn more about dimension visit:

https://brainly.com/question/28688567

#SPJ11

Answer: Dude I would love to help you but I don't understand this and I'm good with math

Step-by-step explanation:

Answer:

a. 1

b. 2.

Step-by-step explanation:

a) There are a total of 10 numbers so we have:

4 * 10 = 3+5+6+8+9+2+1+0+5+x

40 = 39 + x

x = 1.

b) 5*6 = 28 + x

x = 2.

If the null hypothesis is rejected, and the proportion of customers willing to pay more is significantly different from 10%, this would support my hypothesis that customers are willing to pay more for eco-friendly packaging.

Let's say you work for a company that has been using a certain type of packaging material for their products. However, there have been concerns raised about the environmental impact of this material, and the company is considering switching to a more eco-friendly option. You believe that customers would be willing to pay more for products that are packaged with the eco-friendly material, but you need to test this hypothesis.

Variable: The variable that would be tested is whether customers are willing to pay more for products that are packaged with the eco-friendly material.

Guess of value: I would guess that customers would be willing to pay more for eco-friendly packaging, but I'm not sure how much more. Let's say my guess is that customers would be willing to pay 10% more for products packaged with the eco-friendly material.

Hypothesis test: To test this hypothesis, I would conduct a survey where I randomly select a sample of customers and ask them if they would be willing to pay more for products packaged with the eco-friendly material. I would then compare the proportion of customers who are willing to pay more to my guess of the value (10%).

Null hypothesis: The null hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is not significantly different from 10%.

Alternative hypothesis: The alternative hypothesis would be that the proportion of customers willing to pay more for eco-friendly packaging is significantly different from 10%.

 If the null hypothesis is not rejected, this would suggest that customers are not willing to pay more for eco-friendly packaging, and the company may need to reconsider their decision to switch to the more expensive material.

To learn more about proportion visit:

brainly.com/question/30657439

#SPJ11

Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

Learn more on length of an arc here: https://brainly.com/question/2005046