Sum of 8 product of 7

Step-by-step explanation:

in this scenario you can imagine that there is a circle with a radius of 12.4 and it's center in the bottom left corner of the triangle.

for that 70 degree angle in that corner x is cos(70)×12.4, and the height of the triangle is sin(70)×12.4

so,

cos(70) = x/12.4

The second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

The given sequence starts with C(1) = -20. Each subsequent term is obtained by adding 0 to the previous term, which means that the sequence is constant.

The recursive formula for this sequence is given as:

c(1) = -20 and c(n) = c(n-1) + 0

This means that the first term of the sequence is -20, and each subsequent term is obtained by adding 0 to the previous term

Therefore, the second term in the sequence is equal to the first term, which is -20. Hence, the answer is -20.

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The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Answer is x=-1/2y+-21/2

I provided my work below

Answer: 2ayx4a

Step-by-step explanation:

1) First, we will need to simplify each equation:

4ax2y = 8axy

8axy = 8axy

2ayx4a = 8ayx4a

ax8y = 8axy

2) We can now see that 2ayx4a is not the same as the others.

Answer:

Step-by-step explanation:

Area of rectangle = length * width

                             = (x + 4) (5x)

                             = x *5x + 4 *5x

                            = 5x² + 20x

Perimeter of rectangle = 2*(length + width)

                                     = 2*(x + 4 + 5x)

                                     = 2*(6x + 4)

                                   = 2*6x + 2 *4

                                     = 12x + 8

Answer:

Step-by-step explanation:

y - 2 = 3(x - 1)

y - 2 = 3x - 3

y = 3x - 1

Answer:

i so first do (6x4) and then add the total with + 30

\(6(x+4) = 30\\\\\implies x +4 = \dfrac{30}6\\\\\implies x +4 = 5 \\\\\implies x = 5-4 \\\\\implies x =1\)

The equation for the temperature, d, in terms of t (the number of hours since midnight), is:  d = 16 × sin((π/12) × t) + 55

To find an equation for the temperature, we need to determine the amplitude, period, phase shift, and vertical shift of the sinusoidal function.

The amplitude is half the difference between the high and low temperatures, which is (71 - 39) / 2 = 16 degrees. The period is the number of hours in a day, which is 24 hours. Since the temperature is at its highest point at 12:00 PM (midday), there is no phase shift. The vertical shift is the average of the high and low temperatures, which is (71 + 39) / 2 = 55 degrees.

Putting these values together, the equation for the temperature, d, in terms of t can be written as:

d = 16 × sin((2π/24) × t) + 55

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Answer:

1.  There are 609 more fiction books than non-fiction books in the library

2. Cheryl had $900 initially

The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:

\(d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}\)

Given that, the line passes through the points (0,-3) and (7,4).

The equation of the line is given by:

\(y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0\)

Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
\(d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}\)

Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

Answer:

yes

Step-by-step explanation:

The bases are right triangles with side lengths of 12 centimeters, 16 centimeters, and 20 centimeters.

Answer:

yes

Step-by-step explanation:

If you use the formula \(a^{2} +b^{2} =c^{2}\) you get 20 which confirms that is a right triangle

We know that an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.

For an experiment to be considered verifiable, several things should be done. Firstly, the experiment should be designed in a way that allows others to replicate it and obtain the same results. This means that all procedures, materials, and variables used should be clearly documented and made available to others.

Secondly, the experiment should be conducted in a controlled environment, where all external factors that could influence the results are minimized or eliminated.

Thirdly, the data obtained from the experiment should be analyzed and interpreted objectively, without any bias or preconceived notions. Finally, the results should be subjected to peer review and scrutiny by experts in the relevant field to ensure that they are valid and reliable.

By following these steps, an experiment can be considered verifiable, meaning that its results can be trusted and used to inform future research and decision-making.

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

The function value at the minimum is -9

The function is given as:

f(x) = x^2 - 6x

Differentiate the function

So, we have

f'(x) = 2x - 6

Set the function to 0

So, we have

2x - 6 = 0

This gives

2x = 6

Divide by 2

x = 3

Substitute x = 3 in f(x) = x^2 - 6x

f(3) = 3^2 - 6(3)

Evaluate

f(3) = -9

Hence, the function value at the minimum is -9

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The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

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Answer:

I am not certain if its right

Step-by-step explanation:

The odds in favor of winning $5 or more is 3 : 13

The odds of winning $5 or more can be determined by finding the ratio of the total value of tickets that have a value of $5 or greater to the total value of tickets.

Total number  of the tickets that have a value of $5 or more = 25 + 5 = 30

Total number of ticket  = 25 + 5 + 100 = 130

Ratio : 30 : 130

3 ; 13

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Answer:

-7/12

Step-by-step explanation:

The appropriate level of precision for the scale depends on the smallest unit of measurement it can accurately determine. In this case, the scale measures weight to the nearest 0.5 lb.

A. 140 lbs. : This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision. B. 148.75 lbs.: This measurement includes decimal places that the scale cannot accurately determine. It exceeds the precision of the scale and does not show an appropriate level of precision. C. 140.5 lbs: This measurement falls within the precision of the scale. It accounts for the nearest 0.5 lb increment and shows an appropriate level of precision. D. 141 lbs: This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision.

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Answer:

Step-by-step explanation:

1) elimination

2) elimination

3)add

4)subtract

5) Variable

6) add

7) eliminate

8) subtract

9) eliminate

10) adding

11) adding

12) 2

13)2

14) 0

15) (2 , 0)

16) (2 , 0)

17) solution

a) Anaiah currently spending $150 on these goods

b) His behavior is irrational because,

option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

Based on the given information, Anaiah is currently spending $150 on these goods, which is calculated by adding the total cost of eggplants and kiwis as follows:

Cost of 20 eggplants = 20 x $3 = $60

Cost of 30 kiwis = 30 x $3 = $90

Total cost = $60 + $90 = $150

Anaiah is behaving irrationally because he is not spending his entire income of $180, which means he is not maximizing his utility. Additionally, he is spending too much on kiwis, as indicated by the higher marginal utility per dollar spent on the 30th kiwi compared to the 20th eggplant.

This suggests that he would derive more satisfaction from spending more on eggplants and less on kiwis. Lastly, his marginal utility per dollar spent is not the same for both goods, which implies that he is not balancing his spending on each good to achieve the maximum total utility. Therefore, Anaiah could improve his spending behavior by adjusting his purchases to reflect a better balance of marginal utility per dollar spent on each good.

Therefore, the correct options are  option (1) He is not spending his entire income, option (2) He is spending too much on kiwis and option (3) He is not balancing his spending on each good to achieve maximum total utility.

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The complete factor of the polynomial 36x² - 25 is (6x + 5)(6x − 5). Then the correct option is D.

Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.

Factor completely 36x² - 25.

We know that

\(\rm a^2 - b^2 = (a+b)(a-b)\)

(6x)² − 5²

(6x + 5)(6x − 5)

The complete factor of the polynomial 36x² - 25 is (6x + 5)(6x − 5). Then the correct option is D.

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Answer:

The y intercept is the b in y = mx + b

Step-by-step explanation:

The sampling distribution of p is approximately normal with a mean of 0.80 and a standard error of 0.00309.

The sampling distribution of p can be determined using the formula for standard error.

Step 1: Calculate the standard deviation (σ) using the population proportion (p) and the sample size (n).
σ = √(p * (1-p) / n)
  = √(0.80 * (1-0.80) / 220)
  = √(0.16 / 220)
  ≈ 0.0457

Step 2: Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size.
SE = σ / √n
  = 0.0457 / √220
  ≈ 0.00309

Step 3: The sampling distribution of p is approximately normal, centered around the population proportion (0.80) with a standard error of 0.00309.

The sampling distribution of p is a theoretical distribution that represents the possible values of the sample proportion. In this case, we are interested in estimating the proportion of complaints settled for new car dealers. The population proportion of settled complaints is assumed to be the same as the overall proportion of settled complaints in 2016, which is 0.80.

To construct the sampling distribution, we calculate the standard deviation (σ) using the population proportion and the sample size. Then, we divide the standard deviation by the square root of the sample size to obtain the standard error (SE).

The sampling distribution is approximately normal, centered around the population proportion of 0.80. The standard error reflects the variability of the sample proportions that we would expect to see in repeated sampling.

The sampling distribution of p for the selected sample of new car dealer complaints has a mean of 0.80 and a standard error of 0.00309. This information can be used to estimate the proportion of complaints the Better Business Bureau is able to settle for new car dealers.

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Answer:

\(\dfrac{47}{42} \ \ \ \ \ OR \ \ \ \ 1.1\)

Step-by-step explanation:

The objective of this question is to find the  sum of the greatest and least numbers below:

\(\[8\frac15, \qquad -8\frac25, \qquad -\frac{26}{3}, \qquad -\frac{54}7, \qquad \frac{53}{6}.\]\)

To do this ; we will need to find the decimal component of each of them and equate them on a number line before summing the greatest and least numbers.

\(8 \frac{1}{5} = \dfrac{8*5+1}{5} \\ \\ = \dfrac{41}{5} \\ \\ = 8.2\)

\(-8 \frac{2}{5} =- \dfrac{8*5+2}{5} \\ \\ =- \dfrac{42}{5} \\ \\ = -8.4\)

\(-\dfrac{26}{3}= - 8.7\)

\(-\dfrac{54}{7} = - 7.7\)

\(\dfrac{53}{6}= 8.8\)

Thus; the above decimal component of the fractions given are :

8.2, -8.4, -8.7 , -7.7 and 8.8

We are to find the sum of the greatest and the smallest number ; on a number line; we will realize that the positive side is greater than the negative side , As such the greatest number from the positive side will be 8.8 and the smallest number will be -7.7

The sum of 8.8 + ( -7.7 ) = 8.8 - 7.7

= 1.1

i.e

\(\dfrac{53}{6} + (- \dfrac{54}{7} )\)

\(\dfrac{53}{6} - \dfrac{54}{7}\)

\(\dfrac{53}{6} - \dfrac{54}{7} = \dfrac{53*7 - 6*54}{42} \\ \\ = \dfrac{47}{42} \\ \\ = 1.1\)

Answer:

Step-by-step explanation: