After selling half his old games, Sam went and bought 8 new ones. He
now has 30 games. How many did he start with?

From the 32 by 33 rectangular figure, having interior squares, we have

The area of the squares in square units are;

The areas in square units are;

Area of square A = 18 × 18 = 324

Area of square B = 15 × 15 = 225

Area of square E = 10 × 10 = 100

Area of square F = 14 × 14 = 196

Area of square G = 4 × 4 = 16

Area of square H = 7 × 7 = 49

Area of square I = 1 × 1 = 1

Area of a rectangle = Length × Breadth

Therefore;

Area of the entire figure = 32 × 33 = 1056

The perimeter, P, of the rectangular figure is therefore;

P = 2 × 32 + 2 × 33 = 130

Learn more about finding the area of plane figures here;

https://brainly.com/question/2669479

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

Answer:

8+h

Step-by-step explanation:

Simply substitute x = 2+h and x = 2 in.

\(\displaystyle \large{\frac{f(2+h)-f(2)}{h}=\frac{(2+h)^{2} +4(2+h)+5-[(2)^2+4(2)+5]}{h}}\\\displaystyle \large{\frac{f(2+h)-f(2)}{h}=\frac{4+4h+h^2 +8+4h+5-17}{h}}\\\displaystyle \large{\frac{f(2+h)-f(2)}{h}=\frac{h^2 +8h}{h}=h+8}\)

Therefore, the answer is h+8 or 8+h.

Another way is to differentiate the function with respect to x. This equation or expression is rate of changes from 2 to 2+h with h being any numbers.

The definition of derivative is:

\(\displaystyle \large{f\prime(x)= \lim_{h \to 0}\frac{f(x+h)-f(x)}{h}}\)

Notice how both f(2+h)-f(2) over h and the definition of derivative look same except the derivative has limit of h approaching to 0, making h not having any values by default.

Since f(2+h)-f(2) over h does not have limit, we have to add +h when differentiating the function.

\(\displaystyle \large{f\prime(x)=2x+4}\\\displaystyle \large{f\prime(2)=2(2)+4}\\\displaystyle \large{f\prime(2)=8}\)

Since f’(2) is 8 but because f(2+h)-f(2)/h does not have limit of h, therefore we add +h.

\(\displaystyle \large{\frac{f(2+h)-f(2)}{h}=8+h}}\)

The decimals would be ordered as:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.

The decimals will be ordered as shown below:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

Learn more about ordering decimals on:

https://brainly.com/question/20603315

#SPJ1

Answer:

Step-by-step explanation:

Equation:

Answer:

$72.00

Step-by-step explanation:

Answer:

$72

Step-by-step explanation:

I hope this helps!

Answer:

Opinion polls help you determine what your demographic is largely thinking or feeling concerning your project or brand.

By asking your consumers specific questions through polls, you get an overview of the general perspective. And then, you can take the necessary actions.

However, evaluating the pros and cons of opinion polls is crucial to the insight into your consumer demographic.

Step-by-step explanation:

Done 1

Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

Answer:

Step-by-step explanation:

x^3 + 3x^2 - 2x + 3x^2 + 9x - 6

x^3 + 6x^2 + 7x - 6

the solution is A

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

for such more question on Newton-Raphson iteration

https://brainly.com/question/17150870

#SPJ8

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

\(x = \sqrt{\frac{49}{2}}\)

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

More can be learned about the perimeter of a polygon at https://brainly.com/question/3310006

#SPJ1

Answer:

5.75.

Step-by-step explanation:

The mean = (8+5+7+10+3+4+31+12)/ 8

= 80/8

= 10.

Now we calculate the difference of each value from the mean We take the absolute ( positive) differences

10 - 8 = 2

10 - 5 = 5

10 - 7 = 3

10 - 10 = 0

10-3 = 7

10 = 4 = 6

10 - 31 = 21

10 - 12 = 2

Sum of the differences = 46

and the mean deviation  is 46/8 = 5.75.

Answer:

D

Step-by-step explanation:

The greatest common factor of 12 and 24 is 12. The only option which accounts for this is D.

Answer:

\(3\sqrt{22}\)

Step-by-step explanation:

The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)

Multiply

Answer:

C- third option

Step-by-step explanation:

1. you would have to distribute the 1/3 to both x and 9

2. then cancel out the 6 from both sides to get your answer in slope-intercept form

Step-by-step explanation:

Plug

\( {x}^{2} + 1\)

for x.

\(( {x}^{2} + 1) {}^{2} + 1\)

Note that

\((a + b) {}^{2} = 2ab\)

So we have

\( {x}^{4} + 2 {x}^{2} + 2\)

Answer:

4:6, 12:18

Step-by-step explanation:

i think this is correct

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

R1 = 6 ohm

R2 = 3 ohm

Step-by-step explanation:

check the attached picture for step by step solution

The 10% condition when constructing a confidence interval for a population proportion states that the sample size should be less than 10% of the population size.

This is expressed mathematically as follows:

n/N < 0.10

Where n is the sample size and N is the population size. For example, if the population size is 500, then we must ensure that the sample size is less than 50 (500 x 0.10 = 50). This is because if the sample size is larger than 10% of the population size, then the confidence interval will not be reliable. In other words, the results of the confidence interval may be inaccurate and biased.

Learn more about confidence interval here:

https://brainly.com/question/28280095

#SPJ4

Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

\(\log 3+ 9\log x +4 \log y\)

Step-by-step explanation:

Given logarithmic expression:

\(\log 3x^9y^4\)

\(\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay\)

\(\log 3+\log x^9 +\log y^4\)

\(\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax\)

\(\log 3+ 9\log x +4 \log y\)

Answer: 33.6

60 x 56 divided by 100 is 33.6

The written form of the given expression; 3 ones + 12 tenths + 44 hundredths in standard form is; 4.64.

It follows from the task content that the written form of the expression is to be determined in standard form.

Since it follows from place value concept that;

ones is represented as 1;

tenths is represented as 0.1;

hundredths is represented as 0.01;

Therefore, it follows that the sum can be determined as follows;

= (3 × 1) + ( 12 × 0.1 ) + ( 44 × 0.01)

= 3 + 1.2 + 0.44

= 4.64.

Therefore, the standard form of the expression is; 4.64.

Read more on place value concept;

https://brainly.com/question/28600816

#SPJ1

Answer:

4:1 is a ratio

Step-by-step explanation:

It is also equal to 8:2, 12:3, etc.

Answer:

Ratio

Step-by-step explanation:

took test

Answer:

x >3

Step-by-step explanation:

2(2x - 3) > 6

Divide each side by 2

2/2(2x - 3) > 6/2

2x-3 > 3

Add 3 to each side

2x-3+3 > 3+3

2x>6

Divide by 2

2x/2 > 6/2

x >3

Answer:

x > 3

Step-by-step explanation:

First, you're going to divide both sides by two

2( 2x - 3) / 2 and 6/2

After that, you will simplify that into....

2x - 3 > 3

Then you want to add three to both sides like so

2x - 3 + 3 > 3 + 3

Once you're done with that, go ahead and simplify the problem

2x > 6

Then, divide by two on each side

2x/2 > 6/2

Lastly, simplify your answer and that's the solution

x > 3

I hope this helped! :)

Answer:

B. (0, -4) and (4, -4)

Step-by-step explanation:

The solutions are the points of intersection of the circle and the parabola.

(0, -4) and (4, -4)

Answer:

The answer is 5 and 10.hbbbb