Use the approach in Gauss's problem to find the sums of the arithmetic sequences below

(do not use formulas).

>

c. 3+ 6 + 9 + ... + 300

Answer:

g=4 h=6

Step-by-step explanation:

3g +h = 18 (Equation 1)

2g+3h=26 (Equation 2)

From equation 1

3g+ h =18

h= 18-3g (equation 3)

substitute equation 3 into equation 2

2g+3h= 26

2g+ 3(18-3g)= 26

2g+3×18+3(-3g)=26

2g+54-9g=26

9g-2g= 54-26

7g=28

7g÷7 = 28÷7

g= 4

substitute g into equation 1

3g+h=18

3(4)+ h= 18

12+h= 18

h=18-12

h= 6

Answer:

g = 4; h = g

Step-by-step explanation:

When solving an equation with two variables, the goal is to isolate at least one of the variables so that you can plug it in to the equation to get the other. There are multiple ways to solve this so I'll just be giving one.

3g + h = 18

2g + 3h = 26

In these two equations, I notice that if I multiply the first equation by 3, the two equations will have the same values of h, so I'd be able to isolate g:

9g + 3h = 54

2g + 3h = 26

Now, subtract the second equation from the first to isolate g:

9g + 3h = 54

-2g + 3h = 26

= 7g = 28

= g = 4

Now that we have solved for g, we can plug it into either of the equations and solve for h:

2(4) + 3h = 26

= 8 + 3h = 26

= 3h = 18

= h = 6

And in conclusion, g = 4 and h = 6.

Answer:

whichever paper towel observer's the most juice is the best brand

Answer:

21

Step-by-step explanation:

Answer:

67%

Step-by-step explanation:

the original amount had to increase by 67% in order to equal the final about simply by dividing 2000 by 3000 getting 2/3 which is 0.666667 then multiplying by 100 to get a rate

Answer:40

Step-by-step explanation:

Answer:

B. 40

Step-by-step explanation:

aapeexxxxxab

Answer:

1) A person would need approximately 51 years to eat 855 pounds of apples.

2) A person would need approximately 69 years to eat 1120 pounds of turkey.

3) 6 people in the United States will eat 1260 quarts in next 5 years.

4) The statement is a nonsense.

Step-by-step explanation:

1) According to the German page Statista, a person in the United States had a per capita consumption of 16.91 pounds of fresh apples in 2018/19. If we consider that a person consume at same rate, then the time taken is obtained by dividing total amount of fresh apples by per capita consumption rate:

[tex]x = \frac{855\,pd}{16.91\,\frac{pd}{yr} }[/tex]

[tex]x = 50.562\,years[/tex]

A person would need approximately 51 years to eat 855 pounds of apples.

2) According to the German page Statista, a person in the United States had a per capita consumption of 16.40 pounds of turkey in 2018/19. If we consider that a person consume at same rate, then the time taken is obtained by dividing total amount of turkey by per capita consumption rate:

[tex]x = \frac{1120\,pd}{16.40\,\frac{pd}{yr} }[/tex]

[tex]x = 68.293\,years[/tex]

A person would need approximately 69 years to eat 1120 pounds of turkey.

3) Accoring to the US page Aghires, a person in the United States had a per capita consumption of 42 quarts of pop corn in 2017/2018. The total consumption of the groups equals the product of number of people, time and per capita consumption. That is:

[tex]x = 42\,\frac{qt}{yr}\times 6 \times 5\,yr[/tex]

[tex]x = 1260\,quarts[/tex]

6 people in the United States will eat 1260 quarts in next 5 years.

4) According to the US newspaper The South Florida Reporter, a person in the United States had a per capita consumption of 53 pounds of bread in 2017/2018. Consumption during 80 years can be estimated by knowing the product of time and per capita consumption. That is:

[tex]x = 80\,yr \times 53\,\frac{pd}{yr}[/tex]

[tex]x = 4240\,pd[/tex]

Which is only equivalent to about 10 % of the alleged indicator and, consequently, the statement is a nonsense.

Answer:

jo jjejejejej

Step-by-step explanation:

nenenebejeje

Answer:

y=25 x=11

Step-by-step explanation:

Answer:

w = 42

Step-by-step explanation:

A linear pair is a pair of adjacent angles which add up to 180 degrees(supplimentary).

Given m<1 = w + 5, m<2 = 3w + 7, and the fact that m<1, and m<2 form a linear pair. This relationship can be given by:

m<1 + m<2 = 180.

To solve just substitute the expressions given by the angles, and solve.

m<1 + m<2 = 180

| |

v v

(w+5)+(3w+7) = 180 →

4w + 12 = 180

-12 -12

___________

4w = 168

÷4 ÷4

_______

w = 42

Answer:

Step-by-step explanation:

Step-by-step explanation:

hope this helps! good Night!!

Answer with step-by-step explanation:

6 km = 3.72822715 mi

Answer:

Step-by-step explanation:

Thirty three campaign workers called 12,375 eligible voters to encourage them to do their civic duty.  Which rate best represents the relationship between the eligible voters reached by each campaign worker?

Answer:

a) -2, c) 0.5, e) 14

Step-by-step explanation:

The domain is the x value, which is the number of packages sold in this case.

a) -2: You can't sell a negative number of packages

c) 0.5: You can't sell half a package

e) 14: The company only has 12 packages

Answer:

The answer is below

Step-by-step explanation:

The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm

Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:

r/h = radius of tank/ height of tank

r/h = 400/1200

r = h/3

[tex]\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\[/tex]

[tex]\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min[/tex]

Answer:

[tex]y\in (-\infty ,5][/tex]

Step-by-step explanation:

In this problem, we need to write "Twenty times y is at most 100 in interval notation ".

20 times y means, 20y

Atmost means an inequality which is [tex]\le[/tex]

ATQ,

[tex]20\times y\le 100[/tex]

i.e.

[tex]20y\le 100\\\\y\le 5[/tex]

We can also write it as :

[tex]y\in (-\infty ,5][/tex]

Hence, the required interval notation is [tex]y\in (-\infty ,5][/tex].

The interval notation is [tex]\rm y \epsilon (\infty,6][/tex].

The Interval notation is a method to define a set of numbers between a lower limit and an upper limit by using end-point values.

"Twenty times y is at most 100 in interval notation ".

Here, 20 times y means, 20y at most means an inequality.

Therefore,

The inequality is;

[tex]\rm 20 \times y\leq 100\\\\20y\leq 100\\\\y \leq \dfrac{100}{20}\\\\y\leq 5[/tex]

Hence, the required interval notation is [tex]\rm y \epsilon (\infty,6][/tex].

To know more about Interval notation click the link given below.

https://brainly.com/question/13048073

Step-by-step explanation:

Since lines p || q are parallel to one another, let us find all the 8 angles,

        1 and 7 are vertically opposite angles and they are equal;

    since angle 1 is 75°, then angle 7 is 75°

 Also, angle 7 and 5 are corresponding angles, corresponding angles are equal;

    So,

         angle 5  = 75°

 Angle 5 is vertically opposite to angle 3,

   So,

       angle 3  = 75°

To find angle 4,

    angle 4 and angle 5 are angles on a straight line;  

       sum of angles on a straight line = 180°

     angle 4 + angle 5  = 180°

     angle 4 = 180 - 75 = 105°

Angle 2 and Angle 4 are corresponding angles and they are equal;

    So angle 2 = 105°

Angle 4 and angle 6 are vertically opposite and they are equal;

   angle 6  =  105°

Angle 6 and 8 are corresponding angles, they are equal;

     angle 8 =  105°

Answer:

random numbers

Step-by-step explanation:

because they are randomly picked

Unpredictable numbers that are distributed over a certain range are _Random numbers_.

Random experiments are repeated multiple times to determine its likelihood.  

The number of times an experiment is repeated is better described as number of trials.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Now, Unpredictable numbers that are distributed over a certain range are random numbers because they are randomly picked.

Unpredictable numbers that are distributed over a certain range are _Random numbers_.

To Learn more about Random numbers, click here;

https://brainly.com/question/3798851

#SPJ5

Answer:

(0,0)

Step-by-step explanation:

The x-intercept is what the x value is when y = 0, and on this chart, when y=0, x=0 as well.

Answer:

he should have bought 4-5 unless he under paid but i'd say he bought 4 polo shirts

Step-by-step explanation:

Answer:

y-4=5 (x-2)

Step-by-step explanation:

it's point-slope form.

y-y1 = m or slope (x-x1).

y1 being the y coordinate and x1 being the x coordinate.

if you need slope-intercept it is y=5x-6

Answer:

a)35 people participated in the walk

b)22 people walked more than 14 km

Step-by-step explanation:

12|3 3 6 7 9 9

13| 1 1 4 5 5

14| 0 0 2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17|3 5

Key: 12|3 means 12.3

a)

Count the number of leaves

Number of leaves = 35

So,35 people participated in the walk

b)

Count the number of people who walked more than 14 km

Exclude 14|0

14|  2 3 3 8 8 9

15| 2 2 2 2 2 3 5 5 7

16| 4 5 5 9 9

17|3 5

22 people walked more than 14 km

Answer:

1. 90

2. -12 +5

3. 83

Step-by-step explanation:

90 -12 + 5 = 83

Answer:

The mean of the remaining 3 boys is 51.

Step-by-step explanation:

The mean mark of the entire group ([tex]p_{10}[/tex]), dimensionless, is:

[tex]p_{10} = \frac{1}{10}\cdot \Sigma_{i = 1}^{10} x_{i}[/tex] (Eq. 1)

([tex]p_{10} = 58[/tex])

[tex]\frac{1}{10}\cdot \Sigma_{i=1}^{10} x_{i} = 58[/tex] (Eq. 1b)

Where [tex]x_{i}[/tex] is the mark of the i-th boy, dimensionless.

In addition, we know the following mean marks from statement:

[tex]p_{7} = \frac{1}{7} \cdot \Sigma_{i = 1}^{7} x_{i}[/tex] (Eq. 2)

([tex]p_{7} = 61[/tex])

[tex]\frac{1}{7}\cdot \Sigma_{i=1}^{7} x_{i} = 61[/tex] (Eq. 2b)

[tex]p_{3} = \frac{1}{3}\cdot \Sigma_{i=8}^{10}x_{i}[/tex] (Eq. 3)

Where:

[tex]p_{7}[/tex] - Mean mark of the first 7 boys, dimensionless.

[tex]p_{3}[/tex] - Mean mark of the remaining 3 boys, dimensionless.

By applying sum properties in (Eq. 1b) and using (Eq. 2b) and (Eq. 3), we obtain the mean of the remaining 3 boys:

[tex]\frac{1}{10}\cdot [\Sigma_{i = 1}^{7}x_{i}+\Sigma_{i=8}^{10}x_{i}] = 58[/tex]

[tex]\frac{1}{10}\cdot [7\cdot (61)+3\cdot p_{3}] = 58[/tex]

[tex]7\cdot (61) + 3\cdot p_{3} = 580[/tex]

[tex]3\cdot p_{3} = 153[/tex]

[tex]p_{3} = \frac{153}{3}[/tex]

[tex]p_{3} = 51[/tex]

The mean of the remaining 3 boys is 51.

Answer:Best corral has a width and length of 50 feet, enclosing an area of 2500 square feet. Let's calculate the width (W) of the rectangle as a function of it's length (L). So we have W = (200 - 2*L)/2 W = 100 - L Now the area of the rectangle is A = WL Substitute the equation for W. A = (100 - L)L A = 100L -L^2 Let's make an initial guess of 40 ft and add an error component of e. So we'll use the length of (40+e) and see what we get. A = 100L -L^2 A = 100(40+e) - (40+e)^2 A = 4000 + 100e - (1600 + 80e + e^2) A = 4000 + 100e - 1600 - 80e - e^2 A = 2400 + 20e - e^2 Now looking at those 2 "e" terms is interesting. It's pretty obvious that any negative value of e will cause those term to result in a value less than 0, and decrease the available area. Also any value of e greater than 20 will also cause those 2 values to sum to a negative value and decrease the area. But a value of e in the range of 0 to 20 will result in a positive value and cause the area enclosed to be larger. So it's obvious that 40 feet isn't optimal. Let's pick the middle of the e values that result in something positive (0+20)/2 = 10 and add that to our initial guess, getting a length of 50 and replace length by (50+e) and see what happens. A = 100L -L^2 A = 100(50+e) -(50+e)^2 A = 5000+100e -(2500+100e + e^2) A = 5000+100e - 2500 - 100e - e^2 A = 2500 - e^2 This looks quite promising. Any non-zero value of e will result in the area enclosed being smaller. So the idea value of e is 0. That means that the idea length of the rectangle is 50 feet. And that makes the width 50 feet as well. Mind, this problem could have been also solved using the first derivative of the equation A = 100L -L^2, which would have been A' = 100 - 2L, and then solving for 0. But I did this problem to demonstrate that you don't need to resort to calculus for every maximum type of problem.

Step-by-step explanation:

Answer:

Dance m8

Step-by-step explanation:

Answer:

a. Dance

Step-by-step explanation:

We will find the ratios' common denominators and compare them

Dance: 2/3 girls to boys ratio

soccer: 3/5 girls to boys

Chess: 8/15 girls to boys

Lets find a common factor

all of the denominators (bottom numbers evenly go into 15)

2/3=10/15

3/5=9/15

8/15= 8/15 because it already has 15 as a denominator

The number with the greatest numerator is gonna be our answer;

10/15 or 2/3

Answer:

follows are the solution to this question:

Step-by-step explanation:

Please find the correct question in the attached file:

The formula for calculating the Confidence interval of proportion:

[tex]\to CI=\hat{p} \pm Z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\to \hat{p}=\frac{\text{lower limit +upper limit}}{2}\\[/tex]

      [tex]=\frac{0.48+0.60}{2}\\\\=\frac{1.08}{2}\\\\=0.54[/tex]

The number of learners with access to working at home on a computer:

[tex]= 0.54 \times 300 \\\\=162[/tex]

Lower limit =0.48

upper limit = 0.60

[tex]\to margin \ error = \frac{\text{upper limit - lower limit}}{2}\\[/tex]

                          [tex]=\frac{0.60-0.48}{2}\\\\=\frac{0.12}{2}\\\\= 0.06[/tex]

Answer:

Heating and cooling our homes, lighting office buildings, driving cars and moving freight, and manufacturing the products we rely on in our daily lives are all functions that require energy.

Answer:

driving cars, heating and cooling our homes,and manufacturing products we use everyday such as clothes and toothpaste.

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

HOPE THIS HELPED

Answer

50

Step-by-step explanation:

60 is supplementary to 120 so 60+70=130

and a triangle adds up to 180 so 180-130 would be 50