if the sum of an arithmetic progression of six positive integer terms is 78, what is the greatest possible difference between consecutive terms

The equation y = 3/5 x is graphed on a coordinate plane and attached

The equation is graphed using some points for the input which is x values and solving to get the y values

This is called the table of values used to plot on the coordinate plane

The table of values for y = 3/5 x is formed as follows

For x = -10, y = 3/5 * -10 = -6

For x = -5, y = 3/5 * -5 = -3

For x = 0, y = 3/5 * 0 = 0

For x = 5, y = 3/5 * 5 = 3

For x = 10, y = 3/5 * 10 = 6

table of values

x     y

-10  -6

-5   -3

0     0

5     3

6     6

Learn more about linear graphs at:

brainly.com/question/14323743

#SPJ1

Option (A) 18 = 0.1s

Step-by-step explanation:

Every seventh-grade student at Martin Middle School takes one world language class.

Now we will form the equation as per statement of the question.

Let total students of seventh-grade = s

" one tenth of seventh grade students take  French."

" Students who took French were 18."

So  of s = 18

(0.1)s = 18

therefore, Option (A) 18 = 0.1s is the answer.

Answer

a

Step-by-step explanation:

The probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population of marks on a biology final test that is normally distributed with a mean of 78 and a standard deviation of 6. We want to know the probability that a class of 50 has an average score that is less than 77.
Using the central limit theorem, we can calculate the standard error of the mean as follows:
standard error of the mean = standard deviation / square root of sample size
standard error of the mean = 6 / √50
standard error of the mean = 0.8485
Next, we need to calculate the z-score for a sample mean of 77:
z-score = (sample mean - population mean) / standard error of the mean
z-score = (77 - 78) / 0.8485
z-score = -1.18
We can use a standard normal distribution table or calculator to find the probability associated with a z-score of -1.18. The probability of a sample mean less than 77 is approximately 0.1190 or 11.90%.
Therefore, the probability that a class of 50 has an average score that is less than 77 is approximately 11.90%.

To learn more about probability, click here:

https://brainly.com/question/30034780

#SPJ11

Answer:

A = 16cm

B = 32cm

C = 8cm

D = Sorry the time I learned this I didn't learn it for fractions.

There are two other important distances on a circle, the radius (r) and the diameter (d). The radius, the diameter, and the circumference are the three defining aspects of every circle. Given the radius or diameter and pie you can calculate the circumference.

The diameter is the distance from one side of the circle to the other at its widest points. The diameter will always pass through the center of the circle. The radius is half of this distance.

The formula for working out the circumference of a circle is:

Circumference of circle = π x Diameter of circle

This is typically written as C = πd.

The angle  of EBF is  6w -28°.

It is required to find the angle  of EBF.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.

Given:

ABF = 8w - 6

ABE = 2(w + 11)

According to given question we have,

Angle EBF = ABF - ABE

Angle EBF = 8w - 6 - [2(w + 11)]

Angle EBF = 8w - 6 - [2w + 22]

Angle EBF = 8w - 6 - 2w - 22

Angle EBF = 6w -28°

Therefore, the angle  of EBF is  6w -28°.

Learn more about angle here:

https://brainly.com/question/13954458

#SPJ1

Answer:

C

Step-by-step explanation:

She ate 3, so originally 77 cookies. Divide that by 7 batches, which is the equivalent to C

The equation could be used to determine x, the cost of labor per hour is

92x + 4 = 272. Option D

The equation reads as follows: 4x plus 77 equals 497, where 4x stands for the cost of labor per hour, 77 for the cost of the components, and 497 for the overall sum.

Generally, the equation for the expression  is  mathematically given as

4x + 92 = 272

4x + 92-92 = 272 - 92

4x = 180

x = 45

In conclusion, The equation could be used to determine x,

x = 45

Read more about the equation

https://brainly.com/question/10413253

#SPJ1

Answer:

The perimeter of the sector is :30.5 cm

Step-by-step explanation:

Mathematically, we have the area of the sector as;

e/360 * pi * r^2

r is 8 cm

so we have

58 = e/360 * pi * 8^2

58/64 * 360/pi = e

e = 103.85

To get the perimeter,

we have length of the arc plus 2r

Length of the arc is;

e/360 * 2 * pi * r

add 2 r;

e/360 * 2 * pi * r + 2r

so we have

103.85/360 * 2 * pi * 8 + 2(8)

= 14.5 + 16

= 30.5 cm

Answer: the above answer is correct

Step-by-step explanation:

The margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company is approximately 2.80 years.

(a) The z-critical value for an 85% confidence interval is approximately 1.44.

(b) The margin of error for an 85% confidence interval is approximately 1.19 years.

(c) The margin of error for a 99% confidence interval is approximately 2.80 years.

To find the needed values for the confidence intervals, we can use the formula: Margin of Error = z * (standard deviation / square root of sample size)

(a) To find the z-critical value for an 85% confidence interval, we need to find the z-score corresponding to an area of 0.85 in the standard normal distribution table. The z-critical value for an 85% confidence interval is approximately 1.44.

(b) For an 85% confidence interval, we can calculate the margin of error using the given standard deviation of 4.5 years and the sample size of 181: Margin of Error = 1.44 * (4.5 / sqrt(181)) ≈ 1.19 years

Therefore, the margin of error for an 85% confidence interval to estimate the mean time a general manager had spent with their current company is approximately 1.19 years.

(c) Similarly, for a 99% confidence interval, we can calculate the margin of error using the same standard deviation and sample size: Margin of Error = 2.58 * (4.5 / sqrt(181)) ≈ 2.80 years

Hence, the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company is approximately 2.80 years.

Learn more about Margin of Error here:

brainly.com/question/29100795

#SPJ11

Answer:

Step-by-step explanation:

120=10*12

120=5*2*4*3

120=5*2*2*2*3

120=(2^3)*3*5

Answer:

24/9

Step-by-step explanation:

you would multiply the numerator and the 4 together. you kee the denominator the same

The upper specification limit is 2.520 mm, and the lower specification limit is 2.480 mm.  The process is not capable according to the purchaser's requirement of a capability index of 1.50.

(a) The upper specification limit (USL) is calculated by adding the process mean (2.500 mm) to the upper tolerance (0.020 mm), resulting in 2.520 mm. The lower specification limit (LSL) is calculated by subtracting the lower tolerance (0.020 mm) from the process mean, resulting in 2.480 mm.

(b) The process capability index (Cp) is calculated by dividing the tolerance width (USL - LSL) by six times the standard deviation. In this case, the tolerance width is 0.040 mm (2.520 mm - 2.480 mm) and the standard deviation is 0.004 mm. Therefore, Cp = 0.040 mm / (6 * 0.004 mm) = 1.25.

(c) The purchaser requires a capability index (Cpk) of 1.50, which measures how well the process meets the specification limits. Since Cp (1.25) is less than the desired Cpk (1.50), the process is not capable according to the purchaser's requirement. It is not good enough for the supplier either, as the Cp is less than the desired level.

(d) If the process mean were to drift to 2.497 mm, the Cp value would remain the same at 1.25. Since the Cp value is still less than the desired Cpk of 1.50, the process would still not be good enough for the supplier's needs, even with the changed process mean.

Learn more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

The length of each side of the box is 10 centimeter.

Volume is the amount of space occupied by a three-dimensional figure as measured in cubic units.

Given,

The volume of the cubic box = 1 liter

We know 1 liter= 1000 cubic centimeter

Volume of the cubic box= \(x^3}\)

Then,

\(x^{3}=1000\\ x=\sqrt[3]{1000}\)

x=10 centimeter

Hence, the length of each side of the box is 10 centimeter.

Learn more about volume here

brainly.com/question/1578538

#SPJ4

Answer:

there would be 22 students

Answer:

The answer is that there are 25 students in the class.

Answer:

Step-by-step explanation:

The cost = x * (1 + 0.075) = x * 1.075 = 1.075*x

Answer:

Penelope get to ride 30 rides if she spends $35 in all

Step-by-step explanation:

r= ride

20 +0.50r =35

sibtract 20 on each side

0.50r = 15

divide esach side by 0.50

r= 30

Answer:

30 girls 30:24

Step-by-step explanation:

You would do 24 divided by 4 and get 6. Then you would do 5 times 6 to get 30.

Hope this helps.

Answer:

it should be 20

Step-by-step explanation:

Because if you divide then round

Answer:

132 chocolates

Step-by-step explanation:

We know that after Ramesh arranges his chocolates in rows, the number of rows multiplied by the number of chocolates in each row will give us the total number of chocolates, 17424.

Let the number of rows be x.

From the question, the number of chocolates in each row will also be x.

\(=> x * x = 17424\\\\x^2 = 17424\\\\=> \sqrt{x^2} = \sqrt{17424} \\\\x = 132\)

Therefore, he placed 132 chocolates in each row.

Answer: 11%

Step-by-step explanation:

so, I’m not going anywhere else to go to the store and I’ll let you know if you need anything or do I need to get something for dinner lol you know what I’m going through and I can’t even imagine what you mean by that time and you have have to do that for you too but I’m just trying to get you to do that that I don’t want to do with that and that I’m going to be a pain and I’m sorry I don’t want you to think that you have been in the hospital and you have no desire for me to come in this week I don’t think I can do anything with your dad and you are just not being mean and I can’t even talk to you and I’m not going through all that I know I don’t know what to do but you are not going through all this nonsense I know that I know what I want you do not need me but you know me I love that I don’t know if I will ever do that anymore but you are not even in my mind for a while but you are not so much and I’m sorry I just want to make sure that I have no idea that I’m going to have to be a friend of my best relationshi.

Answer:

317 < 400

The Sum of the squares of the smaller 2 sides (121 + 196 = 317)  < longest side squared (400) So, it is an  OBTUSE SCALENE TRIANGLE.

Source: http://www.1728.org/triantest.htm

Step-by-step explanation:

Answer:

I think it's (B)

Step-by-step explanation:

Answer:

x-int: -0.5; y-int: 1

Step-by-step explanation:

We see the intercepts in the graph.

The y-intercept is at 1.

The x-intercept is at -0.5.

Answer: x-int: -0.5; y-int: 1

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

Read more about Line of best fit at; https://brainly.com/question/1441182

#SPJ1

Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

Answer:

\(3x + y = 3 \\ 3 = x - y \\ 3 = x\)

Answer:

y = -3x - 4

Step-by-step explanation:

We are given the equation 3x + y = 3, and we want to find an equation of the line that is parallel to 3x + y = 3.

This same line also passes through the point (1, -7).

Parallel lines have the same slopes. This means that we'll first need to find the slope of 3x + y = 3.

The equation is written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0. a is usually non-negative as well.

There is a shortcut into finding the slope when the equation is in standard form; the slope of the line is -a/b, where a is the coefficient in front of x and b is the coefficient in front of y).

The coefficient in front of x is 3, and 1 in front of y.

Substitute 3 as a, and 1 as b in -a/b. Don't forget about the - in front of a!

-3/1 = -3

This means the slope of the line is -3.

It is also the slope of the line parallel to it.

We can write the equation of the line we are trying to solve for in standard form, too. However, we could also write it in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept.

As we are already given the slope, we can immediately plug that into the formula.

Replace m with -3.

y = -3x + b

Now we need to find b.

As the equation passes through the point (1, -7), we can use its values to help solve for b.

Substitute 1 as x and -7 as y.

-7 = -3(1) + b

Multiply.

-7 = -3 + b

Add -3 to both sides

-4 = b

Substitute -4 as b into the equation

y = -3x - 4

Answer:

7/18

Step-by-step explanation:

Probability is the ratio of the number of possible outcomes to the number of total outcomes.

Given that there are 9 counters in a bag, 7 are green while 2 are blue.

the probability of picking at random a

Green counter = 7/9

Blue counter = 2/9

The probability that Ria takes one counter of each colour if 2 counter are picked as random is Green and Blue or Blue and Green

This is

=7/9 * 2/8 + 2/9 * 7/8

Recall that when a counter is picked the number of that ball available reduces and so does the total number of counter

=14/72 + 14/72

= 28/72

= 7/18

As per the unitary method, the candy distributor needs to mix 380 kilograms of the 20% fat-content chocolate with 152 kilograms of the 50% fat-content chocolate to create 200 kilograms of a 38% fat-content chocolate.

Let us assume that one kilogram of the 38% fat-content chocolate contains 0.38 kilograms of fat.

Now, we can set up the following equation based on the fat content:

0.2x + 0.5y = 0.38(200)

We can simplify this equation to get:

0.2x + 0.5y = 76

Using the equation above, we can find the total amount of fat in the mixture for each unit of the final mixture.

0.2x + 0.5y = 76

Divide both sides by 200, we get:

0.001x + 0.0025y = 0.38

This equation represents the total amount of fat in one unit of the final mixture.

Therefore, we can set up the following equation:

0.2a + 0.5b = 0.38

This equation represents the total amount of fat in one unit of the final mixture, which is the same as the equation we obtained earlier.

Now, we can use the unitary method to find the value of a and b.

Since one kilogram of the 20% fat-content chocolate contains 0.2 kilograms of fat, and one unit of the final mixture contains 0.38 kilograms of fat, we can write:

0.2a = 0.38

a = 1.9

Similarly, since one kilogram of the 50% fat-content chocolate contains 0.5 kilograms of fat, and one unit of the final mixture contains 0.38 kilograms of fat, we can write:

0.5b = 0.38

b = 0.76

we have found that we need 1.9 units of the 20% fat-content chocolate and 0.76 units of the 50% fat-content chocolate to make one unit of the final mixture.

Amount of 20% fat-content chocolate = 1.9 x 200 = 380 kg

Amount of 50% fat-content chocolate = 0.76 x 200 = 152 kg

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4

Answer:

A = 5/6

Step-by-step explanation:

The line is given by

Ax - 4y = 1

We have a point on the line

(6,1)

Replace x with 6 and y with 1

A(6) - 4(1) = 1

6A -4 = 1

Add 4 to each side

6A -4+4 = 1+4

6A = 5

Divide each side by 6

6A /6 = 5/6

A = 5/6

Answer:

Decay

3

Step-by-step explanation:

Answer:

We can write an equation for the length, L, of the rectangle in terms of its width, w, as:

L = 2w + 9

The area, A, of the rectangle is given by:

A = Lw

Substituting the expression for L into the equation for A, we get:

A = (2w + 9)w

Expanding the right side of the equation, we get:

A = 2w^2 + 9w

Therefore, the quadratic function that represents the area of the rectangle for a given value of w is:

A(w) = 2w^2 + 9w

This function is in standard form, where the coefficient of the squared term is positive. We can also see that the graph of this function is a parabola that opens upwards.