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Given an arithmetic progression -8, -3, 2,.... Determine three consecutive terms in this progression which sum up to 111.​

Answer: x=6.5

Step-by-step explanation:

3(2x - 4) = 8 + 2x + 6

6x-12=14+2x

4x-12=14

4x=26

x=26/4

x=6.5

We get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.

We are given a statement:

The sum of eight and half of a number.

We have to form an expression for the same.

An expression means a combination of numbers and variables.

Let the number be a variable say x.

Now we need the half of a number.

1 / 2 of x = x / 2

Now we need the sum of 8 and x / 2.

So, it will be:

8 + x / 2

= (16 + x) / 2

Therefore, we get the expression for the statement "The sum of eight and half of a number" as (16 + x) / 2.

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The mean and the median value of the given data set is 12.62 and 6.

According to the statement

We have to find that the mean and the median of the following data.

So, For this purpose, we know that the

The mean is found by adding all of the numbers together and dividing by the number of items in the set.

And

The median is the middle number in a sorted, ascending or descending list of numbers

From the given information:

The data set are:

1,20,1, 49, 16, 5, 3, 6

Then

According mean definition,

Mean = 1+20+1+ 49+ 16+ 5+ 3+6/8

Mean = 101/8

Mean = 12.625

Then

The data set is 1,3,5,6,16,20,49.

Median = 8 terms /2

Median = 4th term

Median = 6.

So, The mean and the median value of the given data set is 12.62 and 6.

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Answer:

7.25 feet

Step-by-step explanation:

The probability that one green and one yellow is selected (without replacement) is 3/7.

What are examples and probability?

Probability that one green and one yellow is selected (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows

Pr = [tex]\frac{G}{n} * \frac{Y}{n - 1 } + \frac{Y}{n} * \frac{G}{n- 1}[/tex]  The subtraction means the cellphones are not replaced

This gives

[tex]Pr = \frac{6}{8} * \frac{2}{8 - 1} + \frac{2}{8} * \frac{6}{8 - 1}[/tex]

[tex]Pr = \frac{3}{4} * \frac{2}{7} + \frac{1}{4} * \frac{6}{7}[/tex]

[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]

take lcm

[tex]Pr = \frac{3}{7}[/tex]

Hence, the probability that one green and one yellow is selected (without replacement) is 3/7.

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The branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

It is required to find the statement.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

The branch of statistical studies called descriptive statistics summarizes important aspects of a data set.

Descriptive statistics refers to the summary of important aspects of a data set.

Therefore, the branch of statistical studies called descriptive statistics summarizes important aspects of a data set is true.

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In 25.76 seconds we will fill the total volume of the cylinder.

The total volume of the cylinder is given by the equation:

V = pi*R^2*H

Where pi = 3.14, R is the radius and H is the height.

Here we know that the diameter is 6 inches, then the radius is:

R= 6in/2 = 3in

And the height is 8 inches, then the volume is:

V = 3.14*(3in)^2*8in = 226.08 in^3

We already have 20 cubic inches of water there, so what we need to fill is:

226.08 in^3 - 20in^3 = 206.08in^3

If we fill it at a rate of 8in^3/s, the time in which we will completely fill the cylinder is:

T = 206.08in^3/8in^3/s = 25.76s

In 25.76 seconds we will fill the total volume of the cylinder.

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Answer:

15

Step-by-step explanation:

[tex]-10+\left|6+\left(-17\right)\right|-\left(-14\right)[/tex]
[tex]=-10+\left|6-17\right|+14[/tex]
Subtract.
[tex]=-10+\left|-11\right|+14[/tex]
Now, add.
[tex]=4+\left|-11\right|[/tex]
Apply absolute rule.
[tex]=4+11[/tex]
= 15

Answer:

You would need 9 liters of pure acid and 72 liters of 10% acid to make a mixture of of 81 liters of 20% acid.

Step-by-step explanation:

See attached picture.

Bonjour,

Answer:

16 2/3 = 50/3

Step-by-step explanation:

16 2/3 = 16.6666666…

Change the percent to a decimal number by moving the decimal two places to the left.

Call this x = 0.16666666…

10x = 1.66666666…

100x 16.66666666…

Subtract 100x - 10x = 15

90x = 15

x = 15/90 = 1/6

16 2/3 % = 1/6

Answer:

I am not sure myself but I think the answer is 2.3 hours per week.

Answer: 2000π mm^2

Step-by-step explanation:

A=area of entire circle. B=Area of Inside circle. C=Area of shaded region

A-B=C

π(120/2)^2 -π(80/2)^2=

π(60)^2 -π(40)^2=

3600π-1600π=2000π mm^2

Dilation involves changing the size of a quadrilateral or any shape

The coordinates of the image of the dilation are: [tex]W^{\prime}=(1 / 4,-3), X^{\prime}=(10,0)$, $Y^{\prime}=(7,-9)$[/tex] and [tex]$Z^{\prime}=(4,-9)$[/tex]

This is further explained below

The vertices of the pre-image are given as:

W=(0,-4)

X=(13,0)

Y=(9,-12)

Z=(5,-12)

The scale factor is given as:

k=3 / 4

The center of dilation is given as:

(a, b)=(1,0)

To calculate the vertices of the image, we make use of the following formula [tex]$\left(x^{\prime} y^{\prime}\right)=(k(x-a)+a, k(y-b)+b)$[/tex]

So, we have:

W'=(3 / 4(0-1)+1,3 / 4(-4-0)+0)

W'=(1 / 4,-3)

X'=(3 / 4(13-1)+1,3 / 4(0-0)+0)

X'=(10,0)

Y'=(3 / 4(9-1)+1,3 / 4(-12-0)+0)

Y'=(7,-9)

Z'=(3 / 4(5-1)+1,3 / 4(-12-0)+0)

Z'=(4,-9)

Hence, the coordinates of the image of the dilation are:

W'=(1 / 4,-3),

X'=(10,0),

Y'=(7,-9)

Z'=(4,-9)

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The circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

We are given that:

Length of the shorter arc forming an angle of 45° with the center = 22 cm

AB = 22 cm

C is the center of the circle.

We know that the length of the arc is calculated as:

Length of an Arc = θ × (π / 180) × r

22 = 45 × (3.14 / 180) × r

22 = 0.785 r

r = 22 / 0.785

r = 28.0255

Circumference = 2 π r

Circumference = 2(3.14) (28.0255)

C = 176 cm

Therefore, we get that, the circumference of the circle with arc AB as 22 cm and C as the center will be 176 cm.

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Answer:

32 is it

Step-by-step explanation:

A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to  foot/hour

2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to  miles/minute

1 mile=5280 feet

22 miles/hour=22 × 5280 foot/hour

22 miles/hour=116,160 foot/hour

1 hour=60 minute

125 miles/hour= 125/60 miles/minutes

125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes

Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

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If the samples are large and the standard deviations are small, the differences between the two samples are least likely to be statistically significant.

The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

"Statistical significance precision" tells us, in Redman's words, "whether a result is probably caused by chance via some factor of interest." A significant finding simply means that you should consider it. can be sure that it is true and not that you were just lucky (or unlucky) in the sample you chose.

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Using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

Given the equation, y - 6 = x/4, we can rewrite the equation as:

y = x/4 + 6

For x = 12, we have:

y = 12/4 + 6 = 3 + 6

y = 9

For x = 0, we have:

y = 0/4 + 6 = 0 + 6

y = 6

For y = 4, we have:

4 = x/4 + 6

4 - 6 = x/4

-2 = x/4

-8 = x

x = -8

For y = -3, we have:

-3 = x/4 + 6

-3 - 6 = x/4

-9 = x/4

-36 = x

x = -36

Thus, using the given equation, the missing values in the table are:

x            y

32         14

12          9

0           6

-8          4

-36       -3

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Answer:

16 1/4

Step-by-step explanation:

4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4

Add the 6 and you get 16 1/4

Answer:£1500

7500 divided by 10=750. £750 is 10% so 750x2 which is 1500, is 20%. Therefore, it is reduced by £1500

Answer:

£1500

Step-by-step explanation:

20% = 20/100 = 0.2

7500 - (7500*0.2)

= 7500 - 1500

= 6000

The reduction in price is:

£ 1500

Equation of the book on how many pound the books weigh is T = w*n and the weight of the books is 175/3 pounds.

It is given in the question that the book weighs 4 and 3/8 pounds and the number of copies that are needed to mail are 5.

We have to find the equation to find the weight of 5 copies of the book.

The equation will be:-

Total weight of books = Weight of 1 book * Number of copies of book

Let total weight be T

Let weight of 1 book = w

Let number of copies of a book = n

Hence, equation becomes:-

T = w*n

We can find the total weight of the books.

T = (4 and 3/8 )*5

T = (35/3)*5

T = 175/3 pounds

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Answer:

∠ N = 10° , arc RS = 134°

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc.

(5)

∠ N is an inscribed angle and we require arc LM

the measure of the arcs in a circle = 360°

note LN is the diameter so arc LN = 180°

Then

LM + MN + LN = 360°

LM + 160° + 180° = 360°

LM + 340° = 360° ( subtract 340° from both sides )

LM = 20°

then

∠ N = [tex]\frac{1}{2}[/tex] LM = [tex]\frac{1}{2}[/tex] × 20° = 10°

(6)

∠ Q is an inscribed angle so its intercepted arc is twice its measure

arc RS = 2 × 67° = 134°

Answer:

320 Students

Step-by-step explanation:

Hope this helps :)

Osvoldo did not meet his goal of getting at least 30% carbohydrates

Although a part of your question is missing, you might refer to this full question: Osvoldo has a goal of getting at least 30% of his grams of carbohydrates each day from whole grains. Today, he ate 220 grams of carbohydrates, and 55 grams were from whole grains. Did Osvoldo meet his goal?

Total carbohydrates he ate = 220 grams

Carbohydrates intake from whole grains = 55 grams

Percentage of carbohydrates in whole grains = (Carbohydrates from whole grain/Total carbohydrate intake)*100

=(55/220)*100

=0.25*100

=25%

Osvoldo got 25% carbohydrates as against his goal of at least 30% carbohydrates

Hence, he did not meet his goal of getting at least 30% carbohydrates

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Answer:

493%

Step-by-step explanation:

To convert a decimal to percentage, muiltiply the decimal by 100.

If a bottle weighs 300g and can hold 630ml, then it will weigh approximately 930g when filled with water.

As per the question statement, a bottle weighs 300g and can hold 630ml.

We are required to find out the weight of the bottle when it is filled up with water.

To solve this question, we need to know about the concept of density of a substance, i.e.,

[tex]Density=\frac{Mass}{Volume}\\ or, Mass=[Density*Volume][/tex].

And density of water is 1gm/ml, i.e., 1gm of water has a mass of 1ml.

Using the above info, we will calculate the mass of 630ml of water and then we will have to add up the mass of water and the mas of the bottle to obtain our desired answer.

Using the unitary method, if 1ml of water has a mass of 1gm, then,

630 ml of water has a mass of [tex](630*1)=630\\[/tex] gms.

Hence, total weight of the bottle filled with water will be

[tex](630+300)=930[/tex] gms.

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The difference quotient of the function g(x) = √x is  [√(x+h) -√x]/h

Difference quotient of the function:

Difference quotient of the function means a measure of the average rate of change of the function over an interval.

The difference quotient formula of a function y = f(x) is,

[ f(x + h) - f(x) ] / h

where

f (x + h) is obtained by replacing x by x + h in f(x)

f(x) is the actual function

Given,

Function g(x) = √x where x≥0.

Here we need to find the difference of the quotient of the function.

For that,

First we have to calculate the value of g(x + h),

By simply replacing the value of x as x + h,

So,

g(x + h) = √(x+h)

Now apply the values on the formula in order to solve it,

=> [√(x+h) -√x]/h

We can't simplify it further.

So, the difference quotient of function is,

=> [√(x+h) -√x]/h

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Answer: D

Step-by-step explanation:

took one for the team

DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.

∠TAC = ∠ABC  (The angle between the chord and the tangent is equal to the angle in the alternate segment)

Since, EDCB is a cyclic quadrilateral,

     ∠CBD + ∠CED = 180  ----- I

-      ∠CED + ∠AED = 180   -----II

----------------------------------------------------

   ∠ CBD =  ∠AED

Also, ∠ CBD = ∠ EAT( A is tangent to the circle)

So, ∠ EAT = ∠ AED ( Alternate interior angle)

So, DE || ST

Therefore, DE is parallel to ST as ∠ EAT = ∠ AED which are alternate interior angles.

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