the arithmetic sequence 1, .25, blank, -1.25, blank

Thomas bought 6 plastic cups and 6 glass cups.

For given question,

Let a be the number of glass cups and b be the number of plastic cups.

Thomas bought 12 glass cups and plastic cups.

So, we get an equation

a + b = 12                        .................(1)

The glass cups cost $3.25 and plastic cups cost $2.75

Thomas spent a total of $36

From this information we get equation,

3.25 a + 2.75 b = 36         ............(2)

We have a system of equations.

From equation (1),

a = 12 - b                  .............(3)

Substitute above value of a in equation (2)

3.25 (12 - b) + 2.75 b = 36

39 - 3.25 b + 2.75 b = 36

39 - 0.5 b = 36

-0.5 b = -3

b = 6

This means, Thomas bought 6 plastic cups.

Substitute above value of b in equation (3)

So, a = 12 - 6

a = 6

Thomas bought 6 glass cups.

Therefore, Thomas bought 6 plastic cups and 6 glass cups.

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Extreme values have little impact on the median and quantiles because they all come inside the middle half of the data.

Calculation:

Let’s assume the 24 students in the room range in age from 185, 185, 186, 186,.... 195, 195, 196, 196 months.

The total of x2 is 871252.

The sum of x is 4572.

The mean is 190.5 (4572/24).

The median, which lies between positions 12 and 13, is 190.5.

Standard deviation is (871252/24 -190.52)^0.5 = 3.45

Halfway between the( 18th and 19th)- (6th and 7th)interquartile range

= 6 (193.5 - 187.5).

Include his age of 716 months in the calculations as the teacher now.

Total x2 = 1383908

Total x = 5288

Mean (5288/25) = 211.52

Median (13th) = 191

Standard Deviation is (1383908/25 - 211.522)^0.5 = 103.03

Interquartile range (7th minus 19th) is 194 - 188 = 6

Therefore the mean has changed by 21.02 after the addition of a piece of data that is vastly different from the rest, yet the median has changed by only 0.5.

The interquartile range has remained constant, whereas the standard deviation has increased by over 100 and by a factor of approximately 30.

The result of adding together and dividing the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.

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Based on the calculations, the volume of this object is equal to 68 cubic inches (in³).

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume = πr²h

Where:

For this cylinder, the radius is given by:

Radius = Diameter/2 = 4/2 = 2 inches.

Substituting the given parameters into the formula, we have;

Volume = 3 × 2² × 3

Volume = 3 × 4 × 3

Volume = 36 cubic inches.

Mathematically, the volume of a sphere can be calculated by using this formula:

Volume = 4/3 × πr³

Where:

r represents the radius.

Substituting the given parameters into the formula, we have;

Volume = 4/3 × 3 × 2³

Volume = 4/3 × 3 × 8

Volume = 4 × 8

Volume = 32 cubic inches.

Now, we can find the total volume of this object:

Total volume = 36 cubic inches + 32 cubic inches.

Total volume = 68 cubic inches (in³).

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Answer:

Step-by-step explanation:

Compare both shapes

Find out the length of the red line through Pythagoras theorem

a² + b² = c²

9² + b² = 15²

15²- 9² = b²

144 = b²

√144 = b

b = 12

Red line is 12 and the other length of one side of the triangle is x - 9

The hypotenuse of the other triangle will be equal to:

a² + b² = c²

12² + (x-9)² = c²

144 + x² - 9x -9x + 81 = c²

x² - 18x + 225 = c²

THE HYPOTENUSE OF THE 2ND TRIANGLE = x² - 18x + 225

NOW COMPARE BOTH TRIANGLES

x² - 18x + 225 :    15

       x - 9        :     9

Cross multiply

9(x² - 18x + 225) = 15(x - 9)

9x² - 162x + 2025 = 15x - 135

9x² - 162x - 15x + 2025 + 135 = 0

9x² - 177x + 2160 = 0

Now use the quadratic equation

x = (-b +- √b² - 4ac)/2a

a = 9

b = -177

c = 2160

x = (-(-177) +- √(-177)² - 4(9)(2160))/(2×9)

x = (177 +- √31329 - 77760)/(18)

x = (177 +- √-46431)/18

At this point I have lost hope in the question as i got a negative value under square root which means it can't be solved.
I don't know where I am wrong but I hope the starting parts of the answer help you reach the final answer.

Answer:

111/22 or 5 and 1/22

Step-by-step explanation:

9 and 7/22 equals 205/22

4 and 3/11 equals 47/11

multiply 47/11 times 2/2 to get common denominator

47/11 times 2/2 is 94/22

205/22 minus 94/22 is 111/22 which is also 5 and 1/22

Answer:

1111

Step-by-step explanation:

Answer: Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. If the number is negative, then the absolute value is its opposite: |-9|=9.

Step-by-step explanation:

The height of the rectangular pyramid tent's center pole = 5.5 feet.

Volume of rectangular pyramid = 1/3(length)(width)(height).

Given the following:

Substitute

88 = 1/3(8)(6)(height)

88 = 16(height)

88/16 = height

5.5 = height

Therefore, the height of the rectangular pyramid tent's center pole = 5.5 feet.

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Answer:

the cost per liter of the paint is equal to 24 8/liter

Hope this helps :)

The proof of the expression 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated for pqr = 1.

For the given expression;

pqr = 1. Then pq = 1/r; qr = 1/p; pr = 1/q.

OR, pq = r⁻¹ ; qr = p⁻¹ ; pr = q⁻¹ .

The given expression is;

1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1

Consider LHS part;

= 1/(1+p+pr) + 1/(1+q+pq) + 1/(1+r+qr)

Multiply and divide q in the first part;

=  q/(q+qp+qpr) + 1/(1+q+pq) + 1/(1+r+qr)

Put prq = 1 (given)

=  q/(q+qp+1) + 1/(1+q+pq) + 1/(1+r+qr)

Add 1st and 2nd part;

= (q+1)/(q+qp+1) + 1/(1+r+qr)

Multiply and divide r in the first part;

=  (q+1)r/(rq+rqp+r) + 1/(1+r+qr)

Put prq = 1 (given)

=  (qr+r)/(rq+1+r) + 1/(1+r+qr)

Add both

=  (qr+r+1)/(rq+1+r)

Both will be cancelled;

= 1 = RHS

Therefore, proof for 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1 is evaluated.

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The complete question is-

If pqr = 1, then prove that 1/(1+p+q⁻¹) + 1/(1+q+r⁻¹) + 1/(1+r+p⁻¹) = 1

Answer:

pqr = 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

gnhbn

The given vertices make a right angled triangle as seen below, with the help of vectors.

Vectors refer to the quantities that have both magnitude and direction but not position.

Now,

Given: Three vertices of a triangle: P(1,-3,-2),Q(2,0,-4), and R(6,-2,-5).

To find: whether they make a right angled triangle.

Finding:

Now,

The triangle's three sides can be represented by the following three directional vectors:

Vector (PQ) = <2, 0, -4> - < 1, -3, -2>

=> Vector (PQ) = < 1, 3, -2>

Vector (QR) = < 6, -2, -5> - < 2, 0, -4>

=> Vector (QR) = < 4, -2, -1>

Vector (PR) = < 6, -2, -5> - <1, -3, -2>

=> Vector (PR) = < 5, 1, -3>

Now, finding a pair of vectors whose dot product = 0:

Hence, the sides PQ and QR must be perpendicular so that the given vertices make a right-angled triangle.

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The length of QR in triangle PQR is 6.7 √2 m .

We are given that:

In triangle PQR, we have:

P = 90° and PR = 6.7 m .

Since, it is an isosceles triangle, the other angles will be equal to = 45° ( as the other two triangles will be equal and the sum of angles is 180°) .

We have to find the length of QR

We know that sin θ = Perpendicular / hypotenuse

sin 45° = 6.7 m / H

1 / √2 = 6.7 m / H

H = 6.7 √2 m

Therefore, we get that, the length of QR in triangle PQR is 6.7 √2 m .

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Goran's monthly salary would be $3963.49

In this problem, the Annual salary or his Gross Salary is $63,000 and annual deductions for his salary which includes taxes & health insurance is $15,438.12 annually. The formula to calculate the Net salary is :

                 => Net Salary = Gross Salary - Deductions

By the formula mentioned above, we can calculate Goran's Net salary which he gets Annually. Here, Gross = $63,000, Deductions = $15,438.12 :

                 => Net = 63,000 - 15438.12   => Net Salary = 47,561.88

Goran gets a Net Salary of $47,561.88, Now we have to calculate the equal amount of paychecks he will receive monthly for 12 months.

Monthly Paycheck = Net/12   => 47561.88/12  =>  $3963.49

Hence, Goran's monthly paycheck will be $3963.49

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where is the problem, how can I help you?

Answer:

1.5 or 3/2

Step-by-step explanation:

The scale factor is the factor by which the side lengths of the original shape are multiplied by. In this case, the original shape had side lengths 17 and was multiplied by [tex]x[/tex] to get the scaled shape.

Now we get the equation [tex]17\cdot x=51/2[/tex]. Solving, we get x=1.5

Answer:

Step-by-step explanation:

Answer:

biweekly salary =

365/14=

23

then total salary

of her is =$1230.90

*23

=

Step-by-step explanation:

We get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

We are given the radius of the circle as:

Radius = r = 14 m

We are also given the value of π as:

π = 3.14

We need to find the perimeter and area of the circle.

Perimeter of the circle is given by:

Perimeter = 2 π r

Substituting the values in the formula, we get that:

P = 2 × (3.14) × (14) m

P = 87.92 m.

Area of the circle is given by:

Area = π r²

Substituting the values in the formula, we get that:

Area = (3.14) × (14)²

A = 615.44 m²

Therefore, we get the perimeter of the circle as 87.92 m and area of the circle as 615.44 m².

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The proof for the decimal expansion d₁d₂d₃d₄.... is evaluated.

A number's decimal expansion is its base-10 representation (i.e., in the decimal system).

Now, as per the given question;

We focus on non negative decimal expansions as well as nonnegative real numbers. Every nonnegative decimal expansion, in our opinion, is short form for the limit of a constrained increasing sequential manner of real numbers.

Assume we're given a decimal expansion K. d₁d₂d₃d₄.... where K is a non-negative integer and each value of dj belongs to {0,1,2,3,4,5,6,7,8,9}.

Then Sn is defined as the increasing sequential of real numbers and Sn is also restrained by (sn < k + 1) .

Using Theorem; converges to a real number, which we usually write as K. d₁d₂d₃d₄....

Like. 3.33333 can be written as;

[tex]\lim _{n \rightarrow \infty}\left(3+\frac{3}{10}+\frac{3}{10^2}+\cdots+\frac{3}{10^n}\right)[/tex]

We use the following geometric series fact to calculate this limit:

[tex]\lim _{n \rightarrow \infty} a\left(1+r+r^2+\cdots+r^n\right)=\frac{a}{1-r} \quad \text { for } \quad|r| < 1 .[/tex]

Where a =3 and r = 1/10.

Similarly, for 0.9999.....it can also be written as

[tex]\lim _{n \rightarrow \infty}\left(\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}\right)=\frac{\frac{9}{10}}{1-\frac{1}{10}}=1 .[/tex]

Therefore, 0.9999... and 1.0000... are different decimal expansions for the same number.

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The correct question is-

For a decimal expansion K. d₁d₂d₃d₄....let (sn) be defined. Prove (sn < k + 1) for all n ∈ N. Hint:' [tex]\frac{9}{10}+\frac{9}{10^2}+\cdots+\frac{9}{10^n}=1-\frac{1}{10^n}[/tex]

The distance between the 2 points is 7.3 units.

So,

The formula for the distance between two points P(a, b) and Q(c,d) is:

Use the following formula for the points M(6, 16) and Z(-1, 14):

Which, when rounded to the nearest tenth, equals 7.3 (units).

Therefore, the distance between the 2 points is 7.3 units.

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The graph of the given linear function can be seen in the image below.

Here we want to graph the line:

y = 3x - 2  (I think this is the line, the image is really blurry).

To graph this line (or any line, actually) what you need to do is find two points on the line.

To do so, you need to evaluate the function.

If we use x = 0, then:

y = 3*0 - 2 = -2

So we have the point (0, -2)

If we use x = 1, then:

y = 3*1 - 2 = 1

So we have the point (1, 1)

Now just graph these two points, and then draw a line that passes through both of them, you should get something like the image below.

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Answer:

As a biological stain, iodine is useful for studying plant cells because it stains starch blue-black and in animal tissue, it can help in the demonstration of nuclei and cell membranes

Answer: Iodine is also a useful stain. When studying plant cells, iodine is used. Because it is a starch indicator, it reacts with starch and turns blue-black. Iodine can also be used as a stain on animal cells, making the cell membrane and nucleus appear more visible

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

little marks show that

eh and hg are the same size so

angle e and g are the same

angle h has a red box which means its 90 degrees

that means angle e and angle g are 45 degrees each

3x+6=45

3x=39

x=13

The solution to the division of the polynomial equation is [tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]

Polynomial long division is an extended form of the well-known arithmetic method of long division used in algebra to divide one polynomial with another polynomial of the same or lower degree. Addressing a difficult division issue and breaking it into manageable pieces makes it feasible to solve by using this method.

From the given information, we Divide:

[tex]=\dfrac{(-3x^3+5x^2-6x-7)}{(x+4)}[/tex]

[tex]=-3x^2+\dfrac{17x^2-6x-7}{x+4}[/tex]

Divide: [tex]\dfrac{17x^2-6x-7}{x+4}[/tex]

[tex]=-3x^2+17x + \dfrac{-74x-7}{x+4}[/tex]

Divide: [tex]=\dfrac{-74x-7}{x+4}[/tex]

[tex]=-3x^2+17x -74 +\dfrac{289}{x+4}[/tex]

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-25 is an integer and a rational number.

Now,

Hence, -25 is an integer and a rational number.

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Answer:

y = 1/3x + 3

please correct me if I'm wrong

Yes

We can tell if a triangle can exist based on the relationship between the side lengths.

Side Length Relationships

For a triangle to really exist, the sum of the smaller legs must be greater than the length of the longest leg. This can be expressed with the inequality a + b > c, where a and b are the shorter legs.

Now, we can plug the values we are given into this inequality.

Since the inequality is true, this triangle does exist.

Other Examples

One of the most important things to remember is that the sum of the shorter legs must be greater than, not equal to, the longest leg. So take the sides 4, 6, and 10.

This statement is not true. 10 is not greater than 10; they are equal. Thus, these sides cannot make a triangle.

Additionally, if the 3 numbers are Pythagorean triples, then it will be a right triangle. For example, the sides 5, 12, and 13 will create a right triangle.