What is the range? The range is __

The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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Answer:

Step-by-step explanation:

volume of the sphere=4/3 π (4)³=256 /3 π=256/3 ×3.14≈267.95 m³

Answer:

i hope this helpes

Step-by-step explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer:

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}

The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Answer:

661.39

Step-by-step explanation:

Answer:

  a) 1/5 are Primary 6 girls

  b) 120 Computer Club pupils

Step-by-step explanation:

For problems like this, we assume the designated groups are one of two groups: (boys, girls), (Primary 6, Not Primary 6). That means the fractions in each group total 1.

  3/4 are boys means 1-3/4 = 1/4 are girls.

If 4/5 of the girls are Primary 6, then (4/5)(1/4) = 1/5 of all club pupils are Primary 6 girls

__

1-4/5 = 1/5 of the girls in the club are not Primary 6 girls. 1/4 of the club members are girls, so the fraction of club members who are not Primary 6 girls is ...

  (1/5)(1/4) = 1/20 . . . . club pupils who are girls not from Primary 6

This fraction is 6 girls, so the total number of club pupils is ...

  20×6 = 120 . . . pupils in the computer club

Answer:

Therefore, the earliest time to take the next pill is after 10.85 hours and the latest time is before 15.14 hours have passed.

Step-by-step explanation:

The concentration of the drug in your system after ingesting 100.0 mg can be calculated using the formula:

C = D / V

where C is the concentration, D is the dose, and V is the volume of distribution (assumed to be constant).

At the initial time, t = 0, the concentration is:

C(0) = 100.0 mg / V

After one half-life, t = 16 hours, the concentration is:

C(16) = C(0) / 2 = 50.0 mg / V

After two half-lives, t = 32 hours, the concentration is:

C(32) = C(16) / 2 = 25.0 mg / V

After three half-lives, t = 48 hours, the concentration is:

C(48) = C(32) / 2 = 12.5 mg / V

To find the earliest and latest times to take the next 100.0 mg pill, we need to calculate the concentration at those times and make sure it stays between 20.0 mg and 140.0 mg.

Let's first find the earliest time at which the concentration drops below 20.0 mg.

20.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 20.0 = 2.5

x/16 = log2(2.5)

x = 16*log2(2.5) = 16*0.678 = 10.85

So the earliest time to take the next pill is after 10.85 hours.

Now let's find the latest time at which the concentration goes above 140.0 mg.

140.0 mg / V = C(16 + x) = 50.0 mg / V / (2^(x/16))

Solving for x:

2^(x/16) = 50.0 / 140.0 = 0.3571

x/16 = log2(0.3571)

x = 16*log2(0.3571) = -15.14

So the latest time to take the next pill is before 15.14 hours have passed.

Step-by-step explanation:

------------->Then f(-2)

= f(x) : 3x2 + 2x - 8

= f(-2) : 3(-2)2 + 2(-2) - 8

= f(-2) : (-6)2 + (-4) - 8

= f(-2) : (-12) + (-4) - 8

= f(-2) : (-16) - 8

Step-by-step explanation:

f(x) = 3x2 + 2x – 8

———» Then f(-2)

f(-2) = 3(-2)^2 + 2(-2) - 8

f(-2) = 3((-2) × (-2)) + (2 × (-2)) - 8

f(-2) = 3(4) + (-4) - 8

f(-2) = (3 × 4) + (-4) - 8

f(-2) = 12 + (-4) - 8

f(-2) = 8 - 8

f(-2) = 0

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.

If the body of the mass (m) is moving with a velocity (v), then the body possesses the energy which is known as kinetic energy. The SI unit of the kinetic energy is Joule. Then the formula is given as,

KE = 1/2 x mv²

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec is given as,

KE = 1/2 x 1500 x 31²

KE = 720,750 Joule

KE = 720 kJ

The kinetic energy of a 1500 kg pick-up truck traveling at 31.0 m/sec will be 720 kJ.

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Answer:

Answer:00

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.

b=0b=0

3b−5=03b-5=0

Set the first factor equal to 00.

b=0b=0

Step-by-step explanation:

The result can be shown in multiple forms.

Exact Form:

b=0,53b=0,53

Decimal Form:

b=0,1.¯6b=0,1.6‾

Mixed Number Form:

b=0,123b=0,123

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Let's call the measure of the larger angle as x, and the measure of the smaller angle as y.

When two angles are complementary, their sum is equal to 90º, therefore

The larger of the two is 30° more than twice the smaller, writing this as an equation, we have

If we substitute this expression for x in the first equation, we have

Using this y-value on the first expression, we have

Then, the larger angle is 70º and the smaller angle is 20º.

Answer:

i believe it is b d c

Step-by-step explanation:

Answer: The perimeter of a rectangle is found by adding up all four sides. For this rectangle with a base of 9 ft and a height of 10 ft, the two base sides have a length of 9 ft each, and the two height sides have a length of 10 ft each. Therefore, the perimeter is:

P = 2(9 ft) + 2(10 ft) = 18 ft + 20 ft = 38 ft

So the perimeter of the rectangle is 38 feet.

Step-by-step explanation:

All of these equations are in the form Ax+By = C

The solution of the given system of equations is (-1, -2).

We are aware that a linear system of equations can be solved using a substitution method.

The intersection of the two lines represents the system's solution.

The given equations are-

y = 3x+1 ...eq 1

y = -2x-4  ...eq 2

Put the value of eq 1 in eq2 .

3x+1  = -2x-4

3x + 2x = -4 - 1

5x = -5

x = -5/5

x = -1

Put the x in eq 1.

y = 3(-1)+1

y = -2

Thus, the solution of the given system of equations is (-1, -2).

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The complete question is-

What is the solution to the system of equations-

y=3x+1 ;

y=-2x-4

the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99m².

Why it is and what is diameter?

The diameter of the circle is 17 meters, which means the radius is half of the diameter, or 8.5 meters.

The formula for the area of a circle is:

A = πr²2

where A is the area and r is the radius.

Substituting the value of the radius into the formula, we get:

A = 3.14 x 8.5²2

A = 3.14 x 72.25

A ≈ 226.99

Therefore, the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99 m².

In geometry, the diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord (a line segment connecting any two points on a circle) of the circle, and it divides the circle into two equal halves, also known as hemispheres.

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Answer: -1

Step-by-step explanation:

because x equals to -2, thus the first term is -2 * -2 = 4.

For the second terms,^3 and the square root canceled, so you got the answer still y, which is also -5. Therefore, you add them. and you got the answer (4) + (-5) = -1

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

In prοbability,  experiment refers tο prοcess that generates οutcοme οr event, which cannοt be predicted with certainty. An experiment in prοbability may invοlve flipping  cοin, rοlling  die, drawing  card frοm deck, οr any οther randοm prοcess.

Part A:

The tοtal number οf cards in  hat is:

12 (red) + 17 (blue) + 14 (purple) + 7 (yellοw) = 50 cards

theοretical prοbability οf drawing purple card frοm hat is are:

P(purple) = number οf purple cards / tοtal number οf cards

P(purple) = 14 / 50

P(purple) = 0.28 οr 28%

Part B:

theοretical prοbability οf drawing purple card frοm  hat are 0.28 οr 28%.

The experimental prοbability οf drawing a purple card is:

P(exp) = number οf times a purple card is drawn / tοtal number οf trials

P(exp) = 324 / 1080

P(exp) = 0.3 οr 30%

therefοre, difference between  experimental prοbability and theοretical prοbability is:

P(exp) - P(theοretical) = 0.3 - 0.28

P(exp) - P(theοretical) = 0.02 οr 2%

Therefοre, the experimental prοbability is 2% greater than the theοretical prοbability.

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

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The formula to calculate the volume of a cylinder is

The formula to calculate the volume of a hemisphere is

Hence, the volume of the composite shape can be calculated by using the formula

From the question, we have the following parameters:

r = 12/2 = 6cm (radius is half of the diameter)

h = 26cm

Substituting, using pi as 22/7, we have

The volume is given as 3392.9 cm³.

The correct option is the FIRST OPTION.

Answer: 5

Step-by-step explanation: Diana makes 3 batches of biscuits usinusing 15 cups of flour. 3 batches 5,10,15

i think

1. For every ounce of fertilizer 2.5 more pepper pods can be expected.

2. When no fertilizer is added, 4 pepper pods can be expected.

3. 8 pepper pods. Plug in 1.6 for X: y=2.5(1.6)+4=8

Answer:

1. slope= 2.5

2. y-intercept= 0,4

3.  Plug in 1.6 for X: y=2.5(1.6)+4=8 so it would be 8 .

The equation of a line is y  = -6x + 8 if the line is perpendicular to the line t and passes through (2, -4).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The slope of the line t:

M = 1/6

The slope of the line which is perpendicular to the line t

m = -6

The equation of the line:

y + 4 = -6(x - 2)

y = -6x + 12 - 4

y  = -6x + 8

Thus, the equation of a line is y  = -6x + 8 if the line is perpendicular to the line t and passes through (2, -4).

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f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.

So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.

To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.

Applying the power rule, we differentiate each term separately:

f'(x) = d/dx (x^1) + d/dx (2)

The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.

The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.

Therefore, f'(x) = 1 + 0 = 1.

So, the derivative of f(x) = x + 2 is f'(x) = 1.

To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).

In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).

Applying the power rule and the constant multiple rule, we differentiate each term separately:

f'(x) = d/dx (2 * x^(-2))

Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.

Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.

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Answer:

135 because if you put it in a caluclator that is what you get

We have the next information

the selling cost is $0.75 per cup

They spend $15.62 on all the ingredients

each cup cost $0.04

The profit for each cup will be

In order to break even

In order to break even, they must sell 22 cups

In order to begin making a profit, they must sell 23 cups

Answer:

6.88 is what I think you're looking for

Step-by-step explanation:

Answer: 15

Step-by-step explanation:

If he sold 1/4 then 40 x 1/4 = 10

So he has 30 left

30 x 1/2 = 15

The neighbor bought 15

Using the formula, we can conclude that the 15th term in the following sequence is 59.

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.

The common difference in that mathematical progression is the constant difference.

n: The method for determining the nth term is used to locate a particular term in an arithmetic series.

Step 1:

An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

Therefore, enter the values a = 2 and d = 3 into the formula to determine the nth term.

So, the formula is:

an = a + (n – 1)d

Now, insert the values as follows:

an = a + (n – 1)d

a15 = 3 + (15 – 1)4

a15 = 3 + (14)4

a15 = 3 + 56

a15 = 59

Therefore, using the formula, we can conclude that the 15th term in the following sequence is 59.

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Correct question:

Find the 15th term in the sequence if a1= 3 and d= 4