#8. The half-life of a radioactive kind of tellurium
is 3 hours. How much will be left after 15 hours,
if you start with 60 grams of it?

The third term of this arithmetic sequence is 21.

eleventh term of an arithmetic sequence is 69.

a₁₁ = a + 10 d = 69

also sum of the first three terms is 45

the first three terms are a, a + d, a + 2d

a + a + d + a + 2d = 45

3a + 3d = 45

a + d = 15

a = 15 - d

so, a + 10 d = 69

15 - d + 10d = 69

9d = 69 - 15

9d = 54

d = 6

a = 15 - 6 = 9

a₃ = a + 2d

   = 9 + 2(6)

a₃ = 21

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Answer:

7-isoceles, 8- equilateral 9-scalene

Step-by-step explanation:

isoceles have 2 identical sides unlike scalene, where all sides have different lengths.

is obtuse and acute I think

The slope of the situation is 10.20. Answer (a) is correct.

The cost of the breakfast platter of 12 bagels is $10.20 and the cost of a gallon of coffee is $4.65.

The slope represents the rate of change between two variables, typically represented as y and x. In this case, it's not clear which variables we should use to calculate the slope. If we use the number of bagels as x and the cost as y, then the slope would represent the rate of change in cost per bagel.

Alternatively, if we use the gallons of coffee as x and the total cost as y, then we can calculate the slope. The total cost would be the sum of the cost of bagels and the cost of coffee, which is $10.20 + $4.65 = $14.85.

Using the formula for slope, which is (change in y) / (change in x), we can calculate the slope as follows:

slope = (change in cost) / (change in gallons of coffee)

= ($14.85 - $4.65) / (1 - 0)

= $10.20 / 1

= 10.20

Therefore, the slope of the situation is 10.20. Answer (a) is correct.

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Answer:

2(x+2)² - 18

Step-by-step explanation:

Given

2x² +8x-10

express in the form a(x + b)² + c

Take out common factor 2 from 2x² +8x-10 ==> 2(x² + 4x -5)

x² + 4x - 5 can be converted to the form (x + b)² + c as follows using complete the square technique

(x + b)² = x² +2bx + b²

Comparing  x² +2bx + b² and x² + 4x - 5 we can see that b = 2

So the expression becomes
x² + 4x - 5 = (x+2)³ + c
= x² + 4x + 4 + c

Therefore -5 = 4 - c

c = -5 -4 = -9

Therefore
x² + 4x - 5 = (x+2)³ -9

2(x² + 4x -5) = 2[(x+2)³ -9]

=2(x+2)² -18

ANSWER

Verify

2(x+2)² -18 = 2(x² +4x + 4) - 18 = 2x²+8x +8 - 18 = 2x² + 8x - 10
Thus verified

Answer:

5.18181818182

5.2 (nearest 10th)

Step-by-step explanation:

The tangent line is y=x-1 and differentiation of ln(x) is 1/x

What does differentiation in mathematics mean?

Differentiation is a technique for determining a function's derivative. In mathematics, the technique of differentiation is used to determine the instantaneous rate of change in a function dependent on one of its variables.

                            The most prevalent example is velocity, which is the rate at which a distance changes in relation to time.

The ratio of the vertical to the horizontal distance between any two points on it  is called slope of ray or line or line segment in analytical geometry.

y-y1 = m(x-x1)

If the function passes through (1,0)  and the slope equals to 1 is:

y-0 = 1(x-1)

y=x-1

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The complete question is -

Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.

Answer:

Answer provided in image May it help you !!!

Step-by-step explanation:

The algebraic expression can be written as:

(11 + g)/9

Here we want to write:

"divide the sum of 11 and g by 9"

As an algebraic expression.

The sum of 11 and g can be written as:

(11 + g)

Where g is the variable in this problem.

And now we just divide that by the number 9, then the algebraic expression is the next one:

(11 + g)/9

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The number of different unique cleaning teams should be 1540.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, A class has 10 boys and 12 girls and 3 students are chosen at random.

So, the team of 3 can be chosen as 3 boys, 3 girls, 1 boy 2 girls, and 1 girl and 2 boys and the total teams will be the sum of different combinations which is,

= [tex]^{10}C_3 + ^{12}C_3 + ^{10}C_1\times^{12}C_2 + ^{12}C_1\times^{10}C_2[/tex].

= (10×9×8)/6 + (12×11×10)/6 + 10×(12×11)/2 + 12×(10×9)/2.

= 120 + 220 + 660 + 540.

= 1540.

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A plurality of magnitude can represent the property of number or amount, which exhibits both discontinuity and continuity and in the given situation, we would pay a quantitative amount to the seller.

A property called quantity or amount can take the form of a plurality of magnitude, which shows both discontinuity and continuity.

Comparing quantities can be done by using phrases like "greater," "less," or "equal," as well as by assigning a numerical value that is a multiple of the unit of measurement.

Among the well-known examples of quantitative qualities are mass, time, distance, heat, and angle.

Along with quality, substance, change, and relationship, quantity is one of the fundamental categories of things.

Some quantities serve as states (properties, dimensions, qualities) of things like heavy and light, long and short, broad and narrow, little and large, or much and little, while others are such by their very nature (as numbers).

Therefore, in the given situation, we would pay a quantitative amount to the seller.

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Correct question:

J.D. Power and Associates surveys new automobile owners to learn about the quality of recently purchased vehicles. The following questions were asked in the J.D. Power Initial Quality Survey, May 2012.

What Price did you pay?

The minimum total cost for the company if all of the order constraints are fulfilled is given as follows:

$25.

The cost function is given as follows:

C = 3x + 2y.

Meaning that:

The relevant restrictions to minimize the costs are given as follows:

Since an item y costs less than an item x, considering the second bullet point above, the cost is minimized with an equal amount of x and y.

From the first restriction, they must have at least 10 amounts, hence the cost is minimized with:

x = 5 and y = 5.

And the cost is of:

C = 3 x 5 + 2 x 5

C = $25.

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Answer:

  (3, 6)

Step-by-step explanation:

You want the coordinates of the orthocenter of triangle WXY with vertices W(2,7), X(3, 4), and Y(6, 7).

The orthocenter is the point where the altitudes of the triangle meet. An altitude is the line through a vertex that is perpendicular to the opposite side.

This is an acute triangle, so the orthocenter is within the boundaries of the triangle.

We note that side WY of the triangle is a horizontal line, so the orthocenter will lie on the vertical line through point X. The x-coordinate of point X is 3, so that vertical line has equation x=3.

Side XY can be seen on the graph to have a slope of 1. Or, you can compute it from the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (7 -4)/(6 -3) = 3/3 = 1

Then the point-slope equation of the altitude to that line will have the opposite reciprocal slope, and will go through point W(2, 7):

  y -7 = -1(x -2)

The y-value of the point of intersection of the altitude through W with the altitude through X will be the solution to ...

Substituting for x in the second equation, we have ...

  y -7 = -3 +2

  y = 6 . . . . . . . . . . add 7

The orthocenter is (x, y) = (3, 6).

__

Additional comment

The orthocenter of a right triangle is the vertex where the right angle is located. The orthocenter of an obtuse triangle is outside the triangle.

Answer:

You can put this solution on YOUR website!

100 >= 20t (that's "more than or equal to")

Divide each side by 20

5 >= t [5 is more than or equal to t]

or, conversely, t <= 5 [t is less than or equalequal to 5]

Answer: 1/5

Step-by-step explanation:

The potential energy of the water in a lake is 57 trillion N × m, which is 57 trillion joules (J).

Gravitational potential energy applies in this situation. G P E = m g h is the formula for gravitational potential energy, where: mg stands for weight or mass times gravity (w). The height to which an object can fall before kinetic energy replaces potential energy is denoted by the symbol h. In the example of the lake, we first determine the amount of water using the equation for the volume of a typical cylinder in order to determine the weight of the cylinder: V cy l = π r²L , The weight density of the water per cubic foot, which is about 62 lb, can then be multiplied by this volume: W(water) = (Volume) (Density)

W (water) = (28,000,000 ft² ⋅ 40ft) ( 62 lb ÷ ft³ )

W (water) = 69,440,000,000 lb

To calculate the potential energy, multiply this weight by the height. GPE=mgh

GPE=Wh=(69,440,000,000lb)(600ft)

GPE=41,644,000,000,000ft⋅lb

matching the level of precision by rounding the response to two significant digits. 4.2X10¹³ft⋅lb , or 42 trillion ft-lb.

Because joules are measured in N × m units, multiply the result by fractional equivalencies. 42trillionft × lb × (4.45N ÷ lb) × (m ÷ 3.28ft)

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The probability that fund-raising event is a success and total contributors exceeds $5,000 is 0.0351  or 3.51%

Number of family members = 40

Mean of individual contributions for each family is normally distributed is $115 (μ) and standard deviation(σ) is $35. It is also given that the organizers would call this event a success if the total contributions exceed $5,000

Mean = [tex]\frac{5000}{40}[/tex]

Mean = 125

P-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

P(mean > 125) = P( 2 > [tex]\frac{(125 - 115)\sqrt{40} }{35}[/tex] )

                      = P(2 > 1.81)

                      = 1 - P(2 < 1.81)

1.81 has a pvalue of 0.9649

                      ≅ 0.0351

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Answer:$2.97

Step-by-step explanation: 35 divided by 12 = 2.97

Answer:

The weight is 95.53 ounces of bluegill which has a length of 9.5 inches using linear regression.

Step-by-step explanation:

good luck to you

Answer:

A collection of facts, such as numbers, words, measurements, observations.

Step-by-step explanation:

The volume of the resulting solid is 3,280.953 cm3.

The volume of the resulting solid is calculated by subtracting the volume of the inner sphere (the hole) from the volume of the outer sphere (the ball). The volume of a sphere is calculated by the formula V=4/3πr3. Therefore, the volume of the outer sphere is V1=4/3π(13)3=4,714.286 cm3. Similarly, the volume of the inner sphere is V2=4/3π(7)3=1,433.333 cm3. Subtracting V2 from V1 gives the volume of the resulting solid as V3=4,714.286 - 1,433.333=3,280.953 cm3. Therefore, the volume of the resulting solid is 3,280.953 cm3.

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Answer:

Step-by-step explanation:

can you include a picture please

Even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.

Freelancer, freelancer, or freelance worker are phrases frequently used to describe someone who is self-employed and isn't necessarily long-term dedicated to a certain employer.

Others work independently or use websites or professional associations to find work.

Freelancers are occasionally represented by a business or a temporary agency that resells their services to clients.

Independent contractors must always pay taxes on their wages, regardless of how much they make.

The term "freelancing" is most frequently used in the culture and creative industries, and use of this term may indicate participation in these sectors, even though the term "independent contractor" would be used in a different register of English to designate the tax and employment classes of this type of worker.

Therefore, even if we earned less than the standard deduction, we nonetheless file taxes since, regardless of their income, freelancers are always required to pay tax on their earnings.

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The unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.

The unit kilowatt-hour (kWh) is a measure of energy, not power. Energy is a measure of the amount of work that can be done, and is usually measured in joules. Power, on the other hand, is a measure of the rate at which energy is transformed, and is usually measured in watts.

A kilowatt-hour is the amount of energy used or produced when a power of one kilowatt is used for one hour. For example, if a 100-watt light bulb is left on for 10 hours, it will have used

100 * 10 = 1000 watt-hours or 1 kilowatt-hour of energy.

So to summarize, the unit kilowatt-hour measures the amount of energy used or produced, whereas the rate at which energy is transformed is measured in kilowatts.

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Answer: $33.3

Step-by-step explanation:

1kg of beans cost $3.70 then $3.70x9= $33.3.

Hope this helps.

A system of 4 linear equations in 3 variables x, y, z can have at most one solution.

It is because a system with more than three equations and only three variables will not have a unique solution due to the fact that the dimension of the solution space of 3-dimensional equations is three, so adding an extra equation will result in an over-determined system.

In other words, there are not enough variables in the system to meet the requirements of all the equations, which leads to an over-determined system where there is either no solution or a unique solution. If the system has exactly two solutions, it means that the solution space of the system of equations has a dimension greater than 3, which contradicts the fact that the dimension of the solution space of a system of 3-dimensional equations is 3.

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The short sleeve shirts sold by haley were 405

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: Haley's clothing store sold 540 shirts with ratio of short sleeve to long as 3:9

let 3x and 9x long and short sleeves were sold respectively

Then we have

3x+9x=540

12x=540

x=540/12

x=45

Thus 3x=135 and 9x=405

Hence, The short sleeve shirts sold by haley were 405

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With his average speed of 3mph, Viktor should leave his house by 6:36 am to arrive at the skaring rink on time.

From the case, we know that:

Average speed = 3.0 mph

Distance = 1.2 miles

Arrival time = 7:00 am

Departure time?

Using the average speed concept, we know that average speed can be calculated by dividing the travel distance with the travel time, or it can be formulated as:

Average speed = distance : travel time

3.0 = 1.2 : travel time

travel time = 0.4 hours

After finding the travel time Viktor spend to go from his house to the skating rink, we need to find the departure time for him to arrieve at the skating rink on time. However, we need to convert the travel time into minutes first.

Travel time = 0.4 hours

Travel time = 0.4 x 60 minutes

Travel time = 24 minutes

Arrival time = Departure time + Travel time

7:00 = Departure time + 24 minutes

Departure time = 6:36 am or 24 minutes before 7:00 am

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Answer:

8595.4

Step-by-step explanation:

The formula for volume of cylinder is: V = [tex]\pi[/tex][tex]r^{2} h[/tex]

[tex]\pi[/tex] = 3.14

radius = 12

height = 19

plug in the numbers which would give us = 3.14(12)^2(19)

which gives us 8595.4

The function graphed on the paper could be a quadratic function which has the two real roots equal to 3 and 9.

A parabola is a two dimensional figure on a plane which is U shaped and any point on the parabola is at an equal distance from a fixed point called focus and a fixed line called directrix.

The graph of a function is parabola when the function is quadratic.

Quadratic functions are of the form f(x) = ax² + b x + c.

Given that, the parabola touches the x-axis at 3 and 9.

This indicates that roots of the quadratic equation are 3 and 9.

That is, f(x) = 0, when x = 3 and x = 9.

It may be of the form f(x) = (x - 3)(x - 9) = x² - 3x - 9x + 27 = x² - 12x + 27.

So the function representing the graph on the paper is a quadratic function whose roots are 3 and 9 and the function could be of the form f(x) = x² - 12x + 27.

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