juliana wrote the terms below. –8, –4, 0, 4, 8, 12 what do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence

Answer: yes

Step-by-step explanation:

12    3

4     1

to get to 3 from 12 you divide by 4 and to get from 4 to 1 you also divided by 4

Solution

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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At the optimal solution, 10 trucks will travel the route from Charlotte to St. Louis.

At the optimal solution, the number of trucks that will travel the route from Charlotte to St. Louis will depend on various factors such as the demand for goods, the capacity of the trucks, and the cost of transportation.

To find the optimal solution, we can use the following formula:

Optimal Solution = (Demand for goods) / (Capacity of trucks) * (Cost of transportation)

By plugging in the values for the demand for goods, the capacity of the trucks, and the cost of transportation, we can calculate the optimal number of trucks that will travel the route from Charlotte to St. Louis.

For example, if the demand for goods is 1000 units, the capacity of the trucks is 100 units, and the cost of transportation is $1 per unit, the optimal solution would be:

Optimal Solution = (1000 units) / (100 units) * ($1 per unit) = 10 trucks

Therefore, at the optimal solution, 10 trucks will travel the route from Charlotte to St. Louis.

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The distance Chyna ran is 7 1 / 2 kilometres.

Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5

kilometres

Therefore, the distance Chyna ran in kilometres can be calculated as follows:

Therefore,

Distance Ronaldo ran = 6 3 / 5  = 33 / 5 kilometres

Hence,

Distance Chyna ran = 33 / 5 + 9 / 10

Distance Chyna ran = 66 + 9 / 10

Distance Chyna ran = 75 / 10

Therefore,

Distance Chyna ran = 7 5 / 10

Distance Chyna ran = 7 1 / 2 kilometres

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The measure of the angle x in the isosceles triangles are;

x = 44°

1) x = 80°

An isosceles triangle is a triangle that has a pair of congruent sides and a pair of congruent angles.

The measure of the specified angle are found as follows;

The isosceles triangle that has 92° as the exterior angle, indicates that we get;

Base angles of the isosceles triangle = (180° - 92°)/2 = 44°

Vertical angles theorem, indicates that the vertical angle and the base angles of the second isosceles triangle are congruent.

Base angles of the second isosceles triangle = 44°

1) The angle adjacent to the angle x is a base angle of the isosceles triangle that has a base angle of 70°

The vertex angle of the isosceles triangle = 180° - 2 × 70° = 40°

The measure of the section of the indicated 90° angle that is a part of the isosceles triangle that has angle x as the vertex angle = 90° - 40° = 50°

The measure of angle x found using the relationship between the angles in an isosceles is; x = 180° - 2 × 50° = 80°

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Answer:

5x

Step-by-step explanation:

NOte: it is an expression and not an equation as originally asked.

"Product" means the answer to a multiplication of two numbers.

You are asked to write the answer to 5 and a number being multiplied together.

Let the unknown number be

x

The product is therefore

5x

x

=

5x

Answer:

\(v = \frac{n+y+16}{2}\)

Step-by-step explanation:

2(v-8) = n+y

Distribute

2v-16 = n+y

Move -16 to the other side

2v = n+y+16

Divide everything by 2

\(v = \frac{n+y+16}{2}\)

Answer:

\(v = \frac{n+y}{2} +8\)

Step-by-step explanation:

To find the expression that represents v, we have to isolate v. Our first step is distributing the 2 to both v and 8.

(2(v) - 2(8))

2v - 16 = n + y

Now add 16 to both sides.

2v = n + y + 16

Now divide both sides by 2, this will isolate v and give us the initial value of it.

\(v = \frac{n+y}{2} +8\)

Step-by-step explanation:

It doesn't have neither the greater than or equal to or less than or equal to signs so

To use long division in polynomials, we follow steps similar to normal long division, but we look for the terms from higher degree to lower.

We are dividing:

By:

We want to multiply the divisor by some expression that will make the higher term equal to the higher term of the dividend. The higher term of the dividend is 4x³, to get to that, we can multiply the divisor by 2x²:

Now we have the same term, so we just substract what we have got from the dividend:

Notice that we don't have a third degree term anymore.

So, until now we have done:

- Multiplied the divisor by 2x²

- Got a remainder of -5x² + 3

Now, we just repeat with the remainder.

We want to multiply 2x - 1 so that the higher term is -5x², so we can multiply by -5x/2:

And we do the substraction:

So, now we have got:

- Multiplied the divisor by 2x² and then by -5x/2

- Got a remainder of -5x/2 + 3

Now, we repeat once more:

To get -5x/2, we multiply the divisor by -5/4:

And we substract from the remainder:

So, we have done:

- Multiplied the divisor by 2x² then -5x/2 then -5/4

- Got a remainder of 7/4

This means that th result of the division is:

And the remainder is:

But, the answer wants us to write what the dividend is equal to.

Let's write first in the division form:

Notice that we result is the quotient plus the remainder divided by the divisor.

If we multiply both sides by the divisor, we will get:

That is the answer.

The benefits of using the theoretical capacity for Zippy, Inc. include providing a maximum production potential based on ideal conditions, aiding in long-term planning, and setting performance benchmarks. Practical capacity considers unavoidable interruptions and breakdowns, providing a more realistic estimate. The negative aspect of a master-budget denominator level is the potential for unused capacity costs, while the positive aspect is using a predetermined cost base for pricing decisions.

Theoretical capacity, based on three shifts and completion of five motorcycles per shift, gives Zippy, Inc. a maximum production potential of 5,400 units per year. This capacity measure helps in long-term planning, resource allocation, and setting performance benchmarks. On the other hand, practical capacity takes into account unavoidable interruptions, breakdowns, and other factors that can impact production. It provides a more realistic estimate of 3,840 units.

Regarding cost-based pricing, the negative aspect of a master-budget denominator level is that it may lead to unused capacity costs. If the estimated demand falls below the master-budget level, there could be underutilized resources, resulting in economic costs for the company. However, the positive aspect of using a master-budget denominator level is that it provides a predetermined cost base for pricing decisions. It helps in setting prices that ensure the company's costs are covered and profitability is achieved.

In summary, theoretical capacity aids in long-term planning and setting benchmarks, while practical capacity considers interruptions. The negative aspect of a master-budget denominator level is unused capacity costs, but it provides a predetermined cost base for pricing decisions, ensuring cost recovery and profitability.

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Observational studies have their merits in certain scenarios, when determining the relationship between two variables, randomized experiments are generally preferred for their ability to establish causal links.

Conducting a randomized experiment is often preferable to an observational study when determining the relationship between two variables. This preference arises due to several reasons that provide stronger evidence for causality and help address potential confounding factors. To illustrate this, let's consider an example involving the effects of a new medication on depression.

In a randomized experiment, researchers can randomly assign participants into two groups: a treatment group that receives the new medication and a control group that receives a placebo or standard treatment. By randomizing the assignment, the researchers ensure that any differences between the groups are due to chance, rather than preexisting characteristics. This randomization helps create comparable groups, reducing the potential for confounding variables.

In contrast, an observational study involves observing individuals as they naturally fall into groups based on their exposure to a variable. In our example, researchers might observe individuals who self-select into taking the new medication or those who choose not to take it. The problem with observational studies is that individuals in different groups may have preexisting differences, making it difficult to attribute any observed effects solely to the medication. Confounding variables, such as underlying health conditions, lifestyle factors, or socioeconomic status, can impact the outcomes and confound the results.

Randomized experiments allow researchers to control and manipulate the independent variable (in this case, the medication) while keeping other factors constant. This control enables them to draw stronger causal conclusions about the relationship between the variables. By comparing the outcomes of the treatment group with the control group, any differences can be more confidently attributed to the medication's effects.

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Answer:

  graph several points and draw a curve through them

Step-by-step explanation:

First of all, I would remove the common factor of 2 from the coefficients. This makes it easier to see how the equation might be factored.

  y = 2(x^2 +8x +15)

The constant 15 has factors 1, 3, 5, 15. The two that add up to 8 are 3 and 5, so this can be further factored as ...

  y = 2(x +3)(x +5)

This tells you the x-intercepts (where y=0) are x=-3 and x=-5.

__

The line of symmetry is halfway between, at x = -4. The vertex value is the value of y at that point:

  y = 2(-4+3)(-4+5) = 2(-1)(1) = -2

So, the minimum is (-4, -2). The graph crosses the x-axs at x=-5 and -3. The overall factor of 2 tells you this is expanded vertically by a factor of 2, so the curve goes up by double the square of the distance from the axis of symmetry: points (-2, 6), (-1, 16), and their reflections across the line of symmetry, (-6, 6), (-7, 16) are all on the curve.

__

So, the graph will start with the points you know:

  (-4, -2), (-5, 0), (-3, 0), (-6, 6), (-2, 6), (-7, 16), (-1, 16)

Then you draw a smooth curve through them.

__

Personally, I like to use a graphing calculator to draw the graph.

Answer:

Step-by-step explanation:

diameter = circumference / π

= 31/π

= 9.9 ins to nearest tenth

If angle m∠KLJ = 78° then m∠OFG = 78°.

The angle o a straight line

An angle is the parent shaped by using rays, referred to as the edges of the attitude, sharing a not unusual endpoint, referred to as the vertex of the attitude. Angles shaped via two rays lie inside the plane that includes the rays. Angles are also shaped through the intersection of two planes. those are known as dihedral angles.

The angle in a straight line says that the sum of all the angles on a straight line is 180°.

opposite vertical angle is the two opposite angles on a parallel line at the point of intersection.

         angle ∠KLJ = 78°°   (opposite vertical angle).

The angle on a straight line is 180°

         angle∠OFG = 78°.

angle ∠KLJ =∠OFG = 78°. (parallel angles)

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It will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

What is Compound Interest ?

Compound interest refers to the process of earning interest on both the initial principal amount as well as any accumulated interest from previous periods. In other words, it is the interest that is earned on the interest that has been accumulated over time.

We can use the formula for compound interest to solve this problem.

Where:

A = the final amount

P = the initial amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this problem, we have:

P = $250

r = 0.06% = 0.0006 (as a decimal)

n = 12 (since the interest is compounded monthly)

A = 3P = $750

Substituting these values into the formula, we get:

750 = 250\((1 + 0.0006/12) ^{12t}\)

Dividing both sides by 250, we get:

3 =\((1 + 0.0006/12) ^{12t}\)

Taking the natural logarithm of both sides, we get:

㏒(3) = 12t ㏒(1 + 0.0006÷12)

Solving for t, we get:

t = ㏒(3)/(12 ㏒(1 + 0.0006÷12))

Plugging this into a calculator, we get:

t ≈ 387.3 months

Therefore, it will take about 387.3 months (or about 32.3 years) to triple the balance of the account.

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The fraction of shirts that are either black or white in Tamara's clothing shop is 1/2.

Let's assume there are 100 shirts in Tamara's clothing shop. Given that 1/4 of the shirts are black and another 1/4 are white, we can calculate the number of black shirts and white shirts separately.

Number of black shirts = (1/4) * 100 = 25

Number of white shirts = (1/4) * 100 = 25

To find the fraction of shirts that are either black or white, we need to add the number of black shirts and white shirts and divide it by the total number of shirts.

Total number of black or white shirts = Number of black shirts + Number of white shirts = 25 + 25 = 50

Fraction of shirts that are either black or white = (Total number of black or white shirts) / (Total number of shirts) = 50/100 = 1/2

Therefore, the fraction of shirts that are either black or white in Tamara's clothing shop is 1/2.

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Step-by-step explanation:

u need to give the full question

Answer:

A and C

Step-by-step explanation: Edge 2021

The statements which are true about the given rational equation is:

This refers to an equation which has fractions which contains polynomials and can be solved by reducing the fractions to solve the inequality.

With this in mind, we can see that options A and C are both solutions to a rational equation because of their equality of their solutions.

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Answer:

b = 4

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here ( h, k ) = (2, 5 ) , then

y = a(x - 2)² + 5

to find a substitute any point on the parabola into the equation

using (0, 1 ) then

1 = a(0 - 2)² + 5 ( subtract 5 from both sides )

- 4= a(- 2)²= 4a ( divide both sides by 4 )

- 1 = a

then

y = - ( x - 2)² + 5

   = - (x² - 4x + 4) + 5

    = - x² + 4x - 4 + 5

    = - x² + 4x + 1 ← in the form ax² + bx + c

with b = 4

Answer:If im correct the answer is C

Step-by-step explanation:

The probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.  

You can use the central limit theorem to approximate the sample distribution of the sample mean.

The mean of the sample distribution is a rise to the population mean (135 mm)

 the standard deviation of the test distribution is a rise to the population standard deviation isolated by the square root of the test measure, which is \(5/√42\) ≈ 0.7689 mm.

To find the probability that the sample mean is greater than 135.4 millimeters, use the sample distribution to standardize the sample mean and use the standard normal distribution. That is,

\(z = (x - μ) / (σ / √n) = (135.4 - 135) / (5 / √42) ≒ 1.0607\)

where x = sample mean, μ = population mean, σ =population standard deviation, n=sample size, and z =standard value.

The probability that the sample mean exceeds 135.4 millimeters can be found by using a standard normal distribution table or calculator,

to find the area to the right of the Z value of 1.0607. This range is approximately 0.1446 or 14.46%.

Therefore, the probability that the sample mean exceeds 135.4 millimeters is approximately 0.1446.

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its all real solution your right

ex, 1.4

There are 5,040 possible ways to select a president, vice president, treasurer, and secretary from a group of 10 students, where the order in which the positions are filled matters.

Given,

For a group of 10 students,

The number of possibilities for selecting a president, vice president, treasurer, and secretary from a group of 10 students can be expressed using permutation notation as:

P(10, 4) = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040

This means that there are 5,040 possible ways to select a president, vice president, treasurer, and secretary from a group of 10 students, where the order in which the positions are filled matters.

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(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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The functions are as follows:

Function f: R → R, f(x) = x²

Onto function: The function f is not an onto function since some negative numbers do not have square roots in real numbers.

One-to-one function: The function f is not a one-to-one function since for each positive number "x", there exist two values that we can input and get that positive number "x" output.

Example: Consider -4 which is a negative number. It doesn't have a square root in real numbers.

Function g: R → R, G(x) = x³

On to function: The function g is onto since every real number can be obtained by the function g.

One-to-one function: The function g is one-to-one since for each input "x" there is only one output.

Example: Consider the values x = 2 and x = -2. On inputting these values into the function, we get outputs 8 and -8 respectively. Thus, we get two different outputs for the same value h(x) = x³Function h: Z → Z, h(x) = x³On to function: The function h is onto since every integer has a cube root.

One-to-one function: The function h is not a one-to-one function since for each negative number "x", there exist two values that we can input and get that negative number "x" output.

Example: Consider the input -2. On input this value into the function, we get the output -8. But -(-2)³ = -8. Thus, we get two different inputs for the same value h(x) = x³.

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Answer: f(-2) = -7

Explanation: If f(x) = 3x - 1, then f(-2) is 3(-2) - 1 which simplifies to -7.

So the value of the function at -2 is -7.