What is the 5th term of the sequence f(1)=2f(n)=−3f(n−1)​

A. 54
B. -162
C. 162
D. -54

Answer:

140.

Step-by-step explanation:

Answer:140

Step-by-step explanation:

The number of ways are there to arrange these people in a row if the men and women alternate is 2880.

The concepts of counting are permutation and combination, and they are used in a variety of contexts. A permutation is a list of the many configurations that may be created from the given set of items. Details are crucial in permutation because the order or sequence is crucial.

The techniques used to count the number of outcomes that can occur under different circumstances are permutation and combination. Combinations and permutations are also referred to as arrangements and choices, respectively. The sum rules and product rules may be used to conveniently apply counting according to the basic idea of counting.

5 men and 5 women sit around a table so that they all seat alternately

Formula used:

n! = n x (n - 1) x (n-2) x....... (n-n1)

According to the question,

5 Men sit alternate in 5! ways

5 women can be seated around the circle in (5 - 1)!

⇒ 5! × 4!

⇒ 5 × 4 × 3 × 2 × 1 × 4 × 3 × 2 × 1

⇒ 120 × 24

⇒ 2880

:. The number of ways is 2880.

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The temperature should be 99.471° F.  If we want only 2.0% of healthy people.

Given that:

μ = 98.20

σ = 0.62

Determine the z-score in the normal probability table in the appendix that corresponds with a probability of:

1 − 0.02 =0.98

It is calculated by subtracting the population mean from the individual raw scores and dividing the difference by the population standard deviation. The process of converting raw scores to standardized scores is called standardization or normalization (although "normalization" can refer to different types of comparisons; see Normalization for more information).

The standardized score is the value x decreased by the mean and then divided by the standard deviation:

​     Z = X - μ / σ

⇒ x = μ+ zσ

      = 98.20+ (2.05)(0.62) = 99.471

Therefore, Only 2% of the healthy people exceed 99.471° F.

Complete Question:

Assume that human body temperatures are normally distributed with a mean of 98.20 F and a standard deviation of 0.62∘F. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

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Answer:

I have graphed it in the explanation part.

Step-by-step explanation:

First, we have to rewrite the two equations in the form y = mx + b.

2x - y = 4

-y = -2x + 4

y = 2x - 4

x - y = -2

-y = -x - 2

y = x + 2

As we see from the graph, the intersect point is at (6, 8)

In the proportion ,  a=-3 when b=4 and c=-3.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here the given is a directly proportional to b and c . then,

=> a ∝ bc

Now converting into equation add constant then

=> a = kbc [ where k is constant]

Now a= 24 when b= 8 and c= 12 then,

=>24=k(8*12)

=> k = 24/(8*12) = 2/8 = 1/4

Then the equation is [tex]a=\frac{1}{4}bc[/tex]

Now b=4 and c=-3 then,

=> a= (1/4)*4*-3 = -3.

Hence a=-3 when b=4 and c=-3.

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Answer:

a = -3

Step-by-step explanation:

ANSWERS:

A. 6 old printers would produce the batch of magazines in less time than 2 new printers
B. Using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers

EXPLANATIONS:

a) To determine which option would produce a batch of magazines in less time, we need to compare the printing rates of each option.

The old printers can produce a batch of magazines in 30 minutes, which means their printing rate is:

5 printers / 30 minutes = 1/6 printers per minute

The new printers can produce the same batch of magazines in 16 minutes, which means their printing rate is:

4 printers / 16 minutes = 1/4 printers per minute

If we use 6 old printers, their printing rate would be:

6 printers / 30 minutes = 1/5 printers per minute

If we use 2 new printers, their printing rate would be:

2 printers / 16 minutes = 1/8 printers per minute

Therefore, 6 old printers would produce the batch of magazines in less time than 2 new printers.

b) To determine how much less time it would take to produce the batch of magazines with 6 old printers, we can set up a proportion:

1/5 printers per minute = 1/x minutes

Solving for x, we get:

x = 5 minutes

Therefore, using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers.

The lengths of the missing sides are:

x = 6

y = 3√2

Here we can see a right triangle, we want to find the two missing lengths in it.

We know the measure of one angle, and the length of the adjacent cathetus of it, then we can use trigonometric relations:

cos(a) = (adjacent cathetus)/hypotenuse

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the values that we know, we will get:

cos(45°) = 3√2/x

Solving for x:

x = ( 3√2)/cos(45°) = 3√2*(2/√2) = 6

And to get the value of y we use the other:

tan(45°) = y/ ( 3√2)

1 = y/ ( 3√2)

( 3√2) = y

These are the lengths.

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Answer:

Mary is 36 years old

Her son is 12 years old

Step-by-step explanation:

Let's assume, that Mary's son is x years old and Mary is 3x years old

Let's write 2 equations according to the given information:

x = 3x (Mary is 3 times older than her son)

3x + 12 = 2(x + 12) (after 12 years, she will be 2 times older than her son)

3x + 12 = 2x + 24

3x - 2x = 24 - 12

x = 12

That means, Mary's son is 12 years old

Mary is 3 × 12 = 36 years old

This is used to calculate the height of the object at any time t during its flight.

The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.

The acceleration due to gravity is taken to be -9.8 m/[tex]s^2[/tex] (negative since it acts downward), and the formula for the height is derived from the equation of motion:

h(t) = -1/2 [tex]gt^2[/tex] + vt + hi

Where:

g = 9.8 m/[tex]s^2[/tex] (acceleration due to gravity)

t = time (in seconds)

v = initial velocity (in meters per second)

hi = initial height (in meters)

The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).

This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/[tex]s^2[/tex] until it reaches the maximum height and then starts to fall back down.

So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.

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Putting the negative sign to the numerator, we have the value of x = -6/7.

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

The given equation is:

x³ = -216/343

To solve for x, we can take the cube root of both sides of the equation:

∛(x³) = -∛(216/343)

x = -∛(216/343)

Solving for numerator:

216 =  6 × 6 × 6

∛216 = 6

Solving for denominator:

343 = 7 × 7 × 7

∛343  = 7

Therefore,

x = -∛(216/343)

x = -(6/7)

x = -6/7

Putting the negative sign to the numerator, we have the value of x = -6/7.

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Answer:

See below

Step-by-step explanation:

Helping in the name of Jesus.

The area of the bases of the second triangular pyramid will be 3 times the first one.

What is a triangular pyramid?

A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.

We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 90 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 90 = A * 5

⇒ A = 18 square inches.

Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 270 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 270 = A * 5

⇒ A = 54 square inches.

Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.

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Answer:

≈ 0,9

Step-by-step explanation:

To the nearest tenth:

[tex] \frac{20}{23} ≈0.9[/tex]

Yes, there could be total number 50 kids in the group. If there are 50 kids in the group, then more than half of them would be boys, which means there would be at least 26 boys in the group.

Let B be the number of boys and G be the total number of kids in the group.

Given that more than 1/2 are boys, we have B > G/2. Also, given that the boys are less than 2/3 of the group, we have B < 2G/3.

If there are 50 kids in the group, then we have:B > 50/2

B > 25B < 50(2/3)

B < 33.33

B ≤ 33 (since B is an integer)

Therefore, the number of boys in the group can be any integer between 26 and 33, inclusive.

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The function is linear because as the x-value increases, the y-values increases.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(0 - 1)

Slope (m) = -2/-1

Slope (m) = 2

Based on the information provided above at point (0, 9), an equation that models the line is represented by this mathematical equation;

y = mx + c

y = 5x + 9

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2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

A circle is a two-dimensional object in geometry made up of all points in a plane that seem to be equidistant from a certain point known as the centre. The radius of a circle is the distance from the centre to any point on the circle. The diameter is the length of a line joining two points on a circle and running through its centre. The area of a circle is the space inside of it, and the circumference is the distances around the edge. Tangent lines perpendicular to radii, inscribed and encircled angles in relation to the diameter, and a constant diameter to diameter ratio (pi) are only a few of the crucial characteristics of circles.

given

The circle has a radius of 7 feet, and its area is:

A=r2 = (22/7)x7/2 = 154 square feet

The circle is divided into six equal sections, each of which will have the following area:

6 / 154 = 25.67 square feet (rounded to two decimal places)

An region of two of the pieces will include:

2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

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Answer: divide 1/5 by the price of the CD

Formula: A = P(1+r/n)(nt)

Step-by-step explanation: , if you have a $1,000 CD with a term of three years and an APY of 5%, you can multiply $1,000 by 5% to find the interest

Answer:

20% of his money

Step-by-step explanation:

it's 1/5 of 100% of his money

Answer:

the height of the water in Container B is 22.48 feet.

Step-by-step explanation:

Answer:

12.2 miles

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Here, A represents the airport, C represents Centerville, and N represents Newberry. We want to find the distance x between N and A.

Since Centerville is 7 miles due north of the airport, the distance AC is 7 miles. Since the distance between Centerville and Newberry is 10 miles, we can use the Pythagorean theorem to find the distance AN. So the distance between Newberry and the airport is approximately 12.2 miles.

Determine the proper prism's base. The base takes the form of the prism's base. Calculate the base's area. The appropriate prism's height should be measured. Multiply the base's area by the prism's height.

A prism is a three-dimensional geometric object with two parallel, congruent bases and rectangular sides connecting the bases. The prism's name is derived from the design of its base. For instance, the bases of a triangular prism, rectangular prism, and so on, are all triangular. The distance between the two parallel bases of a prism determines its height. The formula V = Bh, where B is the area of the base and h is the height of the prism, can be used to determine the volume of a prism.

The formula V = Bh can be explained as follows:

Determine the proper prism's base. The base takes the form of the prism's base. The base, for instance, might be a triangle, square, rectangle, or any other polygon.

Calculate the base's area. The formula's B stands in for this.

The appropriate prism's height should be measured.

To get the volume, multiply the base's area by the prism's height.

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Answer:

96

Step-by-step explanation:

Because it is

Answer:

1/6

Step-by-step explanation:

There is a 1/3 chance that you will get either a blue, red or green.
It is also a 1/2 chance that you will get an even number on a die.
1/3x1/2=1/6.

Therefore our answer is 1/6

The point with the y-coordinate of 0 splits the directed line segment from J to K into a 5:1 ratio.

An X coordinate value denotes a location that is relative to a point of reference to the east or west. A Y coordinate value denotes a location that is relative to a point of reference to the north or south.

Considering J (1, -10) and K (7, 2)

In this case, let's suppose that point L divides the directed line segment from J to K into a 5:1 ratio.

We know that from coordinate geometry's inherent characteristics.

The point's coordinates are (x1, y1), (x2, y2) where they meet in the ratio of m:n.

[tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]

Now putting the respective values,

= ([tex](\frac{(5 .1)(1 .1) }{5 +1} , \frac{(5 . 2)(1 . (-10))}{5+1}[/tex]

= (6, 0)

Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

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Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex] the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

We know that the product of two factors is equal to zero only when at least one of the factors is zero.

[tex](x + 4) \ (2x - a) = 0[/tex]

This equation has two factors:  [tex](x + 4)[/tex] and [tex](2x - a)[/tex] . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.

Setting  [tex](x + 4)[/tex] equal to zero, we get:

[tex]x + 4 = 0[/tex]

[tex]x = -4[/tex]

This means that  [tex]-4[/tex] is one of the solutions of the equation.

Setting  [tex](2x - a)[/tex] equal to zero, we get:

[tex]2x - a = 0[/tex]

[tex]2x = a[/tex]

[tex]x = a/2[/tex]

This means that [tex]a/2[/tex] is another solution of the equation.

Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex]  , we can substitute these values into the expression we found for x in terms of a to get:

[tex]a/2 = 4[/tex] or  [tex]a/2 = -4[/tex]

Solving for a in each case, we get:

[tex]a = 8[/tex] or [tex]a = -8[/tex]

Therefore, the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

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A stratified random sample is preferred when the population is heterogeneous, ensuring a proportional representation of each subgroup, and allowing for more accurate comparisons and reliable inferences about the population.

When the community under study is heterogeneous, which means it can be broken down into different divisions or sectors, a stratified random sample is usually favored over a basic random sample.

In this situation, a stratified random sample makes it possible for each stratum to be proportionally reflected in the sample, guaranteeing that each subset is properly represented. When analyzing the differences or parallels between various subgroups, this method can be especially helpful.

For instance, a business might want to poll to find out how satisfied customers are with its offerings. They might choose to select a stratified random sample based on customer demographic categories or regions as opposed to a straightforward random sample.

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The question is -

Provide an example of when you might want to take a stratified random sample instead of a simple random sample and explain what the advantages of a stratified random sample might be.

Answer:

C. cos A = 1 and sin B = 1.

Step-by-step explanation:

The angles in a triangle must add up to 180°. Since angle C is 90°, angles A and B must add up to 90°. Therefore, the sine of angle A and the sine of angle B must both equal 1. Since the sine of an angle is equal to the cosine of its complement, cos A = 1 and sin B = 1.

The repeated measures studies require fewer subjects than matched subjects studies with the same number of outcomes is that repeated measures designs reduce intersubject variability.

In repeated measures studies, each participant is measured multiple times under different conditions or treatments.

Whereas, In a matched-subjects study, each participant in the treatment group is compared to participants in the control group.

Intersubject variability can be large, and differences between treatment and control groups may be attributed to differences in these individual characteristics.

However, in a repeated-measures design, each participant served as its own control, reducing inter-subject variability.

This makes it easier to recognize differences in treatment conditions and can increase effect sizes.

Therefore, a repeated measures study may require fewer subjects to achieve the same statistical power as a matched subjects study with the same number of outcomes.

However, it is important to note that repeated measures designs may have their own limitations:  Potential Order Effect or Practice Effect.

These limitations should be carefully considered when designing a study, and an appropriate design should be chosen based on the research question and the nature of the data.

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The calculated length of AC from the right triangles is 320 units

from the question, we have the following parameters that can be used in our computation:

The right triangle

The length of the segment AC is calculated as

sin(30) = 160/AC

Make AC the subject

So, we have

AC = 160/sin(30)

When evaluated, we get

AC = 320

Hence the length of AC is 320 units

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