find the sum of 6 terms in the sequence 3,6,12, ...

The value of the net force acting on the block will be equal to 79N.

Force may be defined as the product of mass and acceleration, and it acts on the body in order to move the body. Since, the external force is acting on the block there will be a frictional force which opposes the block to move. The frictional force may be represented by f(k) and is given by

f(k) = external force - (ma)

f(k) = 40N - (5×6)

f(k) = 40N - 30N

f(k) = 10N and since it opposes the external force then the sign will be negative that is f(k) = -10N.

Also, there is a force of gravity acting on the body which will be equal to mg where 'g' is the acceleration due to gravity.

Now, force of gravity = mg

= 5×9.8 = 49N

Now, net force acting on the block = 40N - 10N + 49N

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Step-by-step explanation:

you can ask questions for clarification

Answer:

3

Please refer to the photo below:

The body mass index of a person 65 inches tall with a weight of 175 pounds is 29.12

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The body mass index (BMI) is given by:

BMI = [mass in pounds / (height in inches)²] * 703

Given mass = 175 pounds, height = 65 in, hence:

BMI = [175/65²] * 703 = 29.12

BMI = 29.12

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Answer:

6

Step-by-step explanation:

Answer:

6kg

Step-by-step explanation:

5 to 30 ratio

1 to 6 ratio

Answer:

30/5=6

6 kg beans for $1

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By using Binomial probability distribution, the mean number of adults who would have bank savings accounts is 32.

For every survey, there are only two possible outcomes.

First- they have bank savings accounts,

second- they do not.

So, by using the binomial probability distribution we can solve this problem.

Probability of exactly Y successes in ‘n’ repeated trials, with ‘p’ probability.

Probability = p

Successes repeated = n  times

The  value of the binomial distribution is:

E(Y) = n x p

In this problem, we have that:

p = 0.64

If we were to survey among 50 randomly selected adults, the mean number of adults who would have bank savings accounts is,

E(Y) when, n = 50

So,

E(Y)= n x p

= 50 x 0.64

= 32

Hence ,our required answer is 32 adults who would have bank savings accounts

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Only height, because when you have an expression that relies only on multiplication (not addition or subtraction), we'll say:

cb = a

Tripling either c or b will also triple a. For example:

(8)(3) = 24

(8 + 8 + 8)(3) = 24(3)
(24)(3) = 24(3)

This will be true even if you multiply c by any other number.

So, in the expression v = πr²h, any term except r can be tripled with the result of tripling v. We exclude r because r has an exponent, which means tripling r will more than triple v.

The length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.

The given values in the question are-

The width of the field = w.

The length of the field = 2x+1

The area of the field =  600 m².

The formula of area of rectangular field;

A = length×width

Put the values;

600 = (2x+1)x

Simplifying the equation;

600 = 2x² + x

2x² + x - 600 = 0.

Find the factors of the above quadratic equation using quadratic formula.

x = 2.08, neglecting negative value.

Thus, the width is x = 2.08 m.

length = 2x + 1

length = 5.16 m.

Thus, the length and width of the rectangular field is found as width x = 2.08 m and length = 5.16 m.

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The rules of exponents which can be used to solve the expression as given in the task content are; Product rule, Negative rule and Quotient rule.

It follows from the task content that the rules which can be used to correctly solve the expression as given in the task content be determined.

Since the expression given is;

10³ * 10-⁷ * 10²

We can therefore have rewrite 10-⁷ using the negative rule so that we have; 1/10⁷.

Also, the product rule can be used on; 10³ * 10² so that we have; 10⁵.

Ultimately, the quotient rule can be used on the resulting expression; 10⁵/10⁷ so that we have; 10-².

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Answer:

What is this, give context and I'll help you.

Step-by-step explanation:

Need more context.

The solution for the system of linear inequalities is y <-3 and x < 10.5

Linear inequalities are inequalities that have constant average rates of change.

A system of linear inequalities is a collection of at least two linear inequalities

In this case, the system of inequalities is given as

2x - 3y < 12

y < -3

Substitute y < -3  in 2x - 3y < 12

2x - 3(3) < 12

Evaluate the like terms

2x - 9 < 12

This gives

2x < 21

Divide by 2

x < 10.5

Hence, the solution is y <-3 and x < 10.5

See attachment for the graph where the green line represents y <-3 and the other represents 2x - 3y < 12

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Answer:

60000

Step-by-step explanation:

Answer:

Step-by-step explanation:

6 × [tex]10^{4}[/tex] =

6 × 10000 =

60000

the given family of functions is the general solution of the differential equation on the indicated interval y=[tex]7/2e^{x} -7/2e^{-x}[/tex]

What is differential equation?

Equations which involves functions and its derivative is known as differential equation. these equations are highly used to model behaviour of complex system.

How to solve?

y(x) = [tex]C_{1} e^{x}+C_{2}e^{-x}[/tex]

y(0) = [tex]C_{1} +C_{2}[/tex]

0 =[tex]C_{1} +C_{2}[/tex]  --------------------------------------------------(1)

y'(x) =   [tex]C_{1}e^{x} -C_{2}e^{-x}[/tex]

y'(0) =  [tex]C_1- C_{2} }[/tex]

7 =  [tex]C_{1}-C_{2}[/tex] -------------------------------------------------(2)

From Equation 1 and 2

[tex]C_{1} +C_{2}[/tex] = 0

[tex]C_{1} -C_{2}[/tex] = 7

[tex]C_{1}[/tex] = 7/2

[tex]C_{2}[/tex] = -7/2

y=[tex]7/2e^{x} -7/2e^{-x}[/tex]

the complete question is

The given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem. y = c1ex + c2e−x, (−∞, ∞); y'' − y = 0, y(0) = 0, y'(0) = 7

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From the statement, we know that stack of 30 science flashcards has:

• 10 with insects,

• 8 with trees,

• 8 with flowers,

• 4 with birds.

The probability of selecting a tree or a flower is given by:

4/15

Answer : 3(x - 5)(x + 5)

example 3(x 2 - 25)

               3x2 - 75

sorry about what happened but I hope this helps have a great day

Answer:

23.8/5.6=4.25

Step-by-step explanation:

Answer:

4.25

Step-by-step explanation:

[tex] \sf \: 23.8 / 5.6 =4.25[/tex]

[tex] \sf----------------------------------[/tex]

The solution of the equation b² = 48 is b = 4√3

The equation can be solved as follows;

b² = 48

Therefore, we are to find the value of b in the equation.

The value of b comes with a square sign, so we have to remove the square to make b stand alone in the equation.

By removing the square sign we have to square root both sides.

Hence,

b² = 48

square root both sides of the equation

b² = 48

√b² = √48

Therefore,

b = √16 × 3

b = 4√3

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Answer: In simplest form it would be 6 1/40

Step-by-step explanation:

[tex] \frac{241}{40} [/tex]

but in mixed number

[tex]6\frac{1}{4} [/tex]

Answer:

The farmer had to do 27 loads.

Step-by-step explanation:

Basically the easy way to do this is to grab a calculator (or the paper and pen way) and keep adding 336 until you get to 8914.

Once you add it all you will see there is a remainder of his corn left (that has not been delivered):178

Even though it isn't a full 336, the farmer would still have to make another trip.

336*26=8,736

So, adding the remainder into it's own load, we would get:

27.

The statements that are true in the lines of construction of the straightedge and compass construction which makes use of congruent circles, are;

Line EF is the perpendicular bisector of segment BD

Line EF is the bisector of angle BAC

Geometric figures are constructed using a compass and a straightedge, by using outlined steps or procedures.

From the diagram, given that the circumference of the circle with center B passes through the center of the circle with center D, and vice versa, we have;

Circle B is congruent to circle D

The steps to construct a perpendicular bisector to the segment BD includes;

Therefore;

The steps to construct the angle bisector of angle BAC

The angle bisector can be constructed by using the following steps

Which gives;

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∠1 and ∠4 are supplementary angle in transversal line .

What is a transversal angle?

1) ∠6 ≅ ∠8   congruent angle.

2) ∠6 = ∠1 and ∠8 = ∠3    are Verical angles.

3) ∠1 and ∠4 are supplementary angle.

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Construct a probability mass function (pmf) for x, the dollar amount won by a contestant in this game is 1/18.

What is a probability math example?

from above total number of chips =4+6+5+2+1 =18

hence Probabilty of win 0 P(0)=4/18

P(1) =6/18

P(5) =5/18

P(10) =2/18

P(100)=1/18

x     P(x)     xP(x)

0    0.22     0.00

1     0.33      0.33

5     0.28       1.39

10      0.11       1.11

100     0.06      5.56

                       8.39

therefore expeted value =8.39

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We determine the scale factor by comparing the lengths of corresponding sides of the square.

The length of O’N’=15 and the length of the corresponding segment ON =9.
Then, we compute the scale factor:
O’N’=kON

15=9k

k=15/9=5/3.

The scale factor is k=5/3.

Answer:

m arcRP = 125°

m arcQS = 125°

m arcSP = 55°

m arcQR = 55°

Step-by-step explanation:

An arc is the curve between two points on the circumference of a circle.

An arc measure equals its corresponding central angle measure.

Vertical Angles Theorem:  When two straight lines intersect, the opposite vertical angles are congruent.

Angles on a Straight Line Theorem:  The sum of angles formed on a straight line is equal to 180°.

As m∠ROP = 125°

Therefore, m arcRP = 125°

Given the measure of angle ROP is 125°, and an arc measure equals its corresponding central angle measure, the measure of arc RP is 125°.

Using the Vertical Angles Theorem:

⇒ m∠QOS = 125°

Therefore, m arcQS = 125°

Using the Vertical Angles Theorem, the measure of angle QOS is equal to the measure of angle ROP, so the measure of angle QOS is 125°. As an arc measure equals its corresponding central angle measure, the measure of arc QS is 125°.

Using the Angles on a Straight Line Theorem:

⇒ m∠SOP = 180° - 125° = 55°

Therefore, m arcSP = 55°

Using the Angles on a Straight Line Theorem, the measure of angle SOP is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc SP is 55°.

Using the Angles on a Straight Line Theorem:

⇒ m∠QOR = 180° - 125° = 55°

Therefore, m arcQR = 55°

Using the Angles on a Straight Line Theorem, the measure of angle QOR is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc QR is 55°.

===================================================

Explanation:

The car is initially worth 44000 pounds.

It loses 25% of its value after the first year, but keeps the remaining 75% of it.

75% of 44000 = 0.75*44000 = 33000

The car is worth 33000 pounds at the end of year 1. This is effectively the "starting" value when we change the rate of depreciation.

------------------

The new percentage of the depreciation rate is x%

The car loses x% of its value each year

But it keeps the remaining (100-x)% of the value from year to year. Refer to the previous section.

x% = x/100

(100-x)% = (100-x)/100 = 100/100 - x/100 = 1 - 0.01x

The 1 - 0.01x is the value of b in the exponential equation y = a*b^t

The value of 'a' is the "starting" value of 33000 pounds.

The t represents the number of years after that first year (so that means we have t+1 years total).

The equation we have is

y = a*b^t

y = 33000(1 - 0.01x)^t

The teacher mentions "after 3 years" which means we'll have t+1 = 3 solve to t = 2 which is what we'll plug in along with  y = 25555

Let's solve for x.

y = 33000(1 - 0.01x)^t

25555 = 33000(1 - 0.01x)^2

25555/33000 = (1 - 0.01x)^2

0.77439393939393 = (1 - 0.01x)^2

(1 - 0.01x)^2 = 0.77439393939393

1 - 0.01x = sqrt(0.77439393939393)

1 - 0.01x = 0.87999655646709

-0.01x = 0.87999655646709-1

-0.01x = -0.1200034435329

x = -0.1200034435329/(-0.01)

x = 12.00034435329

Due to rounding error, it appears that it should be x = 12 since your teacher mentions x is an integer.

Also, 12.00034435329 is pretty close to 12.

If it decays at 12% per year, then the car keeps the remaining 88% since 100-12 = 88

Therefore 0.88 is the base of the exponential, it's the value of b.

Computing 33000(0.88)^2 gets us 25,555.2 which isn't too far from the goal of 25,555 pounds.

------------------

We found the exponential decay equation to be

y = 33000(0.88)^t

where t is the number of years after that first year. We have t+1 years total.

Your teacher asks how much the car will be worth after 4 years, so we'll plug in t = 3 because it's the solution to t+1 = 4.

In other words, we're working 3 years after that first year is up, so 3+1 = 4 total years.

Plug in t = 3 to find the following

y = 33000(0.88)^t

y = 33000(0.88)^3

y = 22,488.576

Rounding to the nearest pence gets us 22,489.58 which is the value of the car after 4 years. You can verify this with a spreadsheet table as I have shown in the diagram below. The highlighted rows mention values on your screenshot.

I'll round to the nearest pound since the other car values mentioned were whole numbers rather than decimal ones.

The 22489.58 rounds to 22490

------------------

For the final part, we'll need logarithms to solve the equation. Logarithms are useful to isolate the exponent.

We'll plug in y = 14520 and solve for t

y = 33000(0.88)^t

14520 = 33000(0.88)^t

14520/33000 = (0.88)^t

0.44 = (0.88)^t

Log[ 0.88^t ] = Log[ 0.44 ]

t*Log[ 0.88 ] = Log[ 0.44 ]

t = Log[ 0.44 ]/Log[ 0.88 ]

t = 6.42227097958021

This rounds up to t = 7

Round up instead of down because we want to clear the hurdle of passing the 14520 marker.

Recall once again that t is the number of years after the first year.

So t = 7 represents t+1 = 7+1 = 8 years in total that have passed by. Therefore, after 8 years is when the car's value is below 14520 pounds. Refer to the table diagram below.

Use the Pythagorean theorem to solve for c using the lesser two sides.

The answer is A.

Metric measurement are given below:

The meter, liter, and gram are the corresponding base units for length (distance), capacity (volume), and weight (mass) in the metric system. To measure smaller or larger amounts, we use units that are derived from metric units.

The three most used base units in the metric system are the meter, gram, and liter. The liter is a unit of volume equal to 1.05 quarts, the meter is a unit of length equal to 3.28 feet, and the gram is a unit of mass about equivalent to 0.0022 pounds (or roughly the mass of a paper clip).

Given Data

a) 2.4 meters

b. 0.4 kilometers

c. 0.04 hectometers

d. 240 decimeters

_ 40 dekameters

_ 0.24 hectometers

_400 centimeters

_ 2400 millimeters

a) 2.4 meters = 2400 millimeters

b) 0.4 kilometers = 400 centimeters

c) 0.04 hectometers =  40 dekameters

d) 240 decimeters = 0.24 hectometers

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The image of (-8,6) after a reflection over the line y = -x is (-6, 8).

Given:

The image of (-8,6) after a reflection over the line y = -x.

The x-coordinate and y-coordinate of a point change positions and are negated when it is reflected across the line y = -x.

So, the reflection of the point (-8, 6) across the line y = -x is (-6, 8).

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