1. If a rubber ball is dropped from a height of 10 feet, the function
f(x) = 20 (0.6)* gives the height in feet of each bounce, where
x is the bounce number. What will be the height of the 5th bounce?
Round to the nearest tenth of a foot.





2. A population of pigs is expected to increase at a rate of 4% each
year. If the original population is 1000, the function f(x) = 1000 (1.04)*
gives the population in x years. What will be the population in 12 years?


Please help

Answer: To determine the estimated age of the artifact, we can use the half-life of carbon-14 and the percentage of carbon-14 that is present in the artifact.

The half-life of carbon-14 is the amount of time it takes for half of the carbon-14 in a sample to decay. In this case, the half-life of carbon-14 is 7,730 years.

The percentage of carbon-14 that is present in the artifact is 44%. This means that the artifact contains 44% of the carbon-14 that it would have had when it was originally made.

To determine the age of the artifact, we can use the formula:

age = (half-life / log(2)) * log(percentage of carbon-14 / 100)

Substituting the values from the problem into the formula, we get:

age = (7,730 years / log(2)) * log(44% / 100)

age = (7,730 years / 0.693) * log(0.44)

age = 11,095 years * (-0.847)

age = -9,432 years

Therefore, the estimated age of the artifact is -9,432 years.

It is important to note that this is just an estimate, and the actual age of the artifact may be different. Carbon-14 dating is only accurate up to a certain point, and the accuracy of the age determination depends on several factors, including the initial concentration of carbon-14 in the sample and the presence of any contaminants.

The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

According to the question,

We have the following information:

Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.

Now, let's take the percent to be x.

We have the following expression:

2400*x/100 = 125

24x = 125

x = 125/24

x = 5.21%

Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

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Step-by-step explanation:

the same as every other individual outcome of a roll of 2 dice : 1/6 × 1/6 = 1/36

Equation of the line in slope intercept form is y = x - 5, when slope is 1 and a point on the line is (-12, -17).

Slope of a line is the degree of inclination of that line.

In other words, slope of a line can be calculated by taking the change in y coordinates to the change in x coordinates when x coordinate and y coordinate of two points are given.

Equation of a line in slope-intercept form is,

y = mx + c

where, m is the slope and c is the y-intercept.

y- intercept is the y-coordinate of a point where the line touches with the Y-axis. x coordinate will be zero at this point.

We have m = 1 and a point (x, y) = (-12, -17)

Substituting these values in the equation,

-17 = (1 × -12) + c

-17 + 12 = c

c = -5

Substituting m = 1 and c = -5, equation in slope intercept form can be written as,

y = x - 5

Hence, the equation of the line in slope intercept form when slope = 1 and passing through the point (-12, -17) is y = x - 5.

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(2) The statements and reasons in the two-column method are presented as follows;

Statement [tex]{}[/tex]                                           Reasons

1. [tex]\overline{BD}[/tex] bisects ∠ABC [tex]{}[/tex]                          1. Given

2. ∠BAD ≅ ∠BCD   [tex]{}[/tex]                            2. Given

3. ∠ABD ≅ ∠CBD    [tex]{}[/tex]                           3. Definition of angle bisector

4. [tex]\overline{BD}[/tex] ≅ [tex]\overline{DB}[/tex]    [tex]{}[/tex]                                    4. Reflexive property

5. ΔABD ≅ ΔCBD     [tex]{}[/tex]                          5. AAS congruency postulate

(3) The two-column method used to prove the congruency of triangles ΔQRS and ΔSTU, is presented as follows;

Statement       [tex]{}[/tex]                                           Reason

1. S is the midpoint of [tex]\overline{QU}[/tex]       [tex]{}[/tex]                 1. Given

2. [tex]\overline{QR}[/tex] ≅ [tex]\overline{ST}[/tex]        [tex]{}[/tex]                                       2. Given

3.  [tex]\overline{RS}[/tex] ≅ [tex]\overline{TU}[/tex]        [tex]{}[/tex]                                       3. Given  

4.  [tex]\overline{QS}[/tex] ≅ [tex]\overline{SU}[/tex]        [tex]{}[/tex]                                  4. Definition of midpoint of [tex]\overline{QU}[/tex]

5. ΔQRS ≅ ΔSTV           [tex]{}[/tex]                            5. SSS congruency postulate

The two column method consists of statements and  the associated reasons arranged sequentially side by side in a two-column tabula format.

The reasons used to prove the above statements are as follows;

Angle bisector

An angle bisector is a segment that divides an angle into  two angles of the same measure.

Reflexive property

The reflexive property of equality states that the value of an object or the measure of a dimension is equal to itself

AAS congruency postulate

AAS which is the acronym for Angle-Angle-Side  congruency, states that  if two angles and a non included side of one triangle are congruent to two angles and the non  included side of  another triangle, then  the two triangles are congruent

Midpoint of a line

The midpoint of a line is a point that divides the line into two segments of the same measure.

SSS congruency postulate

The Side-Side-Side congruency postulate states that two triangles are congruent if three sides are congruent to three sides of the other triangle

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The exists no solution for which the water depth 14 feet in the ocean near the shore.

We determine the function's period since that is the number of it takes hours for the ocean to return to its original depth of a specific number of feet.

The function's duration is 2π/ (π/6.2) = 12.4 hours.

When t = 0, midnight, or 12:00AM, it is low tide.

As a result, the next low tide will occur at 12:24 PM, or t = 12.4, 12.4 hours from now.

A high tide will occur halfway between those two low tides, at t=6.2 hours after midnight, or at 6:12AM.

Another high tide will occur at t=18.6 hours after midnight, or at 6:36 PM, 12.4 hours later.

If t = 0 is used in the equation, the low tide occurs at that time;

d = 35 - 28cos(pi/6.2)t

d = 35-28cos(pi/6.2)0

d = 35-28cos(0)

d = 35-28(1)

d - 35-28

d = 7

Therefore, there will never be 4 feet there because the lowest depth that may exist is 7 feet.

Thus, the exists no solution for which the water depth 14 feet in the ocean near the shore.

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The system of equations that to be used to calculate the number of chicken wings (x) and sliders (y) in the combination meal:

55x + 275y = 1100 and y = 8x.

A system of equations is a collection of one or more equations with multiple variables.

Let x represent each onion ring.

Allow each slider to be represented by y.

That is what we are told;

The calorie count for each onion ring is 55.

The number of calories in each slider is 275.

A combination meal of both contained 1100calories.

Thus;

The equation formed wiil be,

55x + 275y = 1100

It also shows that there are 8 more onion rings than as many sliders.

Thus;

The equation formed is,

y = 8x

Therefore the system of equations in the combination meal are as follows: 55x + 275y = 1100 and y = 8x.

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Answer: x > or = to 4 (Inequality Form), [4, infinity) (Interval Notation)

Step-by-step explanation:

Isolate the equation.

Divide each side by the factors that do not contain x.

Solve for x.

The relationship between the time it takes to boil a pot of water, T (in seconds), and the amount of water, A (in litres),

T ∝ A,

setting up the equation and solving:

2.96 liters of water will boils in 220 seconds.

An equation is a mathematical statement that shows that two expressions are equal.

A proportionality constant is a coefficient that relates two quantities that are proportional to each other. In other words, if two quantities are proportional, their ratio is always the same, and this constant ratio is the proportionality constant.

This proportionality can be written as an equation by introducing a constant of proportionality, k:

T = k * A

We are given that it takes 200 seconds to boil 2.7 litres of water, so we can set up an equation using this information:

200 = k * 2.7

Solving for k, we find that k = 200/2.7 = 74.07407407407407.

Now that we know the value of the constant of proportionality, we can use it to find the amount of water in the pot if it boils in 220 seconds. We can set up the following equation:

220 = 74.07407407407407 * A

Solving for A, we find that the amount of water in the pot is A = 220 / 74.07407407407407 = 2.962962962962963 litres.

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Answer:

D. p = -6

Step-by-step explanation:

1. combine like terms

5/6 P + 7 = 7/6 P + 9

2. subtract 7/6 P from both sides

-2/6 P + 7 = 9

3. subtract 7 from both sides

-2/6 P = 2

4. multiply both sides by -6/2

Answer:

p = -6

Answer: D

Step-by-step explanation:

Answer:

13/15

Step-by-step explanation:

Step 1) Convert to -5/15 - (-18/15)

Step 2) -5/15 - (-18/15)= 13/15

A polynomial function of degree n has at most n real zeros and at most n-1 turning points.

What is polynomial function ?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

What isa Zeros of Polynomials?

Every polynomial will have as many zeros as its degree if we are able to factor it over the entire set of complex numbers, though some of these zeros are repeated and therefore counted more than once. As the function might not be fully factorable over the set of real numbers, if we limit ourselves to the set of real numbers, we might or might not be able to identify this many zeros.

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Answer:

y= 20x+50

Step by Step:

x+y=4 is most likely the equation for line K so the set of equations has infinitely many solutions.

Equation is a declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws. also see equation system.

Given

There must be identical lines made up of the same points for there to be an endless number of solutions. This implies that when expressed in the simplest terms, their equations are also identical.

As a result, x+y Equals 4. Equation here corresponds to B.

2x + 2y = 8

Dividing equation by 2

x + y = 4

As a result, x+y Equals 4. Equation here corresponds to B.
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The time calculation which involve calculating the time in GMT when it is 1:31:45 PM EDT (Eastern Daylight Savings Time) is

The conversion given in the problem is

Eastern Daylight Savings Time = Greenwich mean time GMT - 4

Eastern Daylight Savings Time + 4 = Greenwich mean time GMT

Solving for the time equivalence in Greenwich mean time

Greenwich mean time GMT = Eastern Daylight Savings Time + 4

substituting known values

Greenwich mean time = 1 : 31 : 45 PM + 4

Greenwich mean time = 5 : 31 : 45 PM

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Answer:

either h=12, b=5

or h=5, b=12

Step-by-step explanation:

We'll use a system of equations to solve this. We'll have 2 equations and 2 unknowns. Our 2 unknowns are the 2 other sides, and our 2 equations are as follows:

look for any information given. I see that the area is 30 sq.cm and the perimeter is 30cm. There are our pieces of information.

Our first equation will be the one about how the area is 30 sq.cm (we'll use b for base and h for height:

(1/2)×b×h=30

Our second equation will be the one about how the perimeter is 30cm:

13+b+h=30

These equations both have to be true at the same time, and there are a few techniques for solving a system of equations, but in this case, this way is probably the simplest. We'll get one variable on one side of an equation and then plug it into the other equation using the transitive property.

13+b+h=30

b=30-13-h

b=17-h

now we'll plug in (17-h) for all the b in the first equation:

(1/2)×(17-h)×h=30

17h-h²=60

-h²+17h-60=0

now we'll use quadratic formula (or factor) to find h:

[-17±√(289-240)]/-2

(-17±7)/-2

-24/-2 or -10/-2

12 or 5

h=12

h=5

we'll try both of them in this equation:

13+b+h=30

25+b=30

or 18+b=30

therefore;

either h=12, b=5

or h=5, b=12

Answer:

x = -0.5

Step-by-step explanation:

[tex]factors \: of \: 25 \\ 25 = 5 {}^{2} \\ 5 {}^{(2)x} = 5 {}^{4x + 1} \\ since \: bases \: are \: equal \: \\ hence \: exponents \: are \: equal \\ 2x = 4x + 1 \\ collect \: like \: term \\ 2x - 4x = 1 \\ - 2x = 1 \\ divide \: by \: - 2 \: both \: sides \\ x = - 0.5[/tex]

Answer:

Step-by-step explanation:1.08%

Interest rate required in order for Kiran to end up with $9,500 is 4.55%.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

Given,

Principal amount = $6,600

Time in years = 8 years

Final amount = $9,500

The final amount is calculated in compound interest by the formula,

A = P (1 + [tex]\frac{r}{n}[/tex]) ^ (n t)

Here, P is the principal amount, r is the rate of interest, n is the number of  years.

Substituting in the formula,

9500 = 6600 (1 + [tex]\frac{r}{365}[/tex]) ^(365 × 8)

9500 / 6600 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.4394 = (1 + [tex]\frac{r}{365}[/tex])²⁹²⁰

1.000125 = 1 + [tex]\frac{r}{365}[/tex]

[tex]\frac{r}{365}[/tex] = 0.00125

r = 0.045531

r = 4.5531% ≈ 4.55%

Hence the interest rate to the nearest hundredth of a percent is 4.55%.

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The height of the candle after 11 hours is 20.5 if the slope is -0.5.

The ratio of "vertical change" to "horizontal change" between any two separate points on a line, or any two points, is used to compute slope. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line. The line may be practical, as determined by a road surveyor, or in a diagram that represents a roof or a road as a description or a design.

The absolute value of the slope serves as a proxy for a line's steepness, incline, or grade.

Given, slope m= -0.5

(y-y₁)=m(x-x₁)

Also given that,

x=19, y=16.5 cm

(y-16.5)=m(x-19)

y-16.5= -0.5(x-19)

y-16.5= -0.5x+9.5

0.5x+y-26=0

After 11 hours, the height of the candle is:

x=11

0.5(11)+y-26=0

y=26-5.5

y=20.5

Therefore, the height of the candle after 11 hours is 20.5

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i) The amount of work that Mrs. Maharjan did in 2 days is; ¹/₃ parts

ii) The amount of work that was left to do is; ²/₃ parts

iii) The amount of work that was done by Mrs. Rai is; ²/₃ parts

We are told that Mrs. Maharjan can do ¹/₆ part of a work in 1 day.

Thus;

i) Amount of work done in two days = ¹/₆ + ¹/₆ = ¹/₃ part

This represents the amount of work that Mrs. Maharjan did in 2 days.

(ii) Since Mrs. Maharjan did ¹/₃ part of the work in 2 days, then it means that the amount of work that was left to do is;

1 - ¹/₃ = ²/₃ parts

(iii) Since we are told that Mrs. Rai did the remaining works, the the amount of work that was done by Mrs. Rai is as calculated in ii above.

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Complete question is;

Mrs. Maharjan can do ¹/₆ part of a work in 1 day. She worked for 2 days and left. The remaining parts of the work is done by Mrs. Rai.

(i) How much work did Mrs. Maharjan do in 2 days?

(ii) How much work was left to do?

(iii) How much work was done by Mrs. Rai?​

The slopes and points are:

a) (-3/4) and the point is (4, 9)

b) (-2/3), and the point is (-4, 3)

A line with a slope a and a known point (h, k) can be written as:

y - k = a*(x - h)

So that is the slope-point form of the linear equation.

a) The first linear equation is:

y - 9 = (-3/4)*(x - 4)

Comparing this with the general line above, we can see that the slope is (-3/4) and the point is (4, 9)

b) y = 3 - 2/3 (x +4)

We can rewrite this as:

y - 3 = -(2/3)*(x + 4)

Then in this case the slope is (-2/3), and the point is (-4, 3)

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The analysis of the logical statement from among the  options indicates that the inference that is not true is the option;

A logical statement is one which draws a conclusion based on an hypothesis.

The logical statement which is incorrect can be found by examining the specified statements as follows;

If p then q,

The converse statement , found by switching the positions of the hypothesis and the conclusion is therefore;

q therefore p

The inference is correct

The statement, if not p, not q . q therefore not not p

According to the law of contraposition, a conditional statement is true when the contrapositive statement is also true.

The statement if not p, not q. which is the contrapositive of the statement if q then p

The inference, q, therefore not not q is incorrect

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The ratio of the segments formed on each transversal are equal.

  AB/CB = EF/DF

How do parallel lines work?

In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal.

The equation of the parallel lines are;

y = x, and y = x + 1

The point of intersection of transversal 1 and the parallel lines y, and z

(0.2, 0.2), and (0.3, 0.8)

The length of segment AB = √((0.3 - 0.2)² + (0.8 - 0.2)²) = 0.1·√(37)

The point of intersection of transversal 1 and the parallel lines x, and y

(0.3, 0.8), and (0.4, 1.4)

The length of segment CB = √((0.4 - 0.3)² + (1.4 - 0.8)²) = 0.1·√(37)

The ratio of the lengths of the line segments formed by the transversal 1, AB:CB is found as  follows;

              AB/CB = 0.1 . √37/ 0.1 . √37  = 1

The point of intersection of transversal 2 and the parallel lines y and z are;

(0.8, 0.8), and (0.7, 1.2)

The length of segment EF = √((0.7 - 0.8)² + (1.2 - 0.8)²) = 0.1·√(17)

The point of intersection of transversal 2 and the parallel lines x and y are;

(0.7, 1.2), and (0.6, 1.6)

The length of segment DE = √((0.6 - 0.7)² + (1.6 - 1.2)²) = 0.1·√17

The ratio of the lengths of the line segments formed by the transversal 2, EF:DE is found as  follows;

                EF/DF  =  0.1 . √17/ 0.1 . √17 = 1

Therefore:

The ratio of the lengths of the two line segments formed on each transversal are equal.

                AB/CB = EF/DF

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Answer: w=14

Step-by-step explanation: The way I solve it is if you take 27 and subtract 13 from it, you'll get 14. Hope this helps!

Answer:

w=14

Step-by-step explanation:

hope this helps...

The new coordinate for point B is (0,2). Hence option B is the correct option.

What is coordinate of a point?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by (x,y) the x-value and y-value.

Given that the coordinate of point A and B are (3,0) and (0,4).

The line AB is dilated by 1/2.

This means the scale factor is 1/2.

The x coordinate of point B is 0.

The y coordinate of point B is 4.

Multiply 1/2 with the x coordinate and y coordinate of point B to find the new coordinate of point B:

The new  x coordinate of point B is (0 × 1/2) = 0

The new  y coordinate of point B is (4 × 1/2) = 2.

The new coordinate of point B is (0,2).

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To calculate the total area of the cylinder, we need to use the formula for calculating surface area; SA = 2πr² + 2πrh. In this case, r is equal to 1.5 yards and h is equal to 24 yards:

SA = 2(3.14)(1.5^2) + (2)(3.14)(1.5)(24)

= 28 ft² + 144 ft²

= 172 ft²  

Therefore, we need 172/150 gallons of paint in order to cover both sides of the ilo with one coat each - approximately 1 gallon and 14 fluid ounces or about 1 3/4 gallons of paint will be needed in total

What is Surface Area?

The area is the area occupied by a flat, two-dimensional surface. It is expressed in square units. The surface area of a three-dimensional object is the space taken up by its exterior surface.

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Answer:

You will need to use information from (a)

The function's domain is (a) all real numbers.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set. A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

The formula for the function is: f(x) = Negative 5/6. X in superscript?

The function mentioned above is exponential

There are no input value restrictions for exponential functions

Consequently, the function's domain is (a) all real numbers.

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