18. Identify the constant term in the algebraic expression
*

A.-1
B. 1
C. -2
D. 2

Using a geometric sequence, it is found that the maximum height reached after the 5th bounce is of 43.48 feet.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, the ball is dropped from a height of 101.00 inches onto a hard flat floor, and after each bounce, the height is 19% less, that is, 81% of the previous height, hence the first term and the common ratio are given by:

[tex]a_1 = 101, q = 0.81[/tex]

Then, the height of the nth bounce is given by:

[tex]a_n = 101(0.81)^{n-1}[/tex]

And the height of the 5th bounce is:

[tex]a_5 = 101(0.81)^{5-1} = 43.48[/tex]

The maximum height reached after the 5th bounce is of 43.48 feet.

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Answer:

48.57 USD

Step-by-step explanation:

Just subtract 3500 from 1800 you get 1700

then

1700 divided by 35

The original price of the meal deal if they would have exactly enough money to buy two of the meal deal is $4

let

x = cost of the meal

Both = 2x - 3

3/4x + 1/2x = 2x - 3

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

5/4x = 2x - 3

5/4x - 2x = - 3

(5-8)x/ 4 = -3

-3/4x = -3

x = -3 ÷ -3/4

= -3 × -4/3

= 12/3

x = $4

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The total area with land based on the information given is 3x² + 60x.

Let the width = x

Let the length = (1.5 × x) = 1.5x

Area = 1.5x × x = 1.5x²

The area along with land:

Width = x + 20

Length = 3 × x = 3x

The total area with land:

= Length × Width

= 3x(x + 20)

= 3x² + 60x.

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Answer:

[tex]f^{-1}(x) = (x+7)^2[/tex]

Step-by-step explanation:

[tex]y=f(x) = \sqrt x - 7 \\\\\text{Replace x with y and then solve for y:}\\\\~~~~~~~~x= \sqrt y -7\\\\\implies \sqrt y = x+7\\\\\implies y = (x+7)^2\\\\\implies f^{-1}(x) = (x+7)^2[/tex]

Answer:

no thank you sorry 4h he'll be a great day of school and I have been a while ago but it's a good time 44

Answer:

o

Step-by-step explanation:

It looks like the differential equation is

[tex]\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}[/tex]

Factorize the right side by grouping.

[tex]xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)[/tex]

[tex]xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)[/tex]

Now we can separate variables as

[tex]\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx[/tex]

Integrate both sides.

[tex]\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx[/tex]

[tex]\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx[/tex]

[tex]\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}[/tex]

You could go on to solve for [tex]y[/tex] explicitly as a function of [tex]x[/tex], but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

Answer: 121.375

Step-by-step explanation:

[tex]2^4=16[/tex]

[tex]\frac{1942}{2^4}[/tex]

[tex]\frac{1942}{16}=121.375[/tex]

Answer:

I would say A is the answer.

Any line with a slope different than 3 will intercept the given line only once.

The answer will be any line that is not parallel (nor the same) to the given line.

Remember two lines are parallel if the lines have the same slope and different y-intercept

In this case, the given linear equation is:

6x - 2y = 10

y = 3x - 5

So the slope is 3 and the y-intercept is -5.

Then, any line with a slope different than 3 will intercept this line only once.

An example can be:

y = 314*x

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Answer: Maybe when you Grew from a Baby to a toddler because that would be you growing over time

Step-by-step explanation:

I Hope This Helps!

Answer:

2.25or21/4

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

Expression:

Simplify it in below steps:

Answer:

13

Step-by-step explanation:

Divide 12 by 3 first because of (PEMDAS) you get 4 tge add that to the 9 the you get 13.

P = parentheses

E = exponent

M = multiplication

D = division

A = addition

S = subtraction

Step-by-step explanation:

To find slope : y2- y1 / x2 - x1

we have ( -5 , 1 ) which is ( x1 , y1 )

and ( -2 , 7 ) is ( x2 , y2 )

so; 7 - 1 / -2 - (-5)

6/3

= 2

Answer:

3

Step-by-step explanation:

Using the normal distribution, it is found that 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 33.8, \sigma = 1.2[/tex]

The proportion of full term newborn female infants with a head circumference between 31 cm and 36 cm is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 31, hence:

X = 36:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 33.8}{1.2}[/tex]

Z = 1.83

Z = 1.83 has a p-value of 0.9664.

X = 31:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{31 - 33.8}{1.2}[/tex]

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.9664 - 0.0099 = 0.9565.

0.9565 = 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

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Answer: P(A|B) = P(A)

Step-by-step explanation:

If they are independent, one event being given doesn't impact the probability of the other event.

Answer:b

Step-by-step explanation:

b

Step-by-step explanation:

please can you divide it will give you the answer

x=4

Step-by-step explanation:

4x=16y

x=16divide4

x=4

Answer:

y = 4x

Step-by-step explanation:

Take a pair of coordinates, like

(8,32) ; (4,16)

m = (Δy):(Δx)

   = (32-16) : (8 - 4) = 4

y = mx + c

  = 4x +c

Now substitute the values from one of the 2 coordinates' pair.

16 = 16 + c

c = 0

Therefore,

y = 4x

The surface area of a triangular prism with the 3 sides slant height as 14 the base width as 8 and the base height as 6.9 is 155. 705 in²

The surface area of a triangular pyramid is the total area of all it's faces.

The properties of a triangular prism are;

Surface area = Base Area + 1÷2 (perimeter × base height)

But base area = 1÷2 (base side × height)

Base area = 1÷ 2 (8 × 14) = 0.5 × 112 = 56 in²

Perimeter = sum of all the sides = 14 + 8 + 6.9 = 28. 9 in

Base height = 6. 9in

Surface area = 56 + 1 ÷ 2 ( 28.9× 6. 9) = 56 + 0.5 × 199.41 = 56 + 99. 705 = 155. 705 in²

Surface area = 155. 705 in²

Therefore, the surface area of the triangular prism is 155. 705 in²

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Answer:

(2.405, 1.537)

Step-by-step explanation:

When you graph these, they intersect at (2.405, 1.537).

You can use desmos as a graphing calculator, it is extremely helpful.

Hope this helps!

The calculation that will give us the total surface area of the solid figure that is made up of square faces is: B. 6 × 5 × 5

Area of a square = (side length)².

Therefore are six (6) square faces that make up the solid figure.

Area of the 6 square faces = total surface area of the solid figure = 6(5²)

Total surface area of the solid figure = 6 × 5 × 5

Total surface area of the solid figure is: B. 6 × 5 × 5

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Answer:

Step-by-step explanation:

Part A

There are 5 odd numbers from 1 to 10. All three of them must be odd when drawn. I have to assume that there is no replacements.

Probability (odd) = (5 *  4 * 3) / (10 * 9 * 8) = 60 / 720

Probability (odd) = 0.083333

Part B

This is a little harder because 1 even number will turn everything even. So the way to handle this is to assume that there is (1 - probability(odd)) *720  that you have even

So the chances of an even result is 1 - odd/ total or

(1 - 1/12) * 720 =   660/720 = 0.917

Answer

Odd: 0.0833

Even: 0.917

The number of miles between the two cities is 8.13 miles.

In order to determine  the number of miles between the two cities, we would have to divide 13 kilometers by 1.6 miles. Division is when a number is grouped into equal numbers using another number.

Number of miles = 13 / 1.6 = 8.13 miles

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It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

here, we have,

from the given figure we get,

there is a transformation of ABCD to A'B'C'D".

now,

Reason: choices are translation, reflection, rotation, or dilation, this is translation.

Hence, It's translation B to B’, is the composition of transformations that would map figure ABCD to figure A'B'C'D".

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Answer:

Acute Triangle.

Explanation:

The figure shows an equilateral triangle which has all the angles equal.

Acute Triangles are those who has angles less than 90°

Hence, an equilateral triangle is always an acute triangle.

Additional,

A right angle triangle has 90° angle.

An obtuse triangle has greater than 90° angle.

Step-by-step explanation:

[tex] ln(x) + ln(y) + ln(3) [/tex]

[tex] ln(3xy) [/tex]

Answer:

13 and 44

Step-by-step explanation:

let x and y be the 2 numbers with y < x , then

x - y = 31 ( add y to both sides )

x = y + 31 ( subtract 31 from both sides )

x - 31 = y → (1)

4y = x + 8 → (2)

substitute y = x - 31 into (2)

4(x - 31) = x + 8

4x - 124 = x + 8 ( subtract x from both sides )

3x - 124 = 8 ( add 124 to both sides )

3x = 132 ( divide both sides by 3 )

x = 44

substitute x = 44 into (1)

44 - 31  = y , then

y = 13

the 2 numbers are 13 and 44