Identify the independent and dependent variables in the following situation Julie notices that her plant grows one inch for every liter of water that it receives

Answer:

You need to pay $1,759.50 if you get a 15% discount.

Step-by-step explanation:

100%-15%=85%

0.85x2,070=$1,759.50

Answer:

$6500

Step-by-step explanation:

First you find 3% of 5,000. You get 150. Then you would multiply 150 by 10 since it was in the bank for 10 years. You get 1500. Then you add 5000 and 1500 to get 6500.

Answer:

2.28%

Step-by-step explanation:

As this is normally distributed, we can use z scores to find the percentage.

First, find the z-score for 148.

The z-score that you get is:

(148-160)/2=2

As we see that z=2, we can use a calculator or a z-score chart to find the percentage less than a z score of 2.

I used my chart and found: 2.28%

The x-intercept of the table of values is 12 or (12, 0).

To find the x-intercept of a table that represents a linear relationship between x and y, first write the equation that models the table.

To write the equation, first find the slope (m) using two pairs of values, say, (22, 36) and (27, 54)

Slope (m) = (54 - 36)/(27 - 22)

Slope (m) = 18/5

Write the equation that represents the table of values by substituting (a, b) = (22, 36) and m = 18/5 into y - b = m(x - a):

y - 36 = 18/5(x - 22)

To find the x-intercept, substitute y = 0 into the equation, y - 36 = 18/5(x - 22) to find the value of x:

0 - 36 = 18/5(x - 22)

-36 = 18/5(x - 22)

5(-36) = 18(x - 22)

-180 = 18(x - 22)

-180/18 = x - 22

-10 = x - 22

-10 + 22 = x

12 = x

x = 12

The x-intercept is 12 or (12, 0).

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Answer:

a suprise

Step-by-step explanation:

The probability that an MP3 player manufactured in Fort Meyers is defective is 0.37%.

To calculate the probability that an MP3 player is defective, we need to consider the manufacturing plants and their respective defect rates.

Given:

Plant at Memphis manufactures 50% of the MP3 players, and 1% of those manufactured at that plant are defective.

Plant at Fort Meyers manufactures 20% of the MP3 players, and 3% of those manufactured at that plant are defective.

No information is provided about the defect rate of the third plant.

To find the overall probability of an MP3 player being defective, we need to consider the probability of selecting a defective player from each plant and then weigh it by the probability of selecting a player from each plant.

Let's calculate the overall probability:

Probability of selecting a defective player from Memphis plant = 50% * 1% = 0.50% or 0.005 (since 50% is equivalent to 0.50 in decimal form)

Probability of selecting a defective player from Fort Meyers plant = 20% * 3% = 0.60% or 0.006 (since 20% is equivalent to 0.20 in decimal form)

To calculate the overall probability, we need to weigh these probabilities by the probability of selecting an MP3 player from each plant:

Probability of selecting from Memphis plant = 50% = 0.50 (decimal form)

Probability of selecting from Fort Meyers plant = 20% = 0.20 (decimal form)

Overall probability of selecting a defective MP3 player is given by:

Overall probability = (Probability from Memphis plant * Probability of selecting a defective player from Memphis) + (Probability from Fort Meyers plant * Probability of selecting a defective player from Fort Meyers)

Overall probability = (0.50 * 0.005) + (0.20 * 0.006) = 0.0025 + 0.0012 = 0.0037 or 0.37%

Therefore, the probability that an MP3 player, manufactured in Fort Meyers, is defective is 0.37%.

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Answer:

Hey! your answer should be A. 6 and 8

Step-by-step explanation:

I've attatched an image of what corresponding angles look like. Your best choice would be A

Step-by-step explanation:

I just answered this. please look at your copy post.

The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.

To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.

Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.

The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.

Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.

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Answer:

$1500

Step-by-step explanation:

you can figure it out by going in increments of 4.5 years because that is the info you have from the problem so

47000 4.5 years later is 23500

9 years = 11750

13.5y = 5875

18y = 2937.5

22.5 years later is 1468.75

22.5 years is about 23 years and to the nearest hundred dollars that is $1500 so that is the answer

Hope this helps! :)

we know the car depreciates every 4.5 years, and we also know its by one half or namely the depreciation rate is 50% of its value.

\(\textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &47000\\ r=rate\to 50\%\to \frac{50}{100}\dotfill &0.5\\ t=years\dotfill &23\\ c=period\dotfill &4.5 \end{cases} \\\\\\ A=47000(1 - 0.5)^{\frac{23}{4.5}}\implies A=47000(0.5)^{\frac{46}{9}}\implies A\approx 1400\)

Answer:

70°

Step-by-step explanation:

Because line segment OB and OC are both straight lines, then the measure of angle fromed by this two segments is the same in different locations.

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Based on the data, the mean would be the best measure of center to describe a typical value in the data set.

To create a dot plot, we can list the numbers in order and place a dot above the corresponding value on the number line.

20 ••

21 ••

22 •

23 ••••

24 •••••

25 ••

26 ••

27 •

The dot plot shows a relatively symmetric distribution of the data, with the majority of values clustered around the middle. Therefore, the mean would be a good measure of center to describe a typical value of the data set.

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The required value of the x in the proportional relationship is 8.

Given that,
Variables y and x have a proportional relationship and y = 21 when x = 14. What is the value of x when y = 12 is to be determined.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
y = 21 when x = 14,
y = 12 when x = ?
So y is proportion to x,
21 / 12 = 14 / x
x = 14 (12 / 21)
x = 2 (12 / 3)
x = 2 (4)
x = 8

Thus, the required value of the x in the proportional relationship is 8.

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Answer:

Y=1/5x+ -2

Step-by-step explanation:

Hope this helps

Answer:

y = 3\(\sqrt{5}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

y² = 3 × (3 + 12) = 3 × 15 = 45 ( take square root of both sides )

y = \(\sqrt{45}\) = \(\sqrt{9(5)}\) = \(\sqrt{9}\) × \(\sqrt{5}\) = 3\(\sqrt{5}\)

Answer:

yes

Step-by-step explanation:

they are congruent

the answer is ( a=st2-3t )

Answer: 5

Step-by-step explanation:

To find 20% of something, we can just multiply it by 0.2

25 × 0.2 = 5

Have a good day :)

Answer:

Step-by-step explanation:

angle 2 and angle 7 are alternate exterior angles.so they are always equal.

angle 2=angle 7

Answer:

The illustration is approximately 226 times larder than the actual pollen grain.

Step-by-step explanation:

First of all, we have to write out the size of the actual pollen grain in a manner that is easy for us to work with.

This will be

\((\frac{3}{10}) ^{3}=0.027cm\) wide

The original width of the pollen is 0.027 cm.

Next,

We can take the width of the illustration to be 6.10 cm  wide.

After this,

To get the magnification factor, we will have to use the formula

Magnification = illustrated size/ actual size

This will be the magnification = \(6.10/0.027\) = 255.92 times

Hence, the illustration is approximately 226 times larder than the actual pollen grain.

Answer:

19/50   40%     0.37

Step-by-step explanation:

19/50 = 0.38

0.37 = 0.37

40% = 0.40

40%, 19/50, 0.37

Answer:

It depends on which form you are looking for.

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form: x=37/21

Decimal Form: x=1.761904

Mixed Number Form: x=1  16/21

The value of the iterated integral \(\int\limits^1_0 \int\limits^2_0 (12x^2y^3) dx dy\) is 1.

What is iterated integral ?

An iterated integral is a method for calculating the definite integral of a multivariable function over a region in space. It involves evaluating the integral in stages, by integrating over one variable at a time.

The most common type of iterated integral involves integrating first with respect to one variable, such as x, while holding the other variables constant, and then integrating the resulting function with respect to another variable, such as y. This process is repeated for each variable until all variables have been integrated.

According  to the question:
To evaluate the iterated integral:

\(\int\limits^1_0 \int\limits^2_0 {(12x^2y^3)} dx dy\)

We integrate with respect to x first and then with respect to y.

\(\int\limits^1_0 \int\limits^2_0 {(12x^2y^3)} dx dy\) = \(\int\limits^1_0 \int\limits^2_0 [4x^3y^3]dxdy\)

=\(\int\limits^1_0 [(4(1)^3y^3) - (4(0)^3y^3)] dy\)

= \(\int\limits^1_0 {4y^3} dy\)

= \(\int\limits^1_0[y^4]\)

= 1^4 - 0^4

= 1

Therefore, the value of the iterated integral \(\int\limits^1_0 \int\limits^2_0{(12x^2y^3)} dxdy\) is 1.

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sohcahtoa!

SOH

Sin=Opposite/Hypotenuse

CAH

Cosine=Adjacent/Hypotenuse

TOA

Tangent=Opposite/Adjacent

Part a

\(A(11)=224-16(11)=\boxed{\$48}\)

Part b

\(A(t)=0\\\\224-16t=0\\\\t=\frac{224}{16}\\\\t=\boxed{14 \text{ trips}}\)

a) The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48

b) The number of trips on the toll roads can he take until his account is empty is 14 trips

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A ( t ) = 224 - 16t , where t is the number of trips

a)

The amount of money does Ahmad have left in the account after 11 trips on the toll roads be P

Substituting the value of t = 11 in the equation , we get

A ( 11 ) = 224 - 16 ( 11 )

A ( 11 ) = 224 - 176

A ( 11 ) = $ 48

So , The amount of money does Ahmad have left in the account after 11 trips on the toll roads is $ 48

b)

The number of trips on the toll roads can he take until his account is empty be n

when A ( t ) = 0

224 - 16t = 0

Adding 16t on both sides of the equation , we get

224 = 16t

Divide by 16 on both sides , we get

t = 14 trips

Hence , the equations are solved

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Answer:

\(5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)

Step-by-step explanation:

\(f(x)=x^5\\f'(x)=5x^4\\g(x)=1-\frac{5}{x+8}\\g'(x)=\frac{5}{(x+8)^2}\\\\\frac{d}{dx}f(x)g(x)\\\\=f'(x)g(x)+f(x)g'(x)\\\\=5x^4(1-\frac{5}{x+8})+x^5(\frac{5}{(x+8)^2})\\\\=5x^4-\frac{25x^4}{x+8}+\frac{5x^5}{(x+8)^2}\)