£750 is divided between Bridget, Caroline & Sarah so that Bridget gets twice as much as Caroline, and Caroline gets three times as much as Sarah. How much does Caroline get?

The expression (1.4 × 10¹)(8 × 10⁴) in scientific notation is 1.12 × 10⁵ and for expression (1.1 × 10⁻⁵)(3 × 10²) the  scientific notation is 3.3 × 10⁻³

The given expressions are (1.4 × 10¹)(8 × 10⁴) can be calculated as:

Firstly we will multiply the decimal numbers and whole numbers

1.4 × 8

One point four times eight is equal to eleven point two

= 11.2

Now we multiply the base with ten

10¹ × 10⁴

We know that when the bases are same then the powers will be added in multiplication

= 10⁵

Combining these results, we have 11.2 × 10⁵

Therefore, the result in scientific notation is 1.12 × 10⁵

Similarly, for (1.1 × 10⁻⁵)(3 × 10²)

We will multiply the decimal numbers and whole numbers

1.1 × 3 = 3.3

Now the base with ten will be multiplied

10⁻⁵ × 10²

The bases are same the powers will be added

= 10⁻³

Combining these results, we have 3.3 × 10⁻³

Therefore, the result in scientific notation is 3.3 × 10⁻³

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Answer:

11.   g

12.  f

13.  e    (add all the frequencies)

14.  d

15.  c    (eg. 17.5 -8.5 = 9)

16.  b

17.  a

Let me know if you have any questions.

Hope this helps!

Answer:

41^2 = 41^2

Step-by-step explanation:

a^2 +b^2 =c^2

7^2+24^2 = 25^2

49+576 = 25^2

625 = 25^2

25^2 = 25^2

a^2 +b^2 =c^2

9^2 + 40^2 = 41^2

81+1600=41^2

1681=41^2

41^2 = 41^2

The probability of success on the first roll of the die is 5/6. The expected value of the random variable x1, representing the number of rolls needed to get the first success, is 6/5. The probability of success on subsequent rolls, after the first success, is 5/6. The expected values of x2, x3, x4, x5, and x6 are 6/4, 6/3, 6/2, 6/1, and 6/0, respectively. By applying the linearity of expected value, the average number of rolls needed to get each number at least once, E(X), is 6/5 + 6/4 + 6/3 + 6/2 + 6/1 + 6/0.

In this problem, we are interested in finding the expected value of the number of rolls needed to get each number on the die at least once. To begin, on the first roll, there are 5 out of 6 possible outcomes that are considered a success since we have not rolled them before. Therefore, the probability of success on the first roll is 5/6.

Next, we consider the random variable x1, which represents the number of rolls needed to get the first success. Since this follows a geometric distribution with probability of success p = 5/6, the expected value of x1 is given by 1/p, which is 6/5.

After obtaining the first success, the probability of success on subsequent rolls is (6-1)/6 or 5/6, as there are now 5 remaining numbers that have not been rolled. Therefore, the expected values of x2, x3, x4, x5, and x6 are 6/4, 6/3, 6/2, 6/1, and 6/0, respectively, following the same reasoning as for x1.

Finally, by applying the linearity of expected value, the average number of rolls needed to get each number at least once, E(X), is obtained by summing the expected values of x1, x2, x3, x4, x5, and x6. Thus, E(X) = 6/5 + 6/4 + 6/3 + 6/2 + 6/1 + 6/0, which gives the average number of rolls needed to achieve the desired outcome.

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Answer:

x=1

Step-by-step explanation:

2+1+1+1+4=9

2+x+x+x+4=9

=> 3x + 6 = 9

=> 3x = 9-6

=> 3x = 3

=> x = 3/3

=> x = 1

The simplified form of radical √18 . 3√5 = 9√10

In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol.

For example, ³√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.

The term underneath the radical symbol is called the radicand.

Given radical

√18 . 3√5

⇒ √(9 × 2) . 3√5

⇒ 3√2 . 3√5

⇒ 9(√2.5)

⇒ 9√10

⇒ 28.46

Hence, The radical √18 . 3√5 can be simplified to 9√10 having value = 28.46

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In the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

In the right triangle XYZ, angle X and angle Y are complementary angles.

The complementary angle is either of two angles whose sum is 90 degrees

Therefore,

Angle X + Angle Z = 90 degrees

In trigonometry,

sinθ = Opposite side / Hypotenuse

sin z= 36/85

z= \(sin^{-1}(\frac{36}{85} )\)

z= 25.06

Then the value of cos z is

cos 25.06 = 77/85

Hence, in the right triangle XYZ, angle X and angle Y are complementary angles, is angle sin z= 36/85, then the value of cos z= 77/85

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Hey there!☺

Look at image attached below!

Please flip the image if you want to see it properly.

Hope this helps!

Answer:

;)

Step-by-step explanation:

im just here to collect points cause im poor

The value of the mean and the median is so close. Then the correct option is B.

Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect, and summarise the data.

The data is given below.

32, 33, 34, 35, 37, 37, 38, 38, 39, 40, 42, 42, 43, 44, 44, 45, 45, 45, 47, 50

The mean is calculated as,

Mean = (sum of all values) / (number of values)

Mean = (32 + 33 + 34 + ... + 47 + 50) / 20

Mean = 40.5

The median is calculated as,

Median = middle value

Median = 41

The mode is calculated as,

Mode = most frequent

Mode = 45

The value of the mean and the median is so close. Then the correct option is B.

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Answer:

2.7

Step-by-step explanation:

mean = (1 + 2 + 2 + 3 + 8 + 8)/6 = 4

absolute values of differences:

|1 - 4| = 3

|2 - 4| = 2

|2 - 4| = 2

|3 - 4| = 1

|8 - 4| = 4

|8 - 4| = 4

sum of the absolute values of the differences:

(3 + 2 + 2 + 1 + 4 + 4)/6 = 16

MAD = 16/6 = 2.7

Answer: 2.7

the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

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Thus, triangle obtained is right triangle. This triangle is will be unique and one side and angle is fixed.

In a right triangle, one of the three angles is 90 degrees, while the other two acute angles add up to 90 degrees.

Given data:

One side of triangle = 3 in (say BC)

Angle C = 50 degrees

Angle A = 90 degrees

Construct a triangle using the scale and compass.

The obtained figure is attached.

Thus, triangle obtained is right triangle. This triangle is will be unique and one side and angle is fixed.

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Step-by-step explanation:

Given

y = 2x + 1 .....i)

y = 3x +2 .....ii)

Putting equation II in equation i

3x + 2 = 2x + 1

3x - 2x = 1 - 2

x = -1

Now putting x = -1 in equation i

y = 2* (-1) + 1

= -2 + 1

= - 1

Therefore x = -1 and y = -1

Hope it will help :)

The equation for the nth term of the arithmetic sequence -8, -6, -4, -2, 0,... is A(n) = 2n - 10, where n is the index of the term.

The arithmetic sequence given is -8, -6, -4, -2, 0,.... The common difference between consecutive terms in the sequence is 2.

To find the equation for the nth term of an arithmetic sequence, we can use the formula

a_n = a_1 + (n-1)*d

where a_n is the nth term, a_1 is the first term, n is the index of the term, and d is the common difference.

In this sequence, a_1 = -8 and d = 2. Substituting these values into the formula, we get

a_n = -8 + (n-1)*2

= -8 + 2n - 2

= 2n - 10

Therefore, the equation for the nth term of the sequence is 2n - 10.

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The arc length of the curve x =\(y^4/4 + 1/8y^2\), for 1 <= y <= 5, is approximately 33.93 units.

To find the arc length of the curve, we use the formula for arc length integration. Given the equation x = \(y^4/4 + 1/8y^2\) and the interval 1 <= y <= 5, we want to determine the length of the curve within this range.

First, we differentiate the equation with respect to y to obtain dx/dy. In this case, dx/dy = \(y^3 + 1/4y\). Then, we use the formula for arc length:

L = ∫[a,b] \(\sqrt{(1 + (dx/dy)^2)}\) dy

Plugging in the values from the given interval, a = 1 and b = 5, we integrate the expression \(\sqrt{(1 + (y^3 + 1/4y)^2)}\) with respect to y. Evaluating this integral gives us the arc length of the curve within the specified interval, which is approximately 33.93 units.

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Rewritten form of equations in exponential form will be:\(log_{25}(5) = 1/2:Exponential form: 25^{1/2} = 5\quad \\log_{64}(1/2) = -1/6:Exponential form: 64^{-1/6} = 1/2\quad\\log_{(1/17)}(1/289) = 2:Exponential form: (1/17)^2 = (1/289)\quad , \\log_6(216) = 3:Exponential form: 6^3 = 216\)

\(log_{25}(5) = 1/2\)

Identify the base (b) as 25, the logarithmic expression as \(log_{25}(5) = 1/2\), and the result (y) as 1/2.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 25^(1/2) = 5.

\(log_{64}(1/2)=\frac{-1}{6}\)

Identify the base (b) as 64, the logarithmic expression as log_64(1/2), and the result (y) as -1/6.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 64^(-1/6) = 1/2.

\(log_{(1/17)}(1/289) = 2\)

Identify the base (b) as 1/17, the logarithmic expression as log_(1/17)(1/289), and the result (y) as 2.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: (1/17)^2 = 1/289.

\(log_6(216) = 3\)

Identify the base (b) as 6, the logarithmic expression as log_6(216), and the result (y) as 3.

Apply the definition of logarithms: log base b of x = y if and only if b^y = x.

Rewrite the equation using the exponential form: 6^3 = 216.

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The exponential form of the equation is :

15) \(25^{(1/2)} = 5.\)

16)  \(64^{(\frac{-1}{6})} = \frac{1}{2}.\)

17)  \((\frac{1}{17})^2 = \frac{1}{289}.\)

18)  \(6^3 = 216.\)

How to determine exponential form of equation?

15) \(log_{25}5=\frac{1}{2}\)

Identify the base (b) as 25, the logarithmic expression as , and the result (y) as \(\frac{1}{2}\).

Apply the definition of logarithms:  \(log_b x=y\) if and only if  \(b^y = x\).

Rewrite the equation using the exponential form: \(25^{(1/2)} = 5.\)

16)\(log_{64}\frac{1}{2}=-\frac{1}{6}\)

Identify the base (b) as 64, the logarithmic expression as \(log_{64}\frac{1}{2}\), and the result (y) as -\(\frac{1}{6}\).

Apply the definition of logarithms:  \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form:  \(64^{(\frac{-1}{6})} = \frac{1}{2}.\)

17)\(log_{\frac{1}{17}}\frac{1}{289}=2\)

Identify the base (b) as 1/17, the logarithmic expression as \(log_{\frac{1}{17}}\frac{1}{289}\), and the result (y) as 2.

Apply the definition of logarithms:  \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form: \((\frac{1}{17})^2 = \frac{1}{289}.\)

18) \(log_6216=3\)

Identify the base (b) as 6, the logarithmic expression as \(log_6216\), and the result (y) as 3.

Apply the definition of logarithms:   \(log_b x=y\)if and only if   \(b^y = x\).

Rewrite the equation using the exponential form: \(6^3 = 216.\)

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The interaction plot consistent with the combination of main effects and interactions described is Plot D, which shows an interaction between squirrels and location.

An interaction occurs when the effect of one independent variable (in this case, squirrels) on the dependent variable (cone sizes) depends on the level of another independent variable (location).

Based on the given information, we have the following main effects and interactions:

1. Main effect of location: This means that the location (island vs. mainland) has an independent effect on cone sizes. It suggests that there is a difference in cone sizes between the two locations.

2. Main effect of squirrels: This means that the presence or absence of squirrels has an independent effect on cone sizes. It suggests that the presence of squirrels may influence cone sizes.

3. Interaction between squirrels and location: This means that the effect of squirrels on cone sizes depends on the location. In other words, the presence or absence of squirrels may have a different impact on cone sizes depending on whether the trees are on an island or the mainland.

Among the given interaction plots, Plot D is consistent with these main effects and interactions. It shows that the effect of squirrels on cone sizes differs between the island and mainland locations, indicating an interaction between squirrels and location.

Therefore, Plot D is the interaction plot that aligns with the combination of main effects and interactions described in the question.

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The given graph is a rectangular hyperbola graph because the product of the variables, that is x and y, is constant. The equation of a rectangular hyperbola is y=k/x. k is the constant value. The variables x and y are inversely proportional to each other.

Thus, as x increases, y decreases, and vice versa.GraphA rectangular hyperbola graph with labeled axesThe horizontal axis is labeled in increments of 5s. The vertical axis is labeled in increments of 1mil. a) On the graph, 10.00 ÷ min is 0.1mil. Thus, 10.00 ÷ min corresponds to a point on the graph where the vertical axis is at 0.1mil.b) At 6 in 20-00, the horizontal axis is 6, which corresponds to 30s.

The vertical axis is 20-00 or 2000mil, which is equivalent to 2mil. The coordinates of the point are (30s, 2mil).c) At 10.0000000.00 mes, the horizontal axis is at 100s. The vertical axis is 0, which corresponds to the x-axis. The coordinates of the point are (100s, 0).

d) From 20.00 to 35.00s, the vertical axis is at 4mil. From 20.00 to 35.00s, the horizontal axis is at 3 increments of 5s, which is 15s. The coordinates of the starting point are (20.00s, 4mil). The coordinates of the ending point are (35.00s, 4mil). The point on the graph is represented by a horizontal line segment at y=4mil from x=20.00s to x=35.00s. Similarly, from 0 to 40.00s, the coordinates of the starting point are (0, 10mil).

The coordinates of the ending point are (40.00s, 0). The point on the graph is represented by a curve from (0, 10mil) to (40.00s, 0).

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Therefore, Andrea has 25 dimes in 37 coins, all nickels and dimes and the value of the 37 coins is $3.10.

Let's represent the number of nickels by "n" and the number of dimes by "d".

From the problem, we know that:

n + d = 37 (equation 1) ---(the total number of coins)

0.05n + 0.1d = 3.10 (equation 2) ---(the total value of the coins in dollars)

To solve for d, we can rearrange equation 1 to get:

n = 37 - d

Substitute this expression for n into equation 2 and simplify:

0.05(37-d) + 0.1d = 3.10

1.85 - 0.05d + 0.1d = 3.10

0.05d = 1.25

d = 25

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The possible number of cupcakes is less than or equal to 23

let

The inequality:

2k ≤ 46

divide both sides by 2

k ≤ 46 / 2

k ≤ 23

Therefore, the possible number of cupcakes is less than or equal to 23

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The total number of acres planted for the optimal solution is not provided in the given information.

The amount of fertilizer (in tons) required to produce only corn is not provided in the given information.

The peak number of acres of wheat planted as fertilizer availability varies from 200 tons to 2200 tons in 100-ton increments cannot be determined without additional information.

I can help explain the general approach to answering the questions you mentioned.

To determine the total number of acres planted for the optimal solution, you would need to refer to the problem's constraints and objective function. The optimal solution would be obtained by solving the problem using linear programming techniques such as the simplex method or graphical method. By solving the problem, you can identify the values of the decision variables (such as acres planted) that maximize or minimize the objective function while satisfying the given constraints. The total number of acres planted for the optimal solution would depend on the specific problem setup and the solution obtained.

Similarly, to find out how much fertilizer would be needed to produce only corn, you would need to refer to the constraints and objective function of the problem. The specific requirements and coefficients associated with the corn production and fertilizer usage would determine the amount of fertilizer needed. By solving the problem, you can obtain the value of the decision variable representing fertilizer usage, which would indicate the required amount of fertilizer in tons.

SolverTable is a tool in Excel that allows you to perform sensitivity analysis by varying certain input values and observing the impact on the output. By using SolverTable, you can analyze the relationship between fertilizer availability (input) and acres planted (output) in the given problem. By varying the fertilizer availability from 200 tons to 2200 tons in 100-ton increments, you can observe how the acres of wheat planted change accordingly. The peak number of acres of wheat planted would be the maximum value observed during this range of fertilizer availability.

Since I don't have access to the specific problem you mentioned, I cannot provide precise answers or calculations. Please refer to the problem in your textbook or reference material to obtain the exact values and final answers.

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During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Answer:

False, plants can be anything, take grass and trees and cacti, plant just need photosynthesis.

Step-by-step explanation:

You see, plants aren't based on if they are a flower or not

The landform region is the Atlantic Coastal Plain.

The Atlantic Coastal Plain is a significant landform region that spans along the eastern coast of the United States, extending from Florida in the south to Massachusetts in the north.

It is characterized by relatively flat or gently sloping terrain and is primarily composed of sedimentary deposits, including sand, silt, and clay.

The formation of the Atlantic Coastal Plain can be attributed to processes such as erosion, deposition, and sea-level changes over millions of years. It is a result of sedimentary materials being deposited by rivers and streams, as well as the gradual retreat of the ocean over time.

This region is known for its diverse landscapes, which can include barrier islands, marshes, estuaries, and coastal forests. It is an important area for agriculture, as the fertile soils and favorable climate support various crops.

Additionally, the Atlantic Coastal Plain is home to numerous cities and metropolitan areas, including Miami, Washington D.C., and New York City. It also features several prominent geographic features such as the Chesapeake Bay, Delaware Bay, and Cape Cod.

Overall, the Atlantic Coastal Plain is a significant landform region with a distinct geological history and unique ecological characteristics, playing a vital role in the geography and development of the eastern United States.

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The equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 in the form of y = mx + b is y = (6/49)x - 29/49 .

The function whose tangent line is to be found out is f(x)=(x-5)/(x+1) ;

to find the tangent equation , we differentiate the function ;

the function f(x) is of the form g(x)/h(x) ;

On differentiating g(x) and h(x) , we get that g'(x) = h'(x) = 1 ;

We get ; f'(x) = [1(x+1))-(1(x-5)]/(x+1)² ;

⇒ f'(x) = [x+1-x+5]/(x+1)² ;

⇒ f'(x) = 6/(x+1)² ;

Now, we x = 6 in the derivative to find slope of tangent at that point.

So , ⇒ f'(6) = 6/(6+1)²

⇒ f'(6) = 6/49

Now the slope is =  6/49 ,  the value of y in (6,y) by putting in x = 6 into the original function:

⇒ f(6) = (6 - 5)/(6 + 1)

⇒ f(6) = 1/7

We currently know a point (6,1/7) = (x₁,y₁) and slope of tangent, which is 6/49.

now using  point slope form to find equation of tangent.

⇒ y-y₁ = m(x-x₁)

⇒ y - 1/7 = (6/49)(x-6)

⇒ y = (6/49)x - 29/49

Therefore , The equation of the tangent is y = (6/49)x - 29/49 .

The given question is incomplete , the complete question is

What is the equation of the tangent line of f(x)=(x-5)/(x+1) at x=6 . Enter your answer as an equation in the y = mx + b form ?

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Answer:

I think it would be x = 4

Step-by-step explanation:

Answer:NaN

Step-by-step explanation:

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