Can somebody help me with number 6 please?

The logarithm value of log 1/2 462 to four decimal places is  –8.8517.

The logarithm is the mathematical inverse function to exponentiation.

The logarithm of a number x is the exponent to another fixed term.

It is given the log of 462 to a base of 1/2.

\(log_{0.5} 462 = \frac{log462}{log0.5}\)

 = –8.8517

Therefore, the logarithm value of log 1/2 462 to four decimal places is  

–8.8517.

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\(\begin{cases} f(x)=4x-9\\\\ g(x)=x+1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=4[g(x)]-9\implies f(~~g(x)~~)=4[x+1]-9 \\\\\\ f(~~g(x)~~)=4x+4-9\implies \boxed{f(~~g(x)~~)=4x-5} \\\\[-0.35em] ~\dotfill\\\\ g(~~f(x)~~)=[f(x)]+1\implies g(~~f(x)~~)=[4x-9]+1 \\\\\\ g(~~f(x)~~)=4x-9+1\implies \boxed{g(~~f(x)~~)=4x-8}\)

The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

What is a misleading graph?

A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.

What is a data set?

A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.

Here, we have

2 events with a cost of 1,000-1,499;

4 events with a cost of 1,500 to 1,999;

3 events with a cost of 2,000 to 2,499;

1 event with a cost of 3,000 to 3,499

We concluded from the given dataset that the cost of the event is plotted on the x-axis.

In a given dataset, the entry from 2500 to 2599 is missing.

The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.

Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

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Answer:

7280000000 or 7.28^9 (in scientific notation)

Step-by-step explanation:

this question is asking you to transfer numbers out of scientific notation and multiply them. 10^6 is 1 followed by 6 zeros (good trick to remember) or 1000000. when you multiply anything by a power of 10 you just add that many zeroes to it or move the decimal point one point to the left for every zero. so in this example it is 5.2 times 1000000 which is 5200000. we do the same for the other one and we get 1400. When we multiply these two values we get 7280000000 or 7.28^9

The equations N1/dt = r1N1[(K1 - N1 - ON2)/K1] and ON2/dt = r2N2[(K2 - N2 - BN1)/K2] describe models for population dynamics. These models are used to understand how populations of organisms change over time, based on factors like birth rates, death rates, and available resources.

In these equations, N1 and N2 represent the population sizes of two interacting species. The variables r1 and r2 are the intrinsic growth rates of these species, or the rates at which they reproduce in the absence of limiting factors. K1 and K2 represent the carrying capacities of the environment for each species, or the maximum population sizes that can be sustained by available resources.
The terms ON2 and BN1 represent the effects of interspecific interactions on population growth. ON2 refers to the negative impact of species 2 on the growth rate of species 1, and BN1 refers to the negative impact of species 1 on the growth rate of species 2. These interactions can take many forms, such as competition for resources or predation.
By manipulating these equations, scientists can make predictions about how populations will change over time, and test these predictions against real-world data. These models are particularly useful for understanding how species interact in complex ecosystems, and how human activities like habitat destruction and climate change are affecting these ecosystems.

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We are given a matrix A and a scalar λ and asked to show that λ is an eigenvalue of the matrix and determine a basis for its eigenspace.

To determine if λ is an eigenvalue of matrix A, we need to check if there exists a non-zero vector v such that Av = λv. In other words, if multiplying matrix A by vector v results in a scaled version of v. Given the matrix A = [6, 9; -10, 63] and scalar λ = 5, we can find the eigenvectors by solving the equation (A - λI)v = 0, where I is the identity matrix. Substituting the values, we have: [6-5, 9; -10, 63-5]v = 0. Simplifying the equation, we get: [1, 9; -10, 58]v = 0. Solving the system of linear equations, we can find the eigenvectors v corresponding to the eigenvalue λ = 5.

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Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

Answer:  -6 only (choice B)

This is because the point (0,-6) is on the blue line. This is the y intercept.

Choice C would be true if you wanted to solve f(x) = 0, instead of f(0) itself.

Answer:

-6

Step-by-step explanation:

f(0) means what is the output when the input is 0

x=0 y= -6

The function of f(u) = cos(u)` and `g(x) = sin x`.

We are to write the function `y = cos(sin x)` below in the form `y = f(u)` and `u = g(x)`.

Then, we need to find `dy/dx` as a function of `x`.

Function `y = cos(sin x)` can be written as: `y = f(u)`, where `u = sin x` and `f(u) = cos(u)`.

Thus, `f(u) = cos(sin x)` and `u = sin x`.

Hence, `f(u) = cos(u)` and `g(x) = sin x`.

Now, we can apply the chain rule of differentiation to find `dy/dx` as a function of `x`.

The chain rule states that if `y = f(u)` and `u = g(x)`, then `dy/dx = dy/du * du/dx`.

Here, `f(u) = cos(u)` and `g(x) = sin x`. Thus, `dy/du = -sin(u)` and `du/dx = cos x`.

Therefore, `dy/dx = dy/du * du/dx = -sin(u) * cos x = -sin(sin x) * cos x`.

Thus, `dy/dx = -sin(sin x) * cos x`.

Hence, the functions `f(u)` and `g(x)` are: `f(u) = cos(u)` and `g(x) = sin x`.

Therefore, we have `y = cos(sin x)` in the form `y = f(u)` and `u = g(x)`.

Finally, `dy/dx` as a function of `x` is `-sin(sin x) * cos x`.

Thus, `f(u) = cos(u)` and `g(x) = sin x`.

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a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Multiply both sides by 6:

6M = uh

Then divide both sides by h:

u = (6M)/h

If Jane and Sarah share an amount of £63 and Jane receives "5/9" of  money, then the amount of money Sarah receives is £28..

The total amount that needs to be shared between Jane and Sarah is = £63,

We know that , Jane receives "5/9" of the total amount,

Which means , Jane receives = (5/9)×63 = £35,

The total-sum of money is = £63,

So, We can write,⇒ Total money = Jane + Sarah,

Substituting the values ,

We get,

⇒ 63 = 35 + Sarah,

⇒ Sarah = 63 - 35 = £28.

Therefore, Sarah's share of money is = £28.

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Answer:

the time taken is 4 hours

Step-by-step explanation:

The computation of the time is shown below:

As we know that

Speed = Distance ÷ Time

50 miles per hour = 200 miles ÷ Time

So the time would be

= 200 ÷ 50

= 4 hours

Hence, the time taken is 4 hours

Answer:

m=1/5

Step-by-step explanation:

SImplify

4m-8=-6m-6

then 10m=2

so m=1/5

4(m - 2) = -2(3m + 3)

4m - 8 = -6m -6

4m + 6m = -6 + 8

10m = 2

m = 1/5   or 0.2

4(0.2 - 2) = -2[3(0.2) + 3]

4(-1.8) = -2(0.6 + 3)

- 7.2 = -2(3.6)

- 7.2 = - 7.2

Step-by-step explanation:

To compute a 90% confidence interval for the population proportion with a margin of error of 0.08 and no prior estimate for the population proportion, a sample size of 181 is needed.

To determine the sample size needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, we can use the formula:

n = (z^2 * p * (1 - p)) / E^2

where n is the sample size needed, z is the z-score for the desired confidence level (90% confidence level has a z-score of 1.645), p is the estimated proportion (since no prior estimate is available, we use 0.5 as a conservative estimate), E is the margin of error (0.08)

Substituting the given values, we get:

n = (1.645^2 * 0.5 * (1 - 0.5)) / 0.08^2

n = 180.99

Rounding up to the nearest whole number, we get:

n = 181

Therefore, a sample size of 181 is needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, when no prior estimate for the population proportion is available.

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Answer:

7, 9, 11

Step-by-step explanation:

If x is the smallest of the integers, then x+2 is the next consecutive odd integer, and x+4 is the largest odd integer.

1 less than 3 times the largest is equal to the sum of twice the first and twice the second.

3(x+4) − 1 = 2x + 2(x+2)

3x + 12 − 1  = 2x + 2x + 4

3x + 11 = 4x + 4

7 = x

The integers are 7, 9, and 11.

The average number of viewers over the two weeks is 11. 48 × 10^5 viewers

Average can be defined as a representative of a list of numbers. It is the sum of the numbers divided by how many numbers present in the list.

From the information given, we have that:

Now, let's find the sum

= 5.6 x 10^5 + 4.1 x 10^5

= 22. 96 × 10^5

Let's find the average

Average = 22. 96 × 10^5 / 2

Average = 11. 48 × 10^5 viewers

Thus, the average number of viewers over the two weeks is 11. 48 × 10^5 viewers

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Answer:

9.7 x 105

Step-by-step explanation:

tip: make sure to use the ^ symbol to show to the power of not just copy and paste because it copy and pastes wrong

Answer:

19

Step-by-step explanation:

it’s the only one within Q3

Answer: Yes, it will overload the truck.

Step-by-step explanation:

To begin, form an algebraic equation.

200(r) + 425(f)

Second, substitute your numbers for the variables.

200(18) + 425(11) = ?

Third, multiply your numbers of fridges by the weight of each.

3600 + 4675 = 8275 is the total

Finally, determine whether or not if it is greater than the weight limit the truck has.

7200 < 8275

Therefore, the total weight is greater than the weight limit.

Answer:

A 5c+ 275 > 500

Step-by-step explanation:

Answer:

A set is well-defined so that we can always tell what is and what is not a member of the set

Answer:

B.   2n + 14 ≥ -10

Step-by-step explanation:

twice a number: 2n

... increased by 14: 2n + 14

is at least: 2n + 14 ≥

the opposite of 10: 2n + 14 ≥ -10

Answer:

Your answer is B, 2n + 14 \(\geq\) -10

Hope this helps!

Step-by-step explanation:

* Twice a number *

2 * n

* Increased by 14 *

+ 14

* Is at least *

\(\geq\)

* The opposite of 10 *

-10

The linear regression model can be extended to accommodate certain forms of non-linear relationships between the response and predictor(s).  Polynomial regression is one specific method for incorporating non-linear associations within the linear regression framework.

It involves understanding the flexibility of the linear regression model and the techniques available to address non-linear relationships. While the linear regression model assumes a linear relationship between the response variable and predictors, it can still be useful in accommodating certain types of non-linear relationships.

By applying appropriate transformations to the predictor variables, such as taking their squares, logarithms, or other non-linear functions, we can introduce non-linear associations into the linear regression model. This allows the model to capture curvature or other non-linear patterns in the data.

Polynomial regression is a specific approach to incorporating non-linear relationships within the linear regression framework. It involves adding polynomial terms of the predictor variables to the model, such as squared or cubed terms. By including these polynomial terms, the model can account for non-linear relationships and capture more complex patterns.

It's important to note that while linear regression can be extended to accommodate some non-linear relationships, there may be cases where more advanced non-linear regression techniques or alternative models are necessary to adequately capture complex non-linear associations. Nonetheless, the inclusion of transformed predictor variables and the use of polynomial regression are valuable approaches to address non-linear relationships within the linear regression framework.

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The long jump pit was recently rebuilt to make it level with the runway.  the amount of wood, in meters, is 12.29 meters.

Generally, To determine the amount of wood needed in meters, you will need to convert the length of each piece of wood from feet to meters. You can use the conversion factor that 1 foot is equal to approximately 0.3048 meters.

To convert the length of the wood from feet to meters, you can use the formula:

length in meters = length in feet * 0.3048

Using this formula, you can calculate that 2.75 meters is equal to approximately 9 feet, and 9.54 meters is equal to approximately 31.25 feet.

Therefore, the total amount of wood needed in meters is 2.75 meters + 9.54 meters = 12.29 meters.

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Given:

Vertex of a quadratic function is at (3,-10).

The quadratic function passes through the point (0,8).

To find:

The equation of the quadratic function.

Solution:

The vertex form of a quadratic function is:

\(y=a(x-h)^2+k\)              ...(i)

Where, (h,k) is vertex and a is a constant.

Vertex of a quadratic function is at (3,-10). So, \(h=3,k=-10\).

\(y=a(x-3)^2+(-10)\)

\(y=a(x-3)^2-10\)              ...(ii)

The quadratic function passes through the point (0,8).

Putting \(x=0,y=8\) in (ii), we get

\(8=a(0-3)^2-10\)

\(8+10=a(-3)^2\)

\(18=9a\)

Divide both sides by 9.

\(2=a\)

Putting \(a=2\) in (ii), we get

\(y=2(x-3)^2-10\)

Therefore, the correct option is J.

\( \sf \purple{ \sqrt[4]{15} + \sqrt[4]{81} }\)

\( \sf \red{ \sqrt[4]{15} + 3}\)

\( \sf \pink{ 1.9 + 3}\)

\( \sf \orange{ \approx 4.9}\)

1. 7x-2y = 5 and -7x + 3y = 4

We add both together :
7x - 2y + (-7x + 3y) = 9.
7x - 2y - 7x + 3y = 9
y = 9.

-> x = (5+2x9)/7 = 23/7 (reverse finding x from the first equation.)

2. 5x + y = 7 and 2x - y = 14

We add both together once again :
5x + y + 2x - y = 21
7x = 21
x=3
-> y = 3 x 2 - 14 = -8 (reverse finding y from the second equation.)

3. 5x - 3y = 32 and 2x + 3y = 10

We add both together :
5x - 3y + 2x + 3y = 42
7x = 42
x = 6

-> y = (10-6 x 2)/3 = -2/3 (reverse finding y from the second equation.)

Given:

To combine these logarithms into a single logarithm, the first thing we need to do is to re-write the expression as a single logarithm with coeffient.

Next, we will use the Product Rule to simplify the numerator.

Product Rule states that:

Applying it to the numerator:

We will now have a new expression:

Next, we will factor out the logarithm.

Therefore, the final answer would be:

Cost for each pound of almonds is $1.5 and cost for each pound of jelly beans is $2.5.

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

Let x be the cost of each pound of almond and y be the cost of each pound of jelly beans.

Then from the first purchase, we have the equation,

3x + 5y = 17

Similarly, from the second purchase, we have,

12x + 2y = 23

So the system of equations are

3x + 5y = 17 and 12x + 2y = 23

Solving these, we will get the values of x and y which is the cost of each pound of almond and jelly beans.

3x + 5y = 17

12x + 2y = 23

Multiplying the first equation with 4, we get,

12x + 20y = 68

Subtracting 12x + 2y = 23 from 12x + 20y = 68,

18y = 45

y = $2.5

Substituting y = 2.5 in any of the equation above, we get,

x = $1.5

Hence the cost for each pound of almond and jelly beans are $1.5 and $2.5 respectively.

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