The following are the ages (years) of 5 people in a room:
23, 14, 16, 21, 22
A person enters the room.
The mean age of the 6 people is now 24.
What is the age of the person who entered the room?
years

Answer:

$94

Step-by-step explanation:

To find out how much she has after 5 weeks we need to use how much she has at 1 week. We know she starts the month with $54 and adds $8 at the end of a week. Knowing this we can multiply her amount for 1 week by 5 weeks (8x5), this gets us to $40, but since she started the week with 54 we need to add that to her 5 week's total (54+40), so we get a total of $94 after 5 weeks.

The total amount in Johanna's account after 5 weeks will be $94 if Johanna starts the month with $54 in her savings account at the end of each week, Johanna adds $8 to the account.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Johanna starts the month with $54 in her savings account.

At the end of each week, Johanna adds $8 to the account.

Let x be the total amount in Johanna's account after 5 weeks.

The linear equation in one variable can be framed as:

x = 54 + 8×5

x = 54 + 40

x = $94

Thus, the total amount in Johanna's account after 5 weeks will be $94 if Johanna starts the month with $54 in her savings account at the end of each week, Johanna adds $8 to the account.

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(a)An function the deformation gradient F is F = 1 γ 0,0 2X2 0,0 0 1

(b The right Cauchy-Green deformation tensor C is C = 1+γ²γ 0,

γ 4X2²0,0 0 1 the left Cauchy-Green deformation tensor B is B = 1+γ² γ 0,γ γ²+4X2² 0,0 0 1.

(a) Deformation Gradient F:

The deformation gradient is defined as the derivative of the deformed coordinates x with respect to the initial coordinates X:

F = ∂x/∂X

Given the shear deformation x = φ(X) with x1 = X1 + γX2, x2 = X2X2, and x3 = X3, we can compute the deformation gradient as follows:

F =∂x1/∂X1 ∂x1/∂X2 ∂x1/∂X3

∂x2/∂X1 ∂x2/∂X2 ∂x2/∂X3

∂x3/∂X1 ∂x3/∂X2 ∂x3/∂X3

Taking the partial derivatives:

∂x1/∂X1 = 1, ∂x1/∂X2 = γ, ∂x1/∂X3 = 0

∂x2/∂X1 = 0, ∂x2/∂X2 = 2X2, ∂x2/∂X3 = 0

∂x3/∂X1 = 0, ∂x3/∂X2 = 0, ∂x3/∂X3 = 1

(b) Right and Left Cauchy-Green Deformation Tensors C and B:

The right Cauchy-Green deformation tensor C is defined as the square of the deformation gradient:

C = F²T × F

The left Cauchy-Green deformation tensor B is defined as the square of the transpose of the deformation gradient:

B = F × F²T

Calculating C:

C = F²T × F

C = 1 0 0

γ 2X2 0

0 0 1

1 γ 0

0 2X2 0

0 0 1

C =1+γ² γ 0

γ 4X2² 0

0 0 1

Calculating B:

B = F × F²T

B = 1 γ 0

0 2X2 0

0 0 1

1 0 0

γ 2X2 0

0 0 1

B = 1+γ² γ 0

γ γ²+4X2² 0

0 0 1

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Answer:

Ray KM is an angle bisector of AngleNKL

Step-by-step explanation:

Answer:

Ray KM is an angle bisector of AngleNKL

Step-by-step explanation:

brainlist???????????

In order to divide these polynomials, let's use the following property:

So we have:

Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

Answer:

y = 1.50x

the graph is shown below

Step-by-step explanation:

We are told that y is equal to the total cost of the amount of grapefruit purchased. The amount of grapefruit is represented by x. The price of $1.50 would be our rate or slope for the graph.

With this information, we can create the expression:

y = 1.50x

To find the graph you need, either type it in a graphing calculator, or put in your choice of "x" values to find different coordinate that would be on the graph.

For example:

y = 1.50(2)

y = 3

Coordinate 1 would be (2,3)

y = 1.50(0)

y = 0

Coordinate 2 would be (0,0)

With these two coordinates you can draw a line and match your graph with the right one you need for the answer.

Answer:

45 i think

if not 54

I'm pretty sure it's 45

hope this helped :)

The algebraic expression x³ + 1 as given in the task content can be described as a binomial and a a cubic function as it has order 3.

The expression as given in the task content has 2 terms and hence, it change termed a binomial.

Also, since the greater power of the variable x is 3, it follows that the order of the equation is 3 and it is a cubic algebraic expression.

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The value of the function is dy/dx = f(x) = 6x²-10x-14

Differentiation is an element of personalized learning which involves changing the instructional approach to meet the diverse needs of students. It can involve designing and delivering instruction using an assortment of teaching styles and giving students options for taking in information and making sense of ideas.

the given function f(x) 2x³ -5x² -14x + 8

F(x) =dy/dx = 2*3(x)³⁻¹ -5*2(x²⁻¹) -14(x¹⁻¹)

Therefore the derivative of the function is f(x) = 6x²-10x-14

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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Answer:

48 onces

Step-by-step explanation:

Answer:

48 ounces.

Step-by-step explanation:

The required area of the parallelogram and pentagon is 91 unit² and 75 unit².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

A parallelogram in is shown in figure 1 with the dimensions height = 7 and base = 13,
Area of the parallelogram  = 13 × 7 = 91 unit²

Now,
A pentagon is shown in figure 2,
Area of the pentagon = 5 [1/2 × height × side]
                                 = 5 [1/2 × 5 × 6]

                                 = 75 suqare units.

Thus, the required area of the parallelogram and pentagon is 91 unit² and 75 unit².

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32.56 is the expected weight for a bluegill fish that is 11 inches long.

Equation: What is it?

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation. Without them, one can still create an equation, such as 5 + 10 = 15. There are no variables in the equation below.

given expression:

In(Weight) = -5.28 + 3.44 In(Length)

So, we have to find 11 inches then

In(weight) = -5.28 + 3.44 x 11

               = -5.28 + 37.84

               = 32.56

Hence, 32.56 is the expected weight for a bluegill fish that is 11 inches long.

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Answer: 117?

Step-by-step explanation:

Answer:

It's 0.20

Step-by-step explanation:

The distance between the base of the model tree to the edge of the model bench is  0.2 yard.

A diagram is attached which describe the statement of question.

From diagram attached below, It is observed that both triangles are similar triangles.

The ratio of corresponding sides are same in the similar triangles.

the distance between the base of the model tree to the edge of the model bench is  x.

                     \(\frac{5}{x}=\frac{10}{0.4}\\ \\ 10x=2\\\\x=2/10=0.2yard\)                

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Answer:

To rationalize the denominator of 5/√3+√7, we can multiply the numerator and denominator by the conjugate of the denominator, which is √3-√7.

The product of (√3+√7) and (√3-√7) is the difference of squares, which is (√3)^2 - (√7)^2 = 3-7 = -4.

Thus, we have:

5/√3+√7 * (√3-√7)/(√3-√7) = 5(√3-√7)/(-4) = -5/4(√7-√3)

Therefore, the rationalizing factor is (√3-√7).

The resultant velocity of the two vectors is `778.9 km/h` at an angle of `- 3.43°` (measured from the North in the clockwise direction).

Speed of the boat, `v₁ = 25 km/h

`True bearing, `θ₁ = 270°

`Speed of the wind,

`v₂ = ?`

Bearing of the wind, `θ₂ = 220°`

We know that the velocity components can be obtained as follows:

`v₁ = v₁ cos θ₁ i + v₁ sin θ₁ j

``v₂ = v₂ cos θ₂ i + v₂ sin θ₂ j`

Here, `i` is the unit vector along the East-West direction (or x-axis), and `j` is the unit vector along the North-South direction (or y-axis).

Let the velocity of the boat be `v_b` and the velocity of the wind be `v_w`.Then, the resultant velocity `v_r = v_b + v_w`We need to find the magnitude and direction of `v_r`.

Now,`v_b = v₁ cos θ₁ i + v₁ sin θ₁ j``v_w = v₂ cos θ₂ i + v₂ sin θ₂ j`

Substituting the given values, we get:

`v_b = 25 cos 270° i + 25 sin 270° j` and `v_w = v₂ cos 220° i + v₂ sin 220° j`

Now,`v_b = - 25 j` and `v_w = v₂(-0.766 i - 0.643 j)`

Since the wind is pushing the boat, we take the negative of `v_w`.

Hence, `v_w = -0.766 v₂ i - 0.643 v₂ j``v_r = v_b + v_w = -25 j -0.766 v₂ i - 0.643 v₂ j`

The magnitude of the resultant velocity is `|v_r| = √(766² + 643² + 25²) ≈ 778.9 km/h`.

The direction of the resultant velocity is `θ = tan⁻¹((25/0.766) / (-643/0.766)) ≈ - 3.43° (measured from the North in the clockwise direction).

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The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer:

y = -4

Step-by-step explanation:

When y is directly proportional to x,

= y ∝ x

= y = kx

Finding k

the value of y = -2 when x = 4

-2 = k4

k = -2/4

k = -1/2

. What is the value of y when x = 8

Finding y

y = kx

y = -1/2 × 8

y = -4

The interior angles are 43°, 43° and 94°. and  exterior angle is 86°

Let the interior angles are ∠A, ∠B and ∠C.

From the question, we have

∠A = (5x-12)°

exterior angle = (8x-2)°

As the sides are equal

∠A =∠B = (5x-12)°

∠C = 180°-(8x-2)°

=182°-8x

Sum of interior angles of a triangle is equals to 180 degree.

∠A + ∠B + ∠C = 180°

(5x-12)°+(5x-12)°+182°-8x = 180°

2x+158° = 180°

x = 11°

Interior angles,

∠A =∠B = (5x-12)°

= (5*11-12)°

=43°

∠C =182°-8x

=182°-8*11

=94°

exterior angle = (8x-2)°

=8*11-2

=86°

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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To compare the profiles of temperature and salinity for Argo Float 108683 in the Eastern Tropical North Pacific on April 16, 2012 (Profile 001) and April 16, 2016 (Profile 138), follow these steps:

Locate the data: Visit the Argo Data Management site (http://www.argodatamgt.org/) and search for Argo Float 108683 using the ArgosID. Download the data for the specific dates (April 16, 2012, and April 16, 2016).

Plot the graphs: Using a data analysis tool like Excel or Python, create plots of temperature with depth and salinity with depth for both profiles. Ensure that you label the axes and include units.
Compare the profiles: Examine the shapes of the temperature and salinity profiles for both years, focusing on the mixed layer depth and the main thermocline depths.

Based on general ocean circulation, we would expect temperature profiles in the Eastern Tropical North Pacific to show a well-mixed layer near the surface with a rapid temperature decrease below the mixed layer depth, leading to the main thermocline.

Differences between years could be attributed to several factors, such as variations in seasonal weather patterns, changes in ocean circulation, or anomalies like El Niño events. These factors could affect the mixed layer depth, main thermocline depths, and surface features, leading to differences in the temperature and salinity profiles for the two years.

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the two angles that satisfy sinθ = -√2/2 are 5π/4 and 7π/4.

Why it is?

sinθ = -√2/2 is equivalent to saying that the sine of angle θ is negative and equal to √2/2.

We know that the sine function is positive in the first and second quadrants, and negative in the third and fourth quadrants. Therefore, we can limit our search for angles θ to the third and fourth quadrants where the sine function is negative.

In the third quadrant, the reference angle that satisfies sinθ = √2/2 is π/4, since the sine function is negative in this quadrant. Therefore, the angle θ in the third quadrant that satisfies sinθ = -√2/2 is:

θ = π + π/4 = 5π/4

In the fourth quadrant, the reference angle that satisfies sinθ = √2/2 is also π/4, since the sine function is negative in this quadrant. Therefore, the angle θ in the fourth quadrant that satisfies sinθ = -√2/2 is:

θ = 2π - π/4 = 7π/4

So the two angles that satisfy sinθ = -√2/2 are 5π/4 and 7π/4.

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Using the Factor Theorem, the length of one side of the garden is:

(3x - 4) feet.

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, \codts, x_n\) is given by:

\(f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)\)

In which a is the leading coefficient.

The area of a rectangle is given by the multiplication of it's dimensions. In this problem, it is given by:

A = 9x² - 24x + 16.

The root of 9x² - 24x + 16 = 0 is x = 4/3 with multiplicity 2, hence:

\(x_1 = x_2 = \frac{4}{3}\)

Hence the area can be written as:

\(A = 9\left(x - \frac{4}{3}\right) \times \left(x - \frac{4}{3}\right)\)

Then, to find one side:

9(x - 4/3) = 9x - 12 = 3(3x - 4).

Hence (3x - 4) feet is one side.

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Answer:

3/20

Hope this help <3

Answer:

.85

Step-by-step explanation:

Compound interest formula

\(PV(1+\frac{i}{n})^{nt}\)

Melanie:

\(3800(1+\frac{.02}{4})^{(6*4)\\}\\=3800(1+.005)^{24}\\3800*1.1272=4283.21\)

Sebastian:

\(3800(1+\frac{.02}{12})^{12*6}\\3800(1.0017)^{72}\\3800*1.1274=4284.06\)

4824.06-4283.21= .85

Answer:

Option R

Step-by-step explanation:

The point S is the end point of ray.

What is line?

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

According to the given information,

A ray's endpoint is a single point that denotes the conclusion of a line segment. In this instance, only one of the three lines that extend from point S contains a ray's terminus.

We must comprehend a ray's qualities in order to establish which location is the endpoint of a ray.

A ray originates at a single place and travels in one direction indefinitely. The beginning of the line segment is the endpoint of a ray.

We can see from the provided lines that the vertical line runs from point S via point R. Since it doesn't go on forever in one direction, this is not a ray example.

Similar to the vertical line,

The horizontal line also extends from point S through point T,

But it does not go on forever.

The third line is a ray because it is infinitely long in one direction and extends right and up from point S via point U.

Therefore, point S, the beginning of the line, is the endpoint of this ray.

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Answer:

When we have a function g(x)

We will have a maximum at x when:

g'(x) = 0

g''(x) < 0.

Now we start with:

g(x) = 3*x^4 - 8*x^3

The first derivation is:

g'(x) = 4*3*x^3 - 3*8*x^2

g'(x) = 12*x^3 - 24*x^2

We can rewrite this as:

g'(x) = x^2*(12*x - 24)

Now we want to solve:

g'(x) = 0 =  x^2*(12*x - 24)

We have one trivial solution, that is when x = 0.

The other solution will be when the term inside of the parentheses is equal to zero.

Then we need to solve:

12*x - 24 = 0

12*x = 24

x = 24/12 = 2

Then g'(x) is equal to zero for x = 0, and x = 2.

Notice that both of these points are included in the interval [ -2,2 ]

Now we need to look at the second derivative of g(x):

g''(x) = 3*12*x^2 - 2*24*x

g''(x) = 36*x^2 - 48*x

Ok, now we need to evaluate this in the two roots we found before:

if x = 0:

g''(0) = 36*0^2 - 48*0 = 0

g''(0) = 0

Then we do not have a maximum at x = 0, this is a point of inflection.

if x = 2:

g''(2) = 36*(2^2) - 48*2 = 48

then:

g''(2) > 0

This is an absolute minimum.

Now let's look only at the interval [ -2,2 ]

We know that:

g''(0) =  0

g''(2) > 0

Then at some point, we should have g''(x) < 0 in our interval.

We need to find the first point such that happens, so let's try with the lower limit of the interval but with the first derivation, if g'(x) < 0, this means that the function is decreasing from that point on, then that point will be a maximum in our interval.

x = -2

g'(-2) = (-2)^2*(12*-2 - 24) = -192

And if we look at the function:

g'(x) = x^2*(12*x - 24)

We can easily see that it is negative unitl x = 0, and then it keeps being negative until x = 2.

So in the interval  [ -2,2 ], the function g'(x) is always negative or zero, this means that in the interval  [ -2,2 ], the function g(x) is always decreasing or constant.

Then the absolute maximum of g(x) in the interval  [ -2,2 ]  will be  x = -2

this means that:

g(-2) ≥ g(x) for all x ∈  [ -2,2 ]

Answer:

k = -3

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

31 x 2 = 62

62 + 13 = 75

n = 31

Answer: Your welcome!

Step-by-step explanation:

Using a greater scale, 0-100, makes the data look more spread out, indicating a weaker relationship. Using a smaller scale, 0-10, makes the data look more clustered together, indicating a stronger relationship.