I need help with part C. Statistics-based.

Answer:

The number of discharge days for a patient admitted January 23 to February 15 is 31 - 23 + 15 = 23

The remainder theorem indicates that remainder when the polynomial x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) is 8

The remainder theorem specifies the relationship between the division of a polynomial by a linear factor to the value of the polynomial at a specified point

The remainder when the polynomial expression; x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by x - 1, can be found using the remainder theorem by plugging in x = 1 in the function as follows;

f(1) = 1⁵ - 3 × 1⁴ - 2 × 1³ - 5 × 1² + 5 × 1 + 12 = 8

The remainder when x⁵ - 3·x⁴ - 2·x³ - 5·x² + 5·x + 12 is divided by (x - 1) therefore is 8

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Answer:

Step-by-step explanation:

Let’s define the number of rides that Zeek can ride as “r”.

To determine how many rides Zeek can ride, we need to first subtract the cost of admission from his total budget:

$30 - $13 = $17

This means that Zeek has $17 left to spend on rides. Since each ride costs $2, we can set up the following equation:

$2r = $17

To solve for “r”, we divide both sides of the equation by $2:

r = $8.50

So Zeek can ride a maximum of 8 rides with the $17 he has left after paying for admission. However, since he cannot ride a fraction of a ride, he may be limited to only 8 rides or fewer.

The scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex] where 10 raised to an exponent (-2).

In scientific notation, a number is expressed as the product of a coefficient and a power of 10.

To write the number 0.08 in scientific notation, it as a decimal number multiplied by a power of 10.

So, 0.08 can be written in scientific notation as 8 x [tex]10^{(-2)[/tex].

In scientific notation, the number is written as the product of a coefficient (8) and a power of 10 raised to an exponent (-2), indicating the decimal's position relative to the coefficient.

Therefore, the scientific notation of 0.08 is 8 x [tex]10^{(-2)[/tex].

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After applying factorization of the given functions the evaluated expression comes out to be (2x + 1)(x² - x - 4.8), under the condition the given function is P(x)=2x × 3- 5.6x +1

In order to factorize the given polynomial P(x) = 2x³ - 5.6x + 1, we can apply the Rational Root Theorem. The theorem projects that in an incident when a  polynomial has integer coefficients, then any rational roots must have a numerator that divides the constant term and a denominator that divides the leading coefficient.
For the given case, the leading coefficient is 2 and the constant term is 1.
Hence, any rational roots must be of the form p/q where p divides 1 and q divides 2. This elaborates that the possible rational roots are ±1/2 and ±1.
We can observe these roots applying synthetic division. Using synthetic division with root -1/2 gives us:
-1/2 | 2   0   -5.6   1
    |    -1    0.8  -0.5
    -------------------
          2   -1   -4.8  0.5
This means that P(x) can be factored as:
P(x) = (2x + 1)(x² - x - 4.8)
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Answer: there is one solution

Step-by-step explanation:

12x − 13y = 5

x = 23y + 10

lets substitute x into the first equation.

12(23y + 10) - 13y = 5

276y + 120 - 13y = 5

263y = -115

y = -115/263

substituting for x:

x = 23(-115/263) + 10

x = -2645/263 + 10

x = -15/263

As we can see, we get one value of x;

this means there is one solution

The two numbers are 15 and 15. The product of the two numbers is 225.

Let x and y be the two numbers we are searching for. We know that x + y = 30, so we can settle for y to get y = 30-x. The result of x and y is then, at that point:

[tex]P(x, y) = x(30 - x) = 30x - x^2[/tex]

To find the greatest item, we can take the subsidiary of P(x, y) concerning x and set it equivalent to 0:

dP(x, y)/dx = 30 - 2x = 0

Settling for x, we get x = 15. Subbing x = 15 into y = 30-x, we get y = 15. Hence, the two numbers that have an amount of 30 and produce the biggest conceivable item are 15 and 15.

The result of the two numbers is:

P(15, 15) = 15 * 15 = 225

So the result of the two numbers is 225.

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The perimeter of the given triangle is: 19.2 units

The formula for the distance between two coordinates is:

D = √[(y₂ - y₁)² + (x₂ - x₁)²]

Thus: (0, 3)(4, -2)

Slant distance on left side of triangle = √[(-2 - 3)² + (-3 - 0)²] = 5.8 units

Slant distance on right side of triangle = √[(-2 - 3)² + (4 - 0)²] = 6.40 units

Length of horizontal part of triangle = 7 units

Thus:

Perimeter of triangle = 5.83 + 6.40 + 7 = 19.2 units

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The surface area of the given cylinder is approximately 1758.4 square yards.

To find the surface area of a cylinder, we need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.

Given:

Height (h) = 18 yards

Radius (r) = 10 yards

π (pi) ≈ 3.14

Lateral Surface Area:

The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius and h is the height.

Lateral Surface Area = 2πrh

Substituting the given values, we have:

Lateral Surface Area = 2 × 3.14 × 10 × 18

Lateral Surface Area = 1130.4 square yards (rounded to the nearest hundredth)

Circular Bases:

The area of a circle can be calculated using the formula πr^2, where r is the radius.

Area of a Circular Base = π[tex]r^2[/tex]

Substituting the given radius, we have:

Area of a Circular Base = 3.14 × [tex]10^2[/tex]

Area of a Circular Base = 314 square yards

To find the total surface area, we need to add the lateral surface area and the areas of the two circular bases.

Total Surface Area = Lateral Surface Area + 2 × Area of a Circular Base

Substituting the values, we get:

Total Surface Area = 1130.4 + 2 × 314

Total Surface Area = 1758.4 square yards (rounded to the nearest hundredth)

Therefore, the surface area of the given cylinder is approximately 1758.4 square yards.

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Question

'What is the surface area of this cylinder? What is the surface area of this cylinder? Use I ~ 3.14 and round your answer to the nearest hundredth_ 18 yd 10 yd square yards'

The surface area of the pyramid is approximately 393,560 square feet.

To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base.

The area of the square base is simply the area of a square with side length 500 feet:

Area of base =[tex](side length)^2 = (500 feet)^2[/tex]= 250,000 square feet.

To find the area of each triangular face, we need to know the length of one of the sides of the base and the slant height of the pyramid.

Since the base is a square, all sides have the same length of 500 feet.

Using the Pythagorean theorem, we can find the height of each triangular face:

height = √(slant heigh[tex]t^2[/tex] - base lengt[tex]h^2[/tex]/4)

height = √([tex]60^2 - (500/2)^2[/tex])

height = √(3600 - 62500/4)

height = √(3600 - 15625)

height = √20375

height ≈ 142.76 feet

Now we can find the area of one of the triangular faces:

Area of triangular face = (1/2) x (base length) x (height)

Area of triangular face = (1/2) x 500 feet x 142.76 feet

Area of triangular face ≈ 35,690 square feet

Since there are four triangular faces, the total surface area of the pyramid is:

Total surface area = 4 x (Area of triangular face) + (Area of base)

Total surface area = 4 x 35,690 square feet + 250,000 square feet

Total surface area ≈ 393,560 square feet

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(a) The result of row 1 and row 2 interchange is [3     -2    3]

                                                                                 [2     3     1]

(b) The result of multiplying and adding the matrix is [-1       5     -2]

                                                                                         [3      -2      3]

The row operation of the matrix is calculated as follows;

The given matrix;

[2     3     1]

[3     -2    3]

To interchange row 1 and row 2, we determine it as follows;

R₁ ↔ R₂   = [3     -2    3]

                  [2     3     1]

The product of row 2 and -1 is calculated as;

-1 (R₂) = [-3      2     -3]

The addition of -1(R₂) + R₁ is calculated as;

-1(R₂) + R₁ = [-3      2     -3] + [2     3     1]

-1(R₂) + R₁ = [-1       5     -2]

new matrix =  [-1       5     -2]

                       [3      -2      3]

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Given WX is tangent to OS at point V, the statements that must be true include:

A. m∠TVX =m∠TVX

C. m∠TVW = m∠TSV

D. m∠TUV =m∠TVW

In mathematics, a tangent is a line that touches a curve at exactly one point, without intersecting it at that point. The tangent line at a point on a curve represents the slope of the curve at that point. The concept of tangent is important in calculus, where it is used to calculate derivatives of functions.

TUV = 1/2MTU = TVW

TUV = TVW

Also, MTV = TSV = 2TVW

TVW = TSV

The correct options are A, C and D.

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Answer:20%

Step-by-step explanation:

Answer:

Step-by-step explanation: -36

This given function does not have an end behavior since it is not a polynomial.

The end behavior of a function describes the behavior or trend of the function as the input values (x) approach positive or negative infinity. It helps us understand what happens to the function's values as x becomes very large or very small.

We have three possible cases of end behavior of a function which are;

The end behavior of a function is often determined by using the leading term of the function, which is the term with the highest power of x.

In the given problem;

[tex]f(x) = \frac{8x^6 - 16x^3 + 8}{4x^2 - 4x - 24}[/tex]

The end behavior of this function does not exist because this function is not a polynomial

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Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:

Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts.

Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country.

Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy.

Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths.

Regularly update the data: As the situation evolves, keep track of new data releases and updates.

Calculating the total number of deaths for all countries requires collecting data from various sources and summing up the individual death counts. Here is a step-by-step guide on how to approach this calculation:

Identify reliable sources: Look for reputable sources that provide updated and accurate information on global death counts. Examples include official government health agencies, international health organizations (e.g., WHO), and reputable databases (e.g., Worldometer, Johns Hopkins University).

Gather country-specific data: Access the data provided by these sources and collect the individual death counts for each country. Ensure the data is recent and covers a comprehensive list of countries.

Validate and verify data: Cross-reference the data from multiple sources to ensure consistency and accuracy. Different sources may have slight variations, so it's important to verify the data and use the most reliable figures.

Sum up the death counts: Add up the individual death counts for each country to obtain the total number of deaths. Use a spreadsheet or calculator to perform the calculations accurately.

Regularly update the data: As the situation evolves, keep track of new data releases and updates. Update the total number of deaths accordingly to maintain accuracy.
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The question probable may be:

How to calculate the total number of deaths for all the countries?

​

If the volume is 133 1/3 in³, the value of x is equal to 5 inches.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

133 1/3 = 10 × x ×  2 2/3

400/3 = 10 × x × 8/3

400/3 = 80x/3

80x = 400

x = 400/80

x = 5 inches.

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After considering all the given options we come to the conclusion that the inequality that represents the  values of x for the give triangle ABC is 15/11 < x < 17/5, which is Option A.

Here, the sides of a triangle should gradually satisfy the triangle  inequality theorem which projects that the summation of the lengths considering any two sides of a triangle should be bigger than or equivalent towards the length of the third side.
Then, for the given sides of triangle ABC,
3x+1 + 16 > 8x

Applying this inequality,
x > 15/11
So,
16 + 8x > 3x+1
Applying simplification
x < 17/5
Hence , the inequality that represents the values of x for which triangle ABC exists is 15/11 < x < 17/5.
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Answer:

98 is a whole number

Step-by-step explanation:

0.86 is a decimal

2/5 is a fraction

35% is a percentage

The area of the composite figure is 81 yd². Option D

The composite figure is made up of a rectangle, a triangle and a trapezoid

The formula for the area of a rectangle is expressed as;

Area = length × width

Substitute the values

Area = 7(6)

Multiply the values

Area = 42 yd²

Area of the triangle = 1/2 base ×height

Area of the triangle = 1/2 × 6 ×5 = 30/2 = 15yd²

Area of the trapezoid = a+b/2 h

Substitute the values

Area = 7 + 9/2 (3) = 16/2(3) = 8(3) = 24yd²

Total area = 24 + 15 + 42 = 81 yd²

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The area of the composite figure is 81 cm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Any figure that we can break and form more than one basic shape from is called a composite figure.

The figure consist of two trapezoid

Area of trapezoid 1 = 1/2( a+b) h

= 1/2 ( 12 + 7) 6

= 1/2 × 19 × 6

= 19 × 3

= 57cm²

area of trapezoid 2

= 1/2(a+b) h

= 1/2 ( 7+9) 3

= 1/2 × 16 × 3

= 8 × 3

= 24 cm²

Therefore the area of the composite figure

= 57 +24 = 81 cm²

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x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex], we can use the Factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).the remainder when we divide [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex] by x-7 is 4054.

To check if x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$,[/tex] we can use the factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).

To check if x-7 is a factor, we evaluate the polynomial at x=7:

[tex]f(7) = 7^5+5\cdot7^4-2\cdot7^3+4\cdot7^2+8\cdot7+3976 = 384004$.[/tex]

Since [tex]$f(7)\neq 0$[/tex], we can conclude that x-7 is not a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$.[/tex]

To find the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$[/tex]by x-7, we can use polynomial long division or synthetic division. Using polynomial long division, we get:

  [tex]x^4 + 12x^3 + 82x^2 + 578x + 4046\\x-7 | x^5 + 5x^4 - 2x^3 + 4x^2 + 8x + 3976\\- x^5 + 7x^4[/tex]

    ------------

      [tex]12x^4 - 2x^3 + 4x^2 + 8x\\ 12x^4 - 84x^3[/tex]

          -------------

                     [tex]82x^3 + 4x^2 + 8x\\ 82x^3 - 574x^2[/tex]

                      --------------

                                  [tex]578x^2 + 8x\\ 578x^2 - 4046[/tex]

                                    ------------

                                              4054

Therefore, the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$ by $x-7$ is $4054$.[/tex]

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Answer:

B and D

Step-by-step explanation:

4²= 16

it's a perfect square

2³= 8

it's a perfect cube

Prove in below steps:

Proved

The assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

To estimate the number of fossils after 10 years, we need to solve the given equation. However, since the equation is not provided, we'll assume a simple exponential decay model for the population of fossils.

Let's assume the equation for the population of fossils is:

N(t) = N0 * e^(-kt)

where:

N(t) is the number of fossils after t years,

N0 is the initial number of fossils,

k is a decay constant, and

e is the base of the natural logarithm (approximately 2.71828).

Since the initial number of fossils is given as 100, we have N0 = 100. Now, we need to find the value of the decay constant (k) to estimate the number of fossils after 10 years.

Without further information, it's challenging to determine the exact decay constant. However, let's assume a hypothetical value of k = 0.1 for this example.

Plugging the values into the equation, we get:

N(10) = 100 * e^(-0.1 * 10)

= 100 * e^(-1)

≈ 100 * 0.36788

≈ 36.788

So, with the assumption of a decay constant of k = 0.1, we estimate that there would be approximately 36.788 fossils per cubic meter after 10 years.

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Answer:

B. 2333.59

Step-by-step explanation:

We have been given the following differential equation:

[tex]\dfrac{dN}{dt}=\dfrac{5000}{6+5t}[/tex]

To find the number of fossils N(t) after t = 10 years, we first need to solve the differential equation using integration and the given parameters to create an equation for N(t) in terms of t.

Solving a differential equation means using it to find an equation in terms of the two variables, without a derivative term.

Rearrange the equation so that all the terms containing N are on the left-hand side, and all the terms containing t are on the right-hand side:

[tex]1\;dN=\dfrac{5000}{6+5t}\; dt[/tex]

Integrate both sides:

[tex]\displaystyle \int 1 \;dN=\int \dfrac{5000}{6+5t}\; dt[/tex]

Use the following integration rules:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Integration rulest}\\\\\\$\displaystyle \int n\:\text{d}x=nx+\text{C}$\;\;(where $n$ is any constant value)\\\\\\$\displaystyle \int \dfrac{n}{a+bx}\:\text{d}x=\dfrac{n}{b}\ln |a+bx|+\text{C}$\\\\ \end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int 1\;dN&=\int \dfrac{5000}{6+5t}\; dt\\\\\implies N&=\frac{5000}{5}\ln \left|6+5t\right|+C\\\\N&=1000\ln \left|6+5t\right|+C\end{aligned}[/tex]

As the initial number of fossils is 100, then N = 100 when t = 0.

Substitute these values into the equation and solve for C:

[tex]100=1000\ln \left|6+5(0)\right|+C[/tex]

[tex]C=100-1000\ln (6)[/tex]

Therefore, the equation for N in terms of t is:

[tex]N=1000\ln \left|6+5t\right|+100-1000\ln(6)[/tex]

Use the quotient log rule to simplify:

[tex]N=1000\ln \left|6+5t\right|-1000\ln(6)+100[/tex]

[tex]N=1000\ln \left(\dfrac{\left|6+5t\right|}{6}\right)+100[/tex]

To estimate the number of fossils after 10 years, substitute t = 10 into the equation:

[tex]N=1000\ln \left(\dfrac{\left|6+5(10)\right|}{6}\right)+100[/tex]

[tex]N=1000\ln \left(\dfrac{56}{6}\right)+100[/tex]

[tex]N=2333.59\; \sf (2\;d.p.)[/tex]

Therefore, the number of fossils after 10 years is 2333.59.

Answer:

5, 3

Step-by-step explanation:

A set of two or more equations with the same variables.

A system of linear equations with EXACTLY ONE solution.

A system of linear equations with INFINITELY MANY solutions.

A system of equations with NO solution.

A number representing how many times the Base number should be multiplied by itself.

A chart of the different values for an equation or graph.

Systems of Equations:

A set of two or more equations with the same variables.

These equations are solved simultaneously to find the values of the variables.
Consistent Independent:

A system of linear equations with EXACTLY ONE solution.

This means that the lines represented by the equations intersect at a single point.
Consistent Dependent (Coincident):

A system of linear equations with INFINITELY MANY solutions.

In this case, the equations represent the same line or overlapping lines, and every point on the line is a solution.
Inconsistent:

A system of equations with NO solution.

This occurs when the lines represented by the equations are parallel and never intersect.
Exponent:

A number representing how many times the base number should be multiplied by itself.

For example, in the expression[tex]2^3,[/tex] the exponent is 3, which means 2 should be multiplied by itself 3 times [tex](2 \times  2 \times  2 = 8).[/tex]
T-Table:

A chart of the different values for an equation or graph.

It typically includes two columns: one for the input values (usually x) and one for the corresponding output values (usually y).

T-tables are helpful for understanding the relationship between the variables in an equation and for plotting points on a graph.

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Answer:

A≈201.06cm²

Step-by-step explanation:

A=4πr2

d=2r

Solving forA

A=πd2=π·82≈201.06193cm²