6. (15 points) Metal bar costs $3 per meter and wooden bar costs $2 per meter. If we have $6000 to
purchase both type of bars, what is the maximum area we can enclose at this cost?

The probability that a salesperson hit the quota, given that the salesperson was promoted is 0.88. Therefore, option D is the correct answer

From the tree diagram, there are two ways to obtain the promotion:

0.41 of 0.68 (hit the quota).

0.14 of 0.32 (did not hit the quota).

So, the probability of getting a promotion is:

P(A) = 0.41 × 0.68 + 0.14 × 0.32 = 0.3236.

The probability of both getting a promotion and hitting the quota is:

P(A and B) = 0.41 × 0.68 = 0.2788.

So, the conditional probability is:

P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.88 (approximately).

Therefore, option D is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Salespeople at a certain company must meet a quota each month. On average, they hit the quota 68% of the time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person doesn’t hit the quota, the probability of being promoted is 0.14.

Use the tree diagram to determine the probability that a salesperson hit the quota, given that the salesperson was promoted.

A. 0.28

B. 0.32

C. 0.41

D. 0.88

The population of the town 12 years later will be 224,800 if the current population is 28,100 and the population doubles every 4 years.

Since the population doubles every 4 years, we can use the formula:

P = P0 x [tex]2^{t/4}[/tex]

where P0 is the initial population, t is the time elapsed in years, and P is the population after time t.

In this case, the initial population P0 is 28,100, and we want to know the population after 12 years, so t = 12. Substituting these values into the formula, we get:

P = 28,100  2^(12/4)

  = 28,100 x 2³

  = 28,100 * 8 = 224,800

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Answer:

A≈201.06cm²

Step-by-step explanation:

A=4πr2

d=2r

Solving forA

A=πd2=π·82≈201.06193cm²

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.

Prove in below steps:

Proved

Answer:

Step-by-step explanation:

[tex]8x^5 + 3x^4 - 23x\\= 8x^5+3x^4+0x^3+0x^2-23x+0[/tex]

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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The solution of the equation, | x + 10 / 2x + 1 | = 20 is x = 10 / 39 or x = -30 / 41.

The absolute equation can be solved as follows:

| x + 10 / 2x + 1 | = 20

Therefore,

x + 10 / 2x + 1 = 20  or  x + 10 / 2x + 1 = - 20

cross multiply

x + 10 / 2x + 1 = 20

x + 10 = 20(2x + 1)

x + 10 = 40x + 20

x - 40x  = 20 - 10

-39x = -10

x = 10 / 39

x + 10 / 2x + 1 = - 20

cross multiply

x + 10 = -20(2x + 1)

x + 10 = -40x - 20

x + 40x = -20 - 10

41x = -30

divide both sides of the equation by 41

x = - 30 / 41

Therefore, x = 10 / 39 or x = -30 / 41

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Answer:

5, 3

Step-by-step explanation:

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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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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Answer:

0.34

Step-by-step explanation:

4 or below go down low

5 or above fly like a dove

so the 33 part is lower than 50 so round down

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?

​

Answer:

B and D

Step-by-step explanation:

4²= 16

it's a perfect square

2³= 8

it's a perfect cube

The inverse of function f is [tex]f^{-1}(x)=\frac{4}{x}-3[/tex].

The domain of f is (-∞, -3) U (-3, ∞).

The range of f = (-∞, 0) U (0, ∞)

The domain of f⁻¹ = (-∞, 0) U (0, ∞).

The range of f⁻¹ = (-∞, -3) U (-3, ∞).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value or domain) and dependent value (y-value or range) as follows;

f(x) = y = 4/(3 + x)

x = 4/(3 + y)

3 + y = 4/x

f⁻¹(x) = 4/x - 3

[tex]f^{-1}(x)=\frac{4}{x}-3[/tex]

By critically observing the graph of this rational expression (function)   and its inverse shown in the image attached below, we can reasonably and logically deduce the following domain and range:

Domain of f = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.

Range of f = (-∞, 0) U (0, ∞); {y|y ≠ 0}.

Domain of f⁻¹(x) = (-∞, 0) U (0, ∞); {y|y ≠ 0}.

Range of f⁻¹(x) = (-∞, -3) U (-3, ∞); {x|x ≠ -3}.

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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 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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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'

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

After considering the given data we conclude that the value of the sub question are
A) 16
B) 50
C) 5
D) 7
E) 7
F) 15
G) 2
H) 6
I) 15
J) -15
And the marking the true and false
a) true
b) false
c)true
d) true
e) false

The number properties rule is a set of rules that help you solve mathematical equations. The rule is also known as the order of operations. The acronym PEMDAS is used to remember the order of operations. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right) ¹².

Let's solve the equations using the number properties rule:

A) 5 + 16 = 16 + __

We can solve this equation by subtracting 16 from both sides of the equation.

5 + 16 - 16 = 16 + __ - 16

5 = 16

The equation is not true.

B) 450 + ___ = 50 + 450

We can solve this equation by subtracting 450 from both sides of the equation.

450 + ___ - 450 = 50 + 450 - 450

___ = 50

The answer is 50.

C) 2 + ( 3 + 5 ) = ( 2 + 3 ) + _____

We can solve this equation by simplifying the parentheses first.

2 + (3 + 5) = (2 + 3) + _____

2 + 8 = 5 + _____

10 = 5 + _____

We can solve this equation by subtracting 5 from both sides of the equation.

10 - 5 = 5 - 5

5 = _____

The answer is 5

D) (7 + 4) + 6 = ___+ (4+6)

We can solve this equation by simplifying the parentheses first.

(7 + 4) + 6 = ___+ (4+6)

11 + 6 = ___+ 10

17 = ___+ 10

We can solve this equation by subtracting 10 from both sides of the equation.

17 - 10 = ___+ 10 - 10

7 = ___

The answer is 7

E) 7 + 0 = ________

The answer is 7

F) 15 – 0 = _______

The answer is 15

G) (12 – 8 ) – 2 = _______

We can solve this equation by simplifying the parentheses first.

(12 – 8 ) – 2 = _______

4 - 2 = _______

2 = _______

The answer is 2

H) 12 – (8 – 2 ) = _________

We can solve this equation by simplifying the parentheses first.

12 – (8 – 2) = _________

12 - 6= _________

6= _________

The answer is 6.

I)20 – 5= _____

20 - 5= _____

15= _____

The answer is 15.

J)5 –20= _______

5 - 20= _______

-15= _______

The answer is -15.

Mark as true or false.

a)16+4=4+16 ______________

True

b)15–5=5–15 ______________

False

c)(3+4)+5=3+(4+5) ______________

True

d)(12–4)–2=12–(4–2) ______________

True

e)(10-5)+5=10–(5+5) ______________

False
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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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The required total number of grams is 13.5 gram.

From figure we have,

The masses of 4 samples are the masses are 1.5 gram, 3.5 gram , 5 gram and 5 gram respectively.

To calculate the total number of grams of salt in the 3 samples with the most mass,

Add the masses of the three largest samples.

In this case,

The three largest samples are 3.5 grams, 5 grams, and 5 grams.

We have: 3.5 grams + 5 grams + 5 grams = 13.5 grams

Therefore, the total number of grams of salt in the 3 samples with the most mass is 13.5 grams.

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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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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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Answer:

Step-by-step explanation: -36

Answer:

⟶ We can express the sum 1^2 + 2^2 + 3^2 + ... + 750^2 using summation notation as:

∑i^2, where i goes from 1 to 750.

⟶ Here, the symbol ∑ represents the summation, and i is the index variable, which takes on the values 1, 2, 3, ..., 750. The expression i^2 is the term being summed.

⟶ So the sum can be written as:

∑i^2 = 1^2 + 2^2 + 3^2 + ... + 750^2

⟶ Note that the upper limit of the index variable is 750, which corresponds to the last term in the sum.

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Answer:

[tex]\sum \limits^{750}_{n=1} {n^2}[/tex]

Step-by-step explanation:

General explanation of summation notation

Any sum of terms whose format is the same can be represented more concisely using a Summation symbol.

The Summation symbol is a capital greek letter Sigma:  [tex]\sum[/tex]

The summation will take a general format of each term, and increase a "dummy variable" by 1, summing together terms until the summation is complete.  To write the summation expression, find the common format of each term, and write it using a "dummy variable" to represent the number that is changing.

If the change of the number within each term increases by 1 each time, that makes the transition easier because the dummy variable increases by 1.  If the change of the number within each term does not change by 1 each time, using summation notation can be more challenging, as one needs to develop a formula to represent the amount that it is changing each time.

The common format of each term & the changing number

In our case, each term is some number squared, and the number that is squared changes from 1, to 2, to 3, ... and so on .. up to 750 (changing by 1 each time).  Since the number that is square changes by 1 each time, that will be our "dummy variable".

Using "n" for the "dummy variable", our terms look like [tex]n^2[/tex]

The start and end of the list

Lastly, to specify where the list starts and ends, we write where the list starts (lowest number) at the bottom with the "dummy variable", and where the list ends (largest number) at the top.

So, in the end, the summation would look like this:  [tex]\sum \limits^{750}_{n=1} {n^2}[/tex]

This represents adding a bunch of terms that look like [tex]n^2[/tex], starting at n=1, each time, increasing the value of n by 1, and stopping with the last term when n=750.

Extension of knowledge (NOT about THIS problem)

For a similar example where the changing number doesn't increase by 1 each time, look at a similar sequence of, where it's just the odd numbers squared up to 99:

1^2 + 3^2 + 5^2 + … + 99^2

While the terms do have the format of a number squared, since the number that is squared isn't just increasing by 1 each time, there would need to be a formula to describe how they are increasing.  One way to represent that would be:

[tex]\sum \limits^{50}_{n=1} {(2n-1)^2}[/tex]

Note that this does cause the final endpoint of the dummy variable to not necessarily be intuitive, but the "99 squared" is the 50th term (observe 2*50-1 is 99).

Answer:

19.......

Step-by-step explanation:

correct

Answer:

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

Solve the equation for x:

Answer:

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