What is the range of this data ?
60 65 70 75 80 85 90 95 100

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 3, −2+4i, −2−4i

To find the zeros of the polynomial p(x), we need to find the values of x such that p(x) = 0.

One way to do this is to use the rational root theorem, which states that if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors), then p must divide the constant term and q must divide the leading coefficient.

For the polynomial, [tex]p(x) = x^3 + x^2 + 8x - 60,[/tex] the constant term is -60 and the leading coefficient is 1.

Therefore, the possible rational roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60

We can then use synthetic division or long division to check which of these roots are actually zeros of the polynomial.

Trying the possible roots, we find that x = 3 is a zero of the polynomial, since p(3) = 0.

Using long division or synthetic division, we can then divide p(x) by (x - 3) to get a quadratic factor:

[tex]x^3 + x^2 + 8x - 60 = (x - 3)(x^2 + 4x + 20)[/tex]

The quadratic factor [tex]x^2 + 4x + 20[/tex] has no real roots since its discriminant [tex](b^2 - 4ac)[/tex] is negative. Therefore, the zeros of the polynomial p(x) are:

x = 3 (with multiplicity 1)

x = -2 ± 4i (with multiplicity 1 each)

Therefore, the zeros of the polynomial p(x) are 3, -2 + 4i, and -2 - 4i.

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The mathematical function that is modeled in this table is C) f(x) = 1,000(0.80)ˣ⁻¹.

A mathematical function is described as an equation, expression, rule or law defining the relationship between the independent variable and dependent variable.

For instance, there are many types of functions, including:

Initial value = 1,000

Percentage of decrease = 20%

Decay factor = 0.80 (1 - 0.20)

x          f(x)       Using Option C:

1        1,000      1,000(1)

2         800       1,000(0.80)¹

3         640       1,000(0.80)²

4          512       1,000(0.80)³

Thus, the correct function is Option C.

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The value of p when q is equal to 2 is 108

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means as x increases y reduces and vice versa.

If p is inversely proportional to q, then

p = k/q

p = 18 and q = 12

18 = k/12

k = 18 × 12 = 216

When q =2

p = 216/2

p = 108

therefore the value of p is 108

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Answer:

The volume of the cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height:

V= πr²h = π(4cm)²(10cm) = 160π cm³

The density of the material is given by the mass per unit volume:

density = mass/volume = 500g / 160π= π(4 cm)²(10 cm)

= 160π cm³

The mass and volume are related by density (ρ), which is defined as mass per unit volume:

ρ = m/V

where m is the mass and V is the volume.

Substituting the given values, we get:

ρ = 500 g / 160π cm³

ρ ≈ 0.988 g/cm³

Therefore, the density of the material the cylinder is made of is 0.988 g/cm³.

Answer:

Yes, .023 is a rational number.

Step-by-step explanation:

A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not zero.

To show that .023 is a rational number, we can express it as a fraction in which the numerator and denominator are integers.

We can write:

.023 = 23/1000

Both the numerator (23) and denominator (1000) are integers, so .023 is a rational number.

Answer: 82

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)

The total area of the prism is (a) 120 + 20k in terms of k

From the question, we have the following parameters that can be used in our computation:

The pentagonal prism

The total area of the prism is calculated as

Area = 2 * Pentagon + 5 * Rectangle

Given that

P = 20 and

Apothem, a = k

We have

Pentagon = 1/2 * 20 * k

Pentagon = 10k

Next, we have

Rectangle = 6 * P/5

So, we have

Rectangle = 6 * 20/5

Rectangle = 24

Recall that

Area = 2 * Pentagon + 5 * Rectangle

So, we have

Area = 2 * 10k + 5 * 24

Evaluate

Area = 20k + 120

Hence, the total area of the prism is (a) 120 + 20k

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To find the total area of a prism, we need to add up the area of all its faces. The given prism has a rectangular base with length 20 inches and width 6 inches. The area of the base is therefore 20 x 6 = 120 square inches.

The prism also has two congruent rectangular faces, each with a length of 20 inches and a height of K inches. The area of each face is therefore 20K square inches. Since there are two such faces, their total area is 2 x 20K = 40K square inches.
Finally, the prism has two more rectangular faces, each with a length of 6 inches and a height of K inches. The area of each face is therefore 6K square inches. Since there are two such faces, their total area is 2 x 6K = 12K square inches.
Adding up all the face areas, we get:
120 + 40K + 12K = 120 + 52K
Therefore, the total area (in terms of K) of the prism is 120 + 52K square inches.

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Answer:

x = 8.8 cm

Step-by-step explanation:

This is a right-angled triangle, and we are given two sides, so we can use pythagoras Theoren

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where 'c' is the hypotenuse (the longest side in right angled triangle and is always opposite to the 90 degree angle).

'a' and 'b' are the other two sides.

So now we have:

2.6^2 + x^2 = 9.2^2 (Solve for 'x')

x^2 = 9.2^2 - 2.6^2

x = [tex]\sqrt{9.2^{2} - 2.6^{2} }[/tex]

x = 8.8 cm (2 s.f. as other dimensions are also 2 s.f.)

Answer:

  (x, y) = (2, 1)

Step-by-step explanation:

You want the solution to the system of equations ...

When the coefficients are not nicely related, graphical methods or matrix methods are preferred, as elimination or substitution can result in messy arithmetic with large numbers.

The first attachment shows a calculator's solution using row-reduction of the augmented matrix of coefficients. It tells us the solution is ...

  (x, y) = (2, 1)

A solution similar to the use of Cramer's rule can be found using the cross-multiplication method. For this, we rewrite the equations to general form, and make a list of the coefficients with the x-coefficients repeated at the end of the list:

Now, we form the differences of the cross products in each pair of columns:

  ∆ = (148)(148) -(231)(231) = -31,457

  ∆x = (231)(-610) -(148)(-527) = -62,914

  ∆y = (-527)(231) -(-610)(148) = -31,457

And the solution is ...

  x = ∆x/∆ = -62,914/-31,457 = 2

  y = ∆y/∆ = -31,457/-31,457 = 1

The solution is (x, y) = (2, 1).

__

Additional comment

You might consider this to be "messy arithmetic with large numbers." Yes, it looks that way, but there are actually fewer operations required here than when using the elimination method.

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The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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Answer:

10

Step-by-step explanation:

the side is 13 and 3 so the difference is 10 on that side

on the bottom side it's 3 and if it's the same it's 10

Answer:

t=3.5

Step-by-step explanation:

Divide each term in 7t=24.5 by 7 and simplify.

The positive values of the number Kofi thinks of are 1 and 2.

Let's call the number Kofi thinks of "x".

According to the problem Kofi adds 5 to this number and then multiplies the result by 3.

We can write this as:

3(x + 5)

We know that this expression cannot be greater than 21 so we can set up an inequality:

3(x + 5) ≤ 21

Simplifying the inequality, we get:

x + 5 ≤ 7

Subtracting 5 from both sides, we get:

x ≤ 2

The possible values of the number Kofi thinks of are all the positive integers less than or equal to 2 are 1 and 2.

To check that these values work can plug them back into the expression 3(x + 5) and verify that they give a result less than or equal to 21:

If Kofi thinks of 1, then 3(1 + 5) = 18 is less than 21.

If Kofi thinks of 2 then 3(2 + 5) = 21 is equal to 21 but it satisfies the condition since the problem asks for an answer that "cannot be greater than 21".

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Answer:

(a) 5.3 grams

(b) 0.2 years

Step-by-step explanation:

(a) Step 1:  Since we're already given A0, we simply plug in 0.5 for t to find A(0.5), aka the amount of Thorium-234 remaining after 0.5 years:

[tex]A(0.5)=1000e^(^-^1^0^.^4^9^8^*^0^.^5^)\\A(0.5)=1000e^(^-^5^.^2^4^9^)\\A(0.5)=5.252768542\\A(0.5)=5.3[/tex]

Thus, the amount of Thorium-234 remaining after 0.5 years is approximately 5.3 grams.

(b) We plug in 115 for A(t) and 1000 for A0.  Then, we must solve for t: Thus, our equation to solve for t, time in years, is

[tex]115=1000e^(^-^1^0^.^4^9^8^t^)[/tex]

Step 1:  Divide both sides by 1000.

115/1000 = e^(-10.498t)

0.115 = e^(-10.498t)

Step 2:  Take the natural log (ln) of both sides.

ln(0.115) = ln(e^(-10.498t))

Step 3:  According to the rules of natural logs, we can bring -10.498t down and multiply it by ln(e) on the right-hand side of the equation:

ln(0.115) = -10.498t * ln(e)

ln(0.115) = -10.498t * 1

ln(0.115) = -10.498t

Step 4:  Now, we divide both sides by -10.498 and round the result to find out after about how many years will 115 grams of thorium-234 be remaining:

(ln(0.115) = -10.498t) / -10.498

0.2060223996 = t

0.2 = t

Thus, there will be 115 grams of thorium-234 remaining after about 0.2 years

The output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

To maximize profits, we need to find the output levels of the two goods that will maximize the difference between total revenue and total cost (i.e., profit).

The profit function can be expressed as:

π = TR - TC

  = 15Q1 + 18Q1^2 + 15Q2 + 18Q2^2 - 20 - 2Q1.Q2 - 393

Taking the partial derivative of the profit function with respect to Q1 and setting it equal to zero, we get:

∂π/∂Q1 = 15 + 36Q1 - 2Q2 = 0

Taking the partial derivative of the profit function with respect to Q2 and setting it equal to zero, we get:

∂π/∂Q2 = 15 + 36Q2 - 2Q1 = 0

Using Cramer's rule, we can solve for Q1 and Q2:

Q1 = (2(15) - (15)(36))/(-4) = 52.5

Q2 = (2(15) - (15)(36))/(-4) = 52.5

Therefore, the output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

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Answer:

The expected count of rolls to land showing a 3 is 10.00.

The area of Curtis's triangular frame is 36 square feet. The Option C is correct.

To get area of the frame, we will use formula for the area of a triangle which is [tex]A = 1/2 * b * h[/tex]

B = length of the base

H = perpendicular distance from the base to the vertex.

Substituting the values, we get:

A = 1/2 * 12 feet * 6 feet

A = 1/2 * 72 feets

A = 36 square feet

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Answer:

$103,875.41

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Note: Bi-monthly means every 2 months.

Substitute the given values into the formula and solve for A:

[tex]A=240000\left(1+\dfrac{0.012}{6}\right)^{6 \cdot 30}[/tex]

[tex]A=240000\left(1.002\right)^{180}[/tex]

[tex]A=343875.406934...[/tex]

[tex]A=343875.41[/tex]

So after 30 years, Mr. and Mrs. Rainer will have paid a total of $343,875.41, which includes both the principal and the interest.

To find the amount of interest they paid, subtract the principal:

Interest paid = $343,875.41 - $240,000 = $103,875.41

Therefore, they will have paid $103,875.41 in interest over the 30-year period.

The total amount of the emergency fund is A) $6,516.91

First, we need to calculate the net income after deductions:

Next, we need to calculate the amount of constant expenses:

Fixed prices = 30% of $3,425.88 = $1,027.76

The entire amount saved inside the emergency fund is 5 months' worth of fixed costs:

Emergency fund = $1,027.76 x 5 = $5,138.80

To calculate the quantity inside the 60-day CD

We need to multiply 75% of the emergency fund by means of the interest rate and divide with the aid of 12 to get the monthly interest:

Therefore, the total amount of the emergency fund is:

$5,138.80 + $160.57 + $1,284.70 = $$6,516.91

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Mia's total profit for the month is given as follows:

$200.

The profit function is obtained as the subtraction of the revenue function by the cost function, as follows:

P(x) = R(x) - C(x).

From the table given in this problem, the revenue and the costs are given as follows:

Hence the profit is given as follows:

9500 - 9300 = $200.

As the profit is positive, it is in fact a profit(gain) and not a loss.

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The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR.

To calculate the MIRR, we need to find the future value of the positive cash flows at the end of year 4, using the reinvestment rate equal to the WACC. We can then find the discount rate that equates the present value of the initial investment with the future value of the negative cash flows and the positive future value of the positive cash flows.

Using the financial calculator or spreadsheet software, we can find that the future value of the positive cash flows is $698,711.27, and the MIRR is 27.46%.

Therefore, the MIRR is 27.46%, and based on the MIRR criterion, the project should be accepted if the required rate of return is less than 27.46%.

The correct statement about the relationship between the IRR and the MIRR is that a typical firm’s IRR will be less than its MIRR. This is because the IRR assumes that positive cash flows are reinvested at the IRR, which may not be realistic, while the MIRR assumes that positive cash flows are reinvested at the WACC, which is usually more realistic.

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Some of the reasons why math is important include:

Mathematics teaches us the invaluable skills of critical thinking via logical and systematical reasoning for solving complicated problems. It is, however, essential to know that mathematics is omnipresent in our day-to-day lives but we may not be conscious about it.

Our math-related actions include computing tips, shopping, allocating time for daily tasks as well as cooking meals. With a strong foundation in Mathematics, several career paths such as engineering, finance, accounting or data analysis can materialize for perspective job-visors; hence enabling them towards professional success.

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Yes the boa constrictor population would become a problem, since the population of beetles in this rainforest community were to disappear, the population of poison dart frogs will most likely be affected;

The populations feed on Beetles and serve as food for poison dart frogs.

Since poison dart frogs depend on beetles for food, then, a decrease in the population of the beetles in the forest community will most likely result in a decrease in the population of the poison dart frogs.

In conclusion, we can say that the beetles serve as food for poison dart frogs.

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Answer:

[tex]z^{2} +z-36[/tex]

Step-by-step explanation:

Multiply

Answer:

- 3 , 7 , - 13 , 5x + 2

Step-by-step explanation:

A

to evaluate f(0) substitute x = 0 into f(x)

f(0) = 5(0) - 3 = 0 - 3 = - 3

B

substitute x = 2 into f(x)

f(2) = 5(2) - 3 = 10 - 3 = 7

C

substitute x = - 2 into f(x)

f(- 2) = 5(- 2) - 3 = - 10 - 3 = - 13

D

substitute x = x + 1 into f(x)

f(x + 1)

= 5(x + 1) - 3 ← distribute each term in the parenthesis by 5

= 5x + 5 - 3 ← collect like terms

= 5x + 2

Answer:

A) -3

B) 7

C) -13

D) 5x+2

Step-by-step explanation:

For A, B, and C substitute the value stated in the parenthesis.

A) f(0) means to find the value when x=0, so we substitute 0 where x is in the function.

[tex]5(0)-3[/tex]

Then use PEMDAS and multiply first and then subtract 3 from the product.

[tex]5(0)=0\\0-3=-3[/tex]

B) Take the same steps as before with a different value. Substitute 2 for x.

[tex]5(2)-3\\5(2)=10\\10-3=7[/tex]

C) Also the same thing as the previous problems. Substitute -2 for the value of x.

[tex]5(-2)-3\\5(-2)=-10\\-10-3=-3[/tex]

D) Similar to above substitute x+1 where x is.

[tex]5(x+1)-3\\[/tex]

Then distribute 5(x+1) to get

[tex]5x+1(5)\\5x+5[/tex]

Then simplify the equation

[tex]5x+5-3=5x+2[/tex]

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer: 9530

Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0

In the given figure, after applying the vertical angle and straight line angle property, the values of x and z are 5° and 116° respectively.

Four angles are created when two lines intersect. Vertical angles are those that are opposite each other and are always congruent.

That means, z° = (12x + 56)° ---------- (1)

On a straight line, the angles add up to 180°.

That means, z° + (8x + 24)° = 180° ---------- (2)

Substituting value of z from (1) in (2),

(12x + 56) + (8x + 24) = 180

20x + 80 + 180

20x = 100

x = 5°

Substituting x = 5 in (2),

z + (8*2 + 24) = 180

z + 64 = 180

z = 116°

Therefore, x = 5° and z = 116°.

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Answer:

x = -3 + √117

x = -3 - √117

Step-by-step explanation:

So the equation is x(x+6)=108

first you gotta simplify

x*x + x*6 = 108

x^2 + 6x = 108

x^2 + 6x - 108 = 0

using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a) with a=1, b=6 and c=-108