Suppose the finishing times for cyclists in a race are normally distributed. If the population standard deviation is 16 minutes, what minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean?

The average amount that the roller coaster's height drops over each horizontal foot will be -5 feet.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

Slope = change in y/change in x

Slope = Δy/Δx

A 20-foot horizontal drop is present on a roller coaster.

So, Δx = 20-foot

The roller coaster is 100 feet tall when it is at the bottom of the drop.

So, Δy = -100 feet.

Now, the average rate of change will be,

= -100/20

= -5/1 = -5

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Using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, the total cost of fencing is:

According to the given figure, the total length of fencing will be:

8m + 8m + 6m + 2m + 2m + 6m

32 m

Now, 4% more of the total fence:

4/32 * 100

1.28 m

Now the total fencing length:

32 + 1.28

33.28 m

We know that:
1m = 3.2 ft

33.28m = 109.18 ft

We are given that fencing of 4 feet costs: $27. Then,

109.18/4

27.295 * $27

$736.965

Rounding off: $737 approximately

Therefore, using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

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w is less than 75.

What do you mean by algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

An equation that only uses algebraic expressions is known as an algebraic equation.

Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions.

Given expression:

[tex]\frac{75}{w}=\frac{150}{100}[/tex]

⇒ w = [tex]\frac{75 \times 100}{150 }[/tex]

⇒ w = 50

Convert the value of w into percentage.

w = 50 × 100 % = 500%

Therefore, w is less than 75.

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The distance between the bank and Hiroto's house on the map is 11.5 units.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The distance between the bank and Hiroto's house will be calculated as,

The coordinates are, B(-8,6) and H(3.5,6).

D=√(3.5-(-8))²+(6-6)²

D = √11.5²

D = 11.5

Therefore, the distance between the bank and Hiroto's house on the map is 11.5 units.

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The biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

A formula in Microsoft Excel is an expression that modifies values in a set of cells.

Even if the result is incorrect, these formulas nonetheless return a result.

We may execute calculations like addition, subtraction, multiplication, and division using Excel formulae.

To make complex computations simpler, Excel features prewritten formulas known as functions.

A function takes one or more values, runs an operation, and then outputs the outcome to a cell.

Arguments are the values that you pass to a function.

So, in the given situation of Jenny, the excel formula PV(.035/12, 15*12, -485)will be used to determine the largest mortgage loan she can afford.

Therefore, the biggest mortgage loan Jenny can afford will be determined using the Excel formula PV(.035/12, 15*12, -485) in the situation that has been provided.

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Complete question":
Jenny has decided that she can afford a monthly mortgage payment of $390. She has been offered a 3.5% 20-year mortgage from her bank. What formula could you type into Excel to determine the largest mortgage loan she can afford is?

(A) PV(.035/12, 15*12, -485)

(B) PMT(.035/12, 15*12, -485)

(C) PV(.035, 15*12, -485)

(D) 390*.035/20

The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.

Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.

Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

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The one poison dart frog is 1/4 inch longer than the other.

What is Poison dart frog?

A family of frogs known as the Dendrobatidea that are indigenous to tropical Central and South America go by the common name "poison dart frog." These species are nocturnal and frequently have colorful bodies. These aposematic species have a bright coloration that is linked to the species' toxicity.

Given: Mary saw two poison dart frogs.

One was 7/8 inch long and the other was 5/8 inch long.

So, 7/8 - 5/8 = 2/8 = 1/4

Hence, the one poison dart frog is 1/4 inch longer than the other.

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7) ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) ∠ACD = 102 degree

What do you mean by co interior angle?

Co-interior angles, or consecutive interior angles, are two angles on the same side of a transverse line. Co interior angles are interior angles that add up to 180 degrees. This means that the sum of the two interior angles on the same side of the horizontal side are complementary.

7) Given :

∠EFG = 32 degree

∠GFH = 56 degree

∠EFG = ∠EFG + ∠GFH = 32 + 56 = 88 degree

Therefore, ∠EFG = 88 degree

8) DC and AB are parallel to each other.

AE and AB are perpendicular to each other

CG and AB are perpendicular to each other.

9) As AB and CD are parallel to each other therefore , ∠BAC and ∠ACD are cointerior angle and sum of co interior angles is 180 degree.

6x + 6 + 9x - 6 = 180

15x = 180

x = 180/15 = 12

∠ACD = (9x - 6) degree = 9(12) - 6 = 108 - 6 = 102

Therefore, ∠ACD = 102 degree

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The number written as a fraction in simplest form is 4/5

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

Clausometer = 80%

Turn the percentage to fraction

So, we have the following representation

Clausometer = 80/100

Divide 80 and 100 by 10

So, we have the following representation

Clausometer = 8/10

Divide 8 and 10 by 2

So, we have the following representation

Clausometer = 4/5

Hence, the fraction is 4/5

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The area of the shaded region will be equal to 120 square cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that the sides of the rectangle are 24 cm and 10 cm. The area of the shaded region will be calculated by subtracting the area of the whole rectangle and the area of the triangle which is not shaded.

Area of the shaded region = ( 24 x 10 ) - ( 1/2 x 24 x 10)

Area of the shaded region = 240 - 120

Area of the shaded region = 120 square cm

Therefore, the area of the shaded region will be equal to 120 square cm.

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The critical value that corresponds to a confidence level of 99% is, 2.58.

1 decimal place (tenths) 2 decimal places (hundredths) 3 decimal places (thousandths) 4 decimal places (ten-thousandths)

The confidence level is 99%.

The significance level is:

Compute the critical value as follows:

That is:

Use the z-table for the z-value.

For z = 2.58 the P (Z < z) = 0.995.

And for z = -2.58 the P (Z > z) = 0.005.

Thus, the critical value is, 2.58.

active attachment

"=NORM.INV(0.0635,0,1)"

"=NORM.INV(1-0.0635,0,1)"

Previous concepts

And we can use the following excel codes to find the solution:

"=NORM.INV(0.0635,0,1)"

"=NORM.INV(1-0.0635,0,1)"

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8,9,10 is the value from the given replacement set make-up the solution set for inequality.

In mathematics if a statement of an order relation greater or greatest then or equal to is called inequality. To compute the inequality:

if we replace m with 8 it will be 8+7 which is 15 and less then 18

for 9 its 9+7 which is 16 which is less then 18

and for 10 its 10+7 which is 17 which is less then 18

and for 11 its 11+7 is 18 which is equal to 18 so it would not apply to this equation.

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Answer:

It will take 64 hours

Step-by-step explanation:

It will be more specifically 63.889 hours, but rounding up it's 64

The coordinates to plot the graph after solving the equation will be 0.33 and 1.2.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given expressions to plot, the graph is,

f(x) = 3x - 1 and,  (i)

h(x) = -4x - 5       (ii)

From equation (i),

f(x) = 3x - 1

3x = 1

x = 1/3

x = 0.33

From equation (ii)

h(x) = -4x - 5

-4x = 5

x = -5/4

x = 1.2

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Answer: y = 11x + 31, the y - intercept is 31!

Step-by-step explanation:

The equation that models this situation is y = mx + b

We already have the slope, m, of 11.

since we have 2 coordinates, we can substitute all the known values into the equation.

==> 108 = 11 (7) + b

Multiply.

==> 108 = 77 + b

Take 77 from both sides

==> 108 - 77 = 77 - 77 + b

==> 31 = b

==> This means that the y intercept of this linear function is;

f(x) = 11x + 31

or

y = 11x + 31

The solution set for the inequality - x < 2 is - x < 2.

What is  inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

An inequality in mathematics depicts the connection between two values in an unbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.

-x<2

Multiply both sides by -1 (reverse the inequality)

(-x)(-1)>2(-1)

Simplify

x>-2

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Step-by-step explanation:

Set each binomial equal to 0, solve for x.

[tex](x + 5) = 0[/tex]

[tex]x = - 5[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

The zeroes are -5, and 2(with a multiplicity of 2)

We have a degree of 3.

[tex](x + 5)(x {}^{2} - 4x + 4)[/tex]

the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.

Answer:

look below

Step-by-step explanation:

To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.

In each of the following circumstances:

a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.

b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.

e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.

It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.

The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

A parachutist's rate during a fast drop arrives at 55 meters each second. In your calculations, accept that the meter is equivalent to 3.3 feet.

Convert the speed into feet per second. Then we have

S = 55 x 3.3

S = 181.5 feet per second

The parachutist fall during 15 seconds of free fall will be given as,

D = 181.5 x 15

D = 2,722.5 feet

The speed is 181.5 feet per second. Then the parachutist fall during 15 seconds of free fall will be 2,722.5 feet.

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A corporation—also known as a C corp—is a legal entity distinct from its owners.

A corporation also referred to as a C corp, is a separate legal entity from its owners.

Corporations are able to generate revenue, pay taxes, and face legal consequences.

The strongest protection against personal liability is provided to owners by corporations, although forming a corporation is more expensive than creating other types of entities.

A corporation is a collection of people or a business that has been given legal status as a single entity by the state and is used for specific legal purposes.

Early corporations were created with a charter.

The majority of governments currently permit the registration of new corporations.

Therefore, a corporation—also known as a C corp—is a legal entity distinct from its owners.

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Correct question:
Which form of organization is a separate legal entity?

This bolt should go into the package. The percentage of error is 2.22% which is less than 3%.

What is the meaning of error?

The discrepancy between a variable's observed value and its actual but unseen value

Given that the diameter of each bolt is 0.45 inch.

The percentage of error the diameter of each bolt must be less than 3%.

A bolt picks for a test. The diameter of the bolt is 0.46 inch.

The formula of percent error is

The difference of the diameters/ the original diameter of bolt )× 100%

= [(0.46 - 0.45)/0.45] × 100%

= (0.1/0.45) × 100%

= 0.0222 × 100%

= 2.22%

The percentage of error is less than 3%. So the lot is good to go.

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2,200 caterpillars are expected to become a butterfly in 17.8 days or more.

Formula: Z= (x-bar-mean)/σ: where x-bar is the score to which we are calculating a Z value; mean is just the arithmetic mean of the sample or population, and σ is the standard deviation of the sample or the population. Check attached image 1 below.

Substitute and calculate:

[tex]Z=(17.8-15)/3.5\\\\ Z=0.8[/tex]

For this solution, we are going to b e using Microsoft Excel's tools to calculate the probabilities. Check attached image 2.

[tex]IP(Z\leq 17.8)=0.7881[/tex]

This is the probability that any caterpillar becomes a butterfly in 17.8 days or less. This is how Microsoft Excel calculates probabilities for default. Now, in order to get the probability that the problem asks for (17.8 days or more) we just need to do the following operation:

[tex]1-0.778=0.222[/tex]

[tex](0.222)(10,000)=2,220[/tex]

2,200 caterpillars are expected to become a butterfly in 17.8 days or more.

Answer:

The above answers are incorrect.

Step-by-step explanation:

If the price of one of the goods decreases, the quantity demanded of that good will increase due to the substitution effect. This means that the consumer will choose to buy more of the cheaper good and less of the more expensive good. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

In this case, if the price of one of the goods decreases from $10 to $8, the consumer will likely purchase more of that good and less of the other good, which is a substitution effect. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

Therefore, the correct answer is e. The above answers are incorrect.

The proportional relationship of the table are as follows:

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality.

First table

k =hx

10 = 2x

x = 5

Hence,

k = 5h

h = 1 / 5 k

Second table

k = hx

5 = 4x

x = 5 / 4

Hence,

k = 5 / 4 h

Third table

k = hx

5 = 25x

x = 5 / 25

Hence,

k = 1 / 5 h

h = 5k

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Fe^2 + → Fe^3 + + e^- is an example of oxidation

How many oxidations do Fe3+ and Fe2+ ions have?

For instance, the oxygen ion O2+ has an oxidation number of 2 because it can contribute two electrons, whereas the iron ion Fe3+ has an oxidation number of +3 because it can take on three electrons to establish a chemical bond.

[tex]$\mathrm{Fe}_3 \mathrm{O}_4$[/tex] contains [tex]$\mathrm{F}$ e[/tex] atoms of both[tex]$+2$ and $+3$[/tex]oxidation number.

It is a stoichiometric mixture of[tex]Ferrous $(\mathrm{FeO})$[/tex]

and Ferric [tex]$\left(\mathrm{Fe}_2 \mathrm{O}_3\right)$ oxides combined as $\mathrm{FeO} \cdot \mathrm{Fe}_2 \mathrm{O}_3$.[/tex]

[tex]Oxidation state of oxygen in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ is $-2$.[/tex]Let the oxidation state of [tex]$\mathrm{Fe}$ in $\mathrm{FeO}$ and $\mathrm{Fe}_2 \mathrm{O}_3$ be $\mathrm{x}$ and $y$[/tex]

As we know that the sum of the oxidation states of all the atoms or ions in a neutral compound is zero.

ThereforeOxidation state of [tex]$\mathrm{F}$ e in $\mathrm{F}$ eO-[/tex]

&[tex]x+(-2)=0 \\& \Rightarrow x=2[/tex]

Oxidation state of[tex]$\mathrm{F}$ e in $\mathrm{Fe}_2 \mathrm{O}_3-$[/tex]

&[tex]2(\mathrm{y})+3(-2)=0 \\& \Rightarrow 2 \mathrm{y}=6 \\& \Rightarrow \mathrm{y}=3\end{aligned}[/tex]

Hence the oxidation number of [tex]$\mathrm{Fe}$ in $\mathrm{Fe}_3 \mathrm{O}_4$ are $+2$ and $+3$[/tex]respectively.

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The required equation of conic section that shows eclipse is  [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the standard equation of conic section,

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex]      (1)

From the given diagram,

The center of the eclipse is (2, 4),

Here h = 2, and k = 4

The length of minor axis 2a = 8 ⇒ a = 4

The length of major axis 2b = 12  ⇒ b = 6

Substitute the values of a, b and h, k in equation (1)

[tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex]

The required equation of the given conic section is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

The conic section represents the eclipse.

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By using the concept of function, it can be calculated that-

a) [tex]\frac{g}{f}(-4) = \frac{4}{31}[/tex]

b) The point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex]

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are -

   g(x) = (x + 6)(x  + 6)

  f(x)= -6x+7

   [tex]\frac{g}{f}(x) = \frac{g(x)}{f(x)} = \frac{(x+6)(x+6)}{-6x+ 7} = \frac{(x+6)^2}{-6x + 7}[/tex]

   [tex]\frac{g}{f}(-4) = \frac{g(-4)}{f(-4)} = \frac{(-4+6)^2}{-6(-4) + 7} = \frac{4}{31}[/tex]

b)  [tex]\frac{g}{f}(x)[/tex] is not defined if -6x + 7 = 0

     [tex]\frac{g}{f}(x)[/tex] is not defined if  [tex]x = \frac{7}{6}[/tex]

      So the point [tex]\frac{7}{6}[/tex] is not in the domain of [tex]\frac{g}{f}[/tex].

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