Steven is monitoring the height of one particular step on an escalator that takes passengers from the ground level to the second floor. The height of the Height of Step step in terms of time can be modelled by the graph shown. a) What is the period of the function, and what does it represent in this situation? b) Determine the equation of the axis for this periodic function. c) What do the peaks of the periodic function represent in this situation? Time (s) d) State the range of the function. e) If the escalator completes only 10 cycles before being shut down, what is the domain of the periodic function? f) Steven states that the stair will be at ground level at . Is he correct? Justify your answer.

Answer:

The number of DVDs Raj lost can be calculated by:

24% of 225 DVDs = 0.24 * 225 DVDs = 54 DVDs

So Raj lost 54 DVDs during his move.

The required properties for the algebraic expression are Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

Here,

Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution and square root qualities are the main nine properties of equality.

Algebraic equations involving real numbers can be resolved with the aid of the addition, subtraction, multiplication, and division characteristics of equality.

Thus, the required properties for the algebraic expression are Addition, subtraction, multiplication, division, reflexive, symmetric, transitive, substitution, and square root.

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After examining the first 50 rows of their spreadsheet, the investor is doing a kind of sampling that is called convenience sampling.

Convenience sampling is a type of non-probabilistic sampling method where participants are selected based on their ease of access or availability.

Based on the given situation, the investor has chosen to examine the first 50 rows of the spreadsheet because it is convenient for her, rather than selecting a random sample of the 500 cases measured by the Small Business Administration.

However, convenience sampling can lead to bias and is not considered a rigorous method for estimating population parameters.

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Answer:

2cm

convert 2 cm to mm

20 mm

A) To find out how much you pay in interest on the loan, you can use the formula: Interest = Principal x Rate x Time

Therefore:

Principal = 14,000

Rate = 18% (or 0.18 when expressed as a decimal)

Time = 5 years

So, Interest = 14,000 x 0.18 x 5 = 1,540

B) To find the total amount you pay for the loan, you need to add the principal amount and the interest.

Total amount = Principal + Interest

Total amount = 14,000 + 1,540 = 15,540

Simple Interest:
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The second linear equation will be linearly dependent to the first equation. The graphs of the two linear equation will be parallel to each other.

When two systems of linear equation is given and they do not have a solution that means the  first one is depended on the second one or the second equation is depended on the first set of equations.

The system of linear equations that does not posses a solution is called inconsistent form of linear equation where the multiples of the variables are multiples of each other but the constant is completely different.

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The value of 5/12 in decimal is 0.4167 and in percent is 41.67% .

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 of 100 questions correctly on a test (75/100).

The division is shown by the fractional bar between the "part" and the "whole." By dividing the numerator by the denominator, any fractions may be transformed into decimals. For instance, the fraction 45 denotes the ratio of 4 to 5, or 4/5. By dividing 4 by 5, this fraction may be changed into a decimal.

5/12 can be converted into decimal by dividing 5 by 12 we get 0.4167

5/12 in percent will be (5/12)*100 = 41.67 %

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Simple interest formula-

Amount Received = Principle*[1 + Rate.(Time)]

A= 4000*[1+ 5 (6)]

A= 4000*(1+30)

A= 4000*31

A= $124000

Final Answer - $124000

The number of tornadoes that occur in the United States each year is 1158

Let's call the number of tornadoes in the United States each year "x".

The number of tornadoes in Florida each year is 5.7% of this total

So we can write:

66 = x * 5.7%

Divide both sides by 5.7%

x = 66/5.7%

Evaluate

x = approximately 1158

So, approximately 1162 tornadoes occur in the United States each year.

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Answer:

I have graphed it and attached an image in the explanation.

Step-by-step explanation:

Answer:

The height of the cliff is 408.1 m

Step-by-step explanation:

To find the height of the cliff given a stone is thrown downward from the top of a cliff at 24m/s and hits the ground 7 seconds later, use constant acceleration equations (SUVAT).

Constant Acceleration Equations (SUVAT)

[tex]\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}[/tex]

Note: When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

List the given variables, taking downwards as positive:

Select the SUVAT equation with s, u, a and t in it:

[tex]s=ut+\dfrac{1}{2}at^2[/tex]

[tex]\begin{aligned}\textsf{Substitute the values}: \quad s&=24(7)+\dfrac{1}{2}(9.8)(7)^2\\s&=168+240.1\\s&=408.1\; \sf m \end{aligned}[/tex]

Therefore, the height of the cliff is 408.1 m.

The strongest linear relationship is indicated by a correlation coefficient of -1 or 1. The weakest linear relationship is indicated by a correlation coefficient equal to 0. A positive correlation means that if one variable gets bigger, the other variable tends to get bigger.

Now, According to the question:

The relationship between two variables is generally considered strong when their r value is larger than 0.7. The correlation r measures the strength of the linear relationship between two quantitative variables. Pearson r: r is always a number between -1 and 1.

The magnitude of the correlation coefficient indicates the strength of the association. For example, a correlation of r = 0.9 suggests a strong, positive association between two variables, whereas a correlation of r = -0.2 suggest a weak, negative association.

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Answer:

Coefficient: 45

Constant: 2

Hope this helped!

Step-by-step explanation:

The total distance D traveled by John is 255 miles.

The total distance D traveled by John is given by

D = 45 × 2 + 3 × 55 = 255 miles.

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John travelled 280 kilometres in the first distance and 250 kilometres in the second distance.

This question shows the case of John, who drove at constant speed his car on two roads. The travelled distance (s), in kilometers, is equal to the following formula:

s = v × t

Where:

v - Speed, in kilometers per hour.

t - Time, in hours.

The total time (T), in hours, is found by means of the following expression:

T = t₁ + t₂

T = x₁ / v₁ + x₂ / v₂

Where:

x₁ - Distance traveled in the first road

x₂ - Distance traveled in the second road.

v₁ - Speed taken in the first road.

v₂ - Speed taken in the second road.

T - Total time.

If we know that v₁ = 100 km / h, v₂ = 80 km / h, x₂ = 530 km - x₁ and T = 6 h, then the first distance is:

(530 - x₁) / 100 + x₁ / 80 = 6

[80 · (530 - x₁) + 100 · x₁] / 8000 = 6

42400 - 80 · x₁ + 100 · x₁ = 48000

20 · x₁ = 5600

x₁ = 280 km

And the second distance is:

x₂ = 530 km - 280 km

x₂ = 250 km

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Every vector spaces, iff:e→eis an idempotent linear map as E= Kcr(f) + Im(f)

What is Linear Map?

A linear map is a mapping in mathematics, more specifically in linear algebra. It is also known as a linear transformation, vector space homomorphism, or, in some cases, a linear function. that maintains the operations of vector addition and scalar multiplication between two vector spaces

Given that,

F : E → E is an idempotent linear map i.e FoF =F

F is an idempotent, then for any W in the image of F statistics

W = F(x)

for some x = E

Then F(w) = FoF(x)

F(x)=(W)----- (A)

So F is indeed a projection to Im(F) as a subspace of v

also , Kcr(F) + Im(F) =0

Because if x∈Kcr(f) + Im------(B)

then f(x) = 0 and

f(t)=x for some x∈E

FoF (t) = 0

f(t)=x

x=0

also from A we have

f(x)-w=0

f(x) -f(w)=0

f(x-w)=0

x-w=t

where t∈Kcr (F)

X = W+T

here x is arbitrary

E = Kcr + Im f ------(C)

From (B) and (C) we have E = Kcr(f) + Im (f)

Since E= Kcr(f) + Im, every vector space is an idempotent linear map (f)

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Answer:

Step-by-step explanation:

angle made in 20 min = 120 degree

area swept = (120 * 22 * 42 * 42)÷(360 * 7 * 10 * 10)

= 18.48 cm sq.

Answer:

The Angle is AABC

they met at =46

Answer:

Below

Step-by-step explanation:

5x >= 15     first solve for 'x' by dividing both sides by 5

x >= 5       graph on the number line should be a solid dot at 5 (because it includes '5') and going off to the right....looks like you have it correct.

The product of the solutions of the algebraic equation is -80

An algebraic equation is any equation that contains unknown values, usually represented with alphabets or letter

(x-5)/9 = 5/(x+7)

(x-5)(x+7) = 5 * 9

(x-5)(x+7) = 45

x² - 5x + 7x - 35 = 45

x² + 2x - 35 = 45

x² + 2x - 35 -45 = 0

x² + 2x - 80 = 0

(x − 8)(x + 10) = 0

x−8=0 or x+10=0

x=8 or x=-10

Product of the solutions = 8 * (-10) = -80

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There are 1,08,108 different committees that are possible.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex].

The general formula for combination is:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]  ,where 0 ≤ r ≤ n.

In a committee, we can choose 13 men from 5 men in ¹³C₅ ways. similarly, we can choose 3 women from 9 women in ⁹C₃ ways.

total ways in which we can choose 13 men and 9 women to form a committee= ¹³C₅*⁹C₃

[tex]\frac{13*12*11*10*9}{5*4*3*2*1} *\frac{9*8*7}{3*2*1}[/tex]

⇒154440/120*504/6

⇒1287*84

⇒108180

Hence, there are 1,08,180 committees are possible.

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a) The percentage of individuals who sleep between 4.5 and 9.3 hours is 75%.

b) By using Chebyshev's theorem, the percentage of individuals who sleep between 3.9 and 9.9 hours is 84%.

c) Using the empirical rule, the percentage of individuals who sleep between 4.5 and 9.3 hours day is 95%. But according to Chebyshev's theorem, this percentage is equals to 75%.

According to Chebyshev's theorem, the proportion of any distribution that lies within k standard deviations of the mean is at least equals to 1 − 1/k² , where k is a positive number, k> 1.

a) The average sleep hours per night is = 6.9 hours and standard deviation = 1.2 hours. Therefore, individuals who sleep between 4.5 and 9.3 hours are ± 2.4 hours or 2 standard deviations from the mean. Hence, k = 2. Using above theorem, the proportion of individuals who sleep between 4.5 hours and 9.3 hours = 1 - 1/2² = 1 - 1/4 = 0.75. Hence, the percentage of individuals who sleep between 4.5 hours and 9.3 hours

= 75%.

b) Again, the individuals who sleep between 3.9 and 9.9 hours are ±3 hours or 2.5 standard deviations from the mean. Hence, k = 2.5.

By Chebyshev's theorem, the proportion of individuals who sleep between 3.9 hours and 9.9 hours = 1 - 1/(2.5)² = 0.84 or 84 %.

c) The empirical rule is a rule-of-thumb used in statistics to forecast the behaviour of normally distributed data. Main points of Empirical rule:

The assumption here is that the number of hours of sleep follows a bell-shaped distribution i.e., the data are assumed to be normally distributed and therefore Empirical rule is applicable. As we see in individuals who sleep between 4.5 and 9.3 hours day are 2 standard deviations away from the mean. Therefore, by Empirical rule, the percentage is equals to 95% in this case. Thus, the conclusion is as per Empirical rule 95% of the individuals sampled in the national survey sleep between 4.5 and 9.3 hours. Whereas Chebyshev's theorem estimates that 75% individuals sleep between 4.5 and 9.3 hours.

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Complete question:

The results of a national survey showed that on average adults sleep 6.9 hours per night. Suppose that the standard deviation 1.2 hours. round your answers to the nearest whole number.

a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours.

b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between 3.9 and 9.9 hours.

c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours day. How does this result compare to the value that you obtained using Chebyshev's theorem in part(a)? select answer

Answer: To calculate the compound interest and amount for a given principal, interest rate, and time period, we can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the final amount (principal + interest)

P = the principal (initial investment)

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the investment is held

a. Principal = $5,900; Time = 2 years; Rate = 14%

n = 2 (since the interest is compounded half-yearly)

t = 2

r = 0.14

A = 5900(1+0.14/2)^(22)

A = 5900(1+0.07)^4

A = 59001.07^4

A = 5900*1.298844

A = 7,638.21

So the final amount, including interest, would be $7,638.21

b. Principal = $7,800; Time = 6 years; Rate = 18%

n = 2 (since the interest is compounded half-yearly)

t = 6

r = 0.18

A = 7800(1+0.18/2)^(26)

A = 7800(1+0.09)^12

A = 78001.09^12

A = 7800*2.05832

A = 16,093.32

So the final amount, including interest, would be $16,093.32

Please note that the above calculations are based on the compound interest formula and the assumption that the interest is compounded half-yearly, without taking into account any fees, taxes or any other associated cost.

Step-by-step explanation:

Answer: I do not now

Step-by-step explanation: WHO CARES

Rounding to six decimal places, the estimated area is 0.719638.

The midpoint rule for estimating the area under a curve involves dividing the interval of integration into n subintervals and using the heights of rectangles with width equal to the subinterval width to approximate the area under the curve.

Let's divide the interval [0, 2] into 4 subintervals, each with width 0.5. Then the midpoints of the subintervals are: x1 = 0.25, x2 = 0.75, x3 = 1.25, x4 = 1.75

Using the midpoint rule, the estimated area is given by the sum of the areas of the rectangles:

A = 0.5 * f(0.25) + 0.5 * f(0.75) + 0.5 * f(1.25) + 0.5 * f(1.75) where f(x) = e^(-3x²).

Substituting the values of f(x) into the above expression and evaluating, we get:

A = 0.5 * e^(-3 * 0.25²) + 0.5 * e^(-3 * 0.75²) + 0.5 * e^(-3 * 1.25²) + 0.5 * e^(-3 * 1.75²)

= 0.5 * e^(-0.1875) + 0.5 * e^(-2.25) + 0.5 * e^(-3.9375) + 0.5 * e^(-6.0625)

= 0.5 * (1.208611495 + 0.102011764 + 0.024515807 + 0.000598427)

= 0.5 * (1.439275966)

= 0.719637983

Rounding to six decimal places, the estimated area is 0.719638.

Therefore, Rounding to six decimal places, the estimated area is 0.719638.

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The reasonable values for the domain of f(x) is D = {x ∈ W | x ≤ 50}

The domain of a function is the complete set of possible values of the independent variable.

Given that, f(x) = x, where x is the number of people seated on the bus that has a maximum seating capacity of 50

Let us assume the maximum number of people that can sit on a bus is 50.

We know that, domain is all the possible values of x in set notation.

First, state the type of numbers that can be the number of people seated.

Since you cannot have a negative number of people, you cannot have a part of a person, but you can have 0 people, so the type to be included is W whole.

Therefore, the domain can be defined as, D = {x ∈ W | x ≤ 50}

That mean, the domain is x is an element of all whole numbers, x is less than or equal to 50.

Hence, the reasonable values for the domain of f(x) is D = {x ∈ W | x ≤ 50}

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The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

The length of the ladder is given as 30.58 ft using Trigonometry.

In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Distance is the measurement of an object's horizontal distance from a certain point, whereas height is the measurement of an object's height in the vertical direction.

Trigonometry includes heights and distances, and it has many uses in practical daily life. It is used to determine the distance between any two objects, including celestial bodies or other objects, as well as the height of towers, buildings, mountains, etc. Astronauts, surveyors, architects, and navigators are the main users.

The angle made by the ladder is 62°

Length of the ladder is x ft (say)

Height of the Electric Box is 27 ft

Now ,

sinθ = height of Electric box/ length of ladder

sin62° = 27/x

⇒x = 30.58 ft.

The length of the ladder is given as 30.58 ft using Trigonometry.

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Answer:

3(x - 3) ≤ 27

To solve this inequality, we'll start by isolating x on one side of the equation. To do this, we'll divide both sides of the inequality by 3:

x - 3 ≤ 9

Next, we'll add 3 to both sides of the inequality to get:

x <= 12

So the solution to the inequality is x <= 12.

It is also possible to express the solution in interval notation:

x ∈ (-∞, 12]

Answer:

6 meters

Step-by-step explanation:

refer attachment

7,725 ft² of grass cover the trapezoidal field.

0.5 x (125 + 81) x 75

0.5 x 206 x 75 = 7,725 ft².

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Answer:

316 min

Step-by-step explanation:

Find the area of 1 side of the pyramid:

h = height of the triangle

40² = (50/2)² + h²

h² = 1600 - 625 = 975

h = √975 = 31.225

A = 1/2bh = 1/2(50)(31.225) = 780.6

Atotal = 3(780.6) = 2342

2342(.75) = 1756.4

(1756.4 sf)(18 min/100 sf) = 316.15 min    

Answer: 551.1

Step-by-step explanation:

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