Akira is running around a circular track. Akira runs counterclockwise. From where he starts, it takes him 22 seconds to reach the easternmost point of the track. It takes him 95 seconds to run one complete lap. Bob starts running at the same time as Akira. Bob starts from the northernmost point and runs clockwise. Bob and Akira pass each other for the first time after 26 seconds. How long does Bob take to run one lap of the track? (round off your answer to four decimal digits)

n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1

What is Remainder?

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.

As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.

[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]

[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).

The remainder will be n= (K+1)^3

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The result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the following function:

[tex]f(x)=x^2-8x+4;\;g(x)=4x+3;\;and\;h(x)=x+2.[/tex]

We need to find the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex]

Therefore,

g(x)=4x+3

h(x)=x+2

[tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] =(x+2)/( 4x+3)

Hence, the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).

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The distance that each boy ran is as follows:

Donnie = 24 miles

Karim = 12miles

Shawn = 9 mile.

Ratio is defined as an expression that is used to represent the part of a whole entity or structure.

The total distance covered by the three boys = 46miles.

Distance covered by Donnie = 200% of Karim (ratio 4)

That is;

200/100×4 = 8

Now the ratio of the three boys = 8:4:3

To calculate the distance of each boy is by finding the total ratio of the whole boys such as:

= 8+4+3 = 15

For Donnie = 8/15×45 = 24 miles

For Karim = 4/15×45 = 12 miles

For Shawn = 3/15 × 45 = 9 miles

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Answer:

1. The GCF is 15 and the LCF is 1.

There are 4 common factors: 1, 3, 5, 15

2. The GCF and LCF is 1. This is the only common factor.

Step-by-step explanation:

To find common factors, think about what two numbers you can multiply to get the desired values. The numbers that are the same for both desired values are going to be factors.

The probability that [tex]\bar{x}[/tex] < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.

As given in the question,

Normal distribution with mean 'μ' = 1.59 millimeters

Standard deviation 'σ' = 0.042 millimeters

Sample size 'n' = 20

standard error = σ /√n

                        = 0.042 / √20

                        = 0.00933

Probability that [tex]\bar{x}[/tex] < 1.57  is

X = 1.57

s = 0.0093

P( X < 1.57)

= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]

= P ( z < -2.14 )

Using z - table p value is

= 0.01617

= 0.0162

Therefore, the probability for the [tex]\bar{x}[/tex] < 1.57  is equal to 0.0162.

The complete question is :

A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?

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The present age of Sesay is found as the 35 years.

For the stated question;

Let the age of Sesay five years ago be 'x'.

Then, the age of Muskam is twice of Sesay be '2x'.

The sum of their present ages after 5 years  is;

(x + 5) + (2x + 5) = 100

3x + 10 = 100

3x = 90

x = 30 (Age of Sesay 5 years ago)

Present age of Sesay = x + 5 = 30 + 5 = 35 years.

Thus, the present age of Sesay is found as the 35 years.

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(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

Given that,

A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.

We have to find

(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west

(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.

We know that,

(a) For 6:00 p.m

Sin(θ)=opposite/ hypothesis

θ=29

Opposite=west

Hypothesis =60

Sin(29°)=w/60

w=29.09nm

West= 29.09nm

Cos(θ)=adjacent/ hypothesis

θ=29

Adjacent= south

Hypothesis =60

Cos(29°)= south/60

south=52.475nm

Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.

(b) tan(θ)=opposite/adjacent

Opposite=29.09nm

Adjacent= 52.475nm

Tan(θ)=29.09nm/52.475nm

θ=36.68°

Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.

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As a fraction of c, the length will be 60% at v/c = 0.76

The length of the moving rod = 60%

Using the formula for length contraction-

L = L_o(√(1 - (v²/c²))

Where;

v = The speed of the object

c = The speed of light

L = The length of the object at a moving speed

L_o = The length of the object at rest

Thus,

L = 65%

L_o = 0.65

Substituting the values -

0.65L_o = L_o[√(1 - (v²/c²))]

Dividing both sides by L_o -

0.65 = √(1 - (v²/c²))

Squaring both sides -

0.65² = (1 - (v²/c²))

v²/c² = 1 - 0.65²

v²/c² = 0.5775

Taking the square root of both sides gives;

v/c = 0.76

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The expression that results from applying the law of indices and expression is 5x^(-7/3).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Here,

The resulted expression will be,

(125x)^(7/3)^(-1/3)

125=5^3

(a^n)^m = a^mn

(5x)^3^7/3^-1/3

(5x)^7*-1/3

5x^(-7/3)

The resulted expression will be 5x^(-7/3) using the law of indices and expression.

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The variance for the data set is 18.

What is a variance?

The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.

Here we have to find the variance for this data set.

Given data:

The age of six grandchildren in a family is = 6, 3, 14, 11, 14, 6

The mean = 6+3+14+11+14+6/ 6

                 = 9

The variance = (6-9)² + (3-9)² + (14-9)² +(11-9)² + (14-9)² + (6-9)²/ 6

                      = 9+36+25+4+25+9/  9

                     = 18

Therefore the variance is 18.

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The 90% confidence interval for the mean height of students at UH is (5.885,5.915) feet.

We have given that, an srs of 28 students at UH gave an average height of 5.9 feet and a standard deviation  of 0.1 feet.

i.e n = 28

x = 5.9 feet

s = 0.1 feet

and we have to construct a 90% confidence interval for the mean height of students at UH.

The level of significance, α = 1 - 0.9 = 0.1

The value of 0.9 in z-table is 0.816.

The formula for confidence interval is,

CI = x ± z* (s/[tex]\sqrt{n}[/tex])

Substituting the values,

CI = 5.9 ± (0.816) (0.1/√28 )

   = 5.9 ± (0.816)(0.1/5.291)

   = 5.9 ± (0.816)(0.0189)

CI = 5.9 ± 0.015

CI = 5.9 + 0.015 = 5.915

CI = 5.9 - 0.015 = 5.885

Therefore 90% confidence interval for the mean height of students at UH is 5.885 feet to 5.915 feet.

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The value of the the function h(x) at x = 4 is given as follows:

8.7.

The quadratic regression equations for each table are given as follows:

The function for the first item is defined as follows:

h(x) = 50/(5.5 + 8e^(-0.9x)).

At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:

h(4) = 50/(5.5 + 8e^(-0.9(4))).

Then a calculator is used to obtain the exact value due to the exponential, hence:

h(4) = 8.7.

The regression equations are obtained inserting the points of each table into a quadratic regression calculator.

For the first table, the points are given as follows:

(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).

Hence the equation is of:

y = -0.127x² + 4.699x - 27.777.

For the second table, the points are given as follows:

(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).

Hence the equation is of:

y = 32.86x² - 379.14x + 1229.14.

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A statement in the form p→q has three related implications that are called converse, inverse, and contrapositive.

A statement in the form p→q has three related implications.

Statement: If p then q (p→q)

Converse: If q then p (q→p)

Inverse: If not p then not q (-p → -q)

Contrapositive: If not q then not p (-q → -p)

For the given implications, its converse, inverse, and contrapositive can be written as.

Given statement:

(a)  If a quadrilateral is a parallelogram, then its opposite sides are congruent then its converse, inverse, and contrapositive are:

Converse: If a quadrilateral has opposite sides that are congruent then it's a parallelogram.

Inverse:  If a quadrilateral is not a parallelogram then its opposite sides are not congruent.

Contrapositive: If a quadrilateral has opposite sides that are not congruent then it's not a parallelogram.

(b) If two lines do not intersect, then they are parallel:

Converse: If the two lines do not intersect in the same plane, then they are parallel.

Contrapositive: If the two lines intersect in the same plane, then they are not parallel.

(c) If the sky does not look blue, then it is not nighttime:

Converse: If it is not nighttime, then the sky looks blue.

Inverse:  If the sky does not look blue then it is nighttime.

Contrapositive:  If it is nighttime then the sky does not look blue.

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Answer: The relationship between points R , S , and T is that the sum of the RS and RT will be equal to  RT that is RT=RS+ST

Step-by-step explanation:

An auditor selects a sample of shipping documents to examine whether invoices were created for this sample. The fundamental objective of the audit, Completeness, will be satisfied by this test.

Given,

An auditor picks a sample of shipping papers to examine if the related sales invoices were produced.

We need to determine what kind of audit aim will be the focus of this test's evidence gathering;

Audit purpose;

An audit's objective is to form an unbiased evaluation of the entity's financial statements. It is a component of the opinion if the financial statements give a true and fair picture and have been accurately prepared in accordance with accounting rules.

Here,

The audit objective completion test was carried out by the auditor to acquire proof.

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The question is incomplete. Completed question is given below;

An auditor selects a sample of shipping documents in order to determine if the related sales invoices were prepared. This test would gather evidence concerning which audit objective?

A) Completeness

B) Detail tie-in

C) Occurrence

D) Realizable value

The area of rectangular region r is = 12.

Given:

each diagonal of r has length 5. the perimeter of r is 14.

Let l and b be the length and breadth of a rectangle.

we know that

perimeter of rectangle = 2 ( l + b )

2 ( l + b ) = 14

divide by 2 on both sides

( l + b ) = 14/2

l + b = 7

l = 7 - b

l^2 + b^2 = d^2

( 7 - b )^2 + b^2 = 5^2

7^2 + b^2 - 2 * 7 * b  + b^2 = 25

49 + 2b^2 - 14b = 25

2b^2 - 14b + 24 = 0

on solving b = 4,3

Take any one value

b = 4

l = 7 - 4

l = 3

Area of rectangle = l * b

= 4 * 3

= 12

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Answer: from generation 19 to 20.

Step-by-step explanation:

The greatest percentage increase will occur  from generation 19 to 20 as the exponential power will be highest.

What is exponential growth?

Exponential growth happens once the larger in size you're the quicker you grow that causes you to even larger in size. it's the expansion characterised by interest, or growth. it's known as exponential growth as a result of it will solely be delineate mathematically by inserting time within the exponent or power of the bottom. Population then is adequate to the population at the current times some discretional range to the facility of the expansion rate times the time. The discretional range is sometimes two then the expansion rates is given because the reciprocal of the doubling time.

Main body:

initial population = 25

Total generation = 20

growth rate = 0.2

General formula of exponential function = aˣ

here a = 25 and x = 0.2

⇒25⁰°²

= 1.9

hence total population = 25+2 = 27

So it is clear that in 19 to 20 generation , growth will be highest.

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An equation with variables on both sides that equal 19 is x - 2 = 17.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

Based on the information, the equation will be:

x - 2 = 17

Collect like terms

x = 17 + 2

x = 19

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The statement of the given hypothesis condition is False.

What is hypothesis testing?

A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.

Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.

i.e. [tex]\mu_{1} > \mu_{2}[/tex]

">" sign implies that right-tailed test i.e. one-tailed right-sided.

Hence, the given statement is FALSE.

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Ms. Cole have the 8 pieces of string.

Given,

In the question:

A number line going from 0 to 4. numbers 0, 1, 2, 3, and 4 are marked on the line. marks divide the spaces between each number into 2 equal parts. Ms. Cole has 4 yards of string. she cuts the string into pieces that are each 1 2 yard long.

To find the how many pieces of string does Ms. Cole have?

Now, According to the question:

Total yards of string = 4

Length in yard of each string = 1/2 yards

Number of pieces of string Ms. Cole has :

Total. Yards of string / length in yard of each string

=> 4 / (1/2)

=> 4 * (2 /1)

=> 8/1

=> 8 pieces of string.

Hence, Ms. Cole have the 8 pieces of string.

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The sample size should be 1843 at 99% confidence level with margin of error of 3%.

What is Inferential statistics?

By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.

Given, Margin of error (m) = 0.03

           z (at 99% confidence level)=2.576

We know that, Sample size(n) = (z/m)^2 p (1-p)

In order to find the sample size, we must know the value of proportion.

here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.

Now, we've p = 0.5

∴ Sample size = (z/m)^2 p (1-p)

                        = (2.576/0.03)^2 × 0.5 × (1-0.5)

                        = 1843 (approx).

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If 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

In the given question, if 17% of men are bald, then we have to find the probability that at most 140 in a random sample of 900 men are bald.

As given that; 17% of men are bald.

So,p=0.17

Let X=Number of men that are bald

Sample size, n=900

Here X follows binomial distribution with parameters n= 900 and p =0.17

Since np≥5 and n(1-p)≥5, We can use normal approximation to the binomial with continuity correction.

So,Binomial can be approximated to normal with;

mean, μ=np

μ = 900*0.17

μ = 153

Standard deviation, σ = √np(1-p)

σ = √900*0.17*(1-0.17)

σ = √153*0.83

σ = √126.99

σ = 11.269

So, X→Normal (μ = 153, σ = 11.269)

Then, X= (X-μ)/σ

X=(X-153)/11.269

We need to find the probability that at most 140 in a random sample of 900 men are bald i.e. we need to find P(X≤140)

P(X≤140) =P(X<140+0.5)  [using continuity correction factor]

P(X≤140) =P(X<140.5)

P(X≤140) =P(z<(X-153)/11.269)

P(X≤140) =P(z<(140.5-153)/11.269)

P(X≤140) =P(Z<-1.11)  [z score rounded to 2 decimal places]

P(X≤140)  =0.1335

Hence, if 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

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We can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

What is the null hypothesis?

The null hypothesis is a common statistical theory that asserts that no statistical relationship or significance exists between two sets of observed data and measured phenomena based on a single observed variable.

Hypothesis:

[tex]H_0:\rho_1=0\\H_1:\rho\neq0[/tex]

Test statistic:

[tex]t=r\times\sqrt{\frac{n-2}{1-r^2} }\\\\ t=(0.8691)\times\sqrt{\frac{30-2}{(1-0.8691)^2} } \\\\t=9.2974[/tex]

D.F. = n - 2 = 28

P-value = P-value at t = 9.2974, ∝=0.05, 28 d.f. is

        P-value = 0.000

Conclusion: Since. P-value < ∝=0.05, so we have to reject the null hypothesis.

Hence, we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.

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Answer:

Step-by-step explanation:

1st angle = (2x+6)° = (56 + 6)°= 62°. 2nd angle = x = 28°. Thus, 62° and 28° are the required angles. Answer.

Answer:

Yes

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

for 2 days it's 98

then 300-90=202

202÷0.40=505

By using the concept of reflection and scaling, it can be calculated that

New equation of parabola is [tex]y = -5x^2[/tex]

What is reflection and scaling?

Reflection is a mathematical transformation in which a mirror image of an object can be obtained without changing the shape and size of an object.

To draw an object of size proportional to the size of the original object, scaling is used

The equation of the parabola is [tex]y = x^2[/tex]

If it is reflected across x axis, its equation is [tex]y = -x^2[/tex]

Now  y  = -[tex]x^2[/tex] is scaled vertically by a factor of 5

New equation of parabola

[tex]y = -5x^2[/tex]

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Answer:

6 hours

Step-by-step explanation:

dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?

60h + 50 > 400

subtract 50 from both sides:

60h > 350

divide both sides by 60:

h > 5.8333

rounded: 6 hours

Answer: 5.76 x 10 to the 5th