The value of a correct to 10 decimal places is 3.1415926536
a) Write the value of correct to 5 decimal places.
b) Which value below is nearest to the value of ?
22
355
7
113
A
C
135
43
B
62
35
O

Answer:

No Solution

Step-by-step explanation:

-1 is not equal to -5/3

Answer:

if you have about an 85 now than you shouldn’t go below a b

Step-by-step explanation:

Yes there is sufficient evidence that  the alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

Null hypothesis; H_o ; μ = 402

Alternative hypothesis; H_o ; μ ≠ 402

The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.

Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.

Now, the question we have is a two tailed test. Thus;

The null hypothesis is;

bag filling machine works correctly at the 402 gram setting which is;

H_o ; μ = 402

The alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

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Answer:

n > 3

Step-by-step explanation:

2n - 5 > 1

Add 5 on both sides

2n > 6

Divide by two on both sides to isolate n

n > 3

It takes 51.33 min or 6/7 hrs to travel upstream 4 km.

What is relative velocity?

it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.

speed of boat = 7 km/hr

speed of river = r km/hr

speed upstream = 7-r km/hr

speed downstream = 7+r km/hr

time taken to go upstream 4 km = 4/(7-r)

time taken to go downstream 8 km = 8/(7+r)

as time taken is equal in both scenario:

4/(7-r) = 8/(7+r)

on solving we get:

r = 7/3 km/hr

put this value in time taken for upstream

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

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Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Think about two trains that are traveling in the same direction and at the same pace.

Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.

The other train seems to be moving at a constant speed.

So, we know that:

Speed of boat = 7 km/hr

Speed of river = r km/hr

Now,

Speed upstream = 7-r km/hr

Speed downstream = 7+r km/hr

Time taken to go upstream 4 km = 4/(7-r)

Time taken to go downstream 8 km = 8/(7+r)

As the time taken is equal in both scenarios:

4/(7-r) = 8/(7+r)

On solving we get:

r = 7/3 km/hr

Put this value in time taken for upstream as follows:

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

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The equivalent expression to the given expression is, 7 to the fourth power.

What is equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Because both expressions have the same value for any value of x, 3(x + 2) and 3x + 6 are identical expressions. 3x + 6 = 3 × 4 + 6 = 18.

Consider, the given expression

7 · 7 · 7 · 7

By using:

If a = b · b · b

Here there is multiplication of b 3 times.

So, [tex]a = b^3[/tex]

In the given expression 7 is occur 4 times,

Hence it becomes, [tex]7^4[/tex].

That is  7 to the fourth power.

Therefore, the equivalent expression to the given expression is, 7 to the fourth power.

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The value of n in the sequence is ≅ 15

We should know that Arithmetic progression is a type of sequence in which the consecutive terms are gotten by the addition or subtraction of a constant term known as the common difference.

The given parameters are>

a+6d--13 ........................................  (1)

a+8d=47............................................ (2)

Subtracting equation 1 from [a+8d=47]-[a+8d=-13

⇒ 2d=60

d=30

Put d=30 in equation 1

a+6(30)=-13

a+180=-13

Collecting like terms

a=-13-180

a=-193

The nth term of an AP is given by

nth term = a+(n-1)d

where nth = 217

⇒ 217=-193+(n-1)30

Simplifying the expressing

217+223=30n

440/3=30n/30

n=14.7

Therefore n≅15

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By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,

Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.

So,  |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,

This is true for infinite many [tex]n_k[/tex]

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

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Answer:

Step-by-step explanation:

y = 2x - 1  

when you sub in 0 in x and -1 in y, the y-intercept is -1.

Answer:

tan R = [tex]\frac{45}{28}[/tex]; tan S =[tex]\frac{28}{45}[/tex]

Step-by-step explanation:

The tangent proportion is [tex]\frac{opposite}{adjacent}[/tex].

When R is the reference angle TS (45) is the opposite side and TR is the adjacent side (28).

When S is the reference angle, TR is the opposite side (28) and TS is the adjacent side (45).

There are total of 7 terms in the formula of intersection of 3 sets.

The formula of the given sets is,
n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).

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The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s

Angular velocity is the number of revolution per second of an object.

Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.

The angular velocity is given by ω = 2π/T where T = period of revolution

Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s

So, substituting the period into the equation for the angular velocity, we have

ω = 2π/T

ω = 2π/61200 s

ω = π/30600 s

ω = 0.0001026 rad/s

ω = 1.026 × 10⁻⁴ rad/s

So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s

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The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.

The given statement is H(R) = 4H.

Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R

Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.

Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

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The slope of the line given the information in the table is 1.

The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.

Slope = change in the value of y / change in the value of x

Slope = (0 - - 1) / (1 - 0) = 1

Slope =  (1 - 0) / (2 - 1) = 1

Slope = (2 -1 ) / (3 - 2) = 1

Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.

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Answer:

Step-by-step explanation:

look at the x and axis and the irrational fractions and you should find your slope

The time it will take both the boat and whale to meet is 18minutes(nearest minutes)

Displacement is defined as the change in position of an object in a specified direction. It is measured in meters and it's a vector quantity.

Since velocity = displacement/time

displacement = velocity ×time

The total space between the boat and the whale is 5miles.

Using addition of vectors

5= v2t - v1t

5= 46t - 30t

5 = 16t

t= 5/16 = 0.3hrs

to minutes, = 0.3 ×60 = 18minutes(nearest minutes)

Therefore it will take the boat and the whale 18minutes to meet.

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[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]

Answer:

(2) -18.825

Step-by-step explanation:

follow the law of BODMAS

First open the brackets to get;

5/16 - 5/6x = 16

Then collect liie terms;

5/6x = 5/16 - 16

5/6x = -251/16

x = -18.825

The correct option regarding the heights of the trees include:

The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:

(12 - 5) > (12 - 7)

7 > 5

The mean of tree heights at Yard Works is 8 feet.

The mean of tree height at The Grow Station is 9 feet.

The mean absolute deviation of the tree heights at both yards is 2.

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answer:18

Step-by-step explanation:

From the figure, we can see that ABC and A'B'C are similar triangles.

Because Segment A'B' is parallel to segment AB.

then angleA'B'C=ABC  CA'B'=CAB  A'CB'=ACB

A'B':AB=8:20         rate=0.4

A'C:AC=12:?

12/0.4=AC=30

AC-A’C=30-12=18

The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3

Index form of a number can simply be described as that number written in the form of an exponential expression.

The number can also be written as a single number which is raised to another number.

Some rules of indices to note;

Given that;

(8^(5))/(8^(-9))

Then, we have;

8^5-(-9)

8^5+9

Add the powers

8^14

Hence, the value is 8^14

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The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Rectangular coordinates of a point is written like (x, y, z)

Cylindrical coordinates of a point  is written like (r, θ, z)

Spherical coordinates of a point is written like (p, θ, φ)

First talk about Rectangular vs Cylindrical.

x = rcosθ

y = rsinθ.

z = z

x^2 + y^2  = r^2

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

r^2 = 4+4 = 8.

r = [tex]\sqrt{8}[/tex]

r = 2[tex]\sqrt{2}[/tex]

θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .

z = -1.

So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).

Now let's us talk about Rectangular vs Spherical Coordinates.

x =  pcosθsinφ.

y= psinθsinφ.

z = pcosφ.

p^2 =  x^2+y^2+z^2.

tanθ = y/x

cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3

θ = [tex]tan -1[/tex](y/x) =  0.78rad .

φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad

So Spherical coordinates is (3, 0.78rad, 1.91rad).

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Given Question is incomplete, Complete Question here

The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,

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Answer:

1/2

Step-by-step explanation:

-1(15+4-27)/16

Add 15 and 4 to get 19.

Now you have -1(19-27)/16

Subtract 27 from 19 to get −8.

-1(-8)/16

Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.

-(-1/2)

Simplify

1/2

Answer:

1/2

Step-by-step explanation:

⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆

Calculate:

-(15 + 4 - 27) / 16

-(19-27)/16

-(-8) / 16

= 8/16

Simplify:

= 1/2

Answer:

-y-d

Step-by-step explanation:

7y+2d-3d-8y

7y-d-8y

-y-d

just combine like terms :)

The missing value if the point is a direct variation is -15

From the question, we have the following ordered pairs

(2, -6) and (5, y)

These ordered pairs are direct variation

A direct variation is represented as

k = y/x

This means that

y/5 = -6/2

Evaluate the quotient

y/5 = -3

Multiply both sides by 5

y = -15

Hence, the value of y is -15

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For private colleges:

The sample mean for a private college is 42.70 and the sample standard deviation is = 6.72.

For public colleges:

The sample mean for a private college is 22.30 and the sample standard deviation is = 4.53.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

For Private:

sample mean=42.70

sample standard deviation =6.72

For Public:

sample mean=22.30

sample standard deviation =4.53

Hence,

For private colleges:

The sample mean for a private college is 42.70 and the sample standard deviation is = 6.72.

For public colleges:

The sample mean for a private college is 22.30 and the sample standard deviation is = 4.53.

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Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

Answer:

Figure b

Step-by-step explanation:

the sides are equal

Answer:

A. (18, 1)

Step-by-step explanation: