(1)(a) Use the generalized binomial expansion to expand (1 + x)ā up to the x® and hence
determine (1.05). to 5 decimal places
10 marks​

Hey there! :)

Answer:

10 miles.

Step-by-step explanation:

To solve for the diagonal side, we can simply visualize the sides of the rectangle as sides of a right triangle with the diagonal being the hypotenuse.

We can use the Pythagorean Theorem (a² + b² = c²), where:

a = length of short leg

b = length of long leg

c = length of the diagonal

Solve:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

c = 10 miles. This is the length of the pedestrian route.

Answer:

Solution,

Hypotenuse (h) = R

Perpendicular (p) = 8 miles

Base (b) = 6 miles

Now,

Using Pythagoras theorem:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

Plugging the values:

[tex] {r}^{2} = {(8)}^{2} + {(6)}^{2} [/tex]

Calculate:

[tex] {r}^{2} = 64 + 36[/tex]

[tex] {r}^{2} = 100[/tex]

[tex]r = \sqrt{100} [/tex]

[tex]r = 10 \: miles[/tex]

Length of route = 10 miles

Hope this helps...

Good luck on your assignment...

Answer:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Step-by-step explanation:

Information given

n=100 represent the random sample taken

[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car

[tex]p_o=0.31[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:  

Null hypothesis:[tex]p=0.31[/tex]  

Alternative hypothesis:[tex]p \neq 0.31[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And replacing we got:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Answer:

4 = 4

Step-by-step explanation:

=> 2x = 4

Putting x = 2

=> 2(2) = 4

=> 4 = 4

Answer:

Solution,

X= 2

Now,

2x=4

plugging the value of X,

2*2= 4

4 = 4 ( hence it is true)

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Answer:  see below

Step-by-step explanation:

Inverse is when you swap the x's and y's.

The Slope-Intercept form is [tex]y=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]    which isn't convenient to graph.

So take the points from the original equation (-1, -2) & (0, 3) and switch the x's and y's to get the points (-2, -1) & (3, 0).

Draw a line through points (-2, -1) and (3, 0) to sketch the graph of the inverse.

Answer:

Step-by-step explanation:

According to the central limit theorem, if independent random samples of size n are repeatedly taken from any population and n is large, the distribution of the sample means will approach a normal distribution. The size of n should be greater than or equal to 30. Given n = 100 for both scenarios, we would apply the formula,

z = (x - µ)/(σ/√n)

a) x is a random variable representing the salaries of accounting graduates. We want to determine P( x > 52000)

From the information given

µ = 50402

σ = 6000

z = (52000 - 50402)/(6000/√100) = 2.66

Looking at the normal distribution table, the probability corresponding to the z score is 0.9961

b) x is a random variable representing the salaries of finance graduates. We want to determine P(x > 52000)

From the information given

µ = 49703

σ = 10000

z = (52000 - 49703)/(10000/√100) = 2.3

Looking at the normal distribution table, the probability corresponding to the z score is 0.9893

c) The probabilities of either jobs paying that amount is high and very close.

Answer:

a. ans=1

b. ans=2/5

c. ans=4

hope u understood...

Answer:

the answer is C.

Step-by-step explanation:

64 ÷ 8 = 8

Answer:

c- 8cm squared

Step-by-step explanation:

plato

Answer:

7x+7 is obviously divisible by 7.

put in any value high enough and you can find the two three digit numbers.

Step-by-step explanation:

Two three-digit numbers divisible by 7 are 98 and 105.

Two three-digit numbers divisible by 7 are 98 and 105.To create an expression that is divisible by 7, we can use the property that the difference between two numbers is divisible by 7 if the numbers themselves are divisible by 7.

Let's represent a three-digit number divisible by 7 as "7k" where k is an integer. To find two three-digit numbers divisible by 7, we can use the following expression:

7k - 7

For example, if we substitute k = 15, we get:

7(15) - 7 = 105 - 7 = 98

So, the first three-digit number divisible by 7 is 98.

Similarly, for the second three-digit number, let's substitute k = 16:

7(16) - 7 = 112 - 7 = 105

Therefore, the two three-digit numbers divisible by 7 are 98 and 105.

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Question:

A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders.

What is the number of seats occupied by concessionary ticket holders?.

Answer:

60 seats

Step-by-step explanation:

Given

Number of seats = 270

Occupied Seats = 5/9

Concessionary ticket holders = 40% of occupied Seats

Required

The number of seats occupied by concessionary ticket holders

First the number of occupied seat has to be calculated.

[tex]Occupied\ Seats = \frac{5}{9} * 270[/tex]

[tex]Occupied\ Seats = \frac{1350}{9}[/tex]

[tex]Occupied\ Seats = 150[/tex]

Next is to determine the number of seats occupied by concessionary ticket holders.

[tex]Number = 40\%\ of\ occupied\ seats[/tex]

[tex]Number = 40\%\ of\ 150[/tex]

Convert percentage to decimal

[tex]Number = 0.4 * 150[/tex]

[tex]Number = 60[/tex]

Hence, 60 seats were occupied by concessionary ticket holders.

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Answer:

The answer is given below

Step-by-step explanation:

a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.

u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4

u + v < u - v.

b) Let x be a real number and x² be the square of the real number

x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

The statement is true for x is between 0 and ±1

E.g. for x = 1/2, x² = (1/2)² = 1/4

1/4 < 1/2

c) Let n represent all positive integers. n² is the square of n.

n²≥n means that the square of n is greater or equal to n.

We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself

The statement is true.

1² ≥ 1, 2² ≥ 2 e.t.c

d)  Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b

|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.

We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

Evaluating the expressions given using appropriate illustrations, all the statements are True.

Statement 1 :

Real numbers ar both rational and irrational values and hence can be tweaked using arithmetic operators such as addition. Hence, the Statement is True

Statement 2 :

Real numbers can be expressed or raised to the power of another number such as being squared.

Statement 3 :

The squared Value of all positive integers is always greater than or equal the value.

Statement 4 :

The absolute value of a sum is always less than or equal to the sum of the absolute values two numbers

a = 3 ; b = - 4

|a + b | = |3-4| ≤ |-3|+|4|

|-1| ≤ 3 + 4

-1 ≤ 7

Therefore, all the statements are true.

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Answer:

The answer is "As the number of files increases, the storage space used decreases."

Step-by-step explanation:

When the music files are put into storage they take up space, this causes the storage space to decrease.

Answer:

As the number of files increases, the storage space used increases.

Answer:

The correct answer to the following question will be "60 students".

Step-by-step explanation:

Marta will be taking a sampling frame from some kind of 600 student group.

Mean,

N = 60  

Although the sampling method could perhaps consist of the following components 10% of the population,

⇒  [tex]600\times 10 \ percent[/tex]

⇒  [tex]60[/tex]

In order to view these findings as autonomous, 60 students would then have to analyze Marta lacking replacements.

Marta have to sample 60 students without replacement to treat the observations as independent.  

Given,

Marta is going to take a sample from a population of 600 students.

We have to find the no. of students Marta have to sample without replacement.

The 10% condition states that sample sizes should be no more than 10% of the population. Normally, Bernoulli trials are independent, but it's okay to violate that rule as long as the sample size is less than 10% of the population.

So,

[tex]N=10\% \ of \ 600[/tex]

[tex]N=\frac{10}{100} \times600[/tex]

[tex]N=60[/tex]

Hence, Marta have to sample 60 students without replacement to treat the observations as independent.

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Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

7x-1

Step-by-step explanation:

The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

If f(x) = 5x – 2 and g(x) = 2x + 1,

now, we have to find (f+g)(x).

so, we have,

f(x) = 5x – 2

and g(x) = 2x + 1

now,

(f+g)(x)

=f(x)+g(x)

=5x-2+(2x+1)

=5x-2+2x+1

=7x-1

Hence, The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

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Answer: 132

Step-by-step explanation: To solve this equation we know that x is greater than 81 unless the equation would not make sense. 81 + 51 = 132

Answer: x=132

Step-by-step explanation: Add 51 to 81, as positive 51 is the inverse of -51. You need to get the x alone. Therefore, 51+81=132 and x=132.

Answer:

The x-values of the inflection points of the curve are x = -52 and x = 52.

Step-by-step explanation:

Suppose we have a normal curve with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]

The x-values of the inflection points of the curve are [tex]x = \mu - \sigma[/tex] and [tex]x = \mu + \sigma[/tex]

x ~ N(0, 52)

This means that [tex]\mu = 0, \sigma = 52[/tex]

So

[tex]x = 0 - 52 = -52[/tex]

[tex]x = 0 + 52 = 52[/tex]

The x-values of the inflection points of the curve are x = -52 and x = 52.

Answer:

  Always true

Step-by-step explanation:

If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.

If π is irrational, 2π is also irrational.

It is always true that the product of a rational and an irrational number is irrational.

Answer:

all ways true

Step-by-step explanation:

Answer:

30 dimes and 20 quarters

30×.10=$3.00

20×.25=$5.00

30+20=50

$3+$5=$8

Answer:

0.41

Step-by-step explanation:

Given;

5.6, 5.2, 4.6, 4.9, 5.7, 6.4

To calculate the variance of a given set of ungrouped data, follow the following steps;

(i). First calculate the mean (average) of the data as follows;

[tex]\frac{5.6 +5.2 +4.6+ 4.9 +5.7 +6.4}{6}[/tex] = [tex]\frac{32.4}{6}[/tex] = 5.4

(ii) Secondly, find the deviation of each point data from the mean as follows;

5.6 - 5.4 = 0.2

5.2 - 5.4 = -0.2

4.6 - 5.4 = -0.8

4.9 - 5.4 = -0.5

5.7 - 5.4 = 0.3

6.4 - 5.4 = 1.0

(iii) Thirdly, find the square of each of the results in step ii.

(0.2)² = 0.04

(-0.2)² = 0.04

(-0.8)² = 0.64

(-0.5)² = 0.25

(0.3)² = 0.09

(1.0)² = 1.0

(iv) Fourthly, find the sum of the results in step iii.

0.04 + 0.04 + 0.64 + 0.25 + 0.09 + 1.0 = 2.06

(v) The variance, v, is now the quotient of the result in step (iv) and n-1. i.e

v = [tex]\frac{2.06}{n-1}[/tex]

Where;

n = number of data in the set

n = 6 in this case

Therefore,

v = [tex]\frac{2.06}{6-1}[/tex]

v = [tex]\frac{2.06}{5}[/tex]

v = 0.412

Therefore, the variance is 0.41 to the nearest hundredth

Answer:

.34

Step-by-step explanation:

god this is so boring

Answer:

4.7

Step-by-step explanation:

Given :

initial mean length =4.1  minutes.

Final mean length =5.3 minutes

The mid point of the given interval can be determined by the

[tex]Midpoint \ = \frac{Initial\ Mean\ length\ +Final\ Mean\ length }{2} \\Midpoint \ = \frac{4.1\ +\ 5.3\ }{2} \\Midpoint \ = \frac{9.4 }{2} \\Midpoint \ =4.7\\[/tex]

Therefore 4.7 is the midpoint

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

Answer:

245 might be the answer

Step-by-step explanation:

(7*7*10)/2

Answer:

Step-by-step explanation:

As you show, the weight differences are different for the same week differences, so the table is not linear. A graph (attached) can also show you the table is not linear.

__

The highest rate of weight loss shown in the table is 7 lbs in 3 weeks, or 4 2/3 pounds in 2 weeks. The lowest rate of weight loss shown in the table is 5 lbs in 3 weeks, or 3 1/3 pounds in 2 weeks. Based on the rates shown in the table, we might expect the starting weight to be between 3 1/3 and 4 2/3 pounds more than the first table value:

  Week 0 weight: between 184 1/3 and 185 2/3 lbs, estimated.

_____

A "line of best fit" for the data has a y-intercept of about 185 pounds, which is the midpoint between our two estimates above.

Behold the quotient of F and the product of r,s, and T:  F / (r·s·T)

The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).

The number which is being divided is the dividend.

The number with which we are dividing is the divisor.

The result when a dividend is divided by the divisor is the quotient.

A remainder is the extra portion of a number when it isn't completely divisible.

Given, Are some variables F, r, s, and t.

Now, The product of r,s, and T is,

= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,

F/(r×s×T).

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Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

[tex]z = \frac{X - \mu}{s}[/tex]

In which:

X is the measured value.

[tex]\mu[/tex] is the expected value.

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex] is the standard deviation of the sample. [tex]\sigma[/tex] is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that [tex]\mu = 2.9, \sigma = 0.1[/tex]

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so [tex]X = 3[/tex]

[tex]s = \frac{0.1}{\sqrt{100}} = 0.01[/tex]

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{3 - 2.9}{0.01}[/tex]

[tex]z = 10[/tex]

Answer:

-10

Step-by-step explanation:

If we first note the denominator of fraction numerator sigma over denominator square root of n end fraction equals fraction numerator 0.1 over denominator square root of 100 end fraction equals fraction numerator begin display style 0.1 end style over denominator 10 end fraction equals 0.01

Then, getting the z-score we can note it is z equals fraction numerator x with bar on top minus mu over denominator begin display style 0.01 end style end fraction equals fraction numerator 2.9 minus 3 over denominator 0.01 end fraction equals negative 10

This tells us that 2.9 is 10 standard deviations below the value of 3, which is extremely far away.

Answer:

( x, y ) = ( -20, 20 )

Step-by-step explanation:

Given data

Y = y(x)

3x + 2y = 20 ---------- equation 1

2x + 3y = 20 ---------- equation 2

find (x, y )

solving equation 1 and equation 2

3x + 2y = 20 * 2 = 6x + 2y = 40 --------- EQUATION 3

2x + 3y = 20 * 3 =  6x + 3y = 60 --------- EQUATION 4

cancelling out ( x )

Add both equation 3 and equation 4

5y = 100.  hence  y = 100/5 = 20

back to equation equation 2

2x + 3(20) = 20

2x = - 40

x = -20

attached is the graph  to check the answer