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Using the z-distribution, the z-statistic would be given as follows:

c) z = -2.63.

At the null hypothesis we test if the means are equal, hence:

[tex]H_0: \mu_D - \mu_C = 0[/tex]

At the alternative hypothesis, it is tested if they are different, hence:

[tex]H_1: \mu_D - \mu_C \neq 0[/tex]

For each sample, they are given as follows:

Hence, for the distribution of differences, they are given by:

The test statistic is given by:

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

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Hence:

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

[tex]z = \frac{-2 - 0}{0.76}[/tex]

z = -2.63.

Hence option B is correct.

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Farmer will made 14 basket each of 5 apple and 7 peaches.

what is greatest common factor?

Greatest common factor (GCF) is largest common factor in the given number.

first find common factor of numbers 70 and 98

70 = 2*5*7

98 = 2*7*7

the common factor are 2 and 7

the greatest common factor is 2*7=14

70 apples = 14*5

98 peaches = 14*7

farmer will made 14 basket each of 5 apple and 7 peaches.

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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.

Given:

Find:

Solution:

So, for solving this kind of question first we have to find the greatest common factor, we get;

70 = 2*5*7

98 = 2*7*7

the common factor are 2 and 7

the greatest common factor is 2*7=14

70 apples = 14*5

98 peaches = 14*7

So, the farmer will make 14 baskets each of 5 apples and 7 peaches.

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If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually. This can be obtained by using formulas for simple interest and compound interest.

A = P(1 +Rt/100) , P = principle amount ,R = rate of interest, t = time(in years)

A = P(1 + R/100)^t , P = principal amount, R = rate of interest,                                t = time(in years)

Given that,  

P = $11,000 , R = 8%,  t = 25 years

A = P(1 +Rt/100) = [tex]11000(1+\frac{(8)(25)}{100} )[/tex] = $33,000

A = P(1 + R/100)^t = [tex]11000(1+\frac{8}{100} )^{25}[/tex] = [tex]11000(1.08 )^{25}[/tex] = $75,333.23

Hence If $11,000 is invested, $33,000 is the value of the investment at the end of 25 years if the interest is 8% simple interest and $75,333.23 is the value of the investment at the end of 25 years if the interest is 8% compounded annually.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: If $11,000 is invested in an account for 25 years. Find the value of the investment at the end of 25 years if the interest is:

(a) 8% simple interest

(b) 8% compounded annually

Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top

The function of the height where the man falls is a quadratic function, and the equation of the function is given as:

d = t^2 * 0.25

The height of the building is 500

This means that the value of d is 500.

So, we have;

d = 500

Substitute 500 for d in the equation d = t^2 * 0.25

500 = t^2 * 0.25

Divide both sides of the above equation by 0.25

500/0.25 = t^2 * 0.25/0.25

Evaluate the quotient in the above equation

t^2 = 2000

Take the square root of both sides in the above equation

√t^2 = √2000

Evaluate the exponent

t = 44.7

Hence, it takes the man 44.7 seconds to fall

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A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.

A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.

Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:

x + 4 ≥ 9

x ≥ 9 - 4

x ≥ 5.

This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.

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Answer:

x = 3, -5

Step-by-step explanation:

I just know

Answer:

x= -5

x=3

Step-by-step explanation:

You are factoring here. The standard form of an equation is Ax² + Bx + C.

The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.

C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.

Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:

x+5=0

x = -5

x-3 = 0

x=3

Answer: [tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

Step-by-step explanation:

By inspection, we know the equation of the parabola is [tex]y=x^2 +4[/tex] and the equation of the line is [tex]y=-x+4[/tex].

Since there is an open hole at x=3 for the parabola and a closed hole at x=3 for the line, the function is

[tex]f(x)=\begin{cases} x^2 +4, x < 3 \\ -x+4, x \geq 3 \end{cases}[/tex]

Answer: The function is odd because f(–x) = –f(x).

Step-by-step explanation:

[tex]f(x)=6x^7\\\\f(-x)=6(-x)^7 = -6x^7\\\\\therefore f(x)=-f(-x)[/tex]

The function is odd because f(–x) = –f(x).

The function is given as:

f(x) = 6x^7

A function is odd if the following is true

f(-x) = -f(x)

Calculate f(-x)

f(-x) = 6(-x)^7

f(-x) = -6x^7

Calculate -f(x)

-f(x) = -6x^7

By comparison;

f(-x) = -f(x) = -6x^7

Hence, the function is odd because f(–x) = –f(x).

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Answer: (-2,2)

Step-by-step explanation:

The solution to a system of equations represented graphically is the point where the graphs intersect.

The value of the expression for the given values of the variables is 1/9

From the question, we are to determine the value of the expression for the given values of the variables

The given expression is

[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]

From the given information,

x = 2

y = -5

z = 3

Putting the values of the variables into the expression

[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]

[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]

[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]

[tex](\frac{-12 }{36 }) ^{2}[/tex]

[tex](\frac{-1 }{3 }) ^{2}[/tex]

[tex]= \frac{1}{9}[/tex]

Hence, the value of the expression for the given values of the variables is 1/9

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The probability that Luke will pick a blue ball is 3/8.

We have,

To find the probability of Luke picking a blue ball, we need to determine the total number of balls in the container and the number of blue balls.

Total number of balls

= 4 (yellow balls) + 3 (blue balls) + 1 (red ball)

= 8 balls

Number of blue balls = 3

Now, the probability (P) of picking a blue ball is given by:

P = Number of favorable outcomes (picking a blue ball) / Total number of possible outcomes

P = 3 (number of blue balls) / 8 (total number of balls)

Now, we can simplify the fraction to its lowest terms:

P = 3/8

Thus,

The probability that Luke will pick a blue ball is 3/8.

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The non response bias can happen  if the chosen sample is too small for a study.

This is the term that is used to refer to the type of bias that happens in a research study because the some of the study participants could not participate in the study.

This type of bias is a very serious matter of concern while carrying out research.

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The exact distance and direction that Patrick is from Johnny is; 177.81 ft and 215.52°

Let the distance of Johnny to Patrick be x.

The angle opposite x would be; (90 - 50) + 90 + 30 = 160°

We will therefore use the cosine rule to find x;

X² = A² + B² - 2ABcosx

Where;

A and B are the distance of Johnny to Rob and Rob to Patrick respectively. Thus;

X² = 130² + 50² - 2(130)(50)cos160

X²= 16900 + 2500 + 12216.004

X² = 31616.004

X = 177.81 ft

To get the direction "y" we will use sine rule;

50/siny = 177.809/sin160

50/siny = 177.809/0.342

50/siny = 519.9094

Siny = 50/519.904

Siny = 0.09617

y = sin⁻¹(0.09617)

y = 5.52°

The bearing of Patrick from Johnny is;

5.52 + 30 + 180 = 215.52°

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See the graph in the attached image.

Step-by-step explanation:

OK, let's assume it this way:

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+

Sn=1.1!+2.2!+3.3!+...+n.n!=(2‐1).1!+(3-1).2!+(4-1)3!+...+((n+1)-1).n!=(2.1!-1!)+(3.2!-2!)+(4.3!-3!)+...+((n-1)n!-n!)=(2!-1!)+(3!-2!)+(4!-3!)+...+(n+1)!-n!=(n+1)!-1!=(n+1)!-1

and boom problem solved

Answer:

243/506

Step-by-step explanation:

There are 24 total juice boxes.

18 of them are not grape

You have an 18/24 chance of picking not grape juice

The second time, 1 is removed, then another is removed. This creates:

(18/24)*(18/23)*(18/22) = 243/506

The point of intersection for the pair of linear equations is (-5.5, -4.8)

Linear equations are equations that have constant average rates of change, slope or gradient

The pair of linear equations is given as:

x + y = 0.7

y = 3x + 11.7

Substitute y = 3x + 11.7 in x + y = 0.7

x + 3x + 11.7 = 0.7

Evaluate the like terms

2x = -11

Divide both sides by 2

x = -5.5

Substitute x = -5.5 in y = 3x + 11.7

y = 3*-5.5 + 11.7

Evaluate

y = -4.8

So, we have

x = -5.5 and y = -4.8

Express the above points as an ordered pair, to determine the point of intersection

(x, y) = (-5.5, -4.8)

Hence, the point of intersection for the pair of linear equations is (-5.5, -4.8)

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Considering the probability of success of 0.8 in the Bernoulli trial, the probability of failure is of 0.2.

The probability of failure in a Bernoulli trial is one subtracted by the probability of a success.

In this problem, the probability of a success is of 0.8, hence the probability of failure is:

pF = 1 - 0.8 = 0.2.

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Answer:

x=3,y=1

Step-by-step explanation:

2^x+y=16,3^x-y=9

16=2^4,9=3^2

x+y=4,x-y=2 add both

2x=6,x=3

3-y=2,y=1

Answer:

y = (-3/4)x + 2

Step-by-step explanation:

y = m * x + b   where m is the slope and b is the y-intercept

y = (-3/4)x + b       substituting the slope

4 = 6 + b     =>         b = 2        substituting the point given

y = (-3/4)x + 2

Answer:

19 or 14

Step-by-step explanation:

Since the number is odd you can disqualify all even numbers up to 40 including 0.

Next since this number has 2 digits you can take out all 1 digit numbers.

After that, find perfect squares that also are 1 digit each.

Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.

The difference between Area and Volume lies in the fact that the former relates to plane shapes while the latter takes the concept of solid shapes into account.

The distinctive characteristic of area is the space occupied by a two-dimensional, 2D flat object in a plane while Volume on the other hand is defined as the space covered by a three-dimensional, solid object. The area is quantised in square units while the volume is quantised in cubic units.

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Answer:

Jiri is 25 years old.

Step-by-step explanation:

1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)

2)Pamela +Jiri=41

Substitute equation 1 into equation 2

(J-9)+J= 41

2J-9=41

Add 9 to both sides:

2J=41+9

Divide by 2:

2J=50

J=25

the required Jiri's age is 25 years.

Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9   - - - - (1)
the sum of their ages is 41
x +  y = 41  - - - - (2)

From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25

Thus, the required Jiri age is 25 years

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Answer:

y = 2

Step-by-step explanation:

Algebraic Equation is an equation where alphabets are used to represent numbers.

Solving the above question,

Let the number = y

Therefore,

Sum of the number = y + 3

If it's subtracted from 10 it becomes

10 - ( y + 3 )

The result : 10 - y - 3 = 5

- y = 5 - 10 + 3

- y = -2

Therefore,

y = 2

SOLUTION :

YES as well as NO , two equilateral ∆s can be congruent if any of their side matched to one another,

& CANNOT be congruent if any of their side didn't matched in terms of length (magnitude).

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The graph shows the comparison of the human welfare and ecological footprints.

A graph simply means a diagram that shows the relationship between variables.

From the graph, it can be seen that countries such as Norway, Canada, USA, and Australia meet the minimum criteria for sustainability.

The graph also shows that Sierra Leone is the least developed country among the countries compared as it has the lowest human development index.

The threshold for high human development as given as 0.8. Most African countries had a human development index of 0.5 and below.

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The dimensions of the length and width are 25 meters and 12. 5 meters respectively.

Area of a rectangle

area of rectangle = l × w

where

l = length

w = width

Note that,

Perimeter = 2w+ l

50 = 2w + l

l = 50  - 2w

Hence,

area = w(50 - 2w)

288 = 50w - 2w²

-2w² + 50w - 288 = 0

-w² + 25w - 144 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 25

w = - 25 / 2 ×  -1

w = 12.5 meters

Then, we have that

l = 50  - 2w

Substitute the value of w

l = 50 - 2(12.5)

l = 50 - 25

I = 25 meters

Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.

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Answer:

t >= [tex]\frac{25}{3}[/tex] or 8.33333333333

Step-by-step explanation:

We need to set up an inequality where demand is less than or equal to 0. The inequality looks like this:

50 - 6t <= 0

50 <= 6t

t >= [tex]\frac{25}{3}[/tex] or 8.33333333333