Can you guys help me with this problem, please I need it right now.

The larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60. This can be obtained by forming algebraic equation and finding

Given that one number is 4 more than another,

⇒x = y + 4              (equation (1))

Their sum is 60,

⇒x + y = 60

y + 4 + y = 60      (From (1))

2y + 4 = 60

2y = 56 ⇒ y = 28

x = y + 4 = 28 + 4 ⇒x = 32

Hence the larger number is 32 and the smaller number is 28 given that one number is 4 more than another and their sum is 60.

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The examples and solutions to the functions are illustrated below based on the information given.

1st example: The cost of a bag of rice is $100 and subsequent bags cost $95. Illustrate. the function to calculate the cost for p bags of rice.

The function will be:

C = 100 + (95 × p)

C = 100 + 95p

2nd example: The cost of a pen is $5. Find the cost of s pens.

The function will be:

C = 5 × p

C = 5p

3rd example: Calculate the total amount for m tickets if each ticket is $20.

The function will be;

C = 20 × m

C = 20m

4th example: Bon bought g mangoes at $2 each and d oranges at $3.40 each. Calculate the total cost.

C = (2 × g) + (3.40 × d)

C = 2g + 3.4d

5th example: The average age of k number of boys is 7. Find their total age.

The function will be:

a = (7 × k)

a = 7k

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Question 1: Akira sells lemonade at 50 cents a glass. Let m be the amount of money they make in total for g glasses. Akira only has enough lemonade for 20 glasses.

A) Write a function m(g) to represent the total money (in dollars) they make from lemonade sales.

B) What is the domain of the function? Why?

Answer:

A) m(g) = 0.5g

This is since she makes 0.5 dollars per glass

B) The domain is [tex]0 \leq g \leq 20[/tex] where g is an integer. This is since it's impossible to make less than 0 glasses and they cannot make more than 20.

Question 2: Danyon sells CD's at $20 per CD. He has only 15 CD's left.

A) Write a function m(c) to represent the total money he makes from selling c CD's.

B) What is the domain of the function? Why?

Answer:

A) m(c) = 20c, as he makes 20 dollars per CD.

B) The domain is [tex]0 \leq c \leq 15[/tex] where c is an integer, as he can't make less than 0 CD's, and he has only 15 left.

Question 3: A factory is capable of making 60 units per hour. The factory can only run for 24 hours before cool down, and 150 units have already been made.

A) Write a function u(h) to represent the number of units after h hours.

B) What is the domain of the function? Why?

Answer:

A) u(h) = 60h + 150 as it makes 60 units per hour and 150 are already made.

B) The domain is [tex]0 \leq h \leq 24[/tex] as the factory can't run for negative hours and has to cool down after 24 hours.

Question 4: Alazne sells sunglasses at $7 per pair. She has only 30 left before she needs to re-stock.

A) Write a function m(s) which calculates the amount of money she makes after selling s sunglasses.

B) What is the domain of the function? Why?

Answer:

A) m(s) = 7s, as she gets $7 per pair of sunglasses

B) [tex]0 \leq s \leq 30[/tex] where s is an integer, one cannot have a fraction of a pair and she only has 30. She also cannot sell negative sunglasses.

Question 5: Lincoln works at a burger joint in the summer. He makes $3 from every burger he makes. He already has $22 saved. He cannot make more than 10 burgers a day.

A) Write a function m(b) which calculates how much money he gets after making b burgers.

B) What is an appropriate domain for this function?

Answer:

A) m(b) = 3b + 22, as he already has 22 dollars and makes 3 more for every burger.

B) [tex]0\leq b\leq10[/tex], where b is an integer. This is since he cannot make a fraction of a burger, negative burgers, or more than 10 burgers.

Step-by-step explanation:

You already know that we use tn=an²+bn+c for these kinds of sequences:

4, 7, 14, 25, ...

now

7–3=4

So 2a=4===> a=2

[tex] a_{1} = 4 = = > n = 1 \\ 4 = 2 \times {1}^{2} + b + c = = = = > \\ b + c = 2[/tex]

[tex] a_{2} = 7 = = > n = 2 = = = > \\ 7 = 2 \times {2}^{2} + 2 \times b + c = = = > \\ - 1 = 2b + c[/tex]

b=–3, c=5

So the final result is:

[tex] t_{n} = 2 {n}^{2} - 3n + 5[/tex]

The calculated value of the total area of the figure is 49 square units

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have

Shape = trapezoid

The total area of the trapezoid is calculated as

Area = 1/2 * Sum of parallel sides * Height

So, we have

Area = 1/2 * (11 + 3) * 7

Evaluate

Area = 49

Hence. the total area of the figure is 49 square units

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Answer:

The answer is B) b

Step-by-step explanation:

According to the Trapezoid area formula, the area of the trapezoid is [(2d+a+b) × c] ÷ 2, however the area also equals (d+b) × c.

So d+(a+b)/2=d+b

(a+b)/2=b

a+b=2b

a=b

hope this helps <3

Answer:

The answers are in the image

Step-by-step explanation:

The solutions are in the image

A system equations that can be used to determine after how many months the boys will owe the same amount is

60 x = $ 1000

20 y = $ 600

In mathematics, a system of equations, also known as a system of simultaneous or systems of equations, is a finite system of equations for which we have sought common solutions. A system of equations can be classified in a similar way to simple equations. A system of equations finds application in our everyday life in modeling problems where unknown values can be represented in the form of variables.

In algebra, a system of equations contains two or more equations and looks for common solutions to the equations. "A system of linear equations is a set of equations that are satisfied by the same set of variables."

We need to find a system equations that can be used to determine after how many months the boys will owe the same amount

Let lan take x months to pay $ 1000 to his parents

In 1 month Ian pays $60

In x months Ian pays =

60 x= $ 1000

Let Ken take y months to pay $ 600 to his parents

In 1 month Ian pays $20

In y months Ian pays =

20 y= $ 600

Hence 60 x= $ 1000 and 20 y= $ 600 are the system of equations

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(-4x + 2) / 4 >= 6

-4x + 2 >= 24

-4x >= 22

x <= 22/4 OR x <= 5 1/2 OR x <= 5.5

Hope this helps!

The total surface area of the can of coke is 641.143 cm².

A can of coke has the shape of a cylinder. A cylinder is a three-dimensional object that is made up of a prism and two circular bases. The total surface area of a closed cylinder can be determined by adding the area of all its faces.

Total surface area of the closed cylinder = 2πr(r + h)

Where:

Total surface area of the closed cylinder = (2 x 22/7 x 6) x (6 + 11)

(264 / 7) x (17)

37.714 x 17 = 641.143 cm²

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Answer:

4.8

Step-by-step explanation:

60 percent of 8 is 4.8

I hope this helps!

The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. The events are dependent events.

Given that there are five vowels, which come from the letters A, E, I, O, and U, the likelihood of drawing a vowel is:

5/26

since there are a total of 26 alternatives available. After choosing that, we are left with 25 alternatives, 4 of which are vowels, thus the probability is:

4/25

The final likelihood is thus:

5/26 * (4/25) = 0.031

In other words, the likelihood is 3.1% when choosing a vowel and then another (without replacement).

The first event has an impact on the second event since there are fewer vowels and overall possibilities, hence the events are dependent.

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The relation in option B is a function.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given are 4 relations, A, B, C, D.

From the definition of function, it is clear that, no input value have more than one output value.

A : The value of x = -2 is mapping to 2, 1, 0, -1.

That is, an input value is having more than one output values.

So this is not a function.

B : Here the input values, 0, 1, 2 and 3 maps to -2.

Here the input values are distinct. No input values are mapping to more than one output value.

So this is a function.

C : Here 1 is mapping to -2 and 3. So not a function.

D : For x = 0, there are two y values, 3 and -3.

So this is not a function.

Hence option B is a function.

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The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A

[tex]V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} [/tex]

= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴

= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81

= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81

= 9/4√256 + 800 + 432 - 3125 + 450 - 81

= 9/4√-1268

= 54 cubic yard

Total cost to fill Kenny's entire attic = 54 × $16.75

= $904.50

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Using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.

According to the questions,

Three schools have a chess tournament and four players come from each school. Each player plays against each other from his/her own school.

Formula for Combinations [tex]nC_{r}[/tex] = [tex]\frac{(n-r)!}{r!}[/tex]

[tex]4C_{2}[/tex] = [tex]\frac{4*3}{1*2}[/tex]

     = 6

They are 6 ways to select two schools. Given those 2 schools they are

[tex]4^{2}[/tex] = 16 ways to pair up players 1 from each school. They are 3 games played by each of those 3 pairs.

The total number of games played against other school.

6×16×3 = 288.

Similarly using combinations we can find the number of games played against schoolmates. To find this 4 combinations of 2 is 6 ways to select a pair from the 4 people at given school. They are four schools and they play one game each.

6×4×1 = 24

Thus using combinations, the number of games played against schoolmates is 24.

In order to find the number of games of chess are played only if we add the total number of games played against other school and the total number of games played against schoolmates.

288+24 = 312

Hence, using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.

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The mean and the standard deviation of the following data are 35.75 and 11.6765 respectively.

First, we'll find the mean (X) of the data:

[tex]X =\dfrac{(\sum x \times f) } {\sum f}[/tex]

So, the approximate standard deviation for the monthly cell phone plan cost is 9.87.

The mean is given by

[tex]\mu =\frac{\sum xf}{\sum f}[/tex]

Where x is the midpoint of the class and f is the frequency.

The calculation of mean and the standard deviation is shown in the below table:

    Hence, the mean is calculated as:

mean is   [tex]\mu =\frac{2359.67}{66}[/tex]

                          =35.75

The standard deviation is calculated as:

Standard deviation =[tex]\sigma[/tex] =[tex]\sqrt{\Dfrac{\sum f(x-\bar{x})^2}{n-1}}[/tex]

=[tex]\sqrt{\dfrac{8862.12121}{65}}[/tex]

=11.6765

Thus, the mean and the standard deviation are 35.75 and 11.6765 respectively.

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The table of standard deviation is attached below.

Probability that the lock code consists of all even digits is [tex]1344[/tex] if we choose the [tex]4[/tex] digit lock is randomly from numbers [tex]1,2,3,4,5,6,7,8,9[/tex]

How can we find the probability that the lock code consists of all even digits?

Total numbers are [tex]1,2,3,4,5,6,7,8,9[/tex]

And we choose [tex]4[/tex] digit code

So probability of choosing [tex]4[/tex] numbers from [tex]9[/tex] numbers without reapitation is

[tex]9p_{4} =\frac{9!}{(9-4)!} \\=\frac{9*8*7*6*5!}{5!} \\=3024[/tex]

For All numbers are even , probability the last digit of number is even.

So we have [tex]4[/tex]  even number and if we fix one on last digit and can change other [tex]3[/tex] then the probability is

[tex]4*8P_{3} =4*\frac{8!}{(8-3)!} \\=4*\frac{8*7*6*5!}{5!} \\=1344[/tex]

So the total probability of code lock having all even number is [tex]1344[/tex]

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Answer:

No

Step-by-step explanation:

Am irrational number is a number that can't be expressed by a ratio (fraction). 1/11 is a fraction so it is rational, not irrational.

The amount for the deposit is $25350, monthly payment is $1436.5 and the total amount that Sipho pays is $178492.

Given price of car $169000, deposit of 15%, monthly installments being 1% of left over price and number of years be 9 years.

We have to find the amount of deposit, monthly installments and the total amount paid by Sipho.

We have been told that deposit is 15% of total amount. So the deposit will be 15%*169000=$25350.

Monthly installment is 1% of the left over amount.

left amount=169000-25350=$143650.

Monthly installment being =143650*1/100

=$1436.5

Total amount paid by Sipho=deposit +installment amount  * numberof installments

Number of installments=12*9

=108

Total amount=25350+1436.5*108

=25350+155142

=$178492

Hence deposit is $25350, monthly payment being $1436.5, total amount be $178492.

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Answer:22-0.22y

Step-by-step explanation: we have to decrease 22 by y%

we need to calculate what is y% of 22. y% of 22 simply means y% into 22 that is y% x 22

= 0.01(y) x 22

= 0.22y

= 22 - 0.22y

The graph is a decreasing exponential graph.

Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing the value of y is decreasing very rapidly.

Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.

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Answer: 15x-2

Step-by-step explanation: ?

Answer:

15x - 10

Step-by-step explanation:

[tex]5(3x-2)=5(3x)+5(-2)=15x-10[/tex]

Hope this helps

Answer:

The class and exam medians are almost the same.

Step-by-step explanation:

The median of a box-and-whisker plot is the line inside the box.

• As we can see, the medians of  class and median are very similar, both around 85. This is why the first option is correct.

•The second option is incorrect because the exam median is not much higher than the class median; the difference is very small.

• The third option is incorrect because exam does not have the lowest median. In fact, exam median is slightly higher than class median.

• The fourth option is incorrect because outliers do not affect the median.

Considering that the value of 126.07 is valid for the population, it is a parameter.

In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.

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Step-by-step explanation:

The answer is 8 2 / 5 because ...

[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]

Answer:

Here your ans and dont forget to say dhanwyad ok.

The square of the given number will have 199 digits.

A number with hundred digits is given.

The first two digits of the given number are 2 and 9.

We can use the following formula to find the total number of digits in the square of a number.

2n - 1

Where n is the total number of digits in the given number.

Let us take a number with 2 digits:

29*29 = 841     { 2*2 - 1 = 3}

We can see that the square of the 2-digit number has 3 digits in it.

Let us take a number with 3 digits:

299*299 = 89401     { 2*3 - 1 = 5}

We can see that the square of the 3-digit number has 5 digits in it.

Similarly, we can find the number of digits in the square of a 100-digit as shown below:

2n - 1 = 2*100 - 1

= 200 - 1

= 199

Therefore, we have found that the square of the given number will have 199 digits.

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Answer:

(2, - 1 )

Step-by-step explanation:

4x - 9y = 17 → (1)

6x - 5y = 17 → (2)

multiplying (1) by 6 and (2) by - 4 and adding will eliminate x

24x - 54y = 102 → (3)

- 24x + 20y = - 68 → (4)

add (3) and (4) term by term to eliminate x

0 - 34y = 34

- 34y = 34 ( divide both sides by - 34 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

4x - 9(- 1) = 17

4x + 9 = 17 ( subtract 9 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is (2, - 1 )

A margin of sampling "error" is a statistical calculation for how accurate a poll's results are.

A population parameter's sampling error is the discrepancy between the sample statistic used to estimate it and the parameter itself. For instance, sampling error is the variance between a population mean and a sample mean.

The sampling errors can be placed into four categories:

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Answer:

37.44 cm²

Step-by-step explanation:

To find the width, follow these steps.

10.4*2=20.8

28-20.8=7.2

7.2/2=3.6

The width is 3.6.

To find the area, multiply the width and the length together.

10.4*3.6=37.44

The area of the rectangle is 37.44 cm²

Hope this helps!