Homework Progress
37/ 105 Marks
Gigi is going to buy 100 stickers.
Here is some information about the cost of stickers in two shops.
Stickers4u
Pack of 25 stickers for £2.25
World Stationery
Pack of 10 stickers for £1.75
Buy 1 pack get 1 pack free
Gigi wants to buy the stickers for the best possible price.
Which shop should Gigi buy the 100 stickers from?
You must show how you get your answer.
Show your workin

Answer:

(-2,-4)

Step-by-step explanation:

3x+2=-2x-8

+2x.    +2x

5x+2=-8

   -2. -2

5x=-10

/5.  /5

x= -2

y=3(-2)+2

y=-6+2

y= -4

(-2,-4)

Hopes this helps please mark brainliest

Answer:

Domain: all real numbers

Step-by-step explanation:

The function is:

[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]

The domain of a function is the set of values of the x-coordinates of the points of the function.

In this function, there is no restriction on x, so the domain is all real numbers.

Answer:

-------------------------------

Find y:

a. [tex]123.1(1.069)^3 \approx 150.4[/tex]

b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]

The probability mass function (pmf) of X formally displays the likelihood of events where X=xk.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

We can list the components of RX if X is a discrete random variable since RX is a countable set. In other words, RX=x1,x2,x3,... can be written.

Note that the random variable X here has the potential values x1, x2, x3

While we typically use capital letters to designate random variables, we typically use lowercase letters like x, x1, y, and z to denote the integers in the range.

We are interested in learning the probability that a discrete random variable, X, equals a certain value, xk.

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If the inequality which can be used to determine x is 7.25 + 23.25x ≤ 170 and the number of people who can go the amusement park is 7

The maximum amount that he can spend = $170

The cost of the parking ticket = $7.25

The cost of the ticket including tax = $23.25 per person

Then the inequality will be

7.25 + 23.25x ≤ 170

Subtract both side of the inequality by 7.25

23.25x ≤ 162.75

Divide both side of the inequality by 23.25

23.25x / 23.25 ≤ 162.75/23.25

x ≤ 7.006

Hence, the inequality is 7.25 + 23.25x ≤ 170 and 7 people can go to the amusement park

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The linear equation that represents the given situation is 1.75x + 6.25y + 1.50z = 43.50

Total amount that she spent = $43.50

The cost of drinks = $1.75

The cost of sandwich = $6.25

The cost of chips = $1.50

The linear equation is defined as the equation in which the highest power of the variable is 1

The linear equation the represents this situation is

1.75x + 6.25y + 1.50z = 43.50

Where the number of drinks is x, number of sandwiches is y  and the number of chips is z

Hence, the linear equation is 1.75x + 6.25y + 1.50z = 43.50

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By using Binomial distribution, it can be calculated that

a) Probability that the operation is successful = 0.8290

b)  Number of sensors expected to operate during the 24 hour period  = 14.25

What is Binomial Distribution?
Binomial Distribution is a discrete type probability distribution whose probability mass function is given by

P(X = x) = [tex]{n \choose x}p^xq^{n-x}[/tex]

p is the probability of success and q is the probability of failure.

a) This is a problem on Binomial Distribution

Probability that the operation is successful = P(X [tex]\geq[/tex] 14)

= P(X = 14) + P(X = 15)

P(X = 14) =

[tex]{15 \choose 14}(0.95)^{14}(1- 0.95)^{15 - 14}\\15 \times 0.95^{14}\times 0.05\\0.3657\\[/tex]

P(X = 15) =

[tex]{15 \choose 15} 0.95^{15}(1-0.95)^{15 - 15} = 0.4633[/tex]

Probability that the operation is successful = 0.3657+0.4633 = 0.8290

b) Number of sensors expected to operate during the 24 hour period = [tex]15 \times 0.95[/tex] = 14.25

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Step-by-step explanation:

b.) 8/7≈ 1.1

Final.) and then using the exponential decay formula, 18.1 will be left after

The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.

In this problem, the data-set is given as follows:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.

Hence the mean is of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.

After the change, the data-set is of:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.

Hence the mean will be of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.

Then the increase will be of:

1065 - 1035 = 30.

The median of a data-set is the middle element of the data-set, the value which:

The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.

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The expression used to represent the given phrase is given by x =5 and

y = 26 + 8x and value of the given expression when x =5 is equal to

y = 66.

As given in the question,

Given phrase is:

x equal 5

y equals 26 more than the product of 8 and a number x

Required expression to represent the given phrase is:

x = 5

y = 26 + 8x

Value of the expression y = 26 + 8x when x = 5 is given by :

y = 26 + 8( 5 )

⇒ y = 26 + 40

⇒ y = 66

Therefore, the required expression for the given phrase is x =5 and

y=26 +8x , the value of the expression y = 66 when x = 5.

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The domain when the maximum number of people allowed in the movie theater is 60 people would be: B. 0 ≤ x ≤ 60.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Since the maximum number of people that are allowed in the movie theater is 60 people, we can logically deduce that the input values (x-values) for its function is less than or equal to 60. Therefore, the domain of the function on this graph is given by:

Domain = [0, 60]

Domain = 0 ≤ x ≤ 60.

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Complete Question:

The graph represents the money collected at the movie theater on Saturday. Find the domain when the maximum number of people allowed in the movie theater is 60 people.

40 ≤ y ≤ 160

0 ≤ x ≤ 60

40 ≤ x ≤ 160

0 ≤ y ≤ 60

Answer:

the answer is 0 is less than or equal to x which is less than or equal to 60

Step-by-step explanation:

Domain is the x value

Since the max amount of people is 60, and people is x value the answer i put above is a reasonable domain.

Hope this helps!

Answer: the student forgot to multiple by right side of equation 2 in line 2

Step-by-step explanation: your welcome :)

Answer:

Figure b

Step-by-step explanation:

the sides are equal

Proportional relationship for the given table is true and is define as

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

As given in the question,

Value of x and y in the given table are :

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.

y / x for all the values of x and y:

First values:

y /x = 6.4 / 25.6

      = 0.25

Second values:

y/x = 18.2/ 72.8

    = 0.25

Third values :

y /x = 19.3/ 77.2

      = 0.25

0.25 is equivalent to One fourth ( 1/4).

Constant of proportionality exist = 0.25 or One fourth.

Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.

The complete question is:

Determine if the table how a proportional relationship.

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

Yes, it is proportional because all y over x ratio are equivalent to one third.

No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.

No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3

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The expected value of the random variable b is given as follows:

2.404 books.

The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.

From the histogram given by the image at the end of the answer, the distribution is given as follows:

Then the expected value of the random variable b is obtained as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.

The histogram is given by the image at the end of the answer.

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The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .

In the question ,

it is given that ,

the angle bisector of the exterior angle of a triangle is parallel to a side .

we have to prove that the triangle will be an isosceles triangle .

In the triangle ABC given below , AB is extended to AD ,

SO , the exterior angle will be angle DAC ,

let AE be the bisector of the the angle .

So , the equal angles are angle DAC and angle EAC .

it is given that AE is parallel to BC , where BC is base .

we know that ,

if any line intersects two parallel lines then every pairs of alternative  Interior angles are same and also their corresponding angles are equal .

Here AE is parallel to BC and line BD intersects them ,

So , angle ABC = angle DAE    ( corresponding angles )

angle ACB = angle EAC   ( alternate angles )

Now , as AE is the bisector of angle DAC ,

we have , angle DAC = angle EAC

So , we get , angle ABC = angle ACB .

In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal

that means , AB=AC

Hence , the given Triangle is an isosceles triangle .

Therefore , it is proved that the triangle ABC is an isosceles triangle .

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a) The experimental units are the Acacia Trees.

b) The treatments carried used are; active beehives, empty beehives and no single beehive.

c) The response variable is the damage that the elephants caused to the trees.

Experimental design is defined as the process of carrying out research in a manner that is objective and controlled such that precision is maximized and then specific conclusions can possibly be drawn regarding a hypothesis statement. Generally, the purpose of this is to establish the effect that a factor or independent variable has on a dependent variable.

From this question, it is very clear that the experimental units are the Acacia Trees. This is because they are the primary interest or objective of the research.

The treatments carried out here are the active beehives, empty beehives and no single beehive.

The response variable is defined as the result of the experiment where the explanatory variable is manipulated. In this case, the response variable is the damage that the elephants caused to the trees.

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Answer:

12x² + 10xy + 2y²

Step-by-step explanation:

(3x + y)(4x + 2y) =

= 12x² + 6xy + 4xy + 2y²

= 12x² + 10xy + 2y²

Answer: 34.5

Step-by-step explanation:

    To find the constant of proportionality between miles driven and number of gallons used, we will divide the miles driven by the gallons used.

517.5 / 15 = 34.5

1138.5 / 33 = 34.5

1242 / 36 = 34.5

The expression that can be use to represent the amount owned on rental is 0.1x + 25y

Rick rents a car from a company that charges him $25 per day plus 10 cents per mile driven.

The expression that can be use to represent the amount owned on rental can be represented as follows:

let

x = number of miles driven

y = number of days

Let's convert cent to dollars

100 cents  = 1 dollars

10 cents = ?

cross multiply

amount in dollars = 10 / 100 = 0.1 dollars

Therefore,

the expression = 0.1x + 25y

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The null hypothesis would state that the population mean number of cups of coffee that women would drink 32% the population mean number cups of coffee than men drink.

The term "percentage" comes from the Latin phrase "per centum," which means "by the hundred." With 100 as the denominator, percentages are fractions. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam received 30% on his math test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

A certain number or quantity in every hundred is referred to as a percentage. It is a fraction, and the denominator is 100.

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In the context of hypothesis testing, a test statistic is; c. A value, determined from sample information, used to test the null hypothesis.

Hypothesis testing is defined as the method that is used to find the probability of the hypothesis to be proved in the future on the basis of the small population sample. The null hypothesis is said to be a hypothesis where no important difference between the random variables

The test statistic is defined as a value that is computed from the sample data that is used when making a decision about whether or not to reject the null hypothesis.

Looking at the options and based on the definitions above, option C adequately describes the test statistic.

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The diameter of a dime tells us the circumference of a dime is approximately 299 times larger than human hair.

The diameter of an object is used to calculated the circumference or area of the object. This also helps us to know the width of a circular object.

In this problem, the diameter tells us about the length of the each quantity.

The diameter of a dime tells us how wide the coin is and the diameter if a hair tells us the width of the hair.

Comparing both values

Dime = 17.91mm

Hair = 6.0*10^-2

Divide both quantity together.

17.91 / 6.0*10^-2 = 298.5≅299

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Answer:

[tex]y=\frac{2}{3}x+1\frac{1}{3}[/tex]

Step-by-step explanation:

when a line is parallel the slope is the same for both

y=mx+b is slope intercept form where m is slope and b is intercept

we know the slope is 2/3 so to find b we just fill it in with coordinates

-2=2/3(-5)+b

-2=-10/3+b

+10/3 +10/3

4/3=b

y=2/3x+4/3

hopes this helps please mark brainliest

128 were Daily News readers. 19 read neither while 35 read both. Weekly Gazette A marketing class conducted a survey of 270 shoppers at a mall to find out how many of them read the Weekly Gazette and how many the Daily News.

What is News readers?

150 attendees were surveyed by a marketing class to find out how many read the Weekly Journal and how many the National News. In this section, word problems will be solved using Venn diagrams. The areas of a Venn diagram that indicate quantities as opposed to will have numbers in them. Confidence interval for difference of two formula You may have read statements like the ones below in newspapers, for instance. law in numerous nations.

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The equation of the new function is g(x) = 4(2ˣ)

The exponential equation is given as

f(x) = 2ˣ

Then, we have the transformation to be:

Vertically stretch by a scale factor of 4

The scale factor can be represented as k

So, we have

k = 4

The rule of vertical stretch by a scale factor of k is represented a

g(x) = kf(x)

So, we have

g(x) = 4 * 2ˣ

This gives

g(x) = 4(2ˣ)

Hence, the equation is g(x) = 4(2ˣ)

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Answer:

f(x) = 3x + 4

f(4) = 3(4) + 4 = 12 + 4 = 16

Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.

In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.

Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:

Profit = Revenue - Cost

In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.

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This equation x + (x + 1) + (x + 2) = negative 21 will be used.

Let the first Number is x.

We have to take 3 consecutive integers.

second Number is x+1

third Number is x+2.

Sum of these 3 consecutive integers is x+(x+1)+(x+2).

Sum of these 3 consecutive integers is given as negative21.

so we can write  x+(x+1)+(x+2)=negative 21.

by using above equation we can find the value of 3 numbers.

So the final equation will be x + (x + 1) + (x + 2) = negative 21.

Given Question is incomplete, Complete Question here:

Three consecutive integers have a sum of –21. Which equation can be used to find the value of the three numbers? x + x + x = negative 21 x + 2 x + 3 x = negative 21 x + (x + 1) + (x + 2) = negative 21 x + (x + 2) + (x + 4) = negative 21

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