Evaluate 14 - 2xy when x = -6 and y = 2.

Answer:

A) g(x)= 1/2(x-8)^2-8.   The vertex is (8, -8).

Step-by-step explanation:

A. g(x)= 1/2(x-8)^2-8 is the vertex form of the function.

In general it can be written as

f(x) = a(x - h)^2 + k       where (h, k) is the vertex.

Here the vertex is (8, -8)

For given function g(x), vertex = (8, -8)

The correct answer is option (A)

"The graph of the quadratic function is shaped like a parabola. The form of this quadratic function is called vertex form."

"The vertex of the graph of a quadratic function is the highest or lowest possible output for that function. "

For given example,

We have been given three equivalent forms of a quadratic function g.

[tex]g(x) = \frac{1}{2} (x-8)^2-8\\\\g(x) = \frac{1}{2}(x-12)(x-4)\\\\g(x) = \frac{1}{2}x^2-8x+24[/tex]

In general the vertex form of a function can be written as

f(x) = a(x - h)^2 + k,

where (h, k) is the vertex.

From these functions the function g(x)= 1/2(x-8)^2-8 is vertex type function.

Comparing with the general equation,

we have h = 8 and k = -8

So, the vertex are (8, -8).

The correct answer is option (A)

Learn more about the vertex of the graph here:

https://brainly.com/question/22129666

#SPJ2

Answer:

Ratio of the increase in value to the original value will be 1 : 5

Step-by-step explanation:

This question is incomplete; Here is the complete question.

A house with an original value to $150,000 increased in value to $180,000 in 5 years. what is the ratio of the increase in value to the original value of the house?

Original value of the house = $150000

Value of the house after 5 years = $180000

Appreciation in value of the house after 5 years = $180000 - $150000

= $30000

Now the ratio of the increase in value to the original value = [tex]\frac{\text{Increased value}}{\text{Original value}}[/tex]

= [tex]\frac{30000}{150000}[/tex]

= [tex]\frac{1}{5}[/tex] or 1 : 5

Therefore, ratio of the increase in value to the original value of the house is 1 : 5

Final answer:

To find the ratio of the increase in house value to the original value, subtract the original price from the increased price, then divide by the original price. For a house purchased at $200,000 and increased to $250,000, the ratio would be 0.25, or a 25% increase from the original value.

Explanation:

To calculate the ratio of the increase in value to the original value of a house, you must take the difference between the final value and the original value, then divide this by the original value. Suppose a house was bought for $200,000 and is now worth $250,000, this would be an increase of $250,000 - $200,000 = $50,000. The ratio of increase to original value would thus be $50,000 / $200,000 = 0.25 or 1:4. This indicates that, for every dollar of the original value, the house increased in value by 25 cents. If we wanted to express this as a percentage, we would multiply by 100, giving us a 25% increase in value. However, it's important to remember other factors such as transaction costs, market conditions, and loan repayment when considering the rate of return on a house.

Answer:

Step-by-step explanation:

Answer:

800 months

Step-by-step explanation:

The formula for interest is:

(Capital * saving account * time) / 100

So:

(10000 * 0.06 * x) / (100) = 4800

We clear x:

(10000 * 0.06 * x) = (100) * 4800

x = 480,000 / (10000 * 0.06)

x = 800 months (66.67 years)

To determine the duration for which the deposited $10,000 at 6% interest grew to a total of $14,800 ($10,000 principal + $4,800 interest), the formula for compound interest can be re-arranged to solve for the time variable. You'll use the amount of money accumulated, the principal amount, the annual interest rate, and the assumption that the interest is compounded annually. Plug these values into the formula to calculate the number of years.

You deposited $10,000 into a savings account at 6% interest. To determine how long it took for you to earn $4,800 in interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:

In this case, we can rearrange the formula to solve for t, because you want to find out how many years it took for your investment to turn into A = $10,000 + $4,800 = $14,800. Assuming the interest is compounded annually (n = 1), the formula becomes:

t = ln(A/P) / n * ln(1 + r/n)

Plugging in the numbers gives us:

t = ln($14,800 / $10,000) / ln(1 + 0.06)

By calculating this, you can get the number of years you had the money in the savings account.

Answer:

She would earn in a week (six days) 1482 cents.

Step-by-step explanation:

Given:

Mrs. Hall went to work for the shirt factory.

She earned nineteen cents per hour.

She worked thirteen hours per day.

Now, to find the money she earn in a week (six days).

Money she earned per hour = 19 cents.

As she she worked 13 hours per day.

So, money she earned per day = [tex]19\times 13=247.[/tex]

Now, to get the total money she earned in a week (six days) we multiply 6 by money earned in per day:

[tex]6\times 247[/tex]

[tex]=1482\ cents.[/tex]

Therefore, she would earn in a week (six days) 1482 cents.

The two numbers are 8,13.

Step-by-step explanation:

Let,

smaller number = x

Larger number = x+5

According to given statement;

Smaller number + Bigger number = 3x-3

[tex]x+(x+5)=3x-3\\x+x+5=3x-3\\2x+5+3=3x\\8 = 3x-2x\\8=x\\x=8[/tex]

Smaller number = 8

Larger number = 8+5 = 13

The two numbers are 8,13.

Keywords: algebraic equation, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

The two numbers are 8,13.

The transformation type may be identified by understanding each option: reflection would flip the figure across an axis, translation would slide it, and a 90° counter-clockwise rotation would pivot it around the origin. The right choice depends on the specific positioning of ABCD and A'B'C'D'.

The student's question revolves around identifying the type of transformation that maps quadrilateral ABCD to A'B'C'D'. Without the specific coordinates or a visual representation it's difficult to provide the exact transformation.

However, the choices given are reflections across the X-axis or the Y-axis, translation, or a 90° counter-clockwise rotation.

Reflecting across the X-axis would mean to move every point of ABCD to the opposite side vertically, while the Y-axis reflection would be a horizontal flip. A translation involves sliding the figure in any direction without altering its orientation or shape.

But, the 90° counter-clockwise rotation is a pivot of every point at a 90-degree angle around the origin in the counter-clockwise direction, which appears to be the action described in the subsequent figures and discussion of the merry-go-round example.

The three types of descriptions involving the positive x direction, vertically upward, and horizontally to the right side can be related to the translation movement in the coordinate system.

Answer:

The answer to your question is width = 8ab³

Step-by-step explanation:

Data

Area = 32a³b⁴ u²

length = 4a²b   u

Formula

Area of a rectangle = width x length

Solve for width

                           width = [tex]\frac{Area}{length}[/tex]

Substitution

                          width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]

Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.

                          width = 8 a²b³

Answer:

Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3            vertical asymphotes None Extreme points of a32a^3 0,0

Answer:

The Teenagers spend $172.05 billion dollars in 2001.

Step-by-step explanation:

Given:

Number of billion dollars spent by teenagers in 2000 = $155

Percentage amount increase in 2001 = 11%

We need to find how many billions of dollars did teenagers spend in 2001.

Solution:

First we will find the Number of billion dollar increase in 2001.

Number of billion dollar increase in 2001 can be calculated by Percentage amount increase in 2001 multiplied by Number of billion dollar spent by teenagers in 2000 and then divided by 100.

framing in equation form we get;

Number of billion dollar  increase in 2001 = [tex]\frac{11}{100}\times 155 = \$17.05[/tex]

So no number of billion dollars teenagers spend in 2001 is equal to Number of billion dollars spent by teenagers in 2000 plus Number of billion dollar  increase in 2001 .

framing in equation form we get;

number of billion dollars teenagers spend in 2001 = [tex]\$155+\$17.05 = \$172.05[/tex]

Hence The Teenagers spend $172.05 billion dollars in 2001.

I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.

Final answer:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.

Explanation:

A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.

Answer:

33 hearts sold, 48 roses sold

Step-by-step explanation:

x- number of roses sold

y- number of hearts sold

x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"

5x+3y=339

5(15+y)+3y=339

75+5y+3y=339

8y=339-75

8y=264

y=33

x=15+33=48

The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.

Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.

The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.

Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.

Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.

Simplifying the equation, we get '8x + 75 = 339'.

Subtracting 75 from both sides of the equation, we get '8x = 264'.

Dividing both sides of the equation by 8, we get 'x = 33'.

Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.

Answer:

There were 116 jelly beans in the bag to start with

Explanation:

a. Let's start with Carries brother and his friends.

We are given that Carrie's brother ate 4 jelly beans,  the first teammate ate 6, the second teammate ate 8 and so on.

Noticing the pattern, we can see that each teammate ate 2 jelly beans more that the one preceding him.

We are also given that Carrie's brother has 8 teammates.

This means that:

Carrie's brother ate 4 jelly beans

First teammate ate 4 + 2 = 6 jelly beans

Second teammate ate 6 + 2 = 8 jelly beans

Third teammate ate 8 + 2 = 10 jelly beans

Fourth teammate ate 10 + 2 = 12 jelly beans

Fifth teammate ate 12 + 2 = 14 jelly beans

Sixth teammate ate 14 + 2 = 16 jelly beans

Seventh teammate ate 16 + 2 = 18 jelly beans

Eighth teammate ate 18 + 2 = 20 jelly beans

Now, we calculate the total number of jelly beans eaten by Carrie's brother and his teammates

Total jelly beans = 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 108 jelly beans

b. Next, we move to Carrie:

We are given that Carrie ate 5 jelly beans

Adding that to the total number of jelly beans from part a, we get the total number of eaten jelly beans

Therefore:

Total number of eaten jelly beans = 108 + 5 = 113 jelly beans

c. Getting the number of jelly beans that were in the bag to start with:

We are given that the remaining number of jelly beans in the bag after all has eaten was 3 jelly beans

This means that, if we added the number of eaten jelly beans to the number of remaining jelly beans, we will get the total number of jelly beans that were in the bag to start with

Therefore:

Total number of jelly beans in the bag to start with = 113 + 3 = 116 jelly beans

Hope this helps :)

Final answer:

By calculating the total number of jelly beans eaten and adding the three left in the bag, we find that there were originally 119 jelly beans in Carrie's bag.

Explanation:

To figure out how many jelly beans were in the bag initially, we need to work backwards from the information given. Carrie ate 5 beans and then her brother ate 4. Combining that with the 3 beans left at the end, we have a subtotal of 12 beans (5+4+3). We're told that each of Carrie's brother's teammates ate an increasing number of beans, starting with 6 and increasing by 2 each time.

Let's find the total number of beans eaten by the teammates. Since there are 8 teammates and the number of jelly beans increases by 2 for each subsequent teammate, starting at 6, we have an arithmetic sequence.

To find the total beans eaten by teammates, we sum the arithmetic sequence: T = (n/2) * (first term + last term). Here, n=8, the first term is 6, and the last term is 6 + 2*(8-1) = 20 (since the increase is by 2 for each of the 7 teammates after the first).

T = (8/2) * (6 + 20) = 4 * 26 = 104 beans eaten by all teammates combined.

Adding Carrie's and her brother's consumption to the teammates' total gives us: 12 beans (Carrie and her brother) + 104 beans (teammates) = 116 beans. Therefore, there were 116 + 3 (left in the bag) = 119 jelly beans in the bag to start with.

Answer:P(A/B)=0.08

Step-by-step explanation:

The probability formula to find p(A/B) is :

P(A/B) = p(A n B) / p(A)

Which means that B is contain in A and p(A n B) is p(B)

p(A n B)=p(B)=0.05

p(A)=0.625

Therefore

P(A/B) = p(A n B) / p(A)=p(B) / p(A)

P(A/B)=0.05 / 0.625

P(A/B)=0.08

Answer:No Solution

Step-by-step explanation: the explanation can be found in the attached picture

The given system of linear equations does not have a unique solution, as one equation is a multiple of another. Therefore, this is a dependent system and the solution can be expressed in terms of a parameter satisfying all equations.

In order to solve a system of linear equations, one can use a variety of methods such as substitution, elimination, or matrix method. Let's use the elimination method here. The given system of equations is:

a) x + 2y - 7z = -8, b) 2x + y + z = 23 and c) 3x + 9y - 36z = -63. It is seen that equation c) is simply 3 times equation a), hence these equations are dependent and will not provide any unique solution. The system of equations is therefore dependent and does not have a unique solution. It can be expressed in terms of a parameter which will satisfy all given equations. The solution cannot be expressed in terms of x, y and z.

https://brainly.com/question/20379472

#SPJ3

Answer:

$ 213.50

Step-by-step explanation:

From the question;

Albert spent;

We are required to determine Albert's monthly allowance;

Then;

Deducting $35.5, we get,

$(x/2 - 35.5)

Then, 3/5 of the remainder is on a book

Thus, 1 - 3/5 = 2/5 of the remainder (represents the amount that remained after buying a book and a shirt.

Therefore;

2/5 (x/2 - 35.5) = 28.5

We get;

x/2 - 35.5 = 28.5 (5/2)

x/2 - 35.5 = 71.25

 x/2 = 71.25 + 35.5

  x/2  = $ 106.75

    x = $ 106.75 × 2

       = $ 213.50

Therefore, Albert's monthly allowance is $ 213.50

Answer:

Casandra will run 8 miles on the 9th Day.

Step-by-step explanation:

Given:

Casandra on first day of training  she runs 4 miles

So we can say that;

[tex]a_1=4\ miles[/tex]

Also Given:

each day after that she adds on 0.5 mile.

So we can say that;

Common difference [tex]d=0.5\ miles[/tex]

We need to find on what day she will run 8 miles.

So we can say that;

[tex]T_n = 8[/tex]

Let the number of the day be denoted by 'n'

Solution:

Now By using the formula of Arithmetic Progression we get;

[tex]T_n= a_1+(n-1)d[/tex]

Now substituting the values we get;

[tex]8=4+(n-1)0.5[/tex]

Now by using distributive property we get;

[tex]8 =4+0.5n-0.5\\\\8=3.5+0.5n[/tex]

Now subtracting both side by 3.5 we get;

[tex]8-3.5=3.5+0.5n-3.5\\\\4.5=0.5n[/tex]

Dividing both side by 0.5 we get;

[tex]\frac{4.5}{0.5}=\frac{0.5n}{0.5}\\\\9=n[/tex]

Hence Casandra will run 8 miles on the 9th Day.

Answer: -3

Step-by-step explanation: using the mathematical process

4-(4/4)-6=

4-1-6= -3

Answer:

Actually there are two answers: -3 and 0, depending on how the expression is written.

Step-by-step explanation:

If the rational expression is x - 4/x - 6, we have:

x - 4/x - 6

= 4 - 4/4 - 6

= 4 - 1 - 6 = 4 - 7 = -3

If the rational expression is (x - 4)/(x - 6), we have:

(x - 4)/(x - 6)

= (4 - 4)/(4 - 6)

= 0/-2 = 0

The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.

The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:

P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.

Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.

https://brainly.com/question/23283166

#SPJ3

Answer:

Step-by-step explanation:

area=4×22/7×14²=4×22×28=2464 units²

The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.

To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:

A = 4 * (22/7) * (14)²

A = 4 * (22/7) * 196

A = 4 * 22 * 28

A = 88 * 28

A = 2464

Thus, the surface area of the sphere is 2464 square units.

Answer:

x = 12

Step-by-step explanation:

The figure in the question was split into the triangles in the attachment to the solution.

Now applying the principle of similar triangles, we have:

[tex]\frac{16}{x} = \frac{x}{9}[/tex]

cross-multiplying, we have:

[tex]x^{2} = 16*9 = 144[/tex]

solving for x,

x = 12

Answer:

(5,-3) , (10, -2), (7,-8)

Step-by-step explanation:

The new triangle will be

(5,-3) , (10, -2), (7,-8) by mapping

(x,y) => (x +3, y-5)

Answer:

The 4th graph

Step-by-step explanation:

To determine which graph corresponds to the  [tex]f(x) = \sqrt{x}[/tex]  we will start with inserting some values for x and see what y values we will obtain and then compare it with graphs.

[tex]f(1) = \sqrt{1} = 1\\f(2) = \sqrt{2} \approx 1.41\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]

So, we can see that the pairs (1, 1), (2, 1.41), (4, 2), (3, 9) correspond to the fourth graph.

Do not be confused with the third graph - you can see that on the third graph there are also negative y values, which cannot be the case with the [tex]f(x) =\sqrt{x}[/tex], the range of that function is  [tex][0, \infty>[/tex], so there are only positive y values for [tex]f(x) = \sqrt{x}[/tex]

Answer:

if your on edge its the last one

Step-by-step explanation:

use the graphing calculator and input the equation and it will be fourth graph

Answer:

Option A) inferential statistics        

Step-by-step explanation:

We describe inferential statistic as:

Inferential Statistic:

Thus, the correct answer is

Option A) inferential statistics.

Answer:

Step-by-step explanation:

Answer:

The population of city is 7 million in 2015.

Step-by-step explanation:

It is given that the population of a city, P, in millions, is a function of t, the number of years since 2010.

It means, P = f(t).  

We need to explain the meaning of the statement f(5) = 7 in terms of the population of this city.

f(5) = 7 means the population is 7 millions at t=5.

t = 5 means 5 years after 2010, i.e., 2010+5 = 2015

Therefore, the population of city is 7 million in 2015.

Answer: d. Infinitely many solutions

Step-by-step explanation:

The given equation is expressed as

10-3x +10x-7 = 5x-5+2x+8

The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.

10-3x +10x-7=5x-5+2x+8

10 - 7 + 10x - 3x = 5x + 2x - 5 + 8

7x + 3 = 7x + 3

Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.

7x - 7x + 3 - 3 = 7x - 7x + 3 - 3

0 = 0

It has infinitely many solutions because as any value of x would satisfy both sides of the equation.

Answer:

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

We have to find the area under curve y = x³ from 0 to 1 as limit.

Since Area 'A' = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x[/tex]

The given function is f(x) = x³

Since [tex]x_{i}=a+\triangle x.i[/tex]

Here a = 0 and [tex]\triangle x=\frac{1-0}{n}=\frac{1}{n}[/tex]

[tex]f(x_{i})=(\frac{i}{n})^{3}[/tex]

Now A = [tex]\lim_{n \to \infty} \sum_{i=1}^{n}f(x_{i})\triangle x= \lim_{n \to \infty}\sum_{i=1}^{n}(\frac{i}{n})^{3}(\frac{1}{n})[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}\sum_{i=1}^{n}i^{3}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{n^{4}}( \frac{n(n+1)}{2})^{2}[/tex]    Since 1³ + 2³ + 3³..............n³ = [tex][\frac{n(n+1)}{2}]^{2}[/tex]

[tex]= \lim_{n \to \infty}\frac{n^{2}(n+1)^{2}}{4n^{4}}[/tex]

[tex]= \lim_{n \to \infty}\frac{1}{4}(1+\frac{1}{n})^{2}[/tex]

[tex]=\frac{1}{4}(1+0)[/tex]

[tex]=\frac{1}{4}[/tex]

Therefore, area under the curve is [tex]\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

A continuous function is one that has a set of unique solutions. a function is also said to be continuous if at every interval, there exist no sudden change in the assumed values otherwise the function will be discontinuous.

for example, the sine and cosine function are continuous over a set of real integers.

from the question, any assumed expression of x and integrating over the interval x and infinity will render the function continuous.

Assumed f(x) = cuberoot of x

Integrating and evaluating will prove that the function is continuous, as such a defined function is always a continuous function and not necessarily lipschitz.

Answer:

AB = 14 units

Step-by-step explanation:

Given:

A triangle GHJ with the following aspects:

A, B, C are midpoints of sides GH, HJ and GJ respectively.

AB = [tex]3x+8[/tex]

GJ = [tex]2x+24[/tex]

Midsegment Theorem:

The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.

Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.

[tex]\therefore AB=\frac{1}{2}\times\ GJ[/tex]

Now, plug in the values of AB and Gj and solve for 'x'.

This gives,

[tex]3x+8=\frac{1}{2}(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=\frac{4}{2}=2[/tex]

Now, the length of AB is given by plugging in 2 for 'x'.

[tex]AB=3\times2+8=6+8=14[/tex]

Therefore, the length of midsegment AB is 14 units.

Answer:

14 Units

Step-by-step explanation:

The length of midsegment AB is equal to one-half the length of side GJ. In this case, AB is given by the expression 3x + 8 and GJ is given by the expression 2x + 24.

To find the value of x, we can set the expressions for AB and GJ equal to each other and solve for x.

3x + 8 = 1/2(2x + 24)

We can simplify this equation by distributing the 1/2 to the terms inside the parentheses:

3x + 8 = x + 12

Next, we can subtract x from both sides to isolate the x term:

3x - x + 8 = 12

2x + 8 = 12

Then, we can subtract 8 from both sides:

2x = 4

Finally, we can solve for x by dividing both sides by 2:

x = 2

Now that we have the value of x, we can substitute it back into the expression for AB:

AB = 3(2) + 8

AB = 6 + 8

AB = 14

Therefore, the length of midsegment AB is 14 units.

Answer:

the machine is mixing the nuts are not  in the ratio 5:2:2:1.

Step-by-step explanation:

Given that a machine is supposed to mix peanuts, hazelnuts, cashews, and pecans in the ratio 5:2:2:1.

A can containing 500 of these mixed nuts was found to have 269 peanuts, 112 hazelnuts, 74 cashews, and 45 pecans.

Create hypotheses as

H0: Mixture is as per the ratio 5:2:2:1

Ha: Mixture is not as per the ratio

(Two tailed chi square test)

Expected values as per ratio are calculated as 5/10 of 500 and so on

Exp        250      100    100       50        500

Obs       269      112       74       45         500

O-E          19        -12      -26       -5           0

Chi          1.343   1.286  9.135   0.556   12.318

square

df = 3

p value = 0.00637

Since p value < alpha, we reject H0

i.e. ratio is not as per the given

We perform a chi-square goodness of fit test to analyze if the machine is mixing nuts according to the ratio. We set a null and alternate hypothesis, calculate expected frequencies for each group, calculate chi-square test statistic and compare it with the critical value. If the calculated chi-square is greater than the critical value, we reject the null hypothesis.

This question asks about hypothesis testing using chi-squared tests. In this particular case, we're testing the observed distribution of mixed nuts against the expected distribution given by the ratio 5:2:2:1.

https://brainly.com/question/34171008

#SPJ11

Answer:

the answer is 9/8 or 1 and 1/8

Step-by-step explanation:

divide 3/4 by 2 to get 3/8 and then multiply 3/8 by 3 (since its tripling) to get 9/8 which can also be written as 1 1/8. Hope this helps!