The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3 8 of the items barbecued are veggie burgers, and 1 3 of the items barbecued are corn cobs, what fraction of barbecued items are mushroom caps?

Answers

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The Freeman family barbecued veggie burgers, corn cobs, and mushroom caps. 3/8 of the items barbecued are veggie burgers, and 1/3 of the items barbecued are corn cobs.

Let the total number of berbecued items be x. Therefore:

x = barbecued veggie burgers + barbecued corn cobs + barbecued mushroom caps

Barbecued veggie burgers = (3/8)x, barbecued corn cobs = (1/3)x, Let barbecued mushroom caps be y

Substituting:

x = (3/8)x + (1/3)x + y

Multiply through by 24

24x = 9x + 8x + 24y

24x = 17x + 24y

24y = 24x - 17x

24y = 7x

y = (7/24)x

barbecued mushroom caps = (7/24) of items

7/24 of the items barbecued are mushroom caps

Answer 2

Using fractions, it is found that the fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].

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

The total proportion of all products is 100% = 1.The fraction corresponding to veggie burgers is [tex]\frac{3}{8}[/tex].The fraction corresponding to corn cobs is [tex]\frac{1}{3}[/tex].The fraction corresponding to mushroom caps is x.

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

Thus:

[tex]\frac{3}{8} + \frac{1}{3} + x = 1[/tex]

Solving for x, we find the fraction of mushroom caps.The least common multiple of 3 and 8 is 24.

Then:

[tex]\frac{3\times3 + 8\times1 + 24x}{24} = 1[/tex]

[tex]\frac{17 + 24x}{24} = 1[/tex]

[tex]17 + 24x = 24[/tex]

[tex]24x = 7[/tex]

[tex]x = \frac{7}{24}[/tex]

The fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].

A similar problem is given at https://brainly.com/question/4231000


Related Questions

A car enters a turnpike 22 miles north of a town. The car teavels north at an average speed of 64 miles per hour. How far is the car from the town after 4 hours? Explain how you can use linear function to solve this problem. Then, solve the problem.​

Answers

Answer:

distance traveled can be modeled by a linear functionthe car is 260 miles north of town

Step-by-step explanation:

a) When the speed is constant, the distance traveled is proportional to the travel time, a linear relationship. The distance traveled can be added to the initial distance to obtain the total distance (from town). This relation is a linear function. It can be modeled by the equation ...

  d(t) = 4 + 64t . . . where t is travel time in hours, d(t) is the distance in miles

b) After 4 hours, the distance north of town is ...

  d(4) = 4 +64(4) = 260

The car is 260 miles from the town after 4 hours.

Answer: Distance is a function of time. The constant rate of change is 64. Write the equation y = 64x + 22. Substitute 4 in for x to get 278 miles.

Step-by-step explanation:

y=mx+6 , solve for m

Answers

Answer:

m = [tex]\frac{y-6}{x}[/tex]

Step-by-step explanation:

Given

y = mx + 6 ( subtract 6 from both sides )

y - 6 = mx ( divide both sides by x )

[tex]\frac{y-6}{x}[/tex] = m

Use the graph showing Debra's account balance to answer the question that follows. ^

About how long will it take for Debra's account balance to equal $60?

A - 6 months

B - 6 years

C - 3 months

D - 3 years

Answers

Answer: 2 years

Step-by-step explanation:

In the given graph, we have

Account Balance ($) on y-axis

Time (years) on x-axis.

To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.

Then from there we drop a line to x-axis.

We get x=2.

That is it will take 2 years to get $60 balance in Debra's account.

So the correct answer is 2 years.

plzzzzzzzzz someone help

Answers

Answer: 4

Step-by-step explanation:

Since this inequality gives us a list, we want to choose the greatest number shown because x≤?. Because x has to be less than or equal to a number, it makes the most sense to put the greatest number there. In the list, 4 is the greatest number.

1. What happened when you had a negative plus a negative, (-a) + (-b)?
I
2. What happened when you had a positive plus a negative, a + (-b)?
***Is this the same as a positive minus a positive, a - b?
3. What happened when you had a positive minus a negative, a - (-b)?
4. What happened when you had a negative minus a negative, (-a) - (-b)?​

Answers

Answer:

See Explanation

Step-by-step explanation:

1.

What happens when negative adds to negative; e.g (-a) + (-b)

First, we need to simplify the expression

[tex](-a) + (-b)[/tex]

Open the brackets

[tex]-a - b[/tex]

Factorize

[tex]-(a+b)[/tex]

So, what happens is that: the two numbers are added together and the result is negated;

E.g.

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

2.

What happens when positive is added to negative; e.g. a + (-b)

First, we need to simplify the expression

[tex]a + (-b)[/tex]

Open the brackets

[tex]a - b[/tex]

So, what happens is that: the negative number is subtracted from the positive number

And Yes; [tex]a + (-b)[/tex] is the same as [tex]a - b[/tex] (As shown above)

E.g.

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

3.

What happens when to positive minus a negative; e.g. a - (-b)

First, we need to simplify the expression

[tex]a - (-b)[/tex]

Open the brackets

[tex]a + b[/tex]

So, what happens is that; the two numbers are added together.

E.g.

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

4.

What happens when negative minus a negative; e.g. (-a) - (-b)

First, we need to simplify the expression

[tex](-a) - (-b)[/tex]

Open the brackets

[tex]-a + b[/tex]

Reorder

[tex]b - a[/tex]

So, what happens is that; the first number is subtracted from the second.

E.g.

[tex](-5) - (-3) = 3-5 = -2[/tex]

Beginning 177 miles directly north of the city of Morristown, a van travels due west. If the van is travelling at a speed of 31 miles per hour, determine the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles. (Do not include units in your answer, and round to the nearest hundredth.)

Answers

Answer:

Step-by-step explanation:

From the given information;

let the hypotenuse be a , the opposite which is the north direction be b and the west direction which is the adjacent be c

SO, using the Pythagoras theorem

a² = c² + 177²

By taking the differentiation of both sides with respect to time t , we have

[tex]2a \dfrac{da}{dt} = 2c \dfrac{dc}{dt} + 0[/tex]

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

At c = 71 miles,[tex]a = \sqrt{ (71)^2 +(177)^2}[/tex]

[tex]a = \sqrt{ 5041+31329}[/tex]

[tex]a = \sqrt{ 36370}[/tex]

a = 190.71

SImilarly, [tex]\dfrac{dc}{dt} = \ 31 miles \ / hr[/tex]

Thus, the rate of change of the distance between Morristown and the van when the van has been travelling for 71 miles can be calculate as:

[tex]\dfrac{da}{dt} = \dfrac{c}{a} \dfrac{dc}{dt}[/tex]

[tex]\dfrac{da}{dt} = \dfrac{71}{190.71} \times 31[/tex]

[tex]\dfrac{da}{dt} = 0.37229 \times 31[/tex]

[tex]\mathbf{\dfrac{da}{dt} = 11.54}[/tex]  to the nearest hundredth.

solve the following equations for x (3x-6)=18

Answers

Answer:

x = 8

Step-by-step explanation:

Hello!

What we do to one side of the equation we have to do to the other side.

3x - 6 = 18

Add 6 to both sides

3x = 24

Divide both sides by 3

x = 8

The answer is 8

Hope this helps!

Answer:

x=8

Step-by-step explanation:

(3x-6)=18

Add 6 to each side

(3x-6+6)=18+6

3x= 24

Divide by 3

3x/3 = 24/3

x = 8

Which statement best describes a sequence? a.All sequences have a common difference. b.A sequence is always infinite. c.A sequence is an ordered list. d.A sequence is always arithmetic or geometric.

Answers

Answer:

C

Step-by-step explanation:

A sequence is defined as a list of numbers or objects in a special order.

They may be arithmetic or geometric or neither.

For example

0, 1, 4, 9, 16, 25, ..... ← is the sequence of square numbers.

Note it is neither arithmetic or geometric.

In a triangle ABC,AB=9 and BC =12 which of the following Cannot be the length of AC.

Answers

Step-by-step explanation:

mark it as the brainliest

Answer:

i need help with this too

Step-by-step explanation:

Which is a perfect square? 6 Superscript 1 6 squared 6 cubed 6 Superscript 5 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple

Answers

Answer:

Step-by-step explanation:

Hello, by definition a perfect square can be written as [tex]a^2[/tex] where a in a positive integer.

So, to answer the first question, [tex]6^2[/tex] is a perfect square.

(a,b,c) is a Pythagorean triple means the following

[tex]a^2+b^2=c^2[/tex]

Here, it means that

[tex]x^2=20^2+21^2=841=29^2 \ \ \ so\\\\x=29[/tex]

Thank you.

Answer:

Its B

Step-by-step explanation:

Should I read Fruit's Basket? I need something to keep me busy.

Answers

Answer: Yes

Explanation: Yes because, sometimes you need to do stuff to get things of your head

Please answer this correctly without making mistakes

Answers

Answer:

so to get a third you divide it by 3

first convert it to fraction

so it is 26/3

so do 26/3 divided by 3

so we do keep switch flip

26/3*1/3

so answer is 26/9 or 2 8/9

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]

Step-by-step explanation:

8 2/3 tablespoons of red chilies is required for a recipe.

One-third of the original recipe would mean that the quantity of red chilies will be also one-third.

8 2/3 × 1/3

Convert to an improper fraction.

26/3 × 1/3

Multiply the fractions.

26/(3 × 3) = 26/9

Convert to a mixed fraction.

26/9 = 2 8/9

if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!

Answers

Answer:

5

----------

( n+1)(n+2)

Step-by-step explanation:

5

----------

n ( n+1)

Replace n with n+1

5

----------

(n+1) ( n+1+1)

5

----------

( n+1)(n+2)

Answer: Choice A

We replace every 'n' with n+1 and simplify

[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]

2000 2yrs at 2% How much interest is owed

Answers

Answer:

Rs. 80 is owed.

Step-by-step explanation:

Principle (P) = 2000

Time (T) = 2 years

Rate (R) = 2%

Interest (I) = ?

Here,

I = (P×T×R) / 100

= (2000×2×2) / 100

= (8000) / 100

= Rs. 80

Answer:

P= 2000

T= 2

R=2÷100

I = PTR

= 2000×2×2÷100

2÷100=0.02

2000×2×0.02= 80

So i is 80

i need help will rate you branliest

Answers

Answer:

d. The graph of g(x) is the graph of f(x) reflected over the x-axis.

Step-by-step explanation:

The standard transformation

g(x) = - f(x)

is a simple reflection about the x-axis.

So the answer is the last option.

Answer:

Last one

Step-by-step explanation:

The function we are interested in are g(x) and f(x).

● g(x)= (-1/x)

● f(x)= 1/x

Notice what happens when we input the same values in both functions.

● g(1) = -1/1 = -1

● f(x) = 1/1 = 1

●g(2) = -1/2 = -0.5

● f(2) = 1/2 = 0.5

Notice that we get opposite values by imputing the same number.

Wich means:

●f(x) = -g(x)

So the graph of g(x) is the graph of f(x) reflected over the x axis.

Compute the least-squares regression line for the given data set. Use a TI-84 calculator. Round final answers to four decimal places, as needed.
x 5 7 6 2 1
y 4 3 2 5 1
Regression line equation: ŷ = _______ + _______ x.

Answers

Answer:

   Y = 2.843+ 0.037 X

Step-by-step explanation:

Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are

∑Y = na +b ∑X

∑XY = a∑X + b∑X²

We now calculate ∑X, ∑Y , ∑X², and ∑XY

X                Y                XY              X²

5                  4                 20            25

7                  3              21                49

6                  2                 12            36

2                  5                 10             4

1                    1                1                 1          

21                 15                 64           115  

Thus the normal equation becomes

                                                 5a + 21b =15

                                                21a +115b = 64

Solving these two equations simultaneously we get

                                                105 a + 441b = 315

                                                105a + 575b = 320

                                                            134b= 5

b= 0.037 , a= 2.843

Hence the equation for the required straight line is

                    Y = 2.843+ 0.037 X

Given that the sum of squares for error is 60 and the sum of squares for regression is 140, then the coefficient of determination is:

Answers

Answer:

0.7

Step-by-step explanation:

The coefficient of determination which is also known as the R² value is expressed as shown;

[tex]R^{2} = \frac{sum\ of \ squares \ of \ regression}{sum\ of \ squares \ of total}[/tex]

Sum of square of total (SST)= sum of square of error (SSE )+ sum of square of regression (SSR)

Given SSE = 60 and SSR = 140

SST = 60 + 140

SST = 200

Since R² = SSR/SST

R² = 140/200

R² = 0.7

Hence, the coefficient of determination is 0.7. Note that the coefficient of determination always lies between 0 and 1.

The coefficient of determination of the dataset is 0.7

The given parameters are:

[tex]SSE = 60[/tex] --- sum of squared error

[tex]SSR = 140[/tex] --- sum of squared regression

Start by calculating the sum of squared total (SST)

This is calculated using

[tex]SST =SSE + SSR[/tex]

So, we have:

[tex]SST =60 +140[/tex]

[tex]SST =200[/tex]

The coefficient of determination (R^2) is then calculated using

[tex]R^2 = \frac{SSR}{SST}[/tex]

So, we have:

[tex]R^2 = \frac{140}{200}[/tex]

Divide

[tex]R^2 = 0.7[/tex]

Hence, the coefficient of determination is 0.7

Read more about coefficient of determination at:

https://brainly.com/question/15804563

(Algebra) HELP ME ASAP PLZ

Answers

Answer:

no solution because the answer will be p=2

10 - [ 8p + 3 ] = 9 [ 2p - 5 ]

10 - 8p - 3 = [ 2p - 5 ]

-8p + 10 - 3 = [ 2p - 5 ]

p = 2 We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, the following 2 terms will change sign:

8p, 3

Step-by-step explanation:

Find the sum of the even numbers between 199 to 1999​

Answers

[tex]S_n=\dfrac{n(a_1+a_n)}{2}\\a_1=200\\a_n=1998\\n=?\\\\a_n=a_1+(n-1)d\\d=2\\1998=200+(n-1)\cdot2\\2n-2=1798\\2n=1800\\n=900\\\\S_{900}=\dfrac{900\cdot(200+1998)}{2}=450\cdot 2198=989100[/tex]

The Sum is 989100.

what is sum of Even numbers?

The sum of even numbers formula is determined by using the formula to find the arithmetic progression. The sum of even numbers goes on until infinity. The sum of even numbers formula can also be evaluated using the sum of natural numbers formula. We need to obtain the formula for 2 + 4+ 6+ 8+ 10 +...... 2n.

The sum of even numbers = 2(1 + 2+ 3+ .....n). This implies 2(sum of n natural numbers) = 2[n(n+1)]/2 = n(n+1)

Given:

a1 = 200

an= 1998

So, using formula

S= n(a1 + an)/2

now,

d=2

an= a1+(n-1)d

1998= 200 + (n-1) 2

1998-200= (n-1)2

1798/2=n-1

n= 900

S900= 900( 200 + 1998)/2

        =450*2198

       = 989100

Hence, the sum is 989100.

Learn more about this concept here:

https://brainly.com/question/18837188

#SPJ2

Find the length of a square with a perimeter of 48cmeter

Answers

Answer:

12

Step-by-step explanation:

Perimeter of a square:

4(L)

L = Length

=> 4(L) = 48

=> 4L = 48

=> 4L/4 = 48/4

=> L = 12

The length of the square is 12 cm.

Answer:

12

Step-by-step explanation:

Since the lengths of the sides of a square are equal, divide the perimeter by 4

PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?

Answers

Answer:

8)  1.962 miles

9)  (-2, -1.5)

10) 0.515 miles

Step-by-step explanation:

√(-9 - 5)² + (1 - -4)² = 14.866

14.866 x .132 = 1.962

(-9+5)/2, (1 + -4)/2

-4/2, -3/2

-2, -3/2

√(-2 - 1)² + (-3/2 - -4)² = 3.905

3.905 x .132 = 0.515 miles

4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25

Answers

Answer:

a) Means: 24 and 2; Extremes: 4 and 12

b) Means: 6 and 16; Extremes: 24 and 4

c) Means: 8 and 8; Extremes: 4 and 16

d) Means: 50 and 3; Extremes: 6 and 25

Step-by-step explanation:

The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:

a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.

The Means are the values that appear in the middle of the one line expression, that is: b and c.

Recall as well that the proportion can also be written with fractions:

a : b = c : d  is the same as:   a / b = c / d

so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.

Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx

Answers

Answer:

To find the x-intercept, substitute in  0  for y and solve for x.

To find the y-intercept, substitute in  0 for x  and solve for y.

x-intercept(s):  

(−6,0)

y-intercept(s):  

(0,3)

So I would say -6 and 0 and 2 are in domain

Answer:

-6, 0 ,2 are in the domain

Step-by-step explanation:

The domain is what values that x can take

There are no restrictions on the values that x can take

All real numbers are in the domain

-6, 0 ,2 are in the domain

2
Select the correct answer.
which number is the additive Inverse of -10 ?
O A 10 1
Ос. о
OD. -41
Reset
Next

Answers

Answer:

[tex]\boxed{\sf 10}[/tex]

Step-by-step explanation:

The additive number of any number is the number when added to the number gives a result of zero.

So, if we add 10 to -10 we get a result of zero.

=> -10+10

=> Zero

Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l

Answers

Answer:

B. j(kl)

Step-by-step explanation:

(jk)l

We can change the order we multiply and still get the same result

j(kl)

Answer:

Step-by-step explanation:

its B i did it

Cancel the common factor of the numerator and the denominator and write specified expression

Answers

Step-by-step explanation:

Hello,

I hope you mean to cancel the common factor that exists in numerator and denominator,right.

so, Let's look for the common factor,

here, the expression is,

=4(x-2)/ (x+5)(x-2)

so, here we find the common factor is (x-2)

now, we have to cancel it. And after cancelling we get,

=4/(x+5)

Note:{ we cancel the common factor if the common factors are in multiply form.}

Hope it helps

p-value problem. Suppose the director of manufacturing at a clothing factory needs to determine wheteher a new machine is producing a particulcar type of cloth according to the manufacturer s specification which indicate that the cloth should have mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds. THe p value for this hypothesis testing scenario is

Answers

Answer:

The P-Value is  0.07186  

Step-by-step explanation:

GIven that :

Mean = 70

standard deviation = 3.5

sample size n = 49

sample mean = 69.1

The null hypothesis and the alternative hypothesis can be computed as follows;

[tex]H_o : \mu = 70 \\ \\ H_1 : \mu \neq 70[/tex]

The standard z score formula can be expressed as follows;

[tex]\mathtt{z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]

[tex]\mathtt{z = \dfrac{69.1 - 70}{\dfrac{3.5}{\sqrt{49}}}}[/tex]

[tex]\mathtt{z = \dfrac{-0.9}{\dfrac{3.5}{7}}}[/tex]

z = -1.8

Since the test is two tailed and using the Level of significance = 0.05

P- value = 2 × P( Z< - 1.8)

From normal tables

P- value = 2 × (0.03593)

The P-Value is  0.07186  

Two cards are dealt at random from a standard 52 card deck (without replacement). (Ace, King, Queen, Jack are face cards.)

Required:
a. Find the probability that the first card is a face card and the second is NOT a face card.
b. Find the probability that they are both face cards.
c. Find the probability that the second is a face card given the first is NOT a face card.

Answers

Answer:

The answer is below

Step-by-step explanation:

There are 52 cards in a deck, 12 of these cards are face cards (4 kings, 4 queens and 4 jacks) and 40 are not face cards

a. Find the probability that the first card is a face card and the second is NOT a face card.

There are 12 first card, the probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51, the probability of the second card not being a face card = 40/51. Therefore:

The probability that the first card is a face card and the second is NOT a face card = P(first is face card) × P(second is not face card)  = 12/52 × 40/51 = 40/221

b) Find the probability that they are both face cards.

The probability that the first card is a face card is 12/52.

Since there are no replacement, after picking 1 face card the number of cards remaining is 51 and the number of face card remaining is 11, the probability of the second card is a face card = 11/51. Therefore:

The probability that they are both face cards = P(first is face card) × P(second is face card)  = 12/52 × 11/51 = 11/221

c) Find the probability that the second is a face card given the first is NOT a face card.

The probability that the first card is not a face card = 40/52

Since there are no replacement, after picking the first card the number of cards remaining is, the probability of the second card is a face card = 12/51. Therefore:

The probability that the second is a face card given the first is NOT a face card = P(first is not a face card) × P(second is face card)  = 40/52 × 12/51 = 40/221

One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?

Answers

Answer:

The [tex]L_{ACL}[/tex] of the player is  [tex]L_{ACL} = 56.82 \ mm[/tex]

Step-by-step explanation:

From the question we are told that

       The relationship between the length [tex]L_{ACL}[/tex] to the height is  

            [tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]

       The height of the basketball player  is  [tex]h = 2.13 \ m = 2130 \ mm[/tex]

Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is

          [tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]

         [tex]L_{ACL} = 56.82 \ mm[/tex]

       

A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 83 units of a small appliance with a standard deviation of 5 units. During the same point in time last year, a random sample of 49 stores had mean sales of 78 units with standard deviation 3 units.Required:Construct a 95 percent confidence interval for the difference in population means.

Answers

Answer:

The 95% confidence interval for the difference in population means is (−26.325175  , 36.325175)

Step-by-step explanation:

Given that :

sample size n₁ = 36

sample mean [tex]\over\ x[/tex]₁ = 83

standard deviation [tex]\sigma[/tex]₁ = 5

sample size n₂ = 49

sample mean [tex]\over\ x[/tex]₂= 78

standard deviation [tex]\sigma[/tex]₂ = 3

The objective is to construct a 95% confidence interval for the difference in the population means

Let the population means be [tex]\mu_1[/tex]  and  [tex]\mu_2[/tex]

The 95% confidence interval or the difference in population means can be calculated by using the formula;

[tex](\overline{x_1} - \overline{x_2}) \pm t_{\alpha /2} \ \times s_{p}[/tex]

where;

the pooled standard deviation  [tex]s_{p} = \dfrac{(n_1-1)s_1^2+(n_2-1)s^2_2}{n_1+n_2-2}[/tex]

[tex]s_{p} = \dfrac{(36-1)5^2+(49-1)3^2}{36+49-2}[/tex]

[tex]s_{p} = \dfrac{(35)25+(48)9}{83}[/tex]

[tex]s_{p} = \dfrac{875+432}{83}[/tex]

[tex]s_{p} = \dfrac{1307}{83}[/tex]

[tex]s_p[/tex] = 15.75

degree of freedom = [tex]n_1 +n_2 -2[/tex]

degree of freedom = 36+49 -2

degree of freedom = 85 - 2

degree of freedom = 83

The Critical t- value 95% CI at df = 83 is

t  critical = T.INV.2T(0.05, 83) = 1.9889

Therefore, for the population mean , we have:

= (83 - 78) ± (1.9889 × 15.75)

= 5 ± 31.325175

= 5  - 31.325175 , 5 + 31.325175

= (−26.325175  , 36.325175)

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