Answer:
6.25
Step-by-step explanation:
2.5 *2.5=6.25
Answer:
6.25cm^2.
Step-by-step explanation:
To find the area of a square, you multiply the two sides, 2.5✖️2.5.
This gives the area of 6.25cm^2.
Hope this helped!
Have a nice day:)
Jerry was given some birthday money He puts the money in an account Every month after that he deposits the same amount of money The equation that models this situation y=50x+75 where y is the amount of money int he account and x is the number of deposits What does the y- intercept means in this situation
Answer: He was given $75 for his birthday
Step-by-step explanation:
The y - intercept represents the rate of which the money is being deposited in the account.
What is linear equation in two variable ?"An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero."
"The solution of linear equations in two variables, ax+by = c, is a particular point in the graph, such that when x-coordinate is multiplied by a and y-coordinate is multiplied by b, then the sum of these two values will be equal to c.
Basically, for linear equation in two variables, there are infinitely many solutions."
The given equation is y = 50x + 75
The y intercept represents the amount of money to be deposited in account. The rate of change of money in the account with represent to the months.
Hence, y represents money deposited in the account.
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which decimal is equivalent to 6×100+7×10+4×1/10+8×1/1,000
The answer is 670.408, because 6x100=600, 7x10=70, 4x1/10 as a decimal is 0.4, 8x1/1,000 as a decimal is 0.008. Then, you add all of those [tex]600+70+0.4+0.008=670.408[/tex].
solve the following system of equations
1/2x+1/4y=-2
-2/3x+1/2y=6
x=
y=
Answer:
x = -6
y = 4
Step-by-step explanation:
Rewriting the equations :
2x + y = -84x - 3y = -36Now, solving the two equations using substitution method, we get :
x = -6
y = 4
Answer:
y = 4
x = -6
Step-by-step explanation:
1/2 x + 1/4 y= -2 first equation
-2/3 x + 1/2 y = 6 second equation
solution:
from the first equation:
8(1/2 x + 1/4 y) = -2*8
8x*1/2 + 8y*1/4 = -16
8x/2 + 8y/4 = -16
4x + 2y = -16 third equation
from the second equation
6(-2/3 x + 1/2 y) = 6*6
6x*-2/3 + 6y*1/2 = 36
-12x/3 + 6y/2 = 36
-4x + 3y = 36 fourth equation
from the third & fourth equation:
4x + 2y = -16
-4x + 3y = 36
0 + 5y = 20
5y = 20
y = 20/5
y = 4
from the fourth equation:
-4x + 3y = 36
-4x + 3*4 = 36
-4x + 12 = 36
-4x = 36 - 12
-4x = 24
x = 24/-4
x = -6
Check:
from the first equation:
1/2 x + 1/4 y = -2
1/2 *-6 + 1/4 * 4 = -2
-3 + 1 0 -2
from the second equation:
-2/3 x + 1/2 y = 6
-2/3 * -6 + 1/2 * 4 = 6
4 + 2 = 6
Look at the image for the question.
Answer:
38 cm^2
Step-by-step explanation:
The surface area of a rectangular prism is
SA = 2(lw+wh+lh) where h is the height l is the length and w is the width
SA = 2( 3*1 + 3*4+4*1)
= 2(3+12+4)
= 2(19)
= 38 cm^2
3. Using the identity (a + b)² = (a² + 2ab + b²), evaluate 122²
.....
plz it's request to do answer fast and I will make him or her brainlist
[tex]\\ \sf\longmapsto 122^2[/tex]
[tex]\\ \sf\longmapsto (100+22)^2[/tex]
[tex]\\ \sf\longmapsto 100^2+2(100)(22)+22^2[/tex]
[tex]\\ \sf\longmapsto 10000+4400+484[/tex]
[tex]\\ \sf\longmapsto 14400+484[/tex]
[tex]\\ \sf\longmapsto 14884[/tex]
112²
Using Identity(a + b)² = (a² + 2ab + b²)
Solution⇛122²
⇛(100 + 22)²
⇛(100)² + 2 × 100 × 22 + (22)²
⇛10000 + 4400 + 484
⇛14400 + 484
⇛14884
Roll a dice six times. Find the probability that :
a . The back of the dot appears exactly 4 times ;
Answer:
2/3???
.................
Answer:
0.804% to 3 dec places.
Step-by-step explanation:
If the first 4 throws are a dot and the next 2 are not:
Probability = (1/6)^4 * (5/6)^2
= 25/46656
There are 6C4 ways for this to happen
6C4 = (6*5*4*3)/ (4*3*2*1) = 15 ways.
So The required probability = (25*15)/46656
= 125/15552
= 0.00804
= 0.804%
What is the answer to 11.24 divided by 9
Answer:
1.24
Step-by-step explanation:
oahsofhasdf0as0dfadera
Find the vector and parametric equations for the line through the point P(0, 0, 5) and orthogonal to the plane −1x+3y−3z=1. Vector Form: r
Answer:
Note that orthogonal to the plane means perpendicular to the plane.
Step-by-step explanation:
-1x+3y-3z=1 can also be written as -1x+3y-3z=0
The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).
Let us find a point on this line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively
Therefore, the vector equation is given as:
-1(x-0) + 3(y-0) + -3(z-5) = 0
-x + 3y + (-3z+15) = 0
-x + 3y -3z + 15 = 0
Multiply through by - to get a positive x coordinate to give
x - 3y + 3z - 15 = 0
The company charges $5 per sq ft, AND has a minimum charge of 3 sq ft per order (meaning if a customer orders something SMALLER than 3 sq ft they still are charged as if they ordered 3 sq ft, never less - but if they order something larger than 3 sq ft they just pay regularly by the sq ft). What would you charge someone who orders a piece of glass 12in X 12in
Using the same sq ft charge ($5 per sq ft) and remembering the rule about when to use the minimum charge, what would you charge someone ordering a piece of glass 48in X 48in? *
Answer:
12 inches by 12 inches = 15 dollars
48 inches by 48 inches = 80 dollars
Step-by-step explanation:
12 inches = 1 ft
so 12 inch by 12 inches is 1 ft * 1 ft
1 ft* 1 ft
1 ft^2
This is smaller than 3 ft^2 so they will get charged for 3 ft^2
3 ft^2 = 3 ft^2 * $5 / ft^2 = 15 dollars
48 inches = 48/12 = 4 ft
4ft * 4 ft = 16 ft^2
16 ft^2 = 16 ft^2 * $5 / ft^2 = 80 dollars
Consider the age distribution in the United States in the year 2075 (as projected by the Census Bureau). Construct a cumulative frequency plot and describe what information the plot communicates about the distribution of ages in the future.
Answer:
The cumulative frequency plot is also attached below.
Step-by-step explanation:
The data provided is as follows:
Age Group Frequency
0 - 9 34.9
10 - 19 35.7
20 - 29 36.8
30 - 39 38.1
40 - 49 37.8
50 - 59 37.8
60 - 69 34.5
70 - 79 27.2
80 - 89 18.8
90 - 99 7.7
100 - 109 1.7
Consider the Excel output attached.
The cumulative frequency are computed in the Excel sheet.
The cumulative frequency plot is also attached below.
From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.
Jason can peel 15 potatoes in 25 minutes. Janette can peel 8 potatoes in 1/10 hour. If they start peeling at the same time how many
minutes will it take them to peel 406 potatoes?
9514 1404 393
Answer:
210 minutes
Step-by-step explanation:
Jason's rate of peeling is ...
(15 potatoes)/(25 minutes) = 15/25 potatoes/minute = 3/5 potatoes/minute
Janette's rate of peeing potatoes is ...
(8 potatoes)/(6 minutes) = 4/3 potatoes/minute
Their combined rate is ...
(3/5 +4/3) = (9 +20)/15 = 29/15 . . . . potatotes/minute
Then the time required for 406 potatoes is ...
(406 potatoes)/(29/15 potatoes/minute) = (406×15/29) minutes
= 210 minutes
Given the formula A = 5h (B + b); solve for B.
2
Answer:
B = A/5h - b; You could use
B = (A - 5hb)/5h This just puts everything over a common denominator.
Step-by-step explanation:
A = 5h (B + b) Divide both sides by 5h
A/5h = B + b Subtract b from both sides.
A/5h - b = B
Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41
Answer:
[tex]a\cdot b[/tex] = 1
Step-by-step explanation:
Given that,
Vector [tex]a=5i+7j[/tex]
Vector [tex]b=-4i+3j[/tex]
We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]
We know that,
[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]
So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]
So, the value of [tex]a\cdot b[/tex] is 1.
Answer:
1
Step-by-step explanation:
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
F = 585844 N
Step-by-step explanation:
Given that:
A semicircular plate with radius 7 m is submerged vertically in water so that the top is 3 m above the surface.
The objective of this question is to express the hydrostatic force against one side of the plate as an integral and evaluate it.
To start with the equation of a circle: a² + b² = r²
The equation of circle with radius r = 7 can be expressed as:
a² + b² = 7²
a² + b² = 49
b² = 49 - a²
b = [tex]\sqrt{49 -a}[/tex]
NOW;
The integral of the hydrostatic force with a semicircular plate with radius 7 m and the top is 3 m above the surface can be calculated as follows:
[tex]\mathtt{F = 2 \rho g \int \limits^7_3 (a -3) \sqrt{49 -y^2} \ \ da}[/tex]
[tex]\mathtt{F = 2 \rho g \begin {pmatrix}\dfrac{\sqrt{49 -a^2} \ (2a^2-9a - 98)-(441 \times sin^{-1} (\dfrac{a}{3})) }{6} \end{pmatrix}}[/tex]
where;
density of water is 1000 kg/m3
and acceleration due to gravity is 9.8 m/s
Solving the integral; we have:
F = 2 × 1000 kg/m³ × 9.8 m/s × (29.89)
F = 585844 N
-8=8(-3+a) plz help me and show work simply
Answer:
[tex] - 8 = 8( - 3 + a) \\ - 8 = - 24 + 8a \\ 8a = 16 \\ a = 2[/tex]
Answer:
2
Step-by-step explanation:
-8 = 8a - 24
16 = 8a
a =2
I hope this helps! :)Determine the maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8%.
The maturity value of a 45-day note for $1,250 dated May 23 and bearing interest 8% is $1,262.5
Using this formula
Maturity value=Principal amount+ Interest
Let plug in the formula
Maturity value=$1,250+($1,250*8%*45 days/360 days)
Maturity value=$1,250+$12.5
Maturity value=$1,262.5
Inconclusion the maturity value is $1,262.5
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* 2. Use digits and other symbols to write "One hundred one thousand is
greater than one thousand, one hundred."
Answer:
101,000>1,100
Step-by-step explanation:
101,000>1,100
Answer:
101,000>1,100
Step-by-step explanation:
give 12 consecutive integers, in how many ways can three of these integers be selected to give a sum which divides by 4?
Answer:
55 waysStep-by-step explanation:
Out of 12 consecutive integers:
3 - divide by 4, so the remainder is 03- give remainder of 13- give remainder of 23 - give remainder of 3Sum of 3 integers will be divisible by 4 if the remainders are:
0 - 0 - 0 ⇒ 1 combination0 - 1 - 3 ⇒ 3*3 = 9 combinations0 - 3 - 1 ⇒ 3*3 = 9 combinations1 - 1 - 2 ⇒ 2*3 = 6 combinations1 - 2 - 1 ⇒ 2*3 = 6 combinations2 - 1 - 1 ⇒ 2*3 = 6 combinations3 - 0 - 1 ⇒ 3*3 = 9 combinations3 - 1 - 0 ⇒ 3*3 = 9 combinationsSo total number of combinations is:
1 + 4*9 + 3*6 = 55The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of and use a class width of . Does the frequency distribution appear to be roughly a normal distribution?
Answer:
The frequency distribution does not appear to be normal.
Step-by-step explanation:
The data provided is as follows:
S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}
It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.
The frequency distribution table is as follows:
Class Interval Count
0.00 - 0.19 21
0.20 - 0.39 6
0.40 - 0.59 2
0.60 - 0.79 0
0.80 - 0.99 0
1.00 - 1 . 19 0
1.20 - 1. 39 1
The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.
Thus, the frequency distribution does not appear to be normal.
Maria operates a taco truck in her neighborhood. She has created a graph based on her business performance in the previous year. The price she currently sells tacos for is $2.30. Which two statements correctly interpret this graph? Revenue and Cost Functions 1)Maria’s business is incurring losses. 2)Maria’s costs are rising over time. 3)Maria is running a profitable business. 4)Maria’s total revenue exceeds her total profit. 5)Maria’s total profit exceeds her total revenue.
Answer:
3)Maria is running a profitable business.
4)Maria’s total revenue exceeds her total profit.
Step-by-step explanation:
The graph shows variation of revenue and cost with respect to price of product and not with respect to time .
The price of the product is 2.30 . From this graph , we see that at this price revenue exceeds total cost . So maria is running a profitable business .
Total profit can not exceed total revenue as
Total revenue - total cost = total profit .
So total profit will always be less than total revenue .
Solve systems of equations 15 points NOT CLICKBAIT!!! -6y+11y= -36 -4y+7x= -24
Answer:
x = -264/35
y = -36/5
Step-by-step explanation:
-6y + 11y = -36
-4y + 7x = -24
Solve for y in the first equation.
-6y + 11y = -36
Combine like terms.
5y = -36
Divide both sides by 5.
y = -36/5
Plug y as -36/5 in the second equation and solve for x.
-4(-36/5) + 7x = -24
Expand brackets.
144/5 + 7x = -24
Subtract 144/5 from both sides.
7x = -264/5
Divide both sides by 7.
x = -264/35
Answer: -264/35
Step-by-step explanation:
i did my work on a calculator
determine if the following side lengths create an acute,obtuse,or right triangle. a) 20, 21, 28 b) 3, 6, 4 c) 8, 12, 15
Answer:
a) 20, 21, 28 : acute
b) 3, 6, 4 : obtuse
c) 8, 12, 15 : obtuse
Step-by-step explanation:
You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:
If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.
If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.
If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.
Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):
a) 20, 21, 28
Insert numbers, using 28 as c:
[tex]20^2+21^2[/tex]_[tex]28^2[/tex]
Simplify exponents ([tex]x^2=x*x[/tex]):
[tex]400+441[/tex]_[tex]784[/tex]
Simplify addition:
[tex]841[/tex]_[tex]784[/tex]
Identify relationship:
[tex]841>784[/tex]
The sum of the squares of a and b is greater than the square of c. This triangle is acute.
b) 3, 6, 4
Insert numbers, using 6 as c:
[tex]3^2+4^2[/tex]_[tex]6^2[/tex]
Simplify exponents:
[tex]9+16[/tex]_[tex]36[/tex]
Simplify addition:
[tex]25[/tex]_[tex]36[/tex]
Identify relationship:
[tex]25<36[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
c) 8, 12, 15
Insert numbers, using 15 as c:
[tex]8^2+12^2[/tex]_[tex]15^2[/tex]
Simplify exponents:
[tex]64+144[/tex]_[tex]225[/tex]
Simplify addition:
[tex]208[/tex]_[tex]225[/tex]
Identify relationship:
[tex]208<225[/tex]
The sum of the squares of a and b is less than the square of c. This triangle is obtuse.
:Done.
The correct values are,
a) 20, 21, 28 = Acute
b) 3, 6, 4 = Obtuse
c) 8, 12, 15 = Obtuse
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides are,
a) 20, 21, 28
b) 3, 6, 4
c) 8, 12, 15
Now,
We know that;
If three sides of a triangle are a, b and c.
Then, We get;
If a² + b² = c², then the triangle is right triangle.
If a² + b² > c², then the triangle is acute triangle.
If a² + b² < c², then the triangle is obtuse triangle.
Here, For option a;
⇒ 20, 21, 28
Clearly, a² + b² = 20² + 21²
= 400 + 441
= 841
And, c² = 28² = 784
Thus, a² + b² > c²
Hence, It shows the acute angle.
For option b;
⇒ 3, 6, 4
Clearly, a² + b² = 3² + 4²
= 9 + 16
= 25
And, c² = 6² = 36
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
For option c;
⇒ 8, 12, 15
Clearly, a² + b² = 8² + 12²
= 64 + 144
= 208
And, c² = 15² = 225
Thus, a² + b² < c²
Hence, It shows the obtuse angle.
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If K = (AB)/(A+B) , then B = ?
(a) (A)/(1−A)
(b) (AK)/(A−K)
(c) (AK)/(K−A)
(d) (A+K)/(A)
(e) (A−K)/(AK)
Lets do
[tex]\\ \sf\longmapsto K=\dfrac{AB}{A+B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{A+B}{AB}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{K}=\dfrac{1}{A}+\dfrac{1}{B}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{1}{K}-\dfrac{1}{A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{B}=\dfrac{K-A}{AK}[/tex]
[tex]\\ \sf\longmapsto B=\dfrac{AK}{K-A}[/tex]
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
find the alternateof AHG
Answer:
angle HGD
Step-by-step explanation:
alternate angles are in Z position
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
Does anyone have the solution to this
Step-by-step explanation:
There is 1 root at x = 1, where the function crosses the x-axis.
There are 2 roots at x = -2, where the function touches the x-axis but does not cross.
So there are 3 real roots total.
The function is:
y = (x − 1) (x − (-2))²
y = (x − 1) (x + 2)²
Drag each factor to the correct location on the image.
If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0,
P(x).
Answer:
(x-7) and (x+12) are the factors and the rest are non factors...
What is meant by the term "90% confident" when constructing a confidence interval for a mean? Group of answer choices
Answer:
The question is not complete, below is the complete question:
What is meant by the term 90% confident? when constructing a confidence interval for a mean?
a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.
Answer:
The correct answer is:
If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean. (c)
Step-by-step explanation:
a 90% confidence level means that if repeated samples were taken, 9 out of 10 times, the confidence intervals of the sample chosen will be close to the mean (true value), which is a true representation of the population parameter. when using confidence intervals, there are always margins of allowable accuracy, and this is suggested by using standard diviations snd variances.
I attached a simple document to this answer that will give you more insight into confidence intervals used in statistics.
A schoolteacher would like to know whether or not toothpaste brands are used differentially in her classroom (in other words, is one brand preferred over the others?). She asks her students to report which of three brands they use: Crest, Colgate, or Aquafresh. Below are the numbers of students who use each type of toothpaste (notice there are 45 students total in her class). Test her hypothesis using an alpha level of .05.
Crest Colgate Aquafresh
24 13 8
a. What test is appropriate for this analysis?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the test statistic:
f. Make a decision:
Answer:
Step-by-step explanation:
a. What test is appropriate for this analysis?
A Chi-square test of independence is appropriate for this analysis because it is used to compare two variables or testing relationship on categorical variables.
b. State the null hypothesis:
The null hypothesis is the default hypothesis
[tex]\mathtt{H_o:}[/tex] There is no particular preference for any brand of toothpaste among students.
c. State the alternative hypothesis:
The alternative hypothesis is the research hypothesis which comes in place to challenge the validity of the null hypothesis.
[tex]\mathtt{H_a:}[/tex] There is particular preference for brands of toothpaste among students.
d. Find the critical value:
degree of freedom = n-1
degree of freedom = 3 - 1
degree of freedom = 2
At the level of significance ∝ = 0.05
The confidence interval = 0.95 and degree of freedom = 2, the critical value from the chi-square distribution table = 5.991
e. Calculate the test statistic:
Using the chi square test statistics; we have the following:
Crest Colgate Aquafresh Total
24 13 8 45
Since we have three brands. Then, for each brand, the expected value
= Total /3
= 45/3
=15
Thus:
Chi -square [tex]\mathtt{X^2 = \dfrac{(observed \ value - expected \ value)^2}{expected \ value}}[/tex]
[tex]\mathtt{X^2 = \dfrac{(24 - 15)^2}{15} + \dfrac{(13 - 15)^2}{15} + \dfrac{(8 - 15)^2}{15} }[/tex]
[tex]\mathtt{X^2 = \dfrac{81}{15} + \dfrac{4}{15} + \dfrac{49}{15} }[/tex]
[tex]\mathtt{X^2 = \dfrac{81+4+49}{15}}[/tex]
[tex]\mathtt{X^2 = \dfrac{134}{15}}[/tex]
[tex]\mathtt{X^2 =8.93 }[/tex]
f. Make a decision:
Since the chi-square value is greater than the critical value , we reject the null hypothesis and conclude that the students have particular preference for brands of toothpaste.