Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
a bank teller has 340 one hundred dollar bills. how much money does the bank teller have?
Answer:
$34,000
Step-by-step explanation:
Since a one hundred dollar bill is equal to 100, we simply multiply 340 and 100 together:
340(100) = 34000
Find the sample size needed to estimate the percentage of Democrats among registered voters in Texas. Use a 0.01 margin of error, and use a confidence level of 96% and assume LaTeX: \hat{p}
p
^
=0.28.
Answer:
Step-by-step explanation:
Hello!
You have to determine the sample size to take to estimate the population proportion of Democrats among registered voters in Texas for a 96% interval with a margin of error of 0.01 and sample proportion p'= 0.28
The interval for the population proportion is
p' ± [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
The margin of error of the interval is:
d= [tex]Z_{1-\alpha /2}[/tex]*[tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]
[tex]\frac{d}{Z_{1-\alpha /2}}= \sqrt{\frac{p'(1-p')}{n} }\\(\frac{d}{Z_{1-\alpha /2}} )^2= \frac{p'(1-p)}{n} \\n*(\frac{d}{Z_{1-\alpha /2}} )^2= p'(1-p)\\n= p'(1-p)*(\frac{Z_{1-\alpha /2}}{d} )^2\\[/tex]
[tex]Z_{1-\alpha /2}= Z_{0.98}= 2.054[/tex]
[tex]n= 0.28*(1-0.28)*(\frac{2.054}{0.01} )^2= 8505.33[/tex]
n= 8506 voters
I hope this helps!
please helpppp As soon as possible
Answer: 4 pairs
Step-by-step explanation:
121-16=105. However, 121 can be made by squaring -11 or 11. 16 can be made by squaring 4 or -4. Thus, the choices are 11,4 11,-4 -11,4 -11,-4
Two intersecting lines l and m form an angle of 56° with each other. The reflection of a point (–4, 1) along the line l followed by a reflection along line m will cause a ________ rotation. Question 18 options: A) 56° B) 112° C) 180° D) 28°
Answer:
B) 112°
Step-by-step explanation:
After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:
2·56° = 112°
_____
In the attached, lines l and m are separated by 56°, as required by the problem statement.
can someone help me with this please?!?
Answer:
The answer is 60cm^2.
hope it helps..
Hi, can someone help me on this. I'm stuck --
Answer:
a) Fx=-5N Fy=-5*sqrt(3) N b) Fx= 5*sqrt(3) N Fy=-5N
c) Fx=-5*sqrt(2) N Fy=-5*sqrt(2) N
Step-by-step explanation:
The arrow's F ( weight) component on axle x is Fx= F*sinA and on axle y is
Fy=F*cosA
a) The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(30)= -5 N Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N
b) Now the x component is co directed to axle x , and y component is opposite directed to axle y.
So x component is positive and y components is negative
So Fx = 10*sin(60)= 5*sqrt(3) N Fy= -10*cos(60)= -10*1/2= -5 N
c)The x component and y component both are opposite directed to axle x and axle y accordingly. So both components are negative.
So Fx = - 10*sin(45)= -5*sqrt(2) N
Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N
Simplify the algebraic expression: 7x2 + 6x – 9x – 6x2 + 15. A) x2 + 15x + 15 B) x2 – 3x + 15 C) 13x2 + 3x + 15 D) x4 – 3x + 15
Answer:
B) [tex]x^2-3x+15[/tex]
Step-by-step explanation:
[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]
A) [tex]x^2+15x+15[/tex]
B) [tex]x^2-3x+15[/tex]
C) [tex]13x^2 + 3x + 15[/tex]
D) [tex]x^4-3x + 15[/tex]
━━━━━━━☆☆━━━━━━━
▹ Answer
B. x² - 3x + 15
▹ Step-by-Step Explanation
7x² + 6x - 9x - 6x² + 15
Collect like terms
x² + 6x - 9x + 15
Subtract
x² - 3x + 15
Final Answer
x² - 3x + 15
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The average daily rainfall for the past week in the town of Hope Cove is normally distributed, with a mean rainfall of 2.1 inches and a standard deviation of 0.2 inches. If the distribution is normal, what percent of data lies between 1.9 inches and 2.3 inches of rainfall? a) 95% b) 99.7% c) 34% d) 68%
Answer:
D
Step-by-step explanation:
We calculate the z-score for each
Mathematically;
z-score = (x-mean)/SD
z1 = (1.9-2.1)/0.2 = -1
z2 = (2.3-2.1)/0.2 = 1
So the proportion we want to calculate is;
P(-1<x<1)
We use the standard score table for this ;
P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%
Answer:
68
Step-by-step explanation:
multiply your income by 2 to get your monthly income: $900
Answer:
monthly income=$900
the monthly income was multipled by 2
so, real income was, $900/2
=$ 450
so, $450×2=$900...
The real income is $400.
MultiplicationThe term multiplication refers to the product of two or more than two numbers.
How to find real income?Let us assume that the real income is x.
We have to multiply the real income by 2 to get the monthly income of $900.
This implies that [tex]x\times 2=\$900[/tex],
Solving the above expression, we will get
[tex]x\times 2=\$900\\x=\dfrac{900}{2} \\x=400[/tex]
So, the real income is $400.
Learn more about expression here-https://brainly.com/question/14083225
#SPJ2
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z)
Find the work done.
Answer:
Work done = 0 J
Step-by-step explanation:
work done= ∫ F. dr
= [tex]\int\limits^2_0 {x} \, dx[/tex] + [tex]\int\limits^2_2 {x} \, dx[/tex] + [tex]\int\limits^0_2 {x} \, dx[/tex] + [tex]\int\limits^0_0 {x} \, dx[/tex] + [tex]\int\limits^0_0 {y} \, dy[/tex] + [tex]\int\limits^5_0 {y} \, dy[/tex] + [tex]\int\limits^5_5 {y} \, dy[/tex] + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex] + [tex]\int\limits^1_0 {z} \, dz[/tex] + [tex]\int\limits^1_1 {z} \, dz[/tex] + [tex]\int\limits^0_1 {z} \, dz[/tex]
Work done= x²/2 + y²/2 + z²/2
Applying integral limits for entire pathway
Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2
Work done = 0 J
On a piece of paper, graph y + 2 ≤ -2/3x +4. Then determine which answer choice matches the graph you drew.
Answer:
B
Step-by-step explanation:
You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).
The shading is below the line because y-values are less than (or equal to) values on the line.
Choice B matches the attached graph.
Answer:
it is graph b
Step-by-step explanation:
How can you write arithmetic and geometric sequences using recursive and explicit formulas modeled in a real world context?
Answer:
The answer is below
Step-by-step explanation:
They would be written like this:
Arithmetic Progression:
Explicit formula
Tn = a + (n-1) * d
Recursive formula
Tn = Tn-1 + d
Where a is the first term, d is the common differance and n is the number of terms.
Geometric Progression:
Explicit formula
Tn = a * r ^ (n-1)
Recursive formula
Tn = Tn-1 * r
Where r is common ratio
For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 24 and p = 0.6.
Answer:
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
Step-by-step explanation:
When the normal approximation is suitable?
If np > 5 and np(1-p)>5
In this question:
[tex]n = 24, p = 0.6[/tex]
So
[tex]np = 24*0.6 = 14.4[/tex]
And
[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]
Since both np > 5 and np(1-p)>5, it is suitable to use the normal distribution as an approximation.
5c + 16.5 = 13.5 + 10c
Answer:
Hello!
________________________
5c + 16.5 = 13.5 + 10c
Exact Form: c = 3/5
Decimal Form: c = 0.6
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Answer:
3000+3d=noods
Step-by-step explanation:
An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?
First find the distance it is reflected:
D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.
Now calculate the magnification: -20/ 20 = -1
Now calculate the height:
-1 x 2.50 = -2.50
The negative sign means the image is inverted.
The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.
In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
If the area of a circular cookie is 28.26 square inches, what is the APPROXIMATE circumference of the cookie? Use 3.14 for π.
75.2 in.
56.4 in.
37.6 in.
18.8 in.
Answer:
Step-by-step explanation:
c= 2(pi)r
Area = (pi)r^2
28.26 = (pi) r^2
r =[tex]\sqrt{9}[/tex] = 3
circumference = 2 (3.14) (3)
= 18.8 in
Answer: approx 18.8 in
Step-by-step explanation:
The area of the circle is
S=π*R² (1) and the circumference of the circle is C= 2*π*R (2)
So using (1) R²=S/π=28.26/3.14=9
=> R= sqrt(9)
R=3 in
So using (2) calculate C=2*3.14*3=18.84 in or approx 18.8 in
6th grade math , help me please :)
Answer:
A= 20x
B= 15n
C= 15x+ 9
D= a + 15
E= 9x + 3y
F= 10w + 10z
Step-by-step explanation:
Find the lateral area of a regular square pyramid if the base edges are of length 12 and the perpendicular height is 8.
Answer:
Lateral area of the pyramid = 120 square units
Step-by-step explanation:
In the figure attached,
A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.
Lateral area of a pyramid = Area of the lateral sides
Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]
= [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex] [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]
= [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]
= [tex]3\sqrt{100}[/tex]
= 30 units²
Now lateral area of the pyramid = 4 × 30 = 120 square units
Answer: 240 units^2
Step-by-step explanation:
LA= 1/2 Pl
P= perimeter of base
l= lateral height
l= 8^2 + (12/2)^2 = 10^2
P= 12 x 4 = 48
48 x 10 = 480
480/2 = 240
240 units^2
Ann's $6,900 savings is in two accounts. One account earns 3% annual interest and the other earns 8%. Her total interest for the year is $342. How much does she have in each account?
Answer:
x=4200, y=2700
Step-by-step explanation:
let x be first account
y the second
x+y=6900
0.03x+0.08y=342
solve by addition/elimination)
multiply first equation by 0.03
0.03x+0.03y=207 subtract from second
0.03x+0.03y-0.03x-0.08y=207-342
0.05y=135
y=2700, x=4200
plz give me correct answers
Answer:
Step-by-step explanation:
greatest number=8643
smallest number=3468
difference=8643-3468=5175
6.1. DCCLVI
CDXCIV
(II) 74,746
Suppose we write down the smallest positive 2-digit, 3-digit, and 4-digit multiples of 9,8 and 7(separate number sum for each multiple). What is the sum of these three numbers?
Answer:
Sum of 2 digit = 48
Sum of 3 digit = 317
Sum of 4 digit = 3009
Total = 3374
Step-by-step explanation:
Given:
9, 8 and 7
Required
Sum of Multiples
The first step is to list out the multiples of each number
9:- 9,18,....,99,108,117,................,999
,1008
,1017....
8:- 8,16........,96,104,...............,992,1000,1008....
7:- 7,14,........,98,105,.............,994,1001,1008.....
Calculating the sum of smallest 2 digit multiple of 9, 8 and 7
The smallest positive 2 digit multiple of:
- 9 is 18
- 8 is 16
- 7 is 14
Sum = 18 + 16 + 14
Sum = 48
Calculating the sum of smallest 3 digit multiple of 9, 8 and 7
The smallest positive 3 digit multiple of:
- 9 is 108
- 8 is 104
- 7 is 105
Sum = 108 + 104 + 105
Sum = 317
Calculating the sum of smallest 4 digit multiple of 9, 8 and 7
The smallest positive 4 digit multiple of:
- 9 is 1008
- 8 is 1000
- 7 is 1001
Sum = 1008 + 1000 + 1001
Sum = 3009
Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit
Sum of All = 48 + 317 + 3009
Sum of All = 3374
How do you write 0.0026 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]2.6 \times {10}^{ - 3} [/tex]
Hope this helps you
Answer:
2.6 × 10⁻³
Step-by-step explanation:
To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.
In the decimal 0.0026, the first number that is 1 or higher is 2.
0.0026 ⇒ 2.6
When trying to figure out the exponent, here are some things to keep in mind:
- when you move the decimal to the right, the exponent is negative
- when you move the decimal to the left, the exponent is positive
You moved the decimal to the right three places. So the exponent will be -3.
The result is 2.6 × 10⁻³.
Hope this helps. :)
A group of 20 people were asked to remember as many items as possible from a list before and after being taught a memory device. Researchers want to see if there is a significant difference in the amount of items that people are able to remember before and after being taught the memory device. They also want to determine whether or not men and women perform differently on the memory test. They choose α = 0.05 level to test their results. Use the provided data to run a Two-way ANOVA with replication.
A B C
Before After
Male 5 7
4 5
7 8
7 8
7 8
7 8
5 6
7 7
6 7
Female 5 8
5 6
8 8
7 7
6 6
8 9
8 8
6 6
7 6
8 8
Answer:
1. There is no difference in amount of items that people are able to remember before and after being taught the memory device.
2. There is no difference between performance of men and women on memory test.
Step-by-step explanation:
Test 1:
The hypothesis for the two-way ANOVA test can be defined as follows:
H₀: There is no difference in amount of items that people are able to remember before and after being taught the memory device.
Hₐ: There is difference in amount of items that people are able to remember before and after being taught the memory device.
Use MS-Excel to perform the two-way ANOVA text.
Go to > Data > Data Analysis > Anova: Two-way with replication
A dialog box will open.
Input Range: select all data
Rows per sample= 10
Alpha =0.05
Click OK
The ANOVA output is attaches below.
Consider the Columns data:
The p-value is 0.199.
p-value > 0.05
The null hypothesis will not be rejected.
Conclusion:
There is no difference in amount of items that people are able to remember before and after being taught the memory device.
Test 2:
The hypothesis to determine whether or not men and women perform differently on the memory test is as follows:
H₀: There is no difference between performance of men and women on memory test.
Hₐ: There is a difference between performance of men and women on memory test.
Consider the Sample data:
The p-value is 0.075.
p-value > 0.05
The null hypothesis will not be rejected.
Conclusion:
There is no difference between performance of men and women on memory test.
What is y - 8 = 4(x - 4) in slope intercept form?
Answer:
y=4x-8
Step-by-step explanation:
First you must use the distributive property and get y-8=4x-16.
Then you have to add 8 on both sides so just y is left on the left side.
This will get you y=4x-8 in slope-intercept form.
George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?
This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Learn more about the topic Substitution:
https://brainly.com/question/3388130
The graph of y =ex is transformed as shown in the graph below. Which equation represents the transformed function?
Answer:
B. e^x+3
Step-by-step explanation:
Y=e^x
the graph is moving 3 units up
y= y+3
y=e^x+3
answer = y=e^x+3
Answer: B
Step-by-step explanation:
When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)
Answer:
GOOGLE :)
equation:
y=mx+b
m= slope (how steep the line is(negative is \ positive is /))
b= y intercept (where it is on the vertical line(up and down line))
step by step
1. locate y intercept and plotthe point
2.from that point use slop to find second point and plot
Find AC. (Khan Academy-Math)
Answer:
[tex]\boxed{11.78}[/tex]
Step-by-step explanation:
From observations, we can note that BC is the hypotenuse.
As the length of hypotenuse is not given, we can only use tangent as our trig function.
tan(θ) = opposite/adjacent
tan(67) = x/5
5 tan(67) = x
11.77926182 = x
x ≈ 11.78
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish from each of the 53 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have different mercury than the allowable amount?
Required:
State the random variable, population parameter, and hypotheses.
Answer:
Yes. At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.
The random variable is the sample mean amount of mercury in the bass fish from the lakes of Florida.
The population parameter is the mean amount of mercury in the bass fish of Florida lakes.
The alternative hypothesis (Ha) states that the amount of mercury significantly differs from 1 mg/kg.
The null hypothesis (H0) states that the amount of mercury is not significantly different from 1 mg/kg.
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
Step-by-step explanation:
The question is incomplete.
There is no data provided.
We will work with a sample mean of 0.95 mg/kg and sample standard deviation of 0.15 mg/kg to show the procedure.
This is a hypothesis test for the population mean.
The claim is that the fish in all Florida lakes have different mercury than the allowable amount (1 mg of mercury per kg of fish).
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=1\\\\H_a:\mu\neq 1[/tex]
The significance level is assumed to be 0.05.
The sample has a size n=53.
The sample mean is M=0.95.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.15.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.15}{\sqrt{53}}=0.0206[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.95-1}{0.0206}=\dfrac{-0.05}{0.0206}=-2.427[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=53-1=52[/tex]
This test is a two-tailed test, with 52 degrees of freedom and t=-2.427, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.427)=0.019[/tex]
As the P-value (0.019) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to support the claim that the fish in all Florida lakes have different mercury than the allowable amount.