Answer:
The 95% confidence interval is [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
Step-by-step explanation:
From the question we are told that
The data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
The sample size is [tex]n= 20[/tex]
Given that the confidence level is 95% then the level of significance is
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The degree of freedom is mathematically represented as
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
From the student t-distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 19 } = 2.093[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{ n}[/tex]
[tex]\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}[/tex][tex]\= x = 246.6[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }[/tex]
[tex]\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..[/tex]
[tex]\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...[/tex]
[tex]\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...[/tex] [tex]\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }[/tex][tex]\sigma = 2.87411[/tex]
The margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.093 * \frac{2.87411 }{\sqrt{20} }[/tex]
[tex]E = 1.345[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]245.6 - 1.345 < \mu <245.6 + 1.345[/tex]
=> [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
Students in a large statistics class were randomly divided into two groups. The first group had a midterm exam that was printed on canary paper while the second group had the exam printed on pale green paper. The exam scores of the two groups were then then compared.This experiment was not blind because:_______a. Students were allowed to keep their eyes open while taking the exam.b. The exam was too long.c. The students knew whether or not music was playing while they were taking the exam.d. Some of the students did not study for the exam.e. Students were randomized into the two groups.
Answer:
e. Students were randomized into the two groups.
Step-by-step explanation:
A bag contains 6 RED beads, 3 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?
Answer:
17/20
Step-by-step explanation:
Total no. of beads = 6 + 3 + 11 = 20
We need RED or GREEN bead .
So no. of beads needed = 6 + 11 = 17
So probability of getting GREEN or RED beads = 17/20
What is the measure of r
Answer:
The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°
alex buys six equally priced candy bars for $9:00 what is the unit rate?
Answer:
$1.5 unit
Step-by-step explanation:
According to the given situation, the calculation of the unit rate is shown below:-
Candy bars = 6
Amount of candy bars = $9:00
Unit rate
[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]
Now we will put the values into the above formula
[tex]= \frac{\$9:00}{6}[/tex]
Which gives result
= $1.5 unit
Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.
An open top box is to be made by a 24 in by 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?
Answer:
X= -12 +6√10
X= 6.973
Step-by-step explanation:
Volume of the box= (36-2x)(24-2x)x
Volume of the box
=( 864 -96x -4x²)x
But 864 -96x -4x²
=216 - 24x-x²
Solving for x quadratically
X= (24+12√10)/-2
X= -12 -6√10
X= -30.97
Or
X= (24-12√10)/-2
X= -12 +6√10
X= 6.973
X will definitely be a positive number
So X= -12 +6√10
X= 6.973
Increasing or decreasing the side length of the square that gives the
maximum volume, gives a volume that is less than the maximum.
The side length of the cut out square to get a box with the maximum volume is approximately 4.71 in.Reasons:
The given dimensions of the box = 24 in. by 36 in.
Let x represent the dimensions of the square removed from the corners, we have;
Width of box = 24 - 2·x
Length of box = 36 - 2·x
Height of the box = x
Volume of a box = Width × Length × Height
Therefore;
Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x
At the maximum or minimum point of the volume, we have;
[tex]\displaystyle \frac{dV}{dx} = \mathbf{ \frac{d}{dx} \left(4 \cdot x^3 - 120 \cdot x^2 + 864 \cdot x \right )} = 0[/tex]Which gives;
12·x² - 240·x + 864 = 0
x² - 20·x + 72 = 0
Which gives;
[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]
At x = 10 + 2·√7, we have;
[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]
2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard
Therefore, (10 + 2·√7) is too long to be cut from the cardboard
At x = 10 - 2·√7, we have;
V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3
Therefore;
The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches ≈ 4.71 inches
The size of the square to be cut out each corner is x ≈ 4.71 inchesLearn more here:
https://brainly.com/question/11879766
https://brainly.com/question/14573161
When you woke up this morning, the temperature was -5.8°C. At noon, the temperature was 2.9°C. Which expression and statement describes the situation?
Answer:
-5.8<2.9
Step-by-step explanation:
Find g(-2) + h(4) if g(x)= 5-2x and h(x) = - x2 pls help
Answer:
-7
Step-by-step explanation:
g(x)= 5-2x and h(x) = - x^2
g(-2) + h(4)
First find g(-2)
g(-2) = 5 -2(-2) = 5 +4 = 9
Then find h(4) = - 4^2 = -16
g(-2) + h(4) = 9-16 = -7
Answer:
-7
Step-by-step explanation:
Substitute -2 into g(x) equation,
g(x) = 5 - 2x
g(-2) = [5 - 2(-2)] = 9
Substitute 4 into h(x) equation,
h(x) = -x^2
h(4) = [-(4)^2] = -16
Therefore,
g(-2) + h(4) = 9 + (-16) = -7
a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate
Answer:
1 1/14 lbs
Step-by-step explanation:
We can use ratios to solve
2/3 crate 1 crate
----------------- = -----------------
5/7 lb x lbs
Using cross products
2/3x = 5/7 *1
Multiply each side by 3/2
3/2 * 2/3 x = 3/2 * 5/7
x = 15/14
x = 1 1/14
Answer:
[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]
Step-by-step explanation:
[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]
Write the equation of the line PERPENDICULAR to y = 3/2x + 6 that passes through the point (-3, 4).
Answer:
Step-by-step explanation:
perp. -2/3 slope
y - 4 = -2/3(x + 3)
y - 4 = -2/3x - 2
y = -2/3x + 2
fatima bought an xbox game that is 38.00 plus 9% sales tax what is the sales tax on the xbox game that fatima purchased answer
How do you do these questions? With step by step instructions please
Answer: n = 3 n = 4
Upper Sum ≈ 3.41 Upper Sum ≈ 3.25
Lower Sum ≈ 2.15 Lower Sum ≈ 2.25
Step-by-step explanation:
You are trying to find the area under the curve. Area = height x width.
Height is the y-value at the given coordinate --> f(x)
Width is the distance between the x-values --> dx
n = 3
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3
So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9
f(1/3) = 1 + (1/3)² = 1 + 1/9 --> 10/9
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/3} f(-1) = 2 f(-1/3) = 10/9
{-1/3, 1/3} f(-1/3) = 10/9 f(0) = 1 (vertex lies in this interval)
{1/3, 1} f(1) = 2 f(1/3) = 10/9
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]
*****************************************************************************************
n = 4
First, let's figure out dx: the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)
So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}
For the upper sum, we find the max y-value for each interval
For the lower sum, we find the min y-value for each interval
Next, let's find the height for each of the x-values:
f(x) = 1 + x²
f(-1) = 1 + (-1)² = 2
f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4
f(0) = 1 + (0)² = 1
f(1/2) = 1 + (1/2)² = 1 + 1/4 --> 5/4
f(1) = 1 + (1)² = 2
Interval Max Min
{-1, -1/2} f(-1) = 2 f(-1/2) = 5/4
{-1/2, 0} f(-1/2) = 5/4 f(0) = 1
{0, 1/2} f(1/2) = 5/4 f(0) = 1
{1/2, 1} f(1) = 2 f(1/3) = 5/4
Now, let's find the Area: A = f(x) dx:
[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]
[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]
Point R is on line segment QS. Given RS = 13 and QS = 20, determine the length of QR
Answer:
Length of QR = 7
Step-by-step explanation:
20 - 13 = 7
Amy, Ray, Kim, and Jamal are on a trivia team. They gain points for correct answers
and lose points for incorrect answers. During the contest, Amy gains 3 points, Ray loses
4 points, Kim loses 2 points, and Jamal gains 5 points. How many points does the team
have at the end of the contest?
Answer:
2 points
Step-by-step explanation:
0+3-4-2+5=2 points
The probability of a student passing
an examination is 2/3
If the student
takes three examination, what is the
Probability that he will not
pass
any of them.
===============================================
Explanation:
2/3 is the probability of passing a test, so 1/3 is the probability of failing
Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%
The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.
-------
Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27
do all sets have subsets?
Answer:
yes
Step-by-step explanation:
Skip count by twos.
30,_ _ _ _ _ _ _ _ _,50.
Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 19 total hours and must earn a minimum of $270. If Brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.
Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.
$270-$252=$18, he needs to earn $18 more from clearing tables.
$18÷9=2, so the minimum number of whole hours clearing tables is 2
what is -3.5+(-4.9)=?What is the answer please?
Answer:
The answer is -8.4
y varies inversely with x. If y = 5 when x = 60, find y when x = 150
pre cal
Answer:
y = 2 when x = 150
Step-by-step explanation:
Inverse variation is
xy = k
5*60 = k
300 = k
xy = 300
150y = 300
Divide by 150
150y/150 = 300/150
y = 2
The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.
|x______ | = _______
x = __________ (smaller number here)
x = _______ (larger nember here)
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Answer:
[tex]|x - 85| = 12[/tex]
[tex]x = 73 \ (smaller\ number )[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
Step-by-step explanation:
From the question we are told that
The grade is [tex]k = 85\%[/tex]
The variation is [tex]v = 12 \%[/tex]
Generally the absolute value equation is mathematically represented as
[tex]|x - 85| = 12[/tex]
=> [tex]x -85 = \pm 12[/tex]
So
[tex]x = 85 + 12[/tex]
[tex]x = 97 \ (larger \ number )[/tex]
And
[tex]x = -12 + 85[/tex]
=> [tex]x = 73 \ (smaller\ number )[/tex]
What is 30/35 in simplest form?
Answer: 6/7
Step-by-step explanation:
Find a unit vector that is orthogonal to both i + j and i + k.
Answer: i - j - k
Step-by-step explanation:
Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.
<1,1,0> x <1,0,1>
[tex]det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )[/tex]
the determinate of the matrix: <1,-(1),-1>
or: i - j - k
A factory worker can produce 28 toys in an eight hour day If there are 42 workers in total how many toys are produced every hour
Answer:
147 toys
Step-by-step explanation:
for 1 person, 28toys/8hours = 3.5toys/ 1hour
for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour
~Hope it Helps!~
I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me
Answer:
(√2 + √6)/4.
Step-by-step explanation:
Use the addition formula
sin (A+ B) = sinAcosB + cosAsinB
sin (7pi/12) = sin( 3pi/12 + 4pi/12)
= sin(pi/4 + pi/3) = sin pi/4 cos pi/3 + cos pi/4 sin pi/3
= 1/√2 * 1/2 + 1/√2 * √3/2 (using the 45-45-90 and 30-60-90 triangles)
= 1 / 2√2 + √3/2√2
= √2/4 + √6/4
= (√2 + √6)/4
Emma and Clair are planning to sell lemonade on their street. They have two recipes to choose from. Emma’s recipe calls for the juice of 5 lemons and 2 cups of water. Clair’s recipe calls for the juice of 2 lemons and 1 cup of water. Why will the first recipe taste more “lemony”?
Answer:
Emma's recipe will be more lemony because
5/2=2.5
2/1=2
Step-by-step explanation:
Answer:
The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.
Step-by-step explanation:
Sample Answer
There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?
Answer:
.8L
Explanation:
Logic
The liters of water left are 0.8 liters.
What is an Equation?An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.
The equations are useful in the determination of unknown parameters.
The quantity of water in a water bottle is 1 liter.
The amount of water Tom drank is 200 milliliters.
Let x be the amount of water left in the bottle.
The liter has to be converted into milliliters.
1 liters = 1000 milliliters
The equation formed is,
1000 - 200 = x
x = 1000 - 200
x = 800 milliliters.
The water left in the water bottle is 800 milliliters.
1000 milliliters = 1 liters
800 milliliters = 0.8 liters
To know more about Equation
https://brainly.com/question/10413253
#SPJ5
T is the midpoint of SU, ST = 8x + 11 and TU = 12x-1, find the value of x.
Answer:
x = 3
Step-by-step explanation:
mid point means it bisects the segment into two equals halfs meaning
ST = TU
8x + 11 = 12x - 1
8x + 12 = 12x
12 = 4x
3 = x
Glados
spent the day at the mall, First, she bought
three bikes for $10 each. Later, she found 22
dollar bills. Write the total change
an integer.
to Glado's
funds as an integer
Answer:
8
Step-by-step explanation:
Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?
3 tests at 75% each = 3 x 75 = 225 total points
First two tests = 79 + 84 = 163
Third test needs to be at least: 225 - 163 = 62%
So any score less than 62 would get you into trouble.
A plane is a _____ figure
Answer:
bold
Step-by-step explanation:
hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd
A plane is a two dimensional figure.