The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04
The margin of error is a statistic that describes how much random sampling error there is in survey results.
Given in question,
n = 400
p = 317/400
= 0.7925
Confidence Level = 95%
= 0.95
Formula for margin error, E = [tex]z\sqrt{\frac{p(1-p)}{n} }[/tex]
Confidence level corresponding to 95 % confidence interval, z = 1.96
Therefore,
Margin Error, E = [tex]1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }[/tex]
= 0.0397
≈ 0.04
Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.
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Let F be any nonconstant vector field of the form F = f (x) i + g (y) j + h (z) k and let G be any nonconservative vector field of the form G = f (y, z) i + g (x, z)j + h (x, y) k. Indicate whether the following statements are true or false by placing ''T'' or ''F'' to the left of the statement. 1. G is incompressible 2. F is irrotational 3. G is irrotational 4. F is incompressible
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .
So if we calculate for F:
F has a divergence potentially
divF = df/dx + dg/fy + dh/dz
But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)
For G
G has zero divergence.
divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0
But it may have a curl.
curl(G) = df/dy may be non-zero
df/dz, dg/dx etc may all be non-zero
Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,
div = 0 = incompressible and
curl = 0= irrotational
Thus,
1. G is incompressible- True
2. F is irrotational- True
3. G is irrotational- False
4. F is incompressible- False
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Find the sum of 3x + 2 and 8x
Which of the following is true?
Triangle B C D. The exterior angle at B is labeled 1 and the interior angle is labeled 2. Angle C has measure 70 degrees. The exterior angle at D has measure 130 degrees.
A. m∠BCD − m∠DBC = 10°
B. m∠BCD − m∠DBC = 20°
C. m∠BCD − m∠DBC = 60°
D. m∠BCD − m∠DBC = 80°
Answer:
answer :J LOOK THE DIAGRAM CAREFULLY AND UNDERSTAND
Answer:
A <c - <b = 10
Step-by-step explanation:
7. Solve the proportion.
2/3=a/15
8. Solve the proportion.
4/7=44/m
Answer:
a=10
m=28
Step-by-step explanation:
2/3= 0.666666666666666
a/15=??????
try all numbers divided by 15 untill you found 0.666666666666666 which is =10/15
4/7=0.571428571428571
44/m=???????
do the same as the first one
it will be 44/28=0.571428571428571
Yosef drove 11,190 miles last year. His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon. Determine Yosef's average weekly fuel cost.
$32.12
$24.35
$28.55
$30.05
Yosef's average weekly fuel cost is $24.35.
How to find the the average weekly fuel cost?Yosef drove 11,190 miles last year. His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon.
Yosef average weekly fuel cost can be computed as follows:
Yosef used 11190 / 19 = 588.95 gallons to drive 11190 miles.
Therefore, the average cost of gas last year was 2.15 dollars per gallon.
Therefore, Yosef's average weekly fuel cost would be as follows:
Yosef's average weekly fuel cost = 2.15 x 588.95 ÷ 52 = $1266.23684211 ÷ 52
Yosef's average weekly fuel cost = 24.350708502
Yosef's average weekly fuel cost = $24.35
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Maria is making an apple pie. She needs 1/4 cup of sugar for each pie Maria has 2 1/2 cups of sugar how many pies can she make
The number of cups she can make is 2 cups
How to determine the number of cups she can makeFrom the question, we have the following parameters that can be used in our computation:
Cups of sugar needed = 1/4
Cups of sugar available = 1/2
Assume there exist a proportional relationship between the cups
The number of cups she needs can be calculated using the following equation
number of cups = (1/2)/(1/4)
Evaluate the quotient
number of cups = 2
Hence, the cups is 2 cups
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4-1 3/5 write as a mix number in simplest form
Answer:
Step-by-step explanation:
17/5
Answer:
2 and 2/5
Step-by-step explanation:
4x - 8y = -4
-2x + 8y = -2
Solve by elimination
Answer:
X=1 Y=0
Step-by-step explanation:
Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x
4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0
Now, knowing that y=0, plug y into the second equation:
-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1
PLEASE HELP AGAIN I STILL NEED TO GET THESE DONE
Answer:
........................
A water tank initially contained 57 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many minutes have passed m when the tank contains 35 liters? Round go the nearest tenth
Answer:
8.8 minutes
Step-by-step explanation:
first we figure out how many liters are being lost
57 - 35 = 22
then divide that by 2.5
22 / 2.5 = 8.8
8.8 minutes
Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.L1: x = 5-12t, y = 3+9t, z = 1-3tL2: x = 3+8s, y = -6s, z = 7+2s
The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s are parallel lines .
In the question ,
it is given that ,
the two lines are :
L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t
L2 ⇒ x = 3+8s, y = -6s, z = 7+2s
If the lines are intersecting then :
5 - 12t = 3 + 8s
8s + 12t = 2
4s + 6t = 1 ; .....equation(1)
and 3 + 9t = -6s
3t + 2s + 1 = 0
multiplying both sides by 2 ,
we get ,
6t + 4s + 2 = 0 ....equation(2)
Solving equation(1) and equation(2) , we get
3 ≠ 0 .
So , the lines are not intersecting .
For lines to be parallel , the cross product of their directions must be 0 .
So , [tex]\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|[/tex]
On simplifying further ,
we get ,
⇒ 0i - 0j + 0k
= 0
So , the cross product is 0 , lines will be parallel .
Therefore , the lines L1 and L2 are parallel .
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The size of a population is modeled by the function P that satisfies the logistic differential equation dP/dt=(1/10)P - (1/5000)P^2 , where t is measured in months and P (0) = 50. What is the size of the population at the moment when the population is growing most rapidly? A. 50 B. 250 C.500 D. 2500
The correct answer is A.
500 is the size of the population at the moment of maximum growth.
Given data:
To find the size of the population at the moment when the population is growing most rapidly, we need to determine the maximum value of the derivative dP/dt.
Given the logistic differential equation [tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex], find the derivative by taking the derivative of each term separately:
[tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex]
To find the critical points where the derivative is zero or undefined, set dP/dt equal to zero:
[tex](\frac{1}{10})P - (\frac{1}{5000})P^2=0[/tex]
Simplifying:
[tex](\frac{1}{10})P= (\frac{1}{5000})P^2[/tex]
[tex]10P^2=5000P[/tex]
Dividing both sides by P and rearranging:
[tex]10P(P-500)=0[/tex]
This equation has two solutions: P = 0 and P = 500.
To determine which solution corresponds to the moment when the population is growing most rapidly, examine the second derivative. Taking the second derivative of the logistic differential equation, we have:
[tex]\frac{d^2P}{dt^2} = \frac{1}{10} - \frac{2}{5000}P[/tex]
Evaluating the second derivative at P = 0 and P = 500, we get:
[tex]\frac{d^2P}{dt^2}_{P=0} = \frac{1}{10} - \frac{2}{5000}(0)[/tex]
[tex]\frac{d^2P}{dt^2}_{P=0}= \frac{1}{10} > 0[/tex]
[tex]\frac{d^2P}{dt^2}_{P=500} = \frac{1}{10} - \frac{2}{5000}(500)[/tex]
[tex]\frac{d^2P}{dt^2}_{P=0}= -\frac{1}{10} < 0[/tex]
Since the second derivative is positive at P = 0 and negative at P = 500, the moment when the population is growing most rapidly occurs at P = 500.
Hence, the size of the population at the moment when the population is growing most rapidly is 500.
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An initial balance of $4,000 grows at a rate of 12.3% compounded quarterly. What is the balance after 5 years?
Answer:
7330.36
Step-by-step explanation:
A = P (1+i)^n
n = 4×5 = 20
i = 0.03075
12.3% / 4 = 3.075 × 1/100
= 0.03075
A = 4000 ( 1+ 0.03075 ) ^20
= 7330.36
ING
DO
S
DO
Here's the revenue and expenses for the month. Calculate whether Mia had a profit or loss.
REVENUE
DOG FOOD
$3,500
CAT FOOD
$2,100
PET TREATS
$1,200
PET SUPPLIES $2,750
TOTAL
$9,550
JANUARY ACCOUNTS
FIXED EXPENSES
RENT
$2,000
SALARIES
$2,000
UTILITIES
$1,000
PRODUCT STOCK $4,000
TOTAL
$9,000
$ X
VARIABLE EXPENSES
NEWSPAPER AD $200
TOTAL
$200
ENTER MIA'S TOTAL PROFIT/LOSS FOR THE MONTH IN THE BOX BELOW, THEN CLICK SUBMIT.
SUBMIT
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)
Vertex: (2, 3); point: (0, 2)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]
determine the equation of the line of the line of best fit from the data in the table on the right. x 4 5 6 7 10 y = 14 14 17 19 26
The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.
How to find the line of best fit ?The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.
Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).
The slope of this line would be:
= ( Y2 - Y1 ) / ( X 2 - X1)
= ( 19 - 17 ) / (7 - 6 )
= 2.12
The y intercept would be:
y = mx + c
19 = 2.12 (7 ) + c
c = 4.42
The equation of the line of best fit is then :
y = 2.12 x + 4.42
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Two Truths & One Lie: Which of the 3 statements below is a lie? Explain how you made your decision.
x=2 y=5 z=7
Answer:
The 3rd statement is a lie and other two are truth.
Step-by-step explanation:
when two same numbers with power are divided their respective powers are subtracted.
1.
[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]
Using this formula for
[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]
[tex] {b}^{9 - 5} = {b}^{4} [/tex]
Here RHS =LHS
so the equation is true
2.
[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]
[tex] {b}^{7 - 2} = {b}^{2} [/tex]
Here RHS=LHS,
so the equation is true
3.[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]
[tex] {b}^{8 - 2} = {b}^{8}[/tex]
Here RHS is not equal to LHS
so the equation is false
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One of the legs of a right triangle measures 2 cm and the other leg measures 7 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
Hypotenuse = 7.3 cm
Step-by-step explanation:
We can find the hypotenuse using the Pythagorean Theorem, which is:
[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle and c is the hypotenuse.
By plugging in 2 and 7 for a and b, we have:
[tex]2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c[/tex]
Elvia has a bag of snack mix that contains 5 cereal pieces, 4 peanuts, 5 pretzels, and 1 bagel chip. Suppose that she is equally likely to pick any individual object from the bag. What is the probability that Elvia will randomly pull a pretzel from the bag?
Answer: 33%
Step-by-step explanation: a third of the items in the bag are pretzels.
What % of 780 shirts is 46
Answer:
i think the answer will be 6%
Answer:
below
Step-by-step explanation:
46 / 780 * 100% = 5.9 %
Create a slope intercept equation with given information (3,1) m =0
Answer:
y = x - 2
Step-by-step explanation:
Since m = 0, what we have so far is y=x+b
We have a point, which is (3,1)
Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).
1=3+b
1-3=3+b-3 undo the 3 by subtracting
-2 = b
y = x + -2 simplify
y = x - 2
Solve for x: −8 < x − 1 < 5
−7 < x < 6
7 < x < 6
−7 > x > 6
7 > x > 6
Answer:
- 7 < x < 6
Step-by-step explanation:
- 8 < x - 1 < 5 ( add 1 to each interval )
- 7 < x < 6
Write the equation x^2 - 10x + 17 = 0 in the form (x+p)^2 = q (50 points!)
Answer: (x-5)²=8
Step-by-step explanation:
x²-10x+17=0
x²-2(x)(5)+5²-5²+17=0
(x²-2(x)(5)+5²)-25+17=0
(x-5)²-8=0
(x-5)²-8+8=0+8
(x-5)²=8
Answer:
(x - 5)² = 8
--------------------------
Given
Expression x² - 10x +17.
Convert this to vertex form by completing the square.
Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:
x² - 10x + 17 =
x² - 2*5*x + 5² - 5² + 17 =
(x - 5)² - 25 + 17 = (x - 5)² - 8
(x - 5)² = 8
It takes a bus 1 hour and 30 minutes to travel 42 miles.
Calculate the average speed of the bus in mph.
If your answer is a decimal, give it to 1 d.p.
28 mph is the average speed of the bus in mph.
What is speed?
The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.
Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.
time = (1+ 1/2)hr = 3/2 hr = 1.5 hr
distance = 42 miles
average speed = total distance/total time
42/1.5 = 28 mph
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An isosceles triangle has an angle that measures 140°. What measures are possible for
the other two angles? Choose all that apply.
Recommendations
15⁰
70°
45°
20•
The possible value of other two angles will be 20 degree.
What are the types of triangle?
Basically, there are six different types of triangles in terms of lengths and measurements of triangle lines or angles. The sum of all interior angles of a triangle is always 180 degrees. This is called the angular summation of the triangle. Depending on the length of the sides, triangles can be divided into three types:
scale
Isosceles
equilateral
It is given that an isosceles triangle has an angle that measures 140°
We know that two sides of isosceles triangle are equal and by the property of triangle we know that angle opposite to equal sides are equal therefore remaning two angles of isosceles triangle will be equal.
Let the angles be x
By angle sum property of triangle
x + x + 140 = 180
2x = 180 - 140
2x = 40
x = 40/2 = 20
Therefore, the possible value of other two angles will be 20 degree.
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A store bought a sofa wholesale for 200 and marked it up 15% when the sofa did int sell they reduced the price 15% show why the current price is not 200
Answer:
The current price of sofa is $195.50.
Step by Step explanation:Cost price of the sofa for the store = $200
Now, the store marked it up 15%.
So, marked price of sofa = $200 + 15% of $200
=200 + 30
=$230
Now, it is given that the sofa could not sell at this price. So, the store reduces its price by 15% now.
So, current price of sofa = $230 - 15% of $230
= 230 - 34.5
=$195.5
So, the current price of the sofa is $195.50.
W 5. Suppose that 40% of the cars in a certain town are white A person stands at an intersection waiting white car. Let X= the number of cars that must drive by until a white one drives by. What is the exp value of X?
The no. of cars that must drive by until a white one drives by is 40.
What is a binomial distribution in probability?In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is
[tex]^nC_xp^Xq^{n-x}[/tex].
We know the expected value of a binomial distribution E(x) = np.
Given, Suppose that 40% of the cars in a certain town are white.
Therefore 50% of cars in the town are not which.
Let, The no. of cards in the town be 'n'.
So, p = 40/n and q = 60/n
Therefore from the formula E(x) = np we get,
E(x) = n×40/n
E(x) = 40.
So, The expected value of X is 40.
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Answer: We expect 2.5 cars to
The expected value of X is 2.5.
Step-by-step explanation:
In this case, it is a geometric distribution because we do not have a fixed number of trials.
We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.
In this case:
mu_x=1/0.4 = 2.5
In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).
I lowkey need help like immediately
The answers to all the parts are given below.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.
[A] -
For [x] = 1000ft, we can write -
1000 = -16t² + 1800
16t² = 800
t² = (800/16)
t² = 50
t = 7.07 seconds
[B] -
For [x] = 950ft, we can write -
950 = -16t² + 1800
16t² = 850
t² = 53.125
t² = √(53.125)
t = 7.29 seconds
[C] -
The domain of the function will be -
0 ≤ x ≤ 10
[D] -
The range of the function will be -
0 ≤ h ≤ 1800
Therefore, the answers to all the parts are given above.
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The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 7000 miles.
A) The probability that the tyre wears out before 60000 miles is 0.4221
B) The probability that the tyre lasts more than 83000 miles is 0.49534
The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as
z = (x - u)/s
Where
x = the distance the tyres can run until wear-out
u = mean distance
s = standard deviation
From the information given,
u = 70000 miles
s = 7000 miles
A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as
P(x lesser than 60000)
For x = 60000,
z = (60000 - 70000)/7000 = - 1.42
Looking at the normal distribution table, the corresponding z score is 0.4221
B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as
P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)
For x = 83000,
z = (83000 - 70000)/5000 = 2.6
Looking at the normal distribution table, the corresponding z score is 0.49534
P(x greater than 83000)
= 1 - 0.49534 = 0.50466
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A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
(p-124) / 9 min many liters of water are in the tank after 109 seconds.
for 4 min = 65 + (6.5x4) = 91 lit
for 109 sec = 65 + (9x 109/60) = 81.35 lit
for m min = 65 + (9m) lit
how long time
for 151 lit = (151 - 124)/9 = 3 min
for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec
for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec
for p lit = (p-124) / 9 min
What is liters ?
The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.
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