Answer:
[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]
And the value for n rounded up would be n = 174
Step-by-step explanation:
We have the following info given:
[tex] s= 1.7[/tex] previous estimation for the deviation
[tex] ME=0.03[/tex] the margin of error desired
[tex] Conf =0.98[/tex] represent the confidence
The Margin of error is given by:
[tex] ME = z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
If we solve for the value of n we got:
[tex] n= (\frac{z*\sigma}{ME})^2[/tex]
For this problem we know that the confidence is 98% so then the significance level would be [tex]\alpha=0.02[/tex] and the critical value would be:
[tex] z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] n = (\frac{2.326*1.7}{0.3})^2= 173.73[/tex]
And the value for n rounded up would be n = 174
The diameter, D, of a sphere is 15.2m. Calculate the sphere's volume, V.
Derive R = v0 2 sin2θ0 / g for the range of a projectile on level ground by finding the time t at which y becomes zero and substituting this value of t into the expression for x − x0, noting that R = x − x0.
Answer:
R = V₀² Sin 2θ₀/g
Step-by-step explanation:
Consider a projectile motion with following properties:
R = range of projectile
V₀ = Launch Velocity of Projectile
θ₀ = Launch Angle
V₀ₓ = V₀ Cos θ₀ = x - component of launch velocity
V₀y = V₀ Sin θ₀ = y - component of launch velocity
t = time to reach maximum height
T = 2t = total time of flight
First we use 1st equation of motion in vertical direction to find value of "t":
Vfy = V₀y + gt
where,
Vfy= final vertical velocity at highest point = 0 m/s
g = -g (for upward motion)
V₀y = V₀ Sin θ₀
Therefore,
0 = V₀ Sin θ₀ - gt
t = V₀ Sin θ₀/g
Now the total time of flight will be:
T = 2t = 2 V₀ Sin θ₀/g
Since, the horizontal velocity of the projectile remains uniform throughout the motion. Therefore:
x - x₀ = V₀ₓ T
where,
x - x₀ = R = Range of Projectile
V₀ₓ = V₀ Cos θ₀
Therefore,
R = (V₀ Cos θ₀)(2 V₀ Sin θ₀/g)
R = V₀² (2 Sin θ₀Cos θ₀)/g
since, 2 Sin θ Cos θ = Sin 2θ
Therefore,
R = V₀² Sin 2θ₀/g
the diagram shows a circle drawn inside a square the circle touches the edges of the square
Answer:
69.5309950592 cm²
Step-by-step explanation:
Area of Square:
Area = [tex]Length * Length[/tex]
Area = 18*18
Area = 324 square cm
Area of circle:
Diameter = 18 cm
Radius = 9 cm
Area = [tex]\pi r^2[/tex]
Area = (3.14)(9)²
Area = (3.14)(81)
Area = 254.469004941 square cm
Area of Shaded area:
=> Area of square - Area of circle
=> 324 - 254.469004941
=> 69.5309950592 cm²
Apply the distributive property to factor out the greatest common factor of all three terms. {10a - 25 + 5b} =10a−25+5b =
Answer:
5(2a -5 + b)
Step-by-step explanation:
(10a - 25 + 5b) = 5( 2a - 5 + b)
5(b + 2a - 5) = 5(2a - 5 + b)
Answer:
5(2a -5 + b)
Step-by-step explanation:
solve and find the value of (1.7)^2
Answer:
2.89
Step-by-step explanation:
just do 1.7×1.7=2.89
A pet store has 10 puppies, including 2 poodles, 3 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement find the probability that both select a poodle.
The probability is
Answer:
2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.
Step-by-step explanation:
do some math
You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats. You sample 80 men, and 55% own cats. You sample 100 women, and 30% own cats. Find the test statistic, rounded to two decimal places. 41.11Incorrect
Answer:
Step-by-step explanation:
This is a test of 2 population proportions. Let 1 and 2 be the subscript for the men and women who own cats respectively. The population proportion of men and women who own cats would be p1 and p2 respectively.
p1 - p2 = difference in the proportion of men and women who own cats.
The null hypothesis is
H0 : p1 = p2
p1 - p2 = 0
The alternative hypothesis is
Ha : p1 ≠ p2
p1 - p2 ≠ 0
it is a two tailed test
Sample proportion = x/n
Where
x represents number of success
n represents number of samples
For men
n1 = 80
p1 = 55/100 = 0.55
x1 = p1n1 = 0.55 × 80 = 44
For women,
n2 = 100
p2 = 30/100 = 0.3
x2 = p2n2 = 0.3 × 100 = 30
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (44 + 30)/(80 + 100) = 0.41
1 - pc = 1 - 0.41 = 0.59
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.55 - 0.3)/√(0.41)(0.59)(1/80 + 1/100) = 3.39
Test statistic = 3.39
SOMEONE HELP! I AM GOING TO FAIL THIS WITHOUT U :(
A survey was taken of students in math classes to find
out how many hours per day students spend on social
media. The survey results for the first-, second-, and
third-period classes are as follows:
First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3,0
Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3
Which is the best measure of center for second period
and why?
Answer:
D) Standard deviation, because there are no outliers that affect the center
Find the distance of the line segment joining the two points:
segment joining the two points: (√ 2,0) and(0, - √ 2)
Answer:
2
Step-by-step explanation:
[tex]\sqrt{((\sqrt{2} - 0)^2 + (0 - (-\sqrt{2}))^2)[/tex]
Suppose the finishing times for cyclists in a race are normally distributed and have a known population standard deviation of 9 minutes and an unknown population mean. A random sample of 18 cyclists is talken and gives a sample mean of 146 minutes. Find the confidence interval for the population mean with a 99% confidence level.
0.10 0.05 0.025 0.005 0.01
1.282 1.645 1.960 2.326 2.576
Answer:
The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.576[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.576*\frac{9}{\sqrt{18}} = 5.46[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 146 - 5.46 = 140.54 minutes
The upper end of the interval is the sample mean added to M. So it is 146 + 5.46 = 151.46 minutes
The 99% confidence interval for the population mean is between 140.54 minutes and 151.46 minutes
Of the six members in the Spirit of Woodstock rock band, four can play guitar. There are three who can play keyboards. All of the singers play guitar, and two of the guitarists also play keyboards. Two members do all three. One guitarist doesn’t sing. How many members sing but do not play keyboards?
Answer:
1 can sing but cannot play keyboard.
Step-by-step explanation:
There are six members in the rock band. We need to identify how many person can sing, play guitar and play keyboard. To identify this we will find out number of member for each activity,
Total 6 members
4 can play guitar
3 can pay keyboard
All singers play guitar but one guitarist cannot sing.
There will be 1 singer who cannot play keyboard.
Applying the Segment Addition Postulate
Point D is on segment BC. Segment BC measures 8x
units in length.
С
D
B
What is the length of segment BC?
units
3x + 8
4x + 10
Answer:
144
Step-by-step explanation:
Find: Length of segment BC
CD+DB=BC
3x+8+4x+10=BC
7x+18=BC
BC also equals 8x (given on the screen shot)
7x+18= 8x
x=18
18 times 8 = 144
Check:
3( 18) + 8 + 4(18) + 10
54+8 + 72+10
64+ 80= 144 TRUE
The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random sample of 100 college grads in Illinois is collected. What is the probability that the mean student loan debt for these people is between $31000 and $33000?
Answer:
the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Step-by-step explanation:
Given that:
Mean = 30000
Standard deviation = 9000
sample size = 100
The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:
[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]
[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]
[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]
From Z tables:
[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]
[tex]P(31000 < X <33000) = 0.1331[/tex]
Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331
Use this information to evaluate the following. Hint: do not try to solve for the value of a.
loga 2 = 0.32
loga 3 = 0.50
loga 5 = 0.73
a. loga 15 =
b. loga (5/3) =
c. loga(8a7)
Answer:
a. 1.23
b. 0.23
c. 7.96
Step-by-step explanation:
Use laws of logarithms:
log(a*b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b*log(a)
log_k(k) = 1
a. log_a(15) = log_a(3*5) = log_a(3) + log_a(5) = 0.50 + 0.73 = 1.23
b. log_a(5/3) = log_a(5) - log_a(3) = 0.73 - 0.50 = 0.23
c. log_a(8*a^7) = log_a(8) + log_a(a^7) = log_a(2^3) + log_a(a^7)
= 3log_a(2) + 7log_a(a) = 3(0.32) + 7(1) = 7.96
a geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .
Answer: [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]
Step-by-step explanation:
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₁
[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]
PLEASEEE HELP ME ITS DUE ASAP PLS
Answer:
V ≈ 1436.03 cm³
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3}[/tex]πr³. r represents the radius, which is 7 cm since the diameter is 14 cm, so plug 7 into the equation as r. Also remember that the question states to use 3.14 for pi/π.
V = [tex]\frac{4}{3}[/tex] (3.14)(7)³
V ≈ 1436.03 cm³
Brainliest for correct awnser! Hannah thinks of a number. She multiplies the number by 2, adds 4, and then divides the result by 3. The number she ends up with is 6. What number did Anna start with? If you work backward to solve this problem, what do you do first?A.Multiply 6 by 2B.Multiply 6 by 3C.Divide 6 by 2D.Subtract 4 from 6
Answer:
B. Multiply 6 by 3
Step-by-step explanation:
Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:
B. Multiply 6 by 3
Your step by step for getting the number Hannah started with:
First, multiply 6 with 3:
6 x 3 = 18
Next, subtract 4:
18 - 4 = 14
Next, divide by 2:
14/2 = 7
Hannah started with the number 7.
~
Answer: Hannah started with 7.
B. Multiply 6 by 3
Explanation:
Let the number be y
2 × y = 2y
(2y + 4)/3 = 6
2y + 4 = 6×3 = 18
2y + 4 = 18
2y = 18 - 4 = 14
y = 14/2 = 7
To solve the problem backward, the first step is to multiply 6 by 3.
Express the confidence interval 0.333 less than p less than 0.999 in the form Modifying Above p with caret + or - E. Modifying Above p with caret + or - E = + or -.
We are being asked to express the confidence interval " [tex]0.333 < p < 0.999[/tex] " in the form [tex]P + / - E[/tex]. Well, just take a look at procedure below for the first half of the problem,
[tex]P = ( 0.999 + 0.333 ) / 2,\\E = ( 0.999 - 0.333 ) / 2[/tex]
As you can see, for this first bit we took the average of the numbers, for the second we subtracted one from the other, and now let us approximate each value -
[tex]P = ( About ) 0.666,\\E = ( About ) 0.333[/tex]
And so, [tex]P + / - E[/tex] should be [tex]0.666 + / - 0.333[/tex]. That is our solution!
help with this I don't know how to solve.
Answer:
sinR = 0.7184
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
sin∅ = opposite/hypotenuse
Step 1: Find missing leg length
16² + b² = 23²
b² = 23² - 16²
b = √273
Step 2: Find sinR
sinR = √273/23
sinR = 0.718379
If 3/4 and 12/x are equivalent what is the value of x
Answer:
x = 16
Step-by-step explanation:
Simply set them equal to each other and solve:
3/4 = 12/x
3x = 48
x = 16
Answer:
16
Step-by-step explanation:
3/4 = 12/x
Cross multiply.
3 × x = 12 × 4
3x = 48
Divide both sides by 3.
3/3x = 48/3
x = 16
what is the property of 9 + (8 + 1) = (9 + 8) + 1
Answer:
associative property of addition
Step-by-step explanation:
There are various properties of mathematics.
One of these is called the associative property of addition, which states that for three numbers a, b, and c:
(a + b) + c = a + (b + c)
Basically, this means that given an addition statement, no matter if we change the order of how we solve it (solving a + b first or solving b + c first), we will still obtain the same result.
Therefore, here, it's clearly a representation of the associative property of addition, and that's the answer.
~ an aesthetics lover
Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.
Answer:
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles
Step-by-step explanation:
Step(i):-
Given mean of the Population = 100 miles per day
Given standard deviation of the Population = 23 miles per day
Let 'X' be the normal distribution
Let x₁ = 86
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]
Let x₂= 86
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]
Step(ii):-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)
= P(Z≤ 1.08) - P(Z≤ -0.61)
= 0.5 +A(1.08) - ( 0.5 - A(-0.61))
= A(1.08) + A(0.61) ( A(-Z)= A(Z)
= 0.3599 + 0.2291
= 0.5890
Conclusion:-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles per day
A jug of milk contains 3 quarts of milk. Micheal pour 1 pint of milk from the jug. How many pint of milk is left in the jug
Answer:
5 pints of milk.
Step-by-step explanation:
Note the unit conversion:
1 quart = 2 pint.
There are 3 quarts of milk. Multiply 3 with 2 to get the amount of pints in the jug:
3 x 2 = 6
The jug of milk has 6 pints of milk. Michael then pours 1 pint of milk. Subtract 1 from 6:
6 - 1 = 5
There are 5 pints of milk left in the jug.
~
Answer:
[tex]2.5[/tex]
Step-by-step explanation:
1 quart = 2 pints
1 pint = 0.5 quarts
[tex]3 - 0.5 = 2.5[/tex]
[tex]=2.5q[/tex]
Hope this helps.
What is m<3 ? M<6 is and m<8 is (x+5
Answer:
m∠3 = 115 degrees
Step-by-step explanation:
angle 6 and angle 8 are on a straight line
we know that sum of angles on straight line is 180
therefore
m∠8 = x+5
m∠6 + m∠8 = 180
2x - 5 + x+5 = 180
=> 3x = 180
=> x = 180/3 = 60
Thus,
m∠6 = 2x-5 = 2*60 - 5 = 115
we know that for two parallel lines cut by a transversal
alternate opposite angles are equal
m∠6 and m∠3 are alternate opposite angles
thus
m∠6 = m∠3 = 115 (answer)
Find the square root of 8-2√5
Answer:
1.88
Step-by-step explanation:
8-2√5=3.527864045
square root of 3.527864045=1.87826090972
the question will probably want it to 2d.p (decimal places) which means the answer would be 1.88
Answer:
The square root of 8 - 2√5 is
[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]
Step-by-step explanation:
To find the square root
8-2√5 must be in the form √a - √b where a > b
√ 8 - 2√5 = √a - √b
Square both sides
8 - 2√5 = (√a - √b)²
That's
8 - 2√5 = (a + b) - 2√ab
Since the two surd expressions are equal we can equate them
That's
8 = a + b ........ 1
a = 8 - b ........ 2
2√5 = 2√ab
Simplify
Divide both sides by 2
√5 = √ab
square both sides
We have
5 = ab ....... 3
Substitute a = 8 - b into equation 3
5 = ( 8 - b)b
5 = 8b - b²
b² - 8b + 5 = 0
After solving
b = 4 + √ 11 or 4 - √ 1
Since b is less than a
b = 4 - √11
a = 4 + √11
So the square root of 8 - 2√5 is
[tex] \sqrt{4 + \sqrt{11} } \: - \sqrt{4 - \sqrt{11} } [/tex]
Hope this helps you.
Explain the areas in which you will find integration to be significant in your day to day work as an EHT.
Answer:
Step-by-step explanation:
An EHT is an Environmental Health Technician. Integration (Integral Calculus, if that's what you mean) will be applied to an Environmental Health Technician's job in the following way:
1. In the analysis or examination of samples from an environment, such as soil sample, water sample, domestic waste sample, septic waste sample, etc.
Essentially, Integral Calculus (and other forms of Maths) must be studied, before a person is able to be an Environmental Health Technician.
Degrees in any of the following fields are a necessary criterion;
- Applied Science
- Public Health
- Environmental Science
- Biochemistry
- Health Data Analysis
Determine the product of (4.2 × 10–1) ⋅ (5.7 × 10–1). Write your answer in scientific notation. Question 7 options: A) 239.4 × 10–1 B) 2.394 × 10–1 C) 23.94 × 10–1 D) 239.4 × 10–2
Answer:
Its B
Step-by-step explanation:
B is the proper answer in scientific notation and scientific notation is only one decimal placed
The most common form of scientific notation inserts a decimal point after the first significant digit
What is the measure of angle z in this figure?
Enter your answer in the box.
z =
°
Two intersection lines. All four angles formed by the intersecting lines are labeled. Clockwise, the angles are labeled 124 degrees, x degrees, y degrees, and z degrees.
Answer:
z= 56°
hope u understood it...
Answer:
Z=56
Step-by-step explanation:
Because i said so
What is the area of the sector shown in the diagram below?
Answer:
(B ) . 34.2cm^2
Step-by-step explanation:
[tex]A = \frac{\alpha }{360} \times \pi r^2\\\alpha=20 \\r = 14\\\\A =\frac{20}{360} \times 22/7\times 14^2\\A = 1/18 \times4312/7\\A =34.2 cm^2[/tex]
Which of the following best describes the dashed line shown in the regular
octagon below?
A. Altitude
B. Base
C. Apothem
D. Leg
Answer: Apothem
Step-by-step explanation: Half of an octagon is called an apothem
The dashed line shown in the regular octagon is called an apothem.
What is an octagon?Octagon is an eight-sided two-dimensional geometrical figure. An octagon consists of 8 interior angles and 8 exterior angles. The sum of the interior angles of an octagon is 1080°, and the sum of its exterior angles is 360°.
Given is a regular octagon, we need to determine the asked part of the given octagon is called what,
So, the part asked is called the apothem.
A line from the center of a regular polygon at right angles to any of its sides is called an apothem.
Hence, the dashed line shown in the regular octagon is called an apothem.
Learn more about octagon, click;
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