The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: 6,3,14,11,14,6 round the final answer to one decimal place.
The variance for the data set is 18.
What is a variance?
The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.
Here we have to find the variance for this data set.
Given data:
The age of six grandchildren in a family is = 6, 3, 14, 11, 14, 6
The mean = 6+3+14+11+14+6/ 6
= 9
The variance = (6-9)² + (3-9)² + (14-9)² +(11-9)² + (14-9)² + (6-9)²/ 6
= 9+36+25+4+25+9/ 9
= 18
Therefore the variance is 18.
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A mom mixes 9ounces of juice with 3 ounces of water. What percent of the drink is juice?
Answer: 75%
Step-by-step explanation:
9 + 3 = 12
9/12 = 3/4
3/4 = 75%
the manufacturer of a new compact car claims that the car will average at least 35 miles per gallon in general highway driving. for 100 test runs, the car averaged 35.5 miles per gallon with a standard deviation of 2.5 miles per gallon. suppose that the manufacturer tests the following hypotheses: h subscript 0 : mu equals 35 h subscript 1 : mu greater than 35 consider the 1% significance level. what is the power of the test if the actual average fuel efficiency is 36 miles per gallon?
The power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
What is the standard deviation?
The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.
We want to test [tex]\mu_0 > 35[/tex] at the level [tex]\alpha=0.01[/tex], where the true mean is [tex]\mu_1=36,\sigma\approx4, n=100[/tex]
The power of a right-tailed test is given by
[tex]1-\beta=P(Z > [z_\alpha-\frac{\sqrt{n}}{\sigma}(\mu_1-\mu_0)])\\\\1-\beta=P(Z > [2.33- \frac{\sqrt{100}}{4}(36-35)])\\\\1-\beta=P(z > -0.17)\\\\power=0.5675[/tex]
Hence, the power of the test, if the actual average fuel efficiency is 36 miles per gallon, is 0.5675.
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dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
Answer:
6 hours
Step-by-step explanation:
dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
60h + 50 > 400
subtract 50 from both sides:
60h > 350
divide both sides by 60:
h > 5.8333
rounded: 6 hours
In a urvey of 300 houe wire. It wa dicovered that 150 had read magazine A, 200 had read Magazine B and 156 had read magazine C It wa further dicovered that 48 had read A and B 60 had read B and a while 52 hand read A and a. Find The number of houewive that had read. All three magazine
Answer:b
Step-by-step explanation:
. AB :
=
CB =
AC = 4
Answer:
Step-by-step explanation:
its 20
A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys. Since it is true that some boys do better than girls and some girls do better than boys, the researcher must use a two tailed test.
True OR False
The statement of the given hypothesis condition is False.
What is hypothesis testing?
A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.
Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.
i.e. [tex]\mu_{1} > \mu_{2}[/tex]
">" sign implies that right-tailed test i.e. one-tailed right-sided.
Hence, the given statement is FALSE.
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One historic earthquake had a magnitude of 9.0 on the Richter scale. How many times more intense was this than another historic earthquake that had a magnitude of 8.3? (Round your answer to the nearest whole number.)
Answer:
1
Step-by-step explanation:
9/8.3 = 1.0843, rounded to the nearest whole number is 1
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The value of the the function h(x) at x = 4 is given as follows:
8.7.
The quadratic regression equations for each table are given as follows:
y = -0.127x² + 4.699x - 27.777.y = 32.86x² - 379.14x + 1229.14.How to obtain the value at x = 4?The function for the first item is defined as follows:
h(x) = 50/(5.5 + 8e^(-0.9x)).
At x = 4, the value assumed by the function is obtained replacing the lone instance of x by 4, hence:
h(4) = 50/(5.5 + 8e^(-0.9(4))).
Then a calculator is used to obtain the exact value due to the exponential, hence:
h(4) = 8.7.
How to obtain the regression equations?The regression equations are obtained inserting the points of each table into a quadratic regression calculator.
For the first table, the points are given as follows:
(16, 15), (18, 15.6), (20, 15.7), (21, 15), (23, 13.1), (26, 8.9), (27, 6.6).
Hence the equation is of:
y = -0.127x² + 4.699x - 27.777.
For the second table, the points are given as follows:
(3, 330), (4, 276), (5, 263), (6, 86), (7, 174), (8, 198), (9, 553).
Hence the equation is of:
y = 32.86x² - 379.14x + 1229.14.
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A factory makes components used in jet engines, including reinforced steel washers. The washers are required to have a very precise thickness. The thickness of the washers follow a normal distribution with mean 1. 59 millimeters and standard deviation 0. 042 millimeters. A technician randomly samples washers and calculates the mean of their thicknesses, which is. What is the probability that ?.
The probability that [tex]\bar{x}[/tex] < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.
As given in the question,
Normal distribution with mean 'μ' = 1.59 millimeters
Standard deviation 'σ' = 0.042 millimeters
Sample size 'n' = 20
standard error = σ /√n
= 0.042 / √20
= 0.00933
Probability that [tex]\bar{x}[/tex] < 1.57 is
X = 1.57
s = 0.0093
P( X < 1.57)
= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]
= P ( z < -2.14 )
Using z - table p value is
= 0.01617
= 0.0162
Therefore, the probability for the [tex]\bar{x}[/tex] < 1.57 is equal to 0.0162.
The complete question is :
A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?
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which assessment finding(s) are likely to cause noncompliance with antiretroviral treatment? select all that apply.
A. Poor understanding of HIV
B. Cognitive impairment
C. Substance abuse
D. Unstable housing
What is the value of x?
Enter your answer In the box
X =
A+B+C=180
55+80+x=180
135+x=180
x=180-135
x=45
Is the following relation a function?
Answer:
Yes
Step-by-step explanation:
I WILL OPEN MY ALT AND COMENT AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
b = -3
Step-by-step explanation:
1. Rearrange Terms
-3(3 + 6b) = 36 - 3b
-3(6b + 3) = 36 - 3b
2. Distribute
-3(6b + 3) = 36 - 3b
-18b - 9 = 36 - 3b
3. Rearrange Terms
-18b - 9 = 36 - 3b
-18b - 9 = -3b + 36
4. Add 9 to both sides
-18b - 9 = -3b + 36
-18b - 9 + 9 = -3b + 36 + 9
5. Simplify
-18b - 9 + 9 = -3b + 36 + 9
-18b = -3b + 45
6. Add 3b to both sides
-18b = -3b + 45
-18b +3b = -3b + 45 + 3b
7. Simplify
-15b = 45
8. Divide both sides by the same factor
-15b = 45
[tex]\frac{-15b}{-15}[/tex] = [tex]\frac{45}{-15}[/tex]
9. Simplify
b = -3
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Answer:
WWWWWW
Step-by-step explanation:
A plot of land for sale has a width of x ft. , and a length that is 8ft less than its width. A farmer will only purchase the land if it measures 240 square feet. What value of x will cause the farmer to purchase the land?.
If width i.e. x is 20 ft then the farmer will purchase the land.
Given,
width of land = x ft
length of land = ( x - 8 ) ft
Area of land =240 square feet
To determine x use formula,
Area of land =length * width
[tex]240=(x-8)*x\\\\240=x^2-8x\\\\x^2-8x-240=0\\\\x^2+12x-20x-240=0\\\\x(x+12)-20(x+12)=0\\\\(x+12)(x-20)=0\\\\x=-12\ or\ 20[/tex]
x cannot be negative.
x=20 ft
Thus, if width i.e. x is 20 ft then the farmer will purchase the land.
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I need some help on this fast.
Answer: -2
Step-by-step explanation:
Given the algebraic expression the quantity 125 times x to the seven-thirds power end quantity to the negative one-third power comma, create an equivalent expression.
The expression that results from applying the law of indices and expression is 5x^(-7/3).
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.
Here,
The resulted expression will be,
(125x)^(7/3)^(-1/3)
125=5^3
(a^n)^m = a^mn
(5x)^3^7/3^-1/3
(5x)^7*-1/3
5x^(-7/3)
The resulted expression will be 5x^(-7/3) using the law of indices and expression.
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at what speed, as a fraction of c , will a moving rod have a length 60% that of an identical rod at res
As a fraction of c, the length will be 60% at v/c = 0.76
The length of the moving rod = 60%
Using the formula for length contraction-
L = L_o(√(1 - (v²/c²))
Where;
v = The speed of the object
c = The speed of light
L = The length of the object at a moving speed
L_o = The length of the object at rest
Thus,
L = 65%
L_o = 0.65
Substituting the values -
0.65L_o = L_o[√(1 - (v²/c²))]
Dividing both sides by L_o -
0.65 = √(1 - (v²/c²))
Squaring both sides -
0.65² = (1 - (v²/c²))
v²/c² = 1 - 0.65²
v²/c² = 0.5775
Taking the square root of both sides gives;
v/c = 0.76
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2. Find the slope of the line that passes through (-4,4) and (-4,18)
Answer: 14
Step-by-step explanation:
The equation to find slope is y2-y1/x2-x1 or in simpler terms is rise over run.
We see that the y increase by 14 so the rise is 14 and the x is the same so the run is 0. So the slope is 14.
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a coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 19.0 cm. reflection from the surface of the shell forms an image of the 1.5-cm-tall coin that is 6.50 cm behind the glass shell. part a where is the coin located? express your answer in centimeters. s
The location of the coin next to the convex side of a thin spherical glass shell is 3.68 cm.
According to the question,
Radius of curvature : 19 cm
Size of image formed : 1.5cm
Distance of coin from glass shell : 6.5cm
The position of the coin placed next to the convex side of a thin spherical glass shell is calculated as follows;
1/d = 1/f - 1/d'
where;
d' is the position of the coin's image
d position of the coin
f is focal length
Focal length = r/2 =19/ 2 = 9.5 cm
=> 1/d = 1/9.5 - (-1/6.5)
=> 1/d = 1/9.5 + 1/6.5
=> 1/d = 0.1052 + 0.1538
=> 1/d = 0.259
=>d = 1/0.259
d = 3.86 cm
Thus, the position of the coin placed next to the convex side of a thin spherical glass shell is 3.86 cm.
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Divide. Write your answer in scientific notation.
7 x 10 -5
7 x 10 -6
Answer:
(65) (64)
Step-by-step explanation:
If the area of the pentagon is 36, what is the area of the larger pentagon?
Answer:
64
Step-by-step explanation:
16 ÷ 12 = 1.33 (rounded to 2 decimal places)
1.33 = scale factor
1.33² = area scale factor
1.33² × 36 = 64 (rounded to a whole number)
Answer: 64 would be the area
Step-by-step explanation:
I need help to do this bc my math teacher can’t explain it well-
Answer:
b. 1 1/4
c. 11 3/8
d. 1 4/7
Step-by-step explanation:
b. 3 - 1 3/4
2 4/4 - 1 3/4
[4/4 - 3/4 = 1/4] and [2 - 1 = 1]
1 + 1/4
1 1/4
c. 7 3/8 + 4
Add the whole numbers.
11 3/8
d. 4 - 2 3/7
3 7/7 - 2 3/7
[7/7 - 3/7 = 4/7 and 3 - 2 = 1]
1 + 4/7
1 4/7
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Answer:
The goal is to make the denominators the same.
[tex]\frac{numerator}{denominator}[/tex]
Here's how to solve "b" (I explained it so you can do the other ones)
b.
[tex]3 - 1\frac{3}{4}[/tex]
Turn the 3 into a fraction (you can put any number over 1 and it will be the same)
[tex]\frac{3}{1} - 1\frac{3}{4}[/tex]
Next, let's turn the [tex]1\frac{3}{4}[/tex] into an "improper fraction". Right now, it is a mixed number. Multiply the denominator by the whole number on the left, and then add it to the numerator. The denominator will stay the same.
4 * 1 = 4
4 + 3 = 7
[tex]1\frac{3}{4}[/tex] → [tex]\frac{7}{4}[/tex]
Okay, so now we have this:
[tex]\frac{3}{1} - \frac{7}{4}[/tex]
This is getting easier! But to subtract, we have to make the denominators the same. Let's multiply the top and bottom of [tex]\frac{3}{1}[/tex] by 4.
[tex]\frac{3 * 4}{1 * 4} = \frac{12}{4}[/tex]
Now we have:
[tex]\frac{12}{4} -\frac{7}{4}[/tex]
One final step, subtract the numerators! Leave the denominators as they are.
12 - 7 = 5
Our answer is:
[tex]\frac{5}{4}[/tex]
The frequency table shows how many hours Ashley worked over a thirty day period. Using the frequency table, find the average number of hours Ashley worked per day. (Round to the nearest tenth.)
Responses
A 6.0
B 6.5
C 6.7
D 7.0
E 6.6
The average number of hours that Ashley worked per day is obtained as follows:
Mean = sum of relative frequencies x outcome
What is shown by the relative frequency table?The relative frequency table shows that absolute frequencies of the number of hours worked, that is, the number of days in which each amount of hours was worked.
Then the relative frequencies are obtained by the division of each of the absolute frequencies by the total number of outcomes, which is the sum of all the relative frequencies.
Finally, the mean value is obtained just like the mean of a discrete distribution, with the multiplication of each outcome by it's relative frequency obtained previously.
Missing InformationThe problem is incomplete, hence I gave a general pattern to find the mean of the data-set.
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A ferris wheel is 45 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? minutes How High are you off of the ground after 4 minutes? meters
If the wheel rotates clockwise, the height function is h(t) = 28.5 + 22.5sin(270 - 36t).
The function's central axis for the height of the Ferris wheel's center is given by h = f(t).
= 6 + 45 ÷ 2 = 6 + 22.5 = 28.5 meters.
The wheel rotates at a speed of 36 degrees per minute since the period of revolution is 10 minutes.
The wheel's direction of rotation—clockwise or counterclockwise—is not specified.
Let's look at both situations:
The present angle, assuming it spins clockwise, is equal to 270 – 36t degrees, where t is the duration in minutes.
Then the height function h = f(t)
= 28.5 + 22.5sin(a)
= 28.5 + 22.5sin(270 - 36t)
If the wheel rotates anti-clockwise, the current angle is
b = 270 + 36t degrees.
Then the height function
h = r(t)
= 28.5 + 22.5sin(b)
= 28.5 + 22.5sin(270 + 36t)
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The parabola y=x^2y=x 2 y, equals, x, squared is reflected across the xxx-axis and then scaled vertically by a factor of 555. What is the equation of the new parabola?.
By using the concept of reflection and scaling, it can be calculated that
New equation of parabola is [tex]y = -5x^2[/tex]
What is reflection and scaling?
Reflection is a mathematical transformation in which a mirror image of an object can be obtained without changing the shape and size of an object.
To draw an object of size proportional to the size of the original object, scaling is used
The equation of the parabola is [tex]y = x^2[/tex]
If it is reflected across x axis, its equation is [tex]y = -x^2[/tex]
Now y = -[tex]x^2[/tex] is scaled vertically by a factor of 5
New equation of parabola
[tex]y = -5x^2[/tex]
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a ship leaves port at noon and has a bearing of s 23° w. the ship sails at 10 knots. (a) how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.? (round your answers to two decimal places.) miles south miles west (b) at 6:00 p.m., the ship changes course to due west. find the ship's bearing and distance from port at 7:00 p.m. (round your answers to one decimal place.) s ° w nautical miles
(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
Given that,
A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.
We have to find
(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west
(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.
We know that,
(a) For 6:00 p.m
Sin(θ)=opposite/ hypothesis
θ=29
Opposite=west
Hypothesis =60
Sin(29°)=w/60
w=29.09nm
West= 29.09nm
Cos(θ)=adjacent/ hypothesis
θ=29
Adjacent= south
Hypothesis =60
Cos(29°)= south/60
south=52.475nm
Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) tan(θ)=opposite/adjacent
Opposite=29.09nm
Adjacent= 52.475nm
Tan(θ)=29.09nm/52.475nm
θ=36.68°
Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
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help fast plsssssssss
Answer:
2 2/3
Step-by-step explanation:
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (t/s)|이 6.2 | 10.8 | 14.9 | 18.1 19.4 20.2 Step 1 We will use either Ls or Rs for the upper and lower estimates. Since the runner's speed is an increasing function, then will give the lower estimate, andR will give the upper estimate. ˇ Step 2 The sub-interval widths At for this situation are At- L--JX
The speed of the runner calculated by the properties of average speed is given by 33.45 feet and the upper limit is 43.45 feet in the last 3 seconds.
The first three seconds of a race saw a runner's speed rapidly grow.
The time is therefore 3 seconds.
The table provides her speed at half-second intervals.
We are aware,
Distance x Time = Speed
Similarly
Distance equals speed x time.
Δt equals 0.5 seconds
Then, the minimum distance travelled overall is equal to
0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).
Terms are multiplied and added.
= 0.5 × 66.9
= 33.45 feet
The maximum distance travelled is equal to
0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)
= 0.5 × 86.9
= 43.45 feet
As a result, her maximum distance in three seconds is 43.45 feet, and her maximum distance in three seconds is 33.45 feet.
Velocity is the rate at which an item's position changes as perceived from a certain point of view and as measured by a given unit of time (for example, 60 km/h northbound).
Velocity is also the direction at which an object is travelling. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that deals with the motion of bodies.
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how many different passwords are there that contain only digits and lower-case letters and satisfy the given restrictions? 1) length is 1010.
There are 36^10 ways that contain only digits and lower-case letters and having the length is 10.
What is password?
A password, also known as a passcode, is private information that typically consists of a string of characters and is used to verify a user's identity.
We have to find the number of ways that contain only digits and lower-case letters and having the length is 10.
Since, there are total 10 digits from '0 to 9' and 26 lower case letters from
'a to z'.
The 10 slots in the password can be anything - digits as lower case letters.
that is,
10 + 26 = 36 options for each slot.
So, the total number of ways are, 36^10.
Hence, there are 36^10 ways that contain only digits and lower-case letters and having the length is 10.
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