Answer:
The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195
Step-by-step explanation:
The six measurements are:
202, 164, 157, 177, 113, 213
Sample mean:
Sum of all values divided by the number of values which is 6. So
[tex]S_m = \frac{202+164+157+177+113+213}{6} = 171[/tex]
Sample standard deviation:
Square root of the difference squared between each value and the mean, and divided by 1 subtracted by the sample size. So
[tex]s = \sqrt{\frac{(202-171)^2+(164-171)^2+(157-171)^2+(177-171)^2+(113-171)^2+(213-171)^2}{5}} = 35.69[/tex]
Confidence interval
We have the standard deviation for the sample, which means that the t-distribution will be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.365
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.365\frac{35.69}{\sqrt{6}} = 49[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 171 - 49 = 122 ppm
The upper end of the interval is the sample mean added to M. So it is 171 + 49 = 220 ppm
The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195
In the following algebraic expression, determine the coefficients. -x-12+y 3 The coefficients are
Answer:
-1 and 1/3
Step-by-step explanation:
Answer:
Answer:
-1 and 1/3
Step-by-step explanation:
Step-by-step explanation:
1 . Josie is taking a family vacation and she had to do a last minute grocery shop for the trip. She needs to buy graham crackers for S'mores . A 12 once box is priced at $3.49 and a 16 once box is priced at $3.99. Which is the better deal?
2. Todd drives 450 miles in 9 hours. What is his average speed ?
3. A box of 80 Legos cost $4. How much does 1 lego cost ?
prove trigonometric identity:
[tex] { \sin}^{2} + \cos ^{2} = 1[/tex]
Please show proof and explanation I really need help
from the pic above, hope it helps you
Helpppp Quickk!!! Solve the following ewuation: 3x=-12
Answer:x=-2
Step-by-step explanation:
3 x -2^2
3 x -4 = -12
Answer:
[tex]3 {x}^{2} = - 12 \\ {x}^{2} = - 12 \div 3 \\ {x}^{2} = - 4 \\ x = \sqrt{ - 4 } \\ x = \frac{ + }{} 2[/tex]
Option D, hope it helps!
5/6 = 25/? Fractions
Answer:5/6=25/blank
Step-by-step explanation:so 5/6 the top is times five forget the bottom for now just think of 5 and 25
[5x5] equals 25 so you already got the top
now for the bottom since you multiply the top by five you have to do that to the bottom so that will be [6x5] that equals 30 so you got your answer
[25/30]
find each angle or arc measure
Answer:
176
Step-by-step explanation:
The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.
SO JML is 88*2
372.3 in expanded notation
Answer: Expanded Notation Form:
300 + 70 + 2 + 0.3= 372.3
Step-by-step explanation:
(
CH
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to
(6)?
)
Answer:
[tex]\dfrac{17}{13}[/tex]
Step-by-step explanation:
Given that,
r(x) = 3x - 1 and s(x) = 2x + 1
We need to find an expression equivalent to [tex]\dfrac{r}{s}(6)[/tex].
We know that,
[tex]\dfrac{r}{s}(6)=\dfrac{r(6)}{s(6)}[/tex]
Put x = 6 in the above expression
[tex]=\dfrac{3(6)-1}{2(6)+1}\\\\=\dfrac{18-1}{12+1}\\\\=\dfrac{17}{13}[/tex]
So, the equivalent expression is equal to [tex]\dfrac{17}{13}[/tex].
describe the cross section
Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal distribution, and the three times are independent of one another. The mean values are 20, 15, and 30 min, respectively, and the standard deviations are 1, 2, and 1.5 min, respectively. What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component
Answer:
0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Sum of normal variables:
When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.
The mean values are 20, 15, and 30 min, respectively:
This means that [tex]\mu = 20 + 15 + 30 = 65[/tex]
The standard deviations are 1, 2, and 1.5 min, respectively.
This means that [tex]\sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926[/tex]
What is the probability that it takes at most 1 hour of machining time to produce a randomly selected component?
Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 65}{2.6926}[/tex]
[tex]Z = -1.86[/tex]
[tex]Z = -1.86[/tex] has a pvalue of 0.0314
0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component
The height of a ball dropped from the top of a building 512 feet high is given by h(t) = -16t2 + 512, where t is in seconds and h is in feet. a) When will the ball reach the ground? Approximate your answer to two decimal places. (Hint: The height is O when it hits the ground.)
b) Why can t only be a positive value? Explain in a complete sentence.
Interest rates are expected as a percentage of
Answer:
the principle amount
Step-by-step explanation:
I don't know how to explain it without an analogy so...
If a loan is charging a 10% interest amount of a $120 loan than the interest would be $12.
You multiply the interest rate by the total amount and that's how you find the amount of money you make off of interest.
(The total amount and principle amount are the same thing)
Consider the following regression model: Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε, where the dummy variables Spring, Summer, and Fall represent the qualitative variable Season (spring, summer, fall, winter), and the dummy variable Rain is defined as Rain = 1 if rainy day, Rain = 0 otherwise. What is the regression equation for the winter rainy days?
Answer:
The regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".
Step-by-step explanation:
Given:
Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε ...........(1)
Since there can be only one of spring, summer,fall, and winter at a point in time or in a season, we will have the following when there are winter rainy days:
Spring = 0
Summer = 0
Fall = 0
Rain = 1
Substituting all the relevant values into equation (1) and equating ε also to 0, a reduced form of equation (1) can be obtained as follows:
Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0
Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0
Humidity = (β0 + β5) + β1Temperature
Therefore, the regression equation for the winter rainy days is "Humidity = (β0 + β5) + β1Temperature".
The regression equation for winter rainy days is
Humidity = β0 + β5 + β1Temperature
The regression model is given as:
Humidity = β0 + β1Temperature + β2Spring + β3Summer + β4Fall + β5Rain + ε
To determine the regression equation for winter rainy days, we consider that:
[tex]Rain = 1[/tex]
This also means that:
[tex]Spring = 0[/tex]
[tex]Summer = 0[/tex]
[tex]Fall = 0[/tex]
ε = 0
Because each of these seasons can only happen one at a time, and the current season is winter
So, the regression equation becomes
Humidity = β0 + β1Temperature + (β2 * 0) + (β3 * 0) + (β4 * 0) + (β5 * 1) + 0
Evaluate the products
Humidity = β0 + β1Temperature + 0 + 0 + 0 + β5 + 0
The sum of 0 is 0. So, we have:
Humidity = β0 + β1Temperature + β5
Rewrite as:
Humidity = β0 + β5 + β1Temperature
Hence, the regression equation for winter rainy days is
Humidity = β0 + β5 + β1Temperature
Read more about regression equations at:
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The question is in the attatchment!
Answer:
The answer is 4
A triangle has side lengths of 12 centimeters, 12 centimeters, and 18 centimeters. What kind of triangle is it?
Answer:
isosceles triangle
Step-by-step explanation:
2 sides the same
Point M is located at (6, 7) on the coordinate plane. Point N is located 5 units to the left and 2 units down from point
M.
Answer:
(1,5)
Step-by-step explanation:
x:
6-5=1
y:
7-2=5
5) Round $2.879 to the nearest cent
6) Round 56.8567863 to the nearest tenth (one decimal place)
Can you please help me :)
Answer:
P= -3
X= -18
Y= -7
S= -70
B= -9
M= -5
N= 0
Q= -22
The second slide's answers are attached to this message as a pic ;)
Step-by-step explanation:
Hope it was helpful dear ;)
INDEPENDENT PRACTICE 3. Teresa makes a circular pizza with a 14-inch diameter. Which is the approximate area of her pizza? A. 43.96 in? B. 87.92 in2 C. 153.86 in2 D. 615.44 in?
A. 43.96in?
Step_by_step explanationThe values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-group 20 years to 30 years because they are either 1.5 times the interquartile range (IQR) greater than the upper quartile or 1.5 times the IQR less than the lower quartile. Using the same method for identifying outliers, which of the three values are identified as outliers for the age-group 40 years to 50 years
Answer:
Only 60 is an identified outlier
Step-by-step explanation:
Given
Age group: 40 to 50
[tex]Min = 60[/tex] [tex]Q_1 = 70[/tex] [tex]Median= 73[/tex]
[tex]Q_3 = 76[/tex] [tex]Max = 85[/tex]
Conditions for outlier
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]Value < Q_1 - 1.5 * IQR[/tex]
See attachment for complete question
Required
Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years
First, calculate the IQR of group 40 to 50.
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
Where:
[tex]Q_3 = 76[/tex] and [tex]Q_1 = 70[/tex]
So:
[tex]IQR = 76 - 70[/tex]
[tex]IQR = 6[/tex]
Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)
Testing 60
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]60 > 76 + 1.5 * 6[/tex]
[tex]60 > 76 + 9[/tex]
[tex]60 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]60 < 70 - 1.5 * 6[/tex]
[tex]60 < 70 - 9[/tex]
[tex]60 < 61[/tex] --- True
Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years
Testing 62
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]62> 76 + 1.5 * 6[/tex]
[tex]62 > 76 + 9[/tex]
[tex]62 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]62 < 70 - 1.5 * 6[/tex]
[tex]62 < 70 - 9[/tex]
[tex]62 < 61[/tex] --- False
Because both conditions are false, then 62 is not an outlier of group 40 - 50 years
Testing 84
Condition 1
[tex]Value > Q_3 + 1.5 * IQR[/tex]
[tex]84> 76 + 1.5 * 6[/tex]
[tex]84 > 76 + 9[/tex]
[tex]84 > 85[/tex] --- False
Condition 2
[tex]Value < Q_1 - 1.5 * IQR[/tex]
[tex]84 < 70 - 1.5 * 6[/tex]
[tex]84 < 70 - 9[/tex]
[tex]84 < 61[/tex] --- False
Because both conditions are false, then 84 is not an outlier of group 40 - 50 years
helpppppppppp me
i ned help
Answer:
C) 84 cm²
Step-by-step explanation:
The question is asking for the surface area of the square pyramid. So we need to get the area of all the surfaces, then add them together.
6 cm × 6 cm = 36 cm²
1/2(6 cm × 4 cm) = 12 cm² (There are 4 of these sides)
12 cm² + 12 cm² + 12 cm² + 12 cm² + 36 cm² = 84 cm²
PLEASE I NEED THE ANSWERS FOR THESE THREE QUESTIONS ASAP
Answer:
2) 49
3) 8
4) 85
Hope you still need them and that they are correct!
In Littletown, the probability that a baseball team goes to the city playoffs is
0.20. The probability that the team goes to the state playoffs given that the
team goes to the city playoffs is 0.50.
What is the probability that a randomly selected team from Littletown goes to
the city and state playoffs?
A. 0.15
B. 0.25
C. 0.10
Ο Ο
D. 0.20
SUBMIT
Answer:
C. 0.10
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Goes to the city playoffs
Event B: Goes to the state playoffs.
In Littletown, the probability that a baseball team goes to the city playoffs is 0.20.
This means that [tex]P(A) = 0.2[/tex]
The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.50.
This means that [tex]P(B|A) = 0.5[/tex]
What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?
This is [tex]P(A \cap B)[/tex]. So
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)*P(B|A) = 0.2*0.5 = 0.1[/tex]
The correct answer is given by option C.
i neeed help and quick its due at 3:15
Answer:
it c
Step-by-step explanation:
Please help!
Given that the glass can hold a maximum volume of 60 cm3, what is the height of the glass? Round to the nearest tenth of a centimeter.
Answer:
The volume of cone = Maximum holding of glass = 60 cube cm(cm^3)
Step-by-step explanation:
Cone formula:
[tex] v = \frac{1}{3} \pi \: r {}^{2} h[/tex]
The radius is 3cm and Volume is 60cm^3.
if pi =~ 3 So the "h" is 6.66 cm.
"h" is distance from cone's head to its base.
The "H"( height of glass) = 6.66 + 7 = 13.6 =~ 14
9514 1404 393
Answer:
13.4 cm
Step-by-step explanation:
The volume of the cone is given by ...
V = 1/3πr²h
For the given dimensions, we have ...
60 cm³ = 1/3π(3 cm)²h
20/π cm = h ≈ 6.37 cm . . . . . . . . . . . divide by the coefficient of h
The overall height of the glass, H, is 7 cm more than the value of h.
H = 7 cm +6.4 cm = 13.4 cm
The height of the glass is 13.4 cm.
A rectangular garden measures 26ft by 37ft. Surrounding (and bordering) the garden is a path 2ft wide. Find the area of this path. Be sure to include the correct unit in your answer.
The speed of a boat in still water is 10 km/hr. The boat travels 24 km upstream, turns
around and comes back the same route. The entire trip takes 5 hours, What is the
speed of the current?
Answer:
rate of the current = 2 km/hr
Step-by-step explanation:
d = rt
Let c = rate of the current
Rate of boat downstream = 10 + c
Time going downstream = 24/(10 + c)
Rate of boat upstream = 10 - c
Time going upstream = 24/(10 - c)
Since the total time is 5 hr, then
24/(10 + c) + 24/(10 - c) = 5
24(10 - c) + 24(10 + c) = 5(10 + c)(10 - c)
240 - 24c + 240 + 24c = 500 - 5c^2
480 = 500 - 5c^2
5c^2 = 20
c^2 = 4
c = 2 or -2
Since a rate cannot be negative, the rate of the current = 2 km/hr
Darla made two batches of chocolate chip cookies each batch made 25 cookies darling use 16 total ounces of chocolate chips the chocolate chips were equally distributed through the cookies how many ounces of chocolate chips were in each cookie
Answer:
0.32
Step-by-step explanation:
Equation: 16/(2(25)) = ?
Simplify: 16/50
Solve: .32
There are 0.32 ounces of chocolate in each cookie.
There were 0.64 pounds of Choco chips in each cookie.
What is unit rate?Unit rate is a rate with 1 as the denominator. A rate is a ratio used to compare different amounts of different quantities that are somehow related.
Given that, Darla made 25 cookies with 16 pounds of Choco chips, we need to find the amount of Choco chips used in each cookie,
So,
16 pounds for 25 cookies
Therefore,
1 cookie = 16/25 pounds
1 cookie = 0.64
Hence, there were 0.64 pounds of Choco chips in each cookie.
Learn more about unit rate, click;
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Solve for x 4x+3 2x+9
Answer:
x = 28°
I hope it's helps you
Answer:
X=28
Step-by-step explanation:
(4x+3)+(2x+9)=180
6x+12=180
6x=168
X=28
What’s the sum of 1,015 and 119?
A. 1,314
B. 1,224
C. 896
D. 1,134
Step-by-step explanation:
Sum is addition
1015+119 = 1134
