Answer:
We conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
Step-by-step explanation:
We are given that slab avalanches studied in a region of Canada had an average thickness of μ = 66 cm.
A random sample of avalanches in spring gave the following thicknesses (in cm);
X: 59, 51, 76, 38, 65, 54, 49, 62, 68, 55, 64, 67, 63, 74, 65, 79.
Let [tex]\mu[/tex] = true mean slab thickness in the Vail region
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 66 cm {means that the mean slab thickness in the Vail region is the same as that in the region of Canada}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 66 cm {means that the mean slab thickness in the Vail region is different from that in the region of Canada}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean thickness = [tex]\frac{\sum X}{n}[/tex] = 61.81 cm
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 10.64
n = sample of avalanches = 16
So, the test statistics = [tex]\frac{61.81-66}{\frac{10.64}{\sqrt{16} } }[/tex] ~ [tex]t_1_5[/tex]
= -1.575
The value of t-test statistics is -1.575.
Now, at a 1% level of significance, the t table gives a critical value of -2.947 and 2.947 at 15 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean slab thickness in the Vail region is the same as that in the region of Canada.
resultado de
x²-3x=0
Answer:
x = 3,0
Step-by-step explanation:
x²-3x=0
1- x(x - 3) = 0
2- x = 0 , x = 3
Answer:
X1=0 X2=3
Step-by-step explanation:
Factorize x²-3x=x*(x-3)=0
So x=0 or x-3=0
SO x1=0 x2-3=0
x2=3
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 17 subjects had a mean wake time of 104.0 min. After treatment, the 17 subjects had a mean wake time of 97.5 min and a standard deviation of 21.9 min. Assume that the 17 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 104.0 min before the treatment? Does the drug appear to be effective?
Answer:
The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and 108.7599 minutes.
This interval contains the mean wake time before treatment and which does not prove to be effective
Step-by-step explanation:
GIven that :
sample size n = 17
sample mean [tex]\overline x[/tex] = 97.5
standard deviation [tex]\sigma[/tex] = 21.9
At 95% Confidence interval
the level of significance ∝ = 1 - 0.95
the level of significance ∝ = 0.05
[tex]t_{\alpha/2} = 0.025[/tex]
Degree of freedom df = n - 1
Degree of freedom df = 17 - 1
Degree of freedom df = 16
At ∝ = 0.05 and df = 16 , the two tailed critical value from the t-table [tex]t_{\alpha/2 , 16}[/tex] is :2.1199
Therefore; at 95% confidence interval; the mean wake time is:
= [tex]\overline x \pm t_{\alpha/2,df} \dfrac{s}{\sqrt{n}}[/tex]
= [tex]97.5 \pm 2.1199 \times \dfrac{21.9}{\sqrt{17}}[/tex]
= 97.5 ± 11.2599
= (86.2401 , 108.7599)
Therefore; the mean wake time before the treatment was 104.0 min
The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and 108.7599 minutes.
This interval contains the mean wake time before treatment and which does not prove to be effective
Find the measure of the indicated angle to the nearest degree.
PLEASE HELP ASAP
Answers
A. 26
B. 42
C. 64
D. 48
Answer:
The answer is option C
Step-by-step explanation:
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 37
The hypotenuse is 41
So we have
sin ? = 37/41
? = sin-¹ 37/41
? = 64.4805
? = 64° to the nearest degreeHope this helps you
Answer:
C.) 64
Step-by-step explanation:
I got it correct on founders edtell
A satellite dish is being designed so that it can pick up radio waves coming from space. The satellite dish will be in the shape of a parabola and will be positioned above the ground such that its focus is 50 ft above the ground. Using the ground as the x-axis, where should the base of the satellite be positioned? Which equation best describes the equation of the satellite?
Answer:
[tex]y=\frac{x^2}{100}+2500[/tex]
Step-by-step explanation:
Given that the satellite is in the shape of parabola and will be positioned above the ground such that its focus is 50 ft, above ground.
let the point at the ground be (0,0) and focus (0,50). Thus, The base is at equal distance from the ground and focus that the vertex is at
(h,k) =(0,25).
Obtain the equation that describes the equation of the satellite as,
[tex](x-h)^2 =4a(y-k)\\
\Rightarrow (x-0)^2=4(25)(y-25)\\
\Rightarrow x^2=100(y-25)\\
\Rightarrow x^2 =100y-2500\\
\Rightarrow y=\frac{x^2}{100}+2500[/tex]
Thus, the equation of satellite is [tex]y=\frac{x^2}{100}+2500[/tex]
Answer:
(0, 25); y = one over one hundred x2 + 25
Step-by-step explanation:
If your on question 7 of (04.04 MC)
It should be the third option. (C)
Brainliest for correct awnser! Over what interval is the function in this graph decreasing?
Answer:
Option (1)
Step-by-step explanation:
In the graph attached,
There are three intervals of the function graphed.
1st interval → -∞ < x < -3
2nd interval → -3 ≤ x ≤ 2
3rd interval → 2 < x < ∞
In the 1st interval, value of the function is constant. [represented by a straight horizontal line]
In the second interval, line graphed is slanting down. (slope of the line is negative).
Therefore, value of the function is decreasing in -3 ≤ x ≤ 2
In 3rd interval, slope of the line is positive. Therefore, function is increasing in the 3rd interval.
Option (1) will be the answer.
Answer: -3 ≤ x ≤ 2 is correct
Step-by-step explanation: I just took the exam :)
Find the maximum and minimum values by evaluating the equation
Answer:
min = -9
max =3
Step-by-step explanation:
C = x-3y
x ≥0
x≤3
y≥0
y≤3
The minimum will be be when x is smallest and y is at its max
x =0 and y = 3
C = 0 - 3(3)
C = 0-9 = -9
The minimum is -9
The maximum occurs when x is largest and y is smallest
x =3 and y = 0
C = 3 - 3(0)
C = 3-0 = 3
The max is 3
Find the limit L for the given function f, the point x 0, and the positive number epsilon. Then find a number delta > 0 such that, for all x, 0less thanStartAbsoluteValue x minus x 0 EndAbsoluteValueless thandelta double right arrow StartAbsoluteValue f (x )minus Upper L EndAbsoluteValueless thanepsilon.
Answer:
L = -25 and δ = 0.02
Step-by-step explanation:
The function f, point [tex]x_0[/tex] and ε is missing in the question.
The function, f is f(x) = - 4x - 9
point, [tex]x_0[/tex] = 4
epsilon, ε = 0.08
So by the definition of limit,
[tex]\lim_{x \rightarrow x_0} f(x)= L[/tex]
Therefore,
[tex]\lim_{x \rightarrow 4} (-4x-9)[/tex]
L= -4(4)-9
L= -16-9
L= -25
So, for every ε > 0, for all δ > 0 such that
|f(x) - L| < ε [tex](0<|x-x_0|< \delta)[/tex]
[tex]|f(x)-L|<\epsilon \\|(-4x-9)-(-25)|<0.08\\|-4x+16|<0.08\\|-4(x-4)|<0.08\\|-4||x-4|<0.08\\4|x-4|<0.08\\|x-4|<\frac{0.08}{4}\\|x-4|<0.02\\0<|x-4|<0.02 \ \ \ \ \text{ comparing with}\ 0<|x-x_0|< \delta \\ \therefore \delta = 0.02[/tex]
A business tenant has a percentage lease stating rent payment is greater of 2% of the business’s total gross sales volume or a minimum base rental of $1,000.00 per month. In the past year, sales totaled $435,000. How much rent did the business pay?
Answer:
$12,000
Step-by-step explanation:
By paying the minimum rent, the tenant would pay $1000 * 12 = $12,000.
Rent cannot be less than $12,000.
If the 2% of sales is greater than $12,000, then 2% of sales becomes the rent.
Now we calculate 2% of annual sales.
2% * $435,000 = $8,700
Since the minimum rent, $12,000, is greater than 2% of sales, then rent is $12,000.
Solve the given systems of equations:
x-y+z=1
-3x+2y+z=1
2x-3y+4z=3
Answer:
x = 3/2
y = 2
z = 3/2
Step-by-step explanation:
There are multiple methods to solve these. Message me for the method you need to see step by step.
The domain of the function is given. Find the range.
f(x) = 5x - 1
Domain: (-1,0,1,2)
Range:{6, 1, -4,9)
Range: (-6, 1, -4,9)
Range: (-6,-1, 4, 9)
Range:{+6,+1,+4,+9
Answer:
your third answer
Step-by-step explanation:
its easy just plug in each domain into your function and the result will be the range
Please amswere my school is due tommorow and i meed some help
Answer:
88
Step-by-step explanation:
M : R
3 : 7
R : E
1 : 2
So make Ryan equal
1×7=7
2×7=14
tfo R : E
7 : 14
then add all 3forM+7forR+14forE = 24
192/24=8
so for Ethan, 8×14=112and for Marc, 8×3=24
therefore Ethan has 112-24=88 more stickers than Marc
Enter a range of vaules for x
A range for the values of x:
-2, -1, 0, 1, 2,
Happy to help! You can certainly extend this range
The quotient of a number and -5 has a result of 2. What is the number?
Type the correct answer in the box. Use numerals instead of words.
Answer:
-10
-5 * 2 = -10
Hope this is right
Find a solution to the linear equation y=−x+7 by filling in the boxes with a valid value of x and y.
Answer:
(0,7) and (7,0)
Step-by-step explanation:
When x = 0, y = 7
When y = 0, x = 7
The solution to this equation is: (0,7) and (7,0) and can be graphed on a cartesian plane like the attached graph.
Find the centroid of the quarter of the unit circle lying in the fourth quadrant.
Step-by-step explanation:
In the fourth quadrant, the equation of the unit circle is:
y = -√(1 − x²), 0 ≤ x ≤ 1
The x and y coordinates of the centroid are:
cₓ = (∫ x dA) / A = (∫ xy dx) / A
cᵧ = (∫ y dA) / A = (∫ ½ y² dx) / A
For a quarter circle in the fourth quadrant, A = -π/4.
Solving each integral:
∫₀¹ xy dx
= ∫₀¹ -x √(1 − x²) dx
= ½ ∫₀¹ -2x √(1 − x²) dx
If u = 1 − x², then du = -2x dx.
When x = 0, u = 1. When x = 1, u = 0.
= ½ ∫₁⁰ √u du
= ½ ∫₁⁰ u^½ du
= ½ (⅔ u^³/₂) |₁⁰
= (⅓ u√u) |₁⁰
= 0 − ⅓
= -⅓
∫₀¹ ½ y² dx
= ½ ∫₀¹ (1 − x²) dx
= ½ (x − ⅓ x³) |₀¹
= ½ [(1 − ⅓) − (0 − 0)]
= ⅓
Therefore, the x and y coordinates of the centroid are:
cₓ = (-⅓) / (-π/4) = 4/(3π)
cᵧ = (⅓) / (-π/4) = -4/(3π)
The first and last term of an AP are 1 and 121 respectively. If the sum of the series is 671,find a) the number of terms (n) in the AP b) the common
difference between them
Answer:
(a)11
(b)12
Step-by-step explanation:
The first term, a = 1
The last term, l=121
Sum of the series, [tex]S_n=671[/tex]
Given an arithmetic series where the first and last term is known, its sum is calculated using the formula:
[tex]S_n=\dfrac{n}{2}(a+l)[/tex]
Substituting the given values, we have:
[tex]671=\dfrac{n}{2}(1+121)\\671=\dfrac{n}{2} \times 122\\671=61n\\$Divide both sides by 61\\n=11[/tex]
(a)There are 11 terms in the arithmetic progression.
(b)We know that the 11th term is 121
The nth term of an arithmetic progression is derived using the formula:
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{11}=121\\a=1\\n=11[/tex]
Therefore:
121=1+(11-1)d
121-1=10d
120=10d
d=12
The common difference between them is 12.
Help please someone I have solved this multiple times factoring out the quadratic equations and I keep getting m as -1. But the correct answer says m is -5.
Answer: m = -5
Step-by-step explanation:
[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]
Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:
(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)
Multiply binomials, add like terms, and solve for m:
(m² + 6m + 9) - (3m + 3) = m² - 9
m² + 6m + 9 - 3m - 3 = m² - 9
m² + 3m + 6 = m² - 9
3m + 6 = -9
3m = -15
m = -5
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer
240cm^2 (i think)
Step-by-step explanation:
find the area of each side then add
experts, geniuses, aces and moderators .. need help on the attached. will give brainliest!!! find the derivative of e^x
Which of the following is the minor arc for the circle shown below?
A. AWR
B. AW
C. RAW
D. RA
Answer:
RA
Step-by-step explanation:
Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 120 and a y-intercept of negative 353.
What is the equation of the regression line?
Select the correct choice below and fill in the answer boxes to complete your choice.
A) y=..+(..)^x
B) y=..+(..)^x
C) y=..+(..)^x
D) y=..+(..)^x
Answer:
y = -353 + 120xStep-by-step explanation:
First step is using a linear regression equation:
In a linear regression model y = b0 + b1x
where y be the response variable
and x be the predictor variable.
let b1 = slope
b0 = intercept of the line.
Let the variable ratings be by denoted by x and the variable price be denoted by y.
From the given information it is known that, price (y) is response variable and ratings (x) predictor variable.
Therefore, price can be predicted using ratings.
Second step is to obtain the regression equation of the variables price (y) and ratings (x):
so the slope of the regression equation is 120 and the y-intercept is -353.
then b0 = -353
therefore,
(price)y = b0 + b1x (ratings)
y = -353 + 120x
The equation of the regression line is y = -353 + 120x.
Given that,
The regression equation has a slope of 120 and a y-intercept of negative 353.Based on the above information, the equation is as follows:
y = -353 + 120x
Learn more: brainly.com/question/17429689
What is the simplified expression for 3 y squared minus 6 y z minus 7 + 4 y squared minus 4 y z + 2 minus y squared z?
WILL MARK BRAINLEST
Answer:
7y⁴- 10yz - y²z - 5
Step-by-step explanation:
First collect like terms
3y²+ 4y²- 6yz - 4yz - y²z - 7+2
7y⁴-10yz - y²z - 5
Answer:
Its C
Step-by-step explanation:
Heights for teenage boys and girls were calculated. The mean height for the sample of 46 boys was 195 cm and the variance was 58. For the sample of 66 girls, the mean was 165 cm and the variance was 75. Estimate how much taller teenage boys are using a 85% confidence level. Round answers to the nearest hundredth and provide the point estimate together with the margin of error.
Answer:
With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.
Step-by-step explanation:
Hello!
Given the variables:
X₁: height of a teenage boy.
n₁= 46
[tex]\frac{}{X}[/tex]₁= 195cm
S₁²= 58cm²
X₂= height of a teenage girl
n₂= 66
[tex]\frac{}{X}[/tex]₂= 165cm
S₂²= 75cm²
If the boys are taller than the girls then you'd expect μ₁ > μ₂ or expressed as a difference between the two population means: μ₁ - μ₂ > 0
To estimate the difference between both populations you have to calculate the following interval:
([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) + [tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]
[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{110; 0.925}= 1.450[/tex]
Point estimate: ([tex]\frac{}{X}[/tex]₁- [tex]\frac{}{X}[/tex]₂) = (195-165)= 30
Margin of error:[tex]t_{n_1+n_2-2; 1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S_1}{n_1} +\frac{S_2}{n_2} }[/tex]= 1.450*0.54= 0.783
30 ± 0.783
[29.217; 30.783]
With a 85% confidence level you'd expect the teenage boys to be on average between [29.217; 30.783]cm taller than the girls.
I hope this helps!
The area of a triangle is 14 square inches. The base is 28 inches. What is the height in inches? Do not include units in your answer.
Answer:
Hey there!
A=1/2bh
14=1/2(28)h
14=14h
h=1
Hope this helps :)
Answer:
the height is 1 inchStep-by-step explanation:
Area of a triangle is
[tex] \frac{1}{2} \times b \times h[/tex]
where b is the base
h is the height
From the question
Area = 14in²
b = 14 inches
So we have
[tex]14 = \frac{1}{2} \times 28 \times h[/tex]
which is
[tex]14 = 14h[/tex]
Divide both sides by 14
That's
[tex] \frac{14}{14} = \frac{14h}{14} [/tex]
We have the final answer as
h = 1
Therefore the height is 1 inch
Hope this helps you
x−15≤−6 solve for x pls help
Answer:
x≤9
Step-by-step explanation:
x−15≤−6
Add 15 to each side
x−15+15≤−6+15
x≤9
Answer:
[tex]\boxed{x\leq 9}[/tex]
Step-by-step explanation:
[tex]x-15 \leq -6[/tex]
[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]
[tex]x-15 +15 \leq -6+15[/tex]
[tex]x\leq 9[/tex]
What decimal is equivalent to 10/3?
Answer:
3.33333333 . . .
Step-by-step explanation:
Answer:
3.33333333
Step-by-step explanation:
Its a forever number, i forgot the term i think its called a terminal number, or nonterminal i forget. You divide 10 / 3 and get 3.33333333333333333333 forever
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). • Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) • What is Miguel’s expected value from playing the game? • Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? • What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation.
Answer:
See explanation
Step-by-step explanation:
Step 1Miguel wins $2 is if he pulls two chips with the number 1.
Probability of winning is:
2/4 * 1/3 = 1/6 as there are 4 chips in totalProbability of loosing is:
1- 1/6 = 5/6Step 2Missing values we found in the step 1, can be populated in the table:
Xi === 2 === -1P(Xi) === 1/6 === 5/6Expected Value as per table data:
1/6*2 + 5/6*(-1) = -1/2Expected value is $1/2 loss each time he plays
Step 3To make the game fair, the expected value should be zero.
Then as per the calculation above, let's replace 2, with x, and find its value.
1/6x + 5/6*(-1) = 0 1/6x = 5/6 x= 5So the amount should be $5 to make the game fair.
The graph shows how the length of time a boat is rented is related to the
rental cost. What is the rate of change shown in the graph?
Boat Rental
AY
440
400
380
320
Cost (dollars)
240
200
100
120
80
40
0
Time (hours)
A. $40/hour
B. $80/hour
C. 80 hours/dollar
D. 40 hours/dollar
A slope is also known as the gradient of a line is a number. The correct option is B.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The rate of change shown in the graph is the slope of the given line.
Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).
Therefore, the slope of the line can be written as,
Slope, m = ($400 - $0)/(5-0) hour
= $400/5 hour
= $80/hour
Learn more about Slope of Line:
https://brainly.com/question/14511992
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Help ASAP!!!!
1. Solve for x. Round to the nearest hundredth if necessary.
Answer:
The answer is option B
34.28Step-by-step explanation:
To solve for x we use tan
tan ∅ = opposite / adjacent
From the question
The adjacent is x
The opposite is 19
So we have
tan 29 = 19/ x
x = 19/ tan 29
x = 34.276
x = 34.28 to the nearest hundredthHope this helps
Answer:
x ≈ 34.28
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan29° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{19}{x}[/tex] ( multiply both sides by x )
x × tan29° = 19 ( divide both sides by tan29° )
x = [tex]\frac{19}{tan29}[/tex] ≈ 34.28 ( to the nearest hundredth )
Find the area of the triangle. Round the answer to the nearest tenth. A. 4.4 square units B. 5.2 square units C. 6.8 square units D. 8.8 square units
Answer:
A. 4.4 units²
Step-by-step explanation:
Area of a Triangle: A = 1/2bh
sin∅ = opposite/hypotenuse
cos∅ = adjacent/hypotenuse
Step 1: Draw the altitude down the center of the triangle
- We should get a perpendicular bisector that creates 90° ∠ and JM = KM
- We should also see that we use sin∅ to find the h height of the triangle and that we use cos∅ to find length of JM to find b base of the triangle
Step 2: Find h
sin70° = h/3.7
3.7sin70° = h
h = 3.47686
Step 3: Find b
cos70° = JM/3.7
3.7cos70° = JM
JM = 1.26547
Step 4: Find entire length base JK
JM + KM = JK
JM = KM (Definition of Perpendicular bisector)
2(JM) = JK
2(1.26547) = 2.53095
b = 2.53095
Step 5: Find area
A = 1/2(3.47686)(2.53095)
A = 4.39988
A ≈ 4.4