Answer:
a) 20
Step-by-step explanation:
If x is the kg of 0.700 grade silver, then:
Silver in ingot + silver in 0.700 alloy = silver in 0.750 alloy
10 + 0.7x = 0.75(x + 12)
10 + 0.7x = 0.75x + 9
1 = 0.05x
x = 20
A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).
1. What is the appropriate test?
2. State the null hypothesis:
3. State the alternative hypothesis:
4. Find the critical value:
5. Calculate the obtained statistic:
6. Make a decision:
7. What does your decision mean
Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as
H0 :p 0.5 against Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution
Heads (x) Probability (X=x) Cumulative Decumulative
0 1/16384 (1) 0.000061 0.000061
1 1/16384 (14) 0.00085 0.000911
2 1/16384 (91) 0.00555 0.006461
3 1/16384(364) 0.02222
4 1/16384(1001) 0.0611
5 1/16384(2002) 0.122188
6 1/16384(3003) 0.1833
7 1/16384(3432) 0.2095
8 1/16384(3003) 0.1833
9 1/16384(2002) 0.122188
10 1/16384(1001) 0.0611
11 1/16384(364) 0.02222
12 1/16384(91) 0.00555 0.006461
13 1/16384(14) 0.00085 0.000911
14 1/16384(1) 0.000061 0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) = 0.006461 > 0.025
and
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is
∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps
west and finally 50 steps on a bearing of 3150
.
i. Sketch Musah’s movement
Answer:
Step-by-step explanation:
Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.
Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46
Answer:
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
Step-by-step explanation:
We formulate our null and alternative hypotheses as
H0 u≤ 6 ug Ha : u > 6 ug
The significance level ∝ = 0.05
The test statistic used is
t = X` - u / s/ √n
which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.
The critical region t > t (0.05,11) = 1.796
We compute the t value from the data
Xi Xi²
8.92 79.5664
6.99 48.8601
5.54 30.6916
5.73 32.8329
6.38 40.7044
5.51 30.3601
6.45 41.6025
7.50 56.25
8.48 71.9104
5.56 30.9136
6.90 47.61
6.46 41.7316
80.42 553.0336
Now x` = ∑x/ n = 80.42/12 = 6.70
S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)
= 1/11 (553.034-538.948) = 1.2805
s= 1.1316
Putting the values in the test statistics
t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12
= 2.1698
The critical region t > t (0.05,11) = 1.796
As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?
Answer:
Speed of plane in still air is 270 mph
Wind speed is 30 mph
Step-by-step explanation:
Check the picture.
The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.
What is the distance formula?The distance traveled by an object is the product of the speed of an object and the time taken.
Distance = speed x time
An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.
Let the speed of the plane be x
The speed of wind be y
Distance covered with the wind = (x + y)t
1200 = (x + y)4
(x + y) = 1200/4
(x + y)= 300 .....(a)
Distance covered against the wind = (x - y)t
1200 = (x - y)5
(x - y) = 1200/5
(x - y) = 240 .......(b)
By solving both the equation
(x + y)= 300
(x - y) = 240
Therefore the values will be x= 270mph and y = 30 mph
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The graph below shows the quadratic function f, and the table below shows the quadratic function g.
x -1 0 1 2 3 4 5
g(x) 13 8 5 4 5 8 13
Which statement is true?
A.
The functions f and g have the same axis of symmetry and the same y-intercept.
B.
The functions f and g have different axes of symmetry and different y-intercepts.
C.
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
D.
The functions f and g have the same axis of symmetry, and the y-intercept of f is less than the y-intercept of g.
Answer:
D
Step-by-step explanation:
The true statement is:
The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
As, per the graph and table is:
From the graph of f(x):
Axis of symmetry will be at x = 2
The maximum value of f(x) = 10
From the table of g(x):
Axis of symmetry will be at x = 2
The minimum value of g(x) = 4
thus, The functions f and g have the same axis of symmetry, and the y-intercept of f is greater than the y-intercept of g.
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a golfer hits the golf ball. the quadratic y = -14x^2+84x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?
Answer: 6 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -14x² + 84x
0 = -14x(x - 6)
0 = -14x 0 = x - 6
0 = x 6 = x
x = 0 seconds is when the ball was hit
x = 6 seconds is when the ball landed on the ground
Rewrite to make true: The sequence 8,8,8,8,8, ... is neither arithmetic or geometric.
Answer:
8,8,-8,-8,8, ... is neither arithmetic nor geometric
Step-by-step explanation:
8,8,-8,-8,8, ...
This sequence is neither arithmetic nor geometric
We could also write
8,8,8,8,8, ... this is geometric since we multiply by 1 each time
In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?
Answer:
The number is [tex]N =1147[/tex] students
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 281[/tex]
The standard deviation is [tex]\sigma = 34.4[/tex]
The sample size is n = 2000
percentage of the would you expect to have a score between 250 and 305 is mathematically represented as
[tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]
So
[tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]
[tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]
From the z table the value of [tex]P( z_2 < 0.698) = 0.75741[/tex]
and [tex]P(z_1 < -0.9012) = 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]
[tex]P(250 < X < 305 ) = 0.57[/tex]
The percentage is [tex]P(250 < X < 305 ) = 57\%[/tex]
The number of students that will get this score is
[tex]N = 2000 * 0.57[/tex]
[tex]N =1147[/tex]
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
helppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
Brainliest!
Step-by-step explanation:
36x^-4y^2/5x^2y^-3z^-2
36y^5z^2/5x^6
make everything positive
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
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Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).
Answer:
Step-by-step explanation:
Multiply the following complex numbers:
(7+2i)(2+3i)
Please don’t guess
Answer:
14 + 25l + 6l^2
Step-by-step explanation:
(7 + 2i) (2 + 3i)
=> 14 + 4l + 21l + 6l^2
=> 14 + 25l + 6l^2
This is the correct answer
find the value of each variable and the measure of each angle
Answer:
Left angle = 60°
Top angle = 120°
Right angle = 60°
Step-by-step explanation:
Use what you know about angle relationships to set up equations you can solve for each variable.
The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.
You have two variables, so you need at least two equations (I made three but only used two).
The work is in my attachment, comment of you have questions.
PLEASE HELP SOON! A 2011 study by the National Safety Council estimated that there are nearly 5.7 million traffic accidents year. At least 28% of them involved distracted drivers using a cell phones or texting. The data showed that 11% of drivers at any time are using cell phones. Car insurance companies base their policy rates on accident data that shows drivers have collisions approximately once every 19 years. That's a 5.26% chance per per year. Given.
A - Let dc= event that a randomly selected driver is using a cell phone. what is P(DC)? B - Let ta = event that a randomly selected driver has a traffic accident. what is P(ta) C - how can you determine if cell phone use while driving and traffic accidents are related? D - Give that the driver has an accident, what is the probability that the driver was distracted by a cell phone? Write this event with the correct conditional notation.
Answer:
(A) 0.11
(B) 0.0526
(C) Related
(D) 0.28
Step-by-step explanation:
The data provided is:
DC = event that a randomly selected driver is using a cell phone
TA = event that a randomly selected driver has a traffic accident
(A)
From the provided data:
P (DC) = 0.11
(B)
From the provided data:
P (TA) = 0.0526
(C)
To determine whether the events DC and TA are dependent, we need to show that:
[tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
The value of P (DC ∩ TA) is,
[tex]P(DC\cap TA)=P(DC|TA)\time P(TA)[/tex]
[tex]=0.28\times 0.0526\\=0.014728[/tex]
Now compute the value of P (DC) × P (TA) as follows:
[tex]P (DC) \times P (TA)=0.11\times 0.0526=0.005786[/tex]
So, [tex]P(DC\cap TA)\neq P(DC)\times P(TA)[/tex]
Thus, cell phone use while driving and traffic accidents are related.
(D)
The probability that the driver was distracted by a cell phone given that the driver has an accident is:
P (DC | TA) = 0.28
I need help will rate you brainliest
Answer:
Yes you can
Step-by-step explanation:
To eliminate the denominator
Answer:
No
Step-by-step explanation:
We cannot be certain that x + 3 > 0
If it was negative then the sign of the inequality would change.
To solve find the critical values of the numerator/ denominator, that is
x = 2 and x = - 3
The domain is the split into 3 intervals
(- ∞, - 3 ), (- 3, 2), (2, + ∞ )
Use test points from each interval to determine valid solution
In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are
Answer:
In the error term.
Step-by-step explanation:
A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).
Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.
Find the distance of the translation.
Round your answer to the nearest hundredth.
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
-40=-8(x+2) solve the equation
Answer:
x = 3
Step-by-step explanation:
-40 = -8 (x + 2)
-8 (x + 2) = -40 --- divide both sides by - 8
-8 (x + 2) -40
-------------- = ----------
-8 -8
x + 2 = 5 --- subtract 2 from both sides
x + 2 - 2 = 5 - 2 then simplify
x = 3
Answer:
x=3
Step-by-step explanation:
First, write out the equation as you have been given it:
[tex]-40=-8(x+2)[/tex]
Then distribute the -8 to the terms inside the parenthesis:
[tex]-40=-8x-16[/tex]
Next, add 16 to both sides:
[tex]-40+16=-8x-16+16\\-24=-8x[/tex]
Finally, divide both sides by -8:
[tex]\frac{-24}{-8}=\frac{-8x}{-8}\\3=x[/tex]
Therefore, x=3.
Suppose the radius of a circle is 5 units. What is its circumference?
Answer:
C≈31.42
Step-by-step explanation:
C=2πr
C=2xπx5
C≈31.42
pls mark as brainliest
Write 8:18 as a fraction in simplest form.
Ratio as a Fraction:
Fraction in Simplest Form:
Answer:
[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]
[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]
Step-by-step explanation:
Part 1: Writing a ratio as a fraction
A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,
Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).Therefore, 8:18 as a fraction is 8/18.
Part 2: Fraction in simplest form
To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.
8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.
Instead, if both numbers are even, divide by 2.
8/2 = 4
18/2 = 9
Check to see if the new numerator and denominator can reduce any further.
4/9 = 4/9
The fraction in simplest form is 4/9.
plzz answer this fasttttttttt
Answer:
37°
This is because the square indicates a right angle.
53 - 90 = 37
We have,
∠AOB = 53°∠BOC = x°∠A0C = 90°Now,
AOB + ∠BOC = ∠A0C
⇒ 53° + x° = 90°
⇒ x° = 90° - 53°
⇒ x° = 37°
A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?
Answer:
32/1125Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome of event/Total outcome.
If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.
If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;
Probability of selecting 2 comedies = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).
Probability of selecting 1 action movie = 6/15 = 2/5
Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125
Note that the rented movies will have to be returned hence reason for the replacement.
In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?
Answer:
There are 80 10th graders in the school
Step-by-step explanation:
Let the number of 10th graders be x
There are 25% fewer 11th graders
That mean x - 25% of x
x -0.25x = 0.75x
There are 20% more 11th graders than 12th graders
So if number of 12th graders = y, then
0.75x = y + 20/100 * y = y + 0.2y = 1.2y
Since ;
0.75x = 1.2y
then y = 0.75x/1.2 = 0.625x
So let’s add all to give 190
x + 0.75x + 0.625x = 190
2.375x = 190
x = 190/2.375
x = 80
STUCK Basic geometry A for senior year school
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
in the diagram EF and GH are straight lines. Find the values of a,b,c and d
Let a >= b.
show that gcd(a,b) = gcd(a-b, b)
let [tex] \gcd(a,b)= G[/tex] , $a\ge b$
$\therefore a=G\cdot m$ and $b=G\cdot n$
$a-b=Gm-Gn=G(m-n)$
Now, $\gcd(a-b,b)$ clearly is, $G$
