Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.1, n = 2.
The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]
0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
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In the year 2015, New Jersey had 1,218 people per square mile. The land area of New Jersey is 7,354 square miles. What was the approximate population of New Jersey in 2015? In the year 2015 , New Jersey had 1,218 people per square mile . The land area of New Jersey is 7,354 square miles . What was the approximate population of New Jersey in 2015 ?
Answer:
8,957,172 people
Explanation:
Population = 1,218 people per square mile
Land area of New Jersey = 7,354 square miles
Total population:
people living in per square mile × total land area
1,218 × 7,354
8,957,172
As sample of 105 sanitation workers for the city of Euonymus, Texas, earns an average of $24,375 per year. The average salary for all Euonymus city workers is $24,230, with a standard deviation of $523. Are the sanitation workers overpaid? Conduct both one- and two-tailed tests.
The average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
We have:
Average x = 24375
u = 24230
SD = 523
n = 105
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is not overpaid.
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is overpaid.
u > 24230
Assume significance level = 0.05
From the Z-table:
Z(critical) = 1.645
Now,
Z = (x-u)/(SD/√n)
Z = (24375-24230)/(523/√105)
Z = 2.84
Z > Z(critical)
So, reject the null hypothesis.
The average salary of sanitation workers in the city of Euonymus is overpaid.
Now, from the two-tail test:
Null hypothesis and alternative hypothesis for one-tail test:
H0: the average salary of sanitation workers in the city of Euonymus is 24230
u = 24230
H1: the average salary of sanitation workers in the city of Euonymus is not 24230
u ≠ 24230
Assume significance level = 0.05
From the Z-table for the two-tail test:
Z(critical) = ±1.96
Now,
Z = 2.84
Z > z(critical)
∴ The average salary of sanitation workers in the city of Euonymus is not 24230.
Thus, the average salary of sanitation workers in the city of Euonymus is overpaid from the one-tail test and the average salary of sanitation workers in the city of Euonymus is not 24230 from the two-tail test.
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A rectangular garden is 15 ft longer than it is wide. Its area is 450
ft^2
. What are its dimensions?
Width equals =------
Length equals=-----
Answer:
Width= 15ft and Length= 30 ft
Step-by-step explanation:
Length=15+w
Area=450 ft square
(15+w)(w)=450
w²+15w=450
w²+15w-450=0
(w+30)(w-15)=0
w= -30, 15
width can't be negative so possible answer is 15 ft
Length = 15+15=30 ft
) The correlation between a car’s engine size and its fuel economy (in mpg) is r= -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
Given that, r= -0.774.
To solve such problems we must know about the fraction of the variability in data values or R-squared.
What fraction of the variability in fuel economy is accounted for by the engine size?The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
Fraction of the variability in data values = (coefficient of correlation)²= r²
Now, the variability in fuel economy = r²= (-0.774)²
= 0.599076%= 59.91%
Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.
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A shop is opened at 7.45 am and closed at 6.30 pm on each day from Monday to Friday. Calculate the total time the shop is opened from Monday to Friday.
Answer:
53 hours and 45 minutes
Step-by-step explanation:
since they open for 10 hours and 45 minutes a day.
10*5=50 hours, 45*5=225 minutes
add the minutes and hours together and it is 53 hours and 45 minutes
what is the general term for sequence -6;3;15;30?
Answer:
[tex] \frac{3}{2} n {}^{2} + \frac{9}{2} n - 12[/tex]
Step-by-step explanation:
This sequence is a quadratic sequence meaning that we should find the difference and the constant second difference.
The difference between the 4 terms is in the sequence:
9;12;15
The constant second difference is 3.
Use your method of finding the general term:
2a=3 3a+b=9 a+b+c=-6
a=3/2 3(3/2)+b=9 3/2+9/2+c=-6
b=9/2 c=-12
Standard form for quadratic sequence:
[tex] {an}^{2} + bn + c[/tex]
Therefore your general term is the one stated above in the answer.
Hope that helps!
The distance AB= [?] Round to the nearest tenth.
Answer:
3.6Step-by-step explanation:A = ( -2, 1 )
B = ( 1, -1 )
[tex]\boxed{\bf x_1 : - 2}[/tex] [tex]\boxed{\bf x_2 : 1}[/tex]
[tex]\boxed{\bf y_1 : 1}[/tex] [tex]\boxed{\bf y_2 : - 1}[/tex]
______________________________
[tex]\sf d = \sqrt{(x_2 -x_1) ^{2} + ( y_2 - y_1) ^{2} } [/tex][tex]\sf d = \sqrt{(1 - ( - 2)) ^{2} + ( - 1 - 1) ^{2} } [/tex][tex]\sf d = \sqrt{ {3}^{2} + {( - 2)}^{2} } [/tex][tex]\sf d = \sqrt{(9 + 4)} [/tex][tex]\sf d = \sqrt{13} [/tex][tex]\sf d = 3.6[/tex]______________________________
why is smallest possible angle of a 36-gon 5 degrees instead of 4.72222222222?
The smallest interior angle of the given regular polygon with 36 sides is; 170°
How to find the sum of interior angles of a polygon?The formula for calculating the sum of interior angles of a regular polygon is; S = (n − 2) × 180°
where n is number of sides of the polygon
We are told that number of sides of ploygon is 36. Thus;
S = (36 - 2) × 180°
S = 6120°
Thus;
Smallest possible angle of polygon = 6120/36 = 170°
Sum of external angles of a regular polygon is;
S = 360/n
S = 360/36
S = 10°
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Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base 6.4 inches. Find the surface area. Round to the nearest tenth.
The surface area of the square pyramid will be 78.08 square inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
Given that:-
Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base is 6.4 inches. The surface area will be.
The surface area of the square pyramid will be calculated by the formula:-
[tex]SA = P\times\dfrac{l}{2}[/tex]
[tex]SA = 25.6\times \dfrac{6.1}{2}[/tex]
SA = 78.08 square inches
Therefore the surface area of the square pyramid will be 78.08 square inches.
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The blue dot is at what value on the number line -3 -1
Answer:
It's +2
Step-by-step explanation:
As the positive occurs on the right side of the negatives in the number line so if we keep extending on the right side so we get +2
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} S = square numbers E = even numbers Complete the Venn diagram. E S D E & = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } S = square numbers E = even numbers Complete the Venn diagram . E S D E
Answer:
E = [1,2,3,4,5,6,7,8,9,10,11,12]
S = [4,9]
E = [2,4,6,8,10,12]
The number that satisfies both conditions S and E is [4]
A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
&= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
S = square numbers
This means,
1² = 1
2² = 4
3² = 9
S = {1, 4, 9}
E = even numbers
This means,
E = {2, 4, 6, 8, 10, 12}
Now,
S ∩ E = Numbers that are even and square.
S ∩ E = {4}
Thus,
The numbers in the Venn diagram are given,
S S∩E E
1,9 4 2, 6, 8, 10, 12
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Which measure of center is shown in a box plot?
mean
median
mode
range
Answer:
(b) median
Step-by-step explanation:
A box-plot is a graphical representation of the 5-number summary of a data set. It includes the minimum, maximum, median, and 1st and 3rd quartiles.
__
The measure of center shown in a box plot is the median.
PLEASE HELP
The function
shown.
Select from the drop-down menus to correctly describe the end
f (x).
behavior of
f(x) = -2(0.25) + 1is
As x decreases without bound, the graph of
Choose...
Choose...
As x increases without bound, the graph of
f (x)
‹ƒ (x)
f(x)
1 2
5
4
3
2
1
-4-3-2-11.
3
1
2 3
4 5
4
6
5 6
7 8
Which expression represents a difference of squares?
A. t² +100
B. 4x² - 16x
C. 25k-64
D. 81-49y²
Answer:
D represents a difference of squares.
Answer: Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex]
Step-by-step explanation:
Hii, do you need to know which expression represents a difference of squares? No problem! (:
The Difference of SquaresLet's consider it for a moment. The "difference of squares" means we subtract two numbers squared, like [tex]\boldsymbol{a^2-b^2}[/tex].
Now let's check our choices and see where we subtract two numbers squared.
The only choice like that is Choice [D] - [tex]\boldsymbol{81-49y^2}[/tex].
In choice A, we add 2 numbers; in choices B and C we don't subtract two numbers squared.
Voila! There's our solution, cheers! (:
--
Hope that this helped! Best wishes.
[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]
--
If P(x) is a polynomial with lead term -x7, then
a) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
b) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
c) P(x) goes to negative infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
d) P(x) goes to infinity as x goes to negative infinity, and P(x) goes to infinity as x goes to infinity
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity , Option B is the correct answer.
What is a Polynomial ?A polynomial is an expression which consists of variables , Coefficient , indeterminate and mathematical operations.
The polynomial given has lead term -x⁷
So when x --> ∞ , -x⁷---> - ∞
and when x ---> - ∞ , -x⁷ ----> ∞
Similarly for the function P(x)
So when x --> ∞ , P(x)---> - ∞
and when x ---> - ∞ , P(x) ----> ∞
P(x) goes to infinity as x goes to negative infinity, and P(x) goes to negative infinity as x goes to infinity
Therefore Option B is the correct answer.
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Find the principal needed now (the present value) in order to get $10,000 after 15 years, compounded
semiannually at a rate of 5%.
Answer:
10000×(1+5%)^(15×2)=43219.4238
which of the following would be an acceptable first step in simplifying the expression tan^x/1+sec^x
The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.
Which is the first step to simplifying the given expression?
Here we have the expression:
[tex]\frac{tan(x)}{1 + sec(x)}[/tex]
Remember that:
[tex]tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}[/tex]
Replacing that would be the "step zero", we can write:
[tex]\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }[/tex]
The first step to simplify this, is taking the product between the denominators:
[tex]\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}[/tex]
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Answer:
tanx(1-secx)/(1+secx)(1-secx)
Step-by-step explanation:
aP E
hello, please help me match these!
Answer:
1)x+1
2)x-1
3)x+1,R-1
Step-by-step explanation:
please mark me as brainlest
two variables x and y have corresponding values as shown in the table below. x=2,3,a and y=20,40,104 given that y varies directly as x power 2+1 find (a) value of k (b) value of a
The value of k is 4 and the value of a is 5
How to determine the value of k?The table of values is given as:
x=2,3,a
y=20,40,104
The variation is given as:
[tex]y\ \alpha\ x^2+1[/tex]
Express as an equation
y = k(x^2 + 1)
When x = 2, y = 20.
So, we have:
[tex]20 = k(2^2 + 1)[/tex]
Evaluate the sum
20 = 5k
Divide by 5
k = 4
Hence, the value of k is 4
How to determine the value of a?In (a), we have:
y = k(x^2 + 1)
Substitute 4 for k
y = 4(x^2 + 1)
When x = a, y = 104.
So, we have:
104 = 4(a^2 + 1)
Divide by 4
26 = a^2 + 1
Subtract 1 from both sides
a^2 = 25
Take the square root
a = 5
Hence, the value of a is 5
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S
Which triangle is similar to ABC if sin(A) = cos(A)=√15, and tan(A)=√1
R
5
12
13
T
D
3
12
f
3√15
O
2
K
√15
Σ.
M
O
3
L√6 N
X
6√15
N
O
24
6
Answer: Option 4
Step-by-step explanation:
Similar triangles have congruent angles, so this means that the sines, cosines, and tangents should be the same.
Thus, the side lengths of the triangle we want to find should be multiples of [tex]1, \sqrt{15}, 4[/tex].
This eliminates options (1) and (3).Between options 2 and 4, we know that the Pythagorean theorem is not satisfied by option (2), thus we should eliminate it.
This leaves us with option (4)
How many miles per hour does a sneeze travel? 1 10 100 1000
The average speed of sneeze is about 100 miles per hour.
What is the average speed of sneeze?
The average speed of sneeze is determined from the total distance traveled by the sneeze to the total time of motion of the sneeze.
Averagely a sneeze can travel as fast as 100 miles in an hour, which is equivalent to 44.7 m/s.
Thus, the average speed of sneeze is about 100 miles per hour.
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60 milllimeter equals kilograms
Answer: .00006kg
Step-by-step explanation:
which function has an asymptote at x=5 and an x-intercept of (6,0)?
The function is f(x) = log(x - 5).
What is Asymptotes?A line or curve that acts as the limit of another line or curve.
The complete question is
Which function has an asymptote at x = 5 and an x-intercept of (6,0)? a. f(x) = log(x − 5) b. f(x) = log(x 5) c. f(x) = log x − 5 d. f(x) = log x 5
let us take,
f(x) = log(x - 5)
y = 0, then
0 = log(x-5)
x - 5 = [tex]e^{0}[/tex]
x - 5 = 1
x = 6
So, it can be conclude that the x-intercept is at (6, 0)
Hence, the function is f(x) = log(x - 5).
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A company pays $20 per hour for up to 7 hours of work, and $30 per hour for
overtime hours (hours beyond 7). If x is the total hours worked, and more
than 7 hours have been worked, what is the expression for just the overtime
hours worked?
Answer:
Step-by-step explanation:
current total of hours work earnings (7hrs): $140
total earnings: $980 per week
49 hours work per week (no overtime)
immagine you're working another 4 hours for overtime payment everyday:
current total of hours work earnings (11hrs): $280 including 4 hours overtime ($120)
total working hours: 77 hours per week
total earnings: $1,960 per week
A building has a height of 40 feet and a length of 20 feet. On a scale drawing of the building, the height is 20 centimeters. What is the length of the building on the scale drawing in centimeters?
Answer:
10 centimeters
Step-by-step explanation:
For the height:
40 ft / 20 cm = 2 ft / cm
With this ratio, we find the length as follows:
2 ft / cm = 20 ft / x cm
[tex]2 = \frac{20}{x} [/tex]
[tex]2x = 20[/tex]
[tex]x = 10[/tex]
Answer:
10 cm
Step-by-step explanation:
Look at the answer
ก
3
The graphs below show measurements from cubes with
different side lengths.
Perimeter of 1 Face
24
2
10
2
40
36-
32-
8 28-
2
Side Length
Which pairs of variables have a linear relationship?
Select two options.
side length and perimeter of 1 face
perimeter of 1 face and area of 1 face
O surface area and volume
area of 1 face and surface area
Oside length and volume
The pairs of variables that have a linear relationship is: A. side length and perimeter of 1 face.
What is the Graph of a Linear Equation?The graph of a linear equation that shows a linear relationship between two variables are straight line graphs.
The graph shown is a straight line graph, therefore, it shows a linear relationship. Therefore, the pairs of variables that have a linear relationship is: A. side length and perimeter of 1 face.
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A rope is broken up into 3 pieces. The first piece is three times bigger than the second piece and the third piece is eight feet more than the first piece. How big is each piece if the sun of all pieces is 64 feet ?
what is the range of the ordered pairs shown in the graph
Answer:
D.
Step-by-step explanation:
It contains all the y-values of the points.
Answer:
Coordinates of all points
first = (-1 , 3)
second = (-2, 1 )
third = (-3 , -3)
fourth = (-4 , -5)
option 3
Urgent my safari wont work! 20 pts!!
What’s the square root of 32006???
The function g is related to one of the parent functions g(x) = |x − 1| + 5
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x). Then the parent function is f(x) = |x|.
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x – h | + k
The function g is related to one of the parent functions g(x) = |x − 1| + 5.
Then the parent function f(x) will be
f(x) = |x|
If the function f(x) is shifted right by one unit and upward by 5 units, then the function f(x) will be equal to the function g(x).
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