The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.
What is probability?Probability is the rate of successful outcomes to the total outcomes of an event.
P(E) = n(E)/n(S)
Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.
Calculation:It is given that,
An aerospace company has submitted bids on two separate federal government defense contracts.
The probability of winning the first contract is - 45%
The probability of winning the second contract if they win the first contract is - 73%
The probability of winning the second contract if they lose the first contact is - 45%
So, the probability that they win both contracts is
= (probability of winning the first contract) × (probability of winning the second contract)
= 0.45 × 0.73
= 0.3285 ≅ 0.33
⇒ 33%
Therefore, the probability that they win both contracts is 33%.
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How does the volume of a cylinder with a radius of 4 units and a height of 12 units compare to the volume of a rectangular prism with dimensions 8 units x 8 units x 6 units
Answer:
The volume of the cylinder is smaller than the rectangular prism.
Step-by-step explanation:
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
27.2
Step-by-step explanation:
V = (1/2)(2.6)(5.1)(4.1), which is 27.2 to the nearest tenth
Solve the congruence 3x=2(mod4)
Answer:
Step-by-step explanation:
jello :
3x=2(mod4)
multiply by ; 5
5×3x=5×2(mod4)
15x=10(mod4)
but : 15= -1 (mod4) and 10= 2 (mod4)
-x=2 (mod4)
now multiply by ; -1 you have : x= -2 (mod4)
-2=2(mod4)
conclusion : x=2 (mod4) means : x=4k+2 k in Z
Can someone help me with these problems please!
Answer:
I have just wrote answers
a triangle has two sides of length 2 and 5 and that the angle between these two sides is 60 degrees, what is the length of the third side of the triangle
The length of the third side of the triangle is 4. 33
How to determine the side
We have the length of the two sides to be;
2 and 5
If the angle between them is 60 degrees, then the third side is the opposite side
To find the opposite side, we use the sin ratio, which is
sin 60 = opposite/hypotenuse
sin 60 = x/ 5
Cross multiply
sin 60 × 5 = x
x = 0. 8660 × 5
x = 4. 33
Thus, the length of the third side of the triangle is 4. 33
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What is the slope of the line that passes through the points ( 8 , − 6 ) (8,−6) and ( 8 , − 9 ) (8,−9)? Write your answer in simplest form
As slope is undefined, then the slope of the line is parallel to the x axis.
How to determine the slope of a line
In this problem we have a line that passes through two points, the slope is determined by definition of secant line:
m = [- 9 - (- 6)]/(8 - 8)
m = - 3/0
As slope is undefined, then the slope of the line is parallel to the x axis.
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If 5/6 is 180, what is 1/6?
(please explain as well)
Answer: 36
Step-by-step explanation:
If 5/6 = 180
lets find what 1/6 equals
To do this lets divide 180 by 5 to find 1/6
[tex]\frac{180}{5} =36[/tex]
Therefore, 1/6 = 36
We know 180/5 will give us the answer because 180 is already 5/6 of the total; dividing by 5 will give us 1/6 of the total. Ex: if we had 4/6 of the total, we would divide by 4 to find 1/6.
Anyways, we can check our answer by doing:
36*5 = 216 then taking 5/6 of 216, which should equal 180
[tex]216*\frac{5}{6} =180[/tex]
Therefore, we know 36 is the correct answer
9. shyam travelled 8 km 52 m by bus, 2 km 265 m by car. how much distance did he travel in all
Shyam travel total [tex]10km 317m[/tex] distance ,when he travelled [tex]8 km 52 m[/tex] by bus and [tex]2 km 265 m[/tex] by car .
How to find the total distance travel by Shyam ?
Shyam travelled distance by bus [tex]=8 km 52 m[/tex]
Shyam travelled distance by car [tex]=2 km 265 m[/tex]
Total distance travelled by shyam is
Total distance= distance travelled by car + distance travelled by bus
Total distance
[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]
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12. The average bowling score of the 5-member in Regional High School bowling team is 128. If all the members of the team get the same score except for one, who bowls a 160, what is the score of the rest of the players? (A) 32 (B) 96 (C) 120 (D) 144
Answer:
C
Step-by-step explanation:
The average is the total of the scores divided by 5.
128 x 5 Gives us the total scores of 640. I know that one bowler had a score of 160. I will subtract that from the total of 640. 640-160 = 480. Since the 4 bowlers left, all had the same score, I will divide 480 by 4 to get 120
HELP! 10 POINTS+Braniest
Write the following inverse proportion: y is inversely proportional to x, when y = 5 and x = 8.
The inverse proportionality expression is y =40/x
Inverse proportionIf the variable y is inversely proportional to x, this is expressed as;
y = k/x
where
k is the constant of proportionality
If y = 5 and x = 8. then;
5 = k/8
k = 5 * 8
k = 40
Determine the inverse proportionality
Recall that y = k/x
y = 40/x
Hence the inverse proportionality expression is y =40/x
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Estimate the product 5.25 × 8.89.
Answer:
47.25
Step-by-step explanation:
8.89 is about 9.
So, we have 9(5.25)=9(5)+9(0.25)=45+2.25=47.25
Circle S is shown. Line segment R T is a diameter. The length of S T is 4. Sector R S T is shaded.
The measure of central angle RST is radians.
What is the area of the shaded sector?
4Pi units squared
8Pi units squared
16Pi units squared
20Pi units squared
The area of the sector in radians is calculated as: B. 8π units squared.
What is the Area of a Shaded Sector?The area of a sector where the central angle of the sector that is shaded in a circle is given in radians is calculated using the formula that is expressed as:
Area of sector = (1/2) × r²θ; where we have:
θ = the angle subtended at the center/central angle measure in radians
r = the radius of the circle
Given the following:
The shaded area is half of the circle. Its measure would be 180 degrees which when expressed in radians would be π.
Central angle measure in radians (θ) = π
Radius (r) = 4 units
Plug in the values into the area of sector formula
Area of sector = (1/2) × r²θ = (1/2) × (4²)(π)
Area of sector = (1/2) × (16)(π)
Area of sector = (1 × 16 × π)(2)
Area of sector = (16π)(2)
Area of sector = 8π units squared
In conclusion, the area of the shaded sector in the image given below is calculated as: B. 8π units squared.
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Can someone help me with these problems having trouble and show work please !!
Answer:
(2x-5)(2x-5), 81 meters
Step-by-step explanation:
All of the sides of a square are equal, so to find the area we need to multiply 2x-5 by 2x-5: (2x-5)(2x-5)
Using this equation we can plug in 7 for x:
(2(7)-5)(2(7)-5) =
(14-5)(14-5) =
9*9 = 81
The side lengths of a triangle are 9, 12, and 15. Is this a right triang
O A. Yes, because 9² + 12² > 15².
O B. No, because 9 + 12 ‡ 15.
OC. Yes, because 9² + 12² = 15².
OD. No, because 9² + 12² # 15².
If the hypotenuse of a right triangle is 2 [tex]\sqrt{3}[/tex] units long and one of the legs is [tex]\sqrt{3}[/tex] units long, then how long is the other leg?
[tex]\sqrt{3}[/tex]
2[tex]\sqrt{3}[/tex]
3
Answer:
3
Step-by-step explanation:
a = the other leg:
[tex]a^{2} =(2\sqrt{3} )^{2} -(\sqrt{3}) ^{2} =(4)(3)-3=12-3[/tex]
[tex]a^{2} =9[/tex]
[tex]a=\sqrt{9}[/tex]
[tex]a=3[/tex]
Hope this helps
Consider the three functions:
f(x) = Three-halves(4)x g(x) = Three-halves(4)–x h(x) = –Three-halves(4)x
Which statements are true about the domain and range of f(x), g(x), and h(x)? Check all that apply.
f(x) has a domain of all real numbers.
g(x) has a range of y < 0.
h(x) has a range of y > 0.
g(x) has a domain of all real numbers.
h(x) has a domain of x > 0.
The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:
f(x) has a domain of all real numbers.g(x) has a domain of all real numbers.What is a function?It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.
In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.
In conclusion, the correct options are A and D.
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Answer:
A and D
Step-by-step explanation:
Edge 2022
Im one paragraph, summarize the purpose of the graphic and its key findings
The purpose of the graphic is to show the relationship between different educational qualifications and unemployment rate.
What is Unemployment?This is a situation in which employable individuals look for jobs and are unable to find one.
The key findings in this graphic is that the higher the level of education, the lesser the unemployment rate.
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If im trying to get 20 million dollars and i get 300$ per second how long will it take to reach my goal
Answer:
66666.66 seconds, or 1111.12 minutes
Step-by-step explanation:
Since you are earning 300 dollars per second, and you want to earn 20 million, or 20000000 dollars, you can divide 20 million by 300 to get the time it takes to reach your goal in terms of seconds:
[tex]\frac{20000000}{300}=66666.66[/tex] seconds
It will take you approximately 66667 seconds to reach your goal. If we divide by 60 to get this in terms of minutes, we get that it takes about 1111.12 minutes
Answer:
66.666.6 seconds
1,111.11 minutes
18.518518518499999 hours
Step-by-step explanation:
20,000,000÷300
=66,666.6666666
Change in minutes= 66,666.6666666÷60 =1,111.1111111
Change in hours= 1,111.11111111÷60=18.518518518499999
the accompanying diagram shows a kit that has been secured to skate in the ground with a 20-foot string. the kit is located 12 feet from the ground, directly over point X. what is the distance, in feet, between the skate and point X.
The distance between the skate and point X is 16 feet
Given that the distance between point X and kite is 12 feet
and the distance between stake and kite is 20 feet
We need to find the distance between the stake and point X
Here,
Perpendicular = 12 feet
Hypotenuse = 20 feet
Base = ?
According to Pythagoras Theorem
(Hypotenuse)² = (Perpendicular)²+(Base)²
(20)² = (12)² + (Base)²
∴ (Base)² = 400 - 144
∴ (Base)² = 256
∴ Base = 16 feet
Hence the distance between the Point X and the stake is 16 feet
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A prism with a heart-shaped base is sliced parallel to the base. What shape is formed?
The shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
A prism is a polyhedron made up of n parallelogram faces that connect the n-sided polygon base, the second base, which is a translated duplicate of the first base, and the n faces. The bases are translated into all cross-sections that are parallel to them.
In the question, we are informed that a prism with a heart-shaped base is sliced parallel to the base.
We are asked what shape is formed.
From the above discussion, we know that the bases are translated into all cross-sections that are parallel to them, that is, all cross-sections parallel to the base, will be congruent to the base.
Thus, the shape formed, when a prism with a heart-shaped base is sliced parallel to the base, will be congruent to its base. Hence, it will also be heart-shaped.
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Answer:
Step-by-step explanation:
Heart Shaped
A shipment of 60 highly sensitive accelerometers is to be accepted or rejected based on the testing of 5 chosen randomly from the lot. The shipment will be rejected if more than 1 of the 5 fail. It is known that 10% of the shipment does not meet the specifications. Let X denote the number of units that fail.
The value of X that number of unit fails are 1/12.
According to the statement
we have a given that the there is a shipment of 60 highly sensitive accelerometer. And there is a testing of randomly 5 accelerometers.
And we have to find that the how much units that fails in the specifications.
So,
We find the value of X by use of Probability.
The probability that unit fails = number of units that chosen randomly / total units.
So, substitute the values in it then
The probability that unit fails = 5 / 60
The probability that unit fails = 1 / 12.
The probability that unit fails from 60 accelemoters is 1 / 12.
So, The value of X that number of unit fails are 1/12.
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Questions, are all in picture, please solve
The function represents a cosine graph with axis at y = - 1, period of 6, and amplitude of 2.5.
How to analyze sinusoidal functions
In this question we have a sinusoidal function, of which we are supposed to find the following variables based on given picture:
Equation of the axis - Horizontal that represents the mean of the bounds of the function.Period - Horizontal distance needed between two maxima or two minima.Amplitude - Mean of the difference of the bounds of the function.Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.Then, we have the following results:
Equation of the axis: y = - 1Period: 6Amplitude: 2.5The graph may be represented by a cosine with no angular phase and a sine with angular phase, based on the following trigonometric expression:To learn more on sinusoidal functions: https://brainly.com/question/12060967
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Fill in the coefficients for the polynomial with degree 3, roots: x = 2, X =
-1, and x = 3, and with a leading coefficient of 1
The coefficients for the polynomial with degree 3, roots: x = 2, x =
-1, and x = 3, and with a leading coefficient of 1 is given as -4 and 6. Hence, the polynomial turns out as x³ + (-4)x² + x + 6.
It is given that the polynomial is of degree 3 and its roots are,
x = 2
x = -1
x = 3
Thus, the factors of the polynomial would be,
(x - 2), (x + 1), and (x - 3)
The polynomial an be written in terms of its factors, with a leading coefficient of 1, as follows,
(x - 2)(x + 1)(x - 3)
= (x² -2x + x -2)(x - 3)
= (x² -x -2)(x - 3)
= x³ - 3x² - x² + 3x - 2x + 6
= x³ - 4x² + x + 6
= x³ + (-4)x² + x + 6
Hence, the required coefficients of the polynomial are, (-4) and 6.
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Machine A produces 300 bolts less than three times the number machine B produces. If
machine A produces 4,800 bolts, then how many does machine B produce?
Step-by-step explanation:
what is the best definition of luminous
The minimum point on the graph of the equation y=f(x) is (−1,−3). What is the minimum point on the graph of the equation y=f(x−5)? A. (4,−3) B. (−1,−8) C. (−1,−3) D. (−7,−3)
Answer:
(4, -3)
Step-by-step explanation:
y = f(x -5) means y = f(x) shifted 5 units to the right. So the minimum point would shift 5 units to the right as well.
IS ANYONE ABLE TO HELP ME PLEASE ASAP
Answer:
36
Step-by-step explanation:
To answer this question, we need to first understand the notation (f · x)(-2). This is a composite function, and another way to write this is f(g(-2)). This means that we have to find g(-2) and apply the function f to whatever this value is. Let's start by finding g(-2):
[tex]g(x)=x-2\\g(-2)=-2-2\\g(-2)=-4[/tex]
Now that we know g(-2) is -4, we can apply this to f:
[tex]f(x)=x^2-4x+4\\f(-4)=(-4)^2-4(-4)+4\\f(-4)=16-(-16)+4\\f(-4)=16+16+4\\f(-4)=36[/tex]
Therefore, our answer is 36
The volume of a certain right circular cone is 30 cubic inches. What is the volume, in cubic inches, of a second right circular cone with half the radius and twice the height of the first cone
Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
Circadian rhythms are biological processes that oscillate with a period of approximately 24 hours. That is, a circadian rhythm is an internal daily biological clock. Blood pressure appears to follow such a rhythm. For a certain individual the average resting blood pressure varies from a maximum of 100 mmHg at 2:00 P.M. to a minimum of 80 mmHg at 2:00 A.M.
Find a sine function of the form f(t) = a sin(ω(t − c)) + b
that models the blood pressure at time t, measured in hours from midnight.
The equation becomes of the pressure is P = 90 + 10 sin(π/36(t +4 ))
By observation the sine function should be of form P= 90 + 10 sin(ω(t − c)) as it oscillates about 90 and with a factor of 10. Let time be represented by the variable t in hours from 12.00 AM.
At 2:00 P.M. that is t= 14 hours the pressure is 100 mmHg
Substituting it in the equation we get,
100 = 90 + 10 sin(ω(t − c))
10 = 10 sin(ω(14 − c))
1 = sin(ω(14 − c))
ω(14 − c) = π/2 -1)
At 2:00 A.M. that is t= 2 hours the pressure is 80 mmHg
80 = 90 + 10 sin(ω(t − c))
-10 = 10 sin(ω(2 − c))
3π/2 = ω(2 − c) -2)
dividing 2) with 1) we get
3 = (14 − c) /(2 − c)
6 - 3c = 14 - c
2c = -8
c = - 4
Substituting the value of c in 1) we get,
ω(14 − (-4)) = π/2
ω18 = π/2
ω = π/36
Thus the equation becomes P = 90 + 10 sin(π/36(t +4 ))
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If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation? A. g(x) = 3x − 14 B. g(x) = -3x − 14 C. g(x) = 3x + 14 D. g(x) = -3x + 14If function g is defined by the equation y − 3x = -14, which equation represents the function in function notation? A. g(x) = 3x − 14 B. g(x) = -3x − 14 C. g(x) = 3x + 14 D. g(x) = -3x + 14
The following equation represents the function g in function notation,
g(x) = 3x - 14 [Option (A)]
Definition of a Function
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. A function, in general, represents the idealized relationship between two changing quantities.
Given equation is,
y -3x = -14
⇒ y = -14 + 3x
or y = 3x - 14
Here, y stands for or represents the function g(x) which is a function of independent variable x.
Thus, the correct function notation is as follows,
g(x) = 3x - 14
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