Answer: 5.0693 ounces
Step-by-step explanation:
For a 6 ounce cup to overflow, then the cup content is beyond 6 ounce, at 2%
P(x > 6) = 2% = 0.02; similarly
P(x<6) = 1 - P(x > 6)'.
P(x<6) = 1 - 0.02 = 0.98
The z-score for 0.98 = 2.326
The z - formular for a normally distributed goes thus :
Zscore =(observed score - mean) / standard deviation
Substituting the vamus :
2.326 = (6 - mean) / 0.4
2.326 × 0 4 = 6 - mean
0.9304 = 6 - mean
Mean = 6 - 0.9304
Mean = 5.0693
The angle of depression from an airplane to the top of an air traffic
control tower is 56 degrees. If the tower is 320 feet tall and the airplane
is flying at an altitude of 7,450 feet, how far away is the airplane from the
control tower?
Round this however you need to.
===========================
Work Shown:
Check out the diagram below. We have the following points
A = base of the towerB = point on the ground directly below the airplaneC = top of the towerD = plane's locationE = point used to form the angle of depressionBased on those points, we know that
AC = 320 = height of towerBD = 7450 = height of planeCE = BD - AC = 7450-320 = 7130 = difference between the two heightsWhich allows us to find the distance from C to D. Focus solely on triangle EDC. Use the sine ratio to find x.
sin(angle) = opposite/hypotenuse
sin(angle EDC) = CE/CD
sin(56) = 7130/x
x*sin(56) = 7130
x = 7130/sin(56)
x = 8600.33397283284 approximately
Make sure your calculator is in degree mode.
Kite EFGH is inscribed in a rectangle such that F and H are midpoints and EG is parallel to the side of the rectangle. Which statements describes how the location of segment EG affects the area of EFGH? A.) the area of EFGH is 1/4 of the area of the rectangle if E and G are not midpoints B.) The area of EFGH is 1/2 of the area of the rectangle only if E and G are midpoints C.) The area of EFGH is always 1/2 of the area of the rectangle. D.) The area of EFGH is always 1/4 of the area of the rectangle.
Answer:
C.) The area of EFGH is always ¹/₂ of the area of the rectangle.Step-by-step explanation:
If EG is parallel to the side of the rectangle then lenght of EG is equal to width of rectangle.
If F and H are midpoints of sides of rectangle then FH is parallel to the side of rectangle {wich is perpendicular to the side parallel to EG}. That means the lenght of FH is equal to lenght of rectangle, and FH is perpendicular to EG.
Then FH is sum of hights of triangles EFG and EHG [tex](FH=H_{_{\Delta EFG}}+H_{_{\Delta EHG}})[/tex], and the area of EFGH is sum of areas of triangles EFG and EHG [tex](A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}})[/tex].
So the area of the rectangle: [tex]\bold{A_{rectangle}=EG\cdot FH}[/tex]
The area of the kite:
[tex]A_{kite}=P_{_{\Delta EFG}}+P_{_{\Delta EHG}}\\\\A_{kite}=\frac12 EG\cdot H_{_{\Delta EFG}}+\frac12 EG\cdot H_{_{\Delta EHG}}\\\\ A_{kite}=\frac12 EG\cdot (H_{_{\Delta EFG}}+H_{_{\Delta EHG}})\\\\A_{kite}=\frac12 EG\cdot FH\\\\A_{kite}=\frac12 A_{rectangle}[/tex]
No matter the height of the triangles, so no matter the location of the EG
Which phrase best describes f(x), graphed on the coordinate plane below?
f(x) is an odd function.
f(x) is an even function.
f(x) is both odd and even
f(xl is neither add nor even
Answer: f(x) is an odd function
Step-by-step explanation: The major characteristic of odd functions is that one end of the graph goes down to negative infinity, the other end goes up to positive infinity.
Answer:
f(x) is an odd function.
Step-by-step explanation:
Im needing an answer for this please!
Answer:
x=46 degrees
Step-by-step explanation:
first find the size of the other angles(let call z and y)
the sum of a straight angle is 180:
180=130+z
z=180-130=50
y=180-96=84
sum of angles of triangle =180
x+y+z=180
50+84+x=180
x=180-134=46 degrees
Answer:
46°
Step-by-step explanation:
Angle of a line = 180°
To find the other side of 130°
The other side = 180° - 130° = 50°
To find the other side of 96°
The other side = 180° - 96° = 84°
To find x°
Total angle of a triangle = 180°
180° = x° + 50° + 84°
x° = 180° - 134°
x° = 46°
What the correct answer now
Answer:
11
Step-by-step explanation:
The Law of Cosines is useful when you have two sides of a triangle and the angle between.
v^2 = w^2 +u^2 -2wu·cos(V)
v^2 = 6^2 +16^2 -2·6·16·cos(27°)
v^2 = 292 -171.0733
v ≈ 10.9966
v ≈ 11
What is the domain of the function f(x) = x + 1/ x^2 - 6 + 8?
Answer:
The domain is all values but x=4 and x=2
Step-by-step explanation:
f(x) = (x+1) / ( x^2-6x+8)
Factor the function
f(x) = (x+1) / ( (x-4) ( x-2))
The domain of the function is all values of x except where the function does not exist
This is where the denominator goes to zero
(x-4) ( x-2) =0
Using the zero product property
x-4 =0 x-2 =0
x=4 x=2
The domain is all values but x=4 and x=2
Answer:
Hey there!
This, is the graph of your function:
Thus the domain, or all the possible x values would be all real numbers except 2 and 4, because the lines will only reach 2 and 4 when y is infinity.
Hope this helps :)
The level of water in a dam was decreasing by 20% each day. If the level of water was 1500cm,what was the level after two days?
Answer:900
Step-by-step explanation:
Answer:
960 cm.
Step-by-step explanation:
For the first day:
Subtract the primary level of water by the 20% of it. 20% of 1500 is:
[tex]0.2*1500=300[/tex] (Convert the percent to decimal)
Then subtract 1500 to 300. That would become 1200cm for the first day.
For the second day:
Subtract the level of water from the first day by 20% of it. 20% of 1200 is:
[tex]0.2*1200= 240[/tex]
Then subtract 1200 to 240. That would become 960 for the second day.
The level of the water after 2 days is 960 cm.
Suppose a triangle has sides 3, 4, and 6. Which of the following must be true? A: The triangle in question is not a right triangle. B: The triangle in question may or may not be a right triangle. C: The triangle in question is a right triangle.
Answer:
A: The triangle in question is not a right triangle.
Step-by-step explanation:
If the triangle is a right triangle, then the Pythagorean theorem would hold
a^2 + b^2 = c^2
3^2 + 4^2 = 6^2
9+16 = 36
25 = 36
This is not true so this is not a right triangle
Answer:
A: The triangle in question is not a right triangle.
Step-by-step explanation:
We can use Pythagorean theorem to check.
a² + b² = c²
3² + 4² = 6²
9 + 16 = 36
25 = 36 (not true)
Given: ΔABC, AC = BC, AB = 3 CD ⊥ AB, CD = √3 Find: AC
Answer:
[tex]\boxed{AC = 2.3}[/tex]
Step-by-step explanation:
AD = BD (CD bisects AB means that it divides the line into two equal parts)
So,
AD = BD = AB/2
So,
AD = 3/2
AD = 1.5
Now, Finding AC using Pythagorean Theorem:
[tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse (AC), a is base (AD) and b is perpendicular (CD)
[tex]AC^2= (1.5)^2+(\sqrt{3} )^2[/tex]
[tex]AC^2 = 2.25 + 3[/tex]
[tex]AC^2 = 5.25[/tex]
Taking sqrt on both sides
[tex]AC = 2.3[/tex]
Answer:
[tex]\boxed{2.29}[/tex]
Step-by-step explanation:
The length of AB is 3 units.
The length of CD is [tex]\sqrt{3}[/tex] units.
D is the mid-point of points A and B.
AD is half of AB.
[tex]\frac{3}{2} =1.5[/tex]
Apply Pythagorean theorem to solve for length of AC.
[tex]c=\sqrt{a^2 +b^2 }[/tex]
The hypotenuse is length AC.
[tex]c=\sqrt{1.5^2 +(\sqrt{3}) ^2 }[/tex]
[tex]c=\sqrt{2.25+3 }[/tex]
[tex]c=\sqrt{5.25}[/tex]
[tex]c= 2.291288...[/tex]
1 less than a doubled number is equivalent to 5 more than 3 lots of the number
Answer:
the number is -6 (assuming "3 lots of" means 3 times)
Step-by-step explanation:
Let the number be x
1 less than a doubled number
2x-1
5 more than 3 lots of (times???) the number
3x+5
Solve for x
2x-1 = 3x + 5
-x = 5+1
x = -6
Jenny has a $3,000 balance on her credit card with an 18% interest rate. If she makes no payments on her
card and no late fees were charged how long will it take her debt to double?
Answer:
5 years
Step-by-step explanation:
Firstly, Let's use a function to find how much Jenny owes every year.
Using f(t)=3,000(1.18)^t
We can find the amount of money jenny owes every year.
Now let's try to find how many years it would take her to double her credit card debt.
If we change t=5, we can see that the function gives us an output of 6,863.27 which is double the amount of which she currently owes.
The distance from Parrot Point Airport to the Ivy Cliffs is 291 miles at and angle of 9.1 degrees northeast. There is a wind blowing southeast at 25 miles per hour. You want to make this trip in 3 hours by flying straight there. At what speed* and heading should you fly?
Answer:
The flight speed should be 84.79 miles per hour at angle of 22.92° Northeast
Step-by-step explanation:
The given information are;
The distance from Parrot Point Airport to Ivy Cliffs = 291 miles
The direction from Parrot Point Airport to Ivy Cliffs = 9.1° Northeast
The speed of the wind = 25 miles per hour
The direction of the wind = Southeast
The time for the journey = 3 hours
The component of the wind velocity are;
For Southeast direction which is an inclination of 45°
Speed of the wind = -25 × sin(45) + 25 × cos(45)
Without the wind, the velocity of flight will be V = Displacement/time, which gives;
V = 291/3 = 97 miles/hour = 97 mph
Let the required velocity of flying = X, we have;
X×sin(θ) + X×cos (θ) -25× sin(45) + 25 × cos(45) = 97×sin(9.1) + 97×cos(9.1)
X×sin(θ) -25× sin(45) = 97×sin(9.1)
X×sin(θ) = 97×sin(9.1 )+25× sin(45 ) = 33.02
X×sin(θ) = 33.02
X×cos (θ) + 25 × cos(45) = 97×cos(9.1)
X×cos (θ) = 97×cos(9.1)- 25 × cos(45) = 78.1
X×cos (θ) = 78.1
∴X×sin(θ)/(X×cos (θ)) = tan(θ) = 33.02/78.1 = 0.423
tan⁻¹(0.423) = 22.918≈ 22.92°
X×sin(θ) = 33.02
X = 33.02/(sin(θ)) = 33.02/(sin(22.92°)) = 84.79 miles per hour
Therefore, the flight speed should be 84.79 miles per hour at angle of 22.92° Northeast.
find the zeros or x-intercepts (values of r and s) of a quadratic relation y=x^2-5x+6 by factoring using the sum and product method
Answer:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
Step-by-step explanation:
For this problem we have the following polynomial given:
[tex] y = x^2 -5x +6[/tex]
And for this case we want to find the zeros or x interceps r and s so we want to rewrite the function on this way:
[tex] y = (x-r) (x-s)[/tex]
The reason why we have two zeros is because the degree of the polynomial is 2. If we find two numbers that adding we got -5 and multiplied 6 we solve the problem. For this case the solution is r =3, s =2
[tex] y=(x -2)) (x-3)[/tex]
Select the number of solutions for each system of two linear equations.
Answer:
work is shown and pictured
C, infinitely many solutions.
B, one solution.
C, infinitely many solution.
A system of linear equations:A system of linear equations is a collection of one or more linear equations involving the same variables.
A system of linear equation has
one solution when the graph intersect at a point.no solution when the graphs are parallel.infinitely many solutions when the graphs are exact same line.According to the given questions
the given system of equations
(1). 2x+2y=3 and 4x+4y=6
if we see the graph of the above system of linear equations, the graphs are the" exact at same line".
Hence, they have infinitely many solution.
(2). 7x+5y=8 and 7x+7y =8
if we see the graph of the above system of linear equations, the graphs are intersecting at a single point.
Hence, there is only one solution.
(3). -2x+3y=7 and 2x-3y=-7
if we see the graph of the above system of linear equations, the graphs are exact at same line.
Hence, there is infinitely many solutions.
Learn more about the system of linear equations here:https://brainly.in/question/5130012
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Which of the following is a trinomial?
A. 13x^3
B. 12x2 + 2x+10
c.9/5x2
D. 3x - 15
Answer:
B is a trinomial.
Step-by-step explanation: A trinomial is a math equation with 3 terms connected by plus or minus notations. In these 4 answer choices, choice B is the only one with 3 terms.
Answer
13x^3 i think its the right answer but am not sure :(
Find the domain of each function: g(x)= 1/x−9
Answer:
x ∈ R, x ≠ 9
Step-by-step explanation:
Given
f(x) = [tex]\frac{1}{x-9}[/tex]
The denominator of f(x) cannot be zero as this would make f(x) undefined.
To find the value that x cannot be, equate the denominator to zero and solve for x
x - 9 = 0 ⇒ x = 9 ← excluded value
Thus the domain is x ∈ R, x ≠ 9
PLEASE help me answer this question!!!!
Answer:
[tex]\frac{77\pi }{3}[/tex] cm³
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex]πr³ ( r is the radius )
Here diameter = 4 cm , hence r = 4 ÷ 2 = 2 cm
V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8 = [tex]\frac{32\pi }{3}[/tex] cm³
Thus
combined volume = [tex]\frac{32\pi }{3}[/tex] + 15π = [tex]\frac{32\pi }{3}[/tex] + [tex]\frac{45\pi }{3}[/tex] = [tex]\frac{77\pi }{3}[/tex] cm³
four pencils and a ruler cost $1. six pencils and three rulers cost $2.10. find the cost of three pencils and thirteen rulers.
Answer:
$ 5.65
Step-by-step explanation:
let the cost of a pencil and a ruler be $p and $r respectively.
4p +r= 1 -----(1)
6p +3r= 2.10
divide by 3 throughout:
2p +r= 0.70 -----(2)
Q: 3p +13r= ?
(1) -(2):
(4p +r) -(2p +r)= 1 -0.70
4p +r -2p -r= 0.30 (expand)
2p= 0.30 (simplify)
p= 0.30 ÷2 (÷2 on both sides)
p= 0.15
subst. into (1):
4(0.15) +r= 1
r +0.60= 1
r= 1 -0.60
r= 0.40
cost of three pencils and thirteen rulers
= 3p + 13r
= 3(0.15) + 13(0.40)
= 0.45 + 5.20
= $5.65
Find mQPR. If mQPS=40,mRPS=8x+7,mQPR=9x+16
The table below lists some of the characteristics of the houses on Katrina’s street. Characteristics of Homes For Sale on Katrina’s Street Bedrooms Acres of land Sale price Appraised value Property tax 2 0.17 $230,000 $200,000 $1,220 2 0.20 $210,000 $220,000 $1,232 3 0.20 $275,000 $250,000 $1,400 4 0.24 $275,000 $275,000 $1,540 4 0.52 $360,000 $310,000 $1,736 4 0.75 $350,000 $320,000 $1,792 5 1.23 $375,000 $350,000 $1,960 Which relationship describes a function?
Answer:
your welcome and hope this helps
Pls solve ASAP!! Review the attachment and solve. Pls hurry!
Answer:
A. 3
Step-by-step explanation:
ΔDEC is bigger than ΔABC by 5. For the hypotenuse, 25 is 5 times bigger than 5.
So, side DE on ΔDEC has to be 5 times bigger than side AB on ΔABC.
If side AB equals 3, side DE equals 18 - 3, which is 15.
15 is five times bigger than 3, so the answer is A. 3.
Hope that helps.
Convert 50 degrees into radians (NEED ASAP)
Answer:
0.872665
Step-by-step explanation:
Subtract -134 from the sum of 38 and -87.
Answer:
[tex]\boxed{85}[/tex]
Step-by-step explanation:
Sum of 38 and -87:
=> 38 + (-87)
=> 38 - 87
=> -49
Subtraction of -134 from -49:
=> -49 - (-134)
=> -49 + 134
=> 85
Question 21 of 31
What is the length of AC?
Answer:
C. 126
Step-by-step explanation:
We can use ratios to solve for corresponding side lengths.
[tex]\frac{140-x}{81} =\frac{x}{9}[/tex]
Cross multiply.
[tex]9(140-x)=81x[/tex]
[tex]140-x=9x[/tex]
[tex]140=10x[/tex]
[tex]14=x[/tex]
Plug x as 14.
[tex]140-14=126[/tex]
Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply. A. Reflection across the line y = 2 B. Rotation of 180 C. Rotation of 90 D. Translation two units up
Answer: rotate 180 degrees and reflection across the line y=2
Step-by-step explan
Answer:
Step-by-step explanation:
What is the image of E for a 120° counterclockwise rotation about the center of the regular hexagon?
Answer:
N
Step-by-step explanation:
Since this hexagon has six sides, and to end up back at E again we’d need to rotate 360°, this means for every side we cross it’s a 60° turn.
Therefore, [tex]60 \cdot 2 = 120[/tex]° would be two sides.
Since we are moving counter-clockwise, the image for E would be to the left of it.
Two sides/points to the left of E is N, so the image of E for a 120° counterclockwise rotation around the center of this shape would be N.
Hope this helped!
Which of the following best classifies a quadrilateral with coordinates A(8, 4), B(6, 0), C(3, 2), and D(7, 10)? Trapezoid Parallelogram Kite Rectangle
Answer:
Trapezoid
Step-by-step explanation:
Got it right on quiz
The following that best classifies a quadrilateral with coordinates is :
A) Trapezoid
The following that best classifies a quadrilateral with coordinates is Trapezoid.A trapezoid could be a quadrilateral with one match of inverse sides parallel. In some cases individuals characterize trapezoids to have at slightest one match of opposite sides parallel, and some of the time say there's one and as it were one combine of inverse sides parallel.Thus, the correct answer is A.
Find out more information:
https://brainly.com/question/24200218referrer=searchResults
y<-3x+3
y
a. (1,-5)
b.(1,5)
c.(5,1)
d.(-1,5)
Answer: a
Step-by-step explanation:
substitute the coordinate values for x and y
y<3x+3, (1,-5)
-5<3(1)+3
-5<3+3
-5<6
the coordinate (1,-5) works, so a is the answer
Would a 36-ounce box for $3.72 be a better bargain than a 3-pound box for $5.36?
Answer: 5.79
36
16 cost
Step-by-step explanation:
Can an absolute value function also be a polynomial function? Why or why not?
Answer:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function
Step-by-step explanation:
For this case a polynomial is defined with the following expression:
[tex] p(x) =\sum_{i=1}^n a_i x^i[/tex]For all x on the domain considered and n is finite
And by definition the absolute value function is defined as:
[tex] |x|= x, x \geq 0[/tex]
[tex] |x| =-x , x<0[/tex]
If we use the function [tex] f(x) =|x|[/tex] we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:
An absolute value function CANNOT be considered as a polynomial function