Answer:
[tex]n=35[/tex]
Step-by-step explanation:
From the question we are told that:
Standard Deviation [tex]\sigma=4min[/tex]
Let
[tex]CI=95\%[/tex]
Since
Significance level [tex]\alpha[/tex]
[tex]\alpha =1-CI[/tex]
[tex]\alpha =1-0.95[/tex]
Therefore
[tex]Z_{\alpha/2}=Z_{0.025[/tex]
[tex]Z_{\alpha/2}}=1.96[/tex]
Generally the equation for Sample size is mathematically given by
[tex]n = (Z_{\alpha/2}* \frac{\sigma}{E})^2[/tex]
[tex]n= \frac{1.96 * 3}{1}^2[/tex]
[tex]n=35[/tex]
As the students were approaching the park, they noticed a huge tower that was just
being completed. Lucas and Jacob were part of the group responsible for looking at
advertising. They couldn’t help but to think, one of the main attractions of the park
would be the ride involving this tower. It was a bright, sunny day. As they got off
the bus, they collected the mathematical materials provided by their teacher. These
materials included: pencil, paper, eraser, calculator, measuring tape, a
clinometer (a tool used to measure vertical angles). They walked through the
park until they reached the shadow of the tower. They looked up and couldn’t
believe how high it was
Q: If they are going to advertise, the height of the tower in a brochure that is
being created, they want to be sure of their answer. Describe how they
could use the materials they have and trigonometry to determine the
height of the tower. The explanations should include a detailed diagram,
clear step by step instructions making use of terminology appropriately
and even examples showing the calculations to be used to determine
the height.
The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.
First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.
Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).
So at this point, we know one angle and the adjacent cathetus to that angle.
And we want to find the height of the tower, which is the opposite cathetus to the known angle.
Then we can remember the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing these by the things we know:
tan(θ) = H/S
tan(θ)*S = H
Then, by measuring θ and S, we can find the height.
If you want to read more about triangle rectangles, you can see:
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Pls help!! find the area of the shaded region.
Answer:
134.1
Step-by-step explanation:
Area of the circle = 49π = 153.9 (rounded to the nearest tenth)
Segment area,
49/2(150π/360-sin(150))
= 19.8 (rounded to the nearest tenth)
Subtracting them,
153.9-19.8
= 134.1 cm²
Answered by GAUTHMATH
The area of the shaded region is 134.1 cm²
What is a segment of a circle?
'A segment of a circle is the region that is bounded by an arc and a chord of the circle.'
According to the given problem,
Area of the circle = πr²
= π × 7 × 7 cm²
= 153.9 (rounded to the nearest tenth)
Area of the Shaded region,
= [tex]\frac{r^{2} }{2}( \frac{angle in degrees * \pi }{360 - sin(angle in degrees)} )[/tex]
=[tex]\frac{49}{2}(\frac{150\pi }{360 - sin(150)})[/tex]
= 19.8 (rounded to the nearest tenth)
Subtracting them,
= 153.9 - 19.8
= 134.1 cm²
Hence, we can conclude that the area of the shaded region is 134.1cm²
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Multiply using the FOIL method:
(x + y) (x + 2)
Answer:
x^2 +2x+xy +2y
Step-by-step explanation:
(x + y) (x + 2)
FOIL
first x*x = x^2
outer x*2 =2x
inner y*x= xy
last = y*2 =2y
Add together
x^2 +2x+xy +2y
Answer:
Step-by-step explanation:
F - First ; O - Outside ; I - inside ; L -last
(x + y)(x + 2) = x*x + x*2 +y*x +y*2
= x² + 2x + xy +2y
using trig to solve for missing angles
Answer:
? = 32.20422
Step-by-step explanation:
We know the adjacent side and the hypotenuse
cos ? = adj / hyp
cos ? = 33/39
cos ? = 11/13
Taking the inverse cos of each side
cos ^ -1( cos ?) = cos^-1(11/13)
? = 32.20422
The point-slope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1= 164–12). What is the standard form of the equation for this line?
Answer:
[tex]y = \frac{1}{4}x -2[/tex]
Step-by-step explanation:
Step 1: Find the standard form of the equation
The equation that was given made no sense so I will recreate the entire equation using the point slope formula.
Use the point slope formula
[tex]y - y_{1} = m(x - x_{1})[/tex]
[tex]y - (-3) = m(x - (-4))[/tex]
[tex]y +3 = m(x + 4)[/tex]
Find the slope
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{1-(-3)}{12-(-4)}[/tex]
[tex]m = \frac{1+3}{12+4}[/tex]
[tex]m = \frac{4}{16}[/tex]
[tex]m=\frac{1}{4}[/tex]
Combine them together
[tex]y +3 = \frac{1}{4}(x + 4)[/tex]
Convert to standard form
[tex]y +3 = \frac{1}{4}x + 1[/tex]
[tex]y +3 - 3 = \frac{1}{4}x + 1 - 3[/tex]
[tex]y = \frac{1}{4}x -2[/tex]
Answer: [tex]y = \frac{1}{4}x -2[/tex]
Find the value of x.
r h==ptgggggggggggggggggggggggggggggggggggggggggggggggggggtnnnnnnn
Function f is graphed. According to the graph, is f even, odd, or neither?
Answer:
C
Step-by-step explanation:
f is neither even nor odd
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 3 kg weighs 30 N. Find the weight of an object whose mass is 5 kg
Answer:
[tex]50 N[/tex]
Step-by-step explanation:
To help us find our answer, we need to use Newton's Second law
[tex]F = m \times a[/tex]
Where F is the force (N), m is the mass (Kg) and a is the acceleration (m/s^2, on a planet this would just be the gravity)
So if we know that a person has a mass of 3Kg and weighs 30N, the acceleration (or the gravity on that planet is)
[tex]30 = 3 \times a\\a = 10 m/s^2[/tex]
Now that we know the acceleration we can easily find the weight of the person.
[tex]F = 5 * 10 = 50 N[/tex]
witch is equivalent to 3x+5+7x+2
1. 17
2. 15x+2
3.10x+7
4. 17x
Answer:
option 3
Step-by-step explanation:
Given
3x + 5 + 7x + 2 ← collect like terms
= (3x + 7x) + (5 + 2)
= 10x + 7 → option 3
According to the question
=3x + 5+7x + 2
Combining Like terms
= (3x + 7x) +(5+2)
= 12x + 7
Therefore the correct option is third
10x + 7
Answered by Gauthmath must click thanks and mark brainliest
The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Find the
i)value of x
ii) area
iii)cost of weeding the plot at GHc 0.24 per m²
Answer:
P.=2(2x+5)+2(x-10)=80cm
6x-10=80
x=90/6=15cm
Area= L*W= 35*5=175 squared cm= 0.0175 squared m
Cost= 0.24 * 0.0175 = GHc 0.0042
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The cost of weeding the rectangular plot is 0.0042 GHc.
What is a rectangle?That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
A.) The perimeter of a rectangular plot of land whose length is (2x+5) and width is (x-10) is 80cm. Therefore, we can write,
Perimeter of the rectangel = 2(L+W)
80 = 2[(2x+5)+(x-10)]
80/2 = 2x+5+x-10
40 = 3x -5
40+5 = 3x
x = 15
Hence, the value of x is 15.
B.) The length of the rectangle = (2x+5) = 2(15)+5 = 35 cm = 0.35 m
The width of the rectangle = (x-10) = 15-10 = 5 cm = 0.05 m
Now, the area of the rectangle = L×B = 0.35m × 0.05m = 0.0175m²
C.) Given the cost of weeding 1m² is 0.24, therefore, the cost of weeding the rectangular plot is
Cost = 0.0175 × 0.24 = 0.0042 GHc
Hence, the cost of weeding the rectangular plot is 0.0042 GHc.
Learn more about Rectangle:
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Same promblem as first but different angles
If two parallel lines are intersected by a transversal, then internal opposite angles are equal.
So, x° = 61°
=> x = 60
Because they are internal opposite angles.
Which function is the inverse of h(x) = 18x+7/3 ?
Question 10 options
Answer:
Out of those choices, the answer in the first image makes the most sense
Below is a histogram representing the test scores from Mrs. Jackson's 2nd period History class. How many students scored a 90 or above?
Answer:
either 5 or 6
Step-by-step explanation:
I can't have a direct answer because you didn't get all of the histogram in there, but from what I can conclude from just this there's definitely either 5 or 6.
what is the simplification of 9^8 / 9^7?
Answer:
9
Step-by-step explanation:
We know that a^b / a^c = a^(b-c)
9^8 / 9^7
9^(8-7)
9^1
9
Please solve these radical equations and show the steps so that I can understand them. In my notes, it says the steps are to Isolate the radical, square both sides, solve for the variable, and check for the extraneous solutions so if this is what you are supposed to do please show these steps in action. Thank you for your time.
Answer:
1) X = 0
2) X = 0 or X = 1
Step-by-step explanation:
1)
[tex] \sqrt{6x} + 9 + 2 = 11 [/tex]
6x = 0 since root can only be = 0 if radicand is 0
X = 0
2)
[tex] \sqrt{x} - 3 + 3 = x[/tex]
[tex] \sqrt{x} = x[/tex]
X = x^2 ( We are squaring both sides to simplify)
x-x^2 = 0
x (1-x) = 0 (Factor the expression)
X = 0 or
1 -x = 0
X = 1
Answered by Gauthmath
The quantity of milk consumed in five households in a week is 10L.12.13 L. 11 L and
14 L Find the mean weekly consumption of milk by these bouseholds. Also find the number
of households whose consumption is more than the mean weekly consumption
Answer:
12
Step-by-step explanation:
Add 10l to 12l to13l to11l to 14l=60l the divide 60l by the number of houses which will be 12 and there is your correct answer
Melissa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of 59 and costs an additional 0.15 per mile driven. The second plan has an initial fee of 50 and costs an additional 0.20 per mile driven. For what amount of driving do the two plans cost the same? What is the cost when the two plans cost the same?
Answer:
Step-by-step explanation:
Let
x = cost per mile
y = Total cost
Plan 1:
y = 59 + 0.15x
Plan 2:
y = 50 + 0.20x
Equate the total cost of the two plans
59 + 0.15x = 50 + 0.20x
59 - 50 = 0.20x - 0.15x
9 = 0.05x
x = 9/0.05
= 180
x = 180 miles
y = 50 + 0.20x
= 50 + 0.20(180)
= 50 + 36
= 86
y = 86
1) Tính a) (x+3)^2
b) (2x-1)^2
c) x^2 - 2y^2
d) ( x+2)^3
e)(x-3)^3
Answer:
1. a) x^2 + 6x + 27
b) 4x^2 - 4x + 1
c) x^2 - 4y^2
d) x^3 + 6x^2 + 12x + 8
e) x^3 - 9x^2 + 27x - 27
If you have the time mind helping me on this
you can go for option g cause ans is 14:5
can someone pls help me!! :)
Answer:
I think the answer is B
A car accelerates from rest at 1.0 m/s2 for 20.0 seconds along a straight road. It then moves at a constant speed for half an hour. It then decelerates uniformly to a stop in 30.0 s. Find the total distance covered by the car.
HELP
Answer:
50m
Step-by-step explanation:
speed (m/s2) = distance (m) ÷ time (s)
distance = speed (m/s2) x time (s)
1x20 =20m.
30s = 30m because they do 1 meter per second (every second)
50m in total if not counting the constant for half a hour.
Determinar la altura de una antena que, A cierta hora del día,Arroja una sombra de 2.85 m, En ese preciso momento Marta que Mide 1.65 m Proyecta una sombra de 1.16 m
Answer:
La altura de la antena es 4.054 metros.
Step-by-step explanation:
La altura del objeto es perpendicular a la longitud de la sombra, tanto el triángulo rectángulo de la antena como el triángulo rectángulo de Marta son semejantes. La altura de la antena se determina mediante la siguiente relación:
[tex]\frac{h}{l} = \frac{H}{L}[/tex] (1)
Where:
[tex]h[/tex] - Altura de Marta, en metros.
[tex]l[/tex] - Longitud de la sombra de Marta, en metros.
[tex]L[/tex] - Longitud de la sombra de la antena, en metros.
[tex]H[/tex] - Altura de la antena, en metros.
Si sabemos que [tex]h = 1.65\,m[/tex], [tex]l = 1.16\,m[/tex] y [tex]L = 2.85\,m[/tex], entonces la altura de la antena es:
[tex]H = h\cdot \left(\frac{L}{l} \right)[/tex]
[tex]H = 1.65\,m \times \left(\frac{2.85\,m}{1.16\,m} \right)[/tex]
[tex]H = 4.054\,m[/tex]
La altura de la antena es 4.054 metros.
kendra is 3 times her dauters age plus 7 years kendra is 49 years old. write an equation to find he duaghters age?
Answer:
3x+ 7 =49
Step-by-step explanation:
49-7= 42
42 divided by 3 = 14
her daughter is 14 years old
I truly hope this helped, it makes sense to me. I wasn't sure whether or not you needed a more detailed equation, but that's one.
have a great day!
HELP FAST! D: TWENTY POINTS
A group of friends goes Sky diving, using a parachute to fall in a straight line from (1,45) to (3,36). If they keep going in a straight line, at what coordinates will they land on the x-axis?
Answer:
0 =-4.5X +49.5
x = 11
Step-by-step explanation:
x1 y1 x2 y2
1 45 3 36
(Y2-Y1) (36)-(45)= -9 ΔY -9
(X2-X1) (3)-(1)= 2 ΔX 2
slope= -4 1/2
B= 49 1/2
Y =-4.5X +49.5
5√27-2√48-5√3-√(3-2√3)2
Answer:
4√3
Step-by-step explanation:
5√27-2√48-5√3-(√3-2√3)2
= 5√(3x9)-2√(3x16)-5√3-2√3+4√3
= 5(3)√3-2(4)√3-5√3-2√3+4√3
= 15√3-8√3-5√3-2√3+4√3
= 4√3
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.20 meters per week. After 7 weeks, the sheet is only 2.42 meters thick. Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
Answer:
Step-by-step explanation:
We know that the thickness of the lake decreases at a rate of 0.2 meters per week, so we can write:
S(t)=-0.2t+4
we also know that after 7 weeks, the sheet is only 2.42 meters thick, which means we can write:
S(7)=2.42
S(7)=-0.2*7+X
S(7)=-1.4+X
2.42=-1.4+X
X=3.82
So, the function is: S(t)=--0.2*t+3.82
Answer:
y = 3.8 - 0.2x
Step-by-step explanation:
Khan Academy
Staff
Americans eat 7 billion hot dogs between Memorial Day and Labor Day. If all these hot dogs were laid end to end they
would circle the earth 21.5 times. If the circumference of the Earth is approximately 24,860 miles, and one mile is
5,280 feet, find the length (in inches) of each hot dog. (Round your answer to the nearest tenth)
Answer:
The length of each hot dog is 0.5000 inches.
Step-by-step explanation:
Total number of hot dogs eaten = 7 000 000 000
Circumference of the earth = 24 860 miles
21.5 times the circumference of the Earth = 21.5 x 24 860 miles
= 534490 miles
But,
1 mile = 5280 feet
So that,
534490 miles = X
X = 5280 x 534490
= 287707200 feet
Also,
1 feet = 12 inches
Then,
287707200 feet = Y
Y = 12 x 287707200
= 3452486400 inches
Thus,
the length of each hot dog = [tex]\frac{3452486400}{7000000000}[/tex]
= 0.4932
The length of each hot dog is 0.5000 inches.
can somene explain this to me please?
Answer:
10/3
Step-by-step explanation:
rate of change = gradient
(17-7)/(6-3) = 10/3
basically difference of y values / difference of x values
Find the sin P rounded to the nearest hundredth
Answer:
SOH-CAH-TOA
[tex]\sin \left(x\right)=\frac{6}{\sqrt{49+36}}[/tex] = 40.60°
SOH = SIN = OPP/HYP
SIN(Θ) = 6/[tex]\sqrt{49+36 }[/tex]
Step-by-step explanation:
I don't need a language ABC
Answer:
yes
Step-by-step explanation:
Answer:
?
Step-by-step explanation:
