Using the Empirical Rule, it is found that 68% of the data should be between 25.5 and 30.5.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, we have that:
28 - 2.5 = 25.5.28 + 2.5 = 30.5.Within one standard deviation of the mean, hence, 68% of the data should be between 25.5 and 30.5.
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C
250
4.9 cm
80°
A
3.8 cm
D
B
ABC is a triangle.
D is a point on AB.
Work out the area of triangle BCD.
Give your answer correct to 3 significant figures.
Answer:
[tex]10.4\: \sf cm^2\:(3\:sf)[/tex]
Step-by-step explanation:
[tex]\Large\boxed{\sf Formulae}[/tex]
Sine Rule
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Cosine rule
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
Area of a triangle
[tex]\textsf{Area of a triangle}=\dfrac12ab\sin C[/tex]
where:
C is the anglec is the side opposite the anglea and b are the sides adjacent the angle[tex]\Large\boxed{\sf Calculation}[/tex]
To find the area of ΔBCD, find:
length of CDangle CDBlength of BDThen use the sine rule for area of a triangle
Calculate length CD using cosine rule:
[tex]\implies CD^2=4.9^2+3.8^2-2(4.9)(3.8)\cos 80^{\circ}[/tex]
[tex]\implies CD^2=31.98334186...[/tex]
[tex]\implies CD=5.655381673...\:\sf cm[/tex]
Calculate ∠ADC using sine rule:
[tex]\implies \dfrac{\sin 80}{CD}=\dfrac{\sin ADC}{4.9}[/tex]
[tex]\implies ADC=\sin^{-1}\left(\dfrac{4.9 \sin 80}{CD}\right)=58.568949^{\circ}[/tex]
Therefore, ∠CDB = 180° - 58.568949° = 121.431051°
Use sine rule to calculate DB:
[tex]\implies \dfrac{DB}{\sin 25}=\dfrac{CD}{\sin CBD}[/tex]
[tex]\implies DB=\dfrac{5.655381673\sin25}{\sin 33.568949}=4.322471258..\: \sf cm[/tex]
[tex]\Large\boxed{\sf Solution}[/tex]
Use the sine rule for area of a triangle to find area of ΔBCD:
[tex]\implies A=\dfrac12(CD)(DB)\sin CDB[/tex]
[tex]\implies A=\dfrac12(5.655381673)(4.322471258)\sin (121.431051)[/tex]
[tex]\implies A=10.4\: \sf cm^2\:(3\:sf)[/tex]
WHAT IS -X-5 I AM STUCK ON THIS QUESTIOOOOON
Answer:
Step-by-step explanation:
Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. Write an equation that represents the situation. PLEASE HURRY, I DONT HAVE MUCH TIME, WILL MARK BRAINLIEST.
Answer:
Equations: 40-7=33 and 33÷11=3
Step-by-step explanation:
40-7=33
Since there are 3 sides,(q) then you do 33 divided by 3=11.
Equations: 40-7=33
And
33÷11=3
Find the product of 5.21 and 3.4
Step-by-step explanation:
5.21× 3.4 = 17.714
thank u
The ordered pair (3,-2) is a solution to the system of inequalities,
y<x-3
y2-X-2
True
False
Write the equation of a circle whose diameter is 8 and whose center is (-8, -5)?
if the diameter is 8, then its radius is half that or 4.
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-8}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\\\\ [x-(-8)]^2~~ + ~~[y-(-5)]^2~~ = ~~4^2\implies (x+8)^2+(y+5)^2=16[/tex]
-3 x 7 -:- 5 x 1/7
please show the steps :)
is the sign that you mean ÷ ?
if so:
-3×7÷5×1/7
= -21÷5×1/7
=-21/5 × 1/7
= (-21×1) / (5×7)
= -21/35
=-3/5
=-0.6
Calculate the perimeter of of the shape below. Show you work
Answer:
22 is the perimeter.
Step-by-step explanation:
You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.
HELP!
The function f(x) = ax^2 + bx +c has an axis of symmetry of x = -3. The graph opens downwards and passes through the point (0,5). Write a possible equation for f(x).
Repost bc I forgot something.
You throw a football and it leaves your hand of 5 feet. Its initial velocity is 20 feet per second. What is the maximum height the ball will reach? Also, how long will it take the ball to hit the ground? (Equation used: h(t)= -16t^2 + v0t + h0.)
Please show work
Answer:
The max height is 11.25 feet and the ball will take 1.464 seconds to hit the ground
Step-by-step explanation:
The quickest way to solve this equation is by using the equation that you gave, which is h(t)= -16t^2 + v0t + h0. This equation models the trajectory of the football, which means that at the equation's vertex, we can model what the height of the ball is. Along with that, by finding the positive root of where h(t) = 0, we can find how long it will take for the ball to hit the ground.
First, lets find h0 and v(0)
h0 is the initial height of the ball. So we know that the ball leaves your hand of 5 feet, so h0 = 5. Similarly, the initial velocity is 20 ft/sec, so v0 = 20.
Plugging 5 in for h0 and 20 for v0, we get h(t) = -16t^2 + 20t + 5.
Second, find max height.
To find the vertex of a parabola, use -b/2a to find the time, and plug that into h(t) to get the height.
b=20
a=-16
t = -b/2a = -20/2(-16) = .625 seconds
h(.625) = 11.25 feet
The max height is 11.25 feet
Third, find how long.
To find this, we need to find the t-intercepts of the equation.
set h(t) = 0
-16t^2 + 20t + 5 = 0
Use quadratic formula to find t
t = (- 20 ± [tex]\sqrt{20^{2} - 4(-16)(5)}[/tex])/2(-16)
t = {1.464}, -.214
The ball will take 1.464 seconds to hit the ground.
Find the zeros using the quadratic formula x^2-5x+4=y.
Answer:
(x-4) (x-1)
Step-by-step explanation:
X-4=0
x=4
X-1=0
X=1
if the volume of cubical box is 1728^3 . find the total surface area of the box.
Answer:
864 cm²
Step-by-step explanation: Volume of cube Side^3
Side of Cube= (1728)^1/3 = 12cm Total surface area = 6 x Side^2= 6 x 144 = 864 cm²
What is the area of a square that had side length of x-6?
area square= side²
= (x-6)²
= x²-12x+36
Answer:
36
Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36
a hot air balloon is currently 100 feet above the ground. After 5 minutes, the hit air balloon is 40 feet above the ground. write the equation for the relation
Here is the Answer:
Step-by-step explanation:
Leo buys pasta for 12 people,
(a)
Each person eats 100 grams of pasta.
One packet has 500 grams of pasta.
How many packets must Leo buy?
Answer:
3
Step-by-step explanation:
If each packet has 500 grams, and each person eats 100 grams, then one packet will feed five people (500/100=5). Since he will be buying pasta for 12 people, he will need to buy three packets, because 3*500=1500 grams. While there is some extra, buying only two packets would result in not enough pasta.
Need Help! Please!
Tara found a pair of jeans that were regularly priced at $35. She has a coupon for 15% off. What is the price of the jeans after applying the coupon?
$20
$7
$29.75
$33.50
Answer:
The price is $29.75
Step-by-step explanation:
Because it is 15 percent off, that means that the jeans are priced at 100%-15%=85%. To convert a percent to a decimal, move the decimal two places to the left. This gives us .85. Multiply 35 by .85 and you will get 29.75. Hope this helps!
Albert has a rectangular print that is 1 foot in length and 8 inches in width. He wants to reduce the dimensions of the print proportionally so that the new print has a width of 3 inches. What should be the length of the new print?
Answer:
2.6 inches
Step-by-step explanation:
As shown in the title if length is x,
x * 1/x = 8/3 * x
8 * 1 = 3x
x = 8/3 in
= 2.6 in
The new length of the rectangular print will be 2.68 feet.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width).
Given a rectangular print with dimensions,
Length = 1 foot = 12 inches
Width = 8 inches.
Area = 12(8) = 96 square inches
Now,
The area of the new print should be the same
So,
96 = Length × 3
Length = 32 inches = 2.67 feet.
Hence "The new length of the rectangular print will be 2.68 feet".
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A) Find the area of each triangle.
1)
2 yd
7 yd
Answer:
Area= 7
Explanation: area of triangle is A=bh/2
b=2 h=7
7 x 2 = 14/2 = 7
Tell whether the ratios form a proportion. 14:8 and 28:10
Answer:
no
Step-by-step explanation:
14:8 = 14/8 = 7/4
28:10 = 28/10 = 14/5
Since the fractions are not equal, it is not a proportion.
Answer: no
Find the area of the trapezoid.
8 cm
6 cm
13 cm
A. 78 cm2
B. 48 cm2
C. 63 cm
D. 104
Answer:
c; 63 square cm
Step-by-step explanation:
the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)
this means the height times base 1 and base 2 added together divided by 2
(1/2)(6)(8 + 13) is the equation
this can become 3(21)
which is ultimitaly 63
Answer:
it's gonna be 63cm^2
Step-by-step explanation:
First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2
Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.
Next, we have to find the area for the triangle. The formula is length x width / 2.
So, we have to multiply 6x5 to get 30.
Then, well divide it by 2, which will give us 15cm^2
Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.
Bada-bing, bada-boom, we got 63cm^2 as our answer :)
Will give brainliest if correct
Two large numbers of the Fibonacci sequence are F(49) = 7,778,742,049 and
F(50) = 12,586,269,025. If these two numbers are added together, what
number results?
O A. F(54)
O B. F(51)
O C. F(52)
D. F(99)
SUBMIT
F(51)
===========================================================
Explanation:
The very large numbers are likely put there as a distraction. They aren't needed. Adding any two adjacent Fibonacci numbers will lead to the next term in the sequence. This is simply based on how the special number sequence is defined or set up.
This means F(49)+F(50) = F(51) i.e. adding the 49th and 50th terms will generate the 51st term.
In general,
F(n) + F(n+1) = F(n+2)
where n is a positive integer.
please give me the working for this question and I promise to give you stars and mark you as brainliest thank you.
Answer: 5/9
Step-by-step explanation: 10 6
------ x ----------- = 5
12 9 -----
9
a
С
b
60°
45°
Find a, b, and c.
Answer:
Step-by-step explanation:
Area of polygons please help
Answer:
6+12=18
Step-by-step explanation:
the area of the smaller rectangle+the area of the bigger rectangle=18
Write the equivalent expression to (5x – 3x?) – (5x – 2) · (10x + 7x) in standard form
Answer:
-35x³ - 39x² + 25x
Step-by-step explanation:
First write out the equation which is (5x - 3x²) - (5x - 2)(10x + 7x²). Then distribute 5x - 3x² to -(50x² + 35x³ - 20x - 14x²). After that, combine the like terms and don't forget to distribute the negative as well, 5x - 3x² - 36x² - 35x³ + 20x. Lastly combine all the like terms to end up with this -35x³ - 39x² + 25x.
Hope this helps :)
will give brainlest PLEASEE
Answer:
30 degrees
Step-by-step explanation:
The angles of each side of a hexagon is 120 degrees.
The sum of interior angles in a shape is (n-2) * 180.
So,
(6-2) * 180 = 4 * 180 = 720 degrees
This is the total degrees of the hexagon.
Dividing the total degrees by 6 angles gives us 120 degrees for each angle.
Angle AEF = angle FED - angle AED.
Angle FED = 120 degrees
Angle AED = 90 degrees
120 - 90 = 30 degrees
Please help me calculate the area of all the grey parts of this shape :)
Answer:
.858 cm^2
Step-by-step explanation:
Area of square - area of circle = grey corner areas
(2 * 2) - ( pi * 1^2 ) =
4 - pi = .858 cm^2
A large box of crackers weighs 20 oz. If James needs 3 pounds of crackers for a party, how many boxes of crackers should he buy?
Which of the following addition problems yields a sum that is an irrational number? Select TWO that apply. (answers in picture)
Answer:
probably the answer to the following question is B and C I hove this helps because this numbers cannot be fraction only decimal
How many vertices, edges, and faces are in the polyhedron below? List them.
Based on observation, in this polyhedron, there are a total of six vertices, nine edges, and five faces.
What are vertices?In geometry, this refers to the point where two line meet. In this case, the vertices are A, B, C, D, E, F for a total of six vertices.
What are the edges?This term refers to line segments, for example the line between B and C is an edge. Based on this, there are nine edges in this shape.
What are faces?This refers to flat surfaces; in this, case the total of flat surfaces are five.
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