Answer:
0.2805
Step-by-step explanation:
Given that p = 20% = 0.2, n = 300.
The mean (μ) = np = 0.2 * 300 = 60
The standard deviation (σ) = [tex]\sqrt{np(1-p)}=\sqrt{300*0.2(1-0.2)}=6.93[/tex]
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma }[/tex]
For x = 57:
[tex]z=\frac{57-60}{6.93 } =-0.43[/tex]
For x = 62:
[tex]z=\frac{62-60}{6.93 } =0.29[/tex]
From the normal distribution table, P(57 < x < 62) = P(-0.43 < z < 0.29) = P(z < 0.29) - P(z < -0.43) = 0.6141 - 0.3336 = 0.2805
Um terreno retangular possui o comprimento cinco vezes maior que a largura. Sabendo que o perímetro desse terreno é igual a 180 metros, a largura e o comprimento medem, respectivamente: * 30 m e 150 m 75 m e 15 m 15 m e 75 m 150 m e 30 m 90 m e 90 m
Responder:
15 m e 75 m
Explicação passo a passo:
Deixar :
Largura = x
Comprimento = 5x
Perímetro = 180
Já o terreno tem uma forma retangular; usamos a relação;
Perímetro = 2 (comprimento + largura)
180 = 2 (5x + x)
180 = 2 (6x)
180 = 12x
180/12 = x
15 = x
Largura = x = 15 metros
Comprimento = 5x = 15 * 5 = 75 metros
Medida de largura e comprimento, respectivamente:
15 m e 75 m
can someone explain and answer this for me??
In circle F with m \angle EFG= 122m∠EFG=122 and EF=16EF=16 units, find the length of arc EG. Round to the nearest hundredth.
Given:
In circle F, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units.
To find:
The length of arc EG.
Solution:
It is given that, [tex]m\angle EFG=122^\circ,\ EF=16[/tex] units. It means the central angle of arc EG is 122 degrees and the radius of the circle F is 16 units.
Formula for arc length is:
[tex]s=2\pi r\times \dfrac{\theta}{360^\circ }[/tex]
Where, r is the radius and [tex]\theta [/tex] is the central angle in degrees.
Putting [tex]r=16,\ \theta=122^\circ,\ \pi=3.14[/tex], we get
[tex]s=2(3.14)(16)\times \dfrac{122^\circ}{360^\circ }[/tex]
[tex]s=100.48\times \dfrac{61}{180}[/tex]
[tex]s=34.0515556[/tex]
[tex]s\approx 34.05[/tex]
Therefore, the length of arc EG is 34.05 units.
Find the measurements of ZBOC.
A
5xº
A
B
(2x+20)°
C
O ZBOC= 40
O ZBOC = 10
O ZBOC= 50°
O ZBOC= 90°
Answer:
∠ BOC = 40°
Step-by-step explanation:
∠ AOC = 90° , then
5x + 2x + 20 = 90
7x + 20 = 90 ( subtract 20 from both sides )
7x = 70 ( divide both sides by 7 )
x = 10
Then
∠ BOC = 2x + 20 = 2(10) + 20 = 20 + 20 = 40°
Find the measure of Angle ADE
Answer:
30°
Step-by-step explanation:
because the sum of all interior angles in a triangle is 180 degrees
180°= ∡ADE+∡DAE+∡AED
∡ADE = 180°-∡DAE -∡AED
because the diagonals are perpendicular so they form 90° angles, and ∡BRC≅∡AED(vertical angles)
∡AED =90
To find ∡DAE we need to find the value of y
11y+2 =90
11y =90-2
y=88/11
y=8
∡DAE=7y+4=7 ·8 +4= 56+4 =60°
now we know what we need to find ∡ADE
∡ADE = 180°-∡DAE -∡AED
∡ADE = 180°-60° -90°
∡ADE = 30°
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x = 63.8°
Step-by-step explanation:
[tex]tan x = \frac{opposite}{adjacent} \\\\tan x = \frac{5.9}{2.9}\\\\x= tan^{-1} (\frac{59}{29})\\\\x = 63.82 = 63.8[/tex]
The measure of the angle [x] is equivalent to 26.6°.
What is triangle? What is similarity of triangles?A triangle is a polygon with three edges and three vertices. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.If two triangles are similar, then the ratio of their corresponding angles and sides are in same proportion.Given is a triangle ΔPON as shown in the image.
From the triangle ΔPON, we can write -
tan (x°) = ON/OP
tan (x°) = (5.9/2.9)
tan (x°) = (59/29)
tan (x°) = 2.1
x° = tan⁻¹ (2.1)
x° = 26.6°
Therefore, the measure of the angle [x] is equivalent to 26.6°.
To solve more questions on functions, expressions and polynomials, visit the link below -
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Help please me please please need explanation
9514 1404 393
Answer:
a) see attached
b) 1/3
Step-by-step explanation:
Your grid doesn't come with any coordinate axes, so you will need to draw those and label them. You will also need to determine the number of grid squares for each unit. (I suggest 2 grid squares per unit to give you a little more distance between the points you plot. The attachment shows 5 small squares per unit. You may not have this much space on your graph.)
Plot the points. Once you do this, you can see that their horizontal difference is 3 units and their vertical difference is 1 unit. The right point is above the left point, so the slope is positive:
m = (rise)/(run) = 1/3 . . . slope of the line
Type the correct answer in the box. Use numerals instead of words. Consider the logarithmic function f(x)=log^10(x) The values of f(50) rounded to the nearest hundredth is____
Answer:
1.70
Step-by-step explanation:
Logarithmic functions are the inverses of exponential functions. Hence, exponential functions can be expressed in logarithmic form whereas logarithmic function can be expressed in exponential form. Since log is a function, it is most correctly written as log.
Given that f(x) = log₁₀(x)
To find the value of f(50), we substitute x to be 50 in the logarithm function and solve:
f(50) = log₁₀(50)
f(50) = log₁₀(5 * 10) = log₁₀(5) + log₁₀(10)
f(50) = 1 + log₁₀(5) = 1 + 0.70
f(50) = 1.70
Arwen has half as many pens as Adrienne. Adrienne gives Arwen 3 pens, but still has 6 more than
Arwen. How many pens did Arwen have originally?
subtract w from 8 in algebric expression will be
Answer:
Step-by-step explanation:
according to the question ur algebraic expression is
8-w
The algebric function will be 8-w
x²+y²=2
xy=1
x+y= ?
Answer:
2 or -2
Step-by-step explanation:
x²+y²=2
(x+y)²-2xy=2
(x+y)²=4
x+y=±2
the mass of an adult north pacific right whale is about 70,000 kg, or 7 x 10 4 kg. the mass of a male polar bear is about 700 kg, or 7 x 10 2 kg. about how many times more massive is the right whale than the polar bear?
Please help me ASAP!!!
Answer:
x = 25
Step-by-step explanation:
The two angles form a straight line which is 180 degrees
2x+10 + 4x+20 = 180
Combine like terms
6x+30 = 180
Subtract 30 from each side
6x+30-30 = 180-30
6x = 150
Divide by 6
6x/6 = 150/6
x=25
heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp
Answer: you're screwed dude. i had trouble with that two. you should pack up your stuff and run away before your mom finds out that you failed.
Step-by-step explanation:
Answer:
[tex]\frac{3}{4}[/tex] liter
Step-by-step explanation:
Initial amount of milk = 2 litersUsed in the morning = [tex]\frac{1}{2}[/tex] literMilk left = 2 liters - [tex]\frac{1}{2}[/tex] liter = [tex]1\frac{1}{2}[/tex] liters[tex]1\frac{1}{2}[/tex] liters used in half: [tex]1\frac{1}{2}[/tex] : 2= 3/2 :2 = 3/4 literWhat is the solution to the equation -5p = 24-p?
Op= -6
O p= - 27
Op
O p= 4
O p=
24
25
Answer:
p = -6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-5p = 24 - p
Step 2: Solve for p
[Addition Property of Equality] Add p on both sides: -4p = 24[Division Property of Equality] Divide -4 on both sides: p = -6howdy!!
yr answer is A. -6!!!!
goodluck!!! <33
4. Let g(x) = 2x and h(x) = x2 + 4.
Evaluate (hg)(-2).
20
-16
16
-12
Step-by-step explanation:
everything can be found in the picture
The radius of a circle is 1 millimeter. What is the circle’s circumference?
Step-by-step explanation:
Circumference is
2 x pi x r
r= 1
plug and chug
Solve for z:−8(z+4)=−7(z+−4)+−3
Let's solve your equation step-by-step.
−8(z+4)=−7(z+−4)+−3
Step 1: Simplify both sides of the equation.
-8z-32=-7z+25
Step 2: Add 7z to both sides.
-z-32=25
Step 3: Add 32 to both sides.
-z=57
Answer:-57
Step-by-step explanation:
-8(z+4) = -7(z+-4)+-3
-8z-32= -7z+28-3
-8z-32=-7z+25
-57=z
Which expression is equivalent to √900f^6/100g^4
Answer:
A
Step-by-step explanation:
c and d cannot be since the answer to sqrt((900f^6)/(100g^4)) is 3f³/g²
and not 30f something.
the best answer I see is correct is a.
Which of the following values of t will result in a true statement when substituted into the given equation?
1/2 t - 4 (2 + t) = 20
A. t = 8
B. t = -8
C. t = 11
D. t = -12
Answer: t=-8
Step-by-step explanation:
1/2t-4(2+t)=20 then multiplied by two so t-16-8t=40 -7t=56 then divide -7 by 56 and you will get your answer t=-8
PLEASE HELP MEE!!
Shawntae has 21 coins, a combination of nickels and dimes. The total value of her coins is $1.70.
How many of each coin does Shawntae have?
a. Define the variables and then write a system of equations that represent the situation.
(2 points)
b. Solve the system using either the substitution or elimination method. Show your work.
2 points)
C. In a complete sentence, how many nickels and how many dimes does Shawntae have?
(2 points)
Answer:b im not sure
Step-by-step explanation:
ur welcome .
By using substitution method, the number of nickels is 8 and the number of dimes is 13.
What is substitution method?The substitution method is one of the algebraic methods to solve simultaneous linear equations. It involves substituting the value of any one of the variables from one equation into the other equation.
Representing the nickels as n and the dimes as d, and knowing that a nickel is 5 cents and a dime is 10 cents, we can write two equations from the given data.
n + d = 21
5n + 10d = 170
We use the first equation to derive a value for n.
n + d = 21
Subtract d from each side.
n + d - d = 21 - d
n = 21 - d.........................(1)
We now simplify the second equation by dividing all terms by 5.
5n + 10d = 170
[tex]\frac{5n}{5} +\frac{10d}{5} =\frac{170}{5}[/tex]
n + 2d = 24
substitute n = 21 - d in above equation
(21 - d) + 2d = 24
21 -d +2d = 24
21 + d = 24
d = 24 - 21
d = 13
n = 21 - d
n = 21 - 13
n = 8
Thus, the number of nickels is 8 and the number of dimes is 13.
Find out more information about substitution method here:
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Please help me with this question I will give 20 points
Answer:
Step-by-step explanation:
The banquet room is being carpeted. A floor plan of the room is shown below. Each unit represents 1 yard. The carpet costs $23.50 per square yard. How much will it cost to carpet the room?
Answer:
144.84
Step-by-step explanation:
Answer:
No solution is possible from the information provided.
Step-by-step explanation:
"A floor plan of the room is shown below. "
You failed to provide the floor plan so it is not possible to answer your question.
log3 x+log3 (x+30)=log3 64
Answer:
x = 2
Step-by-step explanation:
[tex] log_{3}x(x+ 30) = log_{3}64 \\ x(x + 30) = 64 \\ {x}^{2} + 30x - 64 = 0 \\ x = 2 \: or \: x = - 32[/tex]
-32 is rejected because in logarithms you cannot use negative value so x=2
I need help with this one
Answer:
8
Step-by-step explanation:
7779.949783~7779.94978
Answer:
The missing digit is 8
Step-by-step explanation:
An educated guess, but i'm pretty sure it's right
What is the simplified expression for 2(x-5)?
2x
-10x
2x-10
2x+5
Answer:
2x-10
Step-by-step explanation:
2(x) - 2(5) = 2x - 10
Brian earns 53 dollars per week working part-time at a book store. He makes one dollar more for each book that he sells. The amount, A (in dollars), that Brian
earns in a week if he sells b books is given by the following function.
4(6) - 53 + b
How much does Brian earn in a week if he sells 34 books?
Solve the triangle. Round your answers to the nearest tenth. Law of sines 6 A. M∠C=34 m ∠ C = 34 , b=25 b = 25 , c=16 c = 16 B. M∠C=34 m ∠ C = 34 , b=25 b = 25 , c=17 c = 17 C. M∠C=34 m ∠ C = 34 , b=22 b = 22 , c=17 c = 17 D. M∠C=34 m ∠ C = 34 , b=27.9 b = 27.9 , c=16 c = 16
Answer:
[tex]A = 43.0^o[/tex]
[tex]B = 55.0^o[/tex]
[tex]BC = 20.0[/tex]
Step-by-step explanation:
I will solve this question with the attached triangle
From the attachment, we have:
[tex]\angle C =82^o[/tex]
[tex]AB = 29[/tex]
[tex]AC = 24[/tex]
Required
Solve the triangle
First, we calculate [tex]\angle B[/tex] using sine law:
[tex]\frac{AC}{\sin(B)} = \frac{AB}{\sin(C)}[/tex]
This gives:
[tex]\frac{24}{\sin(B)} = \frac{29}{\sin(82^o)}[/tex]
[tex]\frac{24}{\sin(B)} = \frac{29}{0.9903}[/tex]
Cross multiply
[tex]\sin(B) * 29 = 24 * 0.9903[/tex]
[tex]\sin(B) * 29 = 23.7672[/tex]
Divide both sides by 29
[tex]\sin(B) = 0.8196[/tex]
Take arcsin of both sides
[tex]B = \sin^{-1}(0.8196)[/tex]
[tex]B = 55.0^o[/tex]
Next, calculate [tex]\angle A[/tex] using:
[tex]A + B + C = 180^o[/tex] --- angles in a triangle
[tex]A + 55^o + 82^o = 180^o[/tex]
Collect like terms
[tex]A = 180^o-55.0^o - 82^o[/tex]
[tex]A = 43.0^o[/tex]
Next, calculate BC using sine laws
[tex]\frac{BC}{\sin(A)} = \frac{AB}{\sin(C)}[/tex]
This gives:
[tex]\frac{BC}{\sin(43.0)} = \frac{29}{\sin(82)}[/tex]
[tex]\frac{BC}{0.6820} = \frac{29}{0.9903}[/tex]
Make BC the subject
[tex]BC = \frac{29*0.6820}{0.9903}[/tex]
[tex]BC = 20.0[/tex]
if 30% of the total army troop are officers and 280 are soldiers.find the number of officer.
Answer:
400 total .... 120 officers
Step-by-step explanation:
.7 X = 280
x=400
Answer:
30% of 280 is 84.
What I did to find the answer was multiply 280 by 3 then divide by 10.
I checked it with a calculator and got the same result being 84.
Can someone please help me out ~ASAP~.
Suppose a triangle has two sides of length 2 and 3 and that the angle between these two sides is 60degrees. What is the length of the third side of the triangle?
Answer:
A) 2
Step-by-step explanation:
The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.
sin(A)/a=sin(B)/b=sin(C)/c
Substitute the known values into the law of sines to find a.
sin(60)/a=sin(60)/2