Answer:
73.6
61.824
.2776
2.3
1.342
.4129
*note* I had trouble reading the standard deviation of the second part, so if it's not 3 then leave a comment and i will fix it*
Step-by-step explanation:
1.)
the mean would be something like 460*.16= 73.6
The variance should be 460*.16(1-.16)= 61.824 which means the standard deviation is √61.824= 7.863
for p to be less than .15 it would have to be less than .15*460= 69
(69-73.6)/7.863= -.59 which has a probability of .2776
2.)
the mean is 2.3
I am not sure if the standard deviation is 3 or .3 (picture is kind of blurry)
I am thinking that it's three which would mean that the standard deviation would be √(3²*(1/5))= 1.342
(2-2.3)/1.342= -.22 = .4129
Martina bought 19 pounds of sugar for $10. How many pounds of sugar did she get per dollar?
Answer:
1.9 poundsStep-by-step explanation:
To solve this divide the amount of sugar by the number of dollars:
19 pounds / 10 dollars = 1.9 pounds per dollarPer 10dollar she brought=19pounds
Per dollar
[tex]\\ \sf\longmapsto \dfrac{19}{10}[/tex]
Write in decimals[tex]\\ \sf\longmapsto 1.9pounds[/tex]
The perimeter of a rectangular piece of plastic is 30 millimeters. The area is 54 square millimeters. What are the dimensions of the piece of plastic?
Answer:
6 mm and 9 mm are the dimensions of the piece of plastic.
Step-by-step explanation:
Keep in mind the formulas for the area and perimeter of a rectangle:
A = lw
P = 2 (l + w)
List the factors of 54:
1, 2, 3, 6, 9, 18, 27, 54
POSSIBLE DIMENSIONS of the piece of plastic:
1 mm and 54 mm:
Area - 54 mm^2
Perimeter - 110 mm
2 mm and 27 mm
Area - 54 mm^2
Perimeter - 58 mm
3 mm and 18 mm
Area - 54 mm^2
Perimeter - 42 mm
6 mm and 9 mm
Area - 54 mm^2
Perimeter - 30 mm
The rectangular piece of plastic with the dimensions 6mm and 9 mm corresponds with the area and perimeter of the piece of plastic mentioned. So these are the correct dimensions.
Hope this helps!
one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2
Step-by-step explanation:
what to find then??.........
The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
-2x + 4y = 10
3x - 2y = -7
A. Multiply the top equation by 2 and the bottom equation by 3.
B. Multiply the bottom equation by 2.
C. Multiply the top equation by -3.
O D. Multiply the top equation by 3 and the bottom equation by -2.
Answer:
Multiply the bottom equation by 2
What are the roots of this equation x^2-4x+9=0?
Answer:
Roots is a fancy word for zero, which is also another fancy word for the x intercept.
You can factor a quad or use the quadratic equation to get zeros.
In this case, its non-factorable. So you gotta use the quadratic.
Using the quadratic equation you get : x = -2 ± √-1 (√5),
which can be rewritten as x = -2 ± i(√5)
Function was : x^2 + 4x + 9
For quad, I identified the following:
A = 1
B = 4
C = 9
I also added a picture of the formula in the attached.
NEED EXPLANATION TOO! THANKS BESTIES
There are 3 different trains running to London. One train
leaves every 10 minutes, another leaves every 35 minutes,
and the last one leaves every 40 minutes. They first leave at
5:30am. What Time do they all leave again at the same time?
Answer:
2:50pm
Step-by-step explanation:
You have to find the least common multiple (LCM) between the 3 times. If you don't know what is the LCM, just say it and I'll try to explain for you in the comments.
10, 35, 40 have as LCM the number 560
So it means they'll leave together 560 minutes after 5:30am
One hour is 60 minutes, so we can divide 560 by 60 to find the time in hours:
560/60 = 9 hours and 20 minutes (the rest of the division will be the minutes)
So, they'll leave together at 2:50pm
if x^2=y^2+z^2
what does x equal?
Answer:
[tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertyAlgebra i
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle x^2 = y^2 + z^2[/tex]
Step 2: Solve for x
[Equality Property] Square root both sides: [tex]\displaystyle x = \sqrt{y^2 + z^2}[/tex]please help me i will give 20 points for this question
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
two triangles are similar what is x
Answer:
x = 10
Step-by-step explanation:
smaller triangle / bigger triangle = 20 / 28
hence,
3x / (4x+2) = 20/28
28(3x) = 20(4x+2)
84x = 80x + 40
4x = 40
x = 10
Can anyone plz solve this question step by step ASAP!
Answer:
40√3 cm²Step-by-step explanation:
Step 1
Find the height:
h² = 8² - (12 - 8)²h² = 64 - 16 = 48h = √48 = 4√3Step 2
Find the area:
A = 1/2(a + b)hA = 1/2(12 + 8)(4√3) = 40√3 cm²77 yd
36 yd
What is the length of the hypotenuse?
C =
yards
Answer:
c = 85 yd
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
c² = 77² + 36² = 5929 + 1296 = 7225 ( take square root of both sides )
c = [tex]\sqrt{7225}[/tex] = 85
Answer:
[tex]85yd[/tex]
Step-by-step explanation:
According to PYTHAGORAS Theorem,
[tex] {c}^{2} = {77}^{2} + {36}^{2} \\ {c}^{2} = 5929 + 1296 \\ {c}^{2} = 7225 \\ c = \sqrt{7225} \\ c= 85yd[/tex]
3. If triangle ABC has the following measurements, find the measure of angle A.
a = 17
b = 21
C = 25
9514 1404 393
Answer:
(a) 42.3°
Step-by-step explanation:
Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.
a² = b² +c² -2bc·cos(A)
cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050
A = arccos(777/1050) ≈ 42.3°
The measure of angle A is about 42.3°.
_____
Additional comment
The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.
Answer:
(a) 42.3°
Step-by-step explanation:
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
A person can run 3 miles per minute. (Convert to miles per hour to decide.)
O True
O False
it depends upon a persons pace a average pace is 9-10 mins
Heyyy could someone please help me out?? Would appreciate it. Thanks in advance!!^^
Answer:
Below,...
Step-by-step explanation:
They are saying that if you add a odd number + a odd number than you'd get a even number,... odd + even = odd,... odd x even = even,... and so on,...
Hope it helps,... Chow!
find the derivative of y=x²+3x
Answer:
[tex]\frac{dy}{dx}[/tex] = 2x + 3
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
y = x² + 3x
[tex]\frac{dy}{dx}[/tex] = 2[tex]x^{(2-1)}[/tex] + 3[tex]x^{(1-1)}[/tex]
= 2x + 3[tex]x^{0}[/tex]
= 2x + 3
Helpppppppppppppppppppppppp im not smart pls don't just say some bull i need help ill just get it deleted
Answer:
a. 6m
b. m-2
c. 5(m-2)
d. 6m +5m -10= 56
E. 11m=66
divide by 6: m=6
Maple Granola= 6$
Apple Granola= 4$
1. Which of the following is an algebraic expression?
a. X+5= 7
b. 5-2x = 3
C. 5x +4- 2x
d. -2 = 3x + 1
1.
C. 5x + 4 - 2x is an algebraic expression
Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST
Answer:
4x+y=-32
Step-by-step explanation:
given,
slope (m) = -4
point: (-8,0)
as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]
so,
b = 0-(-4)×(-8) = -32
y=mx+b
or, y=-4x-32
or, 4x+y=-32
(this is the standard form of the line)
Using the equation y - y1 = m(x - x1)
y - 0 = -4(x - (-8))
y = -4(x + 8)
y = -4x - 32
18 cards are numbered from 11 to 29 if one card is chosen at random, what is the probability that if contains the digit
A father is 51 years old and his son is 19. How many years ago was the father 5 times his son's age?
Answer:
x=11
Step-by-step explanation:
51-x-5*19= -5x
51-5*19= -4x
4x=5*19-51
4x=95-51
4x=44
x=11
Step-by-step explanation:
let x year ago son age was 5 time his father age.
age of son before x year = 19-x
age of father before x year = 51-x
NOW
according to the question
5(19-x) =51-x
95-5x =51-x
95-51 = -X-5x
44 = 4x
x=11
so your ans is 11years ago
For the Parabolay = (x + 7)2 – 3. the equation for the Line Of Symmetry is
Answer:
Hello
Step-by-step explanation:
Axis of symmetry is vertical:
x=-7 (since (-7,-3) is the vertex)
Answer:
x = -7
Step-by-step explanation:
y = (x+7)^2 -3
This is in vertex form
y =a(x-h)^2+k where (h,k) is the vertex and the line of symmetry for a vertical parabola is x=h
y = (x- -7)^2 -3
x = -7
Can someone please do this for me please
Answer:
r=-11
Step-by-step explanation:
7r+2=5(r-4)
7r+2=5r-20
2r=-22
r=-11
What is the estimated value of 2v12 . 3V5 / V30 . V36
Answer:
the correct answer is b and I know this because I just had it
[tex]x - \frac{3\\}{8} = \frac{13}{2}[/tex]
X - 3/8 = 13/2
Add 3/8 to both sides:
X = 13/2 + 3/8
Rewrite 13/2 to have 8 as the denominator:
13/2 x 4 = 52/8
X = 52/8 + 3/8
X = 55/8
Answer:
55/8
Step-by-step explanation:
Add 3/8 to both sides
X - 3/8 = 13/2
X = 13/2 + 3/8
make sure the denominators are equal so we can add. so multiply 4/4 by 13/2 and that equals 52/8
X = 52/8+3/8
X= 55/8
Which of the following choices is a linear function?
O f(x) = x2 – 3x+ 2
O f(x) = 3x3 – 3x + 2
O f(x) = -3x + 2
Answer:
f (x) = x2 - 3x + 2
Step-by-step explanation:
Answer:
f(x)=-3x+2
Step-by-step explanation:
The first one is a quadtratic function because it is in quadtratic form.
The second one is also not linear because it looks like a squiggly line. Sorry I forgot what they are called but I know it is not linear.
That leaves the last one is is linear and should be going down because there is a negative in front of the coefficient. It also has so exponent to prove why it is linear even further.
Hope this helps!
Please help simple alebgra! Write an equation representing the translation of f(x) = 7x + 3 down 4 units.
Will mark brainliest!
9514 1404 393
Answer:
g(x) = 7x -1
Step-by-step explanation:
The y-coordinate of a function tells how many units the function value lies above the x-axis. Translating that value down 4 units is the same as subtracting 4 from the function value.
g(x) = f(x) -4
g(x) = 7x +3 -4
g(x) = 7x -1
the product of 7 and the quotient of 40 divided by 5 is
The quotient of 40 and 5
40÷5=8
=> Product of that number with 7 and 8
So number to find is : 7x8=56
The product of 7 and the quotient of 40 divided by 5 is 56.
What is the quotient?The quotient is the result which is derived by the division of two numbers.
For example, the quotient of 30 divided by 3 is 10.
What is the product of two numbers?The product is the multiplication of two numbers which is written as a*b.
For example, the product of 8 and 9 is 72.
Here given we have to calculate the product of 7 and the quotient of 40 divided by 5.
The quotient of 40 divided by 5 is 40/5= 8
The product of 7 and The quotient of 40 divided by 5= 7*8= 56
Therefore the product of 7 and the quotient of 40 divided by 5 is 56.
Learn more about quotient
here: https://brainly.com/question/673545
#SPJ2
Convert 75 mg into gram
Answer:
[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]