Answer:
µ = 38.2 wpm, = 36.8 wpm
During the assembly of a certain piece of exercise equipment, 3 welds are required during different phases of the assembly process. It is assumed that the welds are performed independently of one another. Due to variation in the materials used and in technique, only 97% of all welds are performed satisfactorily, with the remaining 3% being classified as defective. What percentage of all pieces of this type of equipment will have at least one defective weld
Answer:
99.9973 %
Step-by-step explanation:
This is a binomial probability distribution.
Since the probability of satisfactory welds = 97% = 0.97 and the probability of defective welds = 3% = 0.03.
Since there are 3 welds and we require at least one being defective, our binomial probability is
P(x ≥ 1) = 1 - P(x ≤ 0) = 1 - P(0) = 1 - ³C₀(0.03)³(0.97)⁰ = 1 - 1 × 0.000027 × 1 = 1 - 0.000027 = 0.999973 × 100% = 99.9973%
in 1980, wind turbines in Europe generated about 5 gigawatt-hours of energy. Over the next 15 years, the amount of energy increase by about 59% per year.
NOT A MULTIPLE CHOICE
1a. Write a model giving the amount E of energy t years after 1980.
1b. Use your model determine how much wind energy was generated in 1984.
1c. Determine the year when 80 gigawatt-hours of energy were generated.
9514 1404 393
Answer:
1a. E = 5×1.59^t
1b. 32 GWh
1c. 1986
Step-by-step explanation:
1a. An exponential model looks like
f(t) = a·b^t
where 'a' is the value when t=0, and 'b' is the growth factor in the time period associated with t.
Here, 'a' is 5 (GWh), and 'b' is 1+59% = 1.59. Then the desired model is ...
E = 5·1.59^t . . . . . where t is years after 1980, and E is in GWh.
__
1b. For t=4, we have ...
E = 5·1.59^4 ≈ 31.96 ≈ 32
About 32 GWh was generated in 1984.
__
1c. The value of t for a given value of E is ...
E/5 = 1.59^t . . . . divide by 5
log(E/5) = t·log(1.59) . . . . take logarithms
t = log(E/5)/log(1.59) . . . . divide by the coefficient of t
For E = 80, the years after 1980 are ...
t = log(80/5)/log(1.59) ≈ 5.98
About 80 GWh were generated in 1986.
GR5_Math_U14_FSQ_FY21
Jose and Francis throw a ball in the air and create function models to show the trajectory. The variable x represents time in seconds after the ball was thrown and f(x) represents the height in meters. The path of Jose's ball is represented by the function, f(x)=−4.9x2+25.48x+1.8. The path of Francis's ball is represented by the table. Select the answers from the drop-down menus to complete the statements. Choose... ball is thrown from a greater height off the ground. Choose... the ball reaches a greater maximum height. x f(x) 0 1.6 0.7 18.047 1.4 30.412 2.1 37.615 2.8 40.016 3.5 37.615 4.2 30.412 4.9 18.047 5.6 1.6
Answer:
1.Jose's
2.
Francis's
Step-by-step explanation:
Answer:
Step-by-step explanation:
Micah is writing a function that models the height a dolphin reaches when it propels itself from underwater to the surface, leaps through the air, and reenters the water. The model is represented by the equation h=-16t+96t-128, where h is the height in feet above the surface of the water and t is the time in seconds. According to Micha's model, how long will the dolphin be above the surface of the water?
Answer:
The dolphin will be above the surface of the water for 2 seconds.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
The height of the dolphin after t seconds is given by:
[tex]h(t) = -16t^2 + 96t - 128[/tex]
According to Micha's model, how long will the dolphin be above the surface of the water?
It stays above the surface of the water between the first and the second root. Initially, it is below water, when the first time for which [tex]h(t) = 0[/tex] it crosses the surface upwards, and then the second time for which [tex]h(t) = 0[/tex] it crosses the surface downwards.
We have to find these roots. So
[tex]h(t) = -16t^2 + 96t - 128[/tex]
[tex]-16t^2 + 96t - 128 = 0[/tex]
Multiplying by -16
[tex]t^2 - 6t + 8 = 0[/tex]
[tex]\Delta = (-6)^{2} - 4*1*8 = 36 - 32 = 4[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
4 - 2 = 2
The dolphin will be above the surface of the water for 2 seconds.
Someone help! James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply.
7 x + 4 and 3 x + 5 + 4 x minus 1
1. When x = 2, both expressions have a value of 18.
2. The expressions are only equivalent for x = 4 and x = 6.
3. The expressions are only equivalent when evaluated with even values.
4. The expressions have equivalent values for any value of x.
5. The expressions should have been evaluated with one odd value and one even value.
6. When x = 0, the first expression has a value of 4 and the second expression has a value of 5.
7. The expressions have equivalent values if x = 8.
Answer:
3, 5, and 6
Step-by-step explanation:
What is the slope of y=7x+2
Answer: m = 7
Step-by-step explanation: This equation is written in slope-intercept form which is the same thing as y = mx + b form where m represents the slope of the line and b represents the y-intercept.
Now looking at this equation, we can see that m or the slope of the line is 7.
please help i have 2 more questions!!
Answer:
49°
Step-by-step explanation:
since its a right angle that just subtract from 90
90-41= 49
Answer:
49
Step-by-step explanation:
Because of the square at O, we know that angle XOZ is a right angle and is 90°.
Since angle XOZ is made up of angle XOY and angle YOZ, we can subtract the measure of angle XOZ by the measure of angle XOY to find the measure of angle YOZ, which is equal to x.
x = 90 - 41
x = 49
There are 1125 members in a mountaineering club. The club's secretary surveys 72 randomly
selected members and finds that 63 members are in favor of holding a used gear sale.
a.
Describe the population and the sample
b. What percent of the members in the ample are in favor of holding a used-gear sale?
С.
Estimate the number of club members who would be in favor of holding a used-gear sale.
Answer:
hmmm
Step-by-step explanation:
not sure man
match each quadratic function to its graph
please help me, i will give u brainliest if it is CORRECT
Answer: 25%
Step-by-step explanation:
STEP ONE: Find the total possible ways to roll the dice.
- Each roll has 6 possible numbers
- Each roll is independent
6×6=36 possible combination
STEP TWO: Find the possible ways to roll the dice in odd-odd
- Each roll has 3 odd number (1, 3, 5)
- Each roll is independent
3×3=9 possible combination
STEP THREE: Put it into a fraction
Possibility of odd-odd=(possible odd-odd combination)/(total combination)×100%= 9/36 × 100%=0.25 × 100%= 25%
Hope this helps!! :)
Please let me know if you have any questions
I cant figure out what -2⅘÷(-7) IS
Write an expression that expresses y in terms of x
Answer:
y= 5/2x
Step-by-step explanation:
okay so the diffrence between 10, 12, 14 is 2 and diffrence between 25, 30 and 35 is 5
now... y=mx+b
slope or m= 5/2. y=5/2x
Drag each tile to the table to multiply
(6x – y)(2x – y + 2).
fill the table
2x -y 2
6x 12^2 -6xy 12x
-y -2xy y^2 -2y
3. Audrey measures the distance around the lid of her aquarium. The picture
shows the shape of the lid. If the perimeter of the lid is 56 inches, what is the
missing side length? *
Answer:
Answer: 10 inches
Explanation: You are given one side of the aquarium which is 18 inches. The top and the bottom of the aquarium is 18 inches because that’s what the diagram gives us. So you can multiply 18 x 2=36. Now, to find the missing side length, subtract the perimeter (56 inches) by 36 and you get 20 inches. However, that’s not your final answer because you have to divide 20/2=10 inches. 10 inches is the missing side length for the left and right side lengths
The missing length of the lid of her aquarium in the pricure is 18 inches.
What is the missng length?The shape of the lid of her aquarium is a rectangle. A rectangle is a quadrilateral with four sides.
The perimeter of the rectangle = 2(length + width)
56 = 2(18 + l)
56/2 = 18 + l
28 = 18 + l
l = 28 - 18 = 10 inches
Find attached the required image. To learn more about the perimeter of a rectangle, please check: https://brainly.com/question/3205029
What is the solution set of 3x-4)=20 ?
Answer:
3x - 4 = 20
3x = 20 + 4
3x = 24
x = 24/3
x = 8
Answer:
[tex]3x - 4 = 20 \\3x = 20 + 4 \\ 3x = 24 \\ 3x \div 3 = x \\ 24 \ \div 3 = 8 \\ x = 8 [/tex]
Please help meee I need help
Answer:
5
6
Step-by-step explanation:
To solve, collect like terms
x ≥ 2 + 21/2
x ≥ 4 1/2
the whole number that would be greater than 41/2 would be 5
2. 2.7 + 3.3 > x
6 > x
HELP With this question
Answer:
Step-by-step explanation:
sin 60=CB/18
[tex]\frac{\sqrt{3} }{2} =\frac{CB}{18} \\CB=9\sqrt{3}[/tex]
Can someone help me pls
Answer:
Step-by-step explanation:
Repost with picture and I can help you
sorry I cant answer your question if all you write " is help me pls"
juan has $500 in his bank account. At the end of each month he plans to deposit $75. If these are his only transactions, which expression could be used to show the amount of money Juan will have in his account after m months?
75m+500
You have the 500 as the initial amount and the 75m is how much juan adds each month
Suppose a white dwarf star has a radius of approximately 9.0415 x 10 km. Use the formula 4 to find the approximate surface area of the star.
Please show work and not just a rando scam link ._.
Answer:
I like doods
Step-by-step explanation:
Pp + pp
Ezekiel has a $35 budget for school supplies, and he's already spent half of it on notebooks
and binders. Now he needs some pens. If pens only come in packs of 12 and they cost $5
per pack, what's the maximum number of pens he can afford with the rest of his budget?
A) 42 pens
B) 36 pens
C) 3 pens
D) 3.5 pens
Answer:
B
Step-by-step explanation:
let's list everything out.
$35 for school supplies
$17.5 has already been used
$17.5 is left
pens only come in packs of 12
one pack of pens is $5
ok, so we know its definitely not C or D because they are less than 12
42 is not divisible by 12
since packs only come in 12's then it must be B.
good luck my friend!
use factoring to solve quadratic equation. Check by substitution or by a graphing utility.
4x^2=19x+30
Describe the cross section
Someone please help I need this ASAP
Answer:
Composite area is 400+157=557
or 400 + 50pi
Step-by-step explanation:
First find the area of the square
A=s*s A= 20*20
Area of the square portion is 400
then find the area of the semicircle- we know the diameter of the circle is 20, so the radius is 10.
[tex]A=\frac{1}{2} \pi r^{2}[/tex]
so
[tex]A=\frac{1}{2} \pi 10^{2} \\A=\frac{1}{2}\pi 100\\A=50\pi \\A= 157[/tex]
Composite area is 400+157=557
or 400 + 50pi
In the polyhedron above x=5 m and y==20 m. The volume of the polyhedron is _____ m3. Round your answer to the tenths place.
Answer:
523.6 m³
Step-by-step explanation:
The polyhedron is an oblique cone
Volume of oblique cone = ⅓πr²h
r = x = 5 m
h = y = 20 m
Volume = ⅓*π*5²*20
Volume = ⅓*π*25*20
Volume = 523.598777 ≈ 523.6 m³ (nearest tenth)
solve the system by substitution....
Answer: 2,16
Step-by-step explanation:
In a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9 What is the confidence interval for the population mean μ? <μ
Answer:
Confidence Interval = ( 5.6 < μ < 8.2 )
The interval shows that the mean attractiveness is Above average on a scale of 1 to 10
Step-by-step explanation:
Data Given : 5, 8, 2, 8, 7, 6, 6, 8, 9, 9, 6, 9
a) construct a confidence interval at a 95% confidence level
confidence interval = x ± tcritical ( s / √ n ) ------ ( 1 )
n = 12
μ (mean) = ( 5+8+2+8+7+6+6+8+9+9+6+9 ) / 12 ≈ 6.92
std ( s ) = √ 1/11 *∑( xi- X )^2
= √ 1/11 * ( 5 - 6.92)^2 + ( 8 - 6.92)^2 + ( 2 - 6.92)^2 + ( 8 - 6.92)^2 + ( 7-6.92)^2 + ( 6 - 6.92)^2 + (6 - 6.92 )^2 + ( 8 - 6.92 )^2 + ( 9 - 6.92)^2 + ( 9 - 6.92)^2 + ( 6 - 6.92 )^2 + ( 9 - 6.92 )^2
= √ 1/11 * 46.92 = 2.07
tcritical at ∝ 0.05 , df = 11 = 2.20
Back to equation 1
6.92 ± 2.2 ( 2.07 / √ 12 )
( 6.92 ± 1.31 )
Confidence Interval = ( 5.6 < μ < 8.2 )
5. How much should Chantal budget per month to make sure she has enough
money to pay her car expenses? Last year she had variable expenses of
$2,125.10 and fixed expenses of $4,176.43
Answer:
$525.13
Step-by-step explanation:
cost per month = total expenses / months in a year
total expenses = fixed cost + variable cost
$2,125.10 + $4,176.43 = $6,301.53
cost per month = $6,301.53/ 12 = $525.13
19 fand g are functions such that
12
(c)
and g(x)=3(2x + 1)
(a) Find g(5)
(b) Find gf(9)
Answer:
=3(2(5)+1
=3×10+1
=30+1
=31
Answer:
(a) 33
(b) 27
(c) 1/2
Step-by-step explanation:
(a)
g(x) = 3(2x + 1)
g(5) = 3(2 * 5 + 1)
g(5) = 3(10 + 1)
g(5) = 3(11)
g(5) = 33
(b)
[tex] f(x) = \dfrac{12}{\sqrt{x}} [/tex]
[tex] f(9) = \dfrac{12}{\sqrt{9}} [/tex]
[tex] f(9) = \dfrac{12}{3} [/tex]
[tex] f(9) = 4 [/tex]
g(f(9)) = g(4) = 3(2(4) + 1)
g(f(9)) = 3(9)
g(f(9)) = 27
(c)
[tex] g(x) = 3(2x + 1) [/tex]
[tex] y = 3(2x + 1) [/tex]
[tex] x = 3(2y + 1) [/tex]
[tex] 2y + 1 = \dfrac{x}{3} [/tex]
[tex] 2y = \dfrac{x}{3} - 1 [/tex]
[tex] y = \dfrac{x}{6} - \dfrac{1}{2} [/tex]
[tex] g^{-1}(x) = \dfrac{x}{6} - \dfrac{1}{2} [/tex]
[tex] g^{-1}(6) = \dfrac{6}{6} - \dfrac{1}{2} [/tex]
[tex] g^{-1}(6) = 1 - \dfrac{1}{2} [/tex]
[tex] g^{-1}(6) = \dfrac{1}{2} [/tex]