Answer:
The number of defective bulbs in the shipment should be around 15, give or take 4.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Suppose the probability at a light bulb factory of a bulb being defective is 0.11
This means that [tex]p = 0.11[/tex]
Shipment of 133 bulbs:
This means that [tex]n = 133[/tex]
Mean and standard deviation:
[tex]E(X) = np = 133*0.11 = 14.63[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{133*0.11*0.89} = 3.61[/tex]
Rounding to the nearest integers:
The number of defective bulbs in the shipment should be around 15, give or take 4.
Determine the length of CD.
Question 13 options:
A)
10.77 units
B)
3.74 units
C)
6.32 units
D)
9.17 units
Answer:
The answer is 6.32
Step-by-step explanation:
According to the Altitude Geometric Mean Theorem, the length of the altitude of a triangle is the geometric mean of the lengths of the 2 segments is divides the hypotenuse into.
CD= Altitude
CD^2= 4 times 10
or
CD= The square root of 4 times 10
Square root of 4 times 10 is 6.3245553203
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of CD is 6.32 units. The correct option is C.
What are Similar figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
In ΔBDC and ΔABC, the two angles are given,
∠D = ∠C = 90°
∠B = ∠B {Common}
Therefore, the two triangles are similar triangles, thus, the ratio of the sides can be written as,
CB / AB = CD / AC = DB / CB
Now, the ratio can be solved as,
CB / AB = DB / CB
CB / 14 = 10 / CB
CB² = 14 × 10
CB = √140
Further, in triangle ABC using the Pythagorean theorem, we can write,
AB² = CB² + AC²
14² = (√140)² + AC²
196 - 140 = AC²
AC = √56
Again, using the ratio of the similar triangle, we can write,
CD / AC = DB / CB
CD / √56 = 10 / √140
CD = (√56 × 10)/√140
CD = 6.32 units
Hence, the length of CD is 6.32 units.
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.....................
Answer:
Final volume, V2 = 8.57 liters
Step-by-step explanation:
Given the following data;
Initial volume, V1 = 7.7 liters
Initial pressure, P1 = 6.9 atm
Final pressure, P2 = 6.2 atm
To find the new volume V2, we would use Boyles' law.
Boyles states that when the temperature of an ideal gas is kept constant, the pressure of the gas is inversely proportional to the volume occupied by the gas.
Mathematically, Boyles law is given by;
[tex] PV = K[/tex]
[tex] P_{1}V_{1} = P_{2}V_{2} [/tex]
Substituting into the equation, we have;
[tex] 6.9 * 7.7 = 6.2*V_{2} [/tex]
[tex] 53.13 = 6.2V_{2} [/tex]
[tex] V_{2} = \frac {53.13}{6.2}[/tex]
[tex] V_{2} = 8.57 [/tex]
Final volume, V2 = 8.57 liters
Therefore, the new volume is 8.57 liters.
Answer:
just greeting so that the other one can get a brainliest (would be kind if the favor would be returned :D )
Given f (x) = StartLayout Enlarged left-brace first row x squared minus one-third x, for x not-equals negative 1 second row negative 1, for x = negative 1 EndLayout. What is Limit of f (x) as x approaches negative 1?
Negative five-thirds
Negative four-thirds
Four-thirds
Five-thirds
Answer:
It's C, 4/3! Just did the question and got it right
Step-by-step explanation:
The limit of f(x) as x approaches negative 1 is four thirds.
What is Limits?Limits are defined as the value of a function as the input approaches a certain number. Limits are the concepts used essentially in calculus to define continuity, integrals and derivatives.
Given function is,
[tex]f(x) =\left \{ {{x^{2} -\frac{1}{3}x, x\neq -1 } \atop {-1, x=-1}} \right.[/tex]
We have to find the value of the limit as x approaches to negative 1.
This is not the same value as the value of the function at negative 1. Limit of the function as x approaches some value is the value of the function which is closest to the exact value of the function at the input.
We have,
f(x) = x² - [tex]\frac{1}{3}[/tex] x when x ≠ -1
Substitute x = -1 in the above equation
x² - [tex]\frac{1}{3}[/tex] x = (-1)² - (1 / 3) (-1)
= 1 + [tex]\frac{1}{3}[/tex]
= [tex]\frac{4}{3}[/tex]
[tex]\lim_{x \to -1} x^{2} -\frac{x}{3}[/tex] = [tex]\frac{4}{3}[/tex]
Hence the limit of f(x) = x² - [tex]\frac{1}{3}[/tex] x when x tends to -1 is 4/3.
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Which of the following functions has a vertical asymptote at x=3?
Answer:
the last one: f(x) = 1/(x-3)
Step-by-step explanation:
Vertical asymptote at x=3 means dividing by zero for x=3. If you examine all denominators with x=3, you find that the last one divides by zero (3-3).
The base length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle? (5 points) a 2 square feet b 4 square feet c 6 square feet d 8 square feet
Answer:
B. 4 square feet
Step-by-step explanation:
The formula for area of a triangle is length x height / 2 so 4 x 2 is 8 then divided by 2 is 4.
Answer: 4
Base 4
hight 2
4x2=8 ÷ 2 or 1/2 Equals 4
Formula L x W ÷ 2 or 1/2
What is the common ratio between successive terms in the sequence?
2, 4, 8, -16, 32, -64,
Ο Ο Ο Ο
2
Step-by-step explanation:
[tex]r = \frac{4}{2} \\ r = 2[/tex]
Answer:
-2
Step-by-step explanation:
The "common ratio" is the number you multiply a term by to get the next term.
-4 = 2 x -2
8 = -4 x -2
-16 = 8 x -2
The most economical proportion for a right circular cone is to have its height three times long as its base diameter. What lateral area of the cone would produce a volume of 100m^3.
9514 1404 393
Answer:
∛(2500π)√37 m² ≈ 120.911 m²
Step-by-step explanation:
If the height is 3 times the diameter, it is 6 times the radius. Then the volume is ...
V = 1/3πr²h
V = 1/3πr²(6r) = 2πr³
For a volume of 100 m³, the radius is ...
100 m³ = 2πr³
r = ∛(50/π) m
The lateral area of the cone is computed from the slant height. For this cone, the slant height is found using the Pythagorean theorem:
s² = r² +(6r)² = 37r²
s = r√37
Then the lateral area is ...
LA = πrs
LA = π(∛(50/π) m)(∛(50/π) m)√37
LA = ∛(2500π)√37 m² ≈ 120.911 m²
The lateral area of the economical cone with a volume of 100 m³ is 120.911 m².
What is the lateral area of the cone?The lateral area of the cone is the curved area of the cone, therefore, the total area of the cone is without the base area.
As we know that the volume of the cone is given by the formula,
[tex]V = \dfrac{1}{3}\pi r^2h[/tex]
Now, for the right circular cone to be economical, the height must be 3 times the diameter or it should be 6 times the radius. Therefore, the economical volume can be written as,
[tex]V = \dfrac{1}{3}\pi r^2h\\\\V = \dfrac{1}{3}\pi r^2(6r)[/tex]
Now, if cancel out the 3 in the remainder with the six in the numerator, the volume of the cone can be written as,
[tex]V = 2\pi r^3[/tex]
Further, we need to calculate the lateral area of the cone, whose volume is 100 m³. Now, in order to get the radius of the economic cone with the volume of 100 m³, substitute it with 2πr³,
[tex]V = 2\pi r^3\\\\100 = 2\pi r^3\\\\r = 2.5154\rm\ m[/tex]
We know that in order to calculate the lateral area of the cone we need to calculate the slant height. Thus, according to the Pythagorean theorem, the slant height can be written as
[tex]s^2 = r^2 +(6r)^2\\\\ s^2 = 37r^2\\\\ s = r\sqrt{37}[/tex]
Now, the lateral area of the economical cone with the volume of 100 m³ can be written as,
[tex]LA = \pi rs\\\\LA = \pi \times r \times r\sqrt{37}\\\\LA = \pi \times r^2 \times \sqrt{37}\\\\LA = \pi \times (2.5154)^2 \times \sqrt{37}\\\\LA = 120.911\rm\ m^2[/tex]
Hence, the lateral area of the economical cone with a volume of 100 m³ is 120.911 m².
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plz plz plz plz help me
Answer:
240 plantsStep-by-step explanation:
Find the area of the garden:
A = 1/2bhA = 1/2(8)(15) = 60 m²Number of plants:
60*4 = 240 plantsAnswer:
Solution given:
perpendicular [P]=15m
base[B]=8m
hypotenuse [H]=17m
rate :4 plants per square metre
no of plants=?
we have
Area of triangular garden: ½(P*B)=½(15*8)=60m²
Now
Total no of plants =rate ×Area =4×60=240
Michael needs 240 plants in the garden.
Khloe is thinking of a number that is 2 times the value of Carl's number. Khloe's number is also 2 more than 4 times the value of Carl's number. What is Khloe's number?
0 = 2c +2.
Subtracting 2 from both sides, we get
0-2 = 2c +2 -2
-2 = 2c
Dividing both sides by 2, we get
-2/2 = 2c/2
-1 =c.
Plugging c=-1 in first equation,
k=2(-1) = -2.
So the answer is -2.
What is the additive inverse of 36?
Answer:
The additive inverse of 36 is −36.
Step-by-step explanation:
Answer:
-36.
Step-by-step explanation:
Additive inverses are basically the opposite of the number, for example, since 36 in this case was positive you need to make it negative.
Which expressions are equivalent to -3(t - 7 + 5t + 8)?
Answer: It's B, C, F Hope it helps!
Step-by-step explanation: -3(t-7+5t+8) collect like terms -3(6t+1)
which would give you -18t-3
It C to because 1. expand by distributing terms -(18t+9)+6
2. Remove parentheses -18t-9+6
3. Collect like terms -18t+(-9+6) simplify and it would give you -18t+3 it also F because I collect like terms (-3t-15t)+(21-24) and you simplify and that would give you -18t-3 as well can you make me brainliest bye!
Joseph had 3 gallons of lemonade. He wanted to give each of his 1/8
friends of a gallon. How many friends would receive lemonade?
Write the equation of the line in slope-intercept form.
Answer:
y = 50x+40
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
First find two points on the line
(0,40) and (2 ,140)
The slope is
m= (y2-y1)/(x2-x1)
= (140-40)/(2-0) = 100/2= 50
The y intercept is where it crosses the y axis which is 40
y = 50x+40
A government agency estimates the number of young adults (ages 18 to 24) in a particular country to be 31,000 (in thousands) in 2010 and changing at the rate of −x2 + 90x − 200 thousand per year, where x is the number of years since 2010. Find a formula for the size of this population at any time x. [Hint: Keep all calculations in units of thousands.]
Answer:
[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]
Step-by-step explanation:
From the given information:
Let assume the population is denoted by L
The rate of change of the young adults per year given can be represented as;
[tex]\dfrac{dL}{dx}= -x^2 +90x - 200[/tex]
where;
x = 0 since 2010
[tex]dL = -x^2 +90x -200 dx[/tex]
[tex]L = \int( -x^2 +90x -200 ) \ dx[/tex]
[tex]L = - \dfrac{1}{3}x^3 + 45x^2 -200x +C[/tex]
here;
L(0) = 31000
∴
[tex]- \dfrac{1}{3}(0)^3 + 45(0)^2 -200(0)+C= 31000[/tex]
C = 31000
[tex]\mathbf{L(x)= ( - \dfrac{1}{3})x^3 + 45x^2 -200x +31000}[/tex]
Tyrone is building a skateboard ramp with a piece of plywood that is 33 feet long.He wants the height of the ramp to be 22 feet.To make a strong ramp, the base must form a right angle with the back of the ramp.What will be the length of the base rounded to the nearest tenth of a foot?
please hurry and and please show your work!!
Answer:
24.6 ft
Step-by-step explanation:
Use the Pythagorean theorem.
a^2 + b^2 = c^2
a^2 + (22 ft)^2 = (33 ft)^2
a^2 + 484 ft^2 = 1089 ft^2
a^2 = 605 ft^2
a = 24.6 ft
Answer: 24.6 ft
Help pls this is 5th grade math
Answer:
2 is scalene
3 is right
4 is right
5 is equalatirel
6 is scalene
7 is isocoles
8 is equalatirel
9 is right
Step-by-step explanation:
Answer:
2: scalene
3: right
4: right
5: equilateral
6: scalene
7: isosceles
8: equilateral
9: right
Step-by-step explanation:
2: A scalene triangle has no congruent sides
3: A right triangle has a 90 degree angle
4: A right triangle has a 90 degree angle
5: An equilateral triangle has 3 congruent sides
6: A scalene triangle has no congruent sides
7: An isosceles triangle has 2 congruent sides
8: An equilateral triangle has 3 congruent sides
9: A right triangle has a 90 degree angle
Given that ABCD is an inscribed quadrilateral and m(∠DAB)=78°. What is m (DAB)
Answer:
Step-by-step explanation:
I'm going to go out on a limb here and guess that you are looking for the answer to the measure of arc DAB, since we already know that angle DAB is 78. Angle DAB is an inscribed angle. That inscribed angle intercepts arc DCB, and the theorem for that is that an inscribed angle is half the measure of the arc it intercepts. That means that arc DCB measures twice 78, so arc DCB measures 156 degrees. Since the measure around the outside of any circle is 360 degrees, arc DAB is 360 - 156 which is 204 degrees. If this is not what you are looking for, sorry and be more specific next time.
1. María expandió el siguiente cuadrado de la manera que sigue: (x+3)2 = x² + 9,
¿Está correcta la forma que usó María?
Answer:
La expansión de María[tex](x + 3) {}^{2} = x {}^{2} + 9[/tex]
Correcta expansión[tex](x + 3) {}^{2} \\ = {x}^{2} + 2 \times x \times 3 + 3 {}^{2} \\ = x {}^{2} + 6x + 9[/tex]
Note - (a + b)² = a² + 2ab + b²
✐ La expansión de Mary está mal. Correcta expansión ⇻ x² + 6x + 9
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
# ꧁❣ RainbowSalt2²2² ࿐
What is the answer to this equation 4y+3y+2y=
4y + 3y + 2y = 9y
9y is the answer
Plz mark me brainliest
answer is 100% correct
A rain jacket that usually costs r dollars is available at a discount. Drag and drop two
expressions to show the correct price of the rain jacket in the spaces provided.
10.2r
0.3r
0.4r
0.5r
(0.6r
0.8r
The price of the rain jacket after a 20% discount:
The price of the rain jacket after a 40% discount:
The price of the rain jacket after a 20% discount will be 0.2r and the price of the rain jacket after a 40% discount will be 0.4r.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.
A rain jacket that usually costs r dollars is available at a discount.
Drag and drop two expressions to show the correct price of the rain jacket in the spaces provided.
The price of the rain jacket after a 20% discount will be
→ 0.2r
The price of the rain jacket after a 40% discount will be
→ 0.4r
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girlcome 5324611502
p:1234
Answer:
ok then
Step-by-step explanation:
Answer:
Subscribe to my animations Y0UTUBE channel! Channel name: Let Me Explain Studios. Have a nice day!
Step-by-step explanation:
If Sofia randomly picks a number from 1 to 25, what is the probability that the number will have “1” as one of the digits?
A farmer sells 8.2kg of apples and pears at the farmers market. 4/5 of this weight is apples and the rest is pears. How many kg of pears did she sell at the market?
9514 1404 393
Answer:
1.64 kg of pears
Step-by-step explanation:
If 4/5 of the weight is apples, the remaining 1/5 is pears.
(1/5)(8.2 kg) = 1.64 kg
She sold 1.64 kg of pears.
Answer:
Solution :-Weight of pears = 1 - Weight of apple
=> 1 - 4/5
=> 5 - 4/5
=> 1/5
Now
Weight of pears = ⅕ × 8.2
Weight of pears = 1.64 kg
[tex] \\ [/tex]
A garden table and a bench cost $672 combined. The garden table costs $78 less than the bench. What is the cost of the bench?
Answer:
b = $375
Step-by-step explanation:
b = cost of the bench
t = cost of the table
t = b - 78
b + b - 78 = 672
2b = 750
b = $375
helpp!! last question :( A. (4, 1) B. (4, -1) C. (-4, -4) D. (-4, 1)
Answer:
A
Choice A point is just above (4,-1) by an increase of y by 2
26 divided by a number r
Answer:
26 ÷ r
Step-by-step explanation:
Is your expression.
Using the keywords divide you can identify the expression, its showing you divide 26 by r, r in this case is your unknown value(variable). This expression is showing what you divide. You can also consider this as 26/r
Answer:
26/r
Step-by-step explanation:
So when they say a number they are meaning r.
Now lets break this into two simpler pieces.
When they say dividing by r they mean over r, or:
[tex]\frac{}{r}[/tex]
They say 26 is what is being divided by, which means 26 over, or:
[tex]\frac{26}{}[/tex]
Now we just need to combine these two pieces together:
[tex]\frac{26}{r}[/tex]
So this is your answer!
Hope this helps!
Identify the percent of change as an increase or decrease. $24 to $18
Answer:
Step-by-step explanation:
$24-$18
-6$
it is decrease
so,
decrease %=$6/$24*100
=600/24
=25%
Answer:
its a decrease of 25%
Step-by-step explanation:
1/4 of 24 is 6 and if you subtract 6 from 24 its 18 and 1/4 is 0.25 so its 25%.
What is the length of BD?
Answer:
From -6 to positive 1 the length is 7
Step-by-step explanation:
you still add'em.
Answer:
length of BD is 18
just count on the number line and ×2 because it is counting on by 2
Yesterday, there were 60 problems assigned for math homework. Albert did 30% of them correctly. How many problems did Albert get right?
brainliestt
for righto
Answer:
Hello! answer: 13/16
Hope that helps!