Answer:
a) 0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) 0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
Step-by-step explanation:
The condition of the bags in the sample is independent of the other bags, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
a) What is the probability of selecting and finding that all three bags are overweight?
2.5% are overweight, which means that [tex]p = 0.025[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.025)^{3}.(0.975)^{0} = 0.000016[/tex]
0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) What is the probability of selecting and finding that all three bags are satisfactory?
90% are satisfactory, which means that [tex]p = 0.9[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.9)^{3}.(0.1)^{0} = 0.729[/tex]
0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
Each side of a square is increasing at a rate of 4 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 25 cm2
Answer:
The area of the square is increasing at a rate of 40 square centimeters per second.
Step-by-step explanation:
The area of the square ([tex]A[/tex]), in square centimeters, is represented by the following function:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the side length, in centimeters.
Then, we derive (1) in time to calculate the rate of change of the area of the square ([tex]\frac{dA}{dt}[/tex]), in square centimeters per second:
[tex]\frac{dA}{dt} = 2\cdot l \cdot \frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 2\cdot \sqrt{A}\cdot \frac{dl}{dt}[/tex] (2)
Where [tex]\frac{dl}{dt}[/tex] is the rate of change of the side length, in centimeters per second.
If we know that [tex]A = 25\,cm^{2}[/tex] and [tex]\frac{dl}{dt} = 4\,\frac{cm}{s}[/tex], then the rate of change of the area of the square is:
[tex]\frac{dA}{dt} = 2\cdot \sqrt{25\,cm^{2}}\cdot \left(4\,\frac{cm}{s} \right)[/tex]
[tex]\frac{dA}{dt} = 40\,\frac{cm^{2}}{s}[/tex]
The area of the square is increasing at a rate of 40 square centimeters per second.
Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score
Answer:
Mean scores.
Step-by-step explanation:
The golf player will score in the first round, according to these scores the golf player scores can be predicted. The golf player can perform high in first round but he may score lesser in the second round due to stress or mental pressure. The scores can be predicted taking mean of the scores and adding standard deviation to it.
f(x) = 4x*x is a function?
Answer:
yes it is
Step-by-step explanation:
Wires manufactured for a certain computer system are specified to have a resistance of
between 0.11 and 0.16 ohm. The actual measured resistances of the wires produced by
Company A have a normal probability distribution, with a mean of 0.14 ohms, and a
standard deviation of 0.003 ohms. What is the probability that a randomly selected wire
from Company A’s production lot will meet the specifications?
Answer:
8d68d68fu9d6rf0d
c9yd7xpjd
puf68d6rif7
Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)
(Q.1)
[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]
Then substituting into the DE gives
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]
[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]
and both sides match, so y is indeed a valid solution.
(Q.2)
[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have
[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]
[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]
Integrate both sides (on the left, the numerator suggests a substitution):
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]
Given y (2) = e ³, we find
[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]
[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]
so that the particular solution is
[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]
[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]
[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]
(Q.3) I believe I've already covered in another question you posted.
Help me pls
I put the picture in the attach file below
(Sorry i'm in secondary school but i have a problem with my settings)
Answer:
1,2,4,8
Step-by-step explanation:
1
2
1,2
4
4,1
4,2
4,2,1
8
8,1
8,2
8,2,1
8,4
8,4,1
8,4,2
8,4,2,1
What is the lateral area of a cone with radius 19 cm and slant height 11 cm?
a. 19[tex]\pi[/tex] cm²
b. 30[tex]\pi[/tex] cm²
c. 200[tex]\pi[/tex] cm²
d. 209[tex]\pi[/tex] cm²
Answer:
The answer is 209 pi cm^2
L.A.(Lateral Area) = π19×11 = 209 π
The lateral area of the given cone with a raidus of 19 cm and a slant height of 11 cm is: D. 209π cm²
What is the Lateral Area of a Cone?Lateral area of a cone = πrL, where r is the radius and L is the slant height of the cone.
Given the following:
Slant height (L) = 11 cmRadius (r) = 19 cmLateral area of a cone = π(19)(11)
Lateral area of a cone = 209π cm²
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Will give brainliest answer
1... > equivalent 2...>equivalent 3...>not equivalent mark if u want
Sketch the graph of each line.
7) 2x - y = -4
Answer:
check the attachment
Step-by-step explanation:
2x - y = - 4
- y = - 4 - 2x
y = 2x + 4
slope of the line = 2 with y - intercept 4
A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.
Give your answer rounded to 1 decimal place.
Answer:
height = 3
Step-by-step explanation:
x(x+6) = 27
x^2 + 6x - 27 = 0
(x+9)(x-3) = 0
x = 3
For the expression x-5, what would the value be if x=18?
Answer:
13
Step-by-step explanation:
Answer:
if x is 18 replace 18 where x is in the question so, it will be 18-5 = 13
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Expected value of the hypergeometric distribution:
The expected value is given by:
[tex]E(X) = \frac{nk}{N}[/tex]
Expected number of blue and green balls:
40 balls, which means that [tex]N = 40[/tex]
2 are chosen, which means that [tex]n = 2[/tex]
25 are blue, which means that [tex]k = 25[/tex]
So
[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]
The expected number of winning balls that Heather draws is 0.3.
Given the functions below, find f(x)+g(x)
CHECK MY ANSWERS PLEASE
The answer is (a)..........
The following data show the number of cars passing through a toll booth during a certain time period over 15 days. 18 19 17 17 24 18 21 18 19 15 22 19 23 17 21 Identify the corresponding dotplot.
Answer: third from the top
Step-by-step explanation:
The correct answer is third from the top.
Arranging numbers in ascending order:
15 17 17 17 18 18 18 19 19 19 21 21 22 23 24
Let's count how many times each number occurs in this series of numbers.
row of numbers
15 +
16 not
17 + + +
18 + + +
19 + + +
20 not
21 + +
22 +
23 +
24 +
25 not
Working to
(simplify y
Lisa, an experienced shipping clerk, can fill a certain order in 7 hours, Bill, a new clerk, needs 9 hours to do the
same job. Working together, how long will it take them to fill the order?
it might take 19 hours i might be wrong
Step-by-step explanation:
a. A CD is discounted by 10%, and then from the already discounted price, a further 15% discount is given. If the price now is $12.93, find the original price.
b. What is the total discount percent as compared to the original price?
Answer:
a. $16.90
b. 23.5%
Step-by-step explanation:
a. After the two discounts, the original price is multiplied by ...
(1 -10%)(1 -15%) = 0.90×0.85 = 0.765
Then the original price is found from ...
$12.93 = 0.765 × original price
original price = $12.93 / 0.765 ≈ $16.90
__
b. The effective discount from the original price is ...
1 -0.765 = 0.235 = 23.5%
If JKL - PNM. then M = L and the sides NP and
KJ are proportional.
True
Or
False???
Answer:
True
Step-by-step explanation:
In similarity triangles, corresponding angles are congruent and corresponding sides are in proportion.
You are given the following information about x and y.
x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11
The least squares estimate of b 0 equals ______.
a. 16.41176
b. â1.3
c. 21.4
d. â7.647
Answer:
[tex]b_0 = 16.471[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccc}x & {15} & {12} & {10} & {7} \ \\ y & {5} & {7} & {9} & {11} \ \end{array}[/tex]
Required
The least square estimate [tex]b_0[/tex]
Calculate the mean of x
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{15+12+10+7}{4} =\frac{44}{4} = 11[/tex]
Calculate the mean of y
[tex]\bar y = \frac{\sum y}{n}[/tex]
[tex]\bar y = \frac{5+7+9+11}{4} =\frac{32}{4} = 8[/tex]
Calculate [tex]\sum(x - \bar x) * (y - \bar y)[/tex]
[tex]\sum(x - \bar x) = (15 - 11) * (5 - 8)+ (12 - 11) * (7 - 8) + (10 - 11) * (9 - 8)+ (7 - 11) * (11 - 8)[/tex]
[tex]\sum(x - \bar x) = -26[/tex]
Calculate [tex]\sum(x - \bar x)^2[/tex]
[tex]\sum(x - \bar x)^2 = (15 - 11)^2 + (12 - 11)^2 + (10 - 11)^2 + (7 - 11)^2[/tex]
[tex]\sum(x - \bar x)^2 = 34[/tex]
So:
[tex]b = \frac{\sum(x - \bar x) * (y - \bar y)}{\sum(x - \bar x)^2}[/tex]
[tex]b = \frac{-26}{34}[/tex]
[tex]b_0 = y - bx[/tex]
[tex]b_0 = 5 - \frac{-26}{34}*15[/tex]
[tex]b_0 = 5 + \frac{26*15}{34}[/tex]
[tex]b_0 = 5 + \frac{390}{34}[/tex]
Take LCM
[tex]b_0 = \frac{34*5+ 390}{34}[/tex]
[tex]b_0 = \frac{560}{34}[/tex]
[tex]b_0 = 16.471[/tex]
indicate the following pairs of lines are coinciding, parallel ,perpendicular or neither
currently, the US interest rate is at 2% annually. how long it will take an investor to make 10% of money from an investment if the bank pays simple interest
Answer:
5 years
Step-by-step explanation:
Practice Question
1) VAT (value-added tax) is paid on things that you buy.
The table on the right shows the 2019 VAT rates.
This is how much VAT is charged on certain items
as a percentage of the item's cost.
VẬT (%)
20
5
0.
Items
Chocolate and crisps
Gas and electric
Fruit and vegetables
Currena
Before VAT is added, Simon pays 12p per unit of
electricity plus a fixed charge of £87 per year.
How much does Simon pay in VAT if he uses 3000 units of electricity in one year?
er hour
Shane and Space
Simon will pay £18 in VAT for using 3000 units of electricity in one year.
The VAT rate for gas and electric is 5%.
Therefore, Simon will pay VAT on his electricity usage.
Let's calculate Simon's annual electricity cost without VAT:
Cost per unit of electricity = 12p
= £0.12
Number of units used in one year = 3000
Electricity cost without VAT = Cost per unit × Number of units
= £0.12 × 3000
= £360
Now, let's calculate the VAT amount:
VAT rate = 5% = 0.05
VAT amount = Electricity cost without VAT × VAT rate
= £360 × 0.05
= £18
Therefore, Simon will pay £18 in VAT for using 3000 units of electricity in one year.
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Item 16
What is the area of the triangle in the coordinate plane?
36 units²
38 units²
66 units²
72 units²
Select the correct answer. Which function is continuous across Its domain
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
f(a) exists (i.e. the value of f(a) is finite)the right-hand limit = left-hand limit, and both are finite.right-hand limit = left-hand limit = f(a)Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
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Write the expression in complete factored form.
5n(x - 2) + 8(x - 2) =
x − 2 out of 5n ( x −2 ) + 8 ( x − 2) . ( x − 2 ) ( 5 n + 8 )
I hope this is correct and helps!
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{5n(x - 2) + 8(x - 2) =}[/tex]
[tex]\large\text{DISTRIBUTE 5 and 8 WITHIN the PARENTHESES}[/tex]
[tex]\large\textsf{= 5n(x) + 5(-2) + 8(x) + 8(-2)}[/tex]
[tex]\large\textsf{= 5nx - 10n + 8x - 16}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf (x - 2)(5n + 8)}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
There are 100 cars in a car pack.28 of them are blue and 34 are red. If a car is selected at random from the cars. What is the probability that it is neither red nor blue
Answer:
0.38 = 38% probability that it is neither red nor blue.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
100 cars.
Of those, 28 + 34 = 62 are either blue or red.
100 - 62 = 38 are neither blue of red.
What is the probability that it is neither red nor blue?
38 out of 100, so:
[tex]p = \frac{38}{100} = 0.38[/tex]
0.38 = 38% probability that it is neither red nor blue.
Choose the algebraic description that maps the image ABC onto A'B'C'.
19.Find dy/dx
of the function y = f(x) definded by x²+xy-y2 = 4.
Answer:
2x + y
Step-by-step explanation:
x² + xy - y² = 4
→ Remember the rule, bring the power down then minus 1
2x + y
Given the data points below, compute the sum of squared errors for the regression equation
Y
=
2
+
3
X
.
X
0
3
7
10
Y
5
5
27
31
Answer:
The sum of squared errors for the regression equation is 62.
Step-by-step explanation:
The sum of squared errors can be computed as follows:
X Y Y* = 2 + 3X Y - Y* (Y - Y*)^2
0 5 2 3 9
3 5 11 -6 36
7 27 23 4 16
10 31 32 -1 1
20 68 68 0 62
From the above, we have:
Error = Y - Y*
Error^2 = (Y - Y*)^2
Sum of squared errors = Sum of Error^2 = Total of (Y - Y*)^2 = 62
Therefore, the sum of squared errors for the regression equation is 62.
Find the value of x pls help
9514 1404 393
Answer:
x = 36°
Step-by-step explanation:
The exterior angle is equal to the sum of the remote interior angles. A linear pair is supplementary. So, you can find x either of two ways:
2x = x + (180 -4x) ⇒ 5x = 180 ⇒ x = 36
Or ..
4x = x + (180 -2x) ⇒ 5x = 180 ⇒ x = 36
The value of x is 36°.
Fill in the blanks with the correct verbs given below.
(croak, is ,brush, writes plays, chirp, combines, mows, are look , keeps rises ,has,
reflects leaves, walks, is)
1. Marry ......... to office every morning .Walking is good exercise.
2. We........ our teeth after dinner. It ..........them clean.
3. Salim......... for school everyday at 7:00 a.m.
4. The sun ..........at 5:00 a.m. these days. The days are getting longer.
5. The tiger ......an endangered animal. There are only 1410 tigers left.
6. Vikram Seth......... poetry, fiction and travelogues.
7. Sania Mirza......... tennis. She plays both singles and doubles.
8. Frogs....... ...and birds...........
9. Please ..........for my red shirt. I cannot find it.
10. The gardener ........ the loan once a week.
11. The moon ........the light of the sun.
12. The times of India......... a national newspaper.
13. The UN headquarters...... in Geneva.
14. Maya ........... a pet dog .Its name is Lily.
15. This book....... projects and activities.
Answer:
Fill in the blanks with the correct verbs given below.
(croak, is ,brush, writes plays, chirp, combines, mows, are look , keeps rises ,has,
reflects leaves, walks, is)
1. Marry ...keeps rises...... to office every morning .Walking is good exercise.
2. We...brush..... our teeth after dinner. It .....makes.....them clean.
3. Salim....wakes..... for school everyday at 7:00 a.m.
4. The sun ...rises.......at 5:00 a.m. these days. The days are getting longer.
5. The tiger chirp......an endangered animal. There are only 1410 tigers left.
6. Vikram Seth.....combines........ poetry, fiction and travelogues.
7. Sania Mirza....plays..... tennis. She plays both singles and doubles.
8. Frogs....croak... ...and birds.....chirp......
9. Please ....look......for my red shirt. I cannot find it.
10. The gardener .....mows....... the loan once a week.
11. The moon ...keep rises.....the light of the sun.
12. The times of India......writes....... a national newspaper.
13. The UN headquarters.....is..... in Geneva.
14. Maya ...has........ a pet dog .Its name is Lily.
15. This book....writes..... projects and activities
