Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
What type of line is PQ⎯⎯⎯⎯⎯⎯⎯⎯?
Answer:
median
Step-by-step explanation:
Q is at the midpoint of RS and so PQ is a median
A median is a segment from a vertex to the midpoint of the opposite side.
We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.
First, let's analyze the image:
In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.
Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.
With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.
If you want to learn more, you can read:
https://brainly.com/question/2272632
find the value of...
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
1. You measure 24 textbooks' weights, and find they have a mean weight of 75 ounces. Assume the population standard deviation is 3.3 ounces. Based on this, construct a 90% confidence interval for the true population mean textbook weight.
2. You measure 37 backpacks' weights, and find they have a mean weight of 45 ounces. Assume the population standard deviation is 10.1 ounces. Based on this, construct a 95% confidence interval for the true population mean backpack weight.
3. You measure 30 watermelons' weights, and find they have a mean weight of 37 ounces. Assume the population standard deviation is 4.1 ounces. Based on this, what is the maximal margin of error associated with a 90% confidence interval for the true population mean watermelon weight.
4. A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 16. Which of the following is a correct interpretation of the interval 11.8 < μ < 20.4?
A. There is a 99% chance that the mean of a sample of 16 widgets will be between 11.8 and 20.4.
B. The mean width of all widgets is between 11.8 and 20.4, 99% of the time. We know this is true because the mean of our sample is between 11.8 and 20.4.
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 11.8 and 20.4.
E. There is a 99% chance that the mean of the population is between 11.8 and 20.4.
5. For a confidence level of 90% with a sample size of 23, find the critical t value.
Answer:
(73.845 ; 76.155) ;
(41.633 ; 48.367) ;
1.273 ;
C. With 99% confidence, the mean width of all widgets is between 11.8 and 20.4. ;
1.717
Step-by-step explanation:
1.)
Given :
Mean, xbar = 75
Sample size, n = 24
Sample standard deviation, s = 3.3
α = 90%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 24 - 1 = 23
Tcritical = 1.714
Margin of Error = 1.714 * 3.3/√24 = 1.155
Confidence interval = 75 ± 1.155
Confidence interval = (73.845 ; 76.155)
2.)
Given :
Mean, xbar = 45
Sample size, n = 37
Sample standard deviation, s = 10.1
α = 95%
Confidence interval = mean ± margin of error
Margin of Error = Tcritical * s/√n
Tcritical at 95% ; df = 37 - 1 = 36
Tcritical = 2.028
Margin of Error = 2.028 * 10.1/√37 = 3.367
Confidence interval = 45 ± 3.367
Confidence interval = (41.633 ; 48.367)
3.)
Given :
Mean, xbar = 37
Sample size, n = 30
Sample standard deviation, s = 4.1
α = 90%
Margin of Error = Tcritical * s/√n
Tcritical at 90% ; df = 30 - 1 = 29
Tcritical = 1.700
Margin of Error = 1.700 * 4.1/√30 = 1.273
5.)
Sample size, n = 23
Confidence level, = 90%
df = n - 1 ; 23 - 1 = 22
Tcritical(0.05, 22) = 1.717
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
Seth and Ted can paint a room in 5 hours if they work together. If Ted were to work by himself, it would take him 2 hours longer than it would take Seth working by himself. How long would it take Seth to paint the room by himself if Ted calls in sick?
Answer:
9 hours
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x/x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.Answer:
Step-by-step explanation:
Let
x = number of hours it would take Seth to work by himself
He would paint 1/x in 1 hour
x + 2 = number of hours it would take Ted to work by himself
He would paint 1/(x + 2) in 1 hour
Seth and Ted = 5 hours
They would paint 1/5 in 1 hour
The equation is this:
1/x + 1/(x + 2) = 1/5
(x + 2)+x / x(x+2) = 1/5
x+2+x / x(x+2) = 1/5
2x + 2 / x(x+2) = 1/5
Cross product
2x + 2 = x(x + 2)1/5
2x + 2 = (x² + 2x)1/5
Cross product
5(2x + 2) = x² + 2x
10x + 10 = x² + 2x
x² + 2x - 10x - 10 = 0
x² - 8x - 10 = 0
x = -b ± √b² - 4ac/2a
= -(-8) ± √(-8)² - 4(1)(-10) / 2(1)
= 8 ± √64 - (-40) / 2
= 8 ± √64 + 40) / 2
= 8 ± √104 / 2
= 8 ± 2√26 / 2
= 8/2 ± 2√26/2
= 4 ± √26
= 4 ± 5.0990195135927
= 4 + 5.0990195135927 or 4 - 5.0990195135927
= 9.0990195135927 or -1.0990195135927
Approximately,
x = 9 hours or -1 hour
It can't take Seth negative hours to work
Therefore,
x = number of hours it would take Seth to work by himself = 9 hours
Your EZ Pass account begins with $80. It costs you $4/day. Write an equation
for the amount in your account (A) in terms of the number of days (D).
Answer:
The equation is [tex]A(d) = 80 - 4d[/tex]
Step-by-step explanation:
Linear function:
A linear function for the amount of money in an account after t days is given by:
[tex]A(d) = A(0) - md[/tex]
In which A(0) is the initial value and m is the daily cost.
Your EZ Pass account begins with $80. It costs you $4/day.
This means that [tex]A(0) = 80, m = 4[/tex]
So
[tex]A(d) = A(0) - md[/tex]
[tex]A(d) = 80 - 4d[/tex]
5/6 ÷ 1/3 - 2/3 (2/5)
Answer:
[tex] \frac{67}{30} \: \text{or} \:2 \frac{7}{30} [/tex]
Step-by-step explanation:
5/6 ÷ 1/3 - 2/3 (2/5)
= 5/6 ÷ 1/3 - 2/3 × 2/5= 5/2 - 2/3 × 2/5= 5/2 - 4/15= 67/30 or 2 7/30Hope it helps you! ＼(^ᴥ^)／
If the current through a circuit is 2 A and the resistance of a light bulb in the circuit is 10 Ohms what is tge voltage difference across the light bulb
Answer:
v = ir
2 times 10 = 20v
Step-by-step explanation:
i think it is the one
La señora Alcántara realiza una compra en el supermercado fortuna, ella solo tiene 12,400 pesos ,compra varios artículos y su compra es equivalente a 13,600 pesos. ¿Cuánto tiene que pagar si le realizan un descuento de un 15%? ¿Cuántos le quedaron de lo que tenía en efectivo?
Answer:
She spent = 11560 pesos
Amount left = 840 pesos
Step-by-step explanation:
Mrs. Alcántara makes a purchase at the fortuna supermarket, she only has 12,400 pesos, she buys several items and her purchase is equivalent to 13,600 pesos. How much do you have to pay if they give you a 15% discount? How many was left of what he had in cash?
Amount she has = 12400pesos
Item purchased = 13600 pesos
discount = 15 %
So, the total discount on the item purchased is
= 15 % of 13600
= 0.15 x 13600
= 2040 pesos
So, the amount spent = 13600 - 2040 = 11560 pesos
Amount she left = 12400 - 11560 = 840 pesos
xp-q+1×xq-r+1×xr-p+1
Answer:
Look into the picture
Step-by-step explanation:
Let me know if there's something wrong to my answer
what is the range of the funcion y=x^2
Answer:
Range = [0, infinity)
Step-by-step explanation:
Minimum point of the graph is at (0,0) and it is a u shaped graph. Hence, range is 0 inclusive to infinity
In what ratio of line x-y-2=0 divides the line segment joining (3,-1) and (8,9)?
[tex] \large{ \tt{❁ \: USING \: INTERNAL \: SECTION \: FORMULA: }}[/tex]
[tex] \large{ \bf{✾ \: P(x \:, y \: ) = ( \frac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}} \: ,\: \frac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}) }}[/tex]
[tex] \large{ \bf{⟹ \: ( \frac{8m + 3n}{m + n} , \: \frac{9m -n}{m + n}) }}[/tex]
Since point P lies on the line x - y - 2 = 0 ,[tex] \large{ \bf{ ⟼\frac{8m + 3n}{m + n} - \frac{9m - n}{m + n} - 2 = 0 }}[/tex]
[tex] \large{ \bf{⟼ \: \frac{8m + 3n - 9m + n}{m + n} - 2 = 0 }}[/tex]
[tex] \large{ \bf{⟼ \: \frac{4n - m}{ m + n} - 2 = 0 }}[/tex]
[tex] \large{⟼ \: \bf{ \frac{4n - m}{m + n }} = 2} [/tex]
[tex] \large{ \bf{⟼ \: 4n - m = 2m + 2n}}[/tex]
[tex] \large{ \bf{⟼ \: 4n -2 n = 2m + m}}[/tex]
[tex] \large{ \bf{⟼2n = 3m}}[/tex]
[tex] \large{ \bf{⟼ \: 3m = 2n}}[/tex]
[tex] \large{ \bf{⟼ \: \frac{m}{n} = \frac{2}{3} }}[/tex]
[tex] \boxed{ \large{ \bf{⟼ \: m : \: n = 2: \: }3}}[/tex]
Hence , The required ratio is 2 : 3 .-Hope I helped! Let me know if you have any questions regarding my answer and also notify me , if you need any other help! :)
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math help plz
how to divide polynomials, how to understand and step by step with an example provided please
Answer:
hiiiiiii....!!! how r u
Assume that $4,000 I deposited into an investment account doubled in value over a six year period. What annual interest rate must I have earned over this period? Is the initial amount of the deposit relevant to the calculation of the annual interest rate? Why or why not?
Answer:
Interest rate is about 12.246%
The initial deposit doesn't matter because when you divide both sides by the initial deposit you're always left with (1+i)ⁿ=2
Step-by-step explanation:
[tex]4000(1+i)^6=8000\\(1+i)^6=2\\1+i=\sqrt[6]{2} \\1+i=1.122462048\\i=.12246[/tex]
How Do I do this equation
Answer:
Part A 12 ≤ 6x ≤ 36
Part B 2 ≤ x ≤ 6
Step-by-step explanation:
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not have the disease.
The individual actually had the disease
Yes No
Positive 135 11
Negative 99 145
Answer:
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
11 + 145 = 156 people did not have the disease.
Out of those, 145 tested positive. So
[tex]p = \frac{145}{156} = 0.9295[/tex]
0.9295 = 92.95% probability of getting someone who tests negative, given that he or she did not have the disease.
Find the area of the figure
Please help :)
9514 1404 393
Answer:
66.5 cm²
Step-by-step explanation:
A horizontal line at the "knee" on the right will divide the figure into a 4 cm by 2 cm rectangle, and a trapezoid with bases 4 cm and 9 cm, and height 11-2 = 9 cm. Then the total area of the figure is ...
A = LW + 1/2(b1 +b2)h
A = (4 cm)(2 cm) + (1/2)(4 cm +9 cm)(9 cm) = 8 cm² +58.5 cm²
A = 66.5 cm² . . . . area of the figure
Bob had 10 more cars than Paul. Paul had 15 cars.
Answer:
Bob had 25 cars
Step-by-step explanation:
10+15=25
PLEASE HELP WILL MARK BRAINLIEST!
9514 1404 393
Answer:
7.5
Step-by-step explanation:
Corresponding sides are proportional, so ...
UV/VW = LM/MN
x/6 = 15/12
x = 6(15/12) = 15/2
x = 7.5
2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.
a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).
Answer:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Step-by-step explanation:
for person A, we know that earns $40, then we can write the equation:
-4*z + 3*x + 3*y = $40
For person B, we know that earns $50, then:
1*z + 2*x - 3*y = $50
For person C, we know that earns $130, then:
6*z - 1*x + 4*y = $130
Then we have a system of equations:
-4*z + 3*x + 3*y = $40
1*z + 2*x - 3*y = $50
6*z - 1*x + 4*y = $130
To solve the system, we need to isolate one of the variables in one of the equations.
Let's isolate z in the second equation:
z = $50 - 2*x + 3*y
now we can replace this in the other two equations:
-4*z + 3*x + 3*y = $40
6*z - 1*x + 4*y = $130
So we get:
-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40
6*($50 - 2*x + 3*y) - 1*x + 4*y = $130
Now we need to simplify both of these, so we get:
-$200 + 11x - 9y = $40
$350 - 13*x + 28*y = $130
Now again, we need to isolate one of the variables in one of the equations.
Let's isolate x in the first one:
-$200 + 11x - 9y = $40
11x - 9y = $40 + $200 = $240
11x = $240 + 9y
x = ($240 + 9y)/11
Now we can replace this in the other equation:
$350 - 13*x + 28*y = $130
$350 - 13*($240 + 9y)/11 + 28*y = $130
Now we can solve this for y.
- 13*($240 + 9y)/11 + 28*y = $130 - $350 = -$220
-13*$240 - (13/11)*9y + 28y = - $220
y*(28 - (9*13/1) ) = -$220 + (13/11)*$240
y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66
We know that:
x = ($240 + 9y)/11
Replacing the value of y, we get:
x = ($240 + 9*$3.66)/11 = $24.81
And the equation of z is:
z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36
Then:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
What is the solution to the system of equations below
Answer:
A
Step-by-step explanation:
1/2x-4=-2x-9...u vil get the ans
Determine the mean and variance of the random variable with the following probability mass function. f(x)=(216/43)(1/6)x, x=1,2,3 Round your answers to three decimal places (e.g. 98.765).
Mean:
E[X] = ∑ x f(x) = 1 × f (1) + 2 × f (2) + 3 × f (3) = 51/43 ≈ 1.186
Variance:
Recall that for a random variable X, its variance is defined as
Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²
Now,
E[X ²] = ∑ x ² f(x) = 1² × f (1) + 2² × f (2) + 3² × f (3) = 69/43
Then
Var[X] = 69/43 - (51/43)² = 366/1849 ≈ 0.198
(each sum is taken over x in the set {1, 2, 3})
A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line
Answer:
(in the image)
Step-by-step explanation:
I'm not sure I understood your question completely but I hope this helps.
Find the volume (in cubic yards) of a cylinder with radius 1.2 yards and height 2.9 yards. (Round your answer to one decimal place.)
Answer:
11.8 yd³
Step-by-step explanation:
2.6.58
The lot in the figure shown, except for the house, shed, and driveway, is lawn. One bag of lawn fertilizer
costs $15.00 and covers 3,000 square feet.
Please help :)
Answer:
50 bags ;
£750
Step-by-step explanation:
The dimension of the rectangular lawn is 500ft by 300 ft
The area of the lawn an e obtained thus :
Area of rectangle = Length * width
Area of rectangle = 500 ft * 300 ft
Area of rectangle = 150000 feets
1 bag of fertilizer covers 3000 feets
The minimum bags of fertilizer required :
Area of rectangle / Area covered by 1 bag of fertilizer
Minimum bags of fertilizer required :
(150,000 / 3000) = 50 bags
50 bags of fertilizer
Cost per bag = 15
Total cost = 15 * 50 = £750
40 points! Need help finding.
The cordent plan of the answer is 2
Answer:
The scale factor will just be 2
Step-by-step explanation:
The length of PQ is twice as larger than the length of AB.
so from 12 to 6 or 6 to 12, we multiply 6 by 2 which equals to 12
.4.1 Here are the data from Exercise 2.3.10 on the num-ber of virus-resistant bacteria in each of 10 aliquots: 14 14 15 26 13 16 21 20 15 13 (a) Determine the median and the quartiles. (b) Determine the interquartile range. (c) How large would an observati
Answer:
(a)
[tex]Q_1 = 14[/tex]
[tex]Median = 15[/tex]
[tex]Q_3 = 20[/tex]
(b) [tex]IQR = 6[/tex]
Step-by-step explanation:
Given
[tex]14\ 14\ 15\ 26\ 13\ 16\ 21\ 20\ 15\ 13[/tex]
[tex]n = 10[/tex]
Solving (a): Median and the quartiles
Start by sorting the data
[tex]Sorted: 13\ 13\ 14\ 14\ 15\ 15\ 16\ 20\ 21\ 26[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{10 + 1}{2} = \frac{11}{2} = 5.5th[/tex]
This implies that the median is the average of the 5th and the 6th data;
So;
[tex]Median = \frac{15+15}{2} = \frac{30}{2} = 15[/tex]
Split the dataset into two halves to get the quartiles
[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]
[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]
The quartiles are the middle items of each half.
So:
[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]
[tex]Q_1 = 14[/tex] ---- 14 is the middle item
[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]
[tex]Q_3 = 20[/tex] ---- 20 is the middle item
Solving (b): The interquartile range (IQR)
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 20 - 14[/tex]
[tex]IQR = 6[/tex]
Solving (c): Incomplete details
A cardboard box without a lid is to have a volume of 4,000 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)
Determine the value of z in the figure
5z
130°
A.Z = 30°
B.Z = 45°
C.z = 50°
D.Z = 10°
Hi!
180° - 130° = 50°
5z = 50° || : 5
z = 10°
Answer:
10
Step-by-step explanation:
since 130 and the 5z are complementary angles, by subtracting 130 from 180, you get 50. then you equal in 50 to 5z. 50=5z. to solve, you divide 5 from 50 and your answer is 10.
Marla scored 70% on her last unit exam in her statistics class. When Marla took the SAT exam, she scored at the 70th percentile in mathematics. Explain the difference in these two scores.
Answer:
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
Step-by-step explanation:
Marla scored 70% on her last unit exam in her statistics class.
This means that in her statistics class, Marla got 70% of her test correct.
When Marla took the SAT exam, she scored at the 70th percentile in mathematics.
This means that on the SAT exam, graded on a curve, Marla scored better than 70% of the students.
Explain the difference in these two scores.
The difference is that Marla's exam in her statistics class was graded by percent of correct answers, in her case 70%, while the SAT is graded into a curve, taking other students' grades also into account, and since she scored in the 70th percentile, Marla scored better than 70% of the students.
