Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
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A bottle maker believes that 14% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 622 bottles would be less than 11%
Answer:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
Step-by-step explanation:
For this case we know the following info given:
[tex] p =0.14[/tex] represent the population proportion
[tex] n = 622[/tex] represent the sample size selected
We want to find the following proportion:
[tex] P(\hat p <0.11)[/tex]
For this case we can use the normal approximation since we have the following conditions:
i) np = 622*0.14 = 87.08>10
ii) n(1-p) = 622*(1-0.14) =534.92>10
The distribution for the sample proportion would be given by:
[tex] \hat p \sim N (p ,\sqrt{\frac{p(1-p)}{n}}) [/tex]
The mean is given by:
[tex] \mu_{\hat p}= 0.14[/tex]
And the deviation:
[tex]\sigma_{\hat p}= \sqrt{\frac{0.14*(1-0.14)}{622}}= 0.0139[/tex]
We can use the z score formula given by:
[tex] z=\frac{\hat p -\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And replacing we got:
[tex] z = \frac{0.11-0.14}{0.0139} = -2.156[/tex]
And we can use the normal standard distribution table and we got:
[tex] P(Z<-2.156) =0.0155[/tex]
Matt brought $40.50 to the art supply store. He bought a brush, a sketchbook, and a paint set. The brush was 1 6 as much as the sketchbook, and the sketchbook cost 3 4 the cost of the paint set. Matt had $3.00 left over after buying these items.
Answer:
idk what you mean
Step-by-step explanation:
idk
A system of equations has 1 solution. If 4x - y = 5 is one of the equations, which could be the other equation?
O y=-4x + 5
y = 4x-5
2y = 8x - 10
-2y = -8x - 10
Answer:
[tex]4x -y = 5[/tex]
And if we rewrite this expression we got:
[tex] y= 4x -5[/tex]
If the system have just one solution then we need the slope different and for this reason we can discard the options:
y = 4x-5
-2y = -8x - 10 equivalent to y =4x+5
2y = 8x - 10 equivalent to y = 4x -5
And then the correct answer would be:
y=-4x + 5
Step-by-step explanation:
For this case we have the following equation given:
[tex]4x -y = 5[/tex]
And if we rewrite this expression we got:
[tex] y= 4x -5[/tex]
If the system have just one solution then we need the slope different and for this reason we can discard the options:
y = 4x-5
-2y = -8x - 10 equivalent to y =4x+5
2y = 8x - 10 equivalent to y = 4x -5
And then the correct answer would be:
y=-4x + 5
Answer:
A: y = –4x + 5
Step-by-step explanation:
I got it right on Edge
When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation for each option. Graph each line and use the graph to answer the question. You will need to upload a picture or screenshot of your graphs.
Answer:
it´s b
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
1)
Volume of pyramid = 1/3(Ab)(h)
Where Ab is the area of base, h is height
Volume of cone = 1/3(Ab)(h)
a) Their formula for finding volume is same. Also, their painting heads are same.
b) Pyramids have a tetragonal base while cones have a polygonal base
2) Pyramids
Volume of cone = (1/3) πr²h
Since Area of a circle = πr²
So
Volume of pyramid = (1/3)(A)(h)
So we can use the formula of a circle in cone's formula
Answer:
i dont know but i want points
Step-by-step explanation:
hehehe
Need help finding the answer
Answer:
D
Step-by-step explanation:
When there is an negative sign inside in a radical, then we remove that and put out of the radical classifying as "i". Then, reduce 63 into smallest form and we can write it as 9 and 7. 9 is a perfect square of 3 so we put it outside and the answer is D.
The probability of teenager owning a game system is .72 and the probability of teenager owning a cell phone is .93.
the probability of a teenager owning both gaming system and cell phone is .68
what is the probability of a teenager owning a gaming system or a cell phone? round to the nearest thousandth
Answer: 0.97
Step-by-step explanation:
Formula : For events A and B
P(A or B) = P(A) + P(B) - P(A and B)
Given : The probability of teenager owning a game system is .72.
i.e. P(game system) =0.72
The probability of teenager owning a cell phone is .93.
i.e. P(cell phone) = 0.93
The probability of a teenager owning both gaming system and cell phone is .68
i.e. P( game system and cell phone) = 0.68
Now , the probability of a teenager owning a gaming system or a cell phone is given by :_
P(game system or cell phone) = P(game system) +P(cell phone)- P( game system and cell phone)
= 0.72+0.93-0.68
= 0.97
Hence, the probability of a teenager owning a gaming system or a cell phone is 0.97.
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
2 & 8
-4 & -4
Step-by-step explanation:
x and y are the numbers, as per question:
x= 4+2y and xy= 16
y(4+2y)= 162y²+4y=16y²+2y - 8= 0y²+2y+1 =9(y+1)²=9y+1=3 ⇒ y= 2 ⇒ x= 4+2*2= 8y+1= -3 ⇒ y= -4 ⇒ x= 4+2*(-4)= -4Can someone please help me with this one??
Answer:
x = 3.6 cm
Step-by-step explanation:
By the theorem of intersecting secants,
"If two secants are drawn from a point outside the circle, product of the lengths of the secant segment and its external segment are equal."
3(3 + y) = 2(2 + 6 + 3)
9 + 3y = 2 × 11
3y = 22 - 9
3y = 13
y = [tex]\frac{13}{3}[/tex] cm = 4.33 cm
Now we will apply theorem of intersecting chords to determine the value of x.
" When two chords intersect each other in a circle, product of their segments are equal"
[tex]x\times 5=6\times 3[/tex]
[tex]x=\frac{18}{5}[/tex]
[tex]x=3.6[/tex] cm
Therefore, x = 3.6 cm and y = 4.33 cm
You are going to sell your Samsung so you can get the new iPhone. You purchased your Samsung 2 years ago for $200. It's
value decreases at a rate of 2% each month. To the nearest dollar, how much is your Samsung worth now?
Answer:
[tex]\boxed{\ 123 \ dollars\ }[/tex]
Step-by-step explanation:
its value decreases at a rate of 2% each month
in 2 years there are 12*2=24 months
so the Samsung worth [tex]200(0.98)^{24}\\[/tex]
it gives 123 rounded to the nearest dollar
Answer:
$123
Step-by-step explanation:
initial price= $200
value decrease rate= 2% = 0.98 times a month
time = 2 years
current value= $200*0.98²⁴= $123
What is the equation of the line perpendicular to y = 2/3 x +1 that passes through the point (12, – 6)?
Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
Find the value of x.
Answer:
Step-by-step explanation:
so there’s 25 and 25 it’s kinda like counting money divide it into 4 pieces 25 , 50 , 75 , 100
Answer:
The answer would be x=3
Step-by-step explanation:
Henry, Brian and Colin share some sweets in the ratio 6:4:1. Henry gets 25 more sweets than Colin. How many sweets are there altogether?
Answer:
There are 55 sweets in total.
Step-by-step explanation:
The total number of sweets is t.
Henry, Brian and Colin share some sweets in the ratio 6:4:1.
This means that Henry earns [tex]\frac{6}{6+4+1} = \frac{6}{11}[/tex] of the total(t).
Brian earns [tex]\frac{4}{11}[/tex] of the total.
Colin earns [tex]\frac{1}{11}[/tex] of the total
Henry gets 25 more sweets than Colin.
Henry earns [tex]\frac{6t}{11}[/tex]
Colin earns [tex]\frac{t}{11}[/tex]
So
[tex]\frac{6t}{11} = \frac{t}{11} + 25[/tex]
Multiplying everything by 1
[tex]6t = t + 275[/tex]
[tex]5t = 275[/tex]
[tex]t = \frac{275}{5}[/tex]
[tex]t = 55[/tex]
There are 55 sweets in total.
The distance between (2, 3) and (1,7) is:
Answer:
[tex] \sqrt{17}\: units [/tex]
Step-by-step explanation:
[tex]d = \sqrt{ {(2 - 1)}^{2} + {(3 - 7)}^{2} } \\ \\ = \sqrt{ {(1)}^{2} + {( - 4)}^{2} } \\ \\ = \sqrt{ 1 + 16 } \\ \\ d= \sqrt{17} \\ [/tex]
Answer:
d=√17≈4.12310562561766
Step-by-step explanation:
find the common difference of the arithmetic sequence 4, 10, 16,...
4+6=10+6=16+6=22+6=28...
I hope it is helpful for everyone
Salinas Corporation has net income of $15 million per year on net sales of $90 million per year. It currently has no long-term debt but is considering a debt issue of $20 million. The interest rate on the debt would be 7%. Salinas Corp. currently faces an effective tax rate of 40%. What would be the annual interest tax shield to Salinas Corp. if it goes through with the debt issuance?
Answer:
The annual interest tax shield to Salinas Corp would be of $560,000
Step-by-step explanation:
In order to calculate the annual interest tax shield to Salinas Corp if it goes through with the debt issuance we would have to calculate the following formula:
Annual Interest tax shield = Interest * tax
Interest = debt *rate of interest
Interest=$20 million * 0.07
Interest= $ 1.40 million
tax= 40%
Therefore, Annual Interest tax shield =$1.40 million * 0.40
Annual Interest tax shield = $560,000
The annual interest tax shield to Salinas Corp would be of $560,000
What is five + five
Halley's birthday is on Friday. On Monday she receives 23 birthday cards. On Tuesday she receives 5 birthday cards. On Wednesday she receives 13 birthday cards. On Thursday she receives 17 birthday cards, and on Friday she receives 22 birthday cards. How many total birthday cards does Halley receive?
Answer:
80
Step-by-step explanation:
17+13=30
22+23+5=50
30+50=80
Answer:
80 cards
Step-by-step explanation:
23+5=28
13+17=30
28+30=58
58+22=80
Which equation describes a relationship that is directly proportional?
(A) y = 9
(B) y = 1/5
(C) y = 3x
(D) y = x + 4
Answer:
(C) y = 3x
Step-by-step explanation:
Directly proportional relation is one in which the value of x and y gets increases or decreased in same proportion.
example of such relation can be y = kx
where k is the constant of proportionality which depicts by how much value of y will change in response to change of x.
_______________________________________________
now in the option
A and B
y= 9 , y =1/5
value of y is constant and does not depend on other variable. it value will remain same.
for y = x+4
value of y increases with x but it does not increase proportionally.
let see an example for x =1 , y = 1+4 = 5
x =2 , y = 2+4 = 6
(1,5) and (2,6) are not proportionally changing also this equation is not of form y = kx
thus, it is incorrect option.
_______________________________
(C) y = 3x
here equation is form y =kx . in place of k there is 3
let see an example for x =1 , y = 3*1 = 3
x =2 , y = 3*2 = 6
(1,3) and (2,6) are proportionally changing (1/3 = 2/6) also this equation is of form y = kx
thus, it is correct option.
A researcher reports that the farther college students are from their parents, the more often they communicate with their parents (either by phone or by e-mail). Is this an example of a positive correlation or a negative correlation?
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation exists between two variables, when both variables tend to move along the same direction. In order words, when one particular variable increases, there is also an increase in the other variable.
The case stated above is an example of positive correlation, because, the farther the students are from their parents, the more often they communicate with them. As distance increases, so does the number of, perhaps, phone calls increases as well.
Answer:
Positive correlation
Step-by-step explanation:
A positive correlation occurs whereby in a relationship between two variables, both variable move in the same direction meaning as one increases, the other also increases.
In this study, an increase in distance enforces an increase in communication with the parents.
g(x)4x^2-16x+7 completing the square
By completing the square the function will be, g(x)=4(x-2)²-9
What is standard form of the equation?The standard form of the quadratic equation will be ax²+bx+c=0.
Equate the given equation with standard form of equation and determine the values of a, b, and c.
a=4
b=-16
c=7
For completing the square, add and subtract [tex]\frac{b^2}{4a}=\frac{(-16)^2}{4\times4}=16[/tex] in the given equation.
g(x)=4x²-16x+16-16+7
g(x)=(4x²-16x+16)-9
g(x)=4(x²-4x+4)-9
The term x²-4x+4 is equivalent to (x-2)².
g(x)=4(x-2)²-9
So, the given function is same as g(x)=4(x-2)²-9.
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Please answer this correctly
Answer:
1 flowers
Step-by-step explanation:
The graph shows that only one flower received more than [tex]4\frac{1}{2}[/tex] cups of water and that is the plant that received 5 cups of water.
1 flower
Step-by-step explanation:
the question asks for flowers above the 4 1/2 mark and only 1 flower is there.
1/2x+4=2/3x+1, solve for x
Answer:
x=18
Step-by-step explanation:
Step 1: Subtract 2/3x from both sides.
1/2x+4=2/3x+1
-2/3x -2/3x
= -1/6x+4=1
Step 2: Subtract 4 from both sides.
-1/6x+4=1
-4 -4
= -1/6x=-3
Step 3: Multiply both sides by 6/(-1).
-1/6x=-3
*6/(-1) * 6/(-1)
x=18
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us? 24 72 41 76 15 29 64 93 74 38 99
Answer:
a) 56.82
b) 64
c) there is no mode
d) 57
e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless
Step-by-step explanation:
The first thing is to organize the data from least to greatest:
15 24 29 38 41 64 72 74 76 93 99
a) the mean would be the average of the data, thus:
m = (15 + 24 + 29 + 38 + 41 + 64 + 72 + 74 + 76 + 93 + 99) / 11
m = 56.82
b) the median is the data of half, when the data is organized, in this case the value of half would be the sixth data that is 64.
c) the mode is the value that is most repeated, therefore as none is repeated there is no mode.
d) the midrange is the average between the minimum value and the maximum value:
mr = (15 + 99) / 2
mr = 57
e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless
3u - 3 = 15
give me a lecture so i can try to do it in the future please
Answer:
u=6
Step-by-step explanation:
One rule in algebra is what you do to one side, you do it to other side. So if you multiply a number in one side, multiply the same number in other side. Here in this question, you are trying to find the value of the variable u. Variable is called so because the value of it varies depending on different question. Here u is going to be a constant number which when multipled by 3 and then subtracted by 3 equals 15.
So first step is we try to get constants on one side. So we add 3 on both sides to get rid of 3 on left.
3u - 3 + 3= 15+3
3u= 18
Now we divide by 3 on both sides to get u by itself.
3u/3 = 18/3
u= 6
It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking. Among mildly obese people, minutes of activity varied according to the N(373, 61) distribution. Minutes of activity for lean people had the N(525, 104) distribution. Within what limits do the active minutes for 95% of the people in each group fall
Answer:
Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.
Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Within what limits do the active minutes for 95% of the people in each group fall
By the Empirical Rule, within 2 standard deviations of the mean.
Mildly obese:
Mean = 373, standard deviation = 61.
373 - 2*61 = 251 minutes
373 + 2*61 = 495 minutes
Among mildly obese people, 95% of the people have between 251 and 495 minutes of activity per day.
Lean people:
Mean = 525, standard deviation = 104
525 - 2*104 = 317 minutes
525 + 2*104 = 733 minutes
Among lean people, 95% of the people have between 317 and 733 minutes of activity per day.
2y + 5x – z = 4y + 6x solve for y
(show work)
Answer:
y = -z/2 - x/2
Step-by-step explanation:
2y + 5x – z = 4y + 6x
-5x. -5x
2y - z = 4y + x
+z. +z
2y = 4y + z + x
-4y -4y
-2y = z + x
÷-2. ÷-2
y = -z/2 - x/2
An ethologist is interested in how long it takes a certain species of water shrew to catch its prey. He only has access to a sample of 100 shrews. On multiple occasions each day he lets a dragonfly loose inside the cage of the shrews and times how long it takes until the shrews catch the dragonfly. After months of research the ethologist concludes 1) that the mean prey catching time was 30 seconds, 2) the standard deviation was 5.5 seconds and 3) that the scores he has collected are normally distributed. What is the percentage of shrews that: a) catch a dragonfly in less than 18 seconds; b) catch a dragonfly in between 22 and 45 seconds; c) take longer than 45 seconds to catch a dragonfly? d) take less than 30 seconds to catch its prey;
Answer:
a) 1.46%.
b) 92.33%.
c) 0.32%.
d) 50%
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 5.5[/tex]
a) catch a dragonfly in less than 18 seconds;
This is the pvalue of Z when X = 18. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 30}{5.5}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146
So the percentage of shrews is 1.46%.
b) catch a dragonfly in between 22 and 45 seconds;
This is the pvalue of Z when X = 45 subtracted by the pvalue of Z when X = 22.
X = 45
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 30}{5.5}[/tex]
[tex]Z = 2.73[/tex]
[tex]Z = 2.73[/tex] has a pvalue of 0.9968
X = 22
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 30}{5.5}[/tex]
[tex]Z = -1.45[/tex]
[tex]Z = -1.45[/tex] has a pvalue of 0.0735
0.9968 - 0.0735 = 0.9233
So the answer is 92.33%.
c) take longer than 45 seconds to catch a dragonfly?
From b), when X = 45, Z = 2.73 has a pvalue of 0.9968
1 - 0.9968 = 0.0032
So the answer for this item is 0.32%.
d) take less than 30 seconds to catch its prey;
This is the pvalue of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 30}{5.5}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
So the answer for d) is 50%.
5 inches is blank times big as 1 inch
Answer:
5 inches is 5 times as big as 1 inch
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Which statement is correct?
-Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
-Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
-Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
-Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
The correct answer is C. Mark’s method is correct because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Explanation:
To begin Mark should determine the rate of delivery (number of houses the carrier can deliver in 1 minute). This can be found by dividing the houses by the minutes (36 / 30 = 1.2 houses per minute). This means the 1.2 rate found by Mark is correct; also, in this case, it is important to clarify, the carrier will not deliver to 1.2 houses at the same time, but this is the delivery rate or number used to understand the relationship between the number of houses, and the time.
Moreover, you can use this rate, and multiply it by 7.5 and this will show you how many houses the carrier can deliver in this time (7.5 (minutes) x 1.2 (delivery rate) = 9 houses). Thus, the method is correct, and in it, 1.2 represents the unit rate, this is why even when it is not possible to deliver to 1.2 houses all the process is correct.
Answer:
c
Step-by-step explanation:
i took the test