Answer:
[tex]P(\overline{W})=0.99281[/tex]
Step-by-step explanation:
W denotes the event of screening a driver and getting someone who is intoxicated.
Out of 695 drivers, the man observed that 5 were arrested for driving while intoxicated.
Therefore: [tex]P(W)=\dfrac{5}{695} \approx 0.00719[/tex]
The probability of the complement of event W, [tex]\overline{W}[/tex] denotes the probability of screening a driver and getting someone who is NOT intoxicated.
From probability theory, we know that the sum of the probability of an event and its complement is 1.
[tex]P(W)+P(\overline{W})=1\\P(\overline{W})=1-P(W)\\=1-0.00719\\\\P(\overline{W})=0.99281[/tex]
Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFraction 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction
Answer:
[tex]\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}[/tex]
Step-by-step explanation:
[tex]\log{9}+\dfrac{1}{2}\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\dfrac{9x^{\frac{1}{2}}(x^3+4)}{6}\right)}\\\\=\boxed{\log{\dfrac{3\sqrt{x}(x^3+4)}{2}}}\qquad\text{matches choice A}[/tex]
__
The applicable rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
Answer:
A
Step-by-step explanation:
Just did it on edge2020
Which means "a number n increased by 6.2"?
Answer:
n + 6.2
Step-by-step explanation:
Increased here means addition, addition of 6.2 with the number n.
Suppose you want to have $0.5 million saved by the time you reach the age of 30 years and suppose that you are 20 years old now. If you can earn 5% on your funds, how much would you have to invest today to reach your goal?
Answer:
$306,956,6268
Step-by-step explanation:
Future value, FV = Present value PV [1 + rate]^t
PV = FV/[1 + rate]^t
PV = 500,000/[1.05]^10
PV = $306,956,6268
Add 2/7 + 2/7 Is 4/7 the correct answer
Answer:
Yes
Step-by-step explanation:
The denominator always stays the same
Good Job!
Hope this helps :)
Answer:
yes 4/7 is the answer
Step-by-step explanation:
2/7+2/7
l.c.m is 7
2+2/7
4/7
Please answer this correctly
Answer:
50%
OR
1/2
Step-by-step explanation:
The box and whisker plot shows the time spent from 4 to 6 hours is Quartile 1 to 3 which makes it 50%.
Need help ASAP Thankyou!!!
Answer:
216
Step-by-step explanation:
To find the volume of the pyramid we have to do length * width * height / 3
The length is 9yd
The width is 8yd
The height is 9yd
So 9 * 9 * 8 = 648
648 / 3 = 216
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Give the exact answer in simplest form.
Answer:
2π miles
Step-by-step explanation:
2πr is the formula for the circumference of a circle.
Using that formula, the circumference for this circle is 8π.
Since the circle's full angle is 360°, we can use a ratio to find out how long the 45° arc is.
° : length
360 : 8π
9 : 0.4π
45 : 2π
The 45° is 2π mi long.
If a coin is tossed 3 times, and then a standard six-sided die is rolled 4 times, and finally a group of four cards are drawn from a standard deck of 52 cards without replacement, how many different outcomes are possible?
Answer:
67,365,043,200
Step-by-step explanation:
A coin toss has 2 possible outcomes. A coin tossed 3 times has 2³ = 8 possible permutations.
A standard die has 6 possible outcomes. A die rolled 4 times has 6⁴ = 1296 possible permutations.
The number of ways 4 cards can be chosen from a deck of 52 without replacements is 52×51×50×49 = 6,497,400.
The total number of possible outcomes is:
8 × 1296 × 6,497,400 = 67,365,043,200
Which division sentence is related to the product of a/3 (a/3) when A is not equal to 0?
Answer:
Option 4.
Step-by-step explanation:
Reciprocal of the second fraction turns the product into the division of the two fractions, which equals to 1.
[tex]a/3(a/3)[/tex]
[tex]a/3 \div 3/a=1[/tex]
Two fractions are said to be the reciprocal or multiplicative inverse of each other, if their product is 1.
Answer:
D. a/3 divided by 3/a = 1
Step-by-step explanation:
edge
The function f(x) is given by the set of ordered pairs.
{(8,3), (0, 4), (1, 5), (2, -1), (-6, 10)}
Which is true regarding the function?
f(-3) = 8
f(3) = 5
f(8) = 0
f(-6) = 10
Answer: f(-6) = 10.
Step-by-step explanation: This above equation is the only one that contains both coordinates of one of the ordered pairs in the correct order, so it is the answer.
what is the sum of the 3rd and 5th square numbers????
Answer:
40
Step-by-step explanation:
as 1st sq no is.4 and 2nd sq no. is 36
and their sum is =4+36
=40.....ans
The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representative visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Answer:
The number of ways is [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
Step-by-step explanation:
From the question we are told that
The number of factories visited is [tex]n = 9[/tex]
The number of factories to be visited by a representative r = 5
The number of way to visit the 5 factories is mathematically represented as
[tex]\left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}[/tex]
Where P represents permutation
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}[/tex]
=> [tex]\left 9}\atop } \right. P _5 = 15120[/tex]
The employee benefits manager of a large public university would like to estimate the proportion of full-time employees who prefer adopting the first (plan A) of three available health care plans in the next annual enrollment period. A random sample of the university’s employees and their tentative health care preferences are given in the file Healthcare.xlsx below. Calculate a 88% confidence interval for the proportion of all the university’s employees who favor plan A. What are the values of lower limit and upper limit? Round your answer to 3 decimal places. Healthcare.xlsxPreview the document Group of answer choices (0.217, 0.330) (0.211, 0.323) (0.242, 0.358) (0.180, 0.287)
Answer:
The 88% confidence interval for the population proportion of full-time employees who favor plan A is (0.208, 0.344).
Step-by-step explanation:
The question is incomplete: it lacks the sample data.
We will work with a sample size n=105 and a count of X=29 that prefer adopting the plan A.
We have to calculate a 88% confidence interval for the proportion.
The sample proportion is p=0.276.
[tex]p=X/n=29/105=0.276[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.276*0.724}{105}}\\\\\\ \sigma_p=\sqrt{0.001903}=0.0436[/tex]
The critical z-value for a 88% confidence interval is z=1.555.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.555 \cdot 0.0436=0.0678[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.276-0.0678=0.208\\\\UL=p+z \cdot \sigma_p = 0.276+0.0678=0.344[/tex]
The 88% confidence interval for the population proportion is (0.208, 0.344).
The 88% confidence interval is given by (0.208,0.344) and this can be determined by using the given data.
Given :
The employee benefits manager of a large public university would like to estimate the proportion of full-time employees who prefer adopting the first (plan A) of three available health care plans in the next annual enrollment period.A random sample of the university’s employees and their tentative health care preferences are given in the file Healthcare.First, determine the sample proportion p:
[tex]\rm p=\dfrac{X}{n}=\dfrac{29}{105}[/tex]
P = 0.276
Now, determine the standard error:
[tex]\rm \sigma_p=\sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]\rm \sigma_p=\sqrt{\dfrac{0.276(1-0.276)}{105}}[/tex]
[tex]\sigma_p=0.0436[/tex]
For 88% confidence level the value of z-value is 1.555.
Now, determine the margin of error.
[tex]\rm ME = z\times \sigma_p=1.555\times 0.0436[/tex]
ME = 0.0678
For the confidence interval, the upper and lower bounds are:
[tex]\rm LL = p-z\times \sigma_p=0.276-0.0678= 0.208[/tex]
[tex]\rm UL = p+z\times \sigma_p=0.276+0.0678= 0.344[/tex]
Therefore, the 88% confidence interval is given by (0.208,0.344).
For more information, refer to the link given below:
https://brainly.com/question/10951564
A list of numbers begins iwth the number 6. Each number on the list is 10 more than -2 times the previous terms. what is the fourth number
Answer:
The fourth term is -18
Step-by-step explanation:
an = -2(an-1) +10
This is the recursive formula
a1 = 6
a2 = -2(a1) +10 = -2(6) +10 = -12+10 = -2
a3 = -2(a2) +10 = -2(-2) +10 = 4+10 = 14
a4 = -2(a3) +10 = -2(14) +10 = -28+10 = -18
problem decoded dude
follow meh
Please answer this correctly
Answer:
60%
Step-by-step explanation:
In the spinner there are 5 numbers. 3 of them are odd and 2 of them are even and because each number has 1/5 chance of being chosen, you have a 3/5 chance of choosing an odd number. 3/5 = 60/100 = 60%
Please answer this correctly
Answer:
Step-by-step explanation:
The 50 people might be random, depending on when the question was done.
The 50 people might be random if there's roughly the same number of men as women, but to accomplish this, Isabella would have to pick a time when men would be out shopping.
The 16 are certainly not random, and the question itself is kind of biased. I would say the answer should be no.
"In a tri-state conference, 60% attendees are from California, 25% from Oregon, and 15% from Washington. As it turns out 6 % of the attendees from California, 17% of the attendees from Oregon, and 12% of the attendees from Washington came to the conference by train. If an attendee is selected at random and found to have arrived by train, what is the probability that the person is from Washington?"
Answer:
18.65% probability that the person is from Washington
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Arrived by train.
Event B: From Washington.
15% are from Washington
This means that [tex]P(B) = 0.15[/tex]
12% of the attendees from Washington came to the conference by train.
This means that [tex]P(A|B) = 0.12[/tex]
Probability of arriving by train:
6% of 60%(from California), 17% of 25%(from Oregon) or 12% of 15%(from Washington). So
[tex]P(A) = 0.06*0.6 + 0.17*0.25 + 0.12*0.15 = 0.0965[/tex]
If an attendee is selected at random and found to have arrived by train, what is the probability that the person is from Washington?"
[tex]P(B|A) = \frac{0.15*0.12}{0.0965} = 0.1865[/tex]
18.65% probability that the person is from Washington
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
Let f(x)= x^3 −6x^2+11x−5 and g(x)=4x^3−8x^2−x+12. Find (f−g)(x). Then evaluate the difference when x=−3 x=−3 .
Answer: (f-g)(x)= -138
Step-by-step explanation:
A company borrows $60,000 by signing a $60,000 8% 6 year note that requires equal payments of $12979 at the end of each year. The first payment will record interest expense of $4800 and will reduce principal by
Answer: $8179
Step-by-step explanation:
The principal is the amount of money that is invested at a particular interest rate.
In this scenario, we are informed that a company borrows $60,000 by signing a $60,000 8% 6 year note that requires equal payments of $12979 at the end of each year.
Since the first payment will record interest expense of $4800, then for us to get the amount that the principal will be reduced by, we subtract the interest expense made from the equal payments that are made at each year end. This will be:
= $12979 - $4800
= $8179
Suppose that 13% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked. (Round your answers to four decimal places.) a. What is the (approximate) probability that X is at most 30? b. What is the (approximate) probability that X is less than 30? c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?
Answer:
a)0.8280
b)0.7691
c)0.4503
Step by step Explanation:
It was Given that 13% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).Each shaft is independent of the other and probability for non conforming is the same for each trial.
If X the denote the number among these that are nonconforming and can be reworked. Then
n =200 and
p = 0.13
Then, CHECK THE ATTACHMENT FOR DETAILED EXPLATION
What is the common difference between successive terms in the sequence?
0.36, 0.26, 0.16, 0.06, –0.04, –0.14, ...
–0.1
–0.01
0.01
0.1
Answer:
0.1
Step-by-step explanation:
0.36-0.26=0.1
hope u understand
Answer:
A
Step-by-step explanation:
multiply and remove all perfect square roots. Assume y is positive. √12
Answer:
2√3
Step-by-step explanation:
Step 1: Find perfect square roots
√4 x √3
Step 2: Convert
2 x √3
Step 3: Answer
2√3
what is the recursiveformula for this geometric sequence? 4,-12,36,108
Answer:
a[1] = 4
a[n] = -3·a[n-1]
Step-by-step explanation:
The sequence given is not a geometric sequence, since the ratios of terms are -3, -3, 3 -- not a constant.
If we assume that the last given term is supposed to be -108, then the common ratio is -3 and each term is -3 times the previous one. That is expressed in a recursive formula as ...
a[1] = 4 . . . . . . . . . . . first term is 4
a[n] = -3·a[n-1] . . . . . each successive term is -3 times the previous one
Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees, if $\angle AIB = 109^\circ$.
Answer:
<C = [tex]38^{o}[/tex]
Step-by-step explanation:
Given that: <AIB = [tex]109^{o}[/tex]
<AIB + <BIX = [tex]180^{o}[/tex] (sum of angles on a straight line)
[tex]109^{o}[/tex] + <BIX = [tex]180^{o}[/tex]
<BIX = [tex]180^{o}[/tex] - [tex]109^{o}[/tex]
<BIX = [tex]71^{o}[/tex]
But,
<AIB = <YIX = [tex]109^{o}[/tex] (opposite angle property)
<XIB = <AIY = [tex]71^{o}[/tex] (opposite angle property)
Therefore,
[tex]\frac{A}{2}[/tex] + [tex]\frac{B}{2}[/tex] = [tex]71^{o}[/tex] (Exterior angle property)
[tex]\frac{A + B}{2}[/tex] = [tex]71^{o}[/tex]
A + B = [tex]142^{o}[/tex]
A + B + C = [tex]180^{o}[/tex] (sum of angles in a triangle)
[tex]142^{o}[/tex] + C = [tex]180^{o}[/tex]
C = [tex]180^{o}[/tex] - [tex]142^{o}[/tex]
C = [tex]38^{o}[/tex]
Thus, angle C is [tex]38^{o}[/tex].
The purchasing manager for a chain of grocery stores is interested in customer's preference for non-alcoholic beverages. She wondered if there was a relationship between the customer's beverage preference and the customer's income class. She randomly sampled 500 customers and asked their non-alcoholic beverage preference (soft drinks, energy drinks, fruit juices, vitamin water, or other) and what their income class is (lower class, lower middle class, middle class, upper middle class, upper class). Assuming all conditions are satisfied, which of the following tests should the manager use to test her hypothesis?
A. The chi-square test of homogeneity.
B. The goodness-of-fit chi-square test.
C. The chi-square test of independence.
D. The two-sample z-test for proportions.
Answer:
Option C
Step-by-step explanation:
The chi-square test of independence is used to determined whether there is a relationship between two categorical variable which in this study is to establish if there is a relationship between a customer's beverage preference and his/her income class (these are categorical variables).
The null hypothesis would be that no relationship exists between the variables while the alternative would be that there is a relationship between the two variables.
Estimate 68.41 - 57.570 by first rounding each number to the nearest whole number.
Answer:
≈ 10
Step-by-step explanation:
Step 1: Round 68.41
68
Step 2: Round 57.570
58
Step 3: Subtract
68 - 58 = 10
Answer:
10
Step-by-step explanation:
68.41 - 57.570
Round the terms to the nearest whole number.
68 - 58
Subtract the two terms.
= 10
Find the original price of a pair of shoes if the sale price is $144 after a 25% discount.
Answer:
$192
Step-by-step explanation:
1: Subtract the discount from 100% then divide the sale price by this number (100%-25%=75%, $144/75%=$192)
hope this helped
Answer:
$192
Step-by-step explanation:
144 is actually 75% from the original price x:
0.75 x=144
x=144/0.75= $192
check : 192*0.25= $ 48 discount
192-48= $ 144 price of the shoe
A rectangle is 4.2 centimetres wide and each diagonal is 8.6 centimetres long. What is the measure of the angle between a diagonal and the shorter side of the rectangle, to the nearest tenth of a degree?
Answer:
[tex] 60.8^\circ [/tex]
Step-by-step explanation:
First, let's check side lengths.
Using the Pythagorean theorem we can find the length of the other side of the rectangle.
a^2 + b^2 = c^2
4.2^2 + b^2 = 8.6^2
b^2 = 56.32
b = 7.5
The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.
For the angle in question, the 4.2 cm side is the adjacent leg.
The diagonal of 8.6 cm is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos \alpha = \dfrac{adj}{hyp} [/tex]
[tex] \cos \alpha = \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = \cos^{-1} \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = 60.8^\circ [/tex]
how to solve this? please help me
Answer:
tangent: y = 2x -2normal: y = -1/2x +3Step-by-step explanation:
Differentiating implicitly, you have ...
-y²·dx +(4-x)(2y)dy = 3x²·dx
So, the slope is ...
dy/dx = (3x² +y²)/(2y(4 -x))
At (x, y) = (2, 2), the slope of the curve is ...
dy/dx = (3·2² +2²)/(2·2(4 -2)) = 16/8 = 2
In point-slope form, the equation of the tangent line is then ...
y = m(x -h) +k
y = 2(x -2) +2
y = 2x -2 . . . . equation of tangent line
__
The normal to the curve is perpendicular to the tangent at the same point. The slope of the perpendicular line is the negative reciprocal of the tangent's slope, so is -1/2.
y = (-1/2)(x -2) +2
y = -1/2x +3 . . . equation of normal line