Answer:
The probability that neither test is positive
P(A⁻ ∩ B⁻ ) = 0.0108
Step-by-step explanation:
Step(i) :-
Given the two tests are independently
Test A has probability 0.91 of being positive if the illegal drug has been used
P(A) = 0.91
Test B has probability 0.88 of being positive if the illegal drug has been used
P(B) = 0.88
If events are independently then ,
[tex]P(A n B) = P(A) P(B)[/tex]
Step(ii):-
The probability that neither test is positive (and thus Al gets to keep his job)
[tex]P(A^{-} n B^{-} ) = P(A^{-} ) P(B^{-} )[/tex]
P(A⁻ ∩ B⁻ ) = P(A⁻ ) P(B⁻ )
= ( 1- P(A) ) ( 1 - P(B))
= (1 - 0.91 ) ( 1 - 0.88 )
= (0.09) (0.12)
= 0.0108
The probability that neither test is positive
P(A⁻ ∩ B⁻ ) = 0.0108
Which two consecutive whole numbers is each square root 57 between?
Answer:
Between 7 and 8
Step-by-step explanation:
7^2 = 7 × 7 = 49
8^2 = 8 × 8 = 91
57 is between 49 and 91
hgfdertyhujnbvfdfghnbvcdxfg
Answer:
gehsjskkskskkskdhdhjs
Classify is the function as increasing decreasing or constant l
f(x) = 5x
Anyone know the answer .?
Answer:
Increasing
Step-by-step explanation:
Remember that f(x) is the same as y in slope intercept form y = mx + b.
We don’t have a number for “b” which means the line goes across the origin.
Since 5 replaces m, that is the slope and since it’s positive, it is increasing.
Best of Luck!
Consider the diagram below. Name the angle 3 ways. Select all that apply.
ABC
A
BAC
CBA
CAB
C
B
Answer: A, BAC, CAB
Step-by-step explanation: A already says it’s an angle . BAC & CAB are congruent meaning they are equal . Hope this helped !
Which of the following expressions shows how to rewrite 4 - 5 using the addtive inverse and displays the expression correctly on a number line
Answer: 4 - 5 = 4 + (-5) = -1
Step-by-step explanation: You have to make the 5 into a negative number using parenthesis and do the math.
Answer:
4+(-5)
Step-by-step explanation:
Here is the number line
e. What number, when reduced by 20%, becomes 500?
f. What amount increased by 100% will equal $310
g. After deducting 20% from a sum of money, the remainder is $500. What was the
original amount?
Also what is 1.40 to percent and fraction
Pls help fast
Answer:
E: 625
F: 155
G: 625
Step-by-step explanation:
Hi!
E.
A number, reduced by 20% is 500.
Originally, that number was at 100%.
Reduced = subtraction, so that number = 100%-20%, or 80%.
80% of a number = 500.
80% = .8
.8x = 500
Divide both sides by .8
x = 625
F.
A number that is increased by 100% is a number that is doubled (multiplied by 2).
2x=310
x=155
G.
Originally, the money was at 100%. After being reduced by 20%, the money is at 80% (.8).
.8x = 500
Once again, the answer is 625.
H (?)
To change a decimal to a percent, we multiply by a 100.
1.40 * 100 = 140%
As a fraction: 140/100
Find the product: -4/9 and -3/8
A. -1/9
B. -1/6
C. 1/6
D. 7/17
Answer:
C. 1/6
Step-by-step explanation:
negative times a negative is a positive
4 times 3 is 12
9 x 8 is 72
12/72 can be reduced to 1/6 because the top and bottom are both divisible by 12
Answer: 1/6 C
Step-by-step explanation:
49 × 11 = ________ elevens
Answer:
I believe the awnser is 539 total.
Step-by-step explanation:
If you take the 4 and times it by 1 you get 4.
Same with the nine.
But if you times 49 by 11 you get 539.
Hope this helps!
which Best describes the rule for this pattern 1, -12, 12, -1, . . .
what is the square root of 1/9?
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{\frac{1}{9} } = \sqrt{\frac{1}{3} } {^{2} } \\\\=\frac{1}{3}[/tex]
The square root of the fraction 1/9, would be ± 1/3.
What is a perfect square number?A perfect square number when taken the square root of it results in an integer.
Numbers that are not perfect squares when taken the square root of it are irrational numbers.
One method of obtaining square roots for perfect squares is prime factorization.
A fraction 1/9 is given,
Now, The square root of this fraction would be √(1/9).
= √1/√9.
= 1/√9.
= 1/3, But it can be both ± 1/3 as both results to 1/9.
learn more about square roots here :
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A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular
container costs the company $16, while the cylindrical container costs the company $15. If the company needs to
package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs? Explain.
How many rectangular containers will be necessary to package 6,400 candles?
How many cylindrical containers will be necessary to package 6,400 candles?
Which container should the company use to minimize costs? Explain.
Answer:
a) no
b) 143 rectangular containers
c) 157 cylindrical containers
d) both (preferring rectangular for the bulk of an order)
Step-by-step explanation:
a) If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs?
No.*
For packaging 41 candles or fewer, the cylindrical container costs less than the rectangular one.
For packaging 6400 candles, there will be 10 candles left over if rectangular containers are used for most of the packaging needs. A dollar can be saved by packaging these remaining candles in a cylindrical container.
__
b) How many rectangular containers will be necessary to package 6,400 candles?
6400/45 = 142 10/45
If rectangular containers are used for all, then 143 are needed.
__
c) How many cylindrical containers will be necessary to package 6,400 candles?
6400/41 = 156 4/41
If cylindrical containers are used for all, the 157 are needed.
__
d) Which container should the company use to minimize costs?
The cost of 143 rectangular containers is 143×$16 = $2288
The cost of 157 cylindrical containers is 157×$15 = $2355
The cost of 142 rectangular and 1 cylindrical container is $2287
If only one shape container is used, the company should use rectangular containers to minimize cost. If either shape can be used, cost will be minimized by using one cylindrical container for the remnant of the order.
_____
* This question is directed solely at the cost of materials required for packaging. We have advocated that both rectangular and cylindrical containers be made available. As a practical matter, the cost to the company of maintaining inventory of both sizes of containers may exceed the savings associated with using a cheaper container for smaller orders.
si se reparten 7 tazas de pure entre8 bebes a cada bebe le tocan
Respuesta: [tex]\frac{7}{8}[/tex] de taza o 0.875 tazas
Explicación:
Repartir un número total de objetos entre personas implica dividir el total entre el número de personas. Es decir que en este caso las 7 tazas deben dividirse entre los 8 bebes. Esta división o partición puede representarse por medio de una fracción o por medio de una división:
Fracción: Esta situación puede ser representada como una fracción si se incluye el número total de bebés o partes a repartir como denominador (número de abajo) y el número de tazas o cantidad total como numerador.
[tex]\frac{7}{8}[/tex] de taza
División: Divida el total en la cantidad de partes a repartir
7 tazas ÷ 8 bebes = 0.875 tazas por bebé
Louis is 6 times mary's age. If the difference in their ages is 20 how old is louis
Answer:
louis age is 26
Step by step explanation:
their difference = 20
and Louis is 6 times
then 20 + 6 = 26
Louis is [tex]6[/tex] times Mary's age. If the difference in their ages is 20 then Louis is [tex]24[/tex] years old.
What is age?Age is defined as the length of time that somebody has lived or that something has existed.
Let,
Mary's age [tex]=x[/tex] years
So, Louis' age [tex]= 6x[/tex] years
According to question,
[tex]6x-x=20[/tex]
[tex]5x=20[/tex]
[tex]x=4[/tex]
So, Louis' age [tex]= 24[/tex] years
Hence, we can say that Louis is [tex]24[/tex] years old.
To learn more about ages click here
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Row a has 8 seats. Each row behind row a had 4 more seats
Answer:
u have to finish the question ...
Parker is planning for a school picnic. He would like to have 2 hot dogs per person and 15 extra on hand. How many hot dogs does he need if there are 116 students and 8 teachers? O 131 139 248 263
Answer: The answer is 263
Step-by-step explanation: 116 + 8 = 124 * 2 = 258 + 15 = 263
Answer: 116 + 8 = 124 * 2 = 258 + 15 = 263
what is 20 x 10 to the power of 5
Answer:
2000
Step-by-step explanation:
so if I'm multiplying right. Would it be -2*2 or -2*-2
Here, we have the expression [tex]\frac{x^2 + 4}{2}[/tex] and we're asked
to evaluate the expression when x = -2.
To evaluate an expression, we simply plug
the value of the variable into the expression and solve.
So here, since x = -2, we have [tex]\frac{(-2)^2 + 4}{2}[/tex].
Notice that I used parentheses around the -2.
This is a good idea when substituting numbers in for variables.
Next, the order of operations tell us that exponent comes first.
So we have (-2)² which is 4.
So we have [tex]\frac{4 + 4}{2}[/tex].
Now when we have a division bar, it's important to understand
that it has the same effect on a problem as a set of parentheses
in that it groups terms together.
So this 4 + 4 can be thought of as being inside a set of parentheses.
So we can also write this as [tex]\frac{(4 + 4)}{2}[/tex].
Now simplify the top to get 8 and we have 8/2 which is 4.
that’s what i need help with
Answer:
W=-3 because negative divided by a negative equals a positive
Step-by-step explanation:
Hope this helps!!!
30 POINTS!! PLS SHOW WORK!!
Answer:
[tex]\sin(\theta)=4/5[/tex]
Step-by-step explanation:
Refer to the graph.
From the graph, we can see that our angle is in QII.
In QII, sine is positive and cosine and tangent are negative.
Since our point is at (-3, 4), this means that our adjacent side to our angle is -3 while our opposite side to our angle is 4.
To find sine, we need to find the hypotenuse c.
So, we can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute -3 for a and 4 for b. This yields:
[tex](-3)^2+(4)^2=c^2[/tex]
Square:
[tex]9+16=c^2[/tex]
Add:
[tex]25=c^2[/tex]
Take the square root of both sides:
[tex]c=5[/tex]
So, our hypotenuse is 5.
And our adjacent is -3 and opposite is 4.
Now, remember that:
[tex]\sin(\theta)=\text{opp}/\text{hyp}[/tex]
Substitute 4 for the opposite and 5 for our hypotenuse. This gives us:
[tex]\sin(\theta)=4/5[/tex]
Since sine is positive in QII, we don't need to add any negatives.
And we're done!
Given the function f(a) = 5a + 14, solve for f(a) = 0.
Give an exact answer; do not round.
Answer:
a = 14
Step-by-step explanation:
Step 1: Write out your problem
f (a) = 5a + 14 | f (a) = 0
Step 2: Solve
f (a) = 5 (0) + 14 , Input a.
f (a) = 0 + 14 , 5 x 0 = 0
(a) = 14 , 0 + 14
a = 14
Given:
PQ
⊥
QR
, PR = 20,
SR = 11, QS = 5
Find: The value of PS. EXTRA POINTS
Answer:
[tex]PS=13\text{ units}[/tex]
Step-by-step explanation:
So, we know that PR is 20, SR is 11, and QS is 5.
We also know that PQ is perpendicular to QR, forming the right angle at ∠Q.
We know all the side lengths except for PQ and PS (the one we want to find). Notice that if we find PQ first, we can then use the Pythagorean Theorem to find PS since we already know QS.
So, let's find PQ.
We can see that we can also use the Pythagorean Theorem on PQ. PQ, QR, and PR (the hypotenuse) will be our sides. So:
[tex](PQ)^2+(QR)^2=(PR)^2[/tex]
We know that PR is 20.
QR is the combined length of QS+SR, so QR is 5+11 or 16.
So, substitute:
[tex](PQ)^2+(16)^2=(20)^2[/tex]
Solve for PQ. Square:
[tex](PQ)^2+256=400[/tex]
Subtract 256 from both sides:
[tex](PQ)^2=144[/tex]
Take the square root of both sides:
[tex]PQ=12[/tex]
So, the side length of PQ is 12.
Now, we can use the Pythagorean Theorem again to find PS. Notice that PQ, QS, and PS also form a right triangle, with PS being the hypotenuse. So:
[tex](PQ)^2+(QS)^2=(PS)^2[/tex]
We already know that QS is 5. We also just determined that PQ is 12. Substitute:
[tex](12)^2+(5)^2=(PS)^2[/tex]
Square:
[tex]144+25=(PS)^2[/tex]
Add:
[tex]169=(PS)^2[/tex]
Take the square root of both sides:
[tex]PS=13[/tex]
Therefore, the length of PS is 13 units.
And we're done!
The answer to this is PS=13.
Denise and Donna want to exchange secrets from across a crowded whispering gallery. Recall that a whispering gallery is a room which, in cross section, is half of an ellipse. If the room is 30 feet high at the center and 90 feet wide at the floor, how far from the outer wall should each of them stand so that they will be positioned at the foci of the ellipse? Fill in the blank: Denise and Donna should each stand _____ ft from the outer wall so that they will be positioned at the foci of the ellipse. Round your answer to the nearest whole ft (no decimal places).
Answer:
34 feet
Step-by-step explanation:
From the question, we are told that:
If the room is 30 feet high at the center and 90 feet wide at the floor,
Entire width of the room = 90 feet = 2a
a = 90/2 = 45
Height of the room = b = 30 feet
Foci (c)² = a² - b²
c = √a² - b²
c = √45² - 30²
c = √1125
c = 33.541019662 feet
Approximately to the nearest whole number = 34 feet
Denise and Donna should each stand 34 ft from the outer wall so that they will be positioned at the foci of the ellipse
2(s+2)=4(s+2)
Need Steps!
Answer:
s = -2
Step-by-step explanation:
2(s+2)=4(s+2)
2s + 4 = 4s + 8
2s - 4s = 8 - 4
-2s + 4
s = -2
18x5 – 12x4 + 20x3 + 48x2
9x2
write 3 + 2 x 1/10 +4 x 1/1000 in standard form
The standard form of [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex] is 3.204
Explanation :
Given : [tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}[/tex]
Lets convert fractions into decimals
[tex]\frac{1}{10} =0.1\\\frac{1}{1000}=0.001[/tex]
Now 2 times 0.1 becomes 0.2
Also 4 times 0.001 becomes 0.004
So the given expression becomes
[tex]3+2 \cdot \frac{1}{10} +4 \cdot \frac{1}{1000}\\3+2 \cdot 0.1+4 \cdot 0.001\\3+0.2+0.004\\3.204[/tex]
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4/5 divided by 1/10?
Answer:
the answer to the question is 8
Consider the figure below were line PQ is parallel to line RS
Part A: Solve for a and justify your answer
Part B: Determine m<ABQ
Part C: Determine m<BCR
Plzzz HELP
Answer:
Step-by-step explanation:
A) Find the figure attached. According to the figure, since line PQ is parallel to line RS, then <CBQ = <DCS (corresponding angle)
Also <BCS + <DCS = 180° (sum of angles on a straight line)
Given
<BCS = (5a+14)° and <DCS = <CBQ =(2a-9)°
Substituting this values into the formula to calculate the value of a;
(5a+14)°+(2a-9)° = 180°
5a+2a+14-9 = 180
7a+5 = 180
7a = 180-5
7a = 175
a = 175/7
a = 25°
Hence the value of a is 25°
B) From the diagram <ABQ = <BCS = 5a+14 (corresponding angle)
Substitute a = 25 into the expression
<ABQ = 5(25)+14
<ABQ = 125+14
<ABQ = 139°
C) To get <BCR, we will use the formula;
<BCR + <BCS = 180
Given <ABQ = <BCS = 139°
<BCR = 180 - <BCS
<BCR = 180 - 139
<BCR = 41°
Answer:
Part A: 25
Part B: 139
Part C: 41
Step-by-step explanation:
5a+14+2a-9
a=25
5(25)+14
=139
2(25)-9
=41
Started at −20° and rose 1° each minute
Answer:
-20+1 every minute
Step-by-step explanation:
Suppose that in a sample of 50 college students in Illinois, the mean credit card debt was $346. Suppose that we also have reason to believe (from previous studies) that the population standard deviation of credit card debts for this group is $108. Use this information to calculate a 95% confidence interval for the mean credit card debt of all college students in Illinois.
Answer:
A 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .
Step-by-step explanation:
We are given that in a sample of 50 college students in Illinois, the mean credit card debt was $346. Suppose that we also have reason to believe that the population standard deviation of credit card debts for this group is $108.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean credit card debt = $346
[tex]\sigma[/tex] = population standard deviation = $108
n = sample of college students = 50
[tex]\mu[/tex] = population mean credit card debt
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, a 95% confidence interval for the population mean, [tex]\mu[/tex] is;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96} P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}} }[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]\$346-1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] , [tex]\$346+1.96 \times {\frac{\$108}{\sqrt{50} } }[/tex] ]
= [$316.06, $375.94]
Therefore, a 95% confidence interval for the mean credit card debt of all college students in Illinois is [$316.06, $375.94] .
convert 325 milliliters to liters
Answer:
1000 milliliters in a liter, so 325 mL = 0.325 L
Step-by-step explanation:
