Answer:
130.81
Step-by-step explanation:
Given that :
Mean, μ = 100
Standard deviation, σ = 15
To obtain the upper 2% of scores :
We find the Zscore (value) of the upper 2% from the normal probability distribution table ;
Zscore corresponding to the area in the left of (1 - 0.02) = 2.054
Using this with the Zscore formula :
Zscore = (x - μ) / σ
2.054 = (x - 100) / 15
2.054 * 15 = x - 100
30.81 = x - 100
30.81 + 100 = x
x = 130.81
wo large tanks A and B are each partially filled with 100 gallons of salt water. Initially,80 pounds of salt is dissolved in the solution in tank A, and 30pounds of salt is dissolvedin the solution in tank B. The system is closed so that the wellstirred saline solution ispumped only between tanks A and B. The saline solution in tankA travels to tank Balong a pipe at the rate of 3 gallons per minute, and the salinesolution in B travels totank A at the rate of 2 gallons per minute. Write a system of IVPs that will describe theamount of salt,x1, in tank A at timetand the amount of salt,x2in tank B at timet.
At the start, it's given that x₁ (0) = 80 lb and x₂ (0) = 30 lb.
The amounts of salt in either tank change according to
dx₁/dt = (2 gal/min) (x₂/(100 - t ) lb/gal) - (3 gal/min) (x₁/(100 + t ) lb/gal)
dx₂/dt = (3 gal/min) (x₁/(100 + t ) lb/gal) - (2 gal/min) (x₂/(100 - t ) lb/gal)
To break this down a bit, consider tank A, for instance:
• solution flows in from B at a rate of 2 gal/min
• the volume of liquid in tank B after t minutes is
100 gal + (2 gal/min - 3 gal/min) (t min) = (100 - t ) gal
because the tank starts with 100 gallons of liquid, and 2 gallons are pumped in while 3 gal are pumped out each minute
• at any time t, the solution in B contains x₂ pounds of salt
• the concentration of the solution in A is then x₂/(100 - t ) lb/gal
• multiplying this by the inflow rate tells you how much salt is moving around each minute
Ten people are sitting in a row, and each is thinking of a negative integer no smaller than $-15$. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let $x$ be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of $x$
Correct question is;
Ten people are sitting in a row, and each is thinking of a negative integer no smaller than −15. Each person subtracts, from his own number, the number of the person sitting to his right (the rightmost person does nothing). Because he has nothing else to do, the rightmost person observes that all the differences were positive. Let x be the greatest integer owned by one of the 10 people at the beginning. What is the minimum possible value of x?
Answer:
Minimum possible value of x = -6
Step-by-step explanation:
Since there are 10 people and the rightmost person observes that all the differences from the subtraction or positive.
What this implies is that the person on the far left side of the row will have the largest number which from the quewis denoted as x.
Thus, we can say that the person sitting to the far right end on the row will have the smallest integer.
Since we want to minimize x, and for the fact that we are told that each is thinking of a negative integer no smaller than −15, then we will have to make the rightmost person have an integer of -15.
Since there are 9 people remaining on the row, thus, we add 9 to -15 to get the integer of the person for the leftmost person which will be the minimum he will have.
Thus;
-15 + 9 = -6
If the bearing of Saaman from Ankaase is 171. What is the bearing of Ankaase from Saaman.
Step-by-step explanation:
A. Theta + 180 (when angle is less than 180)
Theta - 180(when angle is greater than 180)
Thus, 171 + 180 = 351°
B. I. Angle CBF + Angle BFG = 180 (Co interior angles)
CBF + 118 = 180
CBF + 118 –118 = 180 –118
CBF = 62°
Ii. 83 + X + CBF = 180 (Angles on a straight line)
83+X+62 =180
145+x=180
145–145+x=180–145
X = 35°
Wendy went to the salon and had 2 1/6 inches of hair cut off. The next day she went back
and asked for another 2 1/6 inches to be cut off. How much hair did she have cut off in all?
Write your answer as a fraction or as a whole or mixed number.
inches.
Answer:
4 1/3 of her hair
Step-by-step explanation:
Just add 2 1/6 + 2 1/6 and there you go
There is the total amount of her hair she cut
Where is the blue dot on the number line ?
Answer:
-1.13
Step-by-step explanation:
the gape between two points is 0.01 so the required answer is -1.13
Describe how you can simplify division question such as 3,200 divided into 80
Answer:
40
Step-by-step explanation:
here
3200/80
1600/40
800/20
400/10
40
Name the property illustrated. 7 + 0 = 7
Answer:
I think it's the zero property
Step-by-step explanation:
Which of the following expressions does not have a greatest common monomial factor?
Answer:
Step-by-step explanation:
17x²y+8y³-4x²
it has no greatest common monomial factor.
Answer:
17x²y+8y³-4x²
Step-by-step explanation:
A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
Answer:
the number A(t) of grams of salt in the tank at a time is A(t)=150-110e-t/50
2a( 3a + b)- 3a(2a+4b)
Answer:
-10ab
STEP BY STEP EXPLANATION
2a (3a + b) -3a(2a +4b)
6a² + 2ab - 6a²- 12ab
2ab-12ab 6a²-6a²
-10ab
Hope this will help you if not then sorry :)
Answer:
[tex]2a( 3a + b)- 3a(2a+4b)[/tex]
Expand by distributing terms.
[tex]6a ^{2} +2ab-3a(2a+4b)[/tex]
Expand by distributing terms.
[tex]6a 2+2ab-(6a^{2} +12ab)[/tex]
Remove parentheses
.[tex]6a ^{2} +2ab-6a^{2} -12ab[/tex]
Collect like terms.
[tex](6a^{2}-6a^{2})+(2ab-12ab)[/tex]
[tex]=-10ab[/tex]
OAmalOHopeO
Johnny has 304 apples, his sister ate 301 of them. How many apples does he have? After His sister ate the apples a magic fairy multiplied the apples by 281893.21 times. Now how many apples does Johnny have. After the faity multiplied the apples a demon can and divided the apples by pi * the square root of 9284. Now how many apples does Johnny have?
Answer:
1. John still has 3 Apples
2. John now has 845679,63 Apples (I'm not sure if you've written the number of the multiplying fairy right...).
3. If the * is multiplying:
John now has 25937228,2 Apples.
Step-by-step explanation:
Just use the calculator.
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{4}{16}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{4}[/tex]
[tex]\\ \sf\longmapsto sin\theta=\dfrac{sin30}{2}[/tex]
[tex]\\ \sf\longmapsto sin\theta=sin15[/tex]
[tex]\\ \sf\longmapsto \theta=15°[/tex]
PLEASE HELP ME ASAP!!!! i dont understand
Answer:
i think it is d
Step-by-step explanation:
because 0^2 is 0 and -8^2is64
then,64+0=64 so i think that is what they mean by that hope it helps
[tex]\frac{1}{3-6y} + \frac{1}{y} = \frac{1}{6\\}[/tex]
Answer:
y = 11 + √ 73/ 4 , 11 − √ 73 /4
Step-by-step explanation:
Guys please help me solve this problem, yes I will mark brainliest
Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced
Question 3
Suppose that we have a 3 ft x 3 ft piece of paper, and we cut out a square piece so that the area of the remaining piece is 5 feet. What is the length of a side of the square?
Answer:
2ft
Step-by-step explanation:
If you have a 3x3 you have a 9ft Sq paper. To have five feet left the removed square must be 4 square feet. 2x2 = 4 therefore 2ft per side
Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically.
Answer:
Therefore, the value of x is 5.
Step-by-step explanation:
We can match each equation to find the solutions.
[tex]8x-40=x^{2}-2x-15[/tex]
[tex]0=x^{2}-2x-8x-15+40[/tex]
[tex]x^{2}-10x+25=0[/tex]
Now, we need solve this quadratic equation.
[tex](x-5)^{2}=0[/tex]
Therefore, the value of x is 5.
I hope it helps you!
Explain why cos(-3π/4)=cos(5π/4).
Answer:
Step-by-step explanation:
Because the cosine is a positive function from which we can deduce [tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{Rule : cos(-\alpha)=cos\alpha } \\\\\\ \cos\bigg(\frac{-3\pi }{4} \bigg)=cos135=-sin45=-\frac{\sqrt{2} }{2} \\\\\\cos\bigg(\frac{5\pi }{4} \bigg)=cos225=-sin45=-\frac{\sqrt{2} }{2}[/tex] Therefore, they are equal
Add.
(3x2 – 2x) + (4x-3)
O A. 7x2- 5x
O B. 12x3 - 14x2 + 6x
O C. 3x2 - 6x + 3
O D. 3x2 + 2x-3
Answer:
O D. 3x2 + 2x-3
Answer:
A.7x2-5x questions 2of 20
At a summer camp the campers can choose one of three programmes: camp craft, water sports or hiking. During the first week of camp the campers chose the programmes in the ratio 7:5:8. During the second week of camp the same number of campers chose the programmes in the ratio 7:6:4. Did more campers choose the camp craft programme in the first or second week? How many more?
Answer: Second week
Step-by-step explanation:
Given
In first week, campers choose programmes in the ratio of [tex]7:5:8[/tex]
In second week, this ratio becomes [tex]7:6:4[/tex]
Suppose 100 campers Joined the camp
Number of hikers who choose camp craft in first week are
[tex]\Rightarrow \dfrac{7}{7+5+8}\times 100=\dfrac{7}{20}\times 100\\\\\Rightarrow 35[/tex]
Number of hikers who choose camp craft in second week are
[tex]\Rightarrow \dfrac{7}{7+6+4}\times 100=\dfrac{7}{17}\times 100\\\\\Rightarrow 41.17\approx 41[/tex]
Therefore, in second week more campers take part in camp craft.
If 100 campers take part then, 6 more campers takes part in camp craft.
Which expression is equivalent to 1/4y−1/2?
( ignore the highlighted answer i don’t know if it’s right or not)
Answer:
1/4( y -2)
Step-by-step explanation:
1/4 y -1/2
Rewriting
1/4 * 1 y - 1/4*2
Factor out the 1/4
1/4( y -2)
Rewrite the radical expression as an expression with rational exponents.
cube root of x to the power of 8
Answer:
Step-by-step explanation:
[tex]\sqrt[3]{x^8}=x^{\frac{8}{3}[/tex] The little number outside is called the index and that always serves as the denominator in the rational exponent. The power on the radicand (the radicand is whatever is inside the radical) serves as the numerator.
What describes the correct way to convert minutes to an hour
Answer:
Yo mean correct way??
yo can divide minute by 60 to convert minute into hour
For example
To convert 10 minute into hour. then we should divide 10 by 60. 10/60
Answer:
In any conversion you have to establish ratios (or rates) for the different units being converted.
The process will be performed by a series of multiplications that will cancel out the "unwanted" units.
multiplication by one (1) does not change the value in an equation.
you have to multiply by a "series of ones" that take into account the units being converted..
for example
1 minute/60 seconds or 1 inch = 2.54 cm or 1 day = 24 hours
in your problem you have minutes... lets say you have 100 minutes
100 minutes * 1 hour minutes cancel and you have 100/60 = 1 [tex]\frac{2}{3}[/tex] hrs
60 minutes
Step-by-step explanation:
Write the ratio $150 : $450 : $750 in its simplest form.
Answer:
1 : 3 : 5
Step-by-step explanation:
Given
$150 : $450 : $750 ( divide each part of the ratio by $150 )
= 1 : 3 : 5
SEE QUESTION IN IMAGE
Answer:
23Data is:
5, 6, 7Mean:
(5 + 6 + 7)/3 = 6Standard deviation:
σ = [tex]\sqrt{((5 - 6)^2+(6-6)^2+(7-6)^2)/3} = \sqrt{2/3}[/tex]Correct choice is d
24Data is:
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5Mean:
(-5 -4 - 3 - 2 - 1 + 0 + 1 + 2 + 3 + 4 + 5)/11 = 0Standard deviation:
σ = [tex]\sqrt{((-5)^2+(-4)^2+(-3)^2+(-2)^2+(-1)^2+0^2+1^2+2^2+3^2+4^2+5^2)/11} = \sqrt{10}[/tex]Correct choice is d
25Data is:
3, 4, 5, 6, 7Mean is:
5Standard deviation:
σ = [tex]\sqrt{((3-5)^2+(4-5)^2+(5-5)^2+(6-5)^2+(7-5)^2)/5} = \sqrt{2}[/tex] ≈ 1.4Correct choice is d
6 less than the product of 5 and a number
A. 5-6n
B. 6+5n
C. 5(n - 6)
D. 5n-6
Answer:
D.
Step-by-step explanation:
5 times a number is 5n. We need to subtract 6 from that, so we have 5n-6 for any value n.
Answer:
D. 5n - 6
Step-by-step explanation:
6 less means -6
The product of 5 and a number means 5 x n which is the same as 5n
And it wants us to subtract 6 from 5n
so we would write it as...
5n - 6
What are the solutions to the system of equations?
{y=2x²−6x+3
{y=x−2
Answer:
x = 1, y = −1
x = 5/2, y = 1/2
Step-by-step explanation:
From the question given above, the following data were obtained:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
We can obtain the solutions to the equation as follow:
y = 2x² − 6x + 3 ........ (1)
y = x − 2 ...... (2)
Substitute the value of y in equation 2 into equation 1
y = 2x² − 6x + 3
y = x − 2
2x² − 6x + 3 = x − 2
Rearrange
2x² − 6x − x + 3 + 2 = 0
2x² − 7x + 5 = 0
Solve by factorization
Obtain the product of 2x² and 5. The result is 10x².
Find two factors of 10x² such that their sum will result to −7x.
The factors are −2x and −5x.
Replace −7x in the equation above with −2x and −5x as shown below:
2x² − 2x − 5x + 5 = 0
2x(x − 1) − 5(x − 1) = 0
(x − 1)(2x − 5) = 0
x − 1 = 0 or 2x − 5 = 0
x = 1 or 2x = 5
x = 1 or x = 5/2
Substitute the value of x into equation 2 to obtain y
y = x − 2
x = 1
y = 1 − 2
y = −1
x = 5/2
y = x − 2
y = 5/2 − 2
y = (5 − 4)/2
y = 1/2
SUMMARY:
x = 1, y = −1
x = 5/2, y = 1/2
Suppose triangle ABC is similar to triangle
PQR with AB:PQ = 5:9
What is the ratio of the area of ABC to PQR?
Answer:
[tex]( \frac{5}{9} ) ^{2} = \frac{25}{81} [/tex]
8 . In which step does a mistake first occur?
(24+3 + 10)-14 + 2
Step 1: (8 + 10) -14 + 2
Step 2: 18 -14+2
Step 3: 4 +2
Step 4: 2
Answer:
Step 1
Step-by-step explanation:
Concepts:
When solving any expression or equation, we must go through the order of operations. The order of operations is a set of rules that tell us which operation we must do first. The set of rules is often represented by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.Solving:
Let's go through the order of operations to solve the expression, so we can see the mistake in the steps.
(24 + 3 + 10) - 14 + 2
1. Add 24 and 3 together
(24 + 3 + 10) - 14 + 2(27 + 10) - 14 + 22. Add 27 and 10 together
(27 + 10) - 14 + 2(37) - 14 + 237 - 14 + 23. Subtract 14 from 37
37 - 14 + 223 + 24. Add 23 and 2 together
23 + 225Now, let's compare these steps to the ones given.
There's a mistake in Step 1 because 24 and 3 was divided instead of added; 24 + 3 = 27, not 8.
cạnh huyền của một tam giác vuông lớn hơn một cạnh góc vuông là 1 cm và tổng của hai cạnh góc vuông lớn hơn cạnh huyền 4 cm hãy tính các cạnh của tam giác vuông này
Answer:
Cạnh huyền=13, cgv1=12, cgv2=5
Step-by-step explanation:
Tam giác ABC
Gọi a là cạnh huyền(đối diện điểm A)
b là cgv đối diện điểm B
c là cgv đối diện điểm C
Theo đề bài: a=b+1 hoặc a=c+1
TH1: a=b+1 ta có hệ pt:
a=b+1 (1)
b+c=a+4 (2)
[tex]b^{2} +c^{2} = a^{2}[/tex] (3)
Thế (1) vào (2) ta được: b+c=b+1+4 => c=5
Thế (1) và c=5 vào (3) ta được: [tex]b^{2} +5^{2} = (b+1)^{2}[/tex]
<=> [tex]b^{2} +25=b^{2} +2b+1[/tex]
<=> 2b=24 => b=12
=> a=b+1=12+1=13
TH2: a=c+1 ta có hpt
a=c+1 (4)
b+c=a+4 (5)
[tex]b^{2} +c^{2} = a^{2}[/tex] (6)
Tương tự tính được a=13,b=5,c=12
Vậy cạnh huyền=13, 1 cạnh góc vuông=5 và 1 cạnh góc vuông=12
