Phone card = $20
You need to minus 17.92 from 20 = $2.08
$2.08 / 0.13 = how many minutes
= 16
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Step-by-step explanation:
An arithmetic sequence is of the form:
[tex]A_n = A_{n-1} + d[/tex]
While a geometric sequence is of the form:
[tex]A_n = A_{n-1}*r[/tex]
notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.
In fact, the pattern is kinda easy to see.
The first term is:
A₁ = 2
the second term is:
A₂ = -10
notice that:
A₂/A₍ = r = -10/2 = -5
The third term is:
A₃ = 50
the quotient between the third term and the second term is:
A₃/A₂ = 50/-10 = -5
Whit this we can already conclude that the n-th term of our sequence will be:
[tex]A_n = A_{n-1}*(-5)[/tex]
Then the summation will be something like:
[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]
We can write:
[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]
Then the summation is just:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
11 + box equals 19 find box
Answer:
8
Step-by-step explanation:
11 + x = 19
Subtract 11 from each side
11+x -11 = 19-11
x = 8
Answer:
8
Step-by-step explanation:
11 + box = 19
=> box = 19 - 11
.°. box = 8
Equation?
Slope?
Y-intercept?
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (4, 2) ← 2 points on the line
m = [tex]\frac{2-(-3)}{4-0}[/tex] = [tex]\frac{2+3}{4}[/tex] = [tex]\frac{5}{4}[/tex]
The line crosses the y- axis at (0, - 3 ) ⇒ c = - 3
y = [tex]\frac{5}{4}[/tex] - 3 ← equation of line
Please Help!! much appreciated! :D
Find the value of y.
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
Can I get help with this? Easy points!
9514 1404 393
Answer:
maximum: 0minimum: -16Step-by-step explanation:
A graphing calculator can quickly show you the boundaries of the feasible region, and can calculate the values of the objective function.
In a class of 5 , there are 3 students who have done their homework. If the teacher 2 chooses 2 2 students, what is the probability that none of them have done their homework?
Answer:
2 over 5
Step-by-step explanation:
This means out of 5 students only three did their work so 5-3=2
And the number of students who did their work over the total number of students in the class to find the probability
The probability that none of them have done their homework is 0.57%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that there are 3 students who have done their homework.
If the teacher 2 chooses 2 students, then;
Total no. of Outcomes= 5
Students who did their homework = 3
Students who didn't do their homework is 5-3 = 2
Probability of no. of students who haven't done their homework.
P(e)= 2/5
Thus P(students who haven't done homework) P(e)=0.57%
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The circumference of a
square orchard is 1600
meters. How many square
meters does the orchard
cover? How many hectares
9514 1404 393
Answer:
160,000 m²16 haStep-by-step explanation:
The side length of a square is 1/4 of the perimeter, so the side length of the square orchard is (1600 m)/4 = 400 m.
The area of a square is the square of the side length, so the area of the orchard is (400 m)² = 160,000 m².
A hectare is 10,000 m², so the area of the orchard in hectares is ...
16·(10,000 m²) = 16 ha
Use a calculator to find the mean of the data. {21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
Answer:
The mean of the data is 21.41
Step-by-step explanation:
To find the mean of a data set you must...
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a data set:
{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
As we know from the definition of the mean:
The mean can be calculated using the formula:
Mean = sum of the data set/number of the data in the data set
Mean = 471/22
Mean = 21.409 ≈ 21.41
Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
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A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is:_______
a. 0.9545.
b. 0.9332.
c. 0.0668.
d. 0.4332.
Answer:
0.9545
Step-by-step explanation:
Given that :
Mean = 300
Standard deviation, σ = 18
Sample size, n = 144
Zscore = (x - mean) ÷ σ/√n
At score, x = 297
Zscore = (297 - 300) / (18/12) = - 2
P(Z< - 2) = 0.02275
At score, x = 303
Zscore = (303 - 300) / (18/12) = 2
P(Z< 2) = 0.97725
P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275 = 0.9545
The probability that the sample mean will be between 297 to 303 is 0.9545.
We have given that ,A population has a mean of 300 and a standard deviation of 18. A sample of 144 observations will be taken.
Mean = 300
Standard deviation, σ = 18
Sample size, n = 144
We have to find the probability that the sample mean will be between 297 to 303
Therefore we use the formula of Z score.
What is the formula of Z score?[tex]Zscore = \frac{ (x - mean)}{\sigma/\sqrt n}[/tex]
At the score, x = 297
Zscore = (297 - 300) / (18/12) = - 2
P(Z< - 2) = 0.02275
At score, x = 303
Zscore = (303 - 300) / (18/12) = 2
P(Z< 2) = 0.97725
Therefore we get,
P(Z < 2) - P(Z < - 2) = 0.97725 - 0.02275 = 0.9545
Therefore,the probability that the sample mean will be between 297 to 303 is 0.9545.
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f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 110 feet. The smallest path bordering the patch of grass measures 55 feet. The smallest angle formed by the paths bordering the patch of grass measures 29º.
What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest
degree. Show all your work.
Answer:
76 degrees
Step-by-step explanation:
First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.
The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that
55 feet/ sin(29 degrees) = 110 / sin(largest angle).
If we say that the largest angle is equal to x, we can say
55 / sin(29°) = 110/sin(x)
multiply both sides by x to remove a denominator
55 * sin(x)/ sin(29°) = 110
multiply both sides by sin(29°) to remove the other denominator
55 * sin(x) = 110 * sin(29°)
divide both sides by 55 to isolate the sin(x)
sin(x) = 110 * sin(29°) / 55
For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say
x = arcsin(110 * sin(29°)/55)
x ≈ 76 degrees
There are about 320 million people living in the United States. Of these, how many would you predict wear corrective lenses?
Answer:
243840000 people
Step-by-step explanation:
The total sample size = 1000
Samole proportion of those who wear corrective lenses :
p = x / n ; n = sample size
p = 762 / 1000 = 0.762
To predict the number of people who wear corrective lenses :
Total population * p
320,000,000 * 0.762
= 243840000 people
Answer:
243840000
Step-by-step explanation:
Write down the name of the solid shape that is being described. "When you cut me in half, the number of faces on one of my halves is double the number of faces that I started with.
Answer:
Cone
Step-by-step explanation:
A cone only has 1 side, and when it's cut in half it has two
f(x) = x2
g(x) = (x +4)^2 - 1
We can think of g as a translated (shifted) version of f.
Hurry I am in summer school and almost done I need help ASAP!
Answer:
down by 1 unit and left by 4 units
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Then
g(x) = (x + 4)² - 1
is f(x) shifted down by 1 unit and shifted left by 4 units
3.3 A circle has a radius of 12cm. An angle of 3.2 radians is subtended at the centre by an arc. Calculate the length of the arc. (3)
Answer:
S = 38.4 centimeters.
Step-by-step explanation:
Given the following data;
Radius, r = 12 cmAngle = 3.2 radsTo find the length of the arc of a circle;
A full circle measures an angle of 360 degrees.
π = 180°
So; Angle, A = 360° = 2π
Therefore, a full circle is equal to 2π in terms of radians (rads).
Also, the circumference (the length of an arc) of a circle is equal to 2πr or Ar.
Mathematically, the length of the arc of a circle is given by the formula;
S = rA
Where;
S is the length of the arc.A is the angle measured in radians.Substituting into the formula, we have;
S = 12 * 3.2
S = 38.4 centimeters.
Which shows the numbers Nine-tenths, 0.3, 0.8, Five-tenths, and Two-tenths in order from least to greatest?
Answer:
[tex]\frac{2}{10}, 0.3, \frac{5}{10},0.8,\frac{9}{10}[/tex]
Step-by-step explanation:
Given
[tex]\frac{9}{10}, 0.3, 0.8,\frac{5}{10}, \frac{2}{10}[/tex]
Required
Order from the least
We have:
[tex]\frac{9}{10}, 0.3, 0.8,\frac{5}{10}, \frac{2}{10}[/tex]
Express all as decimal
[tex]0.9, 0.3, 0.8,0.50, 0.20[/tex]
Rearrange from least
[tex]0.20, 0.3, 0.50,0.8,0.9[/tex]
Express converted numbers as fractions
[tex]\frac{2}{10}, 0.3, \frac{5}{10},0.8,\frac{9}{10}[/tex]
A father's age is thrice the sum of the ages of his two children. After five years, his age will be
twice the sum of their ages. How old is the father?
Answer: 45 years old
Step-by-step explanation:
Given:
- Father's age is thrice the sum of ages of his two children
- After five years, his age will be twice the sum of their ages
Let x be the two children's current age and 3x be the father's current age
Solve:
Set equation
3x + 5 = 2 ( x + 10 )
Expand parenthesis
3x + 5 = 2x + 20
Subtract 5 on both sides
3x + 5 - 5 = 2x + 20 - 5
3x = 2x + 15
Subtract 2x on both sides
3x - 2x = 15
x = 15
15 × 3 = 45 years old
Hope this helps!! :)
Please let me know if you have any questions
5 times a number less than 50 is 250 what is the number
Answer:
x = -40
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
50 - 5x = 250
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 50 on both sides: -5x = 200[Division property of Equality] Divide -5 on both sides: x = -40A boy's mother was 32 years old when he was born. Let a represent the boy's age and m represent the mother's age.
Complete the table using the relationship between a and m.
PLEASE ANSWER!!!!
see the picture attached
A laptop was originally sold for $975. The laptop is now on sale for $828.75.The percent markdown must have been...
Answer:
15% markdown
Step-by-step explanation:
To find the percent markdown
Take the original price minus the new price
975-828.75
146.25
Divide by the original price
146.25/975
.15
Change to percent form
15% markdown
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Pleasant help me out explanation need it
Answer:
for which question???????????????
Answer:
Ok please tell me your question because you forgotten the question your asking dor
Mr. Johnson took up an appointment with Nestle Ghana as an accountant with an annual salary of $164 million. as part of his appointment, he was promised a yearly increment of $24 million. Mr Johnson got promoted to chief accountant after six years of work with an annual salary of $300 million and yearly increment of$36 million.
calculate a) Mr. Johnson's salary in the tenth year of service.
b). Mr. Johnson's total earnings at the end of the tenth year of service.
Answer:
300 million(1+ 36 million) y
Step-by-step explanation:
If Roger were 32 years older, he would be three times as old as he is now. How old is
Roger?
Answer:
16
Step-by-step explanation:
Set up the equation ->
x+32=3x
(you can get this easily by writing the equation down as you read the problem)
--> revisiting x+32=3x
-x on both sides to isolate the number and put the like terms together
We are left with 32=2x
Divide 2 on both sides, and you will get x (his current age) --> x=16
Roger is currently 16 years old.
Answer:
16
Step-by-step explanation:
3x = 32 + x
2x = 32
x = 16
Q25 A train travelling at a speed of 30km/h crosses a bridge 25m long in 12 sec. How long will it take to overtake a another train 25m long travelling at 20km/hr? option given 1. 72 sec 2. 74 sec 3. ,75 sec or data insufficient.
Answer:
WHAT
Step-by-step explanation:
In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?
Answer:
Castles made: N day 1
N - 4 day 2
N - 8 day 3
N - 12 day 4
N - 16 day 5
Total 5 N - 40 = 80
N = 24 total castles day 1
Total castles = 24 + 20 + 16 + 12 + 8 = 80
7
10 points
A6-sided die is rolled. Find P(3 or 5).
O 1
1
36
2
2
1
3
3
6
Answer:
I think the answer is 1/3
Step-by-step explanation:
1/6+1/6
=2/6=1/3
Answer:
1/3
Step-by-step explanation:
The possible outcomes are 1,2,3,4,5,6
The good outcomes are 3 and 5 = 2 good outcomes
P(3 or 5) = number of good outcomes / total outcomes
= 2/6 = 1/3
Using a straightedge and compass, the ancient Greeks were able to construct
many geometric objects.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Find the value of x and y.
60°
6
Answer:
b .
x = 3
y = 3[tex]\sqrt3[/tex]
Step-by-step explanation:
Using the pythagorean identities for 30-60-90° triangle,
we know the ratio of the sides is x - x√3 - 2x
Since 2x = 6
Then smallest side is x (opposite ∠30°) = 6/2 = 3
The other side y , opposite ∠60° will be x√3 or 3√3.
9514 1404 393
Answer:
B. x = 3; y = 3√3
Step-by-step explanation:
You only need to use your sense of triangles to choose the correct answer:
x < y < 6
This relation fits only one answer choice:
x = 3, y = 3√3
_____
Additional comment
For multiple choice questions, it isn't always about working the problem. Usually, it is about knowing what the answer has to look like. The usual criteria are (a) is the answer true; (b) does the answer make sense in the context of the problem statement; (c) can you get this answer if you work the problem in detail. More often than not, the first two criteria will let you choose the correct answer without doing any detailed solving.
