Answer:
She has 60% of money left.
Step-by-step explanation:
You have to find out how much Php that Lei has left :
Php 150 - Php 48 - Php 12 = Php 90
She has a remaining of Php 90. Next, you have to find the percentage by dividing hy original amount and then, multiply by 100 :
(90/150)×100 = (3/5)×100 = 60%
point) Find two numbers differing by 42 whose product is as small as possible Enter your two numbers as a comma separated list; e.g. 2,3. Thc " tw numbers are
The numbers differing by 42 whose product is as small as possible are (- 21 + √(441 + p)) and (- 21 - √(441 + p)).
Let us suppose the numbers to be x and y.
As per the given information, we can write;
xy = p ---- (1)
We have to find two numbers differing by 42 whose product is as small as possible.
If two numbers are differing by 42; then we can say
x - y = 42 ---- (2)
From equation (2), we can say
x = y + 42
Now, substitute the value of x in equation (1), we get;
xy = p(y + 42)y² + 42y - p
= 0
Solving this quadratic equation, we will get;
∆ = 1764 + 4p
∴ y = (- 42 ± √(1764 + 4p)) / 2
Now, to find the minimum value of xy, we need to find the value of y that makes xy minimum.
Therefore, the two numbers that make xy as small as possible are;
y = (- 42 + √(1764 + 4p)) / 2
and
x = y + 42
So, the two numbers are;
y = (- 42 + √(1764 + 4p)) / 2
and
x = y + 42
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A 2-column table with 4 rows titled Drama Club Revenue. Column 1 has entries a percent, a percent, a percent, a percent. Column 2 has entries b dollars, b dollars, b dollars, b dollars.
A drama club made $3,200 from a school play. Seventy-five percent of that amount came from ticket sales. Identify the values of the variables in the model. Then use the model to find the amount of ticket sales.
a =
b =
The amount of ticket sales is $
.
Answer:
A: 25
B: 800
C: 2,400
Step-by-step explanation:
Hopes this helps. :) ( Unless you have already solved ) Just have a good day.
Answer:
A: 25
B: 800
C: 2,400
Step-by-step explanation:
You are planning to completely delta hedge your ABC
share holdings. How many call options
will you need to hedge holding 480 shares of a company, if you know
that the option's delta is 0.6?
In order to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need 3 call options.
To completely delta hedge your holdings of 480 shares of ABC company, you would need to calculate the number of call options required based on the delta of the option. The delta represents the change in the option price relative to the change in the underlying stock price. In this case, since the delta is given as 0.6, it means that for every $1 increase in the stock price, the option price will increase by $0.6.
To calculate the number of call options needed for delta hedging, you can use the following formula:
Number of call options = (Delta * Number of shares) / 100
Plugging in the given values, we have:
Number of call options = (0.6 * 480) / 100
Number of call options = 2.88
Since you cannot have a fractional number of options, you would need to round up to the nearest whole number. Therefore, you would need 3 call options to hedge your 480 shares of ABC company.
In summary, to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need to acquire 3 call options.
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How many 8 in pieces of ribbon can you cut from a 12 ft roll of ribbon?
Answer:
1 1/2
Step-by-step explanation:
12 divided by 8 = 1.5
Answer:
18
Step-by-step explanation:
first convert 12 ft to in. there are 12 inches in 1 ft so 12*12=144
then dived 144/8=18
19.
a. Given the formula A= (1/2)bh , solve for b.
Only answer if you know the question please
Answer: b = 2A/h
Step-by-step explanation:
1/2 bh = A
2 ⋅ 1/2 bh = 2A
bh = 2A
bh/h = 2A/h
b = 2A/h
Simplify the expression: 22
.
5 + (20 + 4)
(6 - 2)
1. A company borrows $100,000 today at 12% nominal annual interest. The monthly payment of a 5-year loan is most nearly?
2. A tractor cost $7,500. After 10 years it has a salvage value of $5000. Maintenance costs are $500 per year. If the interet rate is 10%, the equivalant uniform annual cost is most nearly?
1. The monthly payment of the 5-year loan is approximately $2,225.77.
2. The equivalent uniform annual cost for the tractor is approximately $5,572.50.
1. To calculate the monthly payment of a loan, we can use the formula for an amortizing loan. The formula is:
PMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
PMT = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (annual interest rate divided by 12)
n = Total number of payments (number of years multiplied by 12)
In this case, the principal amount (P) is $100,000, the annual interest rate is 12%, and the loan duration is 5 years.
r = 12% / 12 = 1% per month
n = 5 years * 12 months/year = 60 months
PMT = 100,000 * (0.01 * (1 + 0.01)^60) / ((1 + 0.01)^60 - 1)
PMT ≈ $2,225.77
Therefore, the monthly payment of the 5-year loan is approximately $2,225.77.
2. To calculate the equivalent uniform annual cost, we need to consider the initial cost of the tractor, salvage value, maintenance costs, and the interest rate.
The equivalent uniform annual cost (EUAC) can be calculated using the formula:
EUAC = (Initial cost - Salvage value) + (Annual maintenance cost * Present worth factor)
The present worth factor can be calculated using the formula:
Present worth factor = (1 - (1 + r)^-n) / r
Where:
r = Interest rate (10%)
n = Number of years (10 years)
EUAC = ($7,500 - $5,000) + ($500 * ((1 - (1 + 0.10)^-10) / 0.10))
EUAC = $2,500 + ($500 * ((1 - 0.3855) / 0.10))
EUAC ≈ $2,500 + ($500 * 6.145)
EUAC ≈ $2,500 + $3,072.50
EUAC ≈ $5,572.50
Therefore, the equivalent uniform annual cost for the tractor is approximately $5,572.50.
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An airplane is flying overhead at a constant elevation of 5000 ft. A man is viewing the plane from a position 12000 ft from the base of a radio tower. The airplane is flying horizontally away from the man. If the plane is flying at the rate of 520 ft/sec, at what rate is the distance between the man and the plane increasing when the plane passes over the radio tower?
The rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.
Let's denote the distance between the man and the plane as x and the time elapsed since the plane passes over the radio tower as t. We are given that the plane is flying horizontally away from the man, so the height of the plane remains constant at 5000 ft.
We can set up a proportion based on the similar triangles formed by the man, the plane, and the tower:
x / 12000 = 5000 / t
Cross-multiplying, we have:
xt = 12000 * 5000
xt = 60,000,000
Now, we can differentiate both sides of the equation with respect to time t:
d(xt)/dt = d(60,000,000)/dt
dx/dt * t + x * dt/dt = 0
dx/dt * t + x * 1 = 0
dx/dt = -x/t
We are given that the plane is flying at a rate of 520 ft/sec, so dx/dt = 520 ft/sec.
At the moment the plane passes over the radio tower, the distance x is 12000 ft. We can substitute these values into the equation to find the rate at which the distance between the man and the plane is increasing:
520 = -12000 / t
Solving for t:
t = -12000 / 520 = -23.08 sec (approximately)
Since time cannot be negative, we discard the negative value and take the positive value of t.
Now, we can substitute the value of t into the equation to find dx/dt:
dx/dt = -x / t = -12000 / (-23.08) = 519.92 ft/sec (approximately)
Therefore, the rate at which the distance between the man and the plane is increasing when the plane passes over the radio tower is approximately 519.92 ft/sec.
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which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.) average seasonal temperature in the united states; air-conditioning costs for homes in the united states b.) number of miles driven by paul; number of gallons of gas used by paul's car c.) swimsuit sales throughout the year; sunscreen sales throughout the year d.) steepness of the appalachian trail; john's speed while hiking the appalachian trail
The correct option is c.) swimsuit sales throughout the year; sunscreen sales throughout the year.
Correlation coefficient is a measure of the strength and direction of a relationship between two variables. The correlation coefficient varies from -1 to +1. A correlation of -1 means that a negative association between two variables is perfect, while a correlation of +1 means that there is a positive association between two variables that is perfect. The closer the correlation coefficient is to 0, the weaker the association between two variables is. A correlation coefficient of 0 means that there is no relationship between two variables.From the given options, the data set that is most likely to have a negative association and a correlation coefficient between 0 and -1 is (c) swimsuit sales throughout the year and sunscreen sales throughout the year.The reason behind this is that when it's summer or a hot season, people tend to buy more swimsuits than sunscreen. And when it's winter or a cold season, people tend to buy more sunscreen than swimsuits. Hence, the correlation coefficient between swimsuit sales throughout the year and sunscreen sales throughout the year is most likely to be between 0 and -1 because there is an inverse relationship between these two variables.
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Answer:Steepness of Appalachian Trail; John’s Speed while hiking the Appalachian Trail
Step-by-step explanation:
y-2x=14
Solve the literal equation for y
Answer:
y =2x+14
Step-by-step explanation:
y - 2x= 14
Add 2x to each side
y -2x+2x = 2x+14
y =2x+14
please help, thanks.
Sketch the graph of the line x - y = 4
the answer is in the photo
Which equation is linear?
a
xy = 60
b
y + 1 = x
c
3x – 2y = 5
Answer:
equation B is linear. A linear equation will not contain exponents.
Step-by-step explanation:
Answer:
b and c
Step-by-step explanation:
They both follow the formula of a linear function: y = mx + c, where m is the gradient and c is the y-intercept.
When you rearrange:
a. y = 60/x (this is a reciprocal function)
b. y = x - 1 (says that this linear function has a gradient of 1 and cuts the y-intercept at (0,-1))
c. y = 3x/2 -5/2 (says that this linear function has a gradient of 3/2 and cuts the y-intercept at (0, 5/2))
In a certain country, the true probability of a baby being a boy is 0.528. Among the next seven randomly selected births in the country, what is the probability that at least one of them is a girl? (Round to three decimal places)
The probability that at least one of the seven randomly selected births in the country is a girl is 0.986.
Given that the true probability of a baby being a boy is 0.528. To find the probability that at least one of the seven randomly selected births in the country is a girl, we need to find the probability that none of the seven babies is a girl and then subtract it from 1.
To find the probability that none of the seven babies is a girl, we find the probability that each of them is a boy and then multiply them together.Using the probability of having a boy, we can find the probability of having a girl:p(girl) = 1 - p(boy) = 1 - 0.528 = 0.472Using the multiplication rule for independent events, we can find the probability that none of the seven babies is a girl:
P(seven boys) = P(boy) × P(boy) × P(boy) × P(boy) × P(boy) × P(boy) × P(boy)= 0.528 × 0.528 × 0.528 × 0.528 × 0.528 × 0.528 × 0.528= 0.0137Therefore, the probability that at least one of the seven randomly selected births in the country is a girl is:1 - P(seven boys) = 1 - 0.0137 = 0.9863Rounding the answer to three decimal places, we get: 0.986
Thus, the probability that at least one of the seven randomly selected births in the country is a girl is 0.986.
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You want to buy a new Apple Watch. It costs $279.00, but you have to pay 6% sales tax. How much will the watch cost you with tax?
Answer:
279.06
Step-by-step explanation:
Solve x+9x + 26x+24<0 Show all your work. (6 marks) Application 5 . Given the following function f(x) = x -9x +15x +25 , determine the end behaviour, and x-/y-intercepts. and then sketch the graph (must be done by hand). Show all work for full marks. (8 marks)
The x-intercepts are x = -5/3 and x = 5/3.
The y-intercept is (0, 25).
Solve x+9x^2 + 26x+24 < 0:
To solve this inequality, we can first simplify the expression:
9x^2 + 27x + 24 < 0
Now, we can factorize the quadratic expression:
(3x + 4)(3x + 6) < 0
Next, we determine the critical points by setting each factor to zero:
3x + 4 = 0 --> x = -4/3
3x + 6 = 0 --> x = -2
We now create a sign chart and test the intervals:
scss
Copy code
-∞ -4/3 -2 +∞
(3x + 4) - 0 + +
(3x + 6) - - + +
From the sign chart, we can see that the inequality (3x + 4)(3x + 6) < 0 holds true when -4/3 < x < -2.
Therefore, the solution to the inequality x+9x^2 + 26x+24 < 0 is:
-4/3 < x < -2.
Determine the end behavior, x-/y-intercepts, and sketch the graph of f(x) = x - 9x^2 + 15x + 25:
End Behavior:
As x approaches negative infinity, the leading term -9x^2 dominates, and the function approaches negative infinity. As x approaches positive infinity, the leading term -9x^2 still dominates, and the function also approaches negative infinity.
x-intercepts:
To find the x-intercepts, we set f(x) = 0 and solve for x:
x - 9x^2 + 15x + 25 = 0
Combine like terms:
-9x^2 + 16x + 25 = 0
This quadratic equation can be factored as:
-(3x - 5)(3x + 5) = 0
Setting each factor to zero:
3x - 5 = 0 --> x = 5/3
3x + 5 = 0 --> x = -5/3
Therefore, the x-intercepts are x = -5/3 and x = 5/3.
y-intercept:
To find the y-intercept, we set x = 0 in the equation:
f(0) = 0 - 9(0)^2 + 15(0) + 25 = 25
Therefore, the y-intercept is (0, 25).
Sketching the graph:
Using the information gathered, we can sketch the graph of f(x). It is a downward-opening parabola that intersects the x-axis at x = -5/3 and x = 5/3, and the y-axis at y = 25. The end behavior shows that the graph approaches negative infinity as x approaches negative and positive infinity.
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what’s 12 divided by 9?
Answer:
12/9 = 4/3
Step-by-step explanation:
write it as a fraction, then simplify by dividing numerator and denominator by 3.
Answer:
4/3 or 1.3
Step-by-step explanation:
12 divided by 9
You are 5 dollars in debt. You borrow 12 dollars more. What is the total amount of your debt?
Answer:
17
Step-by-step explanation:
You already owe 5 dollars and if you borrow 12 more, you have to pay that back later. You just add 5 and 12 and get 17.
The total debt is $17.
What is addition?Combining items and counting them as a single, large group is done through addition.
Given that, the debt amount is $5.
Now, you borrowed $12 more, therefore, the total debt is:
5 + 12
= 17
Hence, the total debt is $17.
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Which table of ordered pairs represents a proportional relationship? Х 4 7 10 у 8 11 14 X 5 7 9 y 25 49 81 X у 13 6 10 14 ch 7 Х 3 8 13 у 6 11 18
Answer:
The answer is C
Step-by-step explanation:
it just makes sence,and all the numbers are compatible with each other
Hoped it helped^^
The ordered pairs that represent a proportional relationship is (b)
How to determine the proportional relationship?For an ordered pair to represent a proportional relationship, the following equation must be true:
y^m = kx^n
The first table shows that:
y = x + 4 --- this does not represent proportional relationship
The second table shows that
y = x^2 ---- this represents proportional relationship
Hence, the ordered pairs that represent a proportional relationship is (b)
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Q6. (5+2.5+2.5 Marks) A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y²
A. The size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² can be calculated using a double integral in polar coordinates. B. Differential equation models can be 1. free-falling stone, 2. spring vertical displacement C. The rate of change of temperature at the origin in the direction of the unit vector u = (3,-5) can be determined by T = r² + s².
A. To calculate the size of the tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y², we can use a double integral in polar coordinates. By expressing the paraboloid equation in polar coordinates, we can set up the integral and evaluate it to find the size of the tower.
B. Differential equation models are mathematical representations used to describe various real-life phenomena. For the given examples:
The free-falling stone can be modeled using Newton's second law and the concept of acceleration due to gravity.
The vertical displacement of a spring can be described using Hooke's law and the properties of springs.
Kirchhoff's Second Law, also known as the voltage law, can be used to model the behavior of electrical circuits.
Newton's Law of Cooling is a differential equation that describes the rate of change of temperature of an object as it loses heat to its surroundings.
Growth and decay phenomena, such as population growth or radioactive decay, can be modeled using exponential or logarithmic functions.
C. To calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5), we need to find the gradient of the temperature function T = r² + s². The gradient represents the direction of the steepest increase in a function. By computing the gradient at the origin and taking the dot product with the unit vector u, we can determine the rate of change of temperature in the desired direction.
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(5+2.5+2.5 Marks) A. Use double integral and polar coordinates to calculate the size of a tower bounded by the plane z = 0 and the paraboloid z = 1 - x² - y² B. Design a differential equation model for the following real-life phenomena: 1. free-falling stone, 2. spring vertical displacement, 3. Kirchoff's Second Law for the circuit, 4. Newton's Law of Cooling, and 5. Growth and Decay. C. The external body temperature in the r-s plane is T = r² +s². Calculate the rate of change of temperature at the origin in the direction of the unit vector u = (3,-5).
An author is having a book signing at a store. He agrees to give 5% of his profit to literacy programs and 15% of his profit to his manager. If he makes a profit of $200.00, how much of his profit does he take home?
Answer:
i think that is 146
Step-by-step explanation:
because
Write an equation using "x" as the variable: Bill
won 48 super bouncy balls playing the bean
bag toss at the county fair. At school he gave
two to every student in his math class. He only
had 4 balls remaining.
Answer: 48 = 2x + 4
Step-by-step explanation:
x = number of students Bill gave bouncy balls to
The + 4 is there because he had 4 remaining bouncy balls.
48 is what it equals because that is his total number of bouncy balls that he won.
Hope this helps!
Monica’s school band held a car wash to raise money for a trip to a parade in New York City. After washing 125 cars, they made $775 from a combination of $5.00 quick washes and $8.00 premium washes.
This system of equations models the situation.
x + y =125
5x + 8y = 775
Solve the system to answer the questions.
How many premium car washes were ordered?
premium car washes
How many quick car washes were ordered?
quick car washes
Answer:
50 and 75
Step-by-step explanation:
trust me bro
Answer:
50 and 75
Step-by-step explanation:
Hope this helps :)
If you know two points on a line, why can't you write two different equations for that line?
...........................
Answer:
....................... What's the question?
graph the libne with a Y intercept of -2 and slope of -1/3 what is the X intercept of the line
Answer:
y = -1/3x -2
x-intercept = -6
Step-by-step explanation:
Slope = -1/3
y-intercept = -2
Substitute values into slope intercept form ;
y =mx +b
Where ; m = slope
b =y-intercept
Equation =
[tex]y = -\frac{1}{3} x -2[/tex]
Now graph the equation
x-intercept = ?
[tex]y = -\frac{1}{3} x -2[/tex]
Arrange in standard form and Let y = 0
[tex]y = -\frac{1}{3} x -2\\\\\frac{1}{3} x +y =-2\\\\\frac{1}{3} x +0=-2\\\\\frac{1}{3} x =-2[/tex]
Cross Multiply
[tex]x \times 1 = 3\times -2\\\\x = -6\\\\=(-6,0)[/tex]
So , (-6,-2)
I NEED HELP WITH NUNBER 3 AND 4 PLEAAEE
Answer:
I think the answer is 10 or −2(x-6)
Step-by-step explanation:
Over 9 months, a random sample of 50 women were asked to record their average menstrual cycle length (in days). The sample average was 28.86 days, with a sample standard deviation of 4.24 days.
(a) Calculate the lower bound for the 90% confidence interval for the true average menstrual cycle length.
(b) Calculate the upper bound for the 90% confidence interval for the true average menstrual cycle length.
(c) A researcher hypothesized that women's menstrual cycles are typically the same length as a lunar month - 29.5 days. Does your interval from (a,b) support this hypothesis?
O Not enough information O Yes O No
The lower bound of the 90% confidence interval for the true average menstrual cycle length is 27.4.
a) Calculation for the lower bound of 90% confidence interval: The formula for calculating the confidence interval is, :
Lower Limit = X - Zα/2 × (σ/√n) Where, X = sample mean Zα/2 = 1.645σ = sample standard deviation= sample size Putting the given values into the formula, Lower Limit = 28.86 - 1.645 × (4.24/√50)≈ 27.4
The upper bound of the 90% confidence interval for the true average menstrual cycle length is 30.3.
b) Calculation for the upper bound of 90% confidence interval: The formula for calculating the confidence interval is,:
Upper Limit = X + Zα/2 × (σ/√n) Where ,X = sample mean Zα/2 = 1.645σ = sample standard deviation = sample size Putting the given values into the formula, Upper Limit = 28.86 + 1.645 × (4.24/√50)≈ 30.3
The confidence interval is (27.4, 30.3) and the hypothesized value is 29.5.
c) Hypothesis testing:According to the hypothesis, women's menstrual cycles are typically the same length as a lunar month - 29.5 days. So, we can check if the interval from (a,b) supports this hypothesis or not by comparing the hypothesized value with the confidence interval.
As we see that the hypothesized value is within the interval, we can say that the interval from (a,b) supports the hypothesis. Therefore, the answer is Yes.
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5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
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please help me. this is due today.
Answer:
...
let me c
Step-by-step explanation:
Answers:
It's the last one in the chart
(-3-2i -2(24)=8 -51-6i)
