Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment.
How to find hours of work?to find the business hours of work, Let's start by defining the variables given in the problem:
The initial cost of equipment is $175.
Stevie charges $12 per hour for cleanup.
Stevie wants to make at least $1200.
The number of hours worked is represented by h.
Now, we can set up an equation to solve for h:
Total earnings - Total cost = Desired profit
We can express the total earnings as the product of the hourly rate and the number of hours worked:
Total earnings = $12h
The total cost includes the initial cost of equipment plus any additional costs incurred during cleanup:
Total cost = $175 + additional costs
Since we don't know the value of the additional costs, we'll leave it as a variable.
Substituting these expressions into the equation, we get:
$12h - ($175 + additional costs) = $1200
Simplifying the equation, we get:
$12h - $175 - additional costs = $1200
$12h - $1375 = additional costs + $1200
$12h - $1375 = additional costs
Now we have an equation that relates the number of hours worked to the additional costs incurred during cleanup. We want to find the minimum value of h that satisfies this equation, since Stevie wants to make at least $1200.
To do this, we need to estimate the additional costs incurred during cleanup. Let's assume that Stevie spends an average of $4 per hour on additional costs (e.g., gasoline, trash bags, etc.). Then, the equation becomes:
$12h - $1375 = $4h + $175
Simplifying further, we get:
$8h = $1200
h = 150
Therefore, Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment and the estimated additional costs incurred during cleanup.
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The water hose fills A bucket at 1/3 per minute how many minutes does it take to fill a 2 gallon bucket
It will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
To determine the time required to fill a 2-gallon bucket using a water hose that fills at a rate of 1/3 gallon per minute, you can use a simple calculation.
First, identify the fill rate of the hose, which is 1/3 gallon per minute. Now, consider the bucket's capacity, which is 2 gallons. To find out how many minutes it takes to fill the bucket, divide the total capacity of the bucket by the fill rate:
Time (minutes) = Bucket capacity (gallons) / Fill rate (gallons per minute)
In this case:
Time (minutes) = 2 gallons / (1/3 gallons per minute)
To solve this, you can multiply the numerator and denominator by the reciprocal of the fill rate:
Time (minutes) = 2 gallons * (3 minutes per gallon)
Time (minutes) = 6 minutes
So, it will take 6 minutes for the water hose to fill the 2-gallon bucket at a rate of 1/3 gallon per minute.
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A ninja star, or shuriken, is usually constructed using four congruent isosceles triangles that are placed along the sides of a square. What is the value of x?
a.) 46
b.) 56
c.) 62
d.) 118
The measure of angle x of the ninja star is given by x = 56°
Given data ,
Let the ninja star be represented as an isosceles triangle
Now , it is constructed using four congruent isosceles triangles that are placed along the sides of a square
And , the vertex angle of the triangle is x
In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle
So , the measure of x = 180° - ( 62° + 62° )
On simplifying , we get
x = 56°
Hence , the angle of triangle is x = 56°
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 Solve for the value of p
WILL GIVE BRAINLIEST! A line contains the points R (-5, -3) S (-1, -1) and T (x, 3). Solve for x. Be sure to show and explain all work
The x-coordinate of point T is 7. Thus, point T is (7, 3).
To solve for x, we will use the concept of slope. The slope between any two points on a line remains constant. Let's find the slope between points R(-5, -3) and S(-1, -1):
Slope (m) = (y2 - y1) / (x2 - x1)
m = (-1 - (-3)) / (-1 - (-5))
m = (2) / (4)
m = 1/2
Now, we will use the slope between points S(-1, -1) and T(x, 3):
m = (3 - (-1)) / (x - (-1))
1/2 = (4) / (x + 1)
Now, we will solve for x:
1/2 (x + 1) = 4
x + 1 = 8
x = 7
So, the x-coordinate of point T is 7. Thus, point T is (7, 3).
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A school Community had planned to reduce the number of Grade 9 students per classroom by constructing additional classrooms however they constructed 4 Less rooms than they planned. As the result the number of students per class was 10 more than they planned if there are 1200 grade 9 students in the school determine the current number of classrooms and the number of students per class
The current number of classrooms is 24, and the number of students per class is 70 if there were a total of 1200 students.
Let us assume that the number of classes = x
Number of students per class = 1200/x
Number of classrooms planned = x - 4
Number of students planned per class = 1200/ x+10
Total number of students = 1200
By using the above data, the equations will be written as:
(1200 / x-4) = (1200/x) +10
By multiplying the equation 2 we get:
1200x = 1200x + [tex]x^{2}[/tex] - 4800 - 40x
[tex]x^{2}[/tex] - 480- 4x = 0
(x-24) (x+20) = 0
x = 24
Number of rooms built = x =24
Number of students per class = (1200/24-10) = 60 students
Therefore, we can conclude that the current number of classrooms is 24, and the number of students per class is 60 + 10 =70.
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Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?
If Tamekia and Marsha work for 22 hours, Marsha will earn $27.50 more than Tamekia.
To determine the amount of money each person can earn, we need to know the hourly rate and the number of hours worked. Tamekia estimates that she can earn between $6.00 and $6.25 per hour. Let's assume that she can earn $6.25 per hour. If Tamekia works for 22 hours, her total earnings will be:
Total earnings for Tamekia = Hourly rate x Number of hours worked = $6.25 x 22 = $137.50
Now let's look at Marsha's earnings. Marsha estimates that she can earn between $7.50 and $8.00 per hour. Let's assume that she can earn $7.50 per hour. If Marsha works for 22 hours, her total earnings will be:
Total earnings for Marsha = Hourly rate x Number of hours worked = $7.50 x 22 = $165.00
To determine how much more money Marsha will earn than Tamekia, we need to subtract Tamekia's total earnings from Marsha's total earnings:
Difference in earnings = Total earnings for Marsha - Total earnings for Tamekia = $165.00 - $137.50 = $27.50
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state the parent function of g(x) and describe how the graph of (x) is related to its parent function (questions 3,4,5)
The parent functions of the function equations are x³, x⁴ and x²
Stating the parent functionsThe transformed functions 3 - 5 represent the given parameter
To derive the parent functions, we need to determine the degree of the transformed and use this degree as a guide
By definition, the degree of a function is the highest power in the function
So, we have
Question 3
g(x) = (1/2x + 2)³ + 5
The degree here is 3
This means that the function is a cube function
The parent function of a cube function is y = x³
So, the parent function is g(x) = x³
Question 4
g(x) = x⁴ - 4
The degree here is 4
This means that the function is a polynomial function shifted down by 4 units
The parent function of this is y = x⁴
So, the parent function is g(x) = x⁴
Question 5
g(x) = 1/2(x - 1)² - 4
The degree here is 2
This means that the function is a quadratic function
The parent function of a quadratic function is y = x²
So, the parent function is g(x) = x²
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A random sample of small business stock prices has a sample mean of x¯=$54. 82 and sample standard deviation of s=$8. 95. Use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81. 67. Round your answer to the nearest hundredth
Using the Empirical Rule. The percentage of small business stock prices that are more than $81. 67 is 0.30%
To use the Empirical Rule, we need to assume that the distribution of small business stock prices is approximately normal.
First, we need to find the z-score for $81.67:
z = (81.67 - 54.82) / 8.95 = 2.99
Next, we can use the Empirical Rule to estimate the percentage of small business stock prices that are more than $81.67:
About 99.7% of the data falls within 3 standard deviations of the mean.
Therefore, about 0.3% of the data falls more than 3 standard deviations above the mean.
Since $81.67 is more than 3 standard deviations above the mean, we can estimate that the percentage of small business stock prices that are more than $81.67 is about 0.3%.
Rounded to the nearest hundredth, the estimated percentage is 0.30%.
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First derive a recurrence relation giving on for na 2 in terms of co or cy (or both). Then apply the given initial conditions to find the values of co and Cq. Next determine cn (in terms of n) and, finally, identify the particular solution in terms of familiar elementary functions. y"' + 4y = 0; y(0) = 0, y'(O) = 1 = The recurrence relation is on +2 for n 20. (Type an expression using n, cn, and Cn+1 as the variables.) and C1 = The constants are co = (Type integers or fractions.) The explicit formula for the coefficients is c2n and C2n + 1 for n 20. The particular solution in terms of elementary functions is y(x) =
The given differential equation is y"' + 4y = 0. To derive a recurrence relation, we assume that the solution has the form y = e^rx.
Substituting this in the differential equation, we get the characteristic equation r^3 + 4 = 0. Solving this, we get three roots r = -2i, 2i, 0.
So, the general solution is y = c1cos(2x) + c2sin(2x) + c3. Using the initial conditions y(0) = 0 and y'(0) = 1, we get c1 = 0 and c2 = 1/2.
Therefore, the solution is y = 1/2sin(2x) + c3.
Now, we can find the recurrence relation by writing c3 in terms of c2 and c1. We have c3 = y(0) - (1/2)sin(0) = 0. So, the recurrence relation is cn+2 = -4cn.
Using the initial conditions, we have c1 = 0 and c2 = 1/2. Therefore, the explicit formula for the coefficients is cn = (1/2)(-4)^n-2 for n ≥ 2.
Finally, the particular solution can be found by adding the general solution to the homogeneous solution. Since the roots are imaginary, the particular solution will have the form y = Acos(2x) + Bsin(2x).
Substituting this in the differential equation, we get A = 0 and B = -1/8.
So, the particular solution is y = -1/8sin(2x).
Therefore, the final solution in terms of familiar elementary functions is y = (1/2)sin(2x) - (1/8)sin(2x) = (3/8)sin(2x).
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You ask your best friend to lend you Rs.300 to buy your favorite toy she says she can lend you the money. Only if you give her an extra three rupees for every three months the past before you return it.
Your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
What is rate of interest?The amount a lender charges a borrower for the use of assets, such as money, consumer goods, or physical assets, is known as an interest rate. It is a fraction of the loan's principal, which is the amount borrowed to cover the cost of the purchase or the deposit made with a bank or other financial institution.
If your best friend is charging you an extra ₹3 for every three months that pass before you return the money, then after nine months, you will owe her an extra ₹9 in addition to the original ₹300.
So the total amount you must pay her if you return the ₹300 after nine months would be ₹309.
To calculate the annual rate of interest she is charging you, we can use the formula:
Annual Interest Rate = (Total Interest / Principal) x (12 / Number of Months)
Where the Principal is the original amount borrowed (₹300), the Total Interest is the extra amount you owe her (₹9), and the Number of Months is the time period for which you borrowed the money (9 months).
Plugging in the values, we get:
Annual Interest Rate = (9 / 300) x (12 / 9) = 0.04 or 4%
So, your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.
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The complete question is:
You ask your best friend to lend you ₹300 to buy your favourite toy. She says she can lend you the money only if you give her an extra ₹3 for every three months that pass before you return it. What is the total amount you must pay her if you return it after nine months? What is the annual rate of interest she is charging you?
Cuánto interés ganará lesli si presta l 5000 a pagar en 3años? al:5%simple anual. 10%simple anual. 5%compuesto anual
Lesli ganará $750 de interés si presta $5000 a pagar en 3 años al 5% de interés simple anual.
How much interest will Leslie earn if she lends $5000 to be paid back in 3 years at a simple annual interest rate of 5%, 10%, and a compound annual interest rate of 5%?Para calcular el interés que ganará Leslie en diferentes escenarios, consideraremos los siguientes casos:
A) Tasa simple anual del 5%:
El interés simple se calcula multiplicando el capital prestado por la tasa de interés y el tiempo en años.
Interés = Capital x Tasa x Tiempo
Interés = 5000 x 0.05 x 3 = $750
B) Tasa simple anual del 10%:
De manera similar al caso anterior, el interés se calcula como:
Interés = 5000 x 0.10 x 3 = $1500
C) Tasa compuesta anual del 5%:
En el caso de la tasa de interés compuesta, los intereses se acumulan en cada período. La fórmula para calcular el monto total es:
Monto = Capital x (1 + Tasa)^Tiempo
Monto = 5000 x (1 + 0.05)^3 = $5788.75
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if I draw a marble 48 times a white marble is selected 35 times ana a yellow one is selected 13 times what is the probability of the next one to be yellow
A 13%
B 27%
C 51%
D 63%
The probability of drawing a yellow marble on the next draw is 13/48, which is option A, 13%.
What is the probability of the next marble is yellow?The probability of drawing a yellow marble in the next draw depends on whether the drawing process is with or without replacement.
If the drawing process is with replacement, meaning that the marble is put back into the bag after each draw, then the probability of drawing a yellow marble remains the same at 13/48.
If the drawing process is without replacement, meaning that the marble is not put back into the bag after each draw, then the probability of drawing a yellow marble changes. After 48 draws, there are 35 white marbles and 13 yellow marbles left in the bag.
Therefore, the correct answer is A) 13%.
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Find the mad for this set of data.
swim team
name
age (years) mean
absolute
deviation
1
3
9
10
maddox
enrique
13
10
gloria
9
10
1
mckenna
10
.
10
0
10
10
0
mad =
?
✓ done
asher
hannah
danielle
9
10
1
10
10
0
katy
10
10
0
11
10
1
timothy
gentry
9
10
1
The MAD for this set of data is 0.8.
To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore,To find the MAD (Mean Absolute Deviation) for this set of data, we first need to find the mean of the ages:
Mean = (13 + 10 + 9 + 10 + 10 + 9 + 10 + 10 + 11 + 9) / 10 = 10.1
Next, we find the absolute deviation of each age from the mean:
|13 - 10.1| = 2.9
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|9 - 10.1| = 1.1
|10 - 10.1| = 0.1
|10 - 10.1| = 0.1
|11 - 10.1| = 0.9
|9 - 10.1| = 1.1
Then, we find the average of these absolute deviations:
MAD = (2.9 + 0.1 + 1.1 + 0.1 + 0.1 + 1.1 + 0.1 + 0.1 + 0.9 + 1.1) / 10 = 0.8
Therefore, the MAD for this set of data is 0.8.
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Raymond kept track of the number of hours that he spent
practicing the piano each week for several weeks. he
spent 24.8.6 and 5 hours
what is the range of the data set?
o a 8 hours
o b. 2 hours
o c. 5 hours
6 hours
The range of the data set is 19 hours. None of the options are correct.
The given data set represents the number of hours Raymond spent practicing the piano each week for several weeks: 24, 8, 6, and 5 hours. To calculate the range, follow these steps:
1. Identify the highest and lowest values in the data set.
- The highest value is 24 hours.
- The lowest value is 5 hours.
2. Subtract the lowest value from the highest value to find the range.
- Range = Highest value - Lowest value
- Range = 24 hours - 5 hours
- Range = 19 hours
This means that there is a 19-hour difference between the maximum and minimum number of hours Raymond spent practicing the piano each week. None of the options (a. 8 hours, b. 2 hours, c. 5 hours, and 6 hours) provided matches the correct answer, which is 19 hours.
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Evie rolls a fair number cube with faces labeled 1 through 6. She selects a marble from a bag were 3 are green and 1 is red. Select which point on the number line correctly represents the probability she
will land on an even number and then selects a green marble
The point on the number line that represents the probability of rolling an even number and selecting a green marble is 3/8, which is between 0.3 and 0.4 on the number line.
Will she land on an even number and then selects agreen marble?
The probability of rolling an even number is 3/6, which can be simplified to 1/2, because there are three even numbers (2, 4, and 6) out of six possible outcomes.
The probability of selecting a green marble from the bag is 3/4, because there are three green marbles out of four total marbles in the bag.
To calculate the probability of both events happening together (rolling an even number and selecting a green marble), you multiply the probabilities of each event:
P(even number and green marble) = P(even number) x P(green marble)
P(even number and green marble) = (1/2) x (3/4)
P(even number and green marble) = 3/8
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Consider right angle triangle ABC, right angled at B. If AC=17 units and BC+8 units determine all the trigonometric ratios of angle C
The trigonometric ratios of angle C are sin C = 15/17, cos C = 8/17, and tan C = 15/8.
Since triangle ABC is a right triangle with a right angle at B, and we know AC = 17 units (hypotenuse) and BC = 8 units (adjacent side to angle C), we can use the Pythagorean theorem to find the length of the remaining side, AB (opposite side to angle C).
The Pythagorean theorem states: AB² + BC² = AC²
Plugging in the values we know:
AB² + 8² = 17²
AB² + 64 = 289
To find AB:
AB² = 289 - 64 = 225
AB = √225 = 15 units
Now we can determine the trigonometric ratios of angle C:
1. sine (sin C) = opposite/hypotenuse = AB/AC = 15/17
2. cosine (cos C) = adjacent/hypotenuse = BC/AC = 8/17
3. tangent (tan C) = opposite/adjacent = AB/BC = 15/8
So the trigonometric ratios of angle C are:
sin C = 15/17, cos C = 8/17, and tan C = 15/8.
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Suppose you rent canoes to campers to go down the river for a living. Two summers ago you rented canoes for $35 a day and rented 150 canoes. To entice more campers last summer, you lowered the price by $5 and rented 25 more canoes. This summer you are considering lowering the price again based on the trend you noticed last summer. How much should you rent a canoe for to maximize revenue?
The optimal rental price to maximize revenue is $35, the same as two summers ago.
To determine the optimal canoe rental price to maximize revenue, we can use the concept of price elasticity of demand, which measures the responsiveness of demand to a change in price.
When the price of a product decreases, consumers tend to buy more of it, but the increase in demand may not be proportional to the decrease in price. The price elasticity of demand can help us estimate the percentage change in demand for a given percentage change in price.
In this case, we can use the data from the previous two summers to estimate the price elasticity of demand for canoe rentals. From the data provided, we know that a $5 decrease in price led to an increase of 25 canoes rented.
This means that the price elasticity of demand is approximately -5 (25/5). In other words, for every 1% decrease in price, we can expect a 5% increase in demand.
To determine the optimal rental price, we need to find the point where the marginal revenue from renting an additional canoe is equal to the marginal cost of renting it out. Assuming that the marginal cost of renting out an additional canoe is constant, we can use the price elasticity of demand to estimate the change in revenue due to a change in price.
If we increase the rental price by $1, we can expect to lose 5% of customers (assuming the same elasticity as last summer). This means that for every $1 increase in price, we will lose 7.5 (150*5%) customers. On the other hand, we will gain $35 in revenue for each of the remaining 142.5 canoes rented, resulting in a total revenue of $4,987.5.
If we decrease the rental price by $1, we can expect to gain 5% more customers, resulting in 157.5 canoes rented. However, we will also lose $30 in revenue for each of the 150 original customers who decide to rent at the lower price.
This means that for every $1 decrease in price, we will gain 7.5 customers but lose $4,500 in revenue. The total revenue at a rental price of $34 will be $4,827.5.
This price will result in the same number of customers as two summers ago but with a slightly higher revenue due to inflation.
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Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
71.38 in word form is Seventy-one and thirty-eight hundredths.
What is the decimal number?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.
To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.
For example: 0.25 can be written as "zero and twenty-five hundredths"
Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.
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Antonio and lizeth have a combined income of $83,366. they have 1099
forms which report $1,200 in interest. they also have $4,922 income from
rental property. they can reduce their income by $3,500. what is their
adjusted gross income?
Antonio and lizeth's adjusted gross income is $85,988.
To find their adjusted gross income, we need to start with their total income and subtract any adjustments.
Total income:
Combined income: $83,366
Interest income: $1,200
Rental income: $4,922
Total income before adjustments: $89,488
Adjustments:
Reduce income by $3,500
Adjusted gross income:
$89,488 - $3,500 = $85,988
Therefore, their adjusted gross income is $85,988.
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PART B Corey repeats his process 10 more times and gets these results: 3 green balls, 2 orange balls and 5 purple balls. Explain a possible reason for this outcome.
Based on the results of Corey repeating his process 10 more times, a possible reason for this outcome with 3 green balls, 2 orange balls, and 5 purple balls could be that there is a higher probability of selecting a purple ball compared to the other colors.
Here's a step-by-step explanation:
1. Corey conducted an experiment where he repeated a process 10 times.
2. During these trials, he obtained the following results: 3 green balls, 2 orange balls, and 5 purple balls.
3. The distribution of colors suggests that there is a higher probability of selecting a purple ball (5/10) than a green ball (3/10) or an orange ball (2/10).
4. This outcome could be due to factors such as a larger number of purple balls in the pool from which Corey is selecting or some other bias in the process that increases the likelihood of selecting a purple ball.
In conclusion, the possible reason for the outcome with 3 green balls, 2 orange balls, and 5 purple balls is that there might be a higher probability of selecting a purple ball during Corey's repeated trials.
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Sandra Waterman purchased a 52-week, $2,800 T-bill issued by the U.S. Treasury. The purchase price was $2,791.
a. What is the amount of the discount?
b. What is the amount Ms. Waterman will receive when the T-bill matures?
c. What is the current yield for the 52-week T-bill at the time of purchase?
Note: Enter your answer as a percent rounded to 2 decimal places.
(a) Discount amount is $6. (b) Maturity value is $2,200. (c) Current yield is 0.27%.
Here, we have,
A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.
A product may, for instance, be discounted by $10 from its list price or by 10% from its list price. A sales discount is a lower price that a company offers on a good or service.
Find out how to add discounts to invoices. A sales discount, usually referred to simply as a "discount," offers clients of a business a lower price on one or more of the goods or services being provided.
(a) Discount amount
= Maturity (face) value - Purchase price
=$2,200 - $2,194
=$6
(b) Maturity value
=Face value
=$2,200
(c) Current yield
=Discount amount / Purchase price
=$6 / $2,194
=0.0027, or 0.27%
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question in picture
Answer:
Trapezoid--------------------
First, plot the points and connect together in the given order.
See attached.
As we can see all sides are of different length but two sides seem to be parallel.
Let's find the slopes of segments BC and AD and compare:
m(BC) = (3 - 5)/(5- 1) = - 2/4 = - 1/2m(AD) = (- 8 - (-4))/(5 - (-3)) = - 4 / 8 = - 1/2As se see the slopes are same, so BC and AD are parallel.
Since we have a pair of parallel sides, the quadrilateral is a trapezoid.
find the value of x.
Answer:
x ~= 61.0°
Step-by-step explanation:
This is a trig question. The marked angle is unknown so we will use an inverse trig function to find a missing angle. On your calculator you may need to use the 2nd button or shift to get not just "cos" but the inverse cos. It might look like cos with a -1 exponent or "arccos" or "acos"
So the triangle is a right triangle. The angle is next to one of the given sides. "Next to" is called "adjacent" these mean the same thing. One side is adjacent to the angle. The other given side is the hypotenuse.
The trig function that puts together Adjacent and Hypotenuse is cosine.
cos (angle) = adj/hyp
We know the two sides. Fill them in.
cos (angle) = 31/64
We are looking for the angle.
cos x = 31/64
Use the inverse cos to find the angle.
cos^-1 (31/64) = x
This is a calculator activity. Unless your teacher has given you tables of values (this is how it was done before calculators) you have to use a calculator.
x = 61.0284677763
round to the nearest tenth.
x ~= 61.0
QUESTION 2 2.1. Consider the following pattern. 2.1.1 complete the table. (match-sticks were used to make each shape) (6 marks) Shape No. of match- sticks Rule 1 4 2 7 3 10 4 13 6 10 43 [24] 82 [6]
The completed table based on the given pattern is as follows: Shape 1: 4 matchsticks, Shape 2: 7 matchsticks, Shape 3: 10 matchsticks, Shape 4: 13 matchsticks, Shape 5: 24 matchsticks, Shape 6: 82 matchsticks.
To complete the table based on the given pattern, we need to identify the rule that determines the number of matchsticks for each shape.
Looking at the provided information, we can observe that the first four shapes follow a consistent rule, while the last two shapes seem to deviate from that rule.
For the first four shapes:
Shape 1: 4 matchsticks
Shape 2: 7 matchsticks (Shape 1 + 3 matchsticks)
Shape 3: 10 matchsticks (Shape 2 + 3 matchsticks)
Shape 4: 13 matchsticks (Shape 3 + 3 matchsticks)
Based on this pattern, it appears that each shape adds three additional matchsticks compared to the previous shape.
Now, let's analyze the last two shapes:
Shape 6: 43 matchsticks
Shape 7: 82 matchsticks
From Shape 4 to Shape 6, there is an increase of 3 matchsticks as expected.
However, from Shape 6 to Shape 7, there is an unexpected increase of 39 matchsticks.
Since the given information does not provide a clear pattern or rule for the last two shapes, we cannot accurately determine the number of matchsticks for those shapes.
Therefore, we can complete the table as follows:
Shape 1: 4 matchsticks
Shape 2: 7 matchsticks
Shape 3: 10 matchsticks
Shape 4: 13 matchsticks
Shape 5: (Unknown)
Shape 6: (Unknown).
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This table shows the time it takes students in Homeroom 203 to get to school each morning: 1 Time Less than 10 min 10-19 min 20-29 min 30-39 min 40-49 min 50 min or more Find the experimental probability of a student in this homeroom taking a certain number of minutes to get to school. Make a probability distribution for this data. Number of Students 3, 5, 10, 7, 2, 3
Answer:
Step-by-step explanation:
To find the experimental probability of a student in Homeroom 203 taking a certain number of minutes to get to school, we need to divide the number of students who take that amount of time by the total number of students in the homeroom.
The total number of students in the homeroom is:
3 + 5 + 10 + 7 + 2 + 3 = 30
The probability of a student taking less than 10 minutes to get to school is:
3/30 = 0.1 or 10%
The probability of a student taking 10-19 minutes to get to school is:
5/30 = 0.166 or 16.6%
The probability of a student taking 20-29 minutes to get to school is:
10/30 = 0.333 or 33.3%
The probability of a student taking 30-39 minutes to get to school is:
7/30 = 0.233 or 23.3%
The probability of a student taking 40-49 minutes to get to school is:
2/30 = 0.066 or 6.6%
The probability of a student taking 50 minutes or more to get to school is:
3/30 = 0.1 or 10%
To make a probability distribution, we can list the possible outcomes (in this case, the time it takes to get to school) and their corresponding probabilities:
Time (min) Probability
Less than 10 0.1
10-19 0.166
20-29 0.333
30-39 0.233
40-49 0.066
50 or more 0.1
Note that the probabilities add up to 1, which is what we expect for a probability distribution.
Find the total differential. z = 7x4y5 dz =
The total differential of the function z = 7x^4y^5 is dz is (28x^3y^5)dx + (35x^4y^4)dy.
To find the total differential of the function z = 7x^4y^5, we need to compute the partial derivatives with respect to x and y, and then express dz in terms of dx and dy.
Computing the partial derivative with respect to x,
∂z/∂x = 4 * 7x^3y^5 = 28x^3y^5
Computing the partial derivative with respect to y,
∂z/∂y = 5 * 7x^4y^4 = 35x^4y^4
Express dz in terms of dx and dy,
dz = (∂z/∂x)dx + (∂z/∂y)dy
dz = (28x^3y^5)dx + (35x^4y^4)dy
So, the total differential of the function z = 7x^4y^5 is dz = (28x^3y^5)dx + (35x^4y^4)dy.
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Jenny is planning an extended trip to russia.the table below shows a list of cities which she would like to visit during her stay, along with the amount of money she anticipates needing to spend on travel, lodging, and similar expenses in each city. all costs are given in russian rubles (rub). city cost (rub) izhevsk 4,721 novosibirsk 4,870 nizhny novgorod 6,920 moscow 5,485 chelyabinsk 5,217 saint petersburg 5,960 tolyatti 5,598 yaroslavl 4,901 even though jenny wants to go to each of these cities, her budget is only rub 33,000, so she recognizes that she must change her itinerary and choose not to visit some cities. which of the following pairs of cities will not put jenny back under budget if she drops them? a. moscow and chelyabinsk b. izhevsk and nizhny novgorod c. novosibirsk and saint petersburg d. yaroslavl and tolyatti
The pairs of cities that will not put Jenny back under budget if she drops them are:
a. Moscow and Chelyabinsk
b. Izhevsk and Nizhny Novgorod
To determine which pair of cities Jenny can drop without going over budget, we need to find the total cost of each pair and see if it exceeds her budget of rub 33,000.
a. Moscow and Chelyabinsk:
Total cost = 5,485 + 5,217 = 10,702 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Moscow and Chelyabinsk.
b. Izhevsk and Nizhny Novgorod:
Total cost = 4,721 + 6,920 = 11,641 rubles
This pair of cities is over budget, so Jenny cannot drop any other cities if she wants to visit both Izhevsk and Nizhny Novgorod.
c. Novosibirsk and Saint Petersburg:
Total cost = 4,870 + 5,960 = 10,830 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
d. Yaroslavl and Tolyatti:
Total cost = 4,901 + 5,598 = 10,499 rubles
This pair of cities is under budget, so Jenny can drop this pair without going over budget.
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Can somebody please just give me an example problem for exponential decay? I will give brainliest, thanks!
Example problem:
A radioactive substance has a half-life of 10 years. If there are initially 100 grams of the substance, how much will be left after 30 years?Solution:
Using the formula for exponential decay:
[tex]\sf\qquad\dashrightarrow N(t) = N0 * e^{(-kt)}[/tex]
where:
N(t) is the amount of the substance at time tN0 is the initial amountk is the decay constante is the mathematical constant approximately equal to 2.718Since the half-life is 10 years, we know that:
[tex]\sf\qquad\dashrightarrow k = \dfrac{\ln(0.5)}{10} = -0.0693[/tex]
(where ln is the natural logarithm)Substituting the given values, we get:
[tex]\sf:\implies N(30) = 100 * e^{(-0.0693 * 30)}[/tex]
[tex]\sf:\implies N(30) = 100 * e^{(-2.079)}[/tex]
[tex]\sf:\implies N(30) = 100 * 0.126[/tex]
[tex]\sf:\implies \boxed{\bold{\:\:N(30) = 12.6\: grams\:\:}}\:\:\:\green{\checkmark}[/tex]
Therefore, after 30 years, only 12.6 grams of the radioactive substance will be left.
PLEASE HELP
Find X
(7x+3) 78° 152°
By using concept of interior angle we find the value of X is -7.14 degrees.
The above problem involves finding the value of x in a triangle with two known angles measuring 78° and 152°.
The sum of the interior angles of any triangle is always 180°, so we can use this fact to set up an equation involving the third angle, which is given as 7x +3 degrees.
To solve for x, we first simplify the equation by combining the known angles:
78° + 152° + (7x + 3)° = 180°
Next, we can simplify by adding the two known angles:
230° + 7x° = 180°
This simplifies to:
7x° = -50°
Finally, we can solve for x by dividing both sides by 7:
x = [tex]\frac{-50^\circ}{7}$$[/tex]
Therefore, x is approximately -7.14 degrees.
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Given y = 5x^2 + 3x, find dy/dx when x = - 1 and dx/dt =5. dy/dt = (Simplify your answer.)
To dy/dx when x = - 1 and dx/dt =5. dy/dt =
dy/dt = -35.
To find dy/dt, first we need to find dy/dx. Given y = 5x^2 + 3x, we can differentiate y with respect to x:
[tex]dy/dx = d(5x^2 + 3x)/dx = 10x + 3[/tex]
Now, we need to find dy/dx when x = -1:
[tex]dy/dx(-1) = 10(-1) + 3 = -10 + 3 = -7[/tex]
We are given that dx/dt = 5. To find dy/dt, we use the chain rule:
[tex]dy/dt = dy/dx * dx/dt[/tex]
Substitute the values we found:
dy/dt = (-7) * (5) = -35
So, dy/dt = -35.
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