Answer: 640
Step-by-step explanation:
If 7 carpenters need to share 23 gallons of paint equally how many gallons of point will each carpenter use? between what two whole numbers does your answer lie?
Each carpenter will use 3.28 gallons of paint, which lies between the whole numbers 3 and 4.
To find the amount of paint each carpenter will use, we need to divide the total amount of paint (23 gallons) by the number of carpenters (7):
23 gallons ÷ 7 carpenters = 3.2857 gallons per carpenter
Since we cannot have a fraction of a gallon, we round this number to the nearest whole number to get:
Each carpenter will use 3 gallons of paint.
However, since 3.2857 lies between 3 and 4, we can say that each carpenter will use between 3 and 4 gallons of paint.
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The equation y=mx+b
is used to express the equation of a line. Which solution is a correct way to solve this equation for m
in terms of y
?
The correct way to solve this equation for m in terms of y is m = b - y/x
How to determine the valueIt is important to note that subject of formula is the variable that is made to stand alone in an equation.
It is described as the variable that is being worked out in an equation.
The subject of formula in an equation is worked to stand alone on on end of the equality sign.
Example of equations
x = y - 2
The variable 'x' is the subject of formula
From the information given, we have that;
y= mx+b
collect the terms
mx = b - y
Divide by the coefficient
m = b - y/x
The equation for m is m = b - y/x
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The complete question:
The equation y=mx+b is used to express the equation of a line. Which solution is a correct way to solve this equation for m in terms of y?
In a certain game you have to guess the number that your opponent writes down on a sheet of paper. you get five guesses. after each guess, your opponent has to tell you if your number is too high or too low. each guess is considered ____ the last guess.
After each guess, your opponent has to tell you if your number is too high or too low. each guess is considered fifth attempt the last guess.
Let's dive deeper into the game and understand it from a mathematical perspective. You are given five chances to guess the number your opponent has written down. In each turn, you can guess a number, and your opponent will tell you if the number you guessed is too high or too low. This information is crucial because it helps you to narrow down the possibilities of what the actual number could be.
Now, let's consider the game in mathematical terms. Suppose the number your opponent has written down is called "X." Your goal is to guess X in five attempts. Let's call these attempts "A1, A2, A3, A4, and A5." After each attempt, your opponent will give you a clue that the number you guessed is either too high or too low. Based on this feedback, you can eliminate some possibilities of what the number X could be.
As you can see, with each guess, you are narrowing down the possibilities of what the number X could be. The game is all about using logical reasoning and deduction to guess the number X correctly in five attempts. If you guess the number correctly before your fifth attempt, you win the game.
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The probability that Oscar gets heads and an even number is. The probability that Oscar gets tails and a prime number less than 4 is.
The probability of getting heads and an even number is 1/4, and the probability of getting tails and a prime number less than 4 is 1/6.
How to calculate coin toss probabilities?To solve this, we need to use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.
Let's first find the probability of getting heads and an even number. Since there are two equally likely outcomes when flipping a coin (heads or tails), and three equally likely outcomes when rolling a die (1, 2, 3, 4, 5, or 6), the probability of getting heads and an even number is:
P(heads and even) = P(heads) x P(even)
= 1/2 x 3/6
= 1/4
Next, let's find the probability of getting tails and a prime number less than 4. The prime numbers less than 4 are 2 and 3. So, the probability of getting tails and a prime number less than 4 is:
P(tails and prime) = P(tails) x P(prime)
= 1/2 x 2/6
= 1/6
Therefore, the probability that Oscar gets heads and an even number is 1/4, and the probability that Oscar gets tails and a prime number less than 4 is 1/6.
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PLS HELP ASAP 50 POINTS AND BRAINLEIST!!!
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. what are the relationships between them?
Answer:
See explanation.
Step-by-step explanation:
The arc BX, central angle BCX, and inscribed angle BNX are connected through the following relationships:
1. The central angle BCX subtends the arc BX. This means that the central angle is formed by two radii connecting the center of the circle to the endpoints of the arc BX.
2. The inscribed angle BNX subtends the same arc BX. This means that the inscribed angle is formed by two chords connecting a point on the circumference of the circle to the endpoints of the arc BX.
3. The relationship between the central angle BCX and the inscribed angle BNX is given by the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of the central angle subtending the same arc. In other words, if θ is the measure of the central angle BCX and α is the measure of the inscribed angle BNX, then:
[tex]\alpha =\frac{1}{2}[/tex] θ
(3. 5 points) use the given data in problem 33 (page 302) to answer the following questions. Assume that population data follow normal distribution. (a) (1. 5 points) calculate a two-sided 95% confidence interval for true average degree of polymerization. (b) (one points) does the interval suggest that 440 is a plausible value for true average degree of polymerization? explain. (c) (one point) does the interval suggest that 450 is a plausible value for true average degree of polymerization? explain
If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have __________ solutions.
two
one
no
infinite
If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.
Since the parabola opens upward, its vertex is the minimum point, and therefore, it will have only one solution.
A parabola is a U-shaped curve in mathematics that can be formed by the graph of a quadratic function. It is a type of conic section, along with circles, ellipses, and hyperbolas.
Mathematically, a parabola can be defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. The focus lies on the axis of symmetry of the parabola, and the directrix is perpendicular to the axis of symmetry.
If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.
Your answer: one
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Sariah has just begun training for a half-marathon, which is Latex: 13. 1 13. 1 miles. Since she was on vacation, she started the training program later than the rest of her running club. There are Latex: 6 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran Latex: 3 3 miles. She ran Latex: 4. 5 4. 5 miles the second week and Latex: 6 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance?
If she continues to increase the length of her runs the same way, it will not be enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.
Sariah has just begun training for a half-marathon, which is 13.1 miles. There are 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week.
To determine if there is enough time left in the training program for her to get up to half-marathon distance, let's analyze the pattern of her weekly increases in distance:
Week 2 - Week 1 = 4.5 miles - 3 miles = 1.5 miles increase
Week 3 - Week 2 = 6 miles - 4.5 miles = 1.5 miles increase
Sariah is consistently increasing her weekly mileage by 1.5 miles. With 3 weeks of training already completed, she has 3 more weeks to go. Let's see if she can reach the half-marathon distance of 13.1 miles:
Week 4: 6 miles + 1.5 miles = 7.5 miles
Week 5: 7.5 miles + 1.5 miles = 9 miles
Week 6: 9 miles + 1.5 miles = 10.5 miles
After 6 weeks of training, Sariah will have increased her longest run to 10.5 miles. Unfortunately, this is not enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.
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A worker in a computer factory compared these measurements. 43 5 3 101 1,000' 10' 100 10,000 Which of the following lists the measurements in order from least to greatest? 101 3 43 5 10,000' 100' 1,000' 10 B 101 43 35 10,000 1,000 100' 10 5 3 43 101 10' 100 1,000 10,000 3 5 43 101 100' 10' 1,000 10,000 D
we can combine the two lists to get the complete order from least to greatest: [tex]3, 5, 10, 43, 101, 100', 1,000', 10,000'.[/tex]Thus, option B is correct.
What is the order from least to greatest?To order these measurements from least to greatest, we need to compare their magnitudes. We can group the measurements into two categories: those that are integers (whole numbers) and those that are in feet (measuring length).
Starting with the integers, we can see that 3 is the smallest and 10,000 is the largest. So, the integers can be ordered as follows: [tex]3, 5, 10, 43, 101, 10,000.[/tex]
Next, we can order the measurements in feet. 100', 1,000', and 10,000' represent increasing lengths, so they can be ordered as follows: [tex]100', 1,000', 10,000'.[/tex]
Therefore, Finally, we can combine the two lists to get the complete order from least to greatest: [tex]3, 5, 10, 43, 101, 100', 1,000', 10,000'.[/tex]
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Grading categories: creating equations, reasoning with equations, linear models
mr. bro opened a chick-fil-a on white plains road, and ms. kramer opened a popeye’s across the street. both had to borrow money to open their fast food franchises. after 500 customers, mr. bro was still $4000 in debt. by the time he had served 3000 customers, he was ahead $1000.
after 2000 customers, ms. kramer still owed $6000 to the bank. however, after 4500 customers, she was ahead by $1500.
which restaurant would you rather own? support your answer with mathematical evidence. you must show all work and math calculations. some things we have to see in your solution:
amount each had to borrow to open their restaurant
amount of customers they needed to break even (break even means the total profit is $0)
the solution to your system of equations showing when one restaurant would produce more total income than the other
The calculations for break even point is 5000 customers, and the solution to the system of equations were shown. Mr. Bro's Chick-fil-A franchise would be more profitable as it required less initial borrowing, broke even sooner and generated more income than Ms. Kramer's Popeye's franchise.
To solve this problem, we need to set up a system of equations. Let's use "b" to represent the amount each owner had to borrow to open their restaurant, "x" to represent the number of customers, and "y" to represent the total profit.
For Mr. Bro's Chick-fil-A
After 500 customers: y = -4000
After 3000 customers: y = 1000
We can use these two equations to find the slope of the line: m = (1000 - (-4000)) / (3000 - 500) = 1.8
Using the point-slope form of a line y - (-4000) = 1.8(x - 500)
Simplifying, we get: y = 1.8x - 3400
For Ms. Kramer's Popeye's
After 2000 customers: y = -6000
After 4500 customers: y = 1500
We can use these two equations to find the slope of the line: m = (1500 - (-6000)) / (4500 - 2000) = 1.4
Using the point-slope form of a line: y - (-6000) = 1.4(x - 2000)
Simplifying, we get: y = 1.4x - 5400
Now, we can set the two equations equal to each other to find the break-even point
1.8x - 3400 = 1.4x - 5400
0.4x = 2000
x = 5000
This means that both restaurants need to serve 5000 customers to break even.
To compare the total income of the two restaurants, we can find the y-value for both equations when x = 5000
Chick-fil-A: y = 1.8(5000) - 3400 = $5,000
Popeye's: y = 1.4(5000) - 5400 = $1,000
From this analysis, it is clear that owning Chick-fil-A is more profitable than owning Popeye's.
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Calculate the perimeter and area of the shaded region in the drawing of two circles at right. Round to the nearest tenth. Show all work. 10 5cm 21 cm
The perimeter of the shaded region is approximately 85.67 cm The area of the shaded region is approximately 91.84 cm² (rounded to the nearest tenth).
To calculate the perimeter and area of the shaded region, we first need to find the radius of each circle.
The larger circle has a diameter of 21 cm, which means its radius is 10.5 cm (half of the diameter). The smaller circle has a diameter of 10 cm, so its radius is 5 cm.
To find the perimeter of the shaded region, we need to add the circumference of both circles and subtract the overlap (the length of the shared segment). The circumference of the larger circle is 2π(10.5) ≈ 65.97 cm, and the circumference of the smaller circle is 2π(5) ≈ 31.42 cm.
To find the length of the shared segment, we can use the Pythagorean theorem. The distance between the centers of the circles is 15 cm (the sum of the radii), so we can form a right triangle with legs of 10.5 cm and 5 cm. Using the Pythagorean theorem, we get:
c² = a² + b²
c² = 10.5² + 5²
c² ≈ 137.25
c ≈ 11.72
So the length of the shared segment is approximately 11.72 cm.
Therefore, the perimeter of the shaded region is approximately 65.97 + 31.42 - 11.72 = 85.67 cm (rounded to the nearest tenth).
To find the area of the shaded region, we need to subtract the area of the smaller circle from the area of the larger circle, and then subtract the area of the overlap (the area of the shared segment).
The area of the larger circle is π(10.5)² ≈ 346.36 cm², and the area of the smaller circle is π(5)² ≈ 78.54 cm².
To find the area of the shared segment, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where θ is the central angle of the sector. In this case, the sector has a central angle of 2cos⁻¹(5/10.5) ≈ 105.2°, so:
A = (105.2/360)π(10.5)²
A ≈ 91.84 cm²
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Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
r = 4 cm
4 √2 cm
[? ]%
round to the nearest tenth of a percent.
The probability that a randomly selected point within the circle falls in the red shaded area is approximately 49.3%.
To find the probability that a randomly selected point within the circle falls in the red shaded area, we need to find the ratio of the area of the red shaded region to the total area of the circle.
The area of the circle is π[tex]r^{2}[/tex] = π[tex](4cm)^{2}[/tex] = 16π [tex]cm^{2}[/tex].
The diagonal of the square is equal to the diameter of the circle, which is 8cm. Therefore, the length of each side of the square is 4√2 cm.
The area of the square is (4√2 [tex]cm)^{2}[/tex] = 32 [tex]cm^{2}[/tex].
The area of the red shaded region is the difference between the area of the circle and the area of the square, which is 16π - 32 [tex]cm^{2}[/tex].
So, the probability that a randomly selected point falls in the red shaded area is:
[(16π - 32)/16π] × 100% ≈ 49.3%
Therefore, the probability that a randomly selected point within the circle falls in the red shaded area is approximately 49.3%.
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Suzie paid a total of $324 for c tickets to a rock festival. How much does each ticket cost
If for "c" tickets, Suzie paid an amount of $324, then the cost of each ticket is represented by "324/c".
The number of tickets that Suzie bought is = c tickets, and
Let "x" be the cost of "each-ticket for "rock-festival".
The total amount spent for "c" tickets is = $324,
Therefore, we can write the cost-equation as;
⇒ c × x = 324,
To find the value of "x", we solve for it by dividing both sides of the equation by "c":
⇒ x = 324/c,
So, the cost of each ticket is $324 divided by the number of tickets "c" that Suzie bought.
Therefore, Each tickets cost is 324/c.
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Pls help
the sugar sweet company is going to transport its sugar to market. it will cost $6500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.
let c represent the total cost (in dollars), and let s represent the amount of sugar (in tons) transported. write an equation relating c to s. then use this equation to find the total cost to transport 12 tons of sugar. please give the equation used and total cost to transport 12 tons of sugar.
equation:
total cost to transport 12 tons of sugar:
The total cost to transport 12 tons of sugar is $8,600. The equation relating the total cost (c) to the amount of sugar transported (s) is: c = 175s + 6500
To find the total cost to transport 12 tons of sugar, we substitute s = 12 into the equation: c = 175(12) + 6500, c = 2100 + 6500, c = 8600
Therefore, the total cost to transport 12 tons of sugar is $8,600.
The equation shows that the total cost increases by $175 for each additional ton of sugar transported, and there is also a fixed cost of $6,500 for renting the trucks, which is added to the variable cost.
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Use ≈ 0.4307 and ≈ 0.6826 to approximate the value of each expression. 11. log5 5/3
The value of logarithm log5 5/3 is approximately equal to 0.3174.
Using the approximation of ≈ 0.4307 for log5 2 and ≈ 0.6826 for log5 3, we can approximate the value of log5 5/3 by subtracting the two approximations.
log5 5/3 = log5 5 - log5 3 ≈ 1 - 0.6826 ≈ 0.3174
To explain further, logarithms are a way to express the relationship between exponential growth or decay and the input values. In this case, we are using the base of 5 to represent the exponent and trying to find the logarithm of 5/3.
By using the approximation values of log5 2 and log5 3, we can estimate the value of log5 5/3 by subtracting the two approximations. This approximation is useful in situations where we need a quick estimate of a logarithmic function without having to do complex calculations.
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trains arrive at a specified stop at 15-minute intervals starting at 7am. if a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that she waits a) less than 5 minutes for the train b) more than 10 minutes for the train
The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.
Probability that the passenger waits less than 5 minutes for the train,
Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.
Distribution is uniform,
PDF is a constant function over the interval [7:00am, 7:30am] .
With height 1 / (30 minutes - 0 minutes) = 1/30.
Area under the PDF from 7:00am to 7:05am is,
Probability of waiting less than 5 minutes
= area under PDF from 7:00am to 7:05am
= (1/30) ×(5 - 0) minutes
= 1/6
Probability that the passenger waits less than 5 minutes for the train is 1/6.
Probability that the passenger waits more than 10 minutes for the train is
= Area under the PDF from 7:00am to 7:30am - area under the PDF from 7:00am to 7:10am.
Area under PDF from 7:00am to 7:30am
= (1/30) × (30 - 0) minutes
= 1
Area under PDF from 7:00am to 7:10am
= (1/30) × (10 - 0) minutes
= 1/3
Area under PDF from 7:10am to 7:30am
= 1 - 1/3
= 2/3
Probability of waiting more than 10 minutes
= area under PDF from 7:10am to 7:30am
= (1/30) × (30 - 10) minutes
= 2/3
Probability that the passenger waits more than 10 minutes for the train is 2/3.
Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.
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Solve the following equation:
8 x five sixths
To solve the equation 8 x five sixths, we first convert the fraction to a decimal by dividing the numerator (5) by the denominator (6), which gives us 0.83.
We then multiply 8 by 0.83 to get the final answer of 6.64. Therefore, 8 x five sixths = 6.64.
In general, to multiply a whole number by a fraction, we can convert the fraction to a decimal and then multiply the whole number by the decimal.
Alternatively, we can convert the whole number to a fraction with a denominator of 1 and then multiply the two fractions by cross-multiplying and simplifying.
In this case, we could also write 8 as 8/1 and multiply it by 5/6 to get (8 x 5)/(1 x 6) = 40/6, which simplifies to 6 and 4/6 or 6.67 (rounded to two decimal places). However, converting the fraction to a decimal is often simpler and more practical.
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Javier and ellema both get there cars wash and filled there gas tanks at the same gas station javier pays 26. 96 for a car wash and 5. 6 gallon of gas. Ellema pays 48. 62 for a car wash and 13. 2 gallons of gas
We can start by finding the cost per gallon of gas for each person:
Javier: 5.6 gallons of gas for $26.96, so cost per gallon = 26.96/5.6 = $4.79/gallon
Ellema: 13.2 gallons of gas for $48.62, so cost per gallon = 48.62/13.2 = $3.68/gallon
Now we can find the cost of just the car wash for each person:
Javier: $26.96 - (5.6 gallons * $4.79/gallon) = $-1.344, which doesn't make sense. It's possible there was a mistake in the numbers given.
Ellema: $48.62 - (13.2 gallons * $3.68/gallon) = $1.958, which also doesn't make sense. There may be an error in the given information.
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Part A: Sydney made $18. 50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0. 50 and received a $3 tip from a neighbor. Write an equation to represent this situation. (4 points)
Part B: Daria made a profit of $21. 00 selling lemonade. She sold her lemonade for $0. 75 per cup, received a tip of $3 from a neighbor, but also had to buy each plastic cup she used for $0. 10 per cup. Write an equation to represent this situation. (4 points)
Part C: Explain how the equations from Part A and Part B differ. (2 points)
Part A: The equation to represent this situation is: 0.50x + 3 = 18.50
Part B: The equation to represent this situation is: 0.75x + 3 - 0.10x = 21.00
Part C: The equations differ in the following ways:
1. Sydney's equation involves only the price per cup and the tip, while Daria's equation also considers the cost of the plastic cups.
2. The price per cup for Sydney and Daria are different.
Part A: The equation to represent this situation is:
18.50 = 0.50x + 3
Where x represents the number of cups of lemonade sold.
Part B: The equation to represent this situation is:
21.00 = 0.75x + 3 - 0.10x
Where x represents the number of cups of lemonade sold.
Part C: The equations from Part A and Part B differ in that Part B takes into account the cost of each plastic cup used to serve the lemonade, while Part A only considers the revenue from selling each cup of lemonade and the tip received. This means that the profit in Part B is calculated after deducting the cost of each plastic cup from the revenue earned, while the profit in Part A does not account for any costs incurred.
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which fraction is equivalent to 0.48 in simplest form?
[A] 12/25
[B] 12/50
[c] 24/50
[D] 48/100
Answer:
0.48 = 48/100
48/100 ÷ 4/4 = 12/25
0.48 = 12/25 =A
You doing practice 2
Answer:
there is a lot of words
Step-by-step explanation:
6209
The floor tiles in the jackson family’s kitchen are squares
that measure 8 3
··4
inches to a side. each grid square in the
drawing measures 1
··4
inch to a side.
which is the scale of the drawing?
The scale of the drawing is 1:33 1/3, because the actual size of each grid square in the kitchen floor tile is 33 1/3 times larger than its size in the drawing.
What is the ratio of architectural drawing?The scale of a architectural drawing represents the proportional relationship between the size of an object in the drawing and its actual size in real life.
In this case, the floor tiles in the Jackson family's kitchen are square with a length of 8 3/4 inches on each side, while each grid square in the drawing measures 1/4 inch on each side.
To determine the scale of the drawing, we need to find the ratio between the actual size of a grid square and its size in the drawing.
Using proportions, we can set up an equation to solve for the scale. Let x be the scale of the drawing, then we have:
8 3/4 inches / (1/4 inch) = x
Simplifying the left side of the equation gives us:
35 inches = x
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3. DINING Only 6 out of 100 Américans
say they leave a tip of more than 20%
for satisfactory service in a restaurant.
Out of 1,500 restaurant customers, how
many would you expect to leave a tip of
more than 20%?
The number of Americans to leave a tip of more than 20% in 1500 is 90
Calculating the number of AmericansIf only 6% of Americans leave a tip of more than 20% for satisfactory service in a restaurant, we can assume that the same proportion of restaurant customers will do so.
Therefore, out of 1,500 restaurant customers, we would expect:
6% of 1,500 = (6/100) x 1,500 = 90
So we would expect 90 restaurant customers to leave a tip of more than 20%.
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Bob would like to get his debt-to-income (dti) ratio down to 36%. his current monthly expenses are outlined in the chart below. he would like to lower his dti by paying off some of his credit card debt, lowering his combined minimum monthly credit card payment. what would bob's minimum monthly credit card payment need to be in order to reach his dti goal of 36%? bob's monthly debt and income housing: mortgage $1,250.00 (including mortgage insurance and property taxes) credit: auto loan $349.00 credit cards (combined) $348.00(minimum) income: manager $4,800.00 interest $130.00 a. $175.80 b. $129.00 c. $228.00 d. $274.80
Bob's minimum monthly credit card payment needs to be B) $129.00 to reach his dti goal of 36%.
Bob's total monthly debt payments are $1,947.00 ($1,250.00 mortgage + $349.00 auto loan + $348.00 credit cards). To achieve a dti ratio of 36%, his total monthly debt payments should be no more than $1,728.00 ($4,800.00 * 36%).
Therefore, he needs to reduce his monthly credit card payment by $219.00 ($1,947.00 - $1,728.00). Since his current minimum monthly credit card payment is $348.00, he needs to reduce it to d) $129.00 ($348.00 - $219.00) to reach his dti goal.
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Find the midpoint of the line segment joining (-4,-2) and (2,8) please show how u got your answer!!!
Answer:
(1,3)
Step-by-step explanation:
The midpoint formula is:
[tex](\frac{x1+x2}{2}),(\frac{y1+y2}{2})[/tex]
We have our 2 points, (-4,-2) and (2,8).
For this sake and for this explanation, point 1 is (-4,-2), and point 2 is (2,8).
We can substitute in our values:
[tex](\frac{-4+2}{2}),(\frac{-2+8}{2})[/tex]
substitute
[tex](\frac{2}{2}),(\frac{6}{2})[/tex]
Our midpoint is located at (1,3)
Hope this helps! :)
Answer:
(-1,3)
Step-by-step explanation:
To find the midpoint of a line segment, you want to find the change in x and y.
From (-4,-2) to (2,8), you move right by 6 and up by 10.
The midpoint is exactly half of this, meaning right by 3 and up by 5.
Therefore, the midpoint is (-1,3).
The largest single rough diamond ever found, the cullinan diamond, weighed 3106 carats; how much does the diamond weigh in miligrams? in pounds? (1 carat - 0. 2 grams)
the diamond weighs mg.
the diamond weighs lbs
If the largest single rough diamond ever found, the Cullinan diamond, weighed 3106 carat, it weighs approximately 621,200 milligrams and 1.37 pounds.
The Cullinan Diamond, the largest single rough diamond ever found, weighed 3,106 carats. To convert its weight to milligrams and pounds, we'll use the conversion factor of 1 carat = 0.2 grams.
First, convert carats to grams:
3,106 carats * 0.2 grams/carat = 621.2 grams
Next, convert grams to milligrams:
621.2 grams * 1,000 milligrams/gram = 621,200 milligrams
Lastly, convert grams to pounds:
621.2 grams * 0.00220462 pounds/gram ≈ 1.37 pounds
So, the Cullinan Diamond weighs approximately 621,200 milligrams and 1.37 pounds.
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The diameter of circle a is 8.7 units. find the circumference of the circle.
a. 17.4 units
b. 75.69 units
c. 8.7 units
d. 26.1 units
The circumference of a circle with a diameter of 8.7 units is approximately 27.318 units, calculated using the formula Circumference = πd. So, the correct answer is D).
The formula for the circumference of a circle is given by
Circumference = πd
where d is the diameter of the circle.
Substituting the given value of the diameter of circle a, we get:
Circumference = π x 8.7
Using the approximation of π = 3.14, we get
Circumference = 3.14 x 8.7
Circumference = 27.318 units (rounded to three decimal places)
Therefore, the circumference of the circle with a diameter of 8.7 units is approximately 27.318 units. So, the correct option is D).
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--The given question is incomplete, the complete question is given
" The diameter of circle a is 8.7 units. find the circumference of the circle.
a. 17.4 units
b. 75.69 unit
c. 8.7 units
d. 27.318 units "--
3. let f be a differentiable function on an open interval i and assume that f has no local minima nor local maxima on i. prove that f is either increasing or decreasing on i.
Shown that if f has no local minima nor local maxima on i, then f is either increasing or decreasing on i.
Since f has no local minima nor local maxima on i, it means that for any point x in i, either f is increasing or decreasing in a small interval around x. In other words, either f'(x) > 0 or f'(x) < 0 for all x in i.
Now suppose there exist two points a and b in i such that a < b and f(a) < f(b). We want to show that f is increasing on i.
Consider the interval [a,b]. By the Mean Value Theorem, there exists a point c in (a,b) such that f'(c) = (f(b) - f(a))/(b - a). Since f(a) < f(b), we have (f(b) - f(a))/(b - a) > 0, which implies f'(c) > 0. Since f'(x) > 0 for all x in i, it follows that f is increasing on [a,c] and on [c,b]. Therefore, f is increasing on i.
A similar argument can be made if f(a) > f(b), which would imply that f is decreasing on i.
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Use the diagram to match the terms with the correct example.
1. C is the center
2. EF is a secant line
3. AD is the diameter
4. CD is the radius
5. FD is the arc
6. The region bounded by AC, BC and arc AB is a segment
7. The region bounded by FE and arc FE is a sector
8. EF is the chord
9. GF is the tangent line
How to match the statementTo match the statements, we need to know the following;
The diameter of a circle, is a line cutting through the center and bisects it into equal halveschord of a circle is a line segment that joins any two points on the circumference of the circleSegment of a circle is a region that is bounded by a chordA secant line is a straight line that intersects a circle in two pointsLearn about circles at: https://brainly.com/question/24375372
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Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, `x` kilometres, between Hong Kong and the different destinations and the corresponding airfare, `y`, in Hong Kong dollars (HKD)
The cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.
We start by calculating the Porson's product-moment correlation coefficient between the distance and airfare data. The value of the correlation coefficient ranges from -1 to +1. A value of -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation.
In this case, the correlation coefficient between distance and airfare for Galois Airways flights is 0.948, indicates a strong positive correlation between the distance and airfare.
The regression line is expressed as:
y = a + bx
where y is the dependent variable (airfare), x is the independent variable (distance), a is the intercept (the value of y when x is zero), and b is the slope (the change in y for a one-unit change in x).
The regression equation for Galois Airways flights is:
y = 553.51 + 0.292x
Now, we can use the regression equation to estimate the cost of a flight from Hong Kong to Tokyo, which is 2900 km away.
y = 553.51 + 0.292(2900) = 1429.99 HKD
Therefore, we estimate that the cost of a flight from Hong Kong to Tokyo with Galois Airways is 1429.99 HKD.
Finally, we need to explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo. We can do this by examining the assumptions of linear regression. The two main assumptions are that there is a linear relationship between the variables, and that the residuals (the differences between the actual and predicted values) are normally distributed with constant variance.
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Complete question is Galois Airways has flights from Hong Kong International Airport to different destinations. The following table shows the distance, x kilometres, between Hong Kong and the different destinations and the corresponding airfare, y, in Hong Kong dollars (HKD) Destination Bali, Sydney, Bengaluru. Auckland, Bangkok, Indonesia Australia India Singapore New Thailand Zealand 3400 7400 4000 2600 9200 1700 Distance x, (km Airfare y, (HKD) 1550 3600 2800 1300 4000 1400 The Porson's product-moment correlation coefficient for this data is 0.948, correct to three significant figures. Use your prophio display calculator to find the equation of the regression line y on x. b. The distance from Hong Kong to Tokyo is 2900 km. Use your regression equation to estimate the cost of a flight from Hong Kong to Tokyo with Calois Airways. c. Explain why it is valid to use the regression equation to estimate the airfare between Hong Kong and Tokyo.