Answers
Amount Due at Maturity a. $102,000, b. $30,100, c. $62,620, d. $42,930, e. $40,700.
Describe Interest?Interest is the cost of borrowing money, typically expressed as a percentage of the borrowed amount, called the principal. It is the amount charged by a lender to a borrower for the use of money over a certain period of time. Interest can also refer to the amount earned on money that is invested, such as in a savings account or a bond. The rate of interest depends on factors such as the level of risk associated with the loan, the length of the loan period, and the market rate of interest at the time of borrowing. The amount of interest paid or earned can be calculated using various formulas, including simple interest and compound interest.
To determine the due date and amount of interest due at maturity for each note, we can use the following formula:
Interest = Principal x Rate x Time
where Principal is the face amount of the note, Rate is the annual interest rate, and Time is the time in years (based on a 360-day year).
a. January 5, $100,000, 6%, 120 days
Due Date: May 5
Time: 120/360 = 1/3 year
Interest = $100,000 x 0.06 x 1/3 = $2,000
Amount Due at Maturity = Principal + Interest = $100,000 + $2,000 = $102,000
b. February 15, $30,000, 4%, 30 days
Due Date: March 17 (assuming non-leap year)
Time: 30/360 = 1/12 year
Interest = $30,000 x 0.04 x 1/12 = $100
Amount Due at Maturity = Principal + Interest = $30,000 + $100 = $30,100
c. May 19, $62,000, 8%, 45 days
Due Date: July 3
Time: 45/360 = 1/8 year
Interest = $62,000 x 0.08 x 1/8 = $620
Amount Due at Maturity = Principal + Interest = $62,000 + $620 = $62,620
d. August 20, $42,400, 5%, 90 days
Due Date: November 18
Time: 90/360 = 1/4 year
Interest = $42,400 x 0.05 x 1/4 = $530
Amount Due at Maturity = Principal + Interest = $42,400 + $530 = $42,930
e. October 19, $40,000, 7%, 90 days
Due Date: January 17
Time: 90/360 = 1/4 year
Interest = $40,000 x 0.07 x 1/4 = $700
Amount Due at Maturity = Principal + Interest = $40,000 + $700 = $40,700
Therefore, the due date and amount of interest due at maturity for each note are as follows:
a. Due Date: May 5, Interest: $2,000, Amount Due: $102,000
b. Due Date: March 17, Interest: $100, Amount Due: $30,100
c. Due Date: July 3, Interest: $620, Amount Due: $62,620
d. Due Date: November 18, Interest: $530, Amount Due: $42,930
e. Due Date: January 17, Interest: $700, Amount Due: $40,700
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Related Questions
Use elimination and back substitution to solve for x and y in the system of linear equations below.
Answers
Answer:
(-2,-8)
Step-by-step explanation:
6x + 7y = -68
-2x + 7y = -52
Time the first equation by -1
-6x - 7y = 68
-2x + 7y = -52
-8x = 16
x = -2
Now put -2 in for x and solve for y
6(-2) + 7y = -68
-12 + 7y = -68
7y = -56
y = -8
Let's Check
6(-2) + 7(-8) = -68
-12 - 56 = -68
-68 = -68
So, (-2, -8) is the correct answer.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
the true statements about the circle equation are:
The center of the circle lies on the x-axis. The radius of the circle is 3 units.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Which statements are true about our circle?Remember that the equation of a circle whose center is at(a, b) and has a radius of R units is:
(x -a )²+ (y - b)² = R²
Here the equation is:
x² + y² - 2x - 8 = 0
Completing squares in x we will get:
(x² - 2x) + y² - 8 = 0
(x² - 2x + 1) -1 + y² - 8 =
(x - 1)² + (y - 0)² = 9 = 3²
So the center is (1, 0) and the radius is 3, so the true statements are:
The center of the circle lies on the x-axis. The radius of the circle is 3 units.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Learn more about circle equations at:
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the half life of a drug in the bloodstream is 3 hours. if you took a 600mg dose how much of the drug will remain after one day.will remain after one day? i got 2mg please help
Answers
Say no to drugs. It is not good for the body.
Quadrilateral ABCD has vertices A(2,4), B(5, 4), C(8, 1), and D(5, 1). Graph the image of quadrilateral ABCD after a dilation centered at D with a scale factor of
followed by a reflection in the line x = 1.
Answers
The final image of quadrilateral ABCD after a dilation centered at D with a scale factor of 2, followed by a reflection in the line x = 1, is attached below, where A', B', C', and D' are the new points after the transformation.
What are Transformation and Reflection?
Single or multiple changes in a geometrical shape or figure are called Geometrical Transformation. A geometrical transformation in which a geometrical figure changes his position to his mirror image about some point or line or axis is called Reflection.
First, we need to apply the dilation centered at point D with a scale factor of 2. To do this, we will multiply the coordinates of each point by 2, with D as the center of dilation.
Point D remains the same since the scale factor does not affect it:
D(5, 1)
To find the new coordinates of points A, B, and C, we will use the following formula:
New Point = Center of Dilation + Scale Factor * (Original Point - Center of Dilation)
For point A:
New A = D + 2 * (A - D)
New A = (5, 1) + 2 * (-3, 3)
New A = (-1, 7)
For point B:
New B = D + 2 * (B - D)
New B = (5, 1) + 2 * (0, 3)
New B = (5, 7)
For point C:
New C = D + 2 * (C - D)
New C = (5, 1) + 2 * (3, -3)
New C = (11, -5)
Now that we have the new coordinates, we can reflect the image in the line x = 1. To do this, we will reflect each point across the line x = 1 by replacing the x-coordinate with its reflection across the line.
The equation of line x = 1 is a vertical line passing through x = 1. Therefore, to reflect a point across this line, we need to find the difference between the x-coordinate of the point and the line (which is 1), and subtract that difference from the line.
For point D:
D(5, 1) reflected in x = 1 is (2, 1)
For point A:
New A(-1, 7) reflected in x = 1 is (-3, 7)
For point B:
New B(5, 7) reflected in x = 1 is (-3, 7)
For point C:
New C(11, -5) reflected in x = 1 is (13, -5)
Hence, The final image of quadrilateral ABCD after a dilation centered at D with a scale factor of 2, followed by a reflection in the line x = 1, is attached below, where A', B', C', and D' are the new points after the transformation.
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The area of a circle is the same as the area
of a square whose side is 4 centimeters. The radius of the circle is closest to
F. 16 cm
G. 8 cm
H. 4 cm
J. 2 cm
K. 1 cm
Answers
If they have the same area, then both the square and the circle would be 16 cm^2.
The answer is F.
In the figure, PA and PB are tangent to circle O and PD bisects BPA. The figure is not drawn to scale. HELP PLSS
Answers
The measure of the angle POB is equal to 46°. Thus, option C is correct.
What is a circle, exactly?The cοllectiοn οf all pοints in the plane that make up a circle are all equally spaced frοm a certain pοint knοwn as the "centre," making the fοrm a clοsed twο-dimensiοnal shape. The symmetry line οf reflectiοn is fοrmed by each line that traverses the circle.
Mοreοver, it pοssesses rοtatiοnal symmetry arοund the centre fοr each angle. A circle is a circular shape that can be created by tracing a mοving pοint in a plane sο that its distance frοm a specified pοint remains cοnstant.
Given
Angle AOC = 46°
Now, ΔAOP ≅ ΔBOP
As SSS criteria is possible
Then
By CPCT
∠AOC = ∠BOC = ∠POB
∠POB = 46°
Thus, the measure of the angle POB is equal to 46°. Thus, option C is correct.
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Help I’ll give points thanks
Answers
Step-by-step explanation:
your answers for a. are correct.
b.
(f○g)(x) = f(g(x))
that means we are using the expression of g(x) as input to f(x). so, for f(x), x turns into g(x) = 0.9x
(f○g)(x) = f(g(x)) = 0.9x - 220
what it does is it reduces the price by 10% and then gives on to of that an additional absolute value discount if $220.
Use the ALEKS graphing calculator to solve the system of equations.
5-0.7x=0.2y
-y+0.4x = 4.3
Round to the nearest hundredth.
(x, y) = (.D
X
Ś
Answers
the solution to the system of equations is x = 7.14 and y = 13.57.
Define equationIn mathematics, an equation is a statement that asserts the equality of two mathematical expressions, usually containing one or more variables.
Given equations are:
5 - 0.7x = 0.2y ...........(1)
-y + 0.4x = 4.3 ...........(2)
To solve for x and y, we can use the elimination method, which involves multiplying one or both equations by a constant to eliminate one of the variables. Here's how we can do it:
First, let's multiply equation (1) by 5 and equation (2) by 2 to eliminate the y variable:
25 - 3.5x = y (multiplying equation (1) by 5)
-2y + 0.8x = 8.6 (multiplying equation (2) by 2)
Now we can substitute the expression for y from equation (1) into equation (2) and solve for x:
25 - 3.5x = 0.2(25 - 3.5x) (substituting y from equation (1))
25 - 3.5x = 5 - 0.7x
-2.8x = -20
x = 7.14
Substituting this value of x back into equation (1), we can solve for y:
5 - 0.7(7.14) = 0.2y
y = 13.57
Therefore, the solution to the system of equations is x = 7.14 and y = 13.57.
By using ALEKS graphing calculator, we get the same values of x and y.
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Suppose that people are equally likely to have been born on any of the 7 days of the week. You meet two new friends independently, and ask each of them on what day of the week they were born. (Enter your answers as fractions.)
Answers
The calculated probability of a friend being born on a Friday is 1/7
Probability of a Friend Being Born on a FridayAssuming that people are equally likely to have been born on any of the 7 days of the week, the probability of the first friend being born on a Friday is 1/7 or approximately 0.143.
This is because there is only one day out of the seven days of the week that is Friday, and each day has an equal chance of being chosen.
Therefore, the probability of the first friend being born on a Friday is 1/7.
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Complete question
Suppose that people are equally likely to have been born on any of the 7 days of the week. You meet two new friends independently, and ask each of them on what day of the week they were born. (Enter your answers as fractions.) What is the probability that the first friend was born on a Friday
Result of 6³⁶ pls i Need this
Answers
We know that we would need to make use of the calculator to obtain the value of 6³⁶ as 1.03 * 10^28.
What is the meaning of 6³⁶?The expression 6³⁶ means "6 raised to the power of 36," which is equivalent to multiplying 6 by itself 36 times.
So, 6³⁶ is a very large number. This number is difficult to comprehend, but it has many practical applications in fields such as physics, engineering, and computer science.
We can see that we have to make use of the standard form to write; 1.03 * 10^28 as the result.
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Write a quadratic function f whose only zero is 5.
Answers
Step-by-step explanation:
a quadratic function means it has an "x²" based term as highest x exponent.
and as such it has 2 zeroes.
the request here simply means that both zeros must be equal and 5.
remember, factoring the function expression tells us the zeroes right away.
now we reverse the process.
we know the zeroes (5 - two times).
so we define the factors to have the desired zeroes :
y = (x - 5)(x - 5)
you see what i did there ? we need to have a quadratic equation, and therefore 2 zeroes. both with the value of 5.
y = (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² - 10x + 25
A quadratic function with only one zero can be derived using the vertex form of a quadratic function, where h equals the zero. Hence, a possible quadratic function with five as the only zero is f(x) = (x - 5)^2.
Explanation:
In mathematics, a quadratic function is written in the form f(x) = ax2 + bx + c.
If a quadratic function has only one zero or root, it means that the parabola touches the x-axis at that point only.Considering the given zero from the question, we have the zero equals 5.By using the concept of vertex form of a quadratic function which is f(x) = a(x-h)2 + k, where (h,k) is the vertex of the parabola, we can create a quadratic function with 5 as the only zero by setting h = 5 and a ≠ 0, k can be any value.So, a potential function could be f(x) = (x - 5)2.
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Describe the correlation for an r-value of –0.86.
A.
weak, negative correlation
B.
strong, negative correlation
C.
strong, positive correlation
D.
weak, positive correlation
Answers
B. strong, negative correlation. An r-value of -0.86 shows a significant, negative correlation between the two variables under consideration.
An r-value of -0.86 shows a significant, negative correlation between the two variables under study. This implies that while one variable rises, the other falls, and vice versa. The inverse relationship is indicated by the negative sign, and the strength of the association is indicated by the absolute value of 0.86. A correlation coefficient's range is from -1 to 1, where -1 denotes a perfect negative correlation, 0 denotes no correlation, and 1 denotes a perfect positive correlation. Thus, an r-value of -0.86 denotes a significant, negative correlation between the two variables.
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12. Pure fruit concentrate must be diluted with water in the ratio 1:7.
How many millilitre of concentrate are needed to make 5litres cool drink?
Answers
By answering the presented question, we may conclude that To prepare ratio 5 litres of cold drink, we'll need 625 millilitres of pure fruit concentrate.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit plate, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of integers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
If the concentrate-to-water ratio is 1:7, it signifies that the final product requires 7 parts water for every 1 part concentrate. As a result, the total number of components in the combination is 1+7=8.
To produce 5 litres of the cold drink, we must first establish the quantity of concentrate necessary to make 8 parts, and then multiply this figure by 5 litres.
As a result, we need 1 part concentrate and 7 parts water to create 8 parts.
As a result, we require 1/8th of 5,000 millilitres of concentrate, or 625 millilitres.
To prepare 5 litres of cold drink, we'll need 625 millilitres of pure fruit concentrate.
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What is the area of the triangle shown below if the value of h is 3/4 of the length of the side that is labeled in the figure?
Answers
here is the solution :-)
it’s C, 8.64mm.
:)
A 1-bedroom apartment on the 10th floor of the Downtown Apartment Complex rents for $390 per
month. A 1-bedroom apartment on the 15th floor rents for $440 per month. If the price of the apartment
goes up in equal increments as the floor number increases, what is the monthly rate for a 1-bedroom
apartment on the 34th floor?
Answers
answer :
630
explanation
it's a graph question in the form of a word problem
question says if
(10, 390) & (15, 440) then (34, y)?
if x = 34 then what is y
get slope
m = (440 - 390) / (15 - 10) = 10
get graph
y - y1 = m(x - x1)
y - 440 = 10(34 - 15)
y - 440 = 190
y = 630
chatgpt
HELP ME PLEASE this is due tomorrow
Answers
The cube's surface area would be 96m².
The surface area of the right rectangular prism is 37.5 ft².
The height of the prism is 4/3 in.
The approximate lengths of the sides of the base is height of 9 cm and a base of 8.2 cm.
How to find the surface area ?To find the surface area, first find the side length of the cube. The volume of a cube is V = s³, where s is the side length. So:
64m³ = s³ => s = (64)^(1/3) = 4m
Now, the surface area (SA) of a cube is given by the formula SA = 6s². Plugging in the side length:
SA = 6(4m)² = 6(16m²) = 96m²
To find the surface area of the right rectangular prism:
First, find the Lateral Area (LA): LA = Perimeter × height
Perimeter = (2 ft + 1 1/2 ft) × 2 = 7 ft
Height = 4 1/2 ft
LA = 7 ft × 4 1/2 ft = 31.5 ft²
Now, find the Surface Area (SA): SA = LA + 2B
SA = 31.5 ft² + 2(3 ft²) = 31.5 ft² + 6 ft² = 37.5 ft²
To find the height h of the prism:
First, find the Base Area (B): B = Length × Width
B = 3 in × 7 in = 21 in²
Now, use the Surface Area (SA) formula to find the Lateral Area (LA):
SA = LA + 2B => LA = SA - 2B
LA = 68 2/3 in² - 2(21 in²) = 68 2/3 in² - 42 in² = 26 2/3 in²
Now, use the Lateral Area (LA) formula to find the height (h):
LA = Ph => h = LA / P
Perimeter (P) = 2(Length + Width) = 2(3 in + 7 in) = 20 in
h = (26 2/3 in²) / 20 in = 4/3 in
The right triangular prism has two equilateral triangular bases and three rectangular sides. Since the distance between the bases is 9 cm, we can use the surface area of the prism to find the total area of the three rectangular sides:
Surface area = 2 * A (triangle bases) + Lateral area (rectangular sides)
319.5 cm² = 2 * 29.1 cm² + Lateral area
Lateral area ≈ 261.3 cm²
Each of the three rectangular sides has a height of 9 cm and a base of 8.2 cm.
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A roofer props a ladder against a wall so that the base of the ladder is 4 feet away from the building. If the angle of elevation from the bottom of the ladder to the roof is 63°, how long is the ladder?
what is the answer? thank you
Answers
tan(63°) = opposite/adjacent
In this case, the "opposite" side is the height of the building that the ladder reaches, and the "adjacent" side is the distance between the base of the ladder and the building. We know that the distance between the base of the ladder and the building is 4 feet, so we can plug in the values we have:
tan(63°) = height/4
Now we can solve for the height:
height = 4 * tan(63°)
Using a calculator, we get:
height ≈ 8.32 feet
Therefore, the length of the ladder is approximately:
L = √(4^2 + 8.32^2) ≈ 9.38 feet
So the length of the ladder is approximately 9.38 feet.
I need helllllllllllllllllp
Answers
Answer: A = 3
Step-by-step explanation:
4x-2=10
4x=12
x =12/4
x=3
Find the distance traveled.
Answers
The distance traveled after t seconds is given by:
[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]
How to find the distance traveled after t seconds?Here we know that the particle moves along a straight line with the velocity:
[tex]v(t) = t^2*e^{-2t}[/tex]
Remember that the velocity is the rate of change of the position, so if we want to find the distance traveled after t seconds, we need to integrate this between 0 and t, we will get:
[tex]\int\limits^t_0 {t'^2*e^{-2t'}} \, dt' = -\frac{(2t^2 + 2t + 1)e^{-2t}}{4}[/tex]
That is the expression that gives the distance traveled after t seconds, if we want to get it more exactly, we should take the absolute value, then we get:
[tex]d = |-\frac{(2t^2 + 2t + 1)e^{-2t}}{4}|[/tex]
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Which of the following is the average rate of change over the interval
Answers
Answer:
To find the average rate of change of a function over an interval, you can use the formula:
average rate of change = [f(b) - f(a)] / (b - a)
where a and b are the endpoints of the interval.
In this case, you have the function g(x) = log2(x + 3) - 4 and the interval [-2, 5]. So, plugging in the values, you get:
average rate of change = [g(5) - g(-2)] / (5 - (-2))
First, let's evaluate g(5) and g(-2).
g(5) = log2(5 + 3) - 4 = log2(8) - 4 = 3 - 4 = -1
g(-2) = log2((-2) + 3) - 4 = log2(1) - 4 = 0 - 4 = -4
Now you can substitute these values into the formula:
average rate of change = (-1 - (-4)) / (5 - (-2))
= 3 / 7
And the average rate of change of g(x) over the interval [-2, 5] is 3/7.
Question 11 (5 points)
(Experimental Probability MC)
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows
the frequency of each card drawn.
Card A23
Frequency 47567
Based on the table, what is the experimental probability that the card selected was a K or 6?
a
Ob
Od
100 11-
4
10JQK
Question 12(5 points)
Answers
the correct answer is option b) 0.11. To find the experimental probability of drawing a K or 6, we need to first determine how many K's and 6's are in a standard deck of cards.
A standard deck of cards contains 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards, including an ace, numbered cards 2-10, and face cards (jack, queen, king).
Out of the 52 cards in the deck, there are four K's and four 6's, for a total of eight cards that satisfy the condition of being a K or 6.
To calculate the experimental probability of drawing a K or 6 from the table, we need to add up the frequency of drawing a K and the frequency of drawing a 6, and then divide by the total number of draws (100).
From the table, we see that the frequency of drawing a K is 4, and the frequency of drawing a 6 is 7. Therefore, the total frequency of drawing a K or 6 is:
4 (K's) + 7 (6's) = 11
So the experimental probability of drawing a K or 6 is:
11/100 = 0.11
Therefore, the correct answer is option b) 0.11.
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A test is worth 125 points . How many points (rounded to nearest whole number ) are needed to obtain a score of 85%?
Answers
Step-by-step explanation:
You need to find 85% of 125 points :
85% * 125 = .85 * 125 = ~ 106 points
Please help!! Correct answer gets brainliest!!
Answers
Graph B is correct and shows the rectangular opening.
Looking at the text the question, I notice that each unit means 1 inch. After looking at all the graphs, I found out that B was the correct answer because of the sides. The sides are five inches by two inches and it was the only graph that had these units.
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
Answer: Option B.
Step-by-step explanation:
With the scale of one unit equalling one inch, the only answer option that meets the given requirement of having side lengths that are 5 inches and 2 inches is option B.
Answer A is 4 units by 2 units, Answer B is the needed 5 units by 2 units, Answer C is 7 units by 2 units, and Answer D is 6 units by 2 units. This leaves us with Answer B.
If noah had 5 dollars and diego has 150% as noah how much does Diego.
Answers
Answer: 7.5
Step-by-step explanation: Because Noah has five dollars, 100% of 5 is 5, and 50% of 5 is 2.5 so Diego has 7.5 dollars.
Answer:
$7.5
Step-by-step explanation:
There are two ways to solve this:
1) First, write the equation:
150% of 5
Then calculate:
[tex]\frac{150}{100} *5[/tex]
Finally, simplify 1 zero with the 0 in 15:
1.5 * 5
= $7.5
2) For the second way, because 150 is more than over 100 (percent), you deduct 150 and 100:
150 - 100 = 50
Then find 50% of 50:
[tex]\frac{50}{100} *5[/tex]
Then cancel 1 zero in 100 with the zero in 50:
0.5 * 5
= 2.5
Finally, add the product with the original amount of Noah:
5 + 2.5
= $7.5
A soccer team scored 24 goals in 16 games. Based on this relative frequency, how many goals can the team be expected to score in 10 games?
Answers
The team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.
What is relative frequency?The proportion or percentage of times that even an event or category occurs in a dataset is measured by relative frequency. It is derived by dividing the total number of observations in the dataset by the frequency with which the event or category occurs. In statistics, relative frequency is frequently used to compare the occurrence of various events or categories and to characterise the distribution of a dataset. Also, depending on a sample, it is used to calculate the likelihood that an event will occur in a population.
The goals scored in 10 games can be calculated using proportions:
Given that,
24 goals / 16 games = 1.5 goals per game
For 10 games we have:
1.5 goals per game × 10 games = 15 goals
Hence, the team can be expected to score about 15 goals in 10 games based on their relative frequency of scoring 24 goals in 16 games.
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a digital camera that cost #49 was sold on ebay for 3/7 for the original price.what was the selling price
Answers
Answer: 20.99
Step-by-step explanation: you multiply by 0.428571 which is 3/7
The probability of an event occurring is 0.45.
Which of the options below show the
probability of an event that is less likely to
occur? Select all that apply.
A) 0.42
B) 0.48
C) 0.29
D) 0.37
E) 0.51
Answers
Answer:
An event that is less likely to occur would have a lower probability than 0.45. Therefore, the options that show a probability less than 0.45 are:
A) 0.42
C) 0.29
D) 0.37
So options A, C, and D are the correct answers.
In ΔXYZ, x = 830 cm,
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m∠Y=141° and
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m∠Z=25°. Find the length of z, to the nearest 10th of a centimeter.
Answers
Therefore, the length of z is approximately 2330.0 cm.
What is length?Length is a physical quantity that describes the distance between two points. It is typically measured in units such as meters, feet, inches, centimeters, or kilometers. Length can refer to the size of an object or the distance traveled by an object over a period of time. In geometry, length refers to the size of a line segment, which is the distance between two points in a plane. In physics, length is a fundamental concept that is used to describe the size of objects and the distances between them, and is an important factor in many calculations involving motion, energy, and other physical phenomena.
To find the length of side z, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
Using this law, we have:
[tex]z/sin(141°) = x/sin(25°)[/tex]
Solving for z, we get:
[tex]z = x*sin(141°)/sin(25°)[/tex]
[tex]z = 830*sin(141°)/sin(25°)[/tex]
z ≈ 2329.9 cm
Rounding to the nearest tenth of a centimeter, we get:
z ≈ 2330.0 cm
Therefore, the length of z is approximately 2330.0 cm.
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A forklift operator has the task of moving 43 palettes from one location to another. If the most palettes he can move at one time are 8 what are the minimum number of trips he will have to make from one location to the other in order to move all the palettes?
Answers
The forklift operator can move at most 8 palettes at one time.
What is Forklift operator?A forklift operator is a person who operates a forklift, which is a type of powered industrial truck used to lift and move heavy materials over short distances. Forklift operators are commonly employed in warehouses, manufacturing plants, and other industrial settings where materials need to be moved and stored. They are responsible for loading and unloading trucks, transporting materials to and from storage areas, and positioning materials for storage or processing. Forklift operators must be trained and certified to operate the equipment safely and efficiently.
In the given question,
To move all 43 palettes, the operator needs to make at least 43/8 = 5.375 trips.
Since the operator cannot make a fraction of a trip, he will need to make at least 6 trips in order to move all 43 palettes.
On the first five trips, the operator will move 8 palettes each time, and on the final trip, he will move the remaining 3 palettes.
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The Mitchell family and the Garcia family each used their sprinklers last summer. The Mitchell family's sprinkler was used for 35 hours. The Garcia family's sprinkler was used for 25 hours. There was a combined total output of 1075L of water. What was the water output rate for each sprinkler if the sum of the two rates was 35L per hour?
Answers
Water output rate for Mitchell family's sprinkler was 20 L per hour and for Garcia family's sprinkler was 15 L per hour. Their sum is 35 L per hour and total water output was 1075L of water.
Let's denote the water output rate of the Mitchell family's sprinkler by x and the water output rate of the Garcia family's sprinkler by y. We know that the sum of the two rates is 35 L per hour, so equation:
x + y = 35
We also know that the Mitchell family's sprinkler was used for 35 hours, so it produced a total of 35x liters of water. Similarly, the Garcia family's sprinkler was used for 25 hours, so it produced a total of 25y liters of water. The combined total output of 1075L of water will be written as:
35x + 25y = 1075
We use first equation to solve for one of variables in terms of the other. For example, we solve for y:
y = 35 - x
Now substitute this expression for y into second equation:
35x + 25(35 - x) = 1075
Simplifying the equation:
10x + 875 = 1075
Solve for x:
x = 20
Substitute x value into expression for y:
y = 35 - 20 = 15
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