The monthly payments on the original loan are $899.33.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the monthly payments on the original loan, we can use the formula for the monthly payment of an amortized loan:
M = P (r/12)(1 + r/12)ⁿ/ ((1 + r/12)ⁿ - 1)
where M is monthly payment, P is principal, r is monthly interest rate, n is total number of payments
For the original loan, P = $150,000, r = 0.06/12 = 0.005, and n = 45 years x 12 months/year = 540 months.
Substituting these values into the formula, we get:
M = 150,000(0.005)(1 + 0.005)⁵⁴⁰ / ((1 + 0.005)⁵⁴⁰- 1)
= 899.33
Therefore, the monthly payments on the original loan are $899.33.
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ9
The box plot displays the number of push-ups completed by 9 students in a PE class.
A box plot uses a number line from 9 to 56 with tick marks every 2 units. The box extends from 20 to 42.5 on the number line. A line in the box is at 35. The lines outside the box end at 10 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.
Which of the following represents the value of the median of the data?
10
20
35
55
The value of the median of the data is 35.
What is Algebraic expression?
Algebraic expression can be defined as combination of variables and constants.
A box plot is a graphical representation of a data set that shows the distribution of the data, as well as the central tendency and the variability of the data. In this case, the box plot displays the number of push-ups completed by 9 students in a PE class.
The box plot has a number line from 9 to 56 with tick marks every 2 units. The box extends from 20 to 42.5 on the number line, which means that the middle 50% of the data (i.e., the interquartile range) lies between 20 and 42.5. The line in the box represents the median of the data, which is the value that separates the data set into two equal halves.
In this case, the line in the box is at 35, which means that half of the students completed more than 35 push-ups, while the other half completed fewer than 35 push-ups.
Therefore, the value of the median of the data is 35.
To learn more about Algebraic expression from given link.
https://brainly.com/question/953809
#SPJ1
Find the value of x.
Answer:
43 degrees
Step-by-step explanation:
85 degrees + 25 = 110 and the angle sum for a right triangle will always equal 180 degrees. The outside angle is 62 degrees, so 62 +70= 132. 180-132 is 48. Now you want to solve the angle sum for the shorter wider triangle. We know one angle is 89 degrees, plus the 48 degrees= 137. Now to find ? do 180-137=43. The missing angle for ? is 43 degrees.
I hope this helps :)
Find the surface area of the pyramid. A triangular pyramid. The base triangle has a base of 8 meters and a height of 6.9 meters. The height of a triangular face is labeled 7 meters. The surface area is square meters.
If the base triangle has a base of 8 meters and a height of 6.9 meters. the surface area of the pyramid is 139.6 square meters.
How to find the surface area?First, let's find the area of the base triangle:
Area of base triangle = (1/2) * base * height
Area of base triangle = (1/2) * 8 * 6.9
Area of base triangle = 27.6 square meters
Now, let's find the area of one of the triangular faces:
Area of triangular face = (1/2) * base * height
Area of triangular face = (1/2) * 8 * 7
Area of triangular face = 28 square meters
Since the pyramid has four triangular faces, the total area of the triangular faces is 4 times the area of one triangular face, which is:
4 * 28 = 112 square meters
Total surface area = area of base triangle + area of triangular faces
Total surface area = 27.6 + 112
Total surface area = 139.6 square meters
Therefore, the surface area of the pyramid is 139.6 square meters.
Learn more about surface area here:https://brainly.com/question/16519513
#SPJ1
Given the triangle below, what is the coordinate point for the centroid? B O O (1,2) 0 (21) 32 O 15 21 (5-2) 0 10 C
The coordinate point for the centroid are (8/3, 1/3).
How to determine the coordinate point for the centroid?From the question, we have the following parameters that can be used in our computation:
Coordinates = (1,2), (2, 1) and (5, -2)
To find the centroid of a triangle, you can calculate the average of the x-coordinates and the average of the y-coordinates of its three vertices.
Let (x1, y1), (x2, y2), and (x3, y3) be the coordinates of the vertices of a triangle.
Then, the coordinates of the centroid (xc, yc) are given by:
xc = (x1 + x2 + x3) / 3
yc = (y1 + y2 + y3) / 3
Substitute the known values in the above equation, so, we have the following representation
xc = (1 + 2 + 5) / 3 = 8/3
yc = (2 + 1 - 2) / 3 = 1/3
Hence, the coordinates of the centroid are (8/3, 1/3).
Read more about centroid at
https://brainly.com/question/7644338
#SPJ1
What is the simplest radical form of the expression?
We can write the expression in the simplest form as -
[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex].
What is expression?An expression is a term made up of both constants and variables.
Given is the expression as -
[tex]$(8x^{7} y^{4} )^{2/3} \\[/tex]
We can solve as -
[tex]$(8x^{7} y^{4} )^{2/3} \\[/tex]
[tex](8^{2/3} x^{7\times\frac{2}{3} } y^{4\times\frac{x}{y} 2/3})[/tex]
[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex]
Therefore, we can write the expression in the simplest form as -
[tex]$4x^{2} y^{2} \sqrt[3]{x^{2} y^{2} }[/tex].
To solve more questions on expression, visit the link-
https://brainly.com/question/29131910
#SPJ1
my recipe calls for 4/5 of a cup of flour and I want to make it 1/2 of the recipe how much flour do I need?
Answer:
2/5
Step-by-step explanation:
So if you were to half that the bottom stays the same but the top you divide by two which 4 divided by 2 is 2 so you would need 2/5 cup of flour for your new recipe.
The graph shows the total cost c of buying one parking pass and t tickets to a concert. Write an equation from the graph that could be used to find the total cost c if you buy one parking pass and t tickets to a concert.
The linear equation on the graph is written as:
y = 20x + 10
Which is the equation of the line in the graph?Remember that the general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
By looking at the graph, we can see that the line intercepts the y-axis at y = 10, then the y-intercept is b = 10.
We can write:
y = a*x + 10
Now we can also identify the point (1, 30), replacing the values of that point in the equation above we will get:
30 = a*1 + 10
30 = a + 10
30 - 10 =a
20 =a
Then the linear equation is:
y = 20x + 10
Learn more about linaer equations at:
https://brainly.com/question/1884491
#SPJ1
what is the greatest common factor of 4x^3 y^2 and 12x^2 y?
The greatest common factor of 4x³y² and 12x²y is: 4x²y.
What do you mean by greatest common factor?The GCF is a term used to refer to the largest common factor between any two or more numbers (Greatest Common Factor). The GCF of two natural integers, x and y, is the largest possible number that equally and completely divides both x and y. GCF is typically calculated using the following three techniques: division, multiplication, and prime factorization.
Now in the given question,
4x³y² can be written as = 2×2×x×x×x×y×y
12x²y can be written as = 2×2×3×x×x×y
The common factors among them are:
2×2×x×x×y = 4x²y.
Therefore, the greatest common factor of 4x³y² and 12x²y is: 4x²y.
To know more about greatest common factor, visit:
https://brainly.com/question/11221202
#SPJ1
Sam is collecting money for an animal shelter. He collects $150.00 each day for 6 days. The shelter will use 35% of the money he collects to buy pet food. The rest of the money will be used to buy cleaning supplies.
How much of the money that Sam collects will be used to buy cleaning supplies?
Answer:
$585 dollars will be used for cleaning supplies out of the total of $900 that was collected over the six days.
Step-by-step explanation:
$150.00 (money each day) * 6 (number of days) = $ (total)
[tex]150*6=900[/tex]
$900 in 6 days
100% (total amount) - 35% (pet food) = % (cleaning supplies)
[tex]100-35=65[/tex]
65% of his money will be used for cleaning supplied
Change the percentage into a decimal
65% = [tex]0.65[/tex]
Multiply the total amount of money by the decimal
[tex]900*0.65=585[/tex]
Out of the total $900 dollars he collected over 6 days, $585 dollars will be used for cleaning supplies and the rest ($315) will be used on pet food.
Please help
One side of a 141 square foot rectangular room is 15 feet long. How long is the other side?
Answer:
9.4ft²
Step-by-step explanation:
The formula for the area of a rectangle is base*height, or b*h.
Since we know the final area of the room and one of the side lengths, we can plug those into the formula I just stated so that we get
15*h=141
All that's left to do is solve for h, which is the other side that we are solving for. To do this, we will divide 15 on both sides:
15h/15=141/15
The 15s on the left side cancel out, and we simply divide 141 by 15 to get our final answer of 9.4ft².
Which is the distance between parallel lines with the equations y = -1/3x +3 and y =-1/3x -7
The distance between the parallel lines y = -1/3x + 3 and y = -1/3x - 7 is approximately 9.49 units.
How do parallel lines work?A parallel line is a pair of lines that never cross and are always spaced at the same distance apart. The y-intercepts are different, but they have the same slope. In other terms, two lines are parallel if they have the same slope but distinct y-intercepts. Due to their role in defining and producing forms like rectangles, parallelograms, and trapezoids, parallel lines play a crucial role in geometry and trigonometry. In the actual world, parallel lines are also used in things like roads, railroad tracks, and electrical cables.
The standard equation of the line is given as:
y = mx + c
where, m is the slope.
c is the y-intercept.
Comparing the equation with the given equation we have the slope of the parallel lines as:
y = -1/3x +3 and y =-1/3x -7
slope = m = -1/3
y-intercept of 1st line = (0, 3)
y-intercept of the 2nd line = (0, -7)
The distance between two parallel lines is the perpendicular distance between them.
To calculate the perpendicular distance we find the equation of the perpendicular line.
The slope of the perpendicular line is negative reciprocal of the slope of the two given lines, which is 3.
The point-slope form is:
y - y1 = m(x - x1)
Substituting the values:
y - 3 = 3(x - 0)
y = 3x + 3
The intersection of this perpendicular line with the other line.
3x + 3 = -1/3x - 7
10/3x = -10
x = -3
Substituting x = -3 into either equation of the parallel lines gives:
y = -1/3(-3) - 7 = -6
Using the distance formula we have:
d = √((x2 - x1)² + (y2 - y1)²)
d = √((-3 - 0)² + (-6 - 3)²)
d = √(9 + 81)
d = √(90)
d ≈ 9.49
Hence, the distance between the parallel lines y = -1/3x + 3 and y = -1/3x - 7 is approximately 9.49 units.
Learn more about parallel lines here:
https://brainly.com/question/16701300
#SPJ1
Damian works after school. Each day he earns a set amount, plus an hourly wage. The function f(x) = 12x + 10 models the amount he earns each day for working x hours. What is a reasonable domain for the function?.
Charlotte buys a ticket for a raffle with several prizes. The probability that she wins a
prize is 12%. Which word or phrase describes the probability that Charlotte will win a
prize?
O impossible
unlikely
an equal chance or 50-50
O likely
The word or phrase that describes the probability that Charlotte will win a prize, with a probability of 12%, is D. likely.
What is the probability?Probability refers to the likelihood of an expected outcome occurring, given the many possible chances.
Probability lies between zero and one, depending on the level of certainty or otherwise of the successful outcomes.
In this situation, Charlotte's chances of winning cannot be described as impossible, zero percent, or unlikely.
Charlotte does not have an equal chance or 50-50 odds of winning because the probability is not up to 50%.
Thus, we can conclude that Charlotte has a D. likely opportunity of winning.
Learn more about probabilities at https://brainly.com/question/25870256.
#SPJ1
Please help!! Worth 50 points
The ball with the greater maximum height is the second ball
The ball with the greater maximum heightFrom the question, we have the following parameters that can be used in our computation:
f(t) - 4t^2 + 16t
g(t) = -16t^2 + 64t + 192
Differentiate and set them to 0
-8t + 16 = 0
-32t + 64 = 0
Solve for t
t = 2 in both cases
So, we have
f(2) = -4(2)^2 + 16(2) = 16
g(2) = -16(2)^2 + 64(2) + 192 = 256
Hence, the ball with the greater maximum height is the second ball
Which ball hits the ground firstTo do this, we set the function to 0 and calculate t
So, we have
f(t) = -4t^2 + 16t = 0
g(t) = -16t^2 + 64t + 192 = 0
Using a graphing tool, we have
t = 4
t = 6
This means that the first ball landed first
How to change the termTo change the term, we set the constant term in g(t) = -16t^2 + 64t + 192 to a negative number > -192
Read more about quadratic functions at
https://brainly.com/question/25841119
#SPJ1
Need answer for number 5.
The triangle AEC is similar to triangle BDC.
What are similar triangles?Those triangles look the same but are different in size.
And in similar triangles,
the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.
Given:
5. ΔAEC is a triangle.
Assuming BD is parallel to AE.
The ratio of the corresponding sides,
10/5 = 2
8/4 = 2
The ratio is constant.
A similar triangle is made by drawing a line parallel to one of the triangle's sides.
Therefore, triangle AEC ~ triangle BDC.
To learn more about similar triangles;
https://brainly.com/question/14926756
#SPJ1
A new automobile is purchased for $20,000. If V = 20,000(0.8)x, gives the car’s value after x years, about how long will it take for the car to be worth $8,200?
Answer:
Step-by-step explanation:
We can use the given formula to set up an equation and solve for x:
V = 20,000(0.8)x
where V is the value of the car after x years.
We want to find x when the value of the car is $8,200, so we set V equal to 8,200 and solve for x:
8,200 = 20,000(0.8)x
Dividing both sides by 20,000:
0.41 = 0.8x
Taking the natural logarithm of both sides:
ln(0.41) = x ln(0.8)
Dividing both sides by ln(0.8):
x = ln(0.41) / ln(0.8)
Using a calculator:
x ≈ 6.11
Therefore, it will take about 6.11 years for the car to be worth $8,200.
P(z > c) = 0.8914
Find C
The value of c is given as follows:
c = -1.235.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.For this problem, we have that P(z > c) = 0.8914, meaning that Z when X = c has a p-value of 1 - 0.8914 = 0.1086, hence the value of c is given as follows:
c = -1.235.
More can be learned about the normal distribution at https://brainly.com/question/25800303
#SPJ1
what is the answer for the question
Need help asap! (50 points)
Answer:
8
Step-by-step explanation:
160×5%
[tex]\frac{160 * 5}{100}[/tex] = 8
5 Find the value of x. Q (16x - 22) P R
Solution of equation 16x - 22 = 20x + 14 is x = -8
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given equation
16x - 22 = 20x + 14
Moving like terms to same side
- 20x + 16x = 14 + 22
Adding like terms
-4x = 36
Dividing by -4 on both sides
x = 36/-4
x = -8
Hence, x = -8 is the solution of equation 16x - 22 = 20x + 14.
Learn more about equation here:
https://brainly.com/question/1529522
#SPJ9
Complete question is:
Find the value of x, in equation 16x - 22 = 20x + 14
charlie has x pieces of candy .He shares ten with betsy and is left with 24 pieces of candy.Wich of the fowlling equations best reresents the situation
A)10+x=24
B)x+24=10
C)x-10=24
Answer:
2. x-10=24
Step-by-step explanation:
x is the unknown amount of candy that Charlie has.
He gives ten away (-10).
Now he has 24 pieces.
x-10 = 24
can you help please
Answer:
1: 2.097,2: 1000,3: 1.4282,4: 10000,5: 2.774546,6: 10,7: 2.00141,8: 1000,9: 100,10: 10
Step-by-step explanation:
Multiplication and division I don't know how to explain it lol
During your chemistry lab, you fill a cone-shaped beaker that has a 1-inch diameter and a 2- inch height with lead, which weigh 0.41 pounds per cubic inch. Find the weight of the lead in the beaker.
The weight of the lead in the beaker is 0.21 pounds.
What is volume of a cone?A cone is a three dimensional shape with slant sides and a circular surface. Its volume can be defined as the amount of substance that it can contain.
volume of a cone = 1/3 [tex]\pi[/tex]r^2*h
where r is the radius of its circular surface, and h is its height.
In the given question, we have;
r = d/2 = 1/2
= 0.5 inches
h = 2 inches
Thus,
volume of the cone-shaped beaker = 1/3 [tex]\pi[/tex]r^2*h
= 1/3 *22/7*(0.5)^2*2
= 0.524
The volume of the lead in the cone-shaped beaker is 0.524 cubic inch.
Weight of the lead in the beaker = 0.524*0.41
= 0.2148
The weight of the lead in the beaker is 0.21 pounds.
Learn more about volume of a cone at https://brainly.com/question/28109167
#SPJ1
A baseball coach uses a scatter plot to compare the number of swings taken before a baseball tournament and the number of hits during the baseball tournament. What can the coach conclude about the relationship between the number of swings and the number of hits? PLEASE HELP !!!!!!
Answer: Without seeing the actual scatter plot, it is difficult to make a definitive conclusion about the relationship between the number of swings and the number of hits. However, there are a few things that the coach can look for in the scatter plot to gain some insights:
Positive correlation: If the scatter plot shows a generally upward trend, with more hits occurring as the number of swings increases, this suggests a positive correlation between the two variables. In other words, players who take more swings tend to have more hits during the tournament.
Negative correlation: On the other hand, if the scatter plot shows a generally downward trend, with fewer hits occurring as the number of swings increases, this suggests a negative correlation between the two variables. In this case, players who take fewer swings tend to have more hits during the tournament.
No correlation: If the scatter plot shows no clear trend or pattern, with hits occurring randomly across different numbers of swings, this suggests no correlation between the two variables. In this case, there is no apparent relationship between the number of swings taken and the number of hits during the tournament.
Overall, the coach can use the scatter plot to gain some insights into the relationship between the number of swings and the number of hits, but more advanced statistical analysis may be necessary to make definitive conclusions.
Step-by-step explanation:
muscle has a force of 100LBS and is pulling on a bone at an angle of 15 degrees. muscle B has a force of 150 lbs and is pulling on the same bone at the same spot but at an angle of 30. muscle c has a force of 75Ibs and is pulling at the same spot with an angle of 10. what is the resultant force of the muscles in the terms of the amount of force and direction? draw a diagram, label and show your work
Answer:
To solve this problem, we need to use vector addition. We can start by breaking down each force into its x and y components.
For muscle A:
Force = 100 lbs
Angle = 15 degrees
X-component = 100 * cos(15) = 96.93 lbs
Y-component = 100 * sin(15) = 25.04 lbs
For muscle B:
Force = 150 lbs
Angle = 30 degrees
X-component = 150 * cos(30) = 129.90 lbs
Y-component = 150 * sin(30) = 75.00 lbs
For muscle C:
Force = 75 lbs
Angle = 10 degrees
X-component = 75 * cos(10) = 73.83 lbs
Y-component = 75 * sin(10) = 13.03 lbs
Next, we can add up the x and y components separately:
X-component = 96.93 + 129.90 + 73.83 = 300.66 lbs
Y-component = 25.04 + 75.00 + 13.03 = 113.07 lbs
We can use these components to find the magnitude and direction of the resultant force:
Magnitude = sqrt(X^2 + Y^2) = sqrt((300.66)^2 + (113.07)^2) = 321.23 lbs
Direction = tan^-1(Y/X) = tan^-1(113.07/300.66) = 21.65 degrees (measured counterclockwise from the positive x-axis)
Therefore, the resultant force of the muscles is 321.23 lbs at an angle of 21.65 degrees. Here is a diagram to illustrate the vectors:
Step-by-step explanation:
25.04 lbs 73.83 lbs 129.90 lbs
/\ /\ /\
/ \ / \ / \
/ \ / \ / \
100 lbs 15° 75 lbs 10° 150 lbs 30°
\ / \ / \ /
\ / \ / \ /
\ / \ / \ /
96.93 lbs 13.03 lbs 75.00 lbs
What is the standard form of the equation y = 5x + 3 ?
A. 5x + y = 3
B. 5x-y = 3
C. 5x + y = -3
D. 5x- y = -3
Answer:
D
y=5x-3
0=5x-y+3
5x-y= -3
You want to estimate the average class size of Basic Statistics classes at a certain college. You take a random sample of 50 students who are taking Basic Statistics this semester and ask them how large their class is. You average the results and get an average class size of 38. You then look at an Admissions and Records spreadsheet for this semester for the same college and get an average class size of Basic Statistics equal to 25. This is too large of a difference to attribute to random variation. Also, there's nothing wrong with your sample. What's wrong?
The sample size οf 50 might nοt be large οr randοm enοugh, and there might be sοme systematic bias οr errοr in the data sοurces, leading tο a large difference between the sample mean (38) and Admissiοns and Recοrds data (25) in estimating the average class size οf Basic Statistics classes at the cοllege.
What are the statistics?Statistics is a branch οf mathematics that deals with the cοllectiοn, analysis, interpretatiοn, presentatiοn, and οrganizatiοn οf data. It invοlves the use οf mathematical tοοls and techniques tο extract useful infοrmatiοn frοm data, and tο make decisiοns οr predictiοns based οn that infοrmatiοn.
In the given scenariο, it seems that there might be an issue with the methοd used tο cοllect the data, οr the data sοurces might be different. The sample size οf 50 students is nοt large enοugh tο represent the whοle pοpulatiοn οf Basic Statistics classes at the cοllege, especially if the cοllege has many sectiοns οf the class οr the class size varies widely between sectiοns. Mοreοver, the sample might nοt be truly randοm, as there cοuld be sοme bias in hοw the sample was selected, such as selecting οnly students frοm a particular sectiοn οr time slοt.
Alsο, the difference between the average class size οbtained frοm the sample (38) and the οne οbtained frοm Admissiοns and Recοrds (25) is tοο large tο attribute tο randοm variatiοn, which suggests that there might be sοme systematic bias οr errοr in either the sample οr the Admissiοns and Recοrds data.
Tο get a mοre accurate estimate οf the average class size οf Basic Statistics classes at the cοllege, a larger and mοre representative sample might be needed, οr the data cοllectiοn methοd might need tο be revised.
Hence, The sample size οf 50 might nοt be large οr randοm enοugh, and there might be sοme systematic bias οr errοr in the data sοurces, leading tο a large difference between the sample mean (38) and Admissiοns and Recοrds data (25) in estimating the average class size οf Basic Statistics classes at the cοllege.
To learn more about the statistics, visit:
https://brainly.com/question/15525560
#SPJ1
I need area of this irregular room
The area of the irregular room is 82.5 ft²
How to determine the areaIt is important to note that the area of a triangle is represented with the formula
A = 1/2bh
Given that;
A is the area of the triangleb is the base of the triangleh is the height of the triangleFrom the image shown, we have that;
Area of the figure = sum of the areas of the two triangle
This represented as;
Area = 1/2 × 14(6) + 1/2 × 9(9)
expand the brackets
Area = 1/2 (84) + 1/2(81)
divide the values
Area = 42 + 40. 5
Add the values
Area = 82.5 ft²
Learn about area at: https://brainly.com/question/25292087
#SPJ1
0.004 divided by
0.24
Answer:
0.0166666666666666666666666666666666666666666667
Step-by-step explanation:
USE CALCULATORRRRRR
50 Points!!! Solve each inequality. Then graph the solution set on a number line. Photo attached
50
Step-by-step explanation:
plot it on the number line