Short Answers:
a)N*tan(Θ)
b)arctan(h/N)
c)N*tan(A)
Let * stand for multiplication
Hope this is helpful to someone:)
What is the area of this quadrilateral
Answer : 52.
Explanation : For Triangles ( 3 × 4 ) ÷ 2 Rectangle 10 × 4
The area of this quadrilateral is 52 square feet.
First, I noticed that the rectangle had sides which were 10 feet long and 4 feet tall. (10 × 4)
Second, I noticed that the triangles were 3 feet long and 4 feet tall. (3 × 4) Since this was a triangle, I then divided by 2. (3 × 4) ÷ 2 I then saw there were 2 triangles so I multiplied it by 2. [(3 × 4) ÷ 2] × 2
Lastly, the equation I was left with was (10 × 4) + {[(3 × 4) ÷ 2] × 2} = 5
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
A dog food producer reduced the price of a dog food. With the price at $10 the average monthly sales has
been 19000. When the price dropped to $7, the average monthly sales rose to 25000. Assume that monthly
sales is linearly related to the price.
What price would maximize revenue? $
So the price that would maximize revenue is $2.75.
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values that can be solved for using algebraic methods. An equation can be represented symbolically using mathematical notation, such as using letters, numbers, and mathematical symbols like +, -, x, /, and =. Equations can be used to model and solve a wide variety of problems in mathematics, science, engineering, and other fields.
Here,
We can start by finding the linear equation that relates price and monthly sales. Let's use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where y is the monthly sales, x is the price, m is the slope, and (x1, y1) is a point on the line.
Using the two points we have:
(10, 19000) and (7, 25000)
We can find the slope:
m = (y2 - y1) / (x2 - x1)
m = (25000 - 19000) / (7 - 10)
m = 2000
Now we have:
y - 19000 = 2000(x - 10)
Simplifying:
y = 2000x - 11000
This equation represents the relationship between price and monthly sales.
To maximize revenue, we need to find the price that gives the highest value for the product of price and monthly sales. In other words, we need to find the maximum value of the function:
R(x) = x * y = x(2000x - 11000)
Expanding and simplifying:
R(x) = 2000x² - 11000x
To find the maximum, we need to take the derivative and set it equal to zero:
R'(x) = 4000x - 11000 = 0
Solving for x:
4000x = 11000
x = 2.75
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The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24
Bus 14 is therefore the more reliable bus as a result of its lower IQR.
How to obtain the measures of spread?The dot plot, which depicts the frequency with which each observation appears in the data set, is the first thing we take into account.
The difference between the data set's third and first quartiles is represented by the interquartile range, which is the next factor we take into account.
Because it ignores outliers, the interquartile range is a better indicator of a spread than a data set's range.
We have the following for classes of 15 students:
Since the first seven students make up the first half, the first quartile is represented by the fourth dot, which represents the first half's median.
The final seven students make up the second half, thus the eleventh dot—the first half's median—is in the first quartile.
So, the following are the Bus 14 quartiles:
Q1 = 12.
Q3 = 18.
The IQR is therefore of:
IQR = Q3 - Q1 = 18 - 12 = 6.
Hence, the IQR is:
Q1 = 9.
Q3 = 16.
The IQR is therefore of:
IQR = Q3 - Q1 = 16 - 9 = 7.
Therefore, bus 14 is therefore the more reliable bus as a result of its lower IQR.
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Correct question:
The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick, marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times. A horizontal line starting at 0, with tick, marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 14, with an IQR of 6 Bus 18, with an IQR of 7 Bus 14, with a range of 6 Bus 18, with a range of 7
π ≈ 3.14 and round your ansere to the nearest hundredth 7ft
Answer:
SE π ≈ 3.14 and round your answer to the nearest hundredth
Thus, for 3.14, the number in the hundredth place is 4. To round it, we will look at the third digit after the decimal, which is 0. We know any number lower than 5 is rounded down to zero, so we will round down and the rounded number will be 3.14. Conclusion: 3.14 rounded to the nearest hundredth is 3.14 itself.
Answer: 3.14
Step-by-step explanation: It’s not possible to round the answer so it would just be 3.14
Is there a composition of transformations that maps triangle ABC onto triangle XYZ.
Use the drop down options to accurately complete the sentences below about
transformations involving these two triangles.
Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).
Describe Dilation?Dilation is a geometric transformation that involves changing the size of an object while maintaining its shape and proportions. In dilation, every point of the original figure is expanded or contracted away from a fixed point called the center of dilation.
The ratio of the distance between the center of dilation and each point of the original figure is the same for all corresponding points in the dilated figure. This ratio is called the scale factor, and it determines the degree of dilation.
If the scale factor is greater than 1, the figure is enlarged or dilated, while if the scale factor is less than 1, the figure is reduced or contracted. If the scale factor is negative, the figure is reflected across the center of dilation before being dilated.
Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).
Triangle ABC is similar to Triangle XYZ.
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The equation A equals P quantity 1 plus 0.06 over 4 end quantity all raised to the power of 4 times t represents the amount of money earned on a compound interest savings account with an annual interest rate of 6% compounded quarterly. If after 15 years the amount in the account is $16,497.06, what is the value of the principal investment? Round the answer to the nearest hundredths place.
The value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
What is interest rate?Interest rate refers to the percentage amount charged or paid on a loan or investment, usually expressed as an annual percentage rate (APR). It represents the cost of borrowing or the return earned on an investment.
According to question:The equation you provided represents the compound interest formula:
A = P[tex](1 + r/n)^(n*t)[/tex]
Given that the annual interest rate is 6% and is compounded quarterly (i.e., n = 4), and the amount in the account after 15 years is $16,497.06, These values can be plugged into the equation to find P.
A = $16,497.06
r = 0.06 (6% expressed as a decimal)
n = 4
t = 15
$16,497.06 = P[tex](1 + 0.06/4)^(4*15)[/tex]
Dividing both sides by [tex](1 + 0.06/4)^(4*15)[/tex] to isolate P, we get:
P = $16,497.06 / [tex](1 + 0.06/4)^(4*15)[/tex]
Plugging in the values and solving for P using a calculator, we get:
P ≈ $9,000.39
So, the value of the principal investment (rounded to the nearest hundredth) is $9,000.39.
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−
0.1
+
�
1.7
=
−0.1+
1.7
y
=
0.9
0.9
Answer: Actually, the correct answer is:
−0.1 + 1.7 = 1.6
So, y = 1.6.
Step-by-step explanation:
Write down all of the statements below that are correct.
7.2 cm³ > 720 mm³
0.087 m³ <8700 cm³
300 mm³ = 0.03 cm³
8 m³=8,000,000 cm³
The correct statements for inequality are:
0.087 m³ < 8700 cm³
8 m³ = 8,000,000 cm³
What is inequality?An inequality is a mathematical statement that compares two expressions or values and indicates that one is greater than, less than, or not equal to the other. Inequalities use symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), and "≠" (not equal to) to show the relationship between the two expressions.
Here,
The statement "300 mm³ = 0.03 cm³" is incorrect because 300 mm³ is equal to 0.3 cm³ (since 1 cm = 10 mm).
The statement "7.2 cm³ > 720 mm³" is incorrect because 1 cm³ is equal to 1000 mm³, so 7.2 cm³ is equal to 7200 mm³. Therefore, 7.2 cm³ is less than 720 mm³.
Note: When comparing volumes, it is important to make sure that the units are consistent (e.g. converting all volumes to the same unit of measurement) before making any comparisons.
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Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
A. same line
B. parallel
C. neither perpendicular nor parallel
D. perpendicular
Answer:
B. Parallel
Step-by-step explanation:
Let S1 be the slope of the line passing through the points
(9, - 5) and (5, - 2).
S1 = (- 2 -(- 5))/(5 - 9)
= (- 2 + 5)/(- 4)
= 3/(- 4)
S1 = - 3/4
Let S2 be the slope of the line passing through the points
(- 4, - 2) and (- 8, 1).
S2 = (1 -(- 2))/(-8 -(- 4))
= (1 + 2)/(- 8 + 4)
= 3/(-4)
S2 = - 3/4
Since,
the slope of two lines are same.
They are parallel.
Find the vertex and the
�
x- and
�
y-intercepts of the equation
�
=
�
2
−
2
�
−
8
y=x
2
−2x−8
Then, use the points to graph the parabola.
a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
Preview
b) Identify the
�
x-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None.
�
x-intercept
Preview
c) Identify the
�
y-intercept of the parabola. Enter your answer as an ordered pair.
�
y-intercept
Preview
d) Use the points you found to graph the parabola.
The vertex of the parabola is at (1, -9). The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
What is vertex ?
To find the vertex and the x- and y-intercepts of the equation y = x² - 2x - 8, we can start by completing the square to put the equation in vertex form:
y = x² - 2x - 8
y + 8 = x² - 2x
y + 8 + 1 = x² - 2x + 1
y + 9 = (x - 1)²
So, the vertex of the parabola is at (1, -9). The x-coordinate of the vertex is found by taking the opposite of the coefficient of x in the equation (which is -2) and dividing by two times the coefficient of x (which is 1), giving x = -(-2) / (2*1) = 1. The y-coordinate is found by substituting x = 1 into the equation.
What are the intercepts?
To find the x-intercepts, we set y = 0 and solve for x:
0 = x² - 2x - 8
0 = (x - 4)(x + 2)
So, the x-intercepts are at (-2, 0) and (4, 0).
To find the y-intercept, we set x = 0 and solve for y:
y = 0² - 2(0) - 8
y = -8
So, the y-intercept is at (0, -8).
To graph the parabola, we can use the vertex and intercepts we found.
The vertex is (1, -9), which is the lowest point on the parabola. The x-intercepts are (-2, 0) and (4, 0), which are the points where the parabola crosses the x-axis. The y-intercept is (0, -8), which is the point where the parabola crosses the y-axis.
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establish the identity
The identity is cos²∅+sin²∅= 1.
What is trignometric ratios?
This is the boundary or contour length of a 2D geometric shape.
Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.
The same wire can be used to create a square if all sides are the same length.
The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.
As we can say, the surroundings are one-dimensinal. As a result, you can measure in meters, kilometers, millimeters, etc.
Inches, feet, yards, and miles are other globally recognized units of circumference measurement.
According to our question-
cos(90∘−θ)=sinθ
sin(90∘−θ)=cosθ
cos²∅+sin²∅= 1.
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Here is a scatter plot that shows the age of some used
cars and their prices in 2020, together with the graph of
a linear model for the relationship between price and
age.
Approximate the slope of the linear model shown in the
scatter plot.
The point that appears to be closest to the coordinates (29, 37.7) on the scatter plot is (29,37).
What is scatter plot?A scatter plot is a type of chart that displays values for two variables for a set of data. The data points in a scatter plot are represented by dots or circles, and their position on the chart represents the values of the two variables. One variable is usually plotted on the horizontal axis (x-axis) and the other variable is plotted on the vertical axis (y-axis). By analyzing the pattern of the scatter plot, you can see whether there is a relationship between the two variables, and what kind of relationship it is (positive, negative, or no relationship). Scatter plots are useful for identifying patterns, trends, and relationships in data, and are commonly used in scientific research, engineering, economics, and many other fields.
Here,
To find the foot length closest to 29, we need to look for the point on the scatter plot that has an x-value closest to 29.
Using the equation of the line provided (y=0.3x+29), we can see that when x=29, y=0.3(29)+29=37.7. Therefore, we are looking for the point on the scatter plot with an x-value close to 29 and a y-value close to 37.7.
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Complete question:
Here is a scatter plot that shows the lengths and widths of `20` left feet together with the graph of a model of the relationship between foot length and width. Circle the point that represents the foot length closest to `29`.
Four tomatoes cost $3.40. What is the uint raet? pleease help
Answer: $0.85 per tomato
Step-by-step explanation:
To find the unit rate, we need to determine the cost of one tomato. We can do this by dividing the total cost of the four tomatoes by the number of tomatoes:
$3.40 ÷ 4 = $0.85
Therefore, the cost of one tomato is $0.85. The unit rate can also be expressed as a fraction, which is:
$0.85 per tomato, or 85 cents per tomato
Answer:
The Unit rate is 0.85
Step-by-step explanation:
You divide it by 4
In the xy-plane, a line crosses the y-axis at the point (0, 3) and passes through the point (4, 5). Which of the following is an equation of the line?
Answer:
y = 1/2 x + 3
Step-by-step explanation:
y = mx + b
You need to find the slope (m) and the y-intercept (b) to write the equation
The slope is the change in y over the change in x.
(0,3) (4,5) The y values are 5 and 3. The x values are 4 and 0. You find the change by subtracting.
[tex]\frac{5-3}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
The slope (m) is 1/2.
The y-intercept is the point (0,b). They give us this with the point (0,3) The y-intercept (b) is 3
y = 1/2 x + 3
Helping in the name of Jesus.
Lines BC and DE are both vertical. What is the length of BD?
Answer: I believe it is option (A): 4.5
Step-by-step explanation: If you look closely and examine DE and CE you will see they are the same length, and we know they are 5. But if you compare the lines from a diagonal perspective, BD is not equal to 5 and has to be a bit smaller. The closest option below 5 is therefore 4.5
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The equation of line t is 3X-Y=6. Line m is the image of line t after a dilation with a scale factor of 1/2 centered at the origin. What is the equation of the line m?
Answer: y=3x
Step-by-step explanation: To find the equation of the line m, which is the image of line t after a dilation with a scale factor of 1/2 centered at the origin, we need to follow these steps:
Rewrite the equation of line t in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
3X - Y = 6
-Y = -3X + 6
Y = 3X - 6
So the slope of line t is 3.
Apply the dilation with a scale factor of 1/2 centered at the origin. This means that every point on line t is multiplied by 1/2 in both the x and y directions. The origin (0,0) remains fixed.
The new coordinates of any point on line t after dilation are given by (1/2x, 1/2y).
Use the new coordinates to find the equation of line m. To do this, we need to find the slope of line m and a point on it.
The slope of line m is the same as the slope of line t, which is 3.
To find a point on line m, we can use the fact that the origin remains fixed after dilation. So the point (0,0) is on line m.
Using the slope-intercept form, y = mx + b, we can write the equation of line m as:
y = 3x + b
To find the value of b, we can use the point (0,0):
0 = 3(0) + b
b = 0
Therefore, the equation of line m is y = 3x.
The Equation of line m is y= 3x - 3.
What is Scale Factor?A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.
We have, Equation of line t
3x - y = 6
Take x= 0 then y = -6 and y= 0 then x = 2.
Now, dilate the coordinates by factor 1/2 as
(0, -3) and (1, 0).
So, the Equation of line m is
(x - 0) / (1- 0) = (y - (-3)) / (0 - (-3))
x/1 = y + 3 / 3
3x = y+ 3
y= 3x - 3
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Question 6 (4 marks available)
.
A group of students were given a spelling test.
The table shows their marks.
a) Work out the range of the marks.
b) How many students are in the group?
c) Work out the mean mark of the group.
Represent and Analyse C
Mark
6
7
8
9
10
Frequency
5
4
7
10
4
Answer:
A) Range = 2
B) 30 Students
C) 8 Marks
Step-by-step explanation:
A) Range = Biggest - Smallest
Frequency = How many students achieved that many marks
Range = 9-7 = 2
C) Mean = Times the Marks by the Frequencies, add them together, then divide by total frequency (No. of students)
6x5=30
7x4=28
8x7=56
9x10=90
10x4=40
30+28+56+90+40=244
Total Frequency = 30
244/30=8.13
Round to nearest mark = 8
Hope this helped
Find the value of $1000 deposited for 5 years in an account paying 8% annual interest compounded
Answer: 2%
Step-by-step explanation: i looked it up
What are the roots of 2x2-6x+18=0
Answer:
What are the roots of 2x2-6x+18=0
Step-by-step explanation:
if a college newspaper conducts a poll  and select students at random to answer a survey find the probability of a selected student is a woman or a business major 
Sο, if οur estimatiοns are reasοnably accurate, the likelihοοd that a chοsen student is a wοman οr a business majοr is rοughly 0.6.
what is prοbability ?It describes the likelihοοd οf a specific οccurrence οr grοup οf οutcοmes in a given envirοnment and is a key idea in mathematics and statistics. Prοbability is typically stated as a number between 0 and 1, with 1 denοting a certain event and 0 denοting an impοssibility. By dividing the number οf faοurable οutcοmesv by the tοtal number οf pοssible οutcοmes, οne can determine the prοbability οf an οccurring.
We must sum the prοbabilities οf twο events—the prοbability that the student is a wοman and the prοbability that the student is a business majοr—in οrder tο get the likelihοοd that a certain student is a wοman οr a business majοr.
P(A and B) equals P(A)*P (B)
Using this presumptiοn, we may calculate the likelihοοd that a chοsen student will majοr in business and be a wοman as fοllοws:
P (wοman) = 0.2 * P (business majοr) = 0.1 (10%)
After that, we can enter this value in the previοus equatiοn:
P (wοmen majοring in business) = 0.5 + 0.2 - 0.1 = 0.6 (οr 60%)
Sο, if οur estimatiοns are reasοnably accurate, the likelihοοd that a chοsen student is a wοman οr a business majοr is rοughly 0.6.
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Complete Question:
A college has an undergraduate enrollment of 3500. Of these, 860 are business majors, 1800 are women and 425 are women business majors.
a. Are the events "selecting a woman student" and "selecting a business major" mutually exclusive? Explain.
b. If a college newspaper conducts a poll and selects students at random to answer a survey, find the probability that a selected student is a woman or a business major.
vEvaluate this table.
X 5 10 15 25 40
Y 1 2 3 5 8
The table represents a(n)
multiplicative
relationship
Answer:
y = 1/2 x
Step-by-step explanation:
y = mx + b
We need to find the m (slope) and the b (y-intercept)
The slope is the change in y over the change in x. Use to points on the line to find the slope.
(4,2) and (6,3)
[tex]\frac{3-2}{6-4}[/tex] = [tex]\frac{1}{2}[/tex]
The slope (m) is 1/2.
Use the slope and one of the points to calculate b
I will use the point (4,2)
y = mx + b
2 = 1/2(4) +b
2 = 2 +b Subtract 2 from both sides
0 = b
The y-intercept (b) is 0
y = _m + _
y = 1/2x + 0
y = 1/2 x
Helping in the name of Jesus.
A hiker is climbing at a constant rate of 2.4 miles per hour. Part A If d represents the distance the hiker climbed and h represents the time in hours, write an equation to model the relationship. Explain your answer. ( please help-)
Calculate the mean, median, and mode for each shift and explain calculations.
Morning shifts 8,15,16,18,18,20,21,21,21,56 Evening shifts 3,11,12,14,22,22,30,33,34,47
Answer:
Morning shifts -
Evening shifts -
Step-by-step explanation:
Morning
mean: (8+15+16+18+18+20+21+21+21+56) / 10 = 21.4
median: 10 numbers + 1 / 2 =5.5th number is median. therefore that is 19 (numbers have to be in chronological order to start counting)
mode: (most common number) 21
Evening
mean: (3+11+12+14+22+22+30+33+34+47) / 10 = 22.8
median: 10 numbers + 1 / 2 =5.5th number is median. therefore that is 22
mode: 22
need help pls and thank you
The measures for the triangle are given as follows:
x = 10.7.y = 12.3.z = 21.8.What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The base is composed by two lengths of 6 and 25 - 6 = 19, hence the value of x is obtained applying the Geometric Mean Theorem as follows:
x² = 6 x 19
x = sqrt(6 x 19)
x = 10.7.
The value of y is then the hypotenuse of a right triangles of sides 10.7 and 6, hence:
y² = 10.7² + 6²
y = sqrt(10.7² + 6²)
y = 12.3.
The value of z is then the hypotenuse of a right triangles of sides 10.7 and 19, hence:
z² = 10.7² + 19²
z = sqrt(10.7² + 19²)
z = 21.8.
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Find the length of a circle inscribed in a rhombus if its side and angle are equal: 8 cm and 60 degrees. С=?
The length of the circle is approximately 9.237 cm.
What are the diagonals of a rhombus?
A rhombus is a quadrilateral with all sides of equal length. It also has the following properties regarding its diagonals:
The diagonals bisect each other at 90 degrees.
The diagonals are perpendicular to each other.
The diagonals have the same length.
The diagonals divide the rhombus into four congruent triangles.
In a rhombus with a side of 8 cm and an angle of 60 degrees, the diagonals are equal in length.
The length of the diagonals can be found using the formula:
[tex]$D_1 = \frac{2a}{\sqrt{3}}$[/tex]
where a is the length of the side. Substituting the value of a as 8 cm, we get:
[tex]$D_1 = \frac{2(8)}{\sqrt{3}} \approx 9.237 \text{ cm}$[/tex]
The length of the circle inscribed in the rhombus is equal to the length of the diagonals.
Therefore, the length of the circle is approximately 9.237 cm.
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The circumference of a circle is 6.3mm.
Find the length of the diameter.
Give your answer rounded to 3 SF.
The diameter of the circle is equal to 2.00 mm rounded to 3 significant figures.
What is the diameter of a circleThe diameter of a circle is a straight line that passes through the center of the circle and whose endpoints are on the circumference of the circle. We can use the formula for the circumference of a circle to calculate for the diameter.
circumference of is derived using πD or 2πr, where D is the diameter, π is 22/7, and r the radius.
The given circle have 6.3 mm circumference, so;
6.3 mm = 22/7 × D
D = (6.3 mm × 7)22 {cross multiplication}
D = 44.1 mm/22
D = 2.0045
Therefore, the diameter of the circle is equal to 2.00 mm rounded to 3 significant figures.
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A number, c, rounded to 1 d.p. is 47.3
Another number, d, rounded to 1 d.p. is 4.6
What are the lower and upper bounds of c - d?
The lower bound of c - d is 42.66 and the upper bound of c - d is 42.7.
Calculating the lower and upper bounds of c - d?Given that
c, rounded to 1 d.p. is 47.3d, rounded to 1 d.p. is 4.6To find the upper and lower bounds of c - d, we first need to find the maximum and minimum possible values of c and d.
For c rounded to 1 decimal place, the actual value of c could be between 47.25 and 47.34.
This is because when we round to 1 decimal place, we take the first decimal place and round up or down depending on the second decimal place.
Similarly, we have
d = 4.59 to 4.64
So, we have
c - d = 47.25 - 4.59 to 47.34 - 4.64
Evaluate
c - d = 42.66 to 42.7
Therefore, the lower bound of c - d is 42.66 and the upper bound of c - d is 42.7.
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Margo borrows $1300, agreeing to pay it back with 3% annual interest after 14 months. How much interest will she pay?
Round your answer to the nearest cent, if necessary.
Margo will pay approximately $45.50 in interest on the loan.
What is interest?
Borrowers must pay lenders simple interest as a fee in exchange for a loan.
First, we need to calculate the interest that Margo will pay on the loan.
Interest = Principal x Rate x Time
where:
Principal = $1300
Rate = 3% per year (or 0.03)
Time = 14/12 years (since there are 12 months in a year)
Plugging in the values, we get:
Interest = $1300 x 0.03 x (14/12)
Interest ≈ $45.50
Therefore, Margo will pay approximately $45.50 in interest on the loan.
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"John's T.V". gives you 25% discount on a $987.48 T.V and you pay 6 1/2 sales tax on the balance. If you take out a 2 year loan with an annual interest rate of 15.6%, what will your monthly payment be?
Answer:
To calculate the monthly payment for the TV after the discount, sales tax, and financing, we need to follow these steps:
Step 1: Calculate the discount
Discount = 25% of $987.48
Discount = 0.25 x $987.48
Discount = $246.87
Step 2: Calculate the discounted price of the TV
Price after discount = $987.48 - $246.87
Price after discount = $740.61
Step 3: Calculate the sales tax
Sales Tax = 6.5% of $740.61
Sales Tax = 0.065 x $740.61
Sales Tax = $48.15
Step 4: Calculate the total cost of the TV after discount and sales tax
Total cost = Price after discount + Sales Tax
Total cost = $740.61 + $48.15
Total cost = $788.76
Step 5: Calculate the monthly payment on the 2-year loan with 15.6% annual interest rate using the following formula:
Monthly Payment = (P x r) / (1 - (1 + r)^(-n))
where P is the principal (total cost of the TV), r is the monthly interest rate (15.6% / 12), and n is the number of months (24).
Monthly Interest Rate = 15.6% / 12
Monthly Interest Rate = 0.013
Monthly Payment = ($788.76 x 0.013) / (1 - (1 + 0.013)^(-24))
Monthly Payment = $36.89
Therefore, the monthly payment on the 2-year loan for the TV is $36.89.
Step-by-step explanation:
a) The temperature the day after Hurricane Katrina in August 2005 was 91°F. It then fell three degrees, rose 5 degrees and fell another 2°F. What was the final temperature?