Answer:
1 degree = 60 minutes
Step-by-step explanation:
The DMS method is for Degree Minutes Seconds. That allows you to give a precise location the way it's most commonly used on paper maps. Today, with the electronic maps we mostly use the numeric version (34.234 degrees for example).
So, in the DMS method, one degree is basically like an hour on your clock. It can be divided into 60 minutes. Then, those minutes can be divided into 60 seconds. Just like an hour, a degree has 60 minutes and 3600 seconds.
Final answer:
One degree in the DMS method of angle measurement is divided into 60 minutes. To convert DMS to DD, like with 118 degrees 15 minutes, divide the minutes by 60 and add the result to the degrees, giving you 118.25.
Explanation:
In the DMS method of angle measurement, one degree is equivalent to 60 minutes of angle. This is similar to how an hour of time is divided into 60 minutes. To visualize this, if you consider a full circle being 360 degrees, each degree can be further subdivided into 60 smaller parts, each of these parts is known as a minute of angle.
For example, the conversion of 118 degrees 15 minutes to decimal degrees (DD) is a simple mathematical process. You would divide the minutes by 60 since there are 60 minutes in a degree, resulting in the equation 118 + 15/60, which equals 118.25 degrees. This conversion is an important skill in coordinate conversion activities, where positions are described in DMS format and need to be converted to DD for calculations.
Solve the system by using a matrix equation
2x-3y=3
5x-7y=9
Answer:
The correct answer would be option C
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Suppose Company A produces packages of throat lozenges that are normally distributed with a mean of 38.2 individual lozenges and a standard deviation of 1.7 lozenges.
Company B produces packages of throat lozenges that are normally distributed with a mean of 36.9 individual lozenges and a standard deviation of 2.4 lozenges.
Select from the drop-down menus to correctly complete the statement.
CHOICES ARE COMPANY A AND COMPANY B
Answer: B, A, B
Step-by-step explanation:
Let's find the z-score for both companies using the formula: [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Company A: [tex]z=\dfrac{43-38.2}{1.7}=\large\boxed{2.8}[/tex]
Company B: [tex]z=\dfrac{43-36.9}{2.4}=\large\boxed{2.5}[/tex]
The z-score from Company B is closer to 0 than the z-score of Company A so it it more likely that a package of 43 lozenges is produced by Company B
Since the z-score from Company A is closer to zero than the z-score of Company B, the company that produced a package with 43 lozenges in it is most likely Company A.
To find which company is more likely to produce a package with 43 lozenges, we'll first calculate the z-scores for each company using the formula:
[tex]\[ z = \frac{x - \mu}{\sigma} \][/tex]
Where:
- [tex]\( x \)[/tex] is the number of lozenges in the package (43)
- [tex]\( \mu \)[/tex] is the mean number of lozenges in the package for each company
- [tex]\( \sigma \)[/tex] is the standard deviation of the number of lozenges in the package for each company
For Company A:
[tex]\[ z_A = \frac{43 - 38.2}{1.7} = \frac{4.8}{1.7} \approx 2.82 \][/tex]
For Company B:
[tex]\[ z_B = \frac{43 - 36.9}{2.4} = \frac{6.1}{2.4} \approx 2.54 \][/tex]
Since the z-score for Company A (2.82) is higher than the z-score for Company B (2.54), it indicates that the value of 43 lozenges is relatively further away from the mean for Company A compared to Company B.
Thus, Company A is more likely to produce a package with 43 lozenges.
The correct question is:
Suppose Company A produces packages of throat lozenges that are normally distributed with a mean of 38.2 individual lozenges and a standard deviation of 1.7 lozenges.
Company B produces packages of throat lozenges that are normally distributed with a mean of 36.9 individual lozenges and a standard deviation of 2.4 lozenges.
Select from the drop-down menus to correctly complete the statement.
Since the [tex]$z$[/tex]-score from [tex]$\square$[/tex] is closer to zero than the [tex]$z$[/tex]-score of [tex]$\square$[/tex] , the company that produced a package with 43 lozenges in it is most likely [tex]$\square$[/tex] .
PLEASE HELP! TRYING TO FINISH MATH EARLY! PLEASE ACTUALLY ANSWER, AND NOT JUST TAKE THE POINTS! Thank You! ;3
(05.06 MC)
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y > −4x − 1
y is less than 3 over 2 times x minus 1
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area.
Part B: Is the point (−1, −1) included in the solution area for the system? Justify your answer mathematically.
A) the graph is a linear and the slope is negative and positive .
B) (-1,-1) is not a solution because that point does not appear in the shaded region, therefore there is no solution.
:D
Amber is on a family cell phone plan with 2 other family members. The family gets 720 shared cell phone minutes a month, each family is limited to his or her equal fair share of minutes each month and calls between family members cost zero minutes. How many minutes per day does Amber have to call her friends without going over her monthly minutes if there are 30 days in that month?
Amber plus 2 family members = 3 total people on the plan.
They share the minutes equally so divide the minutes by 3 to find how many she can use:
720 / 3 = 240 minutes per month.
Now divide the monthly minutes by 30 days:
240 / 30 = 8 minutes per day.
Suppose 15% of the apples picked one afternoon are rotten. The following simulations demonstrate how apples can be randomly chosen and then recorded as rotten or not rotten. Which simulation best models the scenario? Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten". Place 15 equally sized pieces of paper in a hat. Of the 15, 3 read "rotten," and the rest read "not rotten". Place 30 equally sized pieces of paper in a hat. Of the 30, 3 read "rotten," and the rest read "not rotten". Place 12 equally sized pieces of paper in a hat. Of the 12, 3 read "rotten," and the rest read "not rotten".
Answer:
Place 20 equally sized pieces of paper in a hat. Of the 20, 3 read "rotten," and the rest read "not rotten".
Step-by-step explanation:
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is . If the coordinates of point D are (5 , 5), the equation of line is y = x + .
Answer with explanation:
Equation of line Passing through two points (a,b) and (c,d) is given by:
[tex]\frac{y-b}{x-a}=\frac{d-b}{c-a}[/tex]
Equation of line Passing through two points (8,0) and (3,7) is given by:
[tex]\rightarrow \frac{y-7}{x-3}=\frac{7-0}{3-8}\\\\\rightarrow \frac{y-7}{x-3}=\frac{7}{-5}\\\\\rightarrow -5 y+35=7 x - 21\\\\\rightarrow 5 y= -7 x +35 +21\\\\ y=\frac{-7 x}{5}+\frac{56}{5}\\\\y=-1.4 x +11.2[/tex]
Comparing with slope intercept form of line,
y= m x+c, where , m is slope and c is y intercept.
⇒Y intercept = 11.2
Equation of line Passing through two points (5,5) and (3,7) is given by:
[tex]\rightarrow \frac{y-7}{x-3}=\frac{7-5}{3-5}\\\\y-7= -1 \times (x-3)\\\\y=7-x+3\\\\y=-x +10[/tex]
Comparing with slope intercept form of line,
y= m x+c, where , m is slope and c is y intercept.
⇒Y intercept = 10
Equation of line is, y= -x +10.
The y-intercept of the line passing through point A (8, 0) and B (3, 7) is 56/5. The equation of the line that passes through these points and point D (5, 5) is y = (-7/5)x + (56/5).
To determine the y-intercept and the equation of a line, we first need to find the slope of the line. The slope (m) is given by the rise over run, which can be calculated using the coordinates of two points on the line. We have point A with coordinates (8, 0) and point B with coordinates (3, 7). The slope is therefore:
m = (Y2 - Y1) / (X2 - X1) = (7 - 0) / (3 - 8) = 7 / (-5) = -7/5
Now, we use the slope-intercept form of a line equation, which is y = mx + b, where b is the y-intercept. We can determine b by substituting the slope and the coordinates of one of the given points (we'll use point A). So:
0 = (-7/5)(8) + b
b = (7/5)(8) = 56/5
Therefore, the y-intercept is 56/5.
Knowing point D with coordinates (5, 5) is also on the line, we can use our slope m and this point to write the equation of the line:
y = (-7/5)x + (56/5)
However, since we know point D lies on this line, we can check if our equation is correct by substituting x = 5 and seeing whether y = 5:
5 = (-7/5)(5) + (56/5)
5 = -7 + 56/5
5 = 5
This confirms that our calculated equation is indeed correct and passes through all given points.
Help on number 6, please explain
So it's asking how many times greater is 6,000 than 600. Simply divide to find that it is 10 times greater.
Hope this helps you!
The 6 in the hundreds place is 100 and the 6 in the thousands place is 1000
So,it's 10x greaterEvaluate cot870°.
1. - sqrt3
2. -1/sqrt3
3. 1/sqrt3
4. sqrt3
ANSWER
[tex] -\sqrt{3}[/tex]
EXPLANATION
The given angle is 870°.
870°-360°-360°=150°
This means that:
870° is coterminal with 150°, hence its terminal side is in the second quadrant.
It makes an acute angle of 30° with the x-axis.
Note that cotangent is negative in the second quadrant,
Hence,
[tex] \cot(870 \degree) = \cot(150 \degree) = - \cot(30 \degree) = - \frac{1}{ \tan(30 \degree) } = - \sqrt{3} [/tex]
The first option is correct.
Answer:
use math-way
Step-by-step explanation:
= - square root of 3
A polynomial function has a zero at 4 (multiplicity 3) and 0 (multiplicity 1)
write is standard and simplifed form
Answer:
Y=3x(x-4)
Step-by-step explanation:
What is the leading coefficient of the polynomial?
23x5 + 12x2 + 19x3 + 15x6
A) 12
B) 15
C) 19
D) 23
ANSWER
B) 15
EXPLANATION
The given polynomial is
[tex]23 {x}^{5} + 12 {x}^{2} + 19 { x }^{3} + 15 {x}^{6} [/tex]
We arrange this polynomial in ascending powers of x to obtain the standard form;
[tex] 15 {x}^{6} + 23 {x}^{5} + 19 { x }^{3} + 12 {x}^{2}[/tex]
The degree of this polynomial is 6.
The coefficient of the leading term is 15
the mean (rounded to the nearest tenth if needed) of the following data set is: 110, 142, 120, 180, 151, 110, 159, 173, 173, 144, 110
A. 142.9
B. 157.2
C. 131
D. 146.8
Answer:
A
Step-by-step explanation:
Add up all of the numbers:
110+142+120+180+ 151+110+159+173+173+144+110 = 1572
Next you divide by how many number there are (there are 11 numbers)
1572 ÷ 11 = 142.9090909
142.9090909 rounded to the nearest tenth is 142.9
Answer:
A. 142.9
Step-by-step explanation:
There are 11 members in the data set, therefore:
The mean = (110+142+120+180+151+110+159+173+173+144+110) / 11
= 1572/11
= 142.9.
Determine whether the function is periodic. If it is periodic, find the period.
f(x) = 3 sin 2x + 4 cos 3x
Answer
a) 2π
Step-by-step explanation:
We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is periodic.
The function is
f(x) = 3*sin(2*x) + 4*cos(3*x)
Which can be seen in the picture below
We can notice that f(x) is periodic. It has periodic amplitudes, and the function has a period T = 6.283 ≈ 2π
The maximum and minimum values are
Max = 6.695
Min = -6.695
A surveyor is dividing a large plot of land that measures 27,512 square miles. He wants to divide the area into 91 equal regions. Estimate how large each area will be. Show your work.
Answer:
302 mi²
Step-by-step explanation:
Actually we're looking for the "unit rate," which here is the number of square miles are in each region:
27,512 mi²
---------------- = 302 mi² approximately (rounded up from 302.33 mi²)
91 regions
Find the exact volume of the cylinder. A) 80π ft3 B) 160π ft3 C) 200π ft3 D) 400π ft3
80 ft^3 is the answer
Answer:
200ft^3
Step-by-step explanation:
in the 1980s, an average mortgage range was around 18.75%. how much less per month would a $125,000 30 year mortgage be today if the current rate were 5%?
Answer:
$1289.48
Step-by-step explanation:
A financial calculator tells you the payment with the higher interest rate is $1960.51, and that with the lower interest rate is $671.03. The difference in payment amounts is ...
$1960.51 -671.03 = $1289.48
Answer:
The current per month mortgages are $1289.54 less than the earlier per month mortgages.
Step-by-step explanation:
The EMI formula is = [tex]\frac{p\times r\times (1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Here p = 125000
For case 1:
r = 18.75/12/100=0.015625
n = [tex]30\times12=360[/tex]
So, putting values in formula we get :
[tex]\frac{125000\times 0.015625\times (1+0.015625)^{360} }{(1+0.015625)^{360}-1 }[/tex]
= $1960.51
For case 2:
r = 5/12/100=0.004166
n = [tex]30\times12=360[/tex]
So, putting values in formula we get :
[tex]\frac{125000\times 0.004166\times (1+0.004166)^{360} }{(1+0.004166)^{360}-1 }[/tex]
= $670.97
Now we will find the difference between both EMI's
[tex]1960.51-670.97=1289.54[/tex] dollars.
Therefore, the current per month mortgages are $1289.54 less than the earlier per month mortgages.
If there are initially 5000bacteria in a culture,and the number of bacteria doubles each hour,the number N of bacteria after t hours can be found using the formula N = 5000 [2 t ^]. About how long will it take the culture to grow to 40000 bacteria?
Answer:
3 hours
Step-by-step explanation:
3 hours as it takes 3 periods to be 40000
If there are initially 5000 bacteria in a culture,and the number of bacteria doubles each hour. The culture will take around 3 hours to reach 40,000 bacteria.
What is bacteria?To determine how long it will take for the culture to grow to 40,000 bacteria, we can use the given formula: N = 5000 * (2^t), where N represents the number of bacteria after t hours.
Substitute N with 40,000 and solve for t:
40,000 = 5000 * (2^t)
Divide both sides by 5000:
8 = 2^t
Since 2^3 = 8 we can conclude that t is equal to 3
Therefore it will take approximately 3 hours for the culture to grow to 40,000 bacteria.
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Identify the volume of the sphere in terms of π. HELP PLEASE!!
Answer:
its C
Step-by-step explanation:
PLEASE HELP DON'T UNDERSTAND THIS AT ALL AND PLEASE SHOW YOUR WORKING WILL CHOOSE THE BEST PERSON TO BE THE BRAINLIEST
Answer:
40 cm
Step-by-step explanation:
Since the figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{4x}{x}[/tex] = [tex]\frac{48}{x+2}[/tex], simplifying gives
4 = [tex]\frac{48}{x+2}[/tex]
Multiply both sides by (x + 2)
4(x + 2) = 48 ( divide both sides by 4 )
x + 2 = 12 ( subtract 2 from both sides )
x = 10
Hence
width = 4x = 4 × 10 = 40
If the r-value or correlation coefficient of a data set is 0.827, what is the coefficient of determination to three decimal places?
A. 0.884
B. 0.627
C. 0.684
D. 0.827
Answer: Option C
[tex]r ^ 2 = 0.684[/tex]
Step-by-step explanation:
The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.
If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.
If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.
Then for a relationship, the coefficient of determination [tex]r ^ 2[/tex] is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.
The coefficient of determination [tex]r ^ 2[/tex] for a linear relationship is calculated as the square of the correlation coefficient.
In this problem we have that the correlation coefficient r is
[tex]r = 0.827[/tex]
then the coefficient of determination is:
[tex]r ^ 2 = 0.827 ^ 2[/tex]
[tex]r ^ 2 = 0.684[/tex]
The answer is option C
the area of a rectangle is 75 square centimeters the rectangle is 5 centimeters wide how long is the rectangle
Answer: 15 cm
Step-by-step explanation:
The formula for calculate the area of a rectangle is:
[tex]A=l*w[/tex]
Where "l" is the lenght and "w" is the width.
You know that the area of this rectangle is 75 square centimeters and the width is 5 centimeters. Then, you can substitute these values into the formula [tex]A=l*w[/tex] and solve for the lenght. Then you get:
[tex]75cm^2=l(5cm)\\\\\frac{75cm^2}{5cm}=l\\\\l=15cm[/tex]
Therefore, the lenght of the rectangle is 15 centimeters.
Answer:
15 centimeters.
Step-by-step explanation:
To find the area of a rectangle, you have to multiply the length by the width.
In this case, the width is 5 centimeters.
So, so find the area, you would have to multiply 5 by the length. Let's call the length "x".
The equation to solve this problem would be:
5x - 75
Now we can solve the equation...
Divide both sides by 5...
5x / 5 = 75 / 5
x = 15
Since x is equal to 15, that means that the length is 15, because we said that the length is equal to x.
Length = x = 15
------------------
Hope this helped!
Select the coordinates of two points on the line y = 8. (2 points) (8, 8) and (8, 0) (8, −8) and (8, 8) (0, 8) and (8, 0) (0, 8) and (8, 8)
(8, 8) and (0, 8). If the equation is y = any number, the second coordinate will always be that number. :)
Please help me out :)
Answer:
A = 25√3 cm²
Step-by-step explanation:
View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure. To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).
opp
Using the sine function sin Ф = --------
hyp
we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:
√3 5√3 cm
sin 60° = -------- = ------------- , which produces the value of hyp:
2 hyp
√3 5√3 cm
-------- = ------------- , which produces the value of hyp:
2 hyp
√3·hyp = 10√3, or hyp = 10 cm
Then the area of this one triangle is A = (1/2)(b)(h), or
A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²
The length of a rectangle, I, is six meters more than it's width, w. If the perimeter of the rectangle is 36 meters what is the length of the rectangle, in meters
Answer:
Length = 12 meters
Step-by-step explanation:
Rectangle
Perimeter P = 2(L + W)
The length of a rectangle, I, is six meters more than it's width, W.
Then L = W + 6
So
P = 2(W + 6 + W)
P = 2 (2W + 6)
P = 4W + 12
Plug in P = 36 meters
36 = 4W + 12
4W = 36 - 12
4W = 24
W = 6 meters
L = 6 + 6
L = 12 meters
A square cement parking lot is being converted to a nature park. Each side of the parking lot is 100 meters long. The plan is to reduce the side lengths of the lot by 8 meters each year to plant greenery. Which function can be used to calculate the area of the cement parking lot, A, after t years?
Answer:
[tex]A(t)=(100-8t)^{2}[/tex]
Step-by-step explanation:
Let
t-----> the number of years
A-----> the area of the cement parking lot
we know that
The function that represent this situation is
[tex]A(t)=(100-8t)^{2}[/tex]
Final answer:
The function A(t) = [tex](100-8t)^2[/tex] can be used to calculate the area of the cement parking lot after t years by substituting the side length (100-8t) into the formula for the area of a square.
Explanation:
The function that can be used to calculate the area of the cement parking lot after t years is: A(t) = [tex](100-8t)^2[/tex].
To calculate the area of the square parking lot at any given time t, you substitute the side length (100-8t) into the formula for the area of a square, A = side [tex]length^2[/tex].
For example, after 2 years, the area A(2) would be[tex](100-8(2))^2[/tex] = [tex]84^2[/tex]= 7056 square meters.
The coordinates of point P on a coordinate grid are (?5, ?6). Point P is reflected across the y-axis to obtain point Q and across the x-axis to obtain point R. What are the coordinates of points Q and R? 1. Q(5, 6) and R(?5, ?6) 2. Q(?5, ?6) and R(5, 6) 3. Q(?5, 6) and R(5, ?6) 4. Q(5, ?6) and R(?5, 6)
Answer:
(5, −6) and R(−5, 6)
Step-by-step explanation:
Answer:
4. Q(5, -6) and R(-5, 6)
Step-by-step explanation:
In the coordinates of point P which is (-5,-6) when you reflect it on the Y axis that means that the Y would be the same but the X will change signs, thats why the point Q is (5.-6) and to reflect it on the X axis the X remains the same but the Y would change the sign this is why point R will be (-5,6).
So point Q is (5,-6) and point R is (-5,6).
Keith bought a baseball for 10.37 and spent 8.29 on toy trucks keith also spent 6.03 on a jacket in total how much did keith spend on toys
Answer:
$18.66
Step-by-step explanation:
Add together the amounts Keith spent on baseball and truck: $10.37 + $8.29 = $18.66. We can ignore the amount he spent on the jacket.
Find the values of x and y.
x = 90
y = 180 - (90 + 47)
y = 43
If a+b(c+d)/e =1 which of the variable a,b,c,d, or e cannot be 0?
A.) b
B.) e
C.) a
D.) d
E.) c
Answer:
B.) e
Step-by-step explanation:
If e is zero and c + d ≠ 0, then the quotient [tex]\frac{c + d}{e}[/tex] will be an undefined number and in that case;
a + b([tex]\frac{c + d}{e}[/tex]) ≠ 1
Please answer this question only if you know the answer! 33 points and brainliest!
Because the teacher only picked 5 students out of all the students it was a sample.
If the teacher had asked every student, it would have been a population.
Answer:
sample
Step-by-step explanation:
The teacher only asked the five students specifically so it is a sample.
Population would be if the teacher asked every student.
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each. The remaining 6 bottles are all of the same capacity. Let b represent the capacity, in pints, of each of the remaining 6 bottles. What is tye capacity of each of the 6 remaining bottles
Answer:
The capacity of the remaining bottles = 4 pints.
Step-by-step explanation:
6*3 + 6*b = 42
6b = 42 - 18
6b = 24
b = 4.
The required quantity of the remaining 6 bottles is 4 pints.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Ben fills 42 pints of juice in 12 bottles. Six bottles have a capacity of 3 pints each.
Let b represent the capacity, in pints, of each of the remaining 6 bottles.,
Now,
42 = 3 × 6 + b × 6
42 = 18 + 6b
6b = 42 - 18
b = 24/6
b = 4
Thus, the required quantity of the remaining 6 bottles is 4 pints.
Learn more about models here:
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