B) 12/13
1) In this triangle, the sine of angle A is given by the opposite leg over the hypotenuse, so we can write it out. Since the hypotenuse is opposite to the right angle:
[tex]\begin{gathered} \sin (A)=\frac{36}{39} \\ \sin (A)\text{ = }\frac{12}{13} \end{gathered}[/tex]Note that we simplified that original ratio 36/39 dividing both numerator and denominator by 3
2) Hence, the answer is B) 12/13
The following data represent the number of people aged 25 to 64 years covered by health Insurance (private or government) in 2018. Approximate the mean and standard deviation for age.Age
Explanation
For the given data, we will have the following:
We are given grouped data, from which we will obtain the mean and standard deviation
Thus, we will have
From the above,
We have the mean to be approximately 44.68.
For the standard deviation
We will have
Thus, we have the standard deviation to be 10.22
4. Take your values from the previous chart (In question 2) and convert them fromCelsius to Fahrenheit. Follow the example below, and use the conversion rule to fillout the chart for degrees Fahrenheit when t = 12 and t = 24. (2 polnts: 1 point foreach row)FO-c«) +32Example(0,-32)C(O)- -3.20FCO) - (-32)+32F(0) - -5.76 +32FO) - 26.24 F12
Conversion of Degrees Celsius to Degrees Fehrenheit.
[tex]\begin{gathered} F(t)=\frac{9}{5}C(t)\text{ + 32 }\ldots eqn(1) \\ \text{Making C(t) the subject of the formula, we get} \\ \text{Subtract 32 from both sides, we get} \\ F(t)\text{ -32=}\frac{9}{5}C(t)+32-32 \\ F(t)\text{ -32 =}\frac{9}{5}C(t) \\ \text{Multiplying both sides by }\frac{5}{9}\text{ , we get} \\ \frac{5}{9}\lbrack F(t)-32\rbrack=\frac{5}{9}\times\frac{9}{5}C(t) \\ \\ \frac{5}{9}\lbrack F(t)\text{ - 32\rbrack = C(t)} \\ C(t)=\frac{5}{9}\lbrack F(t)\text{ -32\rbrack}\ldots eqn(2) \end{gathered}[/tex]Substitute 12 for t in eqn(1), we get
[tex]\begin{gathered} t=12 \\ C(12)=40 \\ F(12)=\frac{9}{5}C(12)\text{ + 32} \\ F(12)=(\frac{9}{5}\times40)\text{ }+32 \\ F(12)=(9\times8)+32 \\ F(12)=72+32=104^oF \end{gathered}[/tex]When t =24,
C(24) = 0 , ( does not exist since the graph did not touch the graph)
[tex]\begin{gathered} t=24 \\ C(24)=0 \\ F(24)=\frac{9}{5}C(24)\text{ + 32} \\ F(24)=(\frac{9}{5}\times0)\text{ +32} \\ F(24)=32^oF \end{gathered}[/tex]Hence, the correct answer are:
t =12, C(12) = 104 degrees Fehrenheit, and
t =24, C(24) = 32 degrees Fehrenheit
I need help writing the formula step by step please if anyone can help
f(x)=x ^2
Translate 8.5 units to the left
f(x)= (x + 8.5 )^2
vertical Stretch of a factor of 3
f(x)= 3 (x + 8.5 )^2
7 units down
f(x)= 3 (x + 8.5 )^2 - 7
When solving an equation with one variable on both sides what are three types of solutions youcan obtain?
whenever you have an equation with one variable on both sides, you might end up with one of the following case:
1. You might end up with an inconsistent equation, therefore there is not solution. Example
x = x+3. If you subtract x on both sides, you get 0=3 which is impossible.
2. You might end up having infinite solutions. Example:
x+6 = x+6. If you subtract x on both sides you get 6 =6 which is true regardless of the value of x.
3. You might end up having only one solution. Example:
3x +2 = x +5
If you subtract x on both sides and subtract 2 on both sides, you get
2x = 3.
then if you divide by two on both sides, you find
x = 3/2. So this equation has one unique solution.
what is three.twenty-seven times one hundred
Answer:
32,700
Step-by-step explanation:
At State College last term, 57 of the students in a Physics course earned As, 79 earned Bs, 102 got Cs, 94 were issued Ds, and 53 failed the course. If this grade distribution was graphed on a pie chart, how many degrees would be used to indicate the A region?
Given:-
57 students in a physics course earned A.
79 students course earned B.
102 students course earned C.
94 students course earned D.
53 students failed the course.
To find:-
How many degrees would be used to indicate the region A.
Total number of students is,
[tex]57+79+102+94+53=385[/tex]Now we find the degrees to indicate the region A. we get,
[tex]\frac{57}{385}\times360=0.1480\times360=53.29[/tex]So the required soluion is 53.29 degrees.
4^6*3^4*2^2/4^2*3^4*2^6
Answer:
16
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors. Hope this helps! <3
Divide. Give the quotient and remainde 2249 = 3 x Quotient: S II I Remainder:
We will find the quotient and remainder as follows:
The quotient is 749 and the remainder is 2.
I need to write an explicit formula for this problem but I have not idea what I'm doing.
Given data:
The given series is -32, -25, -18, -11,....
The commo difference of the given series is,
[tex]\begin{gathered} d=-25-(-32) \\ =-25+32 \\ =7 \end{gathered}[/tex]The expression for the explicit formula for the given series is,
[tex]\begin{gathered} a_n=a+(n-1)d \\ =\text{ -32+(n-1)}(7) \\ =-32+7n-7 \\ =-39+7n \end{gathered}[/tex]The expression for recursive formula is,
[tex]\begin{gathered} a_n=a_{n-1}+d \\ =\lbrack-39+7(n-1)\rbrack+7 \end{gathered}[/tex]✓
3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are the sisters ages.
Jenny's age is 20 years, Lynn is 14 years and Kim is 23 years.
Let's take Jenny as J, Kim as K and, Lynn as L.
From the given statement we get the equation.
As the sum of the age of the three sisters is 57. So we have an equation,
J + K + L = 57 ........(i)
Jenny is 6 years older than Lynn. So the next equation is,
J = 6 + L .......(ii)
Kim is 5 years less than twice her age Lynn. So the equation is,
K = 2L -5 .........(iii)
Putting equations (ii) and (iii) in equation (i)
6 +L + 2L - 5 + L = 57
4L = 56
L = 14
Put the value of L in equations (ii) and (iii)
J = 6 + 14
= 20
K = 2(14) -5
= 28 - 5
= 23
Therefore the age of Jenny is 20 years, Lynn is 14 years and Kim is 23 years.
To know more about the ages refer to the link given below:
https://brainly.com/question/11757623
#SPJ1
Monica has a yearly salary of $29,700. Her employer withholds $2948 in state and federal taxes and $2573 in FICA taxes throughout the year. She has the following monthly costs: transportation is $140, cell phone bill is $65, student loans require $300 in repayment, and rent is $675. She is using the average monthly costs for each of the following in order to gain an idea of other monthly expenses: utilities are $130, internet is $55, health insurance is $278, and groceries are $220. What is Monica’s monthly net pay amount? Round your answer to the nearest cent, if necessary.
Step-by-step explanation:
your teacher is not very precise, I fear.
the yearly salary ($29,700) is the gross pay she gets.
the gross pay minus the taxes ($2,948 and $2,573) is then the net pay she receives.
in many cases the employer also withholds the health insurance premium (and then that has to be subtracted too before getting the net pay).
I just think your teacher means by "net pay" how much she will have left are all the monthly costs.
her annual net pay amount is
$29,700 - $2,948 - $2,573 = $24,179
the monthly net pay is $24,179/12 = $2,014.916666... ≈
≈ $2,014.92
she has to pay monthly
$140
$ 65
$300
$675
$130
$ 55
$278
$220
---------
$1,863
based on her monthly net pay she has left
2,014.916666...
- 1,863
---------------------------
151.9166667 ≈ $151.92
per month
please pick based on what you think your teacher means by net pay : the actual net pay by her employer, or how much money she has monthly left after paying all bills.
#1 - Find the inverse of the function shown. *y = ( 6х + 12)/2
The given function is expressed as
y = (6x + 12)/2
In order to determine the inverse of the given function, we would substitute x for y and y for x. Then we would solve for y. It becomes
x = (6y + 12)/2
x = 3y + 6
3y = x - 6
y = (x - 6)/3
y = x/3 - 2
The inverse is
y = x/3 - 2
If the measure of angle 1 = 2x+3 and the measure of angle 2 = 3x+2, then what is the measure of angle 3?
Answer: 126°
Step-by-step explanation:
Step-by-step explanation: Since every triangle has 180 interior degrees, we can say 2x + 3x + 90° = 180°. Subtract 90° from each side and we get
2x + 3x = 90°
5x = 90°
x = 18°
Plug in x for Angle 2, giving us Angle 2 = 54°
Angle 1 and angle 2 must add up to 180°
Subtract 54° from 180° and we get 126°
2. At 8:00pm, the temperature was 6°F. By midnight thetemperature was -2°F. If the temperature changed at aconstant rate, what integer represents the hourlychange in temperature?
We have to write the facts..
It's a little bit easy to understand if you put that numbers in a table.. like this
Now, they ask you an integer that represents a change per hour, and they say you that assume a constant change... then we complement the table with different values per hour until arrive at midnight..
now, you can see that you have two points.. with two coordinates, and you can find a line equation assuming that you have a constant change like this case...
[tex](x,y)\text{ is a general form of one point.. ok?}[/tex]that you place in the cartesian axes.. like this..
You know that you put x values in the horizontal line and y values in the vertical line..
for example, we're gonna place the point (2,1) that means that 2 in x axe and 1 in y axe..
Write an equation for a line perpendicular to 3 y − 6 x = − 15 and passing through the point (6,-4) y =
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The equation of the line is
3y-6x = -15
Convert the equation to the slope intercept form of the line
3y-6x = -15
3y = 6x-15
y = (6x-15)/3
y = 2x-5
The slope intercept form of the line
y = mx+b
By comparing the result with slope intercept form
slope of the line m = 2
The slope of the line perpendicular will be the negative reciprocal of 2
m = -1/2
Therefore the slope of the line will be
y = (-1/2)x+b
The line is passing through the point (6,-4)
Substitute the values in the equation
-4 = (-1/2)×6+b
-4 = -3+b
b = -4+3
b = -1
Substitute the values in the slope intercept form
The equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4)
y = (-1/2)x - 1
Hence, the equation of the line perpendicular to 3y-6x = -15 and passing through the point (6,-4) is y = (-1/2)x - 1
The complete question is
Write an equation for a line perpendicular to 3y − 6x = −15 and passing through the point (6,-4).
Learn more about slope intercept form here
brainly.com/question/9682526
#SPJ1
Find the surface area of the figure. Round to the nearest hundredths place if necessary.
it cost $54.50 to put 24,000 in your bathroom how much would you expect it to cost if you wanted 36 tiles
Given, the cost of 24 tiles $54.50
Step 1: Calculate how much a tile cost. To obtain the cost per tile
[tex]1\text{ tile cost= \$}\frac{54.50}{24}[/tex]Step 2: Calculate the cost to put 36 tiles (i.e the cost per tile multiply by 36)
[tex]\begin{gathered} =\frac{54.50}{24}\times36 \\ =54.50\times1.5 \\ =\text{ \$81.75} \end{gathered}[/tex]Hence, it will cost $81.75 to put 36 tiles
100 students took an exam, the maximum score was 90. From the graph, 1.what was the median score?2.Also, find the lower quartile score. in reference to the first question. 3. what is the inter-quartile score range score?
0. From the given graph, the cumulative frequency value indicates the number of students, we have 100 total number of students .
• so,Median is half of the students = 100/2 = 50
the value of test score that corresponds with 50 = 55 test score
• This means that the median , 50 students scored 55 % in the exa,m.
2. Finding the lower quartile Q1 :
since we have 100 students , 100/4 = 25, so Q1 = 25
the value that corresponds with cumulative frequency of 25 = 45
• This means that 25 students scores 45 %
3. Finding the Interquartile range :
IQR = Upper Quartile -Lower Quartile
Upper quartile = Q3 = 75 students : 60 %
and lower quartile = 45%
So,
IQR = 60-45
= 15
• This means that 15 students got 35 %
help meeeeeee pleaseee !!!!
The linear equation parallel to y = 3x - 2 that passes through the point (4, 6) is:
y = 3*x - 6
How to find the equation of the parallel line?Here we want to find a linear equation parallel to:
y = 3x - 2
Now, a general linear equation is:
y = m*x + b
Where m is the slope and b is the y-intercept.
Remember that two lines are parallel if and only if the lines have the same slope and different y-intercept.
So our linear equation will be something like:
y = 3*x + c
Now we also want our line to pass through the point (4, 6), then we can replace these values:
6 = 3*4 + c
6 = 12 + c
6 - 12 = c
-6 = c
So the linear equation is:
y = 3*x - 6
Learn more about linear equations:
https://brainly.com/question/4074386
#SPJ1
2. If y = x3 + 2x + 5 and z = x2 + 7x + 1, what is 2y + z in terms of x? (A) 3x3 + 11x + 11 (B) 2x3 + x2 + 9x + 6 (C) 2x3 + x2 + 11x + 11 (D) 2x3 + 2x2 + 18x + 12
the given equation is,
[tex]y=x^3+2x+5[/tex]and
[tex]z=x^2+7x+1[/tex]now the expression is,
2y + z
put the values,
[tex]2(x^3+2x+5)+x^2+7x+1[/tex][tex]\begin{gathered} 2x^3+4x+10+x^2+7x+1 \\ 2x^3+x^2+11x+11 \end{gathered}[/tex]thus, the correct answer is option C
estimate 7271 divided by 12= ?
Answer:
B
Step-by-step explanation:
Because i used a calculator
Answer:
C 700
Step-by-step explanation:
7271 is close to 7000
12 is close to 10
So 7000/10 = 700
help it’ll be greatly appreciated:(
Answer:
hola como estas soy de guatemala
find the length of arc CE. Round to the nearest hundredth.
We go from degrees to radians:
[tex]122\degree=122\degree\cdot\frac{\pi}{180\degree}=\frac{61\pi}{90}[/tex]Now, the length of arc CE is:
[tex]CE=m\measuredangle CDE\cdot CD[/tex]Where CD = 6 units. Using the angle in radians:
[tex]CE=\frac{61\pi}{90}\cdot6=12.78\text{ units}[/tex]Homework: Section 5.2 HomeworkQuestion 1, 5.2.7HW Score: 88.33%, 10.6 of 12 pointsPart 2 of 6« Points: 0 of 1Previous questionA medical practice group consists of seven doctors, 4 women and 3 men. The women are Dre, Jonswold, Hein, O'Conell, and Lee. The men are Drs. Penner, Paquette, and Marland. Supposenew patients are randomly assigned to one of the doctors in the group, Complete parts (a) through (d) below.
Solution
Total numbers of Doctors = 7
Number of female doctors = 4
Number of male doctors = 3
The probability that the patient is assigned to a female doctor is given as
[tex]p=\frac{4}{7}\text{ \lparen as a fraction\rparen}[/tex]To express as a percentage
[tex]undefined[/tex]In class of 35 students, 19 take Spanish, 18 take French and 3 Take neither. Calculate
how many takes:
A) Both French and Spanish
B) Just Spanish
C) Just French
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
Given :
Total numbers of students in class = 35
how many members take spanish = 19
how many members take french = 18
students take neither = 3
To find :
A) Both French and Spanish
B) Just Spanish
C) Just French
Solution :
from venn diagram
a+b+c+d = 35 → 1
b+c = 19 → 2
c+d = 18 → 3
a = 3 → 4
Substract equation 1 and equation 2
a+b+c+d-b-c=35-19
a+d=16 → 5
substract a=3 in the eqution 5
3+d=16
d=13
put d=13 in equation 3
c+d=18
c+13=18
c=5
Students takes both French and Spanish is 5 members
Student takes just Spanish = 14 members
Student takes just French = 13 members
To know more about probability of taking French and Spanish visit
https://brainly.com/question/15683159
#SPJ4
In order for the data in the table to represent a liner function with a rate of change of -8, what must be the value of a
By definition, the Rate of change is also called "Slope".
The slope of a line can be found dividing the difference between the y-coordinates of two points, by the difference between the x-coordinate of those points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case you know that:
[tex]m=-8[/tex]Knowing the following point on the line:
[tex]\mleft(10,27\mright);(11,a)[/tex]You can set up the following (substituting the slope and the coordinates of those point into the formula)
[tex]-8=\frac{27-a}{10-11}[/tex]Now you can solve for "a":
[tex]\begin{gathered} (-8)(-1)=27-a \\ 8-27=a \\ -19=a \\ a=19 \end{gathered}[/tex]The answer is: Third option.
A clock has a minute hand that is 11 inches long and an hour hand that is 9 inches long. What is the
distance between the end of the hands at 9 o'clock? Round your answer to the nearest inch.
10 inches
14 inches
O16 inches
20 inches
The Pythagorean Theorem is used to determine that the distance between the hands at 9 o'clock is 14 inches.
What exactly is the Pythagorean theorem?The Pythagorean theorem, also known as the Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. It states that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.It is implied that a clock has an 11-inch-long minute hand and a 9-inch-long hour hand.
We need to find the distance between the end of the hands at 9 o'clock.
At 9 o'clock, the hands form a right angled triangle.
Let the length of minute hand = x , hour hand = y and the distance between the end of the hands at 9 o'clock = z
Therefore, by using Pythagorean theorem,
x² + y² = z²
11² + 9² = z²
z = [tex]\sqrt{11^{2}+9^{2} }[/tex]
z = [tex]\sqrt{202}[/tex]
z = 14.21 rounded to 14 inch
Using the Pythagorean theorem, the distance between the ends of the hands at 9 o'clock is calculated to be 14 inches.
Learn more about problems based on clocks here:
https://brainly.com/question/2078551
#SPJ13
Line a is parallel to line b. Which list shows accurate angle relationships?
Given:
Line a is parallel to line b.
As shown:
m∠1 = m∠5 ; the corresponding angles are congruent
m∠2 = m∠2 ; the corresponding angles are congruent
So, the answer will be option 2
PLS HELP!
I’ll give brainliest if you also explain!
What are the equations of lines m and q?
Equation of 'm'
(y - 6) = - ³/₅ (x - 2) [point-slope form]
y = - ³/₅ x + ³⁶/₅ [slope-intercept form]
Equation of 'q'
(y - 6) = ⁵/₃ (x - 2) [point-slope form]
y = ⁵/₃ x + ⁸/₃ [slope-intercept form]
How to find the equations of lines m and q?To find the equation for both 'm' and 'q' requires a bit of work. Because neither 'm' nor 'q' has two points to find the slopes of the line, we have to get creative.
The Line 'n' has two points [ (4, 4) & (1, -1) ], and as such we can find the slope of that line. The line 'n' is parallel with 'q' and perpendicular with m.
For finding the slope of 'n'
The slope of the 'n' = (y₂ - y₁) ÷ (x₂ - x₁)
= (4 - (- 1)) ÷ (4 - 1)
= 5 ÷ 3
= ⁵/₃
To estimate the slope of 'q' and 'm'
When two lines exists parallel, they contain the exact slope.
Since 'n' and 'q' exists parallel,
then the slope of q = ⁵/₃
When two lines exists perpendicular, the product of their slopes exists -1. This means that the slopes exists negative-reciprocals of each other.
Since 'n' and 'm' exists perpendicular
then the slope of m = - ³/₅
Write the equation for 'q' and 'm'
We can now utilize the point-slope form (y - y₁) = m(x - x₁)) to write the equation for the lines
For both 'q' and 'm' let (x₁, y₁) be (2, 6)
Equation of 'm'
(y - 6) = - ³/₅ (x - 2) [point-slope form]
y = - ³/₅ x + ³⁶/₅ [slope-intercept form]
Equation of 'q'
(y - 6) = ⁵/₃ (x - 2) [point-slope form]
y = ⁵/₃ x + ⁸/₃ [slope-intercept form]
To learn more about slope-intercept form refer to:
https://brainly.com/question/1884491
#SPJ13
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
the treaty for defeated Germany was Article 231, commonly known as the "War Guilt Clause," which forced the German nation to accept complete responsibility for initiating World War I. Germany was required to make enormous reparation payments