Answers
Answer:
m = 6
n = 2√3
Step-by-step explanation:
Reference angle = 30°
Hypotenuse = 4√3
Opposite = n
Adjacent = m
✔️To find m, apply CAH:
Cos θ = Adj/Hypo
Substitute
Cos 30° = m/4√3
4√3 × Cos 30° = m
4√3 × √3/2 = m (cos 30 = √3/2)
(4*3)/2 = m
6 = m
m = 6
✔️To find n, apply SOH:
Sin θ = Opp/Hypo
Substitute
Sin 30° = n/4√3
4√3 × Sin 30° = n
4√3 × ½ = n (Sin 30 = ½)
2√3 = n
n = 2√3
Related Questions
A searchlight is shaped like a parabola. If the light source is located 3 feet from the base along the axis of symmetry and the depth of the searchlight is 4 feet, what should the width of the opening of the searchlight be?
Answers
9514 1404 393
Answer:
8√3 ≈ 13.86 ft
Step-by-step explanation:
The light source is usually placed at the focus, so the focus-vertex distance is p=3 ft. The equation for the parabola with its vertex at the origin is ...
y = 1/(4p)x^2
y = 1/12x^2
The opening for some y-value extends ±x from the axis of symmetry, so is a total of 2x in width.
For y=4, the corresponding value of x is ...
4 = 1/12x^2
48 = x^2
√48 = x = 4√3
Then the width of the searchlight opening is ...
2(4√3 ft) = 8√3 ft ≈ 13.86 ft
For the equation, complete the solution. 7x + y = −18
Answers
Answer:
x= - 18/7 - 1/7y, y
or if you are solving for y= -18-7x, x
( SEE OTHER IMAGE)
Step-by-step explanation:
See image below:)
Answer:
[tex]x= \frac{- 18 - y }{7}[/tex]
y = - 18 - 7x
Step-by-step explanation:
7x + y = - 18
7x + y - y = - 18 - y
7x = - 18 - y
[tex]\frac{7x}{7}= \frac{- 18 - y }{7}[/tex]
[tex]x= \frac{- 18 - y }{7}[/tex]
7x + y = - 18
7x - 7x + y = - 18 - 7x
y = - 18 - 7x
Find the Value of x
Answers
Answer:
42
Step-by-step explanation:
(adjacent straight angles sum up to 180)
3x+54=180
x=42
Chester has less than $25 to spend at the county fair. The entrance fee is $5, and each ride costs $3. The number of rides, r, that Chester can go on is represented by the inequality 3r + 5 < 25. Select the most amount of rides Chester can go on without overspending
Answers
Answer:
6 rides
Step-by-step explanation:
3r+5<25
3r<20
r<6.67
rides=6
check answer
3r+5<25
3(6)+5<25
18+5<25
23<25
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3
C:3
D:8
are the possible answers
Answers
Answer:
find the quotient of 8 divided by one-third, multiply 8 by
A:1/8
B:1/3( true
C:3
D:8
are the possible answers
For what value of x is the rational expression below equal to zero?
20+2x
5-x
O A. -10
O B. -5
C. 10
O D. 5
Answers
Answer:
A.-10 should be the answer to the question..
The rational expression is zero at x = -10.
What is rational expression?The ratio of two polynomials is known as a rational expression.
The given rational expression can equate to zero
[tex]\frac{20+2X}{5-X} =0[/tex]
Then, 20+2x=0
Therefore, x = (-20/2) = -10.
At x = -10, the given rational expression is zero.
To learn more about rational expression, use the link given below:
https://brainly.com/question/19585906
#SPJ2
if $1995 .00 is Shared equally among 7 men, how much would each get?
Answers
Anwer:$285
Explaination: Division method
$1995.00÷7=$285
A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers?
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a − c = 70
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a − c = 70
Answers
Answer:
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
Step-by-step explanation:
If the total number of people at the movie was 35 people, one of the equations will be a + c = 35.
If $70 was collected in total, the other equation will be 6a + c = 70.
Now, solve this system of equations:
a + c = 35
6a + c = 70
Solve by elimination by multiplying the top equation by -1, then adding the equations together:
-a - c = -35
6a + c = 70
Add these together, and solve for a:
5a = 35
a = 7
Since there were 35 people in total, find how many children attended by subtracting 7 from 35:
35 - 7
= 28
So, there were 28 children and 7 adults.
The equations used were: a + c = 35 and 6a + c = 70
So, the correct answer is:
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
PLEASE HELP!
Determine which of the following lists is in order from smallest to largest.
1. -3,131,0, (-3)^2
2. (-3)^2,-3,0, |3|
3. -3,0,|3|, (-3)^2
4. 0,-3,|3|, (-3)^2
Answers
Answer:
3. -3,0,|3|, (-3)^2
Step-by-step explanation:
Answer:
answer would be option 3
Step-by-step explanation:
help this helps
Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?
To maximize his income, Dr. Lum should teach_______classes for Hilltop College and __________classes for Serra College. His maximum income would be________.
Answers
Answer:
z (max) = 34500 $
x₁ = 2
x₂ = 3
Step-by-step explanation:
Hilltop College
3 hours per week preparing lessons and grading papers
Serra College
4 hours per week preparing lessons and grading papers
Total hours to spend per week preparing lessons 18
Let´s call x₁ numbers of class at Hilltop College
and x₂ numbers of class at Serra College then:
Objective function
z = 6000*x₁ + 7500*x₂
Constraints:
1.- x₁ + x₂ ≤ 5 the total number of class
2.- 3*x₁ + 4*x₂ ≤ 18
3. General constraints x₁ ≥ 0 x₂ ≥ 0 integers
After 6 iteration optimal solution is: From on-line solver
z (max) = 34500 $
x₁ = 2
x₂ = 3
Estimate 9272 - 28 by first rounding each number so that it has only 1 nonzero digit.
Answers
Answer:
8970
Step-by-step explanation:
In order to round 9272 so that it has only 1 nonzero digit, look at the hundred digit, If the number is greater or equal to 5, add 1 to the thousand figure. If this is not the case, add zero
The hundred digit is 2 which is less than 5, so 0 is added to 9. the number becomes 9000
In order to round 28 so that it has only 1 nonzero digit, look at the units digit, If the number is greater or equal to 5, add 1 to the tens figure. If this is not the case, add zero
The units digit is greater than 5, so 1 would be added to tens digit. the number becomes 30
9000 - 30 = 8970
What is the median of the following set of numbers?
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD.
Answers
1 5
12 1 121
1
121
13
O A. 27
ОВ.
COIN
OC. .
12
OD. ????????????????
Median of the given data is 8.5.
What is median?In statistics, the median is the middle value of the given list of data in order. Data or observations can be sorted in ascending or descending order.
Given data,
1 , 5, 12, 1, 121, 1, 121, 13
Arranging in ascending order
1, 1, 1, 5, 12, 13, 121, 121
Number of elements N = 8
When number of elements is odd
Median = (N/2 th term + (N/2)+1 th term)/2
Median = (8/2 th term + (8/2)+1 th term)/2
Median = (4th term + 5th term)/2
Median = (5+12)/2
Median = 17/2
Median = 8.5
Hence, 8.5 is the median of the given data.
Learn more about median here:
https://brainly.com/question/28060453
#SPJ7
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Answers
Answer:
Domain = -6 < x < 3
range = -6 < x < -4
Step-by-step explanation:
The domain is the input values along the x-axis. According to the graph, the x values are within the interval;
Domain= -6 < x < 3
The range is the output values along the y-axis. According to the graph, the y values are within the interval;
range = -6 < x < -4
A right triangle has side lengths 7, 24, and 25 as shown below. Use these lengths to find cos B, tanB, and sin B.
Answers
Answer:
cosB = 7/25 = 0,28
tanB = 24/7 = 3,428571429
sinB = 24/25 = 0,96
A small town experienced an explosive population increase Originally the town had population 170 within 3 years the town's population increased by 400% what is the town current population
Answers
Answer:
Step-by-step explanation:
We need to first find out how much 400% of 170 is and then add that increase to the original 170 people.
4(170) = 680 and
680 + 170 = 850 people after 3 years.
Which rules of exponents will be used to evallate this expression? Select three options.
Answers
A study was done on the batting averages for two baseball players: Hitmore and Bunter. Data were collected over a period of time for baseball parks that are natural and artificial turf. It was found that Hitmore does better overall (.e., has a better batting average). However, for both natural and artificial turf separately, Bunter does better. Which of the following is correct?
This is an example of a negative association between variables.
This is an example of Simpson's Paradox.
"Turf" is a lurking variable in this example
Both (B) and (C) are correct
This situation is mathematically impossible
Answers
Answer:
Both (B) and (C) are correct
Step-by-step explanation:
Explaining in simple terms, The Simpson's paradox simply describes a phenomenon which occurs when observable trends in a relationship, which are obvious during singular evaluation of the variables disappears when each of this relationships are combined. This is what played out when hitmire appears to d well on both of natyraknamd artificial turf when separately compared, but isn't the same when the turf data was combined. Also, performance may actually not be related to the turf as turf may Just be. a lurking variable causing a spurious association in performance.
A pen costs $2 and a ruler costs 50 cents. Write down an expression in dollar for the cost of p pen and r ruler.
Answers
Answer:
.50r + 2p
Step-by-step explanation:
cost of ruler * number of rules + cost of pens * number of pens
.50 *r + 2 *p
.50r + 2p
Consider the following sets of sample data: A: $30,500, $27,500, $31,200, $24,000, $27,100, $28,600, $39,100, $36,900, $35,000, $21,400, $37,900, $27,900, $18,700, $33,100 B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answers
Answer:
[tex]CV=0.2[/tex] ---- dataset 1
[tex]CV = 7.2[/tex] --- dataset 2
Step-by-step explanation:
Given
[tex]A: 30500, 27500, 31200, 24000, 27100,28600, 39100, 36900, 35000, 21400, 37900, 27900, 18700,[/tex][tex]33100[/tex]
[tex]B: 4.29, 4.88, 4.34, 4.17, 4.52, 4.80, 3.28, 3.79, 4.84, 4.77, 3.11[/tex]
Required
The coefficient of variation of each
Dataset A
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{30500+ 27500+31200+24000+ 27100+28600+ 39100+ 36900+ 35000+ 21400+ 37900+ 27900+ 18700+33100}{14}[/tex][tex]\mu = \frac{418900}{14}[/tex]
[tex]\mu = 29921.43[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
So, we have:
[tex]\sigma= \sqrt{\frac{(30500 - 29921.43)^2 +.................+ (18700- 29921.43)^2 + (33100- 29921.43)^2}{13}}[/tex]
[tex]\sigma= \sqrt{\frac{487723571.42857}{14}}[/tex]
[tex]\sigma= \sqrt{34837397.959184}[/tex]
[tex]\sigma= 5902.32[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV=\frac{5902.32}{29921.43}[/tex]
[tex]CV=0.2[/tex] --- approximated
Dataset B
Calculate the mean
[tex]\mu = \frac{\sum x}{n}[/tex]
[tex]\mu = \frac{4.29+ 4.88+ 4.34+ 4.17+ 4.52+ 4.80+ 3.28+ 3.79+ 4.84+ 4.77+ 3.11}{11}[/tex]
[tex]\mu = \frac{46.79}{11}[/tex]
[tex]\mu = 4.25[/tex]
Next, calculate the standard deviation using:
[tex]\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}[/tex]
[tex]\sigma = \sqrt{\frac{(4.29 - 4.25)^2 + (4.88- 4.25)^2 +.........+ (3.11- 4.25)^2}{11}}[/tex]
[tex]\sigma = \sqrt{\frac{3.859}{11}}[/tex]
[tex]\sigma = \sqrt{0.35081818181}[/tex]
[tex]\sigma = 0.593[/tex]
So, the coefficient of variation is:
[tex]CV=\frac{\sigma}{\mu}[/tex]
[tex]CV = \frac{4.25}{0.5903}[/tex]
[tex]CV = 7.2[/tex] -- approximated
In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 23 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm3. An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x=8.16 cm3 and s=0.7 cm3. Conduct the appropriate test at the α=0.01 level of significance.
Answers
Answer:
We do not reject the Null Hypothesis
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=23[/tex]
Population mean [tex]\mu=9.02cm^3[/tex]
Sample mean [tex]\=x=8.16[/tex]
Standard deviation [tex]\sigma=0.7cm^3[/tex]
Significance level [tex]\alpha =0.01[/tex]
Generally the Null and and alternative Hypothesis are as follows
[tex]H_0:\mu=9.02cm^3[/tex]
[tex]H_a:\mu<9.02cm^3[/tex]
Therefore t critical Value is
[tex]t\ critical\ Value=(\alpha,df)[/tex]
[tex]t\ critical\ Value=(0.01,22)[/tex]
Where
[tex]df=n-1\\\\df=23-1=>22[/tex]
Therefore
From t Table
[tex]t value=-2.8[/tex]
Generally the equation for Z Critical is mathematically given by
[tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]t=\frac{8.16-9.02}{\frac{0.7}{\sqrt{23} } }[/tex]
[tex]t=-5.89[/tex]
Therefore
Since the t test statistics is greater than the Critical value
Hence,we do not reject the Null Hypothesis
an isosceles triangle has one angel that measure 30 degree what is the measure of the other two angles that are equal?
Answers
Software Solution (SOS) helps subscribers solve software problems. All transactions are made over the telephone. For the year 2018, 10 engineers, most of whom are recent graduates, handled 119,000 calls. The average yearly salary for software engineers was $58,000. Starting in 2019, the firm retained and hired only software engineers with at least 2 years of experience. SOS raised the engineers’ salary to $73,000 per year. In 2019, eight engineers handled 127,000 calls.
Required:
1. Calculate the partial operational productivity ratio for both years.
2. Calculate the partial financial productivity ratio for both years. (Round your answers to 4 decimal places.)
Answers
Answer:
a. 11900, 15875
b. 0.2052, 0.2175
Step-by-step explanation:
number of engineers in 2018 = 10
calls handled in 2018 = 119000
average salary in 2018 = 58000
number of engineers in 2019 = 8
calls handled = 127000
salary = 73000
a.) operational productivity = output/input
in year 2018 = 119000/10= 11900
in year 2019 = 127000/8 = 15875
b.) ratio for both years = output/amount spent
in year 2018 = 119000/10*58000 = 0.2052
in year 2019 = 127000/8*73000 = 0.2175
Express in roster form. Set of B is the set of all elements x such that x is an element of natural numbers and x is a multiple of 8
Answers
=========================================================
Explanation:
The set of natural numbers is {1,2,3,...} basically anything positive and a whole number.
Any multiple of 8 is of the form 8x. Since x is a natural number, the smallest it can be is x = 1 which corresponds to 8x = 8*1 = 8. So 8 is the first multiple of the set. Then 16 is next because 8x = 8*2 = 16, and so on.
That's how we end up with {8, 16, 24, 32, ...}
The three dots, or ellipses, tell the reader that the pattern goes on forever. This set is infinitely large. We wouldn't stop at 800 because we could plug in say x = 200 to get 8x = 8*200 = 1600 and that's a multiple of 8.
WILL MARL BRAINLIEST IF YOU HELP
Answers
Answer:
C.
Step-by-step explanation:
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
A.
9 + 9 = 18
18 < 22
No triangle
B.
7 + 3 = 10
10 = 10
No triangle
C.
5 + 6 = 11 and 11 > 9 good
5 + 9 = 14 and 14 > 6 good
9 + 6 = 15 and 15 > 5 good
There is a triangle.
Answer: C.
\lim _{x\to 0}\left(\frac{\sqrt{1+3x+x^2}-1}{\arcsin \left(2x\right)}\right)
Answers
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right)[/tex]
Note that as [tex]x \rightarrow 0[/tex], the ratio becomes undefined. Using L'Hopital's Rule, where
[tex]\displaystyle \lim_{x \to c} \dfrac{f(x)}{g(x)} = \lim_{x \to c} \dfrac{f'(x)}{g'(x)} [/tex]
where f'(x) and g'(x) are the derivatives of the functions f(x) and g(x), respectively. Note that
[tex]f(x) = \sqrt{x^2 + 3x + 1} \:\:\text{and}\:\: g(x) = \arcsin 2x[/tex]
[tex]f'(x) = \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})}[/tex]
[tex]g'(x) = \dfrac{2}{\sqrt{1 - 4x^2}}[/tex]
Therefore,
[tex]\displaystyle \lim_{x \to 0} \dfrac{f'(x)}{g'(x)} = \lim_{x \to 0} \dfrac{2x + 3}{2(\sqrt{x^2 + 3x + 1})} \times \left(\dfrac{\sqrt{1 - 4x^2}}{2} \right)[/tex]
or
[tex]\displaystyle \lim_{x \to 0} \left(\dfrac{\sqrt{x^2 + 3x + 1} - 1}{\arcsin 2x} \right) = \dfrac{3}{4}[/tex]
Derek sold her house for $541,600, which was 140% of the amount she paid for it.
Calculate the amount she paid for the property.
Answers
9514 1404 393
Answer:
$386,857.14
Step-by-step explanation:
You have ...
sold = 140% × paid
Dividing by 140% gives ...
paid = sold/1.40 = $541,500/1.40 = $386,857.14
Derek paid $386,857.14 for the property.
Bonjour, connaissez vous une app ou on peut manipuler des elastiques j'en ai besoin. Merci!
Answers
Answer:
Wow sup Comment allez-vous, je suis là pour vous aider à essayer cette application, je ne suis pas vraiment sûr de ce que vous entendez par " Rubber Band App " Mais je pense que cela pourrait aider à l'essayer Exercices de bande de résistance
evaluate the given expression if w= 17, x= 29, and a =8 w+(1/x)+(1/z) a. 17.18 b.8.11 c. 94.13 d. 46.15
Answers
Answer:
a. 17.18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
w = 17
x = 29
z = 8
w + (1/x) + (1/z)
Step 2: Evaluate
Substitute in variables: 17 + (1/29) + (1/8)Add: 3981/232Divide: 17.1595Find the area of the sector in
terms of pi.
120°
24
Area = [?] π
Enter
Answers
Radius= 24/2= 12
Sector area= 120/360 x π(12)^2
Final answer :
Sector area = 48π
Two parallel lines, e and f, are crossed by two transversals.
What is the measure of <15
m<15 = 77°
m< 15 = 83°
m<15 = 93°
m<15= 97°
Answers
9514 1404 393
Answer:
∠15 = 97°
Step-by-step explanation:
At any given transversal of parallel lines, all obtuse angles are congruent, and all acute angles are congruent. Obtuse angle 15 is congruent to the one market 97°.
∠15 = 97°