If cos A = 12/13 , and ∠A is in the fourth quadrant, find the exact value of sin2A.
Answer: 0.71
Step-by-step explanation:
we have that cos(A) = 12/13
then:
A = Acos(12/13) = 22.62°
But A is in the fourth quadrant, so A is actually 22.62° + 180° = 202.62°
Then Sin(2A) = sin(2*202.62°) = 0.71
The pilot of a helicopter sights a fire at an angle of depression of 11°.
The helicopter's altitude is 1700 feet.
To the nearest foot, what is the distance from the helicopter to the fire?
8909 ft
3204 ft
8746 ft
3300 ft
Answer:
The distance from the helicopter to the fire is 8909 feet.
Step-by-step explanation:
Refer the attached figure
The pilot of a helicopter sights a fire at an angle of depression of 11° i.e. [tex]\angle ACB = 11^{\circ}[/tex]
The helicopter's altitude is 1700 feet.i.e.AB = 1700 feet
We are supposed to find the distance from the helicopter to the fire i.e. AC
Using trigonometric ratios
[tex]Sin \theta = Perpendicular}{Hypotenuse}\\\\Sin 11^{\circ}=\frac{AB}{AC}\\\\Sin 11^{\circ}=\frac{1700}{AC}\\\\AC=\frac{1700}{Sin 11^{\circ}}\\\\AC=\frac{1700}{0.1908}\\\\AC=8909.85 feet[/tex]
Hence the distance from the helicopter to the fire is 8909 feet.
A school in New Zealand collected data about the employment status of the mother and father in two-parent families. The two-way table of column relative frequencies below shows the data.
Father works full time Father works part time Father not working
Mother works full time
0.17
0.170, point, 17
0.14
0.140, point, 14
0.13
0.130, point, 13
Mother works part time
0.23
0.230, point, 23
0.14
0.140, point, 14
0.07
0.070, point, 07
Mother not working
0.60
0.600, point, 60
0.71
0.710, point, 71
0.80
0.800, point, 80
Column total
1.00
1.001, point, 00
1.00
1.001, point, 00
1.00
1.001, point, 00
Based on the data, which of the following statements must be true for the two-parent families at that school?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A family where the father works part time is twice as likely as a family where the father is not working to have the mother work part time.
(Choice B)
It is most common for neither parent to be working.
(Choice C)
C
Families where the father works full time are more likely to have the mother working full time than part time.
(Choice D)
D
There are twice as many families where the mother works full time and the father works part time as families where the mother works part time and the father doesn't work.
Answer:A
Step-by-step explanation: 14% of the mothers work part-time in families where the father works part-time while 7% of the mothers work part-time in families where the father is not working.
Probabilities are used to determine how likely or unlikely an event is. From the 2-column table, it is twice as likely to get a family where the father and the mother work part-time than a family where the father doesn't work, and the mother works part-time.
We use the following representation:
[tex]FF \to[/tex] Father works full-time
[tex]FP \to[/tex] Father works part-time
[tex]FW \to[/tex] Father not working
[tex]MF \to[/tex] Mother works full-time
[tex]MP \to[/tex] Mother works part-time
[tex]MW \to[/tex] Mother not working
Next, we test each of the 4 options, till one of the options is true (see attachment)
Choice A:
The claim in choice A is that:
[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]
From the given table, we have:
[tex]P(FP\ and\ MP) = 0.14[/tex] ---- father works part-time and mother works part-time
[tex]P(FW\ and\ MP) =0.07[/tex] ---- father not working and mother works part-time
Put the above values in the following equation
[tex]P(FP\ and\ MP) = 2 \times P(FW\ and\ MP)[/tex]
[tex]0.14 = 2 \times 0.07[/tex]
[tex]0.14 = 0.14[/tex]
The above equation is true.
Hence, choice (A) is true
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please calculate the volume of the cylinder below. use 3.14 as approximation for Pi. (MIDDLE SCHOOL MATH)
the answer is V≈254.47
Vince began practicing piano at 11:15 P.M He stopped at 11:35 P.M How many degrees did the minute hand turn during Vince practice time? Complete the explanation how you found your answer
Answer:
Vince began practicing piano at 11:15 P.M
He stopped at 11:35 P.M
=> He practiced in 35 - 15 = 20 mins = 1/3 hour.
=> 1/3 hour means 1/3 circle, the number of degrees the minute hand turned:
N = (1/3) x 360 = 120 deg (1 circle = 360 deg)
Hope this helps!
:)
Suppose you deposit $1500 in a savings account that pays interest at an annual rate of 6% if no money is added or withdrawn from the account answer the following questions how much will be in the account in four years how much will be in the account after 16 years how many years will it take for the account to contain $2000 How many years will it take for the account to contain $2500
Answer:
In 4 years = $1,893.72
In 16 years = $3,810.53
years to contain $2,000 = 4.9371454128
years to contain $2,500 = 8.766692911
Step-by-step explanation:
In 4 years
A = 1,500 (1 + 0.06)^4
= $1,893.72
In 16 years
A = 1,500 (1 + 0.06)^16
= $3, 810.53
to find number of years
t = ln (A/P) / ln (1+r)
when A = 2,000
t = ln(2,000/1,500) / ln(1+0.06)
= 4.9371454128 years
when A = 2,500
t = ln(2,500/1,500) / ln(1+0.06)
= 8.766692911 years
PS: You can also use log in place of ln
The number of years it will take for the account to contain $2000 is 4.94 years while it will take 8.77 years to contain $2500.
Calculation of future value and the number of years it takesLet:
PV = Present value = $1,500
r = Interest rate = 6%, or 0.06
n = number of years
FVn = Future value after a certain number of years
Therefore, we have:
The amount that will be in the account in four years can be calculated using the future value (FV) formula as follows:
FV4 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^4 = $1,893.72
Therefore, the amount that will be in the account in four years is $1,893.72.
The amount that will be in the account after 16 years can also be calculated using the future value (FV) formula as follows:
FV16 = PV * (1 + r)^n = $1,500 * (1 + 0.06)^16 = $3,810.53
Therefore, the amount that will be in the account after 16 years is $3,810.53.
The number of years will it take for the account to contain $2000 can be calculated using the following formula:
n = (log(FV/PV)) / (log(1+r)) = (log($2,000/$1,500)) / (log(1+0.06)) = 0.1249387366083 / 0.0253058652647703 = 4.94 years
Therefore, the number of years it will take for the account to contain $2000 is 4.94 years.
The number of years it will take for the account to contain $2500 can be calculated using the following formula:
n = (log(FV/PV)) / (log(1+r)) = (log($2,500/$1,500)) / (log(1+0.06)) = 0.221848749616356 / 0.0253058652647703 = 8.77 years
Therefore, the number of years it will take for the account to contain $2000 is 8.77 years.
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-3x+1/2=3/8
Whats x? pls someone help step by step
Answer:
x = -1/24 = -0.042
Step-by-step explanation:
Step 1 : Simplify 3/8
Step 2 :
Rewriting the whole as an Equivalent Fraction
Step 3 :
Calculating the Least Common Multiple
Equation at the end of step 3 :
24x + 1
——————— = 0
8
Last step:
Solving a Single Variable Equation :
5.2 Solve : 24x+1 = 0
Subtract 1 from both sides of the equation :
24x = -1
Divide both sides of the equation by 24:
x = -1/24 = -0.042
Hope this helps.
Michelle wants to run a total of 15 miles per week. She runs 3 miles
each day d that she runs. Will she meet her goal by running 5 days
per week?
Answer:
Yes because 3x5 is 15
Step-by-step explanation:
Which number has the greatest absolute value?
A. -20
B. 0
C. 10
Answer:
-20
Step-by-step explanation:
It is the farthest from 0.
Answer:
A. -20
Step-by-step explanation:
The absolute value means take the positive value
A. -20
abs(-20) = 20
B. 0
abs(0) = 0
C. 10
abs(10) = 10
20 is the largest value
Solve the system of linear equations by adding or subtracting.
3x + 7y = −17
4x − 7y = 10
Enter your answer as an ordered pair.
Answer:
3x + 7y = −17
4x − 7y = 10
Add up both sides of 2 equations, then
7x = -7
=> x = 1
=> y =(3 x 1 - 17)/7 = -14/7 = -2
Hope this helps!
:)
Please help please really important question
Answer: The Median because the distribution is skewed to the right
Step-by-step explanation:
What is the volume of the following rectangular prism?
Answer:
529 units squared
Step-by-step explanation:
At the beginning of the year, students in Mrs. Johnson's class took a survey. It was discovered that 1 /3 of the whole class was born in a summer month. Of those born in the summer, 2 /5 of them were born in July. What fraction of the entire class was born in July?
Answer:
2/15
Step-by-step explanation:
1/3 × 2/5 = 2/15
Ann wants to buy a coffee machine. She knows, that during the holidays, the probability of a discount of more than 10% is 0.87, on weekends, the probability of a discount of more than 10% is 0.38, and on a regular weekday, it is 0.17. On average there are 15 holidays per year, 100 weekends (holiday weekends are excluded) and 250 weekdays. Find the probability of a discount of more than 10% for the randomly chosen day. Find the probability that it was a weekend if it is given that she bought a machine with a discount of more than 10%.
Answer:
Let's denote:
P(discount on 15 holidays) = P(A) = 0.87
P(discount on 100 weekends) = P(B) = 0.38
P(discount on 250 weekdays) = P(C) = 0.17
=> The probability of a discount of more than 10% for the randomly chosen day: P = P(A) x 15/360 + P(B) x 100/360 + P(C) x 250/360
= 0.87 x 15/360 + 0.38 x 100/360 + 0.17 x 250/360
= 0.26
Given she bought a machine with a discount of more than 10%, the probability that it was a weekend would be:
P = 100/(100 + 250 + 15) = 0.27
Hope this helps!
:)
Answer:
1. 0.256
2. 0.406
Step-by-step explanation:
Total days:
15 + 100 + 250 = 365
P(more than 10% discount)
= (0.87×15/365) + (0.38×100/365) +(0.18×250/365)
= 1871/7300
0.2563013699
P(weekend/more than 10% discount)
= (0.38×100/365) ÷ (1871/7300)
= 760/1871
0.4061998931
There are 2,010 Starbucks in California. The population of California is 38.8 million. Which of
the following best represents the Starbucks per capita in Scientific Notation?
1.93 x 104
5.18 x 10-4
51.8
5.18 x 10-5
Answer:
5.18x10-5 is the correct answer
Step-by-step explanation:
Scientific notations are used to represent relatively large and small numbers.
The population per capita is (d) [tex]5.18 \times 10^{-5}[/tex]
The populations are given as:
[tex]Starbucks = 2010[/tex]
[tex]People = 38.8\ million[/tex]
The population of Starbucks per capita is calculated by dividing the population of Starbucks by the population of the people.
So, we have:
[tex]Per\ Capita = \frac{Starbucks}{People}[/tex]
Substitute known values
[tex]Per\ Capita = \frac{2010}{38.8\ million}[/tex]
Divide
[tex]Per\ Capita = 0.00005180412[/tex]
Approximate
[tex]Per\ Capita = 0.0000518[/tex]
Express as scientific notation
[tex]Per\ Capita = 5.18 \times 10^{-5}[/tex]
Hence, the population per capita is (d) [tex]5.18 \times 10^{-5}[/tex]
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Find the area. Will mark brainliest.
Answer:
784
Step-by-step explanation:
Answer:
784
Step-by-step explanation:
34+22=56
28÷2=14
56×14=784
pls help will mark as brainliest
Answer:
C F
Step-by-step explanation:
Answer:
2/10 is equivalent to 1:5
6:30 is equivalent to 1:5
8 to 40 is equivalent to 1:5
Step-by-step explanation:
Take a look at the square pyramid illustrated below. it is a picture of one of the
"Great Pyramids of Egypt." Calculate the total surface area of the Great Pyramid.
Show your work!
A. Surface Area of Great Pyramid = 1,831,583 square feet
B.Surface Area of Great Pyramid = 892,784 square feet
C. Surface Area of Great Pyramid = 1,297,956 square
feet
D. Surface Area of Great Pyramid = 545,672 square feet
Answer:
C. 1,297,956 square ft.
Step-by-step explanation:
480.6*755.9*1/2 (area of triangle)
4 triangles so the above x4
square base=755.9^2
add it all together to get 1,297,955.89 or about 1,297,956
Find the center and radius of the circle.
AY
6
N
-6
-2
6 x
N
-61
The center is O,
and the radius is
Answer:
center: (0,0)
radius: 4 units
Step-by-step explanation:
the circle goes through points (0,4), (0,-4), (4,0), and -4,0).
if you notice, all four points are 4 away from the origin, (0,0). this means that there center is (0,0).
if you start at one of the points and go to the origin, it will be 4 units. that will be your radius
Light travels 1.8x 10 kilometers in one minute. How far does it travel in 9 minutes?
Write your answer in scientific notation.
Answer:
162
Step-by-step explanation:
1.8x10= 18
18x9=162
Please help WILL MARK BRAINLIEST
Answer: I believe D is the correct answer.
Step-by-step explanation:
I just took the test. Hope this Helps!!! PLZ MARK BRAINLIEST!!!
Answer:
Multiply each GDP number by its country's population.
Step-by-step explanation:
The GDP depends on the higher or lower population.
The highest GDP and highest population product all help decide the living standards of the country.
After you have multiplied the countries' GDP by its population you compare.
math question screen shot down below
If you answer this correct I mark you Brainelst:
Martha has eighteen marbles see loses 90 and then throws away her dignity whats the the answer? PS: you have to answer the dignity part to! If not then its wrong!
Answer:
72 and dignity is not important
Step-by-step explanation:
I think
Mark is playing a trivia game on his first turn he lost 100 points his second 55 and his third 65 what is his score after the first three scores.
Answer:
-220
Step-by-step explanation:
Please tell me the answer quick
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Giving Brainliest if correct!!
Adam bought a treadmill and a dirt bike from a sports equipment store for y dollars. He signed an installment agreement requiring an 8% down
payment and monthly payments of x dollars for 18 months. Which expression correctly represents Adam's finance charge?
A. 0.8y
B. 18y
C. 18x-0.92y
D. 18x-0.08y
E. 18y-0.92x
Answer:
D. 18x-0.08y
Step-by-step explanation:
He will make 18 monthly payments of x dollars on the total amount leftover after paying an 8% down payment. So his finance charge is payment minus down payment: 18x-0.08y
The expression correctly represents Adam's finance charge is
C. 18x-0.92y.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
From, The given information,
8% of the downpayment is (8/100)×y = 0.08y and te total monthly payment is 18x.
Therefore,
The phrase that accurately describes Adam's finance charge is,
y = 0.08y + 18x.
y - 0.08y = 18x.
0.92y = 18x.
18x - 0.92y = 0.
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Functions math, please help
Answer:
Slope: 2
Y-intercept: (0,-7)
Step-by-step explanation:
2(x-3)=y+1
distribute the 2 through the parentheses
2x-6=y+1
2x+6=0+1
(change the y to 0)
2x-6=1
add 6 to both sides(+6 cancels out -6)
2x=1+6
divide both sides by 2
x=7/2 or x=3.5
hope this helps!
A dance school offers 5 types of classes: jazz, tap, hip-hop, ballet, and lyrical. It conducts 950 classes over the course of a
year. If it conducts the same number of each type of class, how many jazz classes are given?
19
190
475
945
Answer:190
Step-by-step explanation:
If there are 950 classes over a year and 5 classes then there are 190 classes per class because 950/5=190
Petrolyn motor is a combination of natural oil and synthetic oil. it contains 2 liters of natural oil for every 3 liters of synthetic oil. in order to make 475 liters of Petrolyn oil, how many liters of natural oil are needed?
Answer:
About 158 liters
Step-by-step explanation:
475 / 3 = 158.333...
A mill processes 48 tons of flour in 3 hours. How many tons of flour can the mill process in 8 hours if its rate or production stays the same?
Answer:
128 tons can be processed in 8 hours.
Step-by-step explanation:
48 divided by 3 = 16 (to see how much tons are produced in 1 hr.)
16 x 8
=128
Answer:
128 tons in 8 hours
Step-by-step explanation:
do 48 divided by 3 = 16
to see how much tons get produced in an hr.
then when you do 16x8 which is 128
