Answer:
Approximately 3.2362.
Step-by-step explanation:
Recall that definition of cosecant and sine:
[tex]\displaystyle \sin(\theta) = \frac{1}{ \csc(\theta) }\text{ and } \csc(\theta)=\frac{1}{\sin(\theta)}[/tex]
Since we are given that sin(θ) ≈ 0.3090, this means that cosecant will be:
[tex]\displaystyle \csc(\theta)\approx \frac{1}{0.3090} = 3.2362[/tex]
Answer:
3.236
Step-by-step explanation:
csc=1/sinФ
csc=1/0.3090= 3.236
The population, P (t), of an Ontario city is modeled by the function p(t) = 14t^2 + 650t + 32,000. If t = 0 corresponds to the year 2,000. When was the population 25,000?
Answer:
The population of the city was 25,000 in 1970 and 1983.
Step-by-step explanation:
In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.
[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]
Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.
HELPPP ME PLEASEEEEEEEEE
Answer:
7. a = 50 degrees
b = 50 degrees
c= 50 degrees
d = 75 degrees
8.
Step-by-step explanation:
7.
a. Vertically opposite angles are equal
b. Vertically opposite angles are equal
c Alternate angles
d. Angles on a straight line.
8. 45 + 45 + 65 + 35 + 40 + 30 = 200m
Hope this helps
If a function is defined by the equation y=5x−5, which equation defines the inverse of this function?
Answer:
[tex]\displaystyle y = \frac{1}{5}x+1[/tex]
Or:
[tex]x + 5 = 5y[/tex]
Step-by-step explanation:
We have the function:
[tex]y=5x-5[/tex]
And we want to find its inverse.
To find the inverse of a function, we:
Flip x and y. And solve for y.Hence:
[tex]x=5y-5[/tex]
Solve for y. Add:
[tex]\displaystyle x + 5 = 5y[/tex]
Divide:
[tex]\displaystyle y = \frac{x+5}{5}[/tex]
Simplify. Hence:
[tex]\displaystyle y = \frac{1}{5}x+1[/tex]
In conclusion, the inverse function is:
[tex]\displaystyle y = \frac{1}{5}x+1[/tex]
out of 8000 students of Chitwan district 10% take tuition in various subject before the SLC examination. Among them 40% take tuition in English only,20% in math only and 80 students in other subject. Compare the number of students who take tuition on both subject and the total number of students.
Answer:
Out of 8000 students, 10% take tuition in various subjects before the exam.
10% of 8000 is:
10/100 * 8000 = 800
Among the 800, 40% take tuition in English only and 20% take tuition in Math only.
80 students take tuition in other subjects, therefore, in percentage:
80/800 * 100 = 10%
Therefore, the percentage of students that take tuition in both Math and English is:
100% - (40% + 20% + 10%) = 100% - 70% = 30%
30% of the 800 students take tuition in both subjects. That is:
30/100 * 800 = 240 students
Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.
In percentage:
240/8000 * 100 = 3%
3% of students take tuition in both English and Math.
In Ratio:
3 : 100
3 out of 100 students take tuition in English and Math.
HELP YOU WILL GET 30 POINTS Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After reading for 4 hours, he had 330 pages left to read. How long is the book? _____=pages How long did it take Naoya to read the entire book?______=hours
total number of pages = 550 pages
total amount of time to read the full book = 10 hours
======================================================
Work Shown:
1 hour = 55 pages
4 hours = 220 pages ... multiply both sides by 4
After 4 hours, he had read 220 pages. Since he has 330 still left to read, this brings the total to 220+330 = 550 pages overall
550/55 = 10 hours is the total amount of time needed to read the entire book at a rate of 55 pages per hour. This is assuming the rate is kept constant.
While 10 hours is a lot, it's somewhat plausible to get the full book read in one continuous session. Though he is better off taking (short) breaks every now and then.
Answer:
550 pages
10 hrs
Step-by-step explanation:
he reads 55 pages per hour
4 hrs* 55 pages/hrs=220 pages
the book is 550 pages long
220 pages+330=550 pages
to find the time to read the whole book:
330/55=6 hrs +4 hrs=10
or
550/55=10 hrs
if i were to divide 15.34 by 1.64 what would it be
Answer:
9.35975609756
Step-by-step explanation:
Its about this I just put it into a calculator
Answer:9.353658
Step-by-step explanation:
Add the sum of (−5.4) and 8.2 to the opposite of (−2 3/4 ).
Answer:2
Step-by-step explanation:
-5.4+8.2=14/5 and then opposite of -2 3/4 is 2.
Leslie went out for a jog. When she returned she went to the tap and filled up her 500 mL reusable water bottle. She drank 250 mL at a constant rate in one minute. Her phone rang, she set down the bottle of water and talked to her friend for four minutes. After her phone call she sipped the rest of her bottle at a constant rate in two minutes. Create a voulme vs. time graph for this story.
Answer:
Please find attached the required graph and
Step-by-step explanation:
The values for the information given can be written down as follows;
Time, seconds Volume mL
0, 500
12, 450
24, 400
36, 350
48, 300
60, 250
72 250
84 250
96 250
108 250
120 250
132 250
144 250
156 250
168 250
180 250
192 250
204 250
216 250
228 250
240 250
252 250
264 250
276 250
288 250
300 250
312 225
324, 200
336, 175
348, 150
360, 125
372, 100
384, 75
396, 50
408, 25
420, 0
In the diagram, what is the measure of angle 1 to the nearest degree? a) 82° b) 92° c) 94° d) 98°
Answer:
98
Step-by-step explanation:
7x+4 = 88 because they are vertical angles and vertical angles are equal
7x = 88-4
7x = 84
Divide by 7
7x/7 = 84/7
x = 12
<1 and 7x-2 are supplementary angles since they form a line
<1 + 7x-2 = 180
<1 + 7(12) -2 = 180
<1 +84-2 =180
<1 +82 = 180
<1 = 180-82
<1 = 98
Answer-
98
step by step explanation -
7x+4=88
7x=84
x=12
7x-12=7*(12)-2=82
angle 1=180-82 =
98The diagram shows an incomplete polygon. How do I determine whether it is a regular polygon or not? How should I write my reasoning?
Answer:
see explanations below.
Step-by-step explanation:
The shown sides are all equal.
If it is a regular polygon, it must have all interior angles equal, and all sides equal.
IF
all sides are equal and all angles are equal,
THEN
it is a regular polygon, with 12 sides, because in regular polygons, all exterior angles are equal, and add up to 360 degrees.
No. of sides = 360/(180-150) = 360/30 = 12 sides.
Choose the inequality that represents the following graph.
+
H+
-5 -4 -3
+
4
-2 -1
0
1
2.
3
5
Choose 1 answer:
2<-4
23 -4
2 - 4
2-4
Answer:
x ≤ -4
Step-by-step explanation:
There is a closed circle at -4, which requires and equals sign
The line goes to the left, which is less than
x ≤ -4
What is 2+2 I have no idea please help
Answer:
2+2=4
Step-by-step explanation:
2+2=4
good question like if you have two chocolates and your mom gives you two more than there will be 4 and they will be too delicious
i hope this will help you :)
have a great day
Answer:
2+2=4
Step-by-step explanation:
So you take the 2 numbers 2+2 and you use your finger counting to get to 4. It’s really hard mathematics but you’ll get there. Have a great day!
The company profits increased 20% from last year. If the profits last year were $2,500, what are the company's profits this year? A. $30 B. $300 C. $5,000 D. $3,000
Step-by-step explanation:
last years was $2500.00
20% of $2500 = $500.00
profit this year is $3000.00
Answer:
D
Step-by-step explanation:
What is the surface area of a sphere with a diameter of 16 cm?
Answer:
804.25 cm² (corrected to 2 decimal places)
Step-by-step explanation:
Radius = diameter / 2
= 16/ 2
=8 cm
Surface area of sphere = 4πr²
= 4π8²
=804.25 cm² (corrected to 2 decimal places)
If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)?
Answer:
The answer is
the last graphStep-by-step explanation:
To find the graph which shows (f + g)(x) we must first find (f + g)(x)
That's
f(x) = - x² + 3x + 5
g(x) = x² + 2x
To find (f + g)(x) add g(x) to f(x)
That's
(f + g)(x) = -x² + 3x + 5 + x² + 2x
Group like terms
(f + g)(x) = - x² + x² + 3x + 2x + 5
We have (f + g)(x) as
(f + g)(x) = 5x + 5
Since (f + g)(x) is linear the graph which shows (f + g)(x) is the last graph
Hope this helps you
Answer:
last graph or D
Step-by-step explanation:
Three triangles are shown on the centimetre grid.
A
B
C
(a I already did)
b)
Work out the area of this triangle.
Give your answer as a decimal.
Answer:
C has the largest area. It is 4.5 square units.
Step-by-step explanation:
A:
area = bh/2 = 2 * 3/2 = 3
B:
area = bh/2 = 2 * 3/2 = 3
C:
area = bh/2 = 3 * 3/2 = 4.5
C has the largest area. It is 4.5 square units.
Solve (x - 4)2 = 5.
O A. x-5+
O B. * = 41.5
O C. X = 9 and x = -1
O D. X=-4115
Answer:
x=4_+√5option B is the correct option.
Solution,
[tex] {(x - 4)}^{2} = 5 \\ [/tex]
x-4=_+√5
X=4_+√5
Hope this helps...
Good luck on your assignment...
Answer:
(x-4)^2 =5
x^2-16=5
x^2=5+16
x^2=21
√x^2=√21
x=√21
Step-by-step explanation :
First of all open the bracket which has square
Secondly change the position of 16
Note: when a number changes its place , the symbol also changes
then when you get the value take the square root on both sides
and you'll get the answer
Please Help Me i beg
Answer:
B is P(x)=(x-3)^2 +2
C is P(x)=(x-1)^2 -5
Step-by-step explanation:
i think i am right
What is the solution to the system of equations? y = –5x + 3 y = 1
a(0.4, 1) b(0.8, 1) c(1, 0.4) d(1, 0.8)
Answer:
A
Step-by-step explanation:
We know that the y-coordinate has to be 1 so we can eliminate options C and D. If we plug y = 1 into y = -5x + 3 to solve for x we get:
1 = -5x + 3
-2 = -5x
x = 0.4 so the answer is A.
Your friend is having trouble solving word problems. Create a word problem of your own and provide the answer along with a detailed explanation of how you solved your equation.
Step-by-step explanation:
Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?
Solution :
Let “x km/hr” be the speed of 1st car
Let “y km/hr” be the speed of the 2nd car
Time = Distance/Speed
Speed of both cars while they are traveling in the same direction = (x – y)
Speed of both cars while they are traveling in the opposite direction = (x + y)
5 = 100/(x -y)
x – y = 100/5
x - y = 20
x - y - 20 = 0 ---(1)
1 = 100/(x + y)
x + y = 100
x + y - 100 = 0--b----(2)
x/(100 + 20) = y/(-20 + 100) = 1/(1 + 1)
x/120 = y/80 = 1/2
x/120 = 1/2 y/80 = 1/2
x = 120/2 y = 80/2
x = 60 y = 40
So, the speed of first car = 60 km/hr
Speed of second car = 40 km/hr
Prove that (〖sin〗^2 θ)/(1+cosθ)=1-cosθ
Answer:
proved
Step-by-step explanation:
prove that : (sin^2 θ)/(1+cosθ)=1-cosθ
(sin^2θ)*(1−cosθ)/(1+cosθ)(1+cosθ) =
sin^2Ф)(1-cosФ)/1-cos^2Ф since 1-cos^2Ф=sin^2Ф then:
(sin^2Ф)(1-cosФ)/sin^2Ф =
1-cosФ (sin^2Ф/sin^Ф=1)
proved
Answer:
Step-by-step explanation:
take it befor delete
Gassim bought 2L of colour paints to paint a wall of a villa. He already had 0.75L of colour paint. If he uses 2/5 of colour paints , find the amount of colour paints left?
THNXX for answering : )
Answer:
0.45 litres
Step-by-step explanation:
2/5 multiplied by 2 = 0.8
0.8+0.75= 1.55
2-1.55 = 0.45
Erin travels north and south from Main Station. The distance, in km, of the train from Main Station is
modeled by the function d(t) = t3 - 9t2 + 6t, where North is positive and South is negative. Time
elapsed after the start of a shift, in hours, is represented by t, where t € (0,12]. 'If the shift starts at
noon, determine at which time(s) the train is more than 16 km south of Main Station.
Answer:
The times are t = 9, t = 10, t = 11 and t = 12
Step-by-step explanation:
For the train to be more than 16 km South and since south is taken as negative,
d(t) > -16
t³ - 9t² + 6t > -16
t³ - 9t² + 6t + 16 > 0
Since -1 is a factor of 16, inserting t = -1 into the d(t), we have
d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)
So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16
Factorizing t² - 10t + 16, we have
t² - 2t - 8t + 16
= t(t - 2) - 8(t - 2)
= (t -2)(t - 8)
So t - 2 and t - 8 are factors of d(t)
So (t + 1)(t -2)(t - 8) > 0
when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0
when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0
when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0
when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0
Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8
Since t ∈ (0, 12]
In the interval 0 < t < 2 the only value possible for t is t = 1
d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2
Since d(1) < -16 this is invalid
In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.
So,
d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km
d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km
d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km
d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km
Samuel wants to estimate what 5843 x .00243 is. What should his first step be?
Mei Su had 80 coins. She gave most of them to her friends in such a way that each of her friends got at least one coin and no two of her friends got the same number of coins. What is the largest number of friends to whom Mei Su could have given coins?
Answer: 12 friends.
Step-by-step explanation:
the data we have is:
Mei Su had 80 coins.
She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:
The maximum number of friends that could have coins is when:
friend 1 got 1 coin
friend 2 got 2 coins
friend 3 got 3 coins
friend N got N coins
in such a way that:
(1 + 2 + 3 + ... + N) ≥ 79
I use 79 because "she gave most of the coins", not all.
We want to find the maximum possible N.
Then let's calculate:
1 + 2 + 3 + 4 + 5 = 15
15 + 6 + 7 + 8 + 9 + 10 = 55
now we are close, lets add by one number:
55 + 11 = 66
66 + 12 = 78
now, we can not add more because we will have a number larger than 80.
Then we have N = 12
This means that the maximum number of friends is 12.
Answer:
12
Step-by-step explanation:
my
Please answer this question now in two minutes
Answer:
LJ = CB
Therefore, CJ is 50km
2) A girl starts from a point A and walks 285m to B on a bearing of 078°. She then walks due south to a point C which is 307m from A. What is the bearing of A from C , and is the distance |BC| ?
Answer:
bearing of A from C is - 65.24°
the distance |BC| is 187.84 m
Step-by-step explanation:
given data
girl walks AB = 285 m (side c)
bearing angle B = 78°
girl walks AC = 307 m (side a)
solution
we use here the Cosine Law for getting side b that is
ac² = ab² + bc² - 2 × ab × cos(B) ...............1
307² = 285² + x² - 2 × 285 cos(78)
x = 187.84 m
and
now we get here angle θ , the bearing from A to C get by law of sines
sin (θ) = [tex]\frac{187.84}{307} \times sin(78)[/tex]
sin (θ) = 0.5985
θ = 36.76°
and as we get here angle BAC that is
angle BCA = 180 - ( 36.76° + 78° )
angle BCA = 65.24°
and here negative bearing of A from C so - 65.24°
(please help) List the three lowest numbers that have the following characteristics. Work must be shown. 60 is a multiple of the number 3 is a factor of the number 4 is not a factor of the number
Answer:
3, 6, and 15
Step-by-step explanation:
Notice that if 60 is a multiple, the numbers in question could have the same factors as 60.
So let's look at 60's prime factors:
60 = 2 * 2 * 3 * 5
we also know that 3 is a factor, so the factor 3 must be included in all three options, we also know that 4 is NOT a factor, so both factors 2 cannot be included (but only one of them could).
So, in order to build the lowest possible numbers that verify such conditions, we can use:
3
3 * 2 = 6
since 3 or 2 cannot be repeated, the next smaller would be:
3 * 5 = 15
What are the solutions of the equation x^4 + 6x^2 + 5 = 0? Use u substitution to solve.
Answer:
second option
Step-by-step explanation:
Given
[tex]x^{4}[/tex] + 6x² + 5 = 0
let u = x², then
u² + 6u + 5 = 0 ← in standard form
(u + 1)(u + 5) = 0 ← in factored form
Equate each factor to zero and solve for u
u + 1 = 0 ⇒ u = - 1
u + 5 = 0 ⇒ u = - 5
Change u back into terms of x, that is
x² = - 1 ( take the square root of both sides )
x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and
x² = - 5 ( take the square root of both sides )
x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]
Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]
Find the approximate side lengths and perimeter of quadrilateral WXYZ. If necessary, round your answers to the nearest hundredth.
The approximate length of segment WX is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment XY is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate length of segment YZ is
[tex]\left[\begin{array}{ccc}2\\4.12\\4.47\\5\end{array}\right][/tex]
The approximate perimeter of quadrilateral WXYZ is [tex]\left[\begin{array}{ccc}14\\14.47\\15\\15.59\end{array}\right][/tex]
Answer:
The answer is given below
Step-by-step explanation:
Given that the location of the points are W = (3, 1) , X = (7, -1), Y = (7, -3) and Z = (3,-3)
The distance between two points A(x1, y1) and B(x2, y2) is given by the formula:
[tex]|AB|=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Therefore, the side length of the quadrilaterals are:
[tex]|WX|=\sqrt{(-1-1)^2+(7-3)^2}=\sqrt{20} =4.47[/tex]
[tex]|XY|=\sqrt{(-3-(-1))^2+(7-7)^2}=\sqrt{20} =2\\\\|YZ|=\sqrt{(-3-(-3))^2+(3-7)^2}=\sqrt{20} =4\\\\|ZW|=\sqrt{(-3-1)^2+(3-3)^2}=\sqrt{20} =4[/tex]
The Perimeter of the quadrilateral = |WX| + |XY| + |YZ| + |ZX| = 4.47 + 2 + 4 + 4 = 14.47 units
Answer:
4.47,
2
4
14.47
Step-by-step explanation: