Answer:
[tex] \cos(x) = - \frac{5}{ \sqrt{41} } [/tex]
[tex] \csc(x) = \frac{ \sqrt{41} }{4} [/tex]
[tex] \tan(x) = - \frac{4}{5} [/tex]
Step-by-step explanation:
We know that (-5,4) is the terminal side. This means out legs will measure 5 and 4 if we graph it on a triangle.
We need to find the cos, csc, and tan measure of this point.
We can find cos by using the formula of
[tex] \cos(x) = \frac{adj}{hyp} [/tex]
The adjacent side is -5 and we can find the hypotenuse by doing pythagorean theorem.
[tex] { - 5}^{2} + {4}^{2} = \sqrt{41} [/tex]
So using the info the answer is
[tex] \cos(x) = \frac{ - 5}{ \sqrt{41} } [/tex]
We can find tan but first me must find sin x.
[tex] \sin(x) = \frac{opp}{hyp} [/tex]
[tex] \sin(x) = \frac{4}{ \sqrt{41} } [/tex]
So now we just use this identity,
[tex] \tan(x) = \sin(x) \div \cos(x) [/tex]
[tex] \tan(x) = \frac{ \frac{4}{ \sqrt{41} } }{ \frac{ - 5}{ \sqrt{41} } } = - \frac{4}{5} [/tex]
So tan x=
[tex] - \frac{ 4}{5} [/tex]
We can find csc by taking the reciprocal of sin so the answer is easy which is
[tex] \frac{ \sqrt{41} }{4} [/tex]
If anyone knows answer with steps that will be greatly appreciated :)
Answer:
The area formula is= 1/2(a+b)×height
1/2×20×6=60metres squared
Step-by-step explanation:
kindly correct me if am wrong
The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour period, one defective circuit board was found. (a) Find the probability that it was produced during the first hour of operation during that period. (Round your answer to four decimal places.) (b) Find the probability that it was produced during the last hour of operation during that period. (Round your answer to four decimal places.) (c) Given that no defective circuit boards were produced during the first five hours of operation, find the probability that the defective board was manufactured during the sixth hour. (Round your answer to four decimal places.)
Answer:
a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c) the required probability is 0.2000
Step-by-step explanation:
Given the data in the question;
During a specific ten-hour period, one defective circuit board was found.
Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.
Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.
f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex]; ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]
= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex]; ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]
Now,
a) the probability that it was produced during the first hour of operation during that period;
P( Y < 1 ) = [tex]\int\limits^1_0 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^1_0[/tex]
= [tex]\frac{1}{10} [ 1 - 0 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
b) The probability that it was produced during the last hour of operation during that period.
P( Y > 9 ) = [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]
we substitute
= [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]
= [tex]\frac{1}{10} [y]^{10}_9[/tex]
= [tex]\frac{1}{10} [ 10 - 9 ][/tex]
= [tex]\frac{1}{10}[/tex] or 0.1000
Therefore, the probability that the defective board was produced during the last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000
c)
no defective circuit boards were produced during the first five hours of operation.
probability that the defective board was manufactured during the sixth hour will be;
P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )
= P( 5 < Y < 6 ) / P( Y > 5 )
we substitute
[tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]
[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]
= ( 6-5 ) / ( 10 - 5 )
= 0.2000
Therefore, the required probability is 0.2000
If 15% of the customer's total is $22.05, then the customer's total is
Answer:
$147
Step-by-step explanation:
0.15x = $22.05
Divide both sides by 15
22.05/0.15 = $147
Cho hình thang ABCD vuông tại A và D biết AB=AD=3cm, BC=6cm. Tính góc C và D
Answer:
C=6cm
D=3cm
Step-by-step explanation:
C=6×6cm
36cm
D=3×3cm
=9cm
The diameter of a cone is 34 ft. the height is 16 ft what is the volume in cubic ft?
Answer:
4842.24 cubic feet
Step-by-step explanation:
Use the formula for the volume of a cone, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
The diameter of the cone is 34 ft, so the radius is 17 ft.
Plug in the radius and height into the formula, and solve for the volume:
V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]
V = [tex]\pi[/tex](17)²[tex]\frac{16}{3}[/tex]
V = [tex]\pi[/tex](289)[tex]\frac{16}{3}[/tex]
V = 4842.24
So, the volume of the cone is 4842.24 cubic feet
Answer:
4,841.32 ft³.
Step-by-step explanation:
Let’s assume that this is a right circular cone and that the radius of the cone is r.
For our problem, r = (1/2)d = (1/2)34 = 17.
The volume of the cone is:
V = (1/3)pi r^2 h, where r is the radius and h is the height.
So, V = (1/3)pi(17^2)16 = 4,841.32 ft³.
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
Step-by-step explanation:
For the question 1:
The given is a special right triangle with angle measures of
90-60-30 and side lengths represented by :
a - a[tex]\sqrt{3}[/tex] and 2a
The side length that sees 90 degrees is represented with a
The side length that sees 60 degrees is represented with a[tex]\sqrt{3}[/tex]
The side length that sees 30 degrees is represented with 2a
Here the side length that sees angle measure 60 is given as [tex]\sqrt{6}[/tex]
so a[tex]\sqrt{3}[/tex] = [tex]\sqrt{6}[/tex] to find the value of a we divide [tex]\sqrt{6}[/tex] with [tex]\sqrt{3}[/tex]
[tex]\frac{\sqrt{6} }{\sqrt{3} }[/tex] = [tex]\sqrt{2}[/tex]
so y = [tex]\sqrt{2}[/tex] and x = 2[tex]\sqrt{2}[/tex]
for second question
the square value of hypotenuse is equal to sum of other two side length's square value
10^2 + 6^2 = x^2
100 + 36 = x^2
136 = x^2
[tex]\sqrt{136}[/tex] = x
Find the slope of the graphed line
Answer:
4
Step-by-step explanation:
Pick two points on the line
(0,-5) and (1,-1)
We can find the slope using
m = (y2-y1)/(x2-x1)
= ( -1 - -5)/(1 - 0)
(-1+5)/(1-0)
4/1
= 4
Find the area of the circle around your answer to the nearest 10th
Answer:
A= π ( 3.8)^2
A= 45.36
OAmalOHopeO
Step-by-step explanation:
area is 2xr(times your answer)
Fixed costs are $2000, and the cost of producing each pair of skies is $100. The selling price is $220 (per pair). How many pairs should be sold to make a profit of $29200?
260 pairs
Step-by-step explanation:
220-100= 120
(29200+2000)÷120= 260
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft^2. Find the dimensions of the rectangle.
Answer:
7 x 4
Step-by-step explanation:
Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7
Simplify (-2)-3⋅ (-2)4⋅
Answer: 22
Step-by-step explanation:
−2−(3)(−2)(4)
=22
Last year at a certain high school, there were 56 boys on the honor roll and 150 girls on the honor roll. This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 12%. By what percentage did the total number of students on the honor roll decrease?
Answer:
15.534% decrease
Step-by-step explanation:
Find the new number of boys and girls on the honor roll:
56(0.75) = 42 boys
150(0.88) = 132 girls
Find the new total number of students on the honor roll:
42 + 132 = 174
Find the percent decrease by dividing the difference in the number of students by the original number.
There were originally 206 total students on the honor roll. Find the difference:
206 - 174 = 32
Divide this by the original amount:
32/206
= 0.15534
So, the number of students on the honor roll decreased by approximately 15.534%
Find the sum : (i) 23123, 11001 and 21302 (iii) 21031, 12301 and 32211 (v) 21003, 12346 and 21220 (ii) 32101, 12301 and 1032 (iv) 301242, 123310 and 10002
Answer:
(i) 23123 + 11001 + 21302 = 55426(ii) 32101 + 12301 + 1032 = 45434(iii) 21031 + 12301 + 32211 = 65543(iv) 301242 + 123310 + 10002 = 434554(v) 21003 + 12346 + 21220 = 545691:-
[tex]\\ \sf\longmapsto 23123+11001+21302[/tex]
[tex]\\ \sf\longmapsto 55426[/tex]
2:-
[tex]\\ \sf\longmapsto 21031+12301+32211[/tex]
[tex]\\ \sf\longmapsto 65543[/tex]
3:-
[tex]\\ \sf\longmapsto 21003+12346+21220[/tex]
[tex]\\ \sf\longmapsto 54569[/tex]
4:-
[tex]\\ \sf\longmapsto 32101+12301+1032[/tex]
[tex]\\ \sf\longmapsto 45434[/tex]
5:-
[tex]\\ \sf\longmapsto 301242+123310+10002[/tex]
[tex]\\ \sf\longmapsto 434554[/tex]
I copied the problem
Answer:
Step-by-step explanation:
149 11/16" ÷ 12 = 12.4739583333333333... ft
We subtract off the whole number part and call it 12'
0.4739583333333333 × 12 = 5 11/16 "
149 11/16" = 12' 5 11/46"
120 7/8" ÷ 12 = 10.07291666666
We subtract off the whole number part and call it 10'
0.07291666666 × 12 = 7/8"
120 7/8" = 10' 7/8"
The third one is moot as 0 1/8" equals 0' 1/8"
I suspect your photo framing has cut off some important numbers.
The perimeter of the figure below is 107.5 in. Find the length of the missing side
9514 1404 393
Answer:
7.3 in
Step-by-step explanation:
The sum of the lengths of the sides shown is 100.2 in, so the missing length is ...
107.5 -100.2 = 7.3 . . . inches
There are 5 slots, each containing the letters W, R, L, D or O. One letter is picked at random from each slot. What are the odds that the letters stored in these slots read the word WORLD?
Answer:
1/120
Step-by-step explanation:
For the first letter, you have a 1/5 chance of getting w
On the second you have a 1/4 chance to get the r
Then 1/3 and 1/2
Next you just multiply the bottom numbers
That gives you how many diffrent outcomes there can be. Put that over 1 and you have your answer.
Hope this helps <3
Please help me to find this answer
Step-by-step explanation:
question 1
angle DBA=90°, meaning to find m<D you have to add 90+38 then subtract by 180, because ABD is a triangle
90+18+m<D=180
108+m<D=180
m<D=180-108
=72°
question 2
m<D again in this case angle ABD is also 90
m<D=180-(90+48)
=180-138
=42°
I hope this helps
g(x) = f(x+1) using f(x)= x to the power of 2
Answer:
g(x) = x² + 2x + 1
General Formulas and Concepts:
Algebra I
Terms/Coefficients
ExpandingFunctions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = f(x + 1)
f(x) = x²
Step 2: Find
Substitute in x [Function f(x)]: f(x + 1) = (x + 1)²Expand: f(x + 1) = x² + 2x + 1Redefine: g(x) = x² + 2x + 1If sin x = –0.1 and 270° < x < 360°, what is the value of x to the nearest degree?
Answer:
354°15'38.99''
Step-by-step explanation:
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
2x-1=3
2x=3+1
2x=4
x=2
[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]
(a) Let's try with x = - 1
[tex] \sf \: 2x - 1 = 3 \\\sf 2( - 1) - 1 = 3 \\ \sf- 2 - 1 = 3 \\ \\ \boxed{\bf- 3 \: \bcancel= \: 3}[/tex]
So, x = - 1 is not the solution to the given equation.
______________
(b) Now, try with x = 2
[tex]\sf2x - 1 = 3 \\ \sf2(2) - 1 = 3 \\ \sf4 - 1 = 3 \\ \\ \boxed{\bf3 = 3}[/tex]
Yes, we can see that x = 2 is the correct solution for the equation.
______________
Hope it helps.
RainbowSalt2222
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 212" by 334" on the drawing, how large is the bedroom?
Answer:
53 by 83.5.
just divided the two numbers by 1/4
Answer:
848 and 1336
Step-by-step explanation:
You would actually multiply 212 and 334 by 4.
You need to multiply 1/4 by 4 to get 1.
212 x 4 = 848
334 x 4 =1336
A square and a rectangle have the same area. If the dimensions of the rectangle are 4 ft by 16 ft, how long is a side of the square?
Answer:
8
Step-by-step explanation:
4×16=64
[tex] \sqrt{64 } = 8[/tex]
For what value of x is the parallelogram a rhombus.
Answer:
Step-by-step explanation:
2 × ( 3x + 6 )° + ( 16x + 14 )° = 180°
22x + 26 = 180
22x = 154
x = 7
Evaluate: 2-4
1
O A.
loo
O B.-8
O c.
1
16
O D.-16
Answer:
c is the answer
[tex] \frac{1}{16} [/tex]
The pattern 96, 92, 88, 84, ________ follows the "subtract 4" rule. Study the pattern to find traits that are not obvious in the rule. Explain.
pleas in one or 2 sentences
A tank filled with water begins draining. The number of minutes t since the water began draining from the tank is a function of the number of gallons of water in the tank, v. We will call this function f so that f(t) = v.
Required:
a. Using function notation, represent the of gallons of water in me tank 4 minutes after the water darning from the Ink.
b. Suppose that f(4) = 7, what does this mean in the context of the problem?
Answer:
[tex](a)\ f(4) = v[/tex]
(b) There are 7 gallons left in the tank after 4 minuted
Step-by-step explanation:
Given
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
Solving (a): Notation for gallons remaining at 4 minutes
This means that [tex]t=4[/tex]
[tex]f(t) = v[/tex] becomes
[tex]f(4) = v[/tex]
Solving (b): Interpret f(4) = 7
We have:
[tex]f(t) = v[/tex]
[tex]t \to[/tex] time since water began draining
[tex]v \to[/tex] gallons in the tank
This means that:
[tex]t =4[/tex]
[tex]v =7[/tex]
It can be interpreted as:
There are 7 gallons left in the tank after 4 minuted
What’s v=(324pie)(3)
What happens during a controlled experiment?
No observations are made.
A factor called a prediction is changed.
Many variables are changed at once.
The results of changing the independent variable are observed
Answer:
Step-by-step explanation:
The answer is that 1 variable is allowed to change. The others are held at a constant.
An example would be the growth of a poinsettia. These Christmas plants are very touchy. They respond badly to too much water or not enough water. So you keep the amount of dirt, the amount of sunlight, the amount of support that each plant receives as a constant.
The amount of water is what you change in one of the plants. The one plant (or a few) will measure the growth of the plant.
So the last answer is the one you want.
It is claimed that the average child has no time to go to school. For the child spends 8 hours per day,or one third of his/her time sleeping. Based on a 365 day year, that’s 121.67days sleeping. Also the child spends three hours per day eating. That’s a total of 45 days in the year spent eating. Also the child spends 90 days taking summer vacation. Also the child spends 21 days on Christmas and Easter holiday. Finally, the child has each Saturday and Sunday off. That’s a total of 104 days. In short, we (rounding to whole days accounted for 122+45+90+21+104=382 days of the year taken up by ordinary child inlike activities. This is already more than the 365 days that are known to comprise a year. We conclude that there is certainly no time for the child to attend school. What is wrong with this reasoning?
Answer:
See below.
Step-by-step explanation:
Sleeping:
8/24 * 365 = 121.76 days
Eating:
3/24 * 365 = 45.63 days
Total sleeping and eating: 167 days
Summer Vacation & Holidays:
90 + 21 = 111 days
Saturdays and Sundays: 52 + 52 = 104 days
Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days
It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.
A publisher reports that 54% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 200 found that 44% of the readers owned a personal computer. Is there sufficient evidence at the 0.10 level to support the executive's claim
The null and alternate hypotheses are
H0 : u = 0.44 vs Ha: u > 0.44
Null hypothesis: 44% of readers own a personal computer.
Alternate Hypothesis : greater than 44% of readers own a personal computer.
This is one tailed test and the critical region for this one tailed test for the significance level 0.1 is Z > ±1.28
The given values are
p1= 0.54 , p2= 0.44 ; q2= 1-p2= 0.56
Using z test
Z = p1-p2/√p2(1-p2)/n
Z= 0.54-0.44/ √0.44*0.56/200
z= =0.1/ 0.03509
z= 2.849
Since the calculated value of Z= 2.849 is greater than Z= 1.28 reject the null hypothesis therefore there is sufficient evidence to support the executive's claim.
Null hypothesis is rejected
There is sufficient evidence to support the executive's claim at 0.10 significance level.
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