Answer:
Hello,
Step-by-step explanation:
we must first remember that:
[tex]\boxed{sin(5x)=5sin(x)-20*sin^3(x)+16*sin^5(x)}\\\\[/tex]
Let say t=sin(x)
[tex]sin(x)+cos(x)=1.4\\\\t+\sqrt{1-t^2}=1.4\\\sqrt{1-t^2}=1.4-t\ we\ square\\1-t^2=1.4^2+t^2-2.8*t\\2t^2-2.8*t+0.96=0\\\Delta=2.8^2-4*2*0.96=0.16=0.4^2\\\\t=\dfrac{2.8-0.4}{4} =0.6\ or\ t=\dfrac{2.8+0.4}{4}=0.8\\\\t^3=0,216\ or\ t^3=0,512\\\\t^5=0,07776\ or\ t^5=0,32768\\\\\boxed{sin(5x)=5*0.6-20*0.216+16*0.07776=-0,07584}\\\\or\\\\\boxed{sin(5x)=5*0.8-20*0.512+16*0.32768=-0,99712}[/tex]
f(x)=3x+5 and g(x)=4x2-2 h(x)=x2-3x+1 Find f(x)+g(x)-h(x).
Answer:
f(x)+g(x)-h(x) = 3x² + 6x + 2Step-by-step explanation:
f(x) = 3x + 5
g(x) = 4x² - 2
h(x) = x² - 3x + 1
f(x)+g(x)-h(x) means subtract h(x) from the sum of f(x) and h(x)
f(x)+g(x)-h(x) = 3x + 5 +( 4x² - 2) - (x² - 3x + 1)
Remove the brackets
That's
f(x)+g(x)-h(x) = 3x + 5 + 4x² - 2 - x² + 3x - 1
Group like terms
We have
f(x)+g(x)-h(x) = 4x² - x² + 3x + 3x + 5 - 2 - 1
Simplify
We have the final answer as
f(x)+g(x)-h(x) = 3x² + 6x + 2Hope this helps you
Hope this helps you
15 points work out ratio for x
Answer:
x = 25
Step-by-step explanation:
x : (x+10) = 5:7
Fractional form
x / x+10 = 5/7
Cross multiply:
x * 7 = (x+10) * 5
7x = 5x + 50
7x - 5x = 5x + 50 - 5x
2x = 50
x = 25
Check:
25 : 25 + 10
25 : 35
25/35 = 5/7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
5) Suppose a slice of a 12-inch pizza has an area of 20 square inches. What is the angle of
this slice?
Answer:
The angle of the slice is 63.64 degrees
Step-by-step explanation:
Here in this question, we are concerned with calculating the angle of the slice.
What we should know are as follows;
1. A pizza is a perfect circular shape
2. A 12-inch pizza means the diameter of the pizza is 12 inches and consequently its radius will be 12/2 = 6 inches
3. A slice of a pizza represents a sector of the circle( a sector is part of a circle bounded by 2 radii and an arc)
Mathematically, to calculate the angle of the slice, we simply use the formula for the area of a sector.
Area of sector = theta/360 * pi * r^2
where Area of sector = 20 square inches
theta is the center angle we are looking for
r is the radius of the pizza which is 6 inches
Plugging these values into the area of sector equation, we have
20 = theta/360 * 22/7 * 6^2
20 = theta/10 * 22/7
22 theta = 10 * 20 * 7
theta = 1400/22
theta = 63.64 degrees which is approximately 64 degrees to the nearest degree
state crunchy theorem
Answer: it says that if two different paths connect the same two points.
Step-by-step explanation:
It says that is two different paths connect the same two points, and a function holomorphic everywhere in between the two paths, then the two path integrals of the functions will be same.
what is the least number to be added to 1500 to make it a perfect square?
Answer:
21
Step-by-step explanation:
√1500 ≈ 38.7
round that up to 39 and square it:
39² = 1521
A coin is tossed 4 times. Let E1 be the event "the first toss shows heads" and E2 the event "the second toss shows heads" and so on. That is, Ei is the event that the "i"th toss shows up heads.
A. Are the events e e and f f independent?
B. Find the probability of showing heads on both toss.
Answer:
The events are independent.
The probability of showing heads on both toss is equal to 1/2
Step-by-step explanation:
The sample space for this experiment consists of 2⁴= 16 sample points, as each toss can result in two outcomes we assume that the events are equally likely.
Two events are independent in the sample space if the probability of one event occurs, is not affected by whether the other event has or has not occurred.
In general the k events are defined to be mutually independent if and only if the probability of the intersection of any 2,3,--------, k equals the product of their respective probabilities.
P (A∩B) = P(A). P(B)
P (A∩B) = 1/2. 1/2= 1/4
Head Tail
P(E1)= 1/2 ---------- Coin 1 H,H T,H
1/4 1/4
P(E2)= 1/2 --------------- Coin 2 H, H H,T
1/4 1/4
So the events are independent.
The probability of showing heads on both toss is equal to 1/2
The sample space for this experiment consists of 2⁴= 16 sample points, out of which eight will have heads on both toss.
Or in other words ( 1/4* 1/4) = 2/4 = 1/2
The length of a rectangle is a inches. Its width is 5 inches less than the length. Find the area and the perimeter of the rectangle.
Answer:
[tex]Area = 5a - a^2[/tex] [tex]inches\²[/tex]
[tex]Perimeter = 10\ inches[/tex]
Step-by-step explanation:
Given
Length = a
Width = 5 - a
Required
Determine the Area and Perimeter;
Calculating Area
Area is calculated as thus;
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = a * 5 - a[/tex]
[tex]Area = a * (5 - a)[/tex]
Open Bracket
[tex]Area = 5a - a^2[/tex]
Calculating Perimeter
Perimeter is calculated as thus;
[tex]Perimeter = 2 (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 (a + 5 - a)[/tex]
Collect Like Terms
[tex]Perimeter = 2 (5 + a- a)[/tex]
[tex]Perimeter = 2 (5)[/tex]
Open Bracket
[tex]Perimeter = 10\ inches[/tex]
60feet to meters plaese with work
Answer:
60 Feet = 18.288 Meters
Step-by-step explanation:
foot = 12 inch = 0.3048 m
0.3047 × 60
18.288 meters
Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not solve the equation.
x2+3x−18=0
Answer:
Step-by-step explanation:
Hello, "the constant term has been written on the right side", it means that we add 18 to both sides to get.
[tex]x^2+3x-18=0\\\\x^2+3x=18\\\\\text{We can see the beginning of } (x+\dfrac{3}{2})^2 \\\\x^2+3x=(x+\dfrac{3}{2})^2-\dfrac{3^3}{2^2}=18\\\\(x+\dfrac{3}{2})^2=18+\dfrac{9}{4}=\dfrac{18*4+9}{4}=\dfrac{81}{4}[/tex]
Hope this helps.
Thank you.
Answer:
2.25.
Step-by-step explanation:
x^2 + 3x - 18 = 0
First, we need to write the constant on the right of the equation. So, we add 18 to both sides.
x^2 + 3x = 18.
Now, we find the number that will complete the square. It will be [tex](\frac{b}{2} )^2[/tex].
In this case, b = 3.
[tex](\frac{3}{2} )^2[/tex]
= (1.5)^2
= 2.25.
So, the number that will complete the square to solve the equation is 2.25, or 2 and 1/4, or 9/4.
Hope this helps!
Question 12
A leaking pond loses 16 gallons of water in 5 hours. How many gallons of water will it lose in 41 hours?
Answer:
131.2 gallons
Step-by-step explanation:
1)16/5= 3.2 gallons - of water are lost in 1 hour;
2)3.2*41=131.2 gallons
there was a total of 400 oranges and mangoes at a fruit stall.3/8 of these fruits were mangoes.each orange was priced at 40 cents,and each mango was priced at 60 cents.how much would mr.mead make if he sold 2/3 of the mangoes and 4/5 of the oranges?
Answer:
First find the number of Mango and oranges. 400 divided by 8 = 50. We use 8 because it is the whole part of the percentage. Since, there is 3/8 mangoes, multiply 50* 3= 150 mangoes and 50*5= 250 oranges.
2/3 of 150=100 mangoes. You would find this by dividing 150/3=50 then multiply by 2.
4/5 of 250= 200 oranges. You would find this by dividing 250/5=50 then multiply by 4.
$.40*100= $40.00 mangoes
$.60*200= $120.00 oranges
Mr. Mead would make $160.00
Step-by-step explanation:
Please help, thanks!!!!!
Answer:
[ 2+0+8. 0+0+12][-4+10+2. 0+25+3]
[10. 12]
[8. 28]
Option 3 is the solution
Show the distributive property can be used to evaluate 7x8 4/5
Answer:
308/5
Step-by-step explanation:
It can be Written as
= 7 ×(8 + 4/5 )
= 7 × 8 + 7 × 4/5
= 56 + 28/5
= 280+28
________
5
= 308/5
(G1) The distance from Flagstaff Arizona to
Tucson Arizona is 260 miles. Express this
distance in meters.
A. 418,418 meters
B. 419,000 meters
C. 126,200 meters
D. 260,000 meters
Answer:
A. 418, 418
Step-by-step explanation:
The formula to convert miles to meters is the following:
1 = 1,609.34
so for every 1 mile, you have 1,609.34 meters
so you take your distance in miles and multiply it by 1,609.34
d= 260 x 1,609.34
d = 418, 428.4
11 divided by 9876
Thank youuuu
Answer:
770,7272727272727
Step-by-step explanation:
Answer:
8478 divided by 11= 770.7272727
What is the area of a square with a side length of 32 yards?
Answer:
A=1024 yd.^2
Step-by-step explanation:
A=s^2
Substitute,
A=32^2
So,
A=1024 yd.^2
Answer:
1024 yd²
Step-by-step explanation:
Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.
A(Square) = 32² = 1024
The family trip to Grandma's consisted of both a train ride and a car ride. The average speed of the train ride was 72 miles per hour, and the average speed of the car ride was 62 miles per hour. The entire trip lasted 6 hours.
Let x be the number of hours the train ride lasted. Write an expression for the total distance of the trip, in miles.
Answer:
432
Step-by-step explanation:
x=1hr (6x)=6hours x= 72 hours through train so (6x)=72x6=432
The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P.
Answer:
The AP is 1, 11/2, 10, 29/2, 19, ....
Step-by-step explanation:
Let the first term be a and d be the common difference of the arithmetic progression.
ATQ, a+2d+a+6d=38, 2a+8d=38 and a+8d=37. Solving this, we will get a=1 and d=9/2. The AP is 1, 11/2, 10, 29/2, 19, ....
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Here is the equation
[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]
In the order of operations parentheses go first so we get
[tex]20+3\times11+5+2\times16[/tex]
Next we do the multiplication
[tex]20+33+5+32\\[/tex]
And finally we add them all up
[tex]20+33+5+32=90\\[/tex]
Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 192 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x hat= 167.82 cm, y hat= 81.39 kg,
r = 0.101, P-value = 0.317, and y = - 106 + 1.01x.
Required:
a. Find the best predicted value of y (weight) given an adult male who is 189 cm tall. Use a 0.05 significance level.
b. Find the best predicted value of y hat for an adult male who is 189 tall in ____kg.
When an adult is 189cm tall, his predicted weight in kg is 84.89kg
We have y = -106+1.01x. This is the regression equation
the y value represents weight and it is the predicted valuethe X value represents height and it is the predictorwe are to find y(weight) given that x (height) is 189 cm
y = -106 + 1.01x
y = -106+1.01*189
y = -106+190.89
y = 84.89 kg
In conclusion, when height is 189cm, weight is 84.89 kg
Here is a similar question https://brainly.com/question/16105209?referrer=searchResults.
If M ABD = 65 and DBC=60 then m ABC=
Answer:
∠ ABC = 125°
Step-by-step explanation:
∠ ABC = ∠ ABD + ∠DBC that is
∠ ABC = 65° + 60° = 125°
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x = 55.8
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hypotenuse
cos x = 9/16
Taking the inverse cos of each side
cos^-1 (cos x) = cos^-1 (9/16)
x=55.77113
To the nearest tenth
x = 55.8
Answer:
Relative to x, the side of 16 is the hypotenuse, and the side of 9 is adjacent.
So we think, what trigonometric property relates hypotenuse and adjacent sides of a right triangle?
SOH CAH TOA
We can use the COSINE function to solve in this case, as we have both the ADJACENT SIDE (A) and the HYPOTENUSE (H).
Cosine = Adjacent/Hypotenuse
Cosine (x) = 9/16
Angle x = 55.8 degrees.
Let me know if this helps!
Find the first term in the sequence when u(subscript)31=197 and d= 10.
Answer:
197 = 10(31-1) + a
197 = 300 + a
-103 = a
Please help. I’ll mark you as brainliest if correct! Thank you
Answer:
8 pounds of cheaper candy,
17.5 pounds of expensive candy
Step-by-step explanation:
Let's define some variables. Let's say the amount of pounds of candy that sells for $2.20/lb is x, and the $7.30 is y. Now we can write some equations!
x + y = 25.5
[tex]\frac{2.2x + 7.3y}{25.5} = 5.7[/tex]
We can start substitution. We can say that x = 25.5 - y. Plugging this into our second equation, we get:
y = 17.5
Plugging this in, we find that:
x = 8.
Find the equation of the line that is parallel to f(x) and goes through point (-1,7).
Answer:
y=(3/7)*x+52/7
Step-by-step explanation:
The slope of the line will be (3/7). The equation of line will be y=(3/7)*x+52/7
Type an equation for the
following pattern.
x
1 -2
2
4
3
-6
y=[? ]x+[ ]
4
-8
S
- 10
Answer:
y=-2x
Step-by-step explanation:
first find the slope: (-2-(-4))/(1-2)=2/-1=-2 so m=-2
now we have y=-2x+b, to find b we plug in any of the points
-2=-2(1)+b-2=-2+b b=0so the equation is y=-2x
What’s the answer to this? Help please?!!!
Answer:B
Step-by-step explanation:
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
Tom and Harry are racing go-carts.Tom takes 2mins 8seconds to complete a lap while Harry takes 2minutes to complete a lap.They both start from the start line at the same time.when will they next cross the start line together? show all the workings.
9514 1404 393
Answer:
after 32 minutes
Step-by-step explanation:
They will both cross the start line together after each has completed a number of full laps in the same time that the other has completed an integer number of full laps. That time will be the least common multiple (LCM) of their lap times, 128 seconds and 120 seconds.
The difference of these times (8 seconds) is also a divisor of both times, so that value is the greatest common divisor (GCD) of the two lap times. The LCM can be figured as ...
LCM(120, 128) = 120×128/GCD(120, 128)
LCM = 120×128/8 = 1920 . . . . . seconds
Converting this to minutes, we get ...
(1920 s)/(60 s/min) = 32 min
They will next cross the start line together after 32 minutes.
For any real number r, which of the following must be greater than r?
An expression is a set of numbers, variables, and mathematical operations. The correct option is C, r² + 1.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Since real numbers contain positive integers, negative integers, positive decimals, negative decimals, and zero.
Therefore, For any real number r, the expression that will be always greater than r will be (r²+1). This is because,
√r :- If r=2, then √r will be 1.4142, therefore, √r will be lesser than r.2r :- If r is negative then 2r will also be negative and will be a smaller number than that.r² + 1 :- Irrespective of r is negative or positive, decimal or integer, the given expression will be always greater than r.r³ + 1 :- If the value of r is negative, then the expression will return a smaller negative number.Hence, the correct option is C, r² + 1.
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