sin(x+pi)=-sin(x)=sin(-x)=cos(pi/2)
cos (x+pi)=-cos(x)
So according to the question:
cos(pi/2 +x)=cos(x)
Using the solution of cos, obtain:
(pi/2) + x = 2pi +- (x)
case#1: (pi/2) + x = 2pi + (x)
But here, the value of x is canceled, just
case#2: (pi/2) + x = 2pi - (x)
answer------------>>>>>>>>> x=pi-pi/4
Omar, Amare, and Jack paid a total of $68.25 for dinner and tickets to a concert. The concert
tickets cost $9.75 each. If the 3 friends split the dinner bill equally, how much did each friend
spend on dinner?
Answer:
32.5
Step-by-step explanation:
I I divided ot then added it together
In the 1990s the demand for personal computers in the home went up with household income. For a given community in the 1990s, the average number of computers in a home could be approximated by
q = 0.3456 ln x − 3.045 10,000 ≤ x ≤ 125,000
where x is mean household income. A certain community had a mean income of $15,000, increasing at a rate of $1,500 per year.
1. How many computers per household were there?
2. How fast was the number of computers in a home increasing?
Answer:
dvffdd
Step-by-step explanation:
To which graph does the point (−1, 3) belong?
y ≥ 2x + 6
y ≥ 3x − 1
y ≥ −x + 4
y ≥ −2x + 5
Answer:
second option "y ≥ 3x − 1."
Step-by-step explanation:
Just solved it
What is the volume of the given picture below? ( HELP PLEASE )
HELP HELPP PLEASEEEE!
Answer:
Step-by-step explanation:
volume of pyramid with square base=a^2(h/3)
84=a^2*7/3
84*3/7=a^2
252/7=a^2
36=a^2
[tex]\sqrt{36[/tex]=a
6=a
therefore length=6
1)An octagon can be divided into 8 congruent triangles with base angles that are 67.5°. This octagon has a side length that is 8 cm.
2)What is the area of each triangle?
3)What is the area of the octagon?
4) Use your work from above to derive a generic formula for any octagon with side length that is n units.
Answer:
(a) [tex]Area = 14.7824cm^2[/tex]
(b) [tex]Area = 118.2592cm^2[/tex]
(c) [tex]Area = 4nh[/tex]
Step-by-step explanation:
Given
[tex]\theta = 67.5[/tex]
[tex]b= 8cm[/tex] --- base
[tex]n = 8[/tex] --- triangles
Solving (a) The area of each triangle
First, calculate the height (h) of each triangle using:
[tex]\sin(67.5) = \frac{h}{b/2}[/tex] --- i.e. we consider half of the triangle
[tex]\sin(67.5) = \frac{h}{8/2}[/tex]
[tex]\sin(67.5) = \frac{h}{4}[/tex]
Solve for h
[tex]h =4*\sin(67.5)[/tex]
[tex]h =4*0.9239[/tex]
[tex]h =3.6956[/tex]
The area of each triangle is:
[tex]Area = \frac{1}{2} *b * h[/tex]
[tex]Area = \frac{1}{2} *3.6956 * 8[/tex]
[tex]Area = 14.7824cm^2[/tex]
Solving (b): Area of the octagon
This is calculated as:
Area = 8 * area of 1 triangle
[tex]Area = 8 * 14.7824cm^2[/tex]
[tex]Area = 118.2592cm^2[/tex]
Solving (c): Area of octagon of side length n
In (a), we have:
[tex]Area = \frac{1}{2} *b * h[/tex]
Replace b with n
[tex]Area = \frac{1}{2} *n * h[/tex]
Multiply by 8 (the sides) to get the area of the octagon
[tex]Area = 8 * \frac{1}{2} *n * h[/tex]
[tex]Area = 4nh[/tex]
A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins. Find the experimental probability of landing on each color. Enter your answers as simplified fractions.
Red 12
Yellow 18
Blue 5
Answer:
red: 12/35
yellow: 18/35
blue: 1/7
Step-by-step explanation:
The experimental probability is the total number of each outcome over the total outcomes. The total outcomes would be the sum, 12 + 18 + 5, or 35.
If we are looking for the experimental probability of red, we divide the spins on red by the total:
red - [tex]\frac{12}{35}[/tex]
If we are looking for the experimental probability of yellow, we divide the spins on yellow by the total:
yellow - [tex]\frac{18}{35}[/tex]
If we are looking for the experimental probability of blue, we divide the spins on blue by the total:
blue - [tex]\frac{5}{35}[/tex] = [tex]\frac{1}{7}[/tex]
What is the shape of the base of the cylinder?
Answer:
circle
Step-by-step explanation:
at what rate percent of interest per annum will #700 gain an interest of #84 in 3 years
Answer:
4% per annum
Step-by-step explanation:
Recall :
Simple interest = principal * rate * time
Given that :
Time = 3 ; simple interest = 84 ; principal = 700
84 = 700 * rate * 3
84 = 2100 * rate
Rate = 84 /2100
= 0.04
= 0.04 * 100% = 4% per annum
convert 1 2/5 x 2/3 into a mixed number
please help will mark brainliest for right answer! No links...
Let f(x)=2x^3−x . What is the average rate of change of f(x) from 2 to 8 ?
Answer:
[tex]f(x) = {2x}^{3} - x \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(2 {(8)}^{3} - 8) - (2 {(2)}^{2} - 2)}{2} \\ = \frac{(1016 - 6)}{2} \\ = \frac{1010}{2} \\ = 505[/tex]
Please help!!! Trigonometry is so complicated to me
Answer:
x = 4
Step-by-step explanation:
Given that sin(13x) = cos(9x+2)
Since sintheta = cos(90 - theta)
hence sin (13x) = cos (90 -13x)
Substitute into the original equation
cos (90 -13x) = cos(9x+2)
90-13x = 9x+2
-13x - 9x = 2 - 90
-22x = -88
x = 88/22
x = 4
Hence the value of x is 4
If ST≅SV and m∠SUT=w+10° and m
Answer:
5°
Step-by-step explanation:
3w= w +10
3w-w=10
2w =10
w= 10/2
w= 5
I need the answer to this pls.
Answer:
C
Step-by-step explanation:
The operation is defined on the set R of real numbers by ab=ab+a.
Determine whether or not the operation is associative.
Please I need help.
Answer:
ab=ab+a
We need to check the following:
(ab)c=a(bc) or not
LHS
(ab)c=(ab+a)c
=(ab+a)c+(ab+a)
=abc+ac+ab+a
RHS
a(bc)=a(bc+b)
=a(bc+b)+a
=abc+ab+a
as LHS ≠ RHS, the operation is not associative
Step-by-step explanation:
Solve the equation.Leave your answer as simplest form a fraction
Answer:
n = 15
Step-by-step explanation:
5/2 = n/6 Multiply both sides by 6
6 * 5/2 = 6 n/6
30/2 = n
n = 15
additive inverse of -33
Additive Inverse of -33
༆ANSWER:—————————————————
[tex]\purple{\boxed{\boxed{\tt\pink{➢33}}}}[/tex]
The additive inverse of -33 is 33.Remember!»The opposite of the given integer is called its additive inverse. The sum of a number and its additive inverse is zero. For example, the additive inverse of -4 is 4, so when you add the two integer they sum will be zero.
help me please I have to pass
Answer:
Step-by-step explanation:
15% of 400
15/100*400
15*400/100
6000/100
60
therefore ur answer is 60
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{15}{100} \times 400 \\ =15 \times 4 \\ = 60 [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Which of the following statements are true about solids shown above
Check all that apply
A prism a has a lateral surface are of 60 cm 2
B prism b has a total surface are of 110 cm 2
C prism b has larger surface area
D prisms A and B have different values for lateral surface area
Ans its b and c
Step-by-step explanation:
Chau rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 95 cents for each mile driven. Chau had to pay $198.50
when he returned the truck. For how many miles did he drive the truck?
Let's say John drove 2 miles. He had to pay the base fee of $18.99 and $.75(2) = $1.50, so he paid $20.49 total.
We are given his total, though, and asked to find the mileage.
18.99 + .75m = 199.74
-18.99 -18.99
.75m = 180.75
.75 .75
m = 241
So, John drove 241 miles.
Hope this helps!
I
4 more than a number is 12
Answer:
555
Step-by-step explanation:
Answer:
4 + x = 12
x = 8
Step-by-step explanation:
4 more than a number is 12
I will represent the mystery number as "x"4 + x = 12
x = 8
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n
Answer:
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours
This means that [tex]\mu = 945, \sigma = 21[/tex].
What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
The approximate standard deviation of the sampling distribution of the mean for all samples of size n is [tex]s = \frac{\sigma}{\sqrt{n}} = \frac{21}{\sqrt{n}}[/tex]
For a sample size of n = 26 and a population parameter of p = 0.6, a normal
curve can be used to approximate the sampling distribution.
O A. True
O B. False
Answer:true
Step-by-step explanation:
just took the test < 3
The statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
What is normal curve?Normal curve is used to represent the class shapes in the statistical probability. Mathematically, we can describe the normal curve as -
[tex]$f(x)= {\frac{1}{\sigma\sqrt{2\pi}}}e^{- {\frac {1}{2}} (\frac {x-\mu}{\sigma})^2}[/tex]
where -
f(x) = probability density function
σ = standard deviation
μ = mean
Given is that for a sample size of n = 26 and a population parameter of
p = 0.6, a normal curve can be used to approximate the sampling
distribution.
It is asked to identify whether the given statement regarding the normal curve is true or false. The given statement is - "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution". The given statement is true.
Therefore, the statement : "for a sample size of n = 26 and a population parameter of p = 0.6, a normal curve can be used to approximate the sampling distribution" is true.
To solve more questions on normal curves, visit the link below-
https://brainly.com/question/24201610
#SPJ7
A law firm hires the same number of lawyers every year. At the end of 12 years, the firm has hired 48 lawyers. How many lawyers has the firm hired in the last 5 years?
Answer:
20 lawyers
Step-by-step explanation:
48 ÷ 12 = 4
which means every year 4 lawyers are hired
5 × 4 = 20
so this means the law firm has hired 20 lawyers in the last 5 years
Write the ratio 4.05 : 1.35 in the format n : 1
Answer:
3
Step-by-step explanation:
1.35n is 4.05
4.05÷1.35 is 3
n is 3
Answer:
3 : 1
Step-by-step explanation:
4.05 : 1.35 can be written as [tex]\frac{4.05}{1.35}[/tex] in fraction.
To write 4.05 : 1.35 in "n : 1" ratio format , you need to make the denominator of the fraction as 1.
Divide both the numerator & denominator of the fraction by 1.35.[tex]=> \frac{4.05 \div 1.35}{1.35 \div 1.35}[/tex]
[tex]=> \frac{3}{1}[/tex]
[tex]=> \boxed{3 : 1}[/tex]
Charlotte completed 12 pages of her 18-page report. What percent has she completed thus far?
Answer:
Charlotte has 23 of her book left to read. She can read 29 of it each day.
Step-by-step explanation:
Answer:
66.6666666667%
Step-by-step explanation:
12/18 = x/100
cross product
18x = 12(100)
18x = 1200
18× = 1200
__ _____
18 18
x=66.6666666667%
Sale! 10% OFF
of the original price!
The original price of a ticket to an amusement park is $60. What is the sale price?
Which of the following statements is equivalent to 28 + 16?
Answer:
You need to show the statements or I can't help.
Hurry which one
A.70
B.84
C.112
D.138
Answer:
A = 84 ft^2
Step-by-step explanation:
A = bh where b is the base and h is the height
A = 12*7
A = 84 ft^2
If f(1)=6f(1)=6 and f(n)=nf(n-1)-4f(n)=nf(n−1)−4 then find the value of f(3)f(3).
Answer:
49
Step-by-step explanation:
Answer:6144
Step-by-step explanation:
If f(1)=6f(1)=6 and f(n)=4f(n-1)f(n)=4f(n−1) then find the value of f(6)f(6).
f(1)=
f(1)=
\,\,6
6
f(\color{darkgreen}{2})=
f(2)=
\,\,4f(\color{darkgreen}{2}-1)
4f(2−1)
=
=
\,\,4f(1)
4f(1)
=
=
\,\,4(6)
4(6)
Substitute f(1)=6
f(2)=
f(2)=
\,\,24
24
f(\color{darkgreen}{3})=
f(3)=
\,\,4f(\color{darkgreen}{3}-1)
4f(3−1)
=
=
\,\,4f(2)
4f(2)
=
=
\,\,4(24)
4(24)
Substitute f(2)=24
f(3)=
f(3)=
\,\,96
96
f(\color{darkgreen}{4})=
f(4)=
\,\,4f(\color{darkgreen}{4}-1)
4f(4−1)
=
=
\,\,4f(3)
4f(3)
=
=
\,\,4(96)
4(96)
Substitute f(3)=96
f(4)=
f(4)=
\,\,384
384
f(\color{darkgreen}{5})=
f(5)=
\,\,4f(\color{darkgreen}{5}-1)
4f(5−1)
=
=
\,\,4f(4)
4f(4)
=
=
\,\,4(384)
4(384)
Substitute f(4)=384
f(5)=
f(5)=
\,\,1536
1536
f(\color{darkgreen}{6})=
f(6)=
\,\,4f(\color{darkgreen}{6}-1)
4f(6−1)
=
=
\,\,4f(5)
4f(5)
=
=
\,\,4(1536)
4(1536)
Substitute f(5)=1536
f(6)=
f(6)=
\,\,6144
6144
\text{Geometric Sequence:}
Geometric Sequence:
Common ratio of 4
6,24,96,384,1536,6144, ...
6,24,96,384,1536,6144,...
\text{Final Answer:}
Final Answer:
6144