The required value of θ for the trigonometric function cos(θ)=sin(θ/3-10) is 60°.
What are trigonometric functions?The basic Trigonometric functions are sine, cosine, tangent, secant, cosecant and cotangent.
The given equation is,
cos(θ)=sin(θ/3-10) (1)
To find the value of θ,
Change the whole equation into one trigonometric function,
Since, cos(θ)=sin(90-θ)
Substitute this value in equation (1)
sin(90-θ)=sin(θ/3-10)
⇒90-θ=θ/3-10
⇒4θ/3=80
⇒θ=60
The value of θ is 60°.
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Describe how to create a solid model of a simple coffee mug using sweep and other constructive solid geometry operations
Answer:
Step-by-step explanation:
We are going the use the revolve constructive geometry operation
Step one:
Knowing fully well that the simple mug has a cylindrical shape, and all preliminary settings are in place, like the units may be in inches or mm.
We first need to draft out the section of the mug, this will look like an "L" shape with thickness set to whatever dimension you may have in mind.
The next in line is to create an axis using a construction line parallel to the L shape.
Then use the revolve tool to create the cylindrical shape by selecting the axis as the reference of rotation and the angle of rotation set to 360 degrees.
#3 - 8.5G
Which set of ordered pairs does not show y as a function of x?
A. {(1, -2): (3,-3); (5,-4); (3,-5)}
B. {(2,-2): (4, -2): (6,-2): (8,-2)}
C. {(4,-2): (3,-3): (2, -4): (1,-5)}
D. {(2,-2); (3,-3); (4, -7); (5, -8)}
Answer:
A
Step-by-step explanation:
in order for it to be a function the x needs to have only one y, in this case the x is repeated for two different y's
Find the inverse of g(x)=2x-3
=1/2x-3
Step-by-step explanation:
Convert 86 to base 5.
Answer:
321
Step-by-step explanation:
Conversion of 86 to base 5 will be done through base 10 to base 5 and it will be (321)₅.
How to convert any number into base 10?To convert any number to base 10 we have to multiply its unit digit by 10⁰ and its tenth digit by 10¹.
After it, we need to add it. It will give us a number of the 10 bases.
Conversion of any 10 base number into base 5
To convert any number to base 5 we need to divide by 5 and write the remainder each time thus we need to write the quotient from down to up.
Converting 86 to base 10
⇒ 8ₓ10¹ +8ₓ[tex]10^0[/tex]
⇒ 86₁₀
Converting 86₁₀ into 86₅
When the number 86 is converted in a base of 5 will be (321)₅
Since we need to go down to up to 321₅ will be the correct answer.
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Let V=ℝ2 and let H be the subset of V of all points on the line 4x+3y=12. Is H a subspace of the vector space V?
Answer:
No, it isn't.
Step-by-step explanation:
We have [tex]V=IR^{2}[/tex] and let [tex]H[/tex] be the subset of [tex]V[/tex] of all points on the line
[tex]4x+3y=12[/tex]
We need to find if [tex]H[/tex] is a subspace of the vector space [tex]V[/tex].
In [tex]IR^{2}[/tex] all the possibilities for own subspace of the vector space [tex]IR^{2}[/tex] are :
[tex]IR^{2}[/tex] itself.The vector [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex]All lines in [tex]IR^{2}[/tex] that passes through the origin ( [tex]0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right][/tex] )We know that [tex]H[/tex] is the subset of [tex]IR^{2}[/tex] of all points on the line [tex]4x+3y=12[/tex]
If we look at the equation, the point [tex]\left[\begin{array}{c}0&0\end{array}\right][/tex] doesn't verify it because :
[tex]4x+3y=12\\4(0)+3(0)=12\\0=12[/tex]
Which is an absurd. Therefore, [tex]H[/tex] doesn't contain the origin (and [tex]H[/tex] is a line in [tex]IR^{2}[/tex]). Finally, it can't be a vector space of [tex]V=IR^{2}[/tex]
what is a prime factor
Which is the equation of a line with a slope of −13 - 1 3 and a y-intercept at (0, 1) 0 , 1 ?
what is 5/8 / divided by 1/4?
Answer:
5/2
Step-by-step explanation:
Use a calculator
find coordinates of y = 4x^2+ 40x+112
Step-by-step explanation:
y = 4x²+ 40x+112 (:4)
x²+ 10x+ 28.
28
1. |. 28
2. |. 14
4. |. 7
(x+4)(x+7)=0
x= -4. V. x= -7
Now fill in the x= -4 in y so you get the Y-coordinate and do the same for x= -7
Anseer should be like: 'The coordinates are (x, y) and (x, y)
Question 1 (1 point)
(07.03)
How many solutions does the equation 2y+7=5y+7-3y have?
a
One
Ob
None
ос
Two
od
Infinitely many
Answer:
0 because both equations on either side will cancel out
A store sells regular coffee for $5 a pound and gourmet coffee for $8 a pound. To get rid of 30 pounds of the gourmet coffee, a shopkeeper makes a blend to put on sale for $6 a pound. How many pounds of regular coffee should he use?
Answer:
60 pound
Step-by-step explanation:
Calculation for How many pounds of regular coffee should he use
Let pounds of regular coffee be x
Let value of regular coffee be 5x
Let cost of gourmet coffee be 8
Let value of gourmet coffee be 8*30
Let pounds of mixture be 30+x
Let value of mixture be 6(30+x)
Equation:
5x+(8*30)=6(30+x)
5x+240=6(30+x)
Now Let Solve for x:
5x+240=180+6x
240-180=6x-5x
60=1x
x=60/1
x=60
Therefore, he should use $60 pounds of regular coffee
help plsss i really need it
Answer:
can u re-upload the image i cant see it
Step-by-step explanation:
help i’m timed 6th grade math
Answer:
c
Step-by-step explanation:
because I'm smart and I am in 7th grade
Round 1,497 to the nearest ten
solve inequality.
[tex] | - k - 7| \geqslant 4[/tex]
Answer: k [tex]\leq \\[/tex] -11 or k [tex]\geq[/tex] -3
josie walks 3/4 miles in 1/5 hour. what is josie’s speed in miles per hour
Answer:
Speed = 3.75 miles per hour.
Step-by-step explanation:
Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.
Mathematically, speed is given by the equation;
[tex]Speed = \frac{distance}{time}[/tex]
[tex]S = \frac{d}{t}[/tex]
Given the following data;
Distance, d = 3/4 miles
Time, t = 1/5 hour
Substituting into the equation, we have;
[tex]Speed, S= \frac{3/4}{1/5}[/tex]
[tex]Speed, S = \frac{3}{4}*5[/tex]
[tex]Speed, S = \frac{15}{4}[/tex]
Speed, S = 3.75mph.
Therefore, Josie's speed is 3.75 miles per hour.
For every 2 hours, approximately $1,689 worth of product is sold to consumers. How much money will the company for an entire month (30 days)?
1,01340 cuase 1,689 times 2 equal 3,378 and times 30 equal 101340
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life ( 150,000 miles of driving) of cars of a particular model varies Normally with mean 85 mg/mi and standard deviation 6 mg/mi. A company has 16 cars of this model in its fleet. Using Table A, find the level such that the probability that the average NOX + NMOG level ¯ for the fleet greater than is only 0.01 ?
Answer:
Mg/mi. A Company Has 16 Cars Of This Model In Its Fleet. ... The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in d ... organic gas (NMOG) in the exhaust over the useful life (150,000 miles of driving) of cars of a particular model varies Normally with mean 85 mg/mi and standard deviation 6 mg/mi.
Step-by-step explanation:
Using the normal distribution and the central limit theorem, it is found that the level is 88.49 mg/mi.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for the sampling distribution of sample means of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 85 mg/mi, thus [tex]\mu = 85[/tex]Standard deviation of 6 mg/mi, thus [tex]\sigma = 6[/tex]Sample of 16 cars, thus [tex]n = 16, s = \frac{6}{\sqrt{16}} = 1.5[/tex]This level is the 1 - 0.01 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327. Then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 85}{1.5}[/tex]
[tex]X - 85 = 2.327(1.5)[/tex]
[tex]X = 88.49[/tex]
The level is 88.49 mg/mi.
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Determine the slope m of each line in its most reduced form
Answer:
5/3 1/3 4/3
Step-by-step explanation:
A(n) ______ shows relationships between things you are comparing.
Venn diagram
whole number
integer
Answer:
Venn Diagram
Step-by-step explanation:
Its a graph that's used in listing similarities and differences the other two aren't graphs but math terms
PLEASE HELP PLEASE i really need help
Answer:
The constant of proportionality is 6 because 6x2=12 6x4=24 6x6=36 and it keep going
Step-by-step explanation:
(18/10)(8/3) operación matemática
Answer:
4.8
Step-by-step explanation:
(18/10)(8/3)
18*8= 144
10*3= 30
144/30 =4.8
What is the slope of a line perpendicular to the line whose equation is x +y = 3.
Fully reduce your answer.
Answer:
slope = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x + y = 3 ( subtract x from both sides )
y = - x + 3 ← in slope- intercept form
with slope m = - 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1
A bowling ball is dropped from a height of 50 feet. Write a function that gives the height h (in feet) of the bowling ball after 5 seconds. Find the height of the bowling ball after 1 second. How long does the bowling ball take to hit the ground? Round your answer to the nearest hundredth of a second.
Answer:
Step-by-step explanation:
Graph each function and determine the y-intercept, then use the graph to determine the approximate value of the given expression. (1/4)^x (1/4)^17
a.
0; 1.7
c.
1; 0.7
b.
1; 0.1
d.
0; 1.3
Answer:
b
Step-by-step explanation:
The graph of f(x) = 2x + 3 is a linear function and its y-intercept is y = 2x + 3.
What is linear function?Any function is referred to as linear if it represents a straight line on the coordinate plane. For instance, the linear function represented by the equation y = 3x – 2 looks like a straight line on a coordinate plane. Due to the fact that f(x) can substitute for y, this function can be written as f(x) = 3x - 2.
here, we have,
First find the slope of the line
y - y₁ = m(x - x₁)
0 - 3 = m(-1.5 - 0)
m = 2
From the graph, we can take any of the two points i.e.(0, 3) and put it in slope formula
y - y₁ = m(x - x₁)
So,
y - 3 = 2(x - 0)
y = 2x + 3 (y-intercept)
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Full question:
Graph each function determine which of the functions are linear. find the y-intercept of each function and the slope.
f(x) = 2x + 3
HELP :) GIVING BRAINLIEST
Answer:
5/4
Step-by-step explanation:
Rise/Run
5/4
A jar contains 20 yellow jellybeans, 20 orange jellybeans, 20 red jellybeans and 20 green jellybeans.
Required:
a. In how many ways can you put all the jellybeans in a row?
b. How many ways are there to select a handful of 20 jellybeans?
c. How many ways are there to select a handful of 20 jellybeans that contains at least 3 red?
d. How many ways are there to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange?
Answer:
A)
[tex]\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}[/tex]
B)
[tex]\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}[/tex]
C)
= [tex]\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}[/tex]
D)
= [tex]\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}[/tex]
Step-by-step explanation:
A) How many ways can you put all Jellybeans in a row
Total number of Jellybeans = 80
The first jellybeans = 20 yellow , second is 20 orange jellybeans , third is 20 red jellybeans , fourth is 20 green jellybeans
Therefore the number of ways the Jellybeans can be put in a row is :
[tex]\left \{ {{80} \atop {20}} \} * \left \{ {{60} \atop {20}} \} * \left \{ {{40} \atop {20}} \} * \left \{ {{20} \atop {20}} \}[/tex]
B) How many ways are there to select a handful of 20 jellybeans
lets assume:
yellow jellybeans = a , orange jellybeans = b , red jellybeans = c , green jellybeans = d
a + b + c + d = 20
This is the number Non-negative integer solutions
= [tex]\left \{ {{20+4-1} \atop {4-1}} \} = \left \{ {{23} \atop {3}} \}[/tex]
C) This is also the number of Non-negative integer solutions but in this case the value of C ≥ 3
hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red
= [tex]\left \{ {{17+4+1} \atop {4-1}} \} = \left \{ {{20} \atop {3}} \}[/tex]
D) In this case the value of C ≥ 3 and B ≤ 2
Hence the number of ways to select a handful of 20 jellybeans that contains at least 3 red and at most 2 orange
= [tex]\left \{ {{20} \atop {3}} \} - \left \{ {{17} \atop {3}} \}[/tex]
round 8.193 to the nearest hundredth
Answer:
i looked it up and nothing is showing
Step-by-step explanation:
850-53x m= 720-39x m
i really need to know this. my nine weeks ends at 3 pm today plzz help me
i need to know what m =
Answer:
9.286
Step-by-step explanation:
I'm not guaranteeing this answer. If this is correctly written without any indication of how to deal with x, then here is as much as you can do.
850-53x m= 720-39x m Subtract 720 from both sides.
850 - 720 - 53x = 720 - 720 - 39xm Combine
- 53xm + 130 = - 39xm Add 53x
-53x+53xm + 130 = -39x + 53xm Combine
130 = 14xm Divide by 14
xm = 130/14
xm = 9.28
===============================
You can use the same steps above. I'm abbreviating the steps because they are the same.
I'm sure there is more to the problem, but I can't imagine what it is. If you have additional directions, put it under this answer. I will get it as a comment.
850-53m= 720-39m
850 - 720 - 53m = - 39m
130 - 53m = - 39m
130 = -39m + 53m
130 = 14m
130/14 = m
m =9.286
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a 2
Answer:
1/12
Step-by-step explanation:
There are 12 equally likely outcomes. 1 of the outcomes is a 2. So the probability is 1/12.
Answer:2/12 or simplified 1/6
Step-by-step explanation:
