A car manufacturing company produces blue and black cars only. If 54% of 85658 total
production is blue cars, how many black cars are there?
Answer:
About 39,402.
Step-by-step explanation:
You need to find the 46% of black cars.
1:prove that the tangent at the point (1,-2) to the circle x²+y²=5 also touches the circle x²+y²-8x+6y+20=0 .Also find the point of contact.
2:find the length of tangent to the circle
3x²+3y²-7x-6y=12 drawn from (6,-7)
Circle 1 has center at (0, 0)
The tangent passes through the center and point (1, -2).
Equation of tangent at (1, -2):
x*1 + y*(-2) = 5x - 2y = 5x = 2y + 5If the same line is tangent to circle 2 then they have one common point.
Solve the system:
x = 2y + 5x² + y² - 8x + 6y + 20 = 0Substitute x:
(2y + 5)² + y² - 8(2y + 5) + 6y + 20 = 04y² + 20y + 25 - 16y - 40 + 6y + 20 = 05y² + 10y + 5 = 0y² + 2y + 1 = 0(y + 1)² = 0y + 1 = 0y = -1 ⇒ x = 2(-1) + 5 = -2 + 5 = 3We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.
#2Given circle:
3x² + 3y² - 7x - 6y = 12 and external point (6, -7).Rewrite the equation of the circle as:
3x² + 3y² - 7x - 6y = 12x² + y² - 7/3x - 2y = 4x² - 2*7/6x + 49/36 + y² - 2y + 1 = 4 + 49/36 + 1(x - 7/6)² + (y - 1)² = 229/36The center is (7/6, 1) the radius is √229/36
The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:
t² = d² - r²t² = (6 - 7/6)² + (-7 - 1)² - 229/36t² = 36 - 14 + 49/36 + 64 - 229/36t² = 86 - 180/36t² = 81t = 9Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______
a) sec sqr Theta
b) Cot theta
c) cot (pie/2-Theta)
d) csc sqr theta
Answer:
[tex](a)\ \sec^2(\theta) = 82[/tex]
[tex](b)\ \cot(\theta) = \frac{1}{9}[/tex]
[tex](c)\ \cot(\frac{\pi}{2} - \theta) = 9[/tex]
[tex](d)\ \csc^2(\theta) = \frac{82}{81}[/tex]
Step-by-step explanation:
Given
[tex]\tan(\theta) = 9[/tex]
Required
Solve (a) to (d)
Using tan formula, we have:
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
This gives:
[tex]\frac{Opposite}{Adjacent} = 9[/tex]
Rewrite as:
[tex]\frac{Opposite}{Adjacent} = \frac{9}{1}[/tex]
Using a unit ratio;
[tex]Opposite = 9; Adjacent = 1[/tex]
Using Pythagoras theorem, we have:
[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex]
[tex]Hypotenuse^2 = 9^2 + 1^2[/tex]
[tex]Hypotenuse^2 = 81 + 1[/tex]
[tex]Hypotenuse^2 = 82[/tex]
Take square roots of both sides
[tex]Hypotenuse =\sqrt{82}[/tex]
So, we have:
[tex]Opposite = 9; Adjacent = 1[/tex]
[tex]Hypotenuse =\sqrt{82}[/tex]
Solving (a):
[tex]\sec^2(\theta)[/tex]
This is calculated as:
[tex]\sec^2(\theta) = (\sec(\theta))^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
Where:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos(\theta) = \frac{1}{\sqrt{82}}[/tex]
So:
[tex]\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2[/tex]
[tex]\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2[/tex]
[tex]\sec^2(\theta) = (\sqrt{82})^2[/tex]
[tex]\sec^2(\theta) = 82[/tex]
Solving (b):
[tex]\cot(\theta)[/tex]
This is calculated as:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
Where:
[tex]\tan(\theta) = 9[/tex] ---- given
So:
[tex]\cot(\theta) = \frac{1}{\tan(\theta)}[/tex]
[tex]\cot(\theta) = \frac{1}{9}[/tex]
Solving (c):
[tex]\cot(\frac{\pi}{2} - \theta)[/tex]
In trigonometry:
[tex]\cot(\frac{\pi}{2} - \theta) = \tan(\theta)[/tex]
Hence:
[tex]\cot(\frac{\pi}{2} - \theta) = 9[/tex]
Solving (d):
[tex]\csc^2(\theta)[/tex]
This is calculated as:
[tex]\csc^2(\theta) = (\csc(\theta))^2[/tex]
[tex]\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2[/tex]
Where:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin(\theta) = \frac{9}{\sqrt{82}}[/tex]
So:
[tex]\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2[/tex]
[tex]\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2[/tex]
[tex]\csc^2(\theta) = \frac{82}{81}[/tex]
why mathematical induction is used ?(write a 100 words paragraph)
Answer:
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers ( non-negitive integers). The simplest and most common form of mathematical induction proves that a statement involving a natural number that holds for all values.
Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
Someone please help with this ASAP!!! I will give brainliest
Answer:
12m
7m
2520 m³
Step-by-step explanation:
Answer:
h=7m
top width=12m
v=l*w*h
=28*12*10=3360
volume of the top=3*20*12
720
v of the shape is= 3360-720
=2649
determine whether the variable is qualitative or quantitative
street name and adress
Answer:
C
Step-by-step explanation:
Street name has nothing to do with numerical values, therefore it cannot be quantitative. If we take the two qualitative answers left, one of them says something about numbers, so it cannot be that one. C is the only one left over after process of elimination.
What’s the ratio of 20 to 3
Answer:
666.666666666667%
Step-by-step explanation:
Convert fraction (ratio) - 20 / 3 Answer: -666.666666666667%
f(2) 42 g(x) = 2x +3 Find 4) (. Include any restrictions on the domain. O A. 2.2---3 417 2 > 0 B. 47 2 2 r--3, (1) (a) = (4) (a) x A 을 c. (5) (r) = 1,2*0 OD (1) (a= + 2
Answer:
Option D
Step-by-step explanation:
Given f(x) = [tex]\sqrt[3]{4x}[/tex]
g(x) = 2x + 3
Since, [tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
[tex]=\frac{\sqrt[3]{4x}}{2x+3}[/tex]
This function is defined for the denominator is not equal to zero.
(2x + 3) ≠ 0
x ≠ [tex]-\frac{3}{2}[/tex]
Therefore, Option D will be the correct option.
Executives from Six Flags, a well-known amusement park chain, had interest in constructing a Six Flags theme park in a location near Ames city limits. Experts believed that approximately 15% of the surrounding population would be interested in becoming season ticket holders. A random sample of 500 residents of Story County was collected (of the approximately 80,000 residents of Story County). Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames. The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to ___________.
Answer:
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to 0.248.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Of the 500 people sampled, 124 said that they would be interested in purchasing season tickets to a Six Flags in Ames.
This means that [tex]p = \frac{124}{500} = 0.248[/tex]
The mean of the sampling distribution for the sample proportion when taking samples of size 500 from this population is equal to
By the Central Limit Theorem, it is equal to the sample proportion of 0.248.
x−9≥−12 Express your answer as an inequality.
Answer:
x ≥ −3
Step-by-step explanation:
Step One : Add 9 to both sides.
x − 9 + 9 ≥ −12 + 9
x ≥ −3
There is no more to be done, that is our answer. x ≥ −3.
Hope this helps, please mark brainliest! :)
Circle the answer choice below that does not equal the following:
- 48/16
1) 48/-16
2) -3
3) 3
4) -(48/16)
Answer:
3
Step-by-step explanation:
-48/16 = 48/16
-48/16 = -3/1 = -3
The Sweet Slice Cafe has 6 pastries for sale, including 3 glazed donuts.
What is the probability that a randomly selected pastry will be a glazed donut?
Write your answer as a fraction or whole number.
Answer:
50% or 3/6 (1/2).
Step-by-step explanation:
When purchasing a new Cell Phone Plan you are given two pay options (Both included
unlimited text):
With Plan A, you can pay 23 cents per minute. This can be represented by the equation
C= 0.23m
With Plan B, you can pay 19 cents per minute plus a flat fee of $9.00. This can be
represented by the equation c = 0.19m + 9.00
Complete the following steps to determine how many minutes you would need to use for
Plan B to be less expensive than Plan A
Answer:
225 and greater
Step-by-step explanation:
900/4 or 900 cents/ 4 cents equals 225 on calculator
We use 225 minutes for Plan B to be less expensive than plan A.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
For plan A,
We can pay 23 cents per minute.
This can be represented by the equation,
C= 0.23m
For plan B,
We can pay 19 cents per minute plus a flat fee of $9.00.
This can be represented by the equation,
C = 0.19m + 9.00
Now, To find the minutes for plan B is less expensive than plan B
We can write an inequality that represent,
Plan A < Plan B
0.23m < 0.19m + 9
0.23m - 0.19m < 9
0.04m < 9
Divide 0.04 both side,
m < 225
Thus, We use 225 minutes for Plan B to be less expensive than plan A.
Learn more about the inequality visit:
https://brainly.com/question/16914953
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Can you help me with this question? 15 points and brainliest if right!
Answer:
3/4
Step-by-step explanation:
because it is a linear function it means it has the same slope in every point
so you have to take 2 points and find the slope
I take points (0,1) and (4,4)
m = (y2-y1) / (x2-x1)
note that it does not matter which points you chose to be second or first
m = (4-1) / (4-0) = 3/4
you can solve it from the graph too 3/4 is y/x it means for every 4 unit right move 3 units up
Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for asparagus, B for bacon, P for pepperoni, I for Italian, and V for vinaigrette. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: mushrooms, asparagus. Also, you will add one of following meats: bacon, pepperoni. Lastly, you will decide on one of the following dressings: Italian, vinaigrette.
Answer:
MBI, MBV, ABV, ABI, MPI, MPV, APV, API
Can you help me with this question? 15 points and brainliest if right!!
How to take a screenshot on an HP laptop
Press the Windows key and Print Screen at the same time to capture the entire screen. ...
Open an image editing program (Microsoft Paint, GIMP, Photoshop, and PaintShop Pro will all work).
Open a new image and press CTRL + V to paste the screenshot.
The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can this be accomplished if there are 25 members on the board of directors
Answer:
2400 ways
Step-by-step explanation:
Combination has to do with the idea of selection. Here we need to select a president, a secretary, and a treasurer.
This means to select three out of twenty five persons.
From;
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Thus we have;
25C3 = 25!/(25 - 3)! 3!
=
1.6× 10^25/1.1×10^21 × 6
= 2400 ways
Factorize (2ax-2ay-3by+3bx)
Answer:
That's the answer I searched for and I hope it can help.
#Carryonlearning
Please make me brainliest!
Adam is 9 years old and Billy is 11 years old. What will be the ratio of Adams’ age to Billy’s age in exactly one year’s time? Give your answer in its simplest form. *
Answer:
10 / 12
simplified:
5/6
since 5 is a prime number, we can't simplify this ratio any further
What is the y intercept of the function f (x) = -2/9x + 1/3 ?? Please help ! :0 :)
y intercept of the function f (x) = -2/9x + 1/3
is
[tex] \frac{1}{3} [/tex]
OPTION C
Given f(x) = 52x, evaluate f(–1), f(0), and f(2). Question 1 options:a. 1/25, 0, 625 B. 25, 1, –25 c. 1/25, 0, 25 d. 1/25, 1, 625
Answer:
1/25, 1, 625
Step-by-step explanation:
The value of the function at f(–1), f(0), and f(2) will be 1/25, 1, 625 thus option (d) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
f(x) = [tex]5^{2x}[/tex]
Put x = -1
f(-1) = 5⁻² = 1/5² = 1/625
Put x = 0
f(0) = 5⁰ = 1
Put x = 2
f(2) = 5²ˣ² = 5⁴ = 625
Hence "The function's value at f(-1), f(0), and f(2) is 1/25, 1, 625".
For more about the function,
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Calculating area of rectangle.
Your measurements Another student's measurements
Length (cm) 20.70 20.74
Width (cm) 10.44 10.46
Area (cm2) ________ ________
Required:
Why might two students have different calculated areas when measuring the same rectangle?
Answer:
Your measurements; Area = 216.108 cm²
Another student's measurements; Area = 216.9404 cm²
- Difference in area could be as a result of human error or perhaps that they made use of different measuring tools.
Step-by-step explanation:
For Your measurements;
Length of rectangle = 20.70 cm
Width of rectangle = 10.44 cm
Area of rectangle is given by; A = length × width = 20.7 × 10.44 = 216.108 cm²
For Another student's measurements;
Length of rectangle = 20.74 cm
Width of rectangle = 10.46 cm
Area = 20.74 × 10.46
Area = 216.9404 cm²
The areas they both obtained are not of equal values and this could be as a result of human error or perhaps that they used different measuring tools.
Question in pic, please help
Answer:
The first one
(I can't see it too properly but if the dot on -10 has a hole in it then this is the answer)
Select all the numbers that are solutions to the inequality 4,5,,6>5,5.2>5,5.01>5,0.5
Plzzz answer I’ll give you 10 points
iii; iv; and v
Step-by-step explanation:
I think
What is the result when 16x + 9 is subtracted from 4x + 6
Answer:
(4x+9)-(16x+9) = 4x+9-16x-9
= -12x
Let f(x)= 6x^2+7x-4. Find:
a) f(3)
b) f(m)
c) f(x+1)
SHOW WORK PLEASE.
Answer: b) f(m)
Step-by-step explanation:
Will has a book that he wants to read that book is 36 chapters long if he reads 3 chapters a day how many days will it take Will to read the whole book?
Answer:
It will take Will 12 days to read the whole book.
Step-by-step explanation:
36 ÷ 3
= 12
:))
36 ➗ 3 = 12
12 days .........
10)
X + 80
70°
A) 5
C) -10
B) 8
D) 7
Answer:
C: x=-10
Step-by-step explanation:
Alternate interior angles are congruent to each other meaning that x+80=70 making x equal to -10. I hope this helped and this is one of my favorite units so post more these questions :)
i need help with this!
9514 1404 393
Answer:
64.6
Step-by-step explanation:
One standard deviation is 4.3. Then +2 standard deviations is ...
(+2)(4.3) = +8.6
This amount added to the mean gives ...
56 +8.6 = 64.6 . . . . +2σ from the mean
