Answers
Answer:
c
Step-by-step explanation:
There are three types of variations.
1. Direct
2. Inverse
3. Joint
There is positive proportionality is two variables are positively related to each other.
The equation for direct proportionality =
y = bx
where y = dependent variable
b = constant
x = independent variable
if two variables vary inversely, there is a negative relationship between both variables. the increase in one variable leads to a decrease in the other variable
the equation that represents inverse proportion :
where b = constant of proportionality
Joint variation occurs when the dependent variables value is determined by two or more values
For example, the volume of a cylinder is dependent on the value of the radius and height
Related Questions
HELP ME PLEASE!!!
GIVEN sin0= √23/12
tan0= √23/11
Find cos0
Answers
Answer:
[tex]cos \theta = \frac{11}{12}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]
Suppose b is any integer. If b mod 12 = 7, what is 4b mod 12? In other words, if division of b by 12 gives a remainder of 7, what is the remainder when 4b is divided by 12? Fill in the blanks to show that the same answer will be obtained no matter what integer is used for b at the start. Because b mod 12 = 7, there is an integer m such that b = 12m + . Multiply both sides of this equation by 4 and then simplify the right-hand side to find values of q and r such that 4b = 12q + r with 0 ≤ r < 12. The result is q = and r = . Now 0 ≤ r < 12, and q is an integer because ---Select--- . So the uniqueness part of the quotient remainder theorem guarantees that the remainder obtained when 4b is divided by 12 is . Need Help?
Answers
Answer:
4b mod 12 = 4
Step-by-step explanation:
Since b mod 12 = 7, it implies that there is an integer, m such that
b = 12m + 7.
We desire to find 4b mod 12
So, multiplying b by 4, we have
4b = 4(12m + 7)
4b = 4 × 12 m + 4 × 7
4b = 4 × 12 m + 28
4b = 4 × 12 m + 24 + 4
4b = 4 × 12 m + 12 × 2 + 4
Factorizing 12 out, we have
4b = 12(4m + 2) + 4
Since m is an integer 4m + 2 is an integer since the operation of adding and multiplication is closed for the set of integers.
comparing 4b = 12q + r with 4b = 12(4m + 2) + 4,
q = 4m + 2 and r = 4
So 4b mod 12 = 4, that is the remainder when 4b is divided by 12 is 4.
In this exercise we have to calculate the value of the unknown, so we have:
the value is 4
we know that the equation will be given as:
[tex]b = 12m + 7\\[/tex]
we need to multiply both sides by 4 to become another known equation, like this:
[tex]4b = 4(12m + 7)\\4b = 4 * 12 m + 4 * 7\\4b = 4 * 12 m + 28\\4b = 4 * 12 m + 24 + 4\\4b = 4 * 12 m + 12 * 2 + 4[/tex]
So factoring this equation we will find that:
[tex]4b = 12(4m + 2) + 4[/tex]
Thus, when making a comparison between the two equations, we have that:
[tex]4b = 12q + r \\4b = 12(4m + 2) + 4\\q = 4m + 2\\r = 4[/tex]
See more about factoring at brainly.com/question/6810544
There are 400 animals that live at a zoo. You find that 22 of 65 randomly chosen animals are
monkeys. About how many animals in the entire zoo are likely to be monkeys?
Answers
Answer:
About 135.
Step-by-step explanation:
As the sample is random the number of monkeys likely to be in the zoo
= (22/65) * 400
= 135.38
What is the probability of flipping a coin 10 times and getting heads 5 times? Round your answer to the nearest tenth percent.
Answers
The Probability is 1/2 or .5, .5 rounded to the nearest tenth would be irregular because .5 is already in the tenth place but according to the law of rounding since ut is five it would be rounded up giving the whole number 1
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2
Answers
Answer:
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
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 fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.
This means that [tex]\mu = 14, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?
This is 1 subtracted by the p-value of Z when X = 14.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{14.2 - 14}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
I’m suppose to find the measure of each angle. Thank you
Answers
Answer:
E) π/9
Step-by-step explanation:
The angles are complementary meaning they add up to 90°.
Convert radians to degrees:
7π/18 · 180/π = 70°
Now we know that we need the radian equivalent of 20°.
Convert degrees to radians:
70 · π/180 = π/9
Therefore, the measure of the missing degree is π/9.
Find the lowest common multiple of 10 and 12
Answers
2(5) is 10 2(6) is 12. Lower than that is 1 and that is not viable
Point B has coordinates (4,2). The x-coordinate of point A is - 1. The distance between point A and
point B is 13 units. What are the possible coordinates of point A?
Answers
Answer:
A (-1,-10) ; A (-1,14)
Step-by-step explanation:
[tex]\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169[/tex]
y^2 -4y - 140 = 0
Δ/4 = 4 + 140 = 144
y1 = 2 + 12 = 14
y2 = 2 -12= -10
A bacteria culture is growing at a rate of
r(t) = 7e^0.6t
thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)
Answers
Answer:
[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]
A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.
Answers
Answer:
$30.21
Step-by-step explanation:
100% -25%= 75%
Discounted price of the book
= 75% ×$38
= $28.50
Since the customer must pay an additional 6% of the discounted price,
percentage of discounted price paid
= 100% +6%
= 106%
Total amount paid
= 106% × $28.50
= $30.21
_________________________________
Alternative working:
Original selling price= $38
Since the book is discounted 25%,
100% ----- $38
1% ----- $0.38
75% ----- 75 ×$0.38= $28.50
Since the sales tax is based on the discounted price, we let the discounted price be 100%.
100% ----- $28.50
1% ----- $0.285
106% ----- 106 ×$0.285= $30.21
∴ The total amount the customer pays for the discounted book is $30.21.
13. Find the length of X (in the picture)
Answers
Answer:
x=2
Step-by-step explanation:
the sides are proportional due the angles being equal
since the hypotonuse is 5 on the bigger one and 2.5 on the small one we can infer there is a ×2 difference
so 4÷2=x
x=2
X+ 5
If m(x) =x-1 and n(x) = x-3, which function has the same domain as (mon)(x)?
X+5
O (x)=
11
11
o h(x)=
X-1
11
O (X)=
X-4
11
Oh(x) =
X-3
Answers
Answer:
third option
Step-by-step explanation:
m(n(x)) =
[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]
the domain of this is R/(4)
so as the third option
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,
Now,
(m o n)(x)
= m (n(x)
= m (x - 3)
= (x - 3 + 5) / (x - 3 - 1)
= (x + 2) / (x - 3)
We can not have x = 3.
So,
The domain can not have x = 3.
From the options,
h(x) = 11 / (x - 3) can not have x = 3.
Thus,
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
Trong một lớp học có 50 sinh viên. Hỏi có bao nhiêu cách bầu ra một ban cán sự lớp gồm 3 người: 1 lớp trưởng, 1 lớp phó, 1 bí thư và không kiêm nhiệm chức vụ.
Answers
Answe
SI Si olla amigo lel just spammin here
Step-by-step explanation:
My sister’s house is 1 2/4 times as high as my house. My house is 5 feet high. How high is my sister’s house?
Answers
Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answers
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
If 12 girls can sweep a room in 20hours, how many hours will it take 8 girls to perform the same task, assuming they are sweeping at the same rate?
Answers
Answer:
30 hour
Step-by-step explanation:
girls time
12 20 hour
8 x(let)
now,
12/8=x/20
12×20=8×x
240=8x
x=240/8
x=30,,
Write down the equation of the function whose graph is shown.
will mark brainliest
Answers
Answer:
y = 1(x - 5)² + 3
Step-by-step explanation:
The general formula of a quadratic equation is written as;
y = a(x − h)² + k
Where (h, k) are the x and y coordinates at the vertex.
Our vertex coordinate is (5, 3)
Thus;
y = a(x - 5)² + 3
Now,we are given another coordinate as (8, 12)
Thus;
12 = a(8 - 5)² + 3
12 = 9a + 3
9a = 12 - 3
9a = 9
a = 9/9
a = 1
Thus,the equation is;
y = 1(x - 5)² + 3
Explain why the work is not correct.
Answers
3.42x16.5 show your work plz
Answers
Answer:
= 56.43
Step-by-step explanation:
= 3.42 × 16.5
multiply the numbers= 56.43
Explanation:
There’s an imaga attached showing the steps through ling multiplication. My handwriting is bad and these steps came from the web. Either way it is still correct.
Hope this absolutely helps!
the single discount of two successive discounts 10% and 5% is
Answers
Answer:
14.5%
Step-by-step explanation:
Use the number 100 as an example to find the single discount.
Take a 10% discount off of this:
100(0.9)
= 90
Take a 5% discount:
90(0.95)
= 85.5
So, after the successive discounts, $14.5 was discounted.
This means that the single discount is 14.5%.
So, the answer is 14.5%
[tex]8 \times {2}^{n + 2} = 32[/tex]
What is the value of n
Answers
Step-by-step explanation:
2³×2^n+2=32
2^3+n+2=2⁵
n+5=5
n=0
[tex]_____________________________________[/tex]
[tex]\sf\huge\underline\red{ANSWER:}[/tex]
[tex]\tt n = 0[/tex]
[tex]\sf\huge\underline\red{SOLUTION:}[/tex]
[tex]\tt8 \times {2}^{n + 2} = 32 \\ = \tt {2}^{3} \times {2}^{n + 2} = 32 \\ = \tt {2}^{n + 5} = 32 \\ = \tt {2}^{n + 5} = {2}^{5} \\ = \tt n + 5 = 5 \\ = \tt n = 5 - 5 \\ = \large\boxed{\tt{\green{n = 0}}}[/tex]
[tex]_____________________________________[/tex]
[tex]\large\boxed{\sf{\green{CarryOnLearning}}}[/tex]
[tex]\large\boxed{\sf{\red{MathDemonQueenシ︎✌︎}}}[/tex]
[tex]\large\boxed{\sf{\green{ItsMoreFunInThePhilippines✌︎}}}[/tex]
A cone has a diameter of 4 inches and a height of 9 inches. Find the volume of the cone. Use 3.14 for \large \pi.
Answers
Answer:
37.68 in.^3
Step-by-step explanation:
diameter = 4 in.
radius = diameter/2 = 2 in.
height = 9 in.
[tex] V = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \dfrac{1}{3}(3.14)(2~in.)^2(9~in.) [/tex]
[tex] V = \blue{37.68~in.^3} [/tex]
Use the drawing tools to form the correct answer on the graph. Graph this function. - 2 + 8 = Reset ® Delet Undo Drawing Tools Click on a tool to begin drawing. Select Point 10 Line 8 3 6- 4 2 2 4 6 -2 8 10 -4 -10 -8 -6 -2 7071 Frmentum. All rights reserved.
Answers
Answer:
we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm
The graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
The function is given as:
[tex]f(x) = -2x + 8[/tex]
The above function is a linear function.
A linear function is represented as:
[tex]y =mx + c[/tex]
Where:
m represents the slope, and c represents the y-intercept.
So, by comparison;
[tex]m =-2[/tex]
[tex]c = 8[/tex]
This means that the graph of [tex]f(x) = -2x + 8[/tex] has a slope of -2, and a y-intercept of 8
See attachment for the graph of the function
Read more about linear functions at:
https://brainly.com/question/15602982
Select all the numbers that are rational.
Answers
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
62.5% of a number is 25. What is half of the same number.
Answers
let the number be b
62.5/100 x b = 25
0.625 x b = 25
b =25/0.625
b=40
half of b= 40/2 = 20
Finding the Area of a Circle Given the Radius Th It The area in terms of pi isi mi? The approximated value for the area is A circle has a radius of 3 miles. Use the work shown below to identify the area in terms of pi and the approximate area of the circle. Use 3.14 for a and round the answer to the nearest tenth. A = 2 A= T(3 mi) A = 3.14(9 mi)
Answers
Answer:
I'd use A = πr^2
The area is 28.3 if we're using 3.14 as pi (rounded to the nearest tenth)
Which statement best describes the areas and perimeters of the figures?
Answers
Answer:
The last one!
Step-by-step explanation:
What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta
Answers
Answer:
Your options are not clear
Step-by-step explanation:
[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]
pleaseeeee solve thissss pleaseeee
Answers
Answer:
a.) 15 feet
b.) 3.25 seconds
c.) 17.1125 feet
d.) 12.5 seconds
Step-by-step explanation:
a
This is just asking for the y intercept
to get this just do h(0)= 15
b
This is asking for the x value of the vertex
solve that through -b/2a
-1.3/(2*-.2)= 3.25
c
This is asking for the y value of the vertex
to solve this plug in the x value from b
-.2*3.25²+1.3*3.25+15= 17.1125
d
This is asking for an x intercept
using the quadratic formula...
[tex]\frac{-b(+-)\sqrt{b^2-4*a*c}}{2a}=\frac{-1.3(+-)\sqrt{1.3^2-4*-.2*15}}{2*-.2}= -6, 12.5[/tex]
*note the (+-) before the radical is ± *
logic will tell us that a negative x intercept doesn't make any sense so we only take the positive value, 12.5
In a sale, Ali buys a television for $195.80.
The original price was $220.
Calculate the percentage reduction on the original price.
Answers
11%
Hope this helps! :)
______________
Answer:
[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]
