Answer:
See Explanation
Step-by-step explanation:
(a) Proof: Product of two rational numbers
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
[tex]A = \frac{1}{2}[/tex]
[tex]B = \frac{2}{3}[/tex]
The product:
[tex]A * B = \frac{1}{2} * \frac{2}{3}[/tex]
[tex]A * B = \frac{1}{1} * \frac{1}{3}[/tex]
[tex]A * B = 1 * \frac{1}{3}[/tex]
[tex]A * B = \frac{1}{3}[/tex]
Proved, because 1/3 is rational
(b) Proof: Quotient of a rational number and a non-zero rational number
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
[tex]A = \frac{1}{2}[/tex]
[tex]B = \frac{2}{3}[/tex]
The quotient:
[tex]A / B = \frac{1}{2} / \frac{2}{3}[/tex]
Express as product
[tex]A / B = \frac{1}{2} / \frac{3}{2}[/tex]
[tex]A / B = \frac{1*3}{2*2}[/tex]
[tex]A / B = \frac{3}{4}[/tex]
Proved, because 3/4 is rational
(c) x + y is rational (missing from the question)
Using direct proofs.
Let x and y be
Such that:
[tex]x = \frac{1}{2}[/tex]
[tex]y = \frac{2}{3}[/tex]
The sum:
[tex]x + y = \frac{1}{2} + \frac{2}{3}[/tex]
Take LCM
[tex]x + y = \frac{3+4}{6}[/tex]
[tex]x + y = \frac{7}{6}[/tex]
Proved, because 7/6 is rational
The above proof works for all values of A, B, x and y; as long as they are rational values
HELP ME PLEASEEEEEEEEEE
Answer: B
Step-by-step explanation: A=πr2
The formula for calculating the area of a circle is A = πr2 where pi (π) equals 3.14 and the radius (r) is half the diameter.
You must times 5 by 5 because of exponents and then times it by pie
5 times 5 = 25
25 times pie is 78.5
solve for the indicated variable in the literal equation
Answer:
[tex]x = \frac{y}{3} - \frac{5}{3}[/tex]
Step-by-step explanation:
Given
[tex]y = 5 + 3x[/tex]
Required
Solve for x
Subtract 5 from both sides
[tex]y-5 = 5 -5+ 3x[/tex]
[tex]y-5 = 3x[/tex]
Divide through by 3
[tex]\frac{y}{3} - \frac{5}{3} = x[/tex]
[tex]x = \frac{y}{3} - \frac{5}{3}[/tex]
last week Kellie ran 28 miles. this week she ran 32. what was the percent change in number of miles she ran
write ⅔of 4 as a fraction
Answer:
2/3 of 4=8/3or 2 2/3 is your answer
Answer:
I have 2.66667 As a fraction it is 4/1
Step-by-step explanation:
I'm not completely sure I'm new to this :|
Please help I need due rn
Answer:
4 3/12
Step-by-step explanation:
= 4.25 = 4 1/4 = 4 3/12
madison paid $53.58 in sales tax on her books. the sales tax was 8.6% of the cost of the books. how much did madison's books cost before tax?
Answer:
$48.98
Step-by-step explanation:
first move the decimal of your percent 2 places
8.6% = .086
then multiply by 53.58
.086 × 53 58= 4.60
subtract 4.60 from 53.58
53.58 - 4.60= 48.98
simplify (-4/5)^9/(-4/5)^10
Answer:
[tex]-\frac{5}{4}[/tex]
Step-by-step explanation:
We are given two fractions and are asked to simplify it.
So
[tex](-\frac{4}{5} )^9 / (-\frac{4}{5} )^{10}[/tex]
We can follow the exponent rule of subtracting them since both fractions are the same value.
[tex](-\frac{4}{5} )^{9-10}[/tex]
[tex](-\frac{4}{5} )^{-1}[/tex]
Now do the negative exponent rule :
[tex]\frac{1}{-\frac{4}{5} }[/tex]
Move the negative in between the fraction :
[tex]-\frac{1}{\frac{4}{5} }[/tex]
And apply the fraction switcharoo :
[tex]\frac{5}{4}[/tex]
PLS ANSWER IN 5 MINS
I WILL MARK BRAINLIEST
THE QUESTION IS IN THE PICTURE I ATTACHED
Answer:
[tex]\frac{19}{14}x + \frac{97}{56}[/tex] =
^^^hope this helps! :)
Find the volume of this right rectangular prism. [Type your answer as a number.]
1
Answer:
200 cm3
Step-by-step explanation:
Multiply 10x4x5=200
A data scientist studying a manufacturing process classifies each item produced by the process as either Poor, Acceptable, or Excellent. Assume that the classes of different items are independent of each other and that each item falls into the classes according to the following probabilities:
Poor Acceptable Excellent
0.25 0.6 0.15
The data scientist receives three items produced by the manufacturing process.
Find the chance that:
a. all of items are Acceptable
b. none of the items is Acceptable
c. at least one of the items is Excellent
d. not all of the items are Excellent
e. there is one item of each class
Answer:
0.214 ; 0.064 ; 0.3859 ; 0.9966 ; 0.135
Step-by-step explanation:
Given the distribution :
Poor ___ Acceptable ____ Excellent
0.25 _____ 0.6 _________ 0.15
The data scientist receives three items produced by the manufacturing process.
Find the chance that:
a. all of items are Acceptable
0.6 * 0.6 * 0.6 = 0.6^3 = 0.214
b. none of the items is Acceptable
P(not acceptable) = 1 - p(acceptable) = 1 - 0.6 = 0.4
0.4 * 0.4 * 0.4 = 0.4^3 = 0.064
c. at least one of the items is Excellent
P(atleast one) = 1 - P(none)
P(not excellent) = 1 - 0.15 = 0.85
P(none is excellent) = 0.85^3 = 0.614125
Hence,
P(atleast one is excellent) = 1 - 0.614125 = 0.3859
d. not all of the items are Excellent
P(not all) = 1 - p(All)
P(all excellent) = 0.15^3 = 0.003375
P(not all are excellent) = 1 - 0.003375 = 0.9966
e. there is one item of each class:
P(poor) * p(acceptable) * p(excellent) * (number of classes)!
0.25 * 0.6 * 0.15 * 3!
= 0.135
What is the value of z?
62
Enter your answer in the box.
95
Answer:
Value of z = 23°
Step-by-step explanation:
Given:
∠1 = 62°
∠2 = 95°
∠3 = z°
Find:
Value of z
Computation:
Using angle sum property
∠1 + ∠2 + ∠3 = 180°
62 + 95 + z° = 180
Value of z = 23°
How can 38 over 6 be expressed as a decimal?
A. 5.1 with bar over 1
B. 6.1 with bar over 1
C. 6.3 with bar over 3
Answer:
B
Step-by-step explanation:
C its C hopes this helps
10 points
Michael surveyed every tenth child who entered a state fair about the number of rides they planned
on riding. What is the population for Michael's sample?
A. every tenth child who entered the state fair
B. all the people at the state fair
C. all the children at the state fair
D. every adult with children at the state fair
A
OD
Answer:
C
Step-by-step explanation:
All children at the state fair
Steve is turning half of his backyard into a chicken pen. His backyard is a 24 meter by 45 m rectangle. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner.
How many meters of fencing will Steve need?
Answer: 12 is the awnser
Step-by-step explanation: simple math.
The radius of a sphere is 18 feet. What is the surface area of the sphere? Express the answer in terms of pi. Recall the formula SA = 4pi 2
Answer: 1296π
Step-by-step explanation:
To find the surface are if a square, we have to use the formula:
= 4πr²
= 4 × π × 18²
= 4 × π × 324
= 1296π
Therefore, the surface area of the sphere is 1296π
Answer:
C
Step-by-step explanation:
I did the test right
What’s the answer? Please help
A bacteria with an initial size of 180in2 grows by 27% every minute. What will the size of the bacteria be after 8hours
Answer:
The size of the bacteria after 8 hours will be of [tex]1.2 \times 10^{52}[/tex] squared inches.
Step-by-step explanation:
Exponential function:
An exponential function has the following format:
[tex]F(t) = F(0)(1+r)^{t}[/tex]
In which F(0) is the initial value and F is the growth rate.
A bacteria with an initial size of 180in2 grows by 27% every minute.
This means that [tex]F(0) = 180, r = 0.27[/tex]. So
[tex]F(t) = F(0)(1+r)^{t}[/tex]
[tex]F(t) = 180(1+0.27)^{t}[/tex]
[tex]F(t) = 180(1.27)^{t}[/tex]
In which t is measured in minutes,
What will the size of the bacteria be after 8hours
8 hours has 8*60 = 480 minutes, so this is F(480).
[tex]F(480) = 180(1.27)^{480} = 1.2 \times 10^{52}[/tex]
The size of the bacteria after 8 hours will be of [tex]1.2 \times 10^{52}[/tex] squared inches.
Multiply (X - 4) squared
Answer:
it's the fourth answer
Step-by-step explanation:
(X-4) (X-4)
[tex]x^{2}[/tex]-4x-4x+16
[tex]x^{2}[/tex]-8x+16
The expression is x² + 8x + 16. The correct answer is a) x² + 8x + 16.
To multiply (x - 4)², we can use the concept of expanding a binomial squared. The formula for expanding a binomial squared is:
(a - b)² = a² - 2ab + b²
In this case, a = x and b = 4. Substituting these values into the formula, we have:
(x - 4)² = x² - 2(x)(4) + 4²
= x² - 8x + 16
Therefore, the correct option is a) x² + 8x + 16.
To know more about binomial squared:
https://brainly.com/question/29142274
#SPJ6
Point Q is graft at (N, -2). The distance from P to Q is equal to the distance from P point R. What is the distance from point P to point Q? What is the value of N? Explain how you determine the distance from point B to point Q, and the value in.
Answer:
ndndnjxhdhfjhfjdirudjfjutt
Help ? PLEASE HURRY !
Answer:
Step-by-step explanation:
Sine of U = 8/17
opposite /hypotensue
Fill in the blanks: what numbers will make the equation true? 4 * ___ / 6 + ___ = 11 *
Solve the equation 15=7+b
Answer:
[tex]b=8[/tex]
Can i have brain plzI need help with this
Answer:
76
Step-by-step explanation:
We know that the two angles must add up to 90 which means that
12+x-2=90
solve for x
14+x=90
x= 76
find the positive zero of the function f(x)=x^(2)-5x-7 and round two decimal places
Answer:
6.14
Step-by-step explanation:
Given the function f(x)=x^(2)-5x-7, when f(x) = 0
x^(2)-5x-7 = 0
Using the general formula
x = 5±√5²-4(-7)/21(1)
x= 5±√25+28/2
x = 5±√53/2
x = -5±7.28/2
x = 5+7.28/2 and 5-7.28/2
x = 12.28/2 and -2.28/2
x = 6.14 and -1.14
Hence the positive zero is 6.14
The personnel department of Anna's Wholesale Bakery is preparing annual
reports on employee benefits. Hannah Prosser's gross annual salary is $29,500.
Her benefits total $8,673.25. Hannah's total annual benefits are what percent of
her annual salary?
Answer:
$32,277.80
Step-by-step explanation:
A hotel manager is adding a tile border around the hotel's rectangular pool. let n represent the width of the pool, in feet. the length is 3 more than 3 times the width, as shown. Write two expressions that represent the perimeter of the pool.
Answer:
[tex]2(4n+3)[/tex]
[tex]8n+6[/tex]
Step-by-step explanation:
We are given that
Let n represent the width of pool
Length of pool=[tex]3n+3[/tex]
We have to find two expression which represent the perimeter of the pool.
We know that
Perimeter of rectangle=[tex]2(l+b)[/tex]
Where l=Length of rectangle
b=Width of rectangle
Using the formula
Perimeter of pool=[tex]2(n+3n+3)[/tex]
Perimeter of pool=[tex]2(4n+3)[/tex]
Perimeter of pool=[tex]8n+6[/tex]
Hence, two expressions that represent the perimeter of the pool is given by
[tex]2(4n+3)[/tex]
[tex]8n+6[/tex]
solve triangle. round to the nearest tenth
Answer:
37.5 ( i didn't round cause the answer looked simple already)
Step-by-step explanation:
formula for triangle is base x height divided by 1/2
Base(5) x Height(15) = 75 now divide by 1/2
75 divided by 1/2 = 37.5
(Could i have brainliest if i'm right?)
HURRY , Write the coordinates of the vertices after a reflection across the line x = 5. (will give brainiest)
Answer:
U: (5,9)
W: (7,9)
V: (6,10)
T: (6,7)
Step-by-step explanation:
If the diameter of the circle is 6 cm, find its circumference. [Use 3.14 for π
The circumference of the circle with a diameter of 6 cm will be 18.84 cm.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let d be the diameter of the circle. The circumference of the circle will be given as,
C = πd units
The diameter of the circle is 6 cm. Then the circumference is given as,
C = π x 6
C = 3.14 x 6
C = 18.84 cm
The circumference of the circle with a diameter of 6 cm will be 18.84 cm.
More about the circumference of a circle link is given below.
https://brainly.com/question/27177006
#SPJ1
B. Translate each statement to an equation using k as the constant of variation.
1. m varies directly to a.
2. p varies inversely as q.
3. r varies directly as s and inversely as t.
4. z varies jointly as e and f.
5. F varies directly as the square of t.
6. The distance (d) traveled by a car varies jointly as the rate (r) and the time (t) of travel.
7. The air pressure (P) in inversely proportional to the altitude (h).
8. The amount of water pressure (P) in a closed container varies directly as the volume (V) of the
water.
9. The distance (d) of a falling body varies directly as the square of the time (t) traveled.
1
10. The stiffness (s) of a beam varies jointly as its breadth (b) and depth (d) and inversely as the
square
of its length (L).
2
Answer:
See Explanation
Step-by-step explanation:
To do this, we will make use of the following rules:
Direct Variation: [tex]a\ \alpha\ b[/tex] => [tex]a = kb[/tex]
Inverse Variation: [tex]a\ \alpha\ \frac{1}{b}[/tex] ==> [tex]a = k/b[/tex]
Joint Variation: [tex]a\ \alpha\ bc[/tex] ==> [tex]a= kbc[/tex]
Direct, then inverse variation: [tex]a\ \alpha\ b\ \alpha\ \frac{1}{c}[/tex] ==> [tex]a= kb/c[/tex]
Having highlighted the rules, the solution is as follows:
1. m varies directly to a
[tex]m\ \alpha\ a[/tex]
[tex]m =ka[/tex]
2. p varies inversely as q.
[tex]p\ \alpha\ \frac{1}{q}[/tex]
[tex]p\ = k\frac{1}{q}[/tex]
3. [tex]r\ varies[/tex] directly as s and inversely as t.
[tex]r\ \alpha\ s\ \alpha\ \frac{1}{t}[/tex]
[tex]r = k\frac{s}{t}[/tex]
4. z varies jointly as [tex]e\ and\ f.[/tex]
[tex]z\ \alpha \ ef[/tex]
[tex]z = kef[/tex]
5. F varies directly as the [tex]square\ of\ t.[/tex]
[tex]F\ \alpha\ t^2[/tex]
[tex]F = kt^2[/tex]
6. d varies jointly r and t
[tex]d\ \alpha\ rt[/tex]
[tex]d = krt[/tex]
7. P is inversely proportional to h.
[tex]P\ \alpha\ \frac{1}{h}[/tex]
[tex]P= \frac{k}{h}[/tex]
8. P varies directly as V
[tex]P\ \alpha\ V[/tex]
[tex]P=kV[/tex]
9. d varies directly as the square of t
[tex]d\ \alpha\ t^2[/tex]
[tex]d = kt^2[/tex]
10. s varies jointly as b and d and inversely as the square L
[tex]s\ \alpha\ bd\ \alpha\ \frac{1}{L^2}[/tex]
[tex]s = k\frac{bd}{L^2}[/tex]
The translation of each statement to an equation using k as the constant of variation is
1. m varies directly to a.
m = k × a
m = ka
2. p varies inversely as q
p = k / q
3. r varies directly as s and inversely as t
r = (k × s) / t
r = ks / t
4. z varies jointly as e and f.
z = k × e × f
z = kef
5. F varies directly as the square of t.
F = k × t²
F = kt²
6. The distance (d) traveled by a car varies jointly as the rate (r) and the time (t) of travel.
d = k × r × t
d = krt
7. The air pressure (P) in inversely proportional to the altitude (h).
P = k / h
8. The amount of water pressure (P) in a closed container varies directly as the volume (V) of the
water.
P = k × V
P = kV
9. The distance (d) of a falling body varies directly as the square of the time (t) traveled.
d = k × t²
d = kt²
10. The stiffness (s) of a beam varies jointly as its breadth (b) and depth (d) and inversely as the
square of its length (L).
s = (k × b × d) / L²
s = kbd / L²
Read more:
https://brainly.com/question/472621