Answer:
Ratio = 5:1
= 5 / 1
Number of teachers = 15
Lets take the number of students = x
Therefore,
5:1 = x:15
= 5/1 = x/15
x = 15 × 5
= 75 students
Hope it helps!!
The product of two whole numbers is 936 and the sum is 62. What are the two numbers
Answer:
26 and 36.
Step-by-step explanation:
Let the two whole numbers be a and b. Thus, the product of them is 936 while their sum is 62. In equations, this is:
[tex]ab=936\\a+b=62[/tex]
This is a system of equations. To solve, subtract either a or b from the second equation and substitute it into the first.
For instance, subtract b from both sides in the second equation:
[tex]a+b=62\\a=62-b[/tex]
Substitute this into the first equation:
[tex](62-b)(b)=936[/tex]
Distribute:
[tex]62b-b^2=936[/tex]
Rearrange:
[tex]-b^2+62b=936[/tex]
Divide everything by -1 to make the leading coefficient positive:
[tex]b^2-62b=-936[/tex]
Add 936 to both sides:
[tex]b^2-62b+936=0[/tex]
This is now a quadratic. Solve for b.
To do so, we can factor.
After a bit of testing, we can see that -36 and -26 are possible. Thus:
[tex](b-26)(b-36)=0[/tex]
For for b:
[tex]b=26\text{ or } b=36[/tex]
Thus, b is 26 or 36.
Now, plug these back into the isolated equation to solve for a:
[tex]a=62-b\\a=62-(26) \text{ or } a=62-(36)\\a=36\text{ or } a=26[/tex]
It doesn't really matter which one we choose since they're the same.
Thus, the answer is 26 and 36.
Find the square. Simplify your answer.
(2t - 4)
Answer:
t^2 -4t + 4
Step-by-step explanation:
(2t-4)(2t-4) Use the FOIL Method (first, outside, inside, last)
2t*2t =4t^2 First
2t*-4 = -8t Outside
-4*2t = -8t Inside
-4*-4 = 16 Last
4t^2 -8t -8t + 16 (simplify/add like terms)
(4t^2 -16t + 16)/4 (you can further simplify by dividing each value by 4)
t^2 -4t + 4
Your text suggests you look find an agent that has been in the insurance business for how long??
Answer:
A month at the very least
Step-by-step explanation:
Name the missing coordinate(s) of the triangle
Answer:
R(7a, 0 )
Step-by-step explanation:
R is on the vertical line RQ so will have the same x- coordinate as Q
R is on the horizontal line OR so will have the same y- coordinate as O
Thus coordinates of R = (7a, 0 )
Find the distance between the points (-3,1) and (1,-4)
Answer:
[tex]\sqrt{41} \: \: or \: 6.4 \: \: units[/tex]Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-3,1) and (1,-4)
The distance between them is
[tex]d = \sqrt{ ({ - 3 - 1})^{2} + ({1 + 4})^{2} } \\ = \sqrt{ ({ - 4})^{2} + {5}^{2} } \\ = \sqrt{16 + 25} \\ [/tex]We have the final answer as
[tex] \sqrt{41} \: \: or \: 6.4 \: \: units[/tex]Hope this helps you
There are 10,000 mutual fund managers. 22 claim that they are the best, since their fund beat the relevant index every year for 7 years. However, you think that markets are efficient and that the average fund manager is as likely to deliver a better performance than the index as to underperform the index, before fees.
Part 1 | Attempt 1/10 for 10 pts. What is the probability that the average single fund managers beats the index 7 years in a row (before fees)? 4+ decimals
Part 2 | Attempt 1/10 for 10 pts. How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved? No decimals
Answer:
Part A:
Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]
Part B:
Fund Managers to beat index 7 years=78.125≅78 managers.
Step-by-step explanation:
Part A:
Given data:
Since there are equal chances for delivering equal better performance and of under performance so
Probability of better performance =0.5
Required:
Probability that the average single fund managers beats the index 7 years in a row (before fees)=?
Solution:
Since there is 7 year index:
Probability that average single manager beat the index= [tex](0.5)^7=0.0078125=0.0078 (4\ decimals)[/tex]
Part B:
Given Data:
Number of mutual fund managers=10,000
Probability that average single manager beat the index= 0.0078125 (Calculated in part A)
Required:
How many fund managers would you expect to beat the index 7 years in a row if only luck and no skill was involved?
Solution:
Fund Managers to beat index 7 years=Total number of managers*probability average single member beat the index
Fund Managers to beat index 7 years=10,000*0.0078125
Fund Managers to beat index 7 years=78.125≅78 managers.
If a polygon is a kite, then it is a quadrilateral. Write the inverse of the conditional statement and determine whether it is true or false. A) If a polygon is a quadrilateral, then it is a kite. TRUE B) If a polygon is a quadrilateral, then it is a kite. FALSE C) If a polygon is not a kite, then it is not a quadrilateral. TRUE D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
The correct answer is D) If a polygon is not a kite, then it is not a quadrilateral. FALSE
Explanation:
The statement "If a polygon is a kite, then it is a quadrilateral" as other statements is composed of two parts: the if statement or hypothesis and the conclusion. Additionally, to create the inverse of this statement it is necessary to negate both statements, this means the inverse is "If a polygon is not a kite, then it is not a quadrilateral" because this negates the hypothesis and the conclusion. Besides this, it can be concluded this inverse statement is false because the word "quadrilateral" describes all shapes with four sides, which include not only kites but squares, rectangles, trapezoids, etc. Therefore, a polygon can be quadrilateral without being a kite.
(6^2)^x =1 please help ASAP please
Answer:
x =0Step-by-step explanation:
[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]
[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]
Answer:
x = 0
Simplified: [tex]36^{x} = 1[/tex]
Step-by-step explanation:
How to simplify:
[tex]6^{2}[/tex] = 6 × 6 = 36Plug in 36: [tex]36^{x} = 1[/tex]Order these from least to greatest: -3/4, 0.5, 2/3, -7/3, 1.2 Thank you
Answer:
-7/3
-3/4
0.5
2/3
1.2
You can get these numbers by sorting in your head. Think of a number line and that'll make things easier :)
Answer:
-7/3, -3/4, 0.5, 2/3, 1.2
Step-by-step explanation:
The larger the negative number is the smaller it's value is and its the complete opposite for positive numbers
I have no idea what I’m doing
Answer : The polynomial in standard form is [tex]1a^2+9a+20[/tex]
Step-by-step explanation :
The polynomial in standard form means that the terms are ordered from highest exponent to lowest exponent.
Given: Subtract [tex]9a^2-6a+5[/tex] from [tex]10a^2+3a+25[/tex]
The expression will be :
[tex](10a^2+3a+25)-(9a^2-6a+5)[/tex]
Now open the bracket and change the sign.
[tex]=10a^2+3a+25-9a^2+6a-5[/tex]
Now we are adding or subtracting the like terms, we get:
[tex]=1a^2+9a+20[/tex]
Thus, the polynomial in standard form is [tex]1a^2+9a+20[/tex]
6.8 ÷ 3.4 step by step
Answer:
2
Step-by-step explanation:
Pretend there is no decimal point. We can do this by multiplying both numbers by 10.
After that, it becomes 68/34. You then divide those two, and you get 2 as your answer.
Answer:
2
Step-by-step explanation:
its easy you can do it with calculator or paper -__-
A lunch bill is $12 before tax. If the tax on the bill is 7.5% what is the total cost of the lunch including tax?
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{ \: 12.9 \: \: dollars}}}}}[/tex]
Step-by-step explanation:
Given,
Cost without tax = $ 12
Tax percent = 7.5 %
Cost including tax = ?
First, finding the tax amount :
[tex] \sf{tax \: amount \: = \: 7.5 \: \% \: of \: 12}[/tex]
⇒[tex] \sf{tax \: amount = \frac{7.5}{100} \times 12} [/tex]
⇒[tex] \sf{tax \: amount = 0.9}[/tex] dollars
Finding the total cost of the lunch including tax :
⇒[tex] \sf{total \: cost \: = \: 12 + 0.9}[/tex]
⇒[tex] \sf{total \: cost \: = \: 12.9}[/tex] dollars
Hope I helped!
Best regards ! :D
8x - 6(x + 1) < 4(2x - 9)
Answer:
x > 5
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
8x - 6(x + 1) < 4(2x - 9)
Step 2: Distribute parenthesis
8x - 6x - 6 < 8x - 36
Step 3: Combine like terms
2x - 6 < 8x - 36
Step 4: Subtract 2x on both sides
-6 < 6x - 36
Step 5: Add 36 on both sides
30 < 6x
Step 6: Divide both sides by 6
5 < x
Step 7: Rewrite
x > 5
Plz help me this is for online school I just started I don’t need to be failing already
Answer:
-65, (-35)-100+(-150), -250Step-by-step explanation:
When you work addition and subtraction problems, it is often easier to do them if you can "make a 10" or "make a 100", because adding or subtracting 10 or 100 is easier than with non-zero digits.
__
Here, you are steered toward noticing that there are two elements of the sum that have a total of -100. Those elements are -65 and -35. With the above in mind, you can use the commutative property to rearrange the sum to ...
-65 +(-35) +(-150) . . . . . . . last two terms were swapped
Then the first step is to add -65 and -35:
[tex]\text{It is easier to add }\boxed{-65}\,+\,\boxed{(-35)}\text{ first to get $-100$.}[/tex]
Now, the sum reduces to ...
-100 +(-150) = -250
So, the final sentence becomes ...
[tex]\text{Then add }\boxed{-100+(-150)}\text{ to get }\boxed{-250}\,.[/tex]
Which is the correct answer choice?
Answer:
i think b is answer. i think this is useful to you
PLEASE HELP I WILL GIVE BRAINLIEST
Answer:
1/3
Step-by-step explanation:
√2 is irrational because radicals are irrational. π is also an irrational number. The third option, 1.3985624785461.... is obviously not a terminating decimal, hence, it is also irrational. Therefore, the answer is 1/3. We know this because 1/3 can be written in the form a / b where a and b are rational numbers, in this case, a = 1 and b = 3.
how do find the length of a rectangle
Answer:
L = A÷W
Step-by-step explanation:
The area of a rectangle (A) is related to the length (L) and width (W) of its sides by the following relationship: A = L ⋅ W. If you know the width, it's easy to find the length by rearranging this equation to get L = A ÷ W.
Simplify 8(3 - 2x).
0 24x - 16
16x - 24
24 - 16x
Answer:
24 - 16x
Step-by-step explanation:
8(3 - 2x)
Distribute
8*3 - 8*2x
24 - 16x
What are the values of x & y?
Answer:
X= 60°
Y= 30°
Step-by-step explanation:
In triangle ABD, we have:
AB = BD = AD
Then triangle ABD is equilateral triangle.
Then, all its angles are equal to 60°.
=> X = 60°
____________________________________
ADC is right triangle at D.
So, X and Y are congruent angles (their sum is equal to 90°)
So, X + Y =90°
60° + Y = 90°
Y = 90 - 60
Y= 30°
[tex]hope \: this \: helps[/tex]
A landowner has some land on which he wants to plant trees. He can plant 1,357 trees on landl if he already has 1,289 trees. How many does he have left to purchase?
a 2 day automobile trip of 880 miles is planned. half of the distance is to be traveled each day at 55 miles per hour. how many hours will be driven each day
Answer:
Time travelled each day = 8 hours
Step-by-step explanation:
total distance of 2-day trip = 880 miles
half the distance each day = 880 ÷ 2 = 440 miles
velocity travelled each day = 55 miles per hour
time travelled each day = ???
velocity = (distance trvaelled) ÷ (Time)
55 = 440 ÷ Time
[tex]55=\frac{440}{Time} \\cross-multiplying\\55\ \times\ Time = 440\\Time = \frac{440}{55} \\Time = 8\ hours[/tex]
∴ Time travelled each day = 8 hours
Answer:
9 hours
Step-by-step explanation:
Total distance for the two days = 880 miles
If half of the distance is to be traveled each day, then;
distance each day = 440 miles
speed of the automobile = 55 miles per hour.
Now, let's calculate the number of hours that will be driven each day.
Remember that;
speed = distance / time
=> time = distance / speed [substitute the values of distance and speed]
=> time = (440 miles) / (55 miles/hour)
=> time = 9 hours.
Therefore, the number of hours that will be driven each day is 9
Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
What is the standard error?
Answer:
The standard error is 0.033.
Step-by-step explanation:
We are given that Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year.
Let [tex]\hat p[/tex] = proportion of employees who planned to take an extended vacation next year
[tex]\hat p[/tex] = [tex]\frac{X}{n}[/tex] = [tex]\frac{21}{125}[/tex] = 0.168
n = number of employees at her company = 125
Now, the standard error is calculated by the following formula;
Standard error, S.E. = [tex]\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
= [tex]\sqrt{\frac{0.168(1-0.168)}{125} }[/tex]
= [tex]\sqrt{\frac{0.168 \times 0.832}{125} }[/tex] = 0.033
Hence, the standard error is 0.033.
Answer:
.10 - .23
Step-by-step explanation:
.168 +/- 1.96 ( sqrt ((.168 * .832)/125))
Solve the equation by extracting the square roots. List both the exact solution and its approximation rounded to two decimal places. x2 = 19
Answer:
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
Step-by-step explanation:
[tex] x^2 = 19 [/tex]
[tex] x = \pm \sqrt{19} [/tex]
[tex] x = \pm 4.36 [/tex]
The exact solution is 4.36.
What is square root?Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is value which on getting multiplied by itself gives the original value. Hence, both are vice-versa methods. For example, the square of 2 is 4 and the square root of 4 is 2.
Given:
x² = 19
On taking root on both side
√x² = √19
x= √19
x = 4.3588
Hence, the exact solution and its approximation rounded to two decimal places is 4.36.
Learn more about square root here:
https://brainly.com/question/3120622
#SPJ2
Which graph represents decreasing distance with increasing time?
Answer: im pretty sure its exponential decay?
Step-by-step explanation:
the number of points by a basketball player in the first eight games of a season are shown before. 15,35,18,30,25,21,32,16
Answer:
24
Step-by-step explanation:
Assuming you want to find a mean, the answer is: 24 (sum of all values/number of values)
Range is largest-smallest
Median is middle value
A line extends indefinitely in opposite directions.
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?
Answer:
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old are they each now?
Step-by-step explanation:
Let us suppose two years ago my brother's age was x years
Then, my age was 3x
Three years from now, my brother's age will be (x +2+3) = (x+5) years
And my age will be (3x+2+3) = (3x+5) years
But it is given that i will be twice as old as my brother.
So, 2(x+5)= (3x+5)
or, x= 5 years
So my brother's present age is 5+2= 7 years
And my age is 5*3+2= 17 years
The age of the older brother is 13 and the age of the younger brother is 5.
Two simultaneous equations can be determined from this question:
y = 3x - 2 equation 1
y = 2x + 3 equation 2
Where:
y = older brother's age
x = younger brother's age
Equate equation 1 and equation 2
3x - 2 = 2x + 3
Combine similar terms
3x - 2x = 3 + 2
x = 5
Substitute for x in equation 1
3(5) - 2
15 - 2
y =13
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
10-(2x-3)
A. 7-2x
B. 13+2x
C. 15x
D. 13-2x
Answer:
D.13-2x
Step-by-step explanation:
[tex]10-\left(2x-3\right)\\\\-\left(2x-3\right):\quad -2x+3\\=10-2x+3\\\\\mathrm{Simplify}\:10-2x+3:\\\quad -2x+13[/tex]
Answer:
13 -2x
Step-by-step explanation:
10-(2x-3)
Distribute the minus sign
10 -2x +3
Combine like terms
13 -2x
Use De Morgan’s law for quantified statements and the laws of propositional logic to
show the following equivalences:________
a) ¬ x(P (x) ¬Q(x)) x(¬P (x) Q(x))∀∧≡∃∨
b) ¬ x(¬P (x) = Q(x)) x(¬P (x) ¬Q(x))∀⇒≡∃∧
c) ¬ x(¬P (x) (Q(x) ¬R(x))) x(P (x) (¬Q(x) R(x)))
Answer:
A) ¬(¬q) ≡ q
B) ≡ ( эx) (¬p(x) ∧ ¬q(x)
C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )
Step-by-step explanation:
using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following
from De -Morgan law
¬(A ∨ B ) = ¬ A ∧¬ B
ATTACHED BELOW IS THE COMPLETE SOLUTION
Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
1. Let W{1} be the set of all polynomials of the form p(t) = at^{2}, where a is in {R}.
2. Let W{2} be the set of all polynomials of the form p(t) = t^{2} + a, where a is in {R}.
3. Let W{3} be the set of all polynomials of the form p(t) = at^{2} + at, where a is in {R}.
Answer:
1) W₁ is a subspace of Pₙ (R)
2) W₂ is not a subspace of Pₙ (R)
4) W₃ is a subspace of Pₙ (R)
Step-by-step explanation:
Given that;
1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R
2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R
3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R
so
1)
let W₁ = { at² ║ a∈ R }
let ∝ = a₁t² and β = a₂t² ∈W₁
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)
= c₁a₁t² + c²a₂t²
= (c₁a₁ + c²a₂)t² ∈ W₁
Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁ and scalars c₁, c₂
Thus, W₁ is a subspace of Pₙ (R)
2)
let W₂ = { t² + a ║ a∈ R }
the zero polynomial 0t² + 0 ∉ W₂
because the coefficient of t² is 0 but not 1
Thus W₂ is not a subspace of Pₙ (R)
3)
let W₃ = { at² + a ║ a∈ R }
let ∝ = a₁t² +a₁t and β = a₂t² + a₂t ∈ W₃
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)
= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t
= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃
Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂
Thus, W₃ is a subspace of Pₙ (R)