Answer:
[tex]2.5[/tex] [tex]-1.25[/tex] [tex]\sqrt{16}[/tex] [tex]0.6[/tex]
Step-by-step explanation:
Required
Which of the given parameters can be represented as fraction of integers
Taking them one at a time;
1. 2.5
This can be rewritten as
[tex]2.5 = \frac{2.5}{1}[/tex]
Multiply numerator and denominator by 2
[tex]2.5 = \frac{2.5 * 2}{1 * 2}[/tex]
[tex]2.5 = \frac{5}{2}[/tex]
Hence, 2.5 can be represented as fraction of integers
2. √14
This can be rewritten as
[tex]\sqrt{14} = 3.74165738677...[/tex]
The ... implies that the decimal continues and this cannot be represented as a fraction
3. -1.25
This can be rewritten as
[tex]-1.25 = \frac{-1.25}{1}[/tex]
Multiply numerator and denominator by 4
[tex]-1.25 = \frac{-1.25 * 4}{1 * 4}[/tex]
[tex]-1.25 = \frac{-5}{4}[/tex]
Hence, -1.25 can be represented as fraction of integers
4. 5.33333.....
The ... implies that the decimal continues and this cannot be represented as a fraction
5. √16
[tex]\sqrt{16} = \±4[/tex]
This can be rewritten as
[tex]\sqrt{16} = \±\frac{4}{1}[/tex]
Multiply numerator and denominator by 2
[tex]\sqrt{16} = \±\frac{4 * 2}{1 * 2}[/tex]
[tex]\sqrt{16} = \±\frac{8}{2}[/tex]
Hence, √16 can be represented as fraction of integers
6. 0.6
This can be rewritten as
[tex]0.6 = \frac{0.6}{1}[/tex]
Multiply numerator and denominator by 10
[tex]0.6 = \frac{0.6 * 10}{1 * 10}[/tex]
[tex]0.6 = \frac{6}{10}[/tex]
Hence, 0.6 can be represented as fraction of integers
Solve 64^x = 16^(x−1). (1 point) Select one: a. x = −2 b. x = −1 c. x = negative 1 over 4 d. x = negative 1 over 3
Answer:
a. x = -2
Step-by-step explanation:
64ˣ = 16⁽ˣ⁻¹)
64 = 4³
16 = 4²
4³⁽ˣ⁾ = 4²⁽ˣ⁻¹)
4³ˣ = 4²ˣ⁻²
3x = 2x - 2
x = -2
Answer:
[tex]\huge \boxed{x=-2}[/tex]
Step-by-step explanation:
64^x = 16^(x-1)
Rewrite the bases with base of 4.
(4^3)^x = (4^2)^(x-1)
Multiply exponents.
4^(3x) = 4^(2(x-1))
Cancel same bases.
3x = 2(x-1)
Expand brackets.
3x = 2x - 2
Subtract 2x from both sides.
x = -2
An empty suitcase has a mass of 2 kilograms draw a bar model to find its mass in grams.(1 kilogram=1000grams)
Answer:
2000 kilograms
Step-by-step explanation:
Will mark brainliest for fastest answer and right
Answer:
19
Step-by-step explanation:
10 + 9 = 19. If you look at how many students are above the "30 mark", you will count 10 on the first bar and 9 on the second.
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-10, 12) and point (5, 3) rounded to the nearest tenth?
Answer:
The answer is 17.5 unitsStep-by-step explanation:
Using the distance formula
[tex]d = \sqrt{ ({x2 - x1})^{2} + ({y2 - y1})^{2} } [/tex]the distance between (-10, 12) and (5, 3) is
[tex]d = \sqrt{ ({5 + 10})^{2} + ({3 - 12})^{2} } [/tex][tex]d = \sqrt{ {15}^{2} + ( { - 9})^{2} } [/tex][tex]d = \sqrt{225 + 81} [/tex][tex]d = \sqrt{306} [/tex][tex]d = 3 \sqrt{34} [/tex]d = 17.492855
We have the final answer as
d = 17.5 units to the nearest tenthHope this helps you
Answer:17.5
Step-by-step explanation:
According to a survey, 10% of Americans are afraid to fly. Suppose 1,100 Americans are sampled. What is the probability percentage that 121 or more Americans in the survey are afraid to fly
Answer:
0.137.
Step-by-step explanation:
Given that
Sample size = 1100
Afraid to fly = 10 %
Mean = n x p
Mean = 1100 x 0.1 = 110
Variance = n p q
Variance = 1100 x 0.1 x 0.9 = 99
Standard deviation = [tex]\sqrt{n\times p\times q}[/tex]
S.D.=[tex]\sqrt{1100\times 0.1\times 0.9}[/tex]
S.D.=9.94
By using Normal distribution
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
[tex]Z=\dfrac{121-110}{9.94}[/tex]
Z=1.16
[tex]P(X>121)=P(Z>1.16)=1-0.8643\\P(X>121)=0.137\\[/tex]
Thus the answer will be 0.137.
The answer is 4(d+14) I need that simplified? Help!!
Answer:
4d+56
Step-by-step explanation:
4(d+14) you must do distributive property to simplify this answer.
4d + 56 after distributing remove parentheses
GRIDDED RESPONSE Mark got 18 out of 25
questions correct on his science test. What percent
of the questions did he get correct?
he got 0.08 percent questions correct
Answer:
72%
Step-by-step explanation:
A percentage is a number out of 100. For example, 32/100 is 32%. What you want to do with percentages is multiply the denominator of a fraction so it becomes 100 and multiply that same number to the numerator. Sort of like a ratio!
If Mark got 18/25, we can multiply 25 by 4 to get 100 as the denominator.
Since you multiplied the denominator by 4, you have to multiply the numerator by 4 as well.
18 times 4= 72. So the numerator is 72 and the denominator is 100. The fraction is 72/100, which is 72% since it is out of 100.
Enter the number 99.4177 rounded to the nearest hundredth (two decimal places)
Answer: The number 99.4177 rounded to the nearest hundredth is 99.42.
Step-by-step explanation:
Here's how I got my answer:
Since you need to round to the nearest hundredth, then round to the first two decimal places. So if the number is 5 or greater, then round up. If the number is 4 or lesser, then do not round up.
In this scenario:
99.4177
Round the 1 in the hundredths place up to 2, because 7 is on the greater end. Since they are just asking you for the hundredths place, then do not round anything else.
Hence, your final answer is 99.42.
In the student council election, Davina received 50 votes, Binh received 40 votes and Eden received 80 votes. What is the ratio of Binh’s votes to Davina’s votes in simplest form?
Answer:
4:5
Step-by-step explanation:
Davina received 50 votes
Binh reveived 40 votes
It asked for ratio of Binh’s votes to Davina’s
so the ratio is first Binh's 40 to Davina's 50 that's 40 to 50
It want it in simplest form so you find the greatest common factor of 40 and 50 which is 10.
40/10 and 50/10 is 4 to 5
So the answer is 4:5(The ":" means "to")
The ratio of Binh’s votes to Davina’s votes is 4:5
What is ratio?The comparison of two numbers or quantities by division is known as the ratio.
Given that, In the student council election, Davina received 50 votes, Binh received 40 votes and Eden received 80 votes.
Required ratio = Binh’s votes \ Davina’s votes
= 40/50
= 4/5
Hence, The ratio of Binh’s votes to Davina’s votes is 4:5
For more references on ratios, click;
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tyler brought 7/12 pound of trail mix on a camping trip. he ate 4/12 pound of the trail mix. how much trail mix is left
Answer:
Tyler had 7/12 pound of trail mix
He ate 4/12 of it i.e
7/12-4/12=7-4/12
3/12=1/4
He has 1/4 of trial mix left
The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults, which proportion and solution represent this situation?
Answer:
X/y = 2/5
Y= x+12
Where y = students
X= adults
Number of adults= 8
Number of students= 20
Step-by-step explanation:
The ratio of adults to students on a class field trip is 2 to 5. If there are 12 more students than adults.
Let adult be x
Let student be y
X/y = 2/5
5x= 2y.... equation one
Y= x+12..... equation two
Substituting equation two into equation one
5x= 2(x+12).
5x = 2x +24
3x= 24.
X= 8
Y= x+12
Y= 8+12
Y= 20
Number of adults= 8
Number of students= 20
Please see picture attatched! Joanne wants to join a gym. As a member of the gym, Joanne must pay a registration fee as well as a monthly membership fee. The expression 24.72m + 49.95 represents the total amount Joanne pays for her registration and membership for m months. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description. please look at the picture to see full!
Joanne has to pay monthly membership fees = $24.72 per month
And registration fee = $49.95
Here,
The given expression is 24.72 m + 49.95
Joanne has to pay registration fee as well as monthly membership.
And, m denotes the number of months.
We have to explain the different part of given expression.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Now,
The given expression is ;
⇒ 24.72 m + 49.95
Joanne has to pay registration fee as well as monthly membership.
Where, m denotes the number of months.
From the expression;
⇒ 24.72 m + 49.95
We can see that,
Joanne has to pay monthly membership fees = $24.72 per month
And registration fee = $49.95
To learn more about linear expression visit:
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((4-x)/5)+((x+2)/3)=6 Please Help Soon
Answer: x = 34
Step-by-step explanation:
⁴ ⁻ˣ/₅ + ˣ + 2/₃ = 6
Now resolve into fraction and convert to a linear equation
4 - x /₅ + x + 2/₃ = 6
3( 4 -x ) + 5( x + 2 )/15 = 6
3( 4 - x ) + 5( x + 2 ) = 6 x 15
12 - 3x + 5x + 10 = 90
2x + 22 = 90
2x = 90 - 22
2x = 68
x = 34
1. Use separation of variables to find the solution to the differential equation subject to the given initial condition.
dy/dx = 5y/x, y = 4 while x = 1
2. Find the solution to the differential equation, subject to the given initial condition.
4(du/dt) = u^2, u(0) = 7
Answer:
Step-by-step explanation:
Given the differential equation dy/dx = 5y/x subject to the condition y = 4 and x = 1. Using the variable separable method of solving differential equation, we will have;
dy/dx = 5y/x
Separate the variables
dy/5y = dx/x
Integrate both sides of the expression
[tex]\frac{1}{5}\int\limits \frac{1}{y} \, dy = \int\limits \frac{dx}{x} \\ \\\frac{1}{5}lny = lnx + C\\\\lny = 5lnx+5C\\[/tex]
using the initial condition y = 4 while x = 1
ln4 = 5ln1 + 5C
ln4 = 0+5C
C = ln4/5
Substituting the value of C back into the expression;
[tex]lny = 5 lnx+5(ln4/5)\\lny = 5lnx+ln4\\lny = lnx^5+ln4\\lny = ln(4x^5)\\y = 4x^5[/tex]
Hence the solution to the differential equation is y = 4x⁵
b) Given 4(du/dt) = u²
du/dt = u²/4
du/ u² = dt/4
u⁻²du = 1/4 dt
integrate both sides of the equation
[tex]\int\limit {u^{-2}} \, du = \int\limits\frac{1}{4} \, dt\\\\\frac{u^{-1}}{-1} = \frac{t}{4} + C\\\\\frac{-1}{u} = \frac{t}{4} + C[/tex]
Imputing the initial condition u(0) = 7 i.e when t = 0, u = 7
[tex]\frac{-1}{7} = \frac{0}{4} + C\\\\\frac{-1}{7} = C\\[/tex]
[tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]
Hence the solution to the DE is [tex]\frac{-1}{u} = \frac{t}{4} - \frac{1}{7}[/tex]
The sales tax in your city is 8.8% an item costs $63 before tax how much tax would you pay on that item
Answer:
68.67
Step-by-step explanation:
Round 8.8% to 9%.
multiply 63.00*0.09=68.67
Answer:
$5.54
Step-by-step explanation:
how i found it out
63×.088=5.54
2 x + 3 y = 11 x − 3 y = 1 What is the solution ( x , y ) to the given system of equations?
Answer:
(4, 1 )
Step-by-step explanation:
Given the 2 equations
2x + 3y = 11 → (1)
x - 3y = 1 → (2)
Adding (1) and (2) term by term will eliminate the term in y
3x = 12 ( divide both sides by 3 )
x = 4
Substitute x = 4 into either of the 2 equations and evaluate for y
Substituting into (1)
2(4) + 3y = 11
8 + 3y = 11 ( subtract 8 from both sides )
3y = 3 ( divide both sides by 3 )
y = 1
Solution is (4, 1 )
Find the average rate of change of f(x) with respect to x on the interval. [tex]f(x)=x^2-4 ; [-4,3][/tex]
Answer:
The average rate of function of f on the given interval is -1.
Step-by-step explanation:
Recall that the average rate of change is simply the slope of the function between two points.
We are given the function:
[tex]f(x)=x^2-4[/tex]
And we want to find its average rate of change on the interval [-4, 3].
Evaluate the two endpoints:
[tex]\displaystyle \begin{aligned} f(-4) & = (-4)^2 - 4 \\ \\ & = 16 - 4 \\ \\ & = 12\end{aligned}[/tex]
Likewise:
[tex]\displaystyle \begin{aligned} f(3) & = (3)^2 - 4 \\ \\ & = 9 - 4 \\ \\ & = 5\end{aligned}[/tex]
Recall that slope is given by:
[tex]\displaystyle m = \frac{\Delta y}{\Delta x}[/tex]
Hence, the average rate of change is:
[tex]\displaystyle\begin{aligned} \text{Avg Rate of Change} & = \frac{(5)-(12)}{(3)-(-4)} \\ \\ &= \frac{-7}{7} \\ \\ & = -1\end{aligned}[/tex]
In conclusion, the average rate of function of the given function on the given interval is -
Can please someone help me with this calculus problem? Thanks! ∫(4x-6)(x²-3x+1)^5 dx
Looks like the integral is
[tex]I=\displaystyle\int (4x-6)(x^2-3x+1)^5\,\mathrm dx[/tex]
If you we substitute [tex]y=x^2-3x+1[/tex] and [tex]\mathrm dy=(2x-3)\,\mathrm dx[/tex], we get
[tex]I=\displaystyle2\int(2x-3)(x^2-3x+1)^5\,\mathrm dx=2\int y^5\,\mathrm dy[/tex]
Now use the power rule, and replace y accordingly:
[tex]I=\dfrac{2y^6}6+C=\dfrac{y^6}3+C=\boxed{\dfrac{(x^2-3x+1)^5}3+C}[/tex]
Express as a trinomial (2x+8)(x-3)
Answer:
[tex]\huge\boxed{(2x+8)(x-3)=2x^2+2x-24}[/tex]
Step-by-step explanation:
[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(2x+8)(x-3)=(2x)(x)+(2x)(-3)+(8)(x)+(8)(-3)\\\\=2x^2-6x+8x-24\qquad\text{combine like terms}\\\\=2x^2+(-6x+8x)-24\\\\=2x^2+2x-24[/tex]
Answer:
2x^2+2x-24
Step-by-step explanation:
when you see two parentheses, you should first think : FOIL!
you take the First terms in each of the parentheses which is 2x and x and multiply them. (2x^2)
then you take the Outer terms in the parenthesis which is 2x and -3 and multiply them. (-6x)
then you take the Inside terms which is +8 and x and multiply them. (+8x)
lastly, you take the Last terms which is +8 and -3 and multiply them. (-24)
you should get this : 2x^2-6x+8x-24. combine like terms and there's your answer!
i also advise you to write down all your terms until you are familiar with this foil stuff. don't be ashamed if you need to write them down! you'll get the hang of it! :)
what number goes on top
I'm not sure what you're really talking about.
But I think you are talking about fractions.
In fractions there are two places
The number that goes on the top is numerator.
Solve for non extraneous solution and show work/check please help i need help asap! Please no fake answers ___ 1√x+2+2=6
Answer:
x=14
Step-by-step explanation:
1[tex]\sqrt{x+2}[/tex] +2 = 6 --------------- put nums on 1 side
1[tex]\sqrt{x+2}[/tex] = 4 -------------------by the way, 1
[tex]\sqrt{x+2}[/tex] =4 ------------- square both sides
x+2 = 16 --------------- subtract 2 from both sides
x = 14
Find the area of the surface generated by revolving x equals t plus StartRoot 2 EndRoot, y equals StartFraction t squared Over 2 EndFraction plus StartRoot 2 EndRoot t plus 3 , negative StartRoot 2 EndRoot less than or equals t less than or equals StartRoot 2 EndRoot about the y dash axis. The surface area obtained by revolving the given curve around the y dash axis is
What is the solution to X-7 less than or equal to -4
Answer:
x ≤ 3
we have to transpose -7 from left to right
-6n-2n=16
What are all the steps
Answer:
n = 2
Step-by-step explanation:
- 6n - 2n = 16
- 8n = 16
n = 16/-8
n = -2
Answer:
[tex] - 6n \: - 2n \: = 16[/tex]
[tex] = ) - 8n \: = 16[/tex]
[tex] = )n \: = \frac{16}{ - 8} [/tex]
[tex] = )n \: = - 2[/tex]
PLEASE HELP find distance between points
Step-by-step explanation:
To find the distance between two points, we have to use the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
Let's solve for line PQ first. We plug in the points into the formula and solve from there.
P: (-5, 1)
Q: (-2, -5)
[tex]PQ=\sqrt{(-2+5)^2+(-5-1)^2 }[/tex]
[tex]PQ=\sqrt{(3)^2+(-6)^2 }[/tex]
[tex]PQ=\sqrt{9+36}[/tex]
[tex]PQ=\sqrt{45}[/tex]
[tex]PQ=3\sqrt{5}[/tex]
Now, let's solve line ML.
M: (5, 3)
L: (2, -3)
[tex]ML=\sqrt{(2-5)^2+(-3-3)^2 }[/tex]
[tex]ML=\sqrt{(-3)^2+(-6)^2}[/tex]
[tex]ML=\sqrt{9+36}[/tex]
[tex]ML=\sqrt{45}[/tex]
[tex]ML=3\sqrt{5}[/tex]
Answer: 3√5, 3√5, yes, they are congruent.
The stem-and-leaf plot below displays the ages of 30 attorneys at a small law firm.
Stems Attorneys
4 99
5 00112589
6 1234458
7 1233458
8 0137
9 12
What is the age of the oldest attorney? What is the age of the youngest attorney?
A. The oldest attorney is 102 years old. The youngest attorney is 31 years old.
B. The oldest attorney is 91 years old. The youngest attorney is 48 years old.
C. The oldest attorney is 82 years old. The youngest attorney is 59 years old.
D. The oldest attorney is 92 years old. The youngest attorney is 49 years old.
Answer:
D. The oldest is 92 youngest 49
Step-by-step explanation:
we can get the answer by pairing each of the values on the left hand side that is these values 4 5 6 7 9 with values on the right.
the first age from the top row is 49 the second is 49
from the second row it is 50 50 51 51 52 5 59
from the 3rd row 61 62 63 64 64 65 6
from the forth row t s 71 72 73 73 74 75 7
from the fifth row it is 80 81 83 87
from the sxth row it is 91 92.
each of the numbers have just written out represents age. the oldest age there is 92 whle the youngest s 49. It is simply each number under attorney paired wth stem to make a number.
I added an attachment with the pairing
what is the mathmatical property of 7+(5-8)=(7+5)-8 out of Communicative and assoiative propetys and the other 2
Answer:
This demonstrates the associative property of addition which states that a + (b + c) = (a + b) + c. Basically, it states that it doesn't matter which order you add numbers in, you will always get the same result.
Given that 2^x = 7, find the value of 4^{x-1}.
Answer:
[tex] {4}^{x - 1} = \frac{49}{4} [/tex]
Step-by-step explanation:
My work is in the attachment but I essentially used a hefty bit of Algebraic manipulation to turn 2^x into 4^(x-1) and then isolating that bit.
Comment if you have any questions.
Answer:
49/4
Step-by-step explanation:
4^x-1 = (2^x)^2/4 = 7^2/4 = 49/4
square root (2x)^8 simplified
Answer:
256x^8
Step-by-step explanation:
Convert the following angle to decimal degrees.
a=274° 33' 23"
Answer:
274.556 degrees to the nearest thousandth.
Step-by-step explanation:
33 ' = 33/60 = 0.55 degrees.
23" = 23/60 minutes
= 23/60 / 60 = 0.00639 degrees
So the answer is 274 + 0.55 + 0.00639 degrees
=
274.55639 degrees.