Answer:
3 a^(-2)
3 / a^2
Step-by-step explanation:
(3a) (a^-3)
Multiply
3 a^1 * a^-3
Since we are multiplying, we add the exponents
3 a^ ( 1-3)
3 a^(-2)
If you are not supposed to leave a negative exponent
x^-b = 1 / x^b
3 / a^2
Margaret is going to paint a wall that 'is 8 feet high and 15 feet long. How many square feet will she be covering with paint?
Answer:
120 ft²
Step-by-step explanation:
the question is asking for the area of the wall, which we have been given.
8 ft high by 15 ft wide.
Area of a rectangle is length multiplied by breadth.
so, the area is 8 * 15 = 120 ft²
What is the equation of the line that passes through the points (- 2, 3) and (4, 1)
Answer:
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = ((- 2, 3) and (x₂, y₂ ) = (4, 1)
m = [tex]\frac{1-3}{4+2}[/tex] = [tex]\frac{-2}{6}[/tex] = - [tex]\frac{1}{3}[/tex] , thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 2, 3), then
3 = [tex]\frac{2}{3}[/tex] + c ⇒ c = 3 - [tex]\frac{2}{3}[/tex] = [tex]\frac{7}{3}[/tex]
y = - [tex]\frac{1}{3}[/tex] x + [tex]\frac{7}{3}[/tex] ← equation of line
Is (1,9) a solution to this system of
equations?
y = x + 6
y = 2x + 7?
Answer:
No, the solution of the system is (-1,5)
Solve a combined inequality that is a conjunction of two linear equalities.
1.) solve for n. -1<9+n<17
2.) solve for x. -2<8x-12<_36
Answer:
-10 < n < 85/4 < x ≤ 6Step-by-step explanation:
1. Subtract 9:
-10 < n < 8
__
2. Add 12, then divide by 8:
10 < 8x ≤ 48
10/8 < x ≤ 6
5/4 < x ≤ 6 . . . . . with the fraction reduced
_____
The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...
-1 -9 < 9 +n -9 < 17 -9
This simplifies to the inequality we show above:
-10 < n < 8
Brainliests offered whoever answer my question.
1: find the value of 8 4s. It’s not 84 but it’s 8 and then at the top it’s 4.
2: a mug is 1/7 full. The mug contains 1/3 of a cup of water. Find the capacity of the mug. Write the answer a fraction or mixed number in simplest form.
Problem 1
If you meant to say [tex]8^4[/tex], then you would have four copies of 8 multiplied together
[tex]8^4 = 8*8*8*8 = 4096[/tex]
==============================================
Problem 2
1/7 full = 1/3 cup of water
7*(1/7 full) = 7*(1/3 cup of water) ... multiply both sides by 7
1 full = 7/3 cup of water
So a full mug has 7/3 cups of water. Let's convert this to a mixed number
7/3 = (6+1)/3
7/3 = 6/3 + 1/3
7/3 = 2 + (1/3)
7/3 = 2 & 1/3
The full capacity of the cup is 7/3 cups or 2 & 1/3 cups
7/3 is the improper fraction form
2 & 1/3 is the mixed number form
One way to think of it is to imagine there are 7 cookies and you want to distribute among 3 friends. We could say 7/3 = 2 remainder 1 meaning each person gets 2 full cookies and there's 1 left over. So that's how we'd get 2 & 1/3.
The number 0.2 can be written as 2/10, so is it a rational number?
Answer:
yes it is
Step-by-step explanation:
Hope this helps✨
A woman making $3000 per month has her salary reduced by 20% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise. $ per month What percent change is this from the $3000 per month? %
Answer:
4%
Step-by-step explanation:
Since she first goes down 20% you would do 3000 times 20 which is 60000 and divided by 100 which is 600 and you would subtract 600 from 3000 which is 2400 and then you would multiply that by 30 which is 72000 and then you would divide by 100 which is 720 and add that to 2400 which is 3120 and to find the percent change from 3000 to 3120 you would subtract 3120 by 3000 which is 120 and you would divide that by 3000 which is 0.04 and multiply that by 100 which is 4 so the percent change would be 4%
Please help me with the question below
If the numbers are consecutive multiples of 6, and you want to call the smallest one ' n ', then the next one is (n+6) and the biggest one is (n+12).
Their sum is (3n + 18). That's choice-C .
If you run into the same problem again, you might like to call the middle number ' n '. Then the smallest one is (n-6) and the biggest one is (n+6),
and their sum is just 3n ! This is a lot easier to do in your head.
Total Price: The sales tax rate is 8%. If the sales tax on a 10-speed bicycle is $12, what is the purchase price? The purchase price is $ What is the total price? The total price is $ Get Help: Video eBook Points possible: 1
Answer:
Purchase Price = $150 and Total Price = $162
Step-by-step explanation:
Purchase price = Tax Amount / Tax Percentage (as decimal)
Purchase Price = $12 / .08
Purchase Price = $150
Total Price = Purchase Price + Tax
Total Price = 150 + 12 = $162
I hope this helps!
-The Business Man
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $28 monthly fee and charges an additional
$0.09 for each minute of calls. The second plan has no monthly fee but charges $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answer:
700 Minutes
Step-by-step explanation:
For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.
For the first phone plan, we have a base $28 and additional $0.09 per minute of call. This can be expressed as:
28 + 0.09x Where x is the number of minutes used
For the second phone plan, we have a flat $0.13 per minute of call. This can be expressed as:
0.13x Where x is the number of minutes used
To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.
28 + 0.09x = 0.13x
28 + 0.09x + -0.09x = 0.13x + -0.09x
28 = 0.04x
28 = (1/25)x
28 * 25 = (1/25)x * 25
28 * 25 = x
700 = x
Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.
Cheers.
2. Metcalf School has two third-grade rooms (A and B) and two fourth-grade rooms
(C and D). Together, rooms C and D have 46 students. Room A has 6 more students
than room D. Room B has 2 fewer students than room C. Room D has 22 students.
How many students are there altogether in rooms A and B?
Answer: 50 students
Step-by-step explanation: Room D has 22 students, so room A has 28 (22+6). If room D has 22 students, then room C has 24 students (46-22). Room B has 22 students (26-2). In total, rooms A and B will have 50 students (28+22)
Which number sentence shows the correct placement of the decimal point in the product based on the two factors A: 3.48 x 42.37 = 147.4476 B: 23.2 x 8.8 = 20.416 C: 0.39 x 7.2 = 28.08 D: 43.72 x 9.2 = 4,022.24 I NEED ANSWERS ASAP
Answer:
A
Step-by-step explanation:
Add the number of decimal places of the two numbers being multiplied to know the number of decimal places of the product.
A: 3.48 x 42.37 = 147.4476
2 decimal places + 2 decimal places = 4 decimal places
Only choice A is correct.
If y = 3. what is 6y?
Your question has been heard loud and clear.
If y = 3 , then 6y = 6(3) = 18
Thank you
iff(x) = (x - 3)2
for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3
Answer:
Option B. √x + 3
Step-by-step explanation:
f(x) = (x - 3)²
We can obtain the inverse f¯¹(x) of the above expression as follow:
f(x) = (x - 3)²
Replace f(x) with
f(x) = (x - 3)²
y = (x - 3)²
Next, interchange x and y
y = (x - 3)²
x = (y - 3)²
Make y the subject
x = (y - 3)²
Take the square root of both side
√x = y - 3
Add 3 to both side
√x + 3 = y - 3 +3
√x + 3 = y
y = √x + 3
Finally, replace y with f¯¹(x)
y = √x + 3
f¯¹(x) = √x + 3
Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.) Determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
No singular point due to the exponent in the solution
The interval is [tex]-\infty <0 < \infty[/tex]
b
NONE
Step-by-step explanation:
From the question we are told that
[tex]\frac{dy}{dx} = 9y[/tex]
The generally solution is mathematically represented as
[tex]\frac{dy }{dx} = 9y[/tex]
=> [tex]\frac{dy}{y} = 9dx[/tex]
integrating both sides
[tex]\int\limits {\frac{ dy}{y} } \, = \int\limits {9} \, dx[/tex]
=> [tex]lny = 9x + c[/tex]
=> [tex]y = e^{9x +c }[/tex]
=> [tex]y = e^{9x} e^{c}[/tex]
Here [tex]e^c = C[/tex]
=> [tex]y = C e^{9x}[/tex]
From the above equation we see that the domain for x has no singular point the interval is
[tex]-\infty <0 < \infty[/tex]
Also there is no transient term in the general solution obtained because as [tex]x \to \infty[/tex] there no case where [tex]y \to 0[/tex]
Merlyn had 22 magic tricks to perform. He had completed 4/5 of them when the fire alarm sounded. How many magic tricks had he performed?
Answer:
Merlyn realizo 17,6 trucos de magia
Step-by-step explanatio:
Hizo 17,6 trucos de magia porque 22 dividido 5 es igual a 4,4 entonces despues haces 22 menos 4,4 da 17,6
why is 5.1 a rational number
Answer:
5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number
Step-by-step explanation:
Recall that a rational number is a number that can be written as the quotient of two integer numbers.
In particular the number 5.1 can be written as 51/10 (the quotient of the integers 51 and 10. So it is a rational number.
In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.
a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )
b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.
c. How would the manager of a chain of restaurants use the results of (a) and (b)?
Answer:
a
[tex]0.716 < p < 0.744[/tex]
b
[tex]0.3498 < p < 0.4089[/tex]
c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1003[/tex]
The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]
The number that complained about loud or distracting diners at other tables is [tex]q = 381[/tex]
Given that the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
The sample proportion is mathematically represented as
[tex]\r p = \frac{e}{n}[/tex]
=> [tex]\r p = \frac{732}{1003}[/tex]
=> [tex]\r p = 0.73[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]
[tex]E = 0.01402[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]
[tex]0.716 < p < 0.744[/tex]
Considering question b
The sample proportion is mathematically represented as
[tex]\r p = \frac{q}{n}[/tex]
=> [tex]\r p = \frac{381}{1003}[/tex]
=> [tex]\r p = 0.3799[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]
[tex]E = 0.0300[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]
[tex]0.3498 < p < 0.4089[/tex]
Which is bigger 2.0 or 2
Answer:
both are the same
Step-by-step explanation:
2.0 = 2
hope this helps ^-^
Answer:
Both will be equal as 2.0 can also be written as 2
How to find out if a number is transcendental?
Answer:
A transcendental number is a real number that is not the solution of any single-variable polynomial equation whose coefficients are all integers . All transcendental numbers are irrational numbers . But the converse is not true; there are some irrational numbers that are not transcendental.
Step-by-step explanation:
Solve for y.
2y - x = 3/4 (-y +1 )
Answer:
kyskyskyskyskyskyskys
A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.
Answer: yes
Step-by-step explanation: 8^2+15^2=17^2 =289 and 17^2=289 ... 17 is the largest number so therefore its the largest side(c) .
equation- a+b=c
Solve the following linear equation. If a x is a fraction write as follows
-4/5
-6x+3=-21
X =
Answer:
x-5
Step-by-step explanation:
x=5
cause of the negt 6x and posstive 3 =21 so yeah that it for now so go for it head froce
Consider the following time series: t12345 6 11 9 14 15 a. Construct a time series plot. What type of pattern exists in the data
Answer:
Kindly check explanation and attached picture
Step-by-step explanation:
Given the time-series data:
Time (x) : 1 - - 2 - - 3 - - - 4 - - - 5
Data (yt) :6 - - 11 - - 9 - - 14 - - 15
The pattern which exists within the data is a linear pattern which could be inferred through the observable decrement and Incremental change in the y values at a steady or constant rate with time. The second attachment shows the linear trend line of the data.
What is the standard form equation of the line shown below?
5
4
3
2 +
o
+ +
3 4
2
5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-6
The Tigers had twice as many hits as the yanks.Let x= number of hits by yanks.Then ?= number of hits by tigers
Answer:
2x
Step-by-step explanation:
Since the tigers hit 2 times the number of x you would get that the tigers hit 2 times x or 2x balls
Answer:
2x.
hope it helps u...
plz mark as brainliest...
What’s is 2000+100.000
Answer:
2,100.000
Step-by-step explanation:
Answer:
2000+100.000=2100
Its simple just calculate it in a calculator...
A right angle intersects a line at point M
Answer:
where is the graph
Step-by-step explanation:
Answer:
Step-by-step explanation:
Here is the picture
The average cost of a scientific calculator was $96.50 in 1970. The same type of calculator cost $21 in 2016. Assuming the exponential decay model applies, what will a similar calculator cost in the year 2019? Round your answer tbo the nearest cent.
Answer: the cost of a similar scientific calculate in 2019 will be $19.01
Step-by-step explanation:
Given that;
in 1970 cost of S.C = $96.50
in 2016 cost of same calculator = $21
In 2019 cost of a similar calculator = ?
Assuming the exponential decay model applies
dN/dt = -λN
we know that λ is the decay constant
⇒ N(t) = N₀e^-λt
N(t) is price at time t year, N₀ is initial price,
so t = 0 in 1970 thus N₀ = 96.50
also t = 46 in 2016 thus N₄₆ = 21
substituting into our initial expression
N(t) = N₀e^-λt
N(46) = N₀e^-λ×46
21 = 96.50e^-46λ ⇒ In 21/96.50 = -46λ
= -1.5250 = - 46λ
λ = -1.5250 / -46
λ = 0.03315
t = 0 in 1970 thus N₀ = 96.50
also t = 49 in 2019 thus N₄₉ = ?
so
using our initial expression again
N(49) = N₀ e^-49λ
= 96.5 × e^ (-49 × 0.03315 )
= 96.5 × 0.197014404
= 19.01189 ≈ 19.01
therefore the cost of a similar scientific calculate in 2019 will be $19.01
Complete the table shown below. f(x) = 2x2 - 8x + 6 1 0 2 y 3 4. 6 X= y = Z
Answer:
x = 6, y = -2, z = 0
Step-by-step explanation:
To find x, we have to plug 0 into f(x). Therefore, x = f(0) = 2 * 0² - 8 * 0 + 6 = 6. Similarly, to find y, we have to plug 2 into f(x) so y = f(2) = 2 * 2² - 8 * 2 + 6 = -2. Finally, z = f(3) = 2 * 3² - 8 * 3 + 6 = 0.
Answer:
6, -2, 0
Step-by-step explanation: