We know that there are about 3.785 liters in 1 gallon. From here we could pour 3 whole liters into a one-gallon container without overflowing since 3 < 3.285 liters. But if we try to pour the next whole liter( 4 liters) it would be too much since 4 is greater then 3.785 liters. So the answer is 3 liters.
Hope this helps. <3
What is the sign of − 4 a b −4ab when a > 0 a>0 and b < 0 b<0?
Answer:
The sign is positive.
Step-by-step explanation:
a > 0 and b < 0
So, a·b < 0
⇒ -4·a·b > 0
⇒ -4·a·b - 4·a·b > 0
Hence, the sign will be positive
Answer:
the answer is on top of me
Step-by-step explanation:
my mom is angry at me and im bored
Mantago wants to borrow $20,000 to buy a used car. He examined his budget and decides that he can afford a payment of $425 a month. If his bank offers him an APR of 7.5%, how long should he borrow the money so he can afford his monthly payment?
3.5 years
4.66 years
4.5 years
4 years
Answer:
4.66 years
Step-by-step explanation:
Let us assume that it will take 't' years for him to repay the money that he would borrow.
We can use monthly cashflow formula:
[tex]C=Pr\frac{(1+r)^{12t}}{(1+r)^{12t}-1}[/tex]
Here, we have been given:
Monthly cashflow C=425
Loan amount P=20000
Interest rate AMR = 7.5%. Therefore, we have [tex]r=\frac{0.075}{12}[/tex]
Upon substituting these values in the formula, we get:
[tex]425=20000\cdot \frac{0.075}{12} \frac{(1+\frac{0.075}{12})^{12t}}{(1+\frac{0.075}{12})^{12t}-1}[/tex]
Upon simplifying, we get:
[tex]425=125 \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t}-1}[/tex]
[tex]425=125 \frac{(1.00625)^{12t}}{(1.00625)^{12t}-1}[/tex]
Upon solving this equation using a calculator, we get:
[tex]t=4.66[/tex]
Therefore, correct answer is 4.66 years. That is, second choice from the given options.
Sienna published 2/3 of the poems she wrote in a book. Additionally, published 4 different poems in a newspaper. The total numbers of poems she published was 22. How many poems had sienna written?
Answer:
Subtract the 4 additional poems from what was published first:
22 - 4 = 18
Now 18 is 2/3 of what she wrote.
To find the total poems written divide 18 by 2/3:
18 / 2/3 = 27
Sh wrote 27 poems total.
Please answer this question
Answer:
The average rate is 35 miles per hour
Step-by-step explanation:
To get from town A to town B takes 3 hours. The distance is 100 miles
To get from town B to town c takes 1 hours. The distance is 40 miles
To find the average rate , we need to find the total distance and divide by the total time
Total distance = 100 + 40 = 140 miles
Total time = 3 hrs + 1 hr = 4 hours
distance = rate * time
140 miles = rate * 4 hours
140/4 = rate
35 = rate
The average rate is 35 miles per hour
what is the simplified form of 15x^5/20y^6*6y^4/5x^2
Answer:
The simplified form of the equation is 9x^3/10y^2 Good Luck!
Step-by-step explanation:
Answer:
if you go to a site called math papa it gives you the answer and how to do it
Step-by-step explanation:
If triangle ABC is similar WXY write a proportionality statement for the ratio of the sides of the triangle
There are many ways to answer this. Here is one answer shown below
AB/WX = BC/XY
On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.
On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.
It might help to line up ABC over top WXY so you can pick out the corresponding sides. I show this in the attached image below.
Answer: There are many ways to answer this.
Step-by-step explanation:
On the left side is the ratio of AB over WX. These two sides are the bottom horizontal portions of the triangles. This is a visual indication that they correspond to one another. More concrete proof of this is that AB and WX are the first two letters of the sequences ABC and WXY respectively. The order is very important to help establish pairs like this.
On the right side of that equation above, we have BC and XY as the diagonal sides on the right part of each triangle. They are the last two letters of ABC and WXY respectively, which is a non-visual way to prove these two sides correspond.
what is the area of the piece of red paper after the hole for the photograph has been cut
Answer:
47 squared units.
Step-by-step explanation:
Solve for x.
Enter your answer in the box.
An equilateral triangle A B C. Side B C is the base. Sides A B, B C, and A C are equal. Sides A B, B C, and A C are labeled with single tick marks. Angle A is labeled as left parenthesis 2 y right parenthesis degrees, angle B is labeled left parenthesis 25 x minus 15 right parenthesis degrees.
Answer:
3
Step-by-step explanation:
The salaries of the employees at four companies are summarized below. Answer the questions about them.
Answer:
Range = 24
Step-by-step explanation:
Record of percentage
59, 61, 83, 67, 81, 80, 81
We need to find the range
To find the range , we order the numbers from smallest to largest.
Then Subtract the smallest number from largest number.
When we arrange the numbers it becomes
59, 61, 67, 80, 81, 81, 83
Smallest number is 59 and largest number is 83
Range = 83 - 59 =24
HELP ME WITH THIS AND ILL GIVE YOU BRAINLIST!!!! <3
Answer:
9+8 = 8+991+0 = 91.Step-by-step explanation:
Given expression 9+8.
We need to rewrite it using Commutative Property.
Note: According to Commutative Property of Addition
a + b = b + a
Therefore,
9+8 = 8+9We just need to swap the positions of numbers.
Second expression : 91+0
We need to rewrite it using Identity.
According to Identity property of addition
a+0 = a.
When we add 0 to any number it gives same number.
Therefore,
91+0 = 91.Twenty-five subtracted from one-half a number is 10.What is the number?
Final answer:
The number in question is 70, found by solving the equation 1/2 * x - 25 = 10.
Explanation:
To find a number where half of that number, subtracted by 25, equals 10. We can set up an equation to represent this: 1/2 * x - 25 = 10, where 'x' is the number we are trying to find. To solve for 'x', we first add 25 to both sides of the equation, which gives us 1/2 * x = 35. Then, to isolate 'x', we multiply both sides by 2, resulting in x = 70. Therefore, the number is 70.
Final answer:
To find the number, isolate the variable by performing inverse operations. The number is 70.
Explanation:
To find the number, we need to translate the given information into an equation. Let's assume the number is x. The equation can be written as:
1/2x - 25 = 10.
To isolate the variable x, we first add 25 to both sides of the equation:
1/2x - 25 + 25 = 10 + 25.
This simplifies to 1/2x = 35.
Next, we multiply both sides of the equation by 2 to undo the division by
1/2: 2 × (1/2x) = 2 × 35.
The 1/2 cancels out on the left side, leaving us with x = 70.
Therefore, the number is 70.
a store has apples on sale for $3.00 on two pounds . how many pounds of apples can you buy for $9 if an apple is approximately 5 ounces how many apples can you buy for $9 explain your reasoning
Answer: You can get 6 pounds of apples and approximately 19 apples.
Step-by-step explanation:
There are 16 ounces per pound so 6 pounds is 96 ounces
96/5 = 19.2
You can buy 6 pounds of apples for 9, which is approximately 19 apples.
1. First, let's find out how much one pound of apples costs. Since two pounds cost $3.00, one pound would cost half of that, which is $1.50.
2. Now, if one pound costs $1.50, we can find out how many pounds of apples you can buy for $9 by dividing $9 by the cost per pound: [tex]\( \frac{9}{1.50} = 6 \)[/tex]. So, you can buy 6 pounds of apples for $9.
3. Since 1 pound equals 16 ounces, 6 pounds equal [tex]\( 6 \times 16 = 96 \)[/tex]ounces.
4. If one apple is approximately 5 ounces, then the number of apples you can buy for 96 ounces is [tex]\( \frac{96}{5} \).[/tex]
5. Performing the division, [tex]\( \frac{96}{5} = 19.2 \)[/tex]. Since you can't buy a fraction of an apple, you'd round down to the nearest whole number.
6. So, you can buy approximately 19 apples for $9.
Here's the calculation step by step:
1. Cost per pound: [tex]\( \frac{3.00}{2} = 1.50 \)[/tex] dollars per pound.
2. Pounds you can buy for $9: [tex]\( \frac{9}{1.50} = 6 \)[/tex] pounds.
3. Total ounces: [tex]\( 6 \times 16 = 96 \)[/tex] ounces.
4. Apples you can buy: [tex]\( \frac{96}{5} = 19.2 \)[/tex](rounded down to 19 apples).
[CALCULUS] [HELP PLEASE]
7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.
0.6%
0.9%
1.2%
1.5%
1.8%
A point on a damped spring has motion given by s(t)=2e^(-1.5t) s in(2(pi)t), where s is measured in centimeters and t is measured in seconds. Choose which of these is the graph for the velocity function for 0 < or equal to t < or equal to 4
Answer:
(7)
error percentage is 0.6%
(8)
Graph-C
Step-by-step explanation:
(7)
we are given cube
Let's assume edge of cube =x
so, volume of cube will be
[tex]V(x)=x^3[/tex]
we are given
V=125000
so, we can find 'x'
[tex]125000=x^3[/tex]
[tex]x=50[/tex]
So,
[tex]a=50[/tex]
now, we can use linear approximation formula
[tex]L(x)=V(a)+(x-a)V'(a)[/tex]
[tex]L(x)=V(a)+(\Delta x)V'(a)[/tex]
we have
[tex]\Delta x=0.1[/tex]
we can plug a=50
[tex]L(x)=V(50)+(0.1)V'(50)[/tex]
[tex]V(x)=x^3[/tex]
we can find derivative
[tex]V'(x)=3x^2[/tex]
now, we can plug x=50
[tex]V'(50)=3(50)^2[/tex]
[tex]V'(50)=7500[/tex]
now, we can plug these values
and we get
[tex]L(x)=V(50)+(0.1)\times 7500[/tex]
[tex]L(x)=V(50)+750[/tex]
[tex]L(x)-V(50)=750[/tex]
so, error is
[tex]error=750[/tex]
now, we can find percentage error
Percentage is
[tex]=\frac{750}{125000}\times 100[/tex]
=0.6%
so, error percentage is 0.6%
(8)
we are given
[tex]s(t)=2e^{-1.5t}sin(2\pi t)[/tex]
We will find derivative
To get velocity , we will find derivative
[tex]s'(t)=\frac{d}{dt}\left(2e^{-1.5t}\sin \left(2\pi t\right)\right)[/tex]
we can use product rule
and we get
[tex]s'(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
so, we get velocity equation as
[tex]v(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
now, we can draw graph
we can see that firstly , we get maxima and then minima
so, our graph would be
graph-C........Answer
Final answer:
To estimate the percentage error in volume, use the tangent line approximation and find the derivative of the volume function. Then divide the change in volume by the actual volume and multiply by 100%.
Explanation:
To estimate the percentage error in volume, we need to find the derivative of the volume function with respect to the length of one edge of the cube. The volume of a cube is given by V = a^3, where a is the length of one edge of the cube. So, the volume function is V = a^3.
Using the tangent line approximation, we can approximate the change in volume as the derivative of the volume function multiplied by the change in length of one edge of the cube. The derivative of the volume function is dV/da = 3a^2. The change in length of one edge is ±0.1 cm. So, the change in volume is approximately dV = (3a^2) * (±0.1 cm).
To find the percentage error in volume, we divide the change in volume by the actual volume and multiply by 100%. The actual volume is 125,000 cm^3. So, the percentage error in volume is approximately [(3a^2) * (±0.1 cm)] / (125,000 cm^3) * 100%.
a jar contains 10 marbles six marbles are red and four marbles are blue if two marbles are chosen one at a time with replacement what is the probability that both marbles will be red
Answer:
30%
Step-by-step explanation:
there is a 60% chance of getting a red marble each time. You need to choose a ball twice. 60/2=30. therefore there is a 30% chance of getting two reds.
Final answer:
To find the probability of drawing two red marbles with replacement from a jar of six red and four blue marbles, we multiply the probability of drawing a red marble (3/5) by itself, resulting in 9/25.
Explanation:
The question asks for the probability that both marbles will be red when two marbles are chosen one at a time with replacement from a jar containing six red marbles and four blue marbles.
To find this, we calculate the probability of drawing a red marble, and since we replace the marble each time, this probability does not change with each draw. With six red marbles out of a total of 10, the probability of drawing a red marble on the first draw is 6/10 or 3/5. Since we replace the marble after each draw, the probability remains the same for the second draw.
Therefore, the probability of drawing two red marbles in a row is (3/5) * (3/5), which is 9/25.
evaluate the expression for a=3 and b=10 70/b +5a -2b
Answer:
2
Step-by-step explanation:
evaluate from left to right, substituting the given values into the expression
= [tex]\frac{70}{10}[/tex] + (5 × 3) - (2 × 10)
= 7 + 15 - 20
= 22 - 20
= 2
Substitute the values of a and b to the expression:
[tex]a=3,\ b=10\\\\\dfrac{70}{b}+5a-2b=\dfrac{70}{10}+(5)(3)-(2)(10)\\\\=7+15-20=22-20=\boxed2[/tex]
Identify the constant of proportionality in the equation. 3y = 15x
Answer:
5
Step-by-step explanation:
For direct variation y=kx, where k is the constant of proportionality
We need to get the equation in this form
3y = 15x
Divide each side by 3
3y/3 =15x/3
y = 5x
The constant is 5
The junior class at Central High School has 182 students. The debate club at the school has 14 members who are in the junior class. How many students in the junior class are not on the debate team?
a.13
b.42
c.168
d.178
Answer:
13
Step-by-step explanation:
I believe you would take the number of students and divide by the number of members
Which two values of x are roots of the polynomial below?
Answers: choice A, choice C
Compute the discriminant (use a = 1, b = 5, c = 11)
D = b^2 - 4ac
D = 5^2 - 4*1*11
D = 25 - 44
D = -19
The discriminant is negative, so the two solutions are complex or imaginary. The -19 will be under the root as choice A and choice C show
The graph of g(x) is the graph of f(x)=|x| translated 3 units to the left. What is the equation of g(x)?
Answer:
g(x) = |x + 3|
Step-by-step explanation:
The x is replaced by x + 3
The equation of g(x) is | x + 3 | when g ( x ) is translated 3 units to the left
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)
Horizontal shift (also called phase shift):
Left shift by c units: y = f( x + c ) (same output, but c units earlier) Right shift by c units: y = f ( x - c ) (same output, but c units late)Given data ,
The function f(x) = | x | , this function is needed to be translated 3 units to the right. Therefore, the new function can be written as ,
g ( x ) = f ( x + 3 )
= | x + 3 |
Hence, the equation of g(x) is | x + 3 |.
To learn more about transformation of a function click :
https://brainly.com/question/18220829
#SPJ2
Solve for a. a/g - f = D
Answer:
a = (D+f) * g
Step-by-step explanation:
We want to isolate a
a/g -f =D
Add f to each side
a/g -f+f = D+f
a/g = D+f
Multiply each side by g
a/g *g = (D+f) * g
a = (D+f) * g
[tex]\dfrac{a}{g}-f=D\qquad\text{add f to both sides}\\\\\dfrac{a}{g}=D+f\qquad\text{multiply both sides by }\ g\neq0\\\\\boxed{a=g(D+f)}\qquad\text{use distributive property}\\\\\boxed{a=Dg+fg}[/tex]
bring the fraction: 8/3xy^ 2 to a denominator of 15x^2y^2
If u do dis i really appreciate it!!!!!!!!! thx
Answer:
40x/(15x²y²)
Step-by-step explanation:
8/(3xy²) Multiply by 5/5
= 40/(15xy²) Multiply by x/x
= 40x/(15x²y²)
11 chocolate bars cost 10 dollars
I'm not sure what you're trying to ask, but if you're trying to find the individual cost;
Solution: Cost of 1 candy bar is $0.91
Explanation: The quotient of 10 and 11 is 0.90909090909, which rounds into 0.91
Hope This Helps!!!
-Austint1414
One chocolate bar costs approximately 0.91 dollars.
How much does one chocolate bar cost?Let x be the cost of one chocolate bar.
Given that 11 chocolate bars cost 10 dollars, we set up a proportion:
11 bars / 10 dollars = 1 bar / x dollars
To get cost of one chocolate bar (x), we cross-multiply:
11 * x = 10 * 1
11x = 10
x = 10 / 11
x ≈ 0.91 dollars.
Read more about Cost
brainly.com/question/28147009
#SPJ2
Full question:
11 chocolate bars cost 10 dollars. How much does 1 chocolate bars cost?
what are the first 4 items of the arithmetic sequence in the graph
Answer:
i dont know
Step-by-step explanation:
What shape is a four-sided polygon with 4 right angles and at least 2 equal sides?
1. rectangle
2. diamond
3. square
4. triangle
wich one is correct?
Answer:
the answer is rectangle
Step-by-step explanation:
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n) = 5 + (n-1)(1/6)
[tex]A(n)=5+(n-1)\left(\dfrac{1}{6}\right)=5+\dfrac{1}{6}n-\dfrac{1}{6}=\dfrac{1}{6}n+\dfrac{30}{6}-\dfrac{1}{6}\\\\A(n)=\dfrac{n+29}{3}\\\\\text{Put n = 1, n = 4 and n = 10 to the formula:}\\\\A(1)=\dfrac{1+29}{3}=\dfrac{30}{3}=10\\\\A(4)=\dfrac{4+29}{3}=\dfrac{33}{3}=11\\\\A(10)=\dfrac{10+29}{3}=\dfrac{39}{3}=13[/tex]
Find the range of f(x) =-x+4 for the domain {-3, -2, -1, 1}
Answer:
{3, 5, 6, 7 }
Step-by-step explanation:
to find the range of f(x) substitute the given values of x from the domain into f(x)
f(- 3) = - (- 3) + 4 = 3 + 4 = 7
f(- 2) = - (- 2) + 4 = 2 + 4 = 6
f(- 1) = - (- 1) + 4 = 1 + 4 = 5
f(1) = - 1 + 4 = 3
range y ∈ {3, 5, 6 , 7 }
Equivalent expression for 3(4m - 2) -2 (m + 5)
Answer:
10m-16
Step-by-step explanation:
3(4m-2)-2(m+5)
Distribute 3 into the equation
12m-6 than do the same with -2
-2m-10
combine like terms
10m-16
simplify
Equivalent expressions are expressions that have equal values
The equivalent expression is [tex]10m - 16[/tex]
The expression is given as:
[tex]3(4m - 2) -2 (m + 5)[/tex]Open the brackets
[tex]3(4m - 2) -2 (m + 5) = 12m - 6 - 2m - 10[/tex]
Collect like terms
[tex]3(4m - 2) -2 (m + 5) = 12m- 2m - 6 - 10[/tex]
Evaluate the like terms
[tex]3(4m - 2) -2 (m + 5) = 10m - 16[/tex]
Hence, the equivalent expression is [tex]10m - 16[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
23 lb. 14 oz. − 8 lb. 1 oz.
P.S NO WORK NEEDED.
Answer:
15.8125 lb
Step-by-step explanation:
Answer:
15 lb. 13oz.
Step-by-step explanation:
no need
Write the fact family formed by these numbers 3 9 12
Answer:
The family formed by these numbers is 3x where x is any integer number.
Step-by-step explanation:
We have been given 3 9 12
We can see that given numbers are multiple of 3 so, we can say that the given numbers are from the family of 3x
Where x is any integer number when multiplied by 3 will give the multiple of 3.
Arugula is 6 feet and 10 feet long. what is the ratio of length to width
Answer:
5 : 3
Step-by-step explanation:
the ratio of length : width
= 10 : 6 ← divide both parts of the ratio by 2
= 5 : 3 ← in simplest form