Given:
Initial amount = 8
To find next week's amount, we multiply this week's amount by 4.
To find:
A formula that gives the amount A after T weeks.
Solution:
We have,
Initial amount = 8
According to the question,
Amount of next week = 4 × Amount of this week
Amount after one week is
[tex]A=4\times 8[/tex]
Amount after two week is
[tex]A=4\times (4\times 8)[/tex]
[tex]A=4^2\times 8[/tex]
Amount after T week is
[tex]A=4^T\times 8[/tex]
[tex]A=8(4)^T[/tex]
Therefore, the required formula that gives the amount A after T weeks is [tex]A=8(4)^T[/tex].
Which of the following expressions is equivalent to the one below? 3x + 6y
A.
6(2x + y)
B.
6x + 3y
C.
3(x + 2y)
D.
9(x + y)
I WILL MARK BRAINLIST
Answer:
The answer is D
Step-by-step explanation:
what is the value of the digit in the tens place? 6,423
Answer: 20 :)
Step-by-step explanation:
In a direct variation, y= -1/6 when x=4/3. Write a direct variation equation that shows the relationship between x and y.
Please answer ASAP!
Answer: y = 3x
Step-by-step explanation: For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
A fair six-sided die is rolled. Find the probability of getting a 4.
Answer:
A fair six-sized die is rolled. Find the probability of getting at least a 4.
There are 6 outcomes and three of them are 4, 5 or 6, so the probability of greater than or equal to 4 is 3/6=½.
Solving systems of linear equations algbraically.
Answer:
(3,-6)
Step-by-step explanation:
[1] x - 2y = 15
[2] 2x + 4y = -18
Graphic Representation of the Equations :
-2y + x = 15 4y + 2x = -18
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 2y + 15
// Plug this in for variable x in equation [2]
[2] 2•(2y+15) + 4y = -18
[2] 8y = -48
// Solve equation [2] for the variable y
[2] 8y = - 48
[2] y = - 6
// By now we know this much :
x = 2y+15
y = -6
// Use the y value to solve for x
x = 2(-6)+15 = 3
Solution :
{x,y} = {3,-6}
Solve for x
Enter the solutions from least to greatest.
(x – 7)(-4x − 2) = 0
lesser x =
greater x =
Answer:
X= -1/2 X= 7
Answer:
lesser x= -5 Greater X= 5
Step-by-step explanation:
−x
2
−8
−x
2
x
2
=−33
=−25
=25
Hint #22 / 3
Now we can take the square root of both sides, not forgetting to take both the positive and negative roots of the right-hand side:
\begin{aligned} \sqrt{x^2}&=\sqrt{25} \\\\ x&=\pm 5 \end{aligned}
x
2
x
=
25
=±5
Hint #33 / 3
In conclusion,
\begin{aligned} \text{lesser }x &= -5 \\\\ \text{greater } x &= 5 \end{aligned}
lesser x
greater x
=−5
=5
Manny rolls a number cube labeled 1-6 and spins a spinner with four equal sections, labeled 1, 2, 3, and 4. If both numbers are odd, he wins. Otherwise, Gabriel wins. Use a list to find the sample space. Then find the probability that Gabriel wins.
a.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
b.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
c.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
d.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
Answer:
b
Step-by-step explanation:
Answer:
b.
1, 1; 1, 2; 1, 3; 1, 4; 2, 1; 2, 2; 2, 3; 2, 4; 3, 1; 3, 2; 3, 3; 3, 4; 4, 1; 4, 2; 4, 3; 4, 4; 5, 1; 5, 2; 5, 3; 5, 4; 6, 1; 6, 2; 6, 3; 6, 4;
Step-by-step explanation:
IT'S B
Find the area of a triangle with base of 4 and height of 3x-5
Answer:
Area of a triangle is 1/2B x H
In this case, BH = 0.5(3x-5)·4x
A = 4/2 · (3x²-5x)
Can some one help me find x?
Answer:
x = 20
Step-by-step explanation:
Exterior angles are equal.
7x - 3 = 6x + 17
Add 3 and subtract 6x to both sides.
x = 20 is the answer.
C
Kris is cutting ribbon that each measure 2 ft
long. If Kris is cutting from a piece that measures
8zft
, how many pieces can Kris cut?
Answer:
4
Step-by-step explanation:
because 2+2+2+2=8 pretty self explanatory
Answer:
13
Step-by-step explanation:
A line passes through the point (10, -1) and has a slope of 3/2 .
Write an equation in slope-intercept form for this line.
Answer:
y=3/2x-16
Step-by-step explanation:
The equation of the line passing from points (10, -1) is y = 3x/2 - 16.
What is equation of a line?A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It conveys the slope, x-intercept, and y-intercept of the line and can be expressed in a variety of ways. Y = mx + c and axe + by = c are the two versions of the equation of a straight line that are most frequently employed.
Given slope = 3/2 and points (10, -1)
equation of line is given by y = mx + c
m = 3/2
y = 3/2x + c
substitute points,
-1 = 10*3/2 + c
c = -16
equation of line is y = 3x/2 - 16
Hence the equation is y = 3x/2 - 16.
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A gym membership went from 8700 to 6400. What expression equals the percent of change?
Answer:
(6400-8700)/(8700)*100
Step-by-step explanation:
percent of change = (new value - old value)/(old value) * 100
percent of change = (6400 - 8700)/(8700) * 100
The graph shows the printing rate of Printer A. Printer B can print at a rate of 25 pages per minute. Complete this sentence: The rate for Printer B is (a) ____________ the rate for Printer A because the rate of 25 pages per minute is (b) _____________ the rate of (c) __________ pages per minute for Printer A.
Answer:
a equal to c 25 b greater than
Step-by-step explanation:
Answer:
As per graph the rate of Printer A is 15 pages per minute.
Missing words are:
(a) greater than(b) greater than(c) 15The rate for Printer B is greater than the rate for Printer A because the rate of 25 pages per minute is greater than the rate of 15 pages per minute for Printer A.
4 hours worked for $12; 7 hrs worked for $28 are the pair of ratios equal?
Answer:
no they're not equal
Step-by-step explanation:
you can find the ratio by dividing 12/4 and 28/7. 12/4 = 3 and 28/7 = 4. 3 and 4 are not equal, so no.
What is the annual interest for a principal of $3,500 at a simple annual interest
rate of 2.3%?
Answer:
Step-by-step explanation:
Given principal p =$3500
Time t =1 year
Rate of interest r =2.3%
So annual interest=p×r×t/100
=3500×2×2.3/100
=7000×2.3/100
=16100/100
=161.
So annual interest is $161
Use a double integral in polar coordinates to find the area of the region. The region inside the circle (x − 4)2 + y2 = 16 and outside the circle x2 + y2 = 16
Answer:
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
Step-by-step explanation:
From the information given:
Lets first change the given relations into polar coordinates
So, the region of the inner circle into polar coordinates is as follows:
(x - 4)² + y² = 16
x² + y² - 8x = 0
r² - 8r cos θ = 0
r = 8 cos θ
For the outside circle:
x² + y² = 16
r² = 16
Thus, the intersection point are:
64cos²θ = 16
cos²θ = 1/4
θ = -(π/3) , (π/3)
Now: if we are to represent the sketch on a graph, the region of the integration D will be:
[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]
Therefore, the are of the required region can now be computed as follows:
[tex]A = \int \int _D \ dA[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]
[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]
[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]
[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]
[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]
[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]
[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
The double integral formula for the area of a given curve is described below:
[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)
Where:
[tex]r[/tex] - Distance with respect to origin.[tex]\theta[/tex] - Angle in standard position.We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:
[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]
Now we proceed to integrate the expression:
[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]
[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]
The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.
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What is the REMAINDER of 15,908 divided by 13?
Answer: 1223 and the remainder is 9
Step-by-step explanation:
pleaseeeeeeeeeeeeeeeeee helpppppppppppppppppp
Answer:
Option c is the answer
Step-by-step explanation:
3/5 = 0.6
2 divided by 0.6 = 3.3333333
3.33333 = 10/3
10/3 = 3 1/3
Hope this helps :)
Answer:
3 1/3 or 3, depending on if he can play a fraction of a match
Step-by-step explanation:
The question is asking us how many times 3/5 can go into the whole number 2. to find this we can multiply the denominator of the fraction (5) by the whole number we are trying to get with the fraction (2), and this results in 10. if we put this over the denominator, we get 10/5, which results in 2. to find how many times 3/5 can go into 10/5, we will divide 10/5 by 3/5. this results in 3 and 1/3. so he can play 3 1/3 matches.
17) A dog kennel charges $40 per night for boarding
and $5 for walking your dog.
a) Write an equation in standard form that models the
possible combinations if you plan to spend $200.
b) Graph the equation using x and y intercepts.
I
11
10
5
1 3 4 5 6 7 8 9 10 11 12 13
c) List all combinations that can be used.
Answer:
c
Step-by-step explanation:
If the original quantity is 10 and the new quantity is 15, what is the percent increase?
Given the value of the original quantity and the value of the new quantity, the percentage increase is 50%.
What is percent increase?Percent increase is aimply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.
It is expressed as;
C = ((x₂ - x₁) / x₁)100%
Where x₁ is initial value and x₂ is new value
Given the data in the question;
Initial value x₁ = 10New value x₂ = 15Percentage increase C = ?We substitute the given values into the expression above.
C = ((x₂ - x₁) / x₁)100%
C = ((15 - 10) / 10)100%
C = (5/10)100%
C = 0.5 × 100%
C = 50%
Therefore, given the value of the original quantity and the value of the new quantity, the percentage increase is 50%.
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In science class, Polly learned that trees help make the oxygen that people breathe. One tree makes about 250 pounds of oxygen each year. Polly wonders how much oxygen the trees on her street make. When she gets home, she counts 32 trees on her street. How many tons of oxygen do they make in a year?
Answer:
They make 4 approximately tons of oxygen each year.
Step-by-step explanation:
( 250lbs × 32 ) ÷ 2000 = 4t
250 pounds because each tree makes about 250 pounds of oxygen a year.
× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.
÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.
Which operation would you use to solve for x in the equation 3x = 15?
Answer:
Division
Step-by-step explanation:
3x = 3 times x so, you must do the opposite of multiplication to get rid of the 3, which is division.
The solution of the equation with a single variable 3x = 15 will be 5.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
3x = 15
Divide the equation by 3 into both sides, then we have
3x / 3 = 15 / 3
x = 5
The solution of the equation with a single variable 3x = 15 will be 5.
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HELP ME ASAP
graph f(x)=3x+4 and h(x)=f(x+3)
The standard form for expressing the equation of a straight line is
y = mx + b
Given the functions from the question f(x) = 3x + 4
If h(x) = f(x+3)
Replace x with x+3 in the function f(x) to have;
h(x) = 3(x+3) + 4
h(x) = 3x + 9 + 4
h(x) = 3x + 13
Hence the required graph for both functions are attached below;
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Which of the following is parallel to the line
Answer:
1
Step-by-step explanation:
h
Answer:
I know it is 1
Step-by-step explanation:
Jason left for school and forgot his math homework on the kitchen table. His mother found the homework 10 minutes after Jason left, and started driving 36 mph to catch him. Jason bikes 12 mph.
a.How long will it take Jason's mother to catch him?
b. How many miles has Jason biked when his mother catches him?
c. If Jason's school is 2.5 miles from his apartment, how fast must his mother drive to catch him at the school door?
Answer: 5 minutes
Step-by-step explanation:
a. Jason's mother to catch him after time of 5minutes.
b. Jason biked for distance of 3miles when his mother catches him.
c. Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.
What is speed?
" Speed is defined as the total distance travelled per unit time."
Formula used
[tex]Speed = \frac{total distance travelled}{total time taken}[/tex]
According to the question,
Speed of Jason bike = 12mph
1hour = 12miles
60minutes = 12miles
1minutes = [tex]\frac{12}{60}[/tex] miles
Speed of Jason's mother bike = 36mph
Time after mother found the homework = 10 minutes
After 10 minutes
Jason is at distance = [tex]\frac{12}{60} (10)[/tex]
=2miles
After 15 minutes = [tex]\frac{12}{60} (15)[/tex]
= 3miles
To cover three miles mother has to drive for
1hour = 36miles
60minutes = 36miles
1miles = [tex]\frac{60}{36}[/tex] minutes
3miles = [tex]\frac{60}{36} (3)[/tex]
= 5minutes
If Jason's school is 2.5 miles from his apartment,
Time taken by Jason to reach school door = [tex]\frac{2.5}{12.5} (60)[/tex] minutes
= 12.5 minutes
Time in which mother has to cover distance of 2.5miles
= [tex](12.5-10)[/tex]minutes
= 2.5minutes
Substitute the value in the formula we get,
Speed of mother's bike = [tex]\frac{2.5}{2.5} (60)[/tex] mph
= 60mph
Hence,
a. Jason's mother to catch him after time of 5minutes.
b. Jason biked for distance of 3miles when his mother catches him.
c. Mother has to drive with speed of 60mph to catch him at the school door, if Jason's school is 2.5 miles from his apartment.
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Michael threw a baseball 17.6 meters. His older brother, Kyle, threw a baseball 3.5 times farther than Michael. How far did Kyle throw the baseball?
Answer: 61.6
Step-by-step explanation:
17.6 X 3.5 = 61.6
Answer:
Kyle threw the baseball 61.6 meters
Step-by-step explanation:
You multiply 17.6 by 3.5 which results in 61.6
Jessica is shopping for a new car. She found a blue car that has a 12-gallon gas tank and can go 384 miles on one tank. She found a silver car that has a 14-gallon gas tank and can go 504 miles on one tank. Which car gets better gas mileage?
Best answer = More points!
Answer: Silver
Step-by-step explanation:
Answer:silver
Step-by-step explanation: I did it
the least common multiple of 14 and 22
Answer:
Least Common Multiple (LCM) of 14 and 22 is 154.
Answer:
Least Common Multiple (LCM) of 14 and 22 is 154.
enter decimal numbers in the boxes to complete the order pair that locates point Q on the coordinate plane
Answer:
(1.5,-1.5)
Step-by-step explanation:
Hope this helps you