Using an exponential function, it is found that:
The equation is: [tex]y = 5(3)^x[/tex].After 16 hours, there would be 215,233,605 tribbles.After 8 hours, there would be 32,805 tribbles.What is an exponential function?It is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.In this problem:
The number triples every hour, hence b = 3.Initially, five tribbles were brought on board, hence a = 5.Thus, the equation is: [tex]y = 5(3)^x[/tex]
16 hours later, the amount is:
[tex]y = 5(3)^{16} = 215233605[/tex]
After 16 hours, there would be 215,233,605 tribbles.
8 hours later, the amount is:
[tex]y = 5(3)^{8} = 32805[/tex]
After 8 hours, there would be 32,805 tribbles.
More can be learned about exponential functions at https://brainly.com/question/25537936
A frame around a rectangular family portrait has a perimeter of 138 inches. The length is nine more than three times the width. Find the length and width of the frame.
Given :
Perimeter of the frame is 138 inches.The length is nine more than three times the width⠀
To Find :
The Length and width of the frame .⠀
Solution :
We know that,
[tex]\qquad{ \bold{ \pmb{2(Length + Breadth ) = Perimeter_{(rectangle)}}}}[/tex]
Let's assume the width of the rectangle as x inches. Then the length will become (3x + 9).
⠀
Now, Substituting the given values in the formula :
[tex]\qquad \dashrightarrow{ \sf{2(3x + 9 + x )= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{2(4x + 9 )= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x + 18= 138}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x = 138 - 18}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{8x = 120}}[/tex]
[tex]\qquad \dashrightarrow{ \sf{x = \dfrac{120}{8} }}[/tex]
[tex]\qquad \dashrightarrow{ \bf \: x = 15}[/tex]
⠀
Therefore,
[tex]\qquad { \pmb{ \bf{ Width _{(frame)} = x = 15 \: inches}}}\:[/tex]
[tex]\qquad { \pmb{ \bf{ Length _{(frame)} = (3x + 9) \: = 3(15) + 9 = 54 \: inches}}}\:[/tex]
Solve the linear inequality. Other than ∅, graph the solution set on a number line.
Find the solution set in interval notation.
12x-8≤6x-15
The solution for the linear inequality, in interval notation, is [tex]\:(-\infty \:,\:-\frac{7}{6}][/tex].
InequalityIt is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. Therefore, it is common the use of follow symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than) and > (greater than).
The solutions for inequalities can be given by: graph in a number line or numbers.
For solving this exercise, it is necessary to find a number solution for the given inequality.
12x-8≤6x-15
12x-6x≤ -15+8
6x≤-7
x≤ -7/6
Read more about inequalities here.
brainly.com/question/25275758
Taryn had 7/8 of a pound of sugar. She used some
of the sugar to make muffins. She has 3/8 of a
pound of sugar left. How much sugar did she use to
make muffins?
Answer: 1/2
Step-by-step explanation:
7/8 - 3/8 = 4/8
4/8 = 1/2
Answer:
she used 4/8 of the sugar
Step-by-step explanation:
Find the area (hint: find the value of x first)
Answer:
C. 128 in²
Step-by-step explanation:
We know that the opposite sides of rectangles are congruent, so 8 = 2x. If we divide 8 by 2 and 2x by 2, we get x = 4.
This means that the other side length, (3x + 4), equals 3(4) + 4 = 12 + 4 = 16 inchesNow, the area of a rectangle is l × w, where l = length and w = width. The dimensions of this rectangle are 8 and 16, so 8 × 16 = 128 in².
How many solutions does the equation: 4x+2=12x+6 have?
What is the probability of getting a 7 of spades in a deck of 52 cards?
Answer:
I'm sure it's 1/52
Step-by-step explanation:
because if there is 52 cards and one 7 of spades then it would be a 1 out of 52 chance
Find the area of the kitchen
plss help me plss #2
Answer:
8
Step-by-step explanation:
2 ÷ 1/4 = 8
You can draw 2 squares and make them into quarters for your diagram. Hope this helped!
Answer: There are 8 1/4 inches in 2 inches.
Step-by-step explanation:
1/4 x 4 = 1, so 1/4 x 8 = 2
Diagram can be made to look as splitting 2 inches into 8 parts.
what would be twice a number?
Answer:
2x
Step-by-step explanation:
Substitute the x for a number like 2 and you multiply the 2 numbers together to get the total and in this case it would be 4.
Have a great day!!
Please rate and mark brainliest!!
What is the value of x in the figure?
Enter your answer in the box.
x=
A little square marked on angle means that the angle is 90 degrees.
By the vertical angle theorem, angles opposite each other are equal thus the angle opposite the angle with the little square is also 90 degrees.
That angle is split into two angles that is off measure 22 degrees and x degrees
-- x + 22 = 90 --> x = 68.
Hope that helps!
Answer:
68
Step-by-step explanation:
[tex] \hookrightarrow \: x + 22 = 90(complementary \: angles) \\ [/tex]
[tex] \hookrightarrow \: x + 22 = 90 \\ \hookrightarrow \: x = 90 - 22 \\ \hookrightarrow \: x = 68[/tex]
what's the área of this triangle?
Answer:
192 SQUARE FEET
Step-by-step explanation:
Area of a triangle= 1/2 ×base×height
1/2 of the base =32/2 ft
=16 ft
Let the height be A ft and another side(16 ft) be B ft
We know that, A^2 + B^2 =Hypotenuse^2
OR, A^2 + 16^2 = 20^2
OR, A^2= 400-256
OR, A^2 =144
OR, A= Square root of 144
OR, A=12 ft
By the problem,
1/2 ×Base×Height =Area of half of the triangle
1/2 ×16×12= Area of half of the triangle
96=Area of half of the triangle
AREA OF THE TRIANGLE=96 ×2
AREA OF THE TRIANGLE=192 SQUARE FEET.
HOPE IT HELPS
MARK ME BRAINLIEST
Juanita walks 3 hours and burns 750 calories
Answer:
And............ What?
12. You purchase a new computer for $2,100. The function f(x) = 2100(.5)* gives the value of the
computer
each year, where x is the number
of years since the computer was purchased. What is
the value of the computer after four years?
A. $1050
B. $525
C. $262.50
D. $131.25
Answer:
I think it's C but I never did this before so don't trust me
Step-by-step explanation:
2100 * 5 = 1050 and I divided 1050 by 4 which gave me $262.50
Four years ago Ravi was 8 years older than Priya. If he is now 3times as old as she is, find their present ages?
Answer:
24
Step-by-step explanation:
Hope this helps and please mark me brainliest :D
pahelp pooo, thank u
Answer:
1. 25 cm^2
2. 9 m
3. 4.8x5=24 m^2
4. 56/6=9.33 cm
5. 8x7.2=57.6 m^2
soIve for x. Show your work or no credit 1) -8x + 10x - 5 = 35
Answer:
x=20
Step-by-step explanation:
Angle MNP ~ Angle HJK.
Both triangles are isosceles. if m
Answer:
Angles H, J, M, N
Step-by-step explanation:
Since m<p is 90 degrees it must be the largest angle so both triangles have angle 45-45-90. m<P is equal to m<K. This means that angle h, j, m, and n are equal.
angles M, N, and J.
try drawing diagrams to help you figure out the problem :)
Concert tickets cost $70 each. A college student ordered some tickets online. There
was a service fee of $3.50 per ticket. The student has $367.50. How many tickets
did can he order?
Answer:
The college student can get 5 concert tickets
Step-by-step explanation:
$367.50÷(70+$3.50)
20 students in total. 10
play sports and 12 play music. 2 of them
don't play anything and some are play
both. What's the percentage for students
play both?
Answer:
20%
the above was solved using set
Based on the measures shown, could the figure be a parallelogram?
A Yes, one pair of opposite sides could measure
10 in., and the other pair could measure 13 in.
B Yes, one pair of opposite sides could measure
10 in., and the other pair could measure 8 in.
C No, there are three different values for x when each expression is set equal to 10.
D No, the value of x that makes one pair of sides congruent does not make the other pair of sides congruent.
If 5000 is borrowed with an interest of 12.3% compounded semi-anually
Answer:
312.5
Step-by-step explanation:
P=5000
r=12.5%=0.125
t=6month=0.5years
I=P•r•t
I=(5000)(0.125)(0.5)
I =$312.5
Determine whether f(x) = –52 – 10x + 6 has a maximum or a minimum value. Find that value and explain how you know.
Answer:
minimum
Step-by-step explanation:
Because of the negative infront of 52. The graph opens downward which makes it minimum. Hope this helps
Find the value g(-2), where g is defined below.
g(x) = 2x^2- 4x – 4
Answer:
12
Step-by-step explanation:
For this question, simply plug in -2 for x:
[tex]g(-2)=2(-2)^2-4(-2)-4\\g(-2)=2(4)+8-4\\g(-2)=8+8-4\\g(-2)=12[/tex]
Hope this helps!!
The amount of television viewed byâ today's youth is of primary concern to Parents Against Watching Televisionâ (PAWT). 300 parents of elementaryâ school-aged children were asked to estimate the number of hours per week that their child watches television. The mean and the standard deviation for their responses were 12 and 3â, respectively. PAWT constructed aâ stem-and-leaf display for the data that showed that the distribution of times was aâ symmetric, mound-shaped distribution. Give an interval where you believe approximatelyâ 95% of the television viewing times fell in the distribution.
a. less than 9 and more than 15 hours per week
b. between 3 and 21 hours per week
c. between 6 and 18 hours per week
d. less than 18
Answer:
Option C. between 6 and 18 hours per week
Step-by-step explanation:
We are given that distribution of times is symmetric and mound shaped and this implies that data is normally distributed.
We also know that in the normal distribution the 95% of data lies within 2 standard deviations i.e. mean± 2*standard deviation.
So, 95% of the television viewing times falls in interval
mean± 2*standard deviation
12±2*3
12±6
[6,18]
Thus, [6,18] is an interval where you believe approximately 95% of the television viewing times fell in the distribution.
Which graph represents a proportional relationship?
Answe point me
Step-by-step explanation:
Answer:A
Step-by-step explanation:
Find the slope of the line that passes through the points (-9,-4) and (-16,-8)?
Please help asap! I will gave brainlest!
Find the length of the line below.
A. 2 in.
B. 2 3/16 in.
C. 2 5/16 in.
D. 3 in.
Answer:
A)
Step-by-step explanation:
Starting point is at o and ending point at 2.
So, 2 in
HEY GUYS HELP ME ON THIS ONE PLS DO IT FAST
Answer:
The answer is 72
Step-by-step explanation:
The formula to find the area of a trapezoid
[tex]A= \frac{1}{2}h(b_{1} + b_2{} )[/tex]
First, we can add the bottom base together
5 + 8 + 3 = [tex]16_{2}[/tex]
We know that the height of the trapezoid is 6 and base1 is 8
[tex]A= \frac{1}{2}6(16 + 8)[/tex]
[tex]A=\frac{1}{2}6(24)[/tex]
[tex]A=3(24)[/tex]
[tex]A=72[/tex]
OR
Find the area of the two triangles
[tex]A=\frac{1}{2}5(6)\\\\A=5(3)\\\\A=15\\\\[/tex][tex]A=\frac{1}{2}3(6)\\\\A=3(3)\\\\A=9\\[/tex]
15 + 9 = 24
For the area of the rectangle
6 x 8 = 48
48 + 24 = 72
Jack wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 5
3
4
Mixed number
ft by 3
1
2
ft. Find the area the carpet needs to cover.
The area of the floor the carpet needs to cover is 20 1/8 cm².
What is the area the carpet needs to cover?The floor has the shape of a rectangle. A rectangle is a 2-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
5 3/4 x 3 1/2
23/4 x 7/2 = 161/8 = 20 1/8 cm²
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449