Make sure you tell me what goes in each of the 2 blanks.
Answer:
Future amount = 48(1 + 0.316074)^12
0.31607412Step-by-step explanation:
You want the exponential equation that can be used to find the number of bacteria in a colony after 12 days if it starts with 48 bacteria and triples in 4 days.
Exponential functionThe exponential function can be written in the form ...
future amount = a·b^(t/p)
where 'a' is the initial amount, 'b' is the growth factor in period p.
The problem statement tells you the initial amount is 48, and the factor by which the amount grows is a factor of 3 in 4 days. This lets you write the function as ...
future amount = 48·3^(t/4) . . . . . where t is in days.
RearrangementThis equation can be rearranged so the only exponent is t:
future amount = 48·(3^(1/4))^t = 48·1.316074^t
future amount = 48·(1 +0.316074)^t
Then the amount in 12 days is ...
future amount = 48·(1 +0.316074)^12
The numbers that go in the boxes are 0.316074 and 12.
__
Additional comment
Working from our original equation, we would compute the number after 12 days to be ...
future value = 48·(3)^(12/4)
Putting the growth factor in "1 +" form, this could be ...
future value = 48·(1 +2)^3
and your box numbers would be 2 and 3. We doubt your answer checker will accept this version of the equation.
Either way, the number of bacteria after 12 days is 1296.
If you use 3^(1/4) -1 as the growth rate in the first box, you need to report it to at least 5 significant digits in order for the future value to come out right. We have shown the value with 6 significant figures.
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HELP!!!
50 Points!!!!!
Answer:
i think the first and last one.
Step-by-step explanation:
Solve the following system of equations
by Substitution.
5x + 4y = 7
-2x - 2y = 8
Answer:
y = 9/13
Step-by-step explanation:
x = -4 + y
5(-4 + y) + 4y = 7
-20 + 9y = 7
9y = -13
Answer:
5x + 4y = 7 × -2
-2x - 2y = 8 × 5
-10x - 8y = -14
-10x - 10y = 40
Step-by-step explanation:
2y = -54 ÷2
y = -27
Now substitute the value of y into equation (1)
5x + 4y = 7
5x + 4(-27) = 7
5x = 7 + 108
5x = 115
X = 23
Kara scores 3 points when she completes the first level of a video game. At each level after that she scores 3 times the amount awarded at the previous level. If she completes 4, how many points does she score in all?
Answer:
120
Step-by-step explanation:
If Kara earns 3 times as many points completing the next level than she earned the previous level, to find how many points she earned at level 3, triple the amount of points earned in level 2, which is 9.
9 × 3 = 27
We can confirm this is the correct value by multiplt 27 by 3 to see if it equals 81, which it ineed does.
To find how many points she scored in all, find the sum by adding all of the points together.
3 + 9 + 27 + 81 = 120
She scores 120 points in all.
hope this helps!
A map use the scale 3/4 of an inch to represent 3 miles .if the actual distance between two cities is25 miles ,then what is the length on the map
3/4 inch
3 miles
to find:the length of the map
solution:Based on the given conditions, write:
x= 34/ 4 · 25/ 3
Write as a single fraction:
x= 3 × 25/ 4/ 3
Divide a fraction by multiplying its reciprocal:
x= 3 x 25/ 4 × 1/ 3
Write as a single fraction:
x= 3 x 25/ 4 × 3
Reduce fraction to the lowest term by canceling 25 the greatest common factor:
x= 25/4
therefore,the length of the map is 25/ 4.
The mean of five numbers 3,7,9,12 and x is 8. find the value of x
Answer: 23
Step-by-step explanation: 3+7+9+12+X /5 =8
31 + X = 8
X = 23
What is the mean of 3,0,5,0,7,4,3,10 ?
Answer:
4
Step-by-step explanation:
3+0+5+0+7+4+3+10 = 32
Mean = sum of numbers / how many numbers
mean = 32/8
mean = 4
B
A 85⁰
D
What is the measure of angle B
What is the measure of Angle D
43° C
m/B=
m/D=
Answer:
B =116°
D = 116°
Step-by-step explanation:
one set of opposite angles of a kite equal
For all values of x, f(x)=2x^2 and g(x)= x+1
Solve fg(x) = gf(x)
Answer:
-0.25
Step-by-step explanation:
→ Find fg(x)
2 ( x + 1 )² = 2x² + 4x + 2
→ Find gf(x)
2x² + 1
→ Equate them
2x² + 1 = 2x² + 4x+ 2
→ Move everything to the right hand side
0 = 4x + 1
→ Solve
x = -0.25
Answer:
[tex]-\frac{1}{4}[/tex]
Step-by-step explanation:
Work out fg(x)
To work out fg(x), put the g function into the f function so, the x in f(x) is equal to the x+1 (from the g function) so:
[tex]2(x+1)^{2} = 2 (x^{2} +2x+1) = 2x^{2} + 4x +2[/tex]
So fg(x) = [tex]2x^{2} + 4x +2[/tex]
Work out gf(x)
Do this by substituting the f(x) equation into the g(x) which is:
[tex](2x^{2} )+1[/tex]
So gf(x) = [tex](2x^{2} )+1[/tex]
Work out x
And since fg(x) = gf(x),
[tex]2x^{2} + 4x +2[/tex] = [tex](2x^{2} )+1[/tex]
4x = -1
x =[tex]-\frac{1}{4}[/tex]
The tables below contain integers, fractions or mixed numbers. Select the table whose rations of ordered pairs represent a proportional relationship between x and y.
Answer:
d
Step-by-step explanation:
Which pair of triangles can be proven congruent by SAS?
Answer:
Second option
Step-by-step explanation:
They have two congruent pairs of sides and one congruent pair of angles.
The triangles B can be proven congruent by the SAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
From the Option B) , we get
Let the first triangle be ΔABC
Let the second triangle be ΔBDE
Now , the measure of side AB = measure of side BD
And , the measure of side AC = measure of side BE
And , the measure of ∠ABC = measure of ∠DBE
Therefore , Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are congruent by SAS theorem
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Last one!! I need the steps please! Will mark brainliest!
Answer:
[tex]h(t)=-6(t-2)^2+24[/tex]
Step-by-step explanation:
Given function:
[tex]h(t)=-6t^2+24t[/tex]
where:
h = height (in feet)t = times (in seconds)Rewrite in the form [tex]h(t)=a(t-h)^2+k[/tex]
The quickest way to do this is to expand [tex]h(t)=a(t-h)^2+k[/tex] and compare coefficients with the original function.
[tex]\begin{aligned}h(t)& =a(t-h)^2+k\\ & = at^2-2aht+ah^2+k\end{aligned}[/tex]
Comparing coefficients with [tex]h(t)=-6t^2+24t[/tex]
[tex]\begin{aligned}\implies at^2& =-6t^2\\ a &=-6\end{aligned}[/tex]
[tex]\begin{aligned}\implies -2aht & =24t\\ -2(-6)ht& =24t\\ 12ht & = 24t\\ 12h & = 24\\ h & = 2\end{aligned}[/tex]
[tex]\begin{aligned}\implies ah^2+k & = 0\\(-6)(2)^2+k &=0\\ -24+k & =0\\ k &=24 \end{aligned}[/tex]
Therefore, substituting the found values into the equation:
[tex]h(t)=-6(t-2)^2+24[/tex]
Find the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)
Answer:
(x + 4)^2 + (y - 1)^2 = 61.
Step-by-step explanation:
We need to find the square of the radius and the coordinates of the center.
Center = (-10 + 2)/2 , (-4 + 6)/2
= (-4, 1).
Length of the diameter
= √((-10-2)^2 + (-4-6)^2)
= √(144 + 100)
=√244
So the radius = √244/2
and r^2 = 244/4 = 61,
So the equation of this circle is:
(x - (-4)^2 + (y - 1)^2 = 61
(x + 4)^2 + (y - 1)^2 = 61.
(x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given coordinates of the diameter of circle are (-10,-4) and (2,6)
Diameter=√(x₂-x₁)²+(y₂-y₁)²
x₂=2,x₁=-10, y₁=-4, y₂=6
Diameter=√(2-(-10))²+(6-(-4))²
=√(12)²+(10)²
=√144+100
=√244
We know that Radius=Diameter/2
R=√244/2
Squaring both sides
R²=244/4
R²=61
So the equation of this circle is:
(x - (-4)² + (y - 1)² = 61
(x + 4)²+ (y - 1)² = 61.
Hence (x + 4)²+ (y - 1)² = 61 is the equation of a circle given the coordinates of the diameter: (-10,-4) (2,6)
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The average temperature over a 10-day period in Phoenix was 98 degrees. For the first six days, it was sunny, and the average temperature was 100 degrees. Over the next 4 days, it was cloudy and the temperature dropped. What was the average temperature for those 4 days? Show work.
Answer:
96
Step-by-step explanation:
The average for the first 6 days was 100, and it ended up dropping overall by 2 for the average.
6 days=x/6=100
4 days=x/4=98/100
You can do 96+100/2 which is 98 degrees.
30 POINTS!
Find x if ∠m1 = 2x + 10 and m∠2 = 3x - 6
Answer choices:
42, 24, 4, 16
Answer: 16
Step-by-step explanation:
Please helpppppppppppp
please help me with this
Answer:
Length: 12.39313902 cm
Width: 10.89313102 cm
Step-by-step explanation:
Check the attachment.
Find an ordered pair with (x,y) that is a solution to the equation 3x+y=8
Answer: (2,2)
Step-by-step explanation:
3x+y=8
X=2, y=2
3(2)+2=8
6+2=8
HELPPPPPPPPPPPPPPPPPPPPPPPPPP-
Answer:
Answers are in bold (in order)
Step-by-step explanation:
For the table, the question is asking us to take our x value and put it into the equation. for example:
y = 8x +1 . if x = 0, we can write this as this
y = 8(0) + 1 -> (the brackets mean times)
8 x0 = 0. 0+1 = 1.
if we follow this rule, the values are: 1, 9, 17, 25, 33.
For the function machine, if x = 1, then we can write 1 where the x is. The function machine is telling us that 1 x3 and then -2 = y, y being a random number we don't know. 1 x 3 = 3. That means 3-2 = y . 3-2 = y. So, y = 1 when x = 1.
When x =-9 we can rewrite x as -9. That means that -9 x 3, then -2 = y.
-9 x 3 = -27.
That means that -27 -2 = y
-27 -2 = -29, so when x = -9, y = -29.
For the third part we need to work out the gradient and the equation of the table. The gradient (how much our values go up by) The gradient can be worked out by diving the change in y (our y value) by the change in x (our x value). So, if we take the first two y values, we have -2 and 8. The difference/chance between these two is 10. (-2+10=8). And for the x values, the first two x values are 0 and 1. The difference/change between these two is 1. (1-0=1.) So, all we need to do is divide these values 10/1 = 10. So our gradient is 10. That means that the first box on the function machine will be “x10” to work out the second, we simply do the first box and go from there. If our x = 1, then 1 x 10 = 10. Our table says that when x = 1, y = 8. So to we need to work out the change between these is, to get our answer. To get from 10 to 8, we minus two. So the final box on the function machine must be “-2”
For the last part of the question, we are just substituting in the values of x.
If t = 1, then 4(t-3) is basically 4(1-3)
1-3 = -2. 4(-2) = -8.
so when t =1, s = -8. If you do this for the next two questions, you should get the answers:
s = -28 when t = -4
s = -12 when t = 0
Is 6/12 equivalent to 1/2?
Answer:
yes because 1/2= .5
and 6/12= .5 so they are equivalent
yes
Calculations ↓In order to determine whether or not 6/12 is equivalent to 1/2, we need to reduce the first fraction.
Reduce by dividing the top & bottom by 6 ↓
[tex]^6/_{12}=^1/_2[/tex]
Yes, 6/12 is indeed equivalent to 1/2.hope helpful ~
Four students each hike on different trails. Dave (D) hikes 3 miles more than Sue (S). Jerry (J) hikes 2 miles more than Ezra (E). Ezra hikes farther than Sue. Identify the inequality that correctly represents the distance the students hike
A number cube is rolled 300 times. Predict how many times a number greater than 3 would be rolled.
the area of the triangle below is 12.87 square inches what is the length of the base ??
Answer:
6.6 in (Brainliest please)
Step-by-step explanation:
A= 1/2 b*h
12.87= 1/2 b(3.9)
12.87= 1.95b
12.87/1.95= 1.95b/1.95
6.6=b
can you help me pls by the way i am in 5th grade
Answer:
Step-by-step explanation:
What is the surface area of this right triangular prism?
Enter your answer in the box.
in²
Right triangular prism. The height of the prism is labeled 12 in. The base of the prism is a triangle with sides labeled 13 in., 13 in., and 24 in. There is a dashed line from the vertex of the triangle perpendicular to the 24 in. side that is labeled 5 in.
The surface area of the right triangular prism is : 20,568 [tex]in^{2}[/tex]
using this formula ;SA = bh + (s1 + s2 + s3)*l
Meaning of a triangular prismA traingular prisms is a prism that has triangles as its base. It has two triangles which are called the bases and three rectangles called the lateral faces.
Given data:
where; SA means the surface area
b = base = 24 inh = height = 12 ins1 = side one = 13 s2 = side two = 13 ins3 = side three = 24 inl = length = 5 inTherefore:
SA = 24*12 + ( 13 * 13 * 24 ) * 5
SA = 288 + ( 4056) * 5
SA = 288 + 20280
SA = 20,568 [tex]in^{2}[/tex]
In conclusion, the surface area of the right triangular prisms is 20,568 [tex]in^{2}[/tex]
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Answer:
20,568..............................
Instructions: Find the measure of the angle.
Answer:
Step-by-step explanation:
Remark
The figure inside the circle is a quadralateral. The 4 angles touch the circumference of the circle. The figure is further defined as a cyclic quadrilateral.
One of the properties of such a figure, is that the opposite angles are supplementary. That is they add to 180.
Equation and solution
? + 100 = 180 Subtract 100 from both sides
? + 100 - 100 = 180 - 100
? = 80 degrees
Answer
? = 80
The length of the shadow of an office building is 35 feet. At the same time of the day, Donovan Mitchell, who is 6.1 feet tall, has a shadow of 5 feet. What is the height of the office building?
Answer:
175
Step-by-step explanation:
35 times 5 is 175
Hope This Helped
What is 47 x 89 divided by 58 + 787 x 879000 divided by 78
Answer:
6441.46 (2d.p.)
Step-by-step explanation:
47×89= 4183÷(845)=0.571×879000=502434.319÷78= 6441.46
What is the surface area of this rectangular pyramid? 5 cm 5 cm 5 cm square centimeters
Answer:
you have to multiple 5x5x5
Answer:
68.3 cm^2
Step-by-step explanation:
Assuming slant height is 5 cm : ( the Q does not say)
The base area will be 5 x 5 = 25 cm^2
then you have 4 equilateral triangles of side length 5 cm
total area = 43.3 cm^2
SUM = 68.3 cm^2
For the following quadratic equation, find the discriminant.
8x2 + 14x + 40 = 7x2
Answer:
36
Step-by-step explanation:
8x^2 - 7x^2 +14x +40 = 0
x^2 + 14x + 40 = 0
a = 1, b = 14, c = 40
14^2 - 4*1*40
36
Answer:
36
Step-by-step explanation:
you're welcome hope this helps