Answer:
[tex]f(x) = 4\times (3)^{x}[/tex].
Step-by-step explanation:
Exponential functions are in the form [tex]f(x) = a\, \left(b^{x}\right)[/tex], where [tex]a[/tex] and [tex]b[/tex] are constants with [tex]b > 0[/tex].
In this question, the function should satisfy that [tex]f(2) = 36[/tex] and [tex]f(3) = 108[/tex]. Hence, constants [tex]a[/tex] and [tex]b[/tex] should ensure that:
[tex]a \cdot b^2 = f(2) = 36[/tex], and
[tex]a \cdot b^3 = 108[/tex].
Rewrite the left-hand side of the second equation: [tex]a \cdot b^{3} = a \cdot b^2 \cdot b[/tex].
Substitute the first equation [tex]a \cdot b^{2} = 36[/tex] into the second:
[tex]a \cdot b^2 \cdot b = 108[/tex].
[tex]36\, b = 108[/tex].
[tex]\displaystyle b = \frac{108}{36} = 3[/tex].
Substitute [tex]b = 3[/tex] into either equation (for example, the first equation) and solve for [tex]a[/tex]:
[tex]a \cdot 3^2 = 36[/tex].
[tex]a = 4[/tex].
Hence, the exponential function [tex]f(x) = a\cdot b^{x} = 4 \times (3)^{x}[/tex] should satisfy the requirements of this question.
combine like terms in the expression 10g+14k-3k-8g-10k-2g
Simplify the expression m 4/5x m1/10
Answer:
√x4
Step-by-step explanation:
(x^2+x−3)⋅(x^2−4)
(y^2+6y+8)−(y^2+y−12)
I need help quick just the first one
Answer:9& 5
Step-by-step explanation:
Assignment 1
Mathematics
Question 1
1.1.
Write down the factors of 30.
Answer:
1,2,3,5,6,10,15,30
Step-by-step explanation:
1*30
2*15
3*10
5*6
Proportions to Solve Problems - Item 3335
In a box of 36 pencils, 20 are sharpened.
What is the ratio of sharpened pencils to unsharpened pencils?
Answer:
20:16
Step-by-step explanation:
Subtract the number of sharpened pencils you have from the total number and you have your ratio.
(7x^2- 3y)^2 simplify
Answer:
49x^4-42x^2 y+9y^2
Step-by-step explanation:
Answer:
49x^4-42x^2 y+9y^2
Step-by-step explanation:
A=4
B=16
A² + B
Work out the answer
Answer:
32
Step-by-step explanation:
Plug in the corresponding numbers to the corresponding variables. Note that:
A = 4
B = 16
A² + B
(4)² + 16
Remember to follow PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& roots)
Multiplication
Division
Addition
Subtraction
~
First, solve the power:
(4)² = 4 * 4 = 16
Next, add:
16 + 16 = 32
32 is your answer.
~
X = y-2
2x-y=2
X=
Y=
Answer:
y =4 and x=6 hope it may help u
1) Solve quadratic equations by factoring.
2x^2 + 5x - 12 = 0
Answer:
[tex] x = - 4, \: \: x = 1 \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]2 {x}^{2} + 5x - 12 = 0 \\ \\ 2 {x}^{2} + 8x - 3x - 12 = 0 \\ \\ 2x(x + 4) - 3(x + 4) = 0 \\ \\ (x + 4)(2x - 3) = 0 \\ \\ x + 4 = 0, \: \: 2x - 3 = 0 \\ \\ x = - 4, \: \: x = \frac{3}{2} \\ \\ x = - 4, \: \: x = 1 \frac{1}{2} [/tex]
Yall I just realized I skipped 4 and 5- but here's question 4
I give brainalist and points for an answer and explanation
Answer:
option D
Step-by-step explanation:
diameter of two small circle i.e 14cm
radius of two small circle =7cm
area of the small circle =πr²
area of the small circle=22/7 x7²
area of the small circle=154cm²
Radius of bigger circle =14cmArea of bigger circle=πr²Area of bigger circle=22/7×14²
Area of bigger circle=616cm²
Area of shaded region =area of bigger circle -area of small circle +area of small circle
area of shaded region =616-154+154
area of shaded region=308cm²
i.e approximately 282.74cm²
Need help with this asap!!
Answer:
≈ 53.7° (Option 3)
Step-by-step explanation:
In the figure given above , the lengths of other two sides (excluding hypotenuse) are known to us. So , it would be convenient to use 'tan'.
Length of side opposite to angle 'x' = 15 cm
Length of side adjacent to angle 'x' = 11 cm
Using 'tan' formula - [tex]\tan x = \frac{Side \: opposite \: to \: x}{Side \: adjacent \: to \: x}[/tex] , lets solve this.
[tex]=> \tan x = \frac{15}{11}[/tex]
Using inverse tan function , lets find x.
[tex]=> x = {\tan}^{-1}(\frac{15}{11} )[/tex] ≈ 53.74°
Please help me with this question
70+95 Factor the expression using the GCF
giving brain
Answer:
70 + 95 = 5(14 + 19)
70 + 95 = 5(14 + 19)
gcf = 5
Step-by-step explanation:
70+95
70=2*5*7
95=5*19
70+95=(5*2*7)+(5*19)=(5*14)+(5*19)=5*(14+19)=5*(33)
5*33=165 and 70+95=165 Hope this helps! Please give me brainly!
Which dashed line is an asymptote for the graph
Which set can represent the side lengths of a right triangle?
A. 5,11,12
B.2,4, 2sqrt 5
C.6, 7, sqrt 21
D. 5, 7, 5, sqrt 3
Answer:
B
Step-by-step explanation:
2²+4²
=4+16
=20
=√20
which is the same as
=√4×5
= sqrt of 4 is 2
therefore 2√5
6. Select the figure that can be formed when a cube is cut by a plane parallel to its base.
A. line
B. square
C. trapezoid
D. triangle
7. Select all figures that can be formed when a rectangular pyramid is cut by a plane parallel to its base.
A. point
B. rectangle
C. trapezoid
D. triangle
8. This is a cylinder.
Select all figures that can be formed by a vertical slice perpendicular to the bases of the cylinder.
A. circle
B. line segment
C. rectangle
D. oval
9. A family just removed a big tree from their backyard. The diameter of the circular hole left behind is 7 feet across. Approximately how many square feet of grass will the family need if they want to cover the area where the tree once was?
A. 22 ft²
B. 39 ft²
C. 44 ft²
D. 154 ft²
Answer:
Step-by-step explanation:
6. Cross-section is a square.
:::::
7. Point and rectangle
:::::
8. line segment and rectangle
:::::
area of hole = π3.5² = 12.25π ≅ 39 ft²
4 + (7-5)^4 on an iready lesson can someone help ?? the four is a exponet
What is the difference between change in quantity and change in quantity demanded?
A change in demand means that the entire demand curve shifts either left or right. A change in quantity demanded refers to a movement along the demand curve, which is caused only by a chance in price.
it a tets please help it due today
Gribbles are small, pale white, marine worms that bore through wood. While sometimes considered a pest since they can wreck wooden docks and piers, they are now being studied to determine whether the enzyme they secrete will allow us to turn inedible wood and plant waste into biofuel.1 A sample of 50 gribbles finds an average length of 3.1 mm with a standard deviation of 0.72. Give a best estimate for the length of gribbles, a margin of error for this estimate (with 95% confidence), and a 95% confidence interval.
Answer:
The best estimate for the length of gribbles is of 3.1 mm.
The margin of error for this estimate, with 95% confidence, is of 0.2 mm.
The 95% confidence interval is between 2.9 mm and 3.3 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
Best estimate for the length of gribbles
The best estimate is the sample mean, that is 3.1 mm.
Margin of error:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{0.72}{\sqrt{50}} = 0.2[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The margin of error for this estimate, with 95% confidence, is of 0.2 mm.
Confidence interval:
The lower end of the interval is the sample mean subtracted by M. So it is 3.1 mm - 0.2 mm = 2.9 mm
The upper end of the interval is the sample mean added to M. So it is 3.1 mm + 0.2 mm = 3.3 mm
The 95% confidence interval is between 2.9 mm and 3.3 mm.
Hi pls help me thanks :)
Answer:
B
Step-by-step explanation:
A shirt regularly costs $14, but is on sale for 10% off. Sales tax is 6%. What is the cost of the shirt?
Answer:
13.356
Step-by-step explanation:
10/100 = 1.4
14-1.4 = 12.6
12.6*6% = 13.356
Which of the following polygons is not a regular polygon?
Answer:
b
Step-by-step explanation:
polygons is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit
Answer:
rectangle is the answer can i get a brainlist
Step-by-step explanation:
find the percent of the quantity of 110% of 300
Step-by-step explanation:
hop it help you.......
.....
330
Step-by-step explanation:
100% of 300 = 300
10% of 300 = 30
300 + 30 = 330
Please Im stuck. One box contains 24 bottles of soda. Each bottle contains 0.5 dl. Alex celebrates his birthday and 1/3 of the bottles are drunk. A) How many bottles are drunk? B) How many liters of soda are drunk in total on the birthday?
Answer:
(a) 8 bottles(b) 0,4 LitresStep-by-step explanation:
There are
24 bottles/box0,5 decilitres/bottle = 50mL/bottle = 50 × 24 bottles = 1200mL = 1.2 Litres1/3 of the bottles are drunk = 1/3 × 24 = 8 bottles are drunk (a)8 bottles × 50 mL = 400 mL = 0,4 Litre____________________
#IndonesianPride - kexcvi
A sporting goods store is discounting all
sports balls 55%. Which value is equivalent to this
percent?
A. 15/25
B. 11/20
C. 5/10
D. 5/55
The cost of 3 DVD's and 4 CD's is £62.00. The cost of 4 DVD's and 3 CD's is £64.00. Find the cost of each.
Help!!!
Answer:
the cost of each is £10 and £8 respectively
Step-by-step explanation:
Let us assume the cost of per DVD be x
And the cost of per CD be y
Now as per the question
The following equations should be made
3x + 4y = £62.00
4x + 3y = £64.00
Now multiply by 4 in equation 1 and 3 in equation 2
12x + 16y = £248
12x + 9y = £192
7y = £56
y = £8
Now put the value of y in any of the above equation
3x + 4( £8) = £62
3x + £32 = £62
3x = 30
x = £10
Hence, the cost of each is £10 and £8 respectively
Help me please!
Two-thirds of the students in Hannah's homeroom plan to do some volunteering this summer. Of these students,3/5 plan to volunteer at the community center. What fraction of students in Hannah's homeroom plan to volunteer at the community center this summer.
I would rather not have the answer in a file thank you!
2/3 are volunteering.
3/5 are volunteering at the community center.
Multiply the amount from the community center by the total volunteering:
2/3 x 3/5 = (2x3) / (3/5) = 6/15 this can be reduced to 2/5.
The answer is 2/5
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
This is the correct graph but can it fit on your graph?
Step-by-step explanation:
Answer:
is in the photo
Step-by-step explanation:
hope this helps