Using an exponential function, it is found that the multiplier that would allow you to predict the population of bacteria after 2 hours is of 9.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the growth rate.In this problem, the bacteria triples every hour, hence the rate of change is b = 3, and the equation is:
[tex]y = a(3)^x[/tex]
Hence, after 2 hours:
[tex]y = a(3)^2 = 9a[/tex]
Which means that the multiplier is of 9.
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1. In the figure given below, < ABC and < BDC are right angles; If AB-5cm, AD = 3cm and BD = 4cm (3 points) find BC and DC ?
In the given figure, the length of BC is 6.66 cm and the length of DC is 5.33 cm
TrigonometryFrom the question, we are to determine the length of BC and DC
Considering the diagram,
First, we will determine the measure of angle A
Using SOH CAH TOA
We can write that
[tex]sin A = \frac{4}{5}[/tex]
sin A = 0.8
∴ A = sin⁻¹(0.8)
A = 53.13°
Now, we will determine the measure of angle C
∠A + ∠ABC + ∠C = 180° (Sum of angles in a triangle)
53.13° + 90° + ∠C = 180°
∠C = 180° - 90° - 53.13°
∠C = 36.87°
Also,
Using SOH CAH TOA
[tex]tan C = \frac{BD}{DC}[/tex]
[tex]tan36.87 ^\circ=\frac{4}{DC}[/tex]
[tex]0.7500 = \frac{4}{DC}[/tex]
[tex]DC = \frac{4}{0.75}[/tex]
DC = 5.33 cm
By the Pythagorean theorem,
/BC/² = /BD/² + /DC/²
/BC/² = 4² + 5.33²
/BC/² = 16 + 28.4089
/BC/² = 44.4089
/BC/ = √44.4089
/BC/ = 6.66 cm
Hence, the length of BC is 6.66 cm and the length of DC is 5.33 cm
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Find the perimeter. Area=5.612x10^14
9.2x10^7
Answer:
1.962×10^8 cm
Step-by-step explanation:
The area and perimeter formulas can be use to find the perimeter of this rectangle, given its area and the length of one side.
A = LW
P = 2(L +W)
__
Solving the area formula for width, we have ...
W = A/L
Using that in the perimeter formula, we find the perimeter to be ...
P = 2(L +W) = 2(L +A/L)
Using the given values for area and length, we find the perimeter is ...
P = 2(9.2×10^7 +5.612×10^14/(9.2×10^7)) = 1.962×10^8 . . . cm
The perimeter of the rectangle is 1.962×10^8 cm, or 1962 km.
_____
Additional comment
The width is 6.1×10^6 cm, or 0.61×10^7 cm. Then the sum of length and width is (9.2 +0.61)×10^7 = 9.81×10^7 cm. The perimeter is twice that, or 19.62×10^7 cm = 1.962×10^8 cm. 1 km = 10^5 cm, so this is 1.962×10^3 km, or 1962 km.
Your scientific calculator or spreadsheet can use and present numbers in scientific notation directly. The "E" notation is used in place of "×10^". (This notation is an artifact of the earliest computer languages.)
To which quadrants is tan^-1 x restricted?
A. Quadrants I and IV
B. Quadrants III and IV
C. Quadrants II and III
The quadrants is tan⁻¹x restricted is A. Quadrants I and IV
To answer the question, we need to know what tan⁻¹x is.
What is tan⁻¹x?tan⁻¹x is the inverse trigonometric function of tanx, which is the value of the angle for tanx.
Quadrant in which tan⁻¹x is restrictedTo find the quadrants in which tan⁻¹x is restricted, we know that tanx lies in the range
-∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°.
Since the inverse function of tanx is x.tan⁻¹x lies between -90° and 90°. That is -90° ≤ tan⁻¹x ≤ 90°.Since 90° lies in first quadrant and -90° lies in the fourth quadranttan⁻¹x lies between quadrant I and IV
So, the quadrants is tan⁻¹x restricted is A. Quadrants I and IV
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If 2^2^x = 2^3 what is the value of x
Answer:
[tex]\dfrac 32[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^{2x} = 2^3\\\\\implies \ln\left(2^{2x} \right) = \ln (2^3)\\\\\implies 2x \ln(2) = 3 \ln(2) \\\\\implies 2x = 3\\\\\implies x = \dfrac 32[/tex]
Answer:
B
Step-by-step explanation:
Diberi 1 ½s = ⅗t² + ⅓u², hitung (ii) nilai t apabila u = -6 dan s = 28
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
A major arc will have a measure that is
O A. greater than 180°
OB. less than 180°
O C. equal to 180°
which statements are true regarding undefinable terms in geometry?
Please help on the area for 7 8 9 please all i need help is
The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The area of an Isosceles triangle is expressed as A = (ah)/2
Where a is the dimension of the base and h is the height.
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmArea A = ?A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
Area of the Equilateral triangle is 12.6mm²
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inheight h = ?Area A = ?The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
Area of the Isosceles triangle is 9.61in².
For the Right angled triangle
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsArea A = ?A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
Area of the Right angled triangle is 16.81yds²
Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
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what is true about this linear inequality
y>3/4-2
Inequalities help us to compare two unequal expressions. The statements that are correct are B, D, and E.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The complete question is:
Which statements are true about the linear inequality y >3/4 x – 2? Check all that apply.
-The slope of the line is –2.
-The graph of y >3/4 x – 2 is a dashed line.
-The area below the line is shaded.
-One solution to the inequality is (0, 0).
-The graph intercepts the y-axis at (0, –2)
-The slope of the line is 3/4. Thus, the first statement is false.
-The graph of y >3/4 x – 2 is a dashed line. The given statement is true.
-The area below the line is shaded. The statement is false.
-One solution to the inequality is (0, 0). The given statement is true.
-The graph intercepts the y-axis at (0, –2) The statement is true.
Hence, the statements that are correct are B, D, and E.
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Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. If Leah fell asleep after they had travelled 132 miles, what was the total length of the trip?
The total length of the trip 190.08 miles
How you do it is to add the 44% of 132 to 132
= (132 + (132×44%))
What is the length?Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.
First, you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together.
132 × 0.44 is 58.08 miles.
Then you add that to the rest of the trip, 132 miles.
= (132 + 58/08
=190.08
The total length of the trip was 190.08 miles.
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what is this expression in simplified form?
Answer:
33.17 (A)
Step-by-step explanation:
the square root of 22 times (5x the square root of 2)
is 33.17 rounded to the nearest 10th
and 10 x the square root of 11 is 33.17
(they match)
wright the follwing in decimlal form:3/4
Answer:
3/4 in decimal form is 0.75.
Step-by-step explanation:
I hope this helps! :)
Answer:
0.75
Step-by-step explanation:
3/4 is expressed as 0.75 in the decimal form.
to make a fraction into a decimal you just divide the numerator by the
denominator.
and the numerator is the part of a fraction that is above the line
denominator is at the bottom
so 3 / 4 = 0.75
3/4 in decimal form is 0.75
Hope This Helped
■ Write an equivalent expression.
1 (12x+
(12x + 6x − 21) =
?
x
3
?
Answer:
6x - 7
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] (12x + 6x - 21 ) ← multiply each term in the parenthesis by [tex]\frac{1}{3}[/tex]
= 4x + 2x - 7 ← collect like terms
= 6x - 7
Hey there!
ORIGINAL EQUATION:
1/3(12x + 6x - 21)
COMBINE the LIKE TERMS
= 1/3(18x - 21)
DISTRIBUTE 1/3 WITHIN the PARENTHESES:
= 1/3(18x) + 1/3(-21)
SIMPLIFY:
= 6x - 7
Therefore, the answer should be:
6x - 7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
anything that applies. sec0 is undefined for 0 =
If the sec θ is not defined, then the value of angle θ will be (2n + 1)π/2.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric expression is given below.
⇒ sec θ
If the sec θ is not defined, then the value of angle θ will be (2n + 1)π/2.
Where n is the any integer.
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Work out the circumference of this circle.
Give your answer in terms of pi and state its units
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle given the diameter is :
πd
We simply substitute the value given in the image into our formula to find our answer:
πd = π×14 = 14π
Units will be cm as circumference is a length
This is our final answer as the question states to leave it in pi form .
Hope this helped and brainliest please
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle with radius r = 2πr or 2rπ
The diameter d is twice the radius so circumference = dπ
Here d= 14 so the answer is 14π cm
A jar contains five blue marbles, six red marbles, and four green marbles. What are the odds you will draw a blue marble from this jar?
Answer:
Probability=number of specific outcomes/total of all possible outcomes
There are 5 blue marbles and a total of 15 marbles.
So the probability of drawing a blue marble from the jar is:
5/15
1/3
Step-by-step explanation:
Hope this helps
Considering the results from part a, it follows that the volume of a cylinder can be found in the same way as the volume of a rectangular prism. use your results and what you know about volume to explain how to find the volume of a cylinder with a base radius of r units and a height of h units.
To find the volume of a cylinder we must perform a mathematical operation that is expressed in the following formula V = Π h r².
How to find the volume of a cylinder?To find the volume of a cylinder we must solve the following mathematical formula:
V = Πhr²let's do an exampleOur example cylinder is 10 centimeters high and 6 centimeters in diameter. What is its volume?
To find the volume we substitute the values as follows:
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Which equation is showed in the graph above
Answer: A
It has a negative gradient.
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
Answer:
Step-by-step explanation:
Remark
You can read the y intercept right off the graph. Follow the y axis upwards until the line intercepts the y axis. I think you will find it is at 0,5
So far what you know is
y = mx + 5
Finding m is a little harder. I would use 6,0 and 0,5 as the two points that will define m.
Givens
x1 = 6
x2 = 0
y1 = 0
y2 = 5
Equation
m = (y2 - y1) / (x2 - x1) Put the givens into this equation.
Solution
m = (5 - 0) / (0 - 6)
m = 5/-6
m = - 5/6
Answer
The line is
y = -5/6 x + 5
Which one is the right answer
Answer:
The answer is C. Quadrant 3.
Step-by-step explanation:
Looking up a Unit Circle. We can see that 5pi/4 is in quadrant 3.
5pi/4 is also if in degree angle as 225°
In the expression 67.8046 8.264 - 243.5, all of the numbers are measured quantities and have the same units. Evaluate this expression to the correct number of significant figures.
The result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
How to evaluate the expression?The expression is given as:
67.8046 + 8.264 - 243.5
The highest number of significant figures in the expression is 6 (i.e. 67.8046)
This means that the result must be in 6 significant figures.
Next, we evaluate the expression as follows:
67.8046 + 8.264 - 243.5 = -167.4314
Approximate to 6 significant figures.
67.8046 + 8.264 - 243.5 = -167.431
Hence, the result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
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There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?
Answer:
12.5% is the answer.
Step-by-step explanation:
Sketch a graph of each of the four angles in the same coordinate plane. Label the ordered pairs that intersect the circle. The angles given are 30°, 150°, 210°, 330°
When two straight lines or rays intersect at a shared endpoint, an angle is generated.
What is an angle?When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."
The angle can be drawn as shown below. The angle 30°, 150°, 210°, and 330° will lie in 1st, 2nd, 3rd, and 4th quadrants respectively.
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Determine the scale of a map if the distance between 2 towns is 20km and the map distance is 5cm
The required ratio or scale will be 5cm o the map represent 20km on land
Ratio and scalingScaling is a way of enlarging or reducing the figure on an xy-plane. Given the conversion rate;
Given the following
distance between 2 towns is 20km
The distance on map is 5cm. The required ratio or scale will be 5cm o the map represent 20km on land
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ray and line segment difference
Answer:
A line segment is part of a line that has two endpoints and is finite in length. A ray is a line segment that extends indefinitely in one direction.
Step-by-step explanation:
hope it helps you and give me a brainliest
Answer:
A ray goes in one direction for forever, and also has an arrow.
A line segment is a segment, meaning that it has two end points and doesn't go on forever, it ends.
Step-by-step explanation:
answer fast pls .....
1. In a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example ofIn a sample of 800 students in BNHS, 160, or
20%, are Grade 7 students Based on the above
information, the school's paper reported that "20% of
all the students at BNHS are grade 7." This report is
an example of
a. a sample
b. a population
c. statistical inference
d. descriptive statistics
19.. A statistics professor asked students in a class
their ages. On the basis of this information, the
professor states that the average age of all the
students in the university is 21 years. This is an
example of
a. a census
b. descriptive statistics
c. an experiment
d. statistical inference
20. A tabular summary of a set of data showing the
fraction of the total number of items in several classes
is a
a. frequency distribution
b. relative frequency distribution
c. frequency
d. cumulative frequency distribution
Answer:
1. c. statistical inference
19. d. statistical inference
20. b. relative frequency distribution
Consider the functions below.
f(x) = x² - 6x - 27
g(x) = x - 9
An account earns annual simple interest. Find the balance of
the account.
$250 at 4% for 1 year
HELP FAST
The balance of the account which earns annual simple interest of $250 at 4% for 1 year is $260
How to find simple interest?Principal, P = $250Interest rate, r = 4%Time, t = 1 yearSimple interest = principal × rate × time
= 250 × 4% × 1
= 250 × 0.04 × 1
= $10
Balance = Principal + Simple interest
= $250 + $10
= $260
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If 2a/4=b/4 and b≠0, what does 5b equal in terms of a?
A) 2a/15
B) 5a/6
C) 15/2a
D) 40a/3
Step-by-step explanation:
you must have made a typo here.
none of the answer options are correct for the given problem.
let me just show you what you told me, and how I can solve at least this :
2a/4 = b/4
this simply means (multiply both sides by 4) :
2a = b
so, 5b is then (multiplying both sides by 5) :
5×2a = 5b
10a = 5b
but again, "10a" is not among the offered answers.
so, I don't know if you made a mistake with the basic problem or with the answer options.
Which equation shows an example of the associative property of addition?
Answer:
(2+3)+4 = 2+(3+4) this is an example of associative property