given ABCD is congruent EFGH. solve for x. Round the answers to the nearest hundredth
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As ABCD is congruent withEFGH, it means that both figures have the same mesarurements, even if their orientation is different.
Then, you have that the angle in A is congruente with the angle in E, the angle B is congruent with the angle F, the angle C is congruent with the angle G, the angle D is congruent with the angle H.
[tex]\begin{gathered} \angle A=\angle E \\ \angle B=\angle F \\ \angle C=\angle G \\ \angle D=\angle H \end{gathered}[/tex]Then:
[tex]3x^2-4x+10=16[/tex]You solve the x from the equation above:
1. Equal the equation to 0
[tex]\begin{gathered} 3x^2-4x+10-16=0 \\ 3x^2-4x-6=0 \end{gathered}[/tex]2. Use the quadratic equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex][tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(3)(-6)}}{2(3)} \\ x=\frac{4\pm\sqrt[]{16+72}}{6} \\ x=\frac{4\pm\sqrt[]{88}}{6} \\ x_1=\frac{4-\sqrt[]{88}}{6},x_2=\frac{4+\sqrt[]{88}}{6} \\ x_1=-0.896,x_2=2.230 \end{gathered}[/tex]3. As you get two solutions for x. You need to prove which is the right solution:
with x1:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(-0.896^2)-4(-0.869)+10=16 \\ 11.17\ne16 \end{gathered}[/tex]with x2:
[tex]\begin{gathered} 3x^2-4x+10=16 \\ 3(2.23^2)-4(2.23)+10=16 \\ 15.99\approx16 \end{gathered}[/tex]As you can see the right solution is x2, because if you subtitute the x in the equation of the angle A that must be equal to 16, just the x2 gives an approximate value to 16.
Then, the solution for the x is x=2.23Related Questions
A 12 -inch ruler is closest in length to which one of the following Metric units of measure? 0.030 Kilometers30,000 millimeters30 centimeters30 meters
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Inch is one of the units of measuring length.
Converting from inch to meters,
[tex]1inch=0.0254m[/tex]A 12-inch ruler converted to meters will be;
[tex]12\times0.0254=0.3048m[/tex]Converting the meter equivalent of the ruler into the sub-units of meters measurement,
[tex]\begin{gathered} 0.3048m \\ To\text{ kilometer} \\ 1000m=1\operatorname{km} \\ 0.3048m=\frac{0.3048}{1000}=0.0003048\operatorname{km} \\ \\ To\text{ millimeter} \\ 1m=1000\operatorname{mm} \\ 0.3048m=0.3048\times1000=304.8\operatorname{mm} \\ \\ \\ To\text{ centimeters} \\ \text{1m =100cm} \\ 0.3048m\text{ =0.3048}\times100=30.48\operatorname{cm} \\ \\ \\ To\text{ meters } \\ 12\text{ inch = 0.3048m} \end{gathered}[/tex]From the conversions of metric units of length above, the 12-inch ruler measures 30.48cm which is closest to 30cm
Therefore, the ruler is closest to 30 centimeters
help meeeee pleaseeeee!!!
thank you
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The values of f(4) , f(0) and f(-5) are 16/7, -12 and -7/11 respectively.
We are given the function:-
f(x) = (x + 12)/(2x - 1)
We have to find the values of f(4) , f(0) and f(-5).
Putting x = 4 in the given function, we can write,
f(4) = (4+12)/(2*4-1) = 16/7
Putting x = 0 in the given function, we can write,
f(0) = (0 + 12)/(2*0 - 1) = 12/(-1) = -12
Putting x = -5 in the given function, we can write,
f(-5) = (-5 + 12)/(2*(-5) - 1) = 7/(-10-1) = 7/(-11) = -7/11
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I think of a number.
I add 5 to it and then double the result.
I then subtract 10 from this answer.
I then subtract the original number I thought of.
Using algebra and a pronumeral to represent the number I think of, explain
why I get back to the number I started with.
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Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x
Step-by-step explanation:
I think of a number, represented by the variable/pronumeral x.
I add 5 to it: x + 5
then double the result: 2(x + 5)
I then subtract 10 from this answer: [2(x + 5)] - 10
I then subtract the original number I thought of: [2(x + 5)] - 10 - x
Simplifying the expression will explain why you get the original number.
[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.
The slope and one point on the line are given. Find the equation of the line (in slope-intercept form).(1/4, -4) ; m = -3 y=
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Answer
y = -3x - 13/4
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept.
Substituting into the general equation with m = -3 and the point (1/4, -4), that is, x = 1/4 and y = -4, and solving for b:
[tex]\begin{gathered} -4=(-3)\cdot\frac{1}{4}+b \\ -4=-\frac{3}{4}+b \\ -4+\frac{3}{4}=-\frac{3}{4}+b+\frac{3}{4} \\ -\frac{13}{4}=b \end{gathered}[/tex]Substituting into the general equation with m = -3 and b = -13/4, we get:
[tex]\begin{gathered} y=(-3)x+(-\frac{13}{4}) \\ y=-3x-\frac{13}{4} \end{gathered}[/tex]Kepler's third law of planetary motion states that the square of the time required for a planet to make one revolution about the sun varies directly as the cube of the average distance of the planet from the sun. If you assume that Jupiter is 5.2 times as far from the sun as is the earth, find the approximate revolution time for Jupiter in years.
Show work pls ;-;
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By applying Kepler's third law of planetary motion, the approximate revolution time for Jupiter is equal to 12 years.
What is Kepler's third law?Mathematically, Kepler's third law of planetary motion is given by this mathematical expression:
T² = a³
Where:
T represents the orbital period.a represents the semi-major axis.Note: Earth has 1 astronomical unit (AU) in 1 year of time.
For this direct variation, the value of the constant of proportionality (k) is given by:
T² = ka³
k = T²/a³
k = 1²/1³
k = 1.
When the semi-major axis or the distance of Jupiter from Sun is 5.2, we have;
T² = ka³
T² = 1 × 5.2³
T² = 140.608
T = √140.608
T = 11.858 ≈ 12 years.
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In the diagram below, if < ACD = 54 °, find the measure of < ABD
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Opposite angles in a quadrilateral inscribed in a circle add up to 180, therefore:
[tex]\begin{gathered} m\angle ACD+m\angle ABD=180 \\ 54+m\angle ABD=180 \\ m\angle ABD=180-54 \\ m\angle ABD=126^{\circ} \end{gathered}[/tex]Answer:
b. 126
A typical soda can has a diameter of 5.3 centimeters and height of 12 centimeters. How many square centimeters of aluminum is needed to make the can? My answer is 244. I am confused how I got the answer.
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The can is made up of aluminium.
So the area of the can must be equal to the area of the Aluminium sheet.
The can is in the form of a cylinder with diameter (d) 5.3 cm, and height (h) 12 cm.
Then its area is calculated as,
[tex]\begin{gathered} A=\pi d(\frac{d}{2}+h) \\ A=\pi(5.3)(\frac{5.3}{2}+12) \\ A=243.9289 \\ A\approx244 \end{gathered}[/tex]Thus, the area of the Aluminium sheet required is 244 square centimeters.
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
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The derivative of the function f(x) = √x-5 is 1/2√(x-5)
Given f(x) = √x-5
from the formula d/dx (√x) = 1/2√x
hence d/dx √x-5 = 1/2√x-5
or
d/dx √x-5 = 1/2 (x-5)¹/²
The formula for the derivative of root x is d(x)/dx = (1/2) x-1/2 or 1/(2x). The exponential function with x as the variable and base equal to 1/2 is the root x provided by x. Utilizing the Power Rule and the First Principle of Derivatives, we can get the derivative of root x.
Hence we get the value as 1/2 (x-5)¹/²
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O EQUATIONS AND INEQUALITIESSolving a word problem with three unknowns using a linear...
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Given:
The sum of three numbers is 81, The third number is 2 times the second, The first number us 9 moe than the second.
Required:
We need to find all the numbers
Explanation:
Assume that a, b and c are the first, second and third numbers respectively.
By given ststement
[tex]\begin{gathered} a+b+c=81\text{ .....\lparen i\rparen} \\ c=2b\text{ .....\lparen ii\rparen} \\ a=b+9\text{ .....\lparen iii\rparen} \end{gathered}[/tex]substitute c and a in equation (i)
[tex]\begin{gathered} b+9+b+2b=81 \\ 4b=72 \\ b=18 \end{gathered}[/tex]now put value of b in equation (ii) and (iii)
[tex]c=2*18=36[/tex]and
[tex]a=18+9=27[/tex]FInal answer:
first number a = 27
second number b = 18
third number c = 36
pls help. i dont get it
Answers
Answer:
hey what don't u get? u didn't show the question
Help me please what is the probability of all the letters?
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Given:
• Number of male who survived = 338
,• Number if female sho survived = 316
,• Number f children who survived = 57
,• Number of male who died = 1352
,• Number of female who died = 109
,• Number of children who died = 52
,• Total number of people = 2224
Let's solve for the following:
(a). Probability of the passenger that survived:
[tex]P(\text{survived)}=\frac{nu\text{mber who survived}}{total\text{ number if people }}=\frac{711}{2224}=0.320[/tex](b). Probability of the female.
We have:
[tex]P(\text{female)}=\frac{\text{ number of females}}{total\text{ number }}=\frac{425}{2224}=0.191[/tex](c). Probability the passenger was female or a child/
[tex]P(\text{female or child)}=\frac{425}{2224}+\frac{109}{2224}=\frac{425+109}{2224}=0.240[/tex](d). Probability that the passenger is female and survived:
[tex]P(femaleandsurvived)=\frac{316}{2224}=0.142[/tex](e). Probability the passenger is female and a child:
[tex]P(\text{female and child)=}\frac{425}{2224}\times\frac{109}{2224}=0.009[/tex](f). Probability the passenger is male or died.
[tex]P(male\text{ or died) = P(male) + }P(died)-P(male\text{ and died)}[/tex]Thus, we have:
[tex]P(\text{male or died)}=\frac{1690}{2224}+\frac{1513}{2224}-\frac{1352}{2224}=0.832[/tex](g). If a female passenger is selected, what is the probability that she survived.
[tex]P(\text{survived}|\text{female)}=\frac{316}{425}=0.744[/tex](h). If a child is slelected at random, what is the probability the child died.
[tex]P(died|\text{ child)=}\frac{52}{109}=0.477[/tex](i). What is the probability the passenger is survived given that the passenger is male.
[tex]=\frac{338}{1690}=0.2[/tex]ANSWER:
• (a). 0.320
,• (b). 0.191
,• (c). 0.240
,• (d). 0.142
,• (e). 0.009
,• (f). 0.832
,• (g) 0.744
,• (h). 0.477
,• (i) 0.2
Kaitlin's family is planning a trip from WashingtonD.C., to New York City New York City is 227 miles from Washington, D.C.and the family can drive an average of 55mi / h . About how long will the trip take?
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Kaitlin's family's trip from Washington D.C., to New York City of 227 miles at average rate of 55 miles per hour is 4 hours 8 minutes
How to determine the how long the trip will takeinformation gotten from the question include
Washington D.C., to New York City is 227 miles
Kaitlin's family can drive an average of 55mi / h
Average speed is a function of ratio distance covered with time. this is represented mathematically as
average speed = distance covered / time
55 miles / h = 227 miles / time
time = 227 / 55
time = 4.127 hours
The trip take 4.127 hours
0.127 * 60 = 7.62 ≅ 8 minutes
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Consider the following loan. Complete parts (a)-(c) below.An individual borrowed $67,000 at an APR of 3%, which will be paid off with monthly payments of 347$ for 22 years.a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.The amount borrowed is $____ the annual interest rate is ____, the number of payments per year is _____, the loan term is _____ years, and the payment amount is _____$ b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?There are ____ payments toward the loan and the total amount paid is ____$ c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?The percentage paid toward the principal is _____% and the percentage paid for interest is ____%.(Round to the nearest tenth as needed.)
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b) There are 12 payments per year for 22 years; multiply 12 by 22 to get the total number of payments:
[tex]12\times22=264[/tex]To find the total amount paid, multiply the number of payments by the payment amount:
[tex]264\times347=91,608[/tex]There are 264 payments toward the loan and the total amount paid is $91,608c) Toward principal: $67,000
Toward interest: subtract the principal from the payment amount:
[tex]91,608-67,000=24,608[/tex]Let 91,608 be the 100%, use a rule of three to find the % corresponding to the principal and interest:
[tex]\begin{gathered} Principal: \\ x=\frac{67,000\times100}{91,608}=73.1 \\ \\ Interest: \\ x=\frac{24,608\times100}{91,608}=26.9 \end{gathered}[/tex]The percentage paid toward the principal is 73.1% and the percentage paid for interest is 26.9%-1/2 (2/5y - 2) (1/10y-4)
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we multiply the first parenthesis by its coefficient
[tex]\begin{gathered} ((-\frac{1}{2}\times\frac{2}{5}y)+(-\frac{1}{2}\times-2))(\frac{1}{10}y-4) \\ \\ (-\frac{2}{10}y+\frac{2}{2})(\frac{1}{10}y-4) \\ \\ (-\frac{1}{5}y+1)(\frac{1}{10}y-4) \end{gathered}[/tex]now multiply each value and add the solutions
[tex]\begin{gathered} (-\frac{1}{5}y\times\frac{1}{10}y)+(-\frac{1}{5}y\times-4)+(1\times\frac{1}{10}y)+(1\times-4) \\ \\ (-\frac{1}{50}y^2)+(\frac{4}{5}y)+(\frac{1}{10}y)+(-4) \\ \\ -\frac{1}{50}y^2+(\frac{4}{5}y+\frac{1}{10}y)-4 \\ \\ -\frac{1}{50}y^2+\frac{9}{10}y-4 \end{gathered}[/tex]When a projectile is launched at an initial height of H feet above the ground at an angle of theta with the horizontal and initial velocity is Vo feet per second. the path of the projectile...
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Given,
The initial height of H feet.
The initial velocity of the object is Vo.
The equation of the path of projectile is,
[tex]y=h+x\text{ tan }\theta-\frac{x^2}{2V_0\cos ^2\theta}_{}\text{ }[/tex]This is the expression of the projectle path.
Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)
CRITICAL THINKING Describe two different sequences of transformations in which the blue figure is the image of the red figi 1 1 2 B I y ET
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1) rotation 90° clockwise over the origin and a reflection over the x-axis
2) rotation 90° counter clockwise over the origin and reflection over y-axis
Find all values for which at least one denominator is equal to 0.
Answers
Given:
There are given the expression:
[tex]\frac{4}{x+2}-\frac{5}{x}=1[/tex]Explanation:
To find the value of x that is equal to 0, we need to perform LCM in the denominator and then find the value for x:
Then,
From the given expression:
[tex]\begin{gathered} \frac{4}{x+2}-\frac{5}{x}=1 \\ \frac{4x-5(x+2)}{x(x+2)}=1 \end{gathered}[/tex]Then,
According to the question, the values at least one denominator is equal to .
So,
[tex]\begin{gathered} x(x+2)=0 \\ x=0 \\ x+2=0 \\ x=-2 \end{gathered}[/tex]Final answer:
Hence, the value of x is shown below:
[tex]x\ne0,-2[/tex]
Look at the expression below.2h + y 4h^2_______ - _____9h^2-y^2 3h+yWhich of the following is the least common denominator for the expression?
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Answer:
(3h+y)*(3h-y)
Step-by-step explanation:
We are given the following expression:
[tex]\frac{2h+y}{9h^2-y^2}-\frac{4h^2}{3h+y}[/tex]We want to find the LCD for:
9h²-y² and 3h + y.
3h+y is already in it's most simplified way.
9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:
(3h-y)*(3h+y).
The factors of each polynomial is:
3h + y and (3h-y)*(3h+y)
The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).
So the LCD is:
(3h+y)*(3h-y)
Which is option B.
What are all of the answers for these questions? Use 3 for pi. Please do not use a file to answer, I cannot read it.
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The company's sign has two(2) congruent trapezoids and two(2) congruent right angled triangle.
The area of the figure is:
[tex]A_{\text{figure}}=2A_{\text{trapezoid}}+2A_{\text{triangle}}[/tex]The area of a trapezoid is given by the formula:
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(a+b)h \\ \text{where a and b are opposite sides of the trapezoid} \\ h\text{ is the height} \end{gathered}[/tex]Thus, we have:
[tex]\begin{gathered} A_{\text{trapezoid}}=\frac{1}{2}(1\frac{1}{2}+3)2 \\ A_{\text{trapezoid}}=\frac{1}{2}(1.5+3)2 \\ A_{\text{trapezoid}}=\frac{1}{2}\times4.5\times2=4.5m^2 \end{gathered}[/tex]Area of a triangle is given by the formula:
[tex]A_{\text{triangle}}=\frac{1}{2}\times base\times height[/tex]Thus, we have:
[tex]\begin{gathered} A_{\text{triangle}}=\frac{1}{2}\times2\times1\frac{1}{2} \\ A_{\text{triangle}}=\frac{1}{2}\times2\times1.5=1.5m^2 \end{gathered}[/tex]Hence, the area of the company's sign is:
[tex]\begin{gathered} A=(2\times4.5)+(2\times1.5) \\ A=9+3=12m^2 \end{gathered}[/tex]Count the unit squares, and Ind the surface area of the shape represented byeach net. One cube = 1 ft^2
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The surface area of the figure is the sum of the area of the squares. Since they're all equal, is the amount of squares times the area of one square. We have a total of six squares, with a side length equal to 4 units. The area of a square is given by the product of its side length by itself, therefore, the total surface area of this figure is
[tex]6\cdot(4^2)=6(16)=96[/tex]The area of this figure is 96 ft².
Answer: 72 Square Meters sorry super late
Step-by-step explanation:
provide evidence that this function is not one to one. explain how your evidence supports that g(x) is not one to one
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we have the function
g(x)=(x/3)+2 ---------> interval (-infinite, 1)
g(x)=4x-2 ------> interval [1, infinite)
the given function is not one-to -one function, because don't pass the Horizontal Line Test.
Example
For the horizontal line
y=2
we have the values of
x=0 ---------> g(x)=(x/3)+2
and
x=1 -----------> g(x)=4x-2
that means
two elements in the domain of g(x) correspond to the same element in the range of g(x)
therefore
the function is not one to oneUse the method of equating coefficients to find the values of a, b, and c: (x + 4) (ar²+bx+c) = 2x³ + 9x² + 3x - 4.A. a = -2; b= 1; c= -1OB. a=2; b= 1; c= 1OC. a=2; b= -1; c= -1OD. a=2; b= 1; c= -1
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To find the coefficients we first need to make the multipliation on the left expression:
[tex]\begin{gathered} (x+4)(ax^2+bx+c)=ax^3+bx^2+cx+4ax^2+4bx+4c \\ =ax^3+(4a+b)x^2+(4b+c)x+4c \end{gathered}[/tex]Then we have:
[tex]ax^3+(4a+b)x^2+(4b+c)x+4c=2x^3+9x^2+3x-4[/tex]Two polynomials are equal if and only if their coefficients are equal, this leads to the following equations:
[tex]\begin{gathered} a=2 \\ 4a+b=9 \\ 4b+c=3 \\ 4c=-4 \end{gathered}[/tex]From the first one it is clear that the value of a is 2, from the last one we have:
[tex]\begin{gathered} 4c=-4 \\ c=-\frac{4}{4} \\ c=-1 \end{gathered}[/tex]Plugging the value of a in the second one we have:
[tex]\begin{gathered} 4(2)+b=9 \\ 8+b=9 \\ b=9-8 \\ b=1 \end{gathered}[/tex]Therefore, we conclude that a=2, b=1 and c=-1 and the correct choice is D.
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeEnter a decimal rounded to the nearest hundredth.Enter
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Explanation:
The total number of students is
[tex]n(S)=35[/tex]Concept:
To figure out the probability that a student earns grade A,B or C
Will be calculated below as
[tex]P(A,BorC)=P(A)+P(B)+P(C)[/tex]The Probability of A is
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{5}{35}[/tex]The probabaility of B is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{10}{35}[/tex]The probabaility of C is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{15}{35}[/tex]Hence,
By substituting the values in the concept, we will have
[tex]\begin{gathered} P(A,BorC)=P(A)+P(B)+P(C) \\ P(A,BorC)=\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\frac{30}{35} \\ P(A,BorC)=0.857 \\ P(A,BorC)\approx0.86(nearest\text{ }hundredth) \end{gathered}[/tex]Hence,
The final answer is
[tex]0.86[/tex]Solve.(3.3 × 10³) (2 × 10²)
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Here are the steps in multiplying scientific notations:
1. Multiply the coefficients first.
[tex]3.3\times2=6.6[/tex]2. Multiply the base 10 by adding their exponents.
[tex]10^3\times10^2=10^{3+2}=10^5[/tex]3. Connect the result in steps 1 and 2 by the symbol for multiplication.
[tex]6.6\times10^5[/tex]Hence, the result is 6.6 x 10⁵.
Adding mixed fractions (A)1 1/14 + 3 1/14 =
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Explanation:
To add mixed fractions we have to follow these steps:
[tex]1\frac{1}{14}+3\frac{1}{14}=[/tex]1. Add the whole numbers together
[tex]1+3=4[/tex]2. Add the fractions
[tex]\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7}[/tex]3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.
In this case the sum of the fractions results in a proper fraction, so we can skip this step.
Answer:
The result is:
[tex]4\frac{1}{7}[/tex]
In the diagram, MN is parallel to KL. What is the length of MN? K M 24 cm 6 cm 2 12 cm L O A. 6 cm O B. 18 cm O c. 12 cm D. 8 cm
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To solve this question, we shall be using the principle of similar triangles
Firstly, we identify the triamgles
These are JKL and JMN
JKL being the bigger and JMN being the smaller
Mathematically, when two triangles are similar, the ratio of two of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{JN}{MN}\text{ = }\frac{JL}{KL} \\ \\ \frac{6}{MN}=\text{ }\frac{18}{24} \\ \\ MN\text{ = }\frac{24\times6}{18} \\ MN\text{ = 8 cm} \end{gathered}[/tex]A biologist just discovered a new strain of bacteria that helps defend the human body against the flu virus. To know the dosage that should be given to someone, the doctor must first know if the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are now 12 cells in the dish.
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Part 3
An exponential growth function has the general form:
[tex]f(t)=a\cdot(1+r)^t[/tex]where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:
[tex]f(0)=a(1+r)^0=a\cdot1=a[/tex]Thus, the constant a is the initial value of the function.
Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:
[tex]C(h)=C(0)\cdot(1+r)^h[/tex]Notice that we represented the time by the letter h instead of t.
Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:
[tex]\begin{gathered} C(1)=10\cdot(1+r)^1 \\ \\ 12=10+10r \\ \\ 12-10=10r \\ \\ 10r=2 \\ \\ r=0.2 \end{gathered}[/tex]Thus, the number of cells C(h) is given by:
[tex]C(h)=10\cdot(1.2)^h[/tex]Notice that this is valid for C(15) = 154:
[tex]C(15)=10\cdot(1.2)^{15}\cong154.07\cong154_{}[/tex]Part 1
Then, using this formula, we find:
[tex]\begin{gathered} C(2)=10(1.2)^2\cong14 \\ \\ C(3)=10(1.2)^3\cong17.3\cong17 \\ \\ C(4)=10(1.2)^4\cong20.7\cong21 \\ \\ C(5)=10(1.2)^5\cong24.9\cong25 \\ \\ C(6)=10(1.2)^6\cong29.9\cong30 \\ \\ C(7)=10(1.2)^7\cong35.8\cong36 \\ \\ C(8)=10(1.2)^8\cong43 \\ \\ C(9)=10(1.2)^9\cong51.6\cong52 \\ \\ C(10)=10(1.2)^{10}\cong61.9\cong62 \\ \\ C(11)=10(1.2)^{11}\cong74.3\cong74 \\ \\ C(12)=10(1.2)^{12}\cong89.2\cong89 \\ \\ C(13)=10(1.2)^{13}\cong107 \\ \\ C(14)=10(1.2)^{14}\cong128.4\cong128 \end{gathered}[/tex]Part 2
Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:
Part 4
Using a calculator, we obtain the following graph of the function C(h):
Comparing the graph to the plot of the data, we see that they match.
Part 5
After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):
[tex]C(24)=10(1.2)^{24}\cong795[/tex]Therefore, the answer is 795 cells.
A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Answers
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
Show the steps needed to Evaluate (2)^-2
Answers
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]2^{-2}[/tex]
[tex]\boxed{\textsf{Exponent rule}: \quad a^{-n}=\dfrac{1}{a^n}}[/tex]
Apply the exponent rule to the given expression:
[tex]\implies 2^{-2}=\dfrac{1}{2^2}[/tex]
Two squared is the same as multiplying 2 by itself, therefore:
[tex]\begin{aligned}\implies 2^{-2}&=\dfrac{1}{2^2}\\\\&=\dfrac{1}{2 \times 2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]
Solution
[tex]2^{-2}=\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
Now we have to,
→ find the required value of (2)^-2.
Let's solve the problem,
→ (2)^-2
→ (1/2)² = 1/4
Therefore, the value is 1/4.
A popcorn stand offers buttered or unbuttered popcorn in three sizes: small, medium, and large. What is the P(buttered)
Answers
The popcorn we can order is either buttered or unbuttered.
Therefore, the probability of choosing buttered popcorn is 1/2