Given that the population can be represented by the equation;
[tex]P(t)=\frac{2t^2+75}{2t^2+150}[/tex]The current population (Initial population) is the population at time t=0;
Substituting;
[tex]t=0[/tex][tex]\begin{gathered} P(0)=\frac{2t^2+75}{2t^2+150}=\frac{2(0)^2+75}{2(0)^2+150}=\frac{75}{150} \\ P(0)=0.5\text{ million} \end{gathered}[/tex]Therefore, the current population of the habitat is;
[tex]0.5\text{ million}[/tex]The long term population would be the population as t tends to infinity;
[tex]\begin{gathered} \lim _{t\to\infty}P(t)=\frac{2t^2+75}{2t^2+150}=\frac{2(\infty)^2+75}{2(\infty)^2+150}=\frac{\infty}{\infty} \\ \lim _{t\to\infty}P(t)=\frac{4t}{4t}=1 \end{gathered}[/tex]Therefore, the long term population of the habitat is;
[tex]P(\infty)=1\text{ million}[/tex]You have a set of cards labeled one through ten. Event A is drawing an even card. Event B is drawing a seven or higher. What is the P(A∩B) ?
Hello!
First, let's write the information that we know and then each event:
[tex]Set=\mleft\{1,2,3,4,5,6,7,8,9,10\mright\}[/tex]Event A is drawing an even card:[tex]A=\mleft\lbrace2,4,6,8,10\mright\rbrace[/tex]Event B is drawing a seven or higher:[tex]B=\mleft\lbrace7,8,9,10\mright\rbrace[/tex]When we use the interception symbol (∩), it means that we want to know which numbers are part of both sets simultaneously.
Let's calculate it:
[tex]A\cap B=\mleft\lbrace8,10\mright\rbrace[/tex]The ratio of boys to girls in our class is 1210
The ratio of boys to girls in our class is 12:10
that means
12 divided by 10
so
12/10
simplify
6/5 or 6:5
Can you please help me out
The bag contains,
Red (R) marbles is 9, Green (G) marbles is 7 and Blue (B) marbles is 4,
Total marbles (possible outcome) is,
[tex]\text{Total marbles = (R) + (G) +(B) = 9 + 7 + 4 = 20 marbles}[/tex]Let P(R) represent the probablity of picking a red marble,
P(G) represent the probability of picking a green marble and,
P(B) represent the probability of picking a blue marble.
Probability , P, is,
[tex]\text{Prob, P =}\frac{required\text{ outcome}}{possible\text{ outcome}}[/tex][tex]\begin{gathered} P(R)=\frac{9}{20} \\ P(G)=\frac{7}{20} \\ P(B)=\frac{4}{20} \end{gathered}[/tex]Probablity of drawing a Red marble (R) and then a blue marble (B) without being replaced,
That means once a marble is drawn, the total marbles (possible outcome) reduces as well,
[tex]\begin{gathered} \text{Prob of a red marble P(R) =}\frac{9}{20} \\ \text{Prob of }a\text{ blue marble =}\frac{4}{19} \\ \text{After a marble is selected without replacement, marbles left is 19} \\ \text{Prob of red marble + prob of blue marble = P(R) + P(B) = }\frac{9}{20}+\frac{4}{19}=\frac{251}{380} \\ \text{Hence, the probability is }\frac{251}{380} \end{gathered}[/tex]Hence, the best option is G.
Question 2: 14 ptsOut of the 10,000 people who took their driving test for the first time, it was found that 6500 passed the test onthe first attempt. Estimate the probability that a randomly selected person would pass the driving test on thefirst attempt.A0 0.5, or 50%O 0.65, or 65%O 0.8. or 80%• 0.35, or 35%
To calculate the probability of an event we would use the probability formula as follows;
[tex]P\lbrack E\rbrack=\frac{\text{Number of required outcomes}}{Number\text{ of possible outcomes}}[/tex]From the experiment conducted, 10,000 people took the driving test and 6500 passed the test on the first attempt. Therefore, to find the probability that a person randomly selected would pass the driving test on first attempt;
[tex]\begin{gathered} P\lbrack\text{first attempt\rbrack=}\frac{Number\text{ of required outcomes}}{Number\text{ of all possible outcomes}} \\ P\lbrack\text{first attempt\rbrack=}\frac{6500}{10000} \\ P\lbrack\text{first attempt\rbrack=}\frac{65}{100} \\ P\lbrack\text{first attempt\rbrack=0.65 or 65\%} \end{gathered}[/tex]ANSWER:
The second option is the correct answer.
Which fraction has a value greater than 0.4? A 1/3 B 4/10 C 3/8 D 5/9
Answer:
D 5/9
Step-by-step explanation:
This fraction equates to over 0.5
Answer:
1/2, 5/8, 3/4
Step-by-step explanation:
1/2 is 0.5 5/8 is .625 and 3/4 is .75
Find the distance between the points (0, 4) and (-7, -5).Round to the nearest tenthThe distance between them isunits.alm3
the distance between the points is
[tex]d=\sqrt[]{(-5-4)^2+(-7-0)^2}[/tex][tex]\begin{gathered} d=\sqrt[]{(-9)^2+(-7)^2} \\ d=\sqrt[]{81+49} \\ d=\sqrt[]{130} \end{gathered}[/tex][tex]d=11.401[/tex]rounding off to nearest tenth
d = 11.4
solve by factoring, by square roots, by completing the square, or using the quadratic formulaSolve for x in the equation belowX^2 −15x+54=0
STEP 1: Identify and Set up.
We have a quadratic equation and are asked to solve, i.e, solve for x. We approach this problem via the factoring method.
We look for two factors of the third term, c that add up to the coefficient of x, favtorise and solve.
STEP 2: Execute
[tex]\begin{gathered} x^2-15x+54=0 \\ \text{the factors are -6 and -9} \\ x^2-9x-6x+54=0 \\ Factorizing\text{ gives us:} \\ x(x-9)-6(x-9)=0 \\ (x-9)(x-6)=0 \\ x\text{ is either 9 or 6} \end{gathered}[/tex]x = 9 and x = 6
identify the special product by writing the letter of the answer provided. ( number 7 question in photo. )
(7)
Given the equation;
[tex](y+9)(y-9)=y^2-81[/tex]A binommial is a polynomial that is the sum of two terms, that is;
[tex]y^2-81\ldots.\ldots\ldots\ldots.\text{ is a binommial}[/tex]Thus;
[tex](y+9)(y-9)=y^2-81[/tex]is a binommial that is a product of sum and difference of two terms.
CORRECT OPTION: D
In Exercises ***, find the value of x so that the function has the given value.4. f(x) = 6x; f(x) = -245. g(x) = -10x; g(x) = 15
We have to find the value of x, such that the function:
[tex]f(x)=6x[/tex]takes the value -24. This means that such x has to satisfy:
[tex]\begin{gathered} f(x)=-24 \\ 6x=-24 \end{gathered}[/tex]Now, we just clear out the variable x. We obtain:
[tex]\begin{gathered} x=-\frac{24}{6} \\ x=-4 \end{gathered}[/tex]This means that the value x=-4 makes the function f to be -24.
find f such that the given conditions are satisfiedf’(x)=x-4, f(2)=-1
Given:
[tex]f^{\prime}\left(x\right)=x-4,\text{ and}f\left(2\right)=-1[/tex]To find:
The correct function.
Explanation:
Let us consider the function given in option D.
[tex]f(x)=\frac{x^2}{2}-4x+5[/tex]Differentiating with respect to x we get,
[tex]\begin{gathered} f^{\prime}(x)=\frac{2x}{2}-4 \\ f^{\prime}(x)=x-4 \end{gathered}[/tex]Substituting x = 2 in the function f(x), we get
[tex]\begin{gathered} f(2)=\frac{2^2}{2}-4(2)+5 \\ =2-8+5 \\ =-6+5 \\ f(2)=-1 \end{gathered}[/tex]Therefore, the given conditions are satisfied.
So, the function is,
[tex]f(x)=\frac{x^{2}}{2}-4x+5[/tex]Final answer: Option D
upper menu options: 1 3 7 8left menu options: 10 11 12 15
In order to find the amount of blue paint needed, we can write the following rule of three:
[tex]\begin{gathered} \text{green}\to\text{blue} \\ 1\text{ batch}\to2\frac{3}{8}\text{ oz} \\ 5\text{ batches}\to x\text{ oz} \end{gathered}[/tex]First, let's convert the mixed number into an improper fraction:
[tex]2\frac{3}{8}=2+\frac{3}{8}=\frac{16}{8}+\frac{3}{8}=\frac{19}{8}[/tex]From this rule of three, we can write the following equation and solve it for x:
[tex]\begin{gathered} \frac{1}{5}=\frac{\frac{19}{8}}{x} \\ x\cdot1=5\cdot\frac{19}{8} \\ x=\frac{95}{8} \\ x=\frac{88}{8}+\frac{7}{8} \\ x=11+\frac{7}{8} \\ x=11\frac{7}{8} \end{gathered}[/tex]Therefore the upper menu is 7 and the left menu is 11.
A line has an x-intercept of 12 and a y-intercept of -4. What is the equation of theline?
A line has an x-intercept of 12 and a y-intercept of -4. What is the equation of the
line?
that means
we have the points
(12,0) and (0,-4)
Find the slope
m=(-4-0)/(0-12)
m=-4/-12
m=1/3
Find teh equation in slope intercept form
y=mx+b
we have
m=1/3
b=-4
therefore
y=(1/3)x-4QuestionLet x be a constant. The 5th term of an arithmetic sequence is a5=4x−3. The 9th term of the sequence is a9=12x+9. Find the first term of the sequence. Write your answer in simplest form.
The nth term of an arithmetic sequence is :
[tex]a_n=a_1+d(n-1)[/tex]From the problem, we have :
[tex]\begin{gathered} a_5=4x-3 \\ a_9=12x+9 \end{gathered}[/tex]Substitute a5 and n = 5 :
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_5=a_1+d(5-1) \\ 4x-3=a_1+4d \end{gathered}[/tex]Rewrite the equation as d in terms of x and a1 :
[tex]\begin{gathered} 4x-3=a_1+4d \\ 4x-3-a_1=4d \\ d=\frac{4x-3-a_1}{4} \end{gathered}[/tex]Subsitute a9 and n = 9
[tex]\begin{gathered} a_n=a_1+d(n-1) \\ a_9=a_1+d(9-1) \\ 12x+9=a_1+8d \end{gathered}[/tex]Rewrite the equation as d in terms of x and a1 :
[tex]\begin{gathered} 12x+9=a_1+8d \\ 12x+9-a_1=8d \\ d=\frac{12x+9-a_1}{8} \end{gathered}[/tex]Now, equate two equations of d :
[tex]\begin{gathered} \frac{4x-3-a_1}{4}=\frac{12x+9-a_1}{8} \\ 8(4x-3-a_1)=4(12x+9-a_1) \\ 32x-24-8a_1=48x+36-4a_1 \\ 4a_1-8a_1=48x+36-32x+24 \\ -4a_1=16x+60 \\ a_1=-4x-15 \end{gathered}[/tex]The answer is a1 = -4x-15
If the 5th term of an arithmetic sequence is a5=4x−3. The 9th term of the sequence is a9=12x+9. The first term of the sequence is -4x-15
What is Sequence?a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The nth term of AP
aₙ=a+(n-1)d..(1)
From give we have,
a₅=4x−3
a₉=12x+9.
Substitute n=5 in (1)
a₅=a+4d
4x-3=a+4d
4d=4x-3-a
d=4x-3-a/4...(2)
Substitute n=9 in (1)
a₉=a+8d
12x+9=a+8d
12x+9-a/8=d..(3)
Equate 2 and 3
4x-3-a/4=12x+9-a/8
8(4x-3-a)=4(12x+9-a)
32x-24-8a=48x+36-4a
32x-24-8a-48x-36+4a=0
-16x-4a-60
-16x-60=4a
a=-4x-15
Hence the first term of the AP sequence is -4x-15
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More people are purchasing food from farmers' markets around the country. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 1.71.7% every six months. If there were 74997499 farmers' markets in 2019, how many will there be in 99 years?Given the exponential growth scenario above, answer the following questions:What is the initial value, P0P0 in this problem? What is the growth factor or growth rate (as a decimal value)? What is the nn value, or number of time periods? Question Help Question 1: Read 1
Step 1
Given;
[tex]\begin{gathered} Initial\text{ farmer market=P}_0=7499 \\ b=0.017 \\ n=number\text{ of time periods} \end{gathered}[/tex]Step 2
The exponential function for the question is
[tex]\begin{gathered} P=P_0(1+b)^n \\ P=P_0(1+0.034)^n \\ P=P_0(1.017)^n \end{gathered}[/tex]Step 3
The initial value in this problem is;
[tex]P_0=7499[/tex]Step 4
The growth rate factor as a decimal will be;
[tex]1.017[/tex]Step 5
What is the n value or a number of time periods?
[tex]n=18[/tex]Step 6
How many will there be in 9 years
[tex]\begin{gathered} P=7499(1.017)^{18} \\ P=10157.35207 \\ P\approx10157\text{ farmers' markets} \end{gathered}[/tex]Write an expression for the sequence of operations described below.multiply p by q, then multiply 10 by the resultDo not simplify any part of the expression.
Answer:
p x q x 10
Explanation:
First, we interpret the statement: multiply p by q
[tex]=p\times q[/tex]The result is: p x q
So if we then multiply 10 by the result, we have:
[tex]=p\times q\times10[/tex]This is the required expression.
Name:25. What is an equation in slope-intercept form for the line given?88X•1, -3)1-3, 5)-8A. y = 1/2(x)+(-7/2)B. y = 1/2(x) -(1)C. y = 2(x) +(-5/2)D. y = 2(x)+(-7/2)
Given the points (-3,-5) and (1,-3), we can derive the equation of the line using the formula:
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ by\text{ substituting, we have} \\ \frac{y\text{ - (-5)}}{x\text{ - (-3)}}\text{ =}\frac{-3\text{ - (-5)}}{1\text{ - (-3)}} \\ \frac{y\text{ + 5}}{x\text{ + 3}}\text{ = }\frac{2}{4} \\ 4(y\text{ + 5) = 2(x + 3)} \\ 4y\text{ - 2x + 14 = 0} \\ y\text{ = }\frac{1}{2}x\text{ }-\frac{7}{2} \end{gathered}[/tex]This corresponds to option A
11. Mr. Garcia uses a cylindrical container to protect his diploma. The dimensions of the cylinder are shown in the diagram. IS cm ------ 10 cm Which measurement is closest to the total surface area of the container in square centimeters?
Given data:
The given figure of cylinder.
The total surface area of the cylinder is,
[tex]\begin{gathered} SA=2\pi r(r+h) \\ =2\pi\frac{d}{2}(\frac{d}{2}+h) \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]undefined[/tex]Prove a quadrilateral with vertices G(1,1), H(5,3) and J(0,3) is a rectangle
The quadrilateral is a rectangle because
1) GH is parallel and equal to JI
2) GJ is parallel and equal to HI
3) Angles at the vertices are perpendicular
On New Year's Eve, the probability of a person having a car accident is 0.08. The probability of a person driving while intoxicated is 0.28, and the probability of a person having a car accident while intoxicated is 0.04. What is the probability of a person driving while intoxicated or having a car accident ? A.0.15 B.0.16 C.0.18 D.0.32
Answer:
D. 0.32
Explanation:
The probability of a person driving while intoxicated or having a car accident can be calculated as:
[tex]P=P(\text{Intoxicated)}+P(\text{ Accident) - P(Intoxicated and Accident)}[/tex]So, replacing P(Intoxicated) = 0.28, P(Accident) = 0.08 and P(Intoxicated and Accident) = 0.04, we get
[tex]\begin{gathered} P=0.28+0.08-0.04 \\ P=0.32 \end{gathered}[/tex]Therefore, the answer is
D. 0.32
Sam is collecting pennies. On the first day of the month, Sam is given 16 pennies Each day after than he gets 4 more pennies. Which of the following equations defines how many pennies he has after the nth day
ANSWER:
[tex]d_n=4n+16_{}[/tex]STEP-BY-STEP EXPLANATION:
If n is the number of days that pass.
So each day Sam gets 4 more, which means that he would multiply the number of days by 4, before adding that number to the original number of pennies, which was 16.
Therefore, the equation would be:
[tex]d_n=4n+16_{}[/tex]Which fractions are equivalent to ?Select all that apply. 64 64 yi 764 8 1 4
We are given the following radical expression
[tex]\sqrt[3]{\frac{1}{64}}[/tex]Let us simplify it using the properties of radicals.
The quotient property of radicals is given by
[tex]\sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}[/tex]Let us apply the above property
[tex]\sqrt[3]{\frac{1}{64}}=\frac{\sqrt[3]{1}}{\sqrt[3]{64}}[/tex]Further simplifying the radical
[tex]\frac{\sqrt[3]{1}}{\sqrt[3]{64}}=\frac{1^{\frac{1}{3}}}{64^{\frac{1}{3}}}=\frac{1}{4}[/tex]The cube root of 1 is 1 and the cube root of 64 is 4
Therefore, the correct options are
[tex]\begin{gathered} \frac{\sqrt[3]{1}}{\sqrt[3]{64}} \\ \frac{1}{4} \end{gathered}[/tex]there are 750 seats.the number of seats in a row is 5 less than the number of rows.how many seats are there in a row?
Given:
The total number of seats, T=750.
Let x be the number of seats in a row and y be the number of rows.
It is given that the number of seats in a row is 5 less than the number of rows.
Hence, the number of seats in a row can be expressed as,
[tex]x=y-5\text{ ---(a)}[/tex]Now, expression for the total number of seats can be given by,
[tex]T=xy[/tex]Plug in x=y-5 and T=750 in the above equation and simplify.
[tex]\begin{gathered} 750=(y-5)y \\ 750=y^2-5y \\ y^2-5y-750=0\text{ ---(1)} \end{gathered}[/tex]The equation (1) is in the form of a quadratic equation of the form,
[tex]ay^2+by+c=0\text{ ---(2)}[/tex]Comparing equations (1) and (2), a=1, b=-5 and c=-750.
Now, using discriminant method, the solution of y can be expressed as,
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y=\frac{-(-5)\pm\sqrt[]{(-5)^2-4\times1\times(-750)}}{2\times1} \\ y=\frac{5\pm\sqrt[]{25+3000}}{2\times1}\text{ } \\ y=\frac{5\pm\sqrt[]{3025}}{2} \\ y=\frac{5\pm55}{2}\text{ } \\ y=\frac{5+55}{2}\text{ or y=}\frac{5-55}{2} \\ y=\frac{60}{2}\text{ or y=}-\frac{50}{2} \\ y=30\text{ or y=-25} \end{gathered}[/tex]Since the number of rows cannot be negative, y=30.
Put y=30 in equation (a) to find x.
[tex]\begin{gathered} x=30-5 \\ x=25 \end{gathered}[/tex]Therefore, the number of seats in a row is 25.
A group of people were given a personality test to determine if they were type a or type B. The results are shown in the table below:…Compare P(Male or Type B) with P(Male | Type B)
Given,
The data table of the gender and its type is shown in question tab.
Required
P(male or Type B)
P(Male| type B)
The value of P( male or Type B) is calculated as,
[tex]\begin{gathered} P\left(male\text{ }or\text{ }TypeB\right)\text{ =}\frac{65+38+12}{65+85+38+12} \\ =\frac{115}{200} \\ =\frac{57.5}{100} \\ =0.575 \end{gathered}[/tex]The value of P(Male|Type B) is calculated as,
[tex]\begin{gathered} P(Male|Type\text{ B\rparen=}\frac{38}{50} \\ =\frac{76}{100} \\ =0.76 \end{gathered}[/tex]Here, P( male or Type B) < P(Male|Type B) .
Hence, option (P( male or Type B) < P(Male|Type B) ) is correct.
convert to degrees minutes and seconds54.158°
Convert 54.158 degrees
Firstly, Use the whole number as degree
54 degree
to convert to minutes
(54.548 - 54) x 60
= 0.158 x 60
= 9 minutes
To convert to seconds
(54.158 - 54 - 9/60) x 3600
= (0.158 - 0.15) x 3600
= 0.008 x 3600
= 28.8 seconds
This can be written as
[tex]54^o\text{ 9' 28.8''}[/tex]A gallon of paint will cover 600 ft.² of wall space if I plan to paint a room his walls measure 1200 ft.² how many gallons of paint will I need
solutions to 2y-3x=5
The equation 2y - 3x = 5 has infinitely many solutions.
In this question, we have been given an equation 2y-3x=5
We need to solutions to given equation.
for x = -1,
2y -3(-1) = 5
y = 1
for x = 0,
2y - 3(0) = 5
y = 5/2
y = 2.5
for x = 1,
2y - 3(1) = 5
y = 4
In this way for any real value of x we can find infinitely many values of y.
Therefore, the equation 2y - 3x = 5 has infinitely many solutions.
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Using the cosine law to determine the measure of we could use _______:
Solution
- The Cosine law is given below as:
[tex]\begin{gathered} Given\text{ }\triangle ABC,\text{ with sides }a,b,c\text{ and angles }\angle A,\angle B,\angle C\text{ such that} \\ a\text{ is opposite }\angle A \\ b\text{ is opposite }\angle B \\ c\text{ is opposite }\angle C \\ \\ \text{ We have:} \\ a^2=b^2+c^2-2(bc)\cos\angle A \end{gathered}[/tex]- We can make [tex]\begin{gathered} a^2=b^2+c^2-2bc\cos\angle A \\ \text{ Subtract }b^2\text{ and }c^2\text{ from both sides} \\ \\ a^2-b^2-c^2=-2bc\cos\angle A \\ \\ \text{ Divide both sides by }-2bc \\ \cos\angle A=\frac{a^2-b^2-c^2}{-2bc} \\ \text{ } \\ \text{ Take the cos inverse of both sides} \\ \\ \therefore\angle A=\cos^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex]
Final Answer
The answer is
[tex]\operatorname{\angle}A=\cos^{-1}(\frac{a^{2}-b^{2}-c^{2}}{-2bc})\text{ \lparen OPTION C\rparen}[/tex]Let Fx= x^3 + 2^x2 - 18 For what values of x is f(x) = 9 Enter your answers as a comma-separated list.
We have the following function f(x) = x^3+2x^2 -18. We want to solve the following equation
[tex]x^3+2x^2-18=9[/tex]By subtracting 9 on both sides, we get the equivalent equation
[tex]x^3+2x^2-27=0[/tex]Reflect (1,-4) Over the Y axis and over the X axis.
Answer
Check Explanation
Explanation
To reflect a point A (x, y) over the y-axis, the new coordinates become A' (-x, y)
For the point B(x, y) over the x-axis, the new coordinates become B'(x, -y)
So, reflecting the point (1, -4) over the y-axis, we have (-1, -4)
Reflecting the point (1, -4) over the x-axis, we have (1, 4)
Reflecting (1, -4) over both x-axis and then y-axis, we have (-1, 4)
Hope this Helps!!!
what fraction is equivalent to 2/2
Answer:
4/4,6/6 etc
Step-by-step explanation:
multiply both numerator and denominator with the same number