Since the population doubles every 44 hours, it can be modeled using an exponential equation as follows:
[tex]P(t)=405,000\times2^{\frac{t}{44}}[/tex]Where t is the time since the population was 405,000 measured in hours.
Replace t=176 to find the population after 176 hours:
[tex]\begin{gathered} P(176)=405,000\times2^{\frac{176}{44}} \\ =405,000\times2^4 \\ =405,000\times16 \\ =6,480,000 \end{gathered}[/tex]Therefore, the population after 176 hours will be 6,480,000
Find the quotient. Write your answer in standard form. 3+ O A. + COLO O B.-1 O C. 1-1 OD. llo 011
Option A is correct.
The given complex number is
[tex]\frac{3+i}{3-i}[/tex]Multiply the numerator and denominator by 3+i and solve as follows:
[tex]\begin{gathered} \frac{3+i}{3-1}\times\frac{3+i}{3-i}=\frac{(3+i)^2}{3^2-i^2} \\ =\frac{3^2+i^2+6i}{9+1} \\ =\frac{9-1+6i}{10} \\ =\frac{8+6i}{10} \\ =\frac{8}{10}+\frac{6}{10}i \\ =\frac{4}{5}+\frac{3}{5}i \end{gathered}[/tex]Point P is located at (4, 8) on a coordinate plane. Point Pwill be reflected over the x − axis. What will be thecoordinates of the image of point P?
SOLUTION:
Step 1:
In this question, we are given that:
Point P is located at (4, 8) on a coordinate plane.
Point P will be reflected over the x-axis.
What will be the coordinates of the image of point P?
Step 2:
How do you reflect a point over the x-axis?
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.
The reflection of point (x, y) across the x-axis is (x, -y).
CONCLUSION:
Point P ( 4, 8 ) reflected over the x-axis is ( 4, -8 ) -- OPTION C
I am going to attach a photo of the question. as you can tell the question has already been answered but my teacher wants me to show how she got the answer.
Answer:
The ratio of their surface area is;
[tex]25\colon9[/tex]Explanation:
Given the length of the slant height of the cone as;
[tex]\begin{gathered} l_A=35\text{ in} \\ l_B=21\text{ in} \end{gathered}[/tex]since the cones are similar, the ratio of their sides is;
[tex]\begin{gathered} A\colon B \\ =35\colon21 \\ l^{}_A\colon l^{}_B=5\colon3 \end{gathered}[/tex]The ratio of the total surface area is the square of the ratio of the sides.
[tex]\begin{gathered} S_A\colon S_B=l^2_A\colon l^2_B \\ S_A\colon S_B=5^2_{}\colon3^2_{} \\ S_A\colon S_B=25\colon9 \end{gathered}[/tex]Therefore, the ratio of their surface area is;
[tex]25\colon9[/tex]write the first three terms of sequence A(n+1)=1/2A(n) for n ≥ 1 and A(1)=4write your answer separated by commas, with no space for example 5,6,7
For n= 1
[tex]A(1+1)=\frac{1}{2}A(1)[/tex]but A(1) = 4
[tex]A(2)\text{ = }\frac{1}{2}(4)\text{ = 2}[/tex]For n= 2
[tex]A(2+1)=\frac{1}{2}A(2)[/tex][tex]A(3)=\frac{1}{2}A(2)[/tex]But A(2) = 2
[tex]A(3)\text{ =}\frac{1}{2}(2)=\text{ 1}[/tex]Hence, the first three terms are;
4, 2, 1
An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.i need a step by step run through to understand
Given,
The ratio of the height of a sculpture to the actual height of the dog is 2:3.
The height of the sculpture is 14 inch.
let the height of the dog be h.
Thus,
[tex]\begin{gathered} \frac{14}{h}=\frac{2}{3} \\ \Rightarrow h=14\times\frac{3}{2}=21inch \end{gathered}[/tex]The actual height of the dog is 21 inch.
Compare the numbers oS and 0.05. How many times 0.05 is 0.5? Use place value to explain how you know
We will look at the process of decimal point shifts as follows:
[tex]0\text{.05}[/tex]For the above decimal to be manipulated in such a way such that the result is:
[tex]0.5[/tex]Here we see that the digits in the given decimal and the result are exactly the same. However, the placement of decimal point ( . ) has been changed. Such changes in decimal point places are usually accompained by number multiples of ( 10 ).
Now there are two possibilities for the decimal point to move i.e to the right or to the left. If we move the decimal point to the left then we are reducing the value of the decimal ( smaller number ). In such cases we divide the given decimal by multiples of ( 10 ).
Vice versa, If we move the decimal point to the right then we are increasing the value of the decimal ( larger number ). In such cases we multiply the given decimal by multiples of ( 10 ).
The decimal number given to us is smaller than the result decimal. i.e:
[tex]0.5\text{ > 0.05}[/tex]Hence, the given decimal number must be multipled by multiples of 10.
The general rule in moving the decimal point in either multiplying or dividing the multiples of ( 10 )s. Is to count the number of " 0 s" in the this multiples. E.g if we divide:
[tex]\frac{0.2}{10}\text{ = 0.02}[/tex]In above example we divided by ( 10 ). This has ( one zero ). Hence, we will move the decimal point to the left by ( one place ). Another example:
[tex]\frac{236.58}{10000}\text{ = 0.023658}[/tex]In above example we divided by ( 10000 ). This has ( four zeros ). Hence, we will move the decimal point to the left by ( four places ).
The same case applies to multiplication of multiples of 10; however, the only difference is the direction of decimal point moving i.e right.
So with the help of above guidelines and example we see that:
[tex]0.05\cdot10^x\text{ = 0.5}[/tex]We need to determine the number of zeroes for ( 10s ) for which there is only a one place shift to the right side by the decimal point.
The value must be ( x = 1 ). That is we multiple the given ( 0.05 ) by ( 10 ). 10 has only one zero which allow the decimal point to travel to the right side by one digit place. Hence,
Answer:
[tex]\textcolor{#FF7968}{10}\text{\textcolor{#FF7968}{ times 0.05 is 0.5}}[/tex]Metropolis Elementary recommends a ratio of 2 adults for every 24 children on every field trip.
The school has 20 adults and 350 students.
If everyone goes on a field trip, would that meet the recommendation?
If everyone goes on a field trip, then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
What is ratio?It is the comparison of one quantity with another. For example, if your weight is 30 kg and your father's weight is 90 kg, then the ratio of weight is 1:3.
Given:
The school has 20 adults and 350 students,
The Ratio of adults over children = 2 /24 = 1 / 12, which means for every 12 children there required one adult,
So to find the total adults needed = total students / 12
Total adults needed = 350 / 12 = 29 and 2 children come as a reminder.
Therefore, If everyone goes on a field trip then 29 adults are needed for 350 students, so the recommendation by Metropolis Elementary does not meet.
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Given the equation of a line --3x + 4y = -12, determine the following:What is the slope of the line?I22What is the y-intercept? Enter your answer as an ordered pair in the form (x, y).terceptPls see the picture
Answer:
[tex]\begin{gathered} \text{Slope}=\text{ 3/4} \\ \text{ y-intercept= -3} \end{gathered}[/tex]Step-by-step explanation:
Linear equations are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]Therefore, to determine the slope and y-intercept of the given equation. Isolate "y" using inverse operations:
[tex]\begin{gathered} -3x+4y=-12 \\ 4y=3x-12 \\ y=\frac{3}{4}x-3 \\ \text{ Hence,} \\ \text{Slope}=\text{ 3/4} \\ \text{ y-intercept= -3} \end{gathered}[/tex]calculate the difference quotient and use your results to find the slope of the tangent line
Approximate Slope of a Function
We are given the function:
[tex]H(x)=8\ln x+3[/tex]We will find the approximate value of the slope at (e,11).
It's required to use 3 possible values of the approximation differential h.
Let's use h=0.1 and evaluate the function at x = e + 0.1 = 2.8182818
Compute:
[tex]H(e+0.1)=8\ln 2.8182818+3=11.2890193[/tex]Compute the difference quotient:
[tex]H^{\prime}=\frac{11.2890193-11}{0.1}=2.890193[/tex]Now we use h=0.01:
[tex]H(e+0.01)=8\ln 2.728281828+3=11.02937635[/tex]The difference quotient is:
[tex]H^{\prime}=\frac{11.02937635-11}{0.01}=2.9376353[/tex]Finally, use h=0.001:
[tex]H(e+0.001)=8\ln 2.719281828+3=11.00294249[/tex][tex]H^{\prime}=\frac{11.00294249-11}{0.001}=2.9424943[/tex]The last result is the most accurate, thus the slope of the tangent line is 2.94
a. Use the line of random numbers to obtain and report the resulting list of heads and tails. Use H for heads and T for tails.Q0000 00.000 0.0.000 00000
Given -
An unbiased coin is tossed
To Find -
The list of heads and tails while tossing a coin
Assumption -
The coin is tossed twice
Explaination -
The following table lists some possible arrangements for the experiment
Show exact steps to solve and draw the construction!Don't mind the pink writing.
Step by step:
1. Open the compass to a radius less than half the segment MN.
2. Usin point P as center draw two arcs that intersecs line MN on both sides of the point P (As you use the compass those arcs are in the same distance from point P)
3. Lavel the point of intersection of arcs with line MN (Use any other letter as A and B)
4. Use the points A and B as centers and using the compass draw two arcs (one with each point A and B) above the line that intersects each other.
5. Mark the point of intersection of arcs and link it with point P (as the line needs to go throught P corss point P and continue with the line) . That line is the perpendicular line to MN trought point P)
Error Analysis .... Your friend knows that <1 and <2 are complementary and that <1and <3 are complementary. He concludes that <2 and <3 must becomplementary. What is his error in reasoning? *
In this case, we'll have to carry out several steps to find the solution.
Step 01:
We must analyze the problem to find the error.
Data
∠1 + ∠2 = 90
∠1 + ∠3 = 90
Step 02:
∠1 = 25
25 + ∠2 = 90
∠2 = 90 - 25
= 65
∠1 = 25
25 + ∠3 = 90
∠3 = 90 - 25
= 65
∠2 + ∠3 = 130
The answer is:
∠2 = ∠3
Angle 2 and angle 3 are equal, but they are not always complementary.
Use systems to solve :The length of a rectangle is 2 cm more than itswidth. If the perimeter is 52 cm, find the width.
ANSWER
The width is 12 cm
EXPLANATION
The length L of the rectangle is 2 cm more than its width W. With this we have one equation:
[tex]L=W+2[/tex]Then the perimeter is 52cm, which is the sum of the sides of the rectangle:
[tex]P=W+W+L+L=2W+2L[/tex]Therefore the system to solve is:
[tex]\begin{cases}L=W+2 \\ 52=2W+2L\end{cases}[/tex]Using the substitution method we can solve just for W. Replace L in the second equation by its value in terms of W from the first equation:
[tex]52=2W+2(W+2)[/tex]Use the distributive property to eliminate the parenthesis:
[tex]52=2W+2W+4[/tex]Add like terms:
[tex]52=4W+4[/tex]And solve for W:
[tex]\begin{gathered} 4W=52-4 \\ 4W=48 \\ W=\frac{48}{4} \\ W=12 \end{gathered}[/tex]Therefore, the width of the rectangle is 12cm
4/8 =Express your answer as a whole number or fraction.
Given the fraction:
[tex]\frac{4}{8}[/tex]Let's simplify the fraction.
To simplify, divide the denominator and the numerator by the Greatest Common Factor (GCF).
GCF of 4 and 8 = 4
Hence, we have:
[tex]\frac{4\div4}{8\div4}=\frac{1}{2}=0.5[/tex]Hence, the simplified fraction is:
[tex]\frac{1}{2}[/tex]As a decimal:
[tex]0.5[/tex]ANSWER:
[tex]\frac{1}{2}[/tex]?In the table below, y is a linear function of x.X-214710y09182736What is the y intercept of the function
y intercept : (0,6)
Explanation:
Use the formula:
. y = mx + b
Find m (the slope), using 2 random points of the graph: (-2,0) and (1,9)
. m = (y-y1) / (x-x1)
m = (0-9) / (-2-1)
m = -9 / -3
m = 3
Replace m in the equation:
. y = 3x + b
Find b by replacing y and x by a random point of the graph: (1,9)
. 9 = 3*1 + b
b = 9 - 3
b = 6
Replace b in the equation:
. y = 3x +6
To find the y-intercept replace x by 0 in the equation:
. y = 3*0 +6
y = 0+6
y = 6
=> y-intercept : (0,6)
f(x)=x4-6x2 + 3 (b)(6 pts) Find the intervals where f is concave up and where it is concave down. Locate all inflection points. (You may write on the next page if you need more space for this question.)
The inflection points are (-√3, -6), (0, 3), and (√3, -6). The interval where the function is concave up is (-∞, -1)∪(1, ∞). The interval where the function is concave down is (-1, 1).
We are given a function f(x). The function f(x) is defined as x^4 - 6x² + 3. We need to find all the inflection points of the curve. To find the points of inflection, we need to differentiate the equation of the function with respect to the variable "x". After differentiation, the equation is f'(x) = 4x³ - 12x. We now equate this equation with zero, to get the values of "x".
4x³ - 12x = 0
4x(x² - 3) = 0
So, the values of "x" are ±√3 and 0. Put these values in the original equation to get the corresponding y-coordinates. The points of inflection are (-√3, -6), (0, 3), and (√3, -6). Now we need to find the intervals where the function is concave up and where it is concave down. For this, we need to differentiate the previous equation once again with respect to "x". After differentiation, the equation is f''(x) = 12x² - 12. We now equate this equation with zero, to get the values of "x". If the result is negative, then the function is concave downward. If the result is positive, then the function is concave up.
12x² - 12 = 12(x² - 1) = 0
The values of "x" are -1 and 1.
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The international club at school has 125 members, many of whom speak multiple languages, the most commonly spoken languages in the club are English, Spanish and Chinese.55 students speak Spanish30 students speak Chinese89 students speak English15 students speak Spanish and Chinese20 students speak Chinese and English33 students speak Spanish and English8 students speak allCreate a Venn Diagram
8 students speak all, so it is in the intersection of the three
15 speak Spanish and Chinese, but 15-8=7 do not speak English
20 speak Chinese and English, but 20-8=12 do not speak Spanish
33 speak Spanish and English, but 33-8=25 do not speak Chinese
55 speak Spanish, but 55-25-8-7=15, do not speak English or Chinese
30 speas chinese, but 30-12-8-7=3 do not speak English or Spanish
89 speak English, but 89-12-8-25=44 do not speak Spanish or Chinese
To end our diagram, we add
[tex]44+25+15+7+8+12+3=114[/tex]Then 125-114=11 students don't speak English, Spanish or Chinese
Solve for 3+y/2=-212
You have the following equation:
[tex]3+\frac{y}{2}=-212[/tex]In order to solve the previous equation for y, proceed as follow:
3 + y/2 = -212 subtract 3 both sides
y/2 = -212 - 3 simplify right side
y/2 = -215 multiply by 2 both sides to cancel the denominator left side
y = -215(2)
y = -430
Hence, the solution for y in the given equation is y = -430
find the sum of the first 6 terms of the following sequence. round to the nearest hundredth if necessary.35, 14, 28/5,...sum of a finite geometric series:Sn=a1-a1^r^n/1-r
58.09
ExplanationTo find the sum of a finite geometric series, use the formula,
[tex]S_n=\frac{a(1-r^n)}{(1-r)}[/tex]where
[tex]\begin{gathered} a=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ number of terms} \\ S_n=sumo\text{f the firts n terms} \end{gathered}[/tex]so
Step 1
find the common ratio :
To calculate the common ratio in a geometric sequence, divide the n^th term by the (n - 1)^th term,in other words you can just divide each number from the number preceding it in the sequence
[tex]coomin\text{ ratio =}\frac{n\text{ term }}{(n-1)\text{ term}}[/tex]so
[tex]common\text{ ratio=}\frac{\frac{28}{5}}{\frac{14}{1}}=\frac{28}{70}=0.4[/tex]so r= 0.4
Step 2
Now we can use the formula
a)
let
[tex]\begin{gathered} r=0.4 \\ n=\text{ 6} \\ a=35 \end{gathered}[/tex]b) finally, replace in the formula
[tex]\begin{gathered} S_n=\frac{a(1-r^n)}{(1-r)} \\ S_n=\frac{35(1-0.4^6)}{(1-0.4)} \\ Sn=35*1.62984 \\ Sn=58.0944\text{ } \\ rounded \\ S_n=58.09 \end{gathered}[/tex]therefore, the answer is
58.09
I hope this helps you
finding percent proportions
The total number is 80, Among them 30% are under the age of 7, so the number of players under the age of 7 is,
[tex]30\times\frac{80}{100}[/tex]16.2-(3×4) + (14÷2) I have to tell how many terms the expression has.
The expression we have is:
[tex]16.2-(3\times4)+(14\div2)[/tex]A term in an expression in every part of the said expression, for example, in the expression 10+3, 10 and 3 are terms.
For the case of our expression, each number is a term:
16.2, 3, 4, 14, and 2 are terms.
So in total, we have 5 terms.
Answer: 5 terms
Find the improper fraction with a denominator of 8 that is equivalent to 3 and 1/2
Given:
he improper fraction with a denominator of 8 that is equivalent to 3 and 1/2.
Required:
Find the improper fraction.
Explanation:
[tex]\begin{gathered} \text{ According to question} \\ \frac{x}{8}=3\frac{1}{2} \\ x=8\times3\frac{1}{2} \\ x=8\times\frac{7}{2} \\ x=28 \\ \text{ So, fraction is }\frac{28}{8}. \end{gathered}[/tex]Answer:
[tex]\text{ Improper fraction is }\frac{28}{8}.[/tex]Hernando’s salary was $47,500 last year. This year his salary was cut to $38,475. Find the percent decrease
To determine the percentage of decrease that Hernando's salary was cut, we first calculate the total value, then the ratio of this value to the initial one, then we multiplicate by 100, to get it in percent, as follows:
[tex]\begin{gathered} 47,500-38,475=9,025 \\ \frac{9,025}{47,500}=0.19 \\ 0.19\times100=19\text{ \%} \end{gathered}[/tex]From the solution we developed above, we are able to conclude that the salary of Hernando was cut by 19 %What would be and example of a point , a plane , and a line in a classroom setting?
−6x−y=9−2x+10y=−28 please help me
We have to solve the linear system:
-6x - y = 9
-2x + 10y = -28
Multiply both sides of the first equation by 10:
-60x - 10y = 90
-2x + 10y = -28
Now sum both equations, we get:
-60x - 2x -10y + 10y = 90 - 28
-62x + 0 = 62
-62x = 62
x = 62 / -62
x = -1
Now lets find y. I'm going to use the first equation since it is easier to do the math:
-6x - y = 9
-6(-1) - y = 9
6 - y = 9
-y = 9 - 6
-y = 3
y = -3
So the solution of the linear system is x = -1, y = -3 or simply (-1, -3).
Answer: x = -1 ; y = -3
In which quadrant or ok which axis does the point lie ?
Explanation
We are given the following point:
[tex](-5,-3)[/tex]We are required to determine the quadrant, or the axis it lies on a coordinate plane.
We start by plotting the point thus:
Hence, the answer is:
[tex]III[/tex]The last option is correct.
Consider the quadratic function y=2x2 – 12x + 20.Rewrite the equation in vertex format.
The function:
[tex]y=2x^2-12x+20[/tex]has the form:
[tex]y=ax^2+bx+c[/tex]with a = 2, b = -12, and c = 20.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
The x-coordinate of the vertex, h, is computed as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-12)}{2\cdot2} \\ h=\frac{12}{4} \\ h=3 \end{gathered}[/tex]The y-coordinate of the vertex, k, is found replacing h into the formula of the function, as follows:
[tex]\begin{gathered} k=2h^2-12h+20 \\ k=2\cdot3^2-12\cdot3+20 \\ k=18-36+20 \\ k=2 \end{gathered}[/tex]Finally, the quadratic function in vertex form is:
[tex]y=2(x-3)^2+2[/tex]What is the value of 22 + x ÷ 11 when x = −176?
Answer:
6
Step-by-step explanation:
22 + -176 ÷ 11
b i division m a s
-176 ÷ 11 = -16
22 - 16 = 6
Answer:
points hehehhehehehe points hehehehehhehehehehehehe points hehehehe
Step-by-step explanation:
The domain of a quadratic function is all real numbers. The range of the quadratic function is determined by the vertex of the parabola. If the parabola has a minimum value than the range will be all outputs (less than or greater than) that maximum value. If the parabola has a maximum value then the range will be all outputs (equal to or less than) that maximum value.
Answer:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
Explanation:
The range of a function is the set of values that the y-variable can take. If the parabola has a minimum value, the y-variable can take values greater than or equal to the minimum.
In the same way, if the parabola has a maximum value, the y-variable can take values less than the maximum.
Therefore, the answers are:
If the parabola has a minimum value, the range will be all outputs greater than the maximum value. If the parabola has a maximum value then the range will be all outputs less than that maximum value.
A perfectly vertical stack of dominoes has a volume of 1.8 cubic inches. Another stack of the same number of dominoes is slanted slightly to the right. What is its volume?choice:1.8 cubic inches0.9 cubic incheswe can't tell3.6 cubic inches
If we slanted the dominoes, there is no changes in volume of a dominoes so its volume is 1.8 cubic inches.
Answer: 1.8 cubic inches