Number 50 use the graph to estimate the limits and value of the function or explain why the limits do not exist
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In this case, notice that the graph of G(x) approximates to 1 when x goes to 2 from the left, and also the graph approximates to 1 when x goes to 2 from the right, thus, we have the following limits:
[tex]\begin{gathered} \lim _{x\rightarrow2^-}G(x)=1 \\ \lim _{x\rightarrow2^+}G(x)=1 \end{gathered}[/tex]since both limits are equal, we have that the limit of G(x) when x goest to 2 is:
[tex]\lim _{x\rightarrow2}G(x)=1[/tex]Related Questions
4. Determine the appropriate algebraic model for the graphs below. Note: there is more than one possible answer.
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For graph A,
Using the sine to model the graph
The formula to obtain the model is,
[tex]y=Asin\left(Bx\right)[/tex]where,
[tex]\begin{gathered} A=Amplitude \\ B=\frac{2\pi}{Period} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A=0.75=\frac{3}{4} \\ B=\frac{2\pi}{\pi}=2 \end{gathered}[/tex]Hence, the model is
[tex]y=\frac{3}{4}sin\left(2x\right)[/tex]For graph B
Using the cosine to model the graph
The formula to obtain the model is,
[tex]y=Acos\left(Bx\right)[/tex]Therefore,
[tex]\begin{gathered} A=-2 \\ Period=8\pi,\text{ }\therefore B=\frac{2\pi}{8\pi}=\frac{1}{4} \end{gathered}[/tex]Hence, the model is
[tex]y=-2cos\left(\frac{1}{4}x\right)[/tex]I believe the answer to be this: but I'm not too sure-99.2016I'm not understanding what it mean by win or lose I don't know which one to mark
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Hello there. To solve this question, we'll have to remember some properties about probabilities.
First, remember that there are 4 suits in a standard card deck, each containing 13 different cards.
Most specifically, there are only one of each number in each suit, so this means that there are only 4 cards with the number 5 in a 52 card deck.
The probability of taking three fives in succession from this deck, with replacement, is given by the ratio between the favorable events of taking a 5 (4) and the total number of cards (52), cubed:
[tex]P(\text{taking a 5 three times in succession)}=\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}=\frac{1}{13^3}=\frac{1}{2197}[/tex]Notice the probabilities are the same for each succession because we were replacing the cards. If we weren't replacing, then the probabilites would go down as 4/52 * 3/51 * 2/50, which is not the case.
Obviously, this is the probability of winning and if you get three fives in succesion, you get $70.
To find the probability of not getting 5's three times in succession, simply subtract the probability we found from 1:
[tex]P(\text{not get 5's three times in succession)}=1-\frac{1}{2197}=\frac{2196}{2197}[/tex]Now, we multiply the probabilities by the number in dollars we would get by winning and the number in dollars (negative) we would pay for losing, respectively:
[tex]\begin{gathered} 70\cdot\frac{1}{2197}-10\cdot\frac{2196}{2197} \\ \\ \frac{70}{2197}-\frac{21960}{2197} \\ \\ -\frac{21890}{2197} \end{gathered}[/tex]By calculating the fraction, we get:
[tex]-9.9635[/tex]two integers have a sum of -17 and a difference of 1. what are the integers
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In this problem we can write one equation for each condition so:
[tex]\begin{gathered} x+y=-17 \\ x-y=1 \end{gathered}[/tex]So we solve the second equation for x so:
[tex]x=1+y[/tex]and replace in the first equation :
[tex]\begin{gathered} 1+y+y=-17 \\ 2y=-18 \\ y=-9 \end{gathered}[/tex]and we replace y in the secon equation:
[tex]\begin{gathered} x=1-9 \\ x=-8 \end{gathered}[/tex]So the two integers are: -8 and -9
How do I convert 4 ounces of juice to milliliters
Answers
Each fluid ounce is equivalent to approximately 30 milliliters.
Thus, 4 fluid ounces will be equivalent to 4 times 30 milliliters:
4 fluid ounces ≅ 4 * 30 mililiters = 120 mililiters
To better understand, we can write the proportions:
fl. oz. mL
1 30
4 x
Cross multiplying, we obtain:
1x = 4*30
x = 120 (milliliters)
May I please get help with this. I still can’t figure out the the answers
Answers
Answer:
• m∠C=60
,• m∠D=35
,• m∠E=85
Explanation:
Given that the two triangles are similar, and:
• m∠Y=35°
,• m∠W=85°
Since we are told that the triangles are accurately drawn, then:
[tex]\begin{gathered} \triangle\text{WXY}\sim\triangle\text{ECD } \\ \text{Triangle WXY is similar to triangle ECD} \end{gathered}[/tex]Thus:
[tex]\begin{gathered} m\angle C\cong m\angle X \\ \text{Solve for the measure of angle X in triangle WXY.} \\ m\angle X=180-35\degree-85\degree=60\degree \\ \implies m\angle C=60\degree \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} m\angle D\cong m\angle Y=35\degree \\ m\angle E\cong m\angle W=85\degree \end{gathered}[/tex]The measures of angles C, D and E are 60, 35 and 85 respectively.
this text goes with this question: Francesca wants to glue this 3-inch by 5-inch photo on top of a mat that will increase the length of each side by another x inches. Find an expression representing the area of the mat and use this expression to find the area and cost of the mat for different values of x. i need help with question #9.
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Check values for white and black mat
Area of photo is = 3 x 5 = 15 inches ^2
The area most apropiate for this photo is
69 inches^2, because is the most similar in size
If FRANCESCA wants to save costs ,she should pick WHITE MAT
But , if she is not afraid of cost, then she should pick Black price mat of any size.
A tv screen is 41 cm long and 31 cm high. the length of the diagonal is closest to
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the length of the tv screen is,
l = 41 cm
the width of the tv is
b = 31 cm
the length of the diagonal will be the hypotenuse of the triangle,
so, diagonal length is,
[tex]\text{diagonal}=\sqrt[]{41^2+31^2}[/tex][tex]\text{diagonal}=\sqrt[]{1681+961}[/tex][tex]\begin{gathered} \text{diagonal}=\sqrt[]{2642} \\ \text{diagonal}=51.04 \end{gathered}[/tex]so, the length of the diagonal is closest 51.04 cm
Maria rolls a six- sided die. What is the probability that she rolls a prime number
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We know that there are four prime numbers in a six-sided die, which are 1, 2, 3, 5.
So, the probability would be
[tex]P_{\text{prime}}=\frac{4}{6}=\frac{2}{3}[/tex]Therefore, the probability of rolling a prime number is 2/3.How long do you think it would take for the material to decay to 23% (without doing the actual calculation), make an explanation using the half-life being 12 years
Answers
Solution
The exponential decay can be expressed as;
[tex]A(t)=A_0(\frac{1}{2})^{^{\frac{t}{t_{half}}}}[/tex][tex]\begin{gathered} \Rightarrow0.23=(\frac{1}{2})^{\frac{t}{12}} \\ \\ \Rightarrow\ln(0.23)=\frac{t}{12}\ln(\frac{1}{2}) \\ \\ \Rightarrow t=\frac{12\times\ln(0.23)}{\ln(\frac{1}{2})}=25 \end{gathered}[/tex]Hence, it will take about 25 years. (By calculation)
By Inspection.
12 years is 50%
24 years is 25%
It will take about 24 years to decay to 23%
what would 2b-2*3b-2 be
Answers
Using the following property:
[tex]x^y\cdot x^z=x^{y+z}[/tex]Therefore:
[tex]2b^{-2}3b^{-2}=3\times2(b^{-2+(-2)})=6b^{-4}[/tex]y=|x-6|I need help finding parent function, Type of Translation, Domain and Range
Answers
Parent function: y = |x|
The graph of y=|x-6| is the graph of the parent function translated 6 units to the right. This translation doesn't change the domain of the parent function, which is all Real numbers, neither change the range of the parent function, which is all positive Real numbers including zero.
Write the equation of the line in point-slope form perpendicular to y= -3x+6 passing through the point(-9, -4)
Answers
y + 4 = 1/3(x + 9)
Explanations:The formula for finding the equation of a line perpenicular to another line and passing through a point (x1, y1) is expressed as
[tex]y-y_1=-\frac{1}{m}(x-x_1)[/tex]where:
• m is sthe ,slope of the given line
,• (x1, y1) is the ,point on the line
Determine the slope of the given line
Given the equation y = -3x + 6, the slope of the line is -3
Substitute the slope and the given point into the formula as shown:
[tex]\begin{gathered} y-(-4)=\frac{-1}{-3}(x-(-9)) \\ y+4=\frac{1}{3}(x+9) \\ \end{gathered}[/tex]Hence the required equation in point-slope form is y + 4 = 1/3(x + 9)
Solve the quadratic equation by completing the square. 2x^2-8x-5=0Completing the square gives us: (x- Answer )^2 = AnswerEnter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.x=Answer and x=Answer
Answers
ANSWER
(x-2)^2 = 13/2
x = 4.55 or x = -0.55
STEP BY STEP EXPLANATION
the two triangles are similar. their areas and one side length are given. what is the ratio of the areas? what is the scale factor of the 2 sides? find the length of the corresponding side in the small triangle.
Answers
Let 'x' be the length of the corresponding side in the small triangle. Since both triangles are similar, we have the following equation:
[tex]\begin{gathered} \frac{\text{area of big triangle}}{area\text{ of small triangle}}=(\frac{36}{x})^2 \\ \Rightarrow\frac{81}{49}=\frac{1296}{x^2} \end{gathered}[/tex]solving for 'x', we get:
[tex]\begin{gathered} \frac{81}{49}=\frac{1296}{x^2} \\ \Rightarrow81\cdot x^2=1296\cdot49 \\ \Rightarrow81x^2=63504 \\ \Rightarrow x^2=\frac{63504}{81}=784 \\ \Rightarrow x=\sqrt[]{784}=28 \\ x=28 \end{gathered}[/tex]therefore, the length of the corresponding side in the small triangle is 28 cm.
Now, we can find the ratio of the areas using the first equation. Let A be the area of the big triangle, and le t a be the area of the small triangle, then:
[tex]\begin{gathered} \frac{A}{a}=(\frac{36}{28})^2=1.65_{} \\ \Rightarrow A=1.65\cdot a \end{gathered}[/tex]notice that the area of the big triangle is 1.65 times the area of the small triangle, thus, the ratio of the areas is:
[tex]\frac{81}{49}=\frac{1296}{784}[/tex]Finally, we have the following for the scale factor o the two corresponding sides:
[tex]\begin{gathered} 28\cdot k=36 \\ \Rightarrow k=\frac{36}{28}=\frac{9}{7} \\ k=\frac{9}{7} \end{gathered}[/tex]therefore, the scale factor of the two sides is k = 9/7
Determine the roots algebraically by factoring:4x^4+ 6x^3- 6x^2 -4x=0
Answers
we have the equation
[tex]4x^4+6x^3-6x^2-4x=0[/tex][tex]x(4x^3+6x^2-6x^{}-4)=0[/tex][tex](4x^3+6x^2-6x^{}-4)=0[/tex]Note that
For x=1
[tex]\begin{gathered} (4(1)^3+6(1)^2-6(1)^{}-4)=0 \\ 0=0 \end{gathered}[/tex]x=1 is a root of the given equation
so
Divide
(4x^3+6x^2-6x-4) : (x-1)
4x^2+10x+4
-4x^3+4x^2
---------------------------
10x^2-6x-4
-10x^2+10x
-----------------------
4x-4
-4x+4
-----------
0
therefore
(4x^3+6x^2-6x-4)=(x-1)(4x^2+10x+4)
Solve the quadratic equation
(4x^2+10x+4)=0
a=4
b=10
c=4
substitute in the formula
[tex]x=\frac{-10\pm\sqrt[]{10^2-4(4)(4)}}{2(4)}[/tex][tex]x=\frac{-10\pm\sqrt[]{36}}{8}[/tex]the values of x are
x=-1/2 and x=-2
therefore
(4x^2+10x+4)=4(x+1/2)(x+2)=(4x+2)(x+2)
and the answer is
x(x-1)(4x+2)(x+2)=0I need help with my bottom I don’t understand (11)
Answers
The transformation rule for a reflection across the line y = x is given to be:
[tex](x,y)\Rightarrow(y,x)[/tex]The point Q is given to be:
[tex]Q=(4,-2)[/tex]The transformation will give:
[tex]Q^{\prime}=(-2,4)[/tex]Hannah graphed a line to represent the speed in miles per hour of Car A. On the same graph, she drew a line to represent the speed of Car B. The line on the graph of Car B was steeper than the line of Car A. Which car is faster? Explain
Answers
The line on the graph is stteper means slope of lime is more as compare to other.
So, car B speed line is steeper than speed line of car A, which means slope of speed line for Car B is more as compare to car A.
The more slope of speed line means more acceleration means higher speed.
So Car B is faster as compare to Car A.
The table shows the results of a survey of students and their parents. The students and their parents were asked. "If you had to hour to spend by yourself, would you prefer to read a book or would you prefer to watch TV?" Free Time Survey Read a Book Watch TV Students 18 32 Free Time Survey Read a Book Watch TV Students 18 32 Parents 25 9 Parents 25 9 Based on the results of the survey. which of these statements are true? Select all that apply. A A total of 84 people were survey. B A total of 43 students were surveyed. С Of the parents surveyed, 9 prefer to watch TV.
Answers
Options A,C and E are correct
Here, from the table given in the question, we want to select the correct choice
We shall evaluate the validity of the given options
a) This is correct
Looking at the number of respondents at each point, we can see that the addition of all number of responses gives 84
b) This is incorrect
We check for this looking at the row for the students. On this row, we have 18 and 32 which adds up to 50 and not 43
c) This is correct
We simply look at the row for parents and check under the column of 'watch TV' ; This is where we get this number
d) This is incorrect
We already stated in C above that 9 parents love to watch TV
e) This is correct
To get this we compare numbers. The total number of people that likes to read a book is (18 + 25) which is 43. We can see that this number is greater than (84-43 = 41). This means that the information in the option is correct
Hello, I need some assistance with this homework question please for precalculusHW Q8
Answers
The equation is given as,
[tex]f(x)\text{ = \lparen x-8\rparen}^5+4[/tex]Thus the correct answer is option B.
Geometric transformations refer to:a) The morphing of a commonplace vehicle into a robotic defender of libertyb) The movement of a figure or series of points in a 2 dimensional planec) A process by which an element in the underlying deep structure of a sentenceis converted to an element in the surface structured) The spontaneous change of one element into another by a nuclear process
Answers
The correct option is option B
Here, we are to select which of the options best anser the question.
Simply put, by geometric transformation, we are simply trying to make a new fgure out of an old one on a plane, by using a specific transformation process .
The transformation process may be reflection, translation, dilation or rotation.
The best answer that fits this definition is the option B
Select the correct choice below and fill in any answer boxes in your choice.
Answers
To answer this equation we must first simplify it and apply the general rule of math when it comes to dealing with equations.
Remember the rule that, whatever you do on the left side of the equation you must do the same to the other side.
Let's start.
We are given the equation:
[tex]8x-(5x+2)=5x-12[/tex]Now for our first step let us simplify the left side of the equation first. Since we have a parenthesis in our equation let us remove it by distributing the negative (-) sign outside the parenthesis into the terms inside the parenthesis.
[tex]8x-5x-2=5x-12[/tex]Notice that we can combine 8x and -5x since they are like terms.
[tex]\begin{gathered} 8x-5x-2=5x-12 \\ 3x-2=5x-12 \end{gathered}[/tex]Now we have simplified the left side of the equation and looking at the right side, it can't be simplified further.
Now let us evaluate the equation to find the value of x. Looking at our new equation which is:
[tex]3x-2=5x-12[/tex]We can see that both terms with the same variable are separated, so let us manoeuvre so that they can be together on the same side of the equation.
To do that let us subtract 3x in the left side of our equation in order to cancel the original 3x in there, and do the same to the right side of the equation by the virtue of the general rule we talked about earlier. Now we have an equation that looks like this:
[tex]3x-2-3x=5x-12-3x[/tex]Notice that 3x and -3x on the left side of our equation can be cancelled since they will just add up to 0. And the 5x and -3x on the right side of the equation can be combined since they have like terms. Now our equation becomes:
[tex]-2=2x-12[/tex]Now let us do the same thing to the -12 in the right side of the equation, let us transfer it to the left side of the equation so that we can combine it with -2.
To do that we only have to add 12 on the right side of the equation to cancel out the -12, and do the same to the left side of the equation. Our equation now becomes:
[tex]-2+12=2x-12+12[/tex]Notice again that 12 and -12 on the right side can be cancelled out since they are just equal to 0. And -2 and 12 can be combined since they are like terms. Now our equation becomes:
[tex]10=2x[/tex]Now we have simplified our equation to its simplest form it is now time to evaluate the equation. To do that simply divide both sides by 2 so that only x remains on the right side of the equation, and we can now know the value of x.
[tex]\begin{gathered} \frac{10}{2}=\frac{2x}{2} \\ 5=x \\ x=5 \end{gathered}[/tex]Therefore the value of our x is 5.
Therefore the answer to our question is LETTER A. The solution set is {5}.
Complete the sentence: The value of f(x) is a 4 at x=_______ and the value of f(4)=_________
Answers
The value of f(x) is a 4 at x = -4
and the value of f(4) = -2
Explanation:let f(x) = y
since f(x) = 4, y = 4
we find the value of x when y is 4
We trace the x and y axis:
When y =4, x = -4
The value of f(4) means x would be replaced by 4
So we check on the graph for the value of f(4) or the value of y when x = 4
At x =4, y = -2
The value of f(x) is a 4 at x = -4
and the value of f(4) = -2
In an experiment to study the dependence of hypertension on smoking habits, the following data were collected on 180 individuals:Smoking StatusNonsmokerModerate SmokerHeavy SmokerHypertension StatusHypertension213630No Hypertension482619What is the probability that a randomly selected individual is experiencing hypertension? Given that a heavy smoker is selected at random from this group, what is the probability that the person is experiencing hypertension? Are the events "hypertension" and "heavy smoker" independent? Give supporting calculations.
Answers
First question.
The probability of any event is given by:
[tex]P=\frac{\text{ number of favorable outcomes}}{\text{ number of possible outcomes}}[/tex]In this study we have a total of 87 people with hypertension and 180 people was studied, then we have:
[tex]P=\frac{87}{180}[/tex]Therefore, the probability of selecting an individual with hypertension is 87/180
Second question.
The conditional probability of event B given that event A already happened is given by:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]For this question let B be the event "The person is experiencing hypertension" and let event A be "The person is a heavy smoker". From the table we notice that a total of 49 individuals are heavy smokers and that 30 individuals are both heavy smokers and experiencing hypertension. Then we have:
[tex]P(B|A)=\frac{\frac{30}{180}}{\frac{49}{180}}=\frac{30}{49}[/tex]Therefore, the probability is 30/49
Third questions.
We know that two events are independent if and only if:
[tex]P(A\cap B)=P(A)P(B)[/tex]Using the events as we did in the previous question we have:
[tex]\begin{gathered} P(A\cap B)=\frac{30}{180}=\frac{1}{6}\cong0.17 \\ P(A)P(B)=(\frac{87}{180})(\frac{49}{180})\cong0.13 \end{gathered}[/tex]Clearly the condition is not hold. Which means that the events are dependent
Use fraction tiles to divide. Draw your models below. 1 : 3 = 1.2+ 6 2 2.
Answers
Thus, the requied number of blocks is 12. hence the solution is 12.
As 1/4 takes only 12th part of the whole 3 hence the required solution is 1/12.
Multiply 543.542 and 4 together.
Answers
You have to do the following multiplication
[tex]543.542\cdot4[/tex][tex]undefined[/tex]A student sketched some art on an 8.5 inch × 11inch piece of paper. She wants to resize it to fit an 5 inch × 7 inch fram (as show below)what percent of the original sketch was still able to be included in the frame?
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after a translation 9 units right and 7 units down
Answers
point k = (-2,0)
after a translation 9 units right and 7 units down
k' =(-2+9,0-7) = (7,-7)
M' = (2,-7)
L' = (7,-5)
Estimate the difference of 450.012 and 57.876 to the nearest hundredth.A.392.1B.392.13C.392.136D.392.14
Answers
Given: The two numbers below
[tex]\begin{gathered} 450.012 \\ \text{and} \\ 57.876 \end{gathered}[/tex]To Determine: The difference between the two numbers
See the difference below
Hence, the difference to the nearest hundredth is 392.14, OPTION D
Determine the relationship of AB and CD given the following points A(1,-2),B(3,-5),C(7,2),and D(5,5)
Answers
AB
difference of 2x and -3 y
CD
difference of 2x and -3 y
they are parallel
Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use as an approximation for
Answers
Consider that the area of a triangle with base (b) and height (h) is given by,
[tex]\text{Area of triangle}=\frac{1}{2}\times b\times h[/tex]According to the given problem,
[tex]\begin{gathered} b=56\text{ m} \\ h=56\text{ m} \end{gathered}[/tex]So the area of the triangle becomes,
[tex]\begin{gathered} A_T=\frac{1}{2}\times56\times56 \\ A_T=1568 \end{gathered}[/tex]Consider that the area of the circle with diameter (d) is given by,
[tex]A_C=\frac{\pi}{4}d^2[/tex]According to the given problem,
[tex]d=20\text{ m}[/tex]Then the area of the circle becomes,
[tex]\begin{gathered} A_C=\frac{\pi}{4}(20)^2 \\ A_C=100\pi \\ A_C\approx314.16 \end{gathered}[/tex]Now, the area of the shaded region (A) is calculated as,
[tex]\begin{gathered} A=A_T-A_C \\ A=1568-314.16 \\ A=1253.84 \\ A\approx1254 \end{gathered}[/tex]Thus, the area of the shaded region is 1254 sq. meters approximately.
Therefore, the 3rd option is correct choice.