Select the correct answer from the drop-doen menu.Consider this expression.-3x^2 - 24x - 36What expression is equivalent to the given expression? ___ (X + ___)(X + ___) Blank 1 Options: -3 3 Blank 2 Options: -2 2 -44Blank 3 Options:-9 96-6
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Related Questions
See attachment please help. Asked 2 tutors so far n they could answer. This is for 7 th grade
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Given that Janie and Jasmine are playing three games at an arcade.
Each game requires 2, 3, or 4 tokens.
Where:
m represent number of games that require 2 tokens
n represenrs number of games that require 3 tokens
p represents the number of games that require 4 tokens.
Let's write an expression to represent the total number of tokens that Janie and Jasmine will need to play each game at least once.
The expression for the number of tokens needed to play at least each game once for one person is:
2m + 3n + 4p
For both Janie and Jasmine, we have:
Radius 11 cmFind the surface area to the nearest hundredthusing 3.14 instead of Pi.126.65 cm2138.16 cm21393.11 cm21519.76 cm2
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The area of the circle is given by the formula
[tex]A=\pi r^2[/tex]where r is the radius here.
It is given r = 11.
Hence the area is given by
[tex]\begin{gathered} A=\pi\times11\times11 \\ =3.14\times11\times11 \\ =379.94 \end{gathered}[/tex]if Matthew rolls a number cube 90 times, how many times can he expect it to land on an odd number?
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Answer:
45 times
Explanation:
A six-sided number cube has the following numbers written on its six faces.
1, 2, 3, 4, 5, 6
As can be seen, three of the above numbers (1, 3 and 5) are odd. This means that half of the cube faces have odd numbers printed on them.
[tex]\frac{3\text{odd numbers}}{6\text{ numbers}}=\frac{1}{2}[/tex]Therefore, the probability that a toss would land on an odd number is 1/2 or 50%.
Now if we do 90 tosses, then we expect that 50% of them would give us an odd number.
Therefore, the number of tosses we expect to give an odd number is
[tex]90\times\frac{1}{2}=45[/tex]Hence, we expect the number cube to give us odd numbers 45 times out of 90 tosses.
I only know how to do this with equations. How do you do this with graphs?
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We will determine the domain and rage of each graph as follows:
We use the lines in which we see that there are not clear limits to determine the domain and range.
23.
[tex]\begin{cases}D_f=\mleft\lbrace x\colon x\ne2\mright\rbrace \\ \\ R_f=\mleft\lbrace y\colon y\ne1\mright\rbrace\end{cases}[/tex]25.
[tex]\begin{cases}D_f=\mleft\lbrace x\colon x\ne0\mright\rbrace \\ \\ R_f=\mleft\lbrace-\infty27.[tex]\begin{cases}D_f=\mleft\lbrace x\colon x\ne\pm2\mright\rbrace \\ \\ R_f=\mleft\lbrace y\colon y\le0\land y>1\mright\rbrace\end{cases}[/tex]Hi how is your night going and if u help me thank u so much
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Since the number on the faces of the cube are
1, 2, 3, 4, 5, 6
Then the total outcomes = 6 numbers
We need the multiples of 3
There are only 3 and 6 are the multiplies of 3, then
The outcomes = 2 numbers
The rule of probability is
[tex]P(x)=\frac{n(x)}{Tn}[/tex]n (x) = 2
Tn = 6
[tex]P(\times3)=\frac{2}{6}[/tex]Simplify it by dividing up and down by 2
[tex]\begin{gathered} P(\times3)=\frac{\frac{2}{2}}{\frac{6}{2}} \\ P(\times3)=\frac{1}{3} \end{gathered}[/tex]The probability of choosing a multiple of 3 is 1/3
The answer is B
Mia is at Arby's and is getting her drink. She decides to go crazy andmix Dr. Pepper, Sprite, and Tea together. What is the sample space for the probability of any certain order?
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from the question;
Mia is at Arby's and is getting her drink. She decides to go crazy and
mix Dr. Pepper, Sprite, and Tea together.
from this our sample space will be;
[tex]\lbrace DST,DTS,STD,SDT,TDS,TSD\rbrace[/tex]Where D = Dr. Pepper
S = sprite
T = tea
and this can be combined in different order
The correct opition is A
If the ratio of tourists to locals is 3:4 and there are 120 tourists at the opening of a new muesum, how many locals are in attendance?
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Let the number of locals be "x".
From the information given, we can write two ratios and equate:
[tex]\frac{3}{4}=\frac{120}{x}[/tex]We can easily solve for "x" by cross multiplication >>>
[tex]\begin{gathered} \frac{3}{4}=\frac{120}{x} \\ 3x=4\times120 \\ 3x=480 \\ x=160 \end{gathered}[/tex]So,
The
I will give the rest of the answer choices later . I just need a brief explanation with the answer
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Step 1
The given coordinates of triangle XYZ are
[tex]\begin{gathered} X=(-4,2) \\ Y=(-2,2) \\ Z=(-2,6) \end{gathered}[/tex]The coordinates of the first transformation X'Y'Z' has coordinates
[tex]\begin{gathered} X^{\prime}=(-3,4) \\ Y^{\prime}=(-2,4) \\ Z^{\prime}=(-2,6) \end{gathered}[/tex]Find the reason for the first transformation.
The first transformation is dilation and reduction
[tex]\begin{gathered} In\text{ triangle XYZ} \\ XY=\text{ 2units} \\ YZ=\text{ 4 units} \\ We\text{ can find XZ using Pythagoras theorem} \\ XZ=\sqrt[]{4^2+2^2} \\ XZ=\text{ }\sqrt[]{16_{}+4} \\ XZ=\sqrt[]{20} \\ XZ=2\sqrt[]{5}units \end{gathered}[/tex][tex]\begin{gathered} In\text{ triangle X'Y'Z'} \\ X^{\prime}Y^{\prime}=\text{ 1 unit} \\ Y^{\prime}Z^{\prime}=\text{ 2 units} \\ X^{\prime}Z^{\prime}\text{ = }\sqrt[]{1^2+2^2} \\ X^{\prime}Z^{\prime}=\sqrt[]{5}\text{ units} \end{gathered}[/tex]Hence the dilation was by a scale factor of 1/2 which will bring about a reduction.
Step 2
Find the reasons for the second transformation
The second transformation is a reflection and the triangle X'Y'Z' is reflected over x=1
The height of the TV set is … inchesThe length of the TV set is … inches
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The surface of the TV is depicted in the diagram below.
Then, according to the Pythagoras theorem.
[tex]26^2=h^2+l^2[/tex]And, according to the problem
[tex]l=14+h[/tex]We have two equations and two unknowns; therefore, we can solve the system.
[tex]\begin{gathered} l=14+h \\ \Rightarrow26^2=h^2+(14+h)^2 \\ \Rightarrow26^2=h^2+14^2+28h+h^2 \\ \Rightarrow2h^2+28h-480=0 \\ \Rightarrow h^2+14h-240=0 \end{gathered}[/tex]Solve the quadratic equation as shown below
[tex]\begin{gathered} \Rightarrow(h+24)(h-10)=0 \\ \Rightarrow h=-24,h=10 \end{gathered}[/tex]But h is the height; thus, it has to be a positive quantity. Then, h=10
Finally, we need to find l
[tex]\begin{gathered} h=10 \\ \Rightarrow l=14+10=24 \\ \Rightarrow l=24 \end{gathered}[/tex]The answers are: height equal to 10 and length equal to 24.
Question 6 of 10 What is the slope of the line that contains the points (-1, 2) and (3, 3)? A. -4 B. 4 C.-1/4 D.1/4
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The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Given that the line passes through the points (-1, 2) and (3, 3) then its slope is:
[tex]m=\frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]Draw a number line from 2.2 to 2.3. Label tick marks at hundredths to show 2.21, 2.22, 2.23, and so on. Mark a point at the approximate location of square root of 5 to the thousandths place.
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The value is shown in the red circle on the number line.
I need help figuring out what to put in this boxes starting with question 1
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Given the following question:
Independent means testable, so a variable that can be tested would be considered independent. In this case we aren't testing anything, in fact we are measuring the amount of retrievers that are or aren't on a leash which means it is dependent because we are measuring something.
So your answer will be no it's not independent.
from a 38 in by 38 inch piece of metal, squares are cut of the four corners so that the sides can then be folded up to make a box. Let x represent the length of the sides of the squares, in inches, that are cut out. Express the volume of the box as a function of x
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draw the figure without the squares on each corner
fold the figure to make the box
find the volume of the box
[tex]\begin{gathered} V=x\cdot(38-2x)\cdot(38-2x) \\ V=4x^3-152x^2+1444x \end{gathered}[/tex]it takes Joan two times longer than Jane to file the reports.  together they can file the reports in six minutes. how long will it take each woman to file the reports herself
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Work problems can be express as :
[tex](\frac{1}{a}+\frac{1}{b})t=1[/tex]where a and b are the rates of two person doing one work
and
t = time to finish the work when working together.
From the problem, Joan takes two times longer than Jane.
If Jane can file the report in x minutes, Joan will be 2x minutes.
They can file the report together in 6 minutes so t = 6
Plug in the values to the equation :
[tex](\frac{1}{x}+\frac{1}{2x})\times6=1[/tex]Simplify then solve for x :
[tex]\begin{gathered} (\frac{1}{x}+\frac{1}{2x})\times6=1 \\ \text{Multiply both sides by 2x} \\ 2x\times(\frac{1}{x}+\frac{1}{2x})\times6=2x\times1 \\ (2+1)\times6=2x \\ 3\times6=2x \\ 18=2x\text{ } \\ x=\frac{18}{2}=9 \end{gathered}[/tex]x = 9, so Jane can file the report in 9 minutes.
Since Joan is two times longer than Jane, she can file the report in 18 minutes.
Answers :
Jane = 9 minutes
Joan = 18
Simplify the expression:3(7r+1)=
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We are given a mathematical expression as follows:
[tex]3\cdot(\text{ 7r + 1 )}[/tex]We are asked to simply the above expression.
Whenever we resolve mathematical operators in an expression/equation we use the guidelines of PEMDAS.
The rule PEMDAS gives us the order in which the mathematical operations are carried out. The acronyms full form is:
[tex]\begin{gathered} \P\colon\text{ Parenthesis} \\ E\colon\text{ Exponents} \\ M,D\colon\text{Multiplication, Division} \\ A,S\colon\text{ Addition, Subtraction} \end{gathered}[/tex]Mathematical operators are applied in the order of decreasing importance in an expression as expressed above.
Now, we will go ahead an apply the rule of PEMDAS to simplify our expression. We see that we have to deal with a P: Parenthesis first!
[tex]3\cdot7r\text{ + 3}\cdot1[/tex]Next we will use the Multiplication operator ( M ) and multiply out the respective terms inside the parenthesis as follows:
[tex]21r\text{ + 3}[/tex]Since the above terms ( 21r ) and ( 3 ) are of different domains i.e one is a multiple of a vraible ( r ) and the other one is an integer we can not further simplify the result. Hence, the simplified expression would be:
[tex]\textcolor{#FF7968}{21r}\text{\textcolor{#FF7968}{ + 3}}[/tex]Find the average weekly earnings.Unit rate: $1.15; Units per week: 475, 348, 516,402 (Note: 4 weeks of work)
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Given:
The weekly earning for 4 weeks is,
475, 348, 516,402.
The average of the earning for 4 weeks is,
[tex]\begin{gathered} A=\frac{475+348+516+402}{4} \\ A=\frac{1741}{4} \\ A=435.25 \end{gathered}[/tex]Unit rate is $1.15,
[tex]\begin{gathered} A=1.15\times435.25 \\ A=500.5375 \end{gathered}[/tex]Answer: The average weekly earnings is $500.5375.
The following equation represents the volume of a rectangular prism with a width of winches:V= 2w^3 - 7w^2 +3wa. What is the volume if the width is 5 inches?b. Factor this polynomial completely and describe what each factor means in terms of thedimensions of the rectangular prism.c. If the width is 5 inches, what are the other dimensions? How does this relate to youranswer to part a?d. Graph the polynomial on a graphing calculator or an online graphing application. Whatare the x-intercepts? What do these mean in terms of the situation?e. What are the domain and range in terms of the situation? Justify your answers.
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Solution:
Given:
[tex]V=2w^3-7w^2+3w[/tex]a) When the width is 5 inches,
Substitute w = 5 into the equation.
[tex]\begin{gathered} V=2(5^3)-7(5^2)+3(5) \\ V=2(125)-7(25)+15 \\ V=250-175+15 \\ V=90\text{ }in^3 \end{gathered}[/tex]Therefore, the volume of the prism is 90 cubic inches.
b) Factor the polynomial
[tex]\begin{gathered} 2w^3-7w^2+3w=w(2w^2-7w+3) \\ w(2w^2-w-6w+3)=w(w(2w-1)-3(2w-2)) \\ =w(w-3)(2w-1) \end{gathered}[/tex]Therefore, the completely factored polynomial is w(w-3)(2w-1)
[tex]\begin{gathered} w\text{ is the width} \\ 2w-1\text{ can be the length} \\ w-3\text{ can be the height} \end{gathered}[/tex]c) If w = 5 inches;
[tex]\begin{gathered} l=2w-1 \\ l=2(5)-1 \\ l=10-1 \\ l=9inches \\ \\ \\ \\ h=w-3 \\ h=5-3 \\ h=2inches \end{gathered}[/tex]It relates using the formula of volume of a rectangular prism;
[tex]\begin{gathered} V=lbh \\ V=9\times5\times2 \\ V=90in^3 \\ \\ The\text{ volume in part \lparen a\rparen is also }90in^3 \end{gathered}[/tex]d) The graph of the function is shown below;
The x-intercepts are;
[tex]w=0,w=0.5,w=3[/tex]In terms of the situation, the x-intercepts means when
Match the number to the letterS. Note one number can have multiple graphs Solve Number 10
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SOLUTION
When a graph, let's say y = f(x) has a point of inflection (changes from concave up to concave down), the graph of its derivative y = f '(x) has a maximum or minimum (and so changes from increasing to decreasing or decreasing to increasing respectively).
So, from this explanation, the graphs that change concavity are
Graphs B, C, D, E, J, K, M, and O.
Rewrite 2 log7 2 + 6 log7 5 using properties of logarithms.A. log, (3√10)OB. log, (50.22)OC. log77D. log7 (3² √2)Reset Selection
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The given logarithm expression is:
[tex]2\log_72+6\log_75[/tex]It is required to use the properties of logarithms to rewrite the expression.
Use the Power Property of Logarithm to rewrite each term of the expression:
[tex]\Rightarrow\operatorname{\log}_72^2+\operatorname{\log}_75^6[/tex]Rewrite the expression using the Product Property of Logarithm:
[tex]\Rightarrow\log_7(2^2\cdot5^6)=\log_7(5^6\cdot2^2)[/tex]The answer is B.I need help with a math problem(a) milliliters/liters(b) grams/kilograms(c) millimeters/centimeters/meters/kilometers
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ANSWERS
(a) milliliters
(b) grams
(c) centimeters
EXPLANATION
To answer all of these questions, we have to think about each situation.
(a) In this case, Tammy added cream to her coffee. Unless she is drinking more than 5 liters of coffee, she cannot be adding 5 liters of cream. Therefore, she added 5 milliliters of cream to her coffee.
(b) Here we are talking about the mass of a cellular phone. The size of a cell phone is just big enough to fit in a person's hand and, usually, its weight is designed to be held with one hand. Therefore, if the number is 100, that cannot be 100 kilograms.
Hence, the mass of the cell phone is about 100 grams.
(c) Now we have a pencil and we are talking about its length. Like in the case of the cell phone, a pencil is something we hold with one hand, so it cannot be 19 meters long - and 19 kilometers would not fit in our hands either. So, we have either millimeters or centimeters.
19 millimeters is about the size of the tip of a pencil - the part in the shape of a cone, so 19 millimeters is too short of a pencil. Hence, we can conclude that the length of a new pencil is about 19 centimeters.
A teacher purchased 20 calculators and 10 measuring tapes for her class and paid $495.Later, she realized that she didn't order enough supplies. She placed another order of 8 ofthe same calculators and 1 more of the same measuring tape and paid $178.50.This system represents the constraints in this situation:20c + 10m = 4958c + m = 178.501. Discuss with a partner:a. In this situation, what do the solutions to the first equation mean?b. What do the solutions to the second equation mean?c. For each equation, how many possible solutions are there? Explain how youknow.d. In this situation, what does the solution to the system mean?2. Find the solution to the system. Explain or show your reasoning.3. To be reimbursed for the cost of the supplies, the teacher recorded: "Itemspurchased: 28 calculators and 11 measuring tapes. Amount: $673.50."a. Write an equation to represent the relationship between the numbers ofcalculators and measuring tapes, the prices of those supplies, and the totalamount spent.b. How is this equation related to the first two equations?c. In this situation, what do the solutions of this equation mean?
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1. a.
The solution for the first equation means all possible combinations of prices for calculators and tapes that would make a final cost of $495 for 20 calculators and 10 tapes.
b.
The solution for the second equation means all possible combinations of prices for calculators and tapes that would make a final cost of $178.5 for 8 calculators and 1 tape.
c.
Since each equation has 2 variables, there is an infinite number of solutions for each equation individually. Because we can choose any value of c and calculate the corresponding value of m to solve the equation.
d.
The solution to the system means an unique pair of values (one value for c and one for m) that satisfies both equations at the same time.
2.
In order to find the solution of the system, let's first solve the second equation for m and then use its value in the first equation:
[tex]\begin{gathered} 8c+m=178.5\to m=178.5-8c \\ 20c+10m=495 \\ 20c+10(178.5-8c)=495 \\ 20c+1785-80c=495 \\ -60c=495-1785 \\ -60c=-1290 \\ c=21.5 \\ \\ m=178.5-8\cdot21.5 \\ m=178.5-172 \\ m=6.5 \end{gathered}[/tex]Therefore the calculator costs $21.50 and the tape costs $6.50.
3. a.
28 calculators and 11 tapes cost $673.50, so we have the equation:
[tex]28c+11m=673.5[/tex]b.
This equation has the same solution as the other two equations.
c.
The solution for this equation means all possible combinations of prices for calculators and tapes that would make a final cost of $673.50 for 28 calculators and 11 tapes.
Graph the equation 4x + 5y = -4 by plotting points.
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Answer:
To graph the equation 4x + 5y = -4 by plotting points.
First, To find the points on the line.
Substitute different values of x, to find corresponding values of y.
Let x=-1,
Substitute in the equation we get,
[tex]4(-1)+5y=-4[/tex][tex]5y=-4+4[/tex][tex]y=0[/tex]One of the point on the line is (-1,0)
Let x=-6,
Substitute in the equation we get,
[tex]4(-6)+5y=-4[/tex][tex]-24+5y=-4[/tex][tex]5y=20[/tex][tex]y=4[/tex](-6,4) is the point on the line.
Let x=4,
Substitute in the equation we get,
[tex]4(4)+5y=-4[/tex][tex]16+5y=-4[/tex][tex]5y=-20[/tex][tex]y=-4[/tex](4,-4) is the point on the given line.
Rewrite the equation into slope intercept form y=mx+c, we get,
[tex]y=-\frac{4x}{5}-\frac{4}{5}[/tex]we get the slope of the line is -4/5 and y intercept is -4/5
(
A quality control expert at life batteries wants to test their new batteries. The design engineer claims they have a variance of 8464 with the mean life of 886 minutes. If the claim is true in a sample of 145 batteries what is the probability that the main battery life will be greater than 904.8 minutes? Round answer to four decimal places
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The parameters provided from the question is:
[tex]\begin{gathered} \mu=886 \\ \sigma=\sqrt{8464}=92 \\ \bar{x}=904.8 \\ n=145 \end{gathered}[/tex]Using the z-score formula:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substitute for the values provided and solve for z
[tex]\begin{gathered} z=\frac{904.8-886}{\frac{92}{\sqrt{145}}} \\ z=2.4607 \end{gathered}[/tex]The probability that the main battery life will be greater than 904.8 is given:
[tex]\begin{gathered} P(z>2.4607)=P(0\leq z)-P(02.4607)=0.5-0.4931 \end{gathered}[/tex][tex]P(z>2.4607)=0.0069[/tex]Hence, the probability that the main battery life will be greater than 904.8 is 0.0069
hello! can you help me with this equation 3 minus (-6) ???
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Answer
3 - (-6) = 9
Explanation
3 - (-6)
(minus multiplied by minus gives plus)
3 - (-6)
= 3 + 6
= 9
Hope this Helps!!!
A population of 20,000 is decreasing in size at a rate of 4.6% each year. Let A(t) representthe amount in the population after t years. (same as previous problem)Determine when the population will reach below 5000. Round to the nearest thousandth ofa year.
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solve t when A(t)=5000
[tex]\begin{gathered} 5000=20000-920t \\ 920t=20000-5000 \\ 920t=15000 \\ t=16.3 \end{gathered}[/tex]the population will be below 5000 after 16.3 years
A kite glides horizontally at an altitude of 20m while we unspool the string……Related rates question in calculus
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Given
A kite glides horizontally at an altitude of 20m while we unspool the strin
How to solve (x+9)(x+3)(x-2)<0solution in interval notation
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To solve the inequality, we need to find the values of x
[tex]\begin{gathered} \text{When we have quadratic equatio written as (x - a)(x - b) = 0} \\ We\text{ solve by seperating them individually: }x\text{ - a = 0 or x - b = 0 } \\ \text{We will apply same here:} \\ (x\text{ +9) < 0 or (x + 3) < 0 or (x - 2) < 0} \\ (x\text{ +9) < 0} \\ \text{subtract 9 to both sides:} \\ x\text{ + 9 - 9 < 0 - 9} \\ x\text{ < -9} \end{gathered}[/tex][tex]\begin{gathered} (x\text{ + 3) < 0} \\ subtract\text{ 3 from both sides:} \\ x\text{ + 3 - 3 < 0 - 3} \\ x\text{ < -3} \\ \\ (x\text{ - 2) < 0} \\ \text{add 2 to both sides:} \\ x\text{ - 2 + 2 < 0 + 2} \\ x\text{ < 2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ <-9} \\ (-\infty,\text{ -9)} \\ \text{for x < -3 and x < 2} \\ -3<\text{ x< 2} \\ (-3,2) \\ \text{The solution becomes:} \\ (-\infty\text{ -9) }\cup\text{ (-3, 2)} \end{gathered}[/tex]
Which digit is in the hundredths place?6.537O A. 5B. 6C. 3D. 7
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We can get the place value of all the digits of the number 6.537 as shown in the diagram below
The hundredth
You roll a 6 sided die 2 times what is the probability of rolling a 4 and then rolling a 5
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Given:
A 6-sided die was rolled 2 times.
Required:
Find the probability of rolling a 4 and then rolling a 5.
Explanation:
The total number of outcomes on the die = 1, 2, 3, 4, 5, 6 = 6
The possible outcomes of 4 = 1
The possible outcomes of 5 = 1
The probability of an event is given by the formula:
[tex]P=\frac{number\text{ of possible outcomes}}{Total\text{ number of outcomes}}[/tex]Probability of getting 4 is:
[tex]P(4)=\frac{1}{6}[/tex]Probability of getting 5 is:
[tex]P(5)=\frac{1}{6}[/tex]Since both events are independent of each other.
So the probability of rolling a 4 and then rolling a 5 is:
[tex]\begin{gathered} P=\frac{1}{6}\times\frac{1}{6} \\ P=\frac{1}{36} \end{gathered}[/tex]Final Answer:
The probability of rolling a 4 and then rolling a 5 is
[tex]\frac{1}{36}[/tex]Use this function to predict the amount it will take in 2009 and in 2016 to equal the value of 1 currency unit in 1918
Answers
1) Since we have a Linear Function that models this situation, then we can plug it into that function.
2)
a)
Let's begin by predicting the value of that currency in 2009, i.e. 19 years since 1990:
[tex]\begin{gathered} V(x)=0.4226x+13.4784 \\ V(19)=0.4226(19)+13.4784 \\ V(19)=21.5078\approx21.51 \end{gathered}[/tex]b) Now, in 2016, i.e. 26 years since 1990:
[tex]\begin{gathered} V(26)=0.4226(26)+13.4784 \\ V(26)=24.466\approx24.47 \end{gathered}[/tex]Thus, in 2009 we would need $21.51, and in 2016, $24.47 to equate the value of 1 currency in 1918.