Which of the following illustratesthe associative property ofmultiplication?Enter a, b, c, d, or e.(a + b)(cd) =a. acd + bcdb. (b + a)(cd)c. (ac + bc)d d. [(a + b)c]de. (cd)(a + b)
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The associative property of multiplication states that
[tex](a\cdot b)\cdot c=a\cdot(b\cdot c)[/tex]Given that (a+b)(cd), then its associative counterpart is
[tex](a+b)\mleft(cd\mright)=\lbrack(a+b)c\rbrack d[/tex]Related Questions
help me with this question
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Answer:
Step-by-step explanation:
just 3,2
A bag contains 6 green balls and 4 yellow balls. What is the probability that two balls picked randomly are both of the same color?
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Given:
The number of green balls is G = 6.
The numer of yellow balls is Y = 4.
Explanation:
Determine the total number of balls.
[tex]\begin{gathered} T=6+4 \\ =10 \end{gathered}[/tex]Determine the probability for both selected balls to be green.
[tex]\begin{gathered} P(G)=\frac{6}{10}\cdot\frac{5}{9} \\ =\frac{15}{45} \end{gathered}[/tex]Determine the probability for selected balls to be yellow.
[tex]\begin{gathered} P(Y)=\frac{4}{10}\cdot\frac{3}{9} \\ =\frac{6}{45} \end{gathered}[/tex]Determine the probability for both selected balls to be of same colour.
[tex]\begin{gathered} P=P(G)+P(Y) \\ =\frac{15}{45}+\frac{6}{45} \\ =\frac{21}{45} \\ =\frac{7}{15} \end{gathered}[/tex]Write an equation for a line going through the point (-5, -10) that is parallel to theline 1/5x-1/6y = 7.
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Two lines are parallel if they have the same slope. In order to better visualize the slope of the line we will express it in the slope-intercept form, which is done below:
[tex]\begin{gathered} \frac{1}{5}x-\frac{1}{6}y\text{ = 7} \\ \frac{1}{5}x-7=\frac{1}{6}y \\ \frac{1}{6}y\text{ = }\frac{1}{5}x-7 \\ y\text{ = }\frac{6}{5}x\text{ - 42} \end{gathered}[/tex]We now know that the slope of the line is 6/5, because in this form the slope is always the number that is multiplying the "x" variable. So we need to find a line of the type:
[tex]h(x)\text{ = }\frac{6}{5}x+b[/tex]Therefore the only needed variable is "b", which we can find by applying the known point (-5, -10).
[tex]\begin{gathered} -10\text{ = }\frac{6}{5}\cdot(-5)\text{ + b} \\ -10=-6+b \\ b=-10+6 \\ b=-4 \end{gathered}[/tex]The expression of the line is then:
[tex]h(x)\text{ = }\frac{6}{5}x-4[/tex]fine the value of x in(2x+5)(8x+5)
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We are given the value of two angles as functions of "x"
[tex]\begin{gathered} \text{angle 1 = 2x+5;} \\ \text{angle 2 = 8x+5} \end{gathered}[/tex]These are supplentary angles, that is, their sum is 180 degrees
[tex]\text{angle 1 + angle 2 =180}^{\circ}[/tex]Replacing the values for the angles
[tex](2x+5)+(8x+5)=180[/tex]Now we solve the equation, first by adding similar terms
[tex]10x+10=180[/tex]Now we substract 10 on both sides
[tex]10x=170[/tex]Now we divide by 10 on both sides
[tex]x=\frac{170}{10}=17[/tex]The value of x is 17
Lisa receives a net pay of $619.06 biweekly. She has $143withheld from her pay each pay period. What is her annual gross salary?a. $ 762.06b. $18,289.44c. $19,813.56d. $39,627.12
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Answer:
c. $19,813.56
Explanation:
Given:
• Lisa receives a net pay of $619.06 biweekly.
,• $143 is withheld from her pay each pay period.
We are required to find her annual gross salary.
First, determine her gross salary for each pay period.
[tex]\begin{gathered} \text{Gross Salary}=\text{Net Pay+Deduction} \\ =619.06+143 \\ =\$762.06 \end{gathered}[/tex]Next, determine the number of payment periods.
[tex]\begin{gathered} \text{Lisa is paid biwe}ekly,\text{ that is every 2 weeks.} \\ The\text{ number of weeks in a year}=52 \\ \text{Therefore:} \\ \text{The number of payment periods}=\frac{52}{2}=26 \end{gathered}[/tex]Finally, multiply her gross salary per period by the number of periods to get her annual gross salary.
[tex]\begin{gathered} \text{Gross annual salary}=26\times762.06 \\ =\$$19,813.56$ \end{gathered}[/tex]Lisa's annual gross salary is $19,813.56.
Option C is correct.
write the expanded form of the expression : 7(2x + y)
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ANSWER
14x + 7y
EXPLANATION
We want to write the expanded form of the expression given:
7(2x + y)
To do this, we have to use the distribution property by using the number outside the bracket to multiply each of the terms in the bracket.
So, we have that:
7(2x + y) = (7 * 2x) + (7 * y)
= 14x + 7y
That is the answer.
The average price of a new home in a neighborhood in thousands of dollars (f(x)) is related to the number of years since the neighborhood was built (x) in the function: Use the graph of the function to describe its domain.A. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to 100B. The domain is the average price of homes in a new neighborhood, which is represented by all real numbers from 0 to infinity C. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from zero to infinityD. The domain is the number of years since the neighborhood was built, which is represented by all real numbers from 0 to 100l
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As given by the question
There are given that the graph of the function.
Now,
According to the domain concept, the domain is defined for the input valuewhich is given in the x-axis.
That means, all x-axis input value range is called domain.
Then,
From the given graph:
The domain is the number of years since the neighborhood was built, that represent the range of x-axis 0 ti infinity.
Hence, the correct option is C.
which expressions are equivalent to 5(–2k – 3) + 2k?a) (-5•3)-8kb) -15c) none of em
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Without dividing how can you decide whether the quotient of 7.16 ÷ 4 will be less than or greater than 2
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Answer:
Hope this helps : )
Step-by-step explanation:
We know that the quotient of 7.16 ÷ 4 can be multipled with 4 to get 7.16. So if we multiply 4 × 2, then the product is 8. Now we know that the quotient of 7.16 ÷ 4 is less than 2.
Check:
7.16 ÷ 4 = 1.79
1.79 < 2 ✓
Determine if the following equations are parallel, perpendicular, or neither. 5(x + 3) = 3y + 12 and 5x + 3y = 15
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Solution
We have the following equation:
5(x+3)= 3y+12 (1)
Solving for y we got:
3y= -12+ 5(x+3)
3y = -12 + 5x+15
3y= 5x +3
y= 5/3 x +1
The slope for the first case is: m1= 5/3
5x + 3y = 15 (2)
Solving for y we got:
3y= 15-5x
y= 5 -5/3x
The slope is given by : m2= -5/3
Then m1*m2 is not equal to -1 (NOT perpendicular)
m1 is different from m2 (NOT parallel)
Then are not perpendicular or parallel
Is the ordered our (-2,8) a solution to: y-9=3x
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It is not a solution
1) To get to know that, we need to plug it in the equation and check whether it is true or false.
2) Picking point (-2,8) and plugging -2 into x and 8 into y, we get:
[tex]\begin{gathered} y-9=3x \\ (8)-9=3(-2) \\ -1=-6\:False \end{gathered}[/tex]2) Hence, we can tell that (-2,8) is not a solution to that equation
what is the answer to -8+3v-5-4v
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We solve as follows:
[tex]-8+3v-5-4v=-13-v[/tex]y=4x+6slope: 4y-int: (0,6)why after graphing y-int, is the second point on the line given a slope of 4/1? shouldn't it be 4,0?
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The given line is,
[tex]y=4x+6[/tex]Here, the slope is, 4 and y intecept is 6.
For x = 4, we have,
[tex]y=4\times4+6=16+6=22[/tex]Therefore, the two points on the graph is, (0, 6) and (4, 22).
Now, for y = 1, we have,
[tex]\begin{gathered} 1=4x+6 \\ 4x=-5 \\ x=-\frac{5}{4} \end{gathered}[/tex]order the numbers -7,7,1 and -1 from least to greatest.
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as we move towards the right,the value of the numbers on a number line increases. The numbers to the left of zero are negative while the numbers to the right of zero are positive.
Therefore, by ordering the numbers from least to greatest, it would be
- 7, - 1, 1, 7
Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.
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Given:
Lionfish are considered an invasive species, with an annual growth rate of 69%. A scientist estimates there are 9,000 lionfish in a certain bay after the first year.
The general equation of the growth is:
[tex]P(t)=P_0\cdot(1+r)^t[/tex]Given rate = r = 69% = 0.69
After 1 year, P = 9000
Substitute to find the initial number of Lionfish
So,
[tex]\begin{gathered} 9000=P_0\cdot(1+0.69)^1 \\ 9000=P_0\cdot1.69 \\ P_0=\frac{9000}{1.69}\approx5325 \end{gathered}[/tex]Part (A), we will write an explicit formula f(n) that represents the number of lionfish after n years
so, the formula will be:
[tex]f(n)=5325\cdot1.69^n[/tex]Part (B): we will find the number of lionfish after 6 years
so, substitute with n = 6 into the equation of part (a)
[tex]f(6)=5325\cdot1.69^6=124,073[/tex]So, after 6 years, the number of lionfish = 124,073
Part (C): The scientists remove 1400 fish per year after the first year
So, we the number of lionfish:
[tex]9000-1400=7600[/tex]Then after 2 years, the number of lionfish
[tex]7600\cdot1.69-1400[/tex]After 3 years:
[tex]\begin{gathered} (7600\cdot1.69-1400)\cdot1.69-1400 \\ =7600\cdot1.69^2-1400\cdot1.69-1400 \\ =7600\cdot1.69^2-1400\cdot(1+1.69) \end{gathered}[/tex]So, after (n) years:
[tex]7600\cdot1.69^{n-1}-1400\cdot(1+1.69)^{n-2}^{}[/tex]The graph is shifted 1 unit down and 4 units left
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To answer this question, we need to remember the rules of transformation of functions, these rules are shown below:
Using these rules, we have that the equation that represents the new graph is:
[tex]y=\sqrt[3]{x+4}-1[/tex](−2,1) is a solution to the following system of linear equations6−3=−152+=−3
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We have the following system of linear equations:
[tex]\begin{gathered} 6x-3y=-15 \\ 2x+y=-3 \end{gathered}[/tex]We want to know if the pair (x,y) = (-2,1) is a solution of the system above.
To see if this pair is a solution, we simply replace the values of x and y in the equations above and we verify if the equality holds.
1) Replacing in the first equation we see that:
6x - 3y = 6*(-2) - 3*(1) = -12 -3 = -15 ✓
The equality holds.
2) Replacing in the second equation we see that:
2x + y = 2*(-2) + 1 = -4 + 1 = -3 ✓
The equality holds.
We conclude that (-2,1) is a solution to the system of linear equations.
Answer: True
D (x - 4) B . In the figure shown, what is the value of x? C •E 19 A F
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x = 23
Explanation:Given: triangle ABC and triangle DEF
we need to find the triangle congruency theorem in order to determine the value of x.
AB = DE
AC = DF
∠A = ∠D
the sides BC and EF respectively were not marked.
Since, we were not given the value of the angles but we know they are equal. And two sides of triangle ABC and the corresponding two sides of triangle DEF were given. It means BC is equal to EF.
The sides opposite ∠A = BC
The sides opposite ∠D = EF
BC = EF
x - 4 = 19
collect like terms:
x = 19 + 4
x = 23
A graph shows three linear relationships but different y y-intercepts the following slopes line1: 1 / 5 line 2: 3/5 line 3: 6 / 5 write an equation for each line type your answers in the boxes below
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Explanation
Step 1
we have 3 lines, the slopes and the Y-intercept( or a point of the line)
use :
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ \text{and m is the slope} \end{gathered}[/tex]Step 2
Let
[tex]\begin{gathered} \text{slope}=\frac{1}{5} \\ P(0,5)\text{ gr}een \\ \text{replacing} \\ y-5=\frac{1}{5}(x-0) \\ y=\frac{1}{5}x+5\text{ Equation(1) ( gre}en) \end{gathered}[/tex]Step 3
[tex]\begin{gathered} \text{slope}=\frac{3}{5} \\ P(0,7) \\ \text{replacing} \\ y-y_1=m(x-x_1) \\ y-7=\frac{3}{5}(x-0) \\ y=\frac{3}{5}x+7\text{ function (2) Blue} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \text{slope}=\frac{6}{5} \\ P(0,3)\text{red} \\ \text{replacing} \\ y-y_1=m(x-x_1) \\ y-3=\frac{6}{5}(x-0) \\ y=\frac{6}{5}x+3\text{ Function (3) red} \end{gathered}[/tex]I hope this helps you
Convert each equation to slope-intercept form. Then label the slope & y-intercept.
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C. The equation is
[tex]4x-6y=18[/tex]An equation is in slope-intercept form if it is in the form
[tex]y=mx+c[/tex]Expressing the given equation in slope-intercept
This gives
[tex]\begin{gathered} 4x-6y=18 \\ -6y=-4x+18 \end{gathered}[/tex]Divide through by -6
This gives
[tex]\begin{gathered} -\frac{6y}{-6}=-\frac{4x}{-6}+\frac{18}{-6} \\ y=\frac{2}{3}x-3 \end{gathered}[/tex]Therefore, the slope-intercept form of the given equation is
[tex]y=\frac{2}{3}x-3[/tex]
Where
slope = 2/3
y-intercept = -3
which of the following is equivalent to the logarithmic equation below? log4 64=3
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Combine like terms to simplify the expression: 1.17 -0.07a + (-3.92a) 1.17 - 3.850 Stuck? Watch a video or use a hint.
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The given expression is
[tex]1.17-0.07a+(-3.92a)[/tex]Observe that -0.07a and -3.92a are like terms, let's add them.
[tex]\text{1}.17-3.99a[/tex]Hence, the final expression is 1.17 - 3.99a.What is the value of x? 830 R 620 5х-130 6x – 360
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Question:
Solution:
The entire circumference is equivalent to traveling 360 degrees. Therefore, we have the following equation:
[tex]83+62+(5x-13)+(6x-36)\text{ = 360}[/tex]this is equivalent to:
[tex]83+62-13-36+(5x+6x)\text{ = 360}[/tex]this is equivalent to:
[tex]96\text{ +11x = 360}[/tex]this is equivalent to:
[tex]11x\text{ = 360-96 = 297}[/tex]and solving for x, we obtain:
[tex]x\text{ = }\frac{264}{11}=\text{ 2}4[/tex]then, the correct answer is:
[tex]x\text{ = 2}4[/tex]Multiply. -8. -9/3 . 2/-5Write your answer in simplest form.
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To multiply these numbers, the first step is to writhe "-8" as an improper fraction, to do so, divide it by 1
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})\cdot(-\frac{2}{5})[/tex]Next is to solve the multiplication, to do so, first multiply the first two terms of the multiplication:
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})[/tex]The multiplication is between two negative numbers, when you multiply two negative numbers, the minus signs cancel each other and turn into a positive value, this is called "double-negative"
[tex](-\frac{8}{1})\cdot(-\frac{9}{3})=\frac{8\cdot9}{1\cdot3}=\frac{72}{3}[/tex]Next multiply the result by the third fraction -2/5
This time you are multiplying a positive and a negative number, so the result of the calculation will be negative
[tex]\frac{72}{3}\cdot(-\frac{2}{5})=-\frac{72\cdot2}{3\cdot5}=-\frac{144}{15}[/tex]Final step is to simplify the result, both 144 and 15 are divisible by 3, so divide the numerator and denominator by 3 to simplify the result to the simplest form:
[tex]-\frac{144\div3}{15\div3}=-\frac{48}{5}[/tex]In simple layman’s English please explain the difference between uniform probability models and non-uniform probability models.
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In a uniform probability model, all events have the same chance of occurring. For a non-uniform probability model, all events do not have the same chance of occurring
(c) When the local time in Athens is 09 00, the local time in Berlin is 08 00.
A plane leaves Athens at 13.15
It arrives in Berlin at 1505 local time.
(i) Find the flight time from Athens to Berlin.??
Answers
Answer:
l _ to the cinema at least a week
The flight time from Athens to Berlin is 50 minutes as per the given data.
What is local time?Local time refers to the time in a specific location or time zone. It is the time that is used and observed by people in a particular region or city.
To find the flight time from Athens to Berlin, we need to calculate the time difference between the two cities and subtract it from the elapsed time between the departure and arrival times.
Athens is one hour ahead of Berlin when it is 9:00 AM in Athens, it is 8:00 AM in Berlin. This means that when the plane leaves Athens at 13:15 local time, it is 12:15 in Berlin.
The elapsed time between the departure time (13:15) and the arrival time (15:05) is 1 hour and 50 minutes.
However, we need to account for the time difference between the two cities. Since Berlin is one hour behind Athens, we need to subtract one hour from the elapsed time:
1 hour and 50 minutes - 1 hour = 50 minutes
Therefore, the flight time from Athens to Berlin is 50 minutes.
For more details regarding local time, visit:
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A starship is orbiting lax, a large moon of the planet sylow II. The ships sensor array detects that the temperature on the surface of the moon is -12.3 f. What is the temperature in degrees Celsius
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The temperature in degrees celsius of the surface of the moon is -24.6111.
Fahrenheit and Celsius are directly proportionate to one another due to their relationship. When the temperature rises on the Celsius scale, it likewise rises on the Fahrenheit scale. Similar to how the Celsius scale, the Fahrenheit scale similarly drops in temperature when the Celsius scale does.
The ships sensor array detects that the temperature on the surface of the on is -12.3 F.
To convert the Fahrenheit to Celsius we will use the given formula.
[tex]C=\frac{5}{9}(F-32)[/tex]
Given F=-12.3
Substituting F in the equation, we get
[tex]C=\frac{5}{9}(-12.3-32)[/tex]
[tex]C=\frac{5}{9}(-44.3)[/tex]
[tex]C=\frac{-221.5}{9}[/tex]
[tex]C=-24.6111[/tex]
Therefore, the temperature -12.3 f to Celsius is -24.6111 C on the surface of the moon.
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x+2x+5=x+19please help
Answers
To solve this equation
Step 1:
x + 2x + 5 = + 19
Which of the following pairs of points define a line segment parallel to the x-axis?A. (4,3)(-4,3)B. (4,3)(4,-3)C. (-4,-3)(4,-3)D. (3,4)(-3,-4)
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EXPLANATION:
1.We must first locate the pairs of points.
-Points A:
Find the sum of the first three terms of the geometric series represented by the formula an = (825)(52)(n - 1).
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ANSWER:
2nd option: 78/25
STEP-BY-STEP EXPLANATION:
We have the following geometric series:
[tex]a_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(n-1\right)}[/tex]We calculate the sum, replace n by 1,2,3, just like this:
[tex]\begin{gathered} s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(1-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(2-1\right)}+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^{\left(3-1\right)} \\ s_n=\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^0+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^1+\left(\frac{8}{25}\right)\cdot\left(\frac{5}{2}\right)^2 \\ s_n=\frac{8}{25}+\frac{4}{5}+\frac{8}{4} \\ s_n=\frac{32+80+200}{100} \\ s_n=\frac{312}{100} \\ s_n=\frac{78}{25} \end{gathered}[/tex]The sum of the first 3 terms is 78/25