The circumference of a circle is give by:
[tex]C=2\pi r[/tex]Plugging the value we have for the circunference we can find the radius:
[tex]\begin{gathered} 31.4=2\pi r \\ r=\frac{31.4}{2\pi} \\ r=\frac{15.7}{\pi} \end{gathered}[/tex]Now that we have the radius we remember that the area of a circle is:
[tex]A=\pi r^2[/tex]Plugging the value of r we have that:
[tex]A=\pi(\frac{15.7}{\pi})^2=78.46[/tex]Therefore the area of the circle is 78.46
If Carl wants to buy a $23,999 truck and put a 15% down payment on it, how much money should he save for a down payment?
Money Carl should save for a down payment is $3699.85.
A percentage is a number or ratio expressed as a fraction of 100. A percentage is a dimensionless number, it has no unit of measurement.
Calculation:-
Cost of truck = $23,999
Downpayment = 15% of truck price
So, downpayment value = $23,999 × 15/100
= $3699.85
To calculate the average percent, add all probabilities together as numbered values and divide by the sum of all the sets. Then multiply by using a hundred. The percentage may be calculated by dividing the price with the aid of the entire fee, after which multiplying the end result by a hundred. The method used to calculate the percent is: (value/general price)×100%.
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I need help with 4 problems
1)
[tex]c^2=5^2+5^2[/tex]then the solution is
[tex]c=\sqrt[]{25+25}=\sqrt[]{50}=5\sqrt[]{2}\approx7.1[/tex]Select the correct answer from each drop-down menu.Wayne, Winston, and Wilfred walked for an hour. Winston and Wilfred walked the same number of miles. Winston walked 2 miles less than 2 themiles Wayne walked. Wilfred walked 2 miles more than 3 the miles Wayne walked.A variable selected to solve this problem should represent the number of mileswalked in an hour.In that hour, Wayne would have walkedmiles and Winston and Wilfred would have walkedmiles each. So, WaynewalkedWinston and Wilfred.
SOLUTION:
Winston =
[tex]Win\text{ston = }\frac{3}{2}\text{ (Wayne) - 2}[/tex][tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ wayne }+\text{ }\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - 2 = }\frac{1}{3}\text{ wayne }+\frac{3}{2}[/tex][tex]\frac{3}{2}\text{ wayne - }\frac{1}{3}\text{ wayne = }\frac{3}{2}\text{ + 2}[/tex]Upon simplification, the number of miles wayne walked was 3
Substituting wayne = 3 into the second equation
[tex]\text{Wilfred = }\frac{1}{3\text{ }}\text{ (3) }+\text{ }\frac{3}{2}[/tex]Wilfred = 2.5
Since Wilfred and Winston walked the same number of miles,
Winston = 2.5
The first drop menu is Wilfred
The second drop menu is 3
The third drop menu is 2.5
The fourth drop menu is faster than.
sin data cos data tan datacsc date sec data cot data
P (7/25, 24/25)
Sin data= 24/25
Cos data = 7/25
Tan data= (24/25)/(7/25)= 24/7
Csc data= 1/(24/25)= 25/24
Sec data= 1/(7/25)= 25/7
Cotan data= 1/(24/7)= 7/24
Solve the equation without using a calculator
[tex]x^2+\big(4x^3-3x\big)^2=1[/tex]
Answer:
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Step-by-step explanation:
Given equation:
[tex]x^2+(4x^3-3x)^2=1[/tex]
Expand and equal the equation to zero:
[tex]\begin{aligned}x^2+(4x^3-3x)^2&=1\\x^2+(4x^3-3x)(4x^3-3x)&=1\\x^2+16x^6-24x^4+9x^2&=1\\16x^6-24x^4+x^2+9x^2-1&=0\\16x^6-24x^4+10x^2-1&=0\end{aligned}[/tex]
Let u = x²:
[tex]\implies 16u^3-24u^2+10u-1=0[/tex]
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x)
[tex]\textsf{As\;\;$f\left(\dfrac{1}{2}\right)=0$\;\;then\;$\left(u-\dfrac{1}{2}\right)$\;is a factor of $f(u)$}.[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2+bu+2\right)=0[/tex]
Compare the coefficients of u² to find b:
[tex]\implies b-8 = -24[/tex]
[tex]\implies b = -16[/tex]
Therefore:
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(16u^2-16u+2\right)=0[/tex]
Factor out 2:
[tex]\implies 2\left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
[tex]\implies \left(u-\dfrac{1}{2}\right)\left(8u^2-8u+1\right)=0[/tex]
Zero Product Property
If a ⋅ b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for u.
[tex]\implies u-\dfrac{1}{2}=0 \implies u=\dfrac{1}{2}[/tex]
Use the quadratic formula to solve the quadratic:
[tex]\implies u=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(8)(1)}}{2(8)}[/tex]
[tex]\implies u=\dfrac{8 \pm \sqrt{32}}{16}[/tex]
[tex]\implies u=\dfrac{8 \pm 4\sqrt{2}}{16}[/tex]
[tex]\implies u=\dfrac{2 \pm \sqrt{2}}{4}[/tex]
Therefore:
[tex]u=\dfrac{1}{2}, \quad u=\dfrac{2 - \sqrt{2}}{4}, \quad u=\dfrac{2 + \sqrt{2}}{4}[/tex]
Substitute back u = x²:
[tex]x^2=\dfrac{1}{2}, \quad x^2=\dfrac{2 - \sqrt{2}}{4}, \quad x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
Solve each case for x:
[tex]\implies x^2=\dfrac{1}{2}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{1}{2}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 - \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 - \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 - \sqrt{2}}}{2}[/tex]
[tex]\implies x^2=\dfrac{2 + \sqrt{2}}{4}[/tex]
[tex]\implies x=\pm \sqrt{\dfrac{2 + \sqrt{2}}{4}}[/tex]
[tex]\implies x=\pm \dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
Solutions
[tex]x= \dfrac{\sqrt{2}}{2}, \quad x=-\dfrac{\sqrt{2}}{2},\\\\x=\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x=-\dfrac{\sqrt{2 - \sqrt{2}}}{2}, \quad x= \dfrac{\sqrt{2 + \sqrt{2}}}{2}, \quad x= -\dfrac{\sqrt{2 + \sqrt{2}}}{2}[/tex]
blank +0=9 is a associative b. commutativec identity property
It is an identity property
Any number plus zero will give that number
9. For each fraction, decimal, or percent, write the equivalent number from the list below 0.52, 38, 50, 0.35, 40% , 50 UN 76% 0.82 7 20 13 25
We have
In order to convert a fraction to a decimal, we divide the numerator between the denominator.
[tex]\frac{2}{5}=0.4=40\text{\%}[/tex][tex]0.82=\frac{82}{100}=\frac{41}{50}[/tex][tex]\frac{13}{25}=0.52[/tex][tex]76\text{\%}=\frac{76}{100}=\frac{38}{50}[/tex][tex]\frac{7}{20}=0.35[/tex]ANSWER
2/5=40%
0.82=41/50
13/25=0.52
76%=38/50
7/20=0.35
Find the values that form the boundaries of the critical region for a two-tailed test with a = .05 for eachof the following sample sizes:a. n = 4b. n = 15c. n = 24
Given
a). n = 4
b). n = 15
c). n = 24
Find
values that form the boundaries of the critical region for a two-tailed test with a = .05
Explanation
a) n = 4
degree of freedom = n - 1 = 4 - 1 = 3
so , the t value for critical region =
[tex]\begin{gathered} \pm t_{0.05,3} \\ \pm3.182 \end{gathered}[/tex]b) n = 15
degree of freedom = 15 - 1 = 14
so , t- value =
[tex]\begin{gathered} \pm t_{0.05,15} \\ \pm2.131 \end{gathered}[/tex]c) n = 24
degree of freedom = 24 - 1 = 23
so , t - value =
[tex]\begin{gathered} \pm t_{0.05,23} \\ \pm2.069 \end{gathered}[/tex]Final Answer
Hence , the values that form the boundaries of the critical region for a two-tailed test with a = .05 are
a)
[tex]\pm3.182[/tex]b)
[tex]\pm2.131[/tex]c)
[tex]\pm2.069[/tex]how we do this this is hoighs chbool clac 1 i failed it and i have to reatek it
The equation of the curve is given by:
[tex]y=5+\cot(x)-2\csc(x)[/tex]Differentiating both sides of the equation with respect to x, we have:
[tex]\frac{dy}{dx}=2\cot(x)\csc(x)-\csc^2(x)[/tex]Therefore, the slope of the tangent is given by the value of dy/dx when x= π / 2
[tex]2\cot(\frac{\pi}{2})\csc(\frac{\pi}{2})-\csc^2(\frac{\pi}{2})=-1[/tex]Using the point slope formula, it follows that:
[tex]\begin{gathered} y-3=-1(x-\frac{\pi}{2}) \\ y=-x+\frac{\pi}{2}+3 \end{gathered}[/tex]Therefore, the equation of the tangent at P is given by:
y = -x + π /2 + 3
Find the next number in the series
4, 8, 12, 20,-
●
32
34
36
38
-
Answer:
4, 8, 12, 20, 24, 28, 32, 34, 36, 38, 42, 46, 50...
Step-by-step explanation:
If it's counting by four, then the replacing number(s) are 24 and 28.
The next term of the sequence will be 32
What is the formula to calculate the nth term of an Arithmetic Sequence ?
The formula to calculate the nth term of an Arithmetic Sequence is -
a(n) = a + (n - 1)d
[a] - first term of A.P.
[d] - Common difference of A.P.
[n] - position of term
We have the following series -
4, 8, 12, 20 ...
We can write the [n]th term of this series as -
a[n] = a[n - 1] + a[n - 2]
So, for n = 5, we can write -
a[5] = a[4] + a[3] = 20 + 12 = 32
Hence, the next term of the sequence will be 32.
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For the figure below, give the following. (a) one pair of vertical angles (b) one pair of angles that form a linear pair (c) one pair of angles that are congruent 1/2 1 3 4 5 / 6 7 78
Let's remember the following definitions:
1. Vertical angles are those angles that are opposite to each other and share the same vertex. Their measures are equal (They are congruent).
2. A Linear pair of angles are those adjacent angles formed when two lines intersect each other. They are Supplementary, which means that they add up to 180 degrees.
For this case you can see two lines "l" and "m" that are cut by the line "n".
a) Based on the definitions shown above, you can identify this pair of Vertical angles:
[tex]\angle1\text{ and }\angle4[/tex]Because the are opposite and share the same vertex.
b) You can also identify this pair of angles that form a Linear pair:
[tex]\angle2\text{ and }\angle4[/tex]c) Since you know that Vertical angles are congruent, you can determine that this pair of angles are Vertical angles and congruent:
[tex]\angle6\text{ and }\angle7[/tex]Therefore, the answers are:
a)
[tex]\angle1\text{ and }\angle4[/tex]b)
[tex]\angle2\text{ and }\angle4[/tex]c)
[tex]\angle6\text{ and }\angle7[/tex]f(x)= - 9x+2 Find the domain of the function. Type answer in interval notation.
ANSWER:
Domain: (-∞, ∞)
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=-\:9x+2\:[/tex]The domain of a function is the set of all possible input values of the function. In this case, it would be the interval of values that x can take.
In this function, x can take any value in real numbers.
Therefore, in that case, it will be:
[tex]D=(-\infty,\infty)[/tex]Subtract 14 from 11 the difference is
First it is important to remember that, by definition, the result of a subtraction is called "Difference".
In this case you need to subtract 14 from 11. This can operation can be expressed as following:
[tex]11-14[/tex]Notice that , since 14 is greater than 11 and it is also a negative number, the sign of the result (the difference) must be negative too.
Therfefore, keeping the above on mind, you obtain that the difference is the following:
[tex]11-14=-3[/tex]Describe a situation that could be represented by theequation y=x-0.3x.Be sure to explain what x and y mean in your situation,
We are asked to describe a situation that could be represented by the equation
[tex]y=x-0.3x[/tex]Suppose that y is the number of liters of water in a tank.
And x is the number of hours.
Each hour, 30% (0.3) of the water is evaporated from the tank. (subtracted)
So the equation completely models the above scenario.
[tex]y=x-0.3x[/tex]For example:
What will be the amount of water in the tank after 10 hours?
[tex]undefined[/tex]2x - 11 = -3
What does x equal?
Answer :x=4
Step-by-step explanation:
x equals a point. If you are in the same exact area but at a different x, you dont know how to get to the area where x is. It is important to note that x does not equal a point, but a location.
The two lines y y = x and y = x + 1 are parallel lines.
True
False
By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
The equation of a line that passes through the Origin has the following form:
[tex]y=mx[/tex]Where "m" is the slope of the line.
In this case, you have the first line that passes through the Origin:
[tex]y=x[/tex]You can identify that its slope is:
[tex]m_1=1[/tex]You also know the second equation, which is written in Slope-Intercept form:
[tex]y=x+1[/tex]You can identify that:
[tex]\begin{gathered} m_2=1 \\ b=1 \end{gathered}[/tex]By definition, the slopes of parallel lines are equal. Then, since:
[tex]m_1=m_2[/tex]These lines are parallel.
The answer is: True.
solve quadratic formulax^2-4x+3=0
The general formula for a equation of the form:
[tex]ax^2+bx+c=0[/tex]is:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case we notice that a=1, b=-4 and c=3. Plugging this values in the general formula we get:
[tex]\begin{gathered} x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(3)}}{2(1)} \\ =\frac{4\pm\sqrt[]{16-12}}{2} \\ =\frac{4\pm\sqrt[]{4}}{2} \\ =\frac{4\pm2}{2} \end{gathered}[/tex]then:
[tex]x_1=\frac{4+2}{2}=\frac{6}{2}=3[/tex]and
[tex]x_2=\frac{4-2}{2}=\frac{2}{2}=1[/tex]Therefore, x=3 or x=1.
h (t) = 2t - 2 g(t) = 4t + 5 Find (h(g(t))
ANSWER:
[tex]h(g(t))=8t-8[/tex]STEP-BY-STEP EXPLANATION:
We have the following functions:
[tex]\begin{gathered} h(t)=2t-2 \\ g(t)=4t+5 \end{gathered}[/tex]To calculate h (g (t)) we must do the following:
[tex]\begin{gathered} h\mleft(g\mleft(t\mright)\mright)=2\cdot(4t+5)-2 \\ h(g(t))=8t+10-2 \\ h(g(t))=8t-8 \end{gathered}[/tex]Which expression has a quotient of 63? 1) 4650÷752) 2867÷473) 3276÷52
To find the term with quotient in 63 in from the given option divide each quotient with 63. If the quatiend is divisible that term contain the quotient 63.
The quotient in the first option is 4650. Divide the quotient with 63.
[tex]\frac{4650}{63}=72.38[/tex]The final answer contains decimal places. Thus, there first option does not contain 63 as quotient.
The quotient in the second term is 2867. Divide the quotient with 63.
[tex]\frac{2867}{63}=45.190[/tex]The final answer contains decimal places. Thus, there second option does not contain 63 as quotient.
The quotient in the second term is 3276. Divide the quotient with 63.
[tex]\frac{3276}{63}=52[/tex]The final answer does not contain any decimal places. Thus, the third option contains 63 as quotient.
Thus, the correct option is option 3) 3276÷52.
Art club has 12 members. Each member paysmonthly dues of $12.60. On the first day of themonth, 4 members paid their dues. The remainingmembers paid their dues on the second day of themonth. How much money was collected in dues onthe second day of the month?
Given:
Total number of members in a club is 12
Each member pays $12.60 on every month.
[tex]\begin{gathered} \text{Number of members paid the dues on second day=12-4} \\ \text{Number of members paid the dues on second day=}8 \end{gathered}[/tex][tex]\begin{gathered} \text{Money collected on the second day=8}\times12.60 \\ \text{Money collected on the second day= \$100.80} \end{gathered}[/tex]Money collected on the second day of the month is $100.80
Answer:
100.8
Step-by-step explanation:
12-4 = 8
the 4 is the people who payes the first day the 8 is the people who payes the second day
12.60 eight times = 12.60•8= 100.8
the eight people each payes 12.60 so that would be 12.60 8 times
natural number is also a whole number.TrueFalse
Answer
The statement istrue.
Natural numbers are also whole numbers.
Explanation
Natural numbers are counting numbers.
They are the numbers that are numerically used to count things.
Hence, all natural numbers (counting numbers) are whole numbers.
Hope this Helps!!!
Triangle is rotated 180° around the origin. What will be the coordinates for Triangle J'K'L'? A(6,7)(6,2)(3,7)B(7,-6)(2,-7)(-3,-7)C(-6,-7)(-6,-2)(-3,-7)D(-7,6)(2,-6)(-7,3)
Answer:
A. (6,7)(6,2)(3,7)
Explanation:
From the graph, the coordinates of J, K and L are:
[tex]J(-6,-7),K(-6,-2)\text{ and L}(-3,-7)[/tex]When a point (x,y) is rotated 180° around the origin, we have the transformation rule:
[tex](x,y)\to(-x,-y)[/tex]Therefore, the coordinates for Triangle J'K'L' are:
[tex]J^{\prime}(6,7),K^{\prime}(6,2)\text{ and L'}(3,7)[/tex]The correct choice is A.
Rain equation of a hyperbola given the foci and the asymptotes
The equation for a hyperbola that opens up and down has the following general form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]Where the foci of the hyperbola are located at (h,k+c) and (h,k-c) with c given by:
[tex]c^2=a^2+b^2[/tex]And asymptotes with slopes given by a/b and -a/b.
The hyperbola with the equation that we have to find has these two foci:
[tex](3,2-\sqrt{26})\text{ and }(3,2+\sqrt{26})[/tex]This means that:
[tex]\begin{gathered} (h,k-c)=(3,2-\sqrt{26}) \\ (h,k+c)=(3,2+\sqrt{26}) \end{gathered}[/tex]So we get h=3, k=2 and c=√26.
The slope of the asymptotes have to be 5 and -5 which means that:
[tex]\frac{a}{b}=5[/tex]Using the value of c we have:
[tex]c^2=26=a^2+b^2[/tex]So we have two equation for a and b. We can take the first one and multiply b to both sides:
[tex]\begin{gathered} \frac{a}{b}\cdot b=5b \\ a=5b \end{gathered}[/tex]And we use this in the second equation:
[tex]\begin{gathered} 26=(5b)^2+b^2=25b^2+b^2 \\ 26=26b^2 \end{gathered}[/tex]We divide both sides by 26:
[tex]\begin{gathered} \frac{26}{26}=\frac{26b^2}{26} \\ b^2=1 \end{gathered}[/tex]Which implies that b=1. Then a is equal to:
[tex]a=5b=5\cdot1=5[/tex]AnswerNow that we have found a, b, h and k we can write the equation of the hyperbola. Then the answer is:
[tex]\frac{(y-2)^2}{5^2}-\frac{(x-3)^2}{1^2}=1[/tex]Class Work...Exit Ticket... 11.25.2020 Malik picked forty-five oranges in five minutes. At this rate, how many oranges will she pick per minute. Classwork/Participation. 5 points
Malike picked 45 oranges in 5 minutes
Work = Rate x time
If she can pick 45 oranges in 5 minutes
Mathematically
45 oranges ========= 5minutes
x oranges ========== 1 minute
Introduce cross multiplication
45 * 1 = 5 * x
45 = 5x
Divide both sides by 5
45/5 = 5x/5
x = 45 / 5
x = 9 oranges
Malik can pick 9 oranges in 1 minute
The answer is 9 oranges
what is 8 1/2 / 11 as a mixed number or fraction
Answer: 17/22
Step-by-step explanation:
Answer:
Step-by-step explanation:
Answer:
3.68181818182=33409090909150000000000
Showing the work
Rewrite the decimal number as a fraction with 1 in the denominator
3.68181818182=3.681818181821
Multiply to remove 11 decimal places. Here, you multiply top and bottom by 1011 = 100000000000
3.681818181821×100000000000100000000000=368181818182100000000000
Find the Greatest Common Factor (GCF) of 368181818182 and 100000000000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 2,
368181818182÷2100000000000÷2=18409090909150000000000
Simplify the improper fraction,
=33409090909150000000000
In conclusion,
3.68181818182=33409090909150000000000
7. Angela bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Angela spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Angela used to makejam?
Equation of the Line
Let's use the following variables:
x = pounds of sugar
y = pounds of strawberries
Angela spent a total of $19.40 to make strawberry jam, thus:
1.80x + 2.50y = 19.40
The equation of the line represents the relationship between x and y. Any point that solves the problem must lie in the line.
The image shows the graph of a line, but we need to be sure it represents the equation above. A small checkup will be done as follows:
For x = 0, solve for y:
1.80*(0) + 2.50y = 19.40
y = 19.4 / 2.5 = 7.76
This point corresponds to the y-intercept (0, 7.76). It can be correctly found on the graph.
For y = 0, solve for x:
1.80x + 2.50*(0) = 19.40
x = 19.40 / 1.8 = 10.78
This point corresponds to the x-intercept at (10.78, 0). It can also be found on the graph.
Now we are sure the line is the representation of our equation, the only point that lies on that line is B(8, 2).
If we substitute x = 8, y = 2:
1.80*(8) + 2.50*(2) = 19.40
14.4 + 5 = 19.40
19.40 = 19.40
The equation is satisfied, thus, the answer is:
Point B
4^3/(-12+ 2^2)
(2x2)^2 + (-5 x 2 x 3 ) + 2
[tex] \frac{4^3/(-12 +2^2)}{(2x3)^2 +(-5 x2 x 3)+2} [/tex]
i need help!!
Answer:
-1
Step-by-step explanation:
[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]
Answer the questions below.(a) Here are the prices (In thousands) for 10 houses for sale in a local neighborhood:$285, $286, $287, $290, $292, $295, $300, $301, $306, $307.which measure should be used to summarize the data?MeanMedianMode(b) in a survey, a soft drink company asks people to name as many brands of soft drinks as they can.Which measure glves the most frequently mentioned brand?MeanMedianMode(c) In the past 9 days, Kira has received the following numbers of email advertisements per day:40, 41, 43, 45, 48, 49, 50, 52, 85.Which measure should be used to summarize the data?O MeanMedianMode$2
a.
The data set shows the prices for houses.
Looking at the values, they lie near to the same value.
In this case, we can summarize the prices with the mean or median.
b. The survey was made to find how many names of brands of soft drinks they know. In this case, is important to know which soft drinks are the most popular.
Hence, the measure that gives the most frequently mentioned brand is the mode.
c. Kira has received many emails per day.
The emails also lie near to the same value except for the number of 85.
Where 85 represents an outlier (a value in a data set that is very different).
When we have outliers is better to use the median.
what is a like term?
In an expression, two or more terms are like terms if they have the same variable and exponents.
For example the terms:
2a and -8a → these terms have the same variable "a" and the same exponent "1"
9y³ and 8x⁴ → these terms have different variables "y" and "x" and different exponents "3" and "4", so they are not like terms.
Constants, for example, -10 or 6, are also considered to be like terms.
what is the sum of a 7-term geometric series if the first term is -11, the last term is -45056, and the common ratio is -4
Answer:
[tex]-171,875[/tex]Explanation:
Here, we want to find the sum of the geometric series
Mathematically, we have the mathematical formula to calculate this as follows:
[tex]S_n\text{ = }\frac{a(1-r^n)}{1-r}[/tex]where:
a is the first term which is given as -11
n is the number of terms wich is 7
r is the common ratio which is -4
Substituting the values, we have it that:
[tex]\begin{gathered} S_n\text{ = }\frac{-11(1-(-4))\placeholder{⬚}^7}{1+4} \\ \\ S_n\text{ = }\frac{-11(5)\placeholder{⬚}^7}{5}\text{ = -11 }\times\text{ 5}^6\text{ = -171,875} \end{gathered}[/tex]