The number of people contacted at each level of a phone tree can be represented by f(x) = 3x, where x represents the level.
What is x when f(x) = 27?
Answers
Answer:
Option B is correct
x= 3, At level 3, 27 number of people contacted
Step-by-step explanation:
As per the given statement:
The number of people contacted at each level of a phone tree can be represented by:
[tex]f(x) = 3^x[/tex]
where, x represents the level.
We have to find the value of x when f(x) = 27.
⇒27 = 3^x
We can write 27 as:
[tex]27 = 3 \times 3 \times 3 = 3^3[/tex]
then;
[tex]3^3 = 3^x[/tex]
on comparing we have;
3 = x
or
x = 3
Therefore, the value of x is, 3.
Related Questions
Draw or write to show that the number 18 is an even number
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The number 18 is considered an even number because it can be divided by 2 to result in another integer. This is confirmed by writing 18 as 2 times 9, which results in an even product.
Explanation:In mathematics, an even number is any integer that can be exactly divided by 2 without leaving a remainder. For example, the numbers 2, 4, 6, 8, and 10 are even because each can be divided by 2 to result in another integer. If you divide an even number by 2, the result is always a whole number, and that's not the case with odd numbers. Let us examine the number 18.
If we write 18 as 2 times 9, we see that it has been turned into a product of 2 and another integer (9, in this case). This indicates that 18 is indeed an even number. Therefore, we can be sure of the fact that the number 18 is an even number, because it can be divided by 2 without leaving a remainder.
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Last week, Donnell practiced the piano 3 hours longer than Marcus. Together, Marcus and Donnelly practiced the piano for 11 hours. For how many hours did each young man practice the piano?
Answers
Explain why the point (-3,2) is diffrent from the point (2,-3)?
Answers
Find the average.
11,16,15,22
A.64
B.15
C.17
D.16
Answers
So:
11 + 16 + 15 + 22 = 64
64 / 4 = 16
Your answer is D. 16. Hope this helps!
What is the angle above the x axis (i.e., "north of east") for a vector with components (15 m, 8 m)?
Answers
The dotted line represents the x-axis;
Θ represents the desired angle;
Using trigonometry, we can create and solve an equation to get the angle (Θ);
In this case, you can use use sin or cos, I'll go with sin:
SinΘ = opp/hyp
SinΘ = 8/15
Θ = Sin⁻¹(8/15)
= 32.23.... ⇒ 32.2°
Answer:28.071
Step-by-step explanation:
Given
vector component is (15,8)
i.e. its x component is 15 from origin and y component is 8 m
So angle made by vector with x axis is
[tex]tan\theta =\frac{8}{15}[/tex]
[tex] \theta =tan^{-1}\frac{8}{15} [/tex]
Use the empirical rule to calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all possible bank customer waiting times. (round your answers to 3 decimal places. negative amounts should be indicated by a minus sign.)
Answers
You have $27 to spend at the mall and a coupon for $6 off at your favourite store. A t-shirt costs $11 how many tshirts can you buy using your coupon and money
Answers
which is 2 shirts that cost $ 22.
You will have $5 Leftover.
Since you have a $6 dollar off coupon, you could buy one more t-shirt with
$ 5 (11 - 6 = 5)
So, the amount of t-shirt you could buy WITH coupon is 3 T-shirts.
Simplify each expression. use positive exponents. 1. m^3n^–6p^0
Answers
Which of the following fractions is closest to the decimal 0.35
Answers
1/3
3/5
3/8
5/1/2
You just have to make the division and compare the results>
1 / 3 = 0.333..
3 / 5 = 0.6
3 / 8 = 0.375
5 / 12 = 0.416.....
So which is closest to 0.35? The answer is 1/3
maggie’s brother is 6 years younger than four times her acne. the sum of their ages is 34. how old is maggie
Answers
b = 4m - 6
m + 4m - 6 = 34
5m - 6 = 34
5m = 34 + 6
5m = 40
m = 40/5
m = 8 <=== Maggie's age
b = 4m - 6
b = 4(8) - 6
b = 32 - 6
b = 26 .....brothers age
Should the quotient of an integer divided by a nonzero integer always be a rational number? Why or Why not?
Answers
a certain brand of vitamin C contains 300 mg per tablet. A bottle contains 150 vitamins. How many total grams of vitamin C are in the bottle?
Answers
150 tabletsx(300mg/1 tablet)=150x300=45000 mg=45 grams
Which percent is represented by the diagram below?
1.25%
12.5%
125%
1250%
Answers
10+2.5=12.5
So your answer is B 12.5.
25 out of 100 in the other box.....thats 25%
so u have 125% that is shaded
at a wedding dance couples have new partners nine times during a five minute song how long does one couple dance together
one couple dances toghether for _ of a minute
Answers
Final answer:
To determine how long one couple dances together, divide the total song duration by the number of times partners change plus one. With nine partner changes during a five-minute long song, each couple dances together for 0.5 minutes.
Explanation:
The question involves calculating the amount of time one couple dances together during a wedding dance if couples change partners nine times during a five-minute song. To find the answer, we need to divide the total time of the song by the number of times the partners change.
First, we find out how many times the couples will dance together. If they switch partners nine times, there will be ten different dancing intervals. Next, we divide the total length of the song by the number of intervals:
5 minutes ÷ 10 intervals = 0.5 minutes per interval.
Therefore, one couple dances together for 0.5 of a minute.
Find all the square number that are greater then 20 but less then 50
Answers
6^2 = 36
7^2 = 49
8^2 = 64
So the answer is 5,6,7
Hope this helped!
What is 60000 x 1000?
Answers
The solution is, the value is 60000 x 1000 =60000000.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
60000 x 1000
i.e. we have to multiply 60000 with 1000
so, we get,
60000 x 1000
=60000000
Hence, The solution is, the value is 60000 x 1000 =60000000.
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if x equals 3= xequals 4 then use the equation 2x y -6 x equals 18 Z to find the value of y
Answers
"If x equals 3 and z equals 4, find the value of y in the equation: [tex]12xy-6x=18z.[/tex]"
Input the value of the variables we were given:
[tex]12(3)y-6(3)=18(4)[/tex]
Simplify.
[tex]36y-18=72[/tex]
Add 18 to both sides.
[tex](36y-18)+18=(72)+18[/tex]
Simplify.
[tex]36y=90[/tex]
Divide both sides by 36.
[tex](36y)/36=(90)/36[/tex]
Simplify.
[tex]y=5/2[/tex]
[tex]y=2.5[/tex]
The variable, y is equal to 2.5.
Hope this helps.
-Benjamin
of the 30 girls who tried out for the lacrosse team at euclid Middle School, 12 were selected. Of the 40 boys who tried out but, 16 were selected. Are the ratios of the numbers of students on the team to the number of students trying out the same for both boys and girls? How do you know?
Answers
16/40 = 2/5
yes the ratio is the same, because they both simplify to 2/5
hope this helps
Noel Devine bought a new dishwasher for $320. He paid 20 down and made 10 monthly payments of $34 what actual yearly interest rate did Noel pay?
Answers
Interest= Principal x Rate x Time or I= PRT
Substitute values: I= [$20 + ($10 x $34)] -320 =$40
P= $320
R=?
T=10 months/year
I=PRT
Since R is a missing term, we will solve for R using this formula: R=I/PT
R= [$20 + ($10 x $34)-320] / ($320 x 10 months)
T=10 months÷12 months=0.83
R= ($40)/ $320 X 0.83
R= 40/ 265.6
R=15.06024096
Amount financed
320-20=300
Total payments
34×10=340
Total interest=total payments-amount financed
Total interest=340-300=40
Now to find the yearly interest rate use the formula of
I=(2yc)÷(m×(n+1))
I ?
Y number of months in a year 12
C total interest 40
M amount financed 300
N number of payments 10
I=(2×12×40)÷(300×(10+1))
I=0.2909×100=29.09%
Hope it helps!
Which of these indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency?
a.
The bank lists the initials “NA” after its name.
b.
The bank has the word “Federal” in its name.
c.
The bank is qualified to give loans.
d.
The bank is owned by the government.
Answers
Which of these indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency?
a. The bank lists the initials “NA” after its name.
The full form of N.A is N stands for national and A stands for Association. This inclusion of initials helps the banks to be distinguished as national and legal.
The bank is qualified to give loans indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency.Option a is correct.
What is the role of the Currency Comptroller?All federal savings organizations, national banks, and federal branches and agencies of foreign banks are chartered, governed, and overseen by the Office of the Comptroller of the Currency (OCC).
The OCC is a stand-alone division of the U.S. Department of the Treasury, and the Comptroller of the Currency is in charge of it.
The OCC makes ensuring that national banks and federal savings organizations run securely, fairly access financial services, treat customers fairly, and adhere to all relevant laws and regulations.
Thus, the bank is qualified to give loans indicates that a bank is likely to be answerable to the Office of the Comptroller of the Currency.Option a is correct.
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Solve the equation:
(x^4 - x + y)dx - xdy=0
Answers
[tex]\bf (x^4-x+y)dx-xdy=0\implies \stackrel{\textit{distributing dx}}{x^4dx-xdx+ydx}-xdy=0 \\\\\\ ydx=xdy-x^4dx+xdx\implies y=\cfrac{xdy-x^4dx+xdx}{dx} \\\\\\ y=\stackrel{\textit{distributing the denominator}}{x\cfrac{dy}{dx}-x^4+x}[/tex]
From a rectangular piece of cardboard having dimensions a × b, where a = 20 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box as a function of x.
Answers
The volume of the box as a function of x will be 1400x - 180x² - 4x³.
First and foremost, you should note that the volume of a rectangular prism is given as:
= Length × Width × Height
where,
Length = 70 - 2x
Width = 20 - 2x
Height = x
Volume = Length × Width × Height
Volume = (x)(20 - 2x)(70 - 2x)
Volume = 1400x - 40x² - 140x² + 4x³
Volume = 1400x - 180x² - 4x³
Therefore, the volume of the box as a function of x will be 1400x - 180x² - 4x³.
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A school PTA wants to rent a dunking tank for its annual fundraising carnival. The cost is $80 for the first three hours and then $19.75 for each additional hour or part thereof. How long can the tank be rented if up to $200 is budgeted for this expense?
Answers
The tank can be rented for maximum of 6 hours.
We have school PTA wants to rent a dunking tank for its annual fundraising carnival. The cost is $80 for the first three hours and then $19.75 for each additional hour or part thereof.
We have to determine how long can the tank be rented if up to $200 is budgeted for this expense.
The critical level for the number of bacteria spread is 1000. Starting from 500, if the bacteria count rises by 5 every second, then determine whether after 30 seconds the critical level is passed or not?Initial count = 500
Count increasing per second = 5
Critical level = 1000
Assume that the bacteria count after t seconds is y. Then -
y = 500 + 5t
for t = 30 ↔ y = 150 + 500 = 650 < 1000 → Critical level not passed.
According to question, we have -
Cost for first three hours = $80
Cost for additional hour = $19.75
Total Budget = $200
Assume that the tank can be bought for 'n' hours. Then -
80 + 19.75n ≤ 200
Solving the inequality -
19.75n + 80 - 80 ≤ 200 - 80
19.75n ≤ 120
n ≤ 6.07
or
n ≤ 6
Hence, the tank can be rented for maximum of 6 hours.
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Write the equation of the sphere in standard form. 2x2 + 2y2 + 2z2 = 12x − 24z + 1
Answers
[tex](x-a)^2 + (x-b)^2 + (x-c)^2 = r^2[/tex]
Now, the given equation is :
[tex]2x^2 + 2y^2 + 2z^2 = 12x - 24z + 1 \\ 2x^2 + 2y^2 + 2z^2 - 12x + 24z - 1 = 0 \\[/tex]
combine the x, y and z terms and complete the square for each variable
[tex](2x^2 - 12x) + 2y^2 + (2z^2 + 16z) = 1 \\ (x^2 - 6x) + y^2 + (z^2 + 8z) = 1/2 [/tex]
complete square for x by adding 9 to both sides
we do not complete square for y because there is not a translation on that axis
complete square for z by add 16 to both sides
[tex] (x^2 - 6x + 9) + y^2 + (z^2 - 8x + 16) = 1/2 + 9 + 16 \\ (x - 3)^2 + y^2 + (z - 4)^2 = 25 1/2[/tex]
[tex] (x-a)^{2}+ (y-b)^{2}+ (z-c)^{2}=r^{2}[/tex]
We have the equation:
[tex]2x^2+2y^2+2z^2=12x-24z+1[/tex]
which can be regrouped to fit the standard form, using completing the square as follows:
first divide both sides by 2
[tex]x^2+y^2+z^2=6x-12z+ \frac{1}{2} \\\\(x^2-6x)+y^2+(z^2+12z)= \frac{1}{2}\\\\(x^2-2\cdot3\cdot x)+y^2+(z^2+2 \cdot6 \cdot z)= \frac{1}{2}\\\\(x^2-2\cdot3\cdot x+3^2)-3^2+y^2+(z^2+2 \cdot6 \cdot z+6^2)-6^2= \frac{1}{2}\\\\(x-3)^2+y^2+(x+6)^2=9+36+0.5\\\\(x-3)^2+y^2+(x+6)^2=45.5\\\\\(x-3)^2+y^2+(x+6)^2=( \sqrt{45.5} )^2[/tex]
Answer: [tex](x-3)^2+y^2+(x+6)^2=( \sqrt{45.5} )^2[/tex]
What power can you write to represent the volume of a cube shown? write the power as an expression with a base and an exponent and ,then find the volume of the cube.
Answers
A recipe calls for 400 grams of flour. if leena makes one quarter of the recipe, how many kilograms of flour will she need?
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60,488 rounded to the nearest 10,000
Answers
With the 488 it would be rounded for the nearest hundredth to 500 then if you had to round it to the nearest 1,000 from 60,500 it would be 61,000
So even with 61,000 rounded to the nearest 10,000 it would still be 60,000 in order to get 70,000 it would need to be 65,000 and anything above to be rounded to the 70,000 mark.
Joelle is working on a school report in a word processor. She wants to place a figure which is 13.09 cm wide so that it appears centered on the page. The width of the page is 21.59 cm.
How much margin should she leave on the left so that the figure is centered?
Do I divide the width by 13.09 to get the answer? Not very sure
Answers
Answer:
The answer is 4.25 cm.
Step-by-step explanation:
Given is - Joelle wants to place a figure which is 13.09 cm wide so that it appears centered on the page. The width of the page is 21.59 cm.
To solve, this first we will 13.09 from the 21.59, and then divide that number in half to find the left and right margin.
[tex]21.59-13.09=8.5[/tex]
[tex]\frac{8.5}{2}= 4.25[/tex]
Therefore, the answer is 4.25 cm.
What is the quadratic function
Answers
The volume of a triangular prism is increased by a factor of 8.
By what factor is the surface area of the figure increased?
Answers
we know that
[tex]larger\ volume=original\ volume*(scale\ factor)^{3}[/tex]
and
[tex]larger\ surface\ area=original\ surface\ area*(scale\ factor)^{2}[/tex]
so
Find the scale factor
we know that
[tex](scale\ factor)^{3}=8 \\ scale\ factor=\sqrt[3]{8}=2[/tex]
Find the factor of the surface area increased
[tex](scale\ factor)^{2}=2^{2} =4[/tex]
therefore
the answer is
the surface area increased by a factor of [tex]4[/tex]
The need to cut the plastic by finding the measures of the angles (scale factor) is 4.
We have given,
Marcel is designing a circular necklace that will consist of 4 sections, each with a different color of plastic.
We know that
What is the formula of larger volume?larger volume=original volume×(scaler factor )^3
larger surface area =original surface area× (scaler factor)^2
To find the scale factor
we know that
(scalar factor)^3=8
Taking cube root on both sides
scale factor=2
Find the factor of the surface area increased
(scale factor)^2=2^2=4
Therefore, The surface area increased by a factor of 4.
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