Which description matches the function represented by the values in this
table?
X х
у
14
1
2
56
224
4
896
5
3584
O A. exponential decay
OB. linear growth
O C. linear decay
D. exponential growth
Answers
The given table represents Exponential growth.
Exponential growth:The process of Quantity rising over time is called exponential growth. An exponential function is used to create an exponential growth curve, which represents a pattern of data that shows a rise over time. Where the Exponential decay helps to understand the rapid decrease in a period of time
Here we have
The table
х 1 2 3 4 5
у 14 56 224 896 3584
From the given table, we can observe that
[tex]\frac{14}{56} = \frac{56}{224} = \frac{896}{3584} = \frac{1}{4}[/tex]
Since the absolute value of the common ratio is less than 1 i.e 1/4
And the values are increasing
Therefore,
The given table represents Exponential growth.
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Related Questions
We are given a jar full of thousands of red and blue marbles. We want to estimate the unknown proportion pof red marbles in the jar. To do this, we randomly draw 100 marbles and count reds: it so happens we drew 45 reds. Enter values in decimal form, rounded to four decimal places (or more).
We estimate the proportion of reds in the jar to be
Attach a give-or-take value to this estimate. (That is, estimate the standard error.)
For a 96% confidence interval, about how many standard errors should be added to and subtracted from the estimate?
Set up an approximate 96% confidence interval for the unknown proportion of reds in the jar.
Answers
Answer:
(0.3478, 0.5522)
Step-by-step explanation:
Given:
Total number of red marbles, x = 45
Total number of marbles, n = 100
Phat = x / n = 45 / 100 = 0.45
The confidence interval, C.I is given by :
Phat ± Zcritical * standard error
Phat ± Zcritical * √Phat(1 - Phat) / n
Zcritical at 96% = 2.0537
The standard error = √Phat(1 - Phat) / n
S.E = √(0.45 * 0.55) / 100 = 0.0497493
C.I = 0.45 ± (2.0537 * 0.0497493)
C.I = 0.45 ± 0.10217013741
C. I = (0.3478, 0.5522)
Solve.
x² + 5x – 2=0
Answers
Answer:
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
2
+
5
−
2
=
0
x^{2}+5x-2=0
x2+5x−2=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
−
2
c={\color{#129eaf}{-2}}
c=−2
=
−
5
±
5
2
−
4
⋅
1
(
−
2
)
√
2
⋅
1
Step-by-step explanation:
this should help
by finding A B and c
of the quadratic then applying the quadratic formula.
I hope this helps !!
Use AABC to find the value of sin B.
Answers
Answer:
35/37
Step-by-step explanation:
sin(B)=(AC)/(AB) = 35/37
What is the sine ratio for
Answers
Answer:
the since ratio is 5/4
Step-by-step explanation:
hope this is helpful ask manyRemember, sine is simply opposite/hypotenuse; use the mnemonic SOH-CAH-TOA when needing to calculate each trigonometric function.
Since we’re looking at
Thus, 6/10 can be reduced to 3/5.
Let me know if you need further explanation — good luck.
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
Answers
9514 1404 393
Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
In a die game, you roll a standard 6-sided die twice. If the second number rolled is the same as the first number rolled, you win $25. Otherwise, you lose $2. If you were to play the game 100 times, how much money can you expect to make
Answers
Answer:
You can expect to make $250.
Step-by-step explanation:
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Probability of the second number rolled being the same as the first number rolled:
6 outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)
Out of 36, thus:
[tex]p = \frac{6}{36} = \frac{1}{6}[/tex]
Expected value of 1 game:
1/6 probability of earning $25.
5/6 probability of losing $2.
Thus:
[tex]E = 25\frac{1}{6} - 2\frac{5}{6} = \frac{25 - 10}{6} = 2.5[/tex]
100 games:
100*2.5 = 250
You can expect to make $250.
Find the domain of the function.
f (x) =2/5x+4
Answers
Answer:
(-∞,∞)
Step-by-step explanation:
Answer:
The domain of the function is (-∞, ∞)
hope this helps!
Find the value of x.
x
9
9
7
x = [?]
Answers
Answer:
14
Step-by-step explanation:
evaluate (5^0-4^-1)×3/4
Answers
Answer:
[tex](5^{0} -4^{-1} )(\frac{3}{4} )\\\\=(1-\frac{1}{4^{1}} )(\frac{3}{4} )\\\\=(\frac{4}{4} -\frac{1}{4} )(\frac{3}{4} )\\\\=(\frac{3}{4} )(\frac{3}{4} )\\\\=\frac{9}{16}[/tex]
A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. Make a 3 x 3 matrix showing the wire requirements. Assign the cable types to the rows and the wire types to the columns.
A) [2 1 2 1 2 1 2 1 3].
B) [3 3 2 1 2 1 2 1 1].
C) [3 1 2 3 2 1 2 1 2].
D) [2 1 3 1 2 1 2 1 2].
Answers
Answer:
The answer is (B) but with 2 as the last item in the matrix, instead of 1.
Step-by-step explanation:
The grand topic is MATRICES.
In Matrices, there are rules to follow when creating a matrix - which is a 'row by column' arrangement of objects or figures.
Rule 1: Identify your rows and columns.
What is a row? A row is a 'left to right' arrangement of items; also called a horizontal arrangement of items. What is a column? A column is an 'up to down' arrangement of items; also called a vertical arrangement of items.
Rule 2: Start your arrangement by rows.
Before reaching the instruction in the question, I already arranged the data for cables on the rows and the data for wire colors on the columns. You should follow this rule always; from the first information given in the question.
Rule 3: Nomenclature
This is the naming of a given matrix. In naming a matrix, consider the rows first before the columns. For example, a matrix with three rows and four columns with be called a 3 by 4 matrix and not a 4 by 3 matrix. In the case of this question, there is an equal number of rows and columns, so even if you counted the columns first, it wouldn't be noticed. Nevertheless, always count the rows first.
Having arranged the figures in a 3 by 3 matrix,
The full data on Cable A appears on the first row. The full data on Cable B appears on the second row. The full data on Cable C appears on the third row.
The full data on Black wires appears on the first column. The full data on White wires appears on the second column. The full data on Red wires appears on the third column.
So the answer is [tex]\left[\begin{array}{ccc}3&3&2\\1&2&1\\2&1&2\end{array}\right][/tex]
Kudos!
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches, what is the volume of air inside the cube? (Round to the nearest tenth.)
1357.1 cubic inches
1244.1 cubic inches
1887.4 cubic inches
1226.0 cubic inches
Answers
The volume of air inside the cube is 1887.4 cubic inches. Then the correct option is C.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A ball inside of a cube has a volume of 113 cubic inches. If each side of the cube measures 12.6 inches.
Then the volume of air inside the cube will be given as the difference between the volume of the cube and the sphere.
Air volume = Volume of the cube - Volume of the sphere
Air volume = 12.6³ - 113
Air volume = 2000.376 - 113
Air volume = 1887.376
Air volume ≅ 1,887.4
More about the geometry link is given below.
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Answer:
1887.4 cubic inches
Step-by-step explanation:
1. A helicopter is at a position from two VORS (VHF Omnidirectional
Radio Range, an aircraft navigation system operating in the VHF band -
not covered in chapter) as in the diagram shown below. Given the angles
shown, find the third angle.
Helicopter
74.0°
66.0°
VOR
VOR
Answers
The position of the helicopter and the two VORs forms a triangle and the third angle formed by these three entities is 40 degrees
The diagram is not shown; however, the question can still be answered.
The given angles are:
[tex]\theta_1 = 74.0^o[/tex]
[tex]\theta_2 = 66.0^o[/tex]
Represent the third angle as [tex]\theta_3[/tex]
The helicopter and the 2 VORs form a triangle.
So, we make use of the following theorem to calculate the third angle
[tex]\theta_1 + \theta_2 + \theta_3= 180^o[/tex] ---- sum of angles in a triangle
Substitute known values
[tex]74.0^o + 66.0^o + \theta_3= 180^o[/tex]
[tex]140.0^o + \theta_3= 180^o[/tex]
Collect like terms
[tex]\theta_3= 180 -140.0^o[/tex]
[tex]\theta_3= 40^o[/tex]
Hence, the third angle is 40 degrees.
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Rose walks 2 2/3 km in three-fifths of an hour. If her speed remains unchanged, how many kilometres can she walk in one and three quarters of an hour? Express your answer as a mixed number in lowest terms
Answers
Answer:
Distance = 7 7/9 Km
Step-by-step explanation:
Given the following data;
Distance = 2⅔ = 8/3 Km
Time = ⅗ hour
First of all, we would find her speed;
Speed = distance/time
Speed = (8/3)/(3/5)
Speed = 8/3 * 5/3
Speed = 40/9 km/h
Next, we would find the distance covered when time = 1¾ hours
Distance = speed * time
Distance = 40/9 * 1¾
Distance = 40/9 * 7/4
Distance = 10/9 * 7
Distance = 70/9
Distance = 7 7/9 Km
Please help!! The question is the image below VVV
Answers are also images after the picture.
Answers
Step-by-step explanation:
When adding two fractions with different bases (bottom numbers), we can use this function:
[tex]\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}[/tex]
So, to apply this to the given question:
[tex]\frac{x+3}{x-6} +\frac{1}{x-2}[/tex]
= [tex]\frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}[/tex]
From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.
Multiply top using: (a + b)(c + d) = ac + ad + bc + bd= [tex]\frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}[/tex]
Simplify.= [tex]\frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}[/tex]
Remove parentheses.= [tex]\frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}[/tex]
Simplify again.= [tex]\frac{x^2 +2x-12}{(x-6)(x-2)}[/tex]
Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.
Factor.= [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
Answer:
A) [tex]\frac{x(x+2)}{(x-6)(x-2)}[/tex]
I will give you brainliest if you answer this correctly
Answers
Answer:
Mark Brainliest please
The answer is 1
Step-by-step explanation:
(1 — x^ m-n) ^-1 + (1- x ^n-m)^ -1
1/[1-x^(m-n)] + 1/[1-x^(n-m)]
1/[1-x^m × x^(-n)] + 1/[1-x^n × x^(-m)]
x^n/(x^n - x^m) + x^m/(x^m - x^n)
x^n/(x^n - x^m) - x^m/(x^n - x^m)
Now taking the LCM here, we get
(x^n - x^m)/(x^n - x^m)
need some help with this :)
Answers
===========================================================
Explanation:
All direct variation equations are of the form y = kx, for some constant k.
We know that y = -8 and x = 4 pair up together. Let's use these two values to find k
y = kx
-8 = k*4
-8/4 = k
-2 = k
k = -2
Therefore, we go from y = kx to y = -2x
We can then find y when x = -4
y = -2x
y = -2*(-4)
y = 8
Answer:
y∝x
y=kx
k=y/x
by putting values
k=-8/4
k= -2
now ,if x= -4
as, y=kx
hence, y= (-2)(-4)
y=8
Step-by-step explanation:
The profits for video game companies depend on what game platform the game runs on, which can either be a portible system with a built in screen, or a standard system that you have to hook up to a television. The profit off of a portible game system is $72, while the profit from a standard game system is $90. The store manager has to make at least $360 per day in order to keep the store open. Which graph represents this inequality? Write the inequality that represents the number of games that must be sold everyday to meet or beat the sales goal.
Answers
Step-by-step explanation:
what is the prime product of 120
Answers
Answer:
[tex]2^{3} * 3 * 5[/tex]
Step-by-step explanation:
Determine if the graph of y=x/x^2-4 is symmetrical with respect to the x-axis, the y-axis, or the origin.
a. about the x-axis
b. about the y-axis
c. about the origin
d. all of these
e. none of these
please help i’ll also rate brainliest
Answers
9514 1404 393
Answer:
c. about the origin
Step-by-step explanation:
The function is odd: replacing x with -x gives the negative of the function value:
f(-x) = -f(x)
Odd functions are symmetrical about the origin.
Find the missing side of the right triangle.
Answers
Answer:
√202
Step-by-step explanation:
since it's the hypotenuse you are required to find
x²=11²+9²
x²=121+81
√x²=√202
x=√202
I hope this helps
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answers
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
Answers
9514 1404 393
Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
A popular brand of pen is available in 13 colors and 2 writing tips. How many different choices of pens do you have with this brand?
There are ___ different choices of pens with this brand.
Answers
Answer:
7
Step-by-step explanation:
i had it
A campus deli serves 101 customers over its busy lunch period from 11:30 am to 1:30 pm. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 18 customers are in process at any point in time. What is the average amount of time (in minute) that a customer spends in process?
Answers
Answer:
21.38 minutes
Step-by-step explanation:
the total number served = 101
teh number of hours that is spent in serving from 11.30 to 1.30 = 2 hours
Lq = average number of those that are in line = 18 customers
from here we are to find the flow rate
= [tex]\frac{total served}{service hour}[/tex]
= 101/2 = 50.5
the average time in waiting =
Lq/flow rate
= 18/50.5
= 0.3564 hours
convert to minutes = 0.3564 * 60 minutes
= 21.38 minutes
After analyzing a data set using the one-way ANOVA model, the same data are analyzed using the randomized block design ANOVA model. SS (Treatment) in the one-way ANOVA model is ________ the SS (Treatment) in the randomized block design ANOVA model.
a. Always equal to.
b. Always greater than.
c. Always less than.
d. Sometimes greater than.
Answers
Answer: Always equal to
Step-by-step explanation:
A one way analysis of variance refers to the technique that is used in knowing if there's significant difference between two samples means.
Based on the options given, it should be noted that SS (Treatment) in the one-way ANOVA model is always equal to the SS (Treatment) in the randomized block design ANOVA model.
This is Some next level Geometry
Answers
Step-by-step explanation:
Measure of Angle 1 is 115 due to corresponding angles postulate
Measure of Angle 2 is 65 is linear pair postulate.
A research center poll showed that 76% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
Answers
Answer:
6/25
Step-by-step explanation:
P(have belief) =76/100 = 19/25
P (does not have belief) = 1-19/25 = 6/25
What are 3 ratios that are equivalent to 8 :5
Answers
Answer:
Step-by-step explanation:
8/5 = 16/10 = 24/15
8:5 = 16:10 = 24:15
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Answers
Answer:
The right answer is:
(a) 0.1456
(b) 18.125, 69.1202, 8.3139
Step-by-step explanation:
Given:
N = 24
n = 5
r = 7
The improperly drilled gearboxes "X".
then,
⇒ [tex]P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}[/tex]
(a)
P (all gearboxes fit properly) = [tex]P(x=0)[/tex]
= [tex]\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}[/tex]
= [tex]0.1456[/tex]
(b)
According to the question,
[tex]X = 91+5[/tex]
Mean will be:
⇒ [tex]\mu = E(x)[/tex]
[tex]=E(91+5)[/tex]
[tex]=9E(1)+5[/tex]
[tex]=9.\frac{nr}{N}+5[/tex]
[tex]=9.\frac{5.7}{24} +5[/tex]
[tex]=18.125[/tex]
Variance will be:
⇒ [tex]\sigma^2=Var(X)[/tex]
[tex]=V(9Y+5)[/tex]
[tex]=81.V(Y)[/tex]
[tex]=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}[/tex]
[tex]=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}[/tex]
[tex]=69.1202[/tex]
Standard deviation will be:
⇒ [tex]\sigma = \sqrt{69.1202}[/tex]
[tex]=8.3139[/tex]
find r and s on the triangle
Answers
Answer:
r=24
s=21
Step-by-step explanation:
I use proportion of 2 to 3
I multiply 16 and 3/2 to get r
r=24
I multiply 14 and 3/2 to get s
s=21
