Graph the data set.
{(-1, 0.5), (0, 1), (1, 2), (3, 8), 5, 32)}
Which kind of model best describes the data?
a. quadratic
b. exponential
c. linear
d. cubic
Answers
Answer:
b. Exponential
Step-by-step explanation:
We are given the coordinates as the data set:
[tex]\bold{\{(-1, 0.5), (0, 1), (1, 2), (3, 8), (5, 32)\}}[/tex]
First of all, let us plot the given coordinates on the xy coordinate axis.
Let us have a look at the values of x and y first.
A pair is represented as (x, y) i.e. first value is of 'x' and the second value is of 'y'.
[tex]\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 0.5 \\ 1 & 2 \\ 2 & 4 \\ 3 & 8 \\ 5 & 32\end{tabular}\end{center}[/tex]
If we plot them on the graph, we get the graph as the image attached in the answer area.
Let us join the coordinates using a curve.
If we closely look at the graph, there is a sudden increase with increasing value of 'x'.
Actually the increase is exponential.
Observing the given coordinates, we can see that they are in the form:
[tex](x, 2^x)[/tex]
i.e. [tex]y =2^x[/tex]
So, the exponential model best describes the data.
Correct answer is:
b. exponential
Related Questions
In a different plan for area codes the first digit could be any number from 3 through 6 the second digit was either 5,6,7 or 8 and the third digit could be any number except 5. With this plan how many different area codes are possible?
Answers
Answer:
144 codes are possible
Step-by-step explanation:
Okay for the first digit, we shall be selecting one out of 3,4,5,6.
Meaning we are selecting one out of four choices
The number of ways this can be done is 4C1 ways = 4 ways
For the second digit, we have 5,6,7 or 8, we are still selecting 1 out of 4 selections and the number of ways we can do this is also 4 ways
And lastly , we can choose any digit for the last number expect 5 , so from 0 to 9, we are removing 1 which means we are left with 9 choices
So the number of different area codes possible are ; 9 * 4 * 4 = 144 codes
Identify the point corresponding to Q.
A (-3,-2)
B (1,-1)
C (-3,2)
D (-2,-1)
Answers
Answer:
C (-3,2)
Step-by-step explanation:
Well point Q on the parabola is located on point (1,2),
The corresponding point means the point located all the way to the left of Q which is (-3,2).
Thus,
the point that is corresponding to point Q is C. (-3,2).
Hope this helps :)
what fractons time another equal a whole number
Answers
here is an example of a fraction that equals a whole number
2/2 would equal a whole number. The bottom number is 2. This means the whole is cut into two equal pieces (halves).
The top number is 2, so we are counting two-halves.
After shading two-halves, you see that the whole circle is shaded. Two-halves is equivalent to 1.
You would plot 2/2 at the same location as the whole number 1.
For which value of 0 is cot (0) undefined?
90°
180°
270°
450°
Answers
Answer:
The value of cot theta is undefined for all the options
Step-by-step explanation:
I think the best way to go about this is by the use of a calculator.
All that needs to be done is to input the individual values to see where we have an answer that is out of it.
Now, moving away from the calculators, we know quite well that cot is a derivative of tan.
By knowing the values at which we have tan as undefined, we can appropriately see values where cot too would be undefined.
On a normal scientific calculator, there is no cot functionality.
The way around this is to express
Cot theta as 1/tan theta
Thus cot 90 = 1/cot(90) = calculation error
Cot 180 = 1/tan (180) = calculation error
Cot 270 = 1/tan 270 = calculation error
Cot 450 = 1/tan (450) = calculation error
This shows that the value of cot is undefined for all of these options
Answer:
180
Step-by-step explanation:
which of the graphs best represents f(x)= -2 cos 4x-1?
Answers
Answer:
see file attached
Step-by-step explanation:
The graph of g(x) is a transformation of the graph of f(x)=4x.
Answers
42
Step-by-step explan
Find the 9th term geometric sequence 1,1/2,1/2^2w. Please show the steps.
Answers
Answer:
9th term geometric sequence (a9) = 1 / 256
Step-by-step explanation:
Given:
Geometric sequence 1,1/2,1/2²
First term (a) = 1
Common ratio (r) = A2 / A1 = (1/2) / 1 = 1/2
Number of term (n) = 9
Find:
9th term geometric sequence (a9)
Computation:
[tex]an = ar^{n-1}[/tex]
a9 = ar⁹⁻¹
a9 = (1)(1/2)⁸
a9 = (1/2)⁸
a9 = 1/256
9th term geometric sequence (a9) = 1 / 256
You’re working in a pharmacy, and are making a table to help with dosage amounts for a certain drug. The recommended dosage is 40 milligrams per 2.2 pounds of body weight, divided into three daily doses and taken every 8 hours. You want entries for children weighing 10 pounds, 15 pounds and 30 pounds. The drug comes in a 200 mg5 ml formula. If 1 teaspoon = 5 ml, how many teaspoons are required for each entry? Round your answer to the nearest 14 teaspoon.
Answers
Answer: The children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively.
Step-by-step explanation:
Given, The recommended dosage is 40 milligrams per 2.2 pounds of body weight, divided into three daily doses and taken every 8 hours.
i.e. for 1 pound of body weight required dosage per day= [tex]\dfrac{40}{2.2}=18.18\ ml[/tex]
Each dose consist = [tex]\dfrac{18.18}{3}=6.06\ ml[/tex] drug.
so, 1 pound of body weight required 6.06 ml for each dose.
Then, 10 pounds of body weight require 10 x 6.06 ml drug= 60.6 ml
If 1 teaspoon = 5 ml, then 10 pounds of body weight require (60.6 ml ÷5) = 12.12 ≈12 teaspoons.
15 pounds of body weight require 15 x 6.06 ml drug= 90.9 ml
Then 15 pounds of body weight require (90.9 ml ÷5) = 18.18≈18 teaspoons.
30 pounds of body weight require 30 x 6.06 ml drug= 181.8 ml
Then 30 pounds of body weight require (181.8 ml ÷5) = 36.36 ≈ 36 teaspoons.
Hence, the children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively.
Answer:
A. 1, 1 1/2 , 2 3/4
Step-by-step explanation:
REMEMBER: 1 teaspoon = 5 ml.
For 1 pound of body weight required dosage per day= {40}{2.2}=18.18 ml
Each dose consist = {18.18}{3}=6.06 ml drug.
so, 1 pound of body weight required 6.06 ml for each dose.
Then, 10 pounds of body weight require 10 x 6.06 ml drug= 60.6 ml
If 1 teaspoon = 5 ml, then 10 pounds of body weight require (60.6 ml ÷5) = 12.12 ≈12 teaspoons.
15 pounds of body weight require 15 x 6.06 ml drug= 90.9 ml
Then 15 pounds of body weight require (90.9 ml ÷5) = 18.18≈18 teaspoons.
30 pounds of body weight require 30 x 6.06 ml drug= 181.8 ml
Then 30 pounds of body weight require (181.8 ml ÷5) = 36.36 ≈ 36 teaspoons.
Hence, the children weighing 10 pounds, 15 pounds and 30 pounds require 12 teaspoons , 18 teaspoons, 36 teaspoons respectively which deduct to 1, 1 1/2 , 2 3/4 when converted to the fraction requested in the problem.
A science fair poster is a rectangle 48 inches long and 36 inches wide. What is the area of the poster in square feet?
Be sure to include the correct unit in your answer.
Answers
Answer:
Whats the formula for the area of a rectangle?
L x W. 48 x 36 = 1728 sq inches.
Then divide by (12 x12 ) = 144 to find square feet
Step-by-step explanation:
At 3:30 p.m., Berto’s train was 34 miles past the egg farm, traveling at an average speed of 85 miles per hour. At the same time on a nearby track, Eduardo’s train was traveling at an average speed of 110 miles per hour and had 12 miles to go before it reached the egg farm. To the nearest hundredth of an hour, after how much time will the trains meet up? 0.11 hours 0.25 hours 0.88 hours 1.84 hours green t-shirts
Answers
Answer:
Step-by-step explanation:
Berto’s train was 34 miles past the egg farm .
Eduardo’s train had 12 miles to go before it reached the egg farm.
Distance between two trains = 34 + 12 = 46 miles
This distance has to be reduced to zero for their crossing each other .
Rate at which this distance is reduced = their relative velocity
= 110 - 85
= 25 miles / h [ They are moving in the same direction ]
So, time taken for them to meet each other
= 46 / relative velocity
= 46 / 25
= 1.84 hours .
Answer:
The answer is D or 1.84 hours.
Step-by-step explanation:
I got 100% on this quiz.
how would you solve #81?
Answers
An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown. 110, 130, 150, 170, ...
Answers
Answer:
f(n + 1) = f(n) + 20
Step-by-step explanation:
Let f(x) equals their pay at every hour of X
Where x is the number of hours, then if we go with the trend where f(1)=110, f(2)=130 f(3)=150 f(4)=170 then would see that as they are working every hour they have their pay increased by $20, from f(1)=110+ $20 gives us f(2)=130 and that is after an hour then we can say
1 hour work=$20
Then additional 1hour+ n= $20 + n
Hence,f(n+1)=f(n)+20
$2,500 principal earning 4%, compounded quarterly, after 4 years $40,000.00 $41,600.00 $2,931.45 $2,924.65
Answers
Answer:
Amount= $2933.2
Step-by-step explanation:
The interest of $2,500 principal earning with rate of 4%, compounded quarterly, after 4 years
A= p(1+r/n)^(nt)
P= $2500
r= 4/100= 0.04
t= 4
n = 4*4= 16
A= 2500(1+0.04/16)^(16*4)
A= 2500(1+0.0025)^(64)
A= 2500(1.0025)^64
A= 2500(1.17328)
A= 2933.2
Amount= $2933.2
Solve the quadratic equation by using a numeric approach. x squared + 1.1 x minus 2 = 0 a. x = 1.7 and x = -29.2 c. x = 2.3 and x = -22.2 b. x = 3.7 and x = 29.2 d. x = 1.9 and x = -22.2
Answers
Answer:
None of the options are correct, the correct answers are: x = 0.967 and -2.067
Step-by-step explanation:
[tex]x^2 + 1.1x - 2 = 0[/tex]
Comparing this equation with [tex]ax^2 + bx + c = 0[/tex]
a = 1, b = 1.1, c = -2
Using the almighty formula for solving quadratic equation:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} \\x = \frac{-1.1 \pm \sqrt{1.1^2 - 4(1)(-2)} }{2(1)} \\x = \frac{-1.1 \pm \sqrt{1.1^2 - 4(1)(-2)} }{2(1)} \\x = \frac{-1.1 \pm 3.035 }{2}\\x_1 = \frac{-1.1 + 3.035 }{2} = 0.967\\x_2 = -\frac{-1.1 - 3.035 }{2} = -2.067[/tex]
Answer:
A on edge 2021. Just took practice quiz.
Step-by-step explanation:
x = 1.7 and x = -29.2
In a game, one player throws two fair, six-sided die at the same time. If the player receives a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once
Answers
Answer:
probability that a player wins after playing the game once = 5/9
Step-by-step explanation:
To solve this, we will find the probability of the opposite event which in this case, it's probability of not winning and subtract it from 1.
Since, we are told that there are 2 fair six sided die thrown at the same time and that he receives a five or a one on either die ;
Probability of not winning, P(not win) = 4/6.
Thus;
P(winning) = 1 - ((4/6) × (4/6))
P(winning) = 1 - 4/9 = 5/9
Salma received a $ 70 gift card for a coffee store. She used it in buying some coffee that cost $ 8.28 per pound. After buying the coffee, she had $ 28.60 left on her card. How many pounds of coffee did she buy? Pounds
Answers
Answer:
5 pounds.
Step-by-step explanation:
You can start by subtracting 28.60 from 70 which equals 41.4.
Now you just need to divide 41.4 by 8.28 which equals 5.
So, Salma bought 5 pounds of coffee.
Hope this helps! <3
Please answer it now in two minutes
Answers
Answer:
901.1 km²
Step-by-step explanation:
The area of ∆WXY can be found using the formula, ½*a*b*sin(θ),
Where a and b, are two known sides of the triangle, and θ is the angle between both sides.
To find the area of ∆WXY, follow the steps below:
Step 1: Find XY using the law of sines.
m < W = 180 - (65 + 48) (sum of angles in a ∆)
W = 180 - (113) = 67°
X = 65°
WY = 49 km
XY = ?
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
[tex] \frac{XY}{sin(67)} = \frac{49}{sin(65)} [/tex]
[tex] \frac{XY}{0.92} = \frac{49}{0.91} [/tex]
Cross multiply
[tex] XY*0.91 = 49*0.92[/tex]
Divide both sides by 0.91
[tex] \frac{XY*0.91}{0.91} = \frac{49*0.92}{0.91} [/tex]
[tex] XY = 49.54 [/tex]
XY ≈ 49.5
Step 2: find the area
Area = ½*WY*XY*sin(Y)
Area = ½*49*49.5*sin(48)
Area = ½*49*49.5*0.743
Area = 901.07325
Area = 901.1 km² (nearest tenth)
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
last option
Step-by-step explanation:
It will take 200 / 5 = 40 months for Sara's phone to lose all its value, therefore, the domain is 0 ≤ t ≤ 40 because you can't have negative months. Since negative money is not a thing, the range has to be 0 ≤ V(t) ≤ 200 because it stops at 0 and starts at 200.
The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Answers
Greetings from Brasil...
If we have a translation for left/right, we have to use the expression:
F(X ± C)
if F(X + C), so the function shifted C units to the left
if F(X - C), so the function shifted C units to the right
Bringing to our problem
G(X) = F(X + C)
F(X) = 2X - 1
G(X) = F(X + 7) = 2.(X + 7) - 1
G(X) = F(X + 7) = 2X + 14 - 1
G(X) = F(X + 7) = 2X + 13
G(X) = 2X + 13Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Jim will win
Answers
Answer: [tex]\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items.
Rock beats Scissors, Scissors beat Paper, and Paper beats Rock.
We assume that both Jim and Renee have an equal chance of choosing any one of the hand signs.
Since, there are 3 possibilities, either Jim win or Renee or its a tie.
So, the probability that Jim will win: [tex]\dfrac{\text{Outcomes for Jim to win}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{3}[/tex]
Hence, the required probability is [tex]\dfrac{1}{3}[/tex] .
A simple random sample from a population with a normal distribution of 102 body temperatures has x overbarequals98.40degrees Upper F and sequals0.66degrees Upper F. Construct an 80% confidence interval estimate of the standard deviation of body temperature of all healthy humans. Is it safe to conclude that the population standard deviation is less than 1.80degrees Upper F?
Answers
Answer:
It is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F
Step-by-step explanation:
The given information are;
The sample size, n = 102
The sample mean = 98.4°F
The sample standard deviation = 0.66°F
[tex]\sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{\alpha /2}^{}}}< \sigma < \sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{1-\alpha /2}^{}}}[/tex]
α = 0.2, ∴ α/2 = 0.1
[tex]\chi _{1-\alpha /2}[/tex] = [tex]\chi _{0.9, 101}[/tex] = 83.267
[tex]\chi _{\alpha /2}[/tex] = [tex]\chi _{0.1, 101}[/tex] = 119.589,
Which gives;
[tex]\sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{119.589}^{}}}< \sigma < \sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{83.267}^{}}}[/tex]
0.607 < σ <0.727
Therefore, it is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F.
Different cereals are randomly selected and the sugar content in grams of sugar per grams of cereal are obtained. Use a .05 significance level to test the claim of cereal lobbyist that the mean sugar content for all cereals is less than .3 g. Data set: 0.03, 0.24, 0.30, 0.47, 0.43, 0.07, 0.47, 0.13, 0.44, 0.39, 0.48, 0.17, 0.13, 0.09, 0.45, 0.43
Answers
Answer:
Step-by-step explanation:
Hello!
X: content of sugar of a sample of cereal.
Data set:
0.03, 0.24, 0.30, 0.47, 0.43, 0.07, 0.47, 0.13, 0.44, 0.39, 0.48, 0.17, 0.13, 0.09, 0.45, 0.43
n= 16
[tex]\frac{}{X}[/tex]= 0.295g
S= 0.17g
You have to test if the mean sugar content is less than 0.3g
H₀: μ ≥ 0.3
H₁: μ < 0.3
α: 0.05
Assuming that the variable has a normal distribution, you have to conduct a t test:
[tex]t= \frac{\frac{}{X}-Mu }{\frac{S}{\sqrt{n} } } ~~t_{n-1}[/tex]
[tex]t_{H_0}= \frac{0.295-0.30}{\frac{0.17}{\sqrt{16} } } = -0.12[/tex]
p-value: 0.4533
The p-value is greater than α, the decision is to not reject the null hypothesis.
At a 5% significance level the decision is to not reject the null hypothesis. You can conclude that the average sugar content of the cereal is equal or greater than 0.3g of sugar per gram of cereal.
I hope this helps!
what is the product number of 88 and 26?
Answers
Answer:
2288
Step-by-step explanation:
there are 9000 children in a town the probability that a child is affected by a virus 1/3 how many children are not likely to be affected
Answers
Answer:
6,000 children
Step-by-step explanation:
1/3 of 9,000 is 3,000
Meaning that out of 9,000 children, 3,000 WILL get affected. Since we are trying to figure out how many children will NOT get affected, just subtract the number of infected by the total amount which would be 6,000
what is the value of [3.6]
Answers
Answer:
3
Step-by-step explanation:
You remove the brackets and round down to the nearest whole number which is three..
Edge 2020
~theLocoCoco
Answer:
a
Step-by-step explanation:
edge 2021
How many Real Solutions
Answers
Answer:
D.0
Step-by-step explanation:
Our system of equations is
y= x²+1y=xthen we can conclude that
x²+1 = xx²+1-x = 0x²-x+1 = 0This is a quadratic equation so we will use the dicriminant method:
Let Δ be our dicriminant
a= 1b= -1c= 1Δ = (-1)²-4*1*1 = 1-4 = -3 < 0The dicriminant is negative so this equation has no real solutions
the the system has no real solutions
factor the following trinomials x2-18x+81
Answers
Answer:
(x - 9)(x - 9)
Step-by-step explanation:
Hey there!
Well to factor,
x^2-18x+81
we need to figure out what times what equal 81 and adds together to get -18.
-9*-9 = 81
-9 + -9 = -18
x*x = x^2
Factored - (x - 9)(x - 9)
Hope this helps :)
This is found using the MAN strategy, and can be proven by subbing 9 into the equation for x and the solution equaling zero.
Explain how to determine the following from the graph: Number of times the barnacle went beneath the water level if the boat traveled a distance of 20 m Number of meters of the 20 m trip that the barnacle was underwater
Answers
Answer:
+When the graph is below the x-axis, the barnacle is underwater.
+The graph dips below the x-axis three times between x = 0 and x = 20, so the barnacle goes underwater three times.
+Every time the barnacle goes underwater, the boat travels pi meters (one half the circumference of the wheel) before the barnacle comes back up, so the barnacle covers 3pi meters underwater between x = 0 and x = 20
Step-by-step explanation:
To determine the number of times that the times the barnacle went beneath the water level, it can be illustrated when the graph is below the x-axis.
How to illustrate the graph?It should be noted that the graph dips below the x-axis three times between x = 0 and x = 20, therefore the barnacle goes underwater three times.
Also, every time the barnacle goes underwater, the boat travels pi meters before the barnacle comes back up.
Learn more about graph on:
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how to estimate 5 2/11- 3 2/18
Answers
Answer: The estimated value is: " 2.1 " .
__________________________________
Step-by-step explanation:
__________________________________
We are asked to "estimate" :
5 2/11 - 3/ 2/18 ;
Note: Consider: " 5 2/11 " ;
Note that: "2/11" is close to: "2/10" ; which can be expressed as a decimal value: "0.2 " ;
So, consider this value: "5 2/11 "; as estimated: " 5.2 " .
Now, consider: " 3 2/18 " ;
Note that : "2/18" can easily be reduced to: "1/9 ";
Since: "(2/18)" = "(2÷2) / (18÷2) " = "1/9 " ;
Note that "1/9" is close to "1/10" ; which can be expressed as a decimal value: "0.1 ".
So, consider: "3 2/18 " ; as estimated: " 3.1 " .
__________________________________
So: To estimate: " 5 2/11 - 3 2/18 " ;
__________________________________
Use the following: "5.2 - 3.1 " ;
__________________________________
5.2
- 3. 1
__________________________________
" 2.1 "
___________________________________
The estimated value is: " 2.1 " .
___________________________________
Hope this is helpful to you!
___________________________________
Write an equation of the line that passes through the point (-7, -9) with slope -4
A. Y+7= 4(x +9)
B.y+9= 4(x + 7)
c. y +9= - 4(x + 7)
D. Y+7= - 4(x +9)
Answers
Answer:
y + 9 = - 4 ( x + 7 )
Option C is the correct option
Step-by-step explanation:
Given
Point = ( -7 , - 9 )
Slope = - 4
Equation of line ( Point slope form )
[tex]y - y1 = m(x - x1)[/tex]
when point = ( -7 , - 9 )
[tex]y + 9 = - 4(x + 7)[/tex]Hope I helped...
Best regards!!
The equation of the line is 4x + y = -37 then option C is correct.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given point is ( -7, - 9 ) and the slope is - 4.
The equation of the line is calculated by,
y - y₁ = m ( x - x₁ )
y - 9 = -4 ( x + 7 )
y = -4x -28 - 9
y = -4x -37
4x + y = -37
Therefore, the equation of the line is 4x + y = -37 then option C is correct.
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