the base of a expoential function can be a negative number true or false
Answer:
This would be false
Step-by-step explanation:
Exponents can't be negative
Answer:
An exponential function can not be either 1, 0, or any negative number.
20% of US High School teens vape. A local High School has implemented campaigns to reduce vaping among students and believes that the percentage of students who vape at this High School is lower than the national average. School administration implements a survey of 300 randomly selected students. They find that 51 of the 300 vape.
If the true proportion of students who vape at this school is 20%, what is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 300, p = 0.2[/tex]
So
[tex]\mu = E(X) = np = 300*0.2 = 60[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.2*0.8} = 6.9282[/tex]
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is [tex]P(X \leq 51 + 0.5) = P(X \leq 51.5)[/tex], which is the pvalue of Z when X = 51.5 So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{51.5 - 60}{6.9282}[/tex]
[tex]Z = -1.23[/tex]
[tex]Z = -1.23[/tex] has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300
In a board game, each player must roll a number cube and spin a spinner. The number cube is labeled with the numbers 1 through 6 and the spinner consists of eight equal parts shown below. What is the probability you will roll a 5 and land on blue?
A: 1 over 12
B: 1 over 10
C: 5 over 12
D: 2 over 3
Answer:
i think it is 5/12???
I hope i am right :C, if not you can delete this answer
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day. The table shows the amount of fiber Jodi has eaten today. How many more grams of fiber does she need to get the recommended daily amount of fiber?
The amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
We have:
Some nutritionists recommend that people eat 31,000 milligrams of fiber each day.
The total amount of fiber Jodi took = 19 + 4 + 2(1) = 25 grams
1 gram = 1000 milligrams
25 grams = 25000 milligrams
The amount of fiber she needs to eat
= 31000 - 25000
= 6000 milligrams
or
= 6 grams
Thus, the amount of fiber Jodi needs to eat is 6000 milligrams or 6 grams if the nutritionists recommend that people eat 31,000 milligrams of fiber each day.
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Where do you find your domain restrictions in a rational function?
Answer:
denominator zeros are excluded
Step-by-step explanation:
The domain is the set of values of the independent variable where the function is defined. A rational function is "undefined" where the denominator is zero.
The exclusions of interest are generally those values of the variable that make any denominator be zero.
__
Example:
f(x) = (2/(x-3)) / (4/(x -6))
has denominators of x-3 and x-6. These are zero for x=3 and x=6, so those two values are excluded from the domain of this function. We observe that the function can be simplified to ...
f(x) = (x -6)/(2(x -3))
but x=6 remains excluded from the domain because of its effect in the original function definition.
_____
Additional comment
If the rational function includes functions that have domain restrictions (such as square root, for example), then those restrictions apply as well.
Usually, but not always, the rational functions where you're asked about domain are the ratios of polynomials. So, you need to factor or otherwise find the zeros of any denominator polynomials in such functions.
simplify the numerical expression
12-2³
Answer:
12-2³ = 12 - 8 = 4
Hope this helps!
:)
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x2 + 2x + 7 = 21
Complete question is;
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x² + 2x + 7 = 21 The number of positive solutions to this equation is . The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answer:
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is 2.87.
Step-by-step explanation:
We are given the quadratic equation as;
x² + 2x + 7 = 21
Subtract 21 from both sides to give ;
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
Using quadratic formula, we cam find the roots of the equation.
x = [-b ± √b² - 4ac]/2a
Plugging in the values;
x = [-2 ± √(2² - 4(1*-14))]/2(1)
x = [-2 ± √(4 + 56)]/2
x = [-2 ± √60]/2
x = - 4.87 or 2.87
Thus, this equation has only one positive solution which is the greatest.
Thus, greatest solution is 2.87
What is the value of | 3 | (PLEASE HELPP!!)
Two swimmers at opposite ends of a ninety-foot pool start to swim the length of the pool, one at 3 feet per second and the other at 2 feet per second. If they swim back and forth for twelve minutes, how many times do they pass each other?
Answer:
20 times
Step-by-step explanation:
The faster swimmer can swim twice the length of the pool in ...
(2·90 ft)/(3 ft/s) = 60 s
The slower swimmer can do it in ...
(2·90 ft)/(2 ft/s) = 90 s
The least common multiple of these times is 180 s = 3 minutes, after which time each swimmer will be back where they started.
A graph of position vs. time shows the swimmers pass 5 times in that 3-minute period. 4 of those are passes when they are going in opposite directions. A 5th pass occurs at one end of the pool, when the faster swimmer passes the slower one going in the same direction.
Since there are 5 passes in each 3-minute period, there are 20 passes in 12 minutes.
The swimmers pass each other 20 times in 12 minutes.
A lending institution supplied the following data on loan approvals by four loan officers. Use α = .05 and test to determine whether the loan approval decision is associated with the loan officer reviewing the loan application.
Loan Approval Decision
Loan Officer Approved Rejected
Miller 24 16
McMahon 17 13
Lee 35 15
Sanchez 11 9
Answer:
As chi^2 < 7.815, and P > 0.05, we do not reject null hypothesis.
Thus, there is no significant evidence that the loan approval decision is not independent of the loan officer reviewing the loan application.
Step-by-step explanation:
Find the given attachment
describe the domain and range of y=2(3)^x-2+5
Answer:
Step-by-step explanation:
Answer:
the domain is "the set of all real numbers."
the range of the given function is (5, infinity)
Step-by-step explanation:
This is an exponential function. For the sake of clarity you must enclose "x - 2" inside parentheses: f(x) = 2(3)^(x-2). This function is defined for all real x-values, so the domain is "the set of all real numbers."
Focusing on (3)^x: This has the same shape as the basic exponential y = e^x; the graph starts in Quadrant II and increases with x, more and more rapidly as you pass x = 0. The functions y = e^x and that of y = 3^x are always positive. Likewise in the case of f(x) = 2(3)^(x-2): the function is always positive. If we look at f(x) = 2(3)^(x-2) alone, we conclude that the domain is (0, infinity). But that " + 5 " in y=2(3)^(x-2) + 5 translates the entire graph of f(x) = 2(3)^(x-2) upward by 5 units.
Thus, the range of the given function is (5, infinity).
A file that is 278 megabytes is being downloaded. If the download is 19.9% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
55.3
Step-by-step explanation:
19.9% of 278 = 55.322
55.322 rounded to the nearest tenth = 55.3
Answer:55.3
Step-by-step explanation:
A population of insects can double in 30 days. After
80 days, how many times greater will the population be than
after 30 days?
Answer:
about 2.666 times
Step-by-step explanation:
you know that 80 days have past and it only takes 30 days for the population to double. if you do 80/30 you get 2.666 meaning that the population would of been 2.666 times greater.
The population be than after 30 days about 2.666 times greater.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given; A population of insects can double in 30 days.
After 80 days, We need to find that how many times greater will the population be than after 30 days
We know that 80 days have past and it only takes 30 days for the population to double.
if we do 80/30 = 2.666 meaning that the population would of been 2.666 times greater.
Therefore, The population be than after 30 days about 2.666 times greater.
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In the NFL, a football field is 200 feet longer than it is wide, and the area of the field is 57,600ft^2
What is the width of the field?
(Before you mess this up, the field is not 100 yards long. You must include the lengths of the end Zones.) (And hey wait a second! Before you mess it up now, notice the problem is in
FEET.)
Answer
160ft
Step-by-step explanation:
Let the width be x.
Then the length is (x+200)
The area of the field=57600
Area=length*width
x(x+200)=57600
x^2+200x-57600=0
x=-360 or x=160
The width and length of the football field are 160 feet and 360 feet respectively.
Suppose the width of the field = x
So, the length of the field =x+200
What is the area of a rectangle?The area of a rectangle with length l and width b is lb.
So, the area of the football field =x(x+200)
Given that x(x+200)=57600
[tex]x^{2} +200x=57600[/tex]
[tex]x^{2} +200x-57600=0[/tex]
[tex]x=\frac{-200+\sqrt{200^2-4*1*(-57600)} }{2}[/tex]
x=160
So, the width of the field is 160 feet.
Hence, the width and length of the football field are 160 feet and 360 feet respectively.
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In ΔIJK, the measure of ∠K=90°, KI = 3.8 feet, and JK = 6.7 feet. Find the measure of ∠I to the nearest degree.
Answer:
60
Step-by-step explanation:tanI=
adjacent
opposite
=
3.8
6.7
\tan I = \frac{6.7}{3.8}
tanI=
3.8
6.7
I=\tan^{-1}(\frac{6.7}{3.8})
I=tan
−1
(
3.8
6.7
)
I=60.44\approx 60^{\circ}
I=60.44≈60
∘
what is the name of this 3D shape
Answer:
rectangular prism or cuboid
Step-by-step explanation:
The name of the given 3-D shape is rectangular prism or cuboid
The jogging track is 5/9 of a mile long. If Ashley jogged around it four times how far did she run
Answer:
20/9 mile
Step-by-step explanation:
idk pretty self-explanatory
What is the volume of the cylinder below?
Answer:
The volume of the cylinder is [tex]112\ \text{units}^3[/tex].
Step-by-step explanation:
We have,
Radius of the cylinder is 4 units
Height of the cylinder is 7 units
It is required to find the volume of the cylinder. The formula of the volume of the cylinder is given by :
[tex]V=\pi r^2 h[/tex]
Plugging all the values, we get :
[tex]V=\pi \times (4)^2\times 7\\\\V=112\ \text{units}^3[/tex]
So, the volume of the cylinder is [tex]112\ \text{units}^3[/tex]. The correct option is (b).
In a classic prisoner's dilemma game with money for prizes, players who cooperate with each other both earn good prizes. If, however, your opposing player cooperates but you do not (the term used is defect), you receive an even bigger payout and your opponent receives nothing. If you cooperate but your opposing player defects, he or she receives that bigger payout and you receive nothing. If you both defect, you each get a small prize. Because of this, most players of such games choose to defect, knowing that if they cooperate but their partners don't, they won't win anything. The strategies of U.S. and Chinese students were compared. The researchers hypothesized that those from the market economy (United States) would cooperate less (i.e., would defect more often) than would those from the nonmarket economy (China). Defect Cooperate China 31 36 United States 41 14 What is/are the variable(s) in this study and, if appropriate, what are the levels of any variables you identified?
Answer:
Check the explanation
Step-by-step explanation:
a. there are two categorical variables here:
region with two level : China and US
and cooperation with two level : Defect and cooperate.
b. Chi-square test for association can be used here since the variables are categorical in nature.
Chi-Square Test for Association: C6, Worksheet columns
Rows: C6 Columns: Worksheet columns
defect cooperate All
China 31 36 67
39.54 27.46
US 41 14 55
32.46 22.54
All 72 50 122
Cell Contents: Count
Expected count
Pearson Chi-Square = 9.985, DF = 1, P-Value = 0.002
Likelihood Ratio Chi-Square = 10.231, DF = 1, P-Value = 0.001
Carl pays $45 per month for car insurance. How much does he spend on car insurance in 1 year?
Answer: 540
Step-by-step explanation: because if he pays 45 bucks a month and a year equals 12 then ya do 45x12 and ya get 540
Answer:
Carl spends $540 per year on car insurance
Step-by-step explanation:
Carl pays $45 per month. There are 12 months in 1 year.
All we need to do is multiply the rate per month by the number of months to get our answer.
[tex]45*12=540[/tex]
evaluate 9+(-8)÷4+5(-2)-(-3)
Answer:
hi there
0
Step-by-step explanation
9+[(-8)÷4]+[5(-2)]-(-3)
9+[-2]+-10+3
7+-7
0
Answer:
-57
hope this helped correct me if i'm wrong
The diagram shows 2 different shapes ...................................................................................................................
Thanks in advance
Answer:
A) ?
B) Rhombus
Step-by-step explanation:
For A count the squares inside the shape. I am sorry I had to answer this quickly and did not have time time to count them, but that should be fairly straight forward.
B is Rhombus.
Answer:
P = 12
The height = 6
Base = 4
24*0.5 = 12
B = rhombus
I have 25 pound bags of cat food . Each serving is 1.8 from the bag. How many servings can you get?
Answer:
10 servings
Step-by-step explanation:
try your best
Answer:
13.8 servings
Step-by-step explanation:
25 divided by 1.8
which expression is equivalent p^6)2
So the right answer is p^12.
Look at the attached picture
Hope it will help you
Good luck on your assignment..
Answer:
[tex] {p}^{12} [/tex]
Step-by-step explanation:
[tex]( {p}^{6} ) ^{2} [/tex]
[tex]p ^{6 \times 2} [/tex]
[tex] {p}^{12} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
What is the midline equation of y = 8 cos (5pix+3pi/2)-9
Answer:
[tex]y = -9[/tex]
Step-by-step explanation:
The curve intersects the midline when effect of amplitude is annulled. The midline equation is of the form:
[tex]y = y_{o}[/tex]
The midline equation is:
[tex]y = -9[/tex]
What’s the value of x?
Answer fast please
So the value of X is 15 degree.
Look at the attached picture
Hope it will help you
Good luck on your assignment
AC=180°
[tex]3x + 8x + 15 = 180 \\ 11x = 165 \\ x = 15[/tex]
If MH = 18cm and HA = 29cm, what is MA?
Answer:
The leg MA measures 22.7 centimeters.Step-by-step explanation:
Assuming that's about a right triangle, the image attached shows a representation of this problem.
We use the Pythagorean Theorem to find the missing leg, which we are gonna call [tex]y[/tex]
[tex]29^{2} =18^{2}+y^{2}\\y^{2}=29^{2}-18^{2}\\y=\sqrt{841 - 324} \approx 22.7 \ cm[/tex]
Therefore, the leg MA measures 22.7 centimeters.
Change 460g into kg
Answer:
0.46 kg is your answer
Step-by-step explanation:
We know (by definition) that: 1 g = 0.001 kg.
We can set up a proportion to solve for the number of kilograms.
1 g / 460 g = 0.001 kg / x kg
Now, we cross multiply to solve for our unknown x:
x kg = (460 g / 1 g) * 0.001 kg → x kg = 0.46 kg
Conclusion:
460 g = 0.46 kg
Answer:
460g = 0.46 kg
Step-by-step explanation:
just divide 460/1000 since 1 kg = 1000 grams
Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the water level when the water is 6 m deep. (1 L = 1000cm^3)
Answer:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
Step-by-step explanation:
For a tank similar to a cylinder the volume is given by:
[tex] V = \pi r^2 h[/tex]
For this case we know that [tex] r=5m[/tex] represent the radius, [tex] h = 10m[/tex] the height and the rate given is:
[tex] \frac{dV}{dt}= \frac{100 L}{min}[/tex]
For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:
[tex] \frac{dV}{dt}= \pi r^2 \frac{dh}{dt}[/tex]
And solving for [tex]\frac{dh}{dt}[/tex] we got:
[tex] \frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}[/tex]
We need to convert the rate given into m^3/min and we got:
[tex] Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}[/tex]
And replacing we got:
[tex] \frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}[/tex]
And that represent [tex] 0.127 \frac{cm}{min}[/tex]
When Mustafa threw a beach ball to his friend, its horizontal velocity changed as it traveled through the air. The relationship between the elapsed time, tttt, in seconds, since Mustafa threw the ball, and its horizontal velocity, V(t)V(t)V(t)V, left parenthesis, t, right parenthesis, in cm/s\text{cm/s}cm/sstart text, c, m, slash, s, end text, is modeled by the following function: V(t)=4⋅(0.81)t Complete the following sentence about the percent change of the horizontal velocity of the ball. Every second, %\%%percent of horizontal velocity is the total horizontal velocity of the ball.
Answer:
The rate at which the horizontal velocity of the ball changes every second is, 19%.
Step-by-step explanation:
The exponential decay function is given by:
[tex]y=a(1-r)^{t}[/tex]
Here,
y = final value
a = initial value
r = decay rate
t = time
The relationship between the elapsed time, t, in seconds, since Mustafa threw the ball, and its horizontal velocity, V (t) is:
[tex]V(t)=4\cdot (0.81)^{t}[/tex]
The expression for the horizontal velocity of the ball represents the exponential decay function.
On comparing the two equations we get:
[tex]1-r=0.81\\r=1-0.81\\r=0.19[/tex]
Thus, the rate at which the horizontal velocity of the ball changes every second is, 19%.