Answer:
f ( x ) = $1000 - $25*x
( 40 days, $0 )
( 0 days , $1000 )
Step-by-step explanation:
Solution:-
- Every quarter Hannah receives $1000 in her account for meal plan.
- So for a quarter of a year she has $1000 to spend.
- She spends $25 on food each day; hence, an amount of $25 is deducted each day.
- We can mathematically express the amount remaining in her account after ( x ) days as follows:
y = f(x) = Initial deposit - (per day deduction)*x
Where,
y: The amount remaining in Hannah's account after x days.
- The initial amount is the quarterly deposit of $1000 and per day deduction is her buying food each day for $25.
y= f(x) = $1000 - ($25)*x
- The thing to note is that the above function f(x) is only defined over the domain of a quarter of year i.e from the first day she receives her amount till the next deposit.
- The number of days it will take for Hannah to empty her account can be determined from finding the x-intercept or ( y = f(x) = 0 ) using the function defined above:
f ( x ) = 1000 - 25x = 0
x = 1000 / 25
x = 40 days
- So it will take 40 days for Hannah to empty her account. As an ordered pair it can be written as:
( 40 days , $0 ) ... Answer
- The initial deposit of $1000 corroborates the y-intercept of the function defined f ( x ). Or we can evaluate the derived function at f ( 0 ):
f ( 0 ) = 1000 - 25*0
f ( 0 ) = $1000
- The ordered pair for the y-intercpet would be:
( 0 days , $1000 ) ... Answer
What is t in 197sin(12t)=141
Answer:
t ≈ 0.0664731
Step-by-step explanation:
Use the inverse sine function.
sin(12t) = 141/197
12t = arcsin(141/197)
t = arcsin(141/197)/12
t ≈ 0.0664731 . . . . . . . radians
__
This is the principal value. There are other solutions at values of t that have integer multiples of π/6 added to this. There are also solutions where any of those values is subtracted from π.
_____
In general, angles in math are assumed to be in radians, unless specified otherwise. This angle corresponds to about 3.81°. (In geometry, the usual assumption is that angles are measured in degrees.)
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
There are six space shuttles
visiting your planet. Each
shuttle contains 8 people.
How many people visit
your planet
There are six space shuttles with 8 people inside. Meaning, for every space shuttle, there are 8 people so multiply that by six to get the overall people who visited your planet (48)
Qualification exams for becoming a state-certified welding inspector are based on multiple-choice tests. As in any multiple-choice test, there is a possibility that someone who is simply guessing the answers to each question might pass the test. Let x denote the number of correct answers given by a person who is guessing each answer on a 25-question exam, with each question having five possible answers (for each question, assume only one of the five choices is correct).(a) What type of probability distribution does x have?(b) For the 25-question test, what are the mean and standard deviation of x?(c) The exam administrators want to make sure that there is a very small chance, say, 1%, that a person who is guessing will pass the test. What minimum passing score should they allow on the exam to meet this requirement?
Answer:
(a) The probability distribution of the random variable X is Binomial.
(b) The mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c) The value of x is 0.34.
Step-by-step explanation:
The random variable X is defined as the number of correct answers given by a person who is guessing each answer on a 25-question exam.
There are five possible answer for every question.
This implies that the probability of getting a correct answer is:
P (X) = 0.20.
There are a total of n = 25 questions.
Every answer is independent of the others.
(a)
The random variable X has finite number of independent trials (i.e. 25 questions). There are only two outcomes for each trial, i.e. Success = correct answer and Failure = wrong answer. Each trial has the same probability of success (, i.e. P (X) = 0.25).
Thus, the probability distribution of the random variable X is Binomial with parameters n = 25 and p = 0.20.
(b)
Compute the mean of the random variable X as follows:
[tex]E(X)=np\\=25\times 0.20\\=5[/tex]
Compute the standard deviation of the random variable X as follows:
[tex]SD(X)=\sqrt{np(1-p)}\\=\sqrt{25\times 0.20\times (1-0.20)}\\=2[/tex]
Thus, the mean and standard deviation of the 25-question test are 5 and 2 respectively.
(c)
The sample is large and the probability of success is close to 0.50.
So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:
1. np ≥ 5
2. n(1 - p) ≥ 5
Check the conditions as follows:
[tex]np=25\times 0.20=5=5\\\\n(1-p)=25\times (1-0.20)=20>5[/tex]
Thus, a Normal approximation to binomial can be applied.
So, [tex]X\sim N(5, 2^{2})[/tex]
It is provided that the minimum passing score foe the test is such that only 1% of students who are guessing will pass the test.
That is P (X < x) = 0.01.
⇒ P (Z < z) = 0.01
The value of z is -2.33.
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-2.33=\frac{x-5}{2}\\\\x=5-(2.33\times 2)\\\\x=0.34[/tex]
Thus, the value of x is 0.34.
Suppose that in a random sample of 200 New York City residents 55% can name a player on the Knicks. In a random sample of 120 Toronto residents, 70% can name a player on the Raptors. At the 5% level of significance, determine if we can conclude that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors. C.
a. State the null and alternative hypotheses.
b. Are all criteria for the hypothesis test satisfied?
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
b) Yes.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of all NYC residents that can name a player on the Knicks differs from the proportion of all Toronto residents who can name a player on the Raptors.
As the claim is that the proportions differs, the difference to reject the null hypothesis can be positive or negative. Then, this is a two-tailed test.
The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The conditions to met for this test are:
- The sampling method for each population is simple random sampling.
- The samples are independent.
- Each sample includes at least 10 successes and 10 failures.
[tex]\text{Failures (NY):} \, F=200*0.45=90\\\\\text{Failures (T):} \, F=120*0.3=36\\\\\text{Note: we use failures as they have the lower proportions.}[/tex]
- Each population is at least 20 times as big as its sample.
This conditions are met, so all criteria for the hypothesis test is satisfied.
I need help please and thank you
Answer:
3.33×10⁴
Step-by-step explanation:
You can use the hint, or you can use a common exponent. Here is the latter case.
(3.9×10⁴) -(5.7×10³) = (3.9×10⁴) -(0.57×10⁴) = (3.9 -0.57)×10⁴
= 3.33×10⁴
_____
With a little practice, you can see the effect on exponents of moving the decimal point. Here, we have ...
5.7×10³ = (0.57×10)×10³ = 0.57×(10×10³) = 0.57×10⁴
__
When adding or subtracting in scientific notation, all that is required is that the exponents of all the numbers be the same. The hint says make all the exponents be 0. Above, we have chosen to make them all be 4. You could also use 3:
(3.9×10⁴) -(5.7×10³) = (39×10³) -(5.7×10³) = (39 -5.7)×10³
= 33.3×10³ = 3.33×10⁴
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).
What’s the amplitude,period,equation of axis, and range for y=3sin[2(x+90)]?
Answer:
amplitude: 3period: πaxis: y = 0range: [-3, +3]Step-by-step explanation:
The amplitude is the multiplier of the sine function: 3.
The period is 2π divided by the coefficient of x: 2π/2 = π.
The equation of the axis is any added constant: y = 0.
The range is the axis value ± the amplitude value: from -3 to +3.
Determine the slope.(-5,-4) and (7,-8)
Answer: the slope is -3
Step-by-step explanation:
(Pls see pic for the work)
Simplify: (3x2 - 4x + 6) + (7x - 2)
Answer:
11x-2
Step-by-step explanation:
(3x2 - 4x + 6) + (7x - 2) This is the breakdown. (6 4x + 6)= 4x. + (7x-2) = 11x-2
The function g(x) = x^3 has the point (-3, -27) on its graph. The function g(x) is:
even
odd
Answer:
Odd.
Step-by-step explanation:
You don't need the point, its pretty much useless.
If its even, when you plug -x into the equation, it will stay the same
If its odd, when you plug -x into the equation, the signs will change
g(x) = [tex]x^{3}[/tex]
Lets plug in -x.
g(x) = (-x)³
g(x) = -x³
The equation is different! That means the equation is odd!
Drive-In movie theatres are outdoor movie venues where people park facing a large screen and watch a movie from their own car. Daisy’s Drive-In charges $14.00 for a vehicle and an additional $4.00 per person in the car. Donald’s Drive-In charges $26.00 for a vehicle and an additional $2.00 per person in the car.
Write two equations that represent the 2 drive-in theatres.
Daisy’s Drive-In: ______________________________
Donald’s Drive-In: ______________________________
Answer:
26.00 + 2x = y 14.00 + 4x = y
Step-by-step explanation:
depending on the amount of people in the car determines numbers of the equation so variables had to be placed instead.
Each of the following statements is true or false. Which statements are true?
A. A triangle where at least two angles are acute is called an acute triangle.
B. Some polygons are neither convex nor concave.
C. The sum of the interior angles of a concave pentagon is $540^{\circ}.$
D. The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.
E. The exterior angles of a regular $1000$-gon are greater than the exterior angles of a regular $100$-gon.
Type your answer as an list, separated by commas. For example, if you believe statements A, C, and D are true, type A, C, D.
Answer:
B,D
Step-by-step explanation:
The true statements are given below.
The sum of the interior angles of a concave pentagon is $540^{\circ}.$The interior angles of a regular $1000$-gon are greater than the interior angles of a regular $100$-gon.Why does the Pentagon have 5 sides?The land the Pentagon become first planned to head on become bordered on 5 aspects through roads, so the architects designed a five-sided building.
What is the Pentagon shape?A pentagon is a geometrical form, which has 5 facets and five angles. here, “Penta” denotes five, and “gon” denotes attitude. The pentagon is one of the forms of polygons. The sum of all the indoor angles for a normal pentagon is 540 ranges.
Learn more about the pentagon here https://brainly.com/question/21475963
#SPJ2
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
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).
What is wrong with this math problem?
(6x)(4x^7) = 24x^7
Answer:
(6x)*(4x^7) = (6*4)*(x*x^7) = 24*x^8
(6x)*(4x^7) = 24*x^7 is wrong in calculation of x
Hope this helps!
:)
Answer:
Nothing is wrong with it
x= 1
Step-by-step explanation:
It has a solution; here is the solution.
(6x)(4x^7) = 24 x^ 7
x * 24x^7= 24x^7
x = 24x^7 / 24x^7
x = 1
What is the value of x?
Answer:
5.6
Step-by-step explanation:
We assume that 7 is the measure of the portion of the secant that is inside the circle between the circle and the intersection with the other chord.
The product of segment lengths on the same chord is a constant for chords that intersect at the same point. That is, ...
10x = 8·7
x = 56/10
x = 5.6
_____
Comment on the geometry
If you draw the figure to scale, you find the geometry shown is impossible. The arc measures and chord lengths are incompatible.
What’s the correct answer for this ?
Answer:
Blank 1) 150
Blank 2) (3)²
3) (4)²
4) (x+3)²
5) (y-3)²
6) (x+3)²+(y-3)² = 100
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
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.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
What is the value of | 3 | (PLEASE HELPP!!)
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]
PLEASE HELP
Which of the following lists is ordered from least to greatest?
Answer:
the selected list is correct
Step-by-step explanation:
Negative numbers with larger magnitudes are smaller in value, so -2 is less than -1.5.
A fraction is smaller in value if it has a smaller numerator and the same denominator. It is also smaller in value if it has the same numerator and a larger denominator.
2/5 is smaller than 3/4 because it has both a smaller numerator and a larger denominator. So the ordering of the positive numbers is 2/5, 3/4.
The ordering you want is the one checked.
solve the equation -2 = 3x/5 + 1
[tex] - 2 = \dfrac{3x}{5} + 1 | \times 5 \\ - 10 = 3x + 5 \\ - 3x = 15 | \div ( - 3) \\ x = - 5[/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
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
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
A round cake has a diameter of 30 cm. Angela places the cake on a circular cake board with a diameter 5 cm
longer than that of the cake.
What is the circumference of the cake board?
Give your answer in terms of T.
cm
Stuck? Watch a video or use a hint.
Report a problem
Doble
Answer: Circumference of cake board is 35π cm.
Step-by-step explanation:Since we have given that
Diameter of a round cake = 30 cm
Diameter of a cake board is 5 cm longer than the diameter of a round cake.
So, Diameter of a cake board = 30+5=35 cm
So, radius of a cake board will be
As we know the formula for " Circumference of Circle ":
So, According to question, we get,
Hence, Circumference of cake board is 35π cm.
Answer: 35π cm
Step-by-step explanation:
Denver, Colorado, is
5183ft
above sea level. Convert the height to miles. Round to three decimal places.
Answer:
0.982 mile
Step-by-step explanation:
1 mile = 5280 ft
h = (5183ft) *(1 mile/5280ft) = 0.982 miles
The height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.
What is measurement?Measurement is simply the process of associating numbers with physical quantities and events.
Converting measurements in foot to miles as;
1foot = (1/5280)miles
Given that;
Height of Denver, Colorado = 5183ftHeight in miles = ?Since 1foot = (1/5280)miles
5183ft = ( 5183 / 5280 )miles
5183ft = 0.982miles
Therefore, the height of Denver, Colorado above sea level rounded to three decimal places is 0.982miles.
Learn more about measurements here: https://brainly.com/question/2107310
#SPJ2
In a board game, negative number cards represent moving backward and positive number cards represent moving forward. For example, Dimitri drew a card with -3 and moved backward 3 spaces
Stan draws a card with 0.
What does 0 represent in the board game?
Answer: 0 represents he stays in the same place
jdjejejeeeeeeeeeeeStep-by-step explanation: