The composite function c(x) = 0.8x - 3, and the cost of a $30 item would be $21.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions.
In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Let, 'x' be the original cost of the item.
A store offers a 20% discount on all items,
So, f(x) = [(100 - 20)/100]×x.
f(x) = (80/100)×x.
f(x) = 0.8x.
Again, you also have a $3 coupon.
Let, g(x) = x - 3.
Now, The composition of the functions f(x) and g(x) is f(x) + g(x) = C(x).
C(x) = 0.8x - 3.
Now, The cost of an item is $30.
Therefore, C(30) = 0.8×30 - 3.
C(30) = 24 - 3.
C(30) = 21.
learn more about composite functions here :
https://brainly.com/question/30143914
#SPJ1
In a large population, 58 % of the people have been vaccinated. If 3 people are randomly selected,
what is the probability that AT LEAST ONE of them has been vaccinated?
Give your answer as a decimal to at 4 places.
The probability that at least one of them has been vaccinated is 0.9259.
What is binomial distribution?
The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.
The proportion of people vaccinated is 58%.
Three people are selected at random, that is, n=3
p=0.58,
the probability mass function,
[tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]
[tex]p(X=0)= ^{3}C_{x}0.58^{0}(0.42)^{3-0 } = 0.07408[/tex]
p( X≥1)= 1 - p(X=0)
= 1 - 0.07408
= 0.9259
The probability that at least one of them has been vaccinated is 0.9259.
To learn more about the binomial distribution from the given link
https://brainly.com/question/15246027
#SPJ1
The function describing the predicted velocity as a function of time, v(t), for a student-designed prototype two-stage model rocket during a 5.5 s time interval is given by v(t) = at’ + ßt² + yt, where a = 3.0 m/s4, B = –24 m/s°, and y = 54 m/s2. Due to ignition rates of the fuel in the two stages and external forces acting on the rocket, the design produces a velocity function that has both a local minimum and a local maximum during the time interval. Part F Determine the times at which v(t) has a local minimum and maximum. Express your answer as two numbers separated by a comma.
To determine the times at which v(t) has a local minimum and maximum, we need to find the critical points of the function. A critical point is a value of t for which either the first derivative, v'(t), or the second derivative, v''(t), is equal to zero or does not exist.
The first derivative of v(t) is given by:
v'(t) = a + 2bt + y
Setting v'(t) equal to zero and solving for t, we get:
0 = a + 2bt + y
t = -a / 2b = -(3 m/s^4) / (2(-24 m/s^2)) = 3/48 s
The second derivative of v(t) is given by:
v''(t) = 2b
Since b is negative, v''(t) is negative, so v(t) has a local maximum at t = 3/48 s.
Similarly, since the second derivative is constant and negative, the function v(t) has a local minimum.
Therefore, the times at which v(t) has a local minimum and maximum are 3/48 s and 3/48 s, respectively, expressed as two numbers separated by a comma: 3/48 s, 3/48 s.
To know more about Calculus
https://brainly.com/question/24430269
#SPJ4
How many liters of pure water should be mixed with a 5 liter solution of 80% acid to produce a mixture that is 70% water?
14 litres of an 80% acid solution, Let the amount of water needed to create a solution with 60% water be x litres.
What is the mixing of pure water to produce a mixture?Distilled water or pure water are not mixtures. When there are simply water molecules present, there are no additional pollutants or components in the water, making it pure.
A pure material or compound made of oxygen and hydrogen is called water. A mixture would be water that has other substances physically dissolved in it.
20% * 14=0.2*14=2.8 L of water is what you have now
(2.8+x)/(14+x)=60% (amount of water/total amount of solution must equal 60%)
(2.8+x)/(14+x)=60/100
Simplify the fraction 60/100 to 3/5
(2.8+x)/(14+x)=3/5
Cross multiply
5(2.8+x)=3(14+x)
14+5x=42+3x
5x-3x=42-14
2x=28
X=28/2
X=14 L of pure water must be added
Check:
14+2.8=16.8 and 14+14=28
16.8/28=168/280=42/70=6/10=60/100=60%
Therefore, 60% litres of pure water should be mixed with a 5 litre solution of 80% acid to produce a mixture that is 70% water
Learn more about pure water here:
https://brainly.com/question/14468224
#SPJ1
perimeter of triangle qts
The perimeter of triangle QRS is 36 cm.
What is the perimeter of triangle?Add the lengths of the triangle's sides to find its perimeter. For instance, if a triangle has sides a, b, and c, the perimeter of that triangle is P = a + b + c.In the given triangle QRS,
SQ + RS + RQ = Perimeter of triangle QRS
Locate SQ:
10 cm = SN = SM (tangents drawn from an external point)
2 cm = QL + QN (tangents drawn from an external point)
SN + NQ = SQ
SQ = 10 + 2 = 12 cm
Locate RS:
RM + MS = RS
8 - 2 = 6 cm RM = RL
MS = 10 cm (given)
Therefore,
RS = 6 + 10 = 16 cm
RQ = 8 cm (given) (given)
Thus:
SQ + RS + RQ = Perimeter
Circumference = 12 + 16 + 8 = 36 cm
The complete question:
"Find the perimeter of triangle QRS
Figure is attached below."
To learn more about perimeter refer to :
https://brainly.com/question/24299023
#SPJ1
4068+55n/60+n=64.1 what is the value of n?
Answer:
n=212.9
Step-by-step explanation:
= 4068 + 55n/60 + n = 64.1
= 4068 + 55n = 64.1 ( 60 + n )
= 4068 + 55n = 3846 + 64.1n
= 55n - 64.1 = 3846 - 4068
= - 9.1n = 222
= -9.1n/-9.1 = 222/-9.1
n = 212.9.
a family wants to purchase a house that cost 135,000 they plan to take out a 115,000 mortgage on the house nad put 20,000 as a down payment. the bank informs them that with a 15 year mortgage their monthly payment would be 776.85 and with a 30 year mortgage their monthly payment would be 537.31 determine the amount they would save on the cost of the house if they selected the 25 year mortgage rather than the 30 year mortgage
The amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is $55,398.6
What is the interest rate?Interest is the fee paid for having access to borrowed funds. While the interest rate used to compute interest is often reported as an annual percentage rate, interest expense or revenue is sometimes expressed as a dollar figure (APR). The compensation a lender or financial organization receives for giving out money is called interest.
Given a family wants to purchase a house that cost $135,000,
down payment = $20,000
mortgage = $1,15,000
Case 1: For a 15-year mortgage their monthly payment would be 776.85
there will be 12 payments in a year
total amount to be paid in 15 years = 15*12*776.85
total amount to be paid in 15 years = $1,38,033
Case 2: For a 30-year mortgage their monthly payment would be 537.31
total amount to be paid in 30 years = 30*12*537.31
total amount to be paid in 30 years = $1,93,431.6
the amount they would save on the cost of the house if they selected the 15-year mortgage rather than the 30-year mortgage is
$1,38,033 - $1,93,431.6 = $55,398.6
Hence the amount they would save is $55,398.6.
Learn more about interest rate;
https://brainly.com/question/13324776
#SPJ1
The correct question is,
determine the amount they would save on the cost of the house if they selected the 15 year mortgage rather than the 30 year mortgage.
NO LINKS!!
Water covers 708%, or about 3.61 x 10⁸ km², of the Earth's surface. Approximate the total surface area of the Earth. (Round your answer to the nearest million.)
____________ km²
510,000,000 million km²
Let us represent the total surface area of the earth as = x
We are told in the question that:
Water covers 70.8%, or about 3.61 × 10⁸ km², of the Earth's surface.
70.8% = 0.708
Hence,
0.708 × x = 3.61 × 10⁸
x = 3.61 × 10⁸/0.708
x = 361000000/0.708
x = 509,887,005.65km²
Therefore, the total surface are the earth approximately to the nearest million = 510,000,000 million km²
This is the number "510 million"
=======================================================
Work Shown:
The times 10⁸ means "times 100 million"
3.61 x 10⁸ = 3.61 * 100 million = 361 million
S = surface area of the earth
70.8% of S = water coverage area
70.8% of S = 361 million square km
0.708S = 361 million square km
S = (361/0.708) million square km
S = 509.887 million square km
S = 510 million square km
S = 510,000,000 square km
in triangle abc, m is the midpoint of ab, n is the midpoint of ac, and g is the intersection of bn and cm. the area of triangle gmn is 6. find the area of triangle gbc.
The area of the triangle GBC for the given condition of midpoint with a given area of ΔGMN = 6 equals 24.
In triangle ABC,
M is the midpoint of AB , N is the midpoint of AC
⇒ MN is parallel to BC
G is the intersection of BN and CM.
⇒ G is the centroid.
Centroid divides the line segment BN and CM in the ratio
BG : GN = 2 : 1
CG : GM = 2 : 1
In ΔGMN and ΔGBC ,
MN || BC , BN and CM are transversal.
∠NMG ≅∠BCG ( alternate angles)
∠MNG ≅ ∠CBG ( alternate angles)
∠MGN ≅∠BGC ( vertically opposite angles )
By AA corollary,
ΔGMN is similar to ΔGBC
BG : GN = CG : GM
Area of triangle GMN = 6
Area of ΔGBC / Area of ΔGMN = Square of the sides
⇒ Area of ΔGBC / 6 = ( 2 / 1 )²
⇒ Area of ΔGBC = 4 ( 6)
⇒ Area of ΔGBC = 24
Therefore, the area of the triangle GBC is equal to 24.
Learn more about area here
brainly.com/question/27683633
#SPJ4
PERSEVERE In rectangle ABCD, m∠EAB=(4x+6)° , m∠DEC=(10−11y)° , and m∠EBC=60° . Find the values of x and y.
The measure of angle x = 50° and y = 40°.
What is angle?A angle is formed when two rays intersect. The point of intersection is called the vertex point .
Given is that in rectangle ABCD in which -
m ∠EAB = (4x+6)°
m ∠DEC = (10−11y)°
m ∠EBC = 60°
We can write -
∠AEB = ∠DEC = (10 - 11y)°
Now, we know that the external angle is the sum of two interior opposite angles. So -
∠EBC = (4x + 6) + (10 - 11y)
4x - 11y + 16 = 60
4x - 11y = 54
and
(4x + 6) + (10 - 11y) + 30 = 180
4x - 11y = 144
Solving graphically, we get -
x = 50°
y = 40°
Therefore, the measure of angle x = 50° and y = 40°.
To solve more questions on angles, visit the link below-
brainly.com/question/1041084
#SPJ1
Consider the following distribution of scores with a mean of 50 and a standard deviation of 10. For the letters A, B, C, and D in the boxes beneath the line labeled "z" give the z-scores corresponding to each position in the distribution. One 2-score is already filled in (-1). Suppose you also want to standardize these scores to a "K" scale where the mean of k is 100 and the standard deviation is 20. For the letters E, F, G, and H in the boxes beneath the line labeled "k" give the k-scores corresponding to each position in the distribution. One k-score is already filled in (120).
The value of the z-score corresponding to each position in the distribution is given by = { -2 , -1 , 0 , 1 , 2 }
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the z-scores corresponding to each position in the distribution be z
Now , the equation will be
The mean of the data μ = 50
The standard deviation of the data σ = 10
The value of x for the letters A, B, C, and D is given by { 30 , 50 , 60 , 70 }
Substituting the values in the equation , we get
The Z-score is calculated using the formula:
z = (x - μ)/σ
For letter A ,
z = ( 30 - 50 ) / 10
On simplifying the equation , we get
z = -20/10
z = -2
And , for letter B ,
z = ( 50 - 50 ) / 10
z = 0/10
z = 0
For letter C ,
z = ( 60 - 50 ) / 10
z = 10/10
z = 1
For letter D ,
z = ( 70 - 50 ) / 10
z = 20/10
z = 2
Now , the k-scores of the letters E , F , G and H is calculated by
The mean of the letters = 100
The standard deviation of the letters = 20
So , the k-scores of the letters are = { 60 , 80 , 100 , 140 }
Now , the mean of the data is given by = ( 60 + 80 + 100 + 120 + 140 ) / 5
So , the mean is μ = 500/5 = 100
Hence , the z-scores of the letters are solved
To learn more about z-score click :
https://brainly.com/question/25638875
#SPJ1
use the spinner to identify the probability to the nearest hundredth of the pointer landing on a non-shaded area. 0.66 0.26 0.34 0.60
Option A is the correct answer. The probability of the nearest hundredth of the pointer landing on a non-shaded area is 0.66.
An angle of a circle is an angle that is formed between the radii, chords, or tangents of a circle. It contains a total of 360° degrees all the way around the center.
To know the Probability of the non-shaded area first we have to add the shaded area.
The sum of the shaded angles 48°+45°+122°+52° =145°.
As we know that the total angle of a circle=360°.
Now divide the sum of the shaded angles by the total angle of the circle.
i.e=145°/360°
non-shaded area=0.66
To know more about Angles in a circle:
https://brainly.com/question/14165263
#SPJ4
Iced tea 3/16, Fruit juice, 4/16 Water 7/16 Soda 2/16. What combination of beverages makes up 3/4 of the student votes?
Answer: Iced tea, Water, and Soda, or 12/16
Step-by-step explanation: 3/4 of 16/16 is 12/16, and 7/16+3/16+2/16=12/16
Q. 5. A newspaper boy buys magazines for Rs.13 each and sells them for Rs.18 each. He cannot return the unsold magazine. The past record of sales is as follows:. Sales Prob. 23 .05 24 .10 25 .15 26 .30 27 .20 28 .10 i) Prepare the opportunity loss table ii) Select the optimal act using expected opportunity loss criterion. iii) Find EVPI 29 .05 30 .05
Thus, 25 newspapers are required to make the most profit.
How to find the calculation?Profit is the amount of money you have after covering business expenses.
Gross, operational, and net profits are the three basic categories of profit.
Profit potential, p = S p C + C b
S p = Selling price
C = Unit cost of purchase
C b Goodwill lost per unit due to backorders or shortages
p ′ = 12 − 8 + 1.5
= ₹ 5.5
l = C - C b + C h, where C is the loss per unit.
A = Scrap value/unit
holding cost/unit = C
l = 8 − 2 + 0
l = ₹ 6
p ( S − 1 ) ≤ p /p + l ≤ p ( s )
At this point, p / p + l = 5.5 / 5.5 + 6 = 0.4783 = 47.83 %
Thus, 25 newspapers are required to make the most profit.
The Complete Question.
To Learn more About profit Refer To:
https://brainly.com/question/1078746
#SPJ1
PLEASE PLEASE HELPP!! explanation too !!!
Answer:
correct
Step-by-step explanation:
y=x²
if you calculate the square of x, they all equal to Y
Answer:
Susie is correct
Step-by-step explanation:
The relationship between this function is that each x-value is being multiplied by a square of 2 to get the y-value.
-4²= 16
-2²=4
0²=0
2²=4
4²=16
6²=36
I hope this helps!
please help with my math please, please, please!
Answer: 3 1/3
2/3 x 5 = 10/3 = 3 1/3
2 x 5/3 = 10/3 = 3 1/3
Answer:
[tex]= \dfrac{10}{3}[/tex]
Step-by-step explanation:
We can rewrite any whole number as itself over 1.
For example, [tex]5 = \dfrac{5}{1}[/tex].
We can use this tactic to rewrite one of the given (equivalent) expressions. I'll use the one on the left side of the equation.
[tex]\dfrac{2}{3} \times 5 = \dfrac{2}{3} \times \dfrac{5}{1}[/tex]
Then, we can simplify the multiplication of fractions by multiplying out the both the numerators and denominators.
[tex]= \dfrac{2}{3} \times \dfrac{5}{1}[/tex]
[tex]= \dfrac{2\times 5}{3 \times 1}[/tex]
[tex]= \dfrac{10}{3}[/tex]
During the time interval 4 ≤ t ≤ 8, the rate at which the number of wolves in a forest is changing, in wolves per week, can be modeled by the function
E(t) = 31 cos(0.11t^2), where t is measured in weeks.
What is the rate at which the number of wolves in the
forest is changing at timet = 7? You may use a
calculator and round to the nearest thousandth. Indicate units of measure.
The rate at which the number of wolves in the forest is changing at t = 7 weeks is 20.932 wolves per week.
Finding the rate at which the number of wolves in the forest is changing
To find the rate at which the number of wolves in the forest is changing at t = 7 weeks, we can evaluate the function E(t) at t = 7:
E(7) = 31 cos(0.11 * 7^2) = 31 cos(4.97)
Using a calculator, we can find that cos(4.97) = 0.672. So,
E(7) = 31 X 0.672 = 20.932
This means that the rate at which the number of wolves in the forest is changing at t = 7 weeks is 20.932 wolves per week.
Learn more here to find rate :https://brainly.com/question/12089628
#SPJ1
2. Given that ADEF : ALMN, which angle
is congruent to
Answer:
4/7
Step-by-step explanation:
=> The simplest form of
56
:
98
56:98 is
4
:
7.
4:7.
Step-by-step explanation:
Given ratio -
56
:
98
56:98
We have to reduce it to its simplest form,
For that, we have to find the GCD of the numerator as well as the denominator:
So, the GCD for
56
56 and
98
98 is
14.
14.
Now, divide both the numerator and denominator by the GCD:
=
>
56
÷
14
98
÷
14
=>
98÷14
56÷14
=
>
4
7
=>
7
4
Hence, the simplest form is
4
:
7.
4:7.
Find the radius of a pencil with a volume of 110 π mm³, a cone height of 3mm, and a cylinder height of 10 mm.
The radius of the pencil is 3.32mm
How to determine the radius of the pencilThe formula for determining the volume of a cylinder is expressed as;
V = πr²h
Given that the parameters are;
V is the volume of a cylinderπ takes the value 3. 14 or 22/7r is the radius of the cylinderh is the height of the cylinderFrom the information given, we have that;
The volume of the cylinder = 110 π mm³
The height of the cylinder = 10mm
Now, substitute the values, we get
110π = πr² × 10
Multiply the values
110π = 10πr²
Divide both sides by the coefficient of r², we get;
r² = 110π/10
r² = 11
Find the square root of both sides
r = 3. 32mm
Hence, the value is 3.32mm
Learn about cylinders here:
https://brainly.com/question/76387
#SPJ1
write a formulat to show the relationship between lateral area and the length of a side of the base and slant height in a square pyramid
The formula of the relationship between lateral area and the length of a side of the base and slant height in a square pyramid is 2sh.
The lateral area of a square pyramid is defined as the area covered by its slant of lateral faces. One side of each of these triangles coincides with one side of the base polygon.
The lateral area is the area of the faces of the pyramid without the base.
Each face is a triangle with base "s" and a height the same as the slant height - let's consider it as "h."
The area of each face is =0.5sh.
For the four faces the lateral area is 4*0.5sh=2sh.
To know more about the lateral area:
https://brainly.com/question/1601740
#SPJ4
Need help solving these two questions
The domain and the range of the functions are:
Function 1: Domain & Range = (-∝, +∝)Function 2: Domain = (-∝, -5) U (-5, +∝) & Range = {(3), (5, +∝)}How to determine the domain and the rangeFunction 1
Given that
f(x) = 5x - 2, x < 1
x - 7, x ≥ 1
The functions in the piecewise function are linear functions
Because there are no hole in the domain value, this means that the range and the domain are the set of real numbers
Function 2
Given that
g(x) = -x , x < -5
3, x > -5
The functions in the piecewise function are also linear functions
However, there is a hole in the domain value at x = -5
This means that the domain incudes all real values except -5
While the range is 3 and values greater than 5
Read more domain and range at
https://brainly.com/question/2264373
#SPJ1
The domain and range of the two piecewise functions are:
D = (-∞,∞); R = (-∞,∞)D = (-∞,-5)∪ (-5,∞); R = (3,∞)Please refer to the attached graphs below for each piecewise function's graph.
f(x) = {5x-2, if x < 1}
{x - 7, if x ≥ 1}
From the given function, we can make the first graph. We know that the domain for each function individually are:
f(x) = 5x - 2, if x < 1
dom f(x) = (-∞,1)
Range = (-∞, 3)
f(x) = x - 7, if x ≥ 1
dom f(x) = (1, ∞)
Range = (-6, ∞)
By combining both function's domains and range, we can find the piecewise function domain and range are:
D = (-∞,∞) --> include 1
R = (-∞,∞)
g(x) = {-x, if x < -5}
{3, if x > -5}
From the given function, we know each domain and range are:
g(x) = -x, if x < -5
dom g(x) = (-∞, -5)
Range = (5, ∞)
g(x) = 3, if x > -5
dom g(x) = (-5, ∞)
Range = 3
By combining both functions' domain and range, we got:
dom = (-∞, -5) ∪ (-5,∞) --> not including 5
Range = (3, ∞)
Learn more about Piecewise Functions here: brainly.com/question/17883583
#SPJ1
In a hotel, restaurant sales were 2/3 of accommodation sales. Restaurant sales and accommodation
sales totally were € 200 000 per month, then
A. Restaurant sales were € 60 000 per month
B. Restaurant sales were € 66 666 per month
C. Accommodation sales were 80.000 per month
D. Accommodation sales were € 150 000 per month
E. Accommodation sales were € 120 000 per month
Answer:
E. Accommodation sales were € 120 000 per month
Step-by-step explanation:
[tex]1 + \frac{2}{3} = \frac{5}{3} [/tex]
[tex]restaurant \: sales \: = \frac{200 \: 000}{5} \times 2 = 80 \: 000[/tex]
[tex]accommondation \: sales = \frac{200 \: 000}{5} \times 3 = 120 \: 000[/tex]
there are 56 runners in a race how many ways can the runners finish first, second and third?
The number of ways in which the runners can finish first, second and third as required from the task content is; 166,320 ways.
What is the number of ways in which runners can finish first, second and third?It follows from the task content that the number of ways in which runners can finish first, second and third is to be determined from a total of 56 runners.
On this note, this situation describes an arrangement and hence is best represented as a permutation as follows;
⁵⁶P₃
= 166,320.
Ultimately, the number of ways in which the runners can finish is; 166,320.
Read more on permutations;
https://brainly.com/question/28065038
#SPJ1
Find the slope of the line passing through the points (-4, 4) (-4, -2)
Answer:
(-2 - 4) / (-4 - 4) = -2 / 0 = -2
Step-by-step explanation:
The slope of the line passing through the points (-4 [1] [2], 4) and (-4, -2) is -2. This can be calculated using the formula m = (y2 - y1) / (x2 - x1), which in this case would be (-2 - 4) / (-4 - 4) = -2 / 0 = -2.
You Welcome! :)
Pls help and do it as fast as you can
Answer:
what can i do please send me a question?
The third option from the top is correct
Widgets'R'Us created a monthly expense equation, E = 1.48q + 4,830. The company plans to sell their widgets to retailers at a price of $3.98. How many widgets must be sold to reach the breakeven point?
Using the expense and revenue equations above, if Widgets'R'Us sells 5,430 widgets, what will their profit be?
a) The number of widgets that Widgets"R'U must sell to reach the break-even point is 2,082 units.
b) Using the expense and revenue equations, if Widgets'R'Us sells 5,430 widgets, their profit will be $8,745.
What is the profit equation?The profit equation is total revenue minus total costs.
The profit equation shows that profit is a function of the difference between the total revenue realized from sales and services less the total costs involved in rendering the services or delivering the goods.
At the break-even point, the total revenue equals the total costs. Therefore, there is no profit or loss.
The total cost function, E = 1.48q + 4,830
The total revenue function, R = 3.98q
To break even, the quantity to be sold, q, 1.48q + 4,830 = 3.98q
-2.32q = -4,830
q = 2,082
When q = 5,430:
Profit = 3.98q - (1.48q + 4,830)
= 3.98(5,430) - (1.48 x 5,430 + 4,830)
= 21,611.4 - (12,866.4
= 8,745
= $8,745
Learn more about the profit function at https://brainly.com/question/18529899
#SPJ1
Revisit Exercise 1.2.18 about the study on Rhesus monkeys. When given a choice between two boxes, 30 out of 40 monkeys approached the box that the human had gestured toward, and 10 approached the other box. The purpose is to investigate whether rhesus monkeys can interpret human gestures better than random chance.
1.3.16 For this study:
a. State the null hypothesis and the alternative hypothesis in the context of the study.
b. Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution in an applet.)
c. Interpret the standardized statistic in the context of the study. (Hint: You need to talk about the value of your observed statistic in terms of standard deviations assuming ______ is true.)
d. Based on the standardized statistic, state the conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.
Null hypothesis [tex]H_0[/tex] : p = 0.5 and alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]
The standardized statistic from the data is 3.1623
The observed standardized statistic is 3.1623
Based on the standardized statistic, we conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.
As per the given data: a choice between two boxes, 30 out of 40 monkeys approached the box that the human had gestured toward, and 10 approached the other box.
Here, p = proportion of rhesus monkeys who tan interpret human gestures better.
a) Null hypothesis [tex]H_0[/tex] : p = 0.5
Alternative hypothesis [tex]H_1: $p \neq 0.5$[/tex]
b) Given, [tex]$\hat{p}=\frac{x}{n}=\frac{30}{40}=0.75, p_0=0.5$[/tex]
Standardized test statistic,
[tex]$Z=\frac{\hat{p}-p_0}{\frac{p_0\left(1-p_0\right)}{n}} \stackrel{H_0}{\sim} N(0,1)$[/tex]
Therefore the standardized statistic from the data = 3.1623
c) Assuming [tex]$H_0$[/tex] is true, the value of the observed standardized statistic is 3.1623 standard deviations above the mean(=0).
d) Now, p-value [tex]$=2 \times \min [p(z > 3.1623), p(z \leq 3.1623)]$[/tex]
= 0.00157
Since p-value <0.05, we reject [tex]$H_0$[/tex].
We conclude that there is enough evidence to suggest that these monkeys can interpret human gestures better than random chance.
For more questions on hypothesis
https://brainly.com/question/6862488
#SPJ4
please help me with this question
Answer:
The perimeter is 25.71 cm-------------------------------
The perimeter of given semicircle is the sum of the diameter and half of the circumference:
P = d + πd/2P = 10 + 3.142*10/2 = 10 + 15.71 = 25.71 cmFind the least squares approximating line y=zo + zix for each of the following sets of data points. a. (1, 1), (3, 2), (4, 3), (6, 4) b. (2, 4), (4,3), (7, 2), (8, 1) c. (-1, -1), (0, 1), (1, 2), (2, 4), (3, 6) d. (-2, 3), (-1, 1), (0, 0), (1, -2), (2, -4)
The least squares approximating line y=zo + zix for each of the following sets of data points is (1, 1), (3, 2), (4, 3), (6, 4)
This line is determined by minimizing the distance between the data points and the line. The method of least squares is used in many areas, including regression analysis and trend analysis.
To find the least squares approximating line for a set of data points, you need to use the following formula:
=> y = b0 + b1x,
where b0 is the y-intercept and b1 is the slope of the line.
You can use this formula to find the values of b0 and b1 that minimize the difference between the data points and the line.
For example, let's take a look at the first set of data points (1, 1), (3, 2), (4, 3), (6, 4). To find the least squares approximating line, we need to calculate the values of b0 and b1.
This can be done by using a mathematical formula that involves finding the sum of the squares of the differences between the data points and the line.
Therefore, option (a) is correct.
To know more about lines here.
https://brainly.com/question/25727583
#SPJ4
Find the volume of the triangular prism.
18 ft12 ft20 ft15 ft15 ft
B =
1
2
bh =
1
2
(18)(12) = 108
V = Bh = (()(20)) = ft3
The volume of the triangular prism is 2,160 ft³.
How to find the prism's volume?The volume of a triangular prism can be calculated using the formula V = BH, where B is the area of the base of the triangle and H is the height of the prism.
In this case, the base of the triangle is 1 / 2 bh = 1 / 2 (18 x 12) = 108 square ft. The height of the prism is 20 ft. Therefore, the volume of the triangular prism is V = Bh = ((108 sq ft) (20 ft)) cubic ft = 2,160 ft³.
Find out more on triangular prism here: https://brainly.com/question/1284982
#SPJ1
Which of the following is equal to the rational expression when x≠-6?
x²-36
——
x+6
A. x + 6
B. x-6
C. x² - 6
D. 1
—
x- 6
the option b is equal to the rational expression when x≠-6?
Answer:
[tex]\dashrightarrow \: \frac{ {x}^{2} - 36}{x + 6} \\ \\ \dashrightarrow \: \frac{( \cancel{x + 6})(x - 6)}{\cancel{x + 6}} \\ \\ \dashrightarrow\boxed{ \: x - 6 \: }[/tex]
therefore , option ( B ) is correct.
• Step 2 was done by keeping in mind the algebraic identity "a² - b² = ( a + b )( a - b)"
hope helpful! :)
