The relation {(a, b), (b, c), (c, c)} does not represent a function because for the input value "c", there are two possible output values, "c" and "c". In a function, for each input value, there can only be one output value.
The vertical line test may be used to assess whether or not a relation is a function by looking at its graph.
If each input value results in just one output value, the relationship is classified as a function. If any input value results in two or more outputs, the relationship is not a function.
To establish if a graph reflects a function, use the vertical line test. If a vertical line is dragged across the graph and only touches the graph at one location at any time, the graph is a function. If the vertical line intersects the graph more than once, the graph is not a function.
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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]
Give the first six terms of the following sequences. A.The first term is 1 and the second term is 2. The rest of the terms are the product of the two preceding terms. B..a_1, a_2 = 5, and a_n = 2 times a_n - 1 + 3 times a_n - 2 for n greaterthanorequalto 2. C.g_1 = 2 and g_2 =1. The rest of the terms are given by the formula g_n = n times g_n - 1 + g_n-2.
The first 6 terms of the given sequences are for A: 1, 2, 2, 4, 8, 16
for B: 5, 5, 17, 59, 177, 521, and for C: 2, 1, 3, 6, 15, 45
A. The 1st sequence is a geometric sequence, where each term is the product of the two preceding terms. The 1st term is 1, the 2nd term is 2, and the rest of the terms are calculated as below:
a3 = a1 * a2 = 1 * 2 = 2
a4 = a2 * a3 = 2 * 2 = 4
a5 = a3 * a4 = 2 * 4 = 8
a6 = a4 * a5 = 4 * 8 = 16
So, the first six terms of the sequence are 1, 2, 2, 4, 8, and 16.
B. The 2nd sequence can be calculated by using the formula
an = 2 * an - 1 + 3 * an - 2 for n greater than or equal to 2. The 1st term a1 is 5 and the 2nd term a2 is 5, so the rest of the terms are calculated as below:
a3 = 2 * a2 + 3 * a1 = 2 * 5 + 3 * 5 = 17
a4 = 2 * a3 + 3 * a2 = 2 * 17 + 3 * 5 = 59
a5 = 2 * a4 + 3 * a3 = 2 * 59 + 3 * 17 = 177
a6 = 2 * a5 + 3 * a4 = 2 * 177 + 3 * 59 = 521
So, the first six terms of the sequence are 5, 5, 17, 59, 177, and 521.
C. The 3rd sequence follows the formula gn = n * gn - 1 + gn - 2. The 1st term g1 is 2 and the 2nd term g2 is 1, so the rest of the terms are calculated as below:
g3 = 3 * g2 + g1 = 3 * 1 + 2 = 5
g4 = 4 * g3 + g2 = 4 * 5 + 1 = 21
g5 = 5 * g4 + g3 = 5 * 21 + 5 = 110
g6 = 6 * g5 + g4 = 6 * 110 + 21 = 786
So, the first six terms of the sequence are 2, 1, 3, 6, 15, and 45.
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What to work this problem
The value of ∠x in the given triangle is 33° i.e. B.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
As we know
The sum of all the three angles of a triangle =180°
x+105+42=180
∠x=33°
hence,
The value of ∠x in the given triangle is 33°.
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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.
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Fill in the blank with the most appropriate term A company did a study on the physical activity level and weight gain of its employees. Age was not considered so it might be an example of an Answer 2 Points 1 Tables Keypad Keyboard Shortcuts O Confounding Variable
O Response Variable
O Explanatory Variable O Placebo
O Control Variable
A company did a study on the physical activity level and weight gain of its employees. Age was not considered, so it might be an example of a confounding variable.
A confounding variable is an unmeasured third variable that influences, or confounds, the relationship between an independent and a dependent variable. For example, in a study looking at the relationship between smoking and lung cancer, age may be a confounding variable because people who smoke tend to be older than those who do not.
This would mean that age is influencing both smoking and the risk of lung cancer, so the true effect of smoking on the risk of lung cancer cannot be determined without taking age into account. The presence of a confounding variable can distort the results of an experiment and lead to inaccurate conclusions.
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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.
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Find KJ
What the answer
For the given triangles ΔABC ≈ ΔBKJ, the value of KJ is, 9
What is similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
The triangle, ΔABC
one segment KJ which is intersecting sides AB & BC
ΔABC has one similar triangle inside, which is ΔBKJ
Triangle ΔABC and ΔBKJ similar,
So, we can say ΔABC ≈ ΔBKJ
And it is known that
for similar triangles, ratio of lengths of sides are equal for similar triangles
so, AB/AC = KB/KJ
AB = 2KB
⇒ 2KB/18 = KB/KJ
⇒ 2/18 = 1/KJ
⇒ KJ = 9
Hence, the length of KJ is 9 unit
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To have a balanced budget, you must: *
Ohave your net income equal your spending and savings.
have your gross pay equal your spending and savings.
Ohave your net income equal your gross income.
Ohave your gross pay equal your spending.
1 point
To have a balanced budget, you must B. have your gross pay equal your spending and savings.
What is a balanced budget ?A balanced budget is a financial plan in which expenses are equal to or less than the amount of revenue generated. This means that the government or organization is not spending more money than it takes in and is not running a deficit. The result is a balanced financial position, where there is no debt and assets are equal to liabilities.
This indicates that there is no shortfall and that the person is spending just what they get as their gross income.
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The x-coordinates of the solutions to a system of equations are 3.5 and 6. Which of the following could be the system? （ ）A. y=x+3.5 y=x^2+6B. y=2x-7 y=-(x-6)^2C. y=12x+3 y=-(x-5)^2+7D. y=12x+7 y=-(x-6)^2+3.5
The system of equations that has a solution with x-coordinate of 3.5 and 6 is C. y = 1/2x + 3 and y = -(x - 5)² + 7.
To determine if a coordinate is a solution to a system of equations, substitute the values for the x and y in both equations and check if both resulting equations are true. If both resulting equations are true, then the coordinate is a solution to the system of equations.
A. y = x + 3.5
y = 3.5 + 3.5 = 7
y = x² + 6
7 = 3.5² + 6
7 ≠ 18.25
B. y = x - 7
y = 3.5 - 7 = -3.5
y = -(x - 6)²
-3.5 = -(3.5 - 6)²
-3.5 ≠ -6.25
C. y = 1/2x + 3
y = 1/2(3.5) + 3 = 4.75
y = -(x - 5)² + 7
4.75 = -(3.5 - 5)² + 7
4.75 = 4.75
y = 1/2x + 3
y = 1/2(6) + 3 = 6
y = -(x - 5)² + 7
6 = -(6 - 5)² + 7
6 = 6
D. y = 1/2x + 7
y = 1/2(3.5) + 7 = 8.75
y = -(x - 6)² + 3.5
8.75 = -(3.5 - 6)² + 3.5
8.75 ≠ -2.75
Only the system of equation in option C holds the equations true, hence, C. y = 1/2x + 3 and y = -(x - 5)² + 7 are the system of equations that has the given solution stated in the problem.
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Which of the following numerical expressions results in a positive number? (-67) - 12 - 25 (-67) - (-76) (-67) - (-12) (-67) - (-25)
From the following numerical expressions given, the numerical expression which results in a positive number is (-67) - (-12).
In mathematics, subtraction is the process of finding the difference between two numbers. If two numbers have the same sign (both positive or both negative), the result of their subtraction will have the same sign as the numbers being subtracted.
However, if the numbers have different signs, the result of their subtraction will have the sign of the number with the larger absolute value. In this case, (-67) and (-12) have different signs, but (-12) has a larger absolute value than (-67). Therefore, the result of the subtraction will be positive.
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A cylindrical glass is shown at right. The height of the cup is 7 inches. The radius of
the base is 1.5 inches. Use 3.14 for л.
a. How many bases are included in the surface area of the outside of the glass?
b. Find the total surface area of the outside of the glass.
There are 11 1/3 based in the area outside and the total surface area of the outside of the glass is 80.07 square inches
How many bases are includedFrom the question, we have the following parameters that can be used in our computation:
Height, h = 7 inches
Radius, r = 1.5 inches
π = 3.14
The area of the base is calculated as
Base area = πr²
So, we have
Base area = π * 1.5²
Base area = 2.25π
The surface area of the outside of the glass is
Surface area = 2πr(r + h)
So, we have
Surface area = 2π * 1.5 * (1.5 + 7)
Surface area = 25.5π
The number of base is
Number = 25.5π/2.25π
Evaluate
Number = 11 1/3
The total surface area of the outsideIn (a), we have
Surface area = 25.5π
This gives
Surface area = 25.5 * 3.14
Evaluate
Surface area = 80.07
Hence, the area is 80.07 square inches
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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.
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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.
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
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Express each of the following as the sum Of a whole number and a fraction 9/7
Answer:
1 + 2/7
Step-by-step explanation:
9/7 =
(7+2) / 7 =
7/7 + 2/7 = ==> use distribution
1 + 2/7 ==> 7/7 = 1, so simplify the expression
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."
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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
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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, ∞)
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Need some help here i am looking for real answer
The value of expression y ' (2) is, 135/16.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ y = (x - 1/x)³
Now, We can differentiate with respect to x as;
⇒ y (x) = (x - 1/x)³
⇒ y' (x) = 3 (x - 1/x)² × (1 - (-1/x²))
⇒ y' (x) = 3 (x - 1/x)² (1 + 1/x²)
Substitute x = 2;
⇒ y' (2) = 3 (2 - 1/2)² (1 + 1/2²)
⇒ y' (2) = 3 (3/2)² (1 + 1/4)
⇒ y' (2) = 3 × 9/4 × 5/4
⇒ y' (2) = 135/16
Thus, We get;
⇒ y' (2) = 135/16
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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
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easy question so yall can get your points up what is 5 plus 203 .first one gets best answer
Answer:
208
Step-by-step explanation:
someone help !!
geometry: find the value of x
Answer:
x = 18
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 5 , then
sum = 180° × 3 = 540°
sum the 5 interior angles and equate to 540
3x + 23 + 95 + 7x - 4 + 90 + 9x - 6 = 540
19x + 198 = 540 ( subtract 198 from both sides )
19x = 342 ( divide both sides by 19 )
x = 18
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
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.
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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! :)
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.
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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.
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Gina is going to buy 100 stickers
Gina should buy from Stickers4u.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given:
Gina is going to buy 100 stickers.
If she buys from the shop - Stickers4u,
then the cost is,
= 100/25 x 2.15
= 4 x 2.15
= 8.6.
And if she buys from the World stationary,
then the cost is,
= (100 - 50)/10 x 1.65
= 5 x 1.65
= 8.25
Therefore, she should buy from Stickers4u.
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Find 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.
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in the morning, john drove to his mother's house in the village at an average speed of 60 kilometers per hour. when he was going back to town in the evening, he drove more cautiously and his speed was lower. if john went the same distance in the evening as in the morning, what was john's average speed for the entire trip? (1) in the evening, john drove at a constant speed of 40 kilometers per hour. (2) john's morning drive lasted 2 hours.
John's average speed for the entire trip is 50 km/h. So the minimum average speed for the entire trip would be 60 km/h.
To calculate John's average speed, we need to determine the total distance he covered and the total time he spent driving. Given that John drove 60 km/h for 2 hours in the morning, and 40 km/h for a different amount of time in the evening, we can calculate the total distance as follows:
[tex]d = 60 × 2 + 40 × T[/tex]
where T is the total time spent driving in the evening.
To find John's average speed, we need to divide the total distance by the total time:
Average speed = [tex]d / (2 + T)[/tex]
Since we do not know the value of T, we cannot determine the exact average speed. However, we can determine an upper bound on the average speed by assuming that T is 0 (i.e., John drove back to town immediately after arriving at his mother's house). In this case, John's average speed would be equal to the speed he drove in the morning, which was 60 km/h.
Hence the minimum average speed for the entire trip would be 60 km/h, and the maximum average speed would be equal to the speed he drove in the evening, which was 40 km/h. The average of these two speeds is 50 km/h.
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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 cmPLEASE 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!
