The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
The required details for null hypothesis in given paragraph
The null hypothesis and alternative hypothesis in this case would be:
H₀: The distribution of hockey players' birth months is uniformly distributed.
H₁: The distribution of hockey players' birth months is not uniformly distributed.
The expected counts for each birth month can be calculated as follows:
Expected Count = (Total Number of Players) * (Proportion of Total Players for Each Birth Month)
Since there are 4 birth months and the distribution is assumed to be uniform, the proportion of total players for each birth month is 1/4 = 0.25. Therefore, the expected count for each birth month is:
Expected Count = 188 * 0.25 = 47
To test the null hypothesis, we can then calculate the chi-square statistic using the following formula:
χ² = ∑((O - E)² / E)
where O is the observed count, E is the expected count, and the sum is taken over all birth months.
Plugging in the observed and expected counts, we get:
χ² = ((66 - 47)² / 47) + ((59 - 47)² / 47) + ((34 - 47)² / 47) + ((29 - 47)² / 47)
= 3.87 + 2.04 + 3.87 + 5.57
= 15.35
In this case, df = 3.
Looking up the critical value in the chi-square table with df = 3 and a = 0.05, we find that the critical value is 7.815. Since the chi-square statistic (15.35) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the distribution of hockey players' birth months is not uniformly distributed.
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Answer to these required:
Find the value of x. Leave your answer in simplest radical form.
The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]
Explain Pythagoras theorem.
The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.
The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.
Using Pythagoras theorem in both the triangles,
Find the hypotenuse in above triangle
[tex]h^2=P^2+B^2[/tex]
[tex]h^2=4+4=8[/tex]
h = [tex]2\sqrt{2}[/tex]
Now, using Pythagoras theorem in below triangle,
[tex]h^2=P^2+B^2[/tex]
[tex]5^2 = x^{2} + 8[/tex]
25 = [tex]x^{2}[/tex] + 8
[tex]x^{2}[/tex] = 25 - 8 = 17
x = [tex]\sqrt{17}[/tex]
Therefore, x = [tex]\sqrt{17}[/tex]
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Help me thank u very much
Answer:
y = 3x + 2
y = 1/2 x -1
Step-by-step explanation:
The slope intercept form of a line is
y = mx + b You substitute in the slope for m and the y intercept for b
What is the distance between the points (-2,3) and (5, -1)?
Answer:
√65
Step-by-step explanation:
Compute the Euclidean distance between the following points:
p_1 = (-2, 3) and p_2 = (5, -1)
The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:
sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)
Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):
= sqrt((-2 - 5)^2 + (--1 + 3)^2)
(-1)^2 = 1:
= sqrt((-2 - 5)^2 + (1 + 3)^2)
-2 - 5 = -(2 + 5):
= sqrt((-(2 + 5))^2 + (3 + 1)^2)
2 + 5 = 7:
= sqrt((-7)^2 + (3 + 1)^2)
Multiply each exponent in -7 by 2:
= sqrt((-1)^2×7^2 + (3 + 1)^2)
7^2 = 49:
= sqrt((-1)^2×49 + (3 + 1)^2)
(-1)^2 = 1:
= sqrt(49 + (3 + 1)^2)
3 + 1 = 4:
= sqrt(49 + 4^2)
4^2 = 16:
= sqrt(49 + 16)
| 1 |
| 4 | 9
+ | 1 | 6
| 6 | 5:
Answer: √65
Graph this line y+4=1/4(x+10)
Answer:
goes from(6,0),(10,1),(14,2) in +ve
y + 3 = (x - 6)
“Identify the slope and a point on a line, then graph the line”
How would I graph it with no slope and only one point?
Answer:
see attached
Step-by-step explanation:
Given the equation for a line, y +3 = (x -6), you want to identify the slope and a point on the line, then graph it.
Point-slope formThe point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)
Comparing this to the given equation, you can see ...
k = -3m = 1 . . . . . . . . . . a coefficient of 1 is often "missing" or "implied"h = 6This tells you the slope is 1 and a point on the line is (6, -3).
GraphYou graph this equation by plotting point (6, -3) and drawing a line through it that goes up 1 unit for each 1 unit to the right. A graph is attached.
__
Additional comment
If you like, you can rearrange the equation to slope-intercept form by subtracting 3:
y +3 -3 = (x -6) -3
y = x -9
This tells you another point is -9 on the y-axis.
Tim's mathematics teacher asked him to explain the expression -8. 7. Which answer should Tim give?
A The expression represents 7 groups of 8 positives.
B The expression represents 8 groups of 7 positives.
(C) The expression represents 7 groups of 8 negatives.
(D) The expression represents 8 groups of 7 negatives.
Answer:
C
Step-by-step explanation:
Because it says -8 x 7, the * is negative and the 7 is positive.
The snack bar sold 75% of its inventory of bags of chips. If the snack bar still has 37 bags of chips, how many
bags did they sell?
The bags of chips sold are 111.
What is percentage?The percentage is the term use to tell the hundredth part of something.
Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,
Let the original number of bags of the chips be x,
Since, 75% is already sold, so left number of bags are = 100%-75% = 25%
Therefore,
25% of x = 37
x = 37x4
x = 148
The number of bags sold = 75% of 148
= 75x148/100
= 111
Hence, they sold 111 bags of chips.
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What is the correct to this answer ???????( answers only)
Answer:
x > 24 goes to the bottom
x < 24 goes to the 3rd slot
x ≤ 24 goes to the 1st slot
x ≥ 24 goes to the 2nd slot
Step-by-step explanation:
Hope this helps.
Write an explicit formula for a_n, the n^{\text{th}}n th term of the sequence 6, -24, 96, ...
The explicit formula for the geometric sequence 6, -24, 96, ... is
6 * -4^(n - 1)How to find the formula for the geometric sequenceEvery term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio
The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.
For the given sequence the first term is a = 6
The common ratio is solved as follows
a * r = second term
6 * r = -24
r = -24/6
r = -4
check
-24 * -4 = 96 correct
The nth term of a geometric sequence
= ar^(n - 1)
= a * -4^(n - 1)
checking for the third term
= a * -4^(n - 1)
= 6 * -4^(3 - 1)
= 6 * -4^(2)
= 6 * 16
= 96
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The function f(x) = -x + 2 can be formed by
shifting the function y = -2/3x in which way?
A. vertical shift up 2
B. reflection over the x-axis
C. vertical shift down 2
D. horizontal shift to the left 2
Please Show the Work & thank u
Answer:
A) vertical shift up 2------------------------------
The difference of the functions is:
f(x) - y = - 2/3x + 2 - (- 2/3x) = 2The difference between functions is positive, therefore it is a vertical shift up by 2 units.
Mugs can be packed with up to 6 mugs in each box how many boxes are needed to pack 1528
Choose the slope-intercept form of 3x + 2y = 5. y =
Answer: [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Given: [tex]3x + 2y = 5[/tex]
We are needed to find the slope-intercept form.
We know that the slope-intercept form of an equation is given by
[tex]y = mc + c[/tex]
[tex]3x + 2y = 5[/tex]
[tex]2y = 5 -3x[/tex]
[tex]2y = -3x + 5[/tex]
[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]
To test m for an x distribution that is mound-shaped using
sample size n 30, how do you decide whether to use the normal or the
Student’s t distribution?
To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:
Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.
It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.
What is t distribution?For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.
Hence t-distribution is suitable when the variance which is standard deviation squared is unknown
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Select all that apply.
Which of the following are proportions?
2/8=3/12
3/4=8/10
25/10=5/2
3/4=15/20
In the following proportions:-
A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]
C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]
D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal
What are proportion?
A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.
[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]
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Find an angle θ with 0∘ < θ < 360∘ that has the same:
sine as 30°:∅= degrees
cosine as 30°:∅= degrees
Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees
cosine as 30°:∅= degrees are 150 and 330 degrees.
What is trigonometric function?
Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle
Main Body:
We have to find an angle θ with 0° < θ < 360° that has the same:
(a) sin(30∘)
We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.
sin(30∘)=sin(180∘−30∘)
[∵sin(180∘−θ)=sin(θ)]=sin(150∘)
Thus:
sin as 30∘:θ=150 degrees
(b) cos(30∘)
We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.
cos(30∘)=cos(360∘−30∘)
[∵cos(360∘−θ)=cos(θ)]=cos(330∘)
Thus:cos as 30∘
:θ=330 degrees
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If f(x) = 4x - 5 and g(x) = 6 - 3x, what is f (x) + g(x)?
If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.
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).
We know f(x) + g(x) = (f + g)(x).
Given, f(x) = 4x - 5 and g(x) = 6 - 3x.
∴ f(x) + g(x) = (4x - 5) + (6 - 3x).
f(x) + g(x) = 4x - 3x - 5 + 6.
f(x) + g(x) = x + 1.
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Regroup to express the number in a different way.
71{,}83071,83071, comma, 830 ==equals 7\text{ ten thousands}7 ten thousands7, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus 1\text{ thousand}1 thousand1, start text, space, t, h, o, u, s, a, n, d, end text ++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens3, start text, space, t, e, n, s, end text
71{,}83071,83071, comma, 830 ==equals 6\text{ ten thousands}6 ten thousands6, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus
++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens
Answer:
11 thousands---------------------------------
Given number is 71830.
The last part: 830 is same on both lines.
We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:
71000 - 60000 = 11000It is 11 thousands.
Answer:
11,000 (or) 11 thousands
Step-by-step explanation:
Now we have to,
→ find the missing number.
→ Let the number be x.
Forming the equation,
→ 60,000 + x + 800 + 30 = 71,830
Then the value of x will be,
→ 60,000 + x + 800 + 30 = 71,830
→ x + 60,830 = 71,830
→ x = 71,830 - 60,830
→ [ x = 11,000 ]
Hence, the value of x is 11,000.
A transversal runs across two parallel lines, forming two angles. One measures 80 degrees. How large is the other angle
Answer:
100°
Step-by-step explanation:
180°- 80°= 100°
The angles are supplementary, meaning that they have to add up to 180.
Hope this helps!!! :)
Three less than the product of 7and a number is 4 .
Answer:
Step-by-step explanation:
Let
n--------> the number
we know that
1) the sentence" Three less than the product of seven and a number" represent the expression------>
2) the sentence" is four more than the number"
represent the expression ------->
3) the complete sentence" Three less than the product of seven and a number is four more than the number" represent the expression
represent the expression ------->
therefore
the answer is
(7n-3) =(n+4)
leght multipy by breath
Answer:
equal to area of rectangle
Step-by-step explanation:
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HELP PLEASEEE
A party rental company has chairs and tables to rent. There were two customers who rented both chairs and tables last week. The table below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.
By setting up the equation, we get the system of linear equations are
9x + 7y = 77
3x + 5y = 49
solving these equation Cost to rent a chair = $1.75
cost to rent a table = $8.75
What is system of linear equation?A system of linear equations is a collection of one or more linear equations involving the same variables.
What are the method to solve system of linear equations?There are several methods for solving systems of linear equations, including:
Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.
Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.
Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.
etc.
To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.
First, solve the first equation for y:
9x + 7y = 77
7y = -9x + 77
y = (-9/7)x + 11
Now substitute this expression for y into the second equation:
3x + 5((-9/7)x + 5(11) = 49
3x - (45/7)x + 55 = 49
solving for x :
x = 1.75
Now substitute this value for x back into the first equation to find y:
y = 8.75
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Find a formula for the exponential function passing through the points(-1,4/5) and (1 , 20)
y=
The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
How to derive the exponential function containing two given points
In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:
y = A · [tex]e^{B\cdot x}[/tex]
Where:
x - Independent variable.y - Dependent variable. A, B - Constants.If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:
4 / 5 = A · [tex]e^{-B}[/tex]
20 = A · [tex]e^{B}[/tex]
If we divide the latter expression by the former, then:
25 = [tex]e^{2\cdot B}[/tex]
㏑ 25 = 2 · B
B = (1 / 2) · ㏑ 25
B ≈ 1.609
And the value of A is:
A = 20 / [tex]e^{1.609}[/tex]
A ≈ 4.002
The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
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Aspen incorrectly converted 15/8 to a decimal using long division. Check her work carefully to find the error. Select the digit where she first made a mistake.
The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.
The correct long division is shown below.
This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.
Nina deposited $6,000 in a savings account with simple interest. Six months later, the
account held $6,270. What was the interest rate?
Answer:
Step-by-step explanation: 270
Help me thank y so much
The relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
Is a function, because each element in the domain is mapped to a single element in the range.
Do the ordered pairs represent a function?A relation maps elements from one set, called the domain, into another set, called the range.
For example, the element x mapped into element y is written as (x, y).
Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.
So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).
Here the relation is:
(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)
So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.
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A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
The number of liters in the tank after 109 seconds is 60.5 liters.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
2.5 liters = 1 minute
2.5 liters = 60 seconds
Multiply 109/60 on both sides.
109/60 x 2.5 liters = 109 seconds
4.5 liters = 109 seconds
This means,
4.5 liters is drained after 109 seconds
Now,
The liters of water in the tank.
= 65 - 4.5
= 60.5 liters
Thus,
There are 60.5 liters in the tank.
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
In 11.56 years the given amount of $ 900 will be double.
What is Compound interest:The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.
The formula used for
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest in decimal
n = Number of compounds per year
t = Time period
Here from the given data,
Principal amount, p = $ 900
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 12 [ ∵ compounded mothly ]
Here we need to find the time period
Assume that after 'n' years the amount will be doubled i.e $ 1800
From the given problem,
Amount, A = 900(1+0.06/12)¹²ⁿ
= 900(1+0.06/12)¹²ⁿ
= 900(1 + 0.005)¹²ⁿ
= 900 (1.005)¹²ⁿ
As we assumed after 'n' years the amount is $ 1800
=> 900 (1.005)¹²ⁿ = 1800
=> (1.005)¹²ⁿ = 2
Apply to log on both sides
=> log (1.005)¹²ⁿ = log 2
=> 12n log(1.005) = log 2
=> 12n = log 2/log(1.005)
[ use calculator for log (1.005) and log 2]
=> 12n = 0.301029996/ 0.00216606176
=> 12n = 138.975722
=> n = 11.5813102
=> n = 11.56
Therefore,
In 11.56 years the given amount of $ 900 will be double.
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Write this number in scientific notation.
.0000149
Answer: 1.49 x [tex]10^{-5}[/tex]
Step-by-step explanation:
If η. is an even positive integer, the double factorial notation represents the product of all the even integers from to η. For example 8! = 2 . 4. 6. 8 . What is the units digit of the following sum?
a. 0
b. 2
c. 4
d. 6
e. 8
The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.
What is meant by the term factorials?Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.
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