The total cost equation can be written as:
Total Cost = 32000 + 9000L
What is total cost?
Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.
The total cost equation can be expressed as:
Total Cost = Fixed Cost + Variable Cost
where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.
In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.
If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:
Total Cost = 32000 + 9000L
This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.
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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?
Between 2000 and 2015, the number of twin births in a certain country increased by 14%, to approximately 133,950 . About how many twin births were there in 2000? There were approximately ____ twin births in 2000.
Let the number of twin births in 2000 be x.
According to the problem, the number of twin births in 2015 increased by 14%, which means the number of twin births in 2015 is:
x + 0.14x = 1.14x
We also know that the number of twin births in 2015 is approximately 133,950, so we can set up the following equation:
1.14x = 133,950
Solving for x, we get:
x = 117,500
Therefore, there were approximately 117,500 twin births in 2000.
a country radio station wants to know what the most popular type of music is so they ask their listeners to call in say their favorite type
According to the information, if the radio selects listerners randomly, the sample is random. But if they select listerners are selected without random method the sample may be biased.
Is this an example of sample random or not?If the radio station randomly selected a subset of their listeners and asked them to call in, then the sample would be random. This would help ensure that the sample is representative of the overall population of the radio station's listeners, and would allow for valid conclusions to be drawn about the preferences of the wider population based on the results of the survey.
However, if the radio station did not use a random sampling method, then the sample may be biased and not representative of the overall population of the radio station's listeners. For example, if the radio station only advertised the survey during certain times of day or on certain shows, then the sample may be biased towards listeners who are more likely to be listening during those times or shows. Similarly, if the radio station only advertised the survey on certain social media platforms or websites, then the sample may be biased towards listeners who use those platforms or websites.
Note: This question is incomplete. Here is the complete information:
State whether or not the sample is random. If it is not random, explain why
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Mrs Marcus combines her books and magazines then divides them among 10 different tables. If a represents the number of books and d represents the number of magazines Mrs. marcus has, write an expression to show how many books would be on each table.
An expression to show how many books would be on each table is a/10
To find out how many books would be on each table, we need to divide the total number of books by the number of tables.
First, let's express the total number of books in terms of a and d. Since we are not given any specific numbers for a and d, we can simply use variables to represent them. Therefore, the total number of books is given by a.
Next, we need to divide a by 10, the number of tables. This gives us the expression:
a/10
So, the above expression shows how many books would be on each table if Mrs. Marcus combines her books and magazines and then divides them among 10 different tables.
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Complete question is:
Mrs. Marcus combines her atlases and dictionaries and then divides them among 10 different tables. If a represents the number of atlases and d represents the number of dictionaries Mrs. Marcus has, write an expression to show how many books would be on each table.
in how many months will $8500 grow to $8818.75 at 5% P.A?
Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!
Please help!!
If someone could explain how to solve this question I would appreciate it!
2430+15√2=
Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.
Using a calculator, you can directly evaluate the expression to get:
2430 + 15√2 ≈ 2462.11
Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:
2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21
Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.
Step-by-step explanation:
Question is in image
Answer:
366,699
Step-by-step explanation:
to solve this problem, we can use the following formula for exponential growth:
population = initial population x (1 + growth rate)^time
where the initial population is the current population, the growth rate is the rate of increase per year, and the time is the number of years.
Plugging in the given values, we get:
population = 300,000 x (1 + 0.02)^10
Simplifying, we get:
population = 300,000 x 1.02^10
Using a calculator, we get:
population ≈ 366,698.79
Rounding to the nearest whole number, we get:
population ≈ 366,699
The population in 10 years will be approximately 366,699
Solve for x:
|x|+8 = -3
Answer:
No Solution
Step-by-step explanation:
Because this solution deals with absolute value equations.
50 Points! Multiple choice algebra question. Photo attached. Which represents the correct synthetic division of (x^2-4x+7) divided by (x-2)? Thank you!
Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)
What is the synthetic division?Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.
x - 2 | x^2 - 4x + 7
x^2 - 2x
---------
-2x + 7
-2x + 4
-------
3
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What is the discriminant of the quadratic equation − � 2 − 9 � − 8 = 0 −x 2 −9x−8=0?
we know that
discriminant of quadratic is [tex]b^{2}[/tex]-4ac
putting values we get
81-32
= 49
hence the discriminant is 49
Make x the subject of the formula where x is positive:
2(x-2y) = 6xz+5u
Answer:
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Step-by-step explanation:
2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side
2x - 4y = 6xz + 5u ( add 4y to both sides )
2x = 6xz + 5u + 4y ( subtract 6xz from both sides )
2x - 6xz = 5u + 4y ← factor out x from each term on the left side
x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Anyone know how to find the radius when given this?
Answer:
The radius is 26 units--------------------------
As per given, the distance from the center to both of the chords is same, therefore both chords have same length:
JK = ML4x = 6x - 246x - 4x = 242x = 24x = 12The length of each chord is:
4*12 = 48 unitsUse Pythagorean theorem to find the radius, the distance from the center to one end of the chord:
[tex]QM=\sqrt{QP^2+MP^2}[/tex][tex]QM=\sqrt{10^2+(48/2)^2}=\sqrt{100+576}=\sqrt{676} =26\ units[/tex]what is equivalent to 1 whole and 7/8
An equivalent fraction to 1 whole and 7/8 is 15/8.
What is improper fraction?A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. It is, in other words, a "top-heavy" fraction since the fraction represents a value greater than one full unit.
According to question:1 whole and 7/8 can be written as a mixed number, which is a combination of a whole number and a fraction:
1 whole and 7/8 = 1 + 7/8
To find an equivalent fraction, we can convert the mixed number to an improper fraction by multiplying the whole number by the denominator of the fraction, and then adding the numerator. The result is the numerator of the improper fraction, and the denominator stays the same:
1 + 7/8 = (1 × 8 + 7)/8 = 15/8
Therefore, an equivalent fraction to 1 whole and 7/8 is 15/8.
For instance, the improper fraction 7/4 results from the numerator's (7), which is greater than the denominator (4).
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Let u = - 4i + j v = 4i - 2j and w = - 2j
Find the specified scalar or vector.
5u(3v - 4w)
The result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
In linear algebra, we often use scalars and vectors to perform various operations. Scalars are just ordinary numbers that can be used to multiply or divide vectors. On the other hand, vectors are quantities that have both magnitude and direction.
In this problem, we are given three vectors, u, v, and w, and we are asked to find the result of multiplying 5u by the difference between 3v and 4w.
First, let's calculate 3v - 4w. Since v = 4i - 2j and w = -2j, we can substitute these values to get,
3v - 4w = 3(4i - 2j) - 4(-2j)
= 12i - 6j + 8j
= 12i + 2j
Next, we need to find the scalar product of 5u and 12i + 2j. To find the scalar product of two vectors, we need to multiply the corresponding components and add up the products.
Therefore: 5u(3v - 4w) = 5u(12i + 2j)
= 5(-4i + j)(12i + 2j)
= -20i(12i) + 5i(2j) + 60j(i) - 10j(j)
= -240i + 10j + 60j + 10
= -240i + 70j + 10
So, the result of multiplying 5u by the difference between 3v and 4w is the vector -240i + 70j + 10.
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What inequality matches this graph?
A. x > -5
B. x > -5
C. x < -5
D. x < -5
Answer:
x ≥ -5
Step-by-step explanation:
Since we see the dot is filled in, we know the sign is either ≤ or ≥. Then, we can see that x is greater than -5 as the arrow is pointing in the positive direction (to the right). Therefore, it would be x ≥ -5
find the extreme values of [tex]f(x,y) =x^{2} +y^2\\[/tex]
The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.
∂f/∂x = 2x = 0
∂f/∂y = 2y = 0
From these equations, we can see that the critical point occurs at (x,y) = (0,0).
To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:
∂²f/∂x² = 2
∂²f/∂y² = 2
∂²f/∂x∂y = 0
At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.
Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
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Anita’s and Casey’s bills do not vary from month to month. Anita pays $80 more than Casey does each month. Over the course of 4 months, their combined bills are $1,520.
Part A
Write the system of equations that describes this situation. Let a represent Anita's monthly payment and c represent Casey's monthly payment.
a +
c =
a =
+
Part B
Solve the system to find Anita’s and Casey’s monthly payments.
Anita: $
Casey: $
Answer:
Casey's monthly payment is $150.
Anita's monthly payment is $230.
Step-by-step explanation:
Part A:
The system of equations that describes this situation is:
a + c = Total monthly bill
a = c + 80
where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.
Part B:
To solve the system, we can substitute the second equation into the first equation and get:
(c + 80) + c = Total monthly bill
Simplifying this equation, we get:
2c + 80 = Total monthly bill
We also know that over the course of 4 months, their combined bills are $1,520. So we can write:
4(Total monthly bill) = 1520
Substituting the equation for Total monthly bill from the previous step, we get:
4(2c + 80) = 1520
Simplifying this equation, we get:
8c + 320 = 1520
Subtracting 320 from both sides, we get:
8c = 1200
Dividing both sides by 8, we get:
c = 150
So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:
a = c + 80
a = 150 + 80
a = 230
Therefore, Anita's monthly payment is $230.
What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Answer:
translation
hope this helps:) !!
Find the endpoints of the latus rectum of the parabola below.
Select the correct answer below:
(x + 3)² = -20(y + 1)
The endpoints of the latus rectum of the parabola equation is : f. The endpoints of the latus rectum are (-6, 9) and (-6, -15).
What is the latus rectum?Standard form of the equation of a parabola =y (x - h)² = 4p(y - k)
Where:
(h, k) = vertex
4p = distance between the vertex and focus
Comparing this with (x + 3)² = -20(y + 1) will gives us
(x + 3)² = -20(y + 1)
= (x - (-3))² = -20(y - (-1))
The vertex of the parabola is = (-3, -1)
4p = -20
p = -20/4
p = -5
The line that is perpendicular to the axis of symmetry (line y = -1) and passes through the focus (-3, -6) is known as the latus rectum of a parabola. The line y = - 6—the focus—and the directrix are separated by a distance of 4p = 20.
The vertex which is located at (-3, -1) is the latus rectum's midway. The latus rectum tend to has a length of 20 and passes through the points (-3, -1). Its endpoints must be located on the line x = -3 since it is perpendicular to the axis of symmetry.
The endpoints of the latus rectum are:
(-3, -1 - 10) = (-3, -11) and (-3, -1 + 10) = (-3, 9).
Therefore, the correct option is f.
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Erica spins a spinner with equal sections numbered 1 through 4 and selects a colored tile from a bag. Based on the tree diagram given, what is the probability of spinning a 2 or 3 on the spinner and drawing a blue tile?
Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.
Here,
Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).
The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.
To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:
P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)
= (1/2) x (1/3)
= 1/6
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100 POINTS!!!
Question
Step-by-step explanation:
A.
Sequence 2:
25-2×5=15
25-2×6=13
25-2×7=11
25-2×8=9
25-2×9=7
Ordered pairs :
(13,15)
(16,13)
(19,11)
(21,9)
(24,7)
B.
Sequence1 :
The rule is 3x+2 for x starts by 1, so:
3×1+2=5
3×2+2=8
3×3+2=11
3×4+2=14
3×5+2=17
Sequence2
The rule is 2x+3 forx starts by 6, so :
2×6+3=15
2×7+3=17
2×8+3=19
2×9+3=21
2×10+3=23
Ordered pairs
(5,15)
(8,17)
(11,19)
(14,21)
(17,23)
A single fair dice is rolled. Find the probability of getting a 2?
Answer:
1/6
Step-by-step explanation:
Chances of getting 2 = 1/6
tamara. Find the sum of two number cubes rolled at the same time. The chart below shows all possible sums from 36 possible combinations how many times should tamara expect the sum of two cubes to be equal to five if she rolls the cubes 180 times
Answer:
Step-by-step explanation:
There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.
To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:
(1/36) x 180 = 5
So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.
is y=-x directly proportional or non proportional
Answer: Directly proportional.
Step-by-step explanation:
y = -x is directly proportional for a few reasons.
➜ The graph of this equation is a straight line, so all the ratios of points are equal.
➜ The constant of proportionality (k) is equal to -1.
➜ This line intersects the graph at the origin (0, 0).
➜ See the graph below.
Suppose that the functions f and g are defined as follows.
Answer:
[tex]\dfrac{f}{g}(x) = \boxed{\dfrac{7}{x\left(x-3\right)}\\\\}[/tex]
Domain of [tex]\dfrac{f}{g}: \boxed{\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)}[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \dfrac{7}{x} , g(x) = x - 3[/tex]
[tex]\dfrac{f}{g} = \dfrac{f(x)}{g(x)} = \dfrac{7}{x} \div x - 3\\\\= \dfrac{7}{x} \times \dfrac{1}{x-3}\\\\ = \dfrac{7}{x\left(x-3\right)}[/tex]
To find the domain of
[tex]\dfrac{f}{g} = \dfrac{7}{x\left(x-3\right)}[/tex]
note that this function is defined everywhere in the range (- ∞, ∞) except for x = 0 and x = 3
At these two points, the function is undefined since the denominator becomes 0 and division by 0 is undefined
Therefore the domain consists of three parts expressed in inequality and interval forms
-∞ < x < 0 (-∞, 0)
0 < x < 3 (0, 3)
3 < x < ∞ (3, ∞)
Therefore the domain is obtained by combining these three intervals
- ∞ < x < 0 or 0 < x < 3 or x > 3
In interval notation with union:
[tex]\:\left(-\infty \:,\:0\right)\cup \left(0,\:3\right)\cup \left(3,\:\infty \:\right)[/tex] ANSWER
Question 1 of 10
The function f(x) is shown in this graph.
The function g(x) = -2x - 5.
Compare the slopes and y-intercepts.
A. The slopes are the same but the y - intercepts are different.
What is a slope in a graph?In a graph, the slope is the steepness of a line, which is a measure of how quickly the y-coordinate changes with respect to the x-coordinate. It is represented by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
The slope is often denoted by the letter m, and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
What is Y-intercept in a graph?In a graph, the y-intercept is the point where a line or curve intersects the y-axis. It is the value of the dependent variable (usually denoted by y) when the independent variable (usually denoted by x) is equal to zero.
The y-intercept is often denoted by the letter b, and is expressed as a coordinate point (0, b), where 0 represents the x-coordinate and b represents the y-coordinate. For example, in the equation of a line y = mx + b, the y-intercept is the value of b.
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This is ixl olease help
Answer:
m<H = 62.7°
Step-by-step explanation:
If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.
Answer:
H = 62.7 degrees
Step-by-step explanation:
Because this is a right triangle, we can use one of the trigonometric functions to find angle H:
Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):
sin(H) = 8/9
We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:
arcsin(8/9) = H = 62.7 degrees
What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Question is done below. Just multiple sqrts inside of each other.
The solution to the prompt of multiple square roots is 5.
How to solve for the sum of the multiple square rootsTo obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.
So this gives
√30 =5.47
5.47 + 5.47 + 5.47 + 5.47
= 21.88
=4.67 approximately 5
So. option 5 is the solution.
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Find the circumference and area of the circle.
Answer:
9.38
Step-by-step explanation:
I did the math
The length of circumference of this circle is 21.9911 inches.
The area of this circle is, approximately, 38.4845 (in²).
Step-by-step explanation:For the circumference.1. Formula.The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:
[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.
The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.
Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.
2. Rewrite the formula.So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:
[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]
3. Calculate.We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:
[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].
Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.
The length of circumference of this circle is 21.9911 inches.
-------------------------------------------------------------------------------------------------------
For the area.1. Formula.These are the most commonly used formulas for the area of circles:
[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.
Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.
2. Calculate.Let's use the area formula that directly involves diameter to avoid any conversions.
Substitute letter "d" by the length of the diameter (7 inches).
[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]
Therefore, the area of this circle is, approximately, 38.4845 (in²).
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The mean pulse rate in beats per minute of a certain group of adult males is 76 bpm. The hypothesis test results in a p-value of 0.0075
State a conclusion about the null hypothesis
The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.
How to conclude on the null hypothesis ?It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.
At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.
The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.
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