The measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees.
What is the central angle in a regular 7-sided polygon, rounded to the nearest tenth of a degree?For a regular polygon with 7 sides, we can substitute n = 7 into the formula:
central angle = 360 degrees / 7
central angle ≈ 51.4 degrees
A regular polygon is a polygon with equal sides and equal angles. The measure of each interior angle of a regular polygon with n sides is given by the formula:
interior angle = (n-2) x 180 degrees / n
For example, for a regular polygon with 7 sides:
interior angle = (7-2) x 180 degrees / 7
interior angle = 5 x 180 degrees / 7
interior angle ≈ 128.6 degrees
Since a central angle of a regular polygon is an angle formed by two consecutive radii from the center of the polygon, the measure of a central angle is equal to the measure of the exterior angle.
The measure of an exterior angle of a regular polygon with n sides is given by the formula:
exterior angle = 360 degrees / n
For a regular polygon with 7 sides, we can use the formula above to find the measure of each exterior angle:
exterior angle = 360 degrees / 7
exterior angle ≈ 51.4 degrees
Therefore, the measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees, rounded to the nearest tenth of a degree as requested.
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Write the polynomial in standard form with roots of 1/4 and +5i
The polynomial with roots of 1/4 and +5i in standard form is:
f(x) = x² - (1/4)x² + 25x - (25/4)
To write the polynomial with roots of 1/4 and +5i in standard form, we need to use the fact that the roots of a polynomial are related to its factors. Specifically, if r is a root of a polynomial, then x - r is a factor of the polynomial.
Therefore, if the roots of our polynomial are 1/4 and +5i, then we know that the factors of the polynomial are:
(x - 1/4) and (x - 5i) and (x + 5i)
To get the polynomial in standard form, we need to multiply out these factors and simplify.
(x - 1/4) and (x - 5i) and (x + 5i) = (x - 1/4) and (x² - 25i²)
= (x - 1/4) and (x² + 25)
= x³ + 25x - (1/4)x² - (25/4)
Therefore, the polynomial with roots of 1/4 and +5i in standard form is:
f(x) = x³ - (1/4)x² + 25x - (25/4)
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help please due very soon
Answer:
(D) 7/10
Step-by-step explanation:
You want the rate of change of y with respect to x for the relation ...
(2/5)x -(4/7)y = 3/2
Slope-Intercept formSolving for y, we have ...
2/5x -3/2 = 4/7y . . . . . . . . . . add 4/7y -3/2
(7/4)(2/5)x -(7/4)(3/2) = y . . . . multiply by 7/4
7/10x -21/8 = y . . . . . . . . . . simplify
The rate of change is the coefficient of x: 7/10.
What is the scale factor for the similar figures below?
The scale factor of the similar figure is 2.
What is scale factor?
Scale factor is the ratio of the length of a new object to the original object.
To calculate the scale factor of the similar figures, we use the formula below
Formula:
S.F = New length/Original length.................. Equation 1Where:
S.F = Scale factorFrom the diagram,
Given:
New length = 14Original length = 7Substitute these values into equation 1
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11
Differentiate the function and find the slope of the tangent line at the given value of the independent variable s=8-41², 1=-3 s'(t)=0 The slope of the tangent line is at t= -3.
The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.
Process of finding slope:1. Differentiate the function s(t) with respect to the independent variable t: [tex]s(t) = 8 - 41t^2[/tex].
2. Calculate the derivative s'(t).
3. Evaluate the derivative at the given value of t.
Step 1: Differentiate the function [tex]s(t) = 8 - 41t^2[/tex].
To differentiate this function, we apply the power rule for differentiation.
The derivative of a constant (8) is 0, and the derivative of 41t^2 is -82t
(since we multiply the exponent 2 by the coefficient 41 and then subtract 1 from the exponent).
Step 2: Calculate the derivative s'(t).
s'(t) = 0 - 82t
Step 3: Evaluate the derivative at the given value of t (t = -3).
s'(-3) = -82(-3) = 246
The slope of the tangent line to the function [tex]s(t) = 8 - 41t^2[/tex] at t = -3 is 246.
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Marshall is renting a bike for the day. It costs $13 for up to one hour. After one hour, the price increases to $20. After three hours, the price increases again to $50. The maximum time he can rent the bike is 10 hours total
The piecewise function that represents the situation is therefore:
Costs Possible hours
13 0 < x ≤ 1
20 1 < x ≤ 3
50 3 < x ≤ 10
How to find the piecewise function ?We see that up to one hour, the cost to Marshall would be $ 13 so the possible hours at that price is 0 < x ≤ 1 .
Likewise from one hour, the price goes up to $ 20 which means that possible hours become 1 < x ≤ 3 because the price will increase at 3 hours again.
From 3 hours, the price becomes $ 50 and there are a maximum of 10 hours so the hours become 3 < x ≤ 10 .
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Joshua's mail truck travels 14 miles every day he works
and is not used at all on days he does not work. At the
end of his 100th day of work the mail truck shows a
mileage of 76,762. Model Joshua's truck mileage as a
function of the number of days he has worked. When
will he reach 100,000 miles?
Solving the equation, Joshua will reach 100,000 miles after approximately 1,760 days of work.
To model Joshua's truck mileage as a function of the number of days he has worked, we can use the following equation:
Mileage (M) = 14 * Number of days worked (D) + Initial Mileage (I)
First, we need to determine the initial mileage on the mail truck. To do this, we can use the information given for his 100th day of work:
76,762 = 14 * 100 + Initial Mileage
76,762 = 1,400 + Initial Mileage
Initial Mileage (I) = 76,762 - 1,400
Initial Mileage (I) = 75,362
Now we can rewrite the equation as:
Mileage (M) = 14 * Number of days worked (D) + 75,362
To find when Joshua will reach 100,000 miles, we can set M equal to 100,000 and solve for D:
100,000 = 14 * D + 75,362
24,638 = 14 * D
D ≈ 24,638 / 14
D ≈ 1,759.857
Since Joshua cannot work a fraction of a day, he will reach 100,000 miles after approximately 1,760 days of work.
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FRACTIONS It is John's birthday and his mother decided to give him a birthday party. She bought him three cakes for his party; cake one was sliced into 8 pieces, cake two was sliced into 10 pieces, and cake three was sliced into 12 pieces. If the guests at the party ate 4 slices of cake one, 7 slices of cake two and 5 slices of cake three; calculate the amount of cake that was eaten in total.
There are 30 slices in total, so our denominator would be 30.
Now we simply have to add 4, 7 and 5. The answer to this would be 16.
So the amount of cake eaten in total is 16/30.
If your assignment is for improper fractions, I'm guessing the answer would be 16/3 instead.
Answer:
1 37/60 cakes
Step-by-step explanation:
You want the total cake eaten if 4 of 8 slices, 7 of 10 slices, and 5 of 12 slices were eaten.
SumThe sum of the three fractions is ...
4/8 +7/10 +5/12
= 5/10 +7/10 +5/12 . . . . . . . 4/8 = 1/2 = 5/10
= 12/10 +5/12
= 6/5 +5/12
= (6·12 +5·5)/(5·12) = 97/60 = 1 37/60
The total amount of cake that was eaten was equivalent to 1 37/60 cakes.
__
Additional comment
Your calculator can relieve the tedium of this calculation.
Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall.
What is the length of a straight line between the school and the fire station? Round to the nearest tenth.
The length of the straight line between the school and the fire station is 4.6 miles.
The length of a straight line between the school and the fire station?We can form a right-angled triangle with the school at the right-angle.
The distance between the school and the fire station is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
h^2 = 4.3^2 + 1.7^2
h^2 = 21.38
h ≈ 4.62
Rounding to the nearest tenth, the length of the straight line between the school and the fire station is approximately 4.6 miles.
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Rewrite in standard form.
y
=
3
(
x
−
5
)
2
−
1
The equation y = 3(x - 5)^2 - 1 written in the standard form is y = 3x^2 - 30x + 74
Rewriting the equation in standard formTo rewrite the given equation in standard form, we need to expand and simplify the squared term:
y = 3(x - 5)^2 - 1 [given equation]
y = 3(x^2 - 10x + 25) - 1 [expand (x - 5)^2 using FOIL method]
y = 3x^2 - 30x + 74 [combine like terms]
Therefore, the standard form of the equation is:
y = 3x^2 - 30x + 74
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Will a geometric sequence always grow faster than an arithmetic one?
A geometric sequence is a type of sequence where each term is found by multiplying the previous term by a constant factor. This means that each term is a multiple of the one before it. In contrast, an arithmetic sequence is a type of sequence where each term is found by adding a constant value to the previous term.
This means that each term is a sum of the one before it and a fixed value.
To answer your question, whether a geometric sequence will always grow faster than an arithmetic one depends on the values of the constant factor and fixed value in each sequence. In general, if the constant factor in a geometric sequence is greater than 1, the terms will grow at an increasingly faster rate than in an arithmetic sequence.
However, if the constant factor is between 0 and 1, the terms will grow at a decreasing rate, meaning that the sequence will actually grow more slowly than an arithmetic one.
It's important to note that the rate of growth is not the only factor to consider when comparing geometric and arithmetic sequences. The actual values of the terms in each sequence can also differ significantly, depending on the starting term and the values of the common ratio and common difference.
In some cases, an arithmetic sequence may actually have higher values than a geometric one, even if it grows more slowly.
In summary, whether a geometric sequence will always grow faster than an arithmetic one depends on the specific values of each sequence. However, in general, if the constant factor in a geometric sequence is greater than 1, it will grow faster than an arithmetic sequence.
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Solve the given differential equation 3 4ydx - 4xdy + x³dx = 7dx The solution is= (Type an equation.)
The solution of the given differential equation is y = x + Cx⁴ - x²/4, where C is a constant.
We begin by rearranging the terms as follows:
(4y + x³ - 7)dx = (4x)dy
Integrating both sides, we get:
4xy + (1/4)x⁴ - 7x = 2y² + C
where C is the constant of integration.
Next, we can rearrange this equation to solve for y:
y² = 2xy + (1/8)x⁴ - (7/2)x - C/2
y² - 2xy = (1/8)x⁴ - (7/2)x - C/2
We can complete the square to obtain a more useful expression:
(y - x)² = (1/8)x⁴ - (7/2)x - C/2 + x²
y - x = ±sqrt((1/8)x⁴ - (7/2)x - C/2 + x²)
Simplifying this expression, we get:
y = x ±sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
Taking the positive sign for simplicity, we get the final solution as:
y = x + sqrt(Cx⁴ - (1/4)x⁴ + 7x - C)
where C is the constant of integration.
We can also simplify this solution further by using the identity (a + b)² = a² + 2ab + b² to get:
y = x + Cx⁴ - x²/4
where C is a constant, as desired.
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Pls help with these two equations. Pls
Answer:
11. x = 16
12. x = 26
Step-by-step explanation:
11. ∠1 + ∠2 = 90°
∠1 = 42°
∠2 = 90° - 42° = 48°
3x = 48
x = 16
12. ∠C + ∠D = 180°
∠C = 128°
∠D = 180° - 128° = 52°
2x = 52
x = 26
6 cm
4.4 cm
2 cm
determine the total surface area of the figure.
The total surface area of the given cuboid is 94.4 square centimeter.
Given that, the dimensions of box are length=4.4 cm, breadth=2 cm and Hight=6 cm.
We know that, the total surface area of cuboid = 2(lb+bh+lh)
= 2(4.4×2+2×6+4.4×6)
= 2×47.2
= 94.4 square centimeter
Therefore, the total surface area of the given cuboid is 94.4 square centimeter.
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When the price of a certain product is $40, 25 items can be sold. When the price of the same
product costs $20, 185 items can be sold. On the other hand, when the price of this product
is $40, 200 items will be produced. But when the price of this product is $20, only 100 items
will be produced. Use this information to find supply and demand functions (assume for
simplicity that the functions are linear), and compute the consumer and producer surplus at
the equilibrium price
Based on the information, the equilibrium price is $56.67
How to calculate the equillbriumUsing the first data point, we have:
25 = a - 40b
Using the second data point, we have:
185 = a - 20b
Solving these two equations simultaneously, we get:
a = 325
b = 5/2
So the demand function is:
Qd = 325 - 5/2 P
the supply function is:
Qs = -100 + 5P
325 - 5/2 P = -100 + 5P
425 = 15/2 P
P = $56.67
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Help translations and reflections
Thus, Coordinates of image of points A', B' and C' are- A'(-6, 10), B'(-2, -8), C'(4 , -7)
Explain about the reflection along the y-axis:A figure is transformed into a reflection by a transformational process. In a point, a line, or a plane, figures can be reflected. The image and preimage coincide when reflecting any symbol in a line or a point.
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).Given coordinates of points A, B and C
A(6, 10), B(2, -8), C(-4 , -7)
After reflection (x, y) ---> (-x, y).
Thus, Coordinates of image of points A', B' and C' are-
A'(-6, 10), B'(-2, -8), C'(4 , -7)
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Which best describes the scale factor for each dilation?
Dilation 1 has a scale factor
.
Dilation 2 has a scale factor
.
Dilation 3 has a scale factor
.
The statement "Dilation 2 has a scale factor 2" (option b).
Dilation is a transformation that changes the size of an object but not its shape. It is a type of transformation that enlarges or reduces an object by a certain factor called the scale factor. The scale factor is a ratio of the size of the dilated image to the size of the original image.
Now, let's talk about the scale factor for each dilation you asked about.
For dilation 1, the scale factor is 1. This means that the size of the dilated image is the same as the size of the original image. In other words, there is no change in size. This type of dilation is often referred to as the identity transformation because it doesn't change the shape or size of the original object.
For dilation 2, the scale factor is 2. This means that the size of the dilated image is twice as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '2x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '2y'.
For dilation 3, the scale factor is 3. This means that the size of the dilated image is three times as large as the size of the original image. In mathematical terms, if the original object has a length of 'x', then the length of the dilated image will be '3x'. Similarly, if the original object has a width of 'y', then the width of the dilated image will be '3y'.
Hence the correct option is (b).
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Answer:
Dilation 1 has a scale factor between 0 and 1
Dilation 2 has a scale factor greater than 1
Dilation 3 has a scale factor equal to 1
Step-by-step explanation:
A dth tv connection provides channels in english and other languages in the ratio 7:13. what percentage of the channels are in english
A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.
Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:
(7/20) x 100 = 35%
Therefore, 35% of the channels on this DTH TV connection are in English.
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A force of 80 pounds on a rope is used to pull a box up a ramp inclined at 10 degrees from the horizontal. The rope forms an angle of 33 degrees with the horizontal. How much work is done pulling the box 26 feet along the ramp?
The work done on the displacement is 301.95J
What is the work done in pulling the boxTo determine the work done, we need to find the displacement in which the box moved.
cos θ = adjacent / hypothenuse
cos 33 = adjacent / 80
adjacent = 80 * cos 33
adjacent = 67.1 lbs
The force applied is 67.1lbs
The displacement on the ramp;
sin θ = opposite / hypothenuse
sin 10 = opposite / 26
opposite = 26 * sin 10
opposite = 4.5 ft
The work done in moving the object can be calculated as;
work done = force * displacement
work done = 67.1 * 4.5
work done = 301.95 J
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The height of a right rectangular pyramid is equal to x units. The length and width of the base are units and units. What is an algebraic expression for the volume of the pyramid?
The algebraic expression for the volume of the right rectangular pyramid is (x/3) × (units²).
The volume of a right rectangular pyramid is given by the formula;
V = (1/3) × base_area × height
where base_area is area of the base of the pyramid.
In this case, the length and width of the base are given as units and units, respectively. Therefore, the area of the base is;
base_area = length × width
Substituting the given values, we get;
base_area = units × units = units²
The height of the pyramid is given as x units. Therefore, the volume of the pyramid can be expressed as;
V = (1/3) × (units²) × x
Simplifying the expression, we get;
V = (x/3) × (units²)
Therefore, the algebraic expression for the volume of pyramid is (x/3) × (units²).
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Need help, i have the answer just need the steps
(8^2/7)(8^1/4)
Answer:
Step-by-step explanation:
we can use the laws of exponents, which state that when multiplying terms with the same base, we add their exponents. In this case,both terms have a base of 8, so we can add their exponents of 2/7 and 1/4.
First, let's write 8 as a power of 2: 8 = 2^3. Then we can rewrite the original expression as (2^3)^(2/7) * (2^3)^(1/4). Using the power of a power rule, we can simplify this to 2^(3 * 2/7) * 2^(3 * 1/4).
Next, we can simplify the exponents by finding a common denominator. The smallest common multiple of 7 and 4 is 28, so we can rewrite the exponents as 6/28 and 21/28, respectively. Thus, we have 2^(3 * 6/28) * 2^(3 * 21/28).
Now we can simplify the exponents by multiplying the bases and exponents separately: 2^(18/28) * 2^(63/28). We can simplify the fractions by dividing both the numerator and denominator by 2, giving us 2^(9/14) * 2^(63/28).
Finally, we can add the exponents since we are multiplying terms with the same base: 2^(9/14 + 63/28). We can simplify the exponent by finding a common denominator of 28,
giving us 2^(36/28 + 63/28) = 2^(99/28). This is our final answer, which is an irrational number that is approximately equal to 69.887.
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the relationship between group size and percent woodland appears to be negative and nonlinear. which of the following statements explains such a relationship? responses as the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group decreases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group increases at a fairly constant rate. as the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group increases quickly at first and then more slowly. as the percent of woodland increases, the number of deer observed in a group remains fairly constant.
The statement that explains the negative and nonlinear relationship between group size and percent woodland is given by the percent of woodland increases, the number of deer observed in a group decreases quickly at first and then more slowly.
This statement suggests that as the amount of woodland id increases, when the number of deer in a group decreases.
However, the rate of decrease is not constant, but rather decreases more slowly as the percent of woodland increases.
This suggests that there may be some threshold or tipping point.
At which the relationship between group size and percent woodland becomes less pronounced.
This kind of relationship is not uncommon in ecological studies.
Where factors like habitat availability, food availability, and predation risk can all influence animal behavior and population dynamics.
Nonlinear relationships like this one can help researchers better understand complex interplay between these factors and behavior of animals they study.
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Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum
The common ratio for the geometric series 1, 1/2, 1/4, 1/8, ... is 1/2 and the sum of series is 2 which is finite.
To determine whether the series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is:
S = a/(1-r),
where a is the first term and r is the common ratio.
In this case, a = 1 and r = 1/2, so
S = 1/(1 - 1/2) = 2.
Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
The common ratio of a geometric series is the ratio between consecutive terms. For example, in the series 1, 2, 4, 8, 16, ..., the common ratio is 2 because each term is obtained by multiplying the previous term by 2.
To determine whether a geometric series has an infinite sum, we can use the formula for the sum of an infinite geometric series, which is S = a/(1-r), where a is the first term and r is the common ratio.
If the value of r is between -1 and 1 (excluding -1), then the series has a finite sum. If the value of r is greater than 1 or less than -1, then the series has an infinite sum.
In the given series 1, 1/2, 1/4, 1/8, ..., the common ratio is 1/2. To find the sum of the series, we can use the formula S = a/(1-r) with a=1 and r=1/2, which gives S=2. Since the value of S is finite and not infinite, we can conclude that the given geometric series has a finite sum of 2.
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complete question:
Determine the common ratio for each of the following geometric series and determine which ones have an infinite sum 1,1/2,1/4,1/8....
students in mr gonzales class are researching situations of exponitial decay and creating their graphs mr gonzales asked his students what the situations have in common and their responses are shown below
Therefore , the solution of the given problem of unitary method comes out to be it is consistently a constant proportion or percentage of the preceding value.
A unitary method is what?The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.
Here,
According to the students' responses, all instances of exponential decay share the following characteristics:
They begin with a baseline value. (y-intercept).
They get smaller with time. (or successive periods).
They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.
The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,
it is consistently a constant proportion or percentage of the preceding value.
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The equation 8x − 2y = 25 represents a linear function. Which equation represents the same function?
A. The number of minutes m to cook c cups of rice
B. The volume V of a cube with side length s
C. The distance walked after m minutes at r feet per minute
D. The cost C for t tickets to a museum
HELP OR DIE
None of the options presented represent the same function as the given equation 8x − 2y = 25.
The equation 8x − 2y = 25 represents a linear function in terms of variables x and y. To determine which equation represents the same function, we need to look for an equation that has a similar form.
A. "The number of minutes m to cook c cups of rice" does not have the same form as the given equation, so it does not represent the same function.
B. "The volume V of a cube with side length s" also does not have the same form as the given equation, so it does not represent the same function.
C. "The distance walked after m minutes at r feet per minute" does not match the given equation, so it does not represent the same function.
D. "The cost C for t tickets to a museum does not have the same form as the given equation, so it does not represent the same function.
Therefore, none of the given options represent the same function as the equation 8x − 2y = 25.
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Help asap please!!!!
Ella rolls a die and then flips a coin. The sample space for this compound event is represented in the table (His heads and Tis talls). Complete the table and the sentence beneath it. Die 1 2 3 4 5 6 heads H-1 H-2 H-3 H-5 H-6 Coin tails T-1 T-3 T-4 T-5 The size of the sample space is
The sample space for Ella's compound event where she rolls a die and then flips a coin can be represented in the table below:
Die: 1 2 3 4 5 6
Coin: H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5
The size of the sample space is the total number of possible outcomes, which in this case is the number of rows in the table. We can see that there are 9 rows in the table, so the size of the sample space is 9.
To understand the sample space, we can imagine that each row in the table represents a possible outcome of the compound event. For example, the first row represents the outcome where Ella rolls a 1 on the die and gets heads on the coin. The second row represents the outcome where Ella rolls a 2 on the die and also gets heads on the coin, and so on.
Understanding the sample space is important in probability theory because it allows us to calculate the probability of specific events occurring. By knowing the size of the sample space and the number of favorable outcomes, we can determine the probability of an event happening.
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A college entrance exam had a mean of 80 with a standard deviation of 12 find the actual test score that coincides with a z-score of -1.25
The actual test score that coincides with a z-score of -1.25 is 65 when A college entrance exam had a mean of 80 with a standard deviation of 12 and a z-score of -1.25.
The formula to calculate the actual test score from a z-score is given as,
X = μ + Zσ,
where:
X = the actual or raw test score
μ = the mean
Z = z-score
σ = standard deviation.
Given data:
μ = 80
Z = -1.25
σ = 12
Substuting the values of μ, Z, and σ in the formula, we get;
X = μ + Zσ,
X = 80 + (-1.25)(12)
X = 80 + (-15)
X = 65.
Therefore, the actual test score that coincides with a z-score of -1.25 is 65.
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(a) if f(4) = 6, what is f-|(6)? f-'(6) = (b) Suppose a function can be described by y = f(x). The function and its inverse intersect when y = (c) Consider a linear function f (x) = ax + b where a 70. Is the inverse of this linear function always a linear function? (No answer given) If f(x) = ax + b and a € 0, then f-'(x) =
To find f-1(6), we need to find the value of x that gives f(x) = 6. However, we don't have enough information about the function f to do this. We need to know whether f is a linear function or not.
When the function and its inverse intersect, we have f(x) = f-1(x). Substituting y for both f(x) and f-1(x), we get y = f(y). To find the value of y when this is true, we need to solve for y:
y = f(y)
y = f-1(y)
Substituting y = f(x), we get:
f(x) = f-1(f(x))
f(x) = x
So the function and its inverse intersect when y = x.
If a = 0, then the linear function is f(x) = b, which is a constant function. Constant functions do not have inverses, so the inverse of f(x) = b does not exist.
If a ≠ 0, then the inverse of f(x) = ax + b is given by:
f-'(x) = (x - b) / a
This is also a linear function, so the inverse of a linear function is always a linear function when a ≠ 0.
(a) To find the inverse of a linear function, you need to swap the x and y values. Given that f(4) = 6, the inverse function f^(-1)(6) would yield the value of x when y = 6. Since we know that f(4) = 6, it implies that f^(-1)(6) = 4.
A function and its inverse intersect when the input value (x) is equal to the output value (y). In other words, they intersect when y = x.
(c) Yes, the inverse of a linear function is always a linear function. If f(x) = ax + b, where a ≠ 0, then the inverse function, f^(-1)(x), can be found by swapping x and y values and solving for y. In this case, x = ay + b. Solving for y, we get y = (x - b) / a, which is also a linear function.
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a circular pool has a radius of 32 cm find its area?
write an equation of the line that passes through each pair of points (5, 7), (-8, -4)
Answer:
y = 11x/13 + 36/13
Step-by-step explanation:
We can write the line using y = mx + b form.
To find the slope, m, we can use the formula (y1 - y2) / (x1 - x2):
(7-(-4)) / (5-(-8)) = (7+4) / (5+8) = 11 / 13.
To find b, we can plug in one of the points. Lets use (5, 7).
y = 11/13 * x + b
7 = 11/13 * 5 + b
7 - 55/13 = b
b = 91/13 - 55/13 = (91-55)/13 = 36/13.
Your equation is:
y = 11x/13 + 36/13.
Answer: y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]
Step-by-step explanation:
First, we will find the slope.
[tex]m=\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{-4-7}{-8-5} =\frac{-11}{-13} =\frac{11}{13}[/tex]
Next, we will substitute this slope and a given point in and solve for our y-intercept (b).
y = [tex]\frac{11}{13}[/tex]x + b
(7) = [tex]\frac{11}{13}[/tex](5) + b
(7) = [tex]\frac{11}{13}[/tex](5) + b
7 = [tex]\frac{55}{13}[/tex] + b
b = 7 - [tex]\frac{55}{13}[/tex]
b = [tex]\frac{36}{13}[/tex]
Final equation:
y = mx + b
y = [tex]\frac{11}{13}[/tex]x + [tex]\frac{36}{13}[/tex]
Question
A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create (14, 39, 60, 120) different lunch combo meals.
The number of different combo meals possible in a restaurant that is serving a special dinner combo meal is 90.
We are given that the customers can choose from 5 drinks, 6 main dishes, and 3 desserts. We have to find that how many different combos are possible. It means that we have to do an arrangement for such a situation. Arrangement of things means to group them in a systematic order, in all the possible ways.
We know that the number of possible ways to arrange is n! where n is the number of objects. As we know that the dinner includes 5 drinks, 6 main types of dishes, and 3 types of desserts. The number of different combo meals possible can be found by simply multiplying all the meals. Thus,
n = 5 * 6 * 3
n = 90
Therefore, the number of different combo meals possible in a restaurant that is serving a special dinner combo meal that includes a drink, a main dish, and a dessert is 90.
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