The set G = Zp × is a group under modular multiplication. This is because the set contains all the non-zero elements of Zp, and modular multiplication satisfies the four group properties:
Using Lagrange's Theorem, we can prove Fermat's Little Theorem: that for any integer a not divisible by p, ap-1 ≡ 1 (mod p). Let n be the smallest positive integer such that an ≡ 1 (mod p).
Since a is not divisible by p, the order of a (the smallest value of n) must divide p - 1, or in other words, n | (p - 1). By Lagrange's Theorem, this implies n = p - 1, which in turn implies that ap - 1 ≡ 1 (mod p). This proves Fermat's Little Theorem.
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en thatf(x)=x2−3xandg(x)=x+10f+g=f−g=fg=gf=Use the following functions to: find, simplify, and identify the domain of each of the function combinations.f(x)=x2−11xandg(x)=x+9(a)(f+g)(x)=Domain of(f+g)(x): (b)(f−g)(x)=Domain of(f−g)(x): (c)(fg)(x)=Domain of(fg)(x): (d)(gf)(x)=Domain of(gf)(x)
The function combinations and their respective domains are as follows:
(a) (f+g)(x) = f(x) + g(x) = x^2 - 11x + x + 9 = x^2 - 10x + 9
The domain of (f+g)(x) is all real numbers, since there are no restrictions on the values of x.
(b) (f-g)(x) = f(x) - g(x) = x^2 - 11x - (x + 9) = x^2 - 12x - 9
The domain of (f-g)(x) is also all real numbers, since there are no restrictions on the values of x.
(c) (fg)(x) = f(x) * g(x) = (x^2 - 11x)(x + 9) = x^3 - 2x^2 - 99x
The domain of (fg)(x) is all real numbers, since there are no restrictions on the values of x.
(d) (gf)(x) = g(x) * f(x) = (x + 9)(x^2 - 11x) = x^3 - 2x^2 - 99x
The domain of (gf)(x) is all real numbers, since there are no restrictions on the values of x.
In conclusion, the domain of all the function combinations is all real numbers, since there are no restrictions on the values of x.
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The scale factor of two similar hexagons is 3:7.
The area of the smaller hexagon is 18 m2.
What is the volume of the larger hexagon?
Question 7 options:
5832 m2
36 m2
42 m2
324 m2
98 m2
Since the two hexagons are similar, their corresponding sides are in the same ratio as the scale factor.
Let x be the length of a side of the smaller hexagon, then the corresponding length of a side of the larger hexagon can be expressed as (3/7)x.
The area of a hexagon can be calculated using the formula: A = (3√3/2)s², where s is the length of a side.
Since the area of the smaller hexagon is 18 m², we can solve for x as follows:
18 = (3√3/2)x²
x² = 12/√3
x = 2√3
Now we can calculate the area of the larger hexagon:
Area of the larger hexagon = (3√3/2)(3/7x)² = (3√3/2)(3/7(2√3))² = 54/49 m²
Finally, we can calculate the volume of the larger hexagon, assuming it is a regular hexagonal prism:
Volume of the larger hexagon = Area of hexagon x Height
The height of the hexagonal prism is the same as the length of the side of the larger hexagon, which is (3/7)x:
Volume of the larger hexagon = (54/49) x (3/7)x = 54/343 x² ≈ 0.212 x²
Substituting the value of x, we get:
Volume of the larger hexagon ≈ 0.212 x (2√3)² = 1.272 m³
Therefore, the volume of the larger hexagon is approximately 1.272 m³.
Well, I'm not sure if it's correct but I got 42.
I got this by doing something along the lines of:
1) 18/x = 3/7
2) Cross multiply
3) 3x = 126
4) Divide both sides by 3
5) x = 42
Find the perimeter of the triangle. Please show your work.
Answer:
Perimeter=33
Step-by-step explanation:
2x+3=4x-3
0=2x-8
2x=8
x=4
Input 4 as Variable
2x+3=2(4)+3
=8+3
=11
P=3x11
P=33
vIf the slope of a line is 32, how much vertical change will be present for a horizontal change of 96ft?
A horizontal change of 96ft, there will be a vertical change of 3072ft.
The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line. In other words, the slope is the rise over the run.
If the slope of a line is 32, that means that for every 1 unit of horizontal change, there is a 32 unit vertical change.
So, if the horizontal change is 96ft, we can use the slope formula to find the vertical change:
Vertical change = slope × horizontal change
Vertical change = 32 × 96
Vertical change = 3072
Therefore, for a horizontal change of 96ft, there will be a vertical change of 3072ft.
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2(3) to the power of 3 plus 5
1. a) Indicar tres monomios semejantes a - 3x¹.
b) ¿Vo F? 12ab y -12ab son semejantes.
c) ¿Vo F? 2x²y y 2xy² son semejantes.
d) Escribir dos monomios semejantes de grado 5 y cuya parte literal conste de dos letras.
Answer:
a) -5x, 3x y 7x son monomios semejantes a -3x¹.
b) Verdadero, ya que ambos tienen coeficiente -12 y la misma parte literal ab.
c) Falso, ya que el primer monomio tiene exponente 2 en la variable x y exponente 1 en la variable y, mientras que el segundo monomio tiene exponente 1 en x y exponente 2 en y.
d) 3x²y³ y 2x²y³ son dos monomios semejantes de grado 5 y cuya parte literal consta de las variables x e y elevadas a exponentes 2 y 3 respectivamente.
Let f(x)=x2+6x+11.
What is the minimum value of the function?
Enter your answer in the box.
Step-by-step explanation:
The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:
x = -b/2a
where a = 1 and b = 6 are the coefficients of the quadratic function.
x = -6/2(1) = -3
Substitute x = -3 into the function to find the minimum value:
f(-3) = (-3)^2 + 6(-3) + 11 = 2
Therefore, the minimum value of the function is 2.
A store is planning on having New Year's sale in which all winter coats will be discounted by 60%. Find the sale price of a coat that
has a regular price of $80
Answer:
$32
Step-by-step explanation:
Since the coats are discounted by 60%, we need to find 100-60=40% of the original price.
We need to find 40% of 80.
We can use proportional relationships.
100%=80
10%=8
40%=32
Find angle A on a triangle when A(5x-1) B is unknown and C(2x)?
Answer:
∠A = 64°
Step-by-step explanation:
You have a triangle inscribed in a semicircle with acute angles marked A=(5x-1)° and C=(2x)°.
Right triangleA triangle inscribed in a semicircle is a right triangle. (You know that because angle B is half the measure of 180° arc AC.) That means the two marked angles total 90°:
(5x -1) +(2x) = 90
7x = 91
x = 13
Then angle A is ...
A = (5·13 -1)° = (65 -1)° = 64°
The measure of angle A is 64°.
__
Check:
C = (2x)° = (2·13)° = 26°
Then A+C = 64° +26° = 90°, as required.
What is the constant of proportionality between
�
yy and
�
xx in the graph?
The response to the given question would be that The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
what is proportionality?Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.
It is difficult to estimate the constant of proportionality between two variables, y and x, without first viewing the graph.
Nevertheless, the constant of proportionality may be calculated by dividing any y-value by its corresponding x-value if the two variables are directly proportional, which means that when x rises, y rises as well at a consistent pace.
If y = kx, where k is the proportionality constant, then mathematically, k = y/x at every point on the graph.
The slope of the line is the constant of proportionality if the graph is a straight line through the origin.
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A function is given. g(x)=3−4/5x; x=−5 ,x=4 (a) Determine the net change between the given values of the variable. (No Response) (b) Determine the average rate of change between the given values of the variable. (No Response)
A function is given. g(x)=3−4/5x; x=−5 ,x=4 the net change between the given values of the variable is -7.2. The average rate of change between the given values of the variable is -0.8.
(a) To determine the net change between the given values of the variable, we need to find the difference between the function values at x = -5 and x = 4.
g(-5) = 3 - 4/5(-5) = 3 + 4 = 7
g(4) = 3 - 4/5(4) = 3 - 3.2 = -0.2
Net change = g(4) - g(-5) = -0.2 - 7 = -7.2
(b) To determine the average rate of change between the given values of the variable, we need to find the slope of the secant line between the points (-5, 7) and (4, -0.2).
Average rate of change = (g(4) - g(-5))/(4 - (-5)) = (-7.2)/(9) = -0.8
Therefore, the average rate of change between the given values of the variable is -0.8.
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Solve the proportion.
x/4=2/5
Answer:
[tex]x=1.6[/tex]
Step-by-step explanation:
To solve, first cross-multiply:
[tex]\frac{x}{4} = \frac{2}{5}[/tex]
[tex]5x = (4)(2)[/tex]
Then, solve the equation:
[tex]5x=8[/tex]
[tex]x=\frac{8}{5}[/tex]
[tex]\frac{8}{5} = 1.6[/tex]
[tex]x=1.6[/tex]
Therefore, x = 1.6.
I hope this helps!
1. A wholesaler received a shipment of goods, which is reported to be containing at most 2% defective items. He will accept the shipment if the claim is found true and reject if the percentage of defective items is more. To verity this claim, he draws a sample of 200 items and finds that 10 items are defective. Use 5% level of significance to investigate the claim.
At a 5% level of significance, the claims that a shipment of goods contains at most 2% defective items is accepted.
To investigate the claim that the shipment contains at most 2% defective items, we can use the 5% level of significance. The claim is that the population proportion of defective items is at most 2%, or p0 ≤ 0.02. The sample size is n = 200, and the sample proportion of defective items is pobs = 10/200 = 0.05.
The test statistic is then:
z = (pobs - p0) / √(p0(1-p0) / n)
= (0.05 - 0.02) / √(0.02(1-0.02)/200)
= 1.02.
With a 5% level of significance, we can look up the critical value for a one-tailed z-test and find that it is zα/2 = 1.645. Because 1.02 < 1.645, the test statistic is not greater than the critical value, and thus we fail to reject the null hypothesis that the population proportion of defective items is at most 2%.
In conclusion, with a 5% level of significance, the claim that the shipment contains at most 2% defective items is accepted.
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Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
The system of equations shown models the total costs for taking 10 classes at each.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that Toe Tappers charges a rate for each class plus a one-time registration fee.
Dance World, y = 15x
Toe Tappers, y = 25 + 12.5x
Where x = number of classes
Now Equate the total cost at both dance studios;
15x = 25 + 12.5x
Collect like terms;
15x - 12.5x = 25
2.5x = 25
Divide both sides by 2.5;
2.5x / 2.5 = 25 / 2.5
x = 10 classes
Thus, x = number of classes = 10
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Please help asap i need this badly
Answer:
75 seconds
Step-by-step explanation:
You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.
RemainingSean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.
It takes 75 seconds for Sean to finish the slushy.
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I need help on this asap!!!!!
If Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company
Determining the company that minimizes cost
From the question, we are to determine which company Emma should use when she wants to minimize cost.
Let's assume that Emma needs to travel a distance of d miles to get to the airport.
The cost C of taking the red cab company can be represented by the function:
Cred(d) = 3.50 + 1.25d
Similarly, the cost C of taking the yellow cab company can be represented by the function:
Cyellow(d) = 5.00 + 1.15d
To determine which company Emma should use to minimize cost, we need to find the value of d that makes the cost of each company equal. In other words, we need to solve the equation:
Cred(d) = Cyellow(d)
Substituting the expressions for Cred(d) and Cyellow(d), we get:
3.50 + 1.25d = 5.00 + 1.15d
Simplifying and solving for d, we get:
0.10d = 1.50
d = 15
Hence, if Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company.
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Which graph represents the solution for the open sentence 3|p|−5<7
?
Responses
Number line ranging from negative five to five. A line begins with an open point at negative four and continues to the left without end. A second line begins with an open point at four and continues to the right without end.
Image with alt text: Number line ranging from negative five to five. A line begins with an open point at negative four and continues to the left without end. A second line begins with an open point at four and continues to the right without end.
Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.
Image with alt text: Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.
Number line ranging from negative five to five. A line begins with a closed point at negative four and ends with a closed point at four.
Image with alt text: Number line ranging from negative five to five. A line begins with a closed point at negative four and ends with a closed point at four.
Number line ranging from negative five to five. A line begins with a closed point at negative four and continues to the left without end. A second line begins with a closed point at four and continues to the right without end.
The graph that represents the solution for the open sentence 3|p|−5<7 is:
What is graph?a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables
: the collection of all points whose coordinates satisfy a given relation (such as a function)
: a collection of vertices and edges that join pairs of vertices
Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.
Image with alt text: Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.
In this graph, the open points at -4 and 4 indicate that the values of p that make the inequality true do not include -4.
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find the sine of angle C in this triangle.
The sine of angle C is √30/10.
Trigonometric ratios:Trigonometric ratios are mathematical expressions used to relate the angles and sides of a right-angled triangle.
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
are the fundamental ratios in a right-angle triangle
where
"Opposite" refers to the side opposite to the angle.
"Adjacent" refers to the side adjacent to the angle.
"Hypotenuse" refers to the longest side of the right-angled triangle
Here we have
A right-angle triangle DCB
Where DC = 10 units, CB = √70
From trigonometric ratios,
Sin θ = Opposite side/ Hypotenuse
Sin C = DB/CD
By the Pythagorean theorem
=> DC² = CB² + DB²
=> (10)² = (√70)² + DB²
=> 100 = 70 + DB²
=> DB² = 100 - 70
=> DB = √30
Sin C = √30/10
Therefore,
The sine of angle C is √30/10.
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Determine the Equation of circle A
Answer:
Step-by-step explanation:
When writing the equation for a circle on a plane, we use the format:
[tex](x-x_{1})^2+(y-y_{1})^2=r^2[/tex]
x1 and y1 is the point of the center of the circle, which in this case is (1,-2)
r represents the radius, which is the distance from the center to the edge of the circle, which is (4,-2) - (1,-2) = 3
Our equation is now:
[tex](x-1)^2+(y+2)^2=9[/tex]
the reason why its y+2 is because (y-(-2) = (y+2)
r is squared, which is why it's 9 instead of 3. Hope this helps!
The graph of polygon FGHI is shown. Graph the image of FGHI after a reflection across the line y=-1. Include the line of reflection. Then write the coordinates of the image.
The coordinates of the reflected polygon F'G'H'I' are as follows:
F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).
What is the reflection?In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.
The vertices of the polygon FGHI are as follows:
F(2, -1)
G(5, 2)
H(8, 3)
I(6, 0)
To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.
Now we can reflect each of the points of the polygon across the line y = -1 to get the image:
F(2, -1) stays in the same place because it lies on the line of reflection.
G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.
H(8, 3) is reflected to H'(8, -5), and
I(6, 0) is reflected to I'(6, -2).
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The air temperature decreases about 5°F for each increase of 1,000 feet in altitude. If the outside temperature at ground level in a certain location is 68°F, then the air temperature y is represented by the function y=−5x+68 , where x is the altitude (in thousands of feet).
Which of the following sets of numbers would be appropriate input values for the given situation? Select all that apply.
Multiple select question.
cross out
A)
By answering the above question, we may infer that The input value 0 equation represents the height at sea level, making it an inappropriate value for this function.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
For the predicament, the following input values would be suitable:
B) 1
C) 2
D) 3
E) 4
As the temperature drops by around 5°F for every 1,000 feet of height, we must utilise altitude numbers in thousands of feet to obtain the function's proper input values. Hence, we would utilise a value of 1 as an input for every 1,000 feet of height rise. Consequently, 1, 2, 3, and 4 would be the proper input values, which correspond to altitudes of 1,000, 2,000, 3,000, and 4,000 feet, respectively. The input value 0 represents the height at sea level, making it an inappropriate value for this function.
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Which expressions contain exactly two terms? Choose ALL that are correct. Responses −5+6x+3y2 − 5 + 6 x + 3 y 2 4x 4 x 7−9x 7 − 9 x (x+2)(y−4) ( x + 2 ) ( y − 4 ) 8x2+5x
The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.
The expressions that contain exactly two terms are:
7 - 9x
8x2 + 5x
Therefore, The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.
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Convert the following phrase into a mathematical expression. Use x as the variable. Combine like terms when possible.
A number multiplied by −8, subtracted from the sum of 5 and three times the number
The expression is ____.
The expression will be 5 + 11x.
What is an expression?
An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)
It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.
Explanation: 3 + 7
Let the number to be "x"
Step 1 : the number is multiplied by - 8
So, -8 x
Step 2 : subtracted from the sum of 5 and 3 times the number
So, (5 +3x) - (-8x)
= 5+3x + 8x
= 5 + 11x
Hence, The final expression will be 5 + 11x.
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Solve
5sin(x)−2cos(x)=3
for the first 2 positive solutions
x=
Give your answers accurate to at least 2 decimal places, as a list separated by commas Let
f(x)=5.7sin(x)−3.9cos(x)
. What is the maximum and minimum value of this function?
max=
min=
Report answers accurate to 4 decimal places.
The maximum value of the function is 6.9159 and the minimum value is -6.9159, accurate to 4 decimal places. The answers should be provided as a list separated by commas, so the final answer is:
max = 6.9159, min = -6.9159
The first step in solving 5sin(x)−2cos(x)=3 is to rearrange the equation to isolate the sin(x) term. We can do this by adding 2cos(x) to both sides of the equation:
5sin(x) = 3 + 2cos(x)
Next, we can divide both sides of the equation by 5 to isolate the sin(x) term:
sin(x) = (3 + 2cos(x))/5
Now, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to substitute for cos(x) and solve for sin(x):
sin^2(x) = (3 + 2√(1 - sin^2(x)))/5
Multiplying both sides of the equation by 5 and rearranging gives us:
5sin^2(x) - 2√(1 - sin^2(x)) - 3 = 0
We can use the quadratic formula to solve for sin(x):
sin(x) = (-(-2) ± √((-2)^2 - 4(5)(-3)))/(2(5))
Simplifying gives us:
sin(x) = (2 ± √(28))/10
Using a calculator, we can find the first 2 positive solutions for x:
x = sin^-1((2 + √(28))/10) ≈ 0.72, 2.42
Therefore, the first 2 positive solutions for x are 0.72 and 2.42, accurate to at least 2 decimal places.
To find the maximum and minimum values of f(x)=5.7sin(x)−3.9cos(x), we can use the formula:
max = √(a^2 + b^2)
where a and b are the coefficients of the sin(x) and cos(x) terms, respectively. Substituting in the values for a and b gives us:
max = √((5.7)^2 + (-3.9)^2) ≈ 6.9159
The minimum value of the function is the negative of the maximum value:
min = -6.9159
Therefore, the maximum value of the function is 6.9159 and the minimum value is -6.9159, accurate to 4 decimal places. The answers should be provided as a list separated by commas, so the final answer is:
max = 6.9159, min = -6.9159
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If f (x) = √x
Write the equation for the transformed functions "y1" and "y2"
y1 = 2f (x + 5) -3 Equation : _______
y2 = f(2(x - 5)) + 3 Equation : _______
Given the equation f(x) = x^2 - 9, write the equations for – f(x) and for f(–x)
f(x) = x^2 - 9
f(-x) = (-x)^2 - 9
y1 = 2√(x + 5) - 3
y2 = √(2(x - 5)) + 3
For the second question:
f(x) = x^2 - 9
f(-x) = (-x)^2 - 9
f(-x) = x^2 - 9
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Christian's money from his job increased from $12 hour to $21 hour. What is the percent increase?
Answer:
75%
Step-by-step explanation:
Starting value: 12
Final Value: 21
Subtract final value minus starting value
Divide that amount by the absolute value of the starting value
Multiply by 100 to get percent increase
If the percentage is negative, it means there was a decrease and not an increase.
if the diameter of a cone is 19 yd and the height is 13 yd . What is the volume?
If the diameter of a cone is 19 yd and the height is 13 yd, the volume of this cone is equal to 1,228 cubic yard.
How to calculate the volume of a cone?Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Where:
V represents the volume of a cone.h represents the height.r represents the radius.Radius = diameter/2 = 19/2 = 9.5 cm.
Substituting the given parameters into the volume of a cone formula, we have the following;
V = 1/3 × πr²h
V = 1/3 × 3.14 × 9.5² × 13
Volume, V = 1,228 cubic yard.
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A farmer sells 7.1 kilograms of apples and pears at the farmers market. 2 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmers market?
answer:
4.6 kilograms of pears
question:
I don't know if you meant 2.5 or 25 but ill assume you meant 2.5
Question 4.
A high school sports team is ordering sports drinks online from a company. The price of sports drinks varies, based on the number of drinks purchased. For orders of 50 or fewer sports drinks, the price is $0.80 per drink, plus $10 shipping and handling. When more than 50 sports drinks are ordered, the price is $0.70 per drink, plus $15 shipping and handling. What is the maximum amount of sports drinks you can purchase for $75?
A. 85
B. 81
C. 92
D. 107
Using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.
What is meant by an equatiοn?A mathematical equatiοn is a fοrmula that uses the equals symbοl (=) tο cοnnect twο expressiοns and express their equality. The definitiοn οf an equatiοn in algebra is a mathematical statement that prοves twο mathematical expressiοns are equal. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equatiοns. Yοu can sοlve equatiοns tο determine an unknοwn variable's value, which cοrrespοnds tο an unknοwn quantity. It is nοt an equatiοn if there is nο "equal tο" sign in the statement. That shall be taken intο accοunt as an expressiοn.
Let,
the number οf drinks = x
the tοtal cοst οf the x drinks = y
Then we can write equatiοns using the given infοrmatiοn.
When the οrder cοntains 50 οr fewer spοrts drinks, the equatiοn is:
y = 0.8x + 10
When the οrder cοntains mοre than 50 spοrts drinks, the equatiοn is:
y = 0.7x + 15
Since we have tο find the number οf drinks fοr $75, we can write that:
y = 75
Substituting in the equatiοns,
75 = 0.8x +10
65 = 0.8x
x= 81.25 = 81
75 = 0.7x +15
60 = 0.7x
x = 85.7 = 86
Nοw, 86 > 81
Therefοre using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.
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8x^2+18x+9
Box method
Answer:
144x^3+9
Step-by-step explanation:
First of all multiply 8x^2 and 18x then it is 144