At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.
(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:
f'(t) = 400 + 200cos(πt/12).
At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.
(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:
g'(t) = 200 - 200cos(πt/12).
At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.
the complete question is :
both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?
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Let a function f A B be defined by f(x) 11 B-1-2, 1, 0,2- 4¹5) 0. can you make it one to one and onto both? x-1 F x*-2 with A = {-1, 0, 1, 2, 3, 4) and x+2 find the range off. Is the function one to one and onto both? If not, how a whother each of the functions below is one to one, onto both?
Answer:
The function f: A -> B is defined by:
f(x) = { 11, if x = -1 or x = 2,
-1, if x = 0,
-2, if x = 1,
0, if x = 3 or x = 4 }
The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.
To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.
To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.
Therefore, the function f is one-to-one and onto both.
If the sum of two angles is 90 then angles are called ___angles
If the sum of two angles is 90 degrees, then the angles are called complementary angles.
Complementary angles are a type of angle relationship where two angles add up to exactly 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always equal to 90 degrees.
For example, if angle A measures 30 degrees, and angle B measures 60 degrees, then angle A and angle B are complementary angles, because 30 degrees + 60 degrees = 90 degrees.
Complementary angles are important in geometry and trigonometry, because they often appear in problems involving right triangles. In a right triangle, one of the angles measures 90 degrees, which means that the other two angles must be complementary.
For example, if one angle in a right triangle measures 30 degrees, then the other angle must measure 60 degrees, since 30 degrees + 60 degrees = 90 degrees.
Understanding complementary angles can be useful in a wide range of mathematical and real-world contexts. For example, in construction or engineering, understanding complementary angles can help ensure that structures are built at the correct angle to provide the necessary support and stability.
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subsitute (-3,3) 2y+x=3 y=x+0
Answer:
Point (-3, 3) is not a solution to the system of equations
2y+x=3
y=x+0
Step-by-step explanation:
2y + x = 3
y = x + 0
2(3) + (-3) = 3
6 - 3 = 3
3 = 3
The point works in the first equation.
3 = -3 + 0
3 = -3
The point does not work in the second equation.
a circle with radius is inscribed in a square and circumscribed about another square as shown. which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?
The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.
A fraction is a mathematical expression that represents a part or a proportion of a whole.
Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.
Now, let's consider the area of the circle. The formula for the area of a circle is
=> A=πr².
Therefore, the area of the circle is πr².
The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is
=> (2r)²=4r²,
and the area of the inner square is
=> (r√2)²=2r².
Hence, the area between the two squares is
=> 4r²−2r²=2r².
The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is
=> πr²−2r²=(π−2)r².
Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,
ratio = (π - 2)r² / 2r
We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,
ratio = (π - 2) / 2
This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.
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solve the problem and then click on the correct answer choice. jane must select 3 different items for each dinner she will serve. the items are to be chosen from among 5 different vegetarian and 4 different meat selections. if at least one of the selections must be vegetarian, how many different dinners can jane create?
Jane can select 80 different types of dinner consisting of 3 different items from 5 different vegetarian items and 4 different meat items available.
For finding the various combination of dinners available which has atleast one vegetarian item we will apply combination formula with the given data i.e., [tex]^{n} C_{r} = \frac{n!}{(n-r)!.r!}[/tex]
A combination is a way of selecting items from a collection where the order of selection does not matter.
We will have to apply the formula separately for vegetarian and meat items.
Combinations available
A. 1 vegetarian item and 2 meat items
[tex]^{5} C_{1} and ^{4} C_{2}[/tex] (In combination "and" means to multiply)
= [tex]\frac{5!}{(5-1)!.1!} . \frac{4!}{(4-2)!.2!}[/tex]
= [tex]\frac{5!}{(4)!.1!} . \frac{4!}{(2)!.2!}[/tex]
= [tex]\frac{5.4.3.2.1}{(4.3.2.1).(1)}. \frac{4.3.2.1}{(2.1).(2.1)}[/tex]
= 5.3.2
= 5.6
= 30
B. 2 vegetarian items and 1 meat item
[tex]^{5} C_{2} and ^{4} C_{1}[/tex]
= [tex]\frac{5!}{(5-2)!.2!} . \frac{4!}{(4-1)!.1!}[/tex]
= [tex]\frac{5!}{(3)!.2!} . \frac{4!}{(3)!.1!}[/tex]
= [tex]\frac{5.4.3.2.1}{(3.2.1).(2.1)}. \frac{4.3.2.1}{(3.2.1).(1)}[/tex]
= 5.2.4
= 10.4
= 40
C. 3 vegetarian items and no meat item
= [tex]^{5} C_{3} and ^{4} C_{0}[/tex]
= [tex]\frac{5!}{(5-3)!.3!} . \frac{4!}{(4-0)!.0!}[/tex]
= [tex]\frac{5.4.3.2.1}{(2.1).(3.2.1)}. 1[/tex]
= 5.2
= 10
Now, we will add all the different combination
Total combinations = 30+40+10
= 80 different type of dinners
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Topic: Using the rational theorem to find all zeros of a polynomial
Question: 5x^4-26x^3-64x^2+9x-14
The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 , [tex]\frac{1+i\sqrt{19} }{10}[/tex] and [tex]\frac{1-i\sqrt{19} }{10}[/tex] by Using the rational theorem.
f(x) = [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
Now, put x = -2
f(-2) = [tex]5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14[/tex]
f(-2) = 0
so, -2 is a zero of f(x)
or (x+2) is a factor of [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
putting x = 7
f(7) = [tex]5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14[/tex]
f(7) = 0
so, (x-7) is a factor of [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
Now (x+2)(x-7) would also be a factor so
Divide [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by (x+2)(x-7)
or divide [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by [tex]x^{2} -5x -14[/tex]
The quotient or other factor will be [tex]5x^{2} - x +1[/tex]
[tex]5x^{2} - x +1[/tex]
By factorizing [tex]5x^{2} - x +1[/tex]
The other two zeroes are [tex]\frac{1+i\sqrt{19} }{10}[/tex] and [tex]\frac{1-i\sqrt{19} }{10}[/tex]
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The vertex form of the function is y = (x +)2+.
The vertex form of the function is [tex]y = (x+4)^{2} - 19[/tex]
Vertex form of function:
The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.
The vertex form of the equation is written as,
[tex]y = (x+h)^{2} + k[/tex]
Given function is,
y = x² + 8x + 16 - 3 -16
It is observed that,
x² +8x + 16 = (x+4)²
So that, we can write as above function,
y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16
or
y = (x+4)² - 19
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A company charges a shipping fee that is 4. 5% of the purchase price for all items it ships. What is the fee to ship an item that costs 56$?
The shipping charge of an item on the purchase $56 is $2.52.
PercentagePercentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The percentage of a number is the value of the number out of 100.
For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.
A company charges shipping fee = 4.5% of the purchase price for all items,
Cost of an item =$56
So, shipping fee = 4.5% of 56
= 4.5/100 × 56
= 0.045 × 56
= $2.52
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The monster under your bed loves fruit. To appease him you buy 4 pounds of grapes. You also buy some strawberries. Both fruits cost $1.20 per pound. You spend $6. How many pounds of strawberries did you buy?
Answer:
1 pound of strawberries
Step-by-step explanation:
4 x $1.20 = $4.80
$6 - $4.80 = $1.20
one pound is $1.20
he accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.
a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.
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Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function.
The equation of the polynomial is P(x) = 0.16875(x + 8)(x - 10)
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -8
A root of multiplicity 1 at x = 10
y-intercept = -13.5
A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 8)(x - 10)
The y-intercept is -13.5
So, we have
a * (0 + 8)(0 - 10) = -13.5
This gives
a = 0.16875
Hence, the expression is P(x) = 0.16875(x + 8)(x - 10)
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4. Dilate the figure with the origin as the center of dilation.
(x,y) → (2x, 2y)
The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the quadrilateral be represented as ABCD
Now , the coordinates of ABCD is given as
A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )
Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin
Substituting the values in the equation , we get
A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )
On simplifying the equation , we get
The coordinates of A' is = A' ( -2 , 4 )
The coordinates of B' is = B' ( 4 , 4 )
The coordinates of C' is = C' ( 6 , -2 )
The coordinates of D' is = D' ( 0 , -2 )
Hence , the dilated figure is solved
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8 more than the quotient of a number b and 25 is greater than 6
When eight more than the quotient of a number 'b' and 25 is greater than 6 then the inequality representing the value of b is b > -50.
The expression used to represents :
Quotient of a number b and 25 is equal to b / 25
Next step is :
8 more than the b / 25 is equal to ( b / 25 ) + 8
Then ,
( b / 25 ) + 8 is greater than 6 is given by
⇒ ( b / 25 ) + 8 > 6
Simplify the above inequality for 'b' we get,
⇒ ( b / 25 ) > 6 - 8
⇒ ( b / 25 ) > -2
Multiply both the side by 25 we get,
⇒ b > - 2 × 25
⇒ b > -50
Therefore, the inequality representing the value of 'b' for the condition of quotient and a number is equal to b > -50.
The above question is incomplete , the complete question is:
8 more than the quotient of a number b and 25 is greater than 6 , then the value of b is ?
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Factor the polynomial.
3x³-300x
The result to the factorization of the polynomial is 3x (x + 10) (x - 10).
Polynomial FactorizationFactoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.
= 3x³ - 300x
= 3x(x²) - 300x
= 3x(x²) - 3x(100)
= 3x(x² - 100)
= 3x(x² - 10²)
Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );
where
a = x and b = 10= 3x (x+10) (x−10)
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(a) What additional information is needed to prove the triangles are congruent by ASA Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HLTheorem? Explain.
Part (a)
ASA = angle side angle
To use ASA, we need two angles and a side between those angles. We already have one pair of angles (DFE and GHI). The other pair of angles must be DEF and GIH to have the side sandwiched between the angles.
Answer: We need to know if angle DEF is congruent to angle GIH===================================================
Part (b)
HL = hypotenuse leg
The sides EF and IH are congruent to one another because of the tickmarks. They are the legs of each right triangle. So that takes care of the "L" of "HL". We need to have the hypotenuses congruent to each other to be able to use HL. This theorem only applies to right triangles.
Answer: We need to know if segment DE is congruent to segment GIA cylinder has a radius of 2.5meters. Its volume is 37.5\pi cubic meters. What is the height of the cylinder?
Answer: height = 1.91 m
Step-by-step explanation: Using the formula
V=πr2h
Solving for h
h=V
πr2=37.5
π·2.52≈1.90986m
the multiple linear regression predictive model is thus: and the least squares optimization target is we can find the least squares solution by finding the gradient of with respect to and setting it to zero: what kind of object is ? a real number a vector with the same size as . a matrix of the same size as . a vector with the same size as . unanswered what is ? . . . unanswered savesave your answer submit you have used 0 of 3 attempts
Object is kind of a vector with the same size as the coefficients in the linear regression model.
In the least squares optimization target, the sum of squared errors (SSE) is typically minimized with respect to the coefficients of the linear regression model. The gradient of the SSE with respect to the coefficients is a vector that provides the direction of steepest ascent, or the direction in which the SSE increases the most rapidly. Setting this gradient vector to zero and solving for the coefficients yields the least squares solution to the linear regression problem.
Therefore, in this context, " " is likely a vector of coefficients that are being optimized to minimize the SSE.
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please help me im a bit stck on this question
Find sin a + cos a if sin a * cos a = 3/8
The value of sin a + cos a is √7/2.
Trigonometric identities:Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
Based on the right-triangle theorem, which is known as Pythagoras theorem, there are three Pythagorean trigonometric identities in trigonometry as follows
sin² a + cos² a = 11+tan² a = sec² acosec² a = 1 + cot² aHere we have
sin a × cos a = 3/8
Multiply with 2 on both sides
=> 2(sin a × cos a) = 2(3/8)
=> 2 sin a cos a = 3/4
Add sin²a + cos²a on both sides
=> sin²a + cos²a + 2 sin a cos a = 3/4 + sin²a + cos²a
As we know (a + b)² = a²+ b² + 2ab
=> (sin a + cos a)² = 3/4 + 1
=> (sin a + cos a)² = 7/4
=> sin a + cos a = √7/2
Therefore,
The value of sin a + cos a is √7/2.
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Can someone show meh pls
The tape diagram represents an equation.
Write an equation to represent the image
w 1.3 2.7
The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The length of both tapes is the same. Then the equation is given as,
w + 1.3 = 2.7
Simplify the equation for w, then we have
w + 1.3 = 2.7
w = 1.4
The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.
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in the sketch A is an x-intercept and B is the turning point of the parabola, f(x) =ax^2+bx+c the straight line AB is defined as g(x) =3x+6.D(-1\3:35/6) is a point of f and CD is perpendicular to t x-axis B in the y intercept of f and g
Determine the coordinates of B
The required coordinates of B are (0, 6) for the given parabola.
What is x-Intercept?The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.
To determine the coordinates of B, we can use the information given in the problem.
A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).
The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.
Therefore, we can set x = 0 in both equations to find the y-coordinate of B.
For f(x), we have:
f(0) = a × 0² + b × 0 + c = c
For g(x), we have:
g(0) = 3 × 0 + 6 = 6
Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:
c = 6
So, the coordinates of B are (0, 6).
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A water sample shows 0.04 grams of some trace element for every cubic centimeter of water. Samir uses a container in the shape of a right cylinder with a radius of 8.1 cm and a height of 17.9 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Samir collected? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
To find the volume of the container, we can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height. Plugging in the given values, we get:
V = π * 8.1^2 * 17.9 = 1146.4 cm^3
Since the sample contains 0.04 g of the trace element per cubic centimeter of water, the amount of trace element in the entire container can be found by multiplying the volume of the container by the concentration of the trace element:
0.04 g/cm^3 * 1146.4 cm^3 = 45.86 g
So Samir has collected approximately 45.9 g of the trace element, rounded to the nearest tenth.
Answer:147.6g
Step-by-step explanation
What coordinates did we plot when we graphed the function y = 3x - 4?
You should have 4 answers selected.
1. (-1, -7)
2. (-1, 8)
3. (0, -4)
4. (0, 9)
5. (1, -1)
6. (2, 2)
The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
we graphed the function y = 3x - 4
now, the required coordinates are, which satisfies the graph function.
as, we get,
(-1, -7), satisfies the graph function
(0, -4) , satisfies the graph function
(1, -1), satisfies the graph function
Hence, The solution is, (-1, -7), (0, -4), (1, -1), satisfies the graph function, the coordinates did we plot when we graphed the function y = 3x - 4
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My parents give me an allowance of $60 every month. To earn some extra money I get a job. I make $7.50 an hour at this job. In order to have a social life and hang out with my friends, I am going to need at least $260 every month.
What is the APPROXIMATE minimum amount of hours I will have to work to accomplish my goal? (HINT: use whole numbers for your answer)
I would need to work at least 27 hours to make enough money to reach my goal.
What are arithmatic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:
Allowance per month = $60
Amount of money I need for social life = $260
Additional amount of money I need to make = $260 - $60 = $200
Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:
$200 ÷ $7.50 per hour = 26.67 hours
Since we can't work a fraction of an hour, we need to round up to the nearest whole number.
Therefore, I would need to work at least 27 hours to make enough money to reach my goal.
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Celine's Cupcakes recorded how many cupcakes it recently sold in each flavor. carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6 Considering this data, how many of the next 20 cupcakes sold would you expect to be lemon cupcakes?
So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.
What is Algebraic expression?
An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables can represent unknown values, while the constants represent known values.
Based on the data provided by Celine's Cupcakes, out of the total of 15 cupcakes sold, 6 were lemon cupcakes. This means that the proportion of lemon cupcakes sold is:
6/15 = 0.4
To estimate how many of the next 20 cupcakes sold would be lemon cupcakes, we can assume that the proportion of lemon cupcakes sold will remain the same. Therefore, we can expect that:
0.4 x 20 = 8
Therefore, So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.
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please explain correctly how to get the correct answer thank you.
Answer:
Option C
Step-by-step explanation:
First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.
A. x = 63, and z = 104 and together they equal 170, so not A
B. x = 76 and z = 63 and together they equal 139 so not B
C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.
D. x = 63 and z = 76 and together they equal 139 so not D.
From all of this it must be option C
Marsha uses 8.3 pints of blue paint and white paint to paint her bedroom walls. 3 5 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls? Express your answer in fraction and decimal form.
Answer:
Step-by-step explanation:
4.8
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Answer:
i think it x = 0 and x = 5
Step-by-step explanation:
[tex]y = {x}^{2} - 4x + 2[/tex]
[tex]y = x + 2[/tex]
[tex]x + 2 = {x}^{2} - 4x + 2[/tex]
[tex]0 = {x}^{2} - 4x + 2 - x - 2[/tex]
[tex]0 = {x}^{2} - 5x[/tex]
[tex]0 = x(x - 5)[/tex]
[tex]x = 0[/tex]
(or)
[tex]x - 5 = 0[/tex]
[tex]x = 5[/tex]
what is the slope of the line
Answer:
slope = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line
m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]
nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. let the probability that each delegate sits next to at least one delegate from another country be $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
Contact nations A, B, and C. At the northernmost position for configurations, someone from A is seated. Since the only thing the problem mentions about how delegates can differ is by their country, I decided to represent people in my solution by their respective nations. Now, we can see that there are nCr(8, 2) * nCr(6, 3) = 560 possible arrangements (8 seats choose 2 for the rest of the A country, 6 seats choose 3 for B). It is clear that configurations with three delegates in a row are the ones we don't want. Take note that scenarios for A, B, and C to be together are still valid despite my placing of A at the start.We now apply the inclusion-exclusion principle. Two cases for an A three in a row. First. A, Master A, A: $20 for B seats at nCr(6, 3). Additionally, there is $20 for each "slant" A set. =$60. *3=180. A and B both: Two cases once more! We identify four ways for B to get three in a row: A, Master A, A, and A. $12 is the same for slant. *3 = $36 (AB, BC, or CA). For all three: This time, we have two of the three aforementioned A circumstances, for a total of six. 180-36+6 Equals 150 in the end. The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
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