The rates of change in attendance in week 1-4 is 33, week 4-6 is -11, week 6-10 is -37 people per week
What is rate of change of attendance?The rate of change in attendance with respect to time is calculated by taking the difference in attendance between two weeks and dividing by the number of weeks between those weeks. This is done to find the average rate of change in attendance per week. The formula used is:
[tex]Rate =\frac{Attendance at week 2 - Attendance at week 1}{week 2 - week 1}[/tex]
Weeks 1-4:
The rate of change in attendance with respect to time is 33 people per week. This can be calculated by taking the difference in attendance between weeks 1 and 4 (230-131) and dividing by the number of weeks between those weeks (4-1 = 3).
[tex]rate =\frac{230-131}{4-1}\\[/tex]
hence rate is 33 people per week
Weeks 4-6:
The difference in attendance between weeks 4 and 6 (230 - 208)
The number of weeks between those weeks (6-4 = 2).
[tex]rate =\frac{208-230}{6-4}[/tex]
Hence rate is -11 people per week
Weeks 6-10:
The difference in attendance between weeks 6 and 10 (60-208)
The number of weeks between those weeks (10-6 = 4).
[tex]rate=\frac{60-208}{10-6}[/tex]
Hence rate is -37 people per week
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Colton works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Colton make in a week in which he made $1075 in sales? How much would Colton make in a week if he made xx dollars in sales?
Answer:
Step-by-step explanation:
If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.
Find the radius of the circle, if the big square is 30 square units more than the area of the small square.
Answer:
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:
The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
Here, we have,
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle.
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Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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p.
Sue uses of a pitcher of sweet tea to fill
each of 6 matching glasses. What fraction of
the pitcher does Sue use to fill 1 glass?
Answer:
P. Sue uses 1/6 of the pitcher to fill 1 glass
Step-by-step explanation:
Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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During a fundraiser, Kate wants to sell the same number of $5 candy bars as $2 candy bars. The expression that represents how much money Kate will collect is . Identify any variables, constants, and coefficients and explain what they mean in terms of the expression representing this scenario.
The expression that represents how much money Kate will collect
is y = 5x + 2x.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, During a fundraiser, Kate wants to sell the same number of $5 candy bars as $2 candy bars.
Let, The number of candies she sold be 'x' and the total cost of the candies be 'y'.
Therefore, The phrase that describes the amount of money Kate will bring in is y = 5x + 2x.
y = 7x.
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(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
How many possible triangles can be created if measure of angle A equals pi over 6 comma c = 18, and a = 9?
0 triangles
1 triangle
2 triangles
Cannot be determined based on the given information
If the measure of angle A equals pi over 6, the angle c equals 18, and the angle an equals 9, triangles may be formed.
When do three lines join to make a triangle?You only need to apply the Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side. A triangle will exist if this holds true for each of the three possible added side length combinations.
From the given information, we have that:
m<B = pi/6 = 30 degres
c = 10
b = 5
This shows that we can use the cosine rule to find the third side b of the triangle. Since all the sides are complete, hence we can use the information given to find just 1 triangle
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Use the diagram to find the indicated angle measures. Please do 1, 2, and 3. Please need ASAP!!!!!!!!!!!!!!! 30 POINTS
The measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given m∠B= 57 degrees
m∠c= 51 degrees
segment AD bisects m∠BAC
then m∠ADC we need to find.
As AD is perpendicular to BC, the angle of m∠ADC is 90 degrees.
Given m∠B= 66 degrees
m∠BAD=34 degrees
Now we need to find m∠DAC
m∠DAC will be 34 degrees
Hence, the measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees
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Does the table below represent a proportional relationship?
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)
What is a proportional relationship?Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.
The equation that is used to represent a proportional relationship is:
y = kx
Where:
k = constant of proportionality
Value of k when x is 1:
3 = k
Value of k when x is 2:
6 = 2k
k = 6 / 2
k = 3
Value of k when x is 3:
9 = 3k
k = 9 / 3
k = 3
Value of k when x is 4:
12 = 4k
k = 12 / 4
k = 3
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On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
Help me please 35 points on the line
Answer shown in bold
401924109147The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.
========================================================
Explanations:
Add up all of the values in the Venn diagram to find the total. Therefore, 9+10+14+7 = 40 students were surveyed.We add the values in the "social interaction activities" circle only. There are 9+10 = 19 students here.This time add up the values in the "technology driven activities" to get 10+14 = 24 students.The answer is 10 because this value is in the overlapped region between the two circles. The answer is 9 since this value is in the "social interaction activities" circle, but outside the other circle. The answer is 14 as this value is in the "technology driven activities" circle, but outside the other circle.The answer is 7 because this value is outside both circles.Let me know if you have any questions.
2. Avea checked out 18 books
from the library. Half of them
are nonfiction. How many
nonfiction books did she check
out?
Answer: she checked out 9 nonfiction books
Step-by-step explanation:
18-9=9
The temperature during the night was -4. In the morning the temperature increased by 3. What is the temperature in the morning
Answer:
-1
Step-by-step explanation:
Night: -4
Morning: -4 + 3 = -1
Find the distance between the points
(-5/2, 9/4) and(-1/2,-3/4)
Give the exact distance and an approximate distance rounded to at least 2 decimal places.
Make sure to fully simplify any radicals in first answer
Answer:
Step-by-step explanation:
distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61
Find the LCM of the first five primes
Answer:
The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310
12 divided by four
plus 2 x 6+4
Answer:
19
Step-by-step explanation:
12 divided by four plus 2 x 6+4
assuming that the question is:
12 : 4 + 2 x 6 + 4 =
3 + 12 + 4 = (remember PEMDAS)
19
In the algebraic expression, 6x + 10, x is the (blank), 6 is the (blank), and 10 is the (blank)?
In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.
What are algebraic expressions?
Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.
Examples of algebraic expressions include:
2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)
A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.
A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.
A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.
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for a pendulum with a length of l meters, the time in seconds that it takes the pendulum to swing back and forth is 2L^1/2. how long does it take a pendulum that is 9 meters long to swing back and forth
It will take 9 seconds a pendulum that is 9 meters long to swing back and forth.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
WE are Given the expression of length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth modeled as;
T = 2√L
Given
Length of the pendulum = 9 meters
Required Time (period)
Substitute the given value into the formula
T = 2√L
T = 2√9
T = 2 x 3
T = 6 seconds
Hence the period is 6 seconds
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8z = 4x - 32
Please explain step by step
The solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It consists of an equals sign and two expressions, one on each side of the equals sign. Equations are used to solve for the value of the unknown expressions, and can be used to solve problems in various fields such as physics, chemistry, engineering, and mathematics.
1. Start by isolating the z variable by subtracting 4x from both sides of the equation. This will give us: 8z = -32.
2. Divide both sides of the equation by 8. This will give us: z = -4.
3. Finally, substitute z = -4 into the original equation and solve for x. This will give us: 4x = 32, so x = 8.
Therefore, the solution to the equation 8z = 4x - 32 is z = -4 and x = 8.
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Complete questions as follows-
8z = 4x - 32
Please explain step by step how to solve 8z = 4x - 32.
HELPPP ASPPO!!
4x -y=6
-4x +y =8
which statement correctly describes the system of equations
The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .
what is equations ?A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.
given
Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.
The values of the variables you are solving for will be provided by the coordinate of this point.
The equation system is appropriately described by the formula 4x - y=6.
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Two parallel lines are crossed by a transversal.
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
What is the value of y?
The value of y is 130°
What are corresponding angles?The angles occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.
Given here:
Horizontal and parallel lines b and c are cut by transversal a. At the intersection of lines b and a, the bottom right angle is 50 degrees. At the intersection of lines c and a, the top left angle is y degrees.
Thus the angle adjacent to the 50-degree angle will be 130
but this angle corresponds to the angle y thus y=130 as corresponding angles are equal when a transversal intersects two parallel lines
Hence, The value of y is 130°
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Manuel will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $60 and costs an additional $0.60 per mile driven
The second plan has no initial fee but costs $0.80 per mile driven.
For what amount of driving do the two plans cost the
same?
miles
What is the cost when the two plans cost the same?
3
From the given values and conditions, We need to form a equations and equate both sides to solve for the miles, The answer is 300 miles.
What is a equation?An equation is a statement of equality between two expressions. It typically includes numbers and mathematical operations such as addition, subtraction, multiplication, and division. For example, the equation 2x + 3 = 7 is a statement that the value of the expression 2x + 3 is equal to the value of 7. Equations can also include variables, which represent unknown values that can be solved for.
What is unitary method?The unitary method is a method used in mathematics to solve problems involving units of measurement. It involves expressing the units of measurement as a fraction or multiple of a single unit and then using this fraction or multiple to solve the problem. The method is particularly useful in solving problems involving conversions between different units of measurement. The unitary method is particularly useful in solving word problems where the conversion of units is required. It involves expressing the given information in terms of a single unit and then using that information to find the unknown quantity.
x= miles
60+0.6x=0.8x
0.8x-0.6x=60
0.2x=60
x=60/0.2
=300 miles
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What the answer to this 9 - 3y +3y =4
Answer:
its the answer
Step-by-step explanation:
the answer to the question is the answer
hehe
Geometry need help asap
On solving the provided question, we can say that - here in quadrilateral we have x + 146 + 47 + y = 360 => [tex]x= 83.5[/tex]
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here,
x + 146 + 47 + y = 360
2x + 193 = 360
2x = 167
[tex]x= 83.5[/tex]
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List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.
n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.
What is span in vector space?In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.
The vectors that are in the same span should be a multiple of the vectors
V₁ = (8 2 7 ), V₂ = (-6 4 0 )
Now, V₁ + V₂ = (2 6 7).
So, The five vectors in the span of V₁ and V₂ is,
2×(2 6 7).
= (4 12 14).
- 2×(2 6 7).
= (- 4 - 12 - 14).
3×(2 6 7).
= (6 18 21)
- 3×(2 6 7)
= (- 6 - 18 - 21).
5×(2 6 7).
= (10 30 35).
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Solve for -10 - 9/2 x <80
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
A parade traveled 8 miles in 4 hours. How far did the parade travel per minute?
Answer:
1/30 of a mile per minute.
Step-by-step explanation:
8/4 = 2 miles per hour.
2/60 = 1/30 of a mile per minute.
Use partial quotients to solve 5,140 ÷ 9 = ___.
The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.
What are partial quotients division?Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.
Why do we use partial quotient division?Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.
Now we solve
first 9 multiply with 500 so we get 4500. 5140-4500=640
then 9 multiply with 70 so we get 630. 640-630=10
then 9 multiply with 1 so we get 9. 10-9=1
Hence 500+70+1=571
And our remainder is 1.
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Write the following expression in expanded form:9 to power of 3× 7to the power of 4
Exponential Expressions into Expanded Form into Answer:
[tex]9^{3}[/tex] = 9⋅9⋅9 = 729
[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401
I hope this helps, have a good day!
Answer:
= 9⋅9⋅9 = 729
= 7⋅7⋅7⋅7 = 2401
Step-by-step explanation: