The equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Kevin, Mika, and Cheryl have a total of 45 people sponsoring them for a fun-raiser.
Consider that Kevin has p people sponsoring him, Mika has one more than Kevin, and Cheryl has one more than Mika.
Kevin = p
MIka = m
Cheryl = c
Then m = 1 + p
c = 1 + m
Or
m = c - 1
Now solve both equation;
m = 1 + p = c - 1
p = c - 1 -1
p = c + 2
p = m -1
p = c + 2
Then m - 1 = c + 2
m = c + 3
Hence, the equation for the number of people sponsoring each person are; m = c + 3, p = c + 2.
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Give a brief history about TRIANGLE NUMBERS, including Mathematicians that contributed for its development.
Brief history of triangle numbers
What is Triangle Number?
An equilateral triangle-shaped group of objects is counted using a triangular number or triangle number. Square and cube numbers are two further examples of figurate numbers, which also include triangle numbers.
Students are typically introduced to triangular numbers through the account of Carl Gauss, a well-known mathematician who used the concept of the triangle number formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.
Triangular numbers were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to triangular, square, pentagonal, and other numbers.
After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for triangle numbers of
n(n+1)/2
Drawing triangle numbers is an exercise that could be helpful in establishing a connection between these two concepts.
The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y > x + 2y > -2 x - 7I NEED THE CORDINATES
Given:
There are given that the set of inequality is:
[tex]\begin{gathered} y>x+2 \\ y>-2x-7 \end{gathered}[/tex]Explanation:
From the given system of inequality, we need to draw the graph and find the set of points, where both of the graphs will intersect.
Now,
The graph of the given system of inequality is shown below:
Final answer:
Hence, the set of the point from the given system of inequality is shown below:
[tex](-3,-1)[/tex]Select the correct inequality and graph for the statement. Samuel gets 25 or more for mowing the lawn. PLSSS HELP!!
The statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
What is an inequality?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. There are two types of inequalities namely strict and slack inequalities.
Given is the following statement - "Samuel will get 25 or more for mowing the lawn".
The given statement is -
Samuel will get $25 or more for mowing the lawn.
Assume that Samuel gets $x for mowing the lawn.
Then according to the question, we can write the inequality as -
x ≥ 25
" ≥ " sign to represent either 25 or more.
So, the inequality can be written as x ≥ 25 and the graph number [2] represents the correct graph.
Therefore, the statement "Samuel will get 25 or more for mowing the lawn" can be represented using the inequality → x ≥ 25 and the graph number [2] represents the correct graph.
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[Refer to image attached for complete question]
Write three equations whose graphs are the same line as the equation x - 9y = 3/4
y= 1/9x
y= 1/9x +2/24
y = 1/9x + 3/36
1) To be on the same line, they must share the slope and their points
Let's rewrite that into the standard form
x -9y =3/4
-9y = 3/4 -x
9y = 3/4 +x Divide both sides by 9
y = 1/12 + x/9
y= x/9 + 1/12
2) Since we have the slope 1/9, then we can write the first equation as
y= 1/9x On the same line
y= 1/9x +2/24 2/24 is a multiple of 1/12, therefore on the same line
y = 1/9x + 3/36 3/36 is a multiple of 1/12, therefore on the same line
A Christmas tree is supported by a wire that is 3 meters longer than the height of the tree. The wire is anchored at a point whose distance from the base of the tree is 21 meters shorter than the height of the tree. What is the height of the tree?
The height of the Christmas tree is 12 meters
How to determine the height of the Christmas tree?Represent the height of the tree with h
So, we have the following parameters
Tree height = hBaseline = h - 21Anchor = h + 3The figure that illustrates the above parameters is added as an attachment
From the figure, we have the following equation by Pythagoras theorem
(h + 3)² = h² + (h - 21)²
Expand the exponents
h² + 6h + 9 = h² + h² - 42h + 441
Evaluate the like terms
6h + 9 = h² - 42h + 441
So, we have
h² - 48h + 432 = 0
Expand
h² - 36h - 12h + 432 = 0
Factorize the equation
(h - 36)(h - 12) = 0
Solve for h
h = 36 and h = 12
When h = 36, the baseline will be negative
So, we make use of h = 12
Hence, the tree has a height of 12 meters
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Here is the probability model for the blood type of a randomly chosen person in the United States:Blood Type O А B ABProbability 0.14 0.32 0.01 ?(a) This probability model isA. discrete.B. continuousC. equally likelyD. None of the above.(b) Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that arandomly chosen American can donate blood to Maria?A. 0.01B. 0.15C. 0.33D. None of the above.(c) What is the probability that a randomly chosen American does not have type O blood?A. 0.86B. 0.68C. 0.14D. None of the above
a) A probability distribution is called continuous if its distribution function is continuous.
• Answer a: B. continuous.,
b)
[tex]0.14+0.01=0.15[/tex]• Answer b: B. 0.15
c)
[tex]1-0.14=0.86[/tex]• Answer c: A. 0.86
In a test of a sex-selection technique, results consisted of 284 female babies and 15 male babies. Based on this result, what is the probability of a female being born to
a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a female?
The probability that a female will be born using this technique is approximately
(Type an integer or decimal rounded to three decimal places as needed.)
Does the technique appear effective in improving the likelihood of having a female baby?
O No
O Yes
The probability of having female baby is 0.95
What is probability?
Probability is a discipline of mathematics that deals with statistical models of how probable an event is to exist or how likely a statement is to be true. The probability of an occurrence is a value between 0 and 1 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
The probability of having female baby is = 284/(284 + 15) = 0.95
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x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function?
The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6].
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given function,
x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6
The graph of this function has been plotted below,
The vertex is the point where the function is changing its sign of slope or turning point.
It is clear that at (-4,0) it is changing its slope of sign therefore (-4,0) will be the vertex.
The range is the interval where the function exists since the given function goes from y = 0 to y = 6 so [0,6] will be the range of the function.
Hence "The vertex is the turning point of a function while the range is the interval of the value of the function thus vertex of the given function is at (-4,0) while the range is [0,6]".
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Given the following sequences: I. 2,4,6,8,10... II.2,4,8,16,32... III. a,a + 2, a + 4, a + 6, a +8... Which ones are arithmetic sequences?
ANSWER
The arithmetic sequences are: I and iii
EXPLANATION
The formula for the nth term of an arithmetic sequence is:
[tex]a_n=a_1+d(n-1)[/tex]where a1 is the first term of the sequence and d is the common difference.
For the first sequence I. 2, 4, 6, 8, 10... we can find the common difference by subtracting the first term from the second:
[tex]\begin{gathered} a_2=a_1+d(2-1) \\ a_2=a_1+d \\ d=a_2-a_1 \\ d=4-2 \\ d=2 \end{gathered}[/tex]So the nth term of this sequence is:
[tex]a_n=2+2(n-1)[/tex]Each term of this sequence follows this rule. Therefore this is an arithmetic sequence.
For the second sequence II. 2, 4, 8, 16, 32... there's no common difference because between the first and second term there's a difference of 2, between the second and third there's a difference of 4, and this increases as we move through the sequence. Therefore this is not an arithmetic sequence.
For the third one, III. a, a+2, a+4, a+6, a+8... we can see that there is a common difference:
[tex]\begin{gathered} a_2_{}_{}=a_1+d(2-1) \\ d=a_2-a_1 \\ d=a+2-a \\ d=2 \end{gathered}[/tex]The rule for the nth term is:
[tex]a_n=a+2(n-1)[/tex]Let's find the first 5 terms:
[tex]\begin{gathered} a_1=a+2(1-1)=a \\ a_2=a+2(2-1)=a+2 \\ a_3=a+2(3-1)=a+4 \\ a_4=a+2(4-1)=a+6 \\ a_5=a+2(5-1)=a+8 \end{gathered}[/tex]This shows that each term follows the same rule. Therefore this is an arithmetic sequence.
James spins a basketball on his finger and then passes the ball to his friend.
a. What type of transformation is used when James spins the basketball on
his finger?
b. What type of transformation is used to pass the basketball?
The types of transformations that occur as a result of the motion on the ball are;
A) Rotation
B) Translation
What is the type of transformation?Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.
Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.
Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.
Rotation is a method of transformation that involves turning a given figure at an angle about a reference point.
Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.
A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an angle about a given point.
B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.
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18. A student turned in the following incorrect work. - In what line was the mistake made? - What should the correct step be? - What is the correct final answer?
Be sure to describe your answer in 4-5 sentences.
Answer:
4y³/x³
Step-by-step explanation:
Line 1 is completely correct.
Line 2 has an error.
The 4/1 from line 1 should remain as 4/1 in Line 2, but the student wrote it as 1/4 on Line 2.
To fix it, rewrite Line 2, but change the first fraction, 1/4, to 4/1.
The correct final answer is 4y³/x³
Printer A prints 36 pages every 1.5 minutes. Printer B prints 114 pages every 3 minutes.
Printer C prints 115 pages every 5 minutes. Which printer prints the fastest?
Printer B= 114 pages per 3 minutes. Printer B is the fastest printer. I did scratchwork on paper but I still sent it to you. Sorry my handwriting is sloppy. ; ) I hope it helps.
Solve using substitution. y=103x + 4y = 19
We want to find the solutions for the following system
[tex]\begin{cases}y=10 \\ 3x+4y=19\end{cases}[/tex]We already know the value for the y variable, if we substitute this value on the second equation it is possible to find the x value.
[tex]\begin{gathered} 3x+4\cdot(10)=19 \\ 3x+40=19 \\ 3x=19-40 \\ 3x=-21 \\ x=\frac{-21}{3} \\ x=-7 \end{gathered}[/tex]And those are the results for our system
[tex]\begin{cases}x=-7 \\ y=10\end{cases}[/tex]The length of a rectangular room is 12 feet more than 3 times the height of the room. The floor of the room has an area that is represented by the function below, where h is the height of the room in feet. A(R) 9h2 + 45h + 36 Which statement best describes the width of the room? A. The width is 3 feet shorter than the length. B. The width is 9 feet shorter than the length. C. The width is 9 feet longer than the height. D The width is 3 feet longer than the height.ill send a picture of the question
Okay, here we have this:
Considering the provided information, and that the area of a rectangle is the product of its length and width, we obtain the following:
[tex]\begin{gathered} Width=\frac{Area}{Length} \\ Width=\frac{9h^2+45h+36}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3h+12} \\ =\frac{9\left(h+1\right)\left(h+4\right)}{3\left(h+4\right)} \\ =3\mleft(h+1\mright) \\ =3h+3 \end{gathered}[/tex]Now, to know if the width is greater or less than the length, we will subtract it, then we have:
[tex]\begin{gathered} (3h+12)-(3h+3) \\ =3h+12-3h-3 \\ =12-3 \\ =9 \end{gathered}[/tex]Finally we obtain that the width is feet 9 shorter than the length, so the correct answer is the option B
The perimeter of a triangle is 38 feet. One side of the triangle is one foot longer than the second side. The third side is four feet longer than the second side. Find the lengths of all three sides (in feet). (Enter your answers as a comma-separated list.)
The length of the three sides of the triangle are 11 feet, 12 feet and 15 feet.
How to find the length of a triangle?A triangle is a polygon with three sides.
The perimeter of a triangle is 38 feet.
The perimeter of the triangle is the sum of the whole three sides.
One side of the triangle is one foot longer than the second side.
let
the second side = x
longer side = x + 1
The third side is four feet longer than the second side.
Hence,
Third side = 4 + x
Therefore,
38 = x + x + 1 + x + 4
38 = 3x + 5
3x = 38 - 5
3x = 33
x = 33 / 3
x = 11
Therefore, the sides of the triangle are 11 ft, 12 feet and 15 ft.
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You pick a card at random. Without putting the first card back, you pick a second card at random.4567What is the probability of picking an even number and then picking an even number?Simplify your answer and write it as a fraction or whole number.
Given:
4 5 6 7
Given that you picked a card at random, without replacement, you then pick a second card at random.
Let's find the probability of picking an even number and then picking an even number.
Number of possible events = 4
Number of even numbers = 4, 6, ==> 2 even numbers.
Hence, to find the probability, we have:
[tex]\begin{gathered} P=\frac{2}{4}*\frac{1}{3} \\ \\ P=\frac{2*1}{4*3} \\ \\ P=\frac{2}{12}=\frac{1}{6} \end{gathered}[/tex]Therefore, the probability of picking an even number and then picking an even number is 1/6.
ANSWER:
[tex]\frac{1}{6}[/tex]The square of a negative number
is sixteen more than six times the
negative number. Find the number. The sum of two numbers is
twenty three. And The product of the
two numbers is one hundred
twenty. Find the two numbers.Help me. From: Jessie
The numbers are:
1. The value of x = 5
2. The value of x = 15 or 8 and y = 8 or 15
What is Square?
The word Square means a number multiplied by itself.
The above answers were gotten in the following way:
1. Let the unknown negative number be x
The square of the negative number: x² is
Sixteen more than six times of negative x: 6x+16
It is written as: (x)²=6x+16
Equating to zero, we have:
x²-6x-16=0
Factorizing, we have:
x²-8x+2x-16=0
x(x-8)+2(x-8)=0
x+2=0 and x-8=0
x=-2 and 8
Since the number is negative, x = -2
Therefore, the value of the negative number is -2
2. Given:
Sum of two numbers = 23
Product of two numbers = 120
Calculation:
Let the two numbers be x and y
x+y=23...............equation 1
xy=120..................equation 2
From equation 1, x=23-y
Substitute the value of x in equation 2, we have:
(23-y)y=120
Opening the brackets, we have:
23y-y²=120
Rearranging the equation, we have:
-y²+23y=120
Equating to zero, we have:
-y²+23y-120=0
Multiplying both sides by (-1), we have:
y²-23y+120 = 0
Factorizing, we have:
y²-15y-8y+120=0
y(y-15)-8(y-15)=0
(y-8)(y-15)=0
y=8 or 15
Substituting the values of y in any of the equation. Choosing equation 1, we have:
From Equation 1: x+y=23
When y=8,
x+8=23
x=23-8
x=15
When y=15
x+15=23
x=23-15
x=8
Therefore the values of the two numbers are 15 and 8
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Bruno's hourly salary is $8.75. Last week he worked only 18 hours. How much did he earn
Choose two consecutive points on the graph and find the rate of change. Is the slope the same or different?
Choose two consecutive points on the graph and find the rate of change.
We will start with t = 1000 and t = 1500:
[tex]P(1000)=12.643(1.0027)^{1000}=187.4412[/tex][tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex]Remember that the rate of change is found by the difference in y over the difference in x.
[tex]RATEOFCHANGE=\frac{721.7263-187.4412}{1500-1000}[/tex][tex]RATEOFCHANGE=\frac{534.2851}{500}\approx1.0686[/tex]Let's do it now for t = 1500 and t = 2000.
[tex]P(1500)=12.643(1.0027)^{1500}=721.7263[/tex][tex]P(2000)=12.643(1.0027)^{2000}=2778.9454[/tex]In this case the rate of change would be:
[tex]\text{rateofchange=}\frac{2778.9454-721.7263}{2000-1500}[/tex][tex]\text{rateofchange}=\frac{2057.2191}{500}\approx4.1144[/tex]The slopes are different and due to the type of function they will always increase when taking larger values.
pls help. this is so confusing on how to find the p=S(t)=r+i part of the word problem.
Using a linear function, it is found that:
a) Sales are increasing at a constant rate of 30 purchases/month.
b) The linear function is: p = S(t) = 30t + 3990.
c) The total purchases will be of 5130 in June 2010.
d) The sales will be of 5400 in March of 2011.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have that:
The reference month is of April 2007, hence the intercept is of b = 3990.In 16 months, from April of 2007 to August of 2008, sales increased to 4470, hence the slope is given by: m = (4470 - 3990)/16 = 30.The slope of 30 is the constant rate of purchases per month, and the linear function is given by:
p = S(t) = 30t + 3990.
June 2010 is 3 x 12 + 2 = 38 months after April 2007, hence the purchases will be of:
S(38) = 30 x 38 + 3990 = 5130.
The sales will be of 5400 in t months after April 2007, for which:
S(t) = 5400
Hence:
30t + 3990 = 5400
t = (5400 - 3990)/30
t = 47 months.
One month shy of four year, hence in March of 2011.
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- Lana had a fixed budget for a party. She spent one third of the
budget on decorations. Of the money that remained, she spent
on refreshments and the rest on door prizes for the guests.
If she spent $60 on door prizes, what was her budget?
Lana's fixed budget for a party is $180.
How to find Lana's fixed budget for a party?Let x be Lana's fixed budget for a party.
Lana spent one-third of the budget on decorations.
x - 1/3x = 2x/3
Remaining money,
2x/3 -x + (2x/3-x)-x =0
Since she spent $60 on door prizes
-x/3 + 60 = 0
-x/3 = -60
x = 180
Lana's fixed budget for a party is $180.
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What is the net price of merchandise listing for $5,900 less a trade discount rate of 45%?
A percentage is a number or ratio that represents a fraction of 100.
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
What is a percentage?A percentage is a number or ratio that represents a fraction of 100.
We have,
Merchandise price = $5,900
Discount rate = 45%
45% = 45/100 = 9/20
The net price of the merchandise:
= 5900 - (45% of 5900)
= 5900 - 9/20 x 5900
= 5900 - 9 x 295
= 5900 - 2655
= 3245
Thus,
If there is a trade discount of 45% on the price of the merchandise of $5900, the net price of the merchandise is $3245.
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if your 1952 what year will you be 26?
Answer:
16 January 1952, Wednesday, 70 Years, 8 Months, 26 Days or 848 months, or 3691 weeks, or 25837 days, or 37205280 minutes, or 2232316800 seconds.
Step-by-step explanation:
Answer:
Step-by-step explanation:
answer:1978
What's the radius of 5?
The formula for radius is
radius = diameter/2
If diameter = 5, then
radius = 5/2
radius = 2.5
Discount Pricing A wool suit that was originally priced at $700 is on the 30%-off clearance rack. What is the sale price of the suit?
Answer:
Sale Price = $490
Explanation:
After 30% off, the sale price is 100% - 30% = 70% the original price.
70% of the original price is
[tex]\frac{70\%}{100\%}\times\$700=0.7\times\$700[/tex][tex]=\$490[/tex]which is our answer!
Hence, the sale price of the wool suit is $490.
3х-7-(-2х) +9 simplify
use the theorem that relates the sum of degrees to the number of edges to determine the number of edges in the graph (without drawing the graph) a graph with 4 vertices, each of 2 degree 2
3x+3=2(x+7)
What does x equal?
Answer: x = 11
Step-by-step explanation:
To solve we will isolate the variable, x.
Given:
3x+3=2(x+7)
Distribute:
3x+3=2x+14
Subtract 3 and 2x from both sides of the equation:
x = 11
60x-30/5=18. please help meeeeee. 10 pts worth.
A cylinder shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Question: A cylinder-shaped jelly jar has a radius of 2 cm and a height of 6 cm. How much jelly can the jar hold?
Explanation:
The cylinder-shaped jelly has a volume of gelatin equal to its cylindrical volume. Therefore, we must find the volume of the given cylinder. The volume V of the cylinder with radius r and height h is given by the following formula:
[tex]V=h\pi r^2[/tex]Applying the data of the problem, we obtain:
[tex]V=h\pi r^2=6\text{ * }\pi\text{ * \lparen2}^\text{\rparen}^2\text{ = 24}\pi\text{ =75.398}[/tex]Answer: we can conclude that the correct answer is:
[tex]\text{ 24}\pi\text{ =75.398}[/tex]