A $6 prize was offered at the end
of each hour of cookie sale to the person who sold the most cookies. If there
was more than one winner, the winners shared the prize.
After the first hour, 2 people were tied and split the prize.
• At the end of the second hour, each winner received $1 less than
the winners of the first hour.
How many winners were there at the end of the second hour?
Using proportions, it is found that there were 3 winners at the end of the second hour.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
After the first hour, 2 people were tied and split the prize, hence they received $6/2 = $3.
After the second hour, the winners received $2, hence the number of winners is given by:
n = $6/$2 = 3.
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A ball is thrown vertically upwards from the ground. It rises to a height of 10m and then falls and bounces. After each bounce, it vertically 2/3 the height of which is fell.
i) Find the height to which the ball bounces after the nth impact
ii) Find the total distance travelled by the ball from the first throw to the nth impact with the ground
[tex]{\huge{\fcolorbox{yellow}{red}{\orange{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{blue}{Answer}}}}}}}}}}}}}[/tex]
(i)
[tex] \sf{a_n = 20 \times {( \frac{2}{3} )}^{n - 1} }[/tex]
(ii)
[tex] \sf S_n = 60 \{1 - { \frac{2}{3}}^{n} \} [/tex]
Step-by-step explanation:
[tex]\underline\red{\textsf{Given :-}}[/tex]
height of ball (a) = 10m
fraction of height decreases by each bounce (r) = 2/3
[tex] \underline\pink{\textsf{Solution :-}}[/tex]
(i) We will use here geometric progression formula to find height an times
[tex]{\blue{\sf{a_n = a {r}^{n - 1} }}} \\ \sf{a_n = 20 \times { \frac{2}{3} }^{n - 1} }[/tex]
(ii) here we will use the sum formula of geometric progression for finding the total nth impact
[tex] \orange {\sf{S_n = a \times \frac{(1 - {r}^{n} )}{1 - r} }} \\ \sf S_n = 20 \times \frac{1 - ( { \frac{2}{3} })^{n} }{1 - \frac{2}{3} } \\ \sf S_n = 20 \times \frac{1 - {( \frac{2}{3}) }^{n} }{ \frac{1}{3} } \\ \sf S_n = 3 \times 20 \times \{1 - ( { \frac{2}{3}) }^{n} \} \\ \purple{\sf S_n = 60 \{1 - { \frac{2}{3} }^{n} \}}[/tex]
You start at (7, 8). you move left 3 units and right 3 units. where do you end?
Answer:
You end back at where you started (7,8)
Step-by-step explanation:
You move left so you subtract 3 from (7) because it is x, (8) is Y
Left: 7-3=4
Right: 4+3-7
The midpoint of AB is M(4,-2). If the coordinates of A are (3, -6), what are the
coordinates of B?
Answer:
okay here we go
Step-by-step explanation:
[tex]in \: vectos \: ab \: means \: ob - oa \\ but \: the \: midpoint \: m \: is \: equal \: to \: a \: half \: of \: ab \\ \\ therefore \: m = \frac{1}{2} ab \\ = \frac{1}{2} (ob - oa) \\ = \frac{1}{2} (ob - (3. - 6)) \\ (4. - 2) = \frac{1}{2} (ob - (3. - 6)) \\ (8. - 4) = (ob - (3. - 6)) \\ ob = (11. - 2)[/tex]
Translate the sentence into an inequality.
The difference of twice a number and 3 greater than or equal to 19.
Use the variable c for the unknown number.
Answer:
2c - 3 >= 19
Step-by-step explanation:
Solving it:
2c >= 22
c >= 11
50 Points: Name the similar triangles & Prove the similarity with details
Let's consider the facts at hand:
By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF∠BEC = ∠DFCSides BE = DFBased on the diagram, triangles BCE and triangles DCF are similar
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
Definitions of Theorem I used:
Vertical Angle Theorem: opposite angles of two intersecting lines must be equalAngle-Angle Theorem: if two angles of both triangles are equal, then the given triangles must be similar
Answer this question to get 10 pts!
Answer:
10x8=80 not 800 the answer should be
Step-by-step explanation:
5x8=40
5x50=250
10x8=80 not 800
10x50=500
500+250=750
750+40=790
790+80=870
A parabola has a vertex of (3, 6) and passes through the point (1, 42).
we can model the parabola using a function in the form of f(x) = a(x - h)2 + k, where a, h,
and k represent real numbers.
find the value for a.
The value of the constant a for the parabola will be equal to a=9
What is a parabola?The parabola is an open curve, and a conic section which is produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
Here we have the equation of the parabola:-
f(x)a(x-h)²+k
Since a parabola has a vertex of (3, 6) and passes through the point (1, 42).
By putting the values in the equation we can find the value of a;-
(42)=a(1-3)²+6
4a=42-6
a=36/4
a=9
Hence the value of the constant a for the parabola will be equal to a=9
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The scatter plot shows the profit by the month for a new company during its first year of operation. Which equation most closely models the line of best fit for the scatter plot? A) y = 5x B) y = 2.5x C) y = 5x + 1000 D) y = 2.5x + 1000
The equation most closely models the line of best fit for the scatter plot is y = 2.5x
Equation of a line graphsA line is the defines as the minimum distance between two points. The equation of a line is given in the form y =mx + b
where:
m is the slopeb is the interceptIn order to determine the required equation, we can use the coordinate (3, 5000) and (9, 20000)
Determine the slope
Slope = 20000-5000/9-3
Slope = 15000/6 = 2500
Determine the y-intercept
5000 = 2500(3) + b
b = 5000 - 7500
b = -2500
Determine the equation
y = 2.5x - 2.5
Therefore the equation most closely models the line of best fit for the scatter plot is y = 2.5x
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What is the 83rd term of the sequence 91, 87, 83, 79, ... ( = a1, a2, a3, a4, ...)?
Answer:
Common difference: tₙ = (95x - 4)
Question: How do we find the 83rd term?
Step-by-step explanation:
[tex]t_n = (95x-4)\\83 * 4 = 332\\95x - 332 = -237x\\-237x = -237\\-237[/tex]
Therefore, the answer is -237
A boy’s height is 133 cm at the end of a year. His height increased by 5%. Find the height at the
beginning of the year.
Answer:
126.35cm
Step-by-step explanation:
quick use of a calculator
Answer:
26.6 cm
Step-by-step explanation:
height= 133/5
height of year= 26.6 cm
A city’s bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized. The population of Belmont, MA, is 24,729 and covers an area of 4.66 mi2. The population of Easton, MA, is 23,112 and covers an area of 28.4 mi2. Which city’s residents are more likely to use public buses? Explain.
The residents of Belmont are more likely to use public transportation because the city has the highest population density.
The residents of Easton are more likely to use public transportation because the city has the highest population density.
The residents of both cities will not use the bus line because the population density is too high.
The residents of both cities are equally likely to use public transportation because the population densities are equal.
Answer with explanation:
it is given that city's bus line is used more as the urban population density increases.
Population density is defined as ,total population per unit Area.
→Population Density of Belmont
[tex]=\frac{24729}{4.66}[/tex]
[tex]=5306.65[/tex]
In 1 Square mile,of Belmont approximately 5307 people Resides.
→Population Density of Easton
[tex]=\frac{23112}{28.4}[/tex]
[tex]=813.80[/tex]
In 1 Square mile,of Easton Approximately 813 people Resides.
From Above two,we conclude that
→Population Density of Belmont > Population Density of Easton
Option A: The residents of Belmont are more likely to use public transportation because the city has the highest population density.
what is the area of this right triangle
136
200
280
283
PLS HELP ILL MARK BRAINLEST
Answer:
B: 200 is the correct answer for your question.
Step-by-step explanation:
This was the question in my k12 semester test. Which i have done and B is the correct one.
What is the surface area of a sphere with a radius of 12 units?
•
A. 1447 units-
•
B. 576 units-
C. 5767 units?
288gL unitsz
- - - - - -- - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - -
[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
What is the volume of a sphere with a radius of 12 units?
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
[tex]\sf{Formula \ for \ Volume \ of \ a \ sphere \ :[/tex] [tex]\bigstar\boxed{\bold{V=\displaystyle\frac{4}{3} \pi r^3}}[/tex]
Where
[tex]\tt{V=Volume}\\\tt{\pi =pi}\\\tt{r=radius}[/tex]
Provided Information:-
[tex]\tt{r=12\:units}[/tex]
Plug in:-
[tex]\bold{V=\displaystyle\frac{4}{3} \pi (12)^3}[/tex]
[tex]\bold{V=\displaystyle\frac{4}{3} \pi (1,728)}[/tex]
On further simplification,
[tex]\dashrightarrow\boxed{\boxed{\underline{\bold{V=2304\pi\:m^3}}}}\dashleftarrow[/tex]
Good luck.-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -
Can someone solve this venn diagram for x please. Giving brainiliest
Answer:
x = 38
Step-by-step explanation:
Intersection is occupied by xremaining part of set A = 149 - xremaining part of set B = 160 - xNow,
(149 - x) + (x) + (160 - x) + (2x + 3) = 350149 - x + x + 160 - x + 2x + 3 = 350312 + x = 350x = 350 - 312x = 38The final scores from the last five games of two basketball teams are given. Jumping Jackrabbits: 70, 65, 72, 80, 73 Leaping Lizards: 61, 47, 70, 63, 54
(a) Determine the MAD of each data set. In your work, show the mean and the absolute deviation of each data value in each set.
(b) Compare and interpret the MADs in context of the situation.
Using the Mean Absolute Deviation(MAD) concept, it is found that:
a) The Jumping Jackrabbits have a MAD of 3.6 and the Leaping Lizards of 6.8.
b) The MAD is lower for the Jumping Jackrabbits then for the Leaping Lizards, hence their scores are more consistent.
What is the mean absolute deviation of a data-set?The mean of a data-set is given by the sum of all observations divided by the number of observations.The mean absolute deviation(MAD) of a data-set is the sum of the absolute value of the difference between each observation and the mean, divided by the number of observations.The mean absolute deviation represents the average by which the values differ from the mean.Item a:
For the Jumping Jackrabbits, the mean and MAD are given by:
M = (70 + 65 + 72 + 80 + 73)/5 = 72
MAD = (|70 - 72| + |65 - 72| + |72 - 72| + |80 - 72| + |73 - 72|)/5 = 3.6.
For the Leaping Lizards, the mean and the MAD are given by:
M = (61 + 47 + 70 + 63 + 54)/5 = 59
MAD = (|61 - 59| + |47 - 59| + |70 - 59| + |63 - 59| + |54 - 59|)/5 = 6.8.
The Jumping Jackrabbits have a MAD of 3.6 and the Leaping Lizards of 6.8.
Item b:
The MAD is lower for the Jumping Jackrabbits then for the Leaping Lizards, hence their scores are more consistent.
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A 5ft slide will be installed on a playground. The top of the slide will be 3 ft above the ground. What angle does the slide make with the ground? Round your final answer to the nearest degree.
Answer:
Its 37ft
Step-by-step explanation:
The students in Classroom 101 consist of 13 girls and 7 boys. The students in Classroom 103
consist of 8 girls and 12 boys. You randomly choose one student from each classroom. Find the
probability of the events.
8. Choosing a boy from both classrooms
9. Choosing a girl from Classroom 101 and a boy from Classroom 103
10. Choosing a boy from Classroom 101 and a girl from Classroom 103
11. You randomly choose 2 students from Classroom 101 to compete in
a competition.
a. First Choice: girl Second Choice: girl
b. First Choice: boy
Second Choice: girl
c. First Choice: girl
Second Choice: boy
The probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Total number of students in classroom 101 = 13+7 = 20
Total number of students in classroom 103 = 8+12 = 20
The probability of choosing a boy from both classrooms:
= 19/20
Choosing a girl from Classroom 101 and a boy from Classroom 103:
Since both are independent event.
Probability of choosing a girl from Classroom 101 = 13/20
Probability of choosing a boy from Classroom 103 = 12/20
The probability of choosing a girl from Classroom 101 and a boy from Classroom 103:
= (13/20)(12/20)
= 156/400
= 39/100
Similarly, the probability of Choosing a boy from Classroom 101 and a girl from Classroom 103:
= (7/20)(8/20)
= 56/400
= 7/50
Similarly, we can find remaining probability.
Thus, the probability of choosing a boy from both classrooms is 19/20, the probability of choosing a girl from Classroom 101 and a boy from Classroom 103 is 39/100, and the probability of choosing a boy from Classroom 101 and a girl from Classroom 103 is 7/50
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what is the slope for this graph?
Answer:
the slope is 1
Step-by-step explanation:
you could just leave it as x in the equation
please help, will mark brainliest!!!
Answer:
$ 3513. 63
Step-by-step explanation:
Plug in the numbers :
3200 * e ^(.017 * 5.5) = 3513.63
PLEASE HELP!!!!!!!!!!!!
Answer:
Yes you are correct it is a constant rate of -800
Step-by-step explanation:
Hope this helps. :-)
solve 11 ≤ w + 3.4 i dont know the answer please help me
Answer:
7.6 ≤w
Step-by-step explanation:
Hey there!
In order to solve this inequality, you need to simplify the inequality like the following:
Subtract 3.4 from both sides
7.6 ≤w
This means that w is greater than or equal to 7.6
Which
equation represents a line that passes through (-2, 4) and has a slope of 2/5?
Answer:y - 4 = 2/5(x + 2)
Step-by-step explanation:
Mark me brainliest
NEED ASAP: Carlos builds a robot that moves on small wheels. Each wheel has six 5-inch-long metal spokes that meet in the center. What is the area of the sector between these spokes? Express your answer as a simplified fraction in terms of \piπ.
Answer:
27π/8 inches²
Step-by-step explanation:
= πr² × [3π/(4 × 2π)]
= π(3)² × 3π/8π
= 27π/8 inches²
Write it in exponential form, with only positive exponents
Answer:
the answer is 27 if you have to evaluate
" " " 3 cubed if you have to simplify
Step-by-step explanation:
Please help with this question. 100 points!! I know it is a little long but I could really use the help.
The owners of the resort want to expand and build a row of condos at the western base of the mountain. Because of the amount of snow, the area gets most winters, it is important to have the pitch (steepness) of the roof of each condo at least 60°. To make the condos appealing to skiers and boarders, they want to model the condos after their cabins, but on a larger scale. The cabins have an A-line roof that forms an isosceles triangle as shown, with the base angles at 65° . The base length is 6m. Note: the slant height is the length of the side of the roof. (Picture Below)
Required Formula
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
Part A
Given: base length: 6m, half base: 3m, angle: 65°, let hypotenuse: h
Hence solve,
[tex]\rightarrow \sf cos(x) = \dfrac{a}{h}[/tex]
[tex]\rightarrow \sf cos(65) = \dfrac{3}{h}[/tex]
[tex]\rightarrow \sf h = \dfrac{3}{cos(65)}[/tex]
[tex]\rightarrow \sf h =7.0986\ \approx \ 7.1 \ m[/tex]
The slant height is 7.1 meters when base length is 6 meter.
Part B
Given: base length: 9.6m, half base: 4.8m, angle: 65°, let hypotenuse: n
Hence solve,
[tex]\rightarrow \sf cos (x) = \dfrac{a}{n}[/tex]
[tex]\rightarrow \sf cos (65) = \dfrac{4.8}{n}[/tex]
[tex]\rightarrow \sf n = \dfrac{4.8}{cos (65)}[/tex]
[tex]\rightarrow \sf n = 11.357 \ \approx \ 11.4 \ m[/tex]
The slant height is 11.4 meters when base length is 9.6 meter.
Answer:
A) 7.1 m
B) 11.4 m
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Part AThe slant height of the roof is the hypotenuse of a right triangle.
Considering the information given, use the cos trig ratio to determine the slant height.
A roof's base length is the distance from one corner of the roof to the other. Therefore, the base length of the given right triangle is half the roof base length.
Given:
[tex]\theta[/tex] = 65°A = Half of roof base length = 6 ÷ 2 = 3 mH = Slant heightSubstituting the given values into the formula and solving for H:
[tex]\sf \implies\cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\sf \implies\cos(65^{\circ})=\dfrac{3}{H}[/tex]
[tex]\sf \implies H =\dfrac{3}{\cos(65^{\circ})}[/tex]
[tex]\implies \sf H=7.1 \: m \: (nearest\:tenth)[/tex]
Part BThe slant height of the roof is the hypotenuse of a right triangle.
Considering the information given, use the cos trig ratio to determine the slant height.
A roof's base length is the distance from one corner of the roof to the other. Therefore, the base length of the given right triangle is half the roof base length.
Given:
[tex]\theta[/tex] = 65°A = Half of roof base length = 9.6 ÷ 2 = 4.8 mH = Slant heightSubstituting the given values into the formula and solving for H:
[tex]\sf \implies\cos(\theta)=\dfrac{A}{H}[/tex]
[tex]\sf \implies\cos(65^{\circ})=\dfrac{4.8}{H}[/tex]
[tex]\sf \implies H =\dfrac{4.8}{\cos(65^{\circ})}[/tex]
[tex]\implies \sf H=11.4 \: m \: (nearest\:tenth)[/tex]
1
suppose you deposit $1,500 in a savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account, answer the following questions.
a. how much will be in the account after 4 years?
b. how much will be in the account after 17 years?
c. how many years will it take for the account to contain $2,000?
d. how many years will it take for the account to contain $2,500?
a. after 4 years, the amount in the account will $
(do not round until the final answer. then round to the nearest cent as needed.)
Answer:
a. After 4 years there will be $1,823.26.
b. After 17 years there will be $3,438.03.
c. It will take 6 years with a total balance of $2,010.14.
d. It will take 11 years with a total balance of $2,565.51.
Step-by-step explanation:
Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent.
What additional information would be needed to prove that the triangles are congruent using the ASA congruence theorem?
ON ≅ MN
∠LON ≅ ∠LMN
LN ≅ NM
∠LNO ≅ ∠LNM
Answer:
Step-by-step explanation:
Answer:
D. ∠LNO ≅ ∠LNM
Step-by-step explanation:
Have a good day!
Please help me with this .
Answer:
with what
Step-by-step explanation:
can you please post the picture
look at the picture to see how to add a pic to a question
if 2a+3b=12 and a-3b=0, then what is the value of a?
Answer:
a=4
Step-by-step explanation:
2a+3b=12
+
a-3b=0
3a=12
a=4
