The rule to find the cost and the cost of 7 packages can be given as 15n and $105 respectively.
What is Proportionality?When two quantities have some dependence in their values they can be said proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies value of one quantity is increasing while the other is decreasing.
The table for the given case can be written as follows,
Packages of Golf Balls Cost
1 $15
2 $30
3 $45
4 $60
The relation for proportionality can be obtained as,
15/1 = 30/2 = 45/3 = 60/4 = 15
(A) Suppose n be the number of packages.
Then, the cost is given as 15n.
(B) The cost of 7 packages is as below,
⇒ 15 × 7 = $105
Hence, the answers to both part can be given as 15n and $105 respectively.
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what can you say about the series ∑an in each of the following cases
a) lim |(an+1)/(an)∑|=1
n→[infinity] b) lim nth root(|(an)|=2/3
n→[infinity]
c) lim |(an+1)/(an)|=0.8
n→[infinity]
d) lim |(an+1)/(an)|=3/2
n→[infinity]
e) lim |(an+1)/(an)|=3
n→[infinity]
f) lim nth root(|(an)|=1/2
n→[infinity]
In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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If the radius of a spherical orange is 3.5 cm. find its surface area and volume
Answer:
The surface area of a sphere is given by the formula:
surface area = 4 * pi * r^2
Where r is the radius of the sphere.
Using this formula, the surface area of an orange with a radius of 3.5 cm is:
surface area = 4 * pi * (3.5 cm)^2
= 4 * pi * 12.25 cm^2
= 49.0307 cm^2
The volume of a sphere is given by the formula:
volume = (4/3) * pi * r^3
Where r is the radius of the sphere.
Using this formula, the volume of an orange with a radius of 3.5 cm is:
volume = (4/3) * pi * (3.5 cm)^3
= (4/3) * pi * 42.875 cm^3
= 113.097 cm^3
Step-by-step explanation:
Given ,
Radius of a spherical orange is 3.5 cmTo Find : The Surface Area and the volume of a spherical orange
In order to find the surface area of a spherical orange we use the formula,
[tex]SA = 4\pi r^{2}[/tex]
[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]
[tex]SA =[/tex] [tex]154cm^{2}[/tex]
And now to find the volume of a sphere
[tex]V = \frac{4}{3} \pi r^{3}[/tex]
[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]
[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]
Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]
5. solve for x
6. find MN
please help I need before Saturday at 12:00am
Will report links and random words
Answer:
x = 17, MN = 11
Step-by-step explanation:
Given 2 secants from an external point to a circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.
(5)
7(7 + x) = 8(8 + 13) = 8 × 21 = 168 ( divide both sides by 7 )
7 + x = 24 ( subtract 7 from both sides )
x = 17
(6)
9(9 + 2x - 7) = 10(10 + 8)
9(2x + 2) = 10 × 18 = 180 ( divide both sides by 9 )
2x + 2 = 20 ( subtract 2 from both sides )
2x = 18 ( divide both sides by 2 )
x = 9
Then
MN = 2x - 7 = 2(9) - 7 = 18 - 7 = 11
how do I find the slope of these points
(8,-4) and (2,-4)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]
5. A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting.
a.) Find the probability that exactly one student will be absent from class. (5 points) b.) Find the probability that at least 2 students will be absent from class. (10 points)
Answer:
I think the answer is A
Sorry if i am wrong
Step-by-step explanation:
These two figures are similar. Find the length of side x
Answer:
probably 21
Step-by-step explanation:
In the diagram below of parallelogram ABCD with diagonals AC and BD, m∠1=45° and m∠DCB=120°.Whatisthemeasureof∠2?
Answer:
15degrees
Step-by-step explanation:
From the given diagram
<1+<2 + <DCB = 180
<1+<2+120 = 180
<1+<2 = 180 - 120
<1+<2 = 60
<2 = 60 - <1
<2 = 60 - 45
<2 = 15degrees
Hence the measure <2 is 15degree
please help, I really need to pass this class!
Answer:
y=1.5x+2
Step-by-step explanation:
Mark me brainliest pls
2 is the y intercept so a+ 2 is already part of the equation
slope = y2-y1/x2-x1
6-4.5/2-1 = 1.5
y=1.5x + 2
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution
Step-by-step explanation:
x² - 32 = 4x
x² - 4x - 32 = 0
with a little bit experience we see immediately that this is
(x - 8)(x + 4) = 0
the positive x for this to be true is x = 8.
formally, the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =
= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =
= (4 ± 12)/2 = 2 ± 6
x1 = 2 + 6 = 8
x2 = 2 - 6 = -4
we were right at the beginning.
the positive solution is x = 8.
What is the mean absolute deviation and population standard deviation of this data set? 1, 4, 6, 7, 9, 9
Answer:
a)2.33
b) 2.83
Step-by-step explanation:
What is the mean absolute deviation and population standard deviation of this data set? 1, 4, 6, 7, 9, 9
Step 1
Find the Mean
n = 6
Mean = Sum of values/Number of value
= 1 +4 + 6 +7 + 9+ 9/6
= 36/6
= 6
a) Mean Absolute Deviation
Formula
= |x - Mean|/n
= | (1 - 6)+(4 - 6) + (6 - 6)+(7 - 6)+ (9 - 6) + (9 - 6)|/6
= 5 + 2 + 0 + 1 + 3 + 3/6
= 14/6
= 2.3333333333333
Approximately = 2.33
b) Population Standard deviation
Formula
=√(x - Mean)²/n
= √ (1 - 6)²+(4 - 6)² + (6 - 6)² +(7 - 6)² + (9 - 6)² + (9 - 6)²/6
= √25+ 4+0+ 1+ 9+9/6
= √48/6
= √8
= 2.828427125
Approximately = 2.83
Need answers pls answers
Answer:
Thjs is hard mat
Step-by-step explanation:
I just need points mateeeee
which is equivalent?
Answer:
A
Step-by-step explanation:
Given
[tex]\frac{x}{\sqrt{2} }[/tex]
Multiply numerator/ denominator by [tex]\sqrt{2}[/tex] to rationalise the denominator
= [tex]\frac{x\sqrt{2} }{\sqrt{2}(\sqrt{2}) }[/tex]
= [tex]\frac{x\sqrt{2} }{2}[/tex] → A
(15,17,21,6,3) order each set of integers from least to greatest
Answer: 3, 6, 15, 17, 21
Step-by-step explanation:
What is Jasmine’s mistake?
Answer: She has to interpret who has a job not who doesn't.
Step-by-step explanation:
The clock in Sri's car, which is not accurate, gains time at a constant rate. One day as he begins shopping he notes that his car clock and his watch (which is accurate) both say 12:00 noon. When he is done shopping, his watch says 12:30 and his car clock says 12:35. Later that day, Sri loses his watch. He looks at his car clock and it says 7:00. What is the actual time
The actual time is 6:30.
Since Sri's car clock is not accurate, it is gaining time at a constant rate. By knowing that at 12:00 noon the car clock and the watch were in sync, we can estimate that the car clock is gaining 5 minutes per hour.
Therefore, when Sri looks at his car clock at 7:00 and his watch is missing, we can calculate that the actual time is 6:30. This is done by subtracting the 5-minute difference in time between the car clock and the watch at 12:30 (12:35 car clock, 12:30 watch) from the 7:00 car clock. The result is 6:30.
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Luis made an error when he used the distributive property to solve the problem shown. Which sentence describes the error? https://content.thinkthroughmath.com/uploads/media_library/item/31517/L59
Answer:
in step 2, 60 should be multiplied by the quantity 8-15, not by 8
Step-by-step explanation:
i looked at the image they provided and figured this out, and solved it on my own account but the image wont load
Please help I don’t understand this
Answer:
[tex] {8}^{3n} = {8}^{6} \\ 3n = 6 \\ n = 2[/tex]
Answer:
[tex]n = 2[/tex]
Step-by-step explanation:
[tex]( {8}^{n} )^{3} = {8}^{6} [/tex]
[tex] {8}^{n \times 3} = {8}^{6} [/tex]
[tex]n \times 3 = 6[/tex]
[tex]n = \frac{6}{3} [/tex]
[tex]n = 2[/tex]
Hope it is helpful....Find the 19th term of the sequence 5, 8, 11, 14, 17...
59
51
53
56
Answer:
59
Step-by-step explanation:
So, lets look at our numbers in the sequence. So it goes 5 to 8, 8 to 11, 11 to 14, and 14 to 17. This seems like a change in three. So the every 1 term changes the orginal 5 value by 3.
So wouldnt this mean we can multiply the change in terms by the amount of terms? Which is 19*3? Well, sort of. This is the right way of doig this, but we must remember that we already know the first term, 5. So this means we will be doing 18*3.
This gets you 54. Now just add the amount of the 18 terms onto the first term:
54+5
=
59
So your answer is 59.
Hope this helps!
Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
x^2+y^2+8x-6y-15=0
The answers for Center of the circle is (-4,3) and radius is 2√10 units.
How to find the Center of the circle using Algebraic Expressions?(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.
How to simplify Algebraic expressions?Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.
Examples of Algebraic Expressions
2x2+3xy+4x+7
Given,
[tex]x^2+y^2+8x-6y-15=0[/tex]
⇒ x².+8x+16–16+y²-6x+.9–9–15=.0
(x+4)²+(y-3)²-16–9–15=0
I.e. (x+4)²+(y-3)²=40
(x+4)²+(y-3)²={2√10}²
Hence center is (-4,3) and radius is 2√10 units.
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Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangles can be proved congruent by SAS theorem.
Properties of congruent triangles.Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.
To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.
Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;
Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.
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Help please with this maths
The radius of the sphere is 9 cm.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere is 4/3πr³.
We have,
The surface area of a sphere = 324π cm²
4πr² = 324π
r² = 324/4
r² = 81
r = √81
r = ±9
r = -9 cm (rejected)
r = 9 cm
Thus,
The radius is 9 cm.
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What's the value of the following game: You roll a 100 sided die with sides 1-100. You can either take this number of dollars, or pay $1 to roll again. You can keep on paying $1 to roll for as long as you like.
You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
Can a die have 100 sides?The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."
optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.
Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:
1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)
2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1
[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]
[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]
maximizing E w.r.t. x,
dE/dx = 0
2x^2 - 400x + 19600 = 0
x = ( 400+/- sqrt(160000-4*2*19600) ) / 4
Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4
x = 85.85786
We just have to calculate E(x=85) and E(x=86) and compare.
E((x=86) = 87.35 and E(x=85) = 87.33
so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
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What kind of line is y 2x 3?
Answer: It is a straight line
Step-by-step explanation:
Find the measures of the angles
Answer:
（1）：
angle1/2/3/4=90
angle6=51
angle7=40
angle8=89
angle9=51
angle10=40
angle12=50
angle13=130
angle14=50
Step-by-step explanation:
Q1：
angle1 2 3 4 divided 360 into four equal parts
so 360/4=90
angle11=110degree
so angle12 is 180-130=50 degree
because angle 12 3 10 are in triangle
their sum is 180
so angle 10=180-90（angle3）-50（angle12）=40
because angle 10 5 6 sum is 180
so angle 6 is=180-89（angle5）-40（angle10）=51
because angle 5 6 7 sum is 180
angle7=180-51（angle6）-89（angle5）=40
angle8=angle5=89
angle9=angle6=51
angle12 &13sum is 180
so angle13=180-50=130
angle14=angle12=50
How do you find the slope of a logarithmic function?
By taking derivative, slope of the logarithmic function can be found.
The slope of a logarithmic function can be found by taking the derivative of the function with respect to x using the rules of logarithmic differentiation. The general form of the derivative of a logarithmic function is:
d/dx(log(f(x))) = (1/f(x))*(df/dx)
The slope means change in Y with respect to change in X. The slope is the ratio of the rise to run and it shows the steepness of the plane.
The slope is denoted by m.
Example:
Find the slope of y = log(x^2+1)
d/dx(log(x^2+1)) = (1/(x^2+1))*(2x) = 2x/(x^2+1)
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please help with math!!
Answer:
Trinomial
Step-by-step explanation:
If there is 1 term, monomial
2 term - binomial
3 term- trinomial
Indicated angles :
6. Find the measures of the indicated angles. Give reasons for your answers
Answer:
k\
Step-by-step explanation:
j
Which table shows a proportional relationship between x and y?
Answer:
C
Step-by-step explanation:
Put in the form y/x and you should have equivalent fraction
12/4 = 3
15/5 = 3
18/6 = 3
When the fractions are simplified, they all equal 3.
What is the sum of 1/2 plus 3/5 ?
Answer:
1 3 5 6 11
__ + ____ = ___ + ___ = ___ simplified: 1 1/10
2 5 10 10 10
Step-by-step explanation:
Find a common denominator which is 10.
1 1/10 is your answer.
please give the correct answer and no links!
Answer:
KL ≈ 16.6 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos25° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MK}{KL}[/tex] = [tex]\frac{15}{KL}[/tex] ( multiply both sides by KL )
KL × cos25° = 15 ( divide both sides by cos25° )
KL = [tex]\frac{15}{cos25}[/tex] ≈ 16.6 ft ( to the nearest tenth )