If Ajay keeps up his plans for 14 weeks he would have run total of 391 miles.
The sum of n terms of a Geometric Progression ( a,ar,ar²,ar³,...,arⁿ⁻¹ ) is given by
Sₙ=a(rⁿ-1)/(r-1)
where, a=first term
and r = common ratio
In the given question ,
Ajay runs 20 miles in first week , ...(i)
In second week the distance is increased by 5% of the previous week .
So in second week he runs = 20+5% of 20
[tex]=20+\frac{5}{100} *20[/tex]
=20(1+5/100)
=20(105/100)
=[tex]20\times(\frac{21}{20})[/tex] ...(ii)
In third week Ajay runs = 20(21/20) + 5% of 20(21/20)
=[tex]20(\frac{21}{20} )+\frac{5}{100} *20(\frac{21}{20} )[/tex]
=20(21/20)[1+5/100] ..taking 20(21/20) common
[tex]=20(\frac{21}{20} )[\frac{105}{100} ][/tex]
=20(21/20)(21/20)
=20(21/20)² ...(iii)
Similarly in 14th week Ajay Runs = 20(21/20)¹³ . ...(iv)
Total miles run by Ajay = miles run in first week + miles run in 2nd week + ...+ miles run in 14th week.
Substituting the values of equation (i), (ii), (iii) and (iv) we get
Total miles run by Ajay = [tex]20+20(\frac{21}{20} )+20(\frac{21}{20} )^{2} +...+20(\frac{21}{20} )^{13}[/tex]
The above series represent a Geometric Progression with common ratio as (21/20) and first term as 20.
Substituting in the formula for Sum of Geometric Mean we get
[tex]S_{14} =20(\frac{(\frac{21}{20} )^{14} -1}{\frac{21}{20} -1} )[/tex]
S₁₄=20*((1.05)¹⁴-1)/(1.05-1)
=20*(1.9799-1)/0.05
=20*0.9799/0.05
=20*19.598
=391.96
≅391
Therefore , If Ajay keeps up his plans for 14 weeks he would have run total of 391 miles.
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Factor completely.
100-9x²
someone help please
Answer:
[tex](10+3x)(10-3x)[/tex]
Step-by-step explanation:
[tex]100-9x^2\\\sqrt{100} =10\\\sqrt{9} =3\\3*-3=-9\\\sqrt{x^2} = x \\(10-3x)(10+3x)[/tex]
________________________________________________________
Considering both terms are perfect squares, factor using the difference of squares formula:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
In this situation, a = 10 and b = 3x. With this, now plug in your data into the formula.
(10 + 3x) (10 - 3x)
_________________________________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Sheila wants to build a rectangular play space
for her dog. She has 100 feet of fencing and
she wants it to be 5 times as long as it is wide.
What dimensions should the play area be?
The dimensions of the rectangular play area should be: 41.5 x 8.3 feet.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.Now,
Given:
Fencing available = 100 feetLength = 5 times the widthTo find: Length and Width.
Let the width of the rectangular play area be x.
Then, the length = 5x
According to the formula of perimeter of a rectangle,
100 = 2 (x + 5x)
=> 50 = 6x
=> x = 8.3 feet (Approx.)
That is the width of the play area = 8.3 feet
=> Length = 5(8.3) = 41.5 feet.
Hence, The dimensions of the rectangular play area should be: 41.5 x 8.3 feet.
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Which relation is a function of x?
O {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)}
y
2
-6
X
0
0
0
0
9
-7
Ox=3y²-7
X=
-5-4-3-2
5
4
3
2
-2
2 3 4 5 x
Answer:
x=3y2-7
x=3×1-7
x=3-7
x=-4
PLS HELP!!!
Fine the measure of the angle indicated in bold. Then find the measure of the other indicated angle.
The answer for the following questions are:
x= 3x= 10x= 43 = x3 = xx= 8x= 8x=9x=5 x=6What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint.
11. 5+35x + 24x - 2 = 180 (linear pair)
59x = 177
x= 3
12. 15 + 10x = -5 + 12x (corresponding angle)
20 = 2x
x= 10
13. 13x -4 + 8 +9x =180 (linear pair)
22x +4 = 180
22x = 176
x= 4
14. 24x + 3 = 25x (alternate interior angle)
3 = x
15. 32x + 4 = 1 + 33x ( corresponding angle)
3 = x
16. 13x+ 11 = 15x - 5 (alternate interior angle)
-2x = -16
x= 8
17. 15x + 8x -4 = 180 (linear pair)
23x = 184
x=8
18. 9x +16 = 11x -2 ( Vertically opposite angle)
-2x = -18
x=9
19. 5+ 17x = 19x -5 (alternate interior angle)
2x = 10
x=5
20. 8x - 3 + 23x -3 =180 ( Linear pair)
31x = 186
x=6
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questionten times a number, x, is one-half the sum of the number and three. which answer represents this situation? 10x
The solution of the equation 20x = x + 3 will be 3 / 19. Then the correct option is A.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
Ten times a number, x, is one-half the sum of the number and three. Then the equation will be
10x = 1/2(x + 3)
Simplify the equation, then we have
20x = x + 3
19x = 3
x = 3 / 19
Thus, the solution of the equation 20x = x + 3 will be 3 / 19. Then the correct option is A.
Your question was incomplete, probably the question was...
Ten times a number, x, is one-half the sum of the number and three. Which answer represents this situation?
A. 10x = 1/2(x + 3)
B. 10x = 1/2x
C. 10x = 1/2x + 3
D. 10x = (x + 3)
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Solve 0. 504 ÷ 8.
answer choices:
−7. 496
0. 063
0. 630
4. 32
Answer:
0.063
Step-by-step explanation:
0.504 divided by 8 is 0.063
Hope It Helps
Sorry If I'm Wrong
Answer: The answer is 0.630
Step-by-step explanation: The picture proves my answer :D
these are the means and standard deviations for samples of building heights in two different cities. city a city b mean: 120 ft mean: 240 ft standard deviation: 20 ft standard deviation: 12 ftselect the two true statements.
The average building height and the standard deviation for two separate cities' samples are shown. The true statements are:
City A’s heights are more spread out than city B’s heights.
City A has a lower average height than city B.
What is average?In daily life, an average is a number chosen to represent a group of numbers; it is often the sum of the numbers divided by the total number of numbers in the group (the arithmetic mean). The average of the integers 2, 3, 4, 7, and 9, for instance, is 5, which equals 25. An average could alternatively be another statistic like the median or mode, depending on the situation. The median is sometimes used in place of the mean since the mean would be unnaturally high if it included the personal incomes of a few billionaires. The median is the amount below which 50% of personal incomes fall and above which 50% of personal incomes rise.
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Please help with problem 12
The pair of ratios that form a proportion is given by:
B) 5/15 and 4/12.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
A pair of ratios will form a proportion if the division of the denominator by the numerator is the same, hence:
15/5 = 3.12/4 = 3.The pair of ratios that form a proportion is given by:
B) 5/15 and 4/12.
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What is the inequality shown
Answer:
-4 [tex]\leq[/tex] x [tex]\leq[/tex] 3
Step-by-step explanation:
The filled in dots mean that those numbers are included
(2.5+5/3)divided 4/3-2.25
Answer:
7/8
Step-by-step explanation:
add your decimal your fraction inside parentheses then divide it by the rest of the equation
9y=99
Ingrese su respuesta...
The value of y for which the left hand side of the equation is equal to Right hand side is 11.
What is a solution of a linear equation?Solution of a linear equation is the value of the variable for which the left hand side and right hand side of the equation are equal.
Given is the following equation -
9y = 99
In order to solve the equation. we have to find the value of y for which 9y is equal to 99. Now -
9y = 99
Divide both sides by 9 -
9y/9 = 99/9
y = 11
Therefore, the value of y for which the left hand side of the equation is equal to Right hand side is 11.
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[The given question is written in Spanish. The following is the statement converted onto English as
9y=99 Enter your answer.}
determine if the numerical value describes a parameter or a statistic. a recent poll of 2707 home owners in michigan showed that the average price of their houses is $265,000
The numerical value is a statistic.
What is a statistic?A parameter is a value that is used to describe a whole population. A statistic is a number that describes a sample.
There would be more than 2707 homeowners in Michigan. Thus, only a sample of all homeowners was used. Since a sample was used the numerical value is a statistic.
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Find the value of x in each case please
The value of x as given in the diagram is 18
Supplementary anglesThe sum of supplementary angles is 180 degrees. From the given figure;
The measure of the angle 2x and 8x are supplementary such that;
2x + 8x = 180
10x = 180
Divide both sides by 10 to have:
10x/10 = 180/10
x = 18
Hence the value of x as given in the diagram is 18
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Agnes scored 82 on her first test, 69 on her second test, and 84 on her third test. Suppose Agnes has one more test in the semester and what’s to finish with a mean im score of 80
What score does she need on her last test to finish with a mean score of 80?
Answer:
Agnes would need to score a 85 to get an average of 80.
Step-by-step explanation:
[tex]\frac{82+69+84+x}{4}[/tex] = 80 multiply both sides by 4
82+69+84+X = 320
235+X = 320 subtract both sides by235
x = 85
Simplify. (7^{6})^{2}(7
6
)
2
The result of the exponent given is 7^12
Solving exponentsIn order for us to solve the exponential expression given, we will use the law of exponent below;
(a^m)^n = a^mn (multiply the powers)
Given the expression
[tex](7^{6})^{2}[/tex]
Multiply the exponents to have;
7^6(2)
7^12
Hence the result of the exponent given is 7^12
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Gwen davis is a middle school math teacher. she starts today's lesson by introducing the topic of percent increase and percent decrease and reviewing decimals and percents. then, she develops student understanding by explaining and modeling the process of solving percent increase and percent decrease problems. based on the strategy gwen has chosen, what should her next step be
Grew Davis next step would be to give homework for the students and conduct a test in the next week .
Gwen Davis is a middle school math teacher.
she starts today's lesson by introducing the topic of percent increase and percent decrease and reviewing decimals and percent
How do I calculate a percentage decrease?
Percentage decrease formula can be obtained by simply dividing the decreased value by the original value and multiplying that with 100. Here, Decreased Value = Original Value – New Value.
How do you calculate a 20% increase?
Multiply the original value by 0.2 to find the amount of a 20 percent markup, or multiply it by 1.2 to the original value
Hence , Grew Davis next step would be to give homework for the students and conduct a test in the next week .
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The approximate mean age is _____ years.
(Round to one decimal place as needed.)
Age
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
23
22
24
15
31
48
34
18
4
Fraction between 0.3 and 0.2
Answer:
1/4
Step-by-step explanation:
(0.2+0.3) / 2 = 0.25
0.25 = 25% = 25/100 = 1/4
Answer: 3/2
Step-by-step explanation:
[tex]\displaystyle\\0.3:0.2=\\\\\frac{3}{10} :\frac{2}{10}=\\\\ \frac{3}{10}*\frac{10}{2} =\\\\\frac{(3)(10)}{(10)(2)}=\\\\ \frac{3}{2}[/tex]
How many times larger is (1.088 x 101) than (8 x 10−1)?
13.6
8.704
7.35
0.136
Answer:
0.136
Step-by-step explanation:
If we want to find out how many times larger a number is, they need to have the same amount of exponents to make it easier.
We can move the decimal point in (8 * 10^-1) (which equals 0.8) by 1 to the right, so it's exponent is now 1, same as the (1.088 * 10^1). Now we can divide.
1.088/8 is 0.136, so that is your answer.
Evaluate each expression. Express the result in scientific notation.
Answer:
4. [tex]6.3 \times 10^4[/tex]
6. [tex]3.75 \times 10^{-19}[/tex]
Step-by-step explanation:
9.45 * 10^10 / (1.5 * 10^6) = 9.45 / 1.5 * 10^10 / 10^6 = 6.3 * 10^4
9 * 10^(-11) / (2.4 * 10^8) = 9 / 2.4 * 10^(-11) / 10^8 = 3.75 * 10^(-19)
In the figure, the radius of the large circle is three times the radius of the small circle. About what percent of the large circle is covered by the small circle?
I NEED THIS NOW PLEEEEEASE!!
The percent of the large circle is covered by the small circle will be 33.3%.
How to calculate the percentage?It should be noted that the radius of the small circle will be r.
The radius of the big circle will be 3r.
Therefore, the percent of the large circle is covered by the small circle will be:
= r / 3r × 100
= 1/3 × 100
= 33.3%
The percent of the large circle is covered by the small circle will be 33.3%.
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Jane ordered a few moving boxes from a local store as she is relocating to Atlanta.
She returned 28 damaged boxes. She allotted the remaining boxes equally for
each of the four rooms from which her belongings had to be packed. If 5 boxes
were used for each
room, how many boxes did she receive from the store
initially?
48 boxes did she receive from the store initially in probability.
How does probability explain work?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.Basic probability is governed by three primary rules: the addition rule, the multiplication rule, and the complement rule.Since there is a 50% chance that the outcome will be heads, we can anticipate 50 heads. But when we actually test it, we may get 48 heads, 55 heads, or anything else at all, though it will typically be a figure close to 50.Based on the given conditions formulate = 28 + 5 * 4
Calculate the product or quotient = 28 + 20
calculate the sum or difference = 48
get the result = 48
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Estimate the average rate of change over the interval [-1, 0]. Show your work below or on the graph.
Which choice is a correct equation for the graph shown below?
A y = 2x + 20
B. y = 3x + 1
C. y = 10x + 5
D. y = 15x + 35
Answer:
C
Step-by-step explanation:
y = mx +b The b is where the graph crosses the y axis. If you look a the graph it is crossing at 5. The m is the slope. It is the change in y over the change in x. If you start at 5 and go up10 and over 1, you will be on the line. So our slope is 10/1 which is just 10
Answer:
C
Step-by-step explanation:
it starts on 5 and goes up by 10
The rectangle below has an area of x^2+8x+15x
2
+8x+15x, squared, plus, 8, x, plus, 15 square meters and a width of x+3x+3x, plus, 3 meters.
What expression represents the length of the rectangle?
A rectangle with a width of x plus three and an unknown length. The area of the rectangle is x squared plus eight x plus fifteen.
The length of the given rectangle is x + 5 meters.
What is a rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal.Given:
Area of rectangle = x² + 8x + 15 sq.metersWidth = x + 3 metersTo find: Length of the rectangle
Finding:
Let 'a' be the length of the rectangle.
We know that area of a rectangle = length * width
On substituting the given values in the above formula, we get:
=> x² + 8x + 15 = a (x + 3)
=> a = [tex]\frac{x^2+8x + 15}{x+3}[/tex]
=> a = [tex]\frac{(x+5)(x+3)}{x+3}[/tex]
=> a = x + 5
Hence, The length of the given rectangle is x + 5 meters.
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Write the equation of the line in fully simplified slope-intercept form.
x
Me podrian ayudar con estos dos problemas? porfavor es urgente:(
unit 2 sample work due aug 29 3 of 103 of 10 items question order the integers from least to greatest: -9, 5, 2, -8, 0, 10, -12 0, 2, 5, -8, -9, 10, -12 0, 2, 5, -8, -9, 10, -12 -12, -9, -8, 0, 2, 5, 10 -12, -9, -8, 0, 2, 5, 10 -9, -8, 0, 2, 5, 10, -12 -9, -8, 0, 2, 5, 10, -12 -8, -9, -12, 0, 2, 5, 10
The integers from least to greatest is -12<-9<-8<0<2<5<10.
The given set of numbers are -9, 5, 2, -8, 0, 10, -12.
We need to order the integers from least to greatest.
What is ascending order of integers?Ascending order refers to the arrangement of numbers or other items in increasing order from smallest to largest. Numbers that we see on a number line from left to right are examples of ascending order. We usually represent it by putting commas between numbers or by using the 'less-than symbol (<)' between numbers.
With negative numbers, the highest number with the negative sign has the least value.
So, -12<-9<-8<0<2<5<10.
Therefore, the integers from least to greatest is -12<-9<-8<0<2<5<10.
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with a random sample, each individual has the same chance of being selected. with a simple random sample, all samples of the same size have the same chance of being selected.
A subset of a statistical population called a simple random sample is one in which each member has an equal chance of being chosen.
What is Probability sampling?
A probability Slice is a process of opting for a sample from a population when the selection is grounded on the randomization principle, frequently known as chance or arbitrary selection. In general, a probability slice is more delicate, time-consuming, and precious than a non-probability slice.A random/ arbitrary sample is similar to a straightforward arbitrary sample. The distinction between the two is that any object in the population has an equal probability of being named with a simple arbitrary slice. Every item doesn't inescapably have an equal chance of being chosen in an arbitrary slice.
A random/ arbitrary sample is one that was named at arbitrary. It should really be labeled as a sample that was chosen at arbitrary. In order to help bias and other negative goods, arbitrary samples are employed. In fact, it's not as easy as it seems to opt for a arbitrary sample that involves further than simply opting for 100 people from a population of 1000. Make sure your arbitrary sample is actually random/ arbitrary before using it.
The liability of a straightforward random/ arbitrary slice, a subset of a statistical population called a simple random/ arbitrary sample is one in which each member has an equal chance of being chosen. A straightforward arbitrary sample is intended to offer an objective definition of a group.
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(ross p1.15) consider a group of 20 people. if everyone shakes hands with everyone else, how many handshakes take place?
190 handshakes take place.
What is Combinations?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. The sequence in which the chosen components are chosen is crucial in permutations, too. For instance, the arrangements ab and ba are distinct in permutations but equivalent in combinations (regarded as one arrangement).
Combinatorics is the study of combinations, although mathematics and finance are two other fields that employ combinations.
EXPLNATION : For a handshake you need two people. Therefore, select two from twenty, that is, 20C2 ways. It is 20*19/2 = 190.
In general, if there are ’n’ number of people there can be nC2 handshakes.
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