Answer:
79 years old
Step-by-step explanation:
Let his age be x
400-3x=163
400-163=3x
237=3x
Divide both side by 3
237/3 =3x/3
79=x
The man's age (x) =79 years old
To celebrate its grand opening a store is giving customers gift certificates which customer is the first to get two gift certificates every 8th gets a $50 gift certificate and every 6th person gets a $10 gift certificate
Answer:
The 24th Customer is the first to get two gift certificates.
Since, 2 x 2 x 2 x 2 x 3 = 24
The first customer to receive two gift certificates is the customer at the 24th position in the sequence of customers.
The LCM of 8 and 6 is 24. This means that the first customer to receive two gift certificates will be the one who appears at the 24th position in the sequence.
To calculate the position of this customer, we can consider the multiples of 24:
24, 48, 72, and so on.
The 24th customer is the first to receive two gift certificates, as they satisfy both the every-8th and every-6th customer criteria.
The Greatest Common Factor (GCF) and the Least Common Multiple (LCM) are fundamental concepts in number theory. The GCF of two or more numbers is the largest positive integer that divides all the given numbers without leaving a remainder. On the other hand, the LCM of two or more numbers is the smallest positive multiple that is divisible by all the given numbers.
In this scenario, the GCF and LCM were used to determine the customer who would receive two gift certificates. The GCF was not explicitly required to solve this particular problem, but it is a useful concept in various mathematical contexts.
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Complete Question:
To celebrate its grand opening, a store is giving -customers gift certificates. Which customer is the first to get two gift certificates? Every 8 th customer gets Every 6th customer gets a $10 gift certificate. 200 4-2 Find Greatest Common Factor and Least Common Multiple
Sam deposited $4400 in a savings account earning 6% compounded monthly. If she makes no other deposits or withdrawals, how much will she have in her account in two years?
Group of answer choices
$4959.50
$4928.00
$9342.76
$9328.00
Answer: $4959.50
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 4400
r = 6% = 6/100 = 0.06
n = 12 because it was compounded 12 times in a year.
t = 2 years
Therefore,
A = 4400(1 + 0.06/12)^12 × 2
A = 4400(1+0.005)^24
A = 4400(1.005)^24
A = 4959.5
Solve sin theta + 1 = cos2 theta on the interval
Step-by-step explanation:
Hope it helps you in your learning process.
Answer:
Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]
Step-by-step explanation:
sin(theta) + 1 = cos^2(theta) - sin^2(theta)
sin(theta) + 1 = (1 - sin^2(theta)) -sin^2(theta)
sin(theta) = -2sin^2(theta)
2sin^2(theta) + sin(theta) = 0
sin(theta)[2sin(theta) + 1] = 0
sin(theta) = 0 and 2sin(theta) + 1 = 0
sin(theta) = 0 and sin(theta) = -1/2
Θ = 0, [tex]\frac{7\pi }{6}[/tex], [tex]\frac{11\pi }6}[/tex]
Trista had 95 correct out of 100 problems on her math test. The ratio of correct answers to total problems is . Written in fraction form, this is . Written as a percent, Trista got of the problems correct.
Answer:
Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]
Percent form = 95%
Trisha got 95% of her problems correct.
Step-by-step explanation:
Given:
Total number of questions (N) = 100
Number of correct questions (C) = 95
Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:
Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]
Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,
Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]
Therefore, Trisha got 95% of her problems correct.
Answer:
1: the first one
2:the third one
3:the third one
Step-by-step explanation:
A company that sells seeds wants to check that at least 90% of its corn seeds are viable. An independent testing lab plants 1000 randomly chosen seeds and observes that 903 of them germinate. What does this data imply about the claim that 90% of the seeds are viable?
Answer:
The data claims that 90% of the seeds are viable meaning that 90% of the seeds are likely to germinate and grow into healthy plants under good conditions.90% 0f 1000seeds gives 900seeds,and 903seeds germinated so the claim is true
Step-by-step explanation:
Total number of seeds=1000
Seeds that germinate =903
90% of 1000=>90/100×1000 =900seeds.
In the context of data patterns in a time series, a(n) _____ is a one-time variation that is explainable.
Final answer:
In a time series, an explainable one-time variation is known as an outlier. Outliers can be important for understanding data, but they differ from inexplicable random components which include variations not explained by trend, cyclical, or seasonal patterns.
Explanation:
In the context of data patterns in a time series, a one-time variation that is explainable is usually referred to as an outlier. An outlier can be a potential key to understanding the data or it may be due to some abnormality or error. In a time series, data is analyzed over time to determine components such as the trend, cyclical, seasonal, and random components.
Trend component displays the long-term progression of the series, the cyclical component deals with fluctuations occurring at non-fixed intervals, the seasonal component reflects regular variations within a specific period, like quarters within a year, and the random component comprises those elements that cannot be attributed to the trend, cyclical, or seasonal patterns.
It's essential to distinguish outliers from the random components, which are, by definition, inexplicable variations. However, if an outlier can be explained by a particular event or change, it's not part of the random component but a distinct deviation from the expected pattern.
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (3, StartFraction 108 Over 5 EndFraction), (2, 36), (1, 60), (0, 100). Which function represents the given graph? f(x) = 100 · (Three-fifths)x f(x) = (100 · Three-fifths)x f(x) = 100 + Three-fifthsx f(x) = 100 · (Two-fifths)x
Answer:
[tex]f(x)=100(\frac{3}{5} )^x[/tex]
Step-by-step explanation:
Since the exponential function approaches y=0, its equation is of the form,
[tex]f(x)=a(b^x)[/tex]
The point (0,100) is this graph so it must satisfy its equation
[tex]100=a*b^0[/tex]
[tex]100=a(1)[/tex]
a=100
The equation now becomes:
[tex]f(x)=100*b^x[/tex]
We now substitute the point (1,60)
[tex]60=100*b^1[/tex]
[tex]b=\frac{60}{100} =\frac{3}{5}[/tex]
Therefore the required equation is [tex]f(x)=100(\frac{3}{5} )^x[/tex]
Answer:
the correct answer is A
Step-by-step explanation:
Lyric is fencing her garden, which is in the shape of a right triangle. She measures the base to be 10 feet, the height to be 7 feet. How many feet of fencing will Lyric need to enclose the triangular garden? (round to the nearest tenth)
Answer:
Step-by-step explanation:
The perimeter of a plane figure is the distance around the figure.
Lyric's garden is triangular. The formula for determining the perimeter of a triangle is expressed as
Perimeter = a + b + c
Where a, b and c are the side lengths of the triangle.
Since the triangle is a right angle triangle, to determine the length, c of the third side, we would apply Pythagoras theorem. It is expressed as
Hypotenuse² = opposite side² + adjacent side²
c² = 10² + 7² = 100 + 49
c = √149 = 12.2 feet
The number of feet of fencing that Lyric needs to enclose the triangular garden is
10 + 7 + 12.2 = 29.2 feet
Final answer:
Lyric will need approximately 29.2 feet of fencing to enclose her garden, which is calculated using the Pythagorean theorem to find the hypotenuse of the right triangle and then adding all sides for the perimeter.
Explanation:
To determine how much fencing Lyric will need for her garden, we have to find the perimeter of the right triangle. We are given the base and the height, which are 10 feet and 7 feet respectively.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Calculating,
Hypotenuse = √(base2 + height2)
= √(102 + 72)
= √(100 + 49)
= √149
= 12.2 feet (rounded to the nearest tenth)
Now, to find the total amount of fencing required, we add the lengths of all three sides of the triangle:
Total fencing needed = base + height + hypotenuse
= 10 feet + 7 feet + 12.2 feet
= 29.2 feet (rounded to the nearest tenth)
Therefore, Lyric will need approximately 29.2 feet of fencing to enclose her garden.
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Do not include parentheses in your answer.6x3 + 11x2 - 4x -4 / 3x - 2
Answer:
The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
Step-by-step explanation:
We have attached the division for your reference.
Given:
Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]
Divisor= [tex]3x - 2[/tex]
Explaining the division we get;
Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]
Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]
Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.
Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.
A chicken broth container is in the shape of a rectangular prism, with a length of 9.5 centimeters, a width of 6 centimeters, and a height of 16.5 centimeters. The container is 90% full. How many liters of chicken broth are in the container? ( ) 3 1 L 1000 cm = Round your answer to the nearest hundredth.
Answer:
846,45cm³
Step-by-step explanation:
V = 9.5 * 6 * 16.5
V = 940.5cm³
90% = 940.5 * 0.9 = 846,45cm³
Answer:
0.85 liters
Step-by-step explanation:
Step 1. Find the volume of the full prism
V=9.5 x 6 × 16.5 = 940.5 [tex]cm^{3}[/tex]
Step 2. Find 90% of the full volume of the prism
90% x 940.5 = 0.9 × 940.5 = 846.45 [tex]cm^{3}[/tex]
Step 3. Convert [tex]cm^{3}[/tex] to liters (1 liter = 1000 [tex]cm^{3}[/tex] )
846.45 [tex]cm^{3\\[/tex] = 0.84645 ≈ 0.85
Answer - 0.85 liters
Help meh!
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
Answer:
The answer is B) 3
Step-by-step explanation:
The reason why is because 1 is less than OR equal to x and 3 is less than or equal to x and is x = 3 then it fits both descriptions the best.
Answer:
-3
Step-by-step explanation:
3 is the average rate of change for the exponential graph shown over the interval 1 ≤ x ≤ 3.
Start by determining the two distinct points: (1, 2) and (3, −4).
Therefore,
Δf(x)
Δx
=
−4 − 2
3 − 1
=
−6
2
= −3
City Park: You are desinigng a marble planter for a city park. You want the length of the planter to be sic times the height, and the width to be three times the height.The sides should be one foot thick. BEcause the planter will be on the sidewalk, it doesnot need a bottom. What should the outer dimensions of the planter be if it is to hold 4 cubic feet of dirt.
Answer: 6 feet x 3 feet
Step-by-step explanation:
Let the height be given by= x
The length is= 6x -2 (1) from both sides= 6x-2
The width is= 3x-2(1) from both sides= 3x-2
The total volume= length * width * height
4=(6x-2)*(3x-2)*x
Solving we get,
x=1 and other factor is not the valid option.
So the outer dimensions should be 6 feet x 3 feet
Please help, I was absent for this day so I don't know how to do this.
Answer:
Step-by-step explanation:
An arc is a portion of the circle's circumference bounded by 2 radii
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle or angle which the 2 radii subtends at the center of the circle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 5 inches
θ = 170 degrees
Therefore,
Length of arc = 170/360 × 2 × π × 5
Length of arc = 4.7222π feet
rounding up to 2 decimal places, it becomes
4.72π feet
What does twice 3 means
Answer:
Could be 6
Step-by-step explanation:
The reason I'm saying could is that I don't know of any mathematical system that uses the word twice. I could very easily be wrong. As far as I know twice means double, though.
Twice 3 most likely means like two times of 3,or 3 of something two times.or 3 times two..I hope thi helps in any way.
FIND THE INVERSE OF -5 + 7i
Answer:
Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i
hope it helps
Step-by-step explanation:
A motorcyclist heading east through a small Iowa town accelerates after he passes a signpost at x=0 marking the city limits. His acceleration is constant (4.0 m/s2). At time t =0 he is 5 m east of the signpost and has a velocity of 15 m/s. (a) find his position and velocity at time t=2 sec. (b) where is the motor cyclist when his velocity is 25 m/s?
Answer:
a) 43 m b) 55 m
Step-by-step explanation:
a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s
Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]
S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])
S = 30 + 8 = 38 m , Therefroe;
car is (38 + 5)m from the sign post
car is 43 m from the sign post at t = 2 secs
b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]
[tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)
625 - 225 = 8S
S = 50 m
Car is (50 + 5) m from the sign post
Car is 55 m from the sign post at V = 25 m/s
At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.
Explanation:Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.
(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:
Position (x) = x0 + v0*t + 0.5*a*t2 = 5 m + 15 m/s*2s + 0.5*4.0 m/s2* (2s)2 = 29 mVelocity (v) = v0 + a*t = 15 m/s + 4.0 m/s2*2s = 23 m/s
(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.
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please help me with this giving lots of points
x° = 43° and y° = 120°
Solution:
Given ABCD is a parallelogram.
∠A = (y + 9)°, ∠C = (3x)°, ∠D = (x + 8)°
In a parallelogram, sum of the adjacent angles = 180°
⇒ ∠C + ∠D = 180°
⇒ (x + 8)° + (3x)° = 180°
⇒ x° + 8° + 3x° = 180°
⇒ 4x° + 8° = 180°
⇒ 4x° = 180° – 8°
⇒ 4x° = 172°
⇒ x° = 43°
Substitute x° = 43° in ∠C.
∠C = (3x)°
= 3 × 43°
∠C = 129°
In parallelogram, opposite angles are equal.
⇒ ∠A = ∠C
⇒ ∠A = 129°
⇒ (y + 9)° = 129°
⇒ y° = 129° – 9°
⇒ y° = 120°
Hence the value of x° = 43° and y° = 120°.
Answer:
120 degrees
Step-by-step explanation:
PLZ HURRY IT'S URGENT!!
Which fraction represents the ratio 9 to 6 in simplest form?
1/6
6/9
3/2
9/2
Answer:
3/2
Step-by-step explanation:
Answer:
3/2
Step-by-step explanation:
9 to 6 means
[tex]\dfrac{9}{6}[/tex]
Now we will cancel that fraction - we will divide numerator and denominator both by 3:
9 divided by 3 equals 3
6 divided by 3 equals 2
Hence,
[tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]
The sum of six fifths 6 5 and six timessix times a number is equal to four fifths 4 5 subtracted from seven timesseven times the number. Find the number.
Answer :
The required number is 2.
Step-by-step explanation:
Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.
To find : The number ?
Solution :
Let the number be 'x'.
The sum of six fifths and six times a number i.e. [tex]\frac{6}{5}+6x[/tex]
Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]
According to question,
[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]
[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]
[tex]x=\frac{10}{5}[/tex]
[tex]x=2[/tex]
The required number is 2.
At the North campus of a performing arts school 30% of students are music majors at the South campus 80% of the students are music majors the campuses are merged into one East campus if 45% of the 1000 students at the East campus our music majors, how many students did the north and south campuses have before the merger?At the North campus of a performing arts school 30% of students are music majors at the South campus 80% of the students are music majors the campuses are merged into one East campus if 45% of the 1000 students at the East campus are music majors, how many students did the north and south campuses have before the merger
Answer:
It should be option B
Step-by-step explanation:
To find the number of students the North and South campuses had before the merger, set up an equation and solve for the unknowns. Use the given percentages and total number of students to determine the number of music majors at each campus.
Explanation:To find the number of students the North and South campuses had before the merger, we can set up two equations based on the given information. Let's assume the number of students at the North campus is N and the number of students at the South campus is S.
From the information provided, we know that 30% of the students at the North campus are music majors, so the number of music majors at the North campus is 0.3N. Similarly, 80% of the students at the South campus are music majors, so the number of music majors at the South campus is 0.8S.
Since the campuses are merged into the East campus, which has 1000 students and 45% of them are music majors, we can set up the equation 0.45(1000) = 0.3N + 0.8S to represent the total number of music majors at the East campus. From this equation, we can solve for N and S to find the number of students at the North and South campuses before the merger.
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Tina wrote mathematical expressions for five statements. Her work is shown. Statement Tina's Expressions A The product of a number and seven. 7n B The sum of three consecutive numbers. n+(n+1)+(n+2) C The square of a number times three. 3n2 D Twice the sum of a number and 8. 2n+8 E The cube of a number divided by two. n3÷2 Did Tina write the correct expressions? Select Correct or Incorrect for each expression. Select Linear or Nonlinear to correctly identify each of Tina's expressions.
Answer:
See explanation
Step-by-step explanation:
Linear expression is usually an expression of 1st degree.
A. The product of a number and seven [tex]=7\cdot n=7n[/tex]
Correct, linear
B. The sum of three consecutive numbers.
Let the smallest number be n, the next number is n + 1 and the last number is n + 2. Then their sum is
[tex]n+(n+1)+(n+2)[/tex]
Correct, linear
C. The square of a number times three.
Let the number be n, then its square is [tex]n^2[/tex] and the square of a number times three is
[tex]n^2\cdot 3=3n^2[/tex]
Correct, nonlinear
D. Twice the sum of a number and 8.
If the number is n, then the sum of the number anf 8 is n + 8. Twice the sum is
[tex]2\cdot (n+8)=2(n+8)[/tex]
Incorrect, linear
E. The cube of a number divided by two.
If the number is n, then its cube is [tex]n^3.[/tex] The cube of the number divided by 3 is
[tex]n^3\div 3[/tex]
Correct, nonlinear
A kind of lava , block lava , is moving away from the base of a volcano at a rate of 1.5 meters per day . If the lava continues to flow at this rate, how far away has the lava flowed from the base if the volcano in 30 days
Final answer:
The block lava has flowed 45 meters from the base of the volcano after 30 days, based on a rate of 1.5 meters per day.
Explanation:
To calculate how far the block lava has flowed from the base of a volcano after 30 days at a rate of 1.5 meters per day, we simply multiply the rate of flow by the number of days.
Distance traveled = Rate × Time
Distance traveled = 1.5 meters/day × 30 days = 45 meters.
So, if the lava continues to flow at this constant rate, after 30 days, it will have moved 45 meters away from the base of the volcano. This calculation offers valuable insights into the potential extent of volcanic activity, aiding in risk assessment and mitigation strategies for areas surrounding the volcano.
Students at Hampton Middle School sold T-shirts as a school fundraiser. Sylvie asked 12 random seventh-grade students how many T-shirts they sold for the fundraiser. The number of T-shirts each student sold is listed below. 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7 What is the mean of the data set rounded to the nearest tenth? a. 4.0 shirts b. 4.1 shirts c. 4.5 shirts d. 4.9 shirts
Answer:
b. 4.1 shirts
Step-by-step explanation:
Given data:
number of terms = 12
Terms given are 3, 4, 8, 5, 2, 5, 0, 5, 3, 4, 3, 7
Mean = (sum of terms)/ (number of terms)
Mean = (3 +4+ 8+ 5+2+5+0+ 5+ 3+ 4+3+ 7)/12
Mean = 49/12
Mean = 4.083
Mean = 4.1 (to the nearest tenth)
Answer:
Answer is 4.1 shirts.
Step-by-step explanation:
PLZ HELP THIS IS TIMED!!!!
Which formula can be used to describe the sequence? Negative two-thirds, −4, −24, −144,... f(x) = 6(negative two-thirds) Superscript x minus 1 f(x) = −6(Two-thirds) Superscript x minus 1 f(x) = Negative two-thirds(6)x − 1 f(x) = Two-thirds(−6)x − 1
Answer:
For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Step-by-step explanation:
Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
To find the formula to describe the given sequence :
Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...
First find the common ratio
[tex]r=\frac{a_2}{a_1}[/tex] here [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]
[tex]=\frac{-4}{\frac{-2}{3}}[/tex]
[tex]=\frac{4\times 3}{2}[/tex]
[tex]=\frac{12}{2}[/tex]
[tex]r=6[/tex]
[tex]r=\frac{a_3}{a_2}[/tex] here [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]
[tex]=\frac{-24}{-4}[/tex]
[tex]=6[/tex]
[tex]r=6[/tex]
Therefore the common ratio is 6
Therefore the given sequence is geometric sequence
The nth term of the geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
The formula which describes the given geometric sequence is
[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...
Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not
put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...
we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]
[tex]=-\frac{2}{3}(6)^0[/tex]
[tex]=-\frac{2}{3}[/tex]
Therefore [tex]f(1)=-\frac{2}{3}[/tex]
put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]
[tex]=-\frac{2}{3}(6)^1[/tex]
[tex]=-\frac{12}{3}[/tex]
Therefore [tex]f(2)=-4[/tex]
put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]
[tex]=-\frac{2}{3}(6)^2[/tex]
[tex]=-\frac{2(36)}{3}[/tex]
Therefore [tex]f(3)=-24[/tex]
Therefore the sequence is f(1),f(2),f(3),...
Therefore the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...
Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified
Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence
Answer:
a
Step-by-step explanation:
There are 100 bags each with 100 coins, but only one of these bags has gold coins in it. The gold coin has weight of 1.01 grams and the other coins has weight of 1 gram. We are given a digital scale, but we can only use it once. How can we identify the bag of gold coins?
Answer:
So, with one measurement, we can determine the bag of gold coins.
Step-by-step explanation:
We will number the bags with numbers from 1 to 100. Then we will take one coin from the first bag, from the second we will take 2 coins, from the third we will take 3 coins. We will continue the process to the last bag, from which we will take all 100 coins. Then we'll put it all on a digital scale.
Depending on how many numbers in the decimal notation we mean what the bag of gold coins is. For example, if the decimal number is .02, we will conclude that 2 is a bag of gold coins. For example, if the decimal number is .33, we would conclude that 33 is a bag of gold coins. If there are no decimal numbers, we conclude that the gold bag is the last bag on the digital scale, because 100 · 1.01 = 101.
So, with one measurement, we can determine the bag of gold coins.
A student and a pet run straight towards each other at constant speed, starting with a separation of 30 m. They meet somewhere in between. Draw a picture at the beginning and another at the end, and establish a coordinate system. Give names to important quantities.
Answer:
View graph
Step-by-step explanation:
we have that at constant speed the student and the pet must travel equal distances in equal times, so they must be in the middle of the distance with the same travel time
As can be seen in graph 2 the distance of P = -15 m, and that of S = 15, the sign is due to the orientation, P goes to the left and S to the right
The perimeter of square JKLM is 48 units. Square J K L M is shown. The length of J K is x + 3. What is the value of x? 6 9 12 15
Answer:
x = 9
Step-by-step explanation:
if the perimeter os square JKLM is 48
each side has 48/4
so each side has 12
now if JK is x + 3 = 12
we only need to solve that
x + 3 = 12
x = 12 -3
x = 9
Answer:
B. 9
Step-by-step explanation:
On Saturday a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards. A second group r
Question: on saturday, a minor league baseball team gave away baseball cards to each person entering the stadium. One group received 28 baseball cards . a second group received 68 baseball cards. If each person entering the stadium received the same number of cards, what was the greatest possible number of cards that each person could have received?
Answer:
4 baseball cards
Step-by-step explanation:
Since each person entering the stadium receive the same number of cards, we look for the Highest Common Factors HCF of the number of members of the groups.
The factors of 28 = 1 x 2² x 7
The factors of 68 = 1 x 2² x 17
Looking at the factors, the higest common factor HCF is 2² or 4.
This implies that the higest possible number of baseball cards that each person would have received is 4 baseball cards
Let M be the midpoint of side \overline{AB} of \triangle ABC. Angle bisector \overline{AD} of \angle CAB and the perpendicular bisector of side \overline{AB} meet at X. If AB = 40 and MX = 9, then how far is X from line {AC}?
Final answer:
To find the distance from X to line AC, we can use the angle bisector theorem and the fact that M is the midpoint of AB. By substituting the known values, we can solve for the distance d and find that X is 12 units away from line AC.
Explanation:
We are given that M is the midpoint of side AB of triangle ABC. Angle bisector AD of angle CAB and the perpendicular bisector of side AB meet at X. We are also given that AB = 40 and MX = 9.
To find the distance from X to line AC, we can use similar triangles. Let's denote the distance from X to line AC as d. According to the angle bisector theorem, we have:
AD/CD = AB/CB
Since M is the midpoint of AB, we have:
MD = MB = AB/2 = 40/2 = 20
Therefore, we can rewrite the angle bisector theorem as:
AD/(AD + CD) = AB/CB
Substituting the known values, we get:
9/(9 + d) = 40/20
Cross multiplying, we have:
20 * 9 = 40 * (9 + d)
Simplifying, we find:
d = 12
Therefore, X is 12 units away from line AC.
Question 6 options: What is the approximate area of a circle with a diameter of 56 cm? Use your calculator button for π. Round your answer FOUR decimal places. _________cm2
The area of circle is 2463.0086 cm².
Step-by-step explanation:
Given,
Diameter of circle = 56 cm
Radius of circle = [tex]\frac{Diameter}{2}[/tex]
Radius of circle = [tex]\frac{56}{2}=28\ cm[/tex]
We know that;
Area of circle = [tex]\pi r^2[/tex]
Area of circle = [tex]\pi *(28)^2[/tex]
Area of circle = π * 784
Area of circle = 2463.00864041 cm²
Rounding off to four decimal places
Area of circle = 2463.0086 cm²
The area of circle is 2463.0086 cm².
Keywords: area, circle
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