The complete question is:
A geometric sequence is defined recursively by
[tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]
(a) Write out the first four terms of this sequence.
(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.
Answer:
The 9th term is larger than 1/10.Explanation:
You are given the first term, [tex]a_(1)=40[/tex] , and the recursive formula
[tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]
Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).
(a) First four terms of the sequence
[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]
Those are the first four terms.
(b) 9th term
You can write the explicit formula of the sequence as:
[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]
Thus, for the 9th term, n = 9, and the term is:
[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]
Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.
25 gal
min
sec
Helppppp
every 10 customer get a free coke at the movie theater. Every 12 customer gets a free popcorn. what number customer will get both a free coke and a free popcorn?
Answer:
The 60th customer will get both a free coke and a free popcorn.
Step-by-step explanation:
i) every 10 customer gets a free coke
ii) every 12 customer gets a free popcorn
iii) therefore the first customer who will get both a free coke and a free popcorn will be given by the Lowest Common Multiple of 10 and 12 which is 60, as 10 goes in to 60 by 6 times and 12 goes into 60 by 5 times.
Answer:
The 60th customer will get both a free coke and a free popcorn.
Step-by-step explanation:
The radius of a circle is 13cm .a chord is a distance of 5cm from the centre.the length of the chord is ?
Answer:
24 cm
Step-by-step explanation:
The triangle formed by the chord, its bisector, and a radius is a right triangle with hypotenuse 13 and one side of length 5. These are two of the numbers in the 5-12-13 Pythagorean triple, so we know that half the chord has length 12.
The chord is 24 cm long.
_____
In case you haven't memorized some of the more commonly used Pythagorean triples, you can find the half-chord length (h) using the Pythagorean theorem:
13² = 5² + h²
169 -25 = h²
√144 = h = 12
The half-chord length is 12, so the full chord length is 24 centimeters.
6. The following set of numbers indicates the number of natural satellites (moons) of each of the planets in our solar system. Find the
mode.
0, 0, 1, 2, 63, 61, 27, 13
A. 20.9
OB. 13
C. 63
D.O.
The answer is...
Answer:
D.O.
The mode of the given set of numbers is 0.
Explanation:The mode in statistics refers to the number or value that appears most frequently in a set of data. To find the mode of the given set of numbers, we count how many times each number appears:
0 appears twice
1 appears once
2 appears once
63 appears once
61 appears once
27 appears once
13 appears once
Since 0 appears the most frequently, it is the mode of the set. Therefore, the correct answer is Mode: 0.
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A vial of medicine contain 60 ounces of medicine. If a dose consists of 3 ounces, how many doses the vial contain?
Answer:
The answer is 20 doses
Rewrite 9(10+11+12) using the distributive property of multiplication over addition
Answer:
90 + 99 + 108
Step-by-step explanation:
The 3 number being added should be multiplied by 9.
10 x 9 = 90.
11 x 9 = 99.
12 x 9 = 108.
Therefore, 90 + 99 + 108.
Answer: 9*10 + 9*11 + 9*12
Step-by-step explanation:
The distributive property of multiplication states that when a number is multiplied by the sum of several numbers, the first number can be distributed to all of those numbers and multiplied by each of them separately.
9(10 + 11 + 12) = 9*10 + 9*11 + 9*12
Spymoreif 3x= 27, then x = 9 what algebraic property?
Division property of equality is used
Solution:
Given that,
If 3x = 27 then x = 9
We have to find the algebraic property used here
Division property is used here
The division property of equality is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same.
Given equation is:
3x = 27
Divide both the sides by 3
[tex]\frac{3x}{3} = \frac{27}{3}\\\\x = 9[/tex]
Thus division property of equality is used
The algebraic property used in changing 3x = 27, to x = 9 is the Division Property of Equality. This property means that if both sides of an equal equation are divided by the same nonzero number, then the resulting equation remains true.
Explanation:The algebraic property that applies when rearranging the equation 3x = 27, to x = 9 is known as the Division Property of Equality. This property states that when both sides of an equation are divided by the same nonzero number, the result is an equivalent equation.
To demonstrate this, in the given equation 3x = 27 we can apply the Division Property of Equality by dividing both sides of the equation by 3. This will give: 3x/3 = 27/3 which simplifies to x = 9, thus demonstrating the division property of equality.
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A four-quart container holds 128 ounces of water. How much water does a one-quart container hold?
Answer:
32 oz
Step-by-step explanation:
4 quart -----------> hold 128 oz
1 quart -------------> holds 128 ÷ 4 oz = 32 oz
Answer:
It holds 32 oz of water
Step-by-step explanation:
Which expression is equivalent to |b|>2 ?
b > –2 and b < 2
b < –2 or b > 2
b < –2 and b > 2
b > –2 or b < 2
Answer:
b < –2 or b > 2
Step-by-step explanation:
The given expresion is
[tex] |b| \: > \: 2[/tex]
By the definition of absolute value function.
|x|=x, if x>0
|x|=-x, if x<0
This implies that:
[tex] b \: > \: 2 \: or \: - b \: > \: 2[/tex]
Divide the second inequality by -2 and reverse the sign
[tex]b \: > \: 2 \: or \: b \: < \: - 2[/tex]
Option B is correct
The expression |b| > 2 is equivalent to b < -2 or b > 2, indicating that the value of b is either greater than 2 or less than -2.
The expression |b| > 2 is equivalent to the situation where b is greater than 2 or less than -2. The absolute value sign indicates the distance of b from 0 on a number line, without considering direction. Therefore, if |b| is greater than 2, b must lie outside the interval from -2 to 2, since anything within that interval would have an absolute value less than or equal to 2.
This means that the correct expression equivalent to |b| > 2 is b < -2 or b > 2. When b is positive, it must be greater than 2 to satisfy the inequality. When b is negative, to have an absolute value greater than 2, it must be less than -2.
What is the factored form of the expression 35xy + 25x? 5(7xy + 5x) 5x(7y + 5) 25x(10y + 1) 10x(25y + 15)
Answer:
5(7xy + 5x)
Step-by-step explanation:
35xy+25x
divide both sides by 5
we have 5(7xy+5x)
Answer:5x(7y+5)
Step-by-step explanation:
This was the correct answer on my test
identify the slope
The height of a triangle is 7 cm longer than its base. The area of the triangle is 60 cm². What is the base of the triangle? Enter your answer in the box. cm
Base of triangle is: 8 cm
Step-by-step explanation:
Let h be height of triangle and
b be the base
According to given statement "The height of a triangle is 7 cm longer than its base."
[tex]h = b+7[/tex]
Area of triangle = 60 square cm
The formula for the area of triangle is given by:
[tex]A = \frac{1}{2} * b * h\\60 = \frac{1}{2} * b * (b+7)\\120 = b(b+7)\\120 = b^2+7b\\b^2+7b-120 = 0\\b^2+15b-8b-120 = 0\\b(b+15)-8(b+15) = 0\\(b+15)(b-8) = 0\\Now\\b+15 = 0 => b=-15\\b-8 = 0 => b = 8[/tex]
As the length cannot be negative,
Base = 8 cm
Height = b+7 = 8+7 =15 cm
Keywords: Triangle, base
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Find the measure of one interior angle in each regular polygon. Round your to nearest tenth if necessary.
The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
To solve the given problem, it is necessary to know about the polygon. A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.For example: -
The triangle is a polygon that has 3 interior angles. The square is a polygon that has 4 interior angles. The pentagon is a polygon that has 5 interior angles.
The formula for the interior angle of a regular polygon is given by,
[tex]= \dfrac{ (n-2) \times 180}{n}[/tex]
Here, n is the number of sides.
Then the calculation is given as,
For triangle ( n = 3 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (3-2) \times 180}{3}\\\\=60 \;\rm degrees[/tex]
For square ( n = 4 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (4-2) \times 180}{4}\\\\=90 \;\rm degrees[/tex]
For pentagon ( n = 5 sides ),
[tex]= \dfrac{ (n-2) \times 180}{n}\\\\= \dfrac{ (5-2) \times 180}{5}\\\\=108 \;\rm degrees[/tex]
Thus, we can conclude that the interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
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The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
We have to determine, The measure of one interior angle in each regular polygon.
A polygon is a closed curve that consist a set of line segments connected together, such that there is a no intersection between the segments.
A regular polygon refers to a multi-sided convex figure where all the sides are equal in length and all the angles have equal degree measures.
The formula for the interior angle of a regular polygon is given by,
[tex]= \frac{(n-2)\times180}{n}[/tex]
Where, n is number of sides.
The triangle is a polygon that has 3 interior angles.
The square is a polygon that has 4 interior angles.
The pentagon is a polygon that has 5 interior angles.
For triangle ( n = 3 sides ),
[tex]= \frac{(3-2)\times 180}{3} \\\\= \frac{180}{3} \\\\= 60degree[/tex]
For square ( n = 4 sides ),
[tex]= \frac{(4-2)\times 180}{4} \\\\= \frac{360}{4} \\\\= 90degree[/tex]
For pentagon ( n = 5 sides ),
[tex]= \frac{(5-2)\times 180}{5} \\\\= \frac{540}{5} \\\\= 108degree[/tex]
Hence, The interior angles of each regular polygon are 60 degree, 90 degree and 108 degree respectively.
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6 over 7 divided by 3???
Answer:
2/7
Step-by-step explanation:
Repeat the following procedure for the four given numbers.\
Multiply the number by 2. Add 4 to the product. Divide this sum by 2. Subtract 2 from the quotient.
The first number is 2. The result is ??
let g (x) = 3x+2 and f (x) = x-2 / 3 find the value. g (f(2))
A. 1
B. 0
C. 2
D. 1/3
Answer: OPTION C.
Step-by-step explanation:
In order to solve the given exercise, you can follow these steps:
1. Given the following function f(x):
[tex]f(x)=\frac{x-2}{3}[/tex]
You must substitute [tex]x=2[/tex] into the function f(x). Then:
[tex]f(2)=\frac{(2)-2}{3}[/tex]
2. Evaluating, you get:
[tex]f(2)=\frac{0}{3}\\\\f(2)=0[/tex]
3. Now, the next step is to substitute [tex]f(2)[/tex] into the function g(x):
[tex]g (x) = 3x+2\\\\g (f(2)) = 3(0)+2[/tex]
4. Finally, evaluating, you get the following result:
[tex]g (f(2)) = 0+2\\\\g (f(2)) =2[/tex]
You can identify that it matches with the Option C.
To find the value of g(f(2)), we first calculate f(2) which equals 0, then we substitute that into g(x) to get g(0) which equals 2. Therefore, g(f(2)) is 2.
Explanation:The question asks for the value of g(f(2)) given two functions g(x) = 3x + 2 and f(x) = (x - 2) / 3. To find the value, we first evaluate f(2), and then plug that result into g(x).
First, we evaluate f(2): f(2) = (2 - 2) / 3 = 0 / 3 = 0.Next, we use this result in g(x): g(f(2)) = g(0) = 3(0) + 2 = 0 + 2 = 2.The answer to the given function composition g(f(2)) is 2, which corresponds to option C.
Find the product of factors of 2^4 multiplied by x^5
Answer:
16x^5
Step-by-step explanation:
use photomath it will help u with math problems if u need it.
The measures of two complementary angles are complementary angles are in the ratio 1:3. What are the measures of the angles?
The measure of angles are 22.5 degree and 67.5 degree
Solution:
Given that, measures of two complementary angles are in ratio 1 : 3
one angle : another angle = 1 : 3
Let the first complementary angle 1x
Let the another complementary angle be 3x
If the angles are complementary, then their sum is 90 degrees
Therefore,
1x + 3x = 90
4x = 90
x = 22.5
Then, first angle = 1x = 1(22.5) = 22.5
Another angle = 3x = 3(22.5) = 67.5
Thus the measure of angles are 22.5 degree and 67.5 degree
What is a possible equation for a function with an x-intercept of (-5,0) and a y-intercept of (0,3)?
Answer:
The equation of a straight line is
-3 x+5 y=15
Step-by-step explanation:
Given x - intercept of (-5,0) and y- intercept is (0,3)
here (-5,0 ) point lie on x- axis and (0,3) this point lie on y- axis
we know that the x- intercept 'a' and y- intercept 'b' formula is
[tex]\frac{x}{a} +\frac{y}{b} = 1[/tex]
so given x - intercept a =-5 and y- intercept is b= 3
now the straight line equation is [tex]\frac{x}{-5} +\frac{y}{3} =1[/tex]
now simplify [tex]\frac{-3 x+5 y}{15} =1[/tex]
[tex]-3 x+5 y=15[/tex]
help me asap pleaseeee
Answer:
see below
Step-by-step explanation:
y=kx
15=1.50(10)
1.50 is the cost of every coffe
10 is the amount of coffes u can get with the 15 dollars
15 is the total money u have
(hopes this helps)
Answer:
y= -1.5x+15
Step-by-step explanation:
y=mx+b
This is the formula to find the equation. M is the slope (rise over run), and b is the y-intercept. Hope this helps.
A six pack of soda costs 3.48 how much does each bottle of soda cost
Final answer:
To determine the cost of each bottle in a $3.48 six pack of soda, divide the total cost by the number of bottles, which results in each bottle costing $0.58.
Explanation:
To find out how much each bottle of soda costs when a six pack of soda costs $3.48, we need to divide the total cost by the number of bottles in a pack. Since there are six bottles in a six pack, we take the total cost of $3.48 and divide it by 6.
The calculation will look like this:
Cost per bottle = Total cost of six pack ÷ Number of bottles
Cost per bottle = $3.48 ÷ 6
Cost per bottle = $0.58
Therefore, each bottle of soda costs $0.58.
Subtract. 29.82 − 8.001 The difference is
Answer:
21.819 is the difference
The answer is 21.819
✍️(◔◡◔) hope this helps
Will mark brainliest+ 10 points
Whats the range of 78,89,93,73,99,87,92,89
Answer:
26
Step-by-step explanation:
Range = highest number minus lowest number.
99-73=26.
Answer:
26
Step-by-step explanation:
Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is 99−73=26.
Please help! Pythagoras question.
The length of swimming course is 345.93 meters.
Step-by-step explanation:
Given,
BC = 80 m
AB = 145 m
Using pythagoras theorem to find AC.
[tex]AC^2+BC^2=AB^2\\AC^2+(80)^2=(145)^2\\AC^2+6400=21025\\AC^2=21025-6400\\AC^2=14625[/tex]
Taking square root on both sides
[tex]\sqrt{AC^2}=\sqrt{14625}\\AC=120.93m[/tex]
Length of swimming course = AB + BC + AC
Length of swimming course = 145 + 80 + 120.93 = 345.93 m
The length of swimming course is 345.93 meters.
Keywords: square root, addition
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12. A bird chirps 10 times a minute. Determine
how many times the bird would chirp in a day.
A. 144 times per day
B. 1,440 times per day
C. 14,400 times per day
D. 144,000 times per day
Answer:
C 14,400
Step-by-step explanation:
If a bird is chirping 10 times a min, and there are 60 min in a day you would multiply those numbers. 10×60=600.
There are 24 hours in a day so multiply 600 with that and you have ur answer. 24×600=14400. Also sorry this is probably old.
A bird chirps 14,400 times in a day.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A bird chirps 10 times a minute.
Now,
Since, A bird chirps 10 times a minute.
We know that;
1 day = 24 hours
= 24 × 60 minutes
= 1,440 minutes
Hence, We get;
A bird chirps in a day = 10 × 1,440
= 14,400 times
Thus, A bird chirps 14,400 times in a day.
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Cecily made a poster in the shape of a qudrilateral. All the angles and sides of the poster are congruent. WHich of the following names the shape of Celcilys poster?
Answer: Square.
Step-by-step explanation:
First it is important to know the following definitions:
1. A Quadrilateral is defined as a polygon that has four sides and, therefore, four vertices.
2. A Square is a Regular Quadrilateral that has the following properties:
- All its sides have equal length.
- Its opposite sides are parallel.
- The measure of each Internal angle is 90 degrees (which are also called "Right angles").
According to the information given in the exercise, the poster Cecily made has the shape of a Quadrilateral. All the angles of this quadrilateral are congruent (this means that they have equal measure) and all the sides are also congruent (they have the same length).
Therefore, based on the explained before, you can conclude that it is a Square.
What is the equation of the line that contains point(3, -2) and has a slope of 5?
y = 5x - 17
y = 5x - 13
y = 5x + 13
y = 5x + 17
Answer:
y = 5x - 17
Step-by-step explanation:
y = mx + c
m = the gradient/slope = 5
y = 5x + c
Substitute (3, -2) into the equation above to find c.
-2 = 5(3) + c
-2 = 15 + c
-2 - 15 = c
-17 = c
y = 5x - 17
Answer:
Step-by-step explanation:
point(3, -2) and has a slope of 5
Slope m = 5
y1 = -2 and x1 = 3
The equation is
y - y1 = m(x - x1)
y + 2 = 5(x - 3)
y + 2 = 5x - 15
y = 5x - 15 - 2
y = 5x - 17
a straight line ab passes through the points a(3,2) and b(7,10).find the slope of ab and state that whether it slopes upward from left or downwards from left
In order to find the slope, we may use the formula:
Slope = (y2−y1)/(x2-x1)
Now, let's identify the values. Say, point a is the first point and b is the second. This means that:
x1 = 3
y1 = 2
x2 = 7
y2 = 10
Let's plug in the values:
=(10-2)/(7-3)
=8/4
=2
Now, to determine if the slope is downward or upward, positive slope means upward from left to right while negative slope means downward from left to right.
So since our slope is positive 2, it is upward.
FINAL ANSWER:
Slope = 2
It slopes upward from left to right.
Alfred does chores to earn money in the summer. The table
shows the amount he earns per chore. Alfred weeded the
garden 6 times over the summer. Write and solve a division
equation to find how much he earned weeding the garden.
The correct answer is (C) $48. Hence the correct option is c.
1. Identify the relevant information:
From the table, we know Alfred earns $8 per time he weeds the garden.
He weeded the garden 6 times.
2. Calculate his total earnings from weeding:
To find the total amount Alfred earned, we multiply the amount he earns per weeding session by the number of times he weeded:
Total earnings = Number of times weeded * Earnings per weeding
Total earnings = 6 times * $8/time = $48
Therefore, Alfred earned $48 from weeding the garden.
Hence the correct option is c.
Complete question:
Alfred does chores to earn money in the summer. The table shows the amount he earns per chore.
Chore Amount Earned ($)
mow lawn $10
wash car $5
weed garden $8
Suppose Alfred weeded the garden 6 times in the summer. How much did he earn weeding?
(A) $30
(B) $60
(C ) $48
(D) $75
The answer is option B - $48. Alfred earned $48 from weeding the garden 6 times, as each weeding earned him $8 and $8 multiplied by 6 gives $48.
The question involves a basic arithmetic calculation to determine how much money Alfred earned for weeding the garden multiple times. We need to multiply the amount Alfred earns per instance of weeding by the number of times he performed the task.
Given that Alfred earns $8 for weeding the garden once and he weeded the garden 6 times over the summer, the total earning from weeding can be calculated as:
Amount Earned Weeding = Earned per Weeding × Number of Weedings
Amount Earned Weeding = $8 × 6 = $48
Therefore, Alfred earned $48 from weeding the garden 6 times in the summer.
The question is:
Alfred does chores to earn money in the summer. The table shows the amount he earns per chore.
Chore Amount Earned ($)
mow lawn $10
wash car $5
weed garden $8
Suppose Alfred weeded the garden 6 times in the summer. How much did he earn weeding?
(A) $30
(B) $60
(C) $48
(D) $75