Answer: The missing term in the given geometric sequence is 20√5 or -20√5.
Step-by-step explanation: We are given to find the missing term in the following geometric sequence :
4, ?, 500, . . .
Let b represents the missing term.
Since the given sequence is a geometric one, so there common ratio r such that
[tex]\dfrac{b}{4}=\dfrac{500}{b}=r\\\\\\\Rightarrow \dfrac{b}{4}=\dfrac{500}{b}\\\\\Rightarrow b^2=4\times500\\\\\Rightarrow b^2=2000\\\\\Rightarrow b=\pm\sqrt{2000}\\\\\Rightarrow b=\pm20\sqrt{5}.[/tex]
Thus, the missing term in the given geometric sequence is 20√5 or -20√5.
what is another pattern in the numbers? Rule: add 1, multiply by 2 first term: 2
Find the solution to the initial value problem (1 + x^{5}) y' + 5 x^{4} y = 5 x^{8}
Convert 0.5% to a decimal. 0.5 0.05 0.005 5.0
Answer:
the answer is o.oo5
Step-by-step explanation:
Translate to an algebraic expression
34 more than q
Sam used 4 gallons of gas to drive 108 miles and 7 gallons of gas to drive 189 miles. Is this a proportional relationship? Explain your reasoning.
The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence? A. The common difference is 1, so the function is f(n + 1) = f(n) + 1 where f(1) = 14. B. The common difference is 4, so the function is f(n + 1) = f(n) + 4 where f(1) = 10. C. The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14. D. The common difference is 14, so the function is f(n + 1) = f(n) + 14 where f(1) = 10.
Answer:
Option C is correct
The common difference is 10,
So, the function is f(n + 1) = f(n) + 10 , where f(1) = 14
Step-by-step explanation:
The recursive function for the arithmetic sequence is given by:
[tex]f(n+1) = f(n)+d[/tex] .....[1]
where, d is the common difference of the two consecutive terms.
Given the arithmetic sequence :
14, 24, 34, 44, 54, .......
First term f(1) = 14
Common difference(d) = 10
Since,
24 -14 = 10
34-24 = 10
44-34 = 10 and so on....
Substitute d = 4 in [1], we have;
[tex]f(n+1) = f(n) + 10[/tex]
Therefore, the recursive function used to generate the sequence is,
[tex]f(n+1) = f(n) + 10[/tex] and f(1) = 10
The common difference is 10, so the function is t(n + 1) = t(n) + 10. Option C is correct.
Given the sequence of numbers 14, 24, 34, 44, 54, ...
This can also be written as (4+10), (14+10) + (24+10), (34+10), (44+10)...
Since 10 is comon to all the terms, the recursive formula will be:
t(n+1) = t(n) + 10
t(n) is the nth term of the remaining sequence 4, 14, 24, 34...
t(n) = a+(n-1)d
t(n) = 4+(n-1)(10)
t(n) = 4 + 10n - 10
t(n) = 10n - 6
Hence the equivalent recursive function will be t(n + 1)= t(n) + 10 with a common difference of 10
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Find the maximum value of the function
WORTH 20 POINTS
Which functions are equivalent to f(x)= 4√162? Check all that apply
Answer:
1,2,5
Step-by-step explanation:
Sarah started 3 miles below the rim of the canyon and hiked until she was 8 miles above the rim. Her brother Sam said she hiked 5 miles. Sarah said she hiked 11 miles.
Who is correct and why?
A. Sam is correct because |3 – 8| = 5.
B. Sam is correct because |–3 – 8| = 5.
C. Sarah is correct because |–3 + 8| = 11.
D. Sarah is correct because |–3 – 8| = 11.
-3 to 0 would be 3 then add 8 = 11 miles.
Sarah is correct
answer is D. Sarah is correct because |–3 – 8| = 11.
Sarah is correct because |–3 – 8| = 11, answer is option D. using number line concept.
What is number line geometery?A number line is a horizontal line that has numbers in equal intervals.The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.
The horizontal straight lines in which the integers are placed in equal intervals increase as we go right.The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.
A vector is an object that has both a magnitude as wel as direction. direction. It is represented by an arrow (head) and the tail which indicates the direction.The length is proportional to the quantity's magnitude.The resultant vector can be calculated using vector addition, and vector subtraction.Unit vector always has a magnitude of one and tells about the direction
explanation:- using number line concept.
-3 to 0 would be 3 then add 8 = 11 miles.
⇒Sarah started 3 miles below the rim = -3
⇒ initially she was above 8 miles
⇒ total distance first from -3 to 0 and than from o to 8
Therefore total distance = |–3 – 8| = 11.
Hence the answer is option D. Sarah is correct because |–3 – 8| = 11.
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Daniel is enrolling for a test prep class. The expression below represents the hourly charges, including the cost for the materials. $30x + $65
1. The constant of the expression represents the ___ A. cost of materials
B. Cost per hour
C. Number of hours
2. and the coefficient of x represents the__ A. Cost per hour
B. cost of materials
C. number of hours
Answer:
(1) The constant of the expression represents the cost of material .
Option (A) is correct .
(2) The coefficient of x represents the cost per hour .
Option (A) is correct .
Step-by-step explanation:
As given the expression
Total cost of hourly wage including the cost for the material = $30x + $65
(1) The constant of the expression represents the cost of material .
Option (A) is correct .
(2) The coefficient of x represents the cost per hour .
Option (A) is correct .
3. The formula to find the surface area of a sphere is to take the radius of the sphere and square it and multiply that amount by pi and then multiply that by 4. This is written algebraically as S=4πr 2 , where S is the surface area, r is the radius, and the value of π is 3.14. Rewrite the equation to solve for the radius of the sphere if you know the sphere’s surface area. Then estimate the radius of a sphere given a surface area of 500 meters2 .
Answer:
6.31 m
Step-by-step explanation:
The surface area (S) of a sphere is a function of its radius (r) according to the following expression.
[tex]S=4\pi r^{2}[/tex]
We can rewrite it to solve for the radius given the surface area.
[tex]S=4\pi r^{2}\\r^{2} =\frac{S}{4\pi} \\r=\sqrt{\frac{S}{4\pi}}[/tex]
When S = 500 m², the radius is
[tex]r=\sqrt{\frac{500m^{2} }{4\pi}}=6.31 m[/tex]
Square 1 has a side length of x, and square 2 has a side length of y. Square 2 is formed by joining the midpoints of the sides of square 1 in order. If x = 2, find the ratio of the perimeter of square 1 to the perimeter of square 2.. . A. 2:1 . B. 1:2 . C. 1: Radical 2 . D. 2: radical 2 Ask for details Follow Report by Btie3oliv8iakram
Answer:
D. 2:√2
Step-by-step explanation:
Graph 24x+25=−6y+7 .
How would I go about doing this? can someone give me a step by step process?
Answer:
Graph is attached below
Step-by-step explanation:
[tex]24x+25=-6y+7[/tex]
To graph the given equation , first we need to solve the equation for y
[tex]24x+25=-6y+7[/tex]
Subtract 7 on both sides
[tex]24x+18=-6y[/tex]
Divide both sides by -6
[tex]y=-4x-3[/tex]
To graph the given equation , make a table.
Assume some random number for x and find out y
x y=-4x-3
-1 1
0 -3
1 -7
Now graph all the points and join it by a line
(-1,1)(0,-3)(1,-7)
The graph is attached below
Claire runs 100 meters in 17 seconds what is her speed in meters per second?
The numbers on two consecutively numbered gym lockers have a sum of 143. What are the locker numbers
Women's shoe size follow a normal distribution with a mean of size 7.5 and a standard deviation of 1.5 sizes. Using the 68-95-99.7 rule, if a store owner wants to stock shoe that fit. 68% of women, what range of sizes should the owner order
To fit 68% of women, the store owner should stock shoe sizes between 6 and 9.
Explanation:To determine the range of shoe sizes that the store owner should order in order to fit 68% of women, we can use the 68-95-99.7 rule, which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean.
In this case, the mean shoe size is 7.5 and the standard deviation is 1.5. So, we can calculate the range by adding and subtracting one standard deviation from the mean:
Lower Bound = Mean - Standard Deviation
Upper Bound = Mean + Standard Deviation
Therefore, the owner should stock shoe sizes between 6 and 9 to fit 68% of women.
What is the amount of the tax per unit?
a. $3
b. $4
c. $2
d. $1?
The amount of the tax per unit imposed by the government, based on the examples provided, is $4 per unit. This specific tax impacts the supply curve and the market's equilibrium, affecting both the consumers' and suppliers’ prices.
The question you're asking about centers on the concept of tax per unit, which is a specific type of tax that governments impose on goods or services. In the information provided, various scenarios are described where a tax is imposed, which affects the prices and the quantity traded of the good. For instance, the imposition of a specific tax of $4 means the supply curve shifts vertically upwards by this amount. The resulting changes in market conditions illustrate how the tax burden is shared between consumers and suppliers.
In the most relevant example, both the government and supplier receive $4 per unit after the imposition of the tax. Therefore, the amount of the tax per unit imposed by the government is $4, which is option (b) in the context of your question.
When going more than 38 miles per hour, the gas mileage of a certain car fits the model y = 43.81 - .395x where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what speed will the car average 15 miles per gallon? (Round to nearest whole number.)
Answer:
d. 73
The car will average 15 miles per gallon at the speed 73 miles per hour
Step-by-step explanation:
Your equation is: y = 43.81 - 0.395x
We need to solve for x if y = 15
So plug 15 into your equation: 15 = 43.81 - 0.395x
Then rearrange your equation to get the variable by itself and change the sign: 0.395x = 43.81 - 15
Subtract 43.81 - 15 = 28.81
0.395x = 28.81
Then divide both sides of the equation by 0.395
0.395x/0.395 = 28.81/0.395
x = 72.9367088608
Then (Round to nearest whole number.)
Giving you your solution of 73
To Conclude:
The car will average 15 miles per gallon at the speed 73 miles per hour
Which angles are corresponding angles?
Estimate 970,390+741,206
Use properties of equality to simplify each of the following expressions so that you can simplify them in your head. Identify the properties used and describe how you used them.
1. 4 • (–3) • 5
2. (2.25 • 23) • 4
4. 5 • 12 • (–2)
5. 35(26)(0)
"most humans find it easier to remember words, rather than numbers. if you tell someone to go to www.icann.org, they can probably remember that. if you told them to go to 192.0.32.7, they would have a difficult time remembering an ip address. computers process in numbers. dns is the process of translating words into numbers. there is a second translation that takes place. humans think in base 10 numbers. computers process in base 2 numbers. the base 10 ip address 192.0.32.7 in base 2 numbers is 11000000.00000000.00100000.00000111. what happens if you cut and paste these base 2 numbers into a browser?"
If you were to cut and paste the base 2 numbers 11000000.00000000.00100000.00000111 into a browser, it would not work as expected.
Why is this so?Browsers expect IP addresses to be provided in the standard base 10 format, not in base 2.
The base 2 representation you mentioned is the binary representation of the IP address 192.0.32.7, but browsers require the IP address to be in decimal format to establish a successful connection.
A browser is a software application used to access and view information on the World Wide Web, displaying webpages and supporting various internet activities.
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Divide. Write your answer as a fraction in simplest form.
9/10÷(−6/5)=
At oxnard university, a student id consists of one letter (26 possibilities) followed by eight digits (10 possibilities). (a) how many unique student ids can be created? number of student ids (b) would one letter followed by three digits suffice for a university with 43,000 students? yes no
A. We are given that the combination is 1 letter and 8 digits, so the total number of unique combinations would be the product of each possibilities.
Total unique ID’s = 26 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
or can also be written as
Total unique ID’s = 26 * 10^8
Solving:
Total unique ID’s = 2.6 x 10^9
B. Let us now calculate the total unique ID’s if there is only 1 letter followed by 3 digits.
Total unique ID’s = 26 * 10^3
Total unique ID’s = 26,000
Since there are 48,000 students and only 26,000 unique ID’s, therefore it is not enough.
NO.
Final answer:
The answer explains the calculation of unique student IDs at a university and determines if a specific ID format is sufficient for a given student count.
Explanation:
(a) To calculate the number of unique student IDs, we multiply the possibilities for each part: 26 possibilities for a letter and 10 possibilities for each of the eight digits:
Total unique student IDs = 26 x (10)^8 = 26 x 100,000,000 =26 x 10^8
(b) For a university with 43,000 students, one letter followed by three digits would have:
Total unique IDs = 26 x (10)^3 = 26 x 1,000 = 26,000, which is more than 43,000 students - so no, it would not suffice.
six Bakers share 7.5 kg of flour equals how much flour did they each receive
True or false: the mean of a normal distribution has no effect on its spread. explain your answer. choose the correct answer below.
a. false. the spread of a normal distribution is completely determined by its mean.
b. true. the spread of a normal distribution is completely determined by its standard deviation.
c. true. the spread of a normal distribution is completely determined by its median.
d. false. the spread of a normal distribution is determined by both its mean and standard deviation.
How do I
Simplify 8-13-(-4)
BODMAS stands for Brackets of Division, Multiplication, Addition, and Subtraction.
In the given equation, the simplified value is -1.
The given equation is:
[tex]8 - 13 - ( - 4)[/tex]
Step 1: In the equation, brackets are present. The brackets will open and the negative sign will be changed to a positive sign, (-) (-) = +.
The equation now becomes:
[tex]8 - 13 + 4[/tex]
Step 2: Based on the BODMAS, after division and multiplication, addition comes.
Solving for the same, we get:
[tex]8 - 9[/tex] [Becaue, -13 + 4 = -9 (+)(-) = (-)]
Step 3: The final value of subtracting -9 from 8, we get:
[tex]8 - 9[/tex] = -1.
Therefore, for the given equation, [tex]8 - 13 - ( - 4)[/tex], the simplified answer is -1.
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If you sell 30 items at $200 a piece and your commission rate is 20%, how much commission do you earn
Answer:
$1200 a
Step-by-step explanation:
You sell 30 items at $200 a piece and your commission rate is 20%
Price of 30 items = 30 × 200 = $6,000
Your commission = 20% × 6,000
= [tex]\frac{20}{100}[/tex] × 6,000
= 0.20 × 6,000
= $1200
You earn $1200 as commission.
write an algebraic expression to model each situation. you have a summer job at a car wash. you earn $8.50 per hour and are expected to pay a one-time fee of $15 for the uniform. if you work x hours per week, how much will you make during the first week? show all your work.
Answer:
The algebraic expression to the model is [tex]8.5x-15[/tex]
Step-by-step explanation:
Consider the provide situation.
You have a summer job at a car wash. you earn $8.50 per hour and are expected to pay a one-time fee of $15 for the uniform.
Let you work for x hours per week and you earn $8.50 per hours, so the money you will earn can be represented as:
8.50 times x or 8.50x
Now you need to pay one time fee of $15 for the uniform.
For the one time fee use a negative sign.
Thus, the required expression is:
[tex]8.50x-15[/tex]
The algebraic expression to the model is [tex]8.5x-15[/tex]
What is 7:9 to 48 states