The common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
Explanation:A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. To find the common ratio in a geometric sequence of fractions, we divide each term by the previous term. Let's calculate the common ratios for the given sequence:
Common ratio between 5/12 and -1/6 = (-1/6) / (5/12) = -1/6 * 12/5 = -2/5Common ratio between -1/6 and 1/15 = (1/15) / (-1/6) = 1/15 * (-6/1) = -2/5Common ratio between 1/15 and -2/75 = (-2/75) / (1/15) = -2/75 * 15/1 = -2/5Common ratio between -2/75 and 4/375 = (4/375) / (-2/75) = 4/375 * (-75/2) = -2/5As we can see, the common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
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Which fraction has a value greater than 0.4
209,767 rounded to the nearest 10,000
During low tide, the beachfront in some places is about 350 from the ocean to the homes . High tide can change the width of a beach at a rate of -17 feet each hour . It takes 6 hours for the ocean to move from low to high tide . What is the change in the width of the beachfront from low to high tide ?
the change in width would be -17 * 6 = -102 feet
distance from the ocean to the houses would be 350-102= 248 feet
Find the GFC of 56 and 84. A factor tree for 84 is given below. The GCF of 84 and 56 is .
The greatest common factor of the given numbers is 4.
The given numbers are 56 and 84.
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers.
Here, the factors of given numbers are
56 = 2×2×2×7
84 = 2×2×3×7
Now, the common factors from the above factorization is 2×2
= 4
Therefore, the greatest common factor of the given numbers is 4.
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In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(−2, 7) and point D(−10, −1), what is another point that could represent a corner of the trail?
(10, 7)
(14, 7)
(12, 7)
(8, 7)
From the coordinate plane, we can see that the enlarged point A refers to point F, and enlarged point D refers to point I. To solve for this problem, we know that the ratios of each side should be similar (both the original and enlarged). Since the given choices have all y values equal to 7, so we have to look for the enlarged point of point G. Let us call that point as point C.
In this case, we take the ratio of side IF and side FG. First solving for length using distance formula:
IF^2 = (2 – 4)^2 + (-4 - -2)^2
IF^2 = 8
IF = sqrt 8
FG^2 = (7 – 4)^2 + (-2 - -2)^2
FG^2 = 9
FG = 3
Therefore the ratio of IF/FG must be equal to the ratio of DA / AC:
IF / FG = DA / AC
Find DA first:
DA^2 = (-10 - -2)^2 + (-1 -7)^2
DA^2 = 128
DA = sqrt 128
So,
sqrt 8 / 3 = sqrt 128 / AC
AC = 12
Finding for point C: y of point C = 7
AC^2 = (x - -2)^2 + (7 – 7)^2
12^2 = (x + 2)^2
x + 2 = 12
x = 10
Answer:
(10, 7)
You walk east 720 feet to get from your house to class. After class, you walk southwest 1,044 feet to meet your friends for lunch. When walking the 756 feet back home from lunch, what direction are you traveling?
Stumped on how to solve this one! The numbers just aren't making sense to me
30=3/5
so 10 miles = 1/5 on the map
there re 5/5 per inch, so 4 inches = 4*5 = 20/5
20*10 = 200
so they are 200 miles apart
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
a. 1 and 3
b. 0 and 2
c. 0
d. 3
HURRY IM BEING TIMED!!
Answer:
Step-by-step explanation:
Given: –x² + 2x + 3 = x² – 2x + 3 .
To find: What are the solution(s) .
Solution: we have given that
–x² + 2x + 3 = x² – 2x + 3 .
On subtracting both side by x² .
-2x² + 2x + 3 = x² - x² - 2x + 3
-2x² + 2x + 3 = -2x +3
On Addition both side by 2x .
-2x² + 2x + 2x + 3 =-2x +2x +3
-2x² + 4x + 3 = 3
On subtracting both side by -3 .
-2x² + 4x + 3 -3 = 3 - 3
-2x² + 4x = 0
Taking common 2x .
2x (- x +2 ) =0 .
On grouping .
2x= 0
so x= 0
Now , -x +2 =0 .
-x = -2 .
On dividing by -1
x= 2
Therefore , option B is 0 and 2 .
How fast was Matt driving if he drove 415 miles in 7 hours?
The speed of Matt nearest to tenth place will be 59.3 miles per hour.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Matt drove 415 miles in 7 hours. Then the speed of Matt is calculated as,
Speed = 415 / 7
Simplify the equation, then we have
Speed = 59.2857 miles per hour
Speed = 59.3 miles per hour
The speed of Matt closest to the 10th spot will be 59.3 miles each hour.
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Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?
The rate of earning money for both activities will be calculated by dividing the amount earned by the total time spent for each of the activity.
Babysitting: rate = ($30 / 5 hours ) = $6 / hour
Doing chores: rate = ($28 / 4 hours) = $7 / hour
Thus, Holly is able to earn money faster when doing the chores compared to when she do the babysitting if she work for the same amount of time for each.
Answer:
The unit rate for doing chores is $1 more than the unit rate for babysitting.
Step-by-step explanation:
30 divided by 5=6 So that means it was six dollars for babysitting.
28 divided by four=7 So that means it was seven dollars for babysitting.
A cheetah runs at a speed of 54 miles for every hour. If the distance traveled, in miles, is d and time, in hours, is t, which equation shows the relationship between d and t?
A.) d = 54t
B.) t = 54d
C.) d = 54 + t
D.) t = 54 + d
you would multiply the number of hours (t) by the speed (54) to find the distance (d)
so A) d=54t
You are a self-employed plumber. Your charges are: $22.50 per hour for labor, $0.50 per mile for travel to and from home, and the cost of materials plus 5%. Your last job was 35 miles from home. You took 4.5 hours to complete the job. The parts cost $350. Your invoice to the customer was for $468.75.
Was the invoice correct? If not, why?
A)No. You did not charge for travel.
B)Yes. The invoice was correct.
C)No. You charged too much for materials. (ANSWER)
D)No. You charged too much for travel.
You downloaded a video game to your computer. You have a 60 minute free trial of the game. It takes 5 minutes to set up the game and 7 minutes to play each level. You want to find out how many levels you can play for free.
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answer:
(4 square root 2, 315°), (-4 square root 2, 135°)
Step-by-step explanation:
the distance around the tire or a motorized scooter is 21.98. the tires make one revolutioneer 1/10 second.Find the speed of the scooter in miles per hour.
for every 1/10 second it travels 21.98 inches
for a full second it travels 21.98 x 10 = 219.8 inches
for 1 minute it travels 219.8 x 60 = 2820 inches / 12 = 235 feet per minute
235*60 = 14100 feet per hour
5280 feet per mile
14100/5280 = 2.67 = 2.7 miles per hour
The speed of the scooter with a tire circumference of 21.98 inches rotating at 1/10 second per revolution is approximately 12.5 mph after converting the distance traveled in inches per second to miles per hour.
To calculate the speed of the scooter in miles per hour, we first need to determine how far the scooter travels in 1 second. Since the tires make one revolution every 1/10 of a second, and the distance around one tire is 21.98 inches, in one second the tire will cover a distance equal to 10 revolutions (because 1 second divided by 1/10 second per revolution equals 10 revolutions). Hence, the scooter travels 21.98 inches imes 10 revolutions = 219.8 inches per second.
To convert this speed to miles per hour, we'll first convert inches to miles (1 mile = 63,360 inches), then seconds to hours (1 hour = 3600 seconds).
Calculate Miles per Hour
Speed in miles per second = 219.8 inches/s imes (1 mile / 63360 inches) = 0.003468 miles per second.
Speed in miles per hour = 0.003468 miles/s imes 3600 s/h = 12.4848 mph.
Therefore, the speed of the scooter is approximately 12.5 mph.
An item has a listed price of $80. If the sales tax rate is 6% , how much is the sales tax (in dollars)?
6% = 0.06
80 x 0.06 = 4.80
the tax is $4.80
Another struggle.... Helppp
Write a conjecture for the pattern of the sequence
To conjecture a sequence, one must identify and extend the observable pattern, much like the quark hypothesis predicted unseen particles, or like recognizing the vowel sounds in specific linguistic patterns.
Explanation:In mathematics, creating a conjecture for a sequence involves analyzing the given numbers or patterns and predicting the next element based on the identified pattern. The process comparable to what the developers of the quark hypothesis did, working to predict unknown elements based on established patterns, can aid us in formulating a conjecture for the sequence in question.
For instance, if we refer to the resonance frequencies of a closed tube which form a pattern represented by the formula An = L / (4n) where n is an odd number, we can conjecture that the next frequency in the sequence would be determined by the next odd integer following the last one used.
Similarly, the binomial theorem expansion shows a pattern of coefficients that can be used to conjecture future terms in a binomial expansion. Analyzing patterns like VCC and VCle that determine whether the vowel sound should be long or short in English offer a linguistic parallel to mathematical pattern predictions.
To create a conjecture for a sequence, examine the values and look for a consistent relationship or rule. An example is adding 3 to the previous term in the sequence.
Explanation:A conjecture for the pattern of a sequence can be created by examining the values in the sequence and looking for a consistent relationship or rule. For example, if the sequence is 1, 4, 7, 10, 13, the conjecture may be that each term is obtained by adding 3 to the previous term. This can be represented mathematically as An = A(n-1) + 3, where An represents the nth term in the sequence.
Sarah is making flower arrangements. She has 15 roses and 10 daisies. If she wants to make all identical arrangements, with no flowers leftover, what is the greatest number of arrangements she can make? And how much of each flower will be in each arrangement
(1-sec x)/(1-cos x) = -sec x
I got up to this:
(cos x - 1)/ (cos x(1 - cos x)
Can you help me verify the following identity?
We are given the trigonometric equation:
(1 - sec x) / (1 - cos x) = - sec x
Since the left side has more terms, then let us work on that side to make it exactly like the right side.
We know that sec = 1 / cos, therefore:
(1 – 1 / cos x) / (1 – cos x) = - sec x
[(cos x – 1) / cos x] / (1 – cos x) = - sec x
[- (1 – cos x) / cos x] / (1 – cos x) = - sec x
Cancelling out the term (1 – cos x):
- 1 / cos x = - sec x
- sec x = - sec x
PROVEN!
The function y=2x+4 has a domain of 2,3,5,7, and 8.
What number is not in the range of the function?
8
12
18
20
Find the product of 0.094 ×0.367
s the work shown below correct? Explain your answer. (11 + 2i ) – (3 – 10i ) = 11 + 2i – 3 – 10i = (11 – 3) + (2i – 10i) = 8 – 8i
Answer:
Given that: [tex](11+2i)-(3-10i)[/tex]
Remove the parentheses, we have;
[tex]11+2i-3+10i[/tex]
Like terms are those terms which have same variables to the same power.
Combine like terms of a constant variable;
[tex](11-3) +2i+10i[/tex]
Similarly, combine like terms of imaginary part, we have;
[tex](11-3) +(2i+10i)[/tex]
Simplify:
[tex]8 +(12i)[/tex]
or
[tex]8+12i[/tex]
Therefore, the correct solution of [tex](11+2i)-(3-10i)[/tex] = [tex]8+12i[/tex]
-4(2x-6)=-(4x-9)-2x+3
Write the equivalent decimal and fraction for each percent.
Percent: 15%
Percent:120%
Percent:36%
Percent:22%
Percent:54%
Percent:205%
_______________________________________________________________
For each fraction or decimal, write the equivalent percent.
3/25 =
4.06 =
0.01 =
1/8 =
2/5 =
0.6%
__________________________________________________________
90% or 120 is:___
3.6 or 5% of:___
37 1/2 or 64 is:____
39 is __% of 52
110% or 55 is____
18 is 40% of ____
27 is ___ % of 108
35 is 25% of ___
28 is __% of 20
82 is ___% of 40
Answer:
15% = 0.15
120% = 1.2
36% = 0.36
:22% = 0.22
54% = 0.54
205% = 2.05
3/25 = 12%
4.06 = 406%
0.01 = 1%
1/8 = 12.5%
2/5 = 40%
0.6% = 60%
Hope this helps :)
On a standard circular 12-hour clock, the numerals 12 and 6 are opposite each other. On the planet Bajor, they use a circular ten-hour clock with the numerals 1 to 10 equally spaced. What pair of opposite numerals on a Bajorian clock has a sum of 11?
Please add an explanation with your answer.
the lines shown below are perpendicular. if the green line has a slope of 1/7, what is the slope of the red line?
Answer: it's -7
Step-by-step explanation:
Answer:
Therefore, the slope of the red line must be -7
Step-by-step explanation:
If the two lines are said to be perpendicular each other, then the multiplicative of their slope is -1.
Let "m1" be the slope a line and "m2" be the slope of the perpendicular line.
So, m1*m2 = -1
Here, let's take "m1" be the slope of the green line and "m2" be the slope of the red line.
They said to be perpendicular to each other.
So, m1*m2 = -1
Given: m1 = 1/7
NOw plug in m1 = 1/7 in the above statement, we get
1/7 *m2 = -1
Let's find the value of m2, multiply both sides by the reciprocal of 1/7
The reciprocal of 1/7 is 7.
7*1/7*m2 = -1*7
7/7.m2 = -7
m2 = -7
Therefore, the slope of the red line must be -7
Tony is training to run a marathon. He has already run 2 miles today and is running additional miles at 6 miles per hour. Write an equation that represents the miles, M, that Tony runs, where h represents the number of hours
Of the 8760 hours in a year, one television was on for
1752 hours. What percent is this?
What is the answer to this.
2 1/3 + 3 1/4