Answer:
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
Step-by-step explanation:
Given
[tex]24, -12, 6,...[/tex]
Required
Write a formula
The above sequence shows a geometric sequence because:
[tex]r = \frac{-12}{24} = \frac{6}{-12} = -\frac{1}{2}[/tex] -- common ratio
The equation is determined using:
[tex]T_n = ar^{n-1}[/tex]
Where
[tex]a = 24[/tex]
Substitute values for a and r
[tex]T_n = 24* (-\frac{1}{2})^{n-1}[/tex]
Apply law of indices:
[tex]T_n = 24* (-\frac{1}{2})^{n} * (-\frac{1}{2})^{-1}[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1/(-\frac{1}{2})[/tex]
[tex]T_n = 24* (-\frac{1}{2})^{n} * 1*-2[/tex]
[tex]T_n = 1*-2*24* (-\frac{1}{2})^{n}[/tex]
[tex]T_n = -48* (-\frac{1}{2})^{n}[/tex]
The above represents the explicit formula
If y varies inversely with x, and y = 48 when x = 6, find y when x = 18.
Answer:
y = 16
Step-by-step explanation:
Given that,
y varies inversely with x i.e.
[tex]y=\dfrac{k}{x}[/tex]
Where
k is a constant of proportionality
Put y = 48 and x = 6 in the above equation to find k.
So,
[tex]k=48\times 6\\\\k=288[/tex]
Now put k = 288 and x = 18 in the above equation to find y.
[tex]y=\dfrac{288}{18}\\\\y=16[/tex]
So, the value of y is equal to 16 when x = 18.
Answer:
16
Step-by-step explanation:
Plz help me! I’m not sure how to do these!
Answer:
Step-by-step explanation:
Wait where is the picture
What is the equation of the line that is parallel to the
given line and passes through the point (-2, 2)?
Answer:
undefined
Step-by-step explanation:
When x=1, then y= ___
Please I need the answer soon.
Answer:
When x = 1, y = -2
Step-by-step explanation:
The equation of this line is y = x - 3, so when x = 1, y would equal 1 - 3 or -2.
Answer:
x=1, then y= -2
If a confidence interval is given from 43.83 up to 61.97 and the mean is known to be 52.90, what is the margin of error?
Answer:
error is 9.07
Step-by-step explanation:
lemme know if its wrong
David measured a line to be 13.5 inches long. If the actual length of the line is 16.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
18.67
Step-by-step explanation:
(l2-l1)/l2 * 100%
where l2=16.6
l1=13.5
Answer:-23
Step-by-step explanation:
What is the value of X on the parallelogram below?
If Tn =n^+2n. Find third term of the sequence
Answer:
The third term of the sequence Tₙ = n² + 2n is:
T₃ = 15
Step-by-step explanation:
Given
As the sequence is given by
Tₙ = n² + 2n
To determine
The third term of the sequence
The third term of the sequence can be determined by substituting n = 3 in the sequence
Tₙ = n² + 2n
T₃ = (3)² + 2(3)
T₃ = 9 + 6
T₃ = 15
Therefore, the third term of the sequence Tₙ = n² + 2n is:
T₃ = 15
3/4 divided by 1/5 PLEASE ANSWER
Answer:
3.75
Step-by-step explanation:
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
To make the answer to 3/4 divided by 1/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
15/4 = 3.75
The answer is rounded to the nearest four decimal points if necessary.
15/4 is an improper fraction and should be written as 3 3/4.
Answer:
3.75
Step-by-step explanation:
Look at pic plz help
Answer:
Mochi is growing quicker.
Step-by-step explanation:
At 3 weeks Mochi was 13 pounds but Kappa was only at 11. Hope this helps! I'd really appreciate brainliest.
Answer:
Mochi
Step-by-step explanation:
by 2 weeks Mochi was at weight 9 while Kappa was at 8 in weight the same time.
What is the equivalent distance of 60,000 centimeters in kilometers?
1 m = 100 cm
1 km = 1000 m
Enter your answer in the box.
60,000 cm =
km
Answer: it would be 0.6
Step-by-step explanation: why?, because, you must divided 60,000 by 100,000. To get the kilometer 0.6 I hope this helps :), I also took the test!.
Answer:
0.6
Step-by-step explanation:
the answer above is correct
3x+4y=11 x-2y=2 solve the system of equations
select all the sides lengths that will form a triangle?
A. 14 IN, 5 IN, 9 IN
B. 11 CM, 13, CM, 12 CM
C. 25 MM, 12 MM, 12 MM
D. 10 FT, 24FT, 26 FT
E. 5 YD, 5, YD, 5, YD
F. 18 CM, 46, CM, 26 CM
Thank you! :)
B
Step-by-step explanation:
11CM, 13CM, 12CM forms a triangle
Select the statement that describes a unit rate. Javon read 1 book. Javon is running 3 miles. Javon has 4 balls and 1 bat. Javon is bicycling 7 miles per hour.
Answer:
The last one
Step-by-step explanation:
Micah is twice as old as Richard. Richard is three times as old as Ken. Ken is six years old. How old is Micah?
Answer:
36
Step-by-step explanation:
Ken = 6 yo
6 *3 = 18
Richard = 18 yo
8 * 2 = 36
Micah = 36
The age of Micah is 36 years.
What is arithmetic operation?A subfield of mathematics known as arithmetic operations deals with the study and application of numbers to all other subfields of mathematics. Operations like addition, subtraction, multiplication, and division make up the bulk of it.
These fundamental mathematical operations (+, -, ×, and ÷) that we use every day.
Given age of Ken = 6 years
let age of Micah be m and age of Richard be r
acc. to condition
Micah is twice as old as Richard
m = 2r
Richard is three times as old as Ken
r = 3 ken
r = 3 x 6
r = 18
Richard age is 18 years.
m =2r
m = 2 x 18
m = 36 years
Hence age of Micah is 36 years.
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In Ellen's math class, there are 2 boys for every 3 girls. If there are 21 girls in the class, how many boys are in the class?
Answer: 14 boys
Step-by-step explanation:
ratio 2:3
7 divided by 21 = 3, so 7 times 2 equals 14
Answer:
14
Step-by-step explanation:
Divide 21 by 3, you get 7. Multiply 7 by 2, you get 14.
Which of the following is the solution of the system of equations shown?
(2,-2)
(2,2)
(-2,2)
(-2,-2)
Answer:
(-2,-2)
Step-by-step explanation:
The graph doesn't have unit marks, but you can see that the x- and y-coordinates of the intersection are equal, and they are both negative.
(-2,-2)
Can someone solve this please
Answer:
4. 2.4
5. [tex]0.123 = \frac{123}{1000}[/tex]
6. IV
Step-by-step explanation:
4. 3 < 5, so we don't add a tenth when rounding. Hence the answer is 2.4
5. [tex]0.123 = \frac{123}{1000}[/tex]. Because [tex]123[/tex] isn't divisible by 2 or 5, we know that this is the most simplified form.
6. Putting the I before the V negates the I. So IV = 5 - 1 = 4.
A zoo worker works 189.25 hours in 23 days. If she works the exact same number of hours per day, how many hours does she work each day?
Julie bought 12
packages of cucumber seeds. Each bag contains 42
seeds. If she plants half of the seeds, how many of the
seeds does she have left?
Answer:
12x42=504
504/2=252
252
Step-by-step explanation:
What is the square root of 7?
Answer:
2.64575
Step-by-step explanation:
What is 7300 rounded to the nearest hundred?
Two angles of a triangle have measures of 55° and 65°.
Which could not be a measure of an exterior angle of the
triangle?
A. 120
B.125
C.130
D.115
The sum of an interior angle and an exterior angle is 180°. Then the 130° is not an exterior angle of the triangle.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
The two angles of a triangle have measures of 55° and 65°. Then the third angle (x) will be
w + 55° + 65° = 180°
w = 180° - 120°
w = 60°
Let the exterior angle be x, y, and z.
The sum of an interior angle and an exterior angle is 180°. Then we have
[tex]\rm x = 180^o - 55^o = 125^o \\\\y = 180^o - 65^o = 115^o \\\\z = 180^o - 60^o = 120^o[/tex]
More about the triangle link is given below.
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Mrs. Shaw writes this equation on the board. She asks the students to find
the solution.
-40 -2(3m + 1/2)= 7m -2
Keith’s work is shown below. What mistake did Keith make?
-40 - 6m + 1 = 7m - 2
-39 - 6m = 7m -2
-39 = 13m - 2
-37 = 13m
-2 11/13 = m
What is the solution of the equation?
Answer:
-37=13m
Step-by-step explanation:
If i want to build a fence around my rectangular yard, what is the area in fencing if one side is 50 feet long and the other is 80 feet wide?
Answer:
70 feet total
Step-by-step explanation:
Answer:
4,000
Step-by-step explanation:
50•80=4,000
p is directly proportional to the cube of q
Answer:
p=q^3
Step-by-step explanation:
The formula for p in terms of q is p = 0.4 q³
What is meaning of Direct Proportion ?Direct Proportion means when one variable changes the other also changes in the same direction by some proportion.
It is given that
p ∝ q³
p = k q³
here k is the proportionality constant
It is also given that when q = 15 , p = 1350
1350 = k * 15³
k = 0.4
Therefore
The formula for p in terms of q is
p = 0.4 q³
The complete question is
p is directly proportional to the cube of q . When , q = 15 , p = 1350
Find a formula for p in terms of q
To know more about Direct Proportion
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The age at which small breed dogs are fully housebroken follows a Normal distribution with mean ms = 6 months and standard deviation ss = 2.5 months. The age at which large breed dogs are fully housebroken follows a Normal distribution with mean mL = 4 months and standard deviation sL = 1.5 months. Let xS – xL represent the sampling distribution. Be sure show all work and conditions. Let the sample size for both sets be 25 dogs. Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 2.5 months more than the sample mean housebroken age for the large breed dogs? Explain your answer.
Answer:
This measure is just 0.17 standard deviations from the mean, so we should not be surprised.
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
If the z-score is lower than -2, or higher than 2.5, the score of X is considered unusual.
Subtraction of normal variables:
When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Let xS – xL represent the sampling distribution.
Mean s 6, means L 4. So
[tex]\mu = 6 - 4 = 2[/tex]
Standard deviation s is 2.5, for L is 1.5. So
[tex]\sigma = \sqrt{2.5^2+1.5^2} = 2.915[/tex]
Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 2.5 months more than the sample mean housebroken age for the large breed dogs? Explain your answer.
We have to find the z-score for X = 2.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 2}{2.915}[/tex]
[tex]Z = 0.17[/tex]
This measure is just 0.17 standard deviations from the mean, so we should not be surprised.
5. A television set is sale at P13,499 in cash or on installment terms, P2,500 each
month for the next 6 months at 9% compounded monthly. If you would be the
buyer what would you prefer cash or installment?
If I were the buyer, I would prefer cash payments to paying in instalment.
In order to determine which payment method I would prefer, I would have to determine the future value of the payment in instalment terms.
The formula for calculating future value = A (B / r)
B = [(1 + r)^n] - 1
P2,500 x (1.09^6 - 1) / 0.09 = P18,808.34
Paying in instalments is more expensive.
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A rectangular playground has width of 320 feet and a length of 1280 feet. Brooklyn makes a
scale model of the playground using a scale of 4 cm: 20 feet. What are the dimensions of
Brooklyn's scale model?
please help
Answer:409600
Step-by-step explanation:I multpiled and got 409600
Corn chips cost 29.5 cents per ounce. If a bag cost $3.87, how many ounces are in the bag of chips?
Answer:
13.1
Step-by-step explanation:
Answer:
Around 13 ounces
Step-by-step explanation: