The terms a1, a2 and a3 do not have a common difference, and the value of a1 in the geometric sequence is 10/9
How to determine the value of the first term?The arithmetic sequence is given as:
a₁, a₂ and a₃
The geometric sequence is given as:
a₄, a₇ and a₁₂
The common ratio of a geometric sequence is:
[tex]r = \frac{T_2}{T_1}[/tex]
So,we have:
[tex]\frac{a_7}{a_4} = \frac{a_{12}}{a_7}[/tex]
Cross multiply
[tex]a_{12} * a_4 = a_7 * a_7[/tex]
Given that a7 = 30, the equation becomes
[tex]a_{12} * a_4 = 30 * 30[/tex]
Evaluate the product
[tex]a_{12} * a_4 = 900[/tex]
Rewrite as:
[tex]a_{4} * a_{12} = 900[/tex]
Express 900 as 10 * 90
[tex]a_{4} * a_{12} = 10 * 90[/tex]
By comparison, we have:
a₄ = 10 and a₁₂ = 90
This means that the geometric sequence is:
10, 30, 90 ---- it has a common ratio of 3
The nth term of a geometric sequence is:
[tex]a_n = ar^{n-1}[/tex]
So, we have:
[tex]a_7 = ar^6[/tex]
[tex]a_4 = ar^3[/tex]
Substitute values for a7 and 14
[tex]ar^6 = 30[/tex]
[tex]ar^4 = 10[/tex]
Divide both equations
[tex]r^2 = 3[/tex]
Take the cube of both sides
[tex]r^6 = 27[/tex]
Substitute [tex]r^6 = 27[/tex] in [tex]ar^6 = 30[/tex]
[tex]a * 27 = 30[/tex]
Divide both sides by 27
[tex]a = \frac{10}{9}[/tex]
Hence, the value of a1 in the geometric sequence is 10/9
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In Autobiography by Abraham Lincoln, Lincoln avoids embellishing on his own life and keeps his portrayal of his life very_____.
A. neutral
B. negative
C. humorous
Abraham Lincoln, in his autobiography, kept his portrayal of his life very: A. neutral.
What is an Autobiography?An autobiography can be described as the account of the of an individual which is authored by the individual whose life is being narrated.
For Abraham Lincoln, the manner in which he described himself sounded quite neutral in the autobiography he authored.
We can conclude that Lincoln kept his portrayal of his life very: A. neutral.
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Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
Answer:
the surface of the teachers table measures 1.5 m by 1m what is its surface area
PLSS HELP ME WITH THIS 20 POINTSS!! The graph below shows a proportional relationship between 2 and 4. What is the constant of proportional y/x
Answer:
3.5.
Step-by-step explanation:
Y = kx where k is the slope of the line
k = y/x
The slope 3/5/1 = 3.5
y/x = 3.5.
You buy milk at $2.48 per gallon. One portion of oatmeal requires 4 ounces of milk. How much does the milk for one portion cost?
Answer:
$0.01
Step-by-step explanation:
Convert gallons to ounces:
0.03125 Gallons of milk per serving
0.03125/2.48=0.0126008
Simplify:
0.01.
One portion costs 1 cent.
NO LINKS!!! For each table, tell whether represents a linear, exponential, inverse, or no relationship. Write an equation each table(if possible).
[tex]\large\boxed{\sf inverse \ variation}[/tex]
[tex]\sf \large\boxed{\sf xy = 12}[/tex]
Explanation:The coordinates are given in the table. Plot the points and draw a smooth curve on the graph. Identify the type of curve it forms.
After identification, it looks like a inverse graph.
Constant variable:
1 × 12 = 122 × 6 = 123 × 4 = 124 × 3 = 126 × 2 = 12Inverse variation: xy = a [a is constant]
Equation: xy = 12 or y = 12/x
Answers:
This is an Inverse variation
The equation is y = 12/x which is the same as saying xy = 12
======================================================
Explanation:
Notice that for each column, the x & y values multiply to 12.
1*12 = 122*6 = 123*4 = 124*3 = 126*2 = 128*1.5 = 1210*1.2 = 1212*1 = 12This tells us that x*y = 12 which rearranges to y = 12/x
All inverse variation equations are of the form y = k/x which is equivalent to xy = k.
As x increases, y decreases, and vice versa.
Which is bigger 1.47 or -1.47
Answer:
1.47 is larger
Step-by-step explanation:
the reason why it's larger is bc the negative sign shows it's below zero
Rewrite in simplest radical form sqrt x * sqrt[4] x each step of your process
I assume the given expression is
[tex]\sqrt x \sqrt[4]{x}[/tex]
We can write each root as a rational power of x, then add the exponents:
[tex]\sqrt x \sqrt[4]{x} = x^{\frac12} x^{\frac14} = x^{\frac12 + \frac14} = x^{\frac34}[/tex]
Then putting it back into radical form, we have
[tex]\sqrt x \sqrt[4]{x} = \sqrt[4]{x^3}[/tex]
Farmer keeps 64 goats. He keeps 5 times as many cows as goats. How many cows does
keep?
Based on a sample of 20 people, the sample mean GPA was 3.25 with a standard deviation of 0.02
The test statistic is:
(to 2 decimals)
The critical value is:
(to 2 decimals)
Using the t-distribution, it is found that:
The test statistic is t = -11.18.The critical value is [tex]t^{\ast} = \pm 2.093[/tex].What are the hypotheses tested?At the null hypothesis, it is tested if the mean GPA of the students is of 3.3, that is:
[tex]H_0: \mu = 3.3[/tex]
At the alternative hypothesis, it is tested if the mean GPA is different than 3.3, hence:
[tex]H_1: \mu \neq 3.3[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 3.25, \mu = 3.3, s = 0.02, n = 20[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.25 - 3.3}{\frac{0.02}{\sqrt{20}}}[/tex]
t = -11.18.
We are testing if the mean is different of a value, hence we have a two-tailed test, with 20 - 1 = 19 df and a standard significance level of 0.05, hence, using a t-distribution calculator, the critical value is [tex]t^{\ast} = \pm 2.093[/tex].
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If x and y vary inversely, and y =6 when x=7, what is the constant of variation
Answer:
x alpha 1/y
: Introducing a constant k
x = k/y
where x = 7, y= 6
7 = k / 6
Cross Multiply
K ( constant) = 42
Answer: k = 42
Step-by-step explanation:
Formula = [tex]y = \frac{k}{x}[/tex]
plug in values:
6 = [tex]\frac{k}{7}[/tex]
multiply both sides by 7
k = 42
PLSS HELP ME WITH THIS! 20 POINTSS!
Answer:
c
Step-by-step explanation:
Someone help ASAP please !! I’ll vote Brainliest !
Answer:
2nd row
Step-by-step explanation:
The y-intercept corresponds to the ordered pair having an x-value of 0. The second row of the table has an x-value of 0, and y-value of 2. Therefore, the y-intercept is (0, 2).
Which ratio is the same as
2/3
Answer:
8/12
Step-by-step explanation:
Which of the following does NOT contribute to global warming?
A. Oil
B. Gas
C. Nuclear power
D. Coal
The race begins at a rate of 1.5 meter per second. What distance, d, is covered after t seconds?
Slope: y-intercept:
Equation:
The distance that would be covered after t seconds = 1.5t meters
Calculation of distanceThe speed of the race=distance/time =1.5m/s
The time given = t seconds
The distance (d) = ?
From the formula of speed = distance/time, make distance the subject of formula,
distance (d) = speed×time
= 1.5×t
= 1.5t meters
Therefore, the distance covered is 1.5t meters after t seconds.
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what 6+6+6+6+6+6=----------------------------
Mark brainiest
Answer:
36
Step-by-step explanation:
calculate the 6+the Other 6 together
Answer:
36
6 + 6 + 6 + 6 + 6 + 6 is the same as saying 6 × 6, because you are adding 6 to itself 6 times, which gives you 36.Guys please help me I'll give more points to whoever is corretc
What is the area of this figure?
The dot plot shows the number of hours, to the nearest
hour, that a sample of 5th- and 7th-grade students
spend watching television each week. How do the
medians compare?
The 5th-grade range is
The 7th-grade range is
The ratio of variation of 5th grade to 7th grade is
Answer:
6 medians.
Step-by-step explanation:
because the medians of 5 and 7 is 6.
If f(c) =x+7 and g(x)= 1/x-13x, what is the domain of (f circle g)(x)
Answer:
last option, {x|x≠13}
Step-by-step explanation:
(f of g)(x) means f(x) x g(x):
(x + 7) x (1 / x - 13) = (x + 7) / (x - 13)
domain is all possible x values which is the denominator, x - 13
x - 13 = 0
Interval notation: (−∞,13)∪(13,∞) this means x does not equal 13
The volume of a cylinder is 1225π cm. The height of the cylinder is 25 cm. What is the radius of the cylinder?
Answer:
Volume of cylinder = pi r^2 h
1225 pi = pi×r^2×25
r^2= 1225/25=49
so, r= 7 cm
PLEASE ANSWER DUE TODAY
Given JAM and segment PB such that PB JM, what is the missing justification in the proof that JP/PA = MB/BA
Answer:
B. AA similarity postulate
y = 3
3y + 78 + 6y + 13
Step-by-step explanation:
the thing you need to do here is put the value of x and just simply the expression.....
= 3y + 78 + 6y + 13
= 3 × 3 + 78 + 6 × 3 + 13
= 9 + 78 + 18 + 13
= 118
[tex]....[/tex]
Answer:
3×3+78+6×3÷13
9+78+18÷13
88.38
Step-by-step explanation:
i m not sure if it's correct since i didn't follow tye bodmas rule properly and it was bit tricky and it comes in decimal so not sure if it's correct
Keep Moving! Read each problem and then, solve
1. What is the probability that you get a white chip from a box with 1 black chip, 1 white chip, and 1 red chip?
2. What is the probability that you get an 8 when you are rolling a number cube? 3. From a letter cube (A, B, C, D, E, and F), what is the probability that a B is on top when you roll the cube?
4. Mila and 3 other applicants apply for a job. What is the probability that Mila gets hired?
The probabilities of cases 1, 2, 3, and 4 will be 1/3, 5/36, 1/6, and 1/4 respectively.
What is probability?Its simple notion is that something will most likely occur. The favorable event's proportion to the overall number of occurrences.
The probability is given as
P = Favorable event / Total event
1. The probability that you get a white chip from a box with 1 black chip, 1 white chip, and 1 red chip will be
P = 1/3
2. The probability that you get an 8 when you are rolling a number cube will be
P = 5/36
3. From a letter cube (A, B, C, D, E, and F), Then the probability that a B is on top when you roll the cube will be
P = 1/6
4. Mila and 3 other applicants apply for a job. Then the probability that Mila gets hired will be
P = 1/4
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Carmella and Carmen simultaneously left the city and drove 120 km to a nearby town. Carmella drove at a speed that was 20 km/hr faster than Carmen. If Carmella arrived in the nearby town 1 hour before Carmen, find the speed that each of them drove.
[tex]\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}[/tex]
Speed of Carmen = 40km/h
and speed of Carmella = 60km/h
Step-by-step explanation:
Let the speed of Carmen = x km/h
Carmella speed will be (x + 20)km/h
Distance = 120 km
Time between Carmen and Carmella = 1 hour
[tex] \sf Time= \frac{distance}{speed} [/tex]
Let the time taken by Carmen be T1
and Carmella be T2
[tex] \sf So \: T_1 = \frac{120}{x} \: and \: T_2 = \frac{120}{x + 20} [/tex]
As there is 1 hour difference so
[tex] \sf T_2 - T_1 = \: 1 hour \\ \\ \\ \sf \implies \frac{120}{x } - \frac{120}{x + 20} = 1 \\ \\ \\ \sf \implies \frac{120(x + 20) - 120x}{x(x + 20)} = 1 \\ \\ \\ \sf \implies 120x + 2400 - 120x = {x}^{2} + 20x \\ \\ \\ \sf \implies 2400 = {x}^{2} + 20x \\ \\ \\ \sf \implies 0 = {x}^{2} + 20x - 2400 \\ \\ \\ \sf \implies 0 = {x}^{2} + 60x - 40x - 2400 \\ \\ \\ \sf \implies0 = x(x + 60) - 40(x + 60) \\ \\ \\ \sf \implies 0 = (x + 60)(x - 40) \\ \\ \\ \sf \implies \red{\boxed{x = 40km}}[/tex]
We have not considered 60 as it will become negative value and negative value is not possible in distance
Speed of Carmen = 40km/h
Speed of Carmella = 40 + 20 = 60km/h
Find the area of EFGH
The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of triangle ABC, hence:
18 ft² = (1/2) * 3 * h
h = 12 ft
Let x represent the height of triangle EFG, hence:
x/12 = 2/3
x = 8 feet
Area of EFG = (1/2) * 2 * 8 = 8 ft²
The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².
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I need help in 13 & 14 :((
Answer:
C and J
Step-by-step explanation:
I need to solve for X
Answer:
x = 10.5
Step-by-step explanation:
Intersecting chord theorem : If two chords intersect within a circle then the product of the measures of the segemnts made up of the chords are equal to each other.
For more reference to this, kindly view the attatched image.
Applying this theorem we would create an equation which would be 2 × x = 7 × 3
We then solve for x
2 × x = 7 × 3
==> simplify both sides
2x = 21
==> divide both sides by 2
x = 10.5
Gary's daily jogging track is 0.9 miles long. In how many days will she have covered a distance of 27 miles?
Answer:
30 days.
Step-by-step explanation:
27 ÷ 0.9 = 30.
Answer:
in 30 days she will reach 27 miles.
Step-by-step explanation:
27 miles / 0.9 miles = 30 days
What is the approximate area of the shaded sector in the circle shown below?
100°
c
18 cm
O A. 31.4 cm2 O B. 565 cm O C. 15.7 cm O D. 283 cm2
Answer:
C
Step-by-step explanation:
Formula to get the area
A = r^2π
A = 16^2π
A= 804.24 cm^2
As per the given data, the approximate area of the shaded sector is 283 square cm, which is option D.
What is area?Area is a measure of the amount of space inside a two-dimensional shape or a flat surface. It is typically measured in square units, such as square meters or square feet.
To find the area of the shaded sector, we need to first find the area of the whole circle, and then multiply it by the fraction of the circle that is shaded.
The area of a circle is given by the formula:
A = [tex]\pi r^2[/tex]
Where r is the radius of the circle. In this case, we are given that the radius of the circle is 18 cm, so we can substitute this value into the formula:
A = [tex]\pi 18^2[/tex]
A = 324π
So, the area of the whole circle is 324π square cm.
The shaded sector has a central angle of 100 degrees, which is a fraction of the total central angle of 360 degrees. So, the fraction of the circle that is shaded is:
100° / 360° = 5/18
Therefore, the area of the shaded sector is:
A = (5/18) * 324π
A = 90π
Using 3.14 as an approximation for π, we get:
A ≈ 90 * 3.14
A ≈ 283
Thus, the approximate area of the shaded sector is 283 square cm, which is option D.
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Solve each equation and check your answer.
1. 2 x + 4 ( 3 − 2 x ) = 3 ( 2 x + 2 ) 6 + 4
2. 4 z + 5 = - 3 z − 8
3. 1 2 − 1 8 q = q − 1 4
Please answer correctly, will choose brainliest.