Answer:
4/3
Step-by-step explanation:
a2 = 324 and a4 = 36
second term is 324 and fourth term is 36
[tex]a_n= a_1(r)^{n-1}[/tex]
To get second term, replace n with 2
[tex]a_2= a_1(r)^{2-1}[/tex]
[tex]a_2= a_1(r)[/tex]
replace a2 with 324
[tex]324= a_1(r)[/tex] -----------> equation 1
To get fourth term , replace n with 4
[tex]a_4= a_1(r)^{4-1}[/tex]
[tex]a_4= a_1(r)^3[/tex]
Replace the value
[tex]36= a_1(r)[/tex] -----------> equation 2
divide second equation by first equation
[tex]36= a_1(r)^3[/tex] divide by [tex]324= a_1(r)[/tex]
1/9 = r^2
take square root on both sides
1/3= r
now we find a1
[tex]324= a_1(r)[/tex]
[tex]324= a_1(\frac{1}{3})[/tex]
multiply by 3 on both sides
972= a_1
So a1= 972, r= 1/3
now find out 7 term by replacing 'n' with 7
[tex]a_7= 972(\frac{1}{3})^{7-1}[/tex]
So 7th term is 4/3
Is is true that the coefficient of the expression 18z-7(-3+2z) of z is 13
find the root of 6x-48=0
Martha took 48 pictures of flowers and 36 pictures of beautiful scenery.she wants to display the pictures so there are the same number of each kind of picture in each display.what is the greatest number of displays she can make?
A web store offers two versions of a popular song. The size of the standard version is 2.5 MB. The size of the high quality is 4.3 MB. Yesterday, there was 1180 downloads of the song, for a total size of 3850 MB. How many downloads of the high quality version were there?
Answer:
250
Step-by-step explanation:
Solve for x: the quantity of x plus 4 / 3 = 2.
A.x = −2 B.x = 2 C.x = 2/ 3 D. x = negative 10/ 3
Write the polynomial in factored form. 4x3 + 8x2 – 96x
Can somebody plz help me
A vending machine needs to be programmed to accept any combination of coins totaling 0.75, excluding pennies, and half dollars. How many combinations are possible?
How many permutations are there of jack, queen, king, ace
If c(x)= [tex] \frac{5}{x-2} [/tex] and d(x) = x + 3, what is the domain of (cd)(x)?
all real values of x
all real values of x except x = 2
all real values of x except x = –3
all real values of x except x = 2 and x = –3
The domain of the composite function (cd)(x), where c(x) = 5/(x-2) and d(x) = x + 3, includes all real values except x = 2 due to a division by zero condition in the function c(x).
Explanation:In this problem, we need to figure out the domain of the combined function (cd)(x). The domain constitutes the set of all real values of x that make the function defined. The first function, c(x) = rac{5}{x-2}, isn't defined for x = 2 because it would lead to a division by zero. The second function, d(x) = x + 3, is defined for all real values since it's a linear function.
When these functions are multiplied to form (cd)(x), the domain will be the intersection of the individual function domains. This means, with c(x) having a restriction with x != 2, the composite function (cd)(x) will maintain this restriction despite d(x) being defined for all real values. So the domain for (cd)(x) is all real values except for x = 2.
Learn more about Domain of Composite Function here:https://brainly.com/question/31810210
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Find the greatest common factor of 16, 27 and 20
20 POINTS PLEASE HELP Write an equation for a trend line and predict the value when x is 15
X 0 3 6 9 12
Y 17.5 35.4 50.5 60.6 66.3
Simplify the expression. (4 − 4i)(−2 + 5i)
What is the LCM of 5 and 6?
Answer: 30
Explanation: To find the least common multiple of lcm of 5 and 6, we begin by listing the first few multiples of each number.
Multiples of 5
1 x 5 = 5
2 x 5 = 10
3 x 5 = 15
4 x 5 = 20
5 x 5 = 25
6 x 5 = 30
Notice that we skipped 0 x 6 in our list of multiples. That's because 0 x 6 is 0 and our least common multiple can't be 0.
Next we list the multiples of 6. When we list the multiples of 6, it's a good idea to keep an eye on the list of multiples for 6 so that we know when we have found a least common multiple.
Multiples of 6
1 x 6 = 6
2 x 6 = 12
3 x 6 = 18
4 x 6 = 24
5 x 6 = 30
Notice that 30 appears in both lists so we can stop here.
This means that the least common multiple of 5 and 6 is 30.
Answer:
30
Step-by-step explanation:
both 6 and 5 go into 30 :)
Is 9.103 greater than 9.13
Answer:
false 9.13 is greater
Step-by-step explanation:
103 thousanths are smaller then 13 hundreths
with decimals the farther you go the lower you get bc its half a number
1/2 to 1/4 to 1/8 it gets smaller
The lenght of a rectangleis 6 inches more thans its width the area of a rectangle is 91 inches find the dimernins
What does it mean when u cant find the mean of a set of numbers?
Answer:
Another word for mean is the "average", your goal is to find the average of the following data set, it's pretty easy, you just have to add up all the numbers in the data set and divide it with the total numbers in the data set.
For example:
Find the mean of the following data set:
4, 1, 8, 5, 7, 3
Mean: 4 + 1 + 8 + 5 + 7 + 3 = 28
then we divide 28 with 6 since there are 6 numbers in the following data set.
Mean: 4 + 1 + 8 + 5 + 7 3 = 28/6 = 4.6
We get the final answer of 4.6!
which exponential functions have been simplified correctly check all that apply
Answer:
Option A, C, D, are the correct options.
Step-by-step explanation:
To check the exponential functions which have been simplified correctly we will take option one by one.
A). [tex]f(x)=5(\sqrt[3]{16})^{x}=5(\sqrt[3]{2^{4}})^{x}=5(2\sqrt[3]{2})^{x}[/tex]
B). [tex]f(x)=2.3(8^{\frac{1}{2}})^{x}=2.3(2.\sqrt{2})^{x}\neq 2.3(4^{x})[/tex]
C). [tex]f(x)=81^{\frac{x}{4}}=(3^{4})^{\frac{x}{4}}=(3^{\frac{4}{4}})^{x}=3^{x}[/tex]
D). [tex]f(x)=\frac{3}{4}(\sqrt{27})^{x}=\frac{3}{4}(\sqrt{3^{3}})^{x}=\frac{3}{4}.(3\sqrt{3})^{x}[/tex]
[tex]f(x)=(24)^{\frac{1}{3}x}=(2^{3}.3)^{\frac{1}{3}x}=(2.3^{\frac{1}{3}})^{x}\neq 2(\sqrt[3]{3})^{x}[/tex]
Exponential functions and their inverses like the natural logarithm are inverse functions, meaning they can undo each other. Simplifications like ln(e^x) result in x, and e^(ln x) simplifies to x. This property is integral to correctly simplifying exponential functions.
Explanation:The exponential functions and their inverses, like the natural logarithm (ln), have specific properties where they can "undo" each other. This relationship allows us to simplify expressions involving exponentials and logarithms. For example, when you have ln(ex), this simplifies to x because the natural logarithm and the exponential function are inverse functions.
Similarly, when applying the exponential function to a natural logarithm, like eln(x), the result is just x. Furthermore, when taking square roots of exponentials, you can adjust the exponent to be evenly divisible by 2 and then take the square root of the base number, followed by dividing the exponent by 2. Also, while dividing exponentials, you subtract the exponents when the bases are the same.
Here is an example of this simplification: to compute the square root of e4, we can write it as e4/2, which simplifies to e2.
Please help! I need to show my work
Mark had $19.00 to spend on stamp packets. They sell for $1.78 each. How many packets can he buy?
Answer:
[tex]10\ stamp\ packets[/tex]
Step-by-step explanation:
Let
x-----> the number of packets that mark can buy
we know that
[tex]1.78x\leq 19[/tex] -----> inequality that represent the situation
Solve for x
Divide by [tex]1.78[/tex] both sides
[tex]x\leq 19/1.78[/tex]
[tex]x\leq 10.67\ stamp\ packets[/tex]
apply the distributive property and the greatest common factor to write an equivalent expression.
32k + 24 = _ (_)
what numbers should be in place of the underscores?
Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
Alexander thought the equivalent quarterly interest rate would be 2%. Is Alexander correct? If he is, explain
why. If he is not correct, state what the equivalent quarterly interest rate is and show how you got your
answer. i need to show my work and everything
One number is four times another. the greater number is xx. write an expression for the lesser number.
A garden table and a bench cost $573 combined. The garden table costs $77 less than the bench. What is the cost of the bench?
64.125 - 20.37 i need the answer
Answer:
43.755 what the other person said but I know that is the answer
Step-by-step explanation:
What’s the ratio of 42¢ to $1.25? (Change dollars to cents)
Answer:
42 125 becuase i got um right bozzzzzzzz
Step-by-step explanation:
What is the measure of x?
A.36
B.72
C.144
D.360
You can jog around the block twice and the park once in 10 min. You can jog around the block twice and the park 3 times in 22 min. Write a system of linear equations that represents this situation. How long does it take to jog around the park?
15. How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000? (Points : 1)
$783
$491
$292
$415
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
Amount for policy = $50,000
If he opt for life insurance @$5.84 per $1000,
then, his amount of premium will be
[tex]50000\times \frac{5.84}{1000}=\$292[/tex]
If he opt for straight policy @ $15.66 per $1000,
then, his amount of premium will be
[tex]50000\times \frac{15.66}{1000}=\$783[/tex]
Difference in both the cases will be
[tex]783-292=\$491[/tex]
Hence, Second option is correct.
If 6 1/2is the lesser number in an inequality, which statement is true about the other number in the inequality?
I KNOW ITS NOT A. But i think it is B. HOPE THIS HELPS!