Find 30th term of the arithmetic sequence, given that the first few terms are given by
6,12,18,..

To find the equation of the function, we use

(h,k) is the vertex

Then, we we replace the values and find the value of "a"

Finally, the equation is,

Subtitute 6 for h and 4 for k into the vertex form of a quadratic function: y = a(x-6)^2+4

Then substitute 0 for x and 0 for y and solve for a:a=-1/9

Answer:

We accept H₀  we have not enough evidence to support that the mean distance between oil changes is less for all luxury cars than that for all compact lower-price cars

Step-by-step explanation:

Luxury cars sample:

sample size    n₁  =  49

sample mean   x₁ = 3178

sample standard deviation   s₁  = 41,80

Compact lower-price cars sample

sample size    n₂  = 38

sample mean   x₂  =  3200

sample standard deviation   s₂  =  50,60

Test Hypothesis:

Null Hypothesis                              H₀          x₁  -  x₂  = 0  or  x₁  = x₂

Alternative Hypothesis                 Hₐ           x₁  -  x₂  <  0   or   x₁ < x₂

CI = 99 %  then significance level is  α = 1 %   α = 0,01

Alternative Hypothesis indicates   that we have to develop a one tail-test to the left

z(c)   for α  0,01     is   z(c)  = -2,32

To calculate  z(s)

z(s)  =  [  (  x₁   -   x₂ 9 ] / √ (s₁²)/n₁  +  (s₂)²/n₂

z(s)  =  (  3178  -  3200 ) / √ 35,66 +  67,38

z(s)  =  ( -  22 / 10,15 )

z(s)  =  - 2,17

Comparing   z(s)  and z(c)

z(s) > z(c)         -  2,17  >  - 2,32

Then  z(s) is in the acceptance region we accep H₀

Using it's concept, it is found that there is a 0.8 = 80% probability that the learner is a senior or a male.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 6 + 4 + 5 = 15 students. Of those, there are 6 seniors, and 6 male non-seniors, hence there are 12 desired outcomes, and the probability is given by:

p = 12/15 = 0.8 = 80%.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

A quadrilateral is a shape that has four straight sides and four angles.

A triangle is a shape that has three straight sides and three angles.

A square is a special type of quadrilateral that has four straight sides of equal length and four right angles.

Answer:

c=1

Step-by-step explanation:

subtract 1 with 10, outcome is 1. subtract both sides by 9 to deduct the 9. and you get 1

Answer:

c = 1

Step-by-step explanation:

The algebra way is to isolate the variable c, and solve for it. The image below shows step-by-step on how to solve it.

Hope this helps! :)

Answer: -23/6

Step-by-step explanation:

Answer:

were is the circle to be to be equated

Answer:

A.

Step-by-step explanation:

I don’t know how to explain it. It’s just that you need to find a number that is 2.5 less than D. So, you just subtract that 2.5 from D.

If a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

The distance travelled by the car with 110 liters of fuel = 250km

To find the rate of fuel consumption we have to apply the unitary method

The distance travelled by the car with 1 liters of fuel = The distance travelled by the car with 110 liters of fuel /110

Substitute the values in the equation

The distance travelled by the car with 1 liters of fuel = 250/110

= 2.5 km

So a car consumes 1 liters of fuel to cover 2.5 km

The rate of fuel consumption = 2.5 km/liter

Hence, if a car consumes 110 liters of fuel with in a distance of 250 km, then the rate of fuel consumption is 2.5 km/liter

Learn more about unitary method here

brainly.com/question/23423168

#SPJ1

Answer:

15 and 3

Step-by-step explanation:

\(x+y=18\\x-y=12\)

the equations are added:

\(2x=30\)

\(x=30/2=15\)

\(15+y=18\\y=18-15\)

\(y=3\)

Hope this helps

Answer:

x=1

y=7

Step-by-step explanation:

5x-4y=-23

-5x-y=-12

Add the two equations together

5x-4y=-23

-5x-y=-12

------------------

0x -5y = -35

Divide each side by -5

  -5y/-5 = -35/-5

     y = 7

Now find x

-5x -y = -12

-5x - 7 = -12

Add 7 to each side

-5x-7+7 = -12+7

-5x = -5

Divide by -5

-5x/-5 = -5/-5

x =1

Answer:

Quotient = 58.5

Step-by-step explanation:

Long division is a method used to divide large numbers by breaking the division down into multiple steps.

Parts of long division:

The divisor is placed to the left of the parenthesis.

The dividend is placed to the right of the parenthesis.

The quotient is placed above the dividend and separated from it by a bar.

To finish the given long division, subtract 64 from 68:

⇒ 68 - 64 = 4

Now divide the result by the divisor:

⇒ 4 ÷ 8 = 0.5

Finally, add 0.5 to 58 to give the final quotient:

⇒ 58 + 0.5 = 58.5

\(\large \begin{array}{r}58.5\\8{\overline{\smash{\big)}\,468\phantom{))}}}\\{-~\phantom{(}\underline{40\phantom{))..}}\\68\phantom{))}\\-~\phantom{()}\underline{\phantom{)}64\phantom{))}}\\4\phantom{))}\\-~\phantom{()}\underline{\phantom{)}\phantom{)}4\phantom{))}}\\0 \phantom{))}\\\end{array}\)

Therefore, from inspection of the given long division:

The expression log₃(x²∛y²) using the laws of logarithms is 2log₃(x) + 2/3log₃(y)

From the question, we have the following parameters that can be used in our computation:

log₃(x²∛y²)

The product law of logarithms states that

log(ab) = log(a) + log(b)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  log₃(x²) + log₃(∛y²)

The power law of logarithms states that

log(aᵇ) =  blog(a)

Using the above as a guide, we have the following:

log₃(x²∛y²) =  2log₃(x) + 2/3log₃(y)

This means that the values of A and B are A = 2 and B = 2/3

Read more about logarithms at

https://brainly.com/question/28041634

#SPJ1

Answer:

False, False, A. 180

Step-by-step explanation:

A flat line is 180 degrees. A right isosceles triangle has one right angle. None of the sides on a scalene triangle are the same.

The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)

In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.

Horizontal translation

g(x) = f(x - k), where k > 0 for a translation in + x direction.

Vertical translation

g(x) = f(x) + k, where k > 0 for a translation in + y direction.

After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down.  Then, we find the following transformation formula:

g(z) = f(z) - 2

To learn more on translations: https://brainly.com/question/12463306

#SPJ1

Answer:

x = -3; substitute it to the other equation.

2(-3) - 7y = 30

-6 - 7y = 30

-7y = 30 + 6

-7y = 36

y = -36/7

we will not round the number because the question is asking for an improper fraction at its simplest form.

Answer:

5.1

Step-by-step explanation:

2*-3 - 7y =30

-6 + 7y = 30

7y = 30 + 6

y = 36 / 7

i.e. y = 5.1

Answer:

--------------------

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

Answer:

Part A: variable = m

coefficient= 35

constant= 75

Part B : she would have $345 in her account .

Part C : No , the coefficient and variable won't change but constant will change ,in this case the constant will be 95 instead of 75.

Step-by-step explanation:

variable = m

constant = 75

coefficient = 35

hope it helps

plz mark as brainliest

Answer:

Step-by-step explanation:

for number 8 we have to use the equation πr^2, so plugging 9 into the equation would give us π(9^2). squaring the 9 gives us 81, and 81 times π equals ~25.

for number 9 we need to use the same equation, πr^2 to find the area, but since we are given the diameter we do not need to use r^2. Instead, we can use π(106) which gives us 333.

Answer:

2176782336

Step-by-step explanation:

Answer

2176782336

Step-by-step explanation:

36x36x36x36x36x36= 2176782336

Answer:

5.89 mi/h

Step-by-step explanation:

This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.

First, we start by drawing a diagram with the velocity vectors.

A= velocity of the first person

B= velocity of the second person

C= velocity in which they are moving away from each other.

Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)

Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.

Law of cosines:

\(C^{2}=A^{2}+B^{2}-2ABcos \gamma\)

so we can solve the formula for C so we get:

\(C=\sqrt{A^{2}+B^{2}-2ABcos \gamma}\)

and now we can substitute the values we know:

\(C=\sqrt{(4)^{2}+(8)^{2}-2(4)(8)cos 45^{o}}\)

\(C=\sqrt{16+64-32\sqrt{2}}\)

\(C=\sqrt{80-32\sqrt{2}} mph\)

if we want an exact answer, then that will be the exact answer, which approximates to:

C=5.89 mph

Answer:

no

Step-by-step explanation:

85x10= 850

75x12= 900

Answer:

no it would not be enough

Step-by-step explanation:

85x10= 850

75x12= 900

The ranking from the lowest to highest APR for the given companies is A, B, D, C.

The correct option is b.

To rank the companies from the lowest to highest Annual Percentage Rate (APR) based on a $600 loan amount, we need to calculate the APR for each company. The formula to calculate APR is APR = (Fees / Loan Amount) * (365 / Terms of Loan).

Let's calculate the APR for each company:

For Company A:

APR_A = ($60 / $600) x (365 / 18) = 0.1 x 20.28 = 2.028%

For Company B:

APR_B = ($80 / $600) x (365 / 12) = 0.1333 x 30.42 = 4.054%

For Company C:

APR_C = ($90 / $600) x (365 / 10) = 0.15 x 36.5 = 5.475%

For Company D:

APR_D = ($110 / $600) x (365 / 14) = 0.1833 x 26.07 = 4.79%

Now, we can rank the companies from the lowest to highest APR:

Company A - APR: 2.028%

Company B - APR: 4.054%

Company D - APR: 4.79%

Company C - APR: 5.475%

To learn more about the percentage;

https://brainly.com/question/24159063

#SPJ1

Answer:

9.4 serving

Step-by-step explanation:

23.5/2.5 = x/1

just divide 23.5 from 2.5 lol

x = 9.4

I'd be sorry if im wrong

First off, you have to make 65 % into an actual number, which is 0.65 (every time you want to convert percentages into numbers, you have to divide that by 100)

Now

0.65 * 8700 = 5655

Answer:  5655

Answer:

At the time the ball was thrown, it was 8 feet above the ground.

h'(x) = -32x + 64 = 0, so x = 2

The ball reaches its maximum height after 2 seconds.

Answer:

b and c

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%