What is the explicit rule for the arithmetic
sequence on which the series is based?

Answer: You will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.

Step-by-step explanation:

Knowing that you have 1-quart containers, you need to make the conversion from quarts to liters. This is:

[tex]1\ quart=0.946\ liters[/tex]

Now, since the gearbox holds 16.3 liters of oil, you can divide the volume of oil the gearbox holds by the volume of a container  (which is 0.946 liters or 1-quart) to calculate how many containers of 1-quart you will need to fill the gearbox with 16.3 liters of oil.

 [tex]number\ of\ containers=\frac{16.3\ liters}{0.946\ liters}=17.2[/tex]

Based on the result, you will need 18 containers of 1-quart to fill the gearbox with 16.3 liters of oil.

You will need 17 one-quart containers of oil to fill the 16.3-liter gearbox.

To determine how many 1-quart containers of oil you will need to fill the 16.3-liter gearbox, we can convert the 16.3 liters to quarts by using the conversion factor of 1 liter = 1.05668821 quarts. So, 16.3 liters would be approximately 17.229 quarts. Since each 1-quart container holds exactly 1 quart of oil, you will need 17 of the 1-quart containers to fill the gearbox with 16.3 liters of oil.

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Answer:

Step-by-step explanation:

The answer is A

Answer:

250 students would

prefer chocolate ice cream

Step-by-step explanation:

50 of 200

+50   +200

100 of 400

+50    +200

150 of 600

+50     +200

200 of 800

+50      +200

250 of 1000

Answer:

The common ratio is 1/3.

Step-by-step explanation:

Divide each term after the first by the previous one.

9/27 = 1/3

also 3/9 = 1/3 and 3 / 3 = 1/3.

Answer:

Step-by-step explanation:

[tex]\text{The common ratio of a geometric sequence}\ a_n:\\\\r=\dfrac{a_{n+1}}{a_n}\\\\\text{We divide next term by the previous one.}\\\\r=\dfrac{9}{27}=\dfrac{9:9}{27:9}=\dfrac{1}{3}\\\\r=\dfrac{3}{9}=\dfrac{3:3}{9:3}=\dfrac{1}{3}\\\\r=\dfrac{1}{3}\\\vdots[/tex]

Answer:

pi as a value of 3.14 or 3.14159.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

x = 13.0

Step-by-step explanation:

We are given the two legs of the right triangle.

We can use the Pythagorean theorem.

a^2 +b^2 = c^2

7^2 +11^2 = x^2

49+121 = x^2

170 = x^2

Take the square root of each side

sqrt(170) = sqrt(x^2)

13.038 = x

To the nearest tenth

13.0 =x

Answer:

4 3/8 yards.

Step-by-step explanation:

1 7/8 + 2 1/2

= 15/8 + 5/2

Make the denominator 8 in both cases ( The LCM = 8):

= 15/8 +  20/8

= 35/8

= 4 3/8.

Answer:

Multiply all the sides

Step-by-step explanation:

Multiply every side together and you should get your answer just make sure you put the right unit hope this helped :)

Answer:

Option C. x=7

Step-by-step explanation:

we know that

If PQ is parallel to BC

then

triangles APQ and ABC are similar

Remember that

If two figures are similar them the ratio of its corresponding sides is proportional

so

[tex]\frac{AP}{AB}=\frac{AQ}{AC}[/tex]

substitute the values

[tex]\frac{x}{x+7+x}=\frac{x-3}{x-3+x+1}[/tex]

Solve for x

[tex]\frac{x}{2x+7}=\frac{x-3}{2x-2}\\ \\x(2x-2)=(2x+7)(x-3)\\ \\2x^{2}-2x=2x^{2}-6x+7x-21\\ \\3x=21\\ \\x=7\ units[/tex]

Answer: Area of Square = 81m^2

Step-by-step explanation:

To find the area of a square you just need to know the side length on one side, and since we know that the perimeter is 36, and all sides of a square are equal we can divide 36/4, to get 9 is your side length.

Now to actually find the area you can just square your side length, so basically 9x9, which gives you 81, your answer!!

Answer:

Area = 81m^2

Step-by-step explanation:

Square has 4 equal sides so 36/4 =  9

9(9) = 81

Hope this helps :)

Answer:

the answer is 1/12

Step-by-step explanation:

it is 1/12 because if there are only a pair you would have 2 dice. and since each die has numbers all the way up to 6 all you have to do is add them. and don't count all the numbers. like add 1+2+3+4+5+6. that's just plain wrong just do add the highest number on each die (6+6)

Answer:

[tex]x=19[/tex]

Step-by-step explanation:

We have the following equation

[tex]3(x+6)=5(x-4)[/tex]

Notice that in this equation the variable that we want to find is x.

Then the equation for the variable x must be solved

After applying the distributive property and simplifying the equation Maria obtained the following result

[tex]19=x[/tex]

This is the same as:

[tex]x=19[/tex]

That means that the value of x for which equality is met is [tex]x = 19[/tex]. Therefore the solution of the equation is [tex]x = 19[/tex]

Answer:

C

Step-by-step explanation:

x apples cost 80

1 apple  costs 80/x

5 apples costs 80*5/x = 400/x

The same calculation works for the oranges.

y oranges cost 75

1 orange = 75/y

6 oranges = 75*6/y

6 oranges = 450/y

The total cost is 450/y + 400/x which is C

y=4

the values of x changes while the y doesn't so it's y=4

Answer:

[tex]y=4[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The equation of the line in Standard form is:

 [tex]Ax + By =C[/tex]

Where A, B, and C are integers.

We can find the slope of this line with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points K(6, 4) and L(-6, 4), we get:

[tex]m=\frac{4-4}{-6-6}=0[/tex]

Substituting the value of "m" and the coordinates of any point on the line into the equation and solving for "b", you get:

[tex]4=0(6)+b\\b=4[/tex]

Therefore, the equation of this line is:

[tex]y=4[/tex]

Answer:

[tex]a_{11} = 14336[/tex]

Step-by-step explanation:

The general formula for the twelfth term of a geometric sequence is:

[tex]a_n = a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term and r is the common ratio

In this case we know that:

[tex]a_1 = 14\\r=-2[/tex]

The equation is:

[tex]a_n = 14(-2)^{n-1}[/tex]

So for [tex]n = 11[/tex] we look for [tex]a_{11}[/tex]

[tex]a_{11} = 14(-2)^{11-1}[/tex]

[tex]a_{11} = 14(-2)^{10}[/tex]

[tex]a_{11} = 14336[/tex]

Answer:

[tex]11^{th}[/tex] term = 14336

Step-by-step explanation:

We are given the first term [tex] a _ 1 = 1 4 [/tex] and  common ratio [tex] r = - 2 [/tex] of a geometric sequence and we are to find the [tex]11^{th}[/tex] term of this sequence.

We know that the formula to find the [tex]n^{th}[/tex] term in a geometric sequence is given by:

[tex]n^{th}[/tex] term = [tex] a r ^ { n - 1 } [/tex]

Substituting the given values in the above formula:

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{11-1}[/tex]

[tex]11^{th}[/tex] term = [tex]14 \times(-2)^{10}[/tex]

[tex]11^{th}[/tex] term = 14336

Answer: X=1 Is the answer on edge 2023 :)

Step-by-step explanation: X=1

To solve the equation 62x - 3 = 6 - 2x + 1x, combine like terms, add and subtract terms to isolate x, and simplify the solution.

To solve the given equation, 62x - 3 = 6 - 2x + 1x:

Therefore, the solution to the equation is x = 9 / 64.

Answer:

$7 000 was loaned at 10 % and

$10 500 was loaned at 14 %

Step-by-step explanation:

                 Let x = amount loaned at 10 %

Then 17 500 - x = amount loaned at 14 %

                0.10x = interest on 10 % loan

0.14(17 500 - x) = interest on 14 % loan

          2170.00 = total interest

[tex]\begin{array}{rcl}0.10x + 0.14(17 500 - x) & = & 2170.00\\0.10x + 2450 - 0.14x & = & 2170.00\\2450 - 0.04x & = & 2170.00\\-0.04x & = & -280\\\\x & = & \dfrac{-280}{-0.04}\\\\x & = & \mathbf{7000}\\\\\end{array}[/tex]

$7000 was loaned at 10 % and

$10 500 was loaned at 14 %

Check:

\[tex]\begin{array}{rcl}0.10\times 7000 + 0.14(17 500 - 7000) & = & 2170\\700 + 0.14(10 500) & = & 2170\\700 + 1470 & = & 2170\\2170 & = & 2170\\\end{array}[/tex]

OK.

Answer:

3.46 x [tex]10^{10}[/tex]

Step-by-step explanation:

Number of cows 6.4 million = 6.4 x [tex]10^{6}[/tex]

production rate for each cow per year = 5400 = 5.4 x 10³

Total amount of milk produced per year,

= 6.4 x [tex]10^{6}[/tex] x 5.4 x 10³

= (6.4) (5.4) x [tex]10^{6+3}[/tex]

= 34.56 x [tex]10^{9}[/tex]

= 3.46 x [tex]10^{10}[/tex]

Answer:

acute

Step-by-step explanation:

The in-line skates will cost $99.891 with the discount.

To find the cost of the in-line skates with the discount, we need to calculate the amount of the discount first. The discount is 10% of the original price, which is $110.99. To calculate the discount amount, we can multiply the original price by 0.10. The discount would be $110.99 x 0.10 = $11.099. The discounted price would be the original price minus the discount amount, so the discounted price would be $110.99 - $11.099 = $99.891.

Answer:

(f+g)(x)​ is 5^x + 5x - 6

Step-by-step explanation:

To find (f + g)(x), we are merely adding up all the terms present in both

f(x)= 5^x + 2x and g(x)= 3x - 6.  5^x is unique and cannot be combined with any other term.  2x and 3x can be combined to obtain 5x.  -6 is unique.

Thus, the sum (f+g)(x)​ is 5^x + 5x - 6.

Answer:

[tex]5^x+5x-6[/tex]

Step-by-step explanation:

[tex]f(x)=5^x + 2x[/tex]

[tex]g(x)= 3x - 6[/tex]

[tex](f+g)(x)[/tex]

[tex]f(x) + g(x)[/tex]

[tex]5^x+2x+3x-6[/tex]

[tex]5^x+5x-6[/tex]

Answer:

Option C) 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem

The equation of the line represented a direct variation

The value of k is equal to [tex]k=y/x[/tex]

we have the points

(1,n) and (n,16)

so

[tex]k=n/1[/tex]

[tex]k=16/n[/tex]

equate

[tex]n/1=16/n[/tex]

solve for n

[tex]n^{2}=16\\ \\n=(+/-)4[/tex]

therefore

The value of n could be 4 or -4

To find the value of n, substitute the given points into the equation y=kx and solve for n. The possible value of n is 4.

To find the value of n, we need to use the given points and equation. Since the line passes through (1,n), we can substitute these values into the equation y=kx to get n=k(1) or n=k. Similarly, substituting the values (n,16) into the equation gives us 16=k(n). By equating these two equations, we can solve for k and n.

Using substitution, we have n=16/n. Solving this equation by multiplying both sides by n, we get n^2=16. Taking the square root of both sides, we have n=±4. Therefore, the value of n that could be possible is 4.

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Answer:

This answer isn't there, but it's correct: 3.5

Step-by-step explanation:

Subtract 1 from both sides of the equation.

2x = 7

Divide both sides of the equation by 2.

x = 7/2

x = 3.5

Final answer:

The solution to the equation 2x + 1 = 8 is x = 3.5, but this option is not listed among the provided answers, suggesting a possible error in the options listed.

Explanation:

The question seeks the solution set for the equation 2x + 1 = 8. To find the value of x, we begin by subtracting 1 from both sides of the equation, resulting in 2x = 7. Next, we divide both sides by 2 to isolate x, yielding x = 3.5. However, it's important to note that the options provided do not seem to match this solution. It's possible there was an error in the transcription of the options since none of them include 3.5.

Answer:

Step-by-step explanation:

The pentagon RSTYZ is a regular polygon. Therefore all angles are congruent.

If m∠RST = 108°, then m∠STY = 108°.

We have the equation:

m∠UTY + m∠STY + m∠STU = 360°.

Substitute m∠STY = 108° and m∠UTY = 115°.

115° + 108° + m∠STU = 360°

223° + m∠STU = 360°          subtract 223° from both sides

m∠STU = 137°

The ratio for the expression "4 added to the difference of d minus 3" can be represented as: (d - 3) + 4.

Expression: "The difference of d minus 3"

This means subtracting 3 from d:

d - 3

Expression: "4 added to the difference of d minus 3"

Add 4 to the result of the previous expression:

(d - 3) + 4

This gives us the entire expression "4 added to the difference of d minus 3.":

(d - 3) + 4

Combine like terms:

d + 1

Therefore, the simplified form of the given expression is (d + 1).

Answer:

[tex]15x+60\leq 100[/tex]

Step-by-step explanation:

Let

x -----> the number of hours that the painter works

we know that

The inequality that represented this situation is equal to

[tex]15x+60\leq 100[/tex]

solve for x

Subtract 60 both sides

[tex]15x\leq 100-60[/tex]

[tex]15x\leq 40[/tex]

Divide by 15 both sides

[tex]x\leq 40/15[/tex]

[tex]x\leq 2.67\ hours[/tex]

The maximum number of hours is 2

The missing parts of the table for [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex] are 1 and 216, respectively.

Let's solve for the missing values step by step.

The function given is [tex]\( y = 6^x \)[/tex]. This means that for each value of [tex]\( x \)[/tex], [tex]\( y \)[/tex] will be [tex]\( 6 \)[/tex] raised to the power of [tex]\( x \)[/tex].

Step 1: Solve for [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]

The exponent law states that any number raised to the power of 0 is 1. Therefore:

[tex]\( y = 6^0 = 1 \)[/tex]

Step 2: Solve for [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex]

To find [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex], we simply raise 6 to the power of 3:

[tex]\( y = 6^3 = 6 \times 6 \times 6 = 216 \)[/tex]

So, the completed table should look like this:

[tex]$\begin{array}{rrrrrrr}x & -2 & -1 & 0 & 1 & 2 & 3 \\ y & \frac{1}{36} & \frac{1}{6} & 1 & 6 & 36 & 216\end{array}$[/tex]

Answer:

Step-by-step explanation:

This is impossible to figure out because 0 = 0x, as defined by the Zero Property of Multiplication. I apologize.