What is the recursive formula for the geometric sequence with this explicit formula?

Answer:  Nick

Step-by-step explanation:

Nick is the one who will go to bed first because he needs the most sleep. Nick needs 10 hours of sleep, then it would be Brad who needs 9 , then Will who needs 8

Nick will be the first to bed on Friday evening out of Will, Brad, and Nick.

On Friday evening, Nick would be the first to bed among Will, Brad, and Nick. Nick needs 10 hours of sleep every night, so to wake up at 6 a.m. on Saturday, he would have to go to bed earlier than Will and Brad who need 8 and 9 hours of sleep, respectively.

To find the number of 5-digit numbers that can be formed using the digits 0-6 without repetition, we use permutations. The answer is 5,040.

To find the number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, 6 (without repetition), we need to use the concept of permutations.

Since repetition is not allowed, for the first digit, we have 7 choices (0 cannot be the first digit). For the second digit, we have 6 choices (since one digit has been used). For the third digit, we have 5 choices (since two digits have been used), and so on.

Therefore, the number of 5-digit numbers that can be formed is 7 x 6 x 5 x 4 x 3 = 5,040.

Answer:

14! Hope you ace your test!!

Step-by-step explanation:

The value of the side 'a' will be 14 units.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The value of a is calculated as:-

Sin 30  =  P / H

Sin  30  =  7  /  a

1  /  2  =  7  /  a

a  =  7  x  2

a  =  14 units

Therefore the value of the side 'a' will be 14 units.

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To find the volume of the new sphere, calculate the volume of the original sphere and then multiply it by the scale factor cubed. Convert the volume from cubic centimeters to cubic inches using the conversion factor: 1 cm³ = 0.0610237 in³. The approximate volume of the new sphere in cubic inches is 255.3 in³.

To find the volume of the new sphere, we need to first find the volume of the original sphere and then multiply it by the scale factor cubed. The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius.

Given that the radius of the original sphere is 5 cm, we can calculate its volume using the formula:

V1 = (4/3)π(5 cm)³ ≈ 523.6 cm³.

Next, we can calculate the volume of the new sphere by multiplying the volume of the original sphere by the scale factor cubed:

V2 = V1 × (2)³ = 523.6 cm³ × 8 ≈ 4188.8 cm³.

Finally, to convert the volume from cubic centimeters to cubic inches, we need to use the conversion factor: 1 cm³ = 0.0610237 in³. Therefore, the approximate volume of the new sphere in cubic inches is:

V2 ≈ 4188.8 cm³ × 0.0610237 in³/cm³ ≈ 255.3 in³.

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Answer: Step 4

Step-by-step explanation:

Rena made the first mistake in step 4 because she left the terms [tex]2^{3} and (-1)^{21}[/tex] in the denominator, when in the previous step they were also in the denominator but raised to -1, which means that they should be in the numerator.

The right step 4 would be:

[tex]\frac{2^{3} (-1)^{21} }{2^{6} } =\frac{-1}{2^{3} } =\frac{-1}{8}[/tex]

Answer: step 4

!!

Step-by-step explanation:

Answer:

the square root of thirteen is 3.6

Step-by-step explanation:

if you put the 13 with the square root box and press the = button you will get the square root of 13 is 3.6

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Step-by-step explanation:

Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.

Latitude distance:

53.41 + 37.81 = 91.22

Longitude distance:

2.99 + 144.96 = 147.95

Answer:

degrees apart in latitude: 91.22

degrees apart in longitude: 147.95

Answer: 0.3 times

Step-by-step explanation:

Answer:

1.3 times

Step-by-step explanation:

The function [tex]f(x)=603(1.3)^{x}[/tex] represents the number of students enrolled at a university, x years after it was founded.

So the sequence will be formed to represent the number of students will be

f(1) = 603(1.3)

f(2) = 603(1.3)²

f(3) = 603(1.3)³

and so on.

Now the common ratio between second and first term will be

= [tex]\frac{(603)(1.3)^{2}}{603(1.3)}=1.3[/tex]

Therefore, second term of the sequence will be 1.3 times of the first term.

Answer will be - "Each year, the number of students will be 1.3 times the number the year before".

Answer:

Option 1

Step-by-step explanation:

Given expression is:

[tex]\frac{(2mn)^{4}}{6m^{-3}n^{-2}} \\=\frac{2^{4}m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{16m^{4}n^{4}}{6m^{-3}n^{-2}}\\=\frac{8*2*m^{4}*n^{4}}{2*3*m^{-3}*n^{-2}} \\=\frac{8*m^{4+3}n^{4+2}}{3}\\=\frac{8m^{7}n^{6}}{3}[/tex]

So option 1 is the correct answer ..

Answer:

A. x = √2

B. x = 1

D. x = -1

E. x = -√2

Step-by-step explanation:

Correct 100%

Without the complete equation, we cannot provide a definitive solution. However, it seems like you are dealing with a quadratic equation where possible solutions can be found using the quadratic formula, '-b ± √ (b² - 4ac) / 2a'. Please provide the full equation for a more precise answer.

The original equation mentioned in your question is missing, but I'll assume you are referring to solutions of the equation x² = √ ( 2x² - 1 ). This equation can be solved by first simplifying the condition as 2(x² - 1)² ≤ 1. Following the standard method for solving quadratic equations, we can use the quadratic formula -b ± √ (b² - 4ac) / 2a. Unfortunately, without a full equation, we cannot provide a comprehensive answer. Please, provide the complete equation for a more accurate solution.

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Answer:

2 lines meet at a shared point.

Step-by-step explanation:

Hope my answer has helped you!

Answer:

Option a: Line slants down.

Step-by-step explanation:

 It is important to remember that the equation of the line in Slope-Intercept form is the following:

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

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

The slope of a line can be positive (The line slopes upwards to the right), negative (The line slopes downwards to the right), zero (Horizontal line), or undefined (Vertical line).

Therefore, the statement that best describes a line in a slope-intercept form when the coeficient of the x-term (The slope) is negative is: "Line slants down".

Answer:

Step-by-step explanation:

[tex]f(x)=0.5|x-4|-3\\\\f(x)=7\Rightarrow0.5|x-4|-3=7\qquad\text{add 3 to both sides}\\\\0.5|x-4|=10\qquad\text{multiply both sides by 2}\\\\|x-4|=20\iff x-4=\pm20\\\\x-4=-20\qquad\text{add 4 to both sides}\\x=-16\\\\x-4=20\qquad\text{add 4 to both sides}\\x=24[/tex]

Answer:

Option B , D and E are correct.

Step-by-step explanation:

We set the denominator equal to zero to find the number to put in division box

So, if 3 is in the division box then the denominator will be

x-3 = 0 => x=3 is the root.

So, Option E is correct

2x^2-2x-12 ÷ x-3 = 2x+4 is correct.

because after division the result given is 2x+4 which is correct.

So, Option B is correct

x-3 is a factor of 2x^2-2x-12 because because when the term is divided we get the remainder 0.

So, Option D is correct

So, Option B,D and E are correct.

Answer:

20/6 or 3.33 or 3 1/3 or 3 hours and 20 mins

Step-by-step explanation:

5/6 * 4 = (5*4)/6 = 20/6

Answer:

she will have praticed 3 hours and 20 min

Step-by-step explanation:

The average rate of change over the entire slide is [tex]\( \frac{1}{10} \)[/tex] feet per foot.

To find the average rate of change over the entire slide, we need to calculate the change in height divided by the change in distance over the entire slide.

Let's denote:

- [tex]\( h_1 \)[/tex] as the initial height (when x = 0),

- [tex]\( h_2 \)[/tex] as the final height (when x = 20).

Given that the height of the slide is 2 feet when ( x = 20 ), we have:

[tex]\[ h_2 = 2 \, \text{feet} \][/tex]

We also know that the height of the slide is 0 feet when ( x = 0 ), so:

[tex]\[ h_1 = 0 \, \text{feet} \][/tex]

Now, the change in height ([tex]\( \Delta h \)[/tex]) over the entire slide is:

[tex]\[ \Delta h = h_2 - h_1 = 2 \, \text{feet} - 0 \, \text{feet} = 2 \, \text{feet} \][/tex]

The change in distance ([tex]\( \Delta x \)[/tex]) over the entire slide is simply the distance traveled, which is:

[tex]\[ \Delta x = 20 \, \text{feet} \][/tex]

The average rate of change over the entire slide ([tex]\( \text{Avg ROC} \)[/tex]) is then:

[tex]\[ \text{Avg ROC} = \frac{\Delta h}{\Delta x} \][/tex]

[tex]\[ \text{Avg ROC} = \frac{2 \, \text{feet}}{20 \, \text{feet}} \][/tex]

[tex]\[ \text{Avg ROC} = \frac{1}{10} \][/tex]

The average rate of change of the slide height is calculated as 0.1 feet per foot, indicating that the height increases by 0.1 feet for every foot along the slide.

Step by step calculation:

The average rate of change of a function over an interval is calculated using the formula:

       Average Rate of Change = (2 - 0) / (20 - 0) = 2 / 20 = 0.1 feet per foot

This means the height increases by 0.1 feet for every foot traveled along the length of the slide.

Answer:

x = 2

Step-by-step explanation:

Given 2 secants intersecting a circle from an external point, then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

(x + 1)(x + 1 + 11) = (x + 4)(x + 4 + 1)

(x + 1)(x + 12) = (x + 4)(x + 5) ← expand both sides

x² + 13x + 12 = x² + 9x + 20

Subtract x² + 9x from both sides

4x + 12 = 20 ( subtract 12 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

Answer:

C

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = [tex]4^{x}[/tex] - 8 - (5x + 6)

              = [tex]4^{x}[/tex] - 8 - 5x - 6 ← collect like terms

              = [tex]4^{x}[/tex] - 5x - 14 → C

Answer:

22.5 pages

Step-by-step explanation:

First divide the page number by the minutes it takes to read them to find pages per minute-

4.5 / 12 = .375

Then take that number and multiply it by the minutes in an hour-

(.375) (60) = 22.5

22.5 pages in one hour.

Answer:

22 1/2 pages

Step-by-step explanation:

60/12 = 5

5(4.5) = 22 1/2

Answer:

No, because they look like they are different sizes. Or you could say the first answer

Hello There!

The answer is "C"

In this problem, you need dilation to map onto each-other.

Dilation is transformation hat changes the size of something

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour - 3 cups of milk

4- cups of flower - 6 cups of milk

6 cups of flower - 9 cups of milk

Please mark brainliest and have a great day!

Answer:

9 cups of milk

Step-by-step explanation:

2 cups of flour need 3 cups of milk

1 cup of milk needs 3/2 cups of milk

:. 6 cups of milk will need

(6 x 3/2) = 18/2

= 9 cups of milk

Answer:

C

Step-by-step explanation:

The vertical line test is basically just drawing a vertical line and seeing if the line intersects the graph more than once. If it does, then it is not a function, if it doesn't than it is a function.

Answer:

C

Step-by-step explanation:

[tex]\bf (-5u)(-5u)(-5u)(-5u)\implies (-5u)^1(-5u)^1(-5u)^1(-5u)^1 \\\\\\ (-5u)^{1+1+1+1}\implies (-5u)^4\implies (-5)^4u^4\implies 625u^4[/tex]

Answer:

350 lightbulbs

Step-by-step explanation:

First, we need to find the rate of lightbulbs that are inspected. This can be calculated as the division between the number of lightbulbs selected for inspection and the number of light bulbs produced. This is:

Rate = 7/400 =0.0175

That means that for every lightbulb produced, 0.0175 are inspected. Then if the factory produces 20000 light bulbs, the number of light bulbs inspected is:

20000*0.0175 = 350 lightbulbs

By solving for the unknown, the number of lightbulbs inspected can be determined as 350.

The quality control manager selects 7 lightbulbs out of 400 for inspection.

To find the number of lightbulbs inspected, we set up a proportion:

7 lightbulbs / 400 lightbulbs = x lightbulbs / 20000 lightbulbs

Solving for x gives:

x = (7/400) * 20000 = 350 lightbulbs inspected.

Answer:

Option B.  AA

Step-by-step explanation:

we know that

Angle-Angle (AA) Similarity Postulate, states that If two angles of one triangle are congruent to two angles of another, then the triangles must be similar

In this problem

In the triangle XYZ

∠X=70°

∠Y=90°

∠Z=90°-70°=20° (remember that angle X and angle Z are complementary)

In the triangle UWV

∠V=20°

∠W=90°

∠U=90°-20°=70° (remember that angle V and angle U are complementary)

therefore

Traingles XYZ and UWV are similar by AA Similarity Postulate

Hello!

Answer:

[tex]\boxed{-10x+7.5}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

[tex]-2.5*4x-(-2.5)*3[/tex]

[tex]-4*2.5x+3*2.5[/tex]

Simplify.

[tex]4*2.5=10[/tex]

[tex]3*2.5=7.5[/tex]

[tex]=-10x+7.5[/tex]

[tex]\boxed{-10x+7.5}[/tex], which is our final answer.

I hope this helps you!

Have a nice day! :)

Thanks!

Answer:

The answer is -10x+7.5

Step-by-step explanation:

That is true.

The diameter is a line that passes through the center of a circle.

Answer: True is the answer

Answer:

(2.5, - 2)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

(2.5, - 2 ) ← point of intersection

Answer:

Option D is the correct answer.

Step-by-step explanation:

Refer the given figure showing the graph.

We can see the point of intersection is (2.5, -2).

Option D is the correct answer.

Alternatively:

2x + y = 3  ---------------------eqn 1

2x - 5y = 15  ---------------------eqn 2

eqn1 - eqn 2 gives

  2x + y - ( 2x - 5y) = 3 - 15

           6y = -12

             y = -2

Substituting in eqn 1

         2x - 2 = 3

            x = 2.5

Point of intersection is (2.5, -2).

Option D is the correct answer.