What is an explicit formula for an arithmetic sequence with a common difference of three and whos second term is nine?

Answer:

12⁽¹⁸⁾

Step-by-step explanation:

The expression is given as ;

12³ × 12⁹× 12⁴× 12²  -----same base, add the powers according to law of indices

12⁽³⁺⁹⁺⁴⁺²⁾  

12⁽¹⁸⁾

Answer:

e or 12¹⁸

Step-by-step explanation:

It took Michelle approximately 16 years to pay off her loan.

We have,

We can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal amount (initial loan)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We can rearrange this formula to solve for t:

t = ln(A/P) / (n * ln(1 + r/n))

Plugging in the given values.

t = ln((12500 + 9425)/12500) / (1 * ln(1 + 0.0754/1))

t = ln(1.753) / (ln(1.0754))

t = 16.02

Thus,

It took Michelle approximately 16 years to pay off her loan.

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Answer:

you can make 4 loafs of bread

Step-by-step explanation:

Answer:

45:12, 90:24, and 135:36

Step-by-step explanation:

These are the answers because:

1) Finding equivalent ratios is the same way of finding equivalent fractions.

2) We could multiply 45 and 12 with 2

45 x 2 = 90

12 x 2 = 24

Then, you get the ratio 90:24

Hope this helps! :D

Answer:

C) 10 is the answer if this helped brainliest would be appreciated ;)

Step-by-step explanation:

Answer:

10cm

Step-by-step explanation:

15cm-9cm=6cm

KL^2=(8^2)+(6^2)

KL^2=64+36

KL^2=100

KL=10cm

Answer:choccy milk  solve all  yo problems

pop a choccy milk

To put the numbers in order from least to greatest, we can use the number line: -3.5 -2.1 -1 -0.5 0.5 2 4 4.2 5 5.8  Two numbers that are opposites and each more than 6 units away from 0 are -7 and 7.

First, let's put the numbers in order from least to greatest:

-3.5, -2.1, -1.5, -1, -0.5, 0.5, 3.5, 4, 4.2, 4.8, 5

Now, let's find two numbers that are opposites and each more than 6 units away from 0. One example would be -7 and 7. These numbers are opposites (since they have the same magnitude but different signs), and they are both more than 6 units away from 0.

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Answer:

When finding the slope of real-world situations, it is often referred to as rate of change. “Rate of change” means the same as “slope.” If you are asked to find the rate of change, use the slope formula or make a slope triangle.

Step-by-step explanation:

(√(2)t^4 - 6√(2)/t) i - √(2)t^3j + (√(2)t^2 - √(2)/t)k is the cross product (a × b).

We have,  a = t, 6, 1/t and b = t², t², 1,

The cross product a × b. In vector algebra, the cross product of two vectors is another vector that is perpendicular to both of them.

A vector product is also known as the vector product of two vectors or the exterior product of two vectors.

The cross product of two vectors a and b is given by:

a × b = |a| |b| sin(θ) n

where |a| and |b| are the magnitudes of vectors a and b, θ is the angle between them, and n is a unit vector perpendicular to both a and b.

To find the cross product of a and b, we first need to calculate the magnitudes of a and b:

|a| = √(t^2 + 6^2 + (1/t)^2) = √(t^4 + 36 + 1/t^2)

|b| = √(t^4 + t^4 + 1) = √(2t^4 + 1)

Next, we need to find the angle between a and b. We can use the dot product to do this:

a · b = |a| |b| cos(θ)

a · b = t(t^2) + 6(t^2) + (1/t)(1) = t^3 + 6t^2 + 1/t

|a| |b| = √(t^4 + 36 + 1/t^2) √(2t^4 + 1)

cos(θ) = (t^3 + 6t^2 + 1/t) / (√(t^4 + 36 + 1/t^2) √(2t^4 + 1))

θ = arccos((t^3 + 6t^2 + 1/t) / (√(t^4 + 36 + 1/t^2) √(2t^4 + 1)))

Now, the cross-product using the formula:

a × b = |a| |b| sin(θ) n

where n is a unit vector perpendicular to both a and b. We can find n by taking the determinant of the matrix:

i j k

t 6 1/t

t^2 t^2 1

n = (t^2 - 6/t)i - (t^3 - t/j)j + (t^2 - t/k)k

a × b = |a| |b| sin(θ) n

a × b = √(t^4 + 36 + 1/t^2) √(2t^4 + 1) sin(θ) ((t^2 - 6/t)i - (t^3 - t/j)j + (t^2 - t/k)k)

Therefore, the cross-product of a and b is:

a × b = (√(2)t^4 - 6√(2)/t) i - √(2)t^3j + (√(2)t^2 - √(2)/t)k

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Answer:

a

Step-by-step explanation:

The span of a set of vectors is the set of all possible linear combinations of those vectors. So, if we have vectors v1, v2, …, vm in Rn, then the span of these vectors will be the set of all possible linear combinations of these vectors. This means that any vector in the span can be expressed as a linear combination of v1, v2, …, vm.

Now, to determine whether the span of these vectors is necessarily a subspace of Rn, we need to check the three subspace axioms: closure under addition, closure under scalar multiplication, and contains the zero vector.
Closure under addition: Let u and v be two vectors in span(v1, v2, …, vm). This means that u and v can be expressed as linear combinations of v1, v2, …, vm. Therefore, their sum u + v can also be expressed as a linear combination of v1, v2, …, vm, and so u + v is also in the span. Thus, the span is closed under addition.
Closure under scalar multiplication: Let c be any scalar and let u be any vector in span(v1, v2, …, vm). This means that u can be expressed as a linear combination of v1, v2, …, vm. Therefore, cu can also be expressed as a linear combination of v1, v2, …, vm, and so cu is also in the span. Thus, the span is closed under scalar multiplication.
Contains the zero vector: Since the zero vector can always be expressed as a linear combination of the vectors v1, v2, …, vm (by taking all coefficients to be zero), it follows that the span contains the zero vector.
Therefore, since the span of v1, v2, …, vm satisfies all three subspace axioms, it is necessarily a subspace of Rn.

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Answer:

x=45 degrees

y=45 degrees

Step-by-step explanation:

Answer: y = 50; x = 34

ABCD is a  quadrilateral inscribed in the circle

=> ∠ABD = ∠ACD

⇔ x = 34°

and ∠ADB = ∠ACB

we also have:

∠DCE + ∠ DCB = 180°

⇔ 96° + x + ∠ACB = 180°

⇔ ∠ACB = 180 - 96 - x = 180 - 96 - 34 = 50

because ∠ADB = ∠ACB => y = 50°

Step-by-step explanation:

Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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The p-value for this hypothesis test, rounded to 3 decimal places, is 0.018.

To find the p-value for this hypothesis test, we need to use the given information and conduct a one-sample proportion test.

Let's define the null hypothesis (H₀) and alternative hypothesis (Hₐ) as follows:

H₀: p = 0.40 (The proportion of nursing majors is 40%)

Hₐ: p > 0.40 (The proportion of nursing majors is greater than 40%)

Given:

Sample size (n) = 400

Number of nursing majors in the sample (x) = 190

First, we calculate the sample proportion, denoted as \(\hat p\), by dividing the number of nursing majors by the sample size:

\(\hat p\) = x / n = 190 / 400 = 0.475

Next, we can calculate the test statistic, which follows an approximate standard normal distribution under the null hypothesis. The test statistic is calculated as:

z = (\(\hat p\) - p₀) / √(p₀(1 - p₀) / n),

where p₀ is the value specified in the null hypothesis.

Substituting the values, we get:

z = (0.475 - 0.40) / √(0.40 * (1 - 0.40) / 400)

= 0.075 / √(0.24 / 400)

= 0.075 / √(0.0006)

≈ 2.073

Now, we need to find the p-value associated with this test statistic. Since the alternative hypothesis is one-tailed (greater than 40%), we want to find the probability of observing a test statistic as extreme as 2.073 or more extreme.

Looking up the z-value in the standard normal distribution table or using a calculator, we find that the cumulative probability (p-value) corresponding to z = 2.073 is approximately 0.018 (rounded to three decimal places).

Therefore, the p-value for this hypothesis test, rounded to 3 decimal places, is 0.018.

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The complete question is:

A college administrator claims that the proportion of students that are nursing majors is greater than 40%. To test this claim, a group of 400 students are randomly selected and its determined that 190 are nursing majors.

The following is the setup for this hypothesis test:

H₀: p=0.40

Hap 0.40

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

Answer:

c. diameter

because when a line intersects the center and even touches the centre is called a diameter

hope it helps.

Answer:

C

Step-by-step explanation:

Diameter

The derivative dy/dx is equal to -2 / (5x) in terms of x and y.

We are asked to find the derivative dy/dx of the implicitly defined function x² × \(y^5\) × \(e^y\) = 0. To find this, we'll use implicit differentiation.
Implicit differentiation means we differentiate both sides of the equation with respect to x, treating y as a function of x, and then solve for dy/dx. So, let's differentiate both sides:
d/dx (x² × \(y^5\) × \(e^y\)) = d/dx (0)
First, we'll differentiate the left side using the product rule and chain rule:
(2x × y^5 × e^y) + (x² × 5y^4 × e^y × dy/dx) = 0
Now, we'll isolate dy/dx by subtracting the first term from both sides and then dividing by the second term:
dy/dx = - (2x × \(y^5\) × \(e^y\)) / (x² × \(5y^4\) ×\(e^y\))
We can simplify this expression by canceling out some common factors:
dy/dx = - (2x) / (5x²)
Further simplification gives:
dy/dx = -2 / (5x)
Thus, the derivative dy/dx is equal to -2 / (5x) in terms of x and y.

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∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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Answer:

429.34

Step-by-step explanation:

I know trust me

Answer:

26 nickels

Step-by-step explanation:

Given that

Total contributed = $1.69

Number of coins = 5

based on the above information,

The number of nickels to be contributed is

Here first we have to determine the prime factors of 169 i.e 13 and 13

This represents that there are 13 member gives their $0.13 per person so it would be $1.69

Also there are 13 cents out of which 3 cents would be 3 pennies the remaining 10 cents would be 2 nickels

So the 13 people contributed to 2 nickels

Therefore,  it would be

= 13 × 2

= 26 nickels

X+y=-5

-x -x

y=-x-5 is the ending equation.

How to graph:

The y-intercept, or point where the graph starts, is -5

From there go down 1, right 1.

M=-x

B=-5

Answer:  m = -1   b = -5

Step-by-step explanation:

Rewrite the equation in "slope-intercept form"   y = mx +b .

m is the slope  

b is the y-intercept, where the graph of the line crosses the y-axis

To rewrite the equation, to get "y" alone on the left side, subtract x from both sides:

x + y = -5

-x + x + y = -x - 5  (left side -x +x =0 so "cancel")

y = -x -5

You get  the slope "m" from the coefficient of x, (invisible 1, sometimes)

since there is a negative sign, the coefficient is -1   That is m, the slope.

A negative slope goes down from left to right.

For  -1, down one over 1 square.

Your graph should look like the screenshot below.

I hope this helps you understand better!

Hector spent $29.75 for 2 DVDs that costs the same amount. The cost of one DVD is $15.95

The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any kind of digital data and has been widely used for video programs (watched using DVD players) or formerly for storing software and other computer files as well. DVDs offer significantly higher storage capacity than compact discs (CD) while having the same dimensions. A standard DVD can store up to 4.7 GB of storage, while variants can store up to a maximum of 17.08 GB. Blank recordable DVD discs (DVD-R and DVD+R) can be recorded once using a DVD recorder and then function as a DVD-ROM. Rewritable DVDs (DVD-RW, DVD+RW, and DVD-RAM) can be recorded and erased many times.

Hector spent $29.75 and $3.15 sales tax

$29.75 + $3.15 = $32.9

$1.00 coupon off his purchase

$32.9 - $1.00 =  $31.90

The cost of one DVD is $31.9/2 = $15.95

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Answers are :

   4.1 :   y = [(3-2k)/(k+1)]x - 12/(k+1)

4.2(a):  k = -1/2

    (b):  k = 17/10

    (c): (3-2k)x = 12

    (d): (k+1)y =12

The given equation is

(3-2k)x + (k+1)y =12   ....(i)

4.1 Rearrange this equation to obtain the form of  y =mx + c

⇒ (k+1)y = (3-2k)x - 12

⇒        y = [(3-2k)/(k+1)]x - 12/(k+1)  is the required form

4.2(a) if (i) is parallel to y = 4x + 7

slope of this line = 4

And slope of line (i)  = (3-2k)/(k+1)

Since these are parallel lines therefore slopes must be equal,

⇒ (3-2k)/(k+1) = 4

⇒ 3-2k = 4k + 4

⇒       k = -1/2

(b) The value of k line passing through (-3, 4)

Put (x, y) = (-3, 4) in (i)

⇒(3-2k)(-3) + (k+1)4 = 12

⇒  -9 + 6k + 4k + 4 = 12

⇒                       10k = 17

⇒                           k = 17/10

(c) line parallel to x axis the put y = 0 in (i)

⇒ (3-2k)x = 12

(d) line parallel to y axis the put x = 0 in (i)

⇒ (k+1)y =12

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From the definition of the fizzle(), the value of fizzle(8) is 6, obtained by recursively applying the formula fizzle(N) = fizzle((N+1)/2) + fizzle(N/2) with intermediate calculations.

The definition of the function fizzle( ) is given as fizzle (1) = 1fizzle (N) = fizzle((N + 1) / 2) + fizzle(N / 2), for N > 1

As per this definition, the value of fizzle(8) can be calculated by

using the formula of fizzle(N) in recursion as fizzle(N) = fizzle((N + 1) / 2) + fizzle(N / 2).

Then, put the value of N as 8.

Now, fizzle(8) will be:

fizzle(8) = fizzle(9 / 2) + fizzle(8 / 2)

fizzle(8) = fizzle(4.5) + fizzle(4)

Now, the value of fizzle(4.5) is same as fizzle(5), so

fizzle(5) = fizzle(6 / 2) + fizzle(5 / 2)

fizzle(5) = fizzle(3) + fizzle(2.5)

Now, the value of fizzle(3) and fizzle(2.5) can be calculated as

fizzle(3) = fizzle(4 / 2) + fizzle(3 / 2)

fizzle(3) = fizzle(2) + fizzle(1.5) = 1 + fizzle(1.5)

fizzle(1.5) = fizzle(2 / 2) + fizzle(1 / 2) = 1 + fizzle(0.5)

fizzle(0.5) = fizzle(1 / 2) + fizzle(0) = 1

Now, substituting the values of fizzle(0.5), fizzle(1.5), fizzle(2), and fizzle(3) in fizzle(5), we get:

fizzle(5) = 1 + fizzle(1.5) + 1 + fizzle(2)

fizzle(5) = 1 + 1 + 1 + 1 = 4

Now, substituting the values of fizzle(4) and fizzle(5) in fizzle(8), we get:

fizzle(8) = fizzle(4.5) + fizzle(4)

fizzle(8) = fizzle(5) + fizzle(4) = 4 + fizzle(2)

Now, the value of fizzle(2) can be calculated as

fizzle(2) = fizzle(3 / 2) + fizzle(1)

fizzle(2) = fizzle(2) + 1 = 1 + 1 = 2

Therefore, the value of fizzle(8) is 4 + fizzle(2) = 4 + 2 = 6.

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Answer:

y = 8x - 64

Step-by-step explanation:

Start with y = mx + b, the slope-intercept equation.  Replace m with 8, x with 7 and y with -8:

-8 = 8(7) + b, or

-8 - 56 + b, or

b = -64

Then the desired equation is

y = 8x - 64

Answer:

Step-by-step explanation:

If you draw a line from the origin (0,0) to L ( the original point ) and a different line from the origin to the image L' you can see the angle of rotation as being

90 degrees and that the rotation is clockwise.  

the rule is (x, y) become ( y, -x)

The y-intercept of the graph of y = f(x) is y_int = 15. The x-intercepts of the graph are x_int = (3, 0) and x_int = (5, 0). The coordinates of the vertex of the parabola are (4, -1).

To find the y-intercept, we set x = 0 in the equation of the quadratic function f(x) = x^2 - 8x + 15:

f(0) = (0)^2 - 8(0) + 15 = 15

So, the y-intercept is at y = 15.

To find the x-intercepts, we set y = 0 in the equation:

x^2 - 8x + 15 = 0

We can factorize this quadratic equation:

(x - 3)(x - 5) = 0

Setting each factor to zero, we find the x-intercepts:

x - 3 = 0 --> x = 3

x - 5 = 0 --> x = 5

Therefore, the x-intercepts are at x = 3 and x = 5.

To find the coordinates of the vertex, we can use the formula for the x-coordinate of the vertex of a quadratic function given by x = -b/2a, where a and b are the coefficients of the quadratic function.

For our quadratic function f(x) = x^2 - 8x + 15, we have a = 1 and b = -8.

x = -(-8) / (2 * 1) = 8 / 2 = 4

Substituting x = 4 into the quadratic function, we find the y-coordinate of the vertex:

f(4) = (4)^2 - 8(4) + 15 = 16 - 32 + 15 = -1

So, the coordinates of the vertex are (4, -1).

The y-intercept of the graph of y = f(x) is y_int = 15. The x-intercepts are x_int = (3, 0) and x_int = (5, 0). The coordinates of the vertex of the parabola are (4, -1).

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