Write an explicit formula for an, the nth term of the sequence 19,24,29

Answer:

Hey!

Your answer is Eight-hundred and forty-three billion, two-hundred and eight million, seven-hundred and thirty-two thousand, eight-hundred and thirty-three.

HOPE THIS HELPS!

Answer:

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Step-by-step explanation:

Let \(\vec u\) and \(\vec a\), from Linear Algebra we get that component of \(\vec u\) parallel to \(\vec a\) by using this formula:

\(\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a\) (Eq. 1)

Where \(\|\vec a\|\) is the norm of \(\vec a\), which is equal to \(\|\vec a\| = \sqrt{\vec a\bullet \vec a}\). (Eq. 2)

If we know that \(\vec u =(2,1,1,2)\) and \(\vec a=(4,-4,2,-2)\), then we get that vector component of \(\vec u\) parallel to \(\vec a\) is:

\(\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)\)

\(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

Lastly, we find the vector component of \(\vec u\) orthogonal to \(\vec a\) by applying this vector sum identity:

\(\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}\) (Eq. 3)

If we get that \(\vec u =(2,1,1,2)\) and \(\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\), the vector component of \(\vec u\) is:

\(\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)\)

\(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\)

The component of \(\vec u\) orthogonal to \(\vec a\) is \(\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)\).

Answer:

Your answer is C.

Step-by-step explanation:

3.4 μm mean 3.4 Micrometers. Wow, that's pretty small.

A and B can instantly be ruled out, since it's micrometers, which are far smaller than meters. And 1 meter is 1e+6 times bigger than a micrometer, which makes D easily ruled out. The only answer you are left with is C, which is correct.

9514 1404 393

Answer:

  y = 0x + 15

Step-by-step explanation:

A line with a slope of 0 is a horizontal line. It has the same y-value everywhere. If it goes through the point (16, 15) with y-coordinate 15, then its y-intercept is 15.

Writing the slope explicitly, the equation is ...

  y = 0x +15

Simplified, the equation is

  y = 15

Answer:

\(-8\)

Step-by-step explanation:

Solving for \(w\) given the equation, \(-3w +5 = 2\):

\(-3w +5 = 2 \\ -3w +5 -5 = 2 -5 \\ -3w = -3 \\ \frac{-3w}{-3} = \frac{-3}{-3} \\ w = 1\)

Solving for \(w -9\) when \(w = 1\)

\(1 -9 \\ -8\)

Answer: 1

Step-by-step explanation:

You have the next:

Side AB is congruent with side CD

Side AC is congruent with side AC

Angle BAC is congruent with angle DCA

SAS congruence of triangles: If any two sides and included angle (angle between those sides) of one triangle are equal to corresponding two sides and included angle of second triangle, then the two triangles are condruent by SAS rule

Angle BAC is the included angle of sides AB and AC in triangle ABC

Angle DCA is the included angle of sides CD and AC in triangle CDA

Then,

Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

Answer:

It would take 4.8 hours if they worked together

Step-by-step explanation:

The garage can be built by Amy's group in 8 hours and can be built by Bob's group in 12 hours.

Let's find what portion of the garage each group completes in one hour, add their contributions, and find the time to finish the garage working together.

Amy's group completes the job in 8 hours, it means that in 1 hour, they complete 1/8 of the garage.

Bob's group completes the job in 12 hours, meaning they complete 1/12 of the garage in 1 hour.

Now we add both contributions per hour:

\(\displaystyle \frac{1}{8}+\frac{1}{12}\)

The LCM of 12 and 8 is 24, thus:

\(\displaystyle \frac{1}{8}+\frac{1}{12}=\frac{3+2}{24}=\frac{5}{24}\)

In one hour, they build 5/24 parts of the garage, so the complete job is finished in 24/5=4.8 hours.

It would take 4.8 hours if they worked together

The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.

A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.

From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).

The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.

Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.

To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.

To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.

Substituting these values into the equation for g(x), we have:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4

Therefore, the exact expression for g(x) is:

g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.

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For the drug used to treat asthma in a clinical trial:

Part 1:

The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.

Part 2:

The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).

Part 3:

The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).

Part 4:

The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

Part 5:

We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.

Part 6:

The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.

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Answer:

B

Step-by-step explanation:

This is a ratio of polynomials.  As n approaches infinity, an approaches 4n / n⁸ = 4 / n⁷, which is a convergent p-series.

Using Limit Comparison Test:

an = (2 + 4n) / (1 + n²)⁴

bn = 4 / n⁷

lim(n→∞) an / bn = 1

The limit is greater than 0, and bn converges, so an also converges.

Answer:

Step-by-step explanation:

1000

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

To prove that tan A = 12/5, we can use the identity that relates the sine and cosine of an angle to its tangent:

tan A = sin A / cos A

We are given that 0.5 * cos A = 13, so cos A = 26.

Substituting this value into the identity above, we get:

tan A = sin A / 26

We are also given that 12 sec A = 13, so sec A = 13/12 = 1.083333.

The reciprocal of sec A is cosec A, so cosec A = 1/1.083333 = 0.9230769.

The sine of an angle is the reciprocal of the cosecant of the angle, so sin A = 1/0.9230769 = 1.083333.

Substituting this value into the identity tan A = sin A / cos A, we get:

tan A = 1.083333 / 26 = 12/5

Therefore, tan A = 12/5.

The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

The vertex form of a parabola is given by:y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2

Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2

Simplifying this, we get:-66 = 16a - 2

Adding 2 to both sides, we get:-64 = 16a

Dividing both sides by 16, we get:a = -4

Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2

Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

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we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.

How to simplify?

To simplify the expression x⁵-x³, we can factor it using the distributive property of multiplication. First, we can factor out x³ from both terms:

x⁵ - x³ = x³(x² - 1)

Now, we can further simplify by recognizing that x² - 1 is a difference of squares, which can be factored into (x + 1)(x - 1). So, we have:

x⁵ - x³ = x³(x² - 1) = x³(x + 1)(x - 1)

This is the fully simplified form of the expression. We can also expand the expression to verify that it is equivalent to the original expression:

x³(x + 1)(x - 1) = (x³ * x) + (x³ * -1) + (x³ * 1) + (x³ * -1) = x⁴ - x³ + x³ - x³ = x⁴ - x³

So, we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.

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Answer:

Slope would be -3/1

Answer:

-3/1 is the slope since you are going down 3 and going to the right one time.

i accidentally answered this one instead of another one sorry

Steven has five times more tickets than Jared.

'Multiplication is an operation that represents the basic idea of repeated addition of the same number.'

According to the given problem,

If we add the number of tickets till it equals Steven's number of tickets,

= 4 + 4 + 4 + 4 + 4

= 20

This can also be represented as 4 × 5 = 20

Hence, we can conclude that Steven has five times more tickets than Jared.

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Answer:

x = 3

Step-by-step explanation:

Using the pythagoras theorem;

hyp^2 = opp^2 + adj^2

(x+2)^2 = 5^2 + (x-3)^2

Expand

x²+4x+4 = 25 + x²-6x+9

x²+4x+4-25-x²+6x - 9 = 0

10x - 30 = 0

10x = 30

x = 30/10

x = 3

Hence the value of x is 3

Answer:

I think its Yes!

Step-by-step explanation:

Hope this helps!!!

The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.

To find the z-score for Sean's SAT score, we use the formula:

z = (x - μ) / σ

where x is Sean's SAT score, μ is the population mean (1500), and σ is the population standard deviation (250). Substituting the values, we get:

z = (1700 - 1500) / 250 = 0.8

Therefore, Sean's z-score on the SAT is 0.8.

To find the z-score for Sean's ACT score, we use the formula:

z = (x - μ) / σ

where x is Sean's ACT score, μ is the population mean (20.4), and σ is the population standard deviation (4.8). Substituting the values, we get:

z = (24 - 20.4) / 4.8 = 0.75

Therefore, Sean's z-score on the ACT is 0.75.

Comparing the z-scores, we can see that Sean's SAT score is slightly higher relative to the mean and standard deviation of the SAT population than his ACT score is relative to the mean and standard deviation of the ACT population.

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The area between the solid line (y=x+4) and the dotted line (y=-2x-2) represents the system of inequalities solution set.

Two linear inequalities system on a coordinate plane. The first has a solid line graphed with a negative slope of one, a negative y-intercept, and a shaded origin area. The area encompassing the origin is shaded, and the second is a dashed vertical line 3 units to the left of the origin.

x ≥ –3; y ≥ x – 2

x > –3; 5y ≥ –4x – 10

x > –3; y ≥ –x + 1

x > –2; y ≥ –x – 1

The solution set for the system of inequalities is represented by the region between the solid line (y=x+4) and the dotted line (y=-2x-2).

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Answer:

Step-by-step explanation:

\(\frac{25}{100} \times 56=\frac{1}{4} \times 56=\frac{56}{4}=14\)

Racer scored 14 points.