if the power series an(x-4)^n converges at x=7 and diverges at x=9

This result is approximate.

=========================================================

Explanation:

mu = 750 = mean

sigma = 75 = standard deviation

The raw scores or x values are x = 750 and x = 825

Let's compute the z score for each x value

z = (x - mu)/sigma

z = (750 - 750)/75

z = 0

and

z = (x - mu)/sigma

z = (825 - 750)/75

z = 1

Therefore P(750 ≤ x ≤ 825) is equivalent to P(0 ≤ z ≤ 1) in this context.

Use a z score table to determine that

P(z ≤ 0) = 0.5

P(z ≤ 1) = 0.84314 approximately

So,

P(a ≤ z ≤ b) = P(z ≤ b) - P(z ≤ a)

P(0 ≤ z ≤ 1) = P(z ≤ 1) - P(z ≤ 0)

P(0 ≤ z ≤ 1) = 0.84314 - 0.5

P(0 ≤ z ≤ 1) = 0.34314 approximately

The value 0.34314 then converts to 34.314% which rounds to 34%

Or you could use the empirical rule as shown below. The pink section on the right is marked 34% which is approximate. This pink section is between z = 0 and z = 1.

Answer: A function is a relation between domain and range such that each value in the domain corresponds to only one value in the range. Relations that are not functions violate this definition. They feature at least one value in the domain that corresponds to two or more values in the range.

Step-by-step explanation:

Answer:

Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.

Step-by-step explanation:

Since Stefan sells Jin a bicycle for $ 125 and a helmet for $ 18, and the total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet, to determine how much did Stefan spend originally and how much money did he make by selling the bicycle and helmet to Jin, the following calculations must be performed:

130 = 125 + 18

100 = X

100 x (125 + 18) / 130 = X

100 x 143/130 = X

14,300 / 130 = X

110 = X

143 - 110 = 33

Therefore, Stefan originally spent $ 110 on the bike and helmet, with which he is making a profit of $ 33.

Answer:

4.41

Step-by-step explanation:

We can use trig to solve for the missing side (specifically cosine).  cos(x)=adjacent side/hypotenuse.  We have the x value (which is the angle shown) which is 25.  We have the adjacent side of that angle which is 4.  We are solving for the hypotenuse (lets call that h).  When we plug in values into the equation cos(x)=adjacent/hypotenuse, we get cos(25)=4/h.  cos 25=0.9063.  So 0.9063=4/h.  Multiply both sides by h and we get 0.9063h=4.  Now divide 0.9063 on both sides to isolate h and we get 4.4135... but since you want hundredths, its 4.41

Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

Answer:

x=3

Step-by-step explanation:

6 times 3 equals 18. 18+2 equals 20. So X=3

Answer:

\( \sf \: x = 3\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2 + 6x = 20

Then the value of x will be,

→ 2 + 6x = 20

→ 6x = 20 - 2

→ 6x = 18

→ x = 18 ÷ 6

→ [ x = 3 ]

Hence, the value of x is 3.

The average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0≤x≤25 using definite integral is 208.33 units.

To calculate the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, we need to find the average value of y over this range.

The equation y = x² represents a parabola that opens upwards. To find the average height, we need to integrate the function y = x² over the given range and then divide by the length of the range.

Let's calculate it step by step:

Calculate the definite integral of y = x² with respect to x over the range 0 to 25:

∫[0,25] \(x^{2}\) dx = \([x^3/3]\) evaluated from 0 to 25

\(= (25^3/3) - (0^3/3)\\= (25^3/3)\\= 16666.67\)

Calculate the length of the range:

Length = 25 - 0 = 25

Divide the definite integral by the length of the range to find the average height:

\(Average height = (25^3/3) / 25\\= (25^2/3)\\= 208.33\)

Therefore, the average height above the x-axis of a point in the region \(0\leq y\leq x^2\), for 0 ≤ x ≤ 25, is approximately 208.33 units.

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A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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The maximum value of the linear equation on the given interval is:

y = 11

We want to find the maximum of the linear function:

y = 2x + 1

On the interval [3, 5]

Notice that we have a line with a positive slope, thus, this is an increasing line.

Then the maximum is just what we get when we evaluate the function on the maximum value of the interval:

y = 2*5 + 1

y = 10 + 1

y = 11

The maximum value is 11.

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Answer:

.0036 kk

Step-by-step explanation:

The right conversion is 3.600000 kk.

I think in the first option you forgot the decimal point right?

The confidence interval about the given mean age is (40.7, 34.3). Since the given mean age of 38.8 years is in the obtained interval, there is no sufficient evidence to conclude that the mean age had changed.

The formula for the confidence interval is

C.I = \(\bar x\) ± z(σ/√n)

Where \(\bar x\) - sample mean; z or z(α/2) - test value; σ - standard deviation of the sample; n - sample size;

Consider the hypothesis,

null hypothesis H0: μ = 38.8

alternate hypothesis Ha: μ ≠ 38.8

It is given that,

sample size n = 32

sample mean \(\bar x\) = 37.5

standard deviation σ = 9.2

Constructing a 95% confidence interval about the mean age:

a) Finding the significance level:

= 1 - (95/100)

= 1 - 0.95

∴ α = 0.05

b) Finding the z-value for the obtained significance level:

z(α/2) = z(0.05/2)

∴ z = 1.96 (From the distribution table)

c) Calculating the lower and upper bounds:

C.I = \(\bar x\)  ± z(σ/√n)

On substituting,

C.I = 37.5 ± (1.96)(9.2/√32)

⇒ 37.5 ± (1.96)(1.626)

⇒ 37.5 ± 3.186(≅3.2)

Upper bound = 37.5 + 3.2 = 40.7

Lower bound = 37.5 - 3.2 = 34.3

Thus, the interval is from 34.3 years to 40.7 years.

Hence the given mean age of 38.8 is included in the interval, the evidence is insufficient to conclude that there is a change in the mean age.

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Answer:

20 is a tenth of 200

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

x=10%(2)

20/x=10/100

200=100x

x=2

Within 5 hours, Trey covered 315 miles. He would need to travel 504 miles in 11 hours at the same speed.

You must ascertain the unit rate. Divide the miles by the hours to arrive at that.

The unit rate should be found to be 63 miles per hour.

You need to double that by 8 (because it takes 8 hours),

Which is 504 miles.

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The total mass of the living things on the farm is 588 kg.

Since on a farm there was a cow, 2 sheep and 3 chickens, to determine what is the total mass of the 1 cow, the 2 sheep, the 3 chickens, and the 1 farmer on the farm, the following calculation must be performed :

Therefore, the total mass of the living things on the farm is 588 kg.

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Answer:

I think No

Step-by-step explanation:

Given:

Volume of a cube = 1.5 m³

To find:

The length of its edge to the nearest tenth of a meter.

Solution:

Let a be the length of its edge.

We know that, volume of a cube is

\(V=a^3\)

where, a is edge.

Volume of a cube = 1.5 m³

\(a^3=1.5\)

Taking cube root on both sides, we get

\(a=\sqrt[3]{1.5}\)

\(a=1.14471424\)

Approximate the value to the nearest tenth (one decimal place) of a meter.

\(a\approx 1.1\)

Therefore, the length of the edge of the cube is about 1.1 meters.

Answer:

35

Step-by-step explanation:

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

The weighted average of a data set is 36.

Here,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

We have to find the weighted average of a data set.

What is Weighted Average?

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.

Now,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

The weighted average is given by the formula;

\(x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}\)

Hence,

The weighted average of a data set;

x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2

x = 360/10 = 36

Hence, The weighted average of a data set is 36.

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Answer:

kristen is at 1065

Step-by-step explanation:

The addition is one of the four fundamental mathematical operations. The height of Kristen's balloon and Gigi's balloon are 1065ft and 1110ft respectively.

The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.

Kristen's balloon rises 225 feet

Kristen's balloon falls 105 feet

Kristen's balloon again rises 445 feet

Hence, the height of Kristen's balloon and Gigi's balloon with respect to the ground are 1065ft and 1110ft respectively.

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The distance between the point (-2, 8, 1) and the line of intersection between the two planes having equations x + y + z = 3 and 5x + 2y + 3z = 8/4 is approximately 5.26 units.

To compute the distance between a point and a line, we need to use the projection of the point onto the line. Let's solve this problem. The two given planes are x + y + z = 35x + 2y + 3z = 2

First, let's determine the line of intersection between these two planes. Let's do this by setting the two equations equal to each other: 5x + 2y + 3z = x + y + z + 2(4x - y - 2z = 2)

We now have two equations with three unknowns. This tells us that there will be an infinite number of solutions. We can get two points on the line of intersection by setting z to 0 and then to 1.

(4x - y = 2)At z = 0:(4x - y = 2)x = 1y = 2(1, 2, 0) is one point on the line.

At z = 1:(4x - y = -2)x = -1/2y = 0(1/2, 0, 1) is the other point on the line.

The direction vector of the line of intersection is given by the cross product of the normal vectors of the two planes. (-1, 8, -7) = (1, 1, 1) × (5, 2, 3)Now, we need to find the projection of (-2, 8, 1) onto the line of intersection.

We use the following formula for this purpose: Projv(w) = (w · v / |v|²) v

We plug in the values and get:(-2, 8, 1) → w(5, 2, 3) → vProjv(w) = (-18/14, 36/14, 4/14) = (-9/7, 18/7, 2/7)

The distance between the point and the line of intersection is the magnitude of the vector that joins the point to the projection. We use the Pythagorean theorem to get this value.

Distance = √[(x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)²]

Distance = √[( -2 - (-9/7) )² + ( 8 - (18/7) )² + ( 1 - (2/7) )²

]Distance = √[ ( -5/7 )² + ( 34/7 )² + ( 5/7 )² ] = √( 1266 / 49 ) ≈ 5.26 units

The distance between the point (-2, 8, 1) and the line of intersection between the two planes having equations x + y + z = 3 and 5x + 2y + 3z = 8/4 is approximately 5.26 units.

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The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Answer:

- 43

Step-by-step explanation:

f ( x ) = - 2x² + 2x - 3

To find : f ( 5 )

f ( 5 ) = f ( x )

Here,

x = 5

f ( 5 ) = - 2x² + 2x - 3

        = - 2 ( 5 )² + 2 ( 5 ) - 3

        = - 2 ( 25 ) + 10 - 3

        = - 50 + 7

f ( 5 ) = - 43

Answer:

-43

Step-by-step explanation:

oon edge

mark me brain

Answer:

A

Step-by-step explanation:

√23 is 4.795

So point A

Answer:

Step-by-step explanation:

Ab + ac

The horizontal distance between the base of the ladder and the wall is approximately 16.06 feet.

To find the flat distance between the foundation of the  stool and the wall, we utilize geometry. For this situation, we can utilize the sine capability, which relates the contrary side of a right triangle to the hypotenuse and the point inverse the contrary side.

Let x be the flat distance between the foundation of the stepping stool and the wall. Then, utilizing the given point of 64 degrees, we can compose:

sin(64) = inverse/hypotenuse

where the hypotenuse is the length of the stepping stool, which is 18 feet.

Addressing for the contrary side, which is the even distance we need to find, we get:

inverse = sin(64) x hypotenuse

inverse = sin(64) x 18

inverse = 16.06 feet

Accordingly, the even distance between the foundation of the stepping stool and the wall is roughly 16.06 feet.

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(x, y) = ( cos 45, sin 45) =

The correct option is A

Answer:

79°

Step-by-step explanation:

An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.

If the angle is 281° it can go 79° more degrees before getting back to the start.

360° - 281° = 79°

Answer:

A 0.4kg object rolling at 2 m/s that's d right answer

Answer:

A 0.4 kg object moving at 4 m.

Step-by-step explanation:

The heavier the object is, the faster it goes. Also the faster is goes and the heavier it is, the more momentum it has.