7. [1/2 Points) DETAILS PREVIOUS ANSWERS TANAPCALC9 11.3.016. Determine whether the geometric series converges or diverges. -1 converges diverges If it converges, Pind its sum. (If an answer does not

Answer:

12-14w

Step-by-step explanation:

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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Answer: 156 degrees

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

x equals 2

Step-by-step explanation:

‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎ ‏‏‎

a) Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b) Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c) Both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities

a. Angular velocity is defined as the rate of change of angular displacement. It is given by the formula:

ω = v / r

where ω is the angular velocity, v is the tangential velocity, and r is the radius of the curve.

For Elaine: ω = 4.2 m/s / 17.3 m = 0.242 rad/s

For Tori: ω = 4.6 m/s / 34.6 m = 0.133 rad/s

Since Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b. Centripetal acceleration is the acceleration directed towards the center of the circular path. It is given by the formula:

a = ω^2 * r

where a is the centripetal acceleration, ω is the angular velocity, and r is the radius of the curve.

For Elaine: a = (0.242 rad/s)^2 * 17.3 m = 0.099 m/s^2

For Tori: a = (0.133 rad/s)^2 * 34.6 m = 0.622 m/s^2

Since Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c. The centripetal acceleration remains the same regardless of the angular velocity. It only depends on the radius of the curve. Therefore, both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities.

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The radius is approximately 3.78 inches.

We can solve the question using the formula for the surface area of a sphere:

S=4πr^2

We are given that the surface area is 225 square inches, so we can substitute this value into the formula and solve for r:

\(225=4\pi r^2\frac{225}{4\pi}\)

      = r^2

r={{225}{4π}}

approx  3.78

A sphere does not have any edges or vertices, like other 3D shapes. The points on the surface of the sphere are equidistant from the center.

Hence, the distance between the center and the surface of the sphere are equal at any point. This distance is called the radius of the sphere.

The Radius of a circle or sphere is equal to the Diameter divided by 2.

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The vector field f(x,y)=⟨1 y, 1 x⟩ is the gradient of f(x,y). When you compute f(1,2)−f(0,1), the result is ⟨1, 1⟩

Given the vector field f(x,y)=⟨1 y, 1 x⟩ is the gradient of f(x,y), you are asked to compute f(1,2)−f(0,1).

Step 1: Evaluate f(1,2) and f(0,1).
f(1,2) = ⟨1(2), 1(1)⟩ = ⟨2, 1⟩
f(0,1) = ⟨1(1), 1(0)⟩ = ⟨1, 0⟩

Step 2: Compute f(1,2) - f(0,1).
To find the difference between two vectors, subtract the corresponding components of the vectors.
f(1,2) - f(0,1) = ⟨2, 1⟩ - ⟨1, 0⟩ = ⟨2-1, 1-0⟩ = ⟨1, 1⟩

Therefore, the vector field f(x,y)=⟨1 y, 1 x⟩ is the gradient of f(x,y). When you compute f(1,2)−f(0,1), the result is ⟨1, 1⟩.

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The expression for the length of the sail is x = 7( tan 50° ).

According to the given question.

The sail of a boat is in the shape of a right triangle.

And, the sail of a boat is a right triangle with an acute angle at the tip equal to 50 degrees and the side of the sail which is the hypotenuse to the right triangle is 7 meters long.

Now, the side that measures 7 meters would be the adjacent because its right next to the angle and its not the hypotenuse because its not the largest side

And, the side which we do not know the length to will be the opposite side because it is opposite from where the angle is.  

So, we have the the measure of the adjacent side and the angle of the tip. And we have to find the expression for the length of the sail.

Let the length of the sail be x meters.

Now, in the given right angled triangle

We can say that

tan A = Opposite side/Adjacent side

⇒ tan 50° = x/7

⇒ x = 7( tan 50° )

Hence, the expression for the length of the sail is x = 7( tan 50° ).

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Answer:

Step-by-step explanation:

80 is the diameter to we need to divide it by 2 to find the radius

80/2= 40

A= 3.14* 40^2

A = 3.14 * 1600

A= 5024

Step-by-step explanation:

We determine the surface area of a rectangular settling tank for a city is 1544.4 m2. The length of each tank is approximately 103 m, and when considering a total of 3 tanks, the combined length is 309 m.

To determine the length of the rectangular settling tank, we need to calculate the surface area first.

1. Flowrate Conversion:

The flowrate is given as 0.5 m3/s.

We need to convert it to m3/h for consistency.

Since there are 3600 seconds in an hour, the flowrate is equal to

0.5 * 3600 = 1800 m3/h.

2. Overflow Rate Calculation:

The overflow rate desired is given as 28 m3/d-m2.

Since there are 24 hours in a day, the overflow rate is equal to

28 / 24 = 1.1667 m3/h-m2.

3. Detention Time Conversion:

The detention time is given as 1.25 hours.

4. Surface Area Calculation:

The surface area can be calculated using the formula:

Surface Area = Flowrate / Overflow Rate.

Therefore,

Surface Area = 1800 / 1.1667

Surface Area = 1544.4 m2.

5. Length Calculation:

Since the width of the tank is given as 15 m, the length can be calculated using the formula:

Surface Area = Length * Width.

Therefore,

Length = Surface Area / Width

Length = 1544.4 / 15

Length = 102.96 m.

Rounded to the nearest 0.5 m, the length of each tank is approximately 103 m.

In total, with 3 tanks, the combined length would be 3 * 103 = 309 m.

In summary, the length of each tank is approximately 103 m, and when considering a total of 3 tanks, the combined length is 309 m.

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Answer:

The measure of angle XYZ will be 120° because the included arc of an inscribed angle will always be twice the measure of the inscribed angle

Answer:wrong. Its 249 degrees

Step-by-step explanation:

Just got it right on the quiz

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

x=0, 5 (-5±√15)/2

Step-by-step explanation:

see images for solution

To find the equilibrium price and quantity, we need to set the quantity supplied equal to the quantity demanded and solve for the price.

Given:
Q = 200 + 3P (quantity supplied)
Qd = 400 - P (quantity demanded)

Step 1: Set Q = Qd
200 + 3P = 400 - P

Step 2: Solve for P
4P = 200
P = 50

Step 3: Substitute P = 50 back into the equations to find the equilibrium quantity.
Q = 200 + 3(50)
Q = 350

Therefore, the equilibrium price is $50 and the equilibrium quantity is 350.

Now, let's consider the case with a tax on buyers.

Given:
Q° = 400 - (2P + T) (quantity demanded after tax)

Step 1: Set Q° = Q (quantity demanded after tax = quantity supplied)
400 - (2P + T) = 200 + 3P

Step 2: Solve for P
5P + T = 200

Step 3: Substitute T = 20 into the equation and solve for P
5P + 20 = 200
5P = 180
P = 36

Step 4: Substitute P = 36 back into the equations to find the new equilibrium quantity.
Q = 200 + 3(36)
Q = 308

Therefore, the new equilibrium price is $36 and the new equilibrium quantity is 308.

The original equilibrium price and quantity are $50 and 350 respectively. After the tax is placed on buyers, the new equilibrium price and quantity become $36 and 308 respectively.

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Answer:

No

Step-by-step explanation:

4a=a*a*a*a

4a is 4 times the variable a, not the variable a added to itself 4 times.

Answer: 49

Step-by-step explanation: just roll with it

Answer:

Solve for the inequality 0≤x≤3

Step-by-step explanation:

( x + 2√3i ) (  x - 2√3i ) is equivalent to this polynomial .

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables.

                     Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

( x + 2√3i ) (  x - 2√3i )

= x² - ( 2√3i)²

= x² - 12 * ( -1)

= x²  + 12

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The complete question is -

Which expression is equivalent to this polynomial? x2 +12

Answer:

98 inches

Step-by-step explanation:

If one side of the prism is 7 inches and the width is double the length, this means that the width of the prism is 14

In order to find the area of a prism, you multiply the length by the width

7*14 = 98

So, the area of the rectangular prism is 98 inches

Hope this helps!

a) -43, -12, -1 1/2

b) 1 1/2. 12, 43

c) it is different

a) -1 1/2, -12, -43

from the least to the greatest:

The higher a negative number , the lesser the value of the number

-43, -12, -1 1/2

b) The absolute values of -1 1/2, -12, -43:

1 1/2, 12, 43

absolute values from least to greatest:

1 1/2. 12, 43

The order of the rational numbers in part (a) is different from the order of the numbers' absolute values in part (b)

c) Absolute values of a negative number gives a positive number. The higher a posititve number, the greater its value. While a higher negative number has a lower value. This makes the result in ordering the data different

After considering the given data and given set of options we conclude that sequence projects a divergence therefore the correct option is diverges.  

To estimate and find whether the sequence \(an = 3 + 5n^2 / 1+n\) converges or diverges, we can apply the following steps:
We can apply divison of both the numerator and denominator of the sequence by \(n^2\) to get an equivalent expression: \(an = (5/n) + 3n / (1/n + 1).\)
As n comes towards infinity, the term 5/n approaches zero and the term 3n approaches infinity.
Hence, the sequence diverges to infinity.
Finally, the sequence \(an = 3 + 5n^2 / 1+n\)diverges.
Then after carefully evaluating we can projects that,l the sequence diverges which can be seen in the given figure.
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The question is incomplete. The complete question is :

In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches.  Answer the following questions about the specified normal distribution.  (a) What height represents the 99th percentile?  (b) What height represents the first quartile?  (Round to two decimal places as needed)

Solution :

Let the random variable X represents the height of women in a country.

Given :

X is normal with mean, μ = \(62.9\) inches and the standard deviation, σ = \(2.81\) inches

Let,

\($Z=\frac{X - 62.9}{2.81}$\) , then Z is a standard normal

a). Let the \(99th\) percentile is = a

The point a is such that,

\($P(X<a)=0.99$\)

\($P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$\)

From standard table, we get : \(P( Z < 2.3263) =0.99\)

∴ \($\frac{(a-62.9)}{281} = 2.3263$\)

  \($a= (2.3263 \times 2.81 ) +62.9$\)

     = 6.536903 + 62.9

     = 69.436903

     = 69.5 (rounding off)

Therefore, the height represents the \(99th\) percentile = 69.5 inches.

b). Let b = height represents the first quartile.

It is given by :

\(P( X < b) =0.25\)

\($P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$\)

From the standard normal table,

\(P( Z < -0.6745) =0.99\)

∴ \($\frac{(b-62.9)}{2.81}= 0.6745$\)

\($b=(0.6745 \times 2.81) +62.9$\)

  = 1.895345 + 62.9

   = 64.795345

   = 64.8 (rounding off)

Therefore, the height represents the 1st quartile is 64.8 inches.

Answer:

626.625

30*15 + \(\pi (7.5)^{2}\)

450 + 176.625 =

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

2nd and 4th

Step-by-step explanation:

16.50÷6=2.75

So the second one is true.

12x2.75=33

So the fourth one is true.

Answer:

The first and fourth statements are true.

Step-by-step explanation:

We know that 6 pounds of blueberries costs $16.50 so 1 pound costs 16.5 / 6 = $2.75. Therefore, the first statement is true. The second statement can't be true because this is a direct proportion. In a direct proportion, when one variable increases, the other increases as well so the price of 2.75 pounds can't be less than the price of 1 pound. The cost of 5 pounds is 2.75 * 5 = 13.75 so the third statement is false. The cost of 12 pounds will be 2.75 * 12 = 33 so the fourth statement is true. The cost of 3 pounds is 2.75 * 3 = 8.25 so the fifth statement is false.

Answer:

5,8

Step-by-step explanation:

A point (-5,8) rotated around the origin 270 degrees counterclockwise will have coordinates (-8, -5).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know when we rotate a point counter-clockwise the coordinates (x, y) becomes (-y, x).

Given, A point (-5,8) around the origin 270 degrees counterclockwise.

∴ The new coordinates of the points will be (-8, -5).

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Answer:

y = 5z - x

Step-by-step explanation:

Given

z = \(\frac{x+y}{5}\) ( multiply both sides by 5 to clear the fraction )

5z = x + y ( subtract x from both sides )

5z - x = y

To find the probability of a balanced coin coming up heads exactly half the time in 14 tosses, we need to use the concept of binomial distribution.

In this case, we have a fixed number of trials (14 tosses) and each trial has two possible outcomes (heads or tails).

The probability of getting heads in a single toss of a balanced coin is 0.5 (50%). Since we want exactly half the tosses to be heads, we need 7 out of the 14 tosses to be heads.

To calculate the probability, we can use the binomial probability formula:

\(P(X = k) = (nCk) * p^k * (1-p)^(n-k)\)

where P(X = k) is the probability of getting exactly k successes in n trials, (nCk) is the combination formula, p is the probability of success, and (1-p) is the probability of failure.

Plugging in the values, we get:

\(P(X = 7) = (14C7) * (0.5^7) * (0.5^(14-7))\)
Calculating this expression will give us the probability of getting exactly 7 heads in 14 tosses.

To find the probability of a balanced coin coming up heads exactly half the time in 14 tosses, we use the binomial distribution formula and calculate P(X = 7).

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Answer:

95%

i think it should be that

Answer:

(6, -11)

Step-by-step explanation:

In this problem, you are given the image and you need to find the pre-image. To do this work backward and do the opposite of the translation. So, to find the pre-image solve \((x+2, y-3)\). Once you plug in the points you get \((6,-11)\) which must be the original point.

Answer:

(6, -11)

Step-by-step explanation: