Construct a difference table to predict the next term of the sequence. −1, 6, 26, 65, 129, 224, 356, . . .

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

Answer:

isoceles is the answer as MLN= MNL

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

The height of the skyscraper is D. 156.26 ft

To determine the height of the skyscraper,  we need to consider the following trigonometric identities listed thus;

From the information given, we have that;

Angle, θ = 38 degrees

The shadow casted is the adjacent side of the angle and is 200 ft

The height off the skyscraper is the opposite side

Now, using the tangent identity, we have that;

tan θ = opposite/adjacent

tan 38 = h/200

cross multiply the values, we get;

h = 200(0.7812)

Multiply the values

h = 156. 26 ft

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Answer:

0.288

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\(\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740\)

Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.

This is 1 subtracted by the pvalue of Z when X = 18.06. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{18.06 - 17.48}{1.027740}\)

\(Z = 0.56\)

\(Z = 0.56\) has a pvalue of 0.712

1 - 0.712 = 0.288

The answer is 0.288

On solving the provided question, we cans say that - here in coordinates S is given by: \((-2,4)\)

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

x-coordinate of \(X = -2\)

y-coordinate of\(S = 4.\)

S is given by: \((-2,4)\)

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On solving the provided question, we cans say that - here in coordinates S is given by: (-2,4)

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

x-coordinate of -2

y-coordinate of 4

S is given by: (-2,4)

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Answer:

y= between 9-10 patients, round down to 9

Step-by-step explanation:

y= 9/4x + 5

y = 9/4(2) + 5

y = 9.5

y= between 9-10 patients, round down to 9

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.

While the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.

Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.

On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.

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Answer: the answer is D which is x = 11

Step-by-step explanation: swap sides so that all variable terms are on the left-hand side. Add 11 to both sides then add 44 and 11 to get 55. after that divide both sides by 5 then 55 divided by 5 to get to 11.

Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Answer:

41.93 degrees

Step-by-step explanation:

The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping

Rewriting 125x^ 3 −27 as (5x) ^3 −3³

The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )

Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.

Hence, (5x−3)(25x ^2 +15x+9)

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Answer:

\(\large\boxed{52 - 7i}\)

Step-by-step explanation:

-(4i – 1 + 3i) + (61 – 10)

Rearrange to easier combine like terms

-(4i + 3i - 1) + (61 - 10)

Simplify

-(7i - 1) + 51

Remover parenthesis, change - sign to + due to double - signs.

-7i + 1 + 51

-7i + 52

Rearrange equation to minimize operations.

\(\large\boxed{52-7i}\)

Hope this helps, let me know if you have any questions!

Answer:

52 - 7i

Step-by-step explanation:

collect like terms -4i + 3i  and 61-10

-(7i-1) + (61 - 10)   Now remove the  ( ) for next step adding terms

- 7i + 1 + 51   add the numbers

-7i  +  52  To get rid of the -7i Reorder the terms changing the sign

52= -7i

Answer:

Step-by-step explanation:

y - 9 = 3(x - 0)

y - 9 = 3x - 0

y = 3x + 9

450.46497

\(We\ know\ that:\)

\(\left\{\begin{matrix}P=400\\r=2\%\\n=1\\t=6\\\end{matrix}\right.\)

________________________________________________

\(Substitute\) \(\left\{\begin{matrix}P=400\\r=2\%\\n=1\\t=6\\\end{matrix}\right.\)\(into\ formula\)

\(F=P*(1+r/n)^n^t\\ F=400\bullet(1+2\bullet\frac{1}{100})^6\)

_________________________________________________

\(Evaluate\ the\ equation/expression:\\ 450.46497\)

I hope this helps you

:)

Answer:

13 and 4

Step-by-step explanation:

Use the quadratic formula for this one, or you could just plug it into an online calculator like the one at www.symbolab.com if you wanted to check your answer...

You could also factor it to (x - 13)(x -4) and set each side equal to zero!

Hopefully this helps- let me know if you have any questions!

Answer:

the zeros are 13 and 4

Step-by-step explanation:

hope this helped! :D

After the pumping of Container A's water into Container B, the volume of water in Container B is 6,286 feet³.

The volume refers to the amount of space in a container.

The volume of a container can be determined using the following formula: πr²h, where:

Diameter = 26 feet

Height = 20 feet

The volume of water in Container A = πr²h

r = radius = diameter/2

= 20/2 = 10 feet

Volume = 22/7 x 10 x 10 x 20

= 22/7 x 100 x 20

=6,285.7

= 6,286 feet³

Diameter = 36 feet

Height = 19 feet

Thus, the volume of Container B after the pumping, which is equal to the volume of water in Container A, is 6,286 feet³.

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After the pumping of Container A's water into Container B, what is the volume of water in Container B?

(3,5) is the answer i think

hope it helpss

The electric current, C, varies inversely as the resistance, R

C =k/R

If C=2 and R=60, solve for k

2 = k /60

2 (60) = k

120 = k

When R = 240:

C=120/R

C = 120/240

C= 0.5

Answer:

Step-by-step explanation:

sin (B) = \(\frac{2}{5}\)

Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

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

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

A translation followed by what is known as a dilation, but the name for dilation may vary depending on your country of origin. A translation would cause ABCD to slide into the location of the second shape. A dilation would scale ABCD to the size of A'B'C'D.

Answer:

x < 3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Gang ima just take them points tbh

Step-by-step explanation:

Answer:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Step-by-step explanation:

The correlation​ matrix provided is:

Variables    Paper     Glass

  Paper           1         0.1853

 Glass        0.1853         1

Te hypothesis for the test is:

H₀: ρ = 0 vs. H₀: ρ ≠ 0

The test statistic is:

r = 0.1853 ≈ 0.185

As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.

The critical value for the two-tailed test is:

\(r_{\alpha/2, (n-2)}=r_{0.05/2, (62-2)}=r_{0.05/2, 60}=0.250\)

The conclusion is:

Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.

Answer:

could be c

Step-by-step explanation:

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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The student made the first error in Step 2. The correct expression for Step 2 should be: 5/6m - 2/3m + 6.

In this step, the student incorrectly combined the constant terms of 12 and -6 to get 12-6=6, instead of 12-6=6m.

To see why this is the case, simplify the original expression step by step:

5/6m + 12 - 2/3m - 6

= (5/6m - 2/3m) + (12 - 6) (group like terms)

= (5/6 * 2/3)m + 6 (simplify fractions and simplify constants)

= 10/18m + 6 (multiply fractions and simplify)

The expression in Step 4 is correct, but it was obtained using an incorrect expression in Step 2.

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