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Spiral Review "y is less than 3"

Question 1
Part A

Write an inequality that represents the sentence "y is less than 3
then Graph the inequality on the number line.

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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Answer:

The minimum separation is  \(z = 1.0292 *10^{-4} \ m\)

Step-by-step explanation:

    From the question we are told that

         The  reading randomized variable are \(D= 2.5 \ mm\) and \(d = 38 \ cm\)

          The diameter of the pupil is  \(d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m\)

            The distance from the paper is \(D = 38 \ cm = 0.38 \ m\)

            The wavelength is  \(\lambda = 555 \ nm = 555 * 10 ^{-9} m\)

Generally the Raleigh's equation for resolution is  

             \(\theta = 1.22 [\frac{\lambda}{D} ]\)

substituting values

               \(\theta = 1.22 * \frac{555*10^{-9}}{0.0025}\)  

              \(\theta = 2.7084*10^{-4} \ rad\)

The minimum separation of two dots is mathematically represented as

            \(z = \theta d\)

substituting values

            \(z = 2.7084*10^{-4} * 0.38\)

             \(z = 1.0292 *10^{-4} \ m\)

Given the below

Multiplication of the vectors in the a+bi form gives

Applying the complex arithmetic rule below

The expansion of the vectors gives

Opening the brackets

Simplifying the above expression

Hence, the answer is

Answer:

I think its the very last one

Step-by-step explanation:

All of the stuff could go in 1 bag. They could also go i 2 bags if you divide all of them by two. You can also put all of them in to 9 bags because 36 divided buy 9 is 4 and 72 divided by 9 is 8 and 18 divided by 9 is 2. And we can odviously do it for the rest because the same # divided by the same # gives you 1 in each bag

Answer:

IS A guys okay A

Step-by-step explanation:

You Suck So Much ohhhhhhhhhhhhhhhhhhhhhhhh

Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

Austin's rate of motion is (1/70)π Radians per second.

To determine Austin's rate of motion in radians per second, we need to use the formula for angular velocity:

ω = Δθ / Δt

Where:

ω = angular velocity (in radians per second)

Δθ = change in angular displacement (in radians)

Δt = change in time (in seconds)

We know that Austin runs three-quarters of a circular track, which means he covers an arc length that is equal to three-quarters of the circumference of the circle. Let's call the radius of the circle "r". Then, the arc length covered by Austin is given by:

s = (3/4) * 2πr

s = (3/2)πr

We also know that it takes Austin 1 minute and 45 seconds to cover this distance. This is the same as 105 seconds (since 1 minute = 60 seconds).

So, Δt = 105 seconds

Now, we can calculate the change in angular displacement (Δθ). The total angle around a circle is 2π radians, so the angle covered by Austin is given by:

Δθ = (3/4) * 2π

Δθ = (3/2)π

Therefore, Austin's rate of motion (ω) in radians per second is:

ω = Δθ / Δt

ω = [(3/2)π] / 105

ω = (3/210)π

ω = (1/70)π radians per second

So, Austin's rate of motion is (1/70)π radians per second.

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Answer:

all of them

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal

Answer:

Should be 3

Step-by-step explanation:

To add the fractions find the LCD then combine

Answer:

3

Step-by-step explanation:

\((\frac{1}{4} +\frac{5}{4} )^2+\frac{3}{4} \\\\(\frac{6}{4})^2+\frac{3}{4} \\\\\frac{9}{4} +\frac{3}{4} \\\\\frac{12}{4} \\\\3\)

Step-by-step explanation:

C you are gonna have 3,120.00 pesos

The inequality that represents possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b is:

             (c+b) ≥ 15

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

It is given that the least number of cupcakes and brownies that Salma should buy is 15.

Let the number of cupcakes purchased be c and the number of brownies purchased, b.  

Then the total number of cupcakes and brownies is c + b

This sum should be greater than or equal to 15.

Then the inequality is (c+b) ≥ 15

Therefore the inequality that represents possible values for the number of cupcakes purchased, c, and the number of brownies purchased, b is:

             (c+b) ≥ 15

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1.

We are told that the coordinates of the image are of the formula:

P'(x-2 , y-3) where x and y are the actual points and x-2 and y-3 are the reflections

Finding the coordinates of point A:

We are given that the coordinates of reflection of A are: A'(-4 , 3)

we also know that reflected point follow the formula: P'(x-2 , y-3)

So, the points of A'(-4 , 3) follow the formula P'(x-2 , y-3)

So, their respective x and y coordinates will be equal

Hence,

x - 2 = -4

x  = -2                 [adding 2 on both sides]

Also,

y - 3 = 3

y  = 6                 [adding 3 on both sides]

Therefore, the coordinates of A are A(-2,6)

Finding the coordinates of B:

We are given the coordinates of B' are B'(-4 , 2)

So,

x - 2 = -4

x = -2             [adding 2 on both sides]

also,

y-3 = 2

y = 5             [adding 5 on both sides]

Therefore, the coordinates of B are: B(-2,5)

Finding the coordinates of C:

We are given that the coordinates of reflection of C are: C'(-2,3)

Using the general formula given in the question:

x - 2 = -2  

x = 0            [adding 2 on both sides]

y - 3 = 3

y = 6            [adding 3 on both sides]

Therefore, the coordinates of C are: C(0,6)

Finally, the coordinates of A, B and C are:

A(-2,6)   ,    B(-2,5)   ,    C(0,6)

__________________________________________________________

2.

Reflecting the pre-image along the x-axis

To reflect along x-axis, we multiply the y-coordinate by -1

Coordinates of the pre-image:

A(-2,6)   ,    B(-2,5)   ,    C(0,6)

Coordinates of points reflected along the x-axis:

A(-2,-6)   ,    B(-2,-5)   ,    C(0,-6)

The zeros of the polynomial p(x) = x³ + x² + 8x - 60 will be (- 2 + √4 i), (- 2 - √4 i) and 3.

Given that:

Polynomial, p(x) = x³ + x² + 8x - 60

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

At x = 3, then we have

p(3) = 3³ + 3² + 8(3) - 60

p(3) = 60 - 60

p(3) = 0

The one zeros are 3. Then the other two zeros are given as,

(x³ + x² + 8x - 60) / (x - 3) = 0

[(x - 3)(x² + 4x + 20)] / (x - 3) = 0

x² + 4x + 20 = 0

x = [-4 ± √(4² - 4 × 1 × 20)] / (2 × 1)

x = - 2 ± √4 i

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a) 90% confident that the true population mean μ is between 91.01 and 102.99.

b) 90% confident that the true population mean μ is between 92.26 and 101.74.

c) 80% confident that the true population mean μ is between 93.79 and 100.21.

d) Using Central Limit Theorem to approximate the population mean as normally distributed, the confidence intervals can still be computed using the same formula as before.

(a) To construct a 90% confidence interval about μ when n = 27, we use the formula:

x ± z × (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the z-score that corresponds to the desired confidence level (in this case, z = 1.645 for a 90% confidence level). Plugging in the values given, we get:

97 ± 1.645 × (13/√27)

which simplifies to:

(91.01, 102.99)

Therefore, we are 90% confident that the true population mean μ is between 91.01 and 102.99.

(b) To construct a 90% confidence interval about μ when n = 18, we use the same formula as before, but with a different z-score (since the sample size is smaller). In this case, we use z = 1.734, and we get:

97 ± 1.734 × (13/√18)

which simplifies to:

(92.26, 101.74)

Therefore, we are 90% confident that the true population mean μ is between 92.26 and 101.74.

(c) To construct an 80% confidence interval about μ when n = 27, we use the same formula as before, but with a different z-score (since the confidence level is different). In this case, we use z = 1.282, and we get:

97 ± 1.282 × (13/√27)

which simplifies to:

(93.79, 100.21)

Therefore, we are 80% confident that the true population mean μ is between 93.79 and 100.21.

(d) The confidence intervals in parts (a)-(c) assume that the population is normally distributed. If the population is not normally distributed, we cannot rely on these intervals to accurately estimate the true population mean. However, if the sample size is sufficiently large (usually n > 30), we can use the Central Limit Theorem to approximate the population mean as normally distributed, and the confidence intervals can still be computed using the same formula as before. If the sample size is small and the population is not normally distributed, other methods may be needed to construct a confidence interval, such as bootstrapping or using a non-parametric approach.

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

The circumference of the drive wheel is 10 feet * 3.14 = 31.4 feet.

The circumference of the vat is 18 feet * 3.14 = 56.52 feet.

The total length of belt needed to go around the drive wheel and the vat is 31.4 + 56.52 = 87.92 feet.

In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.

Proportion shows the relative number of objects or people in the whole.

Proportions are ratios equated to each other.

They are expressed as fractional values, in decimals, percentages, and fractions.

The percentage of Boomers who want to shop in-store = 84%

The sample size of the Boomer Generation = 75

The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)

Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.

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Answer:

the answer is simple, because you have to add up each side of the triangle and match those sides with your choices. btw its C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Use Pythagorean Theorem:

a^2 + b^2 = c^2

For a triangle to be a triangle a^2 +b^2 has to be larger than c^2

25^2 + 13^2 = 653

22^2 = 625  

Answer:

is there multiple choice options, I want to help but I'm not sure why it isn't 4

The required solution of the equations is given as (2, 3, 0).

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
So we are given a system,
3x -2y + 3z = 0
-3x-5y-5z = -21

Substitute x =2, and we get the system,
-2y + 3z = -6
-5y -5z = -15

Multiply equation 1 by -5 and equation 2 by 2 we get the system,
10y - 15z = 30
-10y -10z = -30

Adding the above equations,
z = 0

Now,
-2y = -6
y = 3

Thus, the required solution of the equations is given as (2, 3, 0).

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Answer:

Yes

Step-by-step explanation:

A for loop basically relies on repeating the same code for a pre-set number of times. During which you can make any code repeat inside of it, including indexing through a type of list. Many times a for-loop will use the indexes in a list to calculate the number of times that the loop has to repeat. This is usually done in order to search or apply changes in an array of other types of data structures that have countless values stored in it.

Answer:

1.82 %

Step-by-step explanation:

Divide 100% among 55 students

\(\frac{100}{55} =1.82\)

Hope this helps

Answer:

9 7/8

Step-by-step explanation:

1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.

2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.

3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.

The answer is 55×88=4840

Answer:

25

Step-by-step explanation:

Answer:

8.5 × 10-5

Step-by-step explanation:

moving decimal place -5 times

9514 1404 393

Answer:

  $35.00

Step-by-step explanation:

The number of pints sold is ...

  (12.5 gal)×(8 pt/gal) = 100 pt

Then the total amount received for the milk is ...

  (100 pt)($0.35/pt) = $35.00

Answer:

g(x) = \(\frac{1}{x+11}-9\) is my choice

Step-by-step explanation:

I. If move right is +x and move down is -y

               then f(x) = \(\frac{1}{x}\)

               +x = 11, -y = -9

                so g(x) = \(\frac{1}{x+11}-9\)

Hope that help :D

Answer:

10.21 m

Step-by-step explanation:

       |\

       |     \

       |          \        L

6 m  |               \

       |                    \

       |          36 deg   \

       |-------------------------\

For the 36-deg angle, 6 m is the opposite leg. L is the hypotenuse. The trig ratio that relates the opposite leg to the hypotenuse is the sine.

\( \sin A = \dfrac{opp}{hyp} \)

\( \sin 36^\circ = \dfrac{6~m}{L} \)

\( L = \dfrac{6~m}{\sin 36^\circ} \)

\( L = 10.21~m\)

The company's current ratio is 2.6.

Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.

Current ratio = current asset /current liability

$65,000 / 25,000 = 2.6

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