Compare these rational numbers. Which of the following are true?

i. -2.3 - 1.3
ii. -2.3 -1.3
iii. -2.3> - 3.3
iv. -2.3 -3.3

a.ii and iv
b.ii and iii
c.i and iii
d.i and iv ​

Answer:

(32,48)

Step-by-step explanation:

Notice the pattern? Every time the number multiplies by 2.

The surface area obtained by rotating the curve y = x² from x = 0 to x = 8 about the y-axis is 2048π square units.

We are given that the curve y = x² is rotated from x = 0 to x = 8. So our range of integration is from x = 0 to x = 8.

To use the disk method, we need to express the curve in terms of y instead of x. For the equation y = x², we can rewrite it as x = √y.

The radius of each disk is the distance between the y-axis and the curve. Since we are rotating the curve around the y-axis, the radius will be the value of x for a given y. Therefore, the radius is x = √y.

The area of each disk can be found using the formula for the area of a circle, which is A = πr². In this case, the area is A = π(x²) = π(√y)² = πy.

To find the total surface area, we need to sum up the areas of all the disks. We integrate the area function πy with respect to y from y = 0 to y = 64 (since x = 8 corresponds to y = 64).

Surface Area = ∫(πy)dy from 0 to 64

= π∫y dy from 0 to 64

= π[y²/2] from 0 to 64

= π[(64²/2) - (0²/2)]

= π[2048]

= 2048π square units.

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Answer:

$48

Step-by-step explanation:

The probability of people earning between $45,000 and $65,000 in this large company is approximately 29.46%.

We need to use the standard normal distribution formula, where we standardize the original distribution with mean and standard deviation to a standard normal distribution with mean 0 and standard deviation 1. We can then use a Z-table to find the probability.

First, we calculate the Z-scores for the lower and upper limits of the range of interest:

Z1 = (45,000 - 50,000) / 20,000 = -0.25

Z2 = (65,000 - 50,000) / 20,000 = 0.75

We can then look up the probabilities associated with these Z-scores in a standard normal distribution table. From the table, we find that the probability of a Z-score between -0.25 and 0.75 is 0.2946. To convert this back to the original units, we need to multiply the probability by 100 to get a percentage:0.2946 x 100 = 29.46%.

The normal distribution is a continuous probability distribution, so the probability of exact values is zero. We are calculating the probability of a range of values.

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he interest he will pay if he takes 2 years to pay his parents back is $153.16. The total amount he will pay if he takes 2 years to pay his parents back is $2,341.12.

To calculate the interest Adam will pay, we need to use the simple interest formula:

Interest = Principal x Rate x Time

The principal is the amount borrowed, which is $2,187.96. The rate is 3.5% per year, or 0.035 in decimal form. The time is 2 years.

Interest = $2,187.96 x 0.035 x 2 = $153.16

Therefore, Adam will pay $153.16 in interest if he takes 2 years to pay his parents back.

To calculate the total amount he will pay, we need to add the interest to the principal:

Total amount = Principal + Interest

Total amount = $2,187.96 + $153.16 = $2,341.12

Therefore, Adam will pay a total of $2,341.12 if he takes 2 years to pay his parents back.

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Answer: 45 yrs old

Step-by-step explanation:

Car A  = 9 yrs old

Car B = X yrs old

The ratio for the cars are

Car A : Car B

or

2 : 5

You want to make it easier to read so you make both the ratio number and the given age number (9) the same number.

Multiply Car A age by 2 to make it 18 and the Ratio 2 by 9 to make it 18. This makes them the same number. Since you did this to one side, you have to do it on the other side by multiplying the 5 by 9 which is 45.

Your new ratio is now

18 : 45

This means Car B is 45 yrs old

Answer:

-1728

Step-by-step explanation:

(-12)×(-12)×(-12)

-1728

Answer:

-1728

Step-by-step explanation:

(-12) × (-12)

=144

144×(-12)

= -1728

We get the sides of the triangle as 33, 8.25, and 19.

Given that One side of a triangle is one-fourth the longest side. Third side is 14 feet less than the longest side Perimeter of triangle is 139.We have to find all the three sides of a triangle.

Let the longest side of the triangle be x,

Then one side will be x/4Third side will be x - 14Perimeter = sum of all sides of a triangle Perimeter of triangle

= x + x/4 + x - 14 = (5x + x - 56)/4

= (6x - 56)/4 = 139Multiplying both sides by 4,6x - 56 = 139 x

= (139 + 56)/6 = 33

Therefore, Longest side of the triangle = 33Length of the second side of the triangle = (1/4) × 33 = 8.25Length of the third side of the triangle = 33 - 14 = 19

Now, to check whether the given side lengths make up a triangle or not, we will apply triangle inequality theorem.

Sum of any two sides of the triangle is always greater than the third side. If it holds true for all three sides then the given side lengths make up a triangle.

Let's check for the given sides33 + 8.25 > 19  Yes33 + 19 > 8.25  Yes19 + 8.25 > 33  Yes

Therefore, the given side lengths make up a triangle. Hence, the sides of a triangle are 33, 8.25 and 19. The given problem is related to the lengths of the sides of a triangle.

We are given the relationship between the lengths of two sides of the triangle and the relationship of the third side with the longest side of the triangle.

Also, the perimeter of the triangle is also given. We have to find the three sides of the triangle. To solve the given problem, let the longest side of the triangle be x.

Then, the other two sides will be x/4 and x - 14.

The perimeter of the triangle is the sum of all three sides, i.e., x + x/4 + x - 14.

Putting the values and equating it to 139, we can solve for x. We get x = 33.

Then we can easily calculate the other two sides, which will be 8.25 and 19.

We have to check whether the given side lengths make up a triangle or not by applying the triangle inequality theorem.

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Answer:

19.45

Step-by-step explanation:

The median is the middle number.  Put the data in order from smallest to largest

16.3, 17.8,17.8  ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4

There are 12 pieces of data,

16.3, 17.8,17.8  ,18.0, 18.7,19.3,         19.6,20.1,20.5, 21.9, 25.2 ,25.4

The median lies between the 6th and 7th piece

Add the 6th and 7th together and divide by 2

(19.3+19.6)/2 =19.45

Answer:

\(\large \boxed{\mathrm{19.45}}\)

Step-by-step explanation:

Median of a data set is the middle value.

The data is to be arranged from smallest to largest.

16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4

Find the middle value.

16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4

Average the two middle numbers.

(19.3+19.6)/2 = 19.45

The median of the data set is 19.45.

Answer:

1,000

Step-by-step explanation:

it is right trust me .

Answer:

they increased by 25%

Step-by-step explanation:

16/4 = 4. 16+4 = 20. Because of this, the number of wins increased by 4, or 1/4 of last year's wins. this means it increased by 25%.

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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Answer:

Step-by-step explanation:

It may help you to rewrite this problem in columns:

 2x - 3

-(  x - 1)

------------

   x - 2 (answer) ("x minus 2")

Answer:

3x^4

Step-by-step explanation:

Answer:

495x^10 y^5

Step-by-step explanation:

The acceleration a in reference frame Σ is equal to the acceleration a' in reference frame Σ' via the Galilean transformation.

To derive the transformation for acceleration, we differentiate the above equations with respect to time:

dx'/dt = dx/dt - u

dt'/dt = 1

The left-hand side of the first equation represents the velocity in frame Σ', while the right-hand side represents the velocity in frame Σ. Since the velocity is the derivative of the position, we can rewrite the equation as:

v' = v - u

where v and v' are the velocities in frames Σ and Σ' respectively.

Now, let's consider the acceleration. The acceleration is the derivative of the velocity with respect to time. Taking the derivative of the equation v' = v - u with respect to time, we have:

a' = a

where a and a' are the accelerations in frames Σ and Σ' respectively. This means that the acceleration remains unchanged when we transform from one reference frame to another using the Galilean transformation.

In conclusion, the acceleration a as described by the coordinates in frame Σ is equal to the acceleration a' as described by the new set of coordinates in frame Σ' via the Galilean transformation.

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Answer: The 14 × 34 = 34 × 14 one is true and the bottom one is false? I'm sorry if I'm wrong

Answer:

14•34=34•14 - True

34÷25=25÷15 - False

Step-by-step explanation:

14•34=476 - 34•14=476

34÷25=1.36 - 25÷34=0.74

Answer

equation of L₁ is y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given L₂

x + 2y = 3 ( subtract x from both sides )

2y = - x + 3 ( divide through by 2 )

y = - \(\frac{1}{2}\) x + \(\frac{3}{2}\) ← in slope- intercept form

with slope m = - \(\frac{1}{2}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{2} }\) = 2

slope of L₁ = 2 and passes through (3, - 1 ) , then

y = 2x + c ← is the partial equation of L₁

to find c substitute (3, - 1 ) into the partial equation

- 1 = 6 + c ⇒ c = - 1 - 6 = - 7

y = 2x - 7 ← equation of L₁

The probability that at least two of the balls have the same number is 27.40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes

No. of ways to succeed = 90P8

No. of possible outcomes = 90^8

No. of ways to succeed =

nPr = n! / (n-r)!

90P8 = 90! / (90-8)!

90P8 = 90! / (82)!

90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!

90P8 = 90*89*88*87*86*85*84*83

90P8 = 3.13x10^15

P(no 2 have same number) = 3.13x10^15 / 90^8

P(no 2 have same number) = 0.73

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(at least 2 have same number) = 1 - 0.73

P(at least 2 have same number) = 0.2740 = 27.40%

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The measurement which is closest to the length of each side of the tablecloth is 6.9 feet.

It follows from the task content that the measurement which is closest to the length of each side of the tablecloth in feet.

Total area of the square tablecloth = 48 square feet

Area of a square = Side length²

48 = Side length²

Find the square root of both sides

Side length = √48

= 6.928203230275

Approximately,

Side length = 6.9 feet

Therefore, the side length of the table cloth is 9.6 feet.

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The integral of cos(3πt)i + sin(2πt)j + \(t^3\)k with respect to t is (1/3π)sin(3πt)i - (1/2π)cos(2πt)j + (1/4)\(t^4\)k + c, where c is the constant of integration.

To evaluate the integral, we integrate each component separately.

The integral of cos(3πt) with respect to t is (1/3π)sin(3πt), where (1/3π) is the constant coefficient from the derivative of sin(3πt) with respect to t.

Therefore, the integral of cos(3πt)i is (1/3π)sin(3πt)i.

Similarly, the integral of sin(2πt) with respect to t is -(1/2π)cos(2πt), where -(1/2π) is the constant coefficient from the derivative of cos(2πt) with respect to t.

Thus, the integral of sin(2πt)j is -(1/2π)cos(2πt)j.

Lastly, the integral of \(t^3\) with respect to t is (1/4)\(t^4\), where (1/4) is the constant coefficient from the power rule of differentiation.

Hence, the integral of \(t^3\)k is (1/4)\(t^4\)k.

Putting it all together, the integral of cos(3πt)i + sin(2πt)j + \(t^3\)k with respect to t is (1/3π)sin(3πt)i - (1/2π)cos(2πt)j + (1/4)\(t^4\)k + c, where c represents the constant of integration.

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(a) To find the value of λ, we need to use the formula for the standard deviation of a double exponential distribution:

σ = (1/λ) * sqrt(2)

We are given that the standard deviation is 39.6 km, so we can plug that in and solve for λ:

39.6 = (1/λ) * sqrt(2)
λ = sqrt(2)/39.6

Using a calculator, we get λ ≈ 0.0891.

(b) The mean value of a double exponential distribution is 1/λ, so the mean extent of daily sea-ice change is:

μ = 1/λ
μ = 1/0.0891
μ ≈ 11.2142 km

To find the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value, we need to find the values of x that are within one standard deviation of the mean:

μ - σ = 11.2142 - 39.6 ≈ -28.3858 km
μ + σ = 11.2142 + 39.6 ≈ 61.1998 km

Then, we can use the cumulative distribution function (CDF) of the double exponential distribution to find the probability that the extent of daily sea-ice change falls within this range:

P(μ - σ < X < μ + σ) = F(μ + σ) - F(μ - σ)

where F(x) is the CDF of the double exponential distribution.

Using the formula for the CDF of the double exponential distribution, we get:

P(-28.3858 < X < 61.1998) = [e^(λ*61.1998) - e^(-λ*28.3858)]/[2*λ]

Using the value of λ we found in part (a), we can calculate this probability using a calculator:

P(-28.3858 < X < 61.1998) ≈ 0.9036

Therefore, the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is approximately 0.9036.

To find the value of λ and the probability, we'll work through the given information step by step.

(a) The standard deviation of the double exponential distribution is given by σ = √(2/λ²). We are given that σ = 39.6 km. Solving for λ:

39.6 = √(2/λ²)
(39.6)² = 2/λ²
λ² = 2/((39.6)²)
λ = √(2/((39.6)²))
λ ≈ 0.0506

So, the value of the parameter λ is approximately 0.0506.

(b) To find the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value, we need to calculate the probability for the range (mean - σ) to (mean + σ). Since the mean of a double exponential distribution is 0, we're looking for the probability within the range -39.6 to 39.6 km.

P(-39.6 < x < 39.6) = ∫(-39.6 to 39.6) 0.5λe^(-λ|x|) dx

Using the value of λ = 0.0506, you can integrate the density function over the range -39.6 to 39.6 km. The result is approximately 0.6321.

So, the probability that the extent of daily sea-ice change is within 1 standard deviation of the mean value is approximately 0.6321 or 63.21%.

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Answer:

= 19 R 0

= 19

Step-by-step explanation:

The measure of the angle the minute hand traces in 49 minutes on a clock is 4.084 radians A radian is an angle measure defined by the ratio of an arc length to a radius.

A radian is a measure of angle equal to the radius of a circle, and is defined as the amount of angle subtended by an arc that is equal in length to the radius of the circle. The radian measure of an angle is defined as the ratio of the length of the arc s to the radius r of the arc s of a circle:\(θ = s/r\)

Where,θ is the measure of the angle in radians.s is the arc length. r is the radius of the circle.

One revolution of the clock is equal to 2π radians.

The minute hand of the clock makes one full revolution in 60 minutes. Therefore, in 49 minutes, the minute hand of the clock moves through an angle equal to:

θ = 49/60 × 2π

= 4.084 radians

Thus, the measure of the angle the minute hand traces in 49 minutes is 4.084 radians.

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False, the expressions 2x − 3(x − 4) = 5x + 12 are not equivalent

The expressions are simplified and if the value of both are equal then they are said to be equivalent

Simplifying 2x − 3(x − 4)

= 2x - 3x + 12

= - x + 12

since   2x − 3(x − 4) = - x + 12 ≠ 5x + 12 the expression is said not to be equivalent

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Answer:

To find alternate exterior angles, look at that outside space for each crossed line, on different sides of the transversal.

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest!

You have to find the transversal. Then you have to the interior and exterior angles, and then find it!

Since the area is zero, the coordinates of the centroid are undefined. This means that the centroid does not exist for this region.

To find the centroid of the region bounded by the curves y = x^3 and x = y^3 in the first quadrant, we need to find the area of the region and the coordinates of the centroid.

First, we can find the area of the region by integrating with respect to x:

A = ∫[0, 1] x^3 dx - ∫[0, 1] y^3 dy

= 1/4 - 1/4

= 0

This means that the area of the region is zero, which is not possible. Therefore, we must have made an error in our integration. The error is that the limits of integration for the second integral should be y = 0 to y = 1, not y = 0 to y = x^3. So, let's correct that:

A = ∫[0, 1] x^3 dx - ∫[0, 1] y^3 dy

= 1/4 - 1/4

= 0

Now, the area is zero because the region is symmetric with respect to the line y = x, and the areas on either side of this line cancel each other out.

To find the coordinates of the centroid, we need to integrate with respect to x and y:

x-bar = (1/A) * ∫∫[R] x dA

= (1/0) * ∫[0,1] ∫[y^3, y^(1/3)] x dx dy

= undefined

y-bar = (1/A) * ∫∫[R] y dA

= (1/0) * ∫[0,1] ∫[0, x^3] y dy dx

= undefined

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Answer:

0.875

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

16oz is 1 pound so if we divide 16 by 2 we get 8 add back on the oz and that's your answer

for further help contact me or a verified teacher

1)

\(180 - 138\) (Reason- LINEAR PAIR)

\(42\)

2)

\(138 + x = 180\) (Reason- Co-interior angles are supplementary)

\(x = 180 - 138\)

\(x = 42\)

Hope it helps you.

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