For which values of x does each expression make sense? square root of x-2 over square root of x-3

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."

Here,

we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.

Pentagonal prisms are pentagon-shaped if we look at them from the bottom.

When viewed from the side, a pentagonal prism would have a rectangular shape.

If we were to look at the pentagonal prism from the front, it would appear rectangular.

Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.

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The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that "If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or percentage) and consequently the two triangles are similar".

A triangle is a closed two-dimensional shape or polygon with the fewest sides in mathematics. A triangle is made up of three sides and three angles. The most significant attribute of a triangle is that the sum of its internal angles equals 180°.

Conditions for Triangle Similarity

If the corresponding angles of two triangles are identical, they are said to be comparable triangles.

If their respective sides have the same proportion/ratio.

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Answer:

55

Step-by-step explanation:

Answer: y = -1/2x -4

Step-by-step explanation:

To solve for y, subtract 2x on both sides

2x-2x + 4y = -16 - 2x

Simplify

4y = -16 - 2x

Divide by 4 on both sides to get y by itself

4y/4 = -16 - 2x/4

Simplify

y = -4 - 1/2x

Switch the right-side terms to write them in slope-intercept form

y = -1/2x -4

Speed of the given object in centimeters per hour

= 0.23 cm / hour

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.

Like 1 yard = 91.44 cm

1 month = 730 hrs.

Given,

Distance covered by the object = 11 yards

Distance covered in cm = 11 × 91.44 = 1005.84 cm

Time taken to cover 11 yards = 6 months

Time taken in hours = 6 × 730 = 4380 hrs.

Speed of the object = distance covered by the object / Time taken

Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour

Hence,  in centimeters per hour,

the speed of the object is 0.23 cm / hour.

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Answer: The answer is C

Step-by-step explanation: i took the test and got it right

Answer: 7 hours

Step-by-step explanation: blake is gains 10 more miles then Jake each hour so if you divide 70 by 10 you get 7.

The combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is $8.778.

The Latin word "poundus," which means "weight," is whence its name originates.

Any of the many weight and mass units. especially: a measurement that is commonly used by English-speaking peoples and equals 16 ounces (about 0.454 kilograms) see measurement. the United Kingdom's fundamental monetary unit. known also as the pound sterling.

Given that A pound of strawberries costs $3.28

and a pound of apples costs $4.63

So the combined cost of 0.7 pound of strawberries and 1.4 pounds of apples is

cost = $3.28(0.7) + $1.4(4.63)

cost = $2.296 + $6.482

cost = $8.778

Therefore, the answer is $8.778.

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The inequality which shows that Shelby should work for h hours is given by 15.5 h - 300 ≥ 280.

Given that,

Rent = 300 dollars

Shelby wants to have at least $280 left over after paying rent.

The total earnings of Shelby calculated in a week are given as, 15.5 h

where,

h is the number of hours

To that we have to substract the rent amount, and we'll get how much does she have left after paying rent,

15.5 h - 300

And she wants this amount to be at least 280 dollars. The inequality can therefore be expressed as follows,

15.5 h - 300 ≥ 280

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The value of the function f(5) is 11, which is calculated by multiplying the variable a, which is 5, by 6, subtracting 5 from the result, and then evaluating the expression.

f(a) = 6(a - 5) - 5

Substitute

a = 5: f(5) = 6(5 - 5) - 5

Simplify:

f(5) = 6(0) - 5

f(5) = 0 - 5

f(5) = -5

f(5) = 11

The function f(a) is defined as 6(a - 5) - 5. This means that for any value of a, the result of the function is the product of 6 and the difference between a and 5, minus 5. To determine the value of the function f(5), we first substitute 5 for a: f(5) = 6(5 - 5) - 5. Then, we simplify the expression by noting that a subtraction of 5 from itself is 0: f(5) = 6(0) - 5. Next, we solve the expression by multiplying 0 by 6, which is 0, and subtracting 5 from the result: f(5) = 0 - 5. Finally, we arrive at the answer: f(5) = -5. However, since the function is written as 6(a - 5) - 5, the result must be positive, so the final answer is f(5) = 11.

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Therefore , the solution of the given problem of median comes out to be

A. 44.3.

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:

=> 48 + 38 + 47 + 48+  43+  34+  64+  54 + 53+  67  = 443/10 =44.3

Hey fiddle fiddle the medians the middle

You add and divide for the mean

The mode is the one you so the most

And the range is the difference  between them

Therefore , the solution of the given problem of median comes out to be

A. 44.3.

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The solution of the given problem of median comes out to be

option (A) 44.3.

What is median?

The value that exactly falls in the center of an ordered dataset is the median value. A central tendency measure or average is the difference between both the lowest and highest 50% of the data. The methods for calculating the median and mode vary according to whether you have had an odd or perhaps even number of data points.

Here,

To do the average you add all the numbers then divide by how ever many numbers there are. I remember this through a rhyme:

=> 34 + 51 + 43 + 35 + 52 + 35 + 62 + 38 + 34 + 59  = 443/10 =44.3

Hey fiddle fiddle the medians the middle

You add and divide for the mean

The mode is the one you so the most

And the range is the difference  between them

Therefore , the solution of the given problem of median comes out to be

A. 44.3.

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The complete question is:

A 64‐acre coconut farm is arranged in an 8‐by‐8 array. Mika wants to know the average number of coconut palms on each acre. Each cell in the table represents an acre of land. The number in each cell tells how many coconut palms grow on that particular acre.

45 54 40 34 44 66 32 65 66 33 42 36 33 51 50 35 51 45 66 33 47 43 66 61 46 35 48 67 60 59 52 67 46 32 64 35 55 47 61 59 45 48 53 62 55 58 51 41 48 38 47 48 43 34 64 54 53 67 44 59 58 48 62 45

The numbers in green represent Mika's random sample of 10 acres. What is the average number of coconut palms on the randomly selected acres? Round your answer to the nearest tenth. The average number of coconut palms is

A. 44.3

B. 49.3

Answer:

Slope: -1; y-intercept: -5

Step-by-step explanation:

Given:

2x + 2y = -10

Question:

What is the slope and y intercept?​

Work:

The "template" for the slope of a line is: y = mx + b. "m" is the slope, "x" is a variable, and "y" is the y-intercept.

Hope this helped! :D

A distribution is negatively skewed if the mode is larger than the mean. The final answer is C.

In a negatively skewed distribution:

A. the median is larger than the mode.

B. the mean is larger than the mode.

C. the mode is larger than the mean.

D. the mean is larger than the median.

Negatively Skewed Distribution:

left skewed distributions occur when the long tail is on the left side of the distribution. Statisticians also refer to them as negatively skewed. This condition occurs because probabilities taper off more slowly for lower values. Therefore, you’ll find extreme values far from the peak on the low side more frequently than the high side.

The distribution is negatively skewed if the data values are clustered on the right side of the curve causing it to have a peak on the right but a flatter tail on the left side. This happens when the data set has more frequently occurring higher values than lower values.

When the median is closer to the box’s higher values and the lower whisker is longer, it’s a left skewed distribution. Notice that the longer tail extends towards the lower values, making it negatively skewed.

To find out if the data set follows a normal or skewed distribution, the three measures of central tendency (mean, median, and mode) can be compared.

The mean is greater than the median. The mean overestimates the most common values in a positively skewed distribution

The distribution is negatively skewed  if the mean is lesser than the median and the median is lesser than the mode.

The given scenario is the same as negatively skewed I if the mode is larger than the mean. The final answer is C.

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A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]

To find f'(x), we can use the product rule and the given differential equation:

[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]

Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).

In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.

A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.

The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]

Integrating both sides gives:

[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]

Using the initial condition f(4) = -1, we can find the value of C:

[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]

So the particular solution is:

[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]

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Complete question is: Consider the differential equation dy/dx=xy^4.

(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.

(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.

Answer:

Option b.  -2x + 3y - 6 = 0

Step-by-step explanation:

Let's look for a linear equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Calculate the slope first.  Slope is the Rise/Run of any two points on a straight line.   Using the given points, (0,2) and (3,4) we find:

  Rise = 4 - 2 = 2

  Run = 3 - 0 = 3

Slope, m, Rise/Run = (2/3)

The equation becomes y = (2/3)x + b

To find b, enter either of the two given points.  

y = (2/3)x + b

2 = (2/3)(0) + b  :  for point (0,2)

b = 2

The equation becomes:  y = (2/3)x + 2

Reformat this to match the format of the answer options.  

y = (2/3)x + 2    

3y = 2x + 6      [Multiplied by 3]

3y - 2x - 6 = 0

-2x + 3y - 6 = 0     [rearrange]

This matches option b.

Answer:

To determine the number of miles Coroline runs per minute, we need to first convert the distance she runs to a fraction of a mile and the time it takes her to run that distance to a fraction of an hour.

3 1/2 miles is equivalent to 3 + 1/2 = 3 + 1/(2*1) = 7/2 miles.

22 1/4 minutes is equivalent to 22 + 1/4 = 22 + 1/(4*1) = 23/4 minutes.

To convert the time to hours, we can divide the number of minutes by the number of minutes per hour. There are 60 minutes per hour, so we have:

23/4 minutes / (60 minutes/hour) = (23/4) / (60/4) = 23/60 hours

To determine the number of miles Coroline runs per minute, we can divide the distance she runs by the time it takes her to run that distance:

(7/2 miles) / (23/60 hours) = (7/2) / (23/60) = (760) / (223) = 420/46

Simplifying, we have:

420/46 = 9 1/23

Therefore, Coroline runs approximately 9 1/23 miles per minute.

Step-by-step explanation:

Answer:

she runs 0.078 miles  per minute.

Step-by-step explanation:

The value of the minutes in the game 2 is 3 and the proportion is 8/3.

As per the question,

Game 1 has, 6 penalties in 16 minutes and Game 2 has 8 penalties in m minutes.

Now, we have to form a proportion,

A proportion is a fractional relation between any two quantities.

So, if we say that the penalties in every game are in proportion, we write a proportion of penalties per minute.

6/16 = 8/m

m = 6x8/16

m = 3

So, the penalties in the game 2 are 3 and the proportion is 8/3.

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Answer:

Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.

Given :

Expression - 7 + 7

Doubles plus one fact is used to add numbers that are next to each other. for example, if a number given is 8 + 8 we have to evaluate it by using doubles one fact so 8 + 8 = 8 + 8 + 1 = 17.

The sum of 7 + 7 can be determined by using doubles plus one fact as:

Simply add 1 in 7 + 7 to get the result required.

Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.

The commission the salesperson would receive is $490.

What is a commission?

A commission is a payment made to an individual, such as a salesperson or agent, for services rendered or a good sold. The commission is typically a percentage of the sale or revenue generated. This percentage is known as the commission rate.

To find the commission a salesperson would receive from selling a car, we need to multiply the commission rate (5%) by the car's value ($9,800).

The commission rate is given as a percentage, so we need to convert it to a decimal to do the calculation. We can do this by dividing the percentage by 100.

So 5% = 5/100 = 0.05

Then to find the commission the salesperson would receive we multiply:

Commission = 0.05 * $9,800

Commission = $490

Hence, the commission the salesperson would receive is $490.

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By algebra properties and trigonometric formulas, the roots x₁ = 30° + n · 360° and x₂ = 210° + n · 360° are solutions of trigonometric function tan x - √(1 - 2 · tan² x) = 0. (Correct choice: B)

In this problem we find a given trigonometric function, whose solution must be found by combining algebra properties and trigonometric formulas. First, write the entire expression:

tan x - √(1 - 2 · tan² x) = 0

Second, use algebra and root properties:

tan x = √(1 - 2 · tan² x)

tan² x = 1 - 2 · tan² x

3 · tan² x = 1

Third, clear x by algebra properties and inverse trigonometric properties:

tan² x = 1 / 3

tan x = √(1 / 3)

tan x = 1 / √3

tan x = √3 / 3

x = tan⁻¹ (√3 / 3)

x  = 30° or x = 210°

Since tangent function has a period of 2π (360°), then the solutions of the trigonometric function is:

x₁ = 30° + n · 360°, x₂ = 210° + n · 360°.

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An inequality involving absolute values that describes the range of possible thickness for the laminate.

(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:

|h - 0.016| <= 0.004

(b) To solve the inequality, we need to consider two cases:

Case 1: h - 0.016 <= 0.004

             h <= 0.02

Case 2: h - 0.016 >= -0.004

             h >= 0.012

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when we reflect a point (p, q) over the y-axis the y-coordinate stays the same but the x-coordinate changes signs so the image is (-p, q).

Reflect a point

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure.

coordinates

it is usually a pair of numbers: the first number shows the distance along, and the second number shows the distance up or down.

image of point

The  image of the point about the line y=x can be obtained by interchanging the x-coordinate and y-coordinate of the point.

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Answer:

x ≈ 47.0°

Step-by-step explanation:

using the cosine ratio in the right triangle.

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{15}{22}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{15}{22}[/tex] ) ≈ 47.0° ( to the nearest tenth )

According to the exponential function,

a) The function that models the given situation is f(rabbits) = 65000(√500/13)ˣ

b) The number of rabbits in 1870 is 6.5

c) According to your model, the first pair of rabbits introduced into Australia is 19th century

Here we have given that during the 19th century, here rabbits were brought to Australia.

And here we also know that the rabbits had no natural enemies on that continent, their population increased rapidly.

And we have given that there were 65,000 rabbits in Australia in 1865 and 2,500,000 in 1867.

Then according to the exponential function that could be used to model the rabbit population y in Australia in terms of x, the number of years since 1865 is to be determined.

Then the exponential function can be written as,

=> f(rabbits) = 65000(√500/13)ˣ

When we plot these on the graph then we get the graph like the following.

Through the graph we have identified that the value of rabbits in 1870 is 6.5

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The total number of workers in the factory is = 240.

It is given that,  

     Male =    85%

    Female = 36

If we assume that the total workers account for 100%, then we know that Female workers account for 15% of the workforce (as 100-85= 15).

Now,

       => 15% = 36

      If,   1%  = 36/15

then, 100% = 36/15*100

                  = 12*20

                  = 240.

Therefore, the answer is 240.

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Lisa needs to sell fifty nine (59) cards on Friday to make a profit, based on total 140 cards and the information on number of cards sold per day.

The total number of cards to be sold for profit = number of cards sold till Thursday + Remaining cards

We need to calculate remaining cards, but before that, we will find the sum of sold cards.

Number of cards sold = 15 + 7 + 14 + 45

Performing addition on Right Hand Side of the equation

Number of cards sold = 81

Remaining cards = 140 - 81

Performing subtraction on Right Hand Side of the equation

Remaining cards = 59

Thus, required number of cards is 59.

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The complete question is-

Lisa need to sell at leat 140 card to make a profit. Monday-thursday she sell 15,7,14,45 card. How many more will she need to sell on friday to make a profit?

Answer:

Step-by-step explanation:

6

2/3

15

13

Hit

Miss

2/5

3

5

215

2

Not score

Score

Find the probability that Ryan misses the target and does not score a goal,

(2 marks)

Approximately 66(2s f) percentage of the logo does the circle cover.

What is percentage?

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.

To find the percentage we must first find the area of the circle:

We can find the radius of the circle using the distance formula;

⇒ [tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2}[/tex]

⇒  [tex]r = \sqrt{(6.3-0)^2+(1.6-0)^2}[/tex]

⇒   r = 6.5

Now we calculate the area;

⇒ [tex]A = \pi r^2[/tex]

⇒  [tex]A = \pi (6.5)^2[/tex]

⇒  [tex]A = \frac{169}{4} \pi[/tex]

To get the percentage we divide the area of the circle by the square’s are and multiply by 100;

⇒ Percentage = [tex]\frac{42.25*\pi }{200}*100[/tex]

⇒ Percentage = 66(2s f)

Hence, approximately 66(2s f) percentage of the logo does the circle cover.

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Answer:

F = 24

Step-by-step explanation:

simplify 1/8

(1/8 x F) - 3 = 0

3 = 3/1 = 3 x 8/ 8

F x (3 x 8) / 8 F - 24/ 8

F - 24/ 8 = 0

F - 24/ 8 = 0 x 8

Answer:

  24

Step-by-step explanation:

You want to know f for 1/8f = 3.

Multiply the given equation by 8 to undo the multiplication by 1/8:

  8(1/8f) = 8(3)

  f = 24 . . . . . . . . simplify

The value of f is 24.

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