Write the following ratio as a fraction in lowest terms 55 to 50

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

ion know

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The 1/8 of 32 is 4

3. 4= 12

12 is the 3/8 of 32

Answer:

ujjjhhhggokkkkbfdxfghhhhbb

Answer:

6035ft

Step-by-step explanation:

Given data

Length=x

WIdth= 6x^3 + 1 − x^2

The expression for the perimeter is given as

P= 2L+2W

substitute

P=2(x)+2(6x^3 + 1 − x^2)

open brackets

P=2x+12x^3+3-2x^2

rearrange, the polynomial that models the perimeter of the rectangle is

=12x^3-2x^2+2x+3

Also, the perimeter when length x= 8 is

P=12x^3-2x^2+2x+3

P=12(8)^3-2(8)^2+2(8)+3

P=12*512-2*64+16+3

P=6144-128+19

P=6016+19

P=6035 feet

Hence the perimeter of the rectangle is 6035ft

Answer:

9-3

Subtract 3 from 9 and you get 6

It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

The simplified form of the given expression as a fraction is 7x/x-7

Fractions  are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.

Given the expression below;

(1/7+1/x)/(1/49+1/x²)

Find the LCM to have:

(x+7/7x)/(x²-49)/49x²

Divide to have:

x+7/7x * 49x²/(x²-49)

(x+7) * 7x/(x+7)(x-7)

Cancel out the like terms to have:

1 * 7x/x-7

= 7x/x-7

Hence the simplified form of the given expression as a fraction is 7x/x-7

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Answer:

80 + 30h

Step-by-step explanation:

(10 * 8) + (10 * 3h)

=80 + 30h

\(\Large\boxed{\tt Anwer:~80+30h}\)

\(\tt Step-by-step~explanation:\)

We need to distribute the 10 to 8 and 3h. In order to do this, we can multiply 10 by 8 and 10 by 3h.

\(\tt 10*8=80\\10*3h=30h\)

Then, we add them together to get the answer.

\(\tt 80+30h\)

The standard error represents the average deviation of the sample means from the true population mean. Rounding this value to four decimal places, the standard error of X¯¯¯ is approximtely 0.6500 mpg.

A smaller standard error indicates that the sample means are more likely to be close to the population mean.To calculate the standard error of X¯¯¯, the mean from a random sample of 25 fill-ups by one driver, we can use the formula:

Standard Error (SE) = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

In this case, the standard deviation (σ) is given as 3.25 mpg, and the sample size (n) is 25.

Plugging in these values into the formula, we have:

SE = 3.25 / sqrt(25).

Calculating the square root of 25, we get:

SE = 3.25 / 5.

Performing the division, we find:

SE ≈ 0.65.

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For each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

Let's assume that x pounds of Guatemalan coffee are used per pound of the blend.

Given information:

Cost of Guatemalan coffee = $11/lb

Cost of the other coffee = $5/lb

Desired cost of the blend = $8/lb

Total weight of the blend = 6 pounds

To find the ratio of Guatemalan coffee to the total blend, we can set up the equation:

\((x \times 11 + (6 - x) \times 5) / 6 = 8\)

In this equation, \((x \times 11)\) represents the cost of the Guatemalan coffee in the blend, and\(((6 - x) \times 5)\) represents the cost of the other coffee in the blend.

The numerator is the total cost of the blend, and we divide it by 6 (the total weight of the blend) to find the cost per pound.

Now, let's solve the equation for x:

(11x + 30 - 5x) / 6 = 8

6x + 30 = 48

6x = 48 - 30

6x = 18

x = 18/6

x = 3

Therefore, for each pound of the blend, Cold Beans should use 3 pounds of Guatemalan coffee.

This means that in a 6-pound bag of the blend, they would use \(3 \times 6 = 18\)pounds of Guatemalan coffee.

To summarize, to achieve a cost of $8 per pound for a 6-pound bag of blend, Cold Beans should use 3 pounds of Guatemalan coffee per pound of the blend.

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The probability that the selected product is a hardware product given that is from company B is x/50.

The probability that the selected product is a hardware product given that is from company A is 3/7.

The value of x must be greater than 21 so that the probability in part (a) is greater than the probability in part (b).

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Company A:

Total product = 70

Software product = 40

Hardware product = 30

Company B:

Total product = 50

Software product = y

Hardware product = x

The probability that the selected product is a hardware product given that is from company B.

= x/50 ____(1)

The probability that the selected product is a hardware product given that is from company A.

= 30/70

= 3/7 _____(2)

From (1 ) and (2) we get,

x/50 > 3/7

x > 3/7 x 50

x > 21

Thus,

The probability that the selected product is a hardware product given that is from company B is x/50.

The probability that the selected product is a hardware product given that is from company A is 3/7.

The value of x must be greater than 21 so that the probability in part (a) is greater than the probability in part (b).

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Correction

The revenue function for a school group selling n bookmarks is given by R(n) =2n and the total cost function is given by C(n)=144+0.08n. Determine the number of bookmarks sold at which they break-even.

Answer:

75 bookmarks

Step-by-step explanation:

The break-even point is the point at which revenue earned is equal to the cost of production.

Given the cost and revenue functions respectively:

Cost=Revenue

C(n)=R(n)

144+0.08n=2n

144=2n-0.08n

144=1.92n

Divide both sides by 1.92

n=75

When 75 bookmarks are sold, the school group will break even.

boys: 9

Girls: 12

Ratio boys to girls :

9:12 = 3/4

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

Answer juvhfVO"zohgvjozi nandish pro nbhvmno

Answer:

25%

Step-by-step explanation:

i think it is

i am sorry if wrong

The cost of one candy bar is $2.35.

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service.

Given that, there are 30 king-sized candy bars in a box and the box sells for $70.50, we need to find that how much does each candy bar in the box cost,

Since, the cost of all 30 candies is given collectively, i.e. $70.50,

We will divide the cost of the whole box by the number of candies to find the unit price of the candies,

Unit price = $70.50 / 30

= $2.35

Hence, the cost of one candy bar is $2.35.

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Given:

(1985,46000)

(1997,38080)

(a)

General linear equation is:

here y represent the population and x represent time so equation is:

slope is:

So equation is:

Point (1985,46000)

So equation is:

(b)

population in 2000.

so population in 2000 is 36100.

I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.

It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.

By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.

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Answer:

0.4246

Step-by-step explanation:

Given data:

mean ( u ) = 15 inches

std ( б )= 6 inches

sample size( n ) = 46

ux = mean sample length

Determine the probability that x within 0.5 inch of the claimed population mean

ux = u = 15

бx = б/ √ 46 =  6 /√ 46 = 6 / 6.78 = 0.88

Hence the   P( 14.5 < x < 15.5 )

= P ( [14.5 - 15 / 0.88 ] < z < (15.5 - 15) / 0.88) )

= P ( -0.5682 < z <  0.5682 )

= P ( z < 0.5682 ) - P ( z < -0.5682 )

= 0.7123 - 0.2877  ( from Z table )

= 0.4246

9514 1404 393

Answer:

  69.6°

Step-by-step explanation:

The sum of angles in a triangle is 180°, so angle X is ...

  ∠X = 180° -∠Y -∠Z

  ∠X = 180° -68.4° -42°

  ∠X = 69.6°

Answer:

1)4x+4y=1, 6x−y=1

x+y=4, x−y=2

x+y=−2,x+2y=2

2)2x+y=3, 2x−8y=19

Step-by-step explanation:

hope this helps

have a nice day ^_^

Answer: x = 50

Step-by-step explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.

Answer:

what do u need help with

Step-by-step explanation:

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