What are two algebraic expressions for the square root of x? (what are two ways of writing the square root of x?)​

(1) The area of the trapezoid is 192 square meters.

(2) The area of the circle is A = 144π square cm or A ≈ 452 square cm.

(3) The circumference of the circle is C = 24π cm or C ≈ 75 cm.

(4) The perimeter of the figure is ≈ 110 cm.

(5) The area of the figure is 321 square meters.

The measurement that indicates the size of a region on a plane or curved surface is called the area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

(1)

The height of the trapezoid is 12m and the lengths of the parallel sides are 11m and 21 m.

The area of the trapezoid is:

A = (1/2)(11 + 21)(12)

A = 192 square meters.

(2)

The area of the circle with a radius of 12 cm is:

A = π(12)²

A = 144π

A ≈ 452 square cm.

(3)

The circumference of the circle with a radius of 12 cm is:

C = 2π(12)

C = 24π

C ≈ 75 cm

(4)

To find the perimeter of the figure, first, find the circumference of the semicircle,

The diameter of the semicircle is 30 - 12 = 18.

Therefore, the radius is 18/2 = 9 cm.

Hence, the perimeter of the figure is:

12 + 20 + 30 + 20 + π(9)

≈ 110 cm

(5)

To find the area of the figure, first, find the area of the large horizontal rectangle, then the upper triangular part, and then the lower rectangular part, and add them together.

The area of the large horizontal rectangle is:
(24 + 5) × 8

= 232

The area of the triangular portion is:

(1/2)×(24 + 5 -10 -10)×12

= 54

The area of the small rectangular part is:
5×7

=35

Now, add all the areas together to find the total area of the figure:

232 + 54 + 35

= 321

Hence, the area of the fifth figure is 321 square meters.

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The mean and standard deviation of the number of people with blood type a-positive in 100 randomly selected is μ=85, σ=3.5707

The standard deviation is a statistic that measures the amount of variation or dispersion of a group of values.

Standard deviation is usually abbreviated SD and is most commonly represented in mathematical texts and equations by the lower case Greek letter (sigma) for population standard deviation or the Latin letter s for sample standard deviation.

A low standard deviation indicates that the values are close to the mean of the set (also known as the expected value), whereas a high standard deviation indicates that the values are spread out over a broader range.

Given, The population proportion of success is p=0.85

And also given that the sample size is n=100

b) The population mean is:

μ=np

μ=100(0.85)

μ=85

Therefore, mean=85

And the population standard deviation is:

σ=√np(1-p)

σ=√100(0.85)(1-0.85)

σ=3.5707

Therefore, standard deviation=3.5707

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The complete question is:

" Rh - positive blood appears in 85% of the population in the USA. a) Verify that it's possible to use the normal approximation to binomial distribution if a sample size is 100 randomly selected people. b) Find the mean and standard deviation of the normal distribution."

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

The way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

\(\text{Area of composite figure} = \sum (\text{Area of composing figures})\)

That ∑ sign shows "sum"

Since the considered composite figure consists of a semicircle, trapezoid, and 2 rectangles, so we can find its area by their use.

Thus, the way we can decompose the composite figure to determine its area is given by: Option D: as a semicircle, a trapezoid, and two rectangles.

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Answer:

d

Step-by-step explanation:

i just finished the test

Answer:

AC = 18

Step-by-step explanation:

AC = AB + BC = 7 + 11 = 18

Answer:

(5, 4 )

Step-by-step explanation:

Given the 2 equations

3x - y = 11 → (1)

- 2x - 4y = - 26 → (2)

Multiplying (1) by - 4 and adding to (2) will eliminate the y- term

- 12x + 4y = - 44 → (3)

Add (2) and (3) term by term to eliminate y

- 14x + 0 = - 70

- 14x = - 70 ( divide both sides by - 14 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (1)

3(5) - y = 11

15 - y = 11 ( subtract 15 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

solution is (5, 4 )

The union of two sets contains all the elements contained in either set (or both sets). The intersection of two sets contains only the elements that are in both sets

Therefore the answer is B.

The low temperature in Edmonton was greater than the low temperature in Fort Nelson.

"Ascending order is the method of arrangement of numerical value in  from smallest to greatest value, also known as increasing order."

According to the question,

Temperature of four cities given

Fort Nelson = -29°F

Ottawa = 5°F

Edmonton = -18°F

Whitehorse = -33°F

Arrange all the temperature in ascending order we get,

-33° < -29° < -18° < 5°

temperature of Whitehorse < temperature of Fort Nelson < temperature of Edmonton< temperature of Ottawa

Hence, we conclude that Option(A) is the correct answer.

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The set S is linearly dependent.

To determine if the set S is linearly independent or dependent, we need to see if any of the vectors in the set can be written as a linear combination of the others.

Let's set up the equation:

a(3/2, 3/4, 5/2) + b(4, 7/2, 3) + c(?, -3/2, 2, 6) = (0,0,0)

To solve for a, b, and c, we can create a system of equations using each component:

3a/2 + 4b + c? = 0
3a/4 + 7b/2 - 3c/2 = 0
5a/2 + 3b + 2c = 0
6c = 0

The last equation tells us that c must be 0, since we can't have a non-zero scalar multiplying the zero vector.

Using the first three equations, we can solve for a and b:

a = (-8/3)c?
b = (5/3)c?

Since c can be any non-zero number, we can see that there are infinitely many solutions to this equation, meaning that the set S is linearly dependent.

Therefore, the answer is option B linearly dependent.

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Answer:

24

Step-by-step explanation:

Two negatives make a positive.

11 + 13 = 24

Answer:

24

Step-by-step explanation:

= 11 - ( -13 )

According to sign conventions, - ( - ) = +

= 11 + 13

= 24

\(\rule[225]{225}{2}\)

Hope this helped!

You have the following function:

y = - |x|

which |x| means the absolute value of variable x.

Moreover, you have the following domain:

d:{-1, 0, 1, 2}

In order to determine what is the associated range of the function, consider that the absolute value of any positive or negative number is always the positive number. Thus, when you evaluate the given function for all values of the domain you have:

y = - |-1| = - (1) = -1

y = - |0| = 0

y = - |1| = - (1) = -1

y = - |2| = - (2)= -2

Then, the range is:

r: {-1 , 0 , -1 , -2}

Without further context I can't say much other than the radius is perpendicular to the tangent. In other words, the radius and tangent line form a 90 degree angle. This is one particular radius and its not just any radius. The radius in question must have the point of tangency as its endpoint.

The radius, AB  is perpendicular to the tangent line,  BC  so their slopes are negative reciprocals of one another. Because I generated a circle at random for this activity, this conclusion likely applies to any tangent line to a circle. In other words, the tangent line to any circle is perpendicular to the radius at their point of intersection.

The confidence interval is 0.039. This means that the value lies between the range of -0.039 and 0.039. Therefore, we can express the confidence interval as the mean plus or minus the margin of error.

This will give us a range in which the true population mean lies.Let's assume that the mean is 0.259. Then the lower limit of the range is given by:Lower limit = 0.259 - 0.039 = 0.22 And the upper limit of the range is given by:Upper limit = 0.259 + 0.039 = 0.298Therefore, the confidence interval is: 0.22 to 0.298Now we can see that option A is the correct answer: 0.259+0.22.

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The volume of the tank can be found using the given information as:\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

Assuming that the area bounded is given by a function f(x), the volume of the oil storage tank can be calculated using the formula for the volume of a solid of revolution:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

where a and b are the limits of integration. In this case, the axis of revolution is the x-axis, so we are revolving the area about the x-axis.

Therefore, the volume of the tank can be found using the given information as:

\(Volume=\int\limits^b_a {\pi f(x)^2} \, dx\)

We need more information about the function f(x) or a curve that bounds the area in order to find the limits of integration and calculate the volume.

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18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

The value of side TR is 3.75 units.

A relationship which is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

In Δ PQR,

ST is parallel to QR,

So, using "Basic Proportionality theorem": we get,

⇒ PS / SQ = PT / TR

⇒ 4 / 6 = 2.5 / TR

⇒ TR = 4 × 2.5 / 6

⇒ TR = 3.75

Thus, The value of TR is 3.75 units.

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The complete question is shown in image.

Answer:

They only intersect once. (Correct letter is B)

Step-by-step explanation:

Slope Intercept Form:

2x - 4y = 3

-2x        -2x

________

-4y = -2x + 3

Switch the signs of all of the numerals since you cannot have a negative 'y' value.

4y = 2x - 3

----   ---------

4         4

y= 1/2x - 3/4

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

7y - 5x = 8

    +5x  +5x

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

7y = 5x + 8

----   ---------

7        7

y= 5/7x + 1 1/7

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

After graphing the lines, you then can see that the lines only ever intersect once.

Answer:

0.02

Step-by-step explanation:

2% of 3,000 is 60

3,000 x 0.02 = 60

Answer:

153 cm^2

Step-by-step explanation:

The area is given by

A = b*h

   = 17*9

    =153 cm^2

Answer:

Step-by-step explanation:

A=(b1+b2/2)h

The formula is area= base 1 plus base 2 over 2 times the height.

The two bases are 17 cm.  Let's add that in our formula.

A=(17+17/2)h

17+17= 34.  Since 34 is over 2 in the parentheses, let's simplify that first.

A=(34/2)h

A=(17)h, because 34 divided by 2 is 17

The height, h, is 9 cm.  Let's subsitute that into h.

A=(17)9

17 times 9 equals 153, so the area is 153² cm.  :)

Hello,

\( \frac{p(x)}{q(x)} = \frac{ {x}^{2} - x - 12}{x + 3} = \frac{(x - 4)(x + 3)}{x + 3} = x - 4\)

Answer:

Step-by-step explanation:

Answer:

2.511 square kilometers

The trend line equation to estimate the hiker's elevation after 150 minutes is 2033 feet.

Given that,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

We must determine,

The trend line equation is used to calculate the hiker's elevation after 150 minutes.

In response to the question,

A trend line's equation for the hiker's elevation is y = 9.16x + 659.

Where x is the number of minutes and y is the elevation of the hiker in feet.

Substitute the value of x = 150minute in the given equation to find the trend line to estimate the hiker's elevation after 150minutes.

Therefore,

y = 9.16x + 659

x = 150

y = 9.16(150) + 659

y = 1374 + 659

y = 2033

As a result, the trend line equation for estimating the hiker's elevation after 150 minutes is 2033 feet.

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Answer:

answer is A

Step-by-step explanation:

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Performing the calculation \(\frac{0.32610}{1.830}\) and rounding the answer to the proper number of significant figures gives us approximately 0.178.

To explain the calculation further, we divide 0.32610 by 1.830. The division results in a quotient of 0.1781967213. However, since we need to round the answer to the proper number of significant figures, we look at the least precise number in the given values, which is 1.830 with four significant figures. Therefore, we round the quotient to three significant figures, giving us approximately 0.178 as the final result.

Significant figures are used to indicate the precision of a number or measurement. They include all the certain digits in a number and the first uncertain or estimated digit. When performing mathematical operations, it's important to consider significant figures and round the final result accordingly to maintain accuracy and proper representation of precision.

In this case, the division yields a result with ten significant figures, but we round it to three significant figures since that is the least precise value among the given numbers. This ensures that the answer reflects the appropriate level of precision and adheres to the rules of significant figures.

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Performing the calculation \(\frac{0.32610}{1.830}\) and rounding the answer to the proper number of significant figures gives us approximately 0.178.

To explain the calculation further, we divide 0.32610 by 1.830. The division results in a quotient of 0.1781967213. However, since we need to round the answer to the proper number of significant figures, we look at the least precise number in the given values, which is 1.830 with four significant figures. Therefore, we round the quotient to three significant figures, giving us approximately 0.178 as the final result.

Significant figures are used to indicate the precision of a number or measurement. They include all the certain digits in a number and the first uncertain or estimated digit. When performing mathematical operations, it's important to consider significant figures and round the final result accordingly to maintain accuracy and proper representation of precision.

In this case, the division yields a result with ten significant figures, but we round it to three significant figures since that is the least precise value among the given numbers. This ensures that the answer reflects the appropriate level of precision and adheres to the rules of significant figures.

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Expressions for the real part, imaginary part, magnitude, and angle of complex numbers are determined using the principal value of -π.

To find the real part, imaginary part, magnitude, and angle of complex numbers, we'll consider the given principal value of -π.

Let's denote the complex number as \(z = a + bi\), where a represents the real part and b represents the imaginary part.

The real part, Re(z), is simply a.

The imaginary part, Im(z), is b.

The magnitude, |z|, is calculated using the formula \(|z| = \sqrt{a^2 + b^2}\).

The angle, θ, can be determined using the inverse tangent function: \(\theta = \text{atan2}(b, a)\). However, the given principal value of -π indicates that we should consider the angle in the range of -π to π.

To adhere to the principal value of -π, we can modify the angle by adding or subtracting multiples of 2π until it falls within the desired range. In this case, we can subtract 2π from the calculated angle if it exceeds π.

In summary, by applying the principal value of -π, we can determine the real part, imaginary part, magnitude, and angle of complex numbers using the provided expressions.

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Answer:

Joe would be paying $700 in 5 years time.

Step-by-step explanation:

Answer:

In 4 years Joe would have to pay $1,680 in simple interest.

Step-by-step explanation:

So first of all you want to start by finding what P, r and t would be.

P = Principal amount ($$)

r = interest rate (%)

t = time

Once I found all of those I put them into the equation (l = Prt) and solved. That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)

Have a great day!

Answer:

It will take 3 hours and 20 minutes.

Step-by-step explanation:

10.000:50=200 minutes for 10.000 beats

200 minutes = 3 hours 20 minutes

The value of time to take for the cow's heart to beat 10,000 times is,

⇒ 3 hours 20 minutes

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A cow has a heart rate of 50 beats per minute (bpm).

Hence, The value of time to take for the cow's heart to beat 10,000 times is,

⇒ 10,000 / 50

⇒ 200 minutes

⇒ 3 hours 20 minutes

Thus, The value of time to take for the cow's heart to beat 10,000 times is,

⇒ 3 hours 20 minutes

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Answer:

The experimental probability of rolling anumber less than 3 is 3/20

Step-by-step explanation:

16+14=30

30/200

=3/20

Answer:

7/50

Step-by-step explanation: