Which choice is equivalent to the product below
Square root of 14 multiplied by the square root of 10
A. 4 square root of 35
B. 4 square root of 7
C. 35
D. 2 square root of 35

 [tex]\frac{2}{5+\sqrt{3}}[/tex]  fraction can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex] .

What are fractions?

A fraction is a number that represents a part of a whole. It consists of two numbers, a numerator and a denominator, separated by a horizontal or diagonal line. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts in the whole.

For example, 1/2 represents one part out of two equal parts, or one-half of the whole. Fractions can also represent values less than one, greater than one, or even negative values.

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is 5 - 3^(1/2):

[tex]\frac{2}{5+\sqrt{3}}[/tex] * [tex]\frac{(5-\sqrt{3})}{(5-\sqrt{3})}[/tex]

=       [tex]\frac{2*(5-\sqrt{3})} {(5+\sqrt{3}) (5-\sqrt{3})}[/tex]

= [tex](10 - \sqrt{23}) / (25 - 3)[/tex]

= [tex](10 - \sqrt{23}) / (22)[/tex]

Therefore, [tex]\frac{2}{5+\sqrt{3}}[/tex] can be simplified to [tex](10 - \sqrt{23}) / (22)[/tex]

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Complete question:

simplify the given fraction [tex]\frac{2}{5+\sqrt{3}}[/tex]

The domain of the function shown on the graph is {-3, -2, 2, 3 }.

The domain of a function is the set of all possible input values (also known as the independent variable or x-values ) for which the function produces a valid output (also known as the dependent variable or y-values).

In other words, it is the set of values that can be plugged into the function to produce a meaningful result.

In this case, there are four (4) points on the graph.

The coordinates of the points are;

Since the domain are the set of the x-values, the domain of the function of the graph will be;

Domain : {-3, -2, 2, 3 }

Therefore, option B) {-3, -2, 2, 3 } is the correct answer.

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The number of elements in set A is n = 12 elements of the set A is given by A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the set notation be represented as S

Now , the value of S is

S = {x|x is an even, negative integer and x > - 25}

Now , the value of the set A is given by all the numbers greater than -25 which are negative and even

So , A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }

The number of elements in set A = 12 elements

Therefore , the value of n = 12 elements

Hence , the set A = { -24 , -22 , -20 , -18 , -16 , -14 , -12 , -10 , -8 , -6 , -4 , -2 }

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The linear equation that gives the rule for the given table  x 0 1 2 3 y 0 2 4 6 is y = 2x.

A linear equation is an equation of a straight line in the form of y = mx + b, where m represents the slope of the line, and b represents the y-intercept.

The slope of the linear equation can be found by calculating the change in y over the change in x:

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

Taking (x1,y1) = (0,0) and (x2,y2) = (3,6),

slope=(6 - 0) / (3 - 0)

        = 2

So slope of the linear equation is 2.

Next, we can use the point-slope form of the linear equation to find the equation of the line:

y - y1 = m(x - x1)

Taking (x1,y1) = (0,0) and m = 2,

y - 0 = 2(x - 0)

Simplifying, we get

y = 2x

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If Jenny has 50 square tiles and arranges them in a rectangular array with 4 rows, then she would have a total of 48 tiles, with 2 tiles left over.

If Jenny arranges the tiles in a rectangular array with 4 rows, this means each row will have 50/4 = 12.5 tiles. However, since we cannot have half a tile, we need to round down to the nearest whole number, which is 12.

Therefore, each row will have 12 tiles, and the total number of tiles used will be 4 x 12 = 48. To find out how many tiles are left over, we need to subtract the total number of tiles used from the original number of tiles: 50 - 48 = 2. So, there will be 2 tiles left over.

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The Central Angle of each color is:

Red= 100°

Blue= 150°

Green= 50°

Purple = 60°

According to the definition of a central angle in geometry, it is the angle that the arc of a circle occupies in its centre. The angle's arms are formed by the two radii. Knowing the ratio of the curve to the circle using the central angle is helpful.

To draw a pie chart we have to find the central angle.

For Red

= 20/72 x 360

= 100 degree

For Blue

= 30/72 x 360

= 150

For Green

= 10/72 x 360

= 50

For Purple

= 12/ 72 x 360

= 60

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Answer:

1.3

Step-by-step explanation:

To find the average number of siblings for the group, we need to calculate the total number of siblings and divide by the total number of children.

Out of the 15 children:

5 are only children, so they have 0 siblings each.

3 have 1 sibling each, so there are 3 * 1 = 3 siblings in total.

4 have 2 siblings each, so there are 4 * 2 = 8 siblings in total.

3 have 3 siblings each, so there are 3 * 3 = 9 siblings in total.

The total number of siblings is 0 + 3 + 8 + 9 = 20.

The average number of siblings for the group is 20/15 = 1.3 (rounded to the nearest tenth).

Therefore, the average number of siblings for this group is 1.3.

Answer:

1.3

Step-by-step explanation:

The value of x is 10 if Leg= 8 and Leg=x-4.

This states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

In this scenario we were given

Leg= 8

Leg=x-4

Hypotenuse=x

Therefore : x² = 8² + (x-4)²

x² = 64 + x² - 8x + 16

x² -  x² = 80 - 8x

8x = 80

x = 80/8 = 10

Therefore hypotenuse is 10 and the length of the other side is (10-4) = 6.

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Answer:

To compute the probability that a person who tests positive actually has the disease, we need to use Bayes' theorem:

P(D|P) = P(P|D) * P(D) / P(P)

where:

P(D|P) is the probability of having the disease given a positive test result

P(P|D) is the probability of testing positive given that the person has the disease (also known as sensitivity), which is 1 - false negative rate = 0.92 in this case

P(D) is the incidence rate of the disease, which is 0.4% = 0.004

P(P) is the probability of testing positive, which can be computed using the false positive rate as 1 - specificity = 1 - 0.98 = 0.02

Plugging in the values, we get:

P(D|P) = 0.92 * 0.004 / 0.02 = 0.184

Therefore, the probability that a person who tests positive actually has the disease is 0.184, or about 18.4%.

Answer:

Step-by-step explanation: 5.6 / 8 = 0.7

Answer:

x = 2 (True)

Step-by-step explanation:

Answer:

See the explanation below.

Step-by-step explanation:

You need to calculate the remaining side.

Pythagorean theorem: c^2 = a^2 + b^2

=> 5^2 = 4^2 + b^2

b^2 = 25 - 16 = 9

b = √9 = 3

Draw a right triangle with the sides of 3cm and 4cm are perpendicular to form 90 degrees angle. Then connect the ends of 2 lines to form the hypotenuse which will be 5 cm long.

Answer:

$13,500

Step-by-step explanation:

I = (P·r·t) / 100

I = (9,000·10·15) / 100

I = 1,350,000 / 100

I = $13,500

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Thanks.

The value of k will make V = x + k/x have a relative minimum at x = 3 is k = 9

A relative minimum of a function is the minimum value of the function in a particular interval.

Since we have the function  V = x + k/x. We desire to find the value of k that will make V = x + k/x have a relative minimum at x = 3

So, to find the relative minimum of V, we differentiate with respect to x and equate to zero.

So, V = x + k/x

dV/dx = d(x + k/x)/dx

= dx/dx + kd(1/x)/dx

= 1 - k/x²

Equating dV/dx to zero, we have that

dV/dx = 0

⇒ 1 - k/x² = 0

1 = k/x²

k = x²

For a relative minimum at x = 3, substitute x = 3 into the equation. So, we have that

k = x²

= 3²

= 9

So, k = 9

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Answer:

Step-by-step explanation:

[tex]C=\pi d[/tex]

   [tex]=\pi \times 35[/tex]

   [tex]\approx 109.96 feet[/tex]

Answer:

110. feet approximately

Step-by-step explanation:

circumference means a closed boundary of a curved shape. Mainly known as a circle. To find circumference, use the formula c= π (pie) times diameter.

35 × π ≈ 110

Hope this helps :)

Answer:

Step-by-step explanation:

Perimeter add all the sides.

so let's walk around and combine like terms:

starting on the bottom moving to the left.

3x^2 + x^2= 4x^2 (there are no other squared terms)

back to the bottom moving left again:

-11x-3x+3x+x = -10x (-3x + 3x =0)

so -11x + x = -10x

now add all of the constants

-1 + 2 = 1

so your answer is

4x^2 -10x + 1

The percentage of temperatures for Shanghai that falls between 46 degrees Fahrenheit and 78 degrees Fahrenheit is A. 50 %.

The interquartile range (IQR) of a box and whisker plot is defined as the difference between the third quartile (Q3) and the first quartile (Q1). It represents the spread of the middle 50% of the data.

On a box plot, the interquartile range (IQR) is represented by the box itself. The box extends from the first quartile (Q1) to the third quartile (Q3) and contains the middle 50% of the data.

This means that for Shanghai, the temperatures of 46 degrees Fahrenheit and 78 degrees Fahrenheit represent the IQR which means that this is 50 % of the temperature.

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The full question is:

The box-and-whisker plots below show the mean monthly temperatures (°F) for Mexico City, Mexico, and Shanghai, China. What percent of the temperatures for Shanghai fall between 46°F and 78°F? *

What are functions ?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

What are asymptotes ?

An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity.

There are three types of asymptotes namely:

1) Vertical Asymptotes

2) Horizontal Asymptotes

3) Oblique Asymptotes

The point to note is that the distance between the curve and the asymptote tends to be zero as it moves to infinity or -infinity.

What are domain of a function ?

The domain of a function is the set of values that we are allowed to plug into our function.

This set is the x values in a function such as f(x).

What is range of a function ?

The range of a function is the set of values that the function assumes. This set is the values

that the function shoots out after we plug an x value in. They are the y values.

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The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

In which:

The radical form is given as follows:

[tex]\sqrt[m]{a^n}[/tex]

Meaning that the equivalence relation is given as follows:

[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]

That is:

Hence the relation for the cube root of 21 is given as follows:

[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]

(applying the conversion of the fractional exponent to a radical expression).

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The solution to the system of equations is x = 6 and y = 2.

The system of equations can also be solved using the elimination method.

We are aware that a system of linear equations is a collection of two or more equations with at least two unknown variables. Finding the answers to the unknown variables in a system of equations is the process of solving a linear equation. There are numerous ways to identify the answers to the unknown variables. These include the cross-multiplication method, elimination method, substitution method, and graphic method.

from the question:

A system of equations can be solved in a variety of methods, including substitution, elimination, and matrices. I'll apply the substitution technique here:

x = 8 - y is the result of the first equation.

We can solve for y by substituting this expression for x in the second equation:

-x + 4y = 2

-(8 - y) + 4y = 2 (substituting x = 8 - y)

-8 + 5y = 2 (simplifying)

5y = 10 (adding 8 to both sides)

y = 2 (dividing by 5)

Knowing y, we can now use this quantity to solve one of the initial equations to determine x:

x + y = 8

x + 2 = 8 (substituting y = 2)

x = 6 (subtracting 2 from both sides)

Hence, x = 6 and y = 2 are the answers to the system of equations.

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The constant of proportionality between the side length and the perimeter of the equilateral triangle would be = 3.

The constant of proportionality is defined as the constant value that exists between two variables that are in a direct proportional relationship to each other.

For example, the constant of proportionality (k) between the side lengths and the perimeter of the equilateral triangle= y/X= 15/5= 3 or 24/8 = 3 or 27/9 = 3 or 30/10=3.

Therefore, the constant of proportionality which is the constant value existing between the two variables= 3.

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Answer:

  π/4, 7π/4

Step-by-step explanation:

You want the values of θ in the range 0 ≤ θ ≤ 2π such that cos(θ) = √2/2.

The cosine function has the value √2/2 for angles ±45° = ±π/4 radians and those angles added to an integer multiple of 2π. In the domain of interest, the angles are ...

  θ = π/4 and 7π/4

This can be resolved with d = 25 miles by multiplying equation both sides by

If Jen has driven 15 miles, and this is 3/5 of the total distance, we can use the following equation to find the total distance d:

15 = (3/5) * d

To solve for d, we need to isolate it on one side of the equation. We can start by dividing both sides of the equation by 3/5, which is the same as multiplying by its reciprocal, 5/3:

15 * (5/3) = d

Simplifying the expression on the left side, we get:

25 = d

Therefore, the total distance Jen needs to travel to get to the mall is 25 miles.

In summary, the equation that can be used to find the total distance d, given that Jen has driven 15 miles and this is 3/5 of the total distance, is:

15 = (3/5) * d

Which can be solved for d by multiplying both sides by 5/3, giving:

d = 25 miles

In conclusion, assuming that Jen has driven 15 miles, which is 3/5 of the entire trip, the equation that can be used to determine the whole distance d is:

15 = (3/5) * d

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The probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

Given is a table as shown in the image attached.

It is aske to find the probability that one client drives less than 10,000 miles a year and has an accident. Form the table, we can write the cell corresponding to driving less than 10,000 miles and having the accident as 0.06.

Therefore, the probability that one client drives less than 10,000 miles a year and has an accident is 0.06.

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The rug covers 42 feet of space. We calculate the area of a rectangle to determine it. A rug is woven fabric or animal skin used as a floor covering.

It is a shape with four straight sides and four right angles that is not square, especially if the sides next to it are uneven.

When a 2-D enclosed shape has four sides, four corners, and four right angles (90°), it is referred to as a rectangle. When opposing sides of a diagram are equal and parallel, the shape is referred to as a rectangle.

Area of rectangle = L × B

So, Area of rug =  7 × 6

                         = 42 feet

Therefore the required answer is 42 Feet.

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Answer:

x = 20

Step-by-step explanation:

2x + 24 = 64

2x = 40

x = 20

Let's check

2(20) + 24 = 64

40 + 24 = 64

64 = 64

So, x = 20 is the correct answer.

Answer:

[tex] \sf \: x = 20[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 2x + 24 = 64

Then the value of x will be,

→ 2x + 24 = 64

→ 2x = 64 - 24

→ 2x = 40

→ x = 40 ÷ 2

→ [ x = 20 ]

Hence, the value of x is 20.

The solution is:

Net income = $31,130

Total Assets = Owner's Equity and Liabilities = $104,230

Income can be stated as the consumption and saving opportunity gained by an entity within a specified timeframe, which is normally expressed in monetary terms. Income is that which means difficult to define conceptually and the definition may be different across fields.

here, we have,

The  Income Statement of Profit or Loss and the Statement of Financial Position can be prepared  as follows:

Sugar Almonds Ltd  

Income Statement of Profit or Loss  

For the Year Ended 31st December 2020  

Particulars                                                        $                       $            

Sales Revenue                                                                       93,700

Cost of sales:  

Opening inventory                                      12,000

Purchases                                                   49,000

Closing inventory - income statement   (24,350)  

Cost of sales                                                                         (36,650)  

Gross profit                                                                             57,050

Operating expenses:  

Administrative Expenses                               (850)

Rent paid                                                     (2,000)

Telephone                                                      (900)

Wages                                                         (21,650)

Travel expenses                                             (330)  

Total operating expenses                                                   (25,730)

Interest income (expense):

Interest paid                                                                              (190)  

Net income                                                                             31,130  

Sugar Almonds Ltd  

The Statement of Financial Position  

As at 31st December 2020  

Particulars                                                        $                        $            

Fixed Assets

Premises at cost                                         70,000  

Vehicles at cost                                           5,800  

Total Fixed Assets                                                                 75,800

Current Assets

Cash                                                                 630  

Bank                                                               2,100

Closing inventory - Statmt of fin positn    24,350  

Trade Receivables                                        1,350  

Total Current Assets                                                              28,430  

Total Assets                                                                           104,230

Owner's Equity

Capital                                                      72,000  

Drawings                                                   (6,450)

Net income                                                31,130  

Total Owner's Equity                                                             96,680

Current Liabilities  

Trade Payables                                          6,400  

VAT                                                              1,150  

Total Current Liabilities                                                          7,550  

Owner's Equity and Liabilities                                           104,230

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By answering the above question, we may state that John consequently variable  sold 35 notepads.

A variable is anything that may be altered in the context of an experiment or mathematical idea. A single symbol is frequently used to denote a variable. Generic symbols for variables are the letters x, y, and z. Variables are qualities with a wide range of values that may be investigated. These include characteristics like height, age, wealth, place of birth, academic standing, and kind of residence, to mention a few. The two primary groups of variables can be separated using numerical and categorical approaches.

Let's define the variables first:

Let's call John's sales of notebooks "n" the quantity.

Each notebook costs $1.50, hence the whole profit from notebook sales is $1.50.

John earned a total of $92.50, according to the issue, thus we can create the following equation:

$40.00 + 1.5n = $92.50

Now that "n" is solved, we can:

$1.5n = $92.50 - $40.00

$1.5n = $52.50 \sn = 35

John consequently sold 35 notepads.

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The areas of triangles ABC are

12. The area is 4.8 cm²

13. The area is 61.4 m²

14.  The area is 9.0 ft²

The area of a triangle is the region occupied by the triangle.

12. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2bcsinA

= 1/2 × 7 cm × 4 cm × sin20°

= 7 cm × 2 cm × sin20°

= 14 cm² × sin20°

= 14 cm² × 0.3420

= 4.788 cm²

≅ 4.8 cm²

The area is 4.8 cm²

13. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2absinC

= 1/2 × 10 m × 15 m × sin55°

= 5 m × 15 m × sin55°

= 75 cm² × sin55°

= 75 cm² × 0.8192

= 61.436 cm²

≅ 61.4 cm²

The area is 61.4 cm²

14. Area of triangle ABC

Given that

Area of triangle ABC is A = 1/2acsinB

= 1/2 × 3 ft  × 9 ft × sin42°

= 1/2 × 27 ft² × sin42°

= 13.5 ft² × sin42°

= 13.5 ft² × 0.6691

= 9.033 ft²

≅ 9.0 ft²

The area is 9.0 ft²

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