Question
Evaluate the expression.

4216−−−√3−3=

PLEASEEEEEEE ITS DUE IN AN HOUR

The subtracting fractions calculator online is a free online calculator showing the difference between two fractions.

The fraction represents the components of the whole in mathematics. It is important to keep track of the fraction types while subtracting fractions, whether they are like or unlike fractions. Like fractions are fractions with the same denominators, and unlike fractions are fractions with distinct denominators. When a fraction is similar, the numerator value can simply be removed. The methods to subtract the fractions are listed below if the denominators are the opposite fractions.

Take the denominator's LCM.

Now multiply the numerator and denominator values by the same number to convert the denominator value to the LCM value.

Finally, subtract the values of the fractions.

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Answer:

Step-by-step explanation:

The hole for the function f(x) = √(x-2) is x < 2.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A hole in a graph refers to a point where a function is undefined or missing.

Now,

f(x) = √(x-2)

Now,

To determine where this function is undefined, we need to consider the domain of the function, which is the set of all possible values of x that can be input into the function.

Since the square root function is defined only for non-negative numbers, The expression inside √(x-2) must be greater than or equal to zero:

i.e

x - 2 ≥ 0

Solving for x.

x ≥ 2

Therefore,

The function f(x) = √(x-2) is undefined for any value of x that is less than 2.

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The complete question.

what is the hole for this equation f(x) = √(x-2)?

Answer:

24 : 8

Step-by-step explanation:

24/4 is equal to 6

8/4 is equal to 2

Answer:

24:8

Step-by-step explanation:

The easiest way to do these kinds of problems is by doing some simple division.  Usually you only need to look at the first number, which in this case is 6, and see if any numbers can be divided by this number.  The first ratio is 24:8, and since the other first number can't be divisible by 6, we know the answer is 24:8

Answer:

3.16666667

Step-by-step explanation:

convert in a calculator online

inches to feet

Step-by-step explanation:

x = number of sold sodas

y = number of sold hot dogs

x + y = 124

x = 3y

so,

3y + y = 124

4y = 124

y = 31

x = 3y = 3×31 = 93

there were 93 sodas and 31 hot dogs sold.

Answer: B. 7

The ratio of the two triangles indicates that BOY is 1/2 the size of GRL. Therefore, the ratio of the sides of the triangles is also 1:2. Since the length of BO is given as x + 3, this means that the length of GR must be 2(x + 3) - 1 = 2x + 5. Therefore, the length of GR is 7.

Answer:

5, 10 20, etc.

Step-by-step explanation:

You can skip count like you do in multiplying.

(i) 61/2000

(ii) 9/2

(iii) 261/400

Total no. of drivers = 2000

(i) exactly 3 accidents (18-29 years of age)

[ P(E)= no. of favourable outcomes/total no.of Outcomes]

P(E) = 61/2000

(ii) one or more accidents in a year (30-50 years of age )

= 125 +60 + 22 + 18

= 225

P( E) = 225/ 2000

= 9/2

(iii) having no accidents in one year

= 440 +505 +360

= 1305

P(E) = 1305/2000

=261/400

hope it helps

- Creativexcolours

Answer:

1/2

Step-by-step explanation:

The numbers are: 1, 2, 4, 5, 7, 8, 9, 10

We see that only 7, 8, 9, and 10 are greater than 5

So, 4 possible numbers are greater than 5 in the total of 8 numbers.

So, the probability is 4/8 = 1/2

So, the answer is 1/2.

The measure of angle of a, b, and c are a = 90, b = 9- and c = 60 degrees

From the question, we have the following parameters that can be used in our computation:

The figure

The angle at the circumference in a semicircle is 90°

This means that

a = b = 90 degrees

Also, we have

Angle c and angle with a measure of 60 degrees are equal

This means that

Angle c = 60 degrees

Hence, the measure of the angles are a = 90, b = 9- and c = 60 degrees

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There are 142,506 different committees of 5 students that can be selected from a group of 30 students.

The number of different committees that can be formed by selecting 5 students from a group of 30 students can be calculated using the formula for combinations, which is:

n C r = n! / r!(n - r)!

where n is the total number of items (in this case, the number of students) and r is the number of items to be selected (in this case, 5).

Substituting the values, we get:

30 C 5 = 30! / (5! * (30 - 5)!)

= (30 * 29 * 28 * 27 * 26) / (5 * 4 * 3 * 2 * 1)

= 142,506

Therefore, there are 142,506 different committees of 5 students that can be selected from a group of 30 students.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is a measure of the chance or likelihood of an event happening, expressed as a number between 0 and 1. A probability of 0 means the event will not occur, and a probability of 1 means the event will definitely occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability, and it assumes that all outcomes are equally likely.

There are also other types of probability, including empirical probability (based on observations and data), subjective probability (based on personal judgment and beliefs), and conditional probability (the probability of an event given that another event has occurred).

Probability has applications in many fields, including statistics, science, finance, and engineering. It is used to model and predict the occurrence of events, to make decisions under uncertainty, and to design systems and processes that can minimize risk and maximize the chances of success.

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(f • g)(x) = f(g(x))

         = f(x-1)

         = 2(x-1)^2

Therefore, (f • g)(3) = 2(2)^2 = 8

Answer:

(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.

Step-by-step explanation:

We have, to substitute g(x) into f(x) wherever we see x in f(x),to find (f • g)(x).

Which will give,

(f • g)(x) = f(g(x))

             = f(x-1)

             = 2(x-1)^2

We have to put x = 3 to evaluate this expression,

(f • g)(3) = 2(3-1)^2

             = 2(2)^2

             = 8

Therefore,

(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.

Answer:

X=7

Y=6

Step-by-step explanation:

Divide the 1st equation by 2.

2x+3y=32

2x-y=8

When you subtract those 2 numbers, you get that 4y=24.

Y=6

32-6*3=14=2x

X=7

The given expression is (2⋅3)2−52. Therefore, the simplified expression is 11.

To simplify this expression, we first need to apply the exponent rule, which states that (a⋅b)c = ac⋅bc. In this case, we have:

(2⋅3)2 = 22⋅32

Next, we need to simplify the exponents. We have:

22⋅32 = 4⋅9 = 36

Finally, we need to subtract 52 from 36. We have:

36−52 = 36−25 = 11

Therefore, the simplified expression is 11.

Answer: 11.

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Therefore , the solution of the given problem of probability comes out to be P(not same color) = 236/361.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

There are three cases to consider:

Case 1: both marbles are red

Case 2: both marbles are yellow

Case 3: both marbles are blue

The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):

P(red and red) = (5/19) * (5/19) = 25/361

Similarly, the probability of drawing two yellow marbles is:

P(yellow and yellow) = (6/19) * (6/19) = 36/361

And the probability of drawing two blue marbles is:

P(blue and blue) = (8/19) * (8/19) = 64/361

So, the probability of drawing two marbles that are the same color is:

P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)

P(same color) = (25/361) + (36/361) + (64/361)

P(same color) = 125/361

d. If two marbles are drawn, what's the chance they are NOT the same color?

There are three cases to consider:

Case 1: one marble is red and one marble is yellow

Case 2: one marble is red and one marble is blue

Case 3: one marble is yellow and one marble is blue

The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):

P(red and yellow) = 2 * (5/19) * (6/19) = 60/361

Similarly, the probability of drawing one red marble and one blue marble is:

P(red and blue) = 2 * (5/19) * (8/19) = 80/361

And the probability of drawing one yellow marble and one blue marble is:

P(yellow and blue) = 2 * (6/19) * (8/19) = 96/361

So, the probability of drawing two marbles that are not the same color is:

P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)

P(not same color) = (60/361) + (80/361) + (96/361)

P(not same color) = 236/361

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The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

The difference between the highest and lowest values for a given data collection is the range in statistics.

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. It indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

The range is the difference between the largest and smallest values in a data set.

For the given data, the largest value is 8 and the smallest value is 3.5.

Thus,

range = 8 - 3.5 = 4.5.

Hence, the range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

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Answer:

Step-by-step explanation:The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

Answer:

56.8 AND 33.2

Step-by-step explanation:

Complementary angles add up to 90 degrees, so we can set up the equation:

x + (x - 23.6) = 90

Simplifying the equation, we get:

2x - 23.6 = 90

Adding 23.6 to both sides, we get:

2x = 113.6

Dividing by 2, we get:

x = 56.8

So one angle measures 56.8 degrees, and its complementary angle measures:

90 - 56.8 = 33.2 degrees.

In the given question, the rocket will hit the ground in 7 seconds. The width of the rectangle is 3 cm. Kirk makes the wall in 5.5 hours. The student needs 97 marks.

The relation between the height and the time of the toy rocket has been given in the question as,

h = -4.9t²+33.6t + 4.9

where,

h= height of the rocket after getting launched

t= time after which the rocket has been launched

So, if we have to calculate how much time the rocket takes to reach the ground,

we have to take h=0 (at ground).

So, the equation becomes

0 = -4.9t²+33.6t + 4.9

Now, the roots of this equation will give the time at which the rocket will hit the ground.

So, after calculating we get

t = -0.1428 sec

or

t = 7 sec

since negative time is not possible,

the time at which the rocket will hit the ground is 7 seconds.

The length of the rectangle is = 5b-7 cm

Hence, the area is = b(5b-7) = 24

Hence, the width comes out to be = 3 cm

Kirk would be able to make the wall in 5.5 hours. This is because Jeff can make it one hour earlier than him i.e., K-1 hours. So, we get -

= (K-1) + K = 10

= 2K = 11

= K = 5.5 hours

The student already has 87 + 85 + 91 = 263 marks. He needs at least -

= (263 + x) / 4 = 90

= 97 marks

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Answer: 9. False

              10. True

              11. False

              12. False, it is called an isosceles triangle

Step-by-step explanation:

I

II

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IX

X

XI

XII

XIII

XIV

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XVI

XVII

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XIX

XX

XXI

XXII

XXIII

XXIV

XXV

XXVI

XXVII

XXVIII

XXIX

XXX

XXXI

XXXII

XXXIII

XXXIV

XXXV

XXXVI

XXXVII

XXXVIII

XXXIX

XL

XLI

XLII

XLIII

XLIV

XLV

XLVI

XLVII

XLVIII

XLIX

L

LI

LII

LIII

LIV

LV

LVI

LVII

LVIII

LIX

LX

LXI

LXII

LXIII

LXIV

LXV

LXVI

LXVII

LXVIII

LXIX

LXX

LXXI

LXXII

LXXIII

LXXIV

LXXV

LXXVI

LXXVII

LXXVIII

LXXIX

LXXX

LXXXI

LXXXII

LXXXIII

LXXXIV

LXXXV

LXXXVI

LXXXVII

LXXXVIII

LXXXIX

XC

XCI

XCII

XCIII

XCIV

XCV

XCVI

XCVII

XCVIII

XCIX

C

Therefore , the solution of the given problem of triangle comes out to be ∠ADC  = 100 and ∠DCB  = 39 Degree.

Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons. The corners of a triangle are determined by where its three sides meet. The sum of the angles inside a triangle is 180 degrees.

Here,

Given :

A triangle ADC and Triangle DCB

To find the angle :∠ADC and ∠DCB in the figure

So,

Acc to triangle angle sum property:

43 + 3y + 7 + 2x + 17 = 180

Simplifying, we get:

2x + 3y + 67 = 180

Subtracting 67 from both sides, we get:

2x + 3y = 113

and

61 + 3y - 13 + 4x - 1 = 180

4x + 3y + 47 = 180

4x + 3y = 133

2x + 3y = 113

4x + 3y = 133

-4x - 6y = -226

Adding this to the second equation, we get:

-3y = -93

Dividing both sides by -3, we get:

y = 31

Substituting this value of y into either equation, we can solve for x:

2x + 3(31) = 113

2x + 93 = 113

2x = 20

x = 10

Therefore, the solution is x = 10, y = 31.

Thus,

∠ADC  = 3(31) + 7 = 93 + 7  = 100

∠DCB = 4(10) -1 = 40 -1  =39

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The statement that "The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables" is true.

The correlation coefficient (r) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables. It ranges from -1 to +1, with a value of -1 indicating a perfect negative linear relationship, 0 indicating no linear relationship, and +1 indicating a perfect positive linear relationship. The sign of r indicates the direction of the relationship, with a negative sign indicating an inverse relationship and a positive sign indicating a direct relationship. Thus, the correlation coefficient provides a useful summary of the degree to which two variables are related in a linear fashion.

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All the angle measures are;

m∠A = 160°

m∠B  = 142°

m∠C = 120°

m∠D  = 156°

m∠E = 31°

m∠F = 111°

A hexagon is a six-sided polygon. And a convex hexagon means the hexagon's vertices are pointed outwards.

And no interior angle has an angle measuring of more than 180°.

Given:

The number of sides in the polygon = 6.

The total sum of the irregular angle = (4 - 2) x 180° = 720°.

7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720°.

28x = 720 - 48

x = 24

Substituting all the values of x = 24 to all the interior angle measures,

Now, all the measures are:

m∠A = 7x - 8 = 160°

m∠B = 4x + 46 = 142°

m∠C = 5x = 120°

m∠D = 6x + 12 = 156°

m∠E = x + 7 = 31°

m∠F = 5x - 9 = 111°

Therefore, all the measures are given above.

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The complete question is given in the image below.

The derivative of cosx is -sinx

Derivative defines the change in the dependent variable with respect to a small change in the independent variable

This means that if we have

y = cosx

where x is the independent variable and y is the independent variable, then the derivative of cosx i.e y will be the amount of change in y due to a small change in x.

i.e, dy/dx = -sinx

we also write this as

d/dx (cosx) = -sinx

This can be proved by the first principle where

[tex]f'(x) = \lim_{h \to 0} \frac{ [f(x + h) - f(x)] }{h}[/tex]

Hence we get

d/dx (cosx)

[tex]f'(x) = \lim_{h \to 0} \frac{ [cos(x + h) - cosx] }{h}[/tex]

[tex]= \lim_{h \to 0}\frac{[-2sin\frac{x+h+x}{2} sin\frac{x+h-x}{2}]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-2sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h}[/tex]

[tex]= \lim_{h \to 0}\frac{ [-sin\frac{2x+h}{2} sin\frac{h}{2} ]}{h/2}[/tex]

Now we know that [tex]\lim_{x \to0} \frac{sinx}{x} = 1[/tex]

Hence we get

-sinx

Therefore derivative of cosx = -sinx

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A number from 1 to 20 is any integer between 1 and 20, inclusive of both endpoints. A number from 1 to 20 can be any integer between 1 and 20, inclusive.

The set of numbers from 1 to 20 includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. This set of numbers is commonly used in a variety of contexts, such as in statistics, probability, and mathematics. For example, when rolling a fair six-sided die, the probability of rolling a number from 1 to 20 is 1, since there are no numbers on a six-sided die that are greater than 6.

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A statistic is a number that describes a sample, whereas a parameter is a number that describes the complete population.

To characterise the whole population under consideration, a parameter is utilised. For instance, we could be curious about a butterfly's typical length. Given that it contains data on the whole butterfly population, this qualifies as a parameter.

The most often used sample is a simple random sample. Every practicable sample of the selected size must be given an equal probability of being used. An element is a population characteristic. The statistic is a property of the sample.

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Answer:

Step-by-step explanation:

(1)To write this in standard form, we want the x and y terms on the same side of the equation and the constant on the other side. To do this, we can subtract 3x from both sides:

-3x + y = 1

So the standard form of the equation is:

-3x + y = 1

(2)y = -9/5x + 3

To write this in standard form, we want to eliminate the fraction by multiplying both sides by the denominator (5):

5y = -9x + 15

Next, we can move the x term to the left side by adding 9x to both sides:

9x + 5y = 15

So the standard form of the equation is:

9x + 5y = 15

The value of the triple integral xy dV over the solid tetrahedron with vertices (0,0,0), (9,0,0), (0,8,0), and (0,0,6) is approximately 490.5. The limits of integration for x, y, and z are 0 to 9, 0 to 8 - (8/9)x, and 0 to 6 - (1/3)x - (1/4)y, respectively.

To evaluate the triple integral, we need to set up the limits of integration for the three variables x, y, and z. Since the solid is a tetrahedron with vertices at (0,0,0), (9,0,0), (0,8,0), and (0,0,6), we can write the limits of integration as follows:

0 ≤ x ≤ 9

0 ≤ y ≤ 8 - (8/9)x

0 ≤ z ≤ 6 - (1/3)x - (1/4)y

The limits of integration for x are straightforward, as x ranges from 0 to 9. For y, we need to consider that the solid is bounded by the x-axis (y=0), the y-axis (x=0), and two planes that intersect along the line x=9, y=8. The equation of the plane containing the points (0,8,0), (9,0,0), and (0,0,6) is given by 8x/9 + 6z/9 = 8, which simplifies to y = 8 - (8/9)x - (2/3)z. Solving for z, we get z = (3/2)(4 - (3/4)x - (3/4)y), so the limits of integration for z depend on both x and y.

With these limits of integration, we can set up the triple integral as follows:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) ∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz dy dx

Evaluating the innermost integral with respect to z, we get:

∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz = xyz |z=0 to z=(6-(1/3)x-(1/4)y) = x y (6 - (1/3)x - (1/4)y)

Substituting this expression back into the triple integral and evaluating the remaining integrals, we get:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) x y (6 - (1/3)x - (1/4)y) dy dx

= ∫0⁹ x [(3/4)y²(8/9 - (1/3)x) - (1/12)y³(8/9 - (1/3)x)] |y=0 to y=(8-(8/9)x) dx

= ∫0⁹ x [(3/4)(8/9 - (1/3)x)³ - (1/12)(8/9 - (1/3)x)⁴] dx

≈ 490.5

Therefore, the value of the triple integral is approximately 490.5

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John's purchasing power increased by 0.97%.

What is the inflation?

The definition of inflation in the field of economics is "mean increased money supply, but the general public often refer to a sustained increase in the general price level of goods and services in an economy over a period".

If the inflation rate was 3% and John's salary grew 4%, his salary increased more than the rate of inflation. However, his real increase in purchasing power depends on the difference between his salary growth rate and the inflation rate.

To calculate the change in John's purchasing power, we can use the following formula:

Change in purchasing power = (1 + Salary growth rate) / (1 + Inflation rate) - 1

Plugging in the values, we get:

Change in purchasing power = (1 + 0.04) / (1 + 0.03) - 1

Change in purchasing power = 1.01 / 1.03 - 1

Change in purchasing power = 0.0097 or 0.97%

Hence, John's purchasing power increased by 0.97%.

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