Find the difference. 5 2/3 - 2 1/2 =

A 3 1/6

B 3 2/3

C 3 1/2

D 3 5/6​

The greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

To determine the vertex of the image triangle that is the greatest distance from the origin, we need to follow the given transformations step by step and find the coordinates of the image vertices.

1. Translation: The given triangle is translated 4 units left and 3 units up.

  - Vertex L' is located at (-2 - 4, 5 + 3) = (-6, 8).

  - Vertex E' is located at (1 - 4, 4 + 3) = (-3, 7).

  - Vertex D' is located at (2 - 4, -2 + 3) = (-2, 1).

2. Reflection: The translated triangle is reflected over the line y = 4.

  - The line y = 4 acts as a mirror. The y-coordinate of each vertex remains the same, but the x-coordinate is reflected.

  - Vertex L'' is located at (-(-6), 8) = (6, 8).

  - Vertex E'' is located at (-(-3), 7) = (3, 7).

  - Vertex D'' is located at (-(-2), 1) = (2, 1).

Now, we have the coordinates of the image triangle vertices: L'' (6, 8), E'' (3, 7), and D'' (2, 1).

To determine which vertex is the greatest distance from the origin (0, 0), we can calculate the distances using the distance formula:

- Distance from the origin to L'': √[(6 - 0)² + (8 - 0)²] = √(36 + 64) = √100 = 10.

- Distance from the origin to E'': √[(3 - 0)² + (7 - 0)²] = √(9 + 49) = √58.

- Distance from the origin to D'': √[(2 - 0)² + (1 - 0)²] = √(4 + 1) = √5.

Therefore, the greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

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Answer:

no solution

Step-by-step explanation:

distribute the -5 to the parenthesis

-5w + 20 < -5w - 15

move all the numbers on right and variables on left

20 + 15 < 0

35 < 0

no solution

Answer:

The answer is 3 7/12 Hope this helps :)

Step-by-step explanation:

GIVEN:

We are given a frequency distribution table showing different classes of hours of study and the frequency of each class of data.

Required;

To determine the relative frequency for the third class

Step-by-step solution;

For a relative frequyency, we need to find the number of times an event occurs and express it as a fraction of the total events that occured in the survey/experiment.

The events in this case are hours of study and the occurrence is the total frequency for all classes of hours of study.

The total frequency is;

The relative frequency for the third class therefore would be;

ANSWER:

The relative frequency of the third class therefore is

Answer:

10.4

Step-by-step explanation:

with reference angle 60

perpendicular (p)= 18

base(b)= x

tan 60 = p/b

\(\sqrt{3}\)  = 18/b

b = 10.4

Answer:

360 × 3 ÷ 8 = 135

360 - 135 = 225

Answer:

38

Step-by-step explanation:

Count the unit squares for each side, starting from the left it's 7, 10, 7, 2, 2, 6, 2, and 2

Now add them together:

7 + 10 + 7 + 2 + 2 + 6 + 2 + 2 = 17 + 9 + 8 + 4 = 26 + 12 = 38

Answer: 38 units

Step-by-step explanation: Perimeter is asking for the total length of all the sides that make up a figure. The top border is 10 units, the two outer sides are 7 each (14 in total), if you add all the downward facing edges you get another 10 units, and the two inside sides are 2 units each (4 in total).

10+14+10+4 = 38

The quotient of the \(((3x^{4}+6x^{3}+2x^{2}+9x+10))/((x+2))\) will be      \(4x^{2} -24x+39\).

What is the quotient?

When we divide a number, the result we ultimately get is the quotient. The division is a mathematical operation that involves dividing items into equal groups. It is represented by the symbol (). In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor. The statement of division, which identifies the dividend, quotient, and divisor, is shown in the accompanying figure.

\(((3x^{4}+6x^{3}+2x^{2}+9x+10))/((x+2))\)

=(\(4x^{2} -24x+39\))(x+2)/(x+2)

=\(4x^{2} -24x+39\)

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the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

13: 22 < x < 74

14: Side DF, Side DE, side EF

Step-by-step explanation:

So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.

For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.

Hope this helps!!! :)

Answer:

540

Step-by-step explanation:

Formula for calculating the sum of interior angles is ( n − 2 ) × 180

Where n = number of sides

The polygon shown has 5 sides so n = 5

To find the sum of the interior angles we simply plug in the values of n into the formula

( n − 2 ) × 180

plug in n = 5

( 5 - 2 ) × 180

Subtract 5 and 2

3 × 180

Multiply

= 540

And we are done

Answer:

-8

Step-by-step explanation:

-5x-15=25

-5x=40

x= -8

Answer:

Step-by-step explanation:

that is incorrect.

if it were to be equal, one side should equal each other when multiplied to make the ratio equal.

20-5x=40-10x (when multiplied by 2 on each side)

It CANNOT equal 50, if it were there would not be -10x

20-5x=100-25x

DIVIDE BY 2 to get 50 WOULD GIVE:

20-5x=50-17.5x

Answer:

Yes

Step-by-step explanation:

solve the equation for x , then evaluate and compare both sides

20 - 5x = 50 - 10x ( add 10x to both sides )

20 + 5x = 50 ( subtract 20 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

then

left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10

right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10

since both sides are equal then

20 - 5x = 50 - 10x is true

Answer: the answer is in the screenshot

Step-by-step explanation:

The hypotenuse of each set of legs of a right triangle are:

1. 5 and 6 => √61

2. 4 and 1 => √17

3. 2 and 5 => √29

4. 9 and 12 => 15

In a right triangle, the hypotenuse is the longest side that is opposite to the right angle. The hypotenuse can be determined by finding the square root of the sum of the other two legs.

1. √(5² + 6²) = √61

2. √(4² + 1²) = √17

3. √(2² + 5²) = √29

4. √(9² + 12²) = 15

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The moment of inertia is a measure of the resistance of an object to rotational acceleration around a particular axis.

The moment of inertia of an area is equal to the sum of the products of the areas and the squares of the distances from an axis.Reference ImageFor calculating the moment of inertia of the shaded area about the x-axis, we can consider it as a sum of smaller areas.

The moment of inertia is given by the formula;I = ∫y²dAWhere,I is the moment of inertia of the area about x-axis.y is the perpendicular distance from the centroid of the element to the x-axisdA is the area elementFor the given shaded area, the moment of inertia can be calculated by dividing it into the following areas:A1 = 59 x 73A2 = 73 x 73A3 = (109 x 59) - A1 - A2The centroid of the element is at point O.

Reference ImageThe moment of inertia of each area can be calculated as follows:I1 = (1/12) x (59 x 73³)I2 = (1/12) x (73 x 73³)I3 = (1/12) x [(109 x 59³) - A1 x (82.5)² - A2 x (36.5)²]Where I1 and I2 are the moment of inertia of area A1 and A2 about x-axis, respectively.And, I3 is the moment of inertia of area A3 about x-axis.

Now, we can calculate the total moment of inertia of the shaded area about the x-axis as follows:Ix = I1 + I2 + I3Ix = [(1/12) x (59 x 73³)] + [(1/12) x (73 x 73³)] + [(1/12) x (109 x 59³ - A1 x 82.5² - A2 x 36.5²)]Ix = 86.734 x 10^6 mm⁴

The moment of inertia of the shaded area about the x-axis is 86.734 x 10^6 mm⁴.

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Answer:

Step-by-step explanation:

Answer:

  7/9

Step-by-step explanation:

The slope of the line between two given points is found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (5 -(-2))/(3 -(-6)) = (5+2)/(3+6) = 7/9

The slope of the line is 7/9.

_____

Additional comment

The slope of a line is the same everywhere, so the slope of the segment from (x, y) to A is the same:

  (y -(-2))/(x -(-6)) = 7/9 . . . . use the slope equation

  9(y +2) = 7(x +6) . . . . . . . multiply by 9(x+6)

  9y +18 = 7x +42 . . . . . . eliminate parentheses

  7x -9y = -24 . . . . . . . subtract 9y+42

This is the standard form of the equation for the line through the two points. The slope-intercept form would be ...

  y = 7/9x +8/3

Answer:

2/7

Step-by-step explanation:

This is easy! No need to over think it btw!

1) whenever you divide by a whole number such as in this case;4. You need to put a 1 under 4... like this: 4/1 (so it can become a fraction!)

2) Use KEEP, CHANGE, FLIP when you are dividing fractions!

    8/7 --> you keep that number

    ÷ ---> × = you change the division sign into multplication sign

    4 ---> 1/4  = you put 1 over 4 and flip it which you get from 4/1  --> 1/4

3) Your would look like this....

   8/7 * 1/4 = ?

4) Muliply horizontally; 8 * 1 = 8 , 7 * 4 = 28

5) You get 8/28   Don't forget to simplify!!!

6) 8/4 / 32/4 = 2/7

ALSO, here's an example of KEEP, CHANGE, FLIP:

if any doubt leave a comment

y-intercept form of the equation 20y - 16x = 120 is y = 4x/5 + 6.

When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.

Here m is slope and c is constant.

The given equation is,

20y - 16x = 120

To find the y intercept form of the equation,

Simplify the equation,

20 y = 120 + 16x

Divide by 20 to whole the equation,

y = 120/20 + 16x/20

y = 6 + 4x / 5

y = 4x/5 + 6

The required slope intercept form of the equation is y = 4x/5 + 6.

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Answer:

Step-by-step explanation:

#61

Radius he r and height be h

\(\\ \tt\longmapsto \dfrac{v1}{v2}=\dfrac{\dfrac{1}{3}\pi r^2h}{\pi r^22h}\)

\(\\ \tt\longmapsto \dfrac{v1}{v2}=\dfrac{1/3}{2}\)

\(\\ \tt\longmapsto v1:v2=1:6\)

Cylinder has 6times more volume

#62

For cylinder

\(\\ \tt\longmapsto V=\pi r^2h=\pi 15^2(30)=225(30)\pi=6750\pi cm^3\)

For sphere

\(\\ \tt\longmapsto V=\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\pi 15^3=\dfrac{13500\pi }{3}=4500\pi cm^3\)

Answer:

#61

Radius he r and height be h

r1=r2=r
2h1=h2


Cancel πr^2




Cylinder has 6times more volume

#62

For cylinder

r=15cm
h=30cm


For sphere

r=15cm


Volume left=6750-4500=2250cm^3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

2x + x = 15

3x = 15

x = 15/3

x = 5

SC = x = 5

Answer:

  33°

Step-by-step explanation:

You want angle M in the congruent triangles XYZ and MNL with angle N marked 124° and angle X marked 33°.

The congruence statement tells you corresponding (and congruent) angle pairs are ...

  X and M (33°)

  Y and N (124°)

  L and Z

The measure of angle M is 33°.

__

Additional comment

The measures of angles L and Z are 180° -124° -33° = 23°.

Answer:

Nothing cause your an special and you should know

Step-by-step explanation:

duh

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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Answer:

t = 0.77

Step-by-step explanation:

D(t) = 50 - 23 sin(π(t + 0.23))

The value of the sine function has a maximum of -1 and a minimum of 1.

The average value of the sine function is 0.

At maximum sine value:

D(t) = 50 - 23(1) = 50 - 23 = 27

At minimum sine value:

D(t) = 50 - 23(-1) = 50 + 23 = 73

At average sine value of 0:

D(t) = 50 - 23(0) = 50 - 0 = 50

The average depth of the waves is 50 cm.

Now we need to find at what time, t, that occurs.

D(t) = 50 - 23 sin(π(t + 0.23)) = 50

50 - 23 sin(π(t + 0.23)) = 50

-23 sin(π(t + 0.23)) = 0

sin(π(t + 0.23)) = 0

The value of the sine is 0 at 0, π, 2π, ..., nπ

π(t + 0.23) = nπ

t + 0.23 = n

t = n - 0.23

n is all integers, but here we are concerned with the first occurrence after time equals zero, so we want n = 1.

t = 1 - 0.23

t = 0.77