b. Find m2VBC
D
B
20x + 5
9x-2
C
18

Answer:

2y = 14 the correct answer is C

Answer:

x = - 3, x = 6

Step-by-step explanation:

x² - 3x - 18 = 0 ( add 18 to both sides )

x² - 3x = 18

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- \(\frac{3}{2}\) )x + \(\frac{9}{4}\) = 18 + \(\frac{9}{4}\)

(x - \(\frac{3}{2}\) )² = \(\frac{81}{4}\) ( take square root of both sides )

x - \(\frac{3}{2}\) = ± \(\sqrt{\frac{81}{4} }\) = ± \(\frac{9}{2}\) ( add \(\frac{3}{2}\) to both sides )

x = \(\frac{3}{2}\) ± \(\frac{9}{2}\)

Then

x = \(\frac{3}{2}\) - \(\frac{9}{2}\) = \(\frac{-6}{2}\) = - 3

x = \(\frac{3}{2}\) + \(\frac{12}{2}\) = 6

Answer:

x=3; x=-6

Step-by-step explanation:

and positve

54 people from the region will need to be selected to find one person who carries the genetic trait

47 percent of the people living in a certain region carry a certain genetic trait.

since 47% carry genetic trait

therefore 53% didn't carry genetic trait

because every time we get person not carry genetic trait but after 54 person surety carry genetic trait

people from the region will be selected at random one at a time until someone is found who carries the genetic trait.

0.47 would be your probability of randomly selecting but your'e solving geometrically so think how many trials until successful.

use u x(mean)= 1/.47 to get around 2.13

54 people from the region will need to be selected to find one person who carries the genetic trait

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Using trigonometric identity, cos(A-B) is:

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If sin A = 1/3 and A terminates in Quadrant 1. All trigonometric functions in Quadrant 1  are positive

sin A = 1/3 (sine = opposite/hypotenuse)

adjacent = √(3² - 1²)

               = √8 units

cosine = adjacent/hypotenuse. Thus,

\(cos A = \frac{\sqrt{8} }{3}\)

If cos B = 2/3 and B terminates in Quadrant 4.

opposite = √(3² - 2²)

                = √5

In  Quadrant 4, sine is negative. Thus:

\(sin B = \frac{\sqrt{5} }{3}\)

We have:

cos(A-B) = cosA CosB + sinA sinB

\(cos (A-B) = \frac{\sqrt{8} }{3} * \frac{2}{3} + \left \frac{1}{3} * \frac{\sqrt{5} }{3}\)

\(cos (A-B) = \frac{2\sqrt{8} }{9} + \left\frac{\sqrt{5} }{9}\)

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

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Answer:

4%of n=16

n=16×100/4=400

required number is 400

2×n=2×400=800 is your answer

The number is 400 and 2 times the number is 800

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be = A

Now , the equation will be

4 % of the number is 16

So ,

( 4 / 100 ) x A = 16

Multiply by 100 on both sides of the equation , we get

4A = 1600

Divide by 4 on both sides of the equation , we get

A = 400

Therefore , the value of A is 400

Now , 2 times the number will be = 2 x A

                                                       = 2 x 400

                                                       = 800

Hence , The number is 400 and 2 times the number is 800

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The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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The expression 30m × 2.01m will be 60.3m²

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression will be:

= 30m × 2.01m

= 60.3m²

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Answer: a

Step-by-step explanation:

Because i said so

Answer:

9

Step-by-step explanation:

3x+8=35

3x=27

x=9

the answer is yes they will use the same amount

Answer:

2

Step-by-step explanation:

because there are 2 x'S

Answer:

hiiii lol. so ganfNFnnq6mq6n1j

Answer:

2/15 or 0.13 repeating

Step-by-step explanation:

Answer:

1. 13/15

2. 4/13

3. 3/4

4. 1 1/18

5. 1/4

6. 3 1/6

7. 1

Step-by-step explanation:

i will use the last one as an example, first reduce, so you would find the common denominator, in this case its 6, so you simplify 6/30 to 1/5. then you have 4/5+1/5, so since u have the same denominator, you can add the two numerators above the common denominator, so it would look like 4+1/5. then add the numbers. so you are left with 5/5 which in other words is 1. i hope this helps!

answers look at the photo, hope it helps

The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

Step-by-step explanation:

Answer:

B represents area of the right triangle

Step-by-step explanation:

Given;

Area of a triangle is A = 0.5bh

where;

b is the base of the triangle

h is the height of the triangle

Given, formula for the volume of a prism is V = Bh

For a right triangle prism, the formula for the volume is, V = Bh

Where;

B is the area of the right triangle

h is the height of the prism

Therefore, B represents area of the right triangle

Answer:

-5.9,58%,23/4,5.9

Step-by-step explanation:

-5.9,5.75,5.9,0.58

Answer:

-5.9, 0.58, 5.75, 5.9

Step-by-step explanation:

Begin by writing all four numbers into the same form.  

We'll start with -5.9.

Next, 23/4 = 5 3/4 or 5.75

Next:  5.9 stays as such

Finally, 58%, a percentage, changes to 0.58

Then the four numbers are:

-5.9, 5.75, 5.9 and 0.58

-5.9 is the smallest (and is positioned furthest from the origin to the left.  

0.58 is the next smaillest; it's positive, whereas -5.9 is negative.

The next two numbers are

5.75 and

5.9

Least to greatest, we  have -5.9, 0.58, 5.75, 5.9

Answer:

let me know when theres an answer

Step-by-step explanation:

Answer:

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

Step-by-step explanation:

\(1cm = 10 millimeters \\\\1 cm = \frac{1}{100} meter\\\\1cm = \frac{1}{100000} kilometer\\\\\)

37cm = 370 millimeters

37cm = 0.37 meter

37cm = 0.00037 kilometers

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

41.2

Step-by-step explanation:

1 is in the tenths place.  Because the number the next number is a five, we must round up and 0.20 is the nearest tenth to 0.153.

The mean \(\mu\) is 2, \(E[X(X-1)]\) is 2, and \(\sigma^2\) is 2 for the given distribution.

For the given distribution \(f(x) = \frac{{x!(3-x)!}}{{3!}} \cdot \left(\frac{4}{1}\right)^x \cdot \left(\frac{4}{3}\right)^{3-x}\) with \(x=0,1,2,3\), the mean \(\mu\) is 2, \(E[X(X-1)]\) is 2, and \(\sigma^2\) is 2.

To find the mean \(\mu = E(X)\), we calculate the weighted sum of each value of \(x\) with its corresponding probability:

\(\mu = 0 \cdot f(0) + 1 \cdot f(1) + 2 \cdot f(2) + 3 \cdot f(3)\)

Simplifying the expression, we get:

\(\mu = 0 + 1 \cdot \frac{4}{3} + 2 \cdot \frac{4}{3} + 3 \cdot \frac{4}{3} = 2\)

To find \(E[X(X-1)]\), we calculate the weighted sum of each value of \(x(x-1)\) with its corresponding probability:

\(E[X(X-1)] = 0 \cdot f(0) + 1 \cdot f(1) + 2 \cdot f(2) + 3 \cdot f(3)\)

Simplifying the expression, we get:

\(E[X(X-1)] = 0 + 1 \cdot \frac{4}{3} + 2 \cdot \frac{4}{3} + 3 \cdot \frac{4}{3} = 2\)

Finally, to find \(\sigma^2 = E[X(X-1)] + E(X) - \mu^2\), we substitute the previously calculated values:

\(\sigma^2 = 2 + 2 - 2^2 = 2\)

Hence, the mean \(\mu\) is 2, \(E[X(X-1)]\) is 2, and \(\sigma^2\) is 2 for the given distribution.

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The ground do the ropes intersect each other is at 4 ft.

AB and ED are the poles (perfectly vertical). BE and DA are the ropes that cross at C.

F is the point directly below C on the ground (line AE), which is perfectly flat and horizontal.

The vertical poles are part of parallel lines.

As a consequence, triangles ABC and DEC have congruent angles at B and E, and at A and D (alternate interior). Of course, ABC and DEC also have congruent angles at C (vertical angles).

Triangles ABC and DEC are similar, with corresponding sides in the ratio 2:1

\(\frac{AB}{DE}= \frac{BC}{EC}= \frac{AC}{DC}= \frac{2}{1}\)

In particular,

BC = 2EC and BE = BC + EC = 2EC + EC = 3EC

Right triangles ABE and FCE, with the same angle at E, are also similar, so

\(\frac{AB}{FC}= \frac{BE}{CE}= \frac{3EC}{EC3.1}\) --> AB = 3FC --> \(FC = \frac{AB}{3}= \frac{12 ft}{3} = 4ft\)

The ropes cross 4 ft above the ground.

Hence the answer is the ground do the ropes intersect each other is at 4 ft.

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The scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2) is equal to 78√26/5

To evaluate the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), we first need to parameterize the curve c.

Let t be the parameter such that

x = -1 + 5t,

y = 3 - t,

for 0 ≤ t ≤ 1.

The length of the curve c is given by the integral ∫ c ds, which can be calculated using the formula ∫ a to b \(√(dx/dt)^2 + (dy/dt)^2\) dt. Plugging in the values from the parameterization, we get

\(∫ c ds = ∫ 0 to 1 √(5^2 + (-1)^2) dt = ∫ 0 to 1 √26 dt = √26.\)

Using the parameterization, we can now write the integral as

\(∫ c (3x y) ds = ∫ 0 to 1 (3(-1+5t)(3-t)) √(5^2 + (-1)^2) dt = 78√26/5.\)

Therefore, the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2) is equal to 78√26/5.

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The scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), is approximately equal to

22.229.

We can do this by letting x = t and y = 3 - t/2, where -1 ≤ t ≤ 4.

Then, we can find ds/dt using the formula \(ds/dt = \sqrt{(dx/dt^2 + dy/dt^2)}\), which simplifies to

\(ds/dt = \sqrt{(1 + 1/4) } = \sqrt{(5)/2} .\)

Next, we can substitute x and y in terms of t into the integrand and simplify to get:

\(3x y = 3t(3 - t/2) = 9t - (3/2)t^2\)

Now, we can evaluate the integral by integrating with respect to t from -1 to 4:

\(\int c (3x y) ds = ∫ from -1 to 4 (9t - (3/2)t^2) (\sqrt{(5)/2)}  dt\)

\(= (\sqrt{(5)/2)}  [ (9t^2/2) - (3/8)t^3 ] evaluated from -1 to 4\)

\(= (\sqrt{(5)/2)}  [ (81/2) - (243/8) - (-27/8) + (3/8) ]\)

\(= \sqrt{(5)/2)}  [ (189/8) ]\)

= 22.229
Therefore, the scalar line integral ∫ c (3x y) ds, where c is the line segment from (−1,3) to (4,2), is approximately equal to

22.229.

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To determine which independent variables are significantly related to traffic at the .05 level of significance, you would need to perform a statistical test such as regression analysis.

In a regression analysis, each independent variable is tested to see if it has a statistically significant relationship with the dependent variable (traffic in this case) at a given level of significance (in this case, 0.05).

Here are the steps to perform regression analysis and determine the significant independent variables:

1. Gather your data: Collect data on the dependent variable (traffic) and the independent variables of interest.

2. Choose a regression model: Select the appropriate regression model based on the nature of your data and research question. Common regression models include linear regression, multiple regression, logistic regression, etc.

3. Run the regression analysis: Input your data into the chosen regression model and run the analysis. The output will provide you with coefficients and p-values for each independent variable.

4. Interpret the results: Look at the p-values associated with each independent variable. The p-value represents the probability of observing a relationship as strong as the one found in the sample, assuming there is no true relationship in the population. A p-value less than the chosen level of significance (in this case, .05) indicates a significant relationship between the independent variable and the dependent variable.

5. Identify the significant independent variables: If the p-value for an independent variable is less than .05, then that independent variable is considered significantly related to traffic at the .05 level of significance.

Therefore, to determine which independent variables are significantly related to traffic at the .05 level of significance, you would need to perform a regression analysis and examine the p-values associated with each independent variable.

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Answer: Let X be the amount of money Helen had to start with.

After spending one half of her money on ice cream, she had X - X/2 = X/2 left.

After spending three eighths of her remaining money on soda, she had X/2 - 3X/8 = 5X/8 left.

Since she had $7 left, we have:

5X/8 = 7

X = 56

So, Helen had $56 to start with.

Step-by-step explanation:

Answer:

800 miles.

Step-by-step explanation:

He would travel 800 miles because 320 divided by 10 is 32. 32 multiplied by 25 is 800.

Hope this helps!