how can you Introduce and Represent a ratio

Let [tex]\vec K,\vec L,\vec M,\vec N[/tex] be vectors pointing the vertices K, L, M, and N, respectively.

The side KL is parallel to and has the same length as the vector

[tex]\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k[/tex]

Similarly, the side KN is parallel and as long as

[tex]\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath[/tex]

These vectors have magnitudes

[tex]\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5[/tex]

[tex]\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}[/tex]

and their dot product is

[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6[/tex]

The parallelogram spanned by the vectors [tex]\vec L-\vec K[/tex] and [tex]\vec N-\vec K[/tex] has area equal to the magnitude of their cross product, for which we have the identity

[tex]\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)[/tex]

where [tex]\theta[/tex] is the angle between the sides KL and KN.

From the dot product identity, we have

[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)[/tex]

Then

[tex]\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}[/tex]

Answer:

Step-by-step explanation:

height of the building

The money in dollars that must be put in this cd in order to have $5,000 in 3 years is $4,081.63

The formula for simple interest and procedure we will use to solve this exercise is:

A = P {1 + [(R/100) * T]}

Where:

Information about the problem:

Applying the simple interest formula and isolating the principal (P), we get:

A = P {1 + [(R/100) * T]}

$5,000 = P {1+[(7.5/100) * 3]}

$5,000 = P [1+(0.075*3)]

$5,000 = P (1+0.225)

$5,000 = P (1.225)

P = $5,000/ 1.225

P = $4,081.63

It is the operation in which we calculate the profit produced by a capital loaned at a given percentage.

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Answer:

278

Step-by-step explanation:

First, add 85+95=180.

Then, add 56+42=98

Add 180+98=278

A continuous variable does allow fractional amounts. a discrete variable  does not allow fractional amounts.

Which variables require boundaries, also known as real limits, in their measurement scales?

A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.

What distinguishes a ratio scale from an ordinal scale?

For continuous data, what kind of data would you use?

Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

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Answer: 71 dogs ==> 1st option

Step-by-step explanation:

c=cats. d=dogs.

2d-3=c

d+c=210

d+2d-3=210

3d-3=210

3d=213

d=71 dogs ==> 1st option

Answer:

5

Step-by-step explanation:

This uses the Pythagorean theorem ([tex]f^2 + g^{2} =h^2[/tex]).  So you would take your values 3 and 4 and plug them into the equation.  [tex]3^2+4^2=h^2[/tex].  This becomes [tex]9+16=h^2[/tex].  Simplify and this becomes [tex]25=h^2[/tex].  If you take the square root of both sides you will end with 5 = h.  Therefore your answer is 5.

Answer:

H=5

Step-by-step explanation:

Since it's a right triangle, you can use the Pythagorean Theorem which is [tex]a^2 + b^2 = c^2[/tex] or in this case: [tex]f^2 + g^2 = h^2[/tex]

Substitute 3 in for f and 4 in for g: [tex]3^2 + 4^2 = h^2[/tex]

Add 9 and 16 together, it's 25 and then find the square root of 25 and the square root of h and the answer is 5

[tex]f^2 + g^2=h^2\\3^2 + 4^2 = h^2\\9 + 16 = h^2\\25 = h^2\\\sqrt25 = \sqrt h^2\\5 = h[/tex]

GOOD LUCK! :)

Answer:

21 feet wide and 31 feet long

Step-by-step explanation:

The probability that they will have an ab/ab child is 5%

Probability is how likely an event is to happen. It is measured by the ratio of the number of good cases to the total number of cases that could happen.

ab/ab (female) x ab/ab (male)

Possible alleles: [Find the alleles of the parents first, because the rest can be mixed]

AB (parental)

ab (parental)

Ab (recombinant)

aB (recombinant)

The m.u. tells us that recombinant alleles happen 10% of the time. If a child is (Ab/ab), then (ab) would come from the father, and (Ab) would come from the mother.

Given the mother has allele ab/ab looking at probabilities there is 50%chance that the child will inherit the allele and a 10% chance for the recombination to happen.

P(ab/ab)= (50%) (10%) = 5%

hence the answer is 5%

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Given [tex]-6x-20[/tex]

Proof that it is equal to the [tex]-2x + 4(1 - 3x)[/tex] or not

[tex]-2x + 4(1 - 3x)[/tex]

Distribute

[tex]-2x+ 4-12x[/tex]

[tex]4-14x[/tex]

Not equal to the [tex]-6x-20[/tex] [tex]\neq[/tex] [tex]4-14x[/tex]

So, it is false

What is Distribute in math?

To "distribute" anything is to divide it up or to give someone a piece of it.

What does the mathematical distributive property mean then?

The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.

Distributive property: What Is It?

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.

This characteristic also holds for subtraction.

A(B-C) = AB-AC

This demonstrates that the other two operands share operand A.

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The G.C.F of the given algebraic expression is; ⁴⁹/₆a xy

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

We are given the algebraic expression;

(3 x y * 4x²y * ¹/₁ * 5x³y ^ z * 4)7a * 1/1 * 7*6

Expanding this further gives;

⁴⁹/₆a((3xy * 4x²y * 20x³y ^ z )

Now, the GCF of the terms inside the bracket would be x y. Thus, expanding the GCF  we have;

⁴⁹/₆a xy((3 * 4x * 20x²y^(z - 1))

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False, If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax.

What is parallax explain?

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Using a system of equations, the numbers of each machine made are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The factory needs to make 54 tables each day, hence:

x + y + z = 54.

The number of dining tables made per day should equal the number of coffee tables, hence:

x = y.

Then, on the first equation:

2y + z = 54.

The number of coffee tables should be three more than the number of end tables, hence:

y = z + 3.

Replacing in the equation 2y + z = 54:

2(z + 3) + z = 54

3z = 48

z = 16.

Then:

The numbers of each machine made are given as follows:

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Answer:

2,220,000 mlg

Step-by-step explanation:

This question can be solved by a simple conversion calculation. Thankfully we're converting between two units of measurement with the same base!

So First, let's convert 222 decagrams to grams, and then convert grams to milligrams.

The conversion rates we need are:

1 decagram = 10 grams

1 gram = 1000 milligrams

Now for the math!

[tex]222 dg *\frac{10g}{1dg} =2220g\\then...2220g * \frac{1000mlg}/1g\\\\\\=2,220,000 mlg[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{4}{6} + \frac{2}{4} + \frac{3}{5} = \frac{80}{120} + \frac{60}{120} + \frac{72}{120} = \frac{212}{120}[/tex]

simplest form : [tex]\frac{53}{30}[/tex]

The set of all such points is a sphere center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

what is the sphere?

The standard form of the equation of a sphere with center (a ,b ,c) and radius r is

( x -a)² + ( y-b)² + ( z - c)² = r²

We let P = ( x, y,z ) be an arbitrary point which satisfies the given conditions. Then

[tex]\sqrt{(x - 1)^{2} + ( y - 5)^{2} + (z - 3)^{2} } = 2 \sqrt({x - 6)^{2} + ( y - 2 )^{2} +( z - 3)^{2} }[/tex]

Squaring both sides of this equation and simplifying yields

( x - 1)² + ( y - 5)² + ( z -3)² = 4 [ (x - 6)² + ( y- 6 )² + ( z - 3)²

( 3x² - 46x + 143 ) + ( 3y² - 38y + 119 ) + ( 3z² - 18z + 27 ) = 0

Next, we complete the square for each variable to obtain

( x - 23/3)²  + ( y - 19/3)² + ( z - 3 )² = 332/9

Thus the set of all such points P forms a sphere, with

center c = ( 23/3 , 19/3 , 3 ) r = 2√83/9

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Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Any 1 of the following transformations will work. There are others that are also possible.

translation up 4 units, followed by rotation CCW by 90°.

rotation CCW by 90°, followed by translation left 4 units.

rotation CCW 90° about the center (-2, -2).

Step-by-step explanation:

The order of vertices ABC is clockwise, as is the order of vertices A'B'C'. Thus, if reflection is involved, there are two (or some other even number of) reflections.

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

If we rotate the final figure 90° CW, we find it ends up 4 units north of the starting position. So, another possible transformation is translation up 4 units + rotation 90° CCW.

Of course, rotation 90° CCW in either case is the same as rotation 270° CW.

_____

Answer:

Step-by-step explanation:

The orientation of line CA is to the east. The orientation of line C'A' is to the north, so the figure has been rotated 90° CCW. In general, such rotation can be accomplished by a single transformation about a suitably chosen center. Here, we're told there is a sequence of transformations involved, so a single rotation is probably not of interest.

If we rotate the figure 90° CCW, we find it ends up 4 units east of the final position. So, one possible transformation is 90° CCW + translation left 4 units.

Answer: x=4.7°

Step-by-step explanation:

[tex]m\angle PQS=119^0\\\angle PQR+\angle RQS=\angle PQS\\72^0+(10x)^0=119^0\\72^0+(10x)^0-72^0=119^0-72^0\\10(x^0)=47^0\\[/tex]

Divide both parts of the equation by 10:

[tex]x=4.7^0[/tex]

Answer:

The range = 14

Step-by-step explanation:

Definition: (range of a data set)

the range of a data set is the difference between the greatest and smallest  value.

In a box plot :

We should notice the maximum (generally located at the top right) and the minimum value (generally located at the top left)

Then we make the difference.

97.

In our case :

Max value = 24

Min value = 10

Therefore

The range = 24 - 10 = 14

Answer: 3rd down :D

Step-by-step explanation:

This is because the problem is asking for Q to be in the middle of B and N and the only answer that applys to this is 3 :D.

The expected value for your profit is 2.53.

The probability is the number that indicates the likelihood that an event will occur and is defined as the ratio of favorable outcomes to all outcomes.

Given,

You can solve for the necessary anticipated value below.

There will be 600 tickets available for purchase overall.

So,

$ 5 each and sell go tickets

one $3,000 grand prize = ( 1/600) × 3000

two $500 second prizes = (2/600) × 500

thirteen $40 third prizes = (13/600) × 40

Any discrete variable X's anticipated value is calculated as:

E(x) = ( 1/600) × 3000 + (2/600) × 500 + (13/600) × 40 + (600-1-2-13/600).0-5

E(x) = 2.53

The expected value for your profit is  2.53.

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Answer:

y= 6/5 x -5

Step-by-step explanation:

You have 2 points. (0,-5) and (5,1)

If you use the formula Y2-Y1 / X2-X1,

you will have 1 - (-5) on the numerator, which equals 6

you will have 5 - 0 in the denominator, which equals 5

6/5 is your slope, and the point on the y-intercept is what you put at the end of the equation.

The value of the expression according to the order of operations is -11. Thus option D is correct.

According to the statement

We have to find that the value of the given expression.

So, For this purpose, we know that the

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

From the given information:

The expression are :

(-2)-3-6

Now solve it with the order then

(-2)-3-6 = (-2)-3-6

(-2)-3-6 = -2-3-6

Now add the first two terms

then

(-2)-3-6 = -5-6

Now, Add next two terms

Then

(-2)-3-6 = -11.

The value becomes -11.

So, The value of the expression according to the order of operations is -11. Thus option D is correct.

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The perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

We are given the vertices:

A(-4,4), B(2,-2), and C(-4,-2).

We need to find the perimeter of ABC.

AB = √ ( 2 + 4)² + (-2 - 4)²

AB = √ 6² + 6²

AB = √72

AB = 6 √2 units

BC = √ (-4 - 2)² + ( -2 + 2)²

BC = √ 6²

BC = 6 units

AC = √ ( -4 + 4)² + (-2 - 4)²

AC = √ 6²

AC = 6 units.

Perimeter = AB + BC + AC

Perimeter = 6 √2 + 6 + 6 units

Perimeter = 12 + 6 √2 units.

Perimeter = 12 + 6(1.414) units

Perimeter = 12 + 8.848 units

Perimeter = 20.848 units

Therefore, the perimeter of ABC with vertices A(-4,4), B(2,-2), and C(-4,-2) is 20.848 units.

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I'll help with the question at the bottom of the page. The rest are unfortunately too blurry.

The x is the adjacent side to the reference angle. The 7 is the hypotenuse. The hypotenuse is always opposite the 90 degree angle.

Let's use the trig ratio cosine.

cos(angle) = adjacent/hypotenuse

cos(39) = x/7

7*cos(39) = x

x = 7*cos(39)

x = 5.44002 which is approximate

x = 5.4

Make sure your calculator is in degree mode.

Answer:

picle scoops ina lane

Step-by-step explanation:

Answer:

29.25

Step-by-step explanation:

Answer: I would say 1 gallon

Step-by-step explanation: 1 gallon because 1 gallon would be closer then a shower or a cup