What is the answer to this problem i have

Answer: 57.15[tex]\geq[/tex] 5.99x

Step-by-step explanation:

127.5-70.35[tex]\geq \\[/tex]x

57.15[tex]\geq[/tex] 5.99x

(i) The unit vector d that is perpendicular to both a and b is d = (1/|d|) *

[tex][6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]
[tex]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]

2) Value of [tex]X[/tex]

[tex]Xd|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]

It can be found by taking the cross product of a and b, and then dividing by the magnitude of the resulting vector. The cross product of a and b is given by:

[tex]d = a × b = [(3)(3) - (6x)(2-x), (6x)(4) - (2)(3), (2)(2-x) - (3)(4)]= [9 - 12x + 6x^2, 24x - 6, 4 - 2x - 12]= [6x^2 - 12x + 9, 24x - 6, -2x - 8][/tex]

The magnitude of d is given by:

[tex]|d| = √((6x^2 - 12x + 9)^2 + (24x - 6)^2 + (-2x - 8)^2)= √(36x^4 - 144x^3 + 216x^2 - 144x + 81 + 576x^2 - 288x + 36 + 4x^2 + 32x + 64)= √(36x^4 - 144x^3 + 796x^2 - 400x + 181)[/tex]

The unit vector d is then given by:

[tex]d = (1/|d|) * [6x^2 - 12x + 9, 24x - 6, -2x - 8]= [(6x^2 - 12x + 9)/|d|, (24x - 6)/|d|, (-2x - 8)/|d|][/tex]

(ii) To find the value(s) of x such that d × c has the maximum length, we can take the cross product of d and c and find the magnitude of the resulting vector. The cross product of d and c is given by:

[tex]d × c = [((24x - 6)(-7) - (-2x - 8)(3)), ((-2x - 8)(-1) - (6x^2 - 12x + 9)(-7)), ((6x^2 - 12x + 9)(3) - (24x - 6)(-1))]= [-168x + 42 + 6x + 24, 2x + 8 + 42x^2 - 84x + 63, 18x^2 - 36x + 27 + 24x - 6]= [-162x + 66, 42x^2 - 82x + 71, 18x^2 - 12x + 21][/tex]

The magnitude of d × c is given by:

[tex]|d × c| = √((-162x + 66)^2 + (42x^2 - 82x + 71)^2 + (18x^2 - 12x + 21)^2)= √(26244x^2 - 21384x + 4356 + 1764x^4 - 6964x^3 + 5988x^2 - 5834x + 5041 + 324x^4 - 432x^3 + 756x^2 - 252x + 441)= √(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848)[/tex]

To find the maximum length of d × c, we can take the derivative of |d × c| with respect to x and set it equal to 0:

[tex]d|d × c|/dx = (8032x^3 - 21384x^2 + 63976x - 22470)/√(2008x^4 - 7128x^3 + 31988x^2 - 22470x + 9848) = 0[/tex]

Solving for x gives the value(s) of x that maximize the length of d × c. This can be done using a numerical method or by finding the roots of the polynomial in the numerator.  

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Answer:

Step-by-step explanation:

OK so i'm not really good at this my self but i'll try my best to help you because I don't really do it for the points I do it because I like to help other people. OK so their blocks have a scale factor of k=4.5. OK so I don't know if this is right but what I would do is there are 8 sides to any cube and you have a scale factor of k=4.5 so I would multiply 4.5 and 8 to get a answer of 36ft.

To graph the function h(x) = (x - 5)² + 2, we can use transformations of the function f(x) = x².

A graph of a function is a visual representation of how the output of the function relates to its input.

First, we need to shift the graph of f(x) 5 units to the left, which can be done by subtracting 5 from x in the function:

h(x) = (x - 5)² + 2 = (x - 5)² + 2.

Then, we need to shift the graph of f(x) 2 units up, which can be done by adding 2 to the function: h(x) = (x - 5)² + 2.

Using a graphing tool, you can then plot the points of h(x) to graph it.

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The correct option regarding the amount of coins is given as follows:

c 4 nickels, 10 dimes, 4 quarters

The amounts are obtained by a system of equations, for which the variables are given as follows:

Amy has 18 coins consisting of nickels, dimes, and quarters, hence:

x + y + z = 18.

She has the same amount of nickels as quarters, hence:

x = z.

Thus:

2x + y = 18

y = 18 - 2x.

She has a total of $2.20 worth of coins, hence:

0.05x + 0.1y + 0.25z = 2.2

0.3x + 0.1y = 2.2

Since y = 18 - 2x, the value of x is obtained as follows:

0.3x + 0.1(18 - 2x) = 2.2

0.1x = 0.4

x = 0.4/0.1

x = 4.

Hence the remaining values are given as follows:

Meaning that option c is correct.

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As a result, the floor's perimeter in the size illustration is 38,016 inches.

The perimeter of an object is the space surrounding its border. Find the perimeter of different forms by combining the lengths of their sides.

We can start by finding the scale factor that relates the length of the actual floor to the length of the scale drawing.

The length of the actual floor is 32 feet = 384 inches (since there are 12 inches in a foot).

The length of the scale drawing is given as 16 inches.

Therefore, the scale factor is:

384 inches / 16 inches = 24

This means that one inch on the scale drawing represents 24 inches in the actual floor.

To find the perimeter of the floor in the scale drawing, we need to multiply the perimeter of the actual floor by the scale factor.

The perimeter of the actual floor is:

2(32 feet) + 2(34 feet) = 64 feet + 68 feet = 132 feet

Converting to inches, we get:

132 feet x 12 inches/foot = 1584 inches

Multiplying by the scale factor of 24, we get:

1584 inches x 24 = 38,016 inches

Therefore, the perimeter of the floor in the scale drawing is 38,016 inches.

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Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.

The degree of variation or dispersion in a set of data is measured by standard deviation. It calculates how far the data points, on average, deviate from the mean (average) of the data collection. Finding the square root of the data's variation yields the standard deviation. In statistics, the standard deviation is frequently used to characterise the distribution of data and is significant in areas like science, finance, and economics. It can be used to assess the validity of statistical data and to contrast different groups of data.

given

The following formula must be used to determine the standard deviation of attendees who would favour chicken as the main course:

σ = √(np(1-p))

When we change the numbers, we obtain:

σ = √(780 x 0.38 x 0.62) (780 x 0.38 x 0.62)

σ = √(182.616) (182.616)

σ = 13.509

Therefore, 13.509 is roughly the standard deviation of the number of attendees who would favour chicken.

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Answer:

  1/3

Step-by-step explanation:

You want the difference in medians in terms of the IQR.

The IQR is the difference of the numbers at the ends of the box.

  top distribution: IQR = 12 -6 = 6

  bottom distribution: IQR = 14 -8 = 6

The median of each distribution is the location of the line in the box.

  top distribution: median = 11

  bottom distribution: median = 9

The difference in medians is 11 -9 = 2. The ratio of that to the IQR is ...

  2/6 = 1/3

The difference in medians is 1/3 times the IQR.

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Answer:

30 baskets per minute

Step-by-step explanation:

We know

Shaq shot 420 baskets in 14 minutes.

Find his basket rate in baskets per minute.

We take

420 / 14 = 30 baskets per minute

So, the answer is 30 baskets per minute.

If a regular pentagon and a regular hexagon have the same area, then the regular pentagon will have a smaller perimeter than the regular hexagon.

This is because a regular pentagon has less sides than a regular hexagon, which means that the length of each side of the pentagon will be shorter than the length of each side of the hexagon.

The hexagon would therefore have more distance to cover and more sides to be add up before one can get to the perimeter. The pentagon has three less sides than the hexagon and so would have a smaller perimeter.

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The religious gathering has 144 more boys than girls.

First we need to find out how many people and kids are attending the event.

There were 3 kids for every 4 adults. Thus we have to divide the total gathering number by the sum of their ratios which is 4 + 3 = 7

Adult population=> (4/7) x 560 = 320

Children's number=> 560-320 = 240

We know that every 4/5 children is a boy

Thus,

Number of boys: (4/5) * 240 = 192

By deducting the number of boys from the total number of children, we can calculate the number of girls which is

240-192= 48

There are 192 boys  and 48 girls

The number of more boys than girls is -

192 - 48 = 144

Therefore, the religious gathering had 144 more boys than girls.

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The simplified expression is -12 and 5/12

In mathematics, an expression is a combination of symbols and/or numbers that can be evaluated or simplified to produce a certain value. Expressions can contain variables, constants, operators, and functions, and can be written in a variety of forms, such as algebraic expressions, trigonometric expressions, and exponential expressions.

Negative 4 and 2 over 3 can be written as -(4 x 3 + 2) / 3 = -14 / 3

7 and 3 over 4 can be written as 7 x 4 + 3 / 4 = 31 / 4

Next, you need to find a common denominator for the two fractions, which is 12. To convert -14/3 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 4, giving you -56/12. To convert 31/4 to a fraction with a denominator of 12, you need to multiply the numerator and denominator by 3, giving you 93/12.

Finally, you can subtract the two fractions by subtracting their numerators and keeping the denominator the same:

(-56/12) - (93/12) = -149/12

To convert this improper fraction back to a mixed number, you can divide the numerator by the denominator and get a quotient of -12 with a remainder of -5.

Therefore, the simplified expression is -12 and 5/12 or -12.41667 (rounded to five decimal places).

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Jolina paid 33.33% more than Kendall paid for the coat, as she paid the full price while Kendall received a 25% discount.

To calculate this, first find out how much Kendall paid after the discount. If the original price of the coat was X, then Kendall paid 0.75X, since the discount was 25%. We know that Kendall paid $100 for the coat, so we can set up the equation 0.75X = 100 and solve for X. X turns out to be $133.33.

Since Jolina paid the full price of $133.33 for the coat, the ratio of what Jolina paid to what Kendall paid is:

133.33 / 100 = 4/3 or 1.33:1

Therefore, Jolina paid 33.33% more than Kendall paid for the same coat.

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Step-by-step explanation:

red gumballs=6 blue gumballs=6

yellow gumballs=6 green gumballs=6

purple gumballs=6

total number of gumballs=30

probability of a student selecting a red gumballs

no of red gumballs 6 1

=------------------------ = ----- = -----

no of total gumballs 30 5

To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:

Step 1: Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1

Step 2: Combine like terms on both sides of the equation:
2w = -2

Step 3: Solve for w by dividing both sides of the equation by 2:
w = -1

Therefore, the solution for w is -1.

In HTML format, the answer would be:

<p>To solve the equation -3(w-1)=-5w+1 for w, we will use the following steps:</p>
<ol>
<li>Distribute the -3 on the left side of the equation:
-3w + 3 = -5w + 1</li>
<li>Combine like terms on both sides of the equation:
2w = -2</li>
<li>Solve for w by dividing both sides of the equation by 2:
w = -1</li>
</ol>
<p>Therefore, the solution for w is -1.</p>

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x1 = -2, x2 = 1, and x3 = 5.5

This system of equations can be solved by first combining the equations and then isolating one of the variables. To combine the equations, subtract the first equation from the second equation:

4x1 + 5x2 + 5x3 = 9

- (x1 + x2 + 3x3 = -4)

3x1 + 4x2 + 2x3 = 13

Next, isolate one of the variables. In this case, let's isolate x3:

3x1 + 4x2 + 2x3 = 13

- (2x3) - (-2x3) = 0

3x1 + 4x2 = 13

x3 = \frac{13 - (3x1 + 4x2)}{2}

Now that x3 has been isolated, substitute it into one of the original equations and solve for the remaining two variables:

x3 = \frac{13 - (3x1 + 4x2)}{2}

x1 + x2 + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x2:

x2 = \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4}

Substitute this expression for x2 into one of the original equations and solve for x1:

x1 + \frac{-4 - x1 - 3\left(\frac{13 - (3x1 + 4x2)}{2}\right)}{4} + 3\left(\frac{13 - (3x1 + 4x2)}{2}\right) = -4

Solve for x1 and then plug this value back into the expression for x2 to find x2:

x1 = -2

x2 = 1

x3 = \frac{13 - (-2 + 4x2)}{2}

x3 = \frac{13 - (-2 + 4 \cdot 1)}{2}

x3 = \frac{13 - 2}{2}

x3 = 5.5

Therefore, the solution to the system of equations is x1 = -2, x2 = 1, and x3 = 5.5.

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Answer:

We can use trigonometry to solve this problem.

A is the taller platform, B is the shorter platform, and x is the length of the zipline cable that we want to find.

We can see that the angle between the horizontal and the zipline cable is 12 degrees, so we can use the tangent function to find x:

Therefore, the length of the zipline cable, rounded to the nearest foot, is 209 ft.

Answer:

To solve for f in the equation:

f/3 + 22 = 17

We need to isolate f on one side of the equation. We can start by subtracting 22 from both sides:

f/3 = 17 - 22

Simplifying the right-hand side:

f/3 = -5

To isolate f, we can multiply both sides by 3:

f = -5 * 3

Simplifying:

f = -15

Therefore, the solution to the equation f/3 + 22 = 17 is f = -15.

Answer:

2*(8*8*3+15*15*3)

Step-by-step explanation:

Small cube V=8*8*3

Large cube V=15*15*3

Doubled height is double of each cube V

so 2*[(8*8*3)+(15*15*3)]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{3.8\% of 25}}{\left( \cfrac{3.8}{100} \right)25}\implies \text{\LARGE 0.95}[/tex]

Answer:

To find 3.8% of 25, we can convert the percentage to a decimal and then multiply it by 25:

3.8% = 0.038 (converting percentage to decimal)

0.038 x 25 = 0.95

Therefore, 3.8% of 25 is 0.95.

Answer: X=10

m<UXV = 46 degrees

Step-by-step explanation:

Angle WXV is 90 degrees, We know this because Angle VXY is 90 degrees, so it is the same on the other side Angle WXV is split into two angles  (WXU, and UXV) to find UXV we subtract 44 from 90, which is 46 Degrees, Now we know 5x-4 is equal to 46, 46+4 is 50, 50/5 is 10, so x is 10

The value of x is, 10

And, The value of angle ∠ UXV is, 46°

Given that;

Angle 44° and ∠ UVX is made a right angle.

Hence, We can formulate;

⇒ 44° + ∠ UVX = 90°

⇒ 44° + (5x - 4)° = 90°

⇒ 44 + 5x - 4 = 90

⇒ 5x + 40 = 90

⇒ 5x = 90 - 40

⇒ 5x = 50

⇒ x = 10

Hence, The value of angle ∠ UXV is,

⇒ ∠ UXV = 5x - 4

               = 5 × 10 - 4

              = 50 - 4

              = 46°

Thus, The value of x is, 10

And, The value of angle ∠ UXV is, 46°

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The number of comic books is given as follows:

P/100 x 560.

In which P is the percentage equivalent to comic books on the circle graph.

The number comic books sold at the book fair is given by the proportions in the context of the problem.

The circle graph gives the percentage out of each type of book, hence the percentage of comic books is given as follows:

P/100.

Then the amount of comic books is obtained multiplying the percentage by the total amount of 560 as follows:

P/100 x 560.

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There is only one solution when you solve the system of equations 2x+y=7 and y=-2x+7. The one solutions is (2, 3).

To find the solution, you can use the substitution method. This involves solving one equation for one variable and then substituting that expression into the other equation.

First, solve the second equation for y:
y = -2x + 7

Now, substitute this expression for y into the first equation:
2x + (-2x + 7) = 7

Simplify the equation:
2x - 2x + 7 = 7

Combine like terms:
7 = 7

This equation is always true, which means that there is only one solution for this system of equations. The solution is the point where the two lines intersect, which is (2, 3).

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Answer:

x^2 + 10x + 20

Step-by-step explanation: When you multiply binomials, you are practically taking each term and multiplying it with others until you are out of combinations. However, when the product is represented in standard form, it requires the terms to be set within a specific order that prompts the term at the highest order/power placed on the furthest left side of the expression. The first term x^2 can be referred to as a term of the second power, 10x is seen as one to the first power (x^1 = 1st), and 20 as 0, since it is a constant.

Answer: x⁴ - 9y²

Step-by-step explanation:

The area of a rectangle is length x width so...

Area = (x² + 3y)(x² - 3y)

Simplify:

Area = x⁴ + 3yx² - 3yx² - 9y²

Area = x⁴ - 9y²

Hope this helps!

The equation can be written as: x + 24° = 90°.

The measure of the unknown angle is 66°.

An algebraic equation is an equation that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

Let the measure of the unknown angle be x.

Since the angle in the corner measures 90° and one piece of the tile will have a measure of 24°. We can write the equation as:

x + 24° = 90°

The measure of the unknown angle can be determined as follow:

​x + 24° = 90°

x = 90° - 24°

x = 66°

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Answer:

8358 cubic ft

Step-by-step explanation:

The amount of water each beaker would hold is x/8

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

Number of beakers = 8

Represent the size with x

So, we have the following quotient expression

Size of each beaker = x/Number of beakers

Substitute the known values in the above equation, so, we have the following representation

Size of each beaker = x/8

Hence, the amount is x/8

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