The outer door of an airplane hangar is in the shape of a parabola. The door is 120 feet wide and 90 feet high. (i)Find the equation describing the door’s shape. (3) (ii)If you are 6 feet tall, how far must you stand from the edge of the door to keep from hitting your head? (2)

Answer: 3.5

Step-by-step explanation:

Graphing calculator

You can also solve for the vertex by doing -b/2a (x value of vertex) and then plug that in for t to get the y value.

Answer:

If Lin's father has an 18% tip for the meal, he will need to pay an additional 0.18 x 23.89 = 4.3 dollars as a tip. This brings the total cost of the meal to 23.89 + 4.3 = 28.19 dollars.

Next, a 7% sales tax is applied to the total cost of the meal, which is 28.19 dollars. The amount of sales tax will be 0.07 x 28.19 = 1.97 dollars.

Therefore, the total amount that Lin's father will pay for the meal including the tip and sales tax is 28.19 + 1.97 = 30.16 dollars.

Step-by-step explanation:

The answer is: B, D, and E. The other scenarios do not involve paired samples, so a paired-test for means is not appropriate.

In statistics, the mean (or arithmetic mean) is a measure of central tendency of a set of numerical data. It is the sum of all the values in the data set divided by the total number of values.

In scenario B, the paired samples are the healthy patients and patients with cancer, and we want to test if there is a difference in the mean number of CD4 T cells between these two groups.

In scenario D, the paired samples are husbands and wives, and we want to test if there is a difference in their mean annual income.

In scenario E, the paired samples are the same patients before and after surgery, and we want to test if there is a difference in the mean number of antibodies before and after surgery.

Therefore, the answer is: B, D, and E. The other scenarios do not involve paired samples, so a paired-test for means is not appropriate.

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The Pigeonhole Principle is a counting principle that states that if n items are put into m containers, with n > m, then at least one container should give  more than one item.

This principle is often used in counting problems to find the minimum number of items or containers needed to guarantee a certain outcome.

1. The smallest number of people in a group needed to guarantee that at least two were born in the same month is 13. This is because there are 12 months in a year, so if there are 12 people in the group, it is possible that each person was born in a different month. However, if there are 13 people in the group, by the Pigeonhole Principle, at least two people must have been born in the same month.

2. The smallest number of people are  needed to guarantee that at least two have the same first and last initials is 53. There are 26 letters in the given alphabet, so there are

possible two-letter combinations for initials. If there are 52 people in the group, it is possible that each person has a unique pair of initials. However, if there are 53 people in the group, at least two people must have the same initials by the Pigeonhole Principle.

3. The smallest number of people in a group needed to guarantee that at least two have the same first initial and were born on the same day of the week is 8. There are 7 days in a week, so if there are 7 people in the group, it is possible that each person was born on a different day of the week with a different first initial. However, if there are 8 people in the group, by the Pigeonhole Principle, at least two people must have been born on the same day of the week with the same first initial.

4. The smallest number of people in a group needed to guarantee that at least two were born on the same day of the year, assuming that nobody in the group was born on February 29 in a leap year, is 367. There are 366 possible days of the year (excluding February 29), so if there are 366 people in the group, it is possible that each person was born on a different day of the year. However, if there are 367 people in the group, by the Pigeonhole Principle, at least two people must have been born on the same day of the year.

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Answer: 113.09734

Step-by-step explanation:

Using a system of equations, the cost per pound of strawberries is $6.06.

A system of equations is two or more equations solved simultaneously.

A system of equations is also called simultaneous equations because they are solved concurrently or at the same time.

                 Strawberries     Blueberries   Total Cost

Reed picked    2                       1.8               $15.52

Cara picked     2.5                   2                $21.95

Let the unit cost per pound of strawberries = x

Let the unit cost per pound of blueberries = y

2x + 1.8y = 15.52 ... Equation 1

2.5x + 3.6y = 21.95 ...Equation 2

Multiply Equation 1 by 2:

4x + 3.6y = 31.04  ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 3.6y = 31.04

-

2.5x + 3.6y = 21.95

1.5x = 9.09

x = 6.06

= $6.06

Substitute x = 6.06 in either Equation 1 or 2:

2.5x + 3.6y = 21.95

2.5(6.06) + 3.6y = 21.95

15.15 + 3.6y = 21.95

3.6y = 6.8

y = 1.89

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Cara picked 2.5 pounds of strawberries and 2 pounds of blueberries and paid $21.95.

Answer:

x = 9

Step-by-step explanation:

AD is an angle bisector and divides the side opposite ∠ A into segments that are proportional to the other two sides , that is

[tex]\frac{CD}{BD}[/tex] = [tex]\frac{AC}{AB}[/tex] ( substitute values )

[tex]\frac{x}{6}[/tex] = [tex]\frac{18}{12}[/tex] ( cross- multiply )

12x = 6 × 18 = 108 ( divide both sides by 12 )

x = 9

(a) Desipramine appears to be the most effective treatment for cocaine addiction among the three treatments compared, with a success rate of 58.3%. Lithium has a success rate of 25.0% and Placebo has a success rate of 16.7%.

b) A two-way table that shows the relationship between treatment and success in staying off cocaine has constructed

(a) The effectiveness of the three treatments can be compared by looking at the percentage of subjects who succeeded in staying off cocaine during the study. From the given data, it can be observed that the highest percentage of success was in the Desipramine group (58.3%), followed by the Lithium group (25.0%) and the Placebo group (16.7%). Therefore, Desipramine appears to be the most effective treatment for cocaine addiction among the three treatments compared.

(b) The two-way table showing the relationship between treatment and success in staying off cocaine can be constructed as follows

The table shows the number of subjects in each treatment group who succeeded or failed in staying off cocaine during the study. It also shows the total number of subjects in each treatment group.

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The domain of the inverse function f⁻¹⁽ˣ⁾ is (-2, 5), and the range is [3, 4).

The domain refers to the set of input values for which a function is defined. For example, the domain of the function f(x) = √(x) is all non-negative real numbers, because the square root function is only defined for non-negative inputs.

The range refers to the set of output values that a function can produce, given its domain of input values. In other words, it represents the set of possible values that a function can output.

In the given question,

Since f(x) is a one-to-one function, it has an inverse function f⁽⁻¹⁾⁽ˣ⁾, which can be found by switching the roles of x and y and solving for y.

To find the domain and range of the inverse function f⁽⁻¹⁾⁽ˣ⁾, we can use the fact that the domain of f(x) is equal to the range of f^⁽⁻¹⁾⁽ˣ⁾, and the range of f(x) is equal to the domain of f⁽⁻¹⁾⁽ˣ⁾.

So, we have:

Domain of f(x) = [3, 4)

Range of f(x) = (-2, 5)

Range of f⁽⁻¹⁾⁽ˣ⁾ = Domain of f(x) = [3, 4)

Domain of f⁽⁻¹⁾⁽ˣ⁾ = Range of f(x) = (-2, 5)

Therefore, the domain of the inverse function f⁽⁻¹⁾⁽ˣ⁾ is (-2, 5), and the range is [3, 4).

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The height of the can is 0.238 inches.

What is the volume of cylinder?

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.

Here, we have

Given: Aiden models a can of ground coffee as a right cylinder. He measures its radius as 3 4/3 ​ in and its volume as 12 cubic inches.

We have to find the height of the can.

the volume of the can of ground coffee = πr²h

12 = 3.14×(12/3)²h

12/50.24 = h

h = 0.238inches.

Hence, the height of the can is 0.238 inches.

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Answer:

d. 2,500

Step-by-step explanation:

The conversion formula to convert kg to g is multiply the mass value by 1000

We just multiply 2.5 by 1000

[tex]2.5\times 1000=2500[/tex]

D is correct

Step-by-step explanation:

Sol'n,

Here,

We can see that the Marked Price is Rs.80

a discount of x percent is added such that the new price i.e. SP with discount becomes about Rs.60

Now,

We know that,

Discount Percentage = (MP-SP with discount/SP with discount)×100%

= (80-60/60)×100%

=33.33%

Hence, by this we can conclude the discount percentage to be of about 33.33%..

The inverse of a function is the relation that is formed when the function is transformed over the line [tex]y=x[/tex]

Explanation:

The inverse can be found algebraically by switching x for y and y for x in the equation. You must then isolate y.

[tex]f(x)= 5x + 10[/tex]

[tex]y= 5x + 10[/tex]

[tex]x= 5x + 10[/tex]

[tex]x-10=5y[/tex]

[tex]\dfrac{x-10}{5}=y[/tex]

So, [tex]f^{-1}(x)=\dfrac{x-10}{5}[/tex]

The simplified polynomial in standard form that represents the result of subtracting (z-7)² from 62 is -z² + 14z + 13.

Given that, ( z - 7 )² is subtracted from 62.

To subtract ( z - 7 )² from 62, we first need to first expand this ( z - 7 )².

( z - 7 )²

( z - 7 )( z - 7 )

z( z - 7 ) - 7( z - 7 )

Apply distributive property

z×z - z×7 - 7×z -7×-7

z² - 7z - 7z + 49

z² - 14z + 49

Now, we can substitute this expression into the original equation:

62 - (z² - 14z + 49)

Simplifying, we get:

13 + 14z - z²

-z² + 14z + 13

Therefore, the simplified polynomial is -z² + 14z + 13.

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If we substitute pi as 3.14 we would be doing -

56.52 / 3.14 = 18

18 / 2 = 9.

So the circle's radius would be 9.

BUT if you want it with PI. . .

The answer would be 8.995437385

Answer:

254.19

Step-by-step explanation:

nswer:

Step-by-step explanation:

Step-by-step explanation:

We can use the FOIL method to find the product of (4x − 3)(x + 2):

(4x − 3)(x + 2) = 4x(x) + 4x(2) - 3(x) - 3(2)

= 4x^2 + 8x - 3x - 6

= 4x^2 + 5x - 6

Therefore, the product of (4x − 3)(x + 2) is 4x^2 + 5x − 6. Answer: (A)

Step-by-step explanation:

(4x-3)(x+2)

4x*x,4x*2,-3*x,-3*2

4x2+8x-3x,-6

4x2(8x-3x)-6

4x2+5x-6

so the answer is A

14 - 9x ≥ 50

-9x ≥ 50 - 14

-9x ≥ 36

x ≤ -4

Therefore, the solution to the inequality is x ≤ -4.

Answer:

15,75

Step-by-step explanation:

[tex]4 \frac{2}{3} \times 1 \frac{1}{2} \times 2 \frac{1}{4} = \frac{14}{3} \times \frac{3}{2} \times \frac{9}{4} = \frac{14}{2} \times \frac{9}{4} = \frac{7}{2} \times \frac{9}{2} = \frac{63}{4} = 15 \frac{3}{4} = 15.75[/tex]

Answer:80384

Step-by-step explanation: Uh you multiply the radius squared to get the answer:)

Answer:

First, we need to convert the length of the leather cord to inches because the length of the necklace is given in inches.

3 yards = 3 x 3 = 9 feet (since there are 3 feet in a yard)

9 feet = 9 x 12 = 108 inches (since there are 12 inches in a foot)

Now we can divide the length of the leather cord by the length of each necklace:

108 inches ÷ 28 inches = 3.857

Since we cannot make a fraction of a necklace, we round down to the nearest whole number:

3 necklaces

Therefore, Cindy can make 3 necklaces with the piece of leather cord she has.

After answering the provided question, we can conclude that Therefore, function the derivative of[tex]f(x) = x^2 at x =[/tex]1 is equal to 2.

In mathematics, a function appears to be a relationship among two the numerical sets in which each citizen of the first set (identified as the domain) corresponds to a specific member of the second set (called the range). In other words, a function collects information from one set and produces output from another. The factor x has frequently been used to represent inputs, and the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 represents a general solution whereby each value of x yields a unique value of y.

[tex]f'(x) = lim(h - > 0) [f(x + h) - f(x)] / h \\f(1) = 1 \\f(1+h) = (1+h)^2 \\f(1+h) - f(1) = (2h + h^2) \\lim(h - > 0) [2h + h^2] / h = lim(h - > 0) [2 + h] = 2 \\f'(1) = 2 \\f'(x) = lim(h - > 0) [f(x + h) - f(x)] / h\\[/tex]

[tex]f'(1) = lim(h - > 0) [f(1 + h) - f(1)] / h\\f'(1) = lim(h - > 0) [(1 + h)^2 - 1] / h\\f'(1) = lim(h - > 0) [1 + 2h + h^2 - 1] / h\\f'(1) = lim(h - > 0) [2h + h^2] / h\\f'(1) = lim(h - > 0) h(2 + h) / h\\f'(1) = lim(h - > 0) (2 + h)\\f'(1) = 2\\[/tex]

Therefore, the derivative of[tex]f(x) = x^2 at x =[/tex]1 is equal to 2.

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Answer:

This is a symmetrical shape so that means all of the sides are going to match. To find x you need to look at the opposite side of the shape and see that it’s needs to match the three. In order to do that X would need to equal two so that it would be two times two minus one which would give you the three that you need to match the other side.

Answer:

249.60

Step-by-step explanation:

there 4 triangles

bh1/2

(12)(10.4)1/2= 62.4 (one triangle)

62.4(4)=249.60 (all 4)

Answer:

249.6 cm

Step-by-step explanation:

Ok so the formula for a triangle is (base*height)1/2

Base: 12

Height = 10.4

12 * 10.4 * 1/2 = 62.4

We have 4 triangles

62.4 * 4 = 249.6

As a result, the inn hosted480 visitors in July.

Vertex: What is it?

A vertex is a location in geometry where two or more curves, lines, or edges converge. It is also referred to as the intersection of an object's edges, faces, or facets to form a corner point of a polygon, polyhedron, or other higher-dimensional polytope. Each of the three corners of a triangle, for instance, is a vertex.

x = -b / 2a

where -10 a and 120 b. By replacing these values, we obtain:

x = -120 / 2(-10) = 6

Let the people stayed be x

Because of this, July is the month with the most guests at the inn (6 months after January).

We may change x = 6 into N(x) to get the number of visitors who stayed at the inn during that month:

We must determine the highest value of N in order to determine the month when the inn had the most guests (x).

N(x) = -10x² + 120x + 120

N(6) = -10(6)² + 120(6) + 120 guests.

N(6) = -360 + 720 + 120

N (6) = 360+120

inn hosted 480visitors

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The total amount the electrician will need in retirement savings to meet their retirement income goal is option D,  $1,560,000.

The electrician wants to have an annual retirement income of 80% of their current annual gross wage, which is $78,000. So, the retirement income goal is the following, per year:

0.8 x $78,000 = $62,400  

The electrician plans to draw 4% of their retirement savings in the first year. So, the total amount the electrician needs in retirement savings is as follows:

$62,400 / 0.04 = $1,560,000.

Therefore, the answer is option D $1,560,000. We can conclude we have correctly answered this question.

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Answer:

Step-by-step explanation:

What is a rectangular prism?

A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prism is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.

The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.

How do I find the volume of a rectangular prism?

The rectangular prism volume formula is:

volume = h × w × l,

where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:

Find the box length. For example, it can be equal to 18 in.

Determine its width. Let's say you measured 12 in.

Find out the rectangular prism height. Assume it's 15 in.

Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.

How do I find the area of a rectangular prism?

The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:

surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),

where h is prism height, w is its width, and l is its length.

Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:

Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².

Or save yourself some time and use our rectangular prism calculator.

Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.

How do I calculate the diagonal of a rectangular prism?

To detewrmine the diagonal of a rectangular prism, apply the formula:

diagonal = √(l² + h² + w²)

where h is prism height, w is its width, and l is its length.

Answer:

A=b×h

A=3x5

A=15

ggggggggggg

Max's plan gives a larger revenue, so it is the better plan.

We know that they have a total of 360 tangerines, Holly says that they should put 24 tangerines in each bag and sell each bag for $1.50

If they put 24 per bag, the number of bags will be given by the quotient:

360/24 = 15

And if they sell each bag for $1.50, the revenue is:

R = 15*$1.50 = $22.50

Max says that is better to divide the tangerines in 24 bags and sell each for $1.50, so there are more bags, this time the revenue is:

R = 24*$1.50 = $36.

We can see that with Max's plan the revenue is larger.

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