Two similar trapezoids have areas of 384 cm² and 24 cm². What is their ratio of similarity?

1:2

1:4

2:1

4:1

Answer:

The graph of the given equation is letter A.

Step-by-step explanation:

I used the geogebra application to plot the graph of the equation.

You input the formula and the app will show you its graph.

Answer:

1 inch : 6.4 feet

Step-by-step explanation:

Since the wall is 51.2 feet tall, and then wall on the blueprint is 8 inches long, we can make a scale. So 8 in: 51.2 ft or 1 inch: 6.4 feet.

Answer is

1 inch:6.4 feet

From the equation, you can see that each value in the equation is multiplied (x - 2)

To get it into factored form, you can just factor out (x - 2) from the equation, and you would be left with:

x²(x - 2) - 3(x - 2)

(x - 2)(x² - 3)      Your answer is A

Answer:

Third option.

Step-by-step explanation:

You need to remember that the formula used to calculate the arc lenght is:

[tex]arc\ length=r C[/tex]

Where "r" is the radius and "C" is the central angle in radians.

You need to solve for "C":

[tex]C=\frac{arc\ length}{r}[/tex]

You know the radius and the arc lenght, therefore, you can substitute values to calculate the central angle in radians. Therefore, this is:

[tex]C=\frac{8.0cm}{6.0cm}[/tex]

[tex]C=\frac{4}{3}radians[/tex]

To determine the shipping cost of a 2-pound package, convert the weight to ounces (32 ounces), account for the initial charge for the first 3 ounces (1.95), and add the cost for the remaining 29 ounces at 0.17 each, totaling 6.88.

To calculate the cost of shipping a 2-pound package, we use the given postal rates. Since there are 16 ounces in 1 pound, a 2-pound package equals 32 ounces. The post office charges 1.95 for the first 3 ounces. Every additional ounce costs 0.17. So we subtract the first 3 ounces from the total weight and then calculate the cost for the remaining ounces.

The calculation can be done as follows:

This approach to calculating postage makes it easy to understand the incremental cost structure of shipping packages.

the answer is 256π option B

Answer:

[tex]V = 256\pi \, u^{3}[/tex]

Step-by-step explanation:

The volume of the cylinder is determined by the following formula:

[tex]V = \pi\cdot r^{2}\cdot h[/tex]

Where:

[tex]r[/tex] - Radius of the cylinder's base.

[tex]h[/tex] - Height of the cylinder.

The volume of the cylinder is:

[tex]V = \pi \cdot (8\,u)^{2}\cdot (4\,u)[/tex]

[tex]V = 256\pi \, u^{3}[/tex]

Answer:

Step-by-step explanation:

As we move from (-2, 5) to (1, 3), x increases by 3 and y decreases by 2.

Hence, the slope of this line is m = rise / run = -2/3.

Start with the slope-intercept form y = mx + b.

Substitute 3 for y and 1 for x and -2/3 for m:

3 = (-2/3)(1) + b.

Remove fractions by mult. all three terms by 3:

9 = -2 + b, so b = 11, and y = (-2/3)x + 11

Again, mult. all three terms by 3:

3y = -2x + 33, or, in standard form,

Answer:

[tex]18.98\°[/tex]

Step-by-step explanation:

Let

x-----> the angle of depression

we know that

The sine of angle x is equal to divide the altitude (opposite side to angle x) by the distance from the runway (hypotenuse)

[tex]sin(x)=\frac{2.7}{8.3}[/tex]

[tex]x=arcsin(\frac{2.7}{8.3})=18.98\°[/tex]

Answer:

18.02°

Step-by-step explanation:

Formula to find angle of depression is given as

tan y = opposite / adjacent

where y = angle of depression

Where opposite = height or altitude of a person or thing

adjacent = distance

In this question ,

opposite = altitude of the plane = 2.7 miles

adjacent = distance of the plane from the runaway = 8.3 miles

Angle of depression is calculated as

tan y = ( 2.7/8.3)

y = tan⁻¹ ( 2.7÷8.3)

y = 18.02°

Angle of depression that the plane must make to land safely = 18.02°

[tex]\dfrac{\partial f}{\partial x}=7+8xy^2[/tex]

[tex]\dfrac{\partial f}{\partial y}=8x^2y[/tex]

The first equation gives

[tex]f(x,y)=7x+4x^2y^2+g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]8x^2=8x^2y+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=K[/tex]

for some constant [tex]K[/tex]. So

[tex]f(x,y)=7x+4x^2y^2+K[/tex]

and by the fundamental theorem of calculus,

[tex]\displaystyle\int_C\nabla f\cdot\mathrm d\vec r=f\left(3,\frac13\right)-f(1,1)=25-11=\boxed{14}[/tex]

To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. The function f(x, y) = 0 is such that ∇f = f. To evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f.

To find a function f such that f = ∇f, we need to find a function whose gradient is equal to itself. Let's start by finding the partial derivative of f with respect to x and y. ∂f/∂x = (7 + 8y2)i + 16xyj and ∂f/∂y = 16xyi + 8x2j. Equating both partial derivatives to f gives us the following equations:

7 + 8y2 = (7 + 8y2)i + 16xyj

8x2 = 16xyi + 8x2j

Simplifying these equations, we find:

i = 0

j = 0

Therefore, the function f(x, y) = 0 is such that ∇f = f.

In order to evaluate c·f · dr along the curve c, we need to find the dot product of the tangent vector to c and the function f. The tangent vector to c is given by dr/dt = (-1/t2, 1/t3). Evaluating f at (x, y) = (1, 1/t) gives us f(1, 1/t) = (7 + 8/t2)i + 8/t2j. Taking the dot product of this with (-1/t2, 1/t3) yields:

c·f · dr = ((7 + 8/t2)(-1/t2) + 8/t2/t3)dt = (-7/t4 + 8/t2/t3)dt = (-7/t4 + 8/t5)dt.

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Answer: 4/20

Step-by-step explanation:

Option b is correct. The probability that you and your friend are both chose is 4/20.

The probability provides a means of getting an idea of likelihood of occurrence of different events resulting from a random experiment in terms of quantitative measures ranging between zero and one.

P(E) = number of favorable outcomes/Total number of outcomes

Where,

P(E) is the probability of an event.

An arrangement of objects where the order in which the objects are selected does not matter is called combination.

[tex]C_{n,k} = \frac{n!}{(n-k)!k!}[/tex]

Where,

n is total number of objects in set

[tex]C_{n, k}[/tex] is number of combinations

k is number of choosing objects from the set

According to the given question

We have

Total six people.

And,

There are total [tex]6C_{3}[/tex]  ways to choose the 3 contestants.

⇒ [tex]6C_{3} = \frac{6!}{(6-3)!3!}[/tex] = [tex]\frac{(6)(5)(4)(3!)}{(3!)(3!)}[/tex] = 20

⇒ total number of outcomes = 60

⇒ There are 20 ways to select 3 contestant among 20 people.

Now, the number of ways that, you and your friend are chosen, along with 1 person from a set of 4 is given by

[tex]C_{4,1} = \frac{4!}{1!3!}= 4[/tex]

⇒ total number of favorable outcomes = 4

Therefore,

The probability that you and your friend are both chose = [tex]\frac{4}{20}[/tex]

Hence, option b is correct.

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Answer:

3x(3x-2)(12x-5) D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

This is a game in which you figure out what the terms of the expression have in common.  Clearly, x is a common factor, as 108x³ = x(108x²), -117x² = x(117x) and 30x = x(30).  Factoring out x, we get:

x(108x² - 117x + 30).

Next, note that 3 is a factor common to 108, 117 and 30, so now we have:

x(108x² - 117x + 30) → 3x(36x² - 27x + 10).  Knowing this enables us to eliminate answers A and B, because neither has that factor 3 in it.

Now take a look at D.  This is the only answer choice that produces a '10,' which stems from multiplying -2 and -5.  So the only possible answer choice is D.

ANSWER

The length is 10 inches and the width is 24 inches

EXPLANATION

The diagonal of the rectangular painting is d=26 inches.

Let l and w be the length and width of the painting respectively.

From Pythagoras Theorem,

[tex] {l}^{2} + {w}^{2} = {26}^{2} [/tex]

[tex]{l}^{2} + {w}^{2} = 676..(1)[/tex]

Its area is 240 square inches.

This implies that,

[tex]l \times w = 240[/tex]

[tex]l = \frac{240}{w} ...(2)[/tex]

Put equation (2) into (1).

[tex]{( \frac{240}{w} )}^{2} + {w}^{2} = 676[/tex]

This implies that,

[tex] {w}^{4} - 676 {w}^{2} + 57600 = 0[/tex]

[tex]( {w}^{2} - 100)( {w}^{2} - 576) = 0[/tex]

[tex]{w}^{2} - 100 = 0 \: or \: ({w}^{2} - 576= 0[/tex]

[tex]{w}^{2} = 100 \: or \: {w}^{2} = 576[/tex]

Take positive square root to get,

[tex]{w} = 10\: or \: {w} = 24[/tex]

When w=24,

[tex]l = \frac{240}{24} = 10[/tex]

when w=10

[tex]l = \frac{240}{10} = 24[/tex]

Hence the length is 10 inches and the width is 24 inches.

The dimensions of the painting can be found by setting two equations, one for the area of the rectangle, and another based on the Pythagorean theorem, and solving for the length and the width. The key is to remember that these values must be positive, as they represent physical dimensions.

First, let's recall what we know. The area of a rectangle is given by the formula length x width = area. Here, we know that the area of the painting is 240 square inches.

Next, remembering the Pythagorean theorem, which states that for any right-angle triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides. Here, we can write the Pythagorean theorem as length² + width² = diagonal² (26 inches).

Setting up these two equations, we would solve for length and width. Keep in mind that we're seeking positive and realistic solutions, as these represent the physical dimensions of the painting.

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Answer:

Step-by-step explanation:

Answer:  The correct option is (C). 0.78125.

Step-by-step explanation:  We are given to find the 10th term of the following geometric sequence

400,  200,  100, . . . .

We know that,

the n-th term of a geometric sequence with first term a and common ration r is given by

[tex]a_n=ar^{n-1}.[/tex]

In the given sequence,

first term, a = 400

and

common ration is given by

[tex]r=\dfrac{200}{400}=\dfrac{100}{200}=~.~.~.~=0.5.[/tex]

Therefore, the 10th term of the sequence is

[tex]a_{10}= ar^{10-1}=400\times (0.5)^9=400\times0.001953125=0.78125.[/tex]

Thus, the correct option is (C). 0.78125.

The height of Blue Mountain is determined by setting up two equations based on the tangent of the observed angles of elevation from two different points and solving for the distance to the mountain. The height is then calculated using this distance and rounded to the nearest tenth.

Tony is trying to find the height of Blue Mountain using trigonometry and the angles of elevation observed from two different points. We can solve this problem using right-angled triangles and trigonometric functions (specifically tangent).

Step-by-Step Calculation

First, we use the angle from the first observation point:
tan(23°) = height / distance
Height = distance * tan(23°). We call this height 'h'.

Then, when Tony moves 210 yards closer, the distance from the mountain is 'distance - 210 yards', and we use the angle from this second point:
tan(28°) = height / (distance - 210)
Height = (distance - 210) * tan(28°). We call this height 'h' as well because the height of the mountain doesn't change.

Therefore, we have two equations:
h = distance * tan(23°)
h = (distance - 210) * tan(28°).

By equating the two expressions for 'h', we find the distance 'd':
distance * tan(23°) = (distance - 210) * tan(28°).

We can now solve for 'distance' numerically. After calculating distance, we can use it to find the actual height 'h' using the tangent function with any of the two angles.

Final Result

We round intermediate results to 3 decimal places and the final height to 1 decimal place, giving us the height of Blue Mountain.

Answer:

c=20

Step-by-step explanation:

200=10c

200/10=c

20=c

Answer:

amplitude; [tex]\frac{2}{3}[/tex]

Phase shift; [tex]\pi[/tex] units right

Period;[tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

The given function is

[tex]y=-\frac{2}{3}\cos(3t-3\pi)[/tex]

This function is of the form;

[tex]y=A\sin (Bt+C)[/tex]

The period is given by:

[tex]|A|=|-\frac{2}{3}|= \frac{2}{3}[/tex]

The period is given by:

[tex]T=\frac{2\pi}{|B|}= \frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]

The phase shift is given by;

[tex]\frac{C}{B}=\frac{-\3pi}{3}=- \pi[/tex] or [tex]\pi[/tex] units right.

Answer: Second Option

[tex]\sigma=0.760[/tex]

Step-by-step explanation:

We have the average January surface water temperatures (°C) of Lake Michigan from 2000 to 2009.

5.07, 3.57, 5.32, 3.19, 3.49, 4.25, 4.76, 5.19, 3.94, 4.34

We know that the average [tex]{\displaystyle {\overline {x}}}[/tex] of the data is:

[tex]{\displaystyle {\overline {x}}}=\frac{\sum_{i=1}^{10}x_i}{10}=4.312[/tex]

We also know that the variance [tex]\sigma^2[/tex] is equal to 0.577.

So by definition the standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=\sqrt{\sigma^2}\\\\\sigma=\sqrt{0.577}\\\\\sigma=0.760[/tex]

Answer:0.760

just right by chance

The 3rd one. The number of 8 ounce glasses of milk in 1 gallon. If you read all the options carefully you can see that there’s no way that the other options could be “normally” distributed. The only on that could be “normal” is the 3rd one. Hope I helped!

Answer:

LOLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL

Step-by-step explanation:

Answer:

Part 1) The width of the pad is [tex]1\ m[/tex]

Part 2) The solutions are

[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex]  and [tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]

Step-by-step explanation:

Part 1)

Let

x----> the width of the pad

we know that

[tex](15+2x)(18+2x)=340[/tex]

Solve for x

[tex]270+30x+36x+4x^{2} =340\\ \\4x^{2}+66x-70=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=1\ m[/tex]

see the attached figure

Part 2) we have

[tex]2x^{2} -5x-9=0[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -5x-9=0[/tex]  

so

[tex]a=2\\b=-5\\c=-9[/tex]

substitute in the formula

[tex]x=\frac{5(+/-)\sqrt{-5^{2}-4(2)(-9)}} {2(2)}[/tex]

[tex]x=\frac{5(+/-)\sqrt{97}} {4}[/tex]

[tex]x=\frac{5(+)\sqrt{97}} {4}[/tex]

[tex]x=\frac{5(-)\sqrt{97}} {4}[/tex]

Answer:

55.4 in³

Step-by-step explanation:

The volume (V) of a triangular prism is

V = area of triangular face × length

note the triangle is equilateral with area (A)

A = [tex]\frac{s^2\sqrt{3} }{4}[/tex] ( s is the length of the side )

   = [tex]\frac{16\sqrt{3} }{4}[/tex] = 4[tex]\sqrt{3}[/tex] in², hence

V = 4[tex]\sqrt{3}[/tex] × 8 = 32[tex]\sqrt{3}[/tex] ≈ 55.4 in³

Answer:the answer is 5

Answer:

answer is 5

Step-by-step explanation:

Given that the scatter plot shows the results of a survey in which 10 students were asked the number of hours they spent studying for a test and the score they earned.

The scatter plot shows

2 students got 100, 1 student between 90 and 100 and 2 students got 90.

Others got below 90

Hence no of students who scores 90 or above = 5

Answer:

A) {x | -1 < x < 7}

Step-by-step explanation:

Given in the question two inequalities,

Inequality 1

(x - 2 < 5)

 x < 5 + 2

 x < 7

x is smaller than 7

Inequality 2

(x + 7 > 6)

 x > 6 - 7

 x > -1

x is greater then -1

When (x - 2 < 5) U (x + 7 > 6).

              (x < 7)   U  (x > -1)    

                    -1 <  x  < 7

When combined, x is greater than -1 but smaller than 7

Answer:

d

Step-by-step explanation:

d is most likely

There are 3 trainers and 12 dogs. The correct answer would be an option (D).

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let's assume the number of trainers would be x and dogs would be y

As per the given information, we can write the system of equations as

x+y=15        .....(i)

2x+4y=54   .....(ii)

From equation (i),

x = 15 - y

From equation (ii), and solve for y

2(15-y)+4y=54

30-2y+4y=54

2y=24

y = 12

Substitute the value of y = 12 in equation (iii), and we get the value of x = 3

Hence, there are 3 trainers and 12 dogs.

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Answer: yes, 1 of each

You can also get a second salad or drink because of the total as shown below:

$2.49 × 2 + $.99 × 2 = $6.96

Answer:

a = 5.

Step-by-step explanation:

The graph here is a probability density graph. What will represent [tex]P(X\le a)[/tex] on the graph?

[tex]P(X\le a)[/tex] is the area

The area under the graph between 0 and 9 is a trapezoid. Consider the trapezoid in three slices from left to right:

The area of the leftmost triangle plus that of the rectangle is exactly 0.6. In other words, the area to the left of [tex]a = 5[/tex] between the graph and the x-axis is [tex]0.6[/tex]. [tex]P(X \le 5) = 0.6[/tex]. [tex]a = 5[/tex].

As a side note [tex]a = 5[/tex] shall be the only answer to this question since the area under the graph to the left of [tex]a[/tex] can only increase or stay constant but not decrease as the value of [tex]a[/tex] increases.

I think it’s 11.

A=.5bh

A=1/2x5 1/2x4

=11

Answer:

11

Step-by-step explanation:

5 liter bucket with the 3 liter bucket twice, and then use the 3 liter bucket and the 4 liter bucket twice.

Answer:

[tex]\large\boxed{C.\ (2,\ -45^o)}[/tex]

Step-by-step explanation:

Regular coordinates (x, y)

Polar coordinates (r, φ)

[tex]r=\sqrt{x^2+y^2}\\\\\psi=\arctan\frac{y}{x}[/tex]

We have the point

[tex](\sqrt2,\ -\sqrt2)[/tex]

Substitute:

[tex]r=\sqrt{(\sqrt2)^2+(-\sqrt2)^2}=\sqrt{2+2}=\sqrt4=2\\\\\psi=\arctan\left(\frac{-\sqrt2}{\sqrt2}\right)=\arctan(-1)=-45^o[/tex]

Final answer:

The rectangular coordinates (√2, -√2) are converted to polar coordinates using formulas for radius and angle, resulting in polar coordinates (2, -45°), which matches Option C.

Explanation:

The question involves converting rectangular coordinates to polar coordinates. The given rectangular coordinates are (√2, -√2). To convert these to polar coordinates, we use the formulas r = √(x² + y²) and θ = arctan(y/x). First, calculate the radius r which is √((√2)² + (-√2)²) = √(2 + 2) = √4 = 2. Next, calculate the angle θ which is arctan((-√2)/(√2)) = arctan(-1). In degrees, arctan(-1) is -45°.

However, since polar coordinates represent angles positively in a counter-clockwise direction starting from the positive x-axis, we consider the equivalent positive angle which makes θ = 315°. However, to match the provided options more closely, we note that -45° is an equivalent way of expressing the direction taking the negative angle into consideration.

The correct polar coordinates are (2, -45°), which matches Option C.