A polygon has rotational symmetry of 22.5 degrees. How many sides does the polygon have?

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

24 birds per year for 4 years for the past 16 years would be 24 x 4 x 16 = 1,536

At least 1,536 birds

Based on the text given, the bottom of the plot is 25 meters, while the front is 18 meters.

Based on the question given, we shall assume that the bottom of the plot is given by the variable "x" meters.

Note that:

The front of the plot = 7 meters smaller than the bottom.

So the front can be represented as (x - 7) meters.

Hence the perimeter of a rectangle is calculated by:

2(x + (x - 7)) = 86

2(2x - 7) = 86

4x - 14 = 86

4x = 100

x = 25

The  bottom of the plot is 25 meters, so to get the front of the plot, we have to substitute the value of x into the expression (x - 7):

Hence:

Front = 25 - 7

          = 18 meters

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see transcribed text below

The front of a plot is 7 meters smaller than its bottom, how much are the front and bottom of the plot if its perimeter is 86 meters?

The differential equation of  the amount of a subject memorized in time t > 0 is k. a(t) + da(t)/dt = km, where k is a constant representing the rate  at which a subject is memorized.

Translate the given word problem into an algebraic expression.

Let m be the total amount of a subject to be memorized.

Let  a(t) be the amount memorized in time t > 0.

Let c(t) be the amount that is left to be memorized in time t > 0.

Then,

c(t) = m - a(t)

From the problem, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. It means:

da(t)/dt = k. c(t),  where k is a constant

da(t)/dt = k. (m - a(t))

k. a(t) + da(t)/dt = km

Hence, the differential equation is k. a(t) + da(t)/dt = km

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Answer:

x < 63

Step-by-step explanation:

The equation about the two angles must be true is  

D) cos 36 = sin 54.

What is complementary angles?

We know that when sum of two angles is add upto 90° then that is called as complementary angles and the equation must be cos A = sin B.

Then, \(\angle A+\angle B=90\textdegree\)

Now solving the options then,

A) 54°+54°=108°≠90°

Then the equation is false.

B) Here sin 36=sin 54 is not correct equation.

C) 36°+36°=72°≠90°

Then the equation is false.

D) 36°+54° = 90°=90°

Then the equation is true.

Hence the equation about the two angles must be true is  

D) cos 36 = sin 54.

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You have the following expression:

In order to express the previous number as an expression with the imaginary unit, you consider the following:

where the square root of -1 is the imaginary unit i by definition. Thus, by replacing you obtain:

Hence, the given expression in terms of the imaginary unit is :

Answer:

Step-by-step explanation:

Find the attachment in the diagram below,

In order to get the right match, we will use the conversion

180° = πrad

- For angle 315°;

If 180° = πrad

315° = a

Cross multiplying

180a = 315π rad

a = 315π rad/180

a = 63π/36 rad

a = 7π/4 rad

Hence 315° = 7π/4 rad

- For angle 80°;

If 180° = πrad

80° = b

Cross multiplying

180b = 80π rad

b = 80π rad/180

b = 8π/18 rad

b = 4π/9 rad

Hence, 80° = 4π/9 rad

- For angle 225°;

If 180° = πrad

225° = c  

Cross multiplying

180c = 225π rad

c = 225π rad/180

c = 15π/12 rad

c = 5π/4 rad

Hence, 225° = 5π/4 rad

- For angle 324°;

If 180° = πrad

324° = d

Cross multiplying

180d = 8324π rad

d = 324π rad/180

d = 27π/15 rad

d = 9π/5 rad

Hence, 324° = 9π/5 rad

Answer:

y = 300x + 100

Step-by-step explanation:

y = mx + c

the line intersects the y axis at 100, so c = 100

m = difference between y-coordinates / difference between x-coordinates

m = (400-100)/(1-0) = 300/1 = 300

y = 300x + 100

If the staysail is 10.5 feet and height is 30 feet then the area of the staysail is 157.5 feet²

To find the area of the staysail, we can use the formula for the area of a triangle:

Area of triangle = 1/2 x base x height

In this case, the base of the staysail is given as 10.5 feet and the height is given as 30 feet.

Substituting these values into the formula, we get:

Area of staysail = 1/2 x 10.5 feet x 30 feet

Simplifying the expression, we get:

Area of staysail = 0.5 x 10.5 feet x 30 feet

Area of staysail = 157.5 square feet

Therefore, the area of the staysail is 157.5 square feet. This means that if the staysail were to be laid flat, it would cover an area of 157.5 square feet.

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Answer:

  100 m²

Step-by-step explanation:

The scale factor for volume of similar figures is the cube of the scale factor for linear dimensions. The scale factor for area is the square of that linear dimension scale factor.

If the ratio of volumes is the cube of the scale factor, then the scale factor for the smaller figure in terms of the larger is ...

  \(k=\sqrt[3]{\dfrac{125\text{ m}^3}{729\text{ m}^3}}=\sqrt[3]{\dfrac{5^3}{9^3}}=\dfrac{5}{9}\)

The area of the smaller figure is found from ...

  \(\dfrac{A}{324\text{ m}^2}=\left(\dfrac{5}{9}\right)^2=\dfrac{25}{81}\\\\A=(324\text{ m}^2)\cdot\dfrac{25}{81}=\boxed{100\text{ m}^2}\)

The surface area of the smaller solid is 100 square meters.

__

Additional comment

The least surface area for a given volume is that of a sphere. The larger volume given corresponds to a sphere with a radius of about 5.583 meters. Such a sphere will have an area of about 391.7 square meters. There is no known physical object with a volume of 729 m³ that can have a surface area as little as 324 m².

Answer:

582 cm²

Step-by-step explanation:

The main vertical rectangle in the middle is 13 cm wide. Its length is

10 cm + 7 cm + 10 cm + 7 cm = 34 cm

Then each of the two rectangles on the sides is 10 cm by 7 cm.

area = 13 cm × 34 cm + 2 × 10 cm × 7 cm

area = 582 cm²

The divergence of the vector field F is positive for y > -1/3 and negative for y <  -1/3.

To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.

Here is a sample grid of points and their corresponding vectors:

(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)

(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)

(x, y) = (0, -2) -> F(0, -2) = (0, 2)

(x, y) = (1, -2) -> F(1, -2) = (0, 2)

(x, y) = (2, -2) -> F(2, -2) = (4, 2)

(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)

(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)

(x, y) = (0, -1) -> F(0, -1) = (0, 1)

(x, y) = (1, -1) -> F(1, -1) = (0, 1)

(x, y) = (2, -1) -> F(2, -1) = (2, 1)

... and so on for other values of y and for positive values of y.

To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.

F(x, y) = (xy, x + y^2)

∂F/∂x = y

∂F/∂y = 1 + 2y

divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1

Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).

For divF > 0:

If y > -1/3, then divF > 0.

For divF < 0:

If y < -1/3, then divF < 0.

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Answer:

\( \huge \boxed{ \boxed{ \sf 6\sqrt{3} \: or \: 10.4}}\)

Step-by-step explanation:

to find how far the ladder is from the foot of the wall

we will use tan function because we are given opposite and angle

we need to find adjacent

\( \quad \tan( \theta) = \dfrac{opp} {adj} \)

let adjacent be BC

\( \boxed{ \red{ \boxed{accoding \: to \: the \: question : }}}\)

\( \quad \: \tan( {60}^{ \circ} ) = \dfrac{6}{BC} \)

we will use a little bit algebra to figure out BC

\(\text{And we are done!}\)

Step-by-step explanation:

in triangle ABC

relationship between perpendicular and base is given by tan angle

tan 60=p/b

b=6/tan60=3.46m

the ladder is 3.46m from the foot of the wall.

Answer:

36 inches would be 3 feet

Step-by-step explanation:

Step-by-step explanation:

The 20° angle is equal to the angle next you friend.

since they are interior alternate angles

The height of the ballon is 600 feet

Let x be the missing distance we are looking for

so the missing distance is 1754 feet

Here I represented the situation to visualize the problem

Let h be L be the length of the ladder

so the ladder is 14 ft

Therefore , the solution of the given problem of slope comes out to be less consistent than that of the split-brain patients.

The slope of a line determines how steep it is. Equations predicated on gradients might experience gradient overflow. One can determine the slope by dividing the midpoint of the run (length difference) between two points by the rise (vertical differentiation) between the same two points. The equation of the hill type with the notation y = mx + b is used to model the fixed path problem.

Here,

Given :

A slope having search functions for the control subjects and

the split-brain patients is different because

In general, the control participants' performance was less consistent than that of the split-brain patients.

Therefore , the solution of the given problem of slope comes out to be less consistent than that of the split-brain patients.

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Answer:

Federcio's age possible values are those that are greater than 14 i.e 15, 16, 17 and so on

Step-by-step explanation:

Let Federico's age = x

Three times the difference of Federico’s age, and 4 means:

3(x - 4)

Increased by 7:

3(x - 4) + 7

Is greater than 37:

3(x - 4) + 7 > 37

Solving the inequality:

3x - 12 + 7 > 37

3x - 5 > 37

3x > 37 + 5

3x > 42

x >42/3

x > 14

Federcio's age possible values are those that are greater than 14

The distance from concord to Matthews is solved to be 14.8 miles

Information from the question include

charlotte is 7 miles south of concord

Matthews is 13 miles west of charlotte

the distance from concord to matthews = ?

The required distance is solved using using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 13² + 7²

x² = 169 + 49

x² =  218

x = √218

x = 14.7648

x = 14.8 (to 3 SF)

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The probability that a student's score is between 490 and 500 is 0 (rounded to four decimal places).

To calculate the probability that a student's score is between 490 and 500, we can use the standard normal distribution and the known standard deviation.

First, we need to convert the scores to z-scores, which represent the number of standard deviations away from the mean. We can use the formula:

z = (x - μ) / σ

Where:

x is the score

μ is the mean score of those taking the MCAT on your campus (495 in this case)

σ is the standard deviation of scores for all MCAT takers (10.8)

For 490:

z1 = (490 - 495) / 10.8 = -0.463

For 500:

z2 = (500 - 495) / 10.8 = 0.463

Now, we can use a standard normal distribution table or software to find the probabilities associated with these z-scores.

From Table A or software, the probability corresponding to z = -0.463 is approximately 0.3212, and the probability corresponding to z = 0.463 is also approximately 0.3212.

To find the probability between the scores of 490 and 500, we subtract the cumulative probability associated with z = -0.463 from the cumulative probability associated with z = 0.463:

P(490 ≤ x ≤ 500) = P(z ≤ 0.463) - P(z ≤ -0.463)

= 0.3212 - 0.3212

= 0

Therefore, the probability that a student's score is between 490 and 500 is 0 (rounded to four decimal places).

Please note that this result seems to be inconsistent with the information provided. Double-checking the calculations and assumptions or using more accurate data may be necessary.

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Answer:

5 16/ 17

17 x 5 + 16

85+16

101/17

Step-by-step explanation:

goodluck

Answer:

answer is 101/17

Answer:

(a)18

(b)1089

(c)Sunday

Step-by-step explanation:

The problem presented is an arithmetic sequence where:

We want to determine the number of Sundays in the 120 days before Christmas.

(a)In an arithmetic sequence:

\(\text{The nth term}, T_n=a+(n-1)d\\T_n \leq 120\\$Therefore:$\\1+7(n-1) \leq 120\\1+7n-7\leq 120\\7n-6\leq 120\\7n\leq 120+6\\7n\leq 126\\$Divide both sides by 7$\\n\leq 18\)

Since the result is a whole number, there are 18 Sundays in which Aldsworth advertises.

Therefore, Aldsworth advertised 18 times.

(b)Next, we want to determine the sum of the first 18 terms of the sequence

1,8,15,...

\(\text{Sum of a sequence}, S_n=\frac{n}{2}( 2a+(n-1)d)\\S_{18}=\frac{18}{2}( 2*1+(18-1)*7)\\=9(2+17*7)\\=9(2+119)\\=9*121\\S_{18}=1089\)

The sum of the numbers of days published in all the advertisements is 1089.

(c)SInce the 120th day is the 18th Sunday, Christmas is on Sunday.

Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

We conclude that there is convincing evidence to reject the null hypothesis. Therefore, the data provide convincing evidence that the distribution has changed.

Based on the given information, a chi-square goodness-of-fit test was conducted to determine whether there is convincing evidence that the distribution has changed. The test statistic is 10.13 and the p-value is 0.0175.

To interpret these results, we need to compare the p-value to a predetermined significance level (α), which is usually set at 0.05.

Step 1: Compare the p-value to the significance level
- If the p-value ≤ α, then there is convincing evidence to reject the null hypothesis (i.e., the distribution has changed).
- If the p-value > α, then there is not enough evidence to reject the null hypothesis (i.e., no convincing evidence that the distribution has changed).

In this case, the p-value (0.0175) is less than the typical significance level (0.05)

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Let x be the number of adult tickets sold and 84 - x be the number of children tickets.

105x + 60(84-x) = 7155

Once you find x (number of adult tickets), find the children tickets with 84 - x

We know that the force exerted by the fluid on the porthole is called the fluid force or hydrostatic force. The formula to find the fluid force is given as:F = pAWhere, p is the pressure exerted by the fluidA is the area of the portholeThe force and the pressure are in the direction perpendicular to the surface.

Let's first find the pressure exerted by the fluid on the porthole. The pressure of a fluid at any point is given as:P = hpg Where h is the depth of the point from the surface p is the weight-density of the fluid.The weight-density of seawater is 64 pounds per cubic foot.The depth of the center of the porthole is 13 feet below the surface.Therefore, the pressure exerted by the seawater on the porthole is:

P = hpg= 13 × 64

= 832 pounds per square foot

let's find the fluid force on the porthole.The area of the porthole is 1 square foot.The pressure on the porthole is 832 pounds per square foot.Therefore, the fluid force on the porthole is:F = pA= 832 × 1= 832 pounds Therefore, the fluid force on the porthole is 832 pounds.

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The probability that the player would miss 7 or more shots is given as follows: 17%.

As the probability is greater than 5%, it would not be a surprise.

The binomial distribution formula gives the probability of obtaining a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant throughout the trials.

The mass probability formula is given by the equation presented as follows:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters, along with their meaning, are listed as follows:

The parameter values for this problem are given as follows:

n = 10, p = 0.5.

Hence the probability of 7 or more misses is given as follows:

P(X >= 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

Using a calculator, with the given parameters, the probability is given as follows:

P(X >= 7) = 0.17 = 17%.

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Translations, reflections, and rotations produce a figure that is congruent to the original figure.

When we perform translations, reflections, and rotations on a figure, the resulting figure maintains the same size, shape, and orientation as the original figure. In other words, the transformed figure is congruent to the original figure.

Here's a brief explanation of each transformation:

1. Translations: A translation involves sliding a figure in a particular direction without changing its orientation or shape. Every point of the figure moves the same distance and direction. The resulting figure is congruent to the original because all corresponding sides and angles remain the same length and measure.

2. Reflections: A reflection involves flipping a figure over a line, called the line of reflection. Each point of the figure is mirrored across the line, creating a symmetrical image. The resulting figure is congruent to the original because the distance between corresponding points remains the same, and the angles formed between intersecting lines are preserved.

3. Rotations: A rotation involves turning a figure around a fixed point, known as the center of rotation. The figure is rotated by a specific angle in a clockwise or counter clockwise direction. The resulting figure is congruent to the original because all corresponding angles and side lengths remain unchanged.

In each of these transformations, the congruency of the resulting figure to the original figure is a fundamental property. Congruent figures have the same shape and size, even though they may be positioned differently in space. This property allows us to apply the concept of congruence in geometry to establish relationships, prove theorems, and solve geometric problems.

Therefore, when we perform translations, reflections, and rotations on a figure, we produce a transformed figure that is congruent to the original figure.

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Answer:

h

Step-by-step explanation: