Please help both questions

Answer:

¿Por qué borraste mi comentario? ¿Es porque hablo español? Lo lamento

Step-by-step explanation:

The graph of this equation will exhibit a symmetrical heart-shaped curve.

The equation r² = 64cos(2θ) represents a polar curve.

The given equation is in the form of a polar equation, where r represents the radial distance from the origin, and θ represents the angle measured from the positive x-axis.

The equation r²= 64cos(2θ) represents a cardioid, which is a type of curve. It has a characteristic heart-shaped pattern.

The equation implies that the distance from the origin squared, represented by r, is determined by the cosine function of twice the angle, 2θ, multiplied by 64.

When plotted, the graph of this equation will exhibit a symmetrical heart-shaped curve.

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Approximately 107 people prefer taking a cab based on the given ratios.

To determine the number of people who prefer taking a cab based on the given ratios, we need to find the common ratio between the number of people who prefer buses and cabs.

The ratio of Bus to Train is given as 3:2, which means out of every 5 people, 3 prefer the bus and 2 prefer the train.Similarly, the ratio of Bus to Cab is given as 9:5, which means out of every 14 people, 9 prefer the bus and 5 prefer the cab.

Since the ratios of Bus to Train and Bus to Cab need to be consistent, we can find the common ratio by determining the least common multiple of the denominators, which is 14.

So, for every 14 people, 9 prefer the bus and 5 prefer the cab.To find the number of people who prefer the cab, we need to calculate 5/14 of the total surveyed population:

(5/14) * 300 = 107.14 (approximately)

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Answer: x = 15

Step-by-step explanation:

4x + 2x = 90 (the square in the corner indicates a 90deg angle)

6x = 90

x/6 = 90/6

x = 15

Answer:

A) Bicycle: Circumference: 188.4cm  

                   Distance of 100 Turns: 18840cm

                   Diameter: 60

B) In-line skate: Circumference: 25.12cm

                         Distance of 100 Turns: 2512cm

                          Diameter: 8

C) Skateboard: Circumference:  15.7cm

                         Distance of 100 Turns: 1570cm

                         Diameter: 5

Step-by-step explanation:

The circumference would be one turn. So, you simply multiply the circumferences by 100.

A) 188.4 x 100 = 18840

B) 25.12 x 100 = 2512

C) 15.7 x 100 = 1570

The correct option is not available among the choices provided (A. 49.4, B. 39.5, C. 55.2, D. 50.45).

To find the measure of angle A in triangle ABC using the Law of Sines, we can use the formula:

sin(A)/a = sin(B)/b = sin(C)/c

Given that a = 14, b = 17, and c = 22, we can substitute these values into the formula:

sin(A)/14 = sin(B)/17 = sin(C)/22

To find angle A, we need to solve for sin(A) and then take the inverse sine (arcsin) of that value.

First, let's find sin(B) using the given information:

sin(B)/17 = sin(A)/14

sin(B) = (17 * sin(A))/14

Next, let's find sin(C):

sin(C)/22 = sin(A)/14

sin(C) = (22 * sin(A))/14

Since the sum of angles in a triangle is 180 degrees, we can calculate angle C:

angle C = 180 - angle A - angle B

Now, we can substitute the expressions for sin(B) and sin(C) into the equation:

(22 * sin(A))/14 = (17 * sin(A))/14 + sin(B)

To solve for sin(A), we can multiply both sides of the equation by 14:

22 * sin(A) = 17 * sin(A) + 14 * sin(B)

22 * sin(A) - 17 * sin(A) = 14 * sin(B)

5 * sin(A) = 14 * sin(B)

sin(A) = (14/5) * sin(B)

Finally, we can take the inverse sine (arcsin) of sin(A) to find the measure of angle A:

A = arcsin((14/5) * sin(B))

Now, since the values of angles B and C are not provided, it is not possible to directly determine the measure of angle A using the given information.

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The sampling that would most likely introduce a sampling error is (a) Choosing the first 10 events for the sample

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

The list of options

Also, we have

Tosses = 20

From the list of options, we have

(a) Choosing the first 10 events for the sample

This techique will introduce a sampling error because the selection done by the sampling is not a random selection

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Answer:1 16

Step-by-step explanation:

Solving a quadratic equation, it is found that the largest possible value of a is of a = 5.

A quadratic equation is modeled by the following rule:

y = ax + bx + c

The solutions of the equations are the values of x for which y = 0.

For this problem, the equation is:

a² - 6a - 9 = b.

b = -9 - a, hence we replace in the equation as follows;

a² - 6a - 9 = -9 - a

a² - 5a = 0.

Traditionally, the solutions are given using Bhaskara's formula, however, since the coefficient c is zero, we can solve the equation by elimination as follows:

a² - 5a = 0.a(a - 5) = 0

Then the solutions are:

a = 0.

a - 5 = 0 -> a = 5.

5 > 0, hence the largest possible value of a is of a = 5.

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Answer:

A.) 5541.8

Step-by-step explanation:

Answer:

A. 5541.8 cm²

Step-by-step explanation:

The surface area of a sphere is given by the formula [tex]\boxed{\bold{SA = 4\pi r^2}}[/tex], where r is the radius of the sphere.

In this case, we know that the diameter ips 42 centimeters. This means that the radius is [tex]r = \frac{d}{2} = \frac{42}{2} = 21[/tex] centimeters.

Substituting this into the formula, we get:

[tex]SA = 4\pi (21)^2 = 1764\pi[/tex]

To the nearest tenth, this is 5541.8 square centimeters. Therefore, the surface area of the sphere is 5541.8 square centimeters.

Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group A are concentrated around younger ages such as 6, 8, 9, 11, and 13. In contrast, Group B exhibits a more dispersed distribution of data points across a wider range of ages, including higher ages like 19 and 21.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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The fraction of  the given expression which is 4’-4” + 6’ -2 is 114/1.

First step is to convert the measurements to a common unit.

4' = 4 x 12 = 48 inches

4" = 4 inches

6' = 6 x 12 = 72 inches

2 = 2 inches

Now let substitute the values

48 inches - 4 inches + 72 inches - 2 inches

= 114 inches

To express this as a fraction we need to find the denominator. Let's choose the common denominator of 1 inch.

So, the fraction is:

114 inches / 1 inch

= 114/1

= 114

Therefore the  fraction of 4'-4" + 6' - 2 is 114/1.

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Answer:

-18$

Step-by-step explanation:

Pepe will have a loan of 18$ since they don't have 20 dollars but Billy took it away

peep have 18dollars.

20-2

=18

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

When you deposit x dollars in Account B instead of Account A, you would earn an additional 0.045x dollars in interest per year.

We need to compare the interest earned from each account.

The interest earned for Account A with a 1.5% simple annual interest rate can be computed as follows:

Interest A = (Simple interest rate A / 100) * Principal A

The calculation of the interest earned for Account B with a simple yearly interest rate of 6% is as follows:

Interest B = (Simple interest rate B / 100) * Principal B

Subtracting the interest earned in Account A from the interest earned in Account B yields the difference in interest:

Difference in interest = Interest B - Interest A

Let's plug in the values and calculate the difference:

Difference in interest = ((6 / 100) * x) - ((1.5 / 100) * x)

= (0.06x) - (0.015x)

= 0.045x

Therefore, when you deposit x dollars in Account B instead of Account A, you would earn an additional 0.045x dollars in interest per year.

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Answer:

x = 12.1

Step-by-step explanation:

Answer8000x-10000=14200+5000x

2000x=24200

24200/2000=13.1

The length of EF is  35. 4 yd

To determine the value of the side, we need to know the different trigonometric identities.

These identities are listed as;

From the information given, we have that;

The angle, theta = 40 degrees

Hypotenuse = 55yd

Opposite side = EF

Using the sine identity, we have that;

sin 40 = EF/55

cross multiply the values

EF = 0. 6427(55)

Multiply the values

EF = 35. 4 yd

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A decrease in the term from 30 years to 20 years on any rate will give the greater reduction in total interest paid .

Given,

Circumstances on which interest will be lower .

Now,

Consider decrease in the term from 30 years to 20 years on any rate of interest .

Let us assume the principal to be $100.

Let us assume the rate of interest to be 1% .

Now for simple interest,

Firstly let time period be 30 years .

SI = P*R*T/100

SI = $100 *1*30/100

SI = $30

Secondly the time period will be 20 years

SI = P*R*T/100

SI = $100 *1*20/100

SI = $20

Hence,

The reduction in interest is 33. 33% which is highest among all the other given options .

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Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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The calculated perimeter of the triangle is 3/5

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

The side lengths: 1/5, 1/5 and 1/5

This means that the triangle is an equilateral triangle

The perimeter of an equilateral triangle is calculated as

Perimeter = 3 * side length

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

Perimeter = 3 * 1/5

Evaluate

Perimeter = 3/5

Hence, the perimeter of the triangle is 3/5

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Answer:

24

Step-by-step explanation:

i dont know if its correct

Answer:

7((x-2)(3x+4))

Step-by-step explanation:

Common factor of 7 in this quadratic formula. [tex]7(3x^2-2x-8)[/tex]; -8 * 3x^2 = -24x^2, now find factors of this product that equal to -2x when added. The factors that fit this is -6x and 4x. So, if you make a generic rectangle you can find the product.  You get 7((x-2)(3x+4))

The answer is option (B) 3/8, the probability of getting the color purple is 3/8.

To calculate the probability of getting the color purple, we need to consider the total number of colors and the number of times purple appears.

Given:

Green = 90°

Orange = 90°

Red = 45°

Purple = 135°

There are a total of 360° in a circle, representing all possible outcomes.

To calculate the probability, we divide the number of degrees for purple by the total number of degrees:

Probability of getting purple = Degrees for purple / Total degrees

Degrees for purple = 135°

Total degrees = 360°

Probability of getting purple = 135° / 360°

Simplifying the fraction:

Probability of getting purple = 3/8

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The central angle is approximately 2.357 radians.

To find the central angle, we can use the formula:

Central angle (θ) = arc length ÷ radius

Given:

Arc length (mXY) = 18 in

Radius (ZY) = 7.64 in

Plugging in the values:

Central angle (θ) = 18 in ÷ 7.64 in

Calculating the division:

θ ≈ 2.357 radians

Therefore, the central angle is approximately 2.357 radians.

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The measure is MN = 19. 05 ft

To determine the value of the variable, we have that;

The different trigonometric identities are expressed as;

From the information given, we have that;

The opposite side of the triangle is MN

The adjacent side is 11ft

Using the tangent identity;

tan θ = opposite/adjacent

substitute the values

tan 60 = MN/11

cross multiply the values, we have;

MN = 1.73(11)

MN = 19. 05 ft

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Answer:

The smallest perfect square that is exactly divisible by 10, 12, and 15 is 900.

Step-by-step explanation:

The explanation is:

A perfect square is a number that is the product of two equal integers. For example, 25 is a perfect square because it is 5 times 5.

A number that is exactly divisible by 10, 12, and 15 must have all the prime factors of these numbers in its prime factorization. The prime factors of 10 are 2 and 5, the prime factors of 12 are 2 and 3, and the prime factors of 15 are 3 and 5. Therefore, the number must have at least two 2s, one 3, and one 5 in its prime factorization.

To make the number a perfect square, each prime factor must appear an even number of times. Therefore, we need to add another 2, another 3, and another 5 to the prime factorization. The number becomes 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5, which is equal to 900.

We can check that 900 is a perfect square by finding its square root. The square root of 900 is 30, which is an integer. We can also check that it is exactly divisible by 10, 12, and 15 by dividing it by these numbers. The quotients are all integers: 90, 75, and 60 respectively.

Answer:

  x = -5

Step-by-step explanation:

You want the equation of the vertical line with x-intercept -5.

Every point on a vertical line has the same x-coordinate. The y-coordinate can be anything. The equation of such a line is ...

  x = c . . . . . . . for some constant c

When the line passes through points with an x-coordinate of -5, the constant (c) in the equation is -5.

The equation of the line is x = -5.

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