13. Lindsay was going to visit her grandmother, shop at the mall, and then return home. The route she took was in the shape of a triangle. The distance between each place she visited was 10 miles. What type of triangle is formed by the route she traveled? Explain. answer please answer that question ​

The required exact value of cos(-10π/3) or cos(2π/3) is -1/2.

To find the exact value of the expression cos(-10π/3), we can use the periodicity and symmetry properties of the cosine function.

In this case, we have cos(-10π/3). Since -10π/3 is equivalent to 2π/3 radians (because it completes a full revolution plus an additional 2π), we can rewrite the expression as cos(2π/3).

Now, let's find the exact value of cos(2π/3).

In the unit circle, an angle of 2π/3 (or 120 degrees) is located in the second quadrant. In the second quadrant, the x-coordinate is negative.

Since the cosine function gives the x-coordinate of a point on the unit circle, we can conclude that cos(2π/3) is negative.

Therefore, the exact value of cos(-10π/3) or cos(2π/3) is -1/2.

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The volume of cylinder B can be calculated using the concept of similarity between the cylinders and the relationship between their areas and volumes. Therefore, the volume of cylinder B is approximately 135.346 cm³.

Given that cylinders A and B are mathematically similar, we can establish a ratio between their corresponding measurements. In this case, we are given the area of the cross-section of cylinder A, which is 18 cm², and the dimensions of cylinder B, which has a height of 10 cm and an unknown radius.

To find the volume of cylinder B, we need to determine the corresponding measurements of its cross-section. Since the cylinders are similar, the ratio of their areas is equal to the square of the ratio of their corresponding linear measurements.

Let's assume that the radius of cylinder B is 'r'. Since the height of cylinder B is given as 10 cm, we can calculate the area of its cross-section using the formula for the area of a circle: A = πr².

The ratio of the areas of the cross-sections of cylinders A and B can be expressed as (Area of A) / (Area of B) = 18 / (πr²).

Since the height of cylinder B is twice that of cylinder A (10 cm compared to 5 cm), the ratio of their corresponding linear measurements is 2:1.

Therefore, the ratio of the areas is (2:1)² = 4:1.

Setting up the equation, we have 18 / (πr²) = 4/1.

By rearranging the equation, we can solve for the radius 'r' of cylinder B:

18 = (4/1) * (πr²)

18 = 4πr²

r² = 18 / (4π)

r² = 4.545

r ≈ 2.132 cm

Now that we have the radius of cylinder B, we can calculate its volume using the formula for the volume of a cylinder: V = πr²h.

V = π * (2.132)² * 10

V ≈ 135.346 cm³

Therefore, the volume of cylinder B is approximately 135.346 cm³.

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Answer:

To determine the sample size required to estimate the proportion of consumers who have seen the company's advertisement in the newspaper, we can use the formula for sample size calculation for proportions. The formula is as follows:

n = (Z^2 * p * q) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence corresponds to a Z-score of approximately 2.33)

p = estimated proportion (0.65)

q = 1 - p (the complement of the estimated proportion)

E = maximum error tolerance (+/- 0.05)

Let's plug in the values and calculate the sample size:

n = (2.33^2 * 0.65 * 0.35) / (0.05^2)

n = 339.28

Rounding up to the nearest whole number, the required sample size is 340.

Answer:

0.75 can be written as :-

[tex] \frac{75}{100} [/tex]

and in simplest form it is:-

[tex] \frac{3}{4} [/tex]

so the answer is 3/4

Answer: 187 apples

Step-by-step explanation:

Substitute "year 5" into the equation. y = 15.2(5) +111.

y = 76 + 111

y = 187

The probability that the engine will not fail between 55,000 and 65,000 miles, based on normal distribution probabilities, when the mean failure is 60,000 miles and standard deviation of 5,000 miles is e) 68%.

Normal distribution probability is a continuous probability distribution with symmetrical values that mostly cluster around the mean.

We can compute the normal distribution probability using the normal distribution calculator.

Mean number of miles when a car's engine fails = 60,000 miles

Standard deviation = 5,000 miles

Sample  cutoff = between 55,000 and 65,000 miles

The probability of the engine fail between 55,000 and 65,000 miles = 0.6827.

= 68%.

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a) 25%

b) 40%

c) 35%

d) 32%

e) 68%

The volume of solid figure is,

⇒ V = 113 cm³

We have to given that;

A solid figure is shown with a cylinder and a cone.

Now, We know that;

Volume of cylinder = πr²h

And,

Volume of cone = πr²h / 3

Where, 'r' is radius and 'h' is height.

Here, Height of cylinder = 7 cm

And, Radius of cylinder = 4/2 = 2 cm

Hence, WE get;

Volume of cylinder = πr²h

Volume of cylinder = 3.14 x 2² x 7

Volume of cylinder = 87.9 cm³

And, Height of Cone = 6 cm

Radius of Cone = 4/2 = 2 cm

Hence, WE get;

Volume of Cone = πr²h/3

Volume of Cone = 3.14 x 2² x 6 / 3

Volume of Cone = 25.1 cm³

Thus, The volume of solid figure is,

⇒ V = 87.9 cm³ + 25.1 cm³

⇒ V = 113 cm³

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Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (5/21)

The probability of an event is calculated as the number of elements in that event divided by the total number of elements in the sample space.

For this question, we are told to find the probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning.

Number of patients that are over 60 years and are for regular cleaning = 10

Total number of patients = 2 + 8 + 6 + 4 + 10 + 12 = 42

Probability that a randomly selected appointment is with patients over 60 years old and is for a regular cleaning = (10/42)

                                                                = (5/21)

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Answer: $383.33 per month for the next 4 years

Step-by-step explanation:

The correct answer is save $383.33 per month for the next 4 years. Tuition for one year at a state university is about $12,500, and Greg would like to attend this university. His parents will give him $4,600 for his first year of tuition, so he must save the remaining $7,900. To have enough money to pay for his first year of tuition, Greg must save $383.33 per month for the next 4 years. This is the minimum amount of money he must save, as the other plans require him to save more money than necessary.

Sorry if this is wrong btw fr fr.

Answer:164.58 (D)

Step-by-step explanation:

12,500-4600= 7900

12 months x 4 years makes 48 months, so 7900/48 = 164.58 per month

The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20

The simple interest formula is J = C ∙ i ∙ t, where J is interest, C is principal, i is interest rate, and t is time. To calculate the simple interest, just substitute the values ​​in the formula and perform the calculation.

Calculate the deposit:

[tex]D=R4.80 + 1.20% of R5,000\\=R4.80 + (1.20/100) * R5,000\\= R4.80 + R60\\= R64.80[/tex]

Now, the deposit amount for the branch:

[tex]DB=R8.00 + 1.50% of R5,000\\= R8.00 + (1.50/100) * R5,000\\= R8.00 + R75\\= R83.00[/tex]

The difference will be:

[tex]Difference = R64.80 - R83.00\\Difference = -R18.20[/tex]

The calculated difference is -R18.20, which means the deposit at the branch is higher than the deposit at the ATM by R18.20. Therefore, John's statement is incorrect.

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The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.

We have,

To find the cost of packaging per weight unit, we need to calculate the cost of packaging (C) and divide it by the weight of the chocolates (W).

Given:

Cost of packaging (C) = 1/4 x²

Weight of chocolates (W) = x + 2

To find the cost of packaging per weight unit, we can express it as C/W.

Substituting the given expressions:

C/W = (1/4 x²) / (x + 2)

To simplify the expression, we can first simplify the numerator:

C/W = (1/4 x²) / (x + 2)

= (1/4) x (x² / (x + 2))

= (1/4) x (x(x) / (x + 2))

= (1/4) x (x / (x + 2)) * x

Now, we can rewrite the expression as:

C/W = (1/4) x (x / (x + 2)) x

Therefore,

The cost of packaging per weight unit is given by (1/4) (x / (x + 2)) x.

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The given quadrilateral is a parallelogram by the theorem "The diagonals of a parallelogram bisect each other."

Given is a quadrilateral.

We have to determine that the quadrilateral is a parallelogram or not.

From the shape and the drawing given, the quadrilateral is a parallelogram.

A parallelogram has opposite sides parallel to each other.

Here it is parallel.

Here it is given that the diagonals are bisected by each other, that is two parts of the diagonals are of equal length.

We have a theorem that "The diagonals of a parallelogram bisect each other."

A square, rectangle, rhombus can be included in the group of parallelogram.

So this is a parallelogram.

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The volume of the cone is 301. 44mm³

First, we need to know the formula

the formula that is used for calculating the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters are;

Substitute the values, we have;

Volume = 3.14 × 6² × 8/3

Multiply the values, we have;

Volume = 904.32/3

Divide the values

Volume = 301. 44mm³

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A quadrilateral is a polygon with four sides. All trapezoids have two pairs of parallel sides. Option (a) is correct.

A quadrilateral is a polygon with four sides, and there are several properties and characteristics that can be true about a quadrilateral. Some possible true statements about a quadrilateral include:

1. A quadrilateral has four angles.

2. A quadrilateral has four vertices.

3. The sum of the interior angles of a quadrilateral is always 360 degrees.

4. A quadrilateral can have sides of different lengths.

5. A quadrilateral can have parallel sides.

Compare each of the properties above to the given options.

Options:

a) All trapezoids have two pairs of parallel sides.

b) Only some rectangles have four right angles.

c) All squares are rectangles.

d) Some rhombuses are trapezoids.

We can conclude that option (a) is correct because it correspond to the property 5 of a quadrilateral.

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The equation is an identity is discussed below.

An identity is a mathematical equation that holds true for all values of the variables involved.

In other words, it is true regardless of the specific values of the variables. When an equation is an identity, it means that both sides of the equation are equivalent and represent the same mathematical relationship.

For example, the equation 2x + 3 = 2(x + 1) is an identity because it holds true for all values of x.

When an equation is an identity, it provides a general statement or rule that is universally applicable and does not depend on specific values or conditions. Identifying an equation as an identity is important because it allows us to make general conclusions and deductions that apply in all cases.

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The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

We have,

To factor the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6,[/tex]

we can look for its roots and express it as a product of linear factors.

First, let's check if there are any rational roots using the rational root theorem.

The possible rational roots can be found by taking the factors of the constant term (-6) and dividing them by the factors of the leading coefficient (1).

The factors of -6 are: ±1, ±2, ±3, ±6

The factors of 1 are: ±1

The possible rational roots are: ±1, ±2, ±3, ±6

By testing these values, we find that x = 2 is a root of the polynomial.

Using synthetic division, we can divide the polynomial by (x - 2) to find the quotient.

The quotient is [tex]x^3 + x^2 - 3x - 7.[/tex]

Now, we can continue factoring the quotient.

The polynomial x³ + x² - 3x - 7 does not have any rational roots.

We can try factoring it by grouping or using other factoring methods, but in this case, it does not factor nicely into linear factors.

Therefore,

The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

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Answer:

  c.  100 m

Step-by-step explanation:

You want the length of the shadow of a 100 m tower if the angle of inclination of the sun is 45°.

The tower and its shadow are modeled as legs of a right triangle. When the acute angle in such a triangle is 45°, the triangle is isosceles and the legs are the same length.

The shadow is the same length as the height of the tower: 100 m.

__

Additional comment

You can check this by using the formula:

  S = 100/tan(45°) = 100/1 = 100

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The prove of the statement is described below.

First of all ,

Labeling the given figure

And draw  a diagonal,

In the quadrilateral PQRS,

The side PQ is equal to the side RS.

Therefore,

PQ = RS

And also, the side PQ is parallel to the side RS.

Then,

PQ || RS.

Now, draw the diagonal PR.

We know that a parallelogram's diagonal divides the parallelogram into two congruent triangles.

By the rule of  Side-Angle-Side,

we can show that ∆ PQR ≅ ∆ RSP.

Therefore,

The side QR is parallel to PS

Then,

QR || PS.

Hence,

PQRS is a parallelogram.

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The equation for each circle is given as follows:

36) (x - 2)² + (y - 15)² = 4.

37) (x + 8)² + (y + 18)² = 25.

38) (x - 11)² + (y + 9)² = 49.

39) (x - 13)² + (y + 8)² = 36.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

For item 36, the center is given as follows:

(-3, 11)

After the translation, the center will be given as follows:

(2, 15)

Hence the equation is given as follows:

(x - 2)² + (y - 15)² = 4.

For item 37, the center is given as follows:

(-3, -14)

After the translation, the center will be given as follows:

(-8, -18)

Hence the equation is given as follows:

(x + 8)² + (y + 18)² = 25.

For item 38, the center is given as follows:

(11, -9).

Hence:

(x - 11)² + (y + 9)² = r².

Point (18, -9) is on the circle, hence the radius squared is obtained as follows:

r² = (18 - 11)² + (-9 + 9)²

r² = 49.

Hence the equation is:

(x - 11)² + (y + 9)² = 49.

For item 39, the center is given as follows:

(13, -8).

Hence the equation is:

(x - 13)² + (y + 8)² = r².

Point (7, -8) is on the circumference of the circle, hence the radius squared is obtained as follows:

r² = (7 - 13)² + (-8 + 8)²

r² = 36.

Hence the equation is given as follows:

(x - 13)² + (y + 8)² = 36.

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The volume of the storage nook is 24 cubic feet.

To find the area of 8 puzzles, we multiply the area of one puzzle by 8:

Area of 8 puzzles = 1 square foot * 8 = 8 square feet

Now, to find the volume of the storage nook, we multiply the area of the floor by its height:

Volume of the nook = Area of the floor * Height

= 8 square feet * 3 feet

= 24 cubic feet

Hence, the volume of the storage nook is 24 cubic feet.

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The surface area of the composite solid is 255 square inches.

We will compute the surface area of each component and then add them together to find the surface area of the composite solid.

First, the surface area of the square prism:

Given: The square prism has a width, length, and height of 5 inches each.

Formula for the surface area of a rectangular prism: 2lw + 2lh + 2wh

Surface area of the prism = 2(5 * 5) + 2(5 * 5) + 2(5 * 5)

= 2(25) + 2(25) + 2(25)

= 50 + 50 + 50

= 150 square inches

Next, the surface area of the square pyramid at the bottom:

Given: The slant height of the pyramid on the bottom of the prism = 7.5 inches.

The base of the pyramid is a square with a side length of 5 inches.

Formula to find the lateral surface area of a square pyramid: (perimeter of base) * slant height / 2.

The base is a square, the perimeter is 4 times the side length.

Lateral surface area of the bottom pyramid = (4 * 5) * 7.5 / 2

= 20 * 7.5 / 2

= 150 / 2

= 75 square inches

Then, the Surface area of the square pyramid at the top:

Given: The height of the pyramid on top of the prism = 3 inches.

The base of the pyramid is a square with a side length of 5 inches.

Lateral surface area of the top pyramid = (4 * 5) * 3 / 2

= 20 * 3 / 2

= 60 / 2

= 30 square inches

Finally, we shall find the total surface area by summing up the surface areas of each component in this way:

Total surface area = Surface area of the prism + Surface area of the bottom pyramid + Surface area of the top pyramid

= 150 + 75 + 30

= 255 square inches

Therefore, the surface area of the composite solid = 255 square inches.

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The ball has traveled approximately 25.24 feet Horizontally.The correct answer is D. 25.2 ft.

The horizontal distance traveled by the soccer ball after 0.9 seconds, we can use the equation:

horizontal distance = initial velocity * time * cos(angle)

Substituting the given values:

initial velocity = 39 ft/s

time = 0.9 s

angle = 44°

horizontal distance = 39 ft/s * 0.9 s * cos(44°)

Calculating:

horizontal distance ≈ 39 ft/s * 0.9 s * 0.71934 ≈ 25.24 ft

Therefore, after 0.9 seconds, the ball has traveled approximately 25.24 feet horizontally.

The correct answer is D. 25.2 ft.

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Answer:

Step-by-step explanation:

To find out how many degrees the tank temperature should increase during the heating hours to maintain the average temperature, we need to calculate the temperature difference between the target average temperature of 67°F and the temperature during the unheated hours (50°F).

The difference in temperature is:

67°F - 50°F = 17°F

Since the heating hours account for the remaining hours of the day, which is 24 hours minus the 14 hours when no heating is required, we have:

24 hours - 14 hours = 10 hours

To maintain the average temperature of 67°F, the tank temperature should increase by 17°F during the 10 hours of heating.

To find the increase per hour, we divide the total temperature increase by the number of heating hours:

17°F / 10 hours = 1.7°F

Therefore, the tank temperature should increase by 1.7°F per hour during the heating hours to maintain the average temperature of 67°F.

Answer: 360 degrees.

Step-by-step explanation: The sum of the interior angles in a quadrilateral is always 360.

(you can check using the formula 180(n-2), where n is the number of sides.)

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

Given: AB is parallel to BC

DC is parallel to BC

Angle 1 is congruent to Angle 2

Prove:

AC is congruent to DB

Proof: AB is parallel to BC and DC is parallel to BC.

Therefore, AB is parallel to DC.

Angle 1 is congruent to Angle 2.

Angles 1 and 2 are alternate interior angles, so they are congruent.

Angles 1 and 2 are congruent and AB is parallel to DC, so by the Corresponding Angles Theorem, AC is congruent to DB.

Therefore, AC is congruent to DB.

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