In the similar triangles below , what is the measure of D

45

22.5

63

90

[tex]y = 3 - \frac{x}{7} \\ x = 3 - \frac{y}{7} \\ \frac{y}{7} = 3 - x \\ y = 7(3 - x) \\ y = 21 - 7x \\ y = - 7x + 21 \\ {f}^{ - 1} (x) = - 7x + 21[/tex]

PLEASE GIVE BRAINLIEST

The equation of the translated graph from x² + y² = 7  is (x - 8)² + (y + 4)² = 7

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

x² + y² = 7

The translation is given as

T (-8,4)

This means that

(x, y) = (x - 8, y + 4)

Using the above as a guide, we have the following equation

(x - 8)² + (y + 4)² = 7

Hence, the equation of the translated graph is (x - 8)² + (y + 4)² = 7

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The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.

When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.

In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.

The total points earned in this situation would be 8, which is not equal to 0.

In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.

In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.

Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.

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The probable question may be:

In which of these situations do the quantities combine to make 0?

A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.

B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.

C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.

D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.

A) A and B are neither mutually exclusive nor exaustive.

B) A and C are neither mutually exclusive nor exaustive.

C) A and D are neither mutually exclusive nor exaustive.

D) B and C are neither mutually exclusive nor exaustive.

Two events are exhaustive if at least one of them must happen, and two events are mutually exclusive if only one of them can happen.

In this problem we have the sample set:

S = {1, 2, 3, 4, 5, 6}

A = {1, 3, 5}

B= {1, 2, 3, 5, 6}

C = {3, 5}

D = {3, 4, 5}

a) Events A and B:

These have common elements, so these arent exclusive, and there is an outcome (4) that is not in either set, so the sets aren't exhaustive.

b) A and C.

Similar to the previous case, neither mutually exclusive nor exhaustive.

c)  A and D

Now we have, again, common elements, 3 and 5, but there is an element missing (2), so  neither mutually exclusive nor exhaustive.

d) B and C.

Again, we have common elements (so these are not mutually exclusive) and the element 4 is not in neither of the sets, so these arent exhaustive.

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Answer:

1. The integral of [tex]\(\cos(x) e^{\sin(x)} dx\)[/tex] is [tex]\(e^{\sin(x)} + C\)[/tex], where [tex]\(C\)[/tex] is the constant of integration.

2. The integral of [tex]\(\cos^2(x) dx\)[/tex] can be rewritten using the double-angle formula as [tex]\(\frac{x}{2} + \frac{\sin(2x)}{4} + C\).[/tex]

3. The integral of [tex]\(\frac{\cos(\sqrt{x})}{\sqrt{x}} dx\)[/tex] is [tex]\(2\sin(\sqrt{x}) + C\)[/tex].

4. The integral of [tex]\(\frac{1}{\sqrt[3]{1-7x}} dx\)[/tex]is [tex]\(-\frac{3(1 - 7x)^{2/3}}{14} + C\)[/tex].

5. The integral of [tex]\(\frac{1}{2+5x} dx\)[/tex] is [tex]\(\frac{\ln|2+5x|}{5} + C\)[/tex].

Step-by-step explanation:

Let's break down each integral:

1. Integral of [tex]\(\cos(x) e^{\sin(x)} dx\)[/tex]

  This is a case of a simple substitution. We can let [tex]\(u = \sin(x)\)[/tex], then [tex]\(du = \cos(x) dx\)[/tex]. Substituting these into the integral, we get [tex]\(\int e^u du\)[/tex], which is simply [tex]\(e^u + C\)[/tex]. Substituting back for [tex]\(u\)[/tex], we get [tex]\(e^{\sin(x)} + C\)[/tex].

2. Integral of [tex]\(\cos^2(x) dx\)[/tex]

  The double-angle formula is used here. We know that [tex]\(\cos^2(x) = \frac{1 + \cos(2x)}{2}\)[/tex]. Substituting this into the integral, we get [tex]\(\int \frac{1 + \cos(2x)}{2} dx\)[/tex], which can be separated into two simpler integrals: [tex]\(\frac{1}{2} \int dx + \frac{1}{2} \int \cos(2x) dx\)[/tex]. The integral of [tex]\(dx\) is \(x\)[/tex], and the integral of [tex]\(\cos(2x)\)[/tex] is [tex]\(\frac{1}{2}\sin(2x)\)[/tex]. So, the result is [tex]\(\frac{x}{2} + \frac{\sin(2x)}{4} + C\)[/tex].

3. Integral of \(\frac{\cos(\sqrt{x})}{\sqrt{x}} dx\)

  This is another case of simple substitution. We can let [tex]\(u = \sqrt{x}\)[/tex], then [tex]\(du = \frac{1}{2\sqrt{x}} dx\), or \(2 du = \frac{dx}{\sqrt{x}}\)[/tex]. Substituting these into the integral, we get [tex]\(2 \int \cos(u) du\), which is \(2\sin(u) + C\)[/tex]. Substituting back for [tex]\(u\)[/tex], we get [tex]\(2\sin(\sqrt{x}) + C\)[/tex].

4. Integral of [tex]\(\frac{1}{\sqrt[3]{1-7x}} dx\)[/tex]

  Here, we can let [tex]\(u = 1 - 7x\)[/tex], then [tex]\(du = -7 dx\)[/tex], or [tex]\(-\frac{1}{7} du = dx\)[/tex]. Substituting these into the integral, we get [tex]\(-\frac{1}{7} \int u^{-1/3} du\)[/tex], which is [tex]\(-\frac{3}{7}u^{2/3} + C\)[/tex]. Substituting back for [tex]\(u\)[/tex], we get [tex]\(-\frac{3(1 - 7x)^{2/3}}{14} + C\)[/tex].

5. Integral of [tex]\(\frac{1}{2+5x} dx\)[/tex]

  This is a standard form of integral that results in a natural logarithm. The integral of [tex]\(\frac{1}{a+bx} dx\)[/tex] is [tex]\(\frac{1}{b} \ln |a+bx| + C\)[/tex]. So, the result is [tex]\(\frac{\ln|2+5x|}{5} + C\)[/tex].


Hope This Helps!

The solution to the cube root equation ^3√(x + 1) - 2 = 0 is x = 7.

To solve the cube root equation ^3√(x + 1) - 2 = 0, you can follow these steps:

Isolate the cube root term: Add 2 to both sides of the equation, resulting in ^3√(x + 1) = 2.

Remove the cube root by raising both sides to the power of 3: Cubing both sides gives (^3√(x + 1))^3 = 2^3. This simplifies to x + 1 = 8.

Isolate the variable x: Subtract 1 from both sides of the equation, resulting in x = 8 - 1, which simplifies to x = 7.

In summary, to solve a cube root equation, you need to isolate the cube root term by performing inverse operations on the equation. In this case, adding 2 to both sides isolated the cube root term.

Then, you remove the cube root by raising both sides to the power of 3, which simplifies the equation to x + 1 = 8. Finally, by isolating the variable x, you subtract 1 from both sides to obtain the solution x = 7.

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The slope of the line passing through the points (-2,4) and (1,7) is 1.

To find the slope of a line passing through two points, we can use the formula:

slope (m) = (y2 - y1) / (x2 - x1)

Given the points (-2,4) and (1,7), we can substitute the coordinates into the formula:

m = (7 - 4) / (1 - (-2))

= 3 / 3

= 1

Therefore, the slope of the line passing through the points (-2,4) and (1,7) is 1.

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The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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The fraction in its lowest terms for 7 1/2 percent is 3/40.

To express the mixed number 7 1/2 percent as a fraction in its lowest terms, we need to convert it to a fraction and simplify.

First, we convert the mixed number to an improper fraction:

7 1/2 percent = 7 1/2 / 100

To simplify this fraction, we find the least common multiple (LCM) of the denominator (2) and the percent denominator (100), which is 200.

Now, we can rewrite the fraction with the common denominator:

7 1/2 / 100 = (7 * 2 + 1) / 200 = 15/200

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 200 is 5.

15/200 = (15 ÷ 5) / (200 ÷ 5) = 3/40

Therefore, the fraction in its lowest terms for 7 1/2 percent is 3/40.

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a) The value of k in the slope k/3 is: -4

b) The coordinates of the point P are: (-1, 0)

The general formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

A line that touches the circle at a single point is known as a tangent to a circle. The point where tangent meets the circle is called point of tangency.

The equation is given as:

3x - 4y + 3 = 0

Rewriting this gives:

4y = 3x + 3

y = ³/₄x + 3

Where ³/₄ is he slope

Now, P is the point of tangency and as such will be perpendicular and as such line IP has a slope of:

-1/(³/₄) = -⁴/₃

Thus: k = -4

Thus, to get the coordinates of P:

(y + 4)/(x - 2) = -⁴/₃

At -1, 0, we have the left hand side equal to the right hand side.

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The correct answer is:

a = 43%

b = 88%

To determine the values of a and b in the relative frequency table, we need to analyze the information provided in the Venn diagram and the given table.

From the Venn diagram, we can gather the following information:

The circle labeled "satellite" has a value of 55.

The circle labeled "cable" has a value of 75.

The overlap between the two circles is labeled as 12.

Using this information, we can complete the table:

First column - "Satellite":

Entries: Satellite, Not satellite, Total

Total: 55 (as given in the Venn diagram)

Second column - "Cable":

Entries: Blank, 51%, Blank

To find the value for the "Cable" entry, we need to subtract the overlap (12) from the total number of cable users (75).

Cable: 75 - 12 = 63

Therefore, the entry becomes: Blank, 51%, Blank

Third column - "Not Cable":

Entries: a, b, Blank

To find the value for "a," we subtract the overlap (12) from the total number of satellite users (55).

a: 55 - 12 = 43

To find the value for "b," we subtract the overlap (12) from the total number of households (100).

b: 100 - 12 = 88

Therefore, the entries become: 43, 88, Blank

Fourth column - "Total":

Entries: Blank, Blank, 100%

The total number of households is given as 100% (as stated in the question).

Therefore, the values of a and b in the relative frequency table are:

a = 43% (rounded to the nearest percent)

b = 88% (rounded to the nearest percent)

Hence, the correct answer is:

a = 43%

b = 88%

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Hey

terms are

9k , 7 , k , 4

the variable is

k

coefficients are

9 , -1

The surface area and volume of the second cylinder are given in square millimeters and cubic millimeters, V =

The given dimensions for cylinders are:

r = 1.75 in, h = 2.2 in Surface Area of Cylinder:

S = 2πr² + 2πrh

The surface area formula of a cylinder is  S = (2 * pi * [tex]r^2[/tex]) + (2 * pi * r * h).

S = (2 * 3.14 * 1.75²) + (2 * 3.14 * 1.75 * 2.2)

= 44.33 + 38.49

= 82.82 square inches.

Volume of Cylinder: V = πr²h

The formula to calculate the volume of a cylinder is given by V = pi * [tex]r^2[/tex] * h.

Volume = 3.14 * 1.75² * 2.2 = 20.28 cubic inches.

Volume = π(1.75)²(2.2)

Volume ≈ π(3.0625)(2.2)

Volume ≈ 6.7375π cubic inches

The given dimensions for cylinders are: d = 4.3 mm, h = 2 mm

Surface Area of Cylinder: S = 2πr² + 2πrhS = (2 * 3.14 * 2.15²) + (2 * 3.14 * 2.15 * 2) = 67.65 square millimeters.

Volume of Cylinder: V = πr²hV = 3.14 * 2.15² * 2 = 28.33 cubic millimeters.

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If the school were to switch from Company A to Company B to serve 200 students, they could potentially make savings of around $250 to $350.

Based on the graph provided, the cost of serving school lunches from Company B for 200 students is approximately $1500. As for Company A, the graph shows that the cost starts at $1500 and increases linearly as the number of students served increases.

The graph does not provide an exact data point for 200 students, but based on the trend of the line, the cost for Company A at 200 students would likely fall between $1750 and $1850.

Therefore, if the school were to switch from Company A to Company B to serve 200 students, they could potentially save around $250 to $350. However, these estimates are based on interpolation and the assumption of a linear relationship.

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Triangle MAB and triangle MNP MN=67.2m AM=32m MP=81.9. The length of MB is approximately 39.4 units.

To find the length of MB, we can use the triangle proportionality theorem.

The triangle proportionality theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

In this case, we can consider line NP as the line drawn parallel to side AB. Therefore, we can set up the following proportion:

MN/MA = MP/MB

Substituting the given values:

67.2m/32m = 81.9/MB

To solve for MB, we can cross multiply:

(67.2m)(MB) = (32m)(81.9)

Dividing both sides by 67.2m:

MB = (32m)(81.9)/67.2m

Simplifying:

MB ≈ 39.4

Therefore, the length of MB is approximately 39.4 units.

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[tex]101c - 5c + 4c = 100c \\ \\ 12q - 4 + 10q - 4q + 9 \\ 12q + 10q - 4q - 4 + 9 \\ 18q + 5 \\ \\ 21k - 20k + 3k = 4k \\ \\ 181x + 91x - 23x = 249x[/tex]

    Hence, OPTION (C): If angles XYZ and RST are not congruent, then they are not vertical angles.

Analysis:  p → q  is  ~ q → ~ p

To find the Statement that is logically equivalent to p → q, We need to understand the contrapositive of a conditional statement.

The contrapositive of a statement  p → q  is  ~ q → ~ p, In  this case, p is "Angles XYZ and RST are vertical angles."  and q is angles XYZ and RST are congruent."

The Contrapositive of  p → q  is  ~ q → ~ p

The Contrapositive of "IF angles XYZ and RST are Vertical angles, Then they are Congruent" is "IF angles XYZ and RST are NOT Congruent, Then They are NOT VERTICAL ANGLES."

The statement that is logically equivalent to p → q is "IF angles XYZ and RST are not congruent, then they are not vertical angles.

 Hence, OPTION (C): The statement that is logically equivalent to p → q is "IF angles XYZ and RST are not congruent, then they are not vertical angles.

I hope this helps you!

The logically equivalent statement to 'If angles XYZ and RST are vertical angles, then they are congruent' is 'If angles XYZ and RST are not congruent, then they are not vertical angles.'

In logic and mathematics, the concept of 'if p then q' refers to a specific directional relationship between two statements where 'p' is the hypothesis (or antecedent) and 'q' is the conclusion (or consequent). The statement 'p implies q' can also be logically equivalent to 'If not q, then not p'.

Applying this to your given statements,

The logically equivalent statement to 'If p then q' is 'If not q, then not p'. So, in the context of these statements, 'If angles XYZ and RST are not congruent, then they are not vertical angles' would be the logically equivalent statement. This statement basically means that if the two angles are not equal in measurement, then you cannot call them vertical angles.

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The probability of the intersection of events A and B, P(AB), is 0.04.

When events A and B are independent, the probability of their intersection (AB) can be calculated by multiplying their individual probabilities.

Given that P(A) = 0.4 and P(B) = 0.1, we can find P(AB) as follows:

P(AB) = P(A) * P(B)

Substituting the given values:

P(AB) = 0.4 * 0.1

P(AB) = 0.04

Therefore , the probability of the intersection of events A and B, P(AB), is 0.04.

To understand the intuition behind this, let's consider two independent events, such as flipping a coin and rolling a die. The probability of getting heads on the coin is 0.5, and the probability of rolling a 4 on the die is 1/6. Since these events are independent, the probability of getting both heads on the coin and rolling a 4 on the die is calculated by multiplying their individual probabilities: 0.5 * 1/6 = 1/12. This means that the chance of both events occurring simultaneously is 1 out of 12 possibilities.

Similarly, in the given scenario, the probability of events A and B both occurring (P(AB)) is found by multiplying the probabilities of A and B: 0.4 * 0.1 = 0.04. This means that there is a 4% probability of both events A and B happening together.

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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *[tex](1 - (1 + r)^(-n)) / r[/tex]

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = [tex]13000 * (1 - (1 + 0.10)^(-8)) / 0.10[/tex]

Calculating this expression:

PV = [tex]13000 * (1 - 1.10^(-8)) / 0.10[/tex]

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

[tex]\hrulefill[/tex]

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

[tex]\hrulefill[/tex]

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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The second approximation x2 is 2.875

and the third approximation x3 is 2.806

The root of the equation = [tex]4x^7 + 5x^4 + 3 = 0[/tex]

using Newton's method.

The initial approximation x1 = 3.

Calculate the function value and derivative at x1:

[tex]f(x1) = 4(3)^7 + 5(3)^4 + 3 = 4083\\f'(x1) = 4(7)(3)^6 + 5(4)(3)^3 = 32640[/tex]

We then apply Newton's method formula to find x2:

[tex]x_2 = x_1 - f(x_1)/f'(x1)\\x_2 = 3 - 4083/32640 = 2.875[/tex]

[tex]f(x2) = 4(2.875)^7 + 5(2.875)^4 + 3 \\f(x2) = 46.48\\f'(x2) = 4(7)(2.875)^6 + 5(4)(2.875)^3 \\f'(x2) = 603.75[/tex]

x3 = x2 - f(x2)/f'(x2)

x3 = 2.875 - 46.48/603.75

= 2.806

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(a) Ô₁ = 40° (b) с Ê₁ = 80°

AE || CB is proved using alternate interior angles.

1.1 To calculate the size of the angles:

(a) Ô₁: Since D = 50° and AD is a chord, Ô₁ is the central angle of chord AD. According to the properties of a circle, the measure of a central angle is equal to twice the measure of the inscribed angle it intercepts. Therefore, Ô₁ = 2D = 2 * 50° = 100°.

(b) с Ê₁: Angle с Ê₁ is an inscribed angle that intercepts chord CB. According to the inscribed angle theorem, the measure of an inscribed angle is equal to half the measure of the intercepted arc. In this case, the intercepted arc is AD. Since Ô₁ = 100° and the intercepted arc AD is opposite to Ô₁, с Ê₁ = 180° - Ô₁ = 180° - 100° = 80°.

1.2 To prove that AE || CB:

To prove that AE || CB, we need to show that the corresponding angles are equal.

Let's consider angle AED and angle BDC. Both angles are inscribed angles that intercept the same arc AD. According to the inscribed angle theorem, the measure of an inscribed angle is equal to half the measure of the intercepted arc. Since angle AED and angle BDC intercept the same arc AD, they are equal: AED = BDC.

Additionally, angle AED and angle с Ê₁ are alternate interior angles formed by a transversal (AD) intersecting two parallel lines (AE and CB). According to the alternate interior angle theorem, when two parallel lines are intersected by a transversal, the alternate interior angles are congruent. Therefore, angle AED = с Ê₁.

Since angle AED = с Ê₁ and AED = BDC, we can conclude that с Ê₁ = BDC. This equality of corresponding angles proves that AE is parallel to CB, and thus, AE || CB.

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Therefore, using the midpoint rule with n = 4, the estimated work done by the force in moving the object from x = 2 to x = 18 is approximately 109.6 J.

To estimate the work done by the force in moving an object from x = 2 to x = 18 using the midpoint rule with n = 4, we divide the interval [2, 18] into 4 subintervals of equal width.

The width of each subinterval is given by Δx = (18 - 2) / 4 = 4.

Next, we calculate the midpoint of each subinterval and evaluate the force function at those midpoints.

The midpoints are: x = 4, 8, 12, 16.

Evaluating the force function at the midpoints, we get: f(4) = 5.6, f(8) = 8.8, f(12) = 8, f(16) = 5.

Now, we can calculate the work done in each subinterval by multiplying the force by the width of the subinterval:

W₁ = f(4) * Δx = 5.6 * 4 = 22.4 J

W₂ = f(8) * Δx = 8.8 * 4 = 35.2 J

W₃ = f(12) * Δx = 8 * 4 = 32 J

W₄ = f(16) * Δx = 5 * 4 = 20 J

Finally, we sum up the individual work values to get the total work done:

W = W₁ + W₂ + W₃ + W₄ = 22.4 + 35.2 + 32 + 20 = 109.6 J

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The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

Answer: 4 inches

Step-by-step explanation:

you would take the 20 and minis the 16

Answer:

number added is 38

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{sum}{count}[/tex]

when the count is 10 the mean is 16 , then

[tex]\frac{sum}{10}[/tex] = 16 ( multiply both sides by 10 )

sum = 160

let the number added be x then mean is 18 when count is 11, so

[tex]\frac{160+x}{11}[/tex] = 18 ( multiply both sides by 11 )

160 + x = 198 ( subtract 160 from both sides )

x = 38

the number added is 38

The calculated value of x in the circle is 5

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

The circle

Using the intersection of secant and tangent equation, we have

4 * (4 + x) = 6 * 6

This gives

x * (4 + x) = 36

When solved for x, we have

x = 5

Hence, the value of x is 5

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The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.