Select the correct answer.

Answer:

19.6 units

Step-by-step explanation:

A = base x height

Pythagoras to get the height

height must be vertical in the base

The probability of randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 6 red pieces of candy out of 37 pieces of candy total is 5/222, or approximately 0.0225 or 2.25%.

Let's calculate the probability of the first draw being red. Since there are 6 red pieces of candy out of a total of 37 pieces of candy, the probability of drawing a red candy on the first try is 6/37.

Now, let's calculate the probability of the second draw being red given that the first draw was red. Since we did not replace the first candy before drawing the second one, there are only 5 red candies left out of a total of 36 candies. Therefore, the probability of drawing a second red candy is 5/36.

To find the probability of the combined event of drawing and immediately eating two red candies in a row, we need to multiply the probability of the first event by the probability of the second event, given that the first event occurred. So the probability of both events occurring is:

(6/37) x (5/36) = 5/222 or approximately 0.0225 or 2.25%.

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Complete Question:

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.

Randomly drawing and immediately eating two red pieces of candy in a row from a bag that contains 6 red pieces of candy out of 37 pieces of candy total.

The correct answer is option A:

Least: 9.5 hours; greatest: 14.5 hours.

Since, We have;

The function D(t) has a maximum value of 2.5 + 12 = 14.5 hours when sin(t) = 1, which occurs twice per year when,

t = π/2 + 2πn

or t = 3π/2 + 2πn for integers n.

The function has a minimum value of -2.5 + 12 = 9.5 hours

when sin(t) = -1,

which occurs twice per year when t = -π/2 + 2πn or t = 5π/2 + 2πn for integers n.

Therefore, the least number of daylight hours over the course of a year is 9.5 hours, and the greatest number of daylight hours over the course of a year is 14.5 hours.

So, the correct answer is option A:

Least: 9.5 hours; greatest: 14.5 hours.

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The length of each of the two guy wires that are anchored are 328.85 ft and 323.45 ft

Start by calculatng the height h from the horizontal to the base of the hill

So, we have

tan(7) = h/120

This gives

h = 14.7

The length of the first guy is

Length² = (14.7 + 120)² + (300)²

Evaluate

Length = 328.85

Next, we calculate the base length b as

b² = (120)² + (14.7)²

b = 120.9

The length of the second guy is

Length² = (120.9)² + (300)²

Length = 323.45

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Answer:

B and D are correct. A rhombus is a quadrilateral and a parallelogram.

In order for three sides to make a triangle, if any two sides are added together, their sum should be greater than the third side:

→ 5 + 7 = 12 < 13 (DOES NOT check off the rule)

→ 7 + 13 = 20 > 5 (Checks off the rule)

→ 5 + 13 = 18 > 7 (Checks off the rule)

As shown, even though 2 of the statements check off the rule the third one does not, this means that the sides don't make a triangle.

The angle that has been marked as B can be obtained as 86 degrees.

To solve a triangle, you need to find the measures of its angles and sides. There are different methods to solve a triangle, depending on the information given.

If you are given the measures of all three angles, you can use the fact that the sum of the angles in a triangle is always 180 degrees to find the missing side lengths.

Using the sine rule;

100/Sin C = 130/Sin 55

Sin C = 100 Sin 55/130

C = Sin-1( 100 Sin 55/130)

C = 39 degrees

Now;

B = 180 - (55 + 39)

B = 86 degrees

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The calculated t-value (4.14) is greater than the critical t-value (2.447), we can reject the null hypothesis and conclude that obese patients consume significantly more calories than their normal-weight siblings at a .05 level of significance.

To test whether obese patients consume significantly more calories than their normal-weight siblings, we can perform a paired t-test at a significance level of .05.

First, we need to calculate the differences in calorie intake between each sibling pair:

Sibling Pair Obese Patient Calorie Intake (cal) Normal-Weight   Sibling   Calorie Intake (cal) Difference

  1 2,450 1,500 950

  2 3,500 1,800 1,700

  3 3,000 2,100 900

  4 2,700 2,000 700

  5 2,800 1,900 900

 6 3,400 2,000 1,400

 7 3,000 2,000 1,000

Next, we need to calculate the mean difference and standard deviation of the differences:

Mean difference = (950 + 1,700 + 900 + 700 + 900 + 1,400 + 1,000) / 7 = 1,014.29

Standard deviation of differences = 382.46

Using these values, we can calculate the t-value:

t = (mean difference - 0) / (standard deviation of differences / [tex]\sqrt{n}[/tex])

where n is the number of sibling pairs (in this case, n = 7).

t = (1,014.29 - 0) / (382.46 / [tex]\sqrt{7}[/tex]) = 4.14

Finally, we can compare the t-value to the critical t-value at a .05 level of significance with 6 degrees of freedom (n-1):

t_critical = 2.447

We may rule out the null hypothesis and reach the conclusion that obese individuals consume considerably more calories than their normal-weight siblings at a.05 level of significance because the estimated t-value (4.14) is higher than the critical t-value (2.447).

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Answer: The answer is B. the graph of g (x) is shifted 4 units up.

Step-by-step explanation:

:) <3

Answer: B

Step-by-step explanation:

f(x) is a line that goes through (0,0) as a parent function

y=mx +b  b is your y-intercept

so

g(x) having a b=4

has been shifted up 4 units  B

The equation is solved to a simplified form as x = -4 ±√14

From the information given, we have that the quadratic equation is given as;

x² + 4x = 3

collect the like terms

x² + 4x - 3 = 0

Using the quadratic formula, we have

x = -b±√b² - 4ac/2a

From the equation;

ax + bx + c = 0

a = 1

b = 4

c = -3

Substitute the values

x = -4 ± √(4)² - 4(1)(-3)/2(1)

expand the bracket, we get;

x = -4 ± √16 + 12/2

Add the values

x = -4 ± √28/2

Divide the values

x = -4 ±√14

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Answer: -65.048

Step-by-step explanation:

-13.84(4.7) = -65.048

(you could also use a calculator)

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 75\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 75 = (500)(\frac{r}{100})(1) \implies 75=5r\implies \cfrac{75}{5}=r\implies \stackrel{ \% }{15}=r[/tex]

On solving the query we can say that the alternative theory is that the proportion of the population does not match the proportion of the sample. Ha: p ≠ p = 0.745

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

M is equal to z* * sqrt(p(1-p)/n)

Therefore, the error margin is:

m = 2.576 * sqrt(0.745*(1-0.745)/1000) = 0.034

The 99% confidence interval for the percentage of voters opposed to school bond initiatives is as follows:

0.745 ± 0.034, or (0.711, 0.779)

H0: p = p^ = 0.745

The null hypothesis (Ha) states that the percentage of voters opposed to school bond measures in the sample and the percentage of voters opposed to school bond measures in the population vary. In other words, the alternative theory is that the proportion of the population does not match the proportion of the sample.

Ha: p ≠ p^ = 0.745

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On solving the query we can say that the alternative theory is that the proportion of the population does not match the proportion of the sample.

[tex]H_O: p = p^{= 0.745}[/tex]

What is function?

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

M is equal to z* √(p(1-p)/n)

Therefore, the error margin is:

m = 2.576* √(0.745 (1-0.745)/1000) = 0.034

The 99% confidence interval for the percentage of voters opposed to school bond initiatives is as follows:

0.745 ± 0.034, or (0.711, 0.779)

[tex]H_O: p = p^{= 0.745}[/tex]

The null hypothesis (Ha) states that the percentage of voters opposed to school bond measures in the sample and the percentage of voters opposed to school bond measures in the population vary. In other words, the alternative theory is that the proportion of the population does not match the proportion of the sample.

[tex]H_O: p = p^{= 0.745}[/tex]

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For the functions  f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.

The function g(x) = (4x)² can be rewritten as g(x) = 16x²

Comparing this with f(x) = x², we can see that g(x) is equal to f(x) multiplied by 16.

Therefore, the graph of g(x) is the same as the graph of f(x) except that it is vertically stretched by a factor of 16.

The graph of g(x) is vertically stretched by a factor of 4.

Hence, for the functions  f(x)=x² and g(x) = (4x)² the best statement is the graph of g(x) is vertically stretched by a factor of 4.

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Answer:

[tex]72\ units^3[/tex]

Step-by-step explanation:

Width = 3 units

Height = 4 units

Length = 6 units

Volume = Length * Width * Height

             =  6 * 3 * 4

             = 72 units cubed

Answer:

4th option

Step-by-step explanation:

observing the graph we can say that the racing game is approximately 25% of the total

so

if 1 hour is ----------------------> 100%

 X-----------------------------25%

x=25/100------> 1/4=0.25 hours

convert to minutes

0.25*60---------> 15 minutes

the answer is 15 minutes

Answer: It equals 13.5

Answer:

6,075 / 450 = 13.5

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The solutions are θ = 5π/3 and θ = 4π/3 for equation -10sinθ - 8 = 5√3 - 8, option D is correct.

The given equation is -10sinθ - 8 = 5√3 - 8

Adding 8 to both sides, we get:

-10sinθ = 5√3 - 8 + 8

Simplifying, we get:

-10sinθ = 5√3

Dividing both sides by -10, we get:

sinθ = -5√3/10

Simplifying the fraction, we get:

sinθ = -√3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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The coordinates of the other endpoint of the line segment are (13-8, 6-5), which simplifies to (5,1).

Coordinates are a set of two or more numbers that represent a location on a map, chart, graph, or in a geographic coordinate system. Coordinates can be in a two-dimensional format, such as latitude and longitude, or in a three-dimensional format, such as X, Y, and Z. Coordinates are often used to pinpoint exact locations on a map, such as a house, city, or country. Coordinates can also be used to define an area, such as a region or district.

The midpoint of a line segment is the point which lies in the middle of two other points along the line. The coordinates of the midpoint of a line segment are (8,5). This means that the line segment in question has one endpoint at (13,6) and the other endpoint is located at the midpoint's opposite. The coordinates of the other endpoint of the line segment can be determined by subtracting the midpoint's coordinates from the known endpoint's coordinates.

Therefore, the coordinates of the other endpoint of the line segment are (13-8, 6-5), which simplifies to (5,1). Thus, the coordinates of the other endpoint of the line segment are (5,1).

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The coordinates of the other endpoint are (3, 4).

To find the coordinates of the other endpoint of the line segment, given the midpoint (8,5) and one endpoint (13,6), you can use the midpoint formula.

The midpoint formula is: Midpoint = ((a + b) / 2, (c + d) / 2)

You are given the midpoint (8,5) and one endpoint (13,6), so you can set up the following equations using the midpoint formula:

8 = (13 + b) / 2

5 = (6 + d) / 2

Now, solve for b and d, which represent the coordinates of the other endpoint:

8 * 2 = 13 + b

16 - 13 = b

b = 3

and

5 * 2 = 6 + d

10 - 6 = d

d = 4

So, the coordinates of the other endpoint are (3, 4).

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A consumer is best described as the end user of a product

Answer:  [tex]\frac{3t^{2}-48 }{t-4}[/tex]

Step-by-step explanation:

Rate of change is still rise/run or your y's/x's

When x=4,   y=3(4)²-5=43

When x=t,    y=3t²-5

rate of change =   [tex]\frac{3t^{2}-5-43 }{t-4}[/tex]  = [tex]\frac{3t^{2}-48 }{t-4}[/tex]

The valid solutions are:

n = 2: X ≈ 33.33, Y ≈ 66.67

n = 3: X = 25, Y = 75

Let X and Y be two positive numbers, both greater than 20, such that X + Y = 100 and Y = nX. We are asked to find the values of X and Y for different values of n.

n = 2

Y = 2X

X + Y = 100

X + 2X = 100

3X = 100

X = 100/3 ≈ 33.33

Y = 2 * 33.33 ≈ 66.67

n = 3

Y = 3X

X + Y = 100

X + 3X = 100

4X = 100

X = 100/4 = 25

Y = 3 * 25 = 75

n = 4

Y = 4X

X + Y = 100

X + 4X = 100

5X = 100

X = 100/5 = 20

Y = 4 * 20 = 80

However, the condition states that both numbers must be greater than 20. In this case, X = 20, so this solution does not satisfy the condition. We cannot find the values of X and Y for n = 4, as they do not satisfy the given conditions.

n = 5

Similar to the case with n = 4, for any higher values of n, the value of X will be equal to or smaller than 20, which does not satisfy the given conditions. Therefore, we cannot find the values of X and Y for n = 5, as they do not satisfy the given conditions.

In summary, the valid solutions are:

n = 2: X ≈ 33.33, Y ≈ 66.67

n = 3: X = 25, Y = 75

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Answer:Umm... what grade am I gonna learn that in?

Step-by-step explanation:

Sorry, I tried but I have no idea what that is...

The tax consequences of the distribution to William in 20X3 would be Dividend of $118,500 and a tax basis in the land of $130,000.

The tax consequences would include the dividend that the William Roy, the shareholder, gets from owning the land. This dividend is:

= Market value of land - Mortgage attached

= 130, 000 - 11, 500

= $ 118, 500

Then, William Roy would have to recognize a tax basis on the land for the fair market value. This means that the tax basis would therefore be $ 130, 000.

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Answer:

[tex]2\pi[/tex]

Step-by-step explanation:

First, let's find the area of circle O.

The formula is [tex]\pi r^2[/tex].

Plugging in the radius 3, we get the area is [tex]9\pi[/tex].

To get the area of the sector, we have to find out what fraction of 360 degrees the POQ is.

[tex]\frac{80}{360} = \frac{2}{9}[/tex].

We now multiply [tex]\frac{2}{9}[/tex] by 9, getting 2.

The answer is [tex]2\pi[/tex]

The net to compute the surface area of the three-dimensional figure is 166 square units.

We have,

the surface area of the three-dimension figure:

The surface area is the area calculated for the three-dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure.

A cuboid is a three-dimensional figure having length, width, and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.

For the given cuboid, length l = 8 , width w = 5 and height h = 5.

The surface area of the figure is given by;

SA = 2 (lw+lh+wh)

    =70 + 56 + 40

    = 166

Hence, the net to compute the surface area of the three-dimensional figure is 166 square units.

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Angle C is 25 degrees (Vertically opposite angles)

An angle pair created by the intersection of two straight lines or rays is said to be vertically opposite. Four angles are formed at the intersection point of two lines. Angles created by the junction of two lines that are opposite to one another vertically are known as vertically opposing angles. They are sometimes referred to as pairs of angles that are vertically opposed.

Since we have angles on a straight line;

B + 25 = 180

B = 155 degrees

Since B and D are vertically opposite, D = 155 degrees

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Answer:

17.25

Step-by-step explanation:

3*7.25= 3*7+ 3*0.25=21+0.75=21.75. 21.75-4.5=17.25.

Answer:

376.58 or 20.570824

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

if you change the equation into y=mx +b  form you get y=-7x +4 where m is -7 so the slope would be -7