please help with problem 7, and 9-12

The area of the dilated triangle will be 9cm²

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller.

If one box represent 1 cm and the area of the original shape is calculated as;

A = 1/2bh

base = 2cm and height is 1cm

the area = 1/2 × 2 × 1

= 1cm²

area scale factor = 3² = 9

scale factor = new dimension/original dimension

9 = x/1

x = 9cm²

therefore the new area = 9cm²

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Answer: The area of the floor of the hall is approximately 599.2448 square meters.

Step-by-step explanation: Let's assume the breadth of the hall be x meters. Then, the length of the hall will be 2x meters and the height will be 3x meters.

The volume of the hall can be found as follows:

Volume = Length × Breadth × Height

36000 = 2x × x × 3x

36000 = 6x³

x³ = 6000

x = ∛6000 ≈ 17.32 meters

Therefore, the breadth is approximately 17.32 meters, the length is 2 × 17.32 = 34.64 meters, and the height is 3 × 17.32 = 51.96 meters.

The area of the floor can be found by multiplying the length and breadth:

Area = Length × Breadth

Area = 34.64 × 17.32

Area = 599.2448 m²

Therefore, the area of the floor of the hall is approximately 599.2448 square meters.

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 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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Answer:

[2, ∞)

Step-by-step explanation:

We Know

The solution set to x ≥ 2, meaning the 2 ≤ x < ∞

So, the interval notation is [2, ∞)

The total distance from the waterfalls to the canoes and then to the fishing area is 12.

From 9 and 10 we already know their coordinates. The distance from waterfax: to canoes: 2-(-4) = 6.

The distance from canoes to fishing is also 6. Understand that the total distance = 6+6 = 12

In conclusion, the total distance from the waterfalls to the canoes and then to the fishing area is 12.

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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:

x = 13 is the solution.

Step-by-step explanation:

Here is how it looks for this problem:

(-3)* = (-3) 13 Ignore the base and write an equation for the exponents: x = 13 Solve for x by subtracting 13 from both sides: x - 13 = 0 Add 13 to both sides: x = 13 Check your work by plugging x = 13 into the original equation: (-3)* = (-3) 13 (-3) 13 = (-3) 13 True

Answer:

The Answer may be D

Step-by-step explanation:

The answer is D because it's an one step equation. For something to be linear it must be one step.

Note that in tis case,  the estimated probability of getting at least 14 correct answers is 0.038, or about 3.8%.

The binomial distribution may be used to solve this problem, where the number of trials (n) is 30, the chance of success (p) is 1/5 (since there are 5 alternative responses and only one is accurate), and we wish to know the likelihood of receiving at least 14 correct answers.

We may calculate the cumulative chance of receiving 13 or fewer right answers using a calculator or statistical software. As a result, the likelihood of receiving at least 14 accurate answers is:

1 - 0.962 = 0.038

With random guessing, the estimated probability of getting at least 14 correct answers is 0.038, or about 3.8%.

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The value of cos 2θ is determined as 0.442.

The value of cos 2θ is calculated by applying the following trig identities.

sin θ = 28/53

The value of θ is calculated as;

θ = sin ⁻¹ (28/53)

θ = 31.89⁰

The value of cos 2θ is calculated as follows;

cos 2θ = cos (2 x 31.89)

cos 2θ = cos (63.78)

cos (63.78) = 0.442

Thus, the value of cos 2θ is determined by first calculating the value of θ based on the sine function given.

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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:

D. -7x + 15

Step-by-step explanation:

In order to rewrite the equation as a function of x, we have to isolate y on the left-hand side of the equation:

[tex](21x+3y-45=0)+45\\(21x+3y=45)-21x\\(3y=-21x+45)/3\\y=-7x+15[/tex]

Answer:

A

Step-by-step explanation:

I used desmos to graph the equations and A matches

Answer:

  9

Step-by-step explanation:

Destiny wants to know how many additional people she needs to invite to use up 1.5 L of tea, if each of them and Destiny all get 150 mL of tea.

Let f represent the number of invited friends. We know that 150 mL is 0.150 L, so the amount of tea Destiny wants to serve is ...

  (f +1)(0.150) = 1.50

  f +1 = 10 . . . . . . . . . . . divide by 0.150

  f = 9 . . . . . . . . . . subtract 1

Destiny should invite 9 friends to her tea party.

The answer of the given question based on the line segment is ,  the slope of the perpendicular bisector of the line segment AB is -1/4.

Slope is a measure of the steepness of a line on a graph. It describes the rate at which the line rises or falls as it moves from left to right, and it is defined as ratio of vertical change (rise) to horizontal change (run) between any two points on  line.

To find the slope of the perpendicular bisector of the line segment AB, we first need to find the midpoint of AB:

Midpoint of AB = [(x-coordinate of A + x-coordinate of B)/2, (y-coordinate of A + y-coordinate of B)/2]

= [(2 + 5)/2, (-3 + 9)/2]

= [3.5, 3]

So the midpoint of AB is (3.5, 3).

The slope of  line segment AB is:

slope of AB = (y-coordinate of B - y-coordinate of A)/(x-coordinate of B - x-coordinate of A)

= (9 - (-3))/(5 - 2)

= 4

The slope of a line perpendicular to AB is the negative reciprocal of the slope of AB. So the slope of the perpendicular bisector of AB is:

slope of the perpendicular bisector=-1/slope of AB

= -1/4

Therefore, the slope of the perpendicular bisector of the line segment AB is -1/4.

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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.

Answer:

-2 11/12

Step-by-step explanation:

-2 1/3 x 5/4

-7/3 x 5/4 = -35/ 12

-35/-12= -2 11/12

With comparison to parent function, the transformation is 3 units to right.

The given function is y=√x.

The parent function is the simplest form of the type of function given y=√(x-3).

The transformation from the first equation to the second one can be found by finding a, h, and k for each equation.

y=a√(x-h)+k

Factor a 1 out of the absolute value to make the coefficient of x equal to 1.

y=√x

Factor a 1 out of the absolute value to make the coefficient of x equal to 1.

y=√(x-3).

Here, a=1, h=3 and k=0

To find the transformation, compare the two functions and check to see if there is a horizontal or vertical shift, reflection about the x-axis, and if there is a vertical stretch.

Parent Function: y=√x

Horizontal Shift: Right 3 Units

Vertical Shift: None

Reflection about the x-axis: None

Vertical Compression or Stretch: None

Therefore, with comparison to parent function, the transformation is 3 units to right.

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The claim of the TV network that 4,50,00,000 people watched the coverage of the special event could be correct if the actual number of people who watched the program was anywhere between 4,49,95,000 and 4,50,05,000.

Rounding to the nearest ten lakhs means rounding to the nearest a million.

So, 4,50,00,000 rounded to the nearest ten lakhs is either 4,40,00,000 or 4,60,00,000.

To find the greatest possible and least possible number of people who could have watched the program, we need to consider the range of values that would round to 4,50,00,000.

For the least possible value, we need to subtract 5 lakhs from 4,50,00,000:

4,50,00,000 - 5,00,000 = 4,49,95,000

So, the least possible number of people who could have watched the program is 4,49,95,000.

For the greatest possible value, we need to add 5 lakhs to 4,50,00,000:

4,50,00,000 + 5,00,000 = 4,50,05,000

So, the greatest possible number of people who could have watched the program is 4,50,05,000.

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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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The metallurgist needs to use 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.

Let x: the number of pounds of the alloy containing 34% aluminum that the metallurgist needs to use,

Let y: be the number of pounds of the alloy containing 69% aluminum.

We want to find values for x and y such that when they are mixed together, they will produce 45 pounds of an alloy containing 56% aluminum.

To solve for x and y, lets set up a system of two equations

x + y = 45 (total weight of the final alloy)....eqn 1

0.34x + 0.69y = 0.56(45) (total amount of aluminum in the final alloy)....eqn 2

Simplifying Eqn 2, we get:

0.34x + 0.69y = 25.2

Now we can solve the system of equations by substitution method

Solve Equation 1 for x in terms of y:

x = 45 - y

Substitute x = 45 - y into Equation 2:

0.34(45 - y) + 0.69y = 25.2

Distribute the 0.34:

15.3 - 0.34y + 0.69y = 25.2

Combine like terms:

0.35y = 9.9

Solve for y:

y = 28.2857... (rounded to 3 d.p)

Now we can use this value of y to find x:

x = 45 - y

x = 16.7142... (rounded to 3 decimal places)

Therefore, the metallurgist needs to use approximately 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.

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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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Answer:

[tex]\text{Annual interest rate = 14 \%}[/tex]

Step-by-step explanation:

The formula for computing accrued amount(principal + interest) is given by

[tex]A = P\left (1 + \dfrac{r}{n}\right )^{nt}[/tex]

where

P =principal amount
r = annual interest rate as a decimal
n = number of times compounded per year
t = number of years
A = amount accrued at the end of t years

We are given
A = 62702.95
P = 4000
n = 4 since we are compounding quarterly, i.e. 4 times a year
t = 20

Plugging in known values into the equation we get
[tex]62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{4 \cdot 20}\\\\62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{80}\\\\[/tex]

Switch sides and divide both sides by 4000 to get
[tex]\left(1 +\dfrac{r}{4}\right)^{80} = \dfrac{62702.95}{4000}[/tex]

[tex]1 +\dfrac{r}{4}\right) = \left(\dfrac {62,702.95}{4000}\right)^{\dfrac{1}{80}}\\\\\text{Using a calculator,}\\1 +\dfrac{r}{4}\right) = 1.03499\dots \approx 1.035[/tex]

[tex]\dfrac{r}{4} = 1.035 - 1 = 0.035\\\\r = 4 \times 0.035\\\\\\r = 0.14\\\\\\[/tex]

As a percentage that would be

[tex]0.14 \times 100 = 14\%[/tex]

The slope of the line that represents the relationship is 0.76.

Slope in mathematics relates to how steep a line is. It measures how much the y-coordinate shifts upward or downward for every unit increment in the x-coordinate. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is, in other words, the slope of the line.

The following equation can be used to determine a line's slope: slope = (y2 - y1) / (x2 - x1).

where any two points on the line (x1, y1) and (x2, y2).

Positive, negative, zero, or undefinable slopes are all possible. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

The slope of the line is given by the formula:

slope = (change in y) / (change in x)

Substituting the point from the table we have (0, 0) , (1.3, 1) thus:

m = 1 - 0 / 1.3 - 0

m = 1 / 1.3 = 0.76

Now, using the slope intercept form we have:

y - y1 = m(x - x1)

For (0, 0) we have:

y = 0.76x

Hence, the slope of the line that represents the relationship is 0.76.

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The complete question is:

Since the calculated F-value of 7.098 is greater than the critical value of 5.79, we reject the null hypothesis and conclude that the population variance of total sales during active price competition is higher than during duopoly and tacit collusion at the 5% level of significance.

For the above issue, the null and alternate hypotheses are as follows:

The population variations of total sales under duopoly, active price competition, and tacit cooperation are all identical.

In contrast to duopoly and implicit collusion, total sales population variance is larger under active price competition.

To test the null  hypothesis, we must use a two-tailed F- test with a 5 % threshold of significance. The ratio of the sample variances is used to determine the F- statistic.

F = s1² / s2²

Where:
s1² - Sample Variance (Active price competition)

s2² -  SAmple variance (Duopoy and Tacit collusion)


Since n1-1 = 3
and n2-1 = 6

F = 114.09 / 16.08
F = 7.098

Having derived same, we know that the critical values of F for a two-tailed test with 3 and 6 degrees of freedom at 5% level of significance are:

Critical Value (3) = 5.14
Critical Value (6) = 5.79

Therefore, since the F-value > Critical Value in both cases, we must reject the null hypothesis.

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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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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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