Two similar cones have surface areas of 1883 square meters and 7532 square meters, respectively. If the height of the smaller cone is 36 meters, what is the height of the larger cone?

The probability that the first roll is a total of at least 5 and the second roll is a total of at least 4  is 0.764 or 76.4%.

The probability is the chance that an expected event occurs out of many possible events.

For two independent events happening, we use the rule of multiplication of independent events based on dice probabilities.

The event that the first roll is a total of at least 5 = A

In the event that the second roll is a total of at least 4 = B

The number of faces on each die, n = 6

The probability of event A = ³⁰/₆ = ⁵/₆

The probability of event B = ³³/₃₆ = ¹¹/₁₂

Multiplying the two probabilities, P(A) and P(B) = ⁵/₆ ​× ¹¹/₁₂

= ⁵⁵/₇₂ = 0.764

Thus, there is a ⁵⁵/₇₂ or 0.764 chance that the first roll is at least 5 and the second roll is at least 4.

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By making the financially irresponsible decision of maxing out your credit card limit, you might not have money for an emergency situation.

As, There is no foolproof technique to determine how much you can spend in excess of your credit limit, but you can go over it.

When determining the risk of accepting an over-the-limit transaction, card issuers may take into account a number of criteria, including your prior payment history.

Now, maxing out credit card leads to negative results.

So, either not have money for an emergency situation or not be able to buy the things you need.

But we can still spend after maxing out the limit.

Thus, not have money for an emergency situation is correct option.

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Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .

The prospect of an event happening is assessed by probability. It is a number between zero and 1, where 0 denotes an improbable occurrence and 1 denotes a certain occurrence. For instance, if we flip a fair coin, the odds of obtaining heads are 0.5, or 50%, and the odds of receiving tails are also 0.5, or 50%. In each case, there are various ways to compute probability. In general, if an event has n equally possible results and k of them are favourable, the likelihood that the event will occur is: Event P = k/n . All possible outcomes are thought to be equally likely under what is referred to as the classical probability.

given

Simply put, the likelihood that Marcus won't obtain a seat on the school bus is the complement of the likelihood that he will.

By deducting the probability from 1, one can determine the complement of a probability. So:

Chance of not being seated equals one less than the likelihood of being seated.

The likelihood of not getting a seat is equal to 1 - 0.93.

0.07 percent of people will not receive a seat.

Marcus not getting a seat on the school bus is therefore 0.07 or 7% likely as 0.07 percent of people will not receive a seat .

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Answer: First, let's convert the room's dimensions from feet to yards, since the carpet cost is given per square yard:

17 feet = 5.67 yards (rounded to two decimal places)

16 feet = 5.33 yards (rounded to two decimal places)

Next, we can calculate the area of the room in square yards by multiplying these values:

Area = 5.67 yards × 5.33 yards = 30.23 square yards (rounded to two decimal places)

Finally, we can multiply the area by the cost per square yard to get the total cost:

Total cost = 30.23 square yards × $101/square yard = $3,056.23 (rounded to two decimal places)

Therefore, it will cost $3,056.23 to carpet the room.

The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.

B. m[tex]\widehat{DG}[/tex] = 85°

The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.

The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.

The tangent secant exterior angle measure theorem indicates that we get;

m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])

The question indicates; m[tex]\widehat{GFE}[/tex] = 149°

m∠DBG = 32°

Therefore;

32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])

149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°

m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°

The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°

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The number of gallons of gas Brynen will use in driving to and from work, during the week, obtained using arithmetic operations is 7 5/7 gallons

Arithmetic operations are operations involving addition, subtraction, multiplication, and division.

The distance Brynen travels each way to his new job = 27 miles

The distance his car gets per gallon of gas = 35 miles

The number of gallons he will use in a week (five days of driving in the week), can therefore, be found by arithmetic operations follows;

The distance Brynen travels = 27 × 2 × 5 = 270 miles

The number of gallons = 270 miles/(35 miles/gallon) = 270/35 = 7 25/35

7 25/35 = 7 5/7

The volume of gas he will use to and from work this week is; 7 5/7 gallons

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Step-by-step explanation:

The constant of proportionality is just the slope of the line

using 0,0   and  3,2   points

slope = (y1-y2 ) / ( x1-x2) = (0-3) / ( 0-2) = 3/2 = constant of proportionality

Answer:

Let the width of the rectangle be w. Then the length of the rectangle is 5w.

The perimeter of a rectangle is the sum of all four sides. So, the perimeter of the rectangle is 2w+2(5w)=108 cm.

Simplifying the right side of the equation, we get 12w=108 cm.

Dividing both sides of the equation by 12, we get w=9 cm.

Since the width is 9 cm, the length of the rectangle is 5w=5(9)=45 cm.

Therefore, the length of the rectangle is 45 cm and the width is 9 cm.

The length of the third side is 8units

Pythagoras theorem states that : the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

If a and b are the legs of the triangle and c is the hypotenuse,then

c² = a²+b²

For example , if a = 3 and b = 4 , then

c = √3²+4²

c = √ 9+16

c = √25

c = 5units.

Similarly, c = 10, a= 6, and b is unknown

therefore

10²= 6²+b²

b² = 10²-6²

b² = 100-36

b² = 64

b = √64

b = 8units

therefore the length of the third leg is 8units.

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Answer:

[tex]sec(-\theta)=-3.1[/tex]

[tex]sin(-\theta)=-0.62[/tex]

Step-by-step explanation:

Part a.

[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].

Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.

For any input in the domain, even functions produce the same output if the opposite of the input is used.  In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].

Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.

[tex]sec(-\theta)=-3.1[/tex]

Part b.

The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.

However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph.  Visually, this is an "odd" function.

For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output.  In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].

Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.

[tex]sin(-\theta)=-0.62[/tex]

Answer:

c=12.04

Explanation:

You can use the formula given: c=√a^2+b^2

c=√8^2+9^2=√64+81=√145=12.04

Answer: i gotchu

Step-by-step explanation:

1) Since the base of this function is greater than 1, this means its increasing exponentially (increases from left to right).  So as x approaches positive infinity, y approaches positive infinity as well.

Domain (-∞,∞)   Range (0,∞)

2) If the base changes to 1/9 the function would decrease. So as x approaches positive infinity, y approaches 0 (Check attached screenshot)

3) The "+5" raises the horizontal asymptote up 5 units. So the new equation for the horizontal asymptote is y=5.

The "x-2" shifts the x values to the right by 2 units.

u dont have to pay me, i literally just learned this like a month ago :)

Answer:10.66 years. Punch again to double check

Step-by-step explanation:

A=Pe^(rt)

11700=5850e^(.065t)

isolate the variable expression

2=e^(.065t) divide by 5850

ln2=lne^(.065t) take the natural log of both sides

ln2=.065t. Bring down the power, lne equals

t is about 10.66 years. Divide ln2 by .065

Answer:

the temperature at 7 am was -36.7 degrees.

Step-by-step explanation:

Let's denote the temperature at 7 am by "x". Since the temperature increased by 8.4 C between 7 am and 11 am, we can set up the equation:

x + 8.4 = -28.3

Subtracting 8.4 from both sides, we get:

x = -36.7

Therefore, the temperature at 7 am was -36.7 degrees.

The function shows that the chairs and sofas the manufacturer should produce to earn that profit is C. (6, 12) P= 1,260

The profit function is P = 50x + 80y.

In order to find the optimal production quantities that will maximize the profit function, we need to determine which vertex yields the highest profit.

From the given vertices, we can see that the profit at (0,0) is 0. The profit at (0,15) is 1,200, and the profit at (6,12) is 1,260.

Therefore, the manufacturer should produce 6 chairs and 12 sofas to earn a profit of 1,260.

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The total cost equation is 200,000 + 40n and the break-even revenue is 20,000.

Given that a company is starting a new production, it cost the company $200,000 to construct the factory building.

The cost per unit of production is estimated to be Birr 20.

The company will incur a 20% commission expense.

The price per unit of products is decided to be Birr 50.

We need to find the total cost equation in terms of quantity and determine the break-even quantity.

a) The fixed cost of the company is $200,000, and 40 per unit sell,

Therefore for n units the total cost =

200,000 + 40n

b) BEQ = FC / P−VC

= 200,000 / 50-40

= 20,000

Hence the total cost equation is 200,000 + 40n and the break-even revenue is 20,000.

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The graph of the piecewise function is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

All the five definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.

The definitions are given as follows:

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Answer:

It is called as triangular numbers

Step-by-step explanation:

these numbers can be represented as a triangle of dots

The sum expression [tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex] using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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

[tex][2(4 + \frac9n)^4](\frac9n) + ... + [2(4 + \frac{9n}n)^4](\frac9n)[/tex]

From the above expression, we can see that the different expression in each term is

9/n

So, we introduce a variable

Assuming the variable is i, the i-th term of the expression would be[tex]t(i) = [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

When represented using the sigma notation, we have

[tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

Hence, the sum expression using the sigma notation is [tex]\sum\limits^{n}_{i=1} [2(4 + \frac{9i}n)^4](\frac9n)[/tex]

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Answer: A

Step-by-step explanation:

A dilation is not a rigid transformation, which means it has to scale the object into a different measure. So, enlarging or reducing the size of an object is a dilation.

Answer:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

Step-by-step explanation:

Match the boxes on the left to the answers:

Positive Association

Complementary Angles

Negative Association

Clusters in Data

Supplementary Angle

Non-linear Association

Answer:

  [tex]x=-\dfrac{\sqrt{51}}{10}[/tex]

Step-by-step explanation:

You want the value of x in the third quadrant of a unit circle where y = -7/10.

The radius of a unit circle is 1, so the Pythagorean theorem tells you the magnitude of the value of x is ...

  1² = x² +(7/10)²

  x = -√(1 -49/100) = -√(51/100) . . . . . . x < 0 in the third quadrant

  x = (-√51)/10

Step-by-step explanation:

This is a right triangle , so the Pythagorean theorem applies

c^2 = a ^2 + b^2        c  is the hypotenuse   a and b are the legs

15^2 = 9^2 + x^2

15^2 - 9^2 = X^2

x  = 12 ft

The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.

To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.

In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.

The weights for each component are calculated as follows:

Weight of debt = Market value of debt / Total market value of capital structure

= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.286 or 28.6%

Weight of preferred stock = Market value of preferred stock / Total market value of capital structure

= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.304 or 30.4%

Weight of common equity = Market value of common equity / Total market value of capital structure

= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.410 or 41.0%

These weights can be used to calculate the weighted cost of capital for Romero Company.

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The correct numbers for Derrek and Thomas' football teams are :

According to the information given, Thomas's football team lost 3 yards in their first drive, which means they moved backward 3 yards from the line of scrimmage. This can be represented as -3 on the number line.

On the other hand, Derrek's football team gained 5 yards in their first drive, which means they moved forward 5 yards from the line of scrimmage. This can be represented as +5 on the number line.

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We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

Here, we have,

H0 : μ ≥ 6

H1 : μ < 6

Test statistic :

n = 20

Sample Mean, x = 3

σ = 1.5

Test statistic = (x - μ) ÷ σ/sqrt(n)

Test statistic = (3 - 6) ÷ 1.5/sqrt(20)

Test statistic = - 3 / 0.3354101

Test statistic = −8.944271

Since, sample size is < 30 ;

Obtaining the Critical value using the from T;

Tcritical at 0.05, df = 19 = - 1.729

Tstatistic < Tcritical

−8.944271 < - 1.729

Hence, we reject the Null:

We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.

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The factored form of 64d³ - 24d² is 8d²(8d³ - 3).

The greatest common factor (GCF), also known as the greatest common divisor (GCD), is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that divides evenly into two or more given numbers. For example, the GCF of 12 and 18 is 6, since 6 is the largest number that divides both 12 and 18 without leaving a remainder.

The greatest common factor (GCF) of the given terms is 8d². We can factor it out by dividing each term by 8d²:

64d³/8d² - 24d²/8d²

Simplifying the fractions:

8d³ - 3

Therefore, the factored form of 64d³ - 24d² is 8d²(8d³ - 3).

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The area of the shaded region is 51.75 in².

From the figure

Radius of semicircle = √25² - 20²

                                  =√625-  400 = 15 inch

Now, Area of Trapezium = 1/02 ( a +b ) h

= 1/2 (17 + 37) x 15

= 1/2 (54) x 15

= 27 x 15

= 405 in²

Then, Area of Shaded region

= Area of Trapezium -  Area of semicircle

= (405 - πr²)

= 405 - 353.25

= 51.75 in²

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The sales 12 weeks after release is $586,000 . Option A is the correct answer.

To create a table of values, we can plug in different values of t and find the corresponding values of s:

t s

0 10

1 19.882

2 26.248

3 31.177

4 35.064

5 38.185

6 40.731

7 42.837

8 44.6

9 46.095

10 47.384

11 48.508

12 49.498

To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.

To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.

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