Sylvia read that the height of the Empire State Building is 443.2 m and wants to build a scale model of the building in her room. She knows that the height of the ceiling in her room is 8 ft. Write a scale that would allow a scale model of the Empire State Building in Sylvia's bedroom so that the top of the building would just touch her ceiling.

The probability of rolling a 3 on a pair of standard six-sided dice is 1/36.

There is only one way to roll a 3 on a pair of standard six-sided dice: one die must show a 1, and the other die must show a 2.

The number of possible outcomes when rolling two dice is given by the number of combinations of the two dice, which is 6x6 = 36.

The number of outcomes that result in a sum of 3 is 1 (as explained above). Therefore, the probability of rolling a 3 is:

P(rolling a 3) = number of outcomes that result in a sum of 3 / total number of possible outcomes = 1/36.

So the probability of rolling a 3 on a pair of standard six-sided dice is 1/36.

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Answer:

it is b the 2 one

hope you like it

Answer:

0

Step-by-step explanation:

X is greater than -4 which leads to having to technically add 4 getting you to 0.

-4, -3, -2, -1, **0**

I hope this is correct and helps you!!!!

Answer:

52.6 degrees

Step-by-step explanation:

tan^-1(72/55)

Angle of elevation is equals to 52°7'(approximately).

" Angle of elevation is the angle between the horizontal plane and  line of sight from the point of observation."

Formula used

In a right angled triangle,

tanθ = ( opposite side) / adjacent side)

According to the question,

As shown in diagram

Height of the building (AB) = 72m

Distance between base of the building and point of observation

(BC)= 55m

Angle of elevation = θ

Substitute the value in the formula we have,

 tanθ = AB / BC

          = 72 / 55

⇒ θ = tan⁻¹ (72 /55)

      = tan ⁻¹(1.3091)

      = 52° 7' (approximately)

Hence, angle of elevation is equals to 52°7'(approximately).

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Answer:

Its 180!

Step-by-step explanation:

The annual effective rate of interest is approximately 3.218%.

To find the annual effective rate of interest, we can use the formula for the present value of a perpetuity:

PV = C / i

where PV is the present value, C is the cash flow, and i is the interest rate.

In this case, the present value (PV) is given as 0.5 and the cash flow (C) is 1, as the perpetuity pays 1 at the end of every 6 years. Plugging these values into the formula, we have:

0.5 = 1 / i

Rearranging the equation to solve for i, we get:

i = 1 / 0.5

i = 2

So the annual effective rate of interest (i) is 2.

However, since the interest is paid at the end of every 6 years, we need to convert the rate to an annual rate. We can do this by finding the equivalent annual interest rate, considering that 6 years is the period over which the cash flow is received.

To find the equivalent annual interest rate, we use the formula:

i_annual = \((1 + i)^(^1^ /^ n^)\) - 1

where i is the interest rate and n is the number of periods in one year. In this case, n is 6.

Plugging in the values, we have:

i_annual =\((1 + 2)^(^1 ^/^ 6^) - 1\)

i_annual = \((3)^(^1 ^/^ 6^) - 1\)

i_annual ≈ 0.03218

So the annual effective rate of interest (i_annual) is approximately 3.218%.

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Two plus x divided by twelve equals one divided by three

Case 1 :

Rewrite into numbers : 2 + x /12 = 1/3

-> x/12 = 1/3 - 2 = -5/3

-> x = -5/3 x 12 = -20

Case 2 :

Rewrite into numbers : (2 + x)/12 = 1/3

-> 2 + x = 1/3 x 12 = 4

-> x = 4 - 2 = 2

i dont know if you meant it the right way or the wrong way but ill just put them both

x=2

Step-by-step explanation:

(2+x)/12=1/3

3(2+x)=12

2+x=4

x=4-2

x=2

The range of speeds at which a car can safely make the curve is approximately 70 km/h to 130 km/h.


When a car moves along a banked curve, the friction force plays a crucial role in preventing the car from slipping. To determine the safe range of speeds, we consider two scenarios: when the car goes too slow and when it goes too fast.
1. When the car goes too slow: If the car moves slower than the required speed, the friction force points uphill, away from the center of the curve. In this case, the static friction force needs to provide the centripetal force. Using the equation F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force, we can find the minimum speed at which the friction force can supply the required centripetal force.

2. When the car goes too fast: If the car moves faster than the required speed, the friction force points downhill, toward the center of the curve. The static friction force is not needed for the centripetal force in this case. Instead, the vertical component of the normal force provides the necessary centripetal force. Again, we can use the equation F_friction = μ_s * N to find the maximum speed at which the friction force is still within the limit.
Considering these scenarios, with a coefficient of static friction of 0.40, we find that the safe range of speeds for the car to make the curve is approximately 70 km/h to 130 km/h, rounded to two significant figures.

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Answer:

Add -3+8

Step-by-step explanation:

You would do this first because it is in the brackets. Usually you would do (*) first but those are just there because the 4 is negative and if they were not there it would get confusing and look like this::[-3+8]--4. So the next step would be the [*].

HOPE THIS HELPS!!!

Answer:

Use PEMDAS

Step-by-step explanation:

Parenthesis, If there are none move on to exponents if there are no exponents move to multiplication. No multiplication? use division. If you dont see division use addition and lastly if there is no addition use subtraction. In the equation, it looks like you have to make the -3 and 8 positive. So, since the -4 is in the parenthesis(P) multiply(M) 4 by 3 and 8 once the three is positive. So your final answer would be either C or D

Its the best i could do but good luck. I tried...

If j(x) = 5^(x - 3), using laws of exponents to solve the given expression [j(x + h) - j(x)]/h gives; [j(x + h) - j(x)]/h =  [(5^(x - 3))(5^(h) - 1)]/h

We are given the function as;

j(x) = 5^(x - 3)

Now, we want to solve the expression;

[j(x + h) - j(x)]/h

This gives us;

j(x + h) = 5^(x - 3 + h)

Thus, our expression is now;

[j(x + h) - j(x)]/h = [5^(x - 3 + h) - 5^(x - 3)]/h

Now, according to laws of exponents, we know that;

y³ × y² = y³ ⁺ ²

Thus;

5^(x - 3 + h) = 5^(x - 3) × 5^h

Therefore;

[5^(x - 3 + h) - 5^(x - 3)]/h = [(5^(x - 3))(5^(h) - 1)]/h

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Answer: -3/74

Step-by-step explanation:Maybe easiest way is a calculator but Have a brilliant day of learning!

The cost and selling price of a certain brand of shampoo marked up at 32% can be determined. The cost of the shampoo is the original price, and the selling price is the cost plus the markup.

To find the cost and selling price of the shampoo, we can use the information that the markup is 32% of the selling price.

Let's denote the cost of the shampoo as C and the selling price as S.

According to the given information, the markup is 32% of the selling price. This means the markup amount is 0.32S.

The selling price is the sum of the cost and the markup:

S = C + 0.32S

To solve for S, we can isolate the S term on one side of the equation:

0.68S = C

We know that the store marks up the shampoo at P70.08, which is 32% of the selling price. Therefore, we have:

0.32S = P70.08

Simplifying the equation, we find:

S = P70.08 / 0.32 ≈ P219

Substituting the value of S back into the equation 0.68S = C, we can determine the cost of the shampoo:

0.68 * P219 = C

C ≈ P148.92

Therefore, the cost of the shampoo is approximately P148.92, and the selling price is approximately P219.

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Answer:

2x+3y-z²

Step-by-step explanation:

twice a number =2x

thrice a number =3x

minus z²

HOPE THIS HELPS!!!

Answer:

2x+3y-z²

Step-by-step explanation:

twice a number =2x

thrice a number =3x

minus z²

Answer:

Step-by-step explanation:

a= first form a equation

lets call the cheese c and the buns b

2c+3b=10

c=2+b

3c+4b=12

now its a simultaneous equation

2c+3b=10    x3

3c+4b=12    x2

6c+9b=30

6c+8b=24

1b=6

b=6

now substitute it in to 2c+3b=10

2c+18=10

2c+-8

so c=$4

b= 56 difference 14

56/2=28

28-7

21

28+7=35

so the 2 numbers are 21 and 35

Hello!

1/6 ≈ 0.167

the answer is 0.167

The domain of (f / g)(x) is all real numbers except x = 0. In interval notation, it can be written as (-∞, 0) ∪ (0, ∞).

To find (f + g)(x), we need to add the functions f(x) and g(x):

f(x) = 5/(x + 6)

g(x) = x/(x + 6)

(f + g)(x) = f(x) + g(x) = 5/(x + 6) + x/(x + 6)

To combine the fractions, we need a common denominator, which is (x + 6):

(f + g)(x) = (5 + x)/(x + 6)

Next, let's find the domain of (f + g)(x). The only restriction on the domain would be any value of x that makes the denominator (x + 6) equal to zero. However, there is no such value in this case.

So, the domain of (f + g)(x) is all real numbers, or (-∞, ∞) in interval notation.

To find (f - g)(x), we need to subtract the function g(x) from f(x):

(f - g)(x) = f(x) - g(x) = 5/(x + 6) - x/(x + 6)

Again, we need a common denominator, which is (x + 6):

(f - g)(x) = (5 - x)/(x + 6)

Now, let's find the domain of (f - g)(x). As before, there are no restrictions on the domain.

So, the domain of (f - g)(x) is all real numbers, or (-∞, ∞) in interval notation.

To find (f * g)(x), we need to multiply the functions f(x) and g(x):

(f * g)(x) = f(x) * g(x) = (5/(x + 6)) * (x/(x + 6))

(f * g)(x) = 5x/(x + 6)²

Next, let's find the domain of (f * g)(x). In this case, the only restriction is that the denominator (x + 6) should not equal zero.

So, the domain of (f * g)(x) is all real numbers except x = -6. In interval notation, it can be written as (-∞, -6) ∪ (-6, ∞).

To find (f / g)(x), we need to divide the function f(x) by g(x):

(f / g)(x) = f(x) / g(x) = (5/(x + 6)) / (x/(x + 6))

(f / g)(x) = 5/(x)

Now, let's find the domain of (f / g)(x). The only restriction is that the denominator x should not equal zero.

So, the domain of (f / g)(x) is all real numbers except x = 0. In interval notation, it can be written as (-∞, 0) ∪ (0, ∞).

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Median is 67. We see comparing the medians that the Allstars are likewise taller on average than the Champs. Conclusion is that the Allstars have taller players than the Champs based on central tendency from data.

We may compare the measures of central tendency of the heights of the players on both teams to see which team normally has the tallest players. The median and mean are the two often used measurements of central tendency based on data.

We add together all the heights and divide by the total number of players to determine the mean height for Allstars:

(73+62 + 60 + 63 + 72 + 65 + 69 + 68 + 71 + 66 + 70 + 67 + 60 + 70 + 71) / 15 = 1006 / 15 = 67.1 inches

We add together all the heights for the Champs and divide by the overall player count:

(15) = 996/15 = 66.4 inches (62+69+65+68+60+70+70+58+67+66+75+70+69+67+60)

We can observe from comparing the means that the Allstars are taller on average than the Champs.

Outliers or extremely high or low numbers in the data, however, can have an impact on the mean. We may determine the median, which is the midpoint value when the data is sorted in either ascending or descending order, to further evaluate the data.

We order the data according to Allstars:

60 60 62 63 65 66 67 68 69 70 70 71 71 72 73

The centre number, or median, is 68.

We order the information for the Champs:

58 60 60 62 65 66 67 68 69 70 70 75

The centre number, or median, is 67.

We can observe from comparing the medians that the Allstars are likewise taller on average than the Champs.

We can therefore draw the conclusion that the Allstars typically have taller players than the Champs based on the metrics of central tendency.

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Option (D), the last option is the correct statement, If heights in inches of 200 graduating seniors were summarized in the frequency table;

The median height is greater than or equal to 60 inches but less than 66 inches.

The median is the number value that separates the lower and upper values to halves. The median height is determined by arranging all the given heights in order either from the smallest to highest or from highest to smallest without skipping any measurement of the heights.

After arranging all the heights in order, the median height is usually at the middle.

The reason as to why the median height is greater than or equal to 60 inches but less than 66 inches is because the middle height should not be same as the largest height of 66 inches. It is possible to have multiple 60 inch heights from the 200 seniors. It is also possible to have multiple 66 inch of heights from the 200 seniors.

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Answer:

inteager

Step-by-step explanation:

temperature can express both positive and negative

Answer:

-3-9

Step-by-step explanation:

+(-) = -

The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.

What is linear inequality?

A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.

We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.

The dotted graphs are drawn for the inequalities having < or >

Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.

Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not

1. 3x-2y≤6

⇒ 0≤6

So, the equation is true for the point.

Hence, the third graph represents this equation.

2. 3x-2y<6

⇒ 0<6

So, the equation is true for the point.

Hence, the first graph represents this equation.

3. 3x-2y>6

⇒ 0>6

So, the equation is false for the point.

Hence, the fourth graph represents this equation.

4. 3x-2y≥6

⇒ 0≥6

So, the equation is false for the point.

Hence, the second graph represents this equation.

Hence, the graphs are matched with the inequalities.

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Since, there are multiple questions so, the question answered above is attached below.

The interval of convergence, i, is [-1, 1), which means the series converges for all x values between -1 (inclusive) and 1 (exclusive).

To find the radius of convergence, r, and the interval of convergence, i, of the series ∑((-1)^n * n^4 * x^n) / (6^n), we can use the ratio test.

The ratio test states that for a power series ∑(a_n * x^n), if the limit of the absolute value of the ratio of consecutive terms is L, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to our series:

lim(n->∞) |((-1)^(n+1) * (n+1)^4 * x^(n+1)) / (6^(n+1))| / |((-1)^n * n^4 * x^n) / (6^n)|

Simplifying this expression:

lim(n->∞) |(-1)^(n+1) * (n+1)^4 * x^(n+1) * 6^n| / |((-1)^n * n^4 * x^n) * 6^(n+1)|

Taking out common terms:

lim(n->∞) |(n+1)^4 * 6^n * x^(n+1)| / |n^4 * 6^n * x^n * 6|

Simplifying further:

lim(n->∞) |(n+1)^4 * x * 6| / |n^4 * 6|

As n approaches infinity, we can drop the absolute value signs:

lim(n->∞) [(n+1)^4 * x * 6] / [n^4 * 6]

Simplifying the expression inside the limit:

lim(n->∞) (n^4 + 4n^3 + 6n^2 + 4n + 1) * x * 6 / (n^4 * 6)

Canceling out common terms and simplifying:

lim(n->∞) (1 + 4/n + 6/n^2 + 4/n^3 + 1/n^4) * x

As n approaches infinity, the terms with 1/n^k (where k > 0) tend to zero. Therefore, we are left with:

lim(n->∞) (1) * x

The limit is simply x, which gives us the ratio L.

To apply the ratio test, we set L < 1 and solve for x:

x < 1

Therefore, the radius of convergence, r, is 1.

Now, to determine the interval of convergence, i, we need to check the endpoints of the interval. We evaluate the series at the endpoints x = -1 and x = 1.

For x = -1:

∑((-1)^n * n^4 * (-1)^n) / (6^n) = ∑(n^4) / (6^n)

This series is a convergent p-series with p = 4 > 1. Therefore, it converges at x = -1.

For x = 1:

∑((-1)^n * n^4) / (6^n)

This series does not satisfy the alternating series test because the terms do not approach zero as n approaches infinity. Therefore, it diverges at x = 1.

Hence, the interval of convergence, i, is [-1, 1), which means the series converges for all x values between -1 (inclusive) and 1 (exclusive).

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Answer:

37.68m^3

2143.57 m^3

Step-by-step explanation:

Volume of a cone 1/3(nr^2h)

n = 3.14

(1/3) x (3^2) x 4 x 3.14 = 37.68

Volume of a sphere = 4/3 x pi x r^3

4/3 x 8^3 x 3.14 =

ANSWER:

The total surface area of the triangular prism is 69.77 square millimeters

STEP-BY-STEP EXPLANATION:

We have that the formula surface area of the remaining prism is the following

Replacing:

s1, s2 and s3 are the sides of the triangle, the base and the height are of the triangle and L is the length of the rectangle.

Answer: no solution

Step-by-step explanation:

Given:

44, 38, 21, 37, 48, 43, 28

To find the box-and-Visker plot representing the given data:

Let us write it in ascending order.

21, 28, 37, 38, 43, 44, 48.

The median of the given data is 38.

The median of the first three terms is 28.

The median of the last three terms is 44.

The lowest of the given data is 21.

The highest of the given data is 48.

Hence, the correct option c.

EXPLANATION

We can complete the frequency table by arranging each given value with its corresponding age class, as shown as follows:

Age class Frequency

20-29 1

30-39 4

40-49 2

50-59 7

60-69 11

70-79 4

80-89 1

The complete frequency distribution for the data is,

Age      Frequency

20-29         1

30-39         4

40-49         2

50-59         7

60-69         11

70-79          4

80-89          1

We have to given that;

The following data represents the age of 30 lottery winners.

Now, We can formulate;

By given table,

Age      Frequency

20-29         1

30-39         4

40-49         2

50-59         7

60-69         11

70-79          4

80-89          1

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Answer:

Darrell is 12 years old while Darrell is 18 years old

Step-by-step explanation:

Let Myles age be m and Darrell age be d

Single Myles is older, m > d

Square Darrell’s age and multiply by 2; d^2 * 2 = 2d^2

Subtract from the square of Myles age

m^2 - 2d^2

Result is 6 times the difference between their ages;

m^2 - 2d^2 = 6(m-d) •••••••••••(i)

When add Myles and Darrell age

m+ d

you get 5 times the difference between their ages 5(m-d)

m + d = 5(m-d)

m + d = 5m - 5d

5m - m = 5d + d

4m = 6d

m = 6d/4

m = 1.5d or 3/2d ••••••••(ii)

Put ii into i

(3/2d)^2 - 2d^2 = 6(3/2d - d)

9/4d^2 - 2d^2 = 6(1/2)d

Multiply through by 4

9d^2 - 8d^2 = 12d

d^2 = 12d

d^2 - 12d = 0

d(d -12) = 0

d = 0 or d-12 = 0

d = 0 or 12

d = 12 years

The age cannot be zero (if Darrel age is zero, then Myles age will be zero too, this cannot work as their ages are not equal)

So we choose 12 years

Recall ; m = 3/2 d = 3/2 * 12 = 18 years