A ladder is leaning against a house so that the top of the ladder is 12 feet above the ground. The angle the ladder makes with the ground is 51°. How long is the ladder?

12•sin51°
12/cos51°
12•cos51°
12/sin51°
None of these

Given:

To simplify:

Explanation:

First, let us take LCM of 4 and 8.

The LCM is 8.

Let us make the denominator the same.

Final answer:

The simplest form of the given problem is,

Answer:The discount would be 25%.

Step-by-Step explanation:

1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.

2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.

3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.

Discount given=25%=21.72

Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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Answer:

5

Step-by-step explanation:

5

Answer:

14x=x

inequal or no solution

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

There are only two ways to roll a die and get a number bigger than 2 (not1 or not 2) and smaller than 5 (not 5 and not 6) You can roll a 3 (bigger than 2, smaller than 5) OR you can roll a 4 (also bigger than 2 a, smaller than 5)

There are only 6 different results when you roll a die (1-6).

To write a probability you put the total number of ways on the bottom. Put 2 on top because there's two ways to roll the desired result.

P = 2/6 and simplify

P = 1/3

The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.

This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.

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Answer:

Below

Step-by-step explanation:

The sum of the 5 angles is 540°

● b+(b+45)+90+(2b-90)+(3/2)b = 540

3/2 is 1.5

● b+b+45+90+2b-90+1.5b = 540

● 2b +45+2b+1.5b = 540

● 5.5 b +45 = 540

● 5.5b = 495

● b = 495/5.5

● b = 90°

Answer:

b = 90

Step-by-step explanation:

b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540

b + b + 45 + 90 + 2b - 90 + (3/2)b - 90 = 540 - 90

b + b + 45 + 2b - 90 + (3/2)b = 450

2b + 2b + (45 * 2) + (2 *2b) - (90 * 2) + (2 * (3/2)b) = 450 * 2

2b + 2b + 90 + 4b - 180 + 3b = 900

11b - 90 = 900

11b - 90 + 90 = 900 + 90

11b = 990

b = 990 / 11

b = 90

check:

b + (b + 45) + 90 + (2b - 90) + (3/2)b = 540

90 + (90 + 45) + 90 + (2*90 - 90) + (3/2)*90 = 540

90 + 135 + 90 + 90 + 135 = 540

540 = 540  --- OK

Answer:

100

Step-by-step explanation:

its impossable

The new volume of the cylinder is $100$ cubic feet.

Let the original radius and height of the cylinder be $r$ and $h$, respectively. Therefore, the original volume of the cylinder is given by $\pi r^2 h = 100$. After the radius decreases by $10%$ and the height increases by $10%$, the new radius and height become $0.9r$ and $1.1h$, respectively. The new volume of the cylinder can be calculated as $\pi (0.9r)^2 (1.1h) = 0.891\pi r^2 h$. Since $0.891\pi r^2 h = 100$, the new volume of the cylinder is $100$ cubic feet.

Therefore, the new volume of the cylinder is the same as the original volume, i.e., $100$ cubic fee

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Answer

Option C is correct.

8.0 × 10³ miles = 8 thousand miles.

Explanation

The number given in scientific notation is

8.0 × 10³ miles

= 8.0 × 1000 miles

= 8000 miles

= 8 thousand miles.

Hope this Helps!!!

The population of mice is initially 25,000 and is decreasing at a rate of 25% per year. To determine the population after t years, we can use an exponential decay model by multiplying the initial population by the decay factor raised to the power of the number of years.

The decay factor represents the percentage decrease per year. In this case, the decay factor is 1 - 0.25 = 0.75, which accounts for the 25% decrease each year. The expression for the population after t years can be written as P(t) = 25,000 * (0.75)^t, where P(t) represents the population after t years.

For example, after 1 year, the population would be P(1) = 25,000 * (0.75)^1 = 18,750. After 2 years, the population would be P(2) = 25,000 * (0.75)^2 = 14,063, and so on. By plugging in different values for t, we can calculate the population at different points in time based on the given rate of decrease.

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Answer:

12

Step-by-step explanation:

If Liam drank 2 \(\frac{2}{9}\) cups and used 9  \(\frac{3}{4}\) cups of milk, then you have to find the lowest common multiple of both the fractions, which would be 36. Then you multiply 2 from 2 over 9 by 4, and 3 from 3 over 4 by 9. Then you add the results which will give you 36 over 36 which equals 1. Then you add the whole numbers, 2 + 9 + 1 = 12.

EQUATION: LCM of \(\frac{2}{9}\) and \(\frac{3}{4}\) = 36

                     2 x 4 + 3 x 9 = 36
                     \(\frac{36}{1}\)=1

                     2 + 9 + 1 = 12

Answer:

Step-by-step explanation:

\(7x^{2} +1 = 15x\) and \(63x^{2} +9x= 135x\)

so, divide because to solve for area you multiply so the opposite of multiplication is division, Anyway so \(135x/15x=9x\)

Hope this helps.

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Jimmy's age = (serena age + tyler age) - 1

Answer:

y = \(\frac{1}{3}\) x - 1

Step-by-step explanation:

x - 3y = 6 ⇔ y = \(\frac{1}{3}\) x - 2

y = \(\frac{1}{3}\) x - 1

Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left.  Amir used a total of 1/3L gas in each direction

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

Initial amount = 1L

Remaining amount = 1/3L

The amount of gas he used in each direction is calculated as

Amount used in each direction =(Initial amount - Remaining amount)/2

Substitute the known values in the above equation, so, we have the following representation

Amount used in each direction =(1L - 1/3L)/2

Evaluate

Amount used in each direction =1/3L

Hence, the amount is 1/3L

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Here is the complete question:

Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left. How much gas did he use in each direction?

Answer:

-3.5 -3, -2 1/2, -2, 2.5

Step-by-step explanation:

Answer:

From least (top) to greatest (bottom):

-3.5--in between -4 and -3

-3--on the -3 line

-2 1/5--in between the -3 and the -2

-2--on the -2 line

2.5--in between 2 and 3

Answer:

I'd say A because this question is just like y and xays.

Step-by-step explanation:

The 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

What is confidence interval?

A confidence interval is a statistical tool used to estimate the range of possible values in which a population parameter, such as the mean or proportion, is expected to lie with a certain level of confidence based on the observed sample data.

To find the 95% confidence interval for the population proportion, we use the formula:

CI = p′ ± z*\(\sqrt{(p'q'/n)\)

where:

CI: confidence interval

p′: sample proportion

q′: 1 - p′

z: z-score from the standard normal distribution for the desired confidence level (95% in this case)

n: sample size

Substituting the given values, we get:

CI = 0.167 ± 1.96\(\sqrt{((0.1670.833)/180)\)

Simplifying, we get:

CI = 0.167 ± 0.065

Therefore, the 95% confidence interval for the proportion of the population who prefer brand named items is:

CI = (0.102, 0.232)

This means that we can be 95% confident that the true population proportion of people who prefer brand named items falls within this range.

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The name for a data value that is far above or below the rest is called an outlier.

An outlier is an observation that deviates significantly from other observations in a dataset. It is an extreme value that lies outside the typical range of values and may have a disproportionate impact on statistical analyses and calculations. Outliers can occur due to various reasons, including measurement errors, data entry mistakes, or genuine rare events. Identifying and handling outliers appropriately is important in data analysis to ensure accurate and reliable results.

When dealing with outliers, it is important to assess whether they are the result of errors or genuine extreme values. Statistical techniques, such as box plots, scatter plots, or z-scores, can be used to detect outliers. Once identified, the appropriate action depends on the nature and cause of the outliers. In some cases, outliers may need to be corrected or removed from the dataset, while in other cases, they may provide valuable insights or require further investigation.

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Answer:

b

Step-by-step explanation:

Answer:8087

Step-by-step explanation:’nsnss

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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In the given problem, we are considering a thin bar of length 20 with heat distribution T(1, t), where ST = 82T/16 for 0 < x < 20 and t > 0.

To solve this problem, we use a separation of variables approach.

(i) We assume that the solution to the problem can be written as T(x, t) = X(x)T(t). By substituting this into the heat equation, we obtain X''(x)T(t) = k²X(x)T(t), where k is a constant.

Solving the eigenvalue problem X''(x) = -k²X(x) subject to the boundary conditions X(0) = X(20) = 0, we find the eigenfunctions Xn(x) = sin(nπx/20), where n = 1, 2, 3, ...

Thus, the general solution for T(x, t) is T(x, t) = ΣAn exp(-k²t)sin(nπx/20), where An are constants determined by the initial condition.

(ii) Applying the initial condition T(1, 0) = sin(πx/20) to the general solution, we find T(x, t) = sin(πx/20)exp(-π²t/400).

(b) To find the smallest time when max(T) ≤ 0.001, we need to find the time t when the maximum value of sin(πx/20)exp(-π²t/400) is less than or equal to 0.001. This can be determined numerically.

(c) When both ends of the bar are insulated, we consider the eigenvalues of the Sturm-Liouville problem, which are given as kₙ, k₁, k₂, ...

(i) The first eigenvalue k₀ is determined by the boundary condition T'(0) = 0.

(ii) The fifth eigenvalue k₅ is determined by solving the eigenvalue problem subject to the boundary conditions T'(0) = T'(20) = 0 and choosing the fifth smallest eigenvalue.

(iii) As t approaches infinity, the solution T(x, t) approaches a steady-state solution determined by the eigenfunctions corresponding to the smallest eigenvalues. The specific value of T(x, t) as t approaches infinity for T(2, 0) = 7 can be determined by substituting the corresponding eigenfunctions into the general solution and taking the limit as t goes to infinity.

Please note that the specific numerical values for k₀, k₅, and the steady-state solution T(x, t) as t approaches infinity cannot be determined without additional information or calculations.

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The variable that fits this description is a discrete variable. Discrete variables are often used in statistics and data analysis to describe populations or samples. They are important for identifying patterns and relationships in data and can be used to make predictions or draw conclusions.

A discrete variable is a type of variable that takes on distinct and separate values or categories. These values are typically counted in whole numbers, such as the number of children in a family, the number of cars in a parking lot, or the number of pets in a household.

In contrast, continuous variables can take on any value within a range, such as height, weight, or temperature. These variables are measured on a continuous scale and can take on fractional or decimal values.

Examples of discrete variables include the number of students in a class, the number of coins in a piggy bank, and the number of days in a month. While these variables can take on different values, they are always counted in whole numbers and are not measured on a continuous scale.

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The total accumulated amount needed to support your son's education is approximately $128,019.22.


Let's solve the problem step by step.

⇒ Calculate the future value of the funds needed for four years of university expenses.

PV1 = $40,000 (amount needed each year)

r1 = 5% (annual interest rate)

n1 = 1 (compounded once a year)

t1 = 4 (number of years)

Using the formula for future value (FV = PV × (1 + r/n)^(n × t)), we can calculate the accumulated amount for these four years:

FV1 = $40,000 × (1 + 0.05/1)^(1 × 4)

FV1 = $40,000 × (1.05)^4

FV1 ≈ $46,620.25

⇒ Calculate the future value of the $50,000 gift upon graduation.

PV2 = $50,000 (amount of the gift)

r2 = 5% (annual interest rate)

n2 = 1 (compounded once a year)

t2 = 9 (number of years from your son's 19th birthday to his graduation at age 28)

Using the same formula, we can calculate the accumulated amount for this gift:

FV2 = $50,000 × (1 + 0.05/1)^(1 × 9)

FV2 = $50,000 × (1.05)^9

FV2 ≈ $81,398.97

⇒ Calculate the total accumulated amount by summing up FV1 and FV2.

FV = FV1 + FV2

FV ≈ $46,620.25 + $81,398.97

FV ≈ $128,019.22

Therefore, the total accumulated amount needed to support your son's education is approximately $128,019.22.

Please keep in mind that these calculations assume a constant interest rate of 5% throughout the investment period and do not consider any additional contributions or fluctuations in the interest rate.

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If a function f is differentiable at a point a and f(a) is not equal to zero, then the absolute value function |f| is also differentiable at that point.

The proof involves considering two cases based on the sign of f(a) and showing that the limit of the difference quotient exists for |f| at point a in both cases. However, it is important to note that |f| is not differentiable at the point where f(a) equals zero.

To prove that if f is differentiable at a, then |f| is also differentiable at a, provided that f(a) ≠ 0, we need to show that the limit of the difference quotient exists for |f| at point a.

Let's consider the function g(x) = |x|. The absolute value function is defined as follows:

g(x) = {

x if x ≥ 0,

-x if x < 0.

Since f(a) ≠ 0, we can conclude that f(a) is either positive or negative. Let's consider two cases:

Case 1: f(a) > 0

In this case, we have g(f(a)) = f(a). Since f is differentiable at a, the limit of the difference quotient exists for f at point a:

lim (x→a) [(f(x) - f(a)) / (x - a)] = f'(a).

Taking the absolute value of both sides, we have:

lim (x→a) |(f(x) - f(a)) / (x - a)| = |f'(a)|.

Since |g(f(x)) - g(f(a))| / |x - a| = |(f(x) - f(a)) / (x - a)| for f(a) > 0, the limit on the left-hand side is equal to the limit on the right-hand side, which means |f| is differentiable at a when f(a) > 0.

Case 2: f(a) < 0

In this case, we have g(f(a)) = -f(a). Similarly, we can use the same reasoning as in Case 1 and conclude that |f| is differentiable at a when f(a) < 0.

Since we have covered both cases, we can conclude that if f is differentiable at a and f(a) ≠ 0, then |f| is also differentiable at a.

Note: It's worth mentioning that at the point where f(a) = 0, |f| is not differentiable. The proof above is valid when f(a) ≠ 0.

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