A ladder 25m long leans against a vertical wall 7m height. How far is the foot of the pole away from the wall​

A graph that represents the absolute function f(x) = |x + 4| - 3 is shown on the coordinate plane attached below.

In Mathematics and Geometry, an absolute value function is a type of function that contains an expression, which is placed within absolute value symbols, and it measures the distance of a point on the x-axis to the x-origin (0) of a graph.

By critically observing the transformed absolute value function f(x) = |x + 4| - 3, we can reasonably infer and logically deduce that the parent absolute value function g(x) = |x| was vertically shifted (translated) downward by 3 units and horizontally shifted (translated) to the left by 4 units, in order to produce it as follows;

g(x) = |x|

f(x) = |x + h| - k

f(x) = |x + 4| - 3

In conclusion, we would use an online graphing tool to plot the given absolute value function f(x) = |x + 4| - 3 as shown in the graph attached below.

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Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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a.

The estimated total cost of the grocery items is $36.

b.

The actual total cost of the grocery items is $35.82.

for part a.

We will round each price to the nearest dollar:

$5.12 =  $5

$3.07 = $3

$7.11 = $7

$1.67 = $2

$13.18=  $13

$5.67 = $6

Summing them up, we have:

$5 + $3 + $7 + $2 + $13 + $6 = $36

the estimated total cost of the grocery items is $36.

for part b.

We will calculate the actual total cost of the grocery items by using a calculator:

$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82

In conclusion, we will find the  actual total cost of the grocery items as $35.82.

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Answer:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

The decimal 0.36 can be represented as a fraction in simplest form as 9/25. It can also be expressed as a repeating decimal using a variable.

a) 0.36 can be represented as a fraction in simplest form by using place value to identify the denominator. The number 3 is in the hundredths place value position.

Thus, the denominator is 100. 36 is in the numerator position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.

b) 0.36 can be represented as a fraction in simplest form by identifying the denominator based on place value.

In this case, 6 is in the thousandths place value position, so the denominator is 1000. 36 is in the numerator position. Thus, 0.36 in fraction form is 36/1000 which can be simplified to 9/250.

c) To write 0.36 as a fraction in simplest form, the place value of each digit needs to be considered. 3 is in the tenths place value position and 6 is in the hundredths place value position.

Therefore, 0.36 in fraction form is 36/100 which simplifies to 9/25.The decimal 0.36 can be represented in fraction form as 36/100 or 9/25.

To determine the fraction in simplest form, the denominator must be reduced to its lowest possible value without changing the numerator. The decimal 0.36 with a line on top of 3 and 6 represents a repeating decimal.

To express this number as a fraction, a variable is used.

In this case, the variable x is equivalent to 0.36. By setting up a proportion and solving for x, the answer can be found.

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It should be noted that there will always be two people in attendance who have the same number of friends at the party using the pigeonhole principle.

The pigeonhole principle states that if you have n pigeons and m pigeonholes, and n > m, then at least one pigeonhole must contain more than one pigeon.

In this case, we have n people at the party, and there are m = n - 1 possible numbers of friends that a person can have. This is because a person can either know 0, 1, 2, ..., or n - 1 other people.

Since n > m, the pigeonhole principle tells us that at least two people at the party must have the same number of friends.

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Answer: it stand for 3 million or 3,000,000

Step-by-step explanation:

Answer:

million

Step-by-step explanation:

millions always have six 0's behind it

For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA

For question 3.)

To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;

Sine rule:

a/sinA = b/sinB = c/sinC

where;

a = 8

A = sinA

b = 5

B = SinB

c = 9.45

C = Sin 90°

The three ratios;

= 9.45:sin90°; 5:sinB; 8:sinA

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The Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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

The triangle

Where, we have

tan(28) = 21/x

This means that

x = 21/tan(28)

Evaluate

x = 39.49

using the above as a guide, we have the following:

tan(28) = 21/39.49

tan(28) = 0.5318

Also, we have

sin(28) = 21/√(39.49² + 21²)

sin(28) = 0.4695

Lastly, we have

cos(28) = 39.49/√(39.49² + 21²)

cos(28) = 0.8829

Hence, the Sine, Cosine and Tangent of the angles are sin(28) = 0.4695, cos(28) = 0.8829 and tan(28) = 0.5318

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Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas.  A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.

To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.

Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.

Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.

Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:

Rectangle: Area = length × width

Triangle: Area = (base × height) / 2

Circle: Area = π × radius²

Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.

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The expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

To find the sum of triple the number "j" and 21, we need to multiply "j" by 3 and then add 21 to the result.

Let's break it down step by step:

Multiply "j" by 3: This can be represented as 3 * j, or simply 3j.

Add 21 to the result: We take the product from step 1 (3j) and add 21 to it, resulting in 3j + 21.

In summary, the expression 3j + 21 represents the sum of triple the number "j" and 21. It accounts for multiplying "j" by 3 and then adding 21 to the product. This equation allows us to calculate the desired sum when the specific value of "j" is known.

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Answer:

0.339, or approximately 33.9%

Step-by-step explanation:

We can solve this problem using Bayes' theorem. Let F denote the event that the selected student is female, and J denote the event that the selected student is taking Japanese classes. We want to find the probability of F given J, which we can write as P(F|J).

Using the law of total probability, we can decompose the probability of J as follows:

P(J) = P(J|F)P(F) + P(J|M)P(M)

where M denotes the event that the selected student is male. We can calculate the probabilities on the right-hand side of this equation as follows:

P(J|F) = 0.1 (from the problem statement)

P(F) = 0.51 (from the problem statement)

P(J|M) = 0.2 (from the problem statement)

P(M) = 0.49 (from the problem statement)

Plugging in these values, we get:

P(J) = 0.10.51 + 0.20.49 = 0.149

Now we can use Bayes' theorem to find P(F|J):

P(F|J) = P(J|F)P(F) / P(J)

Plugging in the values we calculated earlier, we get:

P(F|J) = 0.1*0.51 / 0.149 = 0.339

Therefore, the probability that the selected student is female given that they attend Japanese classes is 0.339, or approximately 33.9%.

Hope this helps!

Answer: 600000

Step-by-step explanation: just multiply it man