Estimate the Given Rotation Within 10 degrees:

Answer:

https://geometryhelp.net/triangle-inequality-theorem/

Step-by-step explanation:

This is from that site. Visit it and you may find what you're looking for.

If we want to go from point A to point B, getting there through any intermediate point C, which is not on the straight line between A and B, is going to be longer. This should seem intuitively correct. But we will prove it formally.

Where do triangles come into this? Imagine that the line AB is a side of a triangle, ΔABC. Going from A to B is the straight, short way. Going there by first going to another point, C (which is the side AC) and then from C to B (which is the side CB) is going to be longer.

The percentage of buyers is approximately 68.26% of buyers of new houses paid between \($149,000\) and \($151,000\) .

We are given that the prices of the new homes are normally distributed with a mean of \($150,000\) and a standard deviation of $1000.

Using the 68-95-99.7 rule, we know that: approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the data falls within two standard deviations of the mean, approximately 99.7% of the data falls within three standard deviations of the mean.

In order to determine the proportion of customers who spent between $149,000 and , we must first determine the z-scores for these values:

z1 = (149,000 - 150,000) / 1000 = -1 z2 = (151,000 - 150,000) / 1000 = 1

Now, we can determine the proportion of data that falls between z1 and z2 using the z-table or a calculator. The region to the left of z1 is 0.1587, and the area to the left of z2 is 0.8413, according to the z-table. Thus, the region bounded by z1 and z2 is:

0.8413 - 0.1587 = 0.6826

We can get the percentage of consumers who spent between by multiplying this by 100% is  \($149,000\)  and \($151,000\):

0.6826 x 100% = 68.26%

Therefore, the standard deviation of customers who paid between is \($149,000\) and \($151,000\)  for this model of new homes.

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Answer:

Mary has two friends over, she wants to split half of a cake she has left over into thirds for her and her friends. 1/2 ÷ 3 is 1/6. This means that each friend will get 1/6 of the full cake.

Step-by-step explanation:

I make up stories and know how to divide fractions. To solve a division problem like this you want to take the 3 and turn it into 3/1. then, flip the 1/2 around to it is 2/1. Then, multiply the two together.

Answer:

the answer is 5

Step-by-step explanation:

Answer:

im gouing to use 3 hours as an example so the first hour is 5 dollars and 8 dollars for each additional hour there are 2 additional hours which would be 16 dollars from the additional hours and plus 5 dollars from the first hour so 21 dollars

and the other option like i said earlier 3 hours is the example so 6*2 becasue their are 2 additional hours which is 12 plus 15 dollars from the first hour so 27 dollars

so the answer would be charge 15 dollars for the first hour and 6 for additional hour

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Answer:

Perpendicular (I believe)

Step-by-step explanation:

Answer:

234,100

anything that is below 50 will go down.

Step-by-step explanation:

Answer:

234,100

Step-by-step explanation:

4 below let him go

5 and above bump him up

if youre looking in the hundreds place (the 1) you look to the right to see what number you have, if you follow the saying ^^ then 4 is let go so you just keep 100.

or if you want to look at it on a number line, 143 is closer to 100 than 200 :)

The height of the kite from the ground when the angle is 50 degrees is 232 feet.

The study of the correlations between triangles' sides and angles is the focus of the mathematic branch known as trigonometry. To link the angles of a right triangle to the lengths of its sides, it makes use of trigonometric functions like sine, cosine, and tangent.

Numerous industries, including physics, engineering, and navigation, use trigonometry. It can be used, for instance, to determine a building's height or the separation between two locations on a map, as well as to examine how waves and oscillations behave.

To find the height of the kite above the ground we use the trigonometric identity of tangent.

Thus, we have:

tan(50°) = h/200

Now, using cross multiplication:

h = 200 tan(50°) ≈ 232 feet

Hence, the height of the kite from the ground when the angle is 50 degrees is 232 feet.

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Answer: -3

Step-by-step explanation:

The common ratio of the geometric sequence –4, 12, -36,... is -3.

12/(-4) =-3

-36/(12) = -3

They both multiply -3 for the next number.

Answer: 0.27272727 or 0.27 (with a dash on top of 27)

Step-by-step explanation:

Answer:

D. Both distributions are skewed left, so the interquartile range is the best measure to compare variability.

Step-by-step explanation:

Plotting the data roughly shows that the data is skewed to the left. In other words, data is skewed negatively and that the long tail will be on the negative side of the peak.

In such a scenario, interquartile range is normally the best measure to compare variations of data.

Therefore, the last option is the best for the data provided.

please mark me brainliest :)

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is: ∠A = 39.6°

3) The length of side x is: x = 39.5 mm

The six trigonometric ratios of a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

1) The three main trigonometric ratios of the given triangle are:

sin B = 5/9.43

cos B = 8/9.43

tan B = 5/8

2) The measure of angle A is gotten from:

∠A = cos⁻¹ (47/61)

∠A = 39.6°

3) The length of side x using trigonometric ratios is:

21/x = tan 28

x = 21/tan 28

x = 39.5 mm

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Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

There is no change in its slope as initial and final slope is 1.

What is slope?

In arithmetic, the slope or gradient of a line may be a variety that describes each the direction and therefore the abruptness of the line.

Main body:

formula for slope with two points form is =

y -y₁ =( y₂-y₁ /x₂-x₁ )(x - x₁)

according to question ,

points are (0,0) and (3,3)

y - 0 = (3-0/3-0)(x -0)

y = 3/3 *x

y = x

hence slope of line is 1.

Now points are (0,0) and (-3,-3).

y - 0 = (-3-0/-3-0)(x -0)

y =- 3/-3 *x

y = x

hence slope of line is 1.

So there is no change in its slope.

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The probability that 35 or more people from the sample of 215 customers are concerned about the digital environment is 0.7043.

To calculate the probability that 35 or more people from the sample of 215 customers are concerned about the digital environment, we can use the binomial distribution formula.

The binomial distribution is applicable here because we have a fixed sample size (215 customers) and each customer can be categorized as either concerned or not concerned.

Let's denote p as the probability that a randomly selected customer is concerned about the digital environment.

From the given information, we know that 29% of technology experts believe our lives will be more harmed than helped, so p = 0.29.

The formula for the probability mass function of the binomial distribution is:

\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)

Where:

P(X = k) is the probability of k successes (in this case, customers concerned about the digital environment)

C(n, k) is the number of combinations of n items taken k at a time

\(p^k\) is the probability of k successes

\((1 - p)^{(n - k)\) is the probability of (n - k) failures

Now, let's calculate the probability of having 35 or more customers concerned:

P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 215)

Using this formula, we can calculate the probability using a cumulative approach:

P(X ≥ 35) = 1 - P(X ≤ 34)

Calculating this probability requires summing up a large number of individual probabilities, which can be time-consuming.

Therefore, it is more practical to use statistical software or calculators to obtain an accurate answer.

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\( {( \sqrt{9)} }^{2} \)

\( ={3}^{2} \)

\( = 9\)

\( {9}^ \frac{1}{2} \)

\( = ({3}^{2} ) ^{ \frac{1}{2} } \)

\( = 3 ^{1} \)

\( = 3\)

A repeating decimal is acceptable to use during calculations when you require a certain level of precision

A repeating decimal is acceptable to use during calculations when you require a certain level of precision, but it's important to keep in mind that the result will be an approximation rather than an exact value.

It is commonly used in situations where a rounded value is sufficient and the level of precision doesn't significantly impact the final result.

On the other hand, you should convert a repeating decimal to a fraction for calculations when you need an exact value or when further mathematical operations or comparisons are required.

Converting a repeating decimal to a fraction allows for precise calculations and eliminates any potential rounding errors associated with working with decimal approximations.

Converting a repeating decimal to a fraction involves identifying the repeating pattern and expressing it as a fraction. This allows for exact calculations and maintains the mathematical properties of fractions.

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Answer: 29/21

Quotient: 1

Reminder: 8

Step-by-step explanation:

Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.

Use the 1st  digit 2 from dividend 29

21 & 29 squared root

Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.

1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.

Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.

The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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Answer:

the probability that the two committees have at least one member in common is approximately 0.3622.

Step-by-step explanation:

To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.

Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:

Number of ways to choose 3 people out of 20 without overlap:

C(20,3) = (201918)/(321) = 1140

Number of ways to choose 3 people out of 20 with overlap:

C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680

The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.

The total number of ways to choose two committees of three people each without any overlap is:

C(20,3) * C(17,3) = (1140*680) = 775200

Therefore, the probability that the two committees have no members in common is:

P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378

So the probability that the two committees have at least one member in common is:

P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622

Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.

Answer:

Bill $306 in 18 hours.

Step-by-step explanation:

First we want to figure out the unit rate, or how much he makes in 1 hour.

So we do 204 ÷ 12. Which equals 17. So that means bill makes $17 every hour.

If we are trying to figure out how much he makes in 18 hours, we just need to do 18 * 17, which equals 306.

Answer: 4/16 =1/4

3/6 =1/2

12/18 =2/3

8/5 =1 3/8

Step-by-step explanation:

Answer:

4/16= 1/4 or .25

3/6=1/2 or .5

12/18=2/3

8/5=1 3/5 or 1.6

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

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Answer:

4

Step-by-step explanation:

It's going backwards by two

Answer:

55*54

=2970

Step-by-step explanation:

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.