Open GeoGebra, and follow the steps below to create and compare triangles using the side-angle-side criterion.

Question 1
Create a triangle of your choice on the grid. Measure two of the sides on the triangle and the angle between the two sides. Record the measurements in the table.

Answer:

Area = 8 sq cm

Step-by-step explanation:

This shape is a parallelogram. Its like a rectangle that got tipped over. Area is:

base × height.

We don't know the base that is on the bottom of the image as it is shown. But if you turn it sideways, the 4 can be the base and the 2 is the height.

Area = b × h

= 4 × 2

= 8

The area is 8 sq cm.

Answer:

haro has more

Step-by-step explanation:

To solve this problem, we need to use the z-score formula to convert the given values to standard units. This will allow us to use the normal distribution table to find the percentage of pregnancies that fall within a certain range of lengths.

First, let's find the z-score for a pregnancy lasting more than 274 days:

z = (274 - 266) / 16 = 0.5

Next, let's use the normal distribution table to find the percentage of pregnancies that are longer than 274 days. Since the z-score we calculated is positive, we need to look in the right tail of the distribution. From the table, we find that the percentage of pregnancies that are longer than 274 days is approximately 30.85%.

Now let's find the z-score for a pregnancy lasting less than 246 days:

z = (246 - 266) / 16 = -1.25

To find the percentage of pregnancies that are shorter than 246 days, we need to look in the left tail of the distribution. From the table, we find that the percentage of pregnancies that are shorter than 246 days is approximately 8.38%.

Therefore, the percentage of children that are born from pregnancies lasting more than 274 days is approximately 30.85%, and the percentage of children that are born from pregnancies lasting less than 246 days is approximately 8.38%.

To find the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days, we need to use the z-score formula to convert the lengths of pregnancies to standard units and the standard normal distribution to find the percentage of children who fall within the given range of pregnancy lengths.

The z-score formula is:

z = (x - mu) / sigma

where z is the z-score, x is the raw score, mu is the mean, and sigma is the standard deviation.

In this case, we are given that mu = 266 days and sigma = 16 days. We can use this information to find the z-score for the lower and upper bounds of the pregnancy length range, 246 days and 274 days, respectively.

For the lower bound of the pregnancy length range, we have:

z = (246 - 266) / 16

= -20 / 16

= -1.25

For the upper bound of the pregnancy length range, we have:

z = (274 - 266) / 16

= 8 / 16

= 0.5

Now we can use the standard normal distribution to find the percentage of children who have a z-score between -1.25 and 0.5. The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1, so the percentage of children who fall within the given pregnancy length range is the same as the percentage of children who have a z-score within this range.

To find the percentage of children who have a z-score between -1.25 and 0.5, we can use a standard normal distribution table to look up the z-scores and find the corresponding probabilities. The standard normal distribution table shows the percentage of values that fall within a given range of z-scores, so to find the percentage of children who have a z-score between -1.25 and 0.5, we need to look up the percentage of values that fall within this range.

According to the standard normal distribution table, the percentage of values that fall within the range of z-scores -1.25 to 0.5 is approximately 0.38. Therefore, the percentage of children who are born from pregnancies lasting more than 274 days or less than 246 days is approximately 38%, to the nearest hundredth.

The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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Answer:

Relation 1 & 2 are functions

Relation 3 & 4 are not functions

Step-by-step explanation:

For a relation to be a function every x must have one and only one y

This is not true for relation 3 which has 2 y's at x = m and 2 y's at x = v

This is also not true for relation 4 which has 2 y's at x = 4

Therefore, the standard deviation for the number of people with the genetic mutation in groups of 500 is approximately 6.726.

To find the standard deviation for the number of people with the genetic mutation in groups of 500, we can use the binomial distribution formula.

Given:

Probability of having the genetic mutation (p) = 0.09

Sample size (n) = 500

The standard deviation (σ) of a binomial distribution is calculated using the formula:

σ = √(n * p * (1 - p))

Substituting the given values:

σ = √(500 * 0.09 * (1 - 0.09))

Calculating the standard deviation:

σ ≈ 6.726 (rounded to three decimal places)

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Answer:

m = 2k/v²

Step-by-step explanation:

I think you mean solve for m, not k

Multiply both sides of the equation by 2

2 * 1/2 *(mv²) = 2 * k

Rewrite the expression.

1*(mv²) = 2*k

Multiply mv² by 1

mv² = 2*k

Divide each term by v² and simplify

mv²/v² = 2k/v²

mv²/v² cancel out and you get

m = 2k/v²

Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.

One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.

In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.

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a. The probability that 1 or more nonconforming units are found is 0.2311.

b. The probability that exactly 3 units are nonconforming is 0.000058.

a. To solve the problem, you can use the complement rule. The complement rule states that the probability of an event occurring is 1 minus the probability of the event not occurring. So, in this case, the probability that no nonconforming units are found in a sample of 25 units is:

P(no nonconforming) = (0.99)²⁵ = 0.787.

Therefore, the probability that 1 or more nonconforming units are found is:

P(1 or more nonconforming) = 1 - P(no nonconforming) = 1 - 0.787 = 0.213.

Rounded to four decimal places, this is 0.2311.

b. To solve the problem, you can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k).

Here, n = 25 is the sample size, k = 3 is the number of nonconforming units, and p = 0.01 is the probability of a unit being nonconforming.

Using the formula, we get:

P(X=3) = (25 choose 3) * (0.01)³ * (0.99)²² = 2300 * 0.000001 * 0.5459 = 0.000058.

Rounded to six decimal places, this is 0.000058.

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Answer:

sorry for the late answer, it looks like a b and d

Answer:

x=60

Step-by-step explanation:

divid the numbers

multiply all terms by the same value to eliminate fraction denominator

simplify

Answer:

CD =7.5 AC =20

Step-by-step explanation: you can answer this question by creating a proportion. For the side AB, we can find the total length by adding AE and EB, for a total of 8. Now we can build a proportion, where x equals AC. 12.5/x= 5/8. When you build a proportion, it’s important to make sure you use the same corresponding parts in the same places, for example, in both the fractions we made for the proportion, the total side length was on the bottom. From this proportion, we now cross multiply to get 5x=100. Divide both sides by 5 and you get that the length of AC is 20. We can do the same with CD. The proportion you’d use to find CD would involve the smaller line segment over the total length of the line. This would look like so: x/20=3/8. Cross multiply again and you’d get 60=8x. Divide both sides by 8 and you’d get x=7.5. This means the length of CD is 7.5.

Answer:

Hello!

Step-by-step explanation:

I assume that you have your answer by now so if you don't mind I need some points.

Have a fantastic day!!!

Answer:

13, 14

Step-by-step explanation:

The parameters of the numbers are;

A whole number value = 2 × Another number + 6

The sum of the two numbers is less than 50

Given that the first number is equal to more than twice the second number, we have that the first number is the larger number, while the second number is the smaller number

Where 'x' represents the second number, we get;

x + 2·x + 6 < 50

Simplifying gives;

3·x + 6 < 50

x < (50 - 6)/3 = 14.\(\overline 6\)

x < 14.\(\overline 6\)

Therefore, the numbers for which the inequality holds true are numbers less than 14.\(\overline 6\). From the given option, the numbers are 13, and 14.

Answer:

It's 3

Step-by-step explanation:

Just divide the entire equation by 3 to isolate the y variable on the left side.

y = mx + b (m is the slope)

and in this equation, after you divide by 3, the value of m is 3.

Answer:

Linda needs to raise a minimum of $9,000 to completely pay for her tuition fee for the first year, that is, $250 per month

Step-by-step explanation:

Tuition fee = $14,000 per year

Linda received a $5000 gift that she will use for her first year of college tuition during her 15th birthday

Amount remaining = Tuition fee - gift money received

= $14,000 - $5,000

= $9,000

Linda needs to raise $9,000 in the next three years to contribute to her first year of college tuition

The minimum amount Linda needs to save each month in the next three years to raise $9,000

= Remaining tuition / 3 years

= $9,000 / 3 * 12 months

= $9,000 / 36 months

= $250 per month

Answer:

11,25

Step-by-step explanation:

A sample size of at least 34 consumers is necessary to generate a 95% confidence interval for the percentage of customers who alter their plans with a margin of error of 0.12.

To estimate the sample size needed for a 95% confidence interval with a margin of error of 0.12, we can use the formula:

n = (Z^2 * p* q) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

p = proportion of clients who changed their vacation plans in the preliminary study (19/132 ≈ 0.144)

q = complement of p (1 - p)

E = desired margin of error (0.12)

Plugging in the values, we can calculate the required sample size:

n = \((1.96^2 * 0.144 * (1 - 0.144)) / 0.12^2\)

n ≈ (3.8416 * 0.144 * 0.856) / 0.0144

n ≈ 0.4899 / 0.0144

n ≈ 33.89

Rounding up to the nearest whole number, the estimated sample size needed is approximately 34.

Therefore, to obtain a 95% confidence interval for the proportion of customers who change their plans with a margin of error of 0.12, a sample size of at least 34 clients is required.

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The two theoretical quantities of ANOVA (Analysis of Variance) are:
1. Between-group variance.

2. Within-group variance:

1. Between-group variance.

This is the variance that can be attributed to differences between the group means.

It is calculated by comparing the mean of each group to the overall mean of all the data points.

The larger the between-group variance, the more likely there are significant differences between the groups.
2. Within-group variance:

This is the variance that can be attributed to differences within each group, i.e., the individual differences among the data points in each group.

It is calculated by comparing the individual data points in each group to their respective group mean.

The smaller the within-group variance, the more likely the groups are homogeneous.
In ANOVA, these two quantities are compared using an F-ratio.

If the between-group variance is significantly larger than the within-group variance, it indicates that there are significant differences between the group means, and the null hypothesis can be rejected.

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Answer:

A,C,D

Step-by-step explanation:

Some of the true statements about angles are:

This refers to the formation of two rays which share a common endpoint which are called vertices.

Please note that your question is incomplete so I gave you a general overview to help you get a better understanding of the concept.

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Answer:

$4.70 + $4.75m = $18.95 which is 3 miles in total.

Step-by-step explanation:

First make the numbers without the variables on one side.

4.75m = 18.95-4.70

Then subtract.

4.75m = 14.25

Finally divide the two numbers.

14.25 ÷ 4.75 = 3 miles

Answer:  m = 3  or 3 miles

Answer:

3 miles

Step-by-step explanation:

Pick up fee = $4.70

Charge = $4.75 per mile therefore this is expressed as 4.75 x m (or 4.75m)

18.95 = 4.7 + 4.75m (add the pick up fee plus fare per mile)

Subtract 4.7 from both sides then divide 4.75 from both sides.

This leaves you with m = 3

Answer:

x=-4

Step-by-step explanation:

First, distribute the 4

this makes 4x + 36 = 20

Then, subtract 36 to combine like terms. 4x = -16

divide 4x! x = -4

For the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

As given in the question,

Given number is equal to :

395,621

Round off the given number 395,621 to nearest ten thousand is given by:

395,621 = 300,000 + 95,621

Ten thousand is represented by 95,621 for the given number

95621 is in between two numbers

90,000< 95,621 < 100,000

95,621 is more closer to 100,000

After rounding it off to the nearest ten thousand

300,000+ 100,000 = 400,000

Therefore, for the given number 395,621 round off it to nearest ten thousand is equal to 400,000.

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The Taylor series for the function f(x) = 1/x centered at a = 3 is given by:

1/(x-3) = -1/(3-x) = -1/3 - (x-3)/9 - (x-3)²/27 - (x-3)³/81 - ...

This is a Maclaurin series with the associated radius of convergence R = ∞, since the function is analytic everywhere except at x = 3.

To derive the Taylor series, we first find the derivatives of f(x) = 1/x:

f'(x) = -1/x², f''(x) = 2/x³, f'''(x) = -6/x⁴, f⁴(x) = 24/x⁵, ...

Evaluating these derivatives at x = 3 gives:

f(3) = 1/3, f'(3) = -1/9, f''(3) = 2/27, f'''(3) = -6/81, f⁴(3) = 24/243, ...

Using these values, we can write the Taylor series in sigma notation as:

1/(x-3) = Σ (-1)ⁿ (x-3)ⁿ / 3ⁿ⁺¹, n = 0 to ∞

This series converges for all x such that |x-3| < 3, which gives us the radius of convergence R = 3.

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Answer: Water expands and becomes less dense when it freezes.

Step-by-step explanation:

When a solid is less dense than liquid that it is put in, it will float.

This is the case with icebergs. When water freezes, the molecules move away thereby expanding and increasing the volume of the water.

The larger the volume of an object, the smaller it's density.

The iceberg will therefore have a lower density that enables it to float.

Answer:

C: Water expands and becomes less dense when it freezes.

Step-by-step explanation:

I got it right on edge

Answer:

∠ETM is 56.7

Step-by-step explanation:

168.7 - 112

Answer:

a) (x+6)(x-1)

b) (x+8)(x-5)

c) (x+3)(x-10)

Step-by-step explanation:

The final answer would always have to be two brackets with x and the relevant variables.

x²: You know the possible factors that can be multiplied together would be x and x. Each factor would have to be in different brackets, so we get (x + smth else)(x +smth else)

When factorising quadratic expressions, you need to find the correct pair of factors, that when multiplied together, becomes the constant of the expression. They also need to become the middle term when they are multiplied with the term in the bracket and then added together.

Possible factors for a):

1. 1 × 6 = 6

2. 2 × 3 = 6

You know 1 - 6 = -5, so we shall use the factors 6 and 1.

(x+6)(x-1) = x² -x + 6x - 6

              = x² + 5x - 6

Thus, (x+6)(x-1) is the answer.

Possible factors for b):

1. 1 × 40 = 40

2. 2 × 20 = 40

3. 4 × 10 = 40

4. 5 × 8 = 40

You know 8 - 5 = 3, so we shall use the factors 8 and 5.

(x+8)(x-5) = x² -5x + 8x - 40

               = x² + 3x - 40

Thus, (x+8)(x-5) is the answer.

Possible factors for c):

1. 1 × 30 = 30

2. 2 × 15 = 30

3. 3 × 10 = 30

4. 5 × 6 = 30

You know 3 - 10 = -7, so we shall use the factors 3 and 10.

(x+3)(x-10) = x² -10x + 3x - 30

               = x² - 7x - 40

Thus, (x+3)(x-10) is the answer.

a)

x² - 5x - 6

= x² + x - 6x - 6

= x(x + 1) -6(x + 1)

= (x - 6) (x + 1)

b)

x² + 3x - 40

= x² + 8x - 5x - 40

= x(x + 8) -5(x + 8)

= (x - 5) (x + 8)

c)

x² - 7x - 30

= x² - 10x + 3x - 30

= x(x - 10) + 3(x - 10)

= (x + 3) (x - 10)

The two mathematical expressions 5(3t - 6) and 15t - 30 are equivalent.

Mathematical expressions are equivalent or equal when they have the same value.

Equivalent expressions work the same way despite their different looks.

We determine that two or more mathematical expressions are equivalent when simplified or yield the same value after substituting the variables.

Equivalent mathematical expressions are usually indicated using the equation symbol (=).

5(3t - 6) = 15t - 30

If t = 3

5(3t - 6) = 15

15t - 30 = 15

Thus, if two algebraic expressions are equivalent, then the two expressions have the same value.

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Answer: A

Step-by-step explanation:

We know the y intercept is -6 so the first point will be  (0,-6)   and we also know that the slope is  2/1  so after plotting (0.-6) you will have to go up by two and  1 unit to the right.  

Answer:

The answer is A!

Step-by-step explanation:

I just did it and it is right! Have an absolutaly amazing day! :) :) :) :)