he altitude to the hypotenuse of a triangle with angles of 30 and 60 degrees is 3 units. what is the area of the triangle, in square units? express your answer in simplest radical form.

The best description of the relationship between the y-axis and the line connecting F to F' after reflection over the y-axis is that they are perpendicular to each other.

When a triangle is reflected over the y-axis, its vertices swap their x-coordinates while keeping their y-coordinates the same. Let's consider the points F and F' on the reflected triangle.

The line connecting F to F' is the vertical line on the y-axis because the reflection over the y-axis does not change the y-coordinate. The y-axis itself is also a vertical line.

Since both the line connecting F to F' and the y-axis are vertical lines, they are perpendicular to each other. This is because perpendicular lines have slopes that are negative reciprocals of each other, and vertical lines have undefined slopes.

Therefore, the best description of the relationship between the y-axis and the line connecting F to F' after reflection over the y-axis is that they are perpendicular to each other.

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The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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Multiply 0.5/100 times 44 to find what is 5% of 44 equal to:

Therefore, 0.5% of $44 is equal to $0.22.

Systematic random sampling is sometimes used in place of simple random sampling due to its efficiency, representativeness, ease of implementation, and cost-effectiveness.

Systematic random sampling is sometimes used in place of simple random sampling for several reasons, including:
Efficiency:

Systematic random sampling can be more efficient than simple random sampling, as it involves selecting elements at regular intervals from the population.

This often reduces the time and effort needed to collect data compared to simple random sampling.
Representativeness:

Systematic random sampling may provide a more representative sample of the population.

By selecting elements at regular intervals, it ensures that different segments of the population are included, reducing the potential for sampling bias.
Ease of implementation:

Systematic random sampling is relatively easy to implement, as it involves fewer random selections compared to simple random sampling.

This makes it more practical for large populations or when a sampling frame is not readily available.
Cost-effectiveness:

Systematic random sampling can be more cost-effective than simple random sampling.

Since the process is more efficient, it may require fewer resources, such as time and personnel, to collect data.

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you can solve the equestion by many rules , but in my point of view the easiest rule is subtraction/addition and subtition method .

Ans X=11.5

Y = -39

8x+2y=14 eqn.......1

82+2y=4 eqn .......2

2y= -78 (4-82)

y = - 39

putting value of y in eqn ..1

we get,

8x+ 2×(-39) =14

8x= 14+78

8x=92

x = 92÷8

x=11.5

it's a subtition method..

You can treat x and 2x+1 just as though they are real numbers.

So f(2x+1) = 3(2x+1) - 5 = 6x + 3 - 5 = 6x - 2

In the above, I made use of something called the distributive law which says that if a,b and c are real numbers, then a(b+c) = ab + ac.

Answer:

not sure if they want 19 or 19.00

The Correct choices are :

Answer:

Step-by-step explanation:

The table shown inconsistent change of price over the year. The price drops down and is negative.

Correct choices are:

About 3.22 times larger is the middle school than the football field. the answer in standard form is 592.8 × 3\(\frac{17}{76}\) = 1911

A standard form is a way of expressing a certain mathematical idea, such as an equation, number, or expression, in a way that adheres to a set of rules. The standard form is used to clearly represent extremely large or extremely small numbers.

The number 4,500,000,000 years is used to represent 4.5 billion years, for instance. As you can see, writing a large number like 4.5 billion in its number form is not only difficult but also time-consuming, and there is a chance that we may write a few 0s more or less. The standard form of the number is very helpful in this situation.

In the standard form, 4,500,000,000 = 4.5 109, for instance.

Size of middle school = 18.2 x 105 square feet

                                    = 1911 square feet

Size of football field =  5.7 x 104

                                 = 592.8 square feet

About 3.22 times larger is the middle school than the football field. the answer in standard form is 592.8 × 3\(\frac{17}{76}\) = 1911

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The chances that the coin is unbiased are 0.08 or 8%.

Probability is the measure of the likelihood of an event occurring.

Probability is calculated by dividing the number of successful events by the total number of possible events.

The probability of an event ranges between 0 and 1.

An event with a probability of 0 has no chance of occurring, whereas an event with a probability of 1 is certain to occur.

In the given question, a coin was tossed 500 times.

The result was heads 230 times and tails 270 times.

Let us calculate the probability of getting heads when the coin is tossed.

P(h) = Probability of getting heads = Number of heads/Total number of tosses = 230/500 = 0.46

Similarly, let us calculate the probability of getting tails when the coin is tossed.

P(t) = Probability of getting tails = Number of tails/Total number of tosses = 270/500 = 0.54

The coin is unbiased if the probability of getting heads is equal to the probability of getting tails when the coin is tossed.

P(h) = P(t)0.46

= 0.54 0.54 - 0.46

= 0.08

Thus, the chances that the coin is unbiased are 0.08 or 8%.

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Answer:

£84

Step-by-step explanation:

The total cost of the dishwasher is: £372

The deposit she makes is: £36

Thus, she still has to pay the following amount:

£372 - £36 = £336

And this amount will be divided into 4 equal monthly payments. So, we must divide the amount that she still has to pay by 4.

Each one of this monthly payments will have a value of:

£336 ÷ 4 = £84

the answer is that each monthly payment will be of £84

Answer:

resistant

because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.

Answer:

8x + 5y + 132 = 0

Step-by-step explanation:

Answer:

The first option is correct

Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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Answer:

Step-by-step explanation:

6x - 17 = 3x + 7

3x = 24

x = 8

Answer :

\( \: \)

Step-by-step explanation :

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

\(\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\\)

Here,

\( \: \)

So, substituting the values in the formula we get :

\(\\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}= (7) {}^{2} + (8 {)}^{2} }}} \\ \)

\( \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=49 +64}}} \\ \)

\( \\ {\longrightarrow \pmb{\sf {\qquad (x {)}^{2}=113 }}} \\ \)

\(\\ {\longrightarrow \pmb{\sf {\qquad x= \sqrt{113} }}} \\ \)

\(\\ {\longrightarrow \pmb{\sf {\qquad x \approx10.63 }}} \\ \)

Therefore,

Because the graph passes the vertical line test, we conclude that this represents a function.

When we have a graph, to check if the graph represents a function we need to use the vertical line test.

This test says that if we can't draw any vertical line that intersects the graph in more than one point, then the graph represents a function.

Here we clearly can see that no vertical line intercepts the graph in more than one point, so this is a function.

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Answer:

24 hours

Step-by-step explanation:

160 x 18 = 2880

2880/120 = 24

Yes, triangle inequality theorem apply to all equilateral triangles.

The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.

A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.

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Answer:

(12,-2)

Step-by-step explanation:

look on a number line

count 7 from 5 to the right and left

and put both number into a (x,y) format

Answer:

12 & -2

Step-by-step explanation:

5 + 7 = 12

5 - 7 = -2

The missing values of a, b, c and d in the table can be filled as shown in the image attached.

To find the missing values of of a, b, c and d in the table, we have to factor the polynomials as follow:

No. 1

x² - 6x + 8 = (x - 4)(x - 2)

Thus, a = 1, b = -4, c = 1 and d = -2

No. 2

3x³ - 6x² - 24 = 3x(x - 4)(x + 2)

Thus, a = 1, b = -4, c = 1 and d = 2

No. 3

2x² - 2x - 24 = (x - 4)(2x + 6)

Thus, a = 1, b = -4, c = 2 and d = 6

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If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer

19.50 x 40 = $ 780 a week.

I hope this helps!

Answer:

35

Step-by-step explanation:

1.divide the miles that Oscar drove to get 105÷3=35

Answer:

the X is 35

Step-by-step explanation:

Answer:

83

Step-by-step explanation:

Answer:

x = 59

y = 83

Step-by-step explanation:

First, you need to solve for y in order to solve for x. Using the Triangle Sum Theorem, you will find that y is 83 degrees.

Now, using the Vertical Angles Theorem, you can figure out the third angle of the triangle in which x is, 83.

Using the Triangle Sum Theorem again, you will find that x is 59.

Answer:

I believe the multiplied number would be 4.

39 × 4 = 156

The number is = 4

Step-by-step explanation:

I'm not sure what is 46 at the end of the question.

The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.

The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.

z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.

z = {x-μ}/{σ}  = {-20-0}/{8}  = −2.5

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.

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