15. Triangles ABC and DEF are similar.
Work out the length of BC.
​

Answer:

It is wrong because John forgot another solution. You can see that the line and the quadratic intersect at (5,14) too.

Explanation:

For any 45-45-90 triangle, if each leg is x units long, then the hypotenuse is x*sqrt(2) units long. Comparing that with 16*sqrt(2) must mean x = 16.

a) The function is continuous in it's entire domain.

b) The increasing and decreasing intervals for the function are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.

The lateral limits for the function in this problem are defined as follows:

The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.

The intervals of increase and decrease are given as follows:

The function for this problem is the piece-wise function A(x).

Item a asks if the function is continuous.

Item b asks when the function is increasing and when it is decreasing.

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Answer:

The test statistic is [tex]z = -2.1[/tex]

The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A simple random sample of 400 parts from supplier 1 finds 20 defective.

This means that:

[tex]p_1 = \frac{20}{400} = 0.05, s_1 = \sqrt{\frac{0.05*0.95}{400}} = 0.0109[/tex]

A simple random sample of 200 parts from supplier 2 finds 20 defective.

This means that:

[tex]p_2 = \frac{20}{200} = 0.1, s_2 = \sqrt{\frac{0.1*0.9}{200}} = 0.0212[/tex]

Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Test whether the defective rates of the parts from two suppliers are significant different at the 1% significance level.

At the null hypothesis, we test if they are equal, that is, if the subtraction of the proportions is 0. So

[tex]H_0: p_1 - p_2 = 0[/tex]

At the alternate of the null hypothesis, we test if they are different, that is, if the subtraction of the proportions is different of 0. So

[tex]H_a: p_1 - p_2 \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the sample proportions:

[tex]X = p_1 - p_2 = 0.05 - 0.1 = -0.05[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0109^2 + 0.0212^2} = 0.0238[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.05 - 0}{0.0238}[/tex]

[tex]z = -2.1[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.05, that is, P(|z| < 2.1), which is 2 multiplied by the p-value of Z = -2.1.

Z = -2.1 has a p-value of 0.0179

2*0.0179 = 0.0358.

The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.

Answer:

24xy - 32y

Step-by-step explanation:

4y × 6x =24xy

4y × -8 = -32y

brainliest plz? i got 1000+ points deleted

Answer:

4y(6x-8)

[tex]4y \times (6x - 8)[/tex]

[tex]4y \times - 6x + 8[/tex]

[tex] - 24xy + 8[/tex]

[tex] - 32xy[/tex]

Answer

Number pattern, sequence, finding the algebraic rule and using a ... To illustrate this, consider the following sequence of numbers {1, 3, 5, 7, 9, …}.

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.Here, we get the numbers in the pattern by skip counting by 5. Given are the steps to identify a number pattern.To solve the problems of number pattern, we need first to find the rule being followed in the pattern.

To find out the rule, we need to see the first few numbers in the series.Try to see the difference between consecutive numbers, it will help us understand the relationship between the numbers.Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, … Here, we get the numbers in the pattern by skip counting by 5.

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The complete question is -

How can you use this pattern to find 3° of the number in Series ?

The required solution for the inequality a + 5 > -7 is (-12, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

a + 5 > -7

To find the solution for the inequality,

Simplify the inequality,

a + 5 > - 7

a > - 7 - 5

a > -12

The value of a is greater than -12, implies that,

The solution for the value of the given inequality is (-12, ∞).

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For the arithmetic sequence 4 - 2(n - 1), we have that:

For the geometric sequence 6 x 3^(n - 1), we have that:

An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.

The nth term of an arithmetic sequence is given by the equation presented as follows:

[tex]a_n = a_1 + d(n - 1)[/tex]

In which:

The sequence in this problem is defined as follows:

4 - 2(n - 1)

Which has first term 4 and common difference -2, hence the terms are:

4, 2, 0, -2, -4, -6 and so on...

A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.

The nth term of a geometric sequence is given by the equation presented as follows:

[tex]a_n = a_1 \times q^{n - 1}[/tex]

In which:

The sequence for this problem is given as follows:

6 x 3^(n - 1)

Which has first term of 6 and common ratio of 3, hence the terms are given as follows:

6, 18, 54, and so on...

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The kind of sequence that you will obtain when you list the number of tickets sold over time is given as follows:

A geometric sequence.

A sequence can be classified as either arithmetic or geometric, as follows:

If none of these statements is true, then the function is neither arithmetic or geometric.

A growing amusement park is able to sell 7 times as many tickets each year as it did the year before, which means that there is a constant ratio of 7 between the amounts of tickets sold each year, and thus this sequence is a geometric sequence.

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Area and circumference of the circle are 78.5 m² and 31.4 m respectively.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that, a circle have a radius 5 m

Area of a circle = π × radius²

Circumference = 2π×radius

Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²

Circumference = 3,14 × 2 × 5 = 31.4 m

Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.

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The equation of the line that passes through the points (-2,3) and (2,7) is:

x-y=-5

Therefore, option(C) x-y= -5 is correct answer.

Step-by-step solution:

The algebraic representation of a line's equation is the collection of points that make up the line in a coordinate system.

Given the line passes through the points (-2,3) and (2,7)

So, the equation of the line passing through the two points is given by:

[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{y-3 }{7-3} } =\frac{x-(-2) }{2-(-2) }[/tex]

[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]

[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]

[tex]y-3 = x+2[/tex]

Now rearranging the above equation:

x - y + 3 + 2 = 0

x - y + 5 =0

Therefore, the equation of the line passing through the points (-2,3) and (2,7) is: x-y=-5

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Carlos's score in his first game was 14.

Addition in maths, a process of combining two or more numbers.

Given that, Carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game.

Let the first score be x,

x+x+6x+6+6=60

3x+18 = 60

3x = 42

x = 14

Hence, Carlos's score in his first game was 14.

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The initial value where x=0, y is 12.74 and the exponential function is

y = 12.74(0.7)×.

Option D is correct.

The formula f(x) = [tex]a^x[/tex] defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x.

The quantity drops rapidly at first, then slowly in Exponential Decay. The rate of change slows over time. As time passes, the rate of change slows.

We know the formula for an exponential function is

y= a [tex]b^x[/tex]

where a is initial value and b is growth factor.

Now, we have to find the growth factor as

We can observe from the table that the values of y decrease as x increases.

That is an example of an exponential decay function.

In an exponential decay function, the value of a growth/decay factor b is always smaller than 1.

Thus, the initial value a= 12.74 and growth factor b=0.7 that is less than 1.

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Answer:

D) 4b

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

Answer: 195

Step-by-step explanation:

(0.3x + 66) + (0.1x + 36) = 180. ( 180 because thats the angle of a straight line)

0.3x + 0.1x + 66 + 36 = 180

0.4x + 102 = 180

0.4x = 180 - 102

0.4x = 78

x = 195

The coordinate of the point C is (0, a)

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

A = (0, a)

B = (b, 0)

As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.

This means that we start by calculating the equation of the altitude from B to line AC.

A linear equation is represented as

y = mx + c

Where

slope = m

y-intercept = c

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

slope = (y₂ - y₁)/(x₂ - x₁)

This gives

m(BC) = (0 - 0)/(b - 0) = 0

y-intercept (c) = a

So the equation of the line BC is

y = 0 * x + a

y = a

For line AC, we have

m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.

This means that the equation of the line AC is

x = 0

The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)

At this stage, we have the coordinates of the points from lines AC and BC to be

(0, a) and (0, a)

Next, we calculate the C as follows

C = Midpoints of (0, a) and (0, a)

This gives

C = 1/2 * (0 + 0, a + a)

Evaluate

C = (0, a)

Hence, the coordinate of C is (0, a)

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Answer:

There are a total of 5/35 ways that you and your friend are both chosen

Step-by-step explanation:

ap3x

The complete table is given in the solution.

A ratio is a way to show a relationship or compare two numbers of the same kind. We use ratios to compare things of the same type.

Given that, at Disneyland there are 300 girls go on the ride and 500 boys go on the ride this represents the ratio of girls and boys that go on the ride

The ratio of girls to boys = 3:5

Therefore, The complete table is as follows:-

    Girls                                     Boys                                     Total

     3                                             5                                             8

     6                                             10                                           16

     12                                            20                                          32

     30                                           50                                          80

     300                                         500                                      800

     480                                         800                                      1280

Hence, the complete table is above

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Answer:

45ft is the missing length j.

Answer:

the other side is 5 i think

Answer:

D

Step-by-step explanation:

Both lines are not intersecting each other so that means they don't share a solution

Answer:

volume = 483 cm³

Step-by-step explanation:

area of trapezoid = 1/2(6 + 17)(8.4) = 96.6 cm²

volume = 96.6 x 5 = 483 cm³

[tex]1000ml = 1l \\ 5000ml = \frac{5000}{1000} l = 5l[/tex]

So option C, 5 litres.

Answer:

5 liters

Step-by-step explanation:

So, lets go over what we know:

There is 5000 milliliters.

There are 1000 milliliters in a liter.

To find the amount of liters, we have to divide 5000 by 1000, or total millilileters by millilileters per liter:

5000/1000

=

5

Hope this helps!

By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.

It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)

First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.

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9514 1404 393

Answer:

  d.  13

Step-by-step explanation:

The smallest number is 3.

The largest number is 16.

The range is the difference between these values:

  16 -3 = 13 . . . range of the data

Answer:

no what grade is it I'm so confused

Answer:

3.665

Step-by-step explanation:

Answer:

942

I wish you luck! :D

give person above me brainliest since he/she/non-binary answered first

Answer:

942

Step-by-step explanation:

I just did this on a test and got 100% so I can verify this is right!

Answer:What is a triangle with 2 congruent sides and an obtuse angle

Step-by-step explanation: