Using the information given, select the statement that can deduce the line segments to be parallel. If there are none, then select none.

When m2 = m6
1. AD BC
2. DC AB
3. none

The 90% confidence interval for the population proportion of defective disks is approximately 0.022 to 0.077

To construct a confidence interval for the population proportion of defective disks, we can use the formula for a confidence interval for a proportion:

Confidence Interval = Sample Proportion ± Margin of Error

The sample proportion (p-hat) is calculated by dividing the number of defective disks (16) by the total number of disks in the sample (322):

Sample Proportion (p-hat) = 16/322 ≈ 0.0497

The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

The critical value depends on the desired confidence level. For a 90% confidence level, we can use a Z-score corresponding to a 5% significance level in each tail. This corresponds to a critical value of approximately 1.645.

The standard error is calculated as the square root of [(p-hat * (1 - p-hat)) / n], where n is the sample size.

Standard Error = √[(0.0497 * (1 - 0.0497)) / 322] ≈ 0.0168

Now we can calculate the margin of error:

Margin of Error = 1.645 * 0.0168 ≈ 0.0277

Finally, we can construct the confidence interval:

Confidence Interval = 0.0497 ± 0.0277

Lower Limit = 0.0497 - 0.0277 ≈ 0.0220

Upper Limit = 0.0497 + 0.0277 ≈ 0.0774

Therefore, the 90% confidence interval for the population proportion of defective disks is approximately 0.022 to 0.077.

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Justin and ruby are currently sharing sweets out after school in a ratio of 1:2 respectively. after buying 20 more sweets and sharing them evenly, they now have a ratio of 3:4. So, Justin initially had 5 sweets.

Justin and Ruby initially shared sweets in a ratio of 1:2. Let's represent the number of sweets Justin had as x, and the number of sweets Ruby had as 2x. After buying 20 more sweets and sharing them evenly, the new ratio is 3:4. Now, Justin has 3y sweets and Ruby has 4y sweets.

We can write two equations based on this information:

1) x + 20/2 = 3y (because Justin received half of the 20 new sweets)
2) 2x + 20/2 = 4y (because Ruby received half of the 20 new sweets)

Simplify the equations:

1) x + 10 = 3y
2) 2x + 10 = 4y

Now, we can solve these equations simultaneously to find the value of x and y:

From equation 1, x = 3y - 10

Substitute this value of x into equation 2:

2(3y - 10) + 10 = 4y
6y - 20 + 10 = 4y
6y - 10 = 4y

Rearrange the equation to solve for y:

2y = 10
y = 5

Now that we have the value of y, we can find the value of x:

x = 3y - 10
x = 3(5) - 10
x = 15 - 10
x = 5

So, Justin initially had 5 sweets.

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The probability of randomly selecting a score less than x = 34 from a normal distribution with a mean of µ = 40 and a standard deviation of σ = 8 is approximately 0.2266, or 22.66%.

First, we need to standardize the value of 34 using the formula for standardization:

Z = (x - µ) / σ

Where:

Z is the standard score or z-score,

x is the value of interest,

µ is the mean of the distribution, and

σ is the standard deviation of the distribution.

Plugging in the values, we get:

Z = (34 - 40) / 8 = -0.75

Now that we have the z-score, we can look up the corresponding probability from the standard normal distribution table or use statistical software. The standard normal distribution has a mean of 0 and a standard deviation of 1.

By looking up the z-score of -0.75 in the standard normal distribution table or using software, we find that the corresponding probability is approximately 0.2266. This means that there is a probability of 0.2266, or 22.66%, of randomly selecting a score less than 34 from the given normal distribution.

Alternatively, you can use software or a graphing calculator to directly calculate the probability using the standard normal distribution function. In this case, you would use the formula:

P(Z < -0.75) = Φ(-0.75)

Where Φ represents the cumulative distribution function (CDF) of the standard normal distribution. By evaluating this expression, you would get the same result of approximately 0.2266.

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Answer:

3

Step-by-step explanation:

add perenthasis (10 \ 10) 3

(10\10) is 1

(1)3 = 3

Answer:

65 + 12.5v = m (M being free movie)

Step-by-step explanation:

65 for the original 65 poitns he gets for signing up, then if he gets 12.5 points for every movie he visits then you need to multiply 12.5 times the amount of movies he went to (v) so it would be 65 + 12.5v
v would need to be 11.6

If you do 210 - 65 thats 145, then you do 145 divided by 12.5 which would get you 11.6

When rolling a six-sided die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. Event B is rolling an even number, which means there are three possible outcomes: 2, 4, or 6. Since there are only three possible outcomes in Event B, it is a simple event.
Let's analyze the event and outcomes when rolling a six-sided die.

Event B: Rolling an even number.

Step 1: Identify the possible outcomes.
When rolling a six-sided die, the outcomes are numbers 1 to 6 (1, 2, 3, 4, 5, and 6).

Step 2: Determine the outcomes in the event.
For Event B, the even numbers are 2, 4, and 6. So, there are 3 outcomes in Event B.

Step 3: Decide if the event is a simple event or not.
An event is considered a simple event if it has only one possible outcome. Since Event B has 3 possible outcomes (2, 4, and 6), it is not a simple event.

Event B (rolling an even number) has 3 possible outcomes (2, 4, and 6), and it is not a simple event.

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Answer:

1) By Pythagoras theorem

16² = x² + (√65)²

256 = x² + 65

x² = 256-65

x² = 191

x=√191

x=13.82 or 13.8 ft

2) 15²=x²+10²

225=x²+100

x²=225-100

x²=125

x=√125

x=11.18 or 11.2km

3) 12.36 or 12.4 cm

4) 8.36 or 8.4 mi

To answer your question, we have to check which of the annelid structures or events is not correctly paired with its role in locomotion.

The incorrect pairing is:
E. Chaetae—provides gas exchange surface for body muscles

A chaetae is a chitinous bristle or seta set up in annelid worms. These are set up as packets on the parapodia, paired accessories on the side of the body.

The chaetae are epidermal extracellular structures, and easily visible in utmost polychaetes. The ultra-structure of chaetae is unnaturally analogous for all taxa but there's vast diversity in chaetal morphology. Also, chaetae bear precise characters for determination of species and taxonomic assessment.

The correct role of chaetae in annelids is to assist with traction and movement, not gas exchange.

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Answer:

x=3y-4

Step-by-step explanation:

3x+8=x+6y

so the goal here is to make everything equal to x. first, let's move all the X's to one side by subtracting x on both sides.

2x+8=6y

now we want x alone on one side so we subtract 8 on both sides.

2x=6y-8

divide by 2

x=3y-4

Answer:

x = 3y - 4

Step-by-step explanation:

Given

3x + 8 = x + 6y ( subtract x from both sides )

2x + 8 = 6y ( subtract 8 from both sides )

2x = 6y - 8 ( divide all terms by 2 )

x = 3y - 4

The area of the decorative is (b) 36π square inches.

The area of a circle can be found by using the formula A = πr^2, where A is the area and r is the radius of the circle.

Since the circumference of the mirror is 12π inches, we can use the formula C = 2πr to find the radius of the mirror.

12π = 2πr

r = 6

So, the radius of the mirror is 6 inches.

Then, we can use that information to find the area of the mirror:

A = πr^2

A = π(6^2)

A = 36π square inches.

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The missing number in 6 17 37 10 10 25 12 32 ? is 37.

Based on the provided sequence, the missing number can be determined by observing the pattern within the given numbers. Let's analyze the sequence:

6 17 37 10 10 25 12 32 ?

By examining the sequence, we can identify the following pattern:

The first number, 6, increases by 11 to become 17.

The second number, 17, increases by 20 to become 37.

The third number, 37, increases by 27 to become 64.

At this point, we can see that the pattern alternates between adding the square of an increasing increment and subtracting that same increment from the previous number. So, to continue the pattern:

The fourth number, 10, decreases by 6 to become 4.

The fifth number, 10, decreases by 1 to become 9.

The sixth number, 25, increases by 3 to become 28.

The seventh number, 12, decreases by 4 to become 8.

The eighth number, 32, increases by 5 to become 37.

Therefore, the missing number in the sequence is 37.

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Answer:

below

Step-by-step explanation:

Standard form

ax + gy = c       re-arrange to slope -int form   subtract ax from both sides of the equation

gy = - ax + c       divide thru by 'g'

y = -a/g x + c/g      - a/g would be the slope , m   and c/g would be the y-axis

  intercept , b    for   slope intercept form    y - mx +b  

Answer:

The answer is andrew!

Step-by-step explanation:

andrew 10 + 14 + 8 + 12 + 11/ 5 = 11

leroy 2 + 12 + 9 + 11 + 16/5 = 10

Answer:

So the sequence of the five numbers are;

10,26,74,218,650

Step-by-step explanation:

In this question, we are interested in building a sequence of 5 numbers given the initial term.

Okay, to build this sequence, we will need to look at the rule that guides the building of the new sequence:

The rule is that the next term is 4 less than 3 times the previous term.

Okay, let’s call the next term y, while the previous term is x.

Following what was specified in the question;

y = 3x -4

Recall; the next term(y) is 4 less (-4) than 3 times (3 multiplied by) the previous term (x)

So let’s start with the initial term of 10.

The next term will be;

y = 3(10) -4 = 30-4 = 26

The next term after 26 will be ;

y = 3(26) -4 = 78-4 = 74

The next term after 74 will be;

y = 3(74) -4 = 222-4 = 218

The next term after 218 will be;

y = 3(218) -4 = 650

Answer:

as a decimal its 2.66666666667, as a mixed number its about 2 1/3

Step-by-step explanation:

multiply 2/3 by 4 to get the whole amount of flour

Answer: 5(x-1)

Step-by-step explanation:

5*x = 5x

5*-1 = -5

therefore the answer is 5(x-1)

5x-5 distributed is 5(x-1).

The common factor of 5x and 5 is 5.

5x divided by 5 is 1x or x.

5 divided by 5 is 1.

So the answer is 5(x-1).

Answer:

A

Step-by-step explanation:

Answer: A. -10

Step-by-step explanation:

The number of hours it will take the airplane to fly the given distance would be = 4.5 hours

To calculate the number of hours that can be used for the distance, the following needs to be done. That is;

The number of hours it take to complete 3600 miles = 3 hours

Therefore the number of hours it will take to complete 5400miles = X hours.

That is;

3600 miles = 3 hours

5400 miles = X hours

make X the subject of formula;

X = 5400×3/3600

= 16,200/3600

= 4.5 hours.

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Answer:

410.3

Step-by-step explanation:

Volume of a sphere = (4/3)πr³

V1 = (4/3)(3.14)(3³) = 113 ft³

V2 = (4/3)(3.14)(5³) = 523.3 ft³

V2 - V1= 523.3 - 113 = 410.3

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

When the diameter is known, the formula is Radius = Diameter/ 2.

When the circumference is known, the formula is Radius = Circumference/2π.

When the area is known, the formula for the radius is Radius = ⎷ (Area of the circle/π).

Hi!

\(\spadesuit\) We're given an equation in slope-intercept form.

                          \(\clubsuit~~~\large\boldsymbol{y=mx+b} ~~~\clubsuit\)

where:

\(\clubsuit ~\boldsymbol{m - > slope}\)

\(\clubsuit~~\boldsymbol{b- > y-intercept}\)

Therefore,

\(\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:-7}\\\bold{y-intercept:12}\end{cases}}}}\)

I hope that helped, have a wonderful day. :)

The number of times both the lights red and blue will blink at the same time in 60 seconds is 10 times (Using LCM method to find out the common multiple)

Blue lights blink every 2 seconds.

Red Lights Blink every 3 seconds.

Here we can use the concept of LCM (least common multiple)

This is the method where we can find out the least common multiples among the factors of any two or more numbers.

As 2 and 3 are two non-zero positive integers so we can find out the smallest common multiple of both the numbers that will be divisible by 2 and 3.

Multiples of 2 = 2, 4, 6, 8

Multiples of 3= 3, 6,9, 12

so the least common multiple is 6 here.

LCM of 2 and 3 is 6.

No of the times the red and blue lights will blink at the same time in 60 seconds = 60 / LCM of Blinking of red and Blue light

=60/6

=10

So they will blink 10 times at the same time in 60 seconds.

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They will blink together at 24 second because it is the first number where multiples of 6 and 4 coincide.

A multiple in mathematics refers to the outcome of multiplying two numbers together. Here, the number 7 is multiple by 56. Here's another illustration of a multiple: Fancy facts Because the result of multiplying 0 by any number is 0, 0 is a multiple of all numbers.

The multiplication symbol is frequently misinterpreted by students as "times." They can only define it as a synonym for multiplication, however, when pressed further. (An informal survey of friends at dinner indicated that everyone was aware of this.) One of those words we use frequently and unconsciously is "times."

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Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

Answer:

Step-by-step explanation:

At first,

Let start writing the squares of number 0 to 10,

0²=0

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

Now,

According to your question,

Hence, your given conditions matches with the numbers 64 and 36.

Therefore, the numbers are 64 and 36.

The value of x when the scale factor of Figure A to Figure B is 4:5 is 12.

Therefore, the answer is 12.

Scale factor is the ratio of corresponding dimensions of an object to another object. If scale factor is less than 1, it is scaling down of the figure and if the scale factor is greater than 1, it is scaling up of the figure. Here the ratio is 4:5, so it is less than 1.

As the scale factor is 4:5, the ratio of corresponding sides is 4 is to 5.

That is x/15 = 4/5.

Therefore, x = 4/ 5 × 15

x = 12

-- The question is incomplete without the figure, the complete question is:

__If the scale factor of Figure A to Figure B is

4:5, find the value of x.__

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Answer:

4\(x^{2}\) − 8 − 14

Step-by-step explanation:

1. Simpify

2. Subtract the numbers

3. Combine like terms

4. last but not least rearrange the terms

Hope this helped :)

Answer:

88

Step-by-step explanation:

100 - (9 - 3)2

100 - (6)2 = 100-12 = 88

According to the Pythagoras theorem, the value of x is 8.366.

Here we know that the the Pythagoras theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, this can be expressed as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Based on this we have obtained the following three equations, they are

x² + z ² = 10

x² + 7² = y²

z² = y² + 3²

When we simplify these equations, then we get,

2z² = 60

z² = 30

z = 5.47

Then the value of x is obtained as

=>  x² = 100 - 30

=> x = √70 = 8.366

Finally, the value of y is calculated as

=> y² = x² - 7²

=> y² = 70 - 49 = 21

=> y = 4.58

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Answer:

Step-by-step explanation:

Inches per hour is the rate we are looking for here, which will then be the slope of the linear equation. Slope is the same thing as the rate of change. While this may not seem all that important right now, it's actually a HUGE concept in higher math, especially calculus!

If the pool is filling at a rate of 2 inches per every 4 hours, then by dividing, we get that the rate is 1 inch every 2 hours, which translates to a slope of 1/2. Creating an equation with this slope:

\(w=\frac{1}{2}t\)  Let's check it. We are told that after 4 hours there are 2 inches of water in the pool. That means if we plug in 4 for t and solve for w, we should get w = 2:

\(w=\frac{1}{2}(4)\) and

w = 2. So we're good!