Points A, B, C, and D are collinear and positioned in that order. Find the length indicated.
AC=149, BD= 3x+307, BC= 6x+443, AD= 8x + 717. Find BC

The given expression as a sine function is \(sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

The given expression is:

\(sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )\)

Note that:

\(sin(A+B)=sinAcosB+cosAsinB\)

Applying the addition principle to the given expression, we have:

\(sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

Therefore, the given expression as a sine function is \(sin(\frac{\pi}{5} +\frac{\pi}{2} )\)

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Answer:

Margin of Error concept & example

Step-by-step explanation:

Margin of Error refers to range of values around sample statistic, within confidence interval. It denotes, expected percentage points of difference from real population value.

Example : With 95% Confidence Interval with (lets say 4) percent Margin of Error implies that - statistic is expected to be within 4% deviation around population mean 95% of the time.

It applies to pie case also. People liking chocolate pie are likely to be within ME% around sample percentage, with probability of CI% .

Answer:

\(P(Sports|Senior)= 0.71\)

Step-by-step explanation:

Hello!

You have a two-way table with the information describing students after school activities regarding the grade the student is in.

You have to calculate the probability that a randomly selected student is ins sports given that he is a senior.

This is a conditional probability and you can symbolize it as:

P(Sports|Senior)

Using the definition of the conditional probability we know that:

\(P(Sports|Senior)= \frac{P(Sports n Senior)}{P(senior)}\)

The probability of the intersection of both events "Sports" and "Seniors" can be calculated as the number of students that are in senior years and take sports by the total of students in the sample

P(Sports ∩ Senior)= \(\frac{25}{100}= 0.25\)

The probability of the student being a senior is a marginal probability, you can calculate is as the number of observed students that are in senior year by the total number of students:

P(senior)= \(\frac{35}{100} = 0.35\)

Now you can calculate the asked probability

\(P(Sports|Senior)= \frac{P(Sports n Senior)}{P(senior)}= \frac{0.25}{0.35} = 0.71\)

I hope this helps!

Answer:

Step-by-step explanation:

P ( Sports | Senior ) = \(\frac{P ( Sports|Senior )}{P ( Total Senior)}\)

\(\frac{25}{100} =25\)

\(\frac{35}{100} =35\)

\(\frac{25}{35} =0.714285=\) 0.71

Answer:

The value of \(\frac{14}{8} + \frac{15}{12}\)  = 3

Step-by-step explanation:

Explanation

Given       \(\frac{14}{8} + \frac{15}{12}\)

L.C.M     8 , 12   is  24

       \(\frac{14}{8} + \frac{15}{12} = \frac{14 X 3 + 15 X 2}{24}\)

                  = \(\frac{42 +30}{24} = \frac{72}{24} = 3\)

Final answer:-

The value of \(\frac{14}{8} + \frac{15}{12}\)  = 3

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

Answer:

∠ 16 = 26°

Step-by-step explanation:

∠ 10 = ∠ 2 = 26°  ( corresponding angles )

∠ 12 = ∠ 10 = 26°  ( vertical angles )

∠ 16 = ∠ 12 = 26° ( corresponding angles )

Answer:

D

Step-by-step explanation:

Answer:

-28 1/3

Step-by-step explanation:

-8 1/3= -25/3

3 2/5= 17/5

-25/3*17/5= -28 1/3

Answer:

5

Step-by-step explanation:

The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

8x² + 16x + 3 = 0

using Quadratic formula

The following steps are involved

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)

\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)

\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)

\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)

\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)

\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

\(x = -0.209431\)

or

\(x = -1.79057\)

Therefore, the steps peter could follow will give the result

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

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Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Step-by-step explanation:

Z 00m

336"083"2553

(wZE2XQ) are

Answer:

  2.5%

Step-by-step explanation:

You want the percentage below 335 if the distribution is normal with a mean of 555 and a standard deviation of 110, using the empirical rule.

The z-score of 335 is ...

  Z = (X -µ)/σ

  Z = (335 -555)/110 = -220/110 = -2

The empirical rule tells you that 95% of the distribution is between Z = -2 and Z = 2. That is, 5% of the distribution is evenly split between the tails Z < -2 and Z > 2. Half that value is in each tail.

  P(X < 335) = 5%/2 = 2.5%

The percentage of people taking the test who score below 335 is 2.5%.

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Number of marbles were not chosen = 62 marbles

Number of marbles were in the bag before the game = 86 marbles

Number pf blue marbles were chosen = 24

Number of blue marbles = 40

Number of white marbles = 46 marbles

Total number of marbles = 40 + 46

= 86 marbles

Of the 40 blue marbles, 3/5 fraction were chosen

Number of blue marbles chosen = 40 × (3/5)

= 24 marbles

Part a

Number of bag's marbles were not chosen = 86 - 24

= 62 marbles

Part b

Number of marbles were in the bag before the game = 86 marbles

Part c

Number of blue marbles were chosen = 40 × (3/5)

= 24 marbles

Therefore, the 62 marbles were not chosen. There were 86 marbles before the game and number of blue marbles were chosen is 24 marbles

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Answer:

36

Step-by-step explanation:

Just add 12+12+12 or 12x3

Answer:

36

Step-by-step explanation:

bro if a dozen is 12 then add it 4 times it comes 48 then 3/4 is 36

Answer:

240

Step-by-step explanation:

20%×5=100

48×5=240

Answer:

20% of 240 is 48.

Step-by-step explanation:

Forming the equation,

→ (x/100) × 20 = 48

Now the value of x will be,

→ (x/100) × 20 = 48

→ (20x/100) = 48

→ x/5 = 48

→ x = 48 × 5

→ [ x = 240 ]

Hence, the answer is 240.

Answer:

(x+4)^2  -25

Step-by-step explanation:

x²+8x-9 in the form  (x+k)² +h.

We need to complete the square.

x^2 +8x   -9

Take the coefficient of x.

8

Divide by 2.

8/2 =4

Square it.

4^2 = 16

Add this then subtract i.

x^2 +8x+16    -16   -9

The x^2 +8x+16 becomes  (x+4) ^2  and we can simplify the remaining terms.

(x+4)^2  -25

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Based on the fact that the cross-country course is shaped like a parallelogram, the total length of the cross-country course is 10 miles.

The total length of the cross-country course will be the perimeter of the shape that the course is shaped like.

As this course is shaped like a parallelogram, the total length would therefore be:

= Base + Base + Length + Length

Solving gives:
= 3 + 3 + 2 + 2

= 6 miles

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Answer:

slope = -3

Step-by-step explanation:

slope = -3

Answer:

-1/3

Step-by-step explanation:

we know ,

Here , m= slope

(x1,y1) , (x2,y2) are point of the slope

\(m=\frac{6-2}{-6-6 }\)

or, \(m=\frac{4}{-12 }\)

so , m= -1/3

Answer:

\(1216 = 64 \times 19\)

64 is 4 cubed, and 19 is a prime number between 10 and 20.

Step-by-step explanation:

Answer:

I think it is 2x-3y=-12 not sure but try it

The incorrect statement is the reflection is over x-axis.

Given that an image has been reflected to form another image, we need to find the incorrect statement from the given options,

A reflection is known as a flip.

A reflection is a mirror image of the shape.

An image will reflect through a line, known as the line of reflection.

A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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The incorrect statement is the reflection is over x-axis.

Given that,

an image has been reflected to form another image, we need to find the incorrect statement from the given options,

So, here the image is reflected over y-axis so the rule (x, y) → (-x, y) can be followed,

Also, the orientation of the image is preserved.

Since, the transformation is reflection, so the image and pre-images are congruent.

Hence, the incorrect statement is the reflection is over x-axis.

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The given triangle is a right angled triangle. Therefore, by Pythagoras theoram,

From the figure,

Hence, Option D is the right answer.

Answer: A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The correct option of system of equations that can be used to find the temperature at which the degrees Celsius and the degrees Fahrenheit would be equivalent is the option;

5·F - 9·C = 160

F - C = 0

A system of equation, is a set of equation that have common variables.

The equation for conversion of the temperature in degrees Celsius to the temperature in degrees Fahrenheit is; 9·C = 5·F - 160

When the temperature in degrees Celsius is equivalent to the temperature in degrees Fahrenheit, we get;

F = C

Therefore;

F - C = 0

Similarly, from the specified equation, we get;

9·C = 5·F - 160

5·F - 9·C = 160

The system of equation that would give the temperature where the degrees Celsius and degrees Fahrenheit are equivalent is therefore;

5·F - 9·C = 160

F - C = 0

(Which yields a temperature of 40°)

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