Which theorem states, "The angles in a triangle always add to 180°"?

For a game, Bob has a total of 60 adventure cards. The distribution of cards, c, to players, p, is shown in the table. c = 60 ÷ p

Probability defines the possibility of occurrence of an event. Probability is the unit of measurement for an event's likelihood. It represents the proportion of positive results to all results. For instance: Receiving the numbers 3 and 5 while rolling the dice, as well as getting both an even and an odd number.

The equation would read: c = 60 / 2, which implies c = 30 if p=2. The equation would read 12 = 60 / p, p = 5, 20 = 60 / 3, etc. If c = 12, the equation would read... 12 = 60 / p, and p = 5, and so on, 20 = 60 / 3, and 15 = 60 / 4.

To know more about Table visit:

brainly.com/question/20648466

#SPJ1

Answer:

59

Step-by-step explanation:

Do it in my head.

59 +60 = 119

Answer:

D

Step-by-step explanation:

Because

1 dekameter = 1000 cm

167 / 1000

Answer:

d

Step-by-step explanation:

Answer:

I believe the correct answer is 600,000

Please mark Brainliest!!! =D

1) The probability distribution of the average weekly earnings for employees in general automotive repair shops is the sampling distribution of the sample mean. According to the Central Limit Theorem, if the sample size is large enough, the sampling distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

2) To find the probability that the average weekly earnings is less than $445, we can standardize the sample mean and use a z-table. The z-score for $445 is calculated as follows: z = (445 - 450) / (50 / sqrt(100)) = -1. Using a z-table, we find that the probability that the average weekly earnings is less than $445 is approximately 0.1587.

3) Since we are dealing with a continuous distribution, the probability that the average weekly earnings is exactly equal to any specific value is zero.

4) To find the probability that the average weekly earnings is between $445 and $455, we can subtract the probability that it is less than $445 from the probability that it is less than $455. The z-score for $455 is calculated as follows: z = (455 - 450) / (50 / sqrt(100)) = 1. Using a z-table, we find that the probability that the average weekly earnings is less than $455 is approximately 0.8413. Therefore, the probability that it is between $445 and $455 is approximately 0.8413 - 0.1587 = 0.6826.

5) In answering questions 2-4, we made an assumption about the population distribution based on the Central Limit Theorem. We assumed that since our sample size was large enough (n=100), our sampling distribution would be approximately normal.

6) If we assume that weekly earnings for employees in all general automotive repair shops are normally distributed with a mean of $450 and a standard deviation of $50, then we can calculate the z-score for an employee earning more than $480 in a given week as follows: z = (480 - 450) / 50 = 0.6. Using a z-table, we find that the probability that an employee will earn more than $480 in a given week is approximately 1 - 0.7257 = 0.2743.

The first 4 terms of given recursive formulas will be as follows

The recursive expression provides two pieces of information:

the first term in the sequence.

the pattern rule that takes each term from the previous term.

As we have G(1) = 18, G(n) = 2 · G(n − 1).

It's A geometric sequence with r as 2

∴ G(2) = 2 · G(2 − 1) = 2 · G(1) = 2(18) = 36.

∴ G(3) = 2 · G(3 − 1) = 2 · G(2) = 2(36) = 72.

∴ G(4) = 2 · G(4 − 1) = 2 · G(3) = 2(72) = 144.

As we have H(1) = 3, H(n) = 5 · H(n − 1).

It's A geometric sequence with r as 5

H(2) = 5 · H(2 − 1) = 5 . H(1) = 5(3) = 15.

H(3) = 5 · H(3 − 1) = 5 . H(2) = 5(15) = 75.

H(4) = 5 · H(4 − 1) = 5 . H(3) = 5(75) = 325.

As we have J(1) = 3, J(n) = J(n − 1) + 5

It's an arithmetic sequence with d as 5

J(2) = J(2 − 1) + 5 = J(1) + 5 = 3+5 = 8.

J(3) = J(3 − 1) + 5 = J(2) + 5 = 8+5 = 13.

J(4) = J(4 − 1) + 5 = J(3) + 5 = 13+5 = 18.

As we have M(1) = 3, M(n) = 2 · M(n − 1)

It's A geometric sequence with r as 2

M(2) = 2 · M(2 − 1) = 2 · M(1) = 2(3) = 6.

M(3) = 2 · M(3 - 1) = 2 · M(2) = 2(6) = 12.

M(4) = 2 · M(4 - 1) = 2 · M(3) = 2(12) = 24.

Know more about recursive formulas visit

https://brainly.com/question/1275192

#SPJ9

Answer:

The statement is correct

Step-by-step explanation:

Use the equation of a circle:

x² + y² = r²

x² + y² = 3²

then enter the coordinates of the point (2; √5):

2² + (√5)² = 9

4 + 5 = 9 (that is correct)

The point (2, √5) lies on the circle centered at the origin with radius 3 is True statement.

The standard equation of a circle is given by:

(x-h)² + (y-k)² = r²

Where (h,k) is the coordinates of center of the circle and r is the radius.

We have,

The point  (2, √5) lies on the circle centered at the origin with radius 3.

We know the equation of circle at origin is

x² + y² = r², where r is the radius of circle

So, x² + y² = 3²

Now. to check the point put x= 2 and y= √5 as

x² + y²

= 2² + √5²

= 4 +5

= 9

Thus, the given statement is Correct.

Learn more about Equation of circle here:

https://brainly.com/question/29288238

#SPJ3

Answer:

y-1 = 2(x+4)

Step-by-step explanation:

when switching to point-slope form, change the sign of the x-and-y values

Therefore, the interquartile range for the given data set is 27.5.

The interquartile range (IQR) is a measure of variability or spread of a set of data. It is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1) of a dataset. The quartiles divide the dataset into four equal parts, with each part containing an equal number of data points. The lower quartile (Q1) is the median of the lower half of the dataset, and the upper quartile (Q3) is the median of the upper half of the dataset.

Here,

To find the interquartile range (IQR), we first need to find the median of the data set. The median is the middle value when the data set is arranged in order. To arrange the data set in order, we have:

6, 12, 14, 15, 15, 20, 35, 48, 87

The median is the middle value, which is 15.

Next, we need to find the median of the lower half of the data set (also called the first quartile or Q1). To do this, we take the median of the values below 15:

6, 12, 14, 15, 15

The median of this set is 14.

Similarly, we need to find the median of the upper half of the data set (also called the third quartile or Q3). To do this, we take the median of the values above 15:

20, 35, 48, 87

The median of this set is (35+48)/2 = 41.5.

Finally, the interquartile range is the difference between Q3 and Q1:

IQR = Q3 - Q1

= 41.5 - 14

= 27.5

To know more about interquartile range,

https://brainly.com/question/29204101

#SPJ1

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

To learn more about : percentage

https://brainly.com/question/24877689

#SPJ8

The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y is 8, 0.30x + 0.30y is 6

Set variables to represent the amounts we wish to identify.

To learn more about expression refer to:

https://brainly.com/question/723406

#SPJ1

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Miles is going to spend less than the hours that were spent last week since 2/3 is a fraction.

A fraction represents a part of a whole, and is therefore always less than the whole. For example, 2/3 represents two out of three equal parts of a whole.

The implication of this is that the time that Miles would have to spend on biking in the coming week would be wo out of three equal parts of a whole time that was spent in the last week and this would be less than the time spent last week.

Learn more about fractions:https://brainly.com/question/10354322

#SPJ1

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

Answer:

the last one :)

Step-by-step explanation:

The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

To more on Graph:
https://brainly.com/question/19040584
#SPJ8

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

The task is to create an equation that use the total expense (y) and the total number of bowled games (x). Hence, the way that we will begin is by entering the knowing into the formula of slope intercept form:  y=mx+b.

Thus, we include them in the formula: y=4x+b.

14 = 4(3)+b

Find b

14 = 12+b

14 - 12=b

b = 2

Thus, an equation to show the overall price y of renting shoes and bowling x equipment is: y=4x+b.

Know more about the slope intercept form

https://brainly.com/question/1884491

#SPJ1

Complete question:

The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of the game increases the price by $4. After 3 games, the total cost with shoe rental is $14.

a.write an equation to represent the total cost y to rent shoes and bowl x games.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

baseball player:

number of a bats = 200

ratio (number of hits/number of at bats):

0.2121....

Step 02:

ratio:

The answer is:

number of hits = 42

Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

Answer:

x=177

Step-by-step explanation:

vertically opp angles are equal so 149=x-28, to find x you do 149 +28 whiichis 177

$1.30 and $1.70 is two standard deviations away from the mean on both sides of the mean, and the empirical rule for normal distribution tells us that approximately 95 percent of the data are within two standard deviations of the mean. Hence, option B is the right choice.

Data in a normal distribution is symmetrically distributed and has no skew. When displayed on a graph, the data has the shape of a bell, with most values clustering in a central region and tapering off as they go away from the center.

Because of their structure, normal distributions are sometimes known as Gaussian distributions or bell curves.

The empirical rule, often known as the 68-95-99.7 rule, indicates where the majority of your values fall in a normal distribution:

In the question, we are given that at a nearby frozen yogurt shop, the mean cost of a pint of frozen yogurt is $1.50 with a standard deviation of $0.10.

We are asked that assuming the data is normally distributed, approximately what percent of customers are willing to pay between $1.30 and $1.70 for a pint of frozen yogurt.

Following the empirical rule for a normal distribution, we need to check how many standard deviations from the mean are at $1.30 and $1.70.

$1.30 = $1.50 - 2($0.10)

and $1.70 = $1.50 + 2(0.10).

Thus, $1.30 and $1.70 is two standard deviations away from the mean on both sides of the mean, and the empirical rule for normal distribution tells us that approximately 95 percent of the data are within two standard deviations of the mean. Hence, option B is the right choice.

Learn more about normal distributions at

https://brainly.com/question/4079902

#SPJ2

Answer:

- Use the distributive property to get 4c-12=8

-Divide both sides by 4 to get c-3 = 2

Step-by-step explanation:

- Use the distributive property to get 4c-12=8

\(4(c - 3) = 8 \\ 4 \times c - 4 \times 3 = 8 \\ 4c - 12 = 8\)

Answer:4c-12=8

Step-by-step explanation:

4(c-3)=8

4xc-4x3=8

4c-12=8

Answer:

one side is \(\sqrt{10}\) and other 3\(\sqrt{10}\)

in decimal one side = 3.16

other side =  9.48

Step-by-step explanation:

In right angle

if two sides containing right angle is a and b and h is hypotenuse then

by Pythagoras theorem

a^2 + b^2 = h^2

__________________________________

let one side be x

given

One of the triangle’s legs is 3  times the length of the other leg

then other leg = 3x

given h = 10 cm

applying Pythagoras theorem

\(a^2 + b^2 = h^2\\x^2 + (3x)^2 = 10^2\\x^2 + 9x^2 = 100\\10x^2 = 100\\x^2 = 100/10 = 10\\x = \sqrt{10}\)

Thus, one side is \(\sqrt{10}\) and other 3\(\sqrt{10}\)

\(\sqrt{10} = 3.16\\\)

thus, in decimal one side = 3.16

other side = 3.16*3 = 9.48

Answer:

C

Step-by-step explanation:

the inequality says that x needs to be less than or equal to 2, we know the first number in an ordered pair is x-axis the only number less than 2 is -2

The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

To know more about angles visit:

brainly.com/question/7116550

#SPJ1

Answer:

The population mean is 19.2 to 20.8.

Step-by-step explanation:

The formula of Confidence interval is

CI = mean ± z*\(\frac{s}{\sqrt{n} }\)

where

n = sample size

s  = Population standard deviation.

mean = Sample mean

z(α/2) = Two tailed z-value for significance level of .

Given : Confidence level = 95.44% = 0.9544

Significance level =  α = 1-0.9544 = 0.0456

Now we Use standard z-value table  

z-value for Significance level of 0.0456 :

z(α/2) = z(0.0228) = 1.99 = 2(approximately)

And we are given

n=144

s = 4.8

mean = 20

so the required Confidence interval is

CI = 20± 2*\(\frac{4.8}{\sqrt{144} }\)

     = 20 ± 2*\(\frac{4.8}{12}\)

      = 20 ± (0.8)

      = (20-0.8, 20+0.8 )

       = (19.2 , 20.8)

Therefore the 95.44% CI value  for the population mean of 20 is 19.2 to 20.8.

Answer:

Step-by-step explanation:

1/2(13-5)+(4+8)^2

A. 148

B. 144

C. 20

D. 16

We must follow "PEMDAS" order of operations rules.  Anything inside parentheses must be done first, followed by exponentiation, multiplication and division, and finally additionl and subtraction.

1/2(13-5)+(4+8)^2 has three sets of parentheses enclosing mathematical expressions:  (1/2), (13 - 5) and (4 + 8).  These evaluate to:

                        1/2,       8,               12

and so we now have (1/2)(8) + (12)^2

Exponentiation is next.  We get:  (1/2)(8) + 144

Next is multiplication:                         4      + 144

Last is addition:                                       148

Answer A is correct:  148

8 x 9+4^2-(63/7)

is evaluated in the same way:

8 x 9+4^2-(9), followed by exponentiation:

8*9 + 16 - 9, followed by multiplication:

72 + 16 - 9 = 79 (Answer C)

Using the binomial distribution, it is found that:

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

For this problem, the parameters are given as follows:

n = 8, p = 0.09.

Hence the mean and the standard deviation are, respectively:

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1