Write an inequality to model the situation.
A number exceeds 21.
n ≤ 21
n < 21
n > 21
n ≥ 21

Answer:

35.25

Step-by-step explanation:

Give the data set:

23 37 49 34 35 41 40 26 32 22 38 42

We are expected to calculate the midquartile of the given data set.

22 23 26 32 34 35 37 38 40 41 42 49

First step is to find the lower quartile which comprises of

22 23 26 32 34 35

Here the Q1 is (26+32)/2 = 58/2= 29

Second step to find the upper quartile which comprises of

37 38 40 41 42 49

Here the Q3 is (40+41) /2 = 81/2 = 41.5

Then to find the midquartile which is (Q1+Q3) /2 where Q1 is 29 and Q3 is 41.5

= (29+41.5)/2

= (70.5) /2 = 35.25

Answer:

sin(O) = 2/sqrt(5)   or 2sqrt(1/5)

Step-by-step explanation:

using 1+cot^2(x) = csc^2(x)

we have, taking reciprocal on both sides,

sin(x) = 1/sqrt(1+cot^2(x)

= 1/sqrt(1+(-1/2)^2)

= 1/sqrt(5/4)

= 2/sqrt(5)   or 2sqrt(1/5)

Since angle x is in the second quadrant, sin(x) is positive.

Answer:

.

Step-by-step explanation:

Answer:

a

   [tex]R =13[/tex]

b

  [tex]\= x =8.9[/tex]

c

 [tex]var(x) = 16.57[/tex]

d

 [tex]\sigma = 4.1[/tex]

Step-by-step explanation:

From the question we are given a data set  

      2​, 10​, 15​, 4​, 11​, 10​, 15​, 10​, 2​, 10

     The sample size is  n  = 10

 The range is  

         [tex]R = maxNum - MinNum[/tex]

Where maxNum  is the maximum number on the data set  which is 15

 and  MinNum  is the minimum  number on the data set  which is  2

   So

           [tex]R = 15 - 2[/tex]

           [tex]R =13[/tex]

The mean is mathematically represented as

          [tex]\= x = \frac{\sum x_i}{N}[/tex]

substituting values

          [tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]

         [tex]\= x =8.9[/tex]

The variance is mathematically evaluated as

        [tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]

substituting values

      [tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex]                    [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]

[tex]var(x) = 16.57[/tex]

The standard deviation is  [tex]\sigma = \sqrt{var(x)}[/tex]

substituting values

         [tex]\sigma = \sqrt{16.57}[/tex]

        [tex]\sigma = 4.1[/tex]

Answer:

true

Step-by-step explanation:

Answer:

[tex]2 \times 10 {}^{ - 7} [/tex]

Step-by-step explanation:

[tex] \frac{4 \times 10 {}^{ - 4} }{20 \times 10 {}^{2} } = \frac{0.0004}{2000} = 2 \times 10 {}^{ - 7} [/tex]

Hope this helps ;) ❤❤❤

Answer:

a. P(0 < z < 3.00) =  0.4987

b. P(0 < z < 1.00) =  0.3414

c. P(0 < z < 2.00) = 0.4773

d. P(0 < z < 0.79) = 0.2852

e. P(-3.00 < z < 0) = 0.4987

f. P(-1.00 < z < 0) = 0.3414

g. P(-1.58 < z < 0) = 0.4429

h. P(-0.79 < z < 0) = 0.2852

Step-by-step explanation:

Find the area under the standard normal probability distribution between the following pairs of​ z-scores.

a. z=0 and z=3.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 3.00) = 0.9987

Thus;

P(0 < z < 3.00) = 0.9987 - 0.5

P(0 < z < 3.00) =  0.4987

b. b. z=0 and z=1.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 1.00) = 0.8414

Thus;

P(0 < z < 1.00) = 0.8414 - 0.5

P(0 < z < 1.00) =  0.3414

c. z=0 and z=2.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 2.00) = 0.9773

Thus;

P(0 < z < 2.00) = 0.9773 - 0.5

P(0 < z < 2.00) = 0.4773

d.  z=0 and z=0.79

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 0.79) = 0.7852

Thus;

P(0 < z < 0.79) = 0.7852- 0.5

P(0 < z < 0.79) = 0.2852

e. z=−3.00 and z=0

From the standard normal distribution tables,

P(Z< -3.00) = 0.0014  and P(Z< 0) = 0.5

Thus;

P(-3.00 < z < 0 ) = 0.5 - 0.0013

P(-3.00 < z < 0) = 0.4987

f. z=−1.00 and z=0

From the standard normal distribution tables,

P(Z< -1.00) = 0.1587  and P(Z< 0) = 0.5

Thus;

P(-1.00 < z < 0 ) = 0.5 -  0.1586

P(-1.00 < z < 0) = 0.3414

g. z=−1.58 and z=0

From the standard normal distribution tables,

P(Z< -1.58) = 0.0571  and P(Z< 0) = 0.5

Thus;

P(-1.58 < z < 0 ) = 0.5 -  0.0571

P(-1.58 < z < 0) = 0.4429

h. z=−0.79 and z=0

From the standard normal distribution tables,

P(Z< -0.79) = 0.2148  and P(Z< 0) = 0.5

Thus;

P(-0.79 < z < 0 ) = 0.5 -  0.2148

P(-0.79 < z < 0) = 0.2852

Answer:

There is a solution. The ordered pair is (4, 2).

Step-by-step explanation:

Solve the system of equations by using the substitution method.

[tex]x+y=6\\x=2y[/tex]

Substitute x as 2y in the first equation and solve for y.

[tex]2y+y=6\\ 3y=6\\(3y)/3=6/3\\y=2[/tex]

Substitute y as 2 in the second equation and solve for x.

[tex]x=2(2)\\x=4[/tex]

Answer:

a = 8

b = -8

Step-by-step explanation:

You have the following function:

[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]

A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.

In this case, you need that the function is differentiable for t=2, then, you have:

[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]

If the derivative exists for t=2, it is necessary that the previous derivatives are equal:

[tex]f'(2)=a=4(2)\\\\a=8[/tex]

Furthermore it is necessary that for t=2, both parts of the function are equal:

[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]

Then, a  = 8, b = -8

Answer: x=2 y=-2

(2,-2) one solution

Step-by-step explanation:

Solve by substitution

[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}y=x-4[/tex]

[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]

[tex]2x^2-8x+16=8[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]

[tex]\mathrm{For\:}y=x-4[/tex]

[tex]\mathrm{Subsititute\:}x=2[/tex]

[tex]y=2-4[/tex]        [tex]2-4=-2[/tex]

[tex]y=-2[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=2,\:y=-2[/tex]

Answer:

The answer is option A.

Step-by-step explanation:

Using the properties of logarithms

that's

[tex] log(x) - log(y) = log( \frac{x}{y} ) [/tex]

log 2 - log 14 is

[tex] log(2) - log(14) = log( \frac{2}{14} ) [/tex]

Simplify

We have the final answer as

[tex] log( \frac{1}{7} ) [/tex]

Hope this helps you

Answer:

log ( 1/7)

Step-by-step explanation:

log2-log14

We know that log ( a/b) = log a - log b

log (2 /14)

log ( 1/7)

Answer:

C. in five hours Caroline wraps an odd number of packages

Step-by-step explanation:

for A until hours you would multiply 2 by 9 and 2 by 9 is 18 and that's an even number so it's not A.

A eliminated.

for B in 3 hours 3 by 9 is 27 and that's an odd number so B is automatically eliminated.

for C in 5 hours all you would do is multiply the 9 by 5 and 9 by 5 is 45 and 45 is indeed an odd number so C is your answer.

for D 7 by 9 is 63 and 63 is an odd number so we already know that C is the answer but still we got to check and D is wrong because 63 is not an even number.

Answer:

the difference between the estimator and the population parameter grows smaller as the sample size grows larger.

Step-by-step explanation:

In Statistics, an estimator is a statistical value or quantity, which is used to estimate a parameter.

Generally, parameters are the determinants of the probability distribution. Thus, to determine a normal distribution we would use the parameters, mean and variance of the population.

An estimator is said to be consistent if the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, for an estimator to be consistent it must have both a small bias and small variance.

Also, note that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[\tex]

Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).

A sample variance is an unbiased estimator of the population variance while the sample mean is an unbiased estimator of the population mean.

Generally, a consistent estimator in statistics is one which gives values that are close enough to the exact value in a population.

Answer:

The adult ticket costs $18 and the children ticket costs $13.

Step-by-step explanation:

Let the price of the adult ticket be a.

Let the price of the children ticket be c.

Three adults and four children must pay $106. This implies that:

3a + 4c = 106 _______(1)

Two adults and three children must pay $75. This implies that:

2a + 3c = 75 ________(2)

We have two simultaneous equations:

3a + 4c = 106 _____(1)

2a + 3c = 75 ______(2)

Multiply (1) by 2 and (2) by 3 and subtract (1) from (2):

  6a + 9c = 225

- (6a + 8c = 212)

             c = $13

Put this value of c in (2):

2a + 3*13 = 75

2a + 39 = 75

=> 2a = 75 - 39

2a = 36

a = 36/2 = $18

Therefore, the adult ticket costs $18 and the children ticket costs $13.

Answer:

43 mountain climbers have not climbed either mountain.

Step-by-step explanation:

Total number of mountain climbers, i.e. n(U) = 60

Number of mountain climbers who have climbed Mt. Everest, n(E) = 10

Number of mountain climbers who have climbed Mt. Rainier, n(R) = 15

Number of mountain climbers who have climbed both, n(E [tex]\cap[/tex] R) = 15

Using the formula to find number of climbers who have climbed either of the mountains:

[tex]n(A \cup B) = n(A)+n(B)-n(A\cup B )[/tex]

[tex]\therefore n(E \cup R) = n(E)+n(R)-n(E\cup R )\\\Rightarrow n(E \cup R) = 10+15-8 = 17[/tex]

To find, who have not climbed either mountain:

[tex]n(E\cup B)'=n(U) - n(E\cap B)\\\Rightarrow n(E\cup B)'=60 - 17 = \bold{43}[/tex]

So, the answer is:

43 mountain climbers have not climbed either mountain.

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph.  When the man  

runs toward point A, the relative speed of the train with respect  

to the man is the train's speed plus the man's speed (45 + M).  

When he runs toward point B, the relative speed of the train is the  

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.  

When he runs in the direction of the train the distance he covers  

is 3 units. We can now write that the ratio of the relative speed  

of the train when he is running toward point A to the relative speed  

of the train when he is running toward point B, is equal to the  

inverse ratio of the two distance units or

              (45 + M)          3

              -----------  =      ---

              (45 - M)          2

          90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

Answer: 9 mph

Step-by-step explanation:

Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .

If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5

The remaining distance = 1 - 4/5 = 1/5

If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be

Speed = distance/time

Time = 1/5d ÷ speed

The time it will take the train to cover the entire distance d will be

Time = d ÷ 45

Equate the two time

1/5d ÷ speed = d ÷ 45

Speed = d/5 × 45/d

Speed = 9 mph

Answer:

Henry had the best record for the number of shots made

Step-by-step explanation:

From the given information.

Four friends are on a basketball team.

Henry

Allison

Arthur

Trevor

We are being told that Henry made 0.45  of his shots out of all his attempts

Allison made Arthur made of her shots  of his shots.

i,e Arthur did the work for Allison , so out of Arthur's shot , we have to  figured out Allison shots,

Trevor missed 58% of his shots.

i.e Trevor failed 0.58 of his shot, If he failed 0.58 shot

Then the attempts Trevor made is :

= 1 - 0.58

= 0.42

SO , Trevor made 0.42 shots out of all his attempt

N:B We are not given any information about Arthur's shots , so we can't determine Allison shot as well.

Therefore; we will focus on only Henry and Trevor shots

So ;

Henry made 0.45  of his shots

Trevor made 0.42 out of his shots

We can thereby conclude that :

Henry had the best record for the number of shots made

Answer:

P

Step-by-step explanation:

Count the line endings in each letter as you write it down.

Answer:

I agree with tonb .Ace,he's/she's right

Answer: A. 299.5

Step-by-step explanation:

1248 · 24%

1248 · 0.24=299.50

Answer:-8

Step-by-step explanation:

Answer:

10 termites will destroy 0.000084kg of wood per week

Step-by-step explanation:

Convert milligram to kilogram

1.2mg=(1.2 / 1,000,000)kg

1.2mg=0.0000012kg

1 termite destroys=0.0000012kg per day

10 termites will destroy (per day) =0.0000012×10 termites per day

10 termites in one day will destroy=0.000012kg

There are 7 days in a week

Therefore,

10 termites will destroy=destruction per day × 7 days

=0.000012×7

=0.000084kg per week

Answer:

Hello!! :) The answer to your question is 13,728

Steps will be below.

Step-by-step explanation:

So we will subtract 22,403 and 8,675.

When we do that we will get 13,728

To check your answer we have to do the opposite of subtracting which will be adding.

This is how we check our work: the answer we got was 13,728...we have to take that answer and add it to 8,675 which will give us 22,403

(Both of the numbers are from the question)

At the bottom I attached a picture of how I did the subtracting and how I checked my work.

Sorry for my handwriting......if you can’t understand my handwriting, I attached another picture which is more clearer.

ANSWER TO YOUR QUESTION: 13,728

Brainliest would be appreciated! Thank you :3

Hope this helps! :)

Answer:

The answer is 13,728

Step-by-step explanation:

Check your work with addition.

Answer: try using sine for this equasion

Step-by-step explanation:

Answer:

The options that have two angles, which are A and D prove both triangles to be similar.

Step-by-step explanation:

The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.

The reason being is if two angles are the same between the two triangles, the third can't be different.

Answer:

500km

Step-by-step explanation:

add all the proportions and then divide by 3. with conversion.

Answer:

[tex]\boxed{Mean = 34.33}[/tex]

Step-by-step explanation:

Mean = Sum of Observations / No. Of Observations

Mean = (24+18+37+82+17+26)/6

Mean = 206 / 6

Mean = 34.33

Answer:

60 and 87

Step-by-step explanation:

Question 1: The chance of losing would be 100% - 40% = 60%.

Question 2: Again, we just have to do 100% - 13% = 87%.

Answer:

Below

Step-by-step explanation:

First question:

Jade has a 40% chance of winnig wich could be expressed as 2/5

The chance of losing is the remainning pourcentage from 100%

●100-40 =60%

60% is the chance of losing wich could be expressed as 3/5

The sum of 3/5 and 2/5 is 1 so it's true.

■■■■■■■■■■■■■■■■■■■■■■■■■

Same method for the 2nd question:

The person has a 13 % chance of winning.

The chance of losing is 87%

● 100-13 =87

There is only one distinct triangle possible, with m N= 33º. Therefore, option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔMNO, m = 20, n = 14, and m∠M = 51°.

Now, sin51°/20=sinN/14

0.7771/20=sinN/14

0.038855=sinN/14

sinN=14×0.038855

sinN=0.54397

N=33°

Therefore, option B is the correct answer.

Learn more about the sine rule here:

https://brainly.com/question/22288720.

#SPJ7

Answer:

1.5+1.7/2=1.6

Step-by-step explanation: