a random sample of size 81 is taken from an infinite population with a mean of 50 and a standard deviation of 9. find an approximate probability that the sample mean is within 48 and 51 (round off to second decimal place).

Answers

Answer 1

The approximate probability that the sample mean is within 48 and 51 is 0.82.

How to calculate probability?

n = sample size = 81

σ = standard deviation = 9

μ = population mean = 50

Probability is a chance of something event can occur, for this case the probability measure of the chance of sample mean is between 48 and 51 can occur. So, the probability of the sample mean is between 48 and 51 is,

P(48 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])

= P([tex]\frac{48-50}{\frac{9}{\sqrt{81}}}[/tex]≤ z ≤ [tex]\frac{51-50}{\frac{9}{\sqrt{81}}}[/tex])

= P(-2 ≤ z ≤ 1)

= P(z ≤ 1) - P(z ≤ -2)

using z table and we get,

= 0.8413 - 0.0228

= 0.8185

= 0.82

Thus, the probability is 0.82 for the sample mean is within 48 and 51.

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A Random Sample Of Size 81 Is Taken From An Infinite Population With A Mean Of 50 And A Standard Deviation
A Random Sample Of Size 81 Is Taken From An Infinite Population With A Mean Of 50 And A Standard Deviation

Related Questions

35 Points!!!! 7 2/5= 2/3x −4 1/2
Enter your answer as a mixed number in simplest form in the box.

Answers

Solving for x in the equation 7 2/5 = 2/3x −4 1/2 gives   17 17/20

How to determine the value of x

In the given equation, we find the value of x by applying the following operations

7 2/5 = 2/3x −4 1/2

7 2/5 = 2x/3 −4 1/2

collecting like terms

7 2/5  + 4 1/2 =

2x/3 = 119/10

multiplying by 3

2x = 119/10 * 3

2x = 357/10

dividing by 2

x = 357 / 10 * 1/2

x = 357/20

x = 17 17/20

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What is the average rate of change of the function on the interval from x = 2 to x = 4? f(x)=10(2)x

Answers

Answer:

B because (16-4)/2=6

Step-by-step explanation:

true or false: when two variables are highly correlated, a change in the value of one will cause a change in the value of another.

Answers

The given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

What are variables?

Any feature, characteristic, or circumstance that can exist in various amounts or types is considered a variable.

Independent, dependent, and controlled variables are typically present in an experiment.

The variable that is altered by the scientist is the independent variable.

A false correlation between two variables indicates that their correlation coefficient is almost zero.

When two variables have a strong correlation, altering the value of one will not affect the other.

Therefore, the given statement "a change in the value of one variable will result in a change in the value of the other when the two variables are highly linked" is FALSE.

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A pilot was scheduled to depart at 4:00 pm, but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination.

Answers

Using the equation y=x/4+16, it is possible to estimate how many minutes will pass after 4:00 pm when she reaches her destination.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let x be the time of original flight before delay.

Let y be the new time of flight after delay.

She will to arrive 4 times faster that in original flight time,

y=x/4

The flight is delayed by 16 minutes,

y=x/4+16

The equation that can be used to predict the number of minutes after 4:00 pm she will arrive at her destination will be y=x/4+16.

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Answer:b

Step-by-step explanation: did the test

Type your solutions into this document and be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. PROBLEM 1 A 125-page document is being printed by five printers. Each page will be printed exactly once. (a) Suppose that there are no restrictions on how many pages a printer can print. How many ways are there for the 125 pages to be assigned to the five printers? One possible combination: printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer

Answers

The number of ways there for the 125 pages to be assigned to the four printers = 5^125 ways.

As per the question,

A 125-page document is being printed by four printers.

Each page will be printed exactly once.

There are no restrictions on how many pages a printer can print.

One of the possible combinations is that printer A prints out pages 2-50, printer B prints out pages 1 and 51-60, printer C prints out 61-80 and 86-90 and printer D prints out pages 81-85 and 91-100.

Since, there are no restrictions in printing the pages any printer cannot print even a single page and any printer can print all 125 pages. To print 100 pages we have four printers.

⇒ Number of possible ways a single paper can be assigned to the four printers = 4 ways

⇒ Number of possible ways 125 pages can be assigned to the four printers

=  5 × 5 × 5 × 5 .................... 5 ( a total of 125 terms )

=     ways.

Therefore, In   ways we can assign 125 pages to four printers with no restrictions.

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Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 100x2 + 49y2 = 1

Answers

The area bounded by the sin (100x² + 49y²) dA is calculated by using integration is 2π (1 - cos 1).

An area bounded by the curve: When the two curves intersect then they bound the region is known as the area bounded by the curve.

Evaluate the integral by making an appropriate change of variables.

The equation of the ellipse is 100x² + 49y² = 1

Let cos t = 10x and sin t = 7y. Then we have

or x = 1/10 cost , y = 1/7 sint.

Then

=> 100 (1/10cost)^2 + 49 (1/7 sint)^2 = 1

=> cos^2 t + sin^2t = 1 which suggests a change of variable will be:

[tex]\left \{ {{x(r,t) = r/10cost} \atop {y(r,t)=r/7sint}} \right.[/tex]

where 0≤r≤1 and 0≤t≤2[tex]\pi[/tex]. Then we also have,

100x² + 49y² = r²

So,

=> ∫∫ sin (100x^2 + 49y^2)dA

     R

=> [tex]\\[/tex]2 ∫2[tex]\pi[/tex] ∫[tex]1[/tex]  sinr^2 dr dt

       0     0

=> 4[tex]\pi[/tex] ∫[tex]1[/tex]  rsinr^2 dr

          0    

                       

Now r² is replaced by r, then we get

=> 2[tex]\pi[/tex] ∫[tex]2[/tex]  sinr^2 d(r^2)

          0

=> - 2[tex]\pi[/tex] cos r^2 [tex]\left \{ {{r^2=1} \atop {r^2=0}} \right.[/tex]    

=> -2[tex]\pi[/tex] (cos1-cos0)

=> -2[tex]\pi[/tex] (-1 + cos1)

=> 2[tex]\pi[/tex](1-cos1)

Evaluating the integral by making an appropriate change of variables 2 sin(100x^2 + 49y^2) dA.

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Please help! Question below

Answers

The system of equation that is used to determine the number of cans of soup purchased and the number of frozen dinners purchased is 300x+450(x+5)=6000mg.

What is meant by linear equation?

A linear equation can be generated by equating a linear polynomial over some field with zero coefficients. The values that, when substituted for the unknowns, make the equality true are the solutions of such an equation. The phrase linear equation is frequently used to refer to this specific scenario, in which the variable is appropriately referred to as the unknown.

Each solution in the case of two variables can be regarded as the Cartesian coordinates of a point on the Euclidean plane. A linear equation's solutions form a line in the Euclidean plane, and every line can be seen as a set.

Sodium contains in a can of soup is 300mg

Sodium contains in a can of frozen dinners is 450mg

Let the number of cans of soup purchased be x

Then, the number of frozen dinners purchased=x+5

Total sodium purchased=6000mg

So, 300x+450(x+5)=6000mg

Therefore, the system is 300x+450(x+5)=6000mg

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Two interior angles of a triangle are 54 and 112. What is the measure of the third angle?

Answers

Answer: 14 degrees.

Step-by-step explanation: The sum of the measures of the interior angles of a triangle is always 180 degrees. Therefore, if we know the measures of two of the interior angles of a triangle, we can use this fact to find the measure of the third angle.

In this case, we are given that two of the interior angles of the triangle have measures of 54 and 112 degrees. We can use this information to find the measure of the third angle as follows:

180 degrees = 54 degrees + 112 degrees + x

180 degrees = 166 degrees + x

x = 180 degrees - 166 degrees

x = 14 degrees

Therefore, the measure of the third angle of the triangle is 14 degrees.

   

The function g(x)=2^x-1 models the number of bacteria after x days. In how many days
will there be 256 bacteria?

Answers

So if you take the 2 and square it by 256 then once you get that subtract one then that will get you your answer

nine people sit down for dinner where there are three choices of meals. three people order the beef meal, three order the chicken meal, and three order the fish meal. the waiter serves the nine meals in random order. find the number of ways in which the waiter could serve the meal types to the n

Answers

There are a total of 216 ways in which the waiter could serve the meal types.

Let the beef meal be denoted by B, chicken meal by C, and fish meal F. Now say the nine people order meals BBBCCCFFF respectively and say that the person who receives the correct meal is the first person. We will solve for this case and then multiply by 9 to account for the 9 different ways in which the person to receive the correct meal could be picked.

Now, we need to distribute meals BBCCCFFF to orders BBCCCFFF with 0 matches. The two people who ordered B's can either both get C's, both get F's, or get one C and one F.

If the two B people both get C's, then the three F meals left to distribute must all go to the C people. The F people then get BBC in some order, which gives three possibilities.

If the two B people both get F's, the situation is identical to the above and three possibilities arise.

If the two B people get CF in some order, then the C people must get FFB and the F people must get CCB. This gives 2*3*3 = 18 possibilities.

In total, we see there are 24 possibilities, so the answer is 9*24 = 216

Thus, there are a total of 216 ways in which the waiter could serve the meal types.

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Your question was incomplete. Check for missing part below-

Find the number of ways in which the waiter could serve the meal types to the nine people so that exactly one person receives the type of meal ordered by that person.

the difference of two numbers is 6 . two times the smaller is 3 more than the larger. find the two numbers.

Answers

The larger number is 15 and the smaller number is 9.

What is substitution method?

In order to solve a system of equations, the substitution method is typically used in mathematics. This approach involves first solving the equation for one variable, then changing the value of the variable in the second equation.

Suppose

'a' be the larger number and 'b' be the smaller number.

As the difference of two numbers is 6.

⇒ a - b = 6        ..(1)

As  two times the smaller is 3 more than the larger.

⇒ 2b = 3 + a        ..(2)

From equation (2),

a = 2b - 3

Substitute the value of 'a' in equation (1)

2b - 3 - b = 6

       b - 3 = 6

            b = 6 + 3

            b = 9

Substitute b = 9 in equation (1),

a - 9 = 6

    a = 6 + 9

    a = 15

Hence, the larger number is 15 and the smaller number is 9.

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The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 8000.(a) Find a function n(t) = n0ert that models the population after t hours.(b) Find the population after 1.5 hours.(c) After how many hours will the number of bacteria reach 15,000?(d) Sketch the graph of the population function.

Answers

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

Given that,

One thousand bacteria make up a culture at the beginning. The number of bacteria is 8000 after an hour.

We have to find

(a) Track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, locate the population.

(c) How long will it take for there to be 15,000 bacteria?

(d) Draw the population function's graph.

We know that,

(a) The initial size of the culture is 1000 bacteria.    

So,  

n₀=500

The size of the culture after one hour (for t =1) is 4000 so we extract the equation:

n(1) = 8000

1000er¹=8000

e to the power of r =8

[taking logarithms both side]    

r ln e  =  ln 8                          

r=2.080

[ln e  =  1]

So, we got  

n₀=1000 and r=2.08

The function will be,

n(t)=1000[tex]e^{2.08t}[/tex]

(b) for t = 1.5

n(1.5)=1000[tex]e^{2.08(1.5)}[/tex]

22646

(c) 15000=1000[tex]e^{2.08t}[/tex]

15=[tex]e^{2.08t}[/tex]

Taking log on both sides

ln15= 2.08(t)lne

t=3.68/2.08

t=1.7

(d) Since we have have the exponential equation therefore our graph should be curve not straight line.

Also at t=1, population of bacteria is 4000

Hence the correct graph will be in picture.

Therefore,

(a) n(t)=1000[tex]e^{2.08t}[/tex] track down a function that simulates the population after t hours, n(t) = n₀ert.

(a) After 1.5 hours, the population is 22646.

(c) t=1.7 will it take for there to be 15,000 bacteria

(d) The population function's graph is in the picture.

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Suppose one balloon costs $3. Complete the table to find the cost of different numbers of balloons that Lucy might buy. Using the rate of the table what would be the cost of 23 balloons?

Answers

The linear function y = 3x is used to calculate the cost of 23 balloons as $69

Linear Function

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variable

y = 3x

x = number of balloons

The cost of 1 balloon = $3

the cost of 23 balloon = x

x = 23 * 3

x = 69

The cost of 23 balloon is $69

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at a sale, a sofa is being sold for of the regular price 33% the sale price is 184.80 what is the regular price?

Answers

The regular price is 275.82, according to given question.

What do you mean by regular price?

Regular price is the cost at which a provider continuously and actively sells goods or services to the general public over an extended period of time.

According to data in the given question,

We have the given information:

Sale discount 33% and the sale price 184.80.

Now, we will calculate the regular price:

Let Regular Price = x

33% Discount of x = 33/100 * x

33% Discount of x = 33x/100

Regular price - 33% Discount = Sale price

x-33x/100=184.80

(100x-33x)/100=184.80

67x/100=184.80

67x=18480

x=18480/67

x=275.82

Therefore, the regular price is 275.82.

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Sara has 7,241 beads. She wants to make them into necklaces to sell at a charity fundraiser. She wants to use 13 beads on each necklace. How many necklaces is she able to make?

Answers

Answer:

557

Step-by-step explanation:

7,241 divided by 13 = 557

Solve for b in A = a + b
——-
3


Help ASAP!!

Answers

Answer:  The correct answer is b=2a

Step-by-step explanation:

Solve for b

A = (a + b)/3

Flip the equation

1/3a + 1/3b = a

Add (-1)/3a to both sides.

1/3a + 1/3b + −1/3a = a + −1/3a

1/3b = 2/3a

Divide both sides by 1/3

(1/3b)/(1/3) = (2/3a)/(1/3)

b=2a

Answer:

[tex]b = 3A - a[/tex] (if A and a are two different variables).

[tex]b = 2a[/tex] (If the A and a denote the same variable.

Step-by-step explanation:

[tex]A = \frac{(a + b)}{3}[/tex]

Isolate the variable, b. Note the equal sign, what you do to the one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, multiply 3 to both sides of the equation:

[tex]A (*3) = \frac{(a + b)}{3} (* 3)\\A * 3 = (a + b)[/tex]

Next, subtract a from both sides of the equation:

[tex]A * 3 = a + b\\3A = a + b\\3A (-a) = a (-a) + b\\b = 3A - a[/tex]

[tex]b = 3A - a[/tex] is your answer.

IF, however, you meant to put both lower case variable a (or vice versa), then you can further simplify:

[tex]b = 3a - a\\b = 2a[/tex]

[tex]b = 2a[/tex] is your answer if the a are supposed to be the same variable.

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3. coach walker gets a shipment of 153 uniforms. he puts them in boxes of 10. how many boxes can he fill? how many uniforms will be left over? boxes.

Answers

By using division, it can be calculated that

Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.

What is division?

Division is the process by which value of single unit can be calculated from the value of multiple unit.

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

This is a problem sum on division

Total number of uniforms = 153

Number of uniforms in one box = 10

Number of boxes he can fill = 153 [tex]\div[/tex] 10

The quotient in this case is 15 and the remainder is 3

Coach Walker needs 15 boxes to fill the uniforms and 3 uniforms will be left over.

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Let A be a complex (or real) n x n matrix, and let x in C^n be an eigenvector corresponding to an eigenvalue (lambda) in C Show that for each nonzero complex scalar (nu) , the vector (nu) x is an eigenvector of A

Answers

The vector (nu) x is an eigenvector of A and corresponds to each nonzero complex scalar (nu) (lambda).

Let x in Cn be an eigenvector of A that corresponds to an eigenvalue. Assume that A is a n x n matrix (lambda). Ax = (lambda)x follows.

Let (nu) now be a complex scalar that is nonzero. A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x) = A((nu)x)

As a result, (nu)x is an eigenvector of A that corresponds to (nu) (lambda).

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HELPPPPPPPPPP MEEE YALL ARE SLAY

Answers

Answer:

B) Corresponding angles are congruent, therefore 2x + 42 = 76.

Step-by-step explanation:

Yes, corresponding angles are congruent, however, the given angles do not fit the definition of a corresponding angle.

Instead, they form a straight line, which is 180° in total. If you were to solve using option B), the answer would look instead as:

(2x + 42)° + (76)° = 180°

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there are 3 seniors and 15 juniors in mrs. gillis’s math class. three students are chosen at random from the class. a. what is the probability that the group consists of a senior and two juniors? b. if the group consists of a senior and two juniors, what is the probability that stephanie, a senior, and jan, a junior, are chosen?

Answers

The answer of a) Probability = 0.386 and of b) Probability = 0.017

Explain probability.

Estimating the likelihood that experiments will succeed or fail is one use of probability theory. The likelihood of flipping a coin and getting heads or tails, for example, or the likelihood of making a research error, can all be calculated using probabilities. In order to fully appreciate this area of mathematics, it is crucial to comprehend the formula for computing probabilities in equiprobable sample spaces, as well as the probabilities of the complementary event, etc., as well as the likelihood of two occurrences joining together.

no of seniors = 3

no of juniors = 15

a) probability that a group consist of a senior and two juniors =

[tex]\frac{^{3}C_{1} * ^{15}C_{2}}{^{18}C_{3}} \\= \frac{3*105}{316}=0.386\\[/tex]

b) if the name of a student given then there is only one way to select it

For example = we have to select 1 senior which name is already given means there is only one way to select it, and 2 junior in which one name is given then it can only selected by one way, but still one junior student has to be selected out of remaining 14 student which can be selected by ([tex]^{14}C_{1}=14[/tex]) different ways.

probability = [tex]\frac{1*1*^{14}C_{1} }{^{18}C_{3} }=\frac{14}{316}=0.017[/tex]

Hence the answer of a) is 0.386 and of b) is 0.017

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write in slop form of the equation and each line given the slope and y intercept. slope = 1/2. y intercept = 2​

Answers

Answer:Y=1/2x+2

Step-by-step explanation:

Slope intercept form is y=mx+b

m=slope

b= y intercept

y=1/2x+2

the mean and standard deviation of the heights of american women are 63.8 inches and 4 inches, respectively. find an approximate probability that the mean height of a randomly selected 100 american women is between 63 and 64 inches (round off to second decimal place).

Answers

The probability that the mean height of the American women is between 63 and 64 is 0.6687

The probability of an event occurring is defined by probability. There are numerous instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

Mean = 63.8

S = 4

n = 100

P(63 <=X-bar<=64) = P(63.638/4/[tex]\sqrt{100}[/tex] < z < 64.638/4/[tex]\sqrt{100}[/tex])

=P(0.2 < z < 0.5)

=P(z<0.5) - P(z<-2)

0.6915 - 0.0228

0.6687

So, the probability is 0.6687

p-values from the z table

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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? select two options. x2 (y – 3)2 = 36 x2 (y – 5)2 = 6 (x – 4)² y² = 36 (x 6)² y² = 144 x2 (y 8)2 = 36

Answers

The equation of the circle on the y-axis is x² +(y-3)² = 36.

Here we have to find the equation of the circle

Data provided:

diameter(d) = 12 units

so radius(r) = 6 units

The center lies on the y-axis

The general equation of the circle:

(x-x1)² + (y - y1)² = r²

where (x1, y1) is the point on the circle.

So by putting x1 = 0 and y1 = 3 and r = 6 as the center lies of y-axis

x² + ( y - 3)² = 6²

x² + (y-3)² = 36

Therefore we get the equation as x² + (y-3)² = 36

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find the equation parallel to y=-2x-18 through (-3,2)

Answers

Answer:

y= -2x-4

Step-by-step explanation:

parallel==> a line has the same slope ===> (m = -2)

y= -2x+b

and a line pass through the (-3,2) ===> x=-3, y=2

2= -2(-3)+b

2=6+b (subtract 6 from both sides )

-4=b

y= -2x-4



a box contains 3 donuts cake, 4 jelly cake and 5 chocolate cake. if a person selects one cake at random, find the probability that it is either a donut or a chocolate cake

Answers

Answer:

50%

Step-by-step explanation:

It is a half chance, you could be lucky

If a circular flower bed has a diameter of 18ft.
What is the area of the flower bed?
What is the circumference of the flower bed?

Answers

Answer:

Area = 81 pi

circumstance = 18 pi

Step-by-step explanation:

radius = 9

A paper cup is in the shape of an inverted right circular cone with both height and diameter of 6 inches. It is being filled with water at a rate of 2 cubic inches per minute. How fast is the water level rising when it is 2 inches deep.


Pls give answer in inches per minute

Answers

Using the implicit differentiation, it is found that the water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

What is the volume of a cone?

The volume of the cone of radius r and height h is given as follows:

V = π r² h / 3

Applying implicit differentiation to find the rate of change of the volume as function of time is given as follows:

[tex]\frac{dV}{dt}[/tex] = 2 π  [tex]\frac{rh}{3}[/tex][tex]\frac{dr}{dt}[/tex]  + [tex]\frac{π r² }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

As the radius is constant, hence:

.[tex]\frac{dr}{dt}[/tex]  = 0

Considering that the radius is half of the diameter, the other parameters are:

r = 3 and [tex]\frac{dV}{dt}[/tex] = 2

Hence:

2 = [tex]\frac{π * 3^{2} }{3}[/tex] [tex]\frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt}[/tex] = 6 / 9 π

dh/dt = 0.21.

The water level is rising at the rate of 0.21 inches per second when it is 2 inches deep.

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please help me solve this problem I will give 20 points

Answers

Answer:

94

Step-by-step explanation:

if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pig with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Answer:

Step-by-step explanation:if 3 pairs of mittens equal 30 then 1 pair of mitten is 10

And 1 mitten is 5

2 pigs plus a mitten equal 27 and since one mitten is 5 2 pigs with a hat equal 22 and 1 pit with a hat equal 11

X+11+10=24

x+21=24

x=3

One hat is 3

We can write the last problem like this

2(3)+11x(11-3)

6+11x8

6+88

94

Hopes this helps and I hope this is right with these riddles I’m sure I missed something

Mt.Mckinley is 20,321 ft in elevation. Mt.McKinley is 8,707 ft lower than Mt. Everest. What is the elevation of Mt.Everest?
I need to explain the variable
write an equation
and solve it

Answers

equation: x-8,707=20,321
+8,707 +8,707
x= 29,028 :)

Answer:

29,028 ft.

Step-by-step:

Consider the following:

Mt. Everest - x

Equation:

We are given that Mt. McKinley is 20,321 ft in elevation, and that it is 8,707 ft. lower than Mt. Everest.

When writing this numerically:

20,321 = x - 8,707

Solve for x:

20,321 = x

+8,707     + 8,707

-------------------------

x = 29,028

Mt. Everest is 29,028 ft. in elevation.

Determine if the subset of R^2 consisting of vectors of the form [a b], where a + b = 1 is a subspace. Select true or false for each statement. This set is closed under scalar multiplications This set is a subspace This set is closed under vector addition The set contains the zero vector

Answers

This set is closed under scalar multiplications. Statement 1 is false.

This set is a subspace. This statement is also false because this set does not contain a zero vector so it is not a subspace.

This set is closed under vector addition. This is false. Because let v and w be two vectors such that v=(v1,v2); w=(w1,w2).

The set contains the zero vector. Statement 4 is false because the sum of two zero vectors cannot be equal to 1.

Since v and w are vectors satisfying the condition of space so v1+v2=1;w1+w2=1

Now we check whether v+w also belongs to the same space or not.

v+w=(v1,v2)+(w1,w2)=(v1+w1, v2+w2)

We shall check whether components of v+w also add up to 1.

v1+w1+v2+w2=v1+v2+w1+w2=1+1=2

So it means that this space is not closed under addition too.

Consider a vector v=(v1,v2) from the space.

Obviously v1+v2=1

Now let us take a constant 'c'  and consider the behavior of

cv=c(v1,v2)=(cv1,cv2)

Now we check whether components of this vector add up to 1.

cv1+cv2=c(v1+v2)=c\neq 1

which clearly indicates that vectors of this space are not closed under scalar multiplication.

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