For a certain population of penguins, the distribution of weight is approximately normal with mean 15. 1 kilograms (kg ) and standard deviation 2. 2 kg. Approximately what percent of the penguins from the population have a weight between 13. 0 kg and 16. 5 kg ?.

Using x only once in the inequality, the inequality expression is 8 > x > 2

The mathematical statement is given as

8 is greater than x, and x is greater than 2.

In mathematical expressions, greater than can be represented as >

So, we have the following representations

8 > x, and x > 2

Next, we combine the inequality expressions

This becomes

8 > x > 2

Hence, the inequality expression is 8 > x > 2

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Answer:

*Note: Perimeter is equal to the sum of all side lengths

1.   3cm + 3cm + 5cm + 4cm = 6cm + 9cm = 15cm

2.   3.5cm + 3cm + 3.5cm + 3.5cm + 3cm + 3.5cm

      = 6cm + 7cm + 7cm = 6cm + 14cm = 20cm

3.   2cm + 3cm + 3cm + 3cm + 5cm + 6cm = 5cm + 6cm + 11cm

      = 11cm + 11cm = 22cm

7.   9cm + 9cm + 9cm = 27cm

8.   Perimeter of a rectangle = 2 times the length plus 2 times the width

     P = 2(60m) + 2(48m) = 120m + 96m = 216m

9.   1 roll of 16m of wire = $3,214

     216m/16m = 13.5 rolls of wire

     13.5 rolls($3,214) = $43,389

The expression a⁷- a is divisible by 7 if a is an integer.

Given that,

7 divides a^7−a

To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7

We can write, where k is an integer

a^7−a=7k

a(a^6−1)=7k

Now if a=k then

a^6−1=7

a^6=8

and a=±1.414 so a^7−a=9.898

If a is not equal to k then

a(a^6−1)=a(a^3+1)(a^3−1)=7k

since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.

Hence, The expression a⁷- a is divisible by 7 if a is an integer.

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Answer:

(-1,3)

Step-by-step explanation:

x+4y=11

 -4y.  -4y

x=11-4y

3(11-4y)+5y=12

33-12y+5y=12

33-7y=12

-33.    -33

-7y=-21

/-7.  /-7

y=3

x+4(3)=11

x+12=11

-12.  -12

x=-1

Hopes this helps please mark brainliest

Answer:

x= −1 and y= 3

Step-by-step explanation:

Step One: Rewrite Equations

x+ 4y = 11

3x +5y = 12

Step Two: Solve x +4y = 11 for x:

x +4y = 11

x +4y + −4y = 11 + −4y (Add -4y to both sides)

x = −4y +11

Step Three: Substitute −4y +11 for x in 3x +5y = 12:

3x +5y = 12

3(−4y +11) +5y = 12

−7y +33 = 12 (Simplify both sides of the equation)

−7y +33 +−33 = 12 +−33(Add -33 to both sides)

−7y = −21

(-7y/-7) = (-21/-7) (Divide both sides by -7)

y = 3

I sincerely hope this helped you, good luck on your assignment!

The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.

Sophia planted a tiny sunflower in her backyard at the start of spring.

When she planted the sunflower,

The height of the sunflower = Initial height of the sunflower = 25 inches.

Now, The sunflower then began to grow at a rate of 3 inches per week.

Thus, the growth rate of the sunflower = 3 inches/week

The growth in 9 weeks = 3*9 = 27 inches,

The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.

The growth in w week = 3w inches,

The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.

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The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are told that the triangle P'Q'R' has been transformed from triangle PQR.

Now, the coordinates of triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

The coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, this is clear that the transformation rule used is;

(x, y) → (⁵/₂x, ⁵/₂y)

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The standard form of the equation y = -2/3 x - 1 is 2x + 3y = -3.

The standard form for linear equations in two variables is Ax + By = C. Where,

The equation is represented in slope intercept form. So, let' represent it in standard form.

Therefore,

y = - 2 / 3 x - 1

add 2 / 3 x to both sides of the equation

y = - 2 / 3 x - 1

y + 2 / 3 x  = - 2 / 3 x + 2 / 3 x - 1

y + 2 / 3 x  = - 1

Let's multiply all through by 3 to eliminate the fraction

y + 2 / 3 x  = - 1

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

Therefore, the standard form equation is 2x + 3y = -3

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Answer:

  7.5 in²

Step-by-step explanation:

You want the area of a triangle shown as having a base of 6 inches and a height of 2.5 inches.

The formula for the area of a triangle is ...

  A = 1/2bh

where b is the base length, and h is the height.

The figure shows the base of the triangle as 6 in, and the height as 2.5 in. This means the area is ...

  A = 1/2(6 in)(2.5 in) = 7.5 in²

__

Additional comment

The attachments show the triangle to be overs-specified. If the side dimensions are correct, the area is actually about 7.48 square inches. If the base and height are correct, at least one side length is slightly off.

The total cookies she baked altogether is 28 cookies

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.

Therefore the total cookies put on the plate is 6+4+4= 14cookies

half of all the cookies were put in the plate,

therefore the total cookies made is 14×2= 28cookies.

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The Correct option is D .

System of linear equations,gives us the result that given system has unique solution such that 13x= 6 or x = 6/13 and y = -40/13 .

If a, b, and c are real numbers, the graph of the equation ax + by = c

is a straight line (unless both a and b are zero), so such an equation is called a linear equation in variables x and y. There are three possible types of solutions to a set of linear equations.

given system of equations is

2x - y = 4 --(1)

and 5x + 4y = -10 ---(2)

comparing the above equations with linear system , a1 x + b1 y = c1 and a2 x + b2y = c2

we get, a1 = 2 , a2= 5 , b1 = -1 , b2= 4 , c1= 4 ,

c2= -10

Now, the ratio are

a1/a2 = 2/5 ; b1/b2 = -1/4 ; c1/c2= -4/10 = 2/5

=> a1/a2 not equal to b1/ b2

therefore the given system of equations has unique solution.

Now , we find the soltion of given system using Elimination method,

multipling equation (1) by 4 to making same cofficient of y in both equations of system we get

8x - 4y = 16 --(3) and 5x +4y = -10

adding equation (2) from (3) we get,

8x -4y + 5x + 4y = 16 -10 => 13x = 6 => x = 6/13

putting this value of x in (1)

2×6/13 - y = 4 => y = 12/13-4 = -40/13

Hence , unique solution for given system of equations is x= 6/13 , y = -40/13.

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Complete Question:

Alfred tried to solve the system of equations shown below..

2x - y = 4 and 5x + 4y = -10

He concluded that the system has an infinite number of solutions. Which is the BEST evaluation of Alfred's conclusion?

He is correct. Both equations describe lines that have infinitely many solutions.

He is correct. If the first equation is multiplied by 4 and subtracted from the second equation, the result is -3x +8y = -14 , which means the system has an infinite number of solutions.

He is incorrect. For any positive value of , the corresponding value of is negative, which means the system has no solution.

He is incorrect. If the first equation is multiplied by 4 and added to the second equation, the result is 13x = 6 , which leads to exactly one solution.

The measure of the smallest angle of the quadrilateral is  60° .

In the question ,

it is given that ,

the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .

So , the measure of the largest angle is = 9x

and the measure of the smallest angle is = 4x .

we know that the sum of the measure of all the angles of the quadrilateral is 360° .

that means ,

4x + 5x + 6x + 9x = 360°

24x = 360

dividing both sides by 24 ,

x = 360/24

x = 15 .

the smallest angle is = 4(15) = 60°

Therefore ,  The measure of the smallest angle of the quadrilateral is  60° .

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Answer:

360

Step-by-step explanation:

it has four right angles 90×4 =360

The equation of the graph is a straight line written in slope-intercept form as y = -33.3x + 450. When Misty travelled for 9 hours, he drove 150.3 miles.

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.

The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line

13: The equation of graph in slope-intercept form

But for this case, we will represent our equation using point-slope formula which is y = mx + c

Let's find the slope of the line.

To do this, we will pick any two points and solve for the slope.

A = (0, 450), B = (6, 250)

The equation of slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

m = 250 - 450 / 6 - 0

m = -200/6

m = -33.3

The y-intercept is the point which the line touches the y-axis or y-plane and in this case, the y-intercept is 450.

The equation of the line is y = -33.3x + 450

14: If he has been travelling for 9 hours, how many miles left ?

Using the equation y = -33.3x + 450; put x = 9

y = -33.3(9) + 450

y = 150.3 miles

Misty has 150.3 miles left.

15: If there are 50 miles in the trip left, how many hours has Misty travelled.

Using the equation y = -33.3x + 450

50 = -33.3x + 450

-400 = -33.3x

x = 12 hours

Misty has approximately travelled 12 hours.

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The amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

We will solve the given problem using percentages.

We are given the following;

A salesperson at a jewelry store eams 4% commission each week.

Last week, Heidi sold $750 worth of jewelry.

We need to find the amount Heidi earned in commission and the amount store made from her sale.

Let us find the amount Heidi earned in commission;

$750 * 4% = 750 * 4 / 100 = 7.5 * 4 = 30

So, Heidi earned $30 from the commission.

Let us find the amount store made from her sale;

The amount store earns

= The total amount of sales - commission of Heidi

= $750 - $30

= $720

So, the store earns $720.

Thus, the amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

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Answer:no image I can’t see on mobile

Step-by-step explanation:

h

Out of all the given situations, all are fair gambles,

Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.

The expectation of any game is

E(X) = ∑xp(x)

In the first case

The probability to get a had or tails on flipping a coin is 1/2

Hence the expectation will be

E(X) = 0.5 X 10  +  0.5 X (-10)

= 5 - 5

= 0

Hence this is a fair gamble

In the next gamble, two coins are tosses

The probability to get 2 head is 1/4

The probability to get 2 tails is 1/4

The probability to get one head and one tail is 1/2

Hence,

E(X) = 0.25 X 10  +  0.25 X (-10)  +  0.5 X 0

= 2.5 - 2.5

= 0

Hence this too is a fair gamble

Here,it is given that

Probability              Gain

0.5                            $100

0.25                       - $200

0.25                           $0

Therefore,

E(X) = 0.5 X 100  +  0.25 X (-200)  +  0.25 X 0

= 50  - 50

= 0

Hence, all are fair gambles.

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Correct Question

which of the following is a fair gamble?

one coin toss: win $10 if heads, lose $10 if tails.

two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.

a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.

all of the above are fair gambles.

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Answer: 125

Step-by-step explanation:

100% = 100

25% of 100 = 100/4 = 25

100 + 25% (25) = 125

Answer:

y=12x-7

Step-by-step explanation:

Slope intercept is  y=mx+b

                            y = slope+y-int

always start with variable y =

slope = 12

y=12

slope needs x

y=12x

y-int = -7 so just plug it in as is

y=12x-7

Answer: y = -4/5x - 5

Step-by-step explanation:

So you can view that fancy F with the parenthesis number inside of it as an input, just like X, and when -1 is the output, that means that y=-1, so your first set of numbers is (5,-1) now do the same with the second pair and you get (0,-5), we know that this is the Y intercept because X=0 in this pair.

-5 - (-1) = -4

0-5 = -5

slope = - 4/5

y intercept = -5

The amount to be invested today in order to have $600 in 20 years is $189.66.

When an account pays interest that is compounded quarterly, it means that both the amount invested and the interest that has already been earned increases in value four times in a year.

In order to determine the amount to be invested today, determine the present value of $600.

The formula for calculating present value:

P = FV / [(1 + r)^nm]

Where:

P = 600 / [(1.0145)^80] = $189.66

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Answer: it is 200

Step-by-step explanation:

The percentage of airline passengers covered by this fee is 85.99%.

If the distribution is normal, use the Z-score formula. For a set of means and standard deviations, the measure's z-score X is given by z-score measures how many standard deviations a measure is from its mean. After finding the Z-score, look at the Z-score table to find the p-value associated with that Z-score. This p-value is the probability that the value of the measure is

less than X, the percentile of X Subtracting 1 from the p-value gives the probability that the value of the measure is greater from X means 46 pounds with a standard deviation of 3.7 pounds.

This is the p-value of Z for X = 50 minus 1 as a

ratio. So the p-value of is 0.8599or 0.8599× 100 = 85.99%

So, 85.99% of the airline passengers pay this fee.

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Answer:

If m angle EFD = 75°, then m angle JAB = ??

C

B

A

1.

2.

The image of the given point after the translation will be (-5,1).

The given point is (0,2).

We have to find out the image of the given point after a translation left 5 units and up to 1 units.

Since it is given that there is a translation left 5 units, starting from point (0,2), the image will be on the negative side of x-axis at point 3.

Similarly, it is given that there is also a translation up to 1 units. This implies starting from point (0,2), the image will be on the positive side of y-axis at point 1.

So, the image of the given point after the translation will be (-3,1).

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The valid conclusion about statement A and statement B is "If Figure A is a parallelogram, then Figure A’s angles sum to 360°".

The correct answer option is option D.

A conditional statement can be defined a statement that is written in the form “If A then B,” where A and B are sentences.

For this conditional statement:

Sentence A is called the hypothesis

Sentence B is called the conclusion.

Hypothesis: This is an assumption taken to be true for the purpose of argument or investigation.

Conclusion: This is the proposition that follows as a necessary consequence of the premises in an argument or syllogism.

Hence, “If A then B” means that B must be true whenever A is true.

Therefore, if a figure is a parallelogram, then it is a quadrilateral; If a figure is a quadrilateral, then its angles sum to 360°.

It can be concluded that if a figure is a parallelogram, then it's angles must sum to 360°.

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If the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, the average annual stock return is 11. 3% and you begin your investment portfolio with $2,000,

Suppose the amount he earns in one year is x,

x=  11. 3%. of $2,000

x=220

The portfolio be worth 30 years if the average holds are,

=220 × 30

=$ 6600

The net cost is the sum of the return and the initial investment,

=$ 6600 + $ 2000

=$8600

Thus, if the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

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The required simplified solution of the given subtraction is 16/25. Option D is correct.

Given that,
To Subtract. and determine the lower terms,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 47/50 - 3/10
= [47 - 3×5] / 50
= [47 - 15] /50
= 32 / 50
= 16 / 25

The required simplified solution of the given subtraction is 16/25. Option D is correct.

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Answer:

d) 16/25

Step-by-step explanation:

The problem is,

→ (47/50) - (3/10)

Let's solve the problem,

→ (47/50) - (3/10)

→ (47/50) - (15/50)

→ (47 - 15)/50

→ 32/50

→ (32 ÷ 2)/(50 ÷ 2)

→ 16/25

Hence, answer is 16/25.

Answer:

Step-by-step explanation:

1.3

10/13=1.3

Answer:

[tex]\boxed{\sf \boxed{\sf x=\cfrac{13}{10}}\:or\: \boxed{\sf x=1.3}}[/tex]

Step-by-step explanation:

[tex]\sf 10x= 13[/tex]

Divide both sides by 10:-

[tex]\sf \cfrac{10x}{10}=\cfrac{13}{10}[/tex]

Simplify:-

[tex]\sf x=\cfrac{13}{10}[/tex]

____________________

Hope this helps!

Have a great day!

The distance around the bases in meters will be 27.432 meters.

How many meters are in 1 feet?

In one feet there are 0.3048 meters.

Given is a baseball field measures 90 feet between each base.

Distance between each base in feet = [d] = 90 feet

The distance between each base in meters will be -

D [meters] = 90 x 1 ft

D [meters] = 90 x 0.3048 meters

D [meters] = 27.432 meters

Therefore, the distance around the bases in meters will be 27.432 meters.

Answer:

the correct answer is -32+43

Step-by-step explanation:

I just know