A pet store has 6 cats. Here are their weights (in pounds).9,7 ,7,10,8,8Find the mean weight of these cats.If necessary, round your answer to the nearest tenth

Step-by-step explanation:

6.

the figure can be considered as a combination of a 16×8 rectangle and a 10×8 right-angled triangle on the left side.

for both, perimeter and area, we need to find the length of the missing third side of the right-angled triangle, as this is a part of the long baseline of the overall figure.

as it is a right-angled triangle, we can use Pythagoras :

c² = a² + b²

"c" being the Hypotenuse (the side opposite of the 90° angle, in our case 10 ft). "a" and "b" being the legs (in our case 8 ft and unknown).

10² = 8² + (leg2)²

100 = 64 + (leg2)²

36 = (leg2)²

leg2 = 6 ft

that means the bottom baseline is 16 + 6 = 22 ft long.

a.

Perimeter = 10 + 16 + 8 + 22 = 56 ft

b.

Area is the sum of the area of the rectangle and the area of the triangle.

area rectangle = 16×8 = 128 ft²

area triangle (in a right-angled triangle the legs can be considered baseline and height) = 8×6/2 = 24 ft²

total Area = 128 + 24 = 152 ft²

7.

it was important that the bottom left angle of the quadrilateral was indicated as right angle (90°). otherwise this would not be solvable.

but so we know, it is actually a rectangle.

that means all corner angles are 90°.

therefore, the angle AMT = 90 - 20 = 70°.

the diagonals split these 90° angles into 2 parts that are equal in both corners of the diagonal, they are just up-down mirrored.

a.

so, the angle HTM = AMT = 70°.

b.

MEA is an isoceles triangle.

so, the angles AME and EAM are equal.

the angle AME = AMT = EAM = 70°.

the sum of all angles in a triangle is always 180°.

therefore,

the angle MEA = 180 - 70 - 70 = 40°

c.

both diagonals are equally long, and they intersect each other at their corresponding midpoints.

so, when AE = 15 cm, then AH = 2×15 = 30 cm.

TM = AH = 30 cm.

In this case, the given sample mean of 25.3 is only slightly higher than the population mean of 25, and is well within one standard deviation from the population mean. Therefore, the probability of a sample mean being less than 25.3 is 0.9582.

In statistics, the mean is a measure of central tendency that represents the sum of all values in a dataset divided by the total number of values in that dataset. It is also commonly referred to as the average.

Here,

To find the required probability, we need to calculate the z-score first:

z = (x - μ) / (σ / √n)

z = (25.3 - 25) / (1.3 / √68)

z = 1.73

Looking at the standard normal table, the probability of a z-score being less than 1.73 is 0.9582.

To determine whether the given sample mean would be considered unusual, we need to compare it to the population mean and standard deviation. A sample mean is considered unusual if it falls outside the range of values that are expected to occur with a high probability based on the population mean and standard deviation.

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Answer:

72

Step-by-step explanation:

Answer:

1200 in^2

Step-by-step explanation:

SA = 2B + Ph

SA = 2(8 * 15 / 2) + 40(27)

SA = 1200

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer:

D. (-2, -6) and (5,15)

Step-by-step explanation:

When you set the equations together, you get x^2-3x-10. You then set this equation equal to zero and get (x-5)(x+2) or x=-2 and x=5. Then, plug these x-values into each equation to get your y-values.

Answer:10,9,8

Step-by-step explanation:trust me bro

Answer:

1grgdgfdgdfgdgdgdgdgdg

Step-by-step explanation:

Answer:

40% \((\frac{40}{100})\)

Step-by-step explanation:

According to the given description of the 10 by 10 grid, 40 out of 100 squares are shaded.

Convert into a Fraction:

\(\frac{Shaded}{Squares} =\frac{40}{100}\)

Convert the fraction into a decimal:

\(\frac{40}{100} =0.4\)

Convert the decimal into a percent:

\(0.4*100=40\\\)

40%

So, the grid should represent 40%.

Answer:

40% got it right on the unit test.

Step-by-step explanation:

Step-by-step explanation:

this is a kind of trick question, actually.

with whatever we draw, we produce X values as power of 3.

to be precise, we can have only

3⁰ = 1

3¹ = 3

3² = 9

3⁴ = 81

due to the possible combinations of drawn numbers (e.g. 3 cannot be created by a multiplication of 0s, 1s and 2s).

so, mostly, these results cannot be exact factors of 1024.

1024 cannot be divided by 3, nor by 9 nor by 81.

but 1024 is a multiple of 1 (as is every number).

so, we are looking at the probability to get 0 as multiplication result of the numbers on the 2 drawn balls.

the only possibilities are

1 and 0

2 and 0

out of in total 6 (2×3) different outcomes

1 and 0

1 and 1

1 and 2

2 and 0

2 and 1

2 and 2

the probability of this "0" event is again

number of desired outcomes / number of possible outcomes = 2/6 = 1/3

Answer:

4

Step-by-step explanation:

20/4.3 = 4.7

but you cant buy just a piece of a tube, so the most you can buy is 4

The best estimate of the solution to the system of linear equations is the point are (x,y) will be (0.76, 4.30).

A linear equation in two variables is one that is written in the form axe + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Given:

as x,y are variables,

-3x + y = 2 ..............(1)

- 4x + 7y = 1 ...........(2)

We know that,

The solution of the system of linear equations is the intersection point of both graphs

Multiply equation (1) by 7 on both sides and then subtract it from eq (2)

- 4x + 7y = 1 ...........(2)

-21x + 7y = 14 ..............(1)

⇒- 17 x = -13

⇒ 17 x = 13

⇒ x =\(\frac{13}{17}\)

⇒ x = 0.76

Now on putting value of x  = 0.76 in eq (1) we get

- 3x + y = 2 ............ (1)

⇒- 3(0.76) + y = 2

⇒y = 4.30

The best estimate of the solution to the system of linear equations is the point (x,y) will be (0.76, 4.30).

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Answer: 375 hamburgers

Step-by-step explanation:

Let's assume that x is the number of hamburgers sold on Monday.

According to the problem, the number of cheeseburgers sold is 62 fewer than the number of hamburgers sold. So the number of cheeseburgers sold is x-62.

The total number of hamburgers and cheeseburgers sold is 688. So we can set up an equation:

x + (x-62) = 688

Simplifying this equation, we get:

2x - 62 = 688

Adding 62 to both sides, we get:

2x = 750

Dividing both sides by 2, we get:

x = 375

Therefore, 375 hamburgers were sold on Monday.

The volume of the sphere is approximately 8181.510 cm³.

The volume of a sphere is the amount of space that is enclosed within the surface of a sphere.

It is a measure of the three-dimensional space that is contained within the sphere.

The volume of a sphere is used in a variety of fields, such as physics, engineering, and architecture, to calculate the space enclosed by a sphere or a spherical object, such as a planet or a ball.

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere. Substituting r = 12.5 cm and π = 3.14, we get:

V = (4/3) × 3.14 × (12.5 cm)³

V ≈ 8181.51 cm³

The volume of the sphere is approximately 8181.510 cm³.

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Answer:

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

Find the sum of the volumes of the two given cones.

Cone volume:

Cone 1, d = 4m, h = 8m:

Cone 2, r = 2m, h = 6 m:

Total volume:

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

The present value of the security is $2142.86, rounded to the nearest cent.

Value is a subjective concept that is based on personal beliefs, experiences, and backgrounds. It is the appreciation of something, whether tangible or intangible, that is based on a person's perception of its worth. Value is often used to describe the worth or importance of something or someone, and can be expressed in monetary terms or in terms of the usefulness of something. Ultimately, value is the measure of how much something is worth to an individual.

The present value of this security is $2142.86. This is determined by using the formula:

Present Value = Dividend / (1 + R)t

Where Dividend is the annual dividend of $150, R is the rate of return which is 7%, and T is the time in years which is 1.

Therefore, the present value of the security is:

150 / (1 + 0.07)¹ = $2142.86

Thus, the present value of the security is $2142.86, rounded to the nearest cent.

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer: 5x + 2x + x = (5 + 2 + 1)x = 8x

Step-by-step explanation:

The given expression is: 5x + 2x + x.

We can simplify it by combining the like terms with the same variable, which are the terms with x.

5x + 2x + x = (5 + 2 + 1)x = 8x

Therefore, the expressions equivalent to 5x + 2x + x are:

A. (5+2+1)x

D. 8x

Option B, 8x3, and option C, 8, are not equivalent to the given expression.

Answer:

a and d

Step-by-step explanation:

b and c would not be an option because you still need tobfind the variable for x and you have to get your variables alone.

The value of CE is 14.7 units.

The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.

So that in the given circle with center A, we have;

CE = BD  (diameter of a given circle)

BA = EA = CA = DA    (radius of a given circle)

CE is the diameter of the circle, and BA is the radius, so that;

CE = 2*BA

     = 2*7.35

     = 14.7

CE = 14.7

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simplification of expression will be g - 2

Our expression is  g - 16/4 + 2

16/4 = 4

so we c will write it as

g - 4 + 2

which can be further simplified to

g - 2

Therefore, our simplified expression comes out to be g - 2.

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a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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Complete question:

Two six-sided dice are rolled (one red one and one green one). Some possibilities are (Red= 1, Green=5) or (Red=2, Green=2) etc.

a)How many total possibilities are there?

For the rest of the questions, we will assume that the dice are fair and that all the possibilities in (a) are equally likely.

b)What is the probability that the sum on the two dice comes out to be 11?

c)What is the probability that the sum on the two dice comes out to be 7?

d)What is the probability that the numbers on the two dice are equal?

Answer:

Kindly check explanation

Step-by-step explanation:

Total probabilities :

Total possible outcomes on each dice = 6

Total probabilities = 6² = 36

b)What is the probability that the sum on the two dice comes out to be 11?

Total required outcome = 2

Total possible outcomes = 36

Probability = required outcome / Total possible outcomes

P(sum on both dice = 11) = 2 / 36 = 1/18

c)What is the probability that the sum on the two dice comes out to be 7?

Required outcome = 6

Possible outcomes = 36

P(obtaining a sum of 7) = 6/36 = 1/6

d)What is the probability that the numbers on the two dice are equal

= required outcome / possible outcomes

Required outcome = 1,1 ; 2,2; 3,3; 4,4 ; 5,5 ; 6,6

= 6/36 = 1/6

Answer:

Pretty sure it's 8 units long

Answer:

x - .2x

Step-by-step explanation:

You take the regular price minus the regular price times the discount percentage in decimal form

Answer: \(x=\Large\boxed{-3}\)

Step-by-step explanation:

Given expression

\(7+2x+12=x+16\)

Combine like terms

\(7+12+2x=x+16\)

\(19+2x=x+16\)

Subtract 19 on both sides

\(19+2x-19=x+16-19\)

\(2x=x-3\)

Subtract x on both sides

\(2x-x=x-3-x\)

\(x=\Large\boxed{-3}\)

Hope this helps!! :)

Please let me know if you have any questions

(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

6

Step-by-step explanation:

use the pythagorean theorem

a² + b² = c²

8² + b² = 10²

b² = 100-64

b= (square root of) 36

b=6

Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.

Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.

Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.

At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.

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