Position Height 5 The height and weight of the starting players on the Big Buckets basketball team are given in the table. A. What is the range of the heights? B. What is the mean height? C. What is the range of the weights? Center Forward Forward Guard Guard 206 193 198 172 190 Weight (kg) 91.8 85.3 84.9 78.0 81.5 D. What is the mean weight?

Let A be the event that a family chose at random indicated an intention to buy a new car and let B be the event that a family chose at random bought a new car within 3 months.

We are asked to find P(A'), which is the probability that a family chosen at random had not previously indicated an intention to buy a car.

We can use the given information to write the following conditional probabilities:

P(B | A) = 60%

P(B | A') = 10%

P(A) = 26%

We can use these probabilities to apply Bayes' theorem to find P(A' | B), which is:

P(A' | B) = P(B | A') * P(A') / P(B)

Substituting the values from the problem, we have:

P(A' | B) = (10%) * (100% - 26%) / (60% * 26% + 10% * (100% - 26%))

= (10%) * (74%) / (60% * 26% + 10% * 74%)

= (10%) * (74%) / (15.4% + 7.4%)

= (10%) * (74%) / (22.8%)

= 43.86%

Therefore, the probability that a family chosen at random had not previously indicated an intention to buy a car is 43.86%.

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The initial population size is 367 fish.

The population size after 8 years is 878 fish.

To find the initial population size of the species, we can substitute t = 0 into the population function:

P(0) = 2200 / (1 + 5\(e^{-0.15t\)))

Since e⁰ = 1, the equation simplifies to:

P(0) = 2200 / (1 + 5)

P(0) = 2200 / 6

P(0) ≈ 366.67

So, the initial population size is 367 fish.

To find the population size after 8 years, we substitute t = 8 into the population function:

P(8) = 2200 / (1 + 5\(e^{(-0.15 . 8)\))

P(8) = 2200 / (1 + 5\(e^{(-1.2)\))

P(8) = 2200 / (1 + 5(0.3012))

P(8) = 2200 / (1 + 1.506)

P(8) = 2200 / 2.506

P(8) ≈ 878.35

Thus, the population size after 8 years is 878 fish.

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Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Answer:

x=27°

Step-by-step explanation:

2x+72° = x+<PLM

<PLM = x+72°

3x = x+<PML

<PML = 2x

(x)+(x+72)+(2x)=180°

4x = 108°

x = 27°

The arc length of \(y=2x^{\frac32}\) over [0, 1] is given by the integral,

\(L=\displaystyle\int_0^1\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx\)

Differentiate y with respect to x using the power rule:

\(\dfrac{\mathrm dy}{\mathrm dx}=\dfrac32\times2 x^{\frac32-1}=3x^{\frac12}\)

Then the integral becomes

\(L=\displaystyle\int_0^1\sqrt{1+\left(3x^{\frac12}\right)^2}\,\mathrm dx=\int_0^1\sqrt{1+9x}\,\mathrm dx\)

Substitute u = 1 + 9x and du = 9 dx :

\(L=\displaystyle\int_0^1\sqrt{1+9x}\,\mathrm dx=\frac19\int_1^{10}\sqrt u\,\mathrm du\)

\(L=\displaystyle\frac19\left(\frac23u^{\frac32}\right)\bigg|_1^{10}\)

\(L=\dfrac2{27}\left(10^{\frac32}-1^{\frac32}\right)\)

\(L=\boxed{\dfrac2{27}\left(10^{\frac32}-1\right)}\)

Step-by-step explanation:

10 seconds=1cm

2 seconds=x cm

cross multiply

10 x=2

divide by 10

x=2/10

x=1/5

Answer:

0.2 in 2 seconds

Step-by-step explanation:

hope this helped!

The allusion in this statement is "Sasquatch," referencing a legendary creature known for its large size and used humorously to imply the person's abnormally large shoe size.

The allusion in the given statement is "Sasquatch." Sasquatch, also known as Bigfoot, is a legendary creature often depicted as a large, hairy, and elusive humanoid. In this context, the reference to Sasquatch is used metaphorically to humorously imply that the person's shoe size is abnormally large.

The mention of Sasquatch adds a playful and exaggerated tone to the conversation about shopping for shoes. It serves as a lighthearted way for the dad to comment on the frequency of buying new shoes, suggesting that the person's feet grow rapidly or that they have a high shoe consumption rate.

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Answer:

0.66 melones por niño o 2/3

Step-by-step explanation:

10/15=2/3=0.66

Answer: rectangle

Step-by-step explanation: Because I saw another Brainly answer saying it was rectangle

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.

When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.

Hope this helps.

Step-by-step explanation:

The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.

Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.

Simplifying this, we get 2x - 80 = $670  + 80 2x = $750  x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.

The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.

The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.

Therefore, the cost of the bench is $375, and the cost of the garden table is $295.

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Answer:

The values are \(x=2\sqrt{2}\) and \(y=2\sqrt{6}\).

Step-by-step explanation:

A right triangle is a type of triangle that has one angle that measures 90°.

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse.

                                             \(\sin(\theta)=\frac{opposite \:site}{hypotenuse}\)

To find the value of x we use the above definition. From the diagram we can see that the angle is 30º and the hypotenuse is \(4\sqrt{2}\). Therefore,

\(\sin(30)=\frac{x}{4\sqrt{2} }\\\\\frac{x}{4\sqrt{2}}=\sin \left(30^{\circ \:}\right)\\\\\frac{8x}{4\sqrt{2}}=8\sin \left(30^{\circ \:}\right)\\\\\sqrt{2}x=4\\\\\frac{\sqrt{2}x}{\sqrt{2}}=\frac{4}{\sqrt{2}}\\\\x=2\sqrt{2}\)

To find the value of y we use the above definition. From the diagram we can see that the angle is 60º and the hypotenuse is \(4\sqrt{2}\). Therefore,

\(\sin(60)=\frac{y}{4\sqrt{2} }\\\\\frac{y}{4\sqrt{2}}=\sin \left(60^{\circ \:}\right)\\\\\frac{8y}{4\sqrt{2}}=8\sin \left(60^{\circ \:}\right)\\\\\sqrt{2}y=4\sqrt{3}\\\\\frac{\sqrt{2}y}{\sqrt{2}}=\frac{4\sqrt{3}}{\sqrt{2}}\\\\y=2\sqrt{6}\)

Answer:

C.

Step-by-step explanation:

trust me its correct on EDGE2021

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

The required surface area of the given rectangular prism is 202 square yd.

Here, we have,

Given that,

the surface area of a rectangular prism with a base length of 9 yd, a base width of 5 yd, and a height of 4 yd is to be determined.

We have,

Surface area is defined as the measure of a region or surface is called as surface area.

Here,

The surface area of the rectangular prism is given as,

S = 2(lw + lh + wh)

S = 2 [9×5 + 5×4 + 4×9]

S = 202 square yd.

Thus, the required surface area of the given rectangular prism is 202 square yd.

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Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

What is Sine rule of triangle?

By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Where, a, b, c are sides of a triangle.

Given that;

Measure of ∠A = 27°

Measure of ∠B = 76°

Since, Sum of all angles of triangle = 180°

Hence,

∠A +  ∠B +  ∠C = 180°

27° + 76° + ∠C = 180°

∠C = 180° - 103°

∠C = 77°

So, Measure of ∠C = 77°

Since, By the definition of sine rule,

sin A / a = sin B / b = sin C / c

Since, sin A = sin 27° = 0.95

sin B = sin 76° = 0.566

sin C = sin 77° = 0.99

Hence,

0.95 / a = 0.566 / b = 0.99 / c = 1 / k

Taking terms as;

0.95 / a = 1 / k

a = 0.95 k

And, 0.566 / b = 1 / k

b = 0.566 k

And, 0.99 / c = 1 / k

c = 0.99 k

Hence, Sides of triangles are;

a : b : c = 0.95 k : 0.566 k : 0.99 k

a : b : c = 0.95 : 0.566 : 0.99

Thus, Measure of ∠C = 77°

And,  Sides of triangles are;

a = 0.95

b = 0.566

c = 0.99

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Take into account similar triangles.

Consider that angle 1 is a right angle. Then:

m∠1 = 90°

the angle below the angle of 50° is congruent to it, then, the angle is 50°.

To determine the measure of angle 2, consider that the sum of the interior angles of a triangle is equal to 180°:

50 + 90 + m∠2 = 180°

m∠2 = 180° - 50° - 90°

m∠2 = 40°

Angle 3 is also a right angle, then:

m∠3 = 90°

Hence, the measure of the required angles are:

D) 90, 40, 90

a=34.697, only one triangle is formed.

And B=40°.7'

A≈77°.79'.So, option A is correct.

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one.

Any three points determine a distinct triangle and a distinct plane in Euclidean geometry when they are non-collinear (i.e. a two-dimensional Euclidean space). To put it another way, each triangle is contained in a plane, and there is only one plane that includes that particular triangle. All triangles are contained in one plane if and only if all geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except as otherwise specified, the subject of this article is triangles in Euclidean geometry, more specifically, the Euclidean plane.

Given,

C​=61° 50, c​=31.2, b=23.6

Sine rule:

sin B/b=Sin C/c

sin B=b sin C/c

=(23.6 sin 61° 50)/31.2

sin B=0.65219

sin B=139.3

A+B+C=180

A=180-B-C

A=180-139.3-61.50

A= -20.8 which is not possible.

Because the angle must be positive.

sin B=sin 40.70

A+B+C=180

A=180-40.70-61.50

A=77.79'

sin A/a=sin C/c

a=c sin A/sin C

So, a=34.697

Only one triangle is formed

And B=40°.7'

A≈77°.79'

Hence, option A is correct.

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Answer:

38 remander 8

Step-by-step explanation:

The distance traveled by Kathryn and her mom in an hour will be 64 miles.

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. The speed is a scalar quantity and requires only magnitude to represent.

Given that Kathryn and her mom drive to her grandmother’s house. They travel 32 miles in 30 minutes.

The distance traveled by them in an hour at the same rate will be calculated as:-

In 30 minutes ⇒ 32 miles

In 1 minute ⇒ 32 / 30

In 60 minutes ⇒ ( 32 / 30 ) x 60

In 60 minutes ⇒ 64 miles

Therefore, the distance traveled by Kathryn and her mom in an hour will be 64 miles.

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Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Answer:

The correct answer is:

D. Action: Divide both sides by 4.

E. Property: Division property of equality.

Answer:

$90

Step-by-step explanation:

A=lw

A=20x20

A=40 ft²

40x2.25=$90

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

365 days in a year

366 days in a leap year

Step-by-step explanation:

Answer:

There are d*w*m days in a year.

Step-by-step explanation:

Multiply the number of days per week by the number of weeks per month, and that by the number of months/year- d*w*m. That number will lbe the total nmber of days in a year.