what is the median and range of the data

Step-by-step explanation:

as the description says, the area is a rectangle (8×4) minus the half-circle at the right.

the radius of the (half-)circle is 4/2 = 2, as 4 is the diameter.

the area of the circle is

pi×r² = pi×2² = 4pi

the area of the half-circle is then

4pi/2 = 2pi

the area of the rectangle is

8×4 = 32

the total area is

32 - 2pi = 25.71681469... ≈ 25.7 square units

Answer:

  25.7 square units

Step-by-step explanation:

You want the area of a 4 × 8 rectangle with a semicircle of diameter 4 removed from the end.

The area of the enclosing rectangle is ...

  A = LW

  A = (8)(4) = 32 . . . . . square units

The are of the missing semicircle is ...

  A = 1/2πr² . . . . . . where r is half the diameter

  A = 1/2π(4/2)² = 2π ≈ 6.3 . . . . . square units

Then the area of the figure is ...

  A = rectangle - semicircle = 32 -6.3 = 25.7 . . . . . square units

The area of the figure is about 25.7 square units.

Yes, the ball reach a height of 25 meters from the ground , got the answer by solving equation given .

what is height ?

Height refers to the vertical distance between a point or an object and a reference level, usually the ground or a specific reference point. In the given context, height refers to the vertical distance of the ball from the ground at any given time, as modeled by the function h(t) = -5t² +7t+24.

In the given question,

h(t) = -5t² +7t+24

To find the time it takes for the ball to reach a height of 25 meters, we set h(t) equal to 25 and solve for t:

-5t² + 7t + 24 = 25

Simplifying, we get:

-5t² + 7t - 1 = 0

Using the quadratic formula, we get:

t = (-(7) ± √((7)² - 4(-5)(-1))) / (2(-5))

t = 1.4 seconds or t = 0.143 seconds (rounded to three decimal places)

Therefore, the ball will reach a height of 25 meters after 1.4 seconds or 0.143 seconds.

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Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E

Given data:

S = initial amount = $54

D = the number of days

C = the cost per day = $6

E: the ending amount = $18

Amelia started with S=$54 and spent C=$6 each day at camp.

Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:

C x D = 6D

Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:

S - (C x D) = E

Substituting the values in the equation we get:

54 - 6D = 18

54 - 18 = 6D

36 = 6D

D = 6

Therefore, Amelia was at camp for 6 days.

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Answer:

21

Step-by-step explanation:

20+1=21

Answer:

lbozo

Step-by-step explanation:

The first term of the polynomial in standard form must be 4y⁴

If Julian wrote the last term as -3x⁴, the terms with the highest degree must have a coefficient of 3.

To get the standard form, we need to combine like terms and arrange the terms in descending order of degree.

The polynomial can be simplified as follows:

4x²y²-2y⁴-8xy³+9x³y+6y⁴-2xy³-3x⁴+x²y²

= -3x⁴ + (4x²y² + x²y²) + (-2y⁴ + 6y⁴) + (-8xy³ - 2xy³) + 9x³y

= -3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

Therefore, the standard form of the polynomial is

-3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y

= 4y⁴ + 5x²y² + -3x⁴ - 10xy³ + 9x³y

The term with the highest degree is -3x⁴, and the terms are arranged in descending order of degree. The answer is not one of the options given.

Therefore, the first term of the polynomial in standard form must be 4y⁴.

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The probability that a randomly selected household has a savings account is  57.16%. therefore, correct option is (C) 57.16%.

Given,

A survey revealed that 21.5% of the households had no checking account.

Of those households with no checking account, 40% had savings accounts.= 21.5% × 40%= 0.086%66.9%

had regular checking accounts. Of the households with regular checking accounts,

71.6% had a savings account.= 66.9% × 71.6%= 47.8916%11.6% had now accounts.

Of the households with now accounts,

79.3% had savings accounts.= 11.6% × 79.3%= 9.1828%

Therefore, the probability that a randomly selected household has a savings account is:

0.086 + 47.8916 + 9.1828 = 57.16%

So, the correct option is (C) 57.16%.

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Answer:

Step-by-step explanation:

15 divided by 15 is 1

3.45 divided by 15 is 0.23

The cost per ounce is 23 cents, or $0.23

A shape is moved to the right by 5 units. Transformation: Translation

A shape is flipped over a line. Transformation: Reflection

A shape is rotated 90 degrees clockwise. Transformation: Rotation

A shape is moved diagonally to the left and up by 3 units. Transformation: Translation

A shape is reflected over the line y = x. Transformation: Reflection

In geometry, a translation is a type of transformation that moves every point of a figure or an object in a straight line without changing its size, shape, or orientation. It is also referred to as a slide.

To perform a translation, you select a vector (which determines the distance and direction of the movement) and apply it to every point of the figure or object. For example, if you want to translate a shape 4 units to the right and 2 units up, you would add 4 to the x-coordinates of all the points and add 2 to the y-coordinates of all the points.

Situation 1: A shape is moved to the right by 5 units.

Transformation: Translation

Situation 2: A shape is flipped over a line.

Transformation: Reflection

Situation 3 : A shape is rotated 90 degrees clockwise.

Transformation: Rotation

Situation 4 : A shape is moved diagonally to the left and up by 3 units.

Transformation: Translation

Situation 5: A shape is reflected over the line y = x.

Transformation: Reflection

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Complete question:

Determine if each situation is a rotation, a translation, or a reflection.

The graph that closely matches the function is graph C.

2(6×7) + 2(3×7) + 2(3×6)

= 162

The volume of container M can be calculated using the formula for the volume of a cylinder:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we have:

V = π(3 in)^2(9.5 in)

V ≈ 254.47 cubic inches

Let x be the volume of one box of sugar. According to the problem, the cook emptied one box of sugar into the container, and then added some fraction of another box to completely fill it. This means that the total volume of sugar added is equal to 1 + some fraction of x.

We can set up an equation to solve for x:

1 + (1/n)x = 254.47

where n is the fraction of the second box of sugar added.

Solving for x, we get:

x = (254.47 - 1) n

x = 253.47n

To find the value of n, we can subtract 1 box of sugar from the total volume added, and then divide by the volume of one box:

n = (254.47 - 1) / x

n = 253.47 / x

Substituting the expression for x from above, we get:

n = 253.47 / (253.47n)

n^2 = 253.47 / 1

n ≈ 15.93

Therefore, the volume of one box of sugar is approximately:

x ≈ 253.47 / 15.93

x ≈ 15.91 cubic inches

El cubo tiene cuatro caras numeradas del 1 al 6, lo que significa que hay un total de 4 posibles resultados en los que se puede obtener un 3 o un 5.

La moneda tiene dos caras, y dado que es imparcial, hay una probabilidad del 50% de que caiga en cara.

Entonces, la probabilidad de que se lance el cubo y la moneda al mismo tiempo y se obtenga un 3 o un 5 y una cara es igual a la probabilidad de obtener un 3 o un 5 multiplicada por la probabilidad de obtener una cara en la moneda.

La probabilidad de obtener un 3 o un 5 es de 2/6, o 1/3. La probabilidad de obtener una cara en la moneda es de 1/2.

Por lo tanto, la probabilidad total es:

1/3 x 1/2 = 1/6

La probabilidad de que caiga en cara y sacar un 3 o un 5 es de 1/6 o aproximadamente 0.1667.

Step-by-step explanation:

16 is tangent and the radial (12) is perpendicular

so this is a right triangle

   Use Pythagorean theorem

      ?^2  = 12^2 + 16^2

?^2 = 400

? = 20 units

The value of k is approximately 10.33.

What is the exterior angle?

An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.

In a triangle, the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles. In this problem, the exterior angle to the bottom left interior angle is (5k - 3) degrees, and the corresponding remote interior angle is (9 + k) degrees. Therefore, we can write:

(5k - 3) = (9 + k) + x

where x is the other remote interior angle of the triangle.

Simplifying this equation, we get:

5k - 3 = 9 + k + x

4k = 12 + x

x = 4k - 12

Now, we know that the sum of the interior angles of a triangle is 180 degrees. So, we can write:

(9 + k) + (5k - 3) + x = 180

Substituting x with 4k - 12, we get:

(9 + k) + (5k - 3) + (4k - 12) = 180

Simplifying this equation, we get:

18k - 6 = 180

18k = 186

k = 10.33 (rounded to two decimal places)

Therefore, the value of k is approximately 10.33.

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Answer:

x1 = -2;

x2 = 3

Step-by-step explanation:

[tex]5 {x}^{2} - 5x - 30 = 0[/tex]

Solve this quadratic equation (a = 5; b = -5; c = -30)

[tex]d = {b}^{2} - 4ac = ( { - 5})^{2} - 4 \times 5 \times ( - 30) = 25 + 600 = 625 > 0[/tex]

x1 = (-b - √d) / 2a = (5 - 25) / 2 × 5 = -20 / 10 = -2

[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{5 + 25}{2 \times 5} = \frac{30}{10} = 3[/tex]

Answer:

x = 11

Step-by-step explanation:

[tex] \frac{8}{48} = \frac{x}{x + 55} [/tex]

[tex]8(x + 55) = 48x[/tex]

[tex]8x + 440 = 48x[/tex]

[tex]40x = 440[/tex]

[tex]x = 11[/tex]

The complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph can be seen in the image at the end.

Here we have the function:

f(x)  = -8

This is a constant function, for every input that we use, the output will be the same one, then:

f(-8) = -8

f(-1) = -8

f(1) = -8

Then the complete table is:

x       f(x)

-8       -8

-1        -8

1          -8

And the graph of these 3 points can be seen in the image at the end.

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Answer: 23 meter

Step-by-step explanation:

meters "above"

elevation means the distance above sea level

Answer: 5,250

Step-by-step explanation:

250x3=750

750x7

After answering the presented question, we can conclude that The equation number of trials is predetermined: We're going to roll the dice 20 times.

An equation is a statement in mathematics that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). For example, 2 + 3 = 5 is an equation because the expression on the left-hand side (2 + 3) is equal to the expression on the right-hand side (5).

Equations are used in many areas of mathematics, science, and engineering to describe relationships between quantities and to solve problems. For example, equations are used to model physical phenomena, such as the motion of objects, the behavior of fluids, and the propagation of waves. They are also used in finance, statistics, and many other fields to analyze data and make predictions.

In this case, the random variable X reflects the number of times a specific number appears after rolling a 20-sided die 20 times.

To see if this situation fits the binomial distribution model, we must look at the four conditions listed below:

The trials are impartial: Each throw of the dice is distinct from the others.

There are just two possibilities: Each roll can produce one of the 20 numbers or none at all.

The likelihood of success is constant: The probability of rolling a given number on a 20-sided dice is the same for each roll.

The number of trials is predetermined: We're going to roll the dice 20 times.

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Answer:

156

Step-by-step explanation:

The value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

To find the value of the expression, 2x^2 - 5xy, when x = -3 and y = 8, we just need to substitute the given values into the expression.

So, 2x^2 - 5xy becomes 2*(-3)^2 - 5*(-3)*8 = 2*9 + 15*8 = 18 + 120 = 138

Therefore, the value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.

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To determine the type of vertex created by this quadratic function, we need to find the vertex of the parabola. The vertex of a parabola is the point where the parabola reaches its minimum or maximum value.

The given equation [tex]h(t) = -0.25t^2 + 2t + 4[/tex] represents the height of the basketball as a function of time.

The vertex of a quadratic function in the form of   [tex]f(x) = ax^2 + bx + c[/tex] can be found by using the formula:

[tex]x = -b/2a[/tex]

[tex]y = f(x) = a(x^2) + bx + c[/tex]

where (x,y) is the vertex of the parabola.

Comparing this with the given equation  [tex]h(t) = -0.25t^2 + 2t + 4[/tex] , we see that a = -0.25, b = 2, and c = 4.

Substituting these values in the formula, we get:

[tex]t = -2/(2\times(-0.25)) = 4[/tex]

[tex]h(4) = -0.25(4)^2 + 2(4) + 4 = 6[/tex]

Therefore, the vertex of the parabola is [tex](4, 6)[/tex] . Since the coefficient of the t^2 term is negative, the parabola opens downwards, and the vertex represents the maximum point of the parabola. The quadratic function   [tex]h(t) = -0.25t^2 + 2t + 4[/tex] would create a maximum vertex.

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The volume of a regular snowcone is 56.52 in³.

The price per cubic inch of a regular snowcone is $0.05.

In Mathematics and Geometry, the volume of a cone can be determined by using this formula:

V = 1/3 × πr²h

Where:

By substituting the given parameters into the formula for the volume of a cone, we have the following;

Volume of cone, V = 1/3 × πr²h

Volume of regular snowcone, V = 1/3 × 3.14 × 3² × 6

Volume of regular snowcone, V = 56.52 in³.

For the price per cubic inch, we have:

Price per cubic inch = Cost/Volume

Price per cubic inch = 2.85/56.52

Price per cubic inch = $0.05

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Answer:

12:4

=3:1 (Simplified )