What is the area of a square with side lengths of 7 feet?


A.
28 ft

B.
28 ft2


C.
49 ft2


D.
49 ft

We have been given that probability of the even is 100%. In other words we can say that the probability is 1. It means that the event will certainly occur.

Now, we know that the highest value of probability is 1 and lower value is 0.

Mathematically, we can represents it as

[tex]0\leq P(E)\leq 1[/tex]

If the probability is 0 then the event will never occur.

And if the probability is 1 then event will definitely occur.

Therefore, A certain event has a 100% chance of occurring.

Answer:250

Step-by-step explanation:

Answer:

132 km

Step-by-step explanation:

1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11

2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132

The equation of the parabola with focus (-2,4) and directrix y = 0 is (x + 2) = 8(y - 2). This is derived by finding the vertex and applying the general equation for a vertically oriented parabola.

To find the equation of a parabola with a given focus and directrix, we use the definition that a parabola is the set of all points that are equidistant from the focus and the directrix. In this case, the focus is at (-2,4) and the directrix is y = 0. The vertex of the parabola will thus be halfway between the focus and the directrix, which means it will lie on the line y = 2 (since the focus has a y-coordinate of 4 and the directrix is at y = 0).

The standard form equation of a vertically oriented parabola with its vertex at the origin is x = 4py, where p is the distance from the vertex to the focus (or to the directrix). For a parabola that is shifted to have a vertex not at the origin, the equation is (x-h)² = 4p(y-k) where (h,k) is the vertex.

In this scenario, because the vertex is not at the origin and the parabola opens upwards (since the directrix is below the focus), we'll adjust the standard form equation to take these factors into account. The vertex (h,k) is (-2,2), the focus is (-2,4), thus p = 2. Therefore, the equation is (x + 2)² = 4*2*(y - 2)

We have to use the distance formula to find the distance between (−8, 2.5) and (0, −4.5).

The distance formula states:

" For the given points [tex] A(x_{1},y_{1}) [/tex] and[tex] B(x_{2},y_{2}) [/tex], the distance between A and B is given as:

AB = [tex] \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} [/tex]

We have to find distance between (−8, 2.5) and (0, −4.5). So, [tex] x_{1}= -8, y_{1}= 2.5 , x_{2}=0 , y_{2}=-4.5 [/tex]

AB = [tex] \sqrt{(0+8)^{2}+(-4.5-2.5)^{2}} [/tex]

AB = [tex] \sqrt{64+49} [/tex]

AB = [tex] \sqrt{113} [/tex]

AB = 10.630 units

By rounding to the nearest hundredth, we get

Distance between A and B = 10.63 units.

The area of the canvas covered by the red rose is 370 square inches, calculated by multiplying the width and height of the canvas to find the total area and then taking 50% of that area.

The task is to calculate the area of a canvas that was covered by a red rose painting, which took up 50% of the total canvas area. To find the area covered by the red rose, we first need to calculate the total area of the canvas. The total area (A) of a rectangle is calculated by multiplying its width (W) by its height (H), which gives us the formula:

A = W x H

In this case, Kendra's canvas is 20 inches wide and 37 inches high. Using the formula:

A = 20 inches x 37 inches = 740 square inches

Now, since the red rose covers 50% of the canvas, we simply take 50% of the total area to find the area covered by the red rose:

Area covered by the red rose = 50% of 740 square inches = 0.50 x 740 square inches = 370 square inches

Therefore, the area of the canvas covered by the red rose is 370 square inches.

The number here is will be represented as under -

Let the number be x.

Thus, the 5 times the number will be = 5x.

Now, it says, the number is 68 less than 5 times a number.

The equation so formed will be -

5x - 68 = x

4x = 68

x = 68.

Thus, the number will be 17.

Let us re-check the number,

(5 × 17) - 68 = 17

85 - 68 = 17

17 = 17. Thus, the number will be 17.

9514 1404 393

Answer:

  B. Rectangle

Step-by-step explanation:

The cross section will be a rectangle, as illustrated in the attachment.

The correct answer is B. Rectangle.

 To determine the shape of the cross section, we need to understand the properties of a right triangular prism and the nature of the plane cut. A right triangular prism has two congruent right triangles as its bases, and the lateral faces are rectangles.

When a plane cut is made through points that are vertices of the base right triangle and is perpendicular to the opposite base, the cross section will intersect all the lateral edges of the prism. Since the lateral edges are perpendicular to the base, the cross section will have four right angles, making it a quadrilateral.

Furthermore, because the cut is perpendicular to the opposite base, the cross section will have two pairs of parallel sides. One pair of parallel sides comes from the intersection with the two lateral faces that are parallel to each other, and the other pair comes from the intersection with the base and the top face of the prism, which are also parallel.

 Given these properties, the most specific name for the shape of the cross section is a rectangle, as it is a quadrilateral with four right angles and opposite sides that are parallel and equal in length.

Therefore, the correct answer is B. Rectangle.

Answer:

1/8

Step-by-step explanation:

from my calculations it should be $835.49

Answer:

30

Step-by-step explanation:

To find out how much money Marcia has, a system of linear equations is set up and solved. Sue has $54, which means Marcia has $78 since she has $84 less than three times Sue's amount. They together have $132.

The question involves solving a system of linear equations to determine how much money Marcia has if she has $84 less than three times as much as Sue. Together they have $132. To solve this, let's name the amount Sue has as S, and consequently, Marcia has 3S - $84. Adding both amounts, we get the equation S + (3S - 84) = $132.

Combining like terms gives us 4S - 84 = $132. We solve for S by first adding 84 to both sides, which yields 4S = $216. Dividing both sides by 4 gives us S = $54. Knowing Sue's amount, we can compute Marcia’s by multiplying Sue’s amount by three and then subtracting 84, so 3 x $54 - $84 = $162 - $84 = $78. Therefore, Marcia has $78.

Answer:

12 and 13 or

- 13 and - 12

A quadratic equation r² + r - 156 = 0

Step-by-step explanation:

Let the first number be r, it means that the second will be r + 1.Given that the product of two consecutive integers is 156. we may interpret that to mean that

r(r + 1) = 156

r² + r - 156 = 0

r² + 13r - 12r -156 = 0

(r + 13)(r - 12) = 0

r = -13 0r 12

if r = -13, r + 1 = -12

If r = 12, r + 1 = 13

Answer:  The correct options are (2). A,  (3). A.

Step-by-step explanation:  The calculations are as follows:

(1) We are to given the area of a regular hexagon with radius 5 in.

The AREA of a regular hexagon with side  'a' units is given by

[tex]A=\dfrac{3\sqrt3}{2}a^2.[/tex]

We know that the radius of a regular hexagon is equal to the length of each side, so we have

a = 5 in.

Therefore, the area of the hexagon will be

[tex]A=\dfrac{3\sqrt3}{2}\times 5^2=1.5\times 1.732\times 25=64.95\sim 65~\textup{in}^2.[/tex]

Thus, (A) is the correct option.

(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.

The angle lying between the two sides measure 35°.

we are to find the area of the triangle.

We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by

[tex]A=\dfrac{1}{2}ab\sin \beta.[/tex]

Here, a = 2.75 miles,  b = 1.32 miles  and  β = 35°.

Therefore, the total search area, in the form of triangle is given by

[tex]A=\dfrac{1}{2}\times 2.75\times 1.32\times \sin 35^\circ=1.815\times 0.5735=2.08~\textup{mi}^2.[/tex]

Thus, the correct option is (A) 2.08 mi².

Hence, the correct options are (2). A,  (3). A.

Answer:

.

Step-by-step explanation: