Match each area to its corresponding radius or diameter of the circle.(All areas are approximate.) Tiles area: 221.5584 square units area: 78.5 square units area: 452.16 square units area: 36.2984 square units area: 314 square units area: 886.2336 square units Pairs radius: 12 units arrowBoth diameter: 16.8 units arrowBoth radius: 3.4 units arrowBoth diameter: 10 units arrowBoth

Answer:

[tex]C=\frac{2W}{E^2}[/tex]

Step-by-step explanation:

[tex]W=\frac{CE^2}{2}[/tex]

Solve for C

To solve for C, we need to get C alone

LEts start with eliminating 2 from the denominator

Multiply the equation by 2 on both sides

[tex]2W= CE^2[/tex]

To isolate C, divide both sides by E^2

[tex]\frac{2W}{E^2} =C[/tex]

[tex]C=\frac{2W}{E^2}[/tex]

Answer:

All rectangles can also be classified as which of the following? Select all that apply. r

rhombus  

square  

parallelogram

trapezoid  

quadrilateral

Step-by-step explanation:

In plane geometry, a rectangle is a parallelogram.

Parallelogram: its opposite sides are parallel, it can also be a square, or a rhombus.

In Euclidean geometry, a quadrilateral is a polygon that has four sides and four vertices.

The answer is: Rhombus, square, parallelogram, and quadrilateral.

Final answer:

The height of the trapezoid is 3 feet.

Explanation:

To find the height of a trapezoid with given bases and area, you can use the formula for the area of a trapezoid, which is the average of the two bases multiplied by the height. The formula is as follows:

Area = ½ × (base1 + base2) × height

Given that the area of the trapezoid is 15 square feet and the two bases are 4 feet and 6 feet, the formula becomes:

15 = ½ × (4 + 6) × height

This simplifies to:

15 = ½ × 10 × height

Therefore, we can calculate the height by dividing the area by 5 (which is half of 10):

height = 15 ÷ 5 = 3 feet

So, the height of the trapezoid is 3 feet.

Final answer:

The probability of selecting a person from the 22-29 age bracket or someone who refused to respond is approximately 79.3% out of the total number of people contacted.

Explanation:

The student is asking about finding the probability of selecting either a person from the 22-29 age bracket or someone who refused to respond from a combined group of people contacted in a survey. To solve this problem, we use the addition rule of probability. The total number of people is 376. The number of people who are in the 22-29 age bracket is 284, and the number of people who refused to respond is 14+19=33. However, this would include those who refused from the 22-29 bracket twice, so we subtract the 19 from the 22-29 age group who refused, leaving us with 33-19=14. Thus, the total number in either category is the sum of these, 284+14=298.

The probability (P) of picking someone from the 22-29 age bracket or someone who refused to respond is therefore calculated as:

P = Number in either category / Total number = 298 / 376 ≈ 0.793 or 79.3%

Final answer:

Jerome's hiking speed was calculated by dividing the distance he hiked, three-fourths of a mile, by the time it took him, two-thirds of an hour. This yielded a hiking speed of 1.125 miles per hour.

Explanation:

To calculate Jerome's hiking speed in miles per hour, we need to divide the distance he hiked by the time it took him. Jerome hiked three-fourths of a mile in two-thirds of an hour. To find the speed, we use the formula:

Speed = Distance ÷ Time

Speed = ¾ mile ÷ ⅓ hour

To divide fractions, we multiply by the reciprocal of the denominator:

Speed = ¾ × ⅔ = 3/4 × 3/2 = 9/8

This fraction simplifies to 1⅛ (1.125) miles per hour. So, Jerome's hiking speed was 1.125 miles per hour.

It is important to remember that when we talk about speed, we are referring to the distance traveled over a certain period of time regardless of the direction of travel.

The equation of the line passing through (-1, 0) and (0, -3) is y = -3x - 3, where -3 is the slope, and -3 is also the y-intercept.

The equation of a line can be written in slope-intercept form as y = mx + b, where m is the slope of the line, and b is the y-intercept. To find the slope m, we can use the two points given; the slope is the change in y over the change in x, which is (-3 - 0)/(0 - (-1)) = -3/1 = -3. With the slope found, and knowing that the line passes through the point (0, -3), we can say the y-intercept b is -3. The equation of the line through the points (-1, 0) and (0, -3) is y = -3x - 3.

Final answer:

The surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is calculated using the formula 2lw + 2lh + 2wh, resulting in a total surface area of 142 square inches.

Explanation:

To calculate the surface area of a box with dimensions of 3 inches, 5 inches, and 7 inches, you would use the surface area formula for a rectangular prism. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.

In this case:

Length (l) = 3 inches

Width (w) = 5 inches

Height (h) = 7 inches

Now, plug these dimensions into the formula:

Surface Area = 2(3 inches × 5 inches) + 2(3 inches × 7 inches) + 2(5 inches × 7 inches)

Surface Area = 2(15) + 2(21) + 2(35)

Surface Area = 30 + 42 + 70

Surface Area = 142 square inches

Therefore, the surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is 142 square inches.

Answer:

The given function is

f(x)= 3 [tex]\sqrt\left- |x  \right-2 |+6[/tex] ⇒[Absolute value function]

F(x)=  1.  3[tex]\sqrt {-(x-2)+6}[/tex] =[tex]3\sqrt {-x+2+6}=3\sqrt{-x+8}[/tex] when (x-2≥0→x≥2) ⇒[ Piecewise function]

   2. [tex]3\sqrt{-[-(x-2)]+6}=3\sqrt{x-2+6}=3\sqrt{x+4}[/tex] when [ x-2<0→x<2]⇒[ Piecewise function]

We see there is a shape which is is in the form of dome,point of intersection  of two curves being (2,7.348), symmetrical on both side of line x=2.

Answer: [tex]\sqrt{78}[/tex] and [tex]15[/tex]

Step-by-step explanation:

Given: (1) two numbers [tex]6[/tex] and [tex]13[/tex].

           (2) two numbers [tex]5[/tex] and [tex]45[/tex].

To Find: Geometric number of numbers in [tex](1)[/tex] and [tex](2)[/tex]

Solution:

Let first number be [tex]=\text{a}[/tex]

Let second number be [tex]=\text{b}[/tex]

Geometric mean of two numbers [tex]\text{a}[/tex] and [tex]\text{b}[/tex] is

                                     [tex]\sqrt{\text{a}\text{b}}[/tex]

Now,

[tex](1)[/tex] First number is [tex]=6[/tex]

            Second number is [tex]=13[/tex]

Geometric mean of both numbers is

      [tex]\sqrt{6\times13}[/tex]

      [tex]\sqrt{78}[/tex]

Geometric mean is  [tex]\sqrt{78}[/tex]

[tex](2)[/tex] First number is [tex]=5[/tex]

            Second number is [tex]=45[/tex]

Geometric mean of both numbers is

      [tex]\sqrt{5\times45}[/tex]

      [tex]\sqrt{225}[/tex]

      [tex]15[/tex]

Geometric mean is  [tex]15[/tex]

The expected value of the sum when rolling a pair of 7-sided dice is 8.

When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.

The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).

To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:

Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8

Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.

Answer:

3.61

Step-by-step explanation:

The function cannot be determined with the given information.

The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.

[tex]g-the\ number\\\\\dfrac{2}{3}g+10=g+5\qquad\text{multiply both sides by 3}\\\\2g+30=3g+15\qquad\text{subtract 30 from both sides}\\\\2g=3g-15\qquad\text{subtract 3g from both sides}\\\\-g=-15\qquad\text{change the signs}\\\\\boxed{g=15}[/tex]