A geometric sequence is defined recursively by an = 4an-1 . The first term of the sequence is 0.5. Which of the following is the explicit formula for the nth term of the sequence?
A. 0.5 4n-1
B. 0.5 4n
C. 4 0.5n
D. 4 0.5n-1
E. 0.5 4n+1

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.

[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]

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]

The exact length of the curve x = y^48 + 14y^2, for 1 ≤ y ≤ 2, can be found by differentiating x with respect to y, substituting into the formula for arc length, and solving the integral from y=1 to y=2.

To solve this problem, we use the formula for the arc length of a curve given by a function in parametric form. This formula is L = ∫sqrt(1+(dx/dy)^2)dy, with integration done over the interval [1,2].

In this case, our function is given as x = y^48 + 14y^2. First, we differentiate x with respect to y to get dx/dy = 48y^47 + 28y. We then substitute this into the formula to get L = ∫sqrt(1+(48y^47 + 28y)^2)dy. To solve this integral, you can use a standard calculus method or a calculator with integral functions. Make sure to evaluate the definite integral from y=1 to y=2.

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Answer:

markup, 12.32

selling price, 50.82

Step-by-step explanation:

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%

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 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.

Answer:

60,480

Step-by-step explanation:

I got it correct on founders edtell

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.

To find the equation of a line that is perpendicular to the line 3x - 2y = 5 and passes through the point (-2, 1), we determine that the slope of the perpendicular line must be -2/3. Using the point-slope form, the equation of the desired line is y = (-2/3)x - (1/3).

Finding the Equation of a Perpendicular Line

To write the equation of a line that is perpendicular to another line, you first need to determine the slope of the original line. The given equation, 3x - 2y = 5, can be rewritten in slope-intercept form (y = mx + b) by solving for y:
3x - 2y = 5
=> -2y = -3x + 5
=> y = (3/2)x - (5/2)
The slope (m) of this line is 3/2. Perpendicular lines have slopes that are negative reciprocals of each other. Thus, the slope of the line perpendicular to the original line is -2/3.

To find the equation of the line passing through the point (-2, 1) with this slope, use the point-slope form of the equation:
y - y1 = m(x - x1)
=> y - 1 = (-2/3)(x + 2)
Simplifying, we have:

y - 1 = (-2/3)x - (4/3)
=> y = (-2/3)x - (4/3) + 1
=> y = (-2/3)x -(1/3)

This is the equation of the line that passes through (-2, 1) and is perpendicular to the line 3x - 2y = 5.

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:

16% of his phone bills are more than $76

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 65

Standard deviation = 11

What percentage of his phone bills are more than $76?

76 = 65 + 11

So 76 is one standard deviation above the mean.

By the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% are more than 1 standard deviation from the mean. Since the normal probability distribution is symmetric, 16% of them are more than 1 standard deviation below the mean and 16% are more than 1 standard deviation above the mean. So

16% of his phone bills are more than $76