Write2/3and3/4 as a pair of fractions with a common denominator

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

Given is Y = 10000·(0.97)ˣ

This is an exponential equation whose general form is y = a·bˣ

where 'a' is the initial value and 'b' is the growth or decay factor.

If value of b is greater than 1, then it is growth of population.

If value of b is lesser than 1 but greater than 0, then it is decay of population.

On comparison of the given equation with its general form, we get a = 10000, b = 0.97

So initial value is 10000.

Since value of b is 0.97 i.e. lesser than 1, so it is decay of population.

Hence, the given equation represents "Decay".

Answer:

60,480

Step-by-step explanation:

I got it correct on founders edtell

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]

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.

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%

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.

[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]

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.

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:

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]