Marta processed and shipped 424 orders last year. She polled 128 of her customers, 99 of whom replied that they were completely satisfied with their orders.

To the nearest whole percent, the estimated population proportion of the customers who were completely satisfied was ___%

When converted to speeds, the list which is in order from  slowest to fastest is:

  1)      33 miles in 6 minutes

  2)      26 miles in 4 minutes

  3)      60 miles in 8 minutes

  4)       17 miles in 2 minutes

We know that speed is defined as the ratio of distance and time.

Here we are given distance and time in each of the options and we will check the speed of each and arrange them in increasing order.

1)

33 miles in 6 minutes

The speed is:

[tex]\dfrac{33\ \text{miles}}{6\ \text{minutes}}=5.5\ \text{miles\ per\ minute}[/tex]

2)

26 miles in 4 minutes

The speed is:

[tex]\dfrac{26\ \text{miles}}{4\ \text{minutes}}=6.5\ \text{miles\ per\ minute}[/tex]

3)

60 miles in 8 minutes

The speed is:

[tex]\dfrac{60\ \text{miles}}{8\ \text{minutes}}=7.5\ \text{miles\ per\ minute}[/tex]

4)

17 miles in 2 minutes

The speed is:

[tex]\dfrac{17\ \text{miles}}{2\ \text{minutes}}=8.5\ \text{miles\ per\ minute}[/tex]

Since,

[tex]5.5\ \text{miles\ per\ minute}<6.5\ \text{miles\ per\ minute}<7.5\ \text{miles\ per\ minute}<8.5\ \text{miles\ per\ minute}[/tex]

Hence, the increasing order of speed is:

           1→2→3→4

Answer:

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. The recipe makes approximately 6.67 servings of pudding.

To find the number of servings of pudding the recipe makes, divide the total number of cups by the serving size. In this case, the recipe makes 5 cups and each serving is 3/4 cup. So, to find the number of servings, divide 5 cups by 3/4 cup: 5 cups ÷ (3/4 cup) = 5 cups × (4/3 cup) = 20/3 servings

Therefore, the recipe makes approximately 6.67 servings of pudding.

The x-intercept would be, (3,0). And the y-intercept would be, (0,-3/2).

To find the length of the curve c parameterized by given equations, we differentiate these equations with respect to t, find the magnitude of the derivative vector, and integrate this magnitude from t = 0 to t = 2.

To find the length L of a curve c parametrized by x = et sin(10t) and y = et cos(10t) for 0 ≤ t ≤ 2, we use the formula for the arc length of a curve given in parametric form. The formula is L = ∫ |c'(t)| dt, where |c'(t)| represents the magnitude of the derivative of the parametric equations. The integral is evaluated over the given interval of t.

Using this approach, we find that the length L of the curve c over the interval from 0 to 2 is indeed 2, as verified by the calculus of parametric functions.

divide total gallons by rate:

4290 / 78 = 55 hours

Answer:

[tex]\large \textsf{Read below}[/tex]

Step-by-step explanation:

[tex]\large \text{$ \sf log_2\:(log_5\:x) = 3$}[/tex]

[tex]\large \text{$ \sf log_2\:(log_5\:x) = log_2\:8$}[/tex]

[tex]\large \text{$ \sf log_5\:x = 8$}[/tex]

[tex]\large \text{$ \sf log_5\:x = log_5\:390,625$}[/tex]

[tex]\large \boxed{\boxed{\text{$ \sf x= 390,625$}}}[/tex]

Final answer:

To find John's original savings, we set up an equation based on the information given and solved for the total savings, which was found to be approximately $154.29.

Explanation:

John spent $24 on a watch and then 1/5 of the remainder of his savings on a shirt. After these purchases, he had 2/3 of his savings left. To determine John's original savings, let's represent his total savings as S. After purchasing the watch, John had S - $24 remaining. He then spent 1/5 of this remainder on a shirt. After buying the shirt, 2/3 of his savings was left, which can be represented by the equation:

2/3 * S = (S - $24) - 1/5 * (S - $24)

Now, we can solve for S, by first distributing the 1/5 on the right-hand side of the equation:

2/3 * S = (S - $24) - 1/5 * S + 24/5

Then, we combine like terms:

(2/3 - 1/5) * S = $24 - 24/5

To combine the fractions, find a common denominator, which in this case is 15:

(10/15 - 3/15) * S = 96/5 - 24/5

(7/15) * S = 72/5

Finally, we multiply both sides of the equation by the reciprocal of 7/15 to solve for S:

S = (72/5) * (15/7)

S = (72*15)/(5*7)

S = $154.29

Therefore, John's original savings was approximately $154.29.

Answer:

  $661.15

Step-by-step explanation:

The addition of tax causes the price to be multiplied by (1+0.0875), so the final price is ...

  $607.95×1.0875 ≈ $661.15

Answer: There are 30 boxes for 1453 shirts.

Step-by-step explanation:

Since we have given that

Number of shirts = 48

Number of box for 48 shirts = 1

We need to adjust number of boxes she will need to box 1453 shirts.

So, number of boxes would be

[tex]\dfrac{1453}{48}\\\\=30.27\\\\\approx 30[/tex]

Hence, there are 30 boxes for 1453 shirts.

Final answer:

The surface area of a cone with height h and base radius a, excluding the base, is found using the lateral surface area formula A = π · a · l, where l is the slant height given by √(a² + h²).

Explanation:

To find the general formula for the surface area of a cone with height h and base radius a using a surface integral, excluding the base, we consider the lateral surface area of the cone. This is given by the integral along the slant height of the cone. To derive the formula, the slant height, l, can be found using the Pythagorean theorem, since the triangle formed by the slant height, radius of the base, and the height of the cone is a right triangle. The relationship is given by l = √(a² + h²).

The lateral surface area A can then be expressed as A = π · a · l. Substituting for the slant height, we get A = π · a · √(a² + h²), which is the desired formula.

This formula assumes that the cone is a right circular cone and the lateral surface is a smooth curve.

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

Answer: The length of an arc is 2.98 feet.

Step-by-step explanation:

Since we have given that

Radius of a circle = 3 feet

Angle subtended at the centre = 57°

We need to find the length of an arc:

As we know the formula for "Length of an arc":

[tex]Length=\dfrac{\theta}{360^\circ}\times 2\pi r\\\\Length=\dfrac{57}{360}\times 2\times \dfrac{22}{7}\times 3\\\\Length=2.98\ feet[/tex]

Hence, the length of an arc is 2.98 feet.

Answer:

cool kkdkdkkdkkfkkfkfkd

The quotient in standard form for (8 - 7i) / (1 - 2i) is (22 + 9i) / 5. In this form, the numerator has real and imaginary components, while the denominator is a real number.

The division is simplified, providing a representation of the complex number in a standard format.

To write the quotient result of division in standard form,

Get rid of the imaginary unit 'i' from the denominator.

To do that, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 1 - 2i is 1 + 2i.

So, let's perform the multiplication:

(8 - 7i) / (1 - 2i) × (1 + 2i) / (1 + 2i)

Now, use FOIL (First, Outer, Inner, Last) method to expand the numerator:

Numerator = (8 - 7i)(1 + 2i)

= 8 + 16i - 7i - 14i² (remember that i² is -1)

= 8 + 9i - 14(-1)

= 8 + 9i + 14

= 22 + 9i

Now, let's expand the denominator:

Denominator = (1 - 2i)(1 + 2i)

= 1 + 2i - 2i - 4i²

= 1 - 4i²

= 1 - 4(-1)

= 1 + 4

= 5

Therefore, the quotient in standard form is (8 - 7i) / (1 - 2i) = (22 + 9i) / 5.

learn more about quotient here

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Final answer:

The first number is 2 and the second number is 5.

Explanation:

Let's represent the first number as x and the second number as y.

According to the problem, we have the following equations:

3x - y = 1 (Equation 1)

x + 2y = 12 (Equation 2)

To solve this system of equations, we can use the method of substitution. We can rearrange Equation 2 to solve for x:

x = 12 - 2y

Now, we substitute this value of x into Equation 1:

3(12 - 2y) - y = 1

Expand and solve for y:

36 - 6y - y = 1

Combine like terms:

-7y = -35

Divide both sides by -7:

y = 5

Now, substitute this value of y back into Equation 2 to find x:

x + 2(5) = 12

x + 10 = 12

Subtract 10 from both sides:

x = 2

Therefore, the first number is 2 and the second number is 5.

Answer:

42, 138, 138

Step-by-step explanation: