Suppose that an object is moving along a vertical line. Its vertical position is given by the equation L(t)=4t^2−t+9, where distance is measured in meters and time in seconds. Find the approximate value of the average velocity (accurate up to three or more decimal places) in the given time intervals.
between t1=1 s and t2=4 s :
Vavg = ________ m/s

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

26 units

Step-by-step explanation:

By using the Pythagoras Theorem,

C^2 = A^2 + B^2

Substitute in given values for A and B.

C^2 = 10^2 + 24^2

= 100 + 576

= 676

\(c = \sqrt{676} \\ = 26\)

Hope this helped! ^^

Sidenote: Pythagoras Theorem can only be used on right-angled triangles.

Answer:

18

Step-by-step explanation:

18 ÷ 3 = 6

6 ⋅ 2 = 12

Therefore, 12 is 2/3 of 18.

The simple interest rate on the account is 7.5%.

The simple interest rate can be calculated by dividing the interest earned by the principal balance and the time period. In this case, the interest earned is $56.25, the principal balance is $300, and the time period is two and one-half years.

To find the interest rate, we use the formula:

Simple Interest = Principal × Rate × Time

Substituting the given values:

$56.25 = $300 × Rate × 2.5

To solve for the interest rate, divide both sides of the equation by $750:

Rate = $56.25 / ($300 × 2.5)

Simplifying the calculation:

Rate = $56.25 / $750

Rate = 0.075

Therefore, the simple interest rate on the account is 7.5%.

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Answer:

I would say b

Step-by-step explanation:

Answer:

x = 42

Step-by-step explanation:

Answer:

Octagon

Step-by-step explanation:

A polygon refers to a two-dimensional closed shape consists of straight sides.

Perimeter of a polygon = 24 inches

Length of each side of the polygon = 3 inches

Number of sides of a polygon = Perimeter of a polygon ÷ Length of each side of the polygon = \(\frac{24}{3} =8\)

An octagon is a polygon consisting of 8 sides of same dimension.

So,

Name of polygon is octagon.

The decimals are ordered from smallest to largest as follows: 1.04, 1 ¼, 1 2/5, 1 ½, 1.75, 1.9. The decimals are compared by converting any mixed numbers or fractions into decimal form for easier comparison. After converting, we can compare the decimals numerically and arrange them in ascending order. The correct order is B.

To order the decimals from smallest to largest, we need to compare their numerical values. Let's analyze each decimal and convert any mixed numbers or fractions into decimal form for easier comparison.

1.9 is already in decimal form.

1 1/4 can be converted to a decimal by dividing 1 by 4, which gives us 0.25.

1.04 is already in decimal form.

1 2/5 can be converted to a decimal by dividing 2 by 5, which gives us 0.4.

1 ½ can be converted to a decimal by dividing 1 by 2, which gives us 0.5.

1.75 is already in decimal form.

Now that all the decimals are in decimal form, we can compare them.

From smallest to largest, the order is:

1.04, 1 ¼ (0.25), 1 2/5 (0.4), 1 ½ (0.5), 1.75, 1.9.

So, the correct order is B. 1.04, 1 ¼, 1 2/5, 1 ½, 1.75, 1.9.

In this order, we can see that 1.04 is the smallest decimal, followed by 1 ¼, 1 2/5, 1 ½, 1.75, and finally 1.9, which is the largest decimal.

It is important to note that converting the mixed numbers or fractions to decimal form allowed us to compare all the decimals on the same scale, making it easier to determine their order from smallest to largest.

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With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of option (C) the variability around the regression line

The standard error of the estimate in a regression-based forecast is a measure of the variability of the actual data points around the predicted values of the regression line.

It tells us how much the actual data points are likely to deviate from the predicted values, and provides a measure of the accuracy of the forecast. It is not related to the time required to derive the forecast equation, the maximum error of the forecast, or the time period for which the forecast is valid.

Therefore, the correct option is (C) The variability around the regression line.

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The give question is incomplete, the complete question is:

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of:

A. the time required to derive the forecast equation.

B. the maximum error of the forecast.

C. the variability around the regression line.

D. the time period for which the forecast is valid.

The probability that Zack randomly selects 4 chocolate pastries out of 8 pastries from a population of 20 pastries, of which 12 are chocolate, is approximately 0.206 or 20.6%.

The hypergeometric distribution can be used to calculate the probability of selecting a certain number of objects with a specific characteristic from a population of objects with and without the characteristic, without replacement.

The probability of Zack selecting 4 chocolate pastries out of 8 randomly chosen pastries from a population of 20 pastries, of which 12 are chocolate.

The probability mass function of the hypergeometric distribution is:

\(P(X = k) = (C(N_1,k) \times C(N_2,n - k)) / C(N,n)\)

where:

X is the random variable representing the number of pastries that are chocolate in the sample of 8

k is the number of chocolate pastries in the sample of 8 (in this case, k = 4)

N₁ is the number of chocolate pastries in the population (in this case, N₁ = 12)

N₂ is the number of non-chocolate pastries in the population (in this case, N₂ = 20 - 12 = 8)

n is the sample size (in this case, n = 8)

N is the total number of pastries in the population (in this case, N = 20)

Plugging in the values, we get:

\(P(X = 4) = (C(12,4) \times C(8,8 - 4)) / C(20,8)\)

\(P(X = 4) = (495 \times 70) / 167,960\)

P(X = 4) ≈ 0.206

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The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

k

Step-by-step explanation:

Step-by-step explanation:

dhsiiabkljefklpajv sl

Answer:

Step-by-step explanation:

Can you explain more please?

The rectangular coordinate form of a complex number is represented by the formula z=a+bi. The real axis is the horizontal one, and the imaginary axis is the vertical one. In terms of r and, where r is the vector's length and is the angle it makes with the real axis, we determine the real and complex components.

Rectangular form;-

Rectangular form, on the other hand, is where a complex number is denoted by its respective horizontal and vertical components. In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides.

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The area swept clean by the wiper blade is 221.128 square inches.

To find the area swept clean by the wiper blade, we can calculate the area of the sector of a circle that the blade moves through.

The radius of the circle that the blade moves through is the length of the arm, which is 19 inches.

The angle that the blade moves through is 105 degrees.

To calculate the area of the sector, we need to convert the angle to radians:

105 degrees * (π/180) = 1.8326 radians (rounded to 4 decimal places)

The area of the sector is then:

(1/2) * r^2 * θ = (1/2) * (19^2) * 1.8326 = 325.628 square inches (rounded to 3 decimal places)

However, the area swept clean by the wiper blade is not the full area of the sector, as the blade itself has a width of 11 inches. Therefore, we need to subtract the area of the triangle formed by the blade and the two radii of the sector that intersect at the blade's pivot point.

The length of one of the radii is the length of the arm, which is 19 inches. The length of the other radius is 19 - 8 = 11 inches since the blade is mounted 8 inches from the pivot point.

Using the formula for the area of a triangle:

(1/2) * base * height = (1/2) * 11 * 19 = 104.5 square inches

Therefore, the area swept clean by the wiper blade is:

325.628 - 104.5 = 221.128 square inches (rounded to 3 decimal places)

So the area swept clean by the wiper blade is approximately 221.128 square inches.

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Answer:

3.5%

Step-by-step explanation:

The value of the car decreased by 3.5%. Hope it helps!

Answer:

The rock will take approximately 3.992 seconds to reach the canyon floor.

Step-by-step explanation:

For all \(a\cdot t^{2}+b\cdot t + c = 0\), its roots are determined by the Quadratic Formula:

\(t = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}\)

In this case, it corresponds to instants when rock is either launched or hits the floor. If we know that \(a = -16\), \(b = 0\) and \(c = 255\), the time it takes the rock to reach the canyon floor is:

\(t = \frac{-0\pm\sqrt{(0)^{2}-4\cdot (-16)\cdot (255)}}{2\cdot (-16)}\)

\(t \approx 3.992\,s\)

The rock will take approximately 3.992 seconds to reach the canyon floor.

x = 5/4   or   x = 15/4

Step-by-step explanation:

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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The centerline for the filling weights is 14 ounces, the upper control limit (UCL) is 17.264 ounces, and the lower control limit (LCL) is 10.736 ounces when samples of 10 boxes are taken.

In a statistical process control (SPC) chart, the centerline represents the target or average value of the process. In this case, the average filling weight of the cereal boxes is 14 ounces.

The upper control limit (UCL) and lower control limit (LCL) are calculated to determine the acceptable variation around the centerline. The UCL is set at three standard deviations above the centerline, while the LCL is set at three standard deviations below the centerline. Since the standard deviation of the filling weights is 2 ounces, the UCL can be calculated as follows

UCL = Centerline + (3 * Standard Deviation)

   = 14 + (3 * 2)

   = 14 + 6

   = 20

Similarly, the LCL can be calculated as follows

LCL = Centerline - (3 * Standard Deviation)

   = 14 - (3 * 2)

   = 14 - 6

   = 8

However, in this case, we are asked to provide the UCL and LCL values rounded to three decimal places. To do this, we can use the formula:

UCL = Centerline + (3 * Standard Deviation / sqrt(sample size))

   = \(14 + (3 * 2 / sqrt(10))\)

   ≈ \(14 + (3 * 2 / 3.162)\)

   ≈ \(14 + (6 / 3.162)\)

   ≈ \(14 + 1.897\)

   ≈ 15.897 (rounded to 3 decimal places)

LCL = Centerline - (3 * Standard Deviation / sqrt(sample size))

   = \(14 - (3 * 2 / sqrt(10))\)

   ≈ \(14 - (3 * 2 / 3.162)\)

   ≈ \(14 - (6 / 3.162)\)

   ≈ \(14 - 1.897\)

   ≈ 12.103 (rounded to 3 decimal places)

Therefore, the centerline is 14 ounces, the UCL is approximately 15.897 ounces, and the LCL is approximately 12.103 ounces when samples of 10 boxes are taken.

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The inequality shown by this graph is  y ≥ 2.

the relationship between two non-equal expressions using a symbol like "not equal to," ≠ "greater than >," or "less than <  "

The inequality sign : ≥ or ≤ to use is: or because the line is solid and not dotted.

Given that the points have y-coordinate values of 2, (-5, 2), and (3, 2), respectively, and that the line crosses the y-axis at this point, the proper inequality is:

y ≥ 2

Therefore, y ≥  2 is the inequality.

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The average change per hour is: -4 F/h

So the temperature decreases by 4 degrees Fahrenheit each hour.

To get the average change in degrees per hour, we need to take the quotient between the change in temperature and the number of hours in which this happens.

We know that initially the temperature is 0F

The final temperature is -12F

and this happens on an interval of 3 hours, then the average change per hour is:

(-12F - 0F)/3h = -12F/3h = -4 F/h

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Answer:

6.14 is Rational only

The rate in cups per hour, at which the water is leaking from the faucet

is 5/14 cups per hour.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Josh put an empty cup underneath a leaking faucet. After \(1\frac{3}{4}\) hours Josh collected 5/8 ​cups of water.

Now, \(1\frac{3}{4} = \frac{7}{4}\).

Therefore, The rate in cups per hour, at which the water is leaking from the faucet is,

= (5/8)/(7/4) cups per hour.

= (5/8)×(4/7) cups per hour.

= 5/14 cups per hour.

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If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.

Given There are 12 coins and total money is 32 cents.

Let the number of pennies be x and the number of  nickels be y.

According to question there are 12 coins so the first equation becomes:

x+y=12.

Then we have been told that together they amount to 32 cents.

We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :

1*x+5*x=32

x+5y=32

converting into dollar

0.01x+0.05y=0.32.

Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.

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Answer:-12x

Step-by-step explanation:

just trust me on this

Answer:

394 km

Step-by-step explanation:

197 is 197/60 times as much as 60

so the distance is also that much more: 120 km * 197/60 = 394