44. The length of a road is 380 m, correct to the nearest 10 m. Maria runs along this road at an average
speed of 3.9 m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria​

The time taken to travel the distance 70 Km/h is 11 hours.

Speed tells us how fast something or someone is travelling. You can find the average speed of an object if you know the distance travelled and the time it took.

The formula can be rearranged in three ways:

Given:

time = 9 hours

speed = 85 Km/h

Now, distance

=speed * time

=85 * 9

= 765 km

As, the speed is 70 km/h

time = distance/ speed

time = 765 / 70

time = 10.92

time= 11 hours

Hence, the time taken to travel the distance 70 Km/h is 11 hours.

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The translation of the question is:

A car takes 9 hours to travel a distance with a speed of 85km/h, how long will it take to travel the same distance at 70km/h?

The maximum volume of an open cylinder with surface area equal to 16π and a radius between 1 and 8 feet is 16π cubic feet, and it is achieved when the radius is equal to 2 feet and the height is equal to 4 feet.

The surface area of an open cylinder is given by the formula 2πrh + 2πr^2, where r is the radius and h is the height. We are given that the surface area is equal to 16π, so we have the equation:

2πrh + 2πr^2 = 16π

Simplifying this equation, we get:

r(h + r) = 8

We want to maximize the volume of the cylinder, which is given by the formula V = πr^2h. Using the equation we derived above, we can express the height in terms of the radius:

h = (8 - r^2)/r

Substituting this expression for h into the formula for the volume, we get:

V = πr^2((8 - r^2)/r)

Simplifying this expression, we get:

V = 8πr - πr^3

To find the maximum volume, we need to find the value of r that maximizes this expression. To do this, we take the derivative of the expression with respect to r:

dV/dr = 8π - 3πr^2

Setting this equal to zero, we get:

8π - 3πr^2 = 0

Solving for r, we get:

r = 2

We can verify at this is a maximum by taking the second derivative of the expression with respect to r:

d^2V/dr^2 = -6πr

At r = 2, this is negative, indicating that we have a maximum.

Therefore, the maximum volume is achieved when the radius is equal to 2 feet. Substituting this into the equation we derived for h, we get:

h = (8 - 2^2)/2 = 4

So the maximum volume is:

V = π(2)^2(4) = 16π cubic feet.

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Answer:

√441=21

√361=19

√401=20.02 or 20

The correct pair of constraints that needs to be added to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units is: P24 - P25 <= 80; P25-P24 <= 80. Therefore, the correct option is 5.

Here, the given information is Pij = the production of product i in period j. We need to find the pair of constraints that will specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Thus, let the production of product 2 in period 4 and in period 5 be represented as P24 and P25 respectively.

Therefore, we can write the following inequalities:

P24 - P25 <= 80

This is because the production of product 2 in period 5 can be at most 80 units less than that of period 4. This inequality represents the difference being less than or equal to 80 units.

P25-P24 <= 80

This is because the production of product 2 in period 5 can be at most 80 units more than that of period 4. This inequality represents the difference being less than or equal to 80 units.

Therefore, we need to add the pair of constraints P24 - P25 <= 80 and P25-P24 <= 80 to specify that production of product 2 in period 4 and in period 5 differs by no more than 80 units. Hence, option 5 is the correct answer.

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Answer:

True.

Step-by-step explanation:

(LHS) cos 6∘ cos 42∘ cos 66∘ cos 78∘

1/4 [cos(66∘+6∘) = cos(66∘-6∘)] • [cos(78∘+42∘)+cos(78∘-42∘)]

= 1/4(sin18∘+12)(-12+cos36∘)

[∵cos72∘ = cos(90∘−18∘) = sin18∘]

1/4[(5-√-1)/4+1/2][−1/2+(5-√+1)/4]

[∵sin(18∘ = (5-√-1)/4, and, cos 36∘ = (5-√+1)/4]

1/4(5-√+1)/4(5-√-1)/4 = (5-1)/64

= 4/64 = 1/16 (RHS)

Therefore, the cosine is equal to 1/16.

There is no solution to the system. This means that the equation 2 = -2 in the system is inconsistent.

What is a system of equations?

A system of equations is a collection of two or more equations that are solved simultaneously. Each equation in the system represents a constraint or condition that must be satisfied, and a solution to the system is a set of values that satisfies all of the equations in the system simultaneously.

If you attempt to solve a system of equations and you get a statement like 2 = -2, it means that the equations in the system are inconsistent. An inconsistent system of equations has no solution because there is no set of values that can simultaneously satisfy all of the equations.

Hence, as these equations are contradictory, there is no solution to the system. This means that the equations in the system are inconsistent.

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Answer:

x = 4²

Step-by-step explanation:

Using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

Given

\(log_{4}\) x = 2 , then

x = 4²

Answer:

\(-\frac{6x^4y^3}{z^7}\)

Step-by-step explanation:

\(=-6x^4y^3\frac{1}{z^7}\) <- Apply the exponent rule.
\(=-\frac{6x^4y^3\cdot \:1}{z^7}\) <- Apply the fraction rule.

\(=-\frac{6x^4y^3}{z^7}\)

The sample space for rolling a six-sided number cube is \({1, 2, 3, 4, 5, 6}\)}, representing the six possible outcomes of the experiment.

The sample space for the experiment of rolling a six-sided number cube consists of all the possible outcomes or numbers that can be obtained when the cube is rolled. Since a standard six-sided cube has six faces, each numbered from 1 to 6, the sample space can be represented as     \({1, 2, 3, 4, 5, 6}\)}.

In this case, the sample space is a set containing the individual numbers 1, 2, 3, 4, 5, and 6, which represent the possible outcomes of rolling the cube. Each number in the sample space corresponds to a face of the cube, and when the cube is rolled, one of these numbers will be the result.

It's important to note that each outcome in the sample space is equally likely, assuming the cube is fair and unbiased. Therefore, the probability of obtaining any particular outcome is 1 out of 6 or approximately 0.1667.

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According to the figure the value of B is

The value of B is solved using the principles of segments of chords secants and tangents

The principle is such that

10^2 = 5 * (5 + b)

100 = 25 + 5b

gathering like terms

5b = 100 - 25

5b = 75

isolating b

b = 75 / 5

b = 15

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The product of the given function is \(12y^2(2\sqrt{5y} )\\\)

Given the following radical function expressed as:

This can be further simplified as:

\(=3\sqrt{10}(y^2\sqrt{4}\sqrt{8y} ) \\=3\sqrt{10}(2y^2\cdot 2\sqrt{2}y \\= 3\sqrt{10}(4y^2 \sqrt{2y} ) \\\\\)

Multiply the radical functions to have:

\(=12y^2{\sqrt{20y} \\=12y^2(2\sqrt{5y} )\\\)

Hence the product of the given function is \(12y^2(2\sqrt{5y} )\\\)

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Answer:

25 e books

Step-by-step explanation:

because you multiply the money by 5 which gets you 40. Then you multiply the number of e books by 5 and you get 25.

Answer:

might be -3 might be wrong if so im sry

Answer:

It's just 3 no negative sign

Step-by-step explanation:

To determine how many of the 3103 subjects used at least one prescription medication, we need to examine the data collected on medication usage. The term "prescription medication" refers to medications that are only available with a prescription from a healthcare provider.

This excludes over-the-counter medications that do not require a prescription. The data collected on medication usage should indicate whether each subject used any prescription medication. We can then count the number of subjects who used at least one prescription medication. This information is important in understanding the overall health of the study population and the prevalence of medication usage.

The answer to this question can inform healthcare providers and researchers in developing strategies for medication management and improving patient outcomes.

To determine how many of the 3103 subjects used at least one prescription medication, we must analyze the given data. Start by identifying the number of subjects who have been prescribed medication. This could be presented as a percentage or a raw number in the data.

Once you have found the relevant information, perform the necessary calculations. If the data is in percentage, multiply the total number of subjects (3103) by the percentage (as a decimal). If it's a raw number, no calculations are needed.

Finally, round the result to the nearest integer to determine the number of subjects who used at least one prescription medication.

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Answer:

-13

Step-by-step explanation:

y=mx+b

b=y-mx

Slope NEEDED is -13.

y=-13

The property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition

From the question, we have the following parameters that can be used in our computation:

(2 + 1) + (6 + 5) = (6 +5) +(2 + 1)

In the above expression, we can see that

The terms of the expression are swapped

This can be illustrated as

if a + b = b + a

The name of the property is the commutative property of addition

Hence, the name of the property illustrated in (2 + 1) + (6 + 5) = (6 +5) +(2 + 1) is the commutative property of addition

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The polynomial expression that represents AB + C in simplest form is: x³ + 3x² + 3x  - 1.

Polynomials are algebraic expressions having variables and constants, and may include exponents.

AB + C would be expressed as:

(x + 1)(x² + 2x - 1) + 2x

Expand

x(x² + 2x - 1) +1(x² + 2x - 1) + 2x

x³ + 2x² - x + x² + 2x - 1 + 2x

x³ + 3x² + 3x  - 1 (simplest form)

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The speed of the object at t = 7.4 s is approximately 59.45 m/s.

To find the speed of the object at time t = 7.4 s, we need to calculate the magnitude of its velocity vector at that time.

The velocity vector is the derivative of the position vector with respect to time:

v(t) = dr(t)/dt

Given the position vector r(t) = \((α + βt)i^ + (γ + σt^2)j^,\) we can differentiate it with respect to time to find the velocity vector v(t):

\(v(t) = (d(α + βt)/dt)i^ + (d(γ + σt^2)/dt)j^\)

\(v(t) = βi^ + (2σt)j^\)

Substituting the given values:

β = 3.3 m/s

σ = -3.97 m/s^2

t = 7.4 s

v(t) = (\(3.3 m/s)i^ + (2*(-3.97 m/s^2)*(7.4 s))j^\)

v(t) = \(3.3 m/s i^ - 58.712 m/s j^\)

To find the speed, we need to calculate the magnitude of the velocity vector:

v\(= sqrt((3.3 m/s)^2 + (-58.712 m/s)^2)\)

Calculating this value:

v ≈ 59.45 m/s

Therefore, the speed of the object at t = 7.4 s is approximately 59.45 m/s.

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- The function g(x) = x^2 + 8ln[x+1] is concave up for all values of x.
- The inflection point of the function is x = 0.

To determine the intervals where the function is concave up or concave down, as well as any inflection points for the function g(x) = x^2 + 8ln[x+1], we need to find the second derivative and analyze its sign changes.

Step 1: Find the first derivative of g(x):
g'(x) = 2x + 8/(x+1)

Step 2: Find the second derivative of g(x):
g''(x) = 2 - 8/(x+1)^2

Step 3: Determine where g''(x) = 0 to find the potential inflection points:
2 - 8/(x+1)^2 = 0

Solving this equation, we have:
2(x+1)^2 - 8 = 0
(x+1)^2 = 4
Taking the square root of both sides, we get:
x+1 = ±2
x = -3 or x = 1

Step 4: Analyze the sign changes of g''(x) to determine the intervals of concavity:
We can create a sign chart for g''(x):

Interval | x+1   | (x+1)^2 | g''(x)
---------|-------|---------|-------
x < -3   | (-)   | (+)     | (+)
-3 < x < 1| (-)   | (+)     | (+)
x > 1    | (+)   | (+)     | (+)

From the sign chart, we can see that g''(x) is always positive, indicating that the function g(x) = x^2 + 8ln[x+1] is concave up for all values of x. Therefore, there are no intervals where the function is concave down.

Step 5: Determine the inflection points:
We found earlier that the potential inflection points are x = -3 and x = 1. To determine if they are indeed inflection points, we can look at the behavior of the function around these points.

For x < -3, we can choose x = -4 as a test value:
g''(-4) = 2 - 8/(-4+1)^2 = 2 - 8/(-3)^2 = 2 - 8/9 = 2 - 8/9 = 10/9 > 0

For -3 < x < 1, we can choose x = 0 as a test value:
g''(0) = 2 - 8/(0+1)^2 = 2 - 8/1 = 2 - 8 = -6 < 0

For x > 1, we can choose x = 2 as a test value:
g''(2) = 2 - 8/(2+1)^2 = 2 - 8/9 = 10/9 > 0

Since the sign of g''(x) changes from positive to negative at x = 0, we can conclude that x = 0 is the inflection point of the function g(x) = x^2 + 8ln[x+1].

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Answer: 9 is what I am thinking.

Explanation: So, first you have to know that 2/3 + 1/3 = 3/3 = 1 cup. The answer is 1 and 1/2 cups will make 1 cup when using a 2/3 cup. So, then 1 + 1 + 1 6 times equals 6, then 1/2 + 1/2 6 times equals 3 and 6+3 = 9. There's your answer.

The company should use a warranty period that is equal to 67,467.5 miles.

To determine the warranty period, we need to find the value of the tire life that corresponds to 95% of the tires. We can use the standard normal distribution table to find the value of the z-score that corresponds to the 95th percentile. This value is approximately 1.645.

Now, we can use the formula for the normal distribution to find the tire life value that corresponds to the z-score of 1.645. This formula is:

X = μ + zσ

Where X is the tire life value, μ is the mean of the distribution (65,000 miles), z is the z-score (1.645), and σ is the standard deviation of the distribution (1500 miles).

Plugging in the values, we get:

X = 65,000 + 1.645(1500)

X = 67,467.5

This means that 95% of the tires will have a life of at least 67,467.5 miles.

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Answer:

Step-by-step explanation:

3 hrs covert to mins =180minutes

180/7=25/26 mins thts for one task

B=Completes 2 tasks in an hour

Answer:

So.

The way I see it you want to host a concert and need 200 feet to do so.

To find the are of a rectangle you just multiply

15.6x12.2

it equals around 190 point smth

that is less than 200 so you CAN NOT host the concert

Stay smart :)

-Lynx

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Based on the calculations, the coordinates of the y-intercept are (0, -9).

In Mathematics, the y-intercept of any graph (parabola) occurs at the point where the value of "x" is equal to zero (0). Similarly, the x-intercept refers to the point at which the graph of a function crosses the x-axis and the value of "y" is equal to zero (0).

Mathematically, the slope of any straight line can be calculated by using this formula;

\(Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\)

Substituting the given parameters into the formula, we have;

Slope, m = (-4.5 - 3)/(-3 + 8)

Slope, m = -7.5/5

Slope, m = -1.5.

Mathematically, the standard form of the equation of a straight line is given by;

y - y₁ = m(x - x₁)

At point (-8, 3), we have:

y - 3 = -1.5(x + 8)

y - 3 = -1.5x - 12

y = -1.5x - 12 + 3

y = -1.5x - 9

Therefore, the coordinates of the y-intercept are (0, -9).

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Answer: Quotient: 467 Remainder: 3

Step-by-step explanation:

1871 divided by 4 = 467.75

467 times 4 = 1868

1871 - 1868 = 3

So, therefore the quotient is 467 and the remainder is 3.

Answer:

1

2,3,4

Step-by-step explanation: to

when the number of football is 1 is less expensive than basketball

Answer:

5x-188-2x^x

Step-by-step explanation:

Answer:

Step-by-step explanation:The formula that shows the dependence of the surface area (S) of a cube on the length (a) of one side is:

S = 6a^2

In this formula, "S" represents the surface area and "a" represents the length of one side of the cube. The surface area of a cube is calculated by multiplying the area of one face (which is a^2) by the total number of faces (which is 6 for a cube).

By squaring the length of one side and multiplying it by 6, we obtain the total surface area of the cube.

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