a car averages 35 miles per gallon of gasoline. how many liters of gasoline will be needed for a trip of 450 km? some conversion factors which may be helpful are the following:

Answer:

9

Step-by-step explanation:

if one marble is blue and 9 are other colors than its a 1/10 chance of getting a blue marble

Angular velocity of pendulum is 3.216 rad/s.

In physics, the rotational velocity ( or ), also referred to as the angular frequency vector, is a pseudovector representation of how quickly an object's angular position or orientation varies over time (i.e. how quickly an object rotates or revolves relative to a point or axis). The pseudovector's direction is normal to the instantaneous plane of rotation or angular displacement, and its magnitude equals the rate at which the object is rotating or revolving. Traditionally, the right-hand rule is used to specify the direction of angular motion.

Orbital and spin angular velocities are the two forms of angular velocities.

For a small angle angular velocity of the pendulum is calculated as:

ω[tex]= \sqrt{\frac{g}{l} }[/tex]

Here, g= gravity acceleration and l = pendulum's length.

Conversation of unit of length are,

l=94.7 cm = 94.7 cm * ([tex]\frac{10^{-2}m}{1cm}[/tex]) = 0.947 m

Substitute l = 0.947 m and g = 9.80 [tex]m/s^2[/tex] in the expression ω[tex]= \sqrt{\frac{g}{l} }[/tex]

ω[tex]= \sqrt{\frac{9.80m/s^2}{0.947m} } = 3.216[/tex]

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Answer:

Step-by-step explanation:

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.

Answer: 24

Step-by-step explanation:

t=seconds. h=height

t=3

h=3+55t-16t^2

h=3+55(3)-16(3)^2

h=3+165-16*9

h=168-144

h=24 ft

The ball's height 3 seconds after it was kicked is 24 feet above the ground.

Given that a formula h = 3 + 55t-16t² describes a ball's height above the ground h, which has been kicked vertically upward from a height of 3 feet with an initial speed of 55 feet per second.

We need to find the height of the ball after 3 seconds.

To find the ball's height 3 seconds after it was kicked, we can use the formula provided:

h = 3 + 55t - 16t²

where h represents the height in feet and t represents the time in seconds.

To find the height after 3 seconds (t = 3), plug the value into the formula and calculate:

h = 3 + 55(3) - 16(3)²

Now, perform the calculations step by step:

h = 3 + 55(3) - 16(9)

h = 3 + 165 - 144

h = 24 feet

Hence the required height is 24 feet.

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The probability that four or fewer of the people who called will sign up for a class = 0.9805

For given question,

Eric estimates that one out of every five people who call for information about a class will sign up for the class.

Last week he receive nine calls.

We need to find the probability that four or fewer of the people who called will sign up for a class.

Total number of calls = 9

⇒ n = 9

Since one out of every five people who call for information about a class will sign up for the class.

the probability of success (p) = 1/5

                                                  = 0.2

and the probability of failure (q) = 1 - p

                                                      = 1 - 0.2

                                                      = 0.8

To find the probability that four or fewer of the people who called will sign up for a class.

So, x would take values 0, 1, 2, 3, 4

Using Binomial principal,

For x = 0,

[tex]P(x=0)= ~^9C_0(0.2)^0(0.8)^{9-0}\\\\P(x=0)=0.13422[/tex]

For x = 1,

[tex]P(x=1)= ~^9C_1(0.2)^1(0.8)^{9-1}\\\\P(x=1)=0.30199[/tex]

For x = 2,

[tex]P(x=2)= ~^9C_2(0.2)^2(0.8)^{9-2}\\\\P(x=2)=0.30199[/tex]

For x = 3,

[tex]P(x=3)= ~^9C_3(0.2)^3(0.8)^{9-3}\\\\P(x=3)=0.17616[/tex]

For x = 4,

[tex]P(x=4)= ~^9C_4(0.2)^4(0.8)^{9-4}\\\\P(x=4)=0.06606[/tex]

So, the required probability would be,

P = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

P = 0.1342 + 0.3020 + 0.3020 + 0.1762 + 0.0661

P = 0.9805

Therefore, the probability that four or fewer of the people who called will sign up for a class = 0.9805

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Answer:

4u+4-1=4u-6

4u+3=4u-6

4u+9=4u

9 I think

Step-by-step explanation:

A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

[tex]Z=\frac{x\;-\;u}{\delta}[/tex]

Where:

Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.

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Complete Question:

Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?

a.) it falls in the general region of the population

distribution

b.) it falls in the common region of the distribution

c.) it is likely to come from the healthy distribution

d.) it is unlikely to come from the healthy distribution

Answer:

a = -30

Step-by-step explanation:

In order to solve for a in the equation [tex]\sf 11 = \dfrac{-3}{10} a + 2[/tex], we can follow these steps:

Subtract 2 from both sides of the equation:

[tex]\sf 11 -2= \dfrac{-3}{10} a + 2-2[/tex]

[tex]\sf 9 = \dfrac{-3}{10} a[/tex]

Multiply both sides of the equation by [tex]\sf -\dfrac{10}{3}[/tex]:

[tex]\sf 9 *-\dfrac{10}{3}= \dfrac{-3}{10} a*-\dfrac{10}{3}[/tex]

-30 = a

Therefore, the solution to the equation 11 a + 2[tex]\sf \dfrac{-3}{10} a + 2[/tex] is a = -30.

The equations that are equivalent are B×10p = 2 and D×p = 20.

Given, For $5.00, Jamie purchased a notebook and a box of pencils.

10 pencils are contained in a box, and the notepad costs $3.00.

The price of one pencil can be calculated using the equation 3+10p=5.

According to the question:

3 ₊ 10p = 5

10p = 5 ₋ 3

10p = 2

p = 2/10

p = 0.2

equations can be :

B × 10p = 2 and D × p = 0.20

Hence we get the equations as: B × 10p = 2 and D × p = 0.20

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Answer:

0 = 0

Step-by-step explanation:

Combine like terms: combine x and -2.

rearrange the terms on left side.

subtract 3 from both sides.

simplify (subtract -x and x)

0=0

The statement which must also be true is that: since line a is perpendicular to line P, any plane containing line a is perpendicular to line P.

A line can be defined as a mark with length and direction, that is created by a point that is moving across a surface. Also, a line can vary in length, width, direction, curvature, and color.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences.

From the given conditional statement, we can reasonably and logically deduce that if line a is perpendicular to line P, any plane that contains line a is perpendicular to line P.

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1) The converse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you do not like sea food, then you will go to an Italian restaurant"

2) The inverse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you go to an Italian restaurant, then you don't like sea food"

3) The contrapositive of "If you do no go to an Italian restaurant, then you like sea food" is; If you do not like sea food, then you will go to an Italian Restaurant"

1) The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." Thus, the converse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you do not like sea food, then you will go to an Italian restaurant"

2) The inverse of a conditional statement is when both the hypothesis and conclusion are negated. Thus, the inverse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you go to an Italian restaurant, then you don't like sea food"

3) The contrapositive of a conditional statement is to interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain.". Thus, the contrapositive of "If you do no go to an Italian restaurant, then you like sea food" is; If you do not like sea food, then you will go to an Italian Restaurant"

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Answer:

Equation: 2.50 + 3h = 13.00

Solution: h = 3.50

Step-by-step explanation:

Letting h be the cost of one hamburger:

[tex]2.50 + 3h = 13.00[/tex]

[tex]3h = 10.50[/tex]

[tex]h = 3.50[/tex]

So the cost of one hamburger is $3.50.

answer:

it has a solution

Answer:

1814.85 N

Step-by-step explanation:

Weight = mass * acceleration of gravity

Jayden's weight = 185 * 9.81 = 1814.85 N

Answer:

b. 4

Step-by-step explanation:

A negative number divided by a negative number is a positive number.

Therefore, -12 ÷ -3 = 4.

Answer:

[tex] \sf \large \: V = -1.5[/tex]

Step-by-step explanation:

Let's solve the equation step by step,

v=u+ at

V = 2 + -7(0.5)

V = 2 + -3.5

V = -1.5

The computation shows that the game is not fair

It should be noted that the cube had numbers 1 to 6. Therefore, the difference of 4 can be either 6-2 or 5-1 .

On the other hand, the difference of 5 will only be 6-1.

Therefore, this is not fair

In conclusion, the game is not fair.

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an invertible sheaf l on x is globally generated if and only if for any point p ∈ x, there is a global section of l not vanishing at p

This fact leads to the first assumption naturally, but neither it nor the other implication can be proven.

Vanishing means to leave or cease existing, especially in an abrupt or unexpected manner.

I be a quasicompact sheaf that can be inverted. X

demonstrate the existence of an epimorphism O ⊕I/X →I

OX⊕I→I if and only if for any point p∈X

p∈X there exists a global section of I

L not vanishing at p

If there is an epimorphism, it is asserted on page 121 of Hartshorne's book O ⊕I/X→I

OX⊕I→I Afterward, a family of global parts exists

{si} i∈I

{si}i∈I of I

I such that Ip is generated by {si,}i∈I

{si,p}i∈I as O

X,p

OX,p-module for every p∈X

This fact leads to the first assumption naturally, but neither it nor the other implication can be proven.

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Based on the number of students invited to the office and the number of Volleyball students who left, the number of students who were both prefects and volleyball players are 3 students.

Those who are only prefects are 4 students.

To find the number of students who were both prefects and volleyball players, the formula is

= Number of volleyball players who left + Total number of volleyball players - Number of students called to office

= 7 + 10 - 14

= 3 students

Number of students who were just prefects:
= Number of students called - Number of students who left - Number of students who are prefects and volleyball players

= 14 - 7 - 3

= 4 students

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Answer:

187.5

Step-by-step explanation:

[tex]\sf {If \; y \; varies \; inversely \; as \; x^3\; represented \; by\; y\propto \dfrac{1}{x^3}} \\then\\y = \dfrac{k}{x^3}\; where\; k \;is\; a \;constant\\\\== > k = y\cdot x^3\\\\When y = 12, x = 5 \;means\\\\k = 12.\cdot 5^3 = 12 \cdot 125 = 1500\\\\\sfTherefore \;when\; x = 2\\y = \dfrac{1500}{2^3} = \dfrac{1500}{8} = 187.5\\\\\sf Answer:\;\; \boxed {\sf y = 187.5\; \sf when\; x = 2}[/tex]

Answer:

82 + -71 = 10

Hope this helps! <3

According to the question, the given data for the scalar projection calculation represent the point [tex]P1(x1,y1)[/tex] to the line [tex]ax1+by1+c=0.[/tex]

What is scalar projection?

Scalar projection refers to scalar coordinates in the cartesian coordinates. It is also the length of the vector projection. It is calculated with the help of the dot product with the unit vector direction. It always tells about the magnitude of the projection.

By using scalar projection, calculate the distance from the point [tex]P1[/tex] to the line.

Here,[tex](a, b)[/tex] is perpendicular and the equation can be written as

           [tex]by1 = -ax1-c[/tex]    

          [tex]y1 = -\frac{a}{b}x1-c[/tex]

For this the slope of the given equation can be written as: [tex]-\frac{a}{b}[/tex]

And the distance is : [tex]d = \frac{|ax1+by1+c|}{\sqrt{a2+b2} }[/tex].

Therefore, the calculated distance for the given equation is:[tex]d = \frac{|ax1+by1+c|}{\sqrt{a2+b2} }[/tex]

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The correct answer is other measures of location need not be the same.

What is mean, mode, median and standard deviation?

When the group of numbers have the same mean then the other measures of location need not be the same. That means the standard deviation, median and mode should not be equal. All three widely used parameters that are mean, mode, median and standard deviation are the measure of central tendency.

If the given data has no outlier then mean value and the median value are closer to each other but the mode value is different. Similarly, standard deviation is calculated for the dispersion data. And it means when mean value is same then standard deviation will be different for a group of numbers.

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