Heather drove at a constant rate. She traveled 162 miles in 3 hours. How far did Heather travel in 1 hour?

When 5/9 of the tank is filled in 2 minutes, then it will take 3.6 minutes to fill the entire tank.

The definition of a fraction is a fraction multiplied by another fraction, integer, or a group of variables. Given that the 5/9 tank fills in 2 minutes. The duration of this period in seconds is 60×5= 120 seconds.

So the time taken to fill a 1/9 tank is calculated as follows,

Time taken = 120/5

=24 seconds

The time taken to fill the 9/9 tank (full) is calculated by multiplying 24 seconds and 9, we get,

24×9 = 216 seconds

= 3.6 minutes.

Therefore, the required answer is 3.6 minutes.

The complete question is -

If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?

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Answer:

$12

Step-by-step explanation:

to find sales tax you multiply the cost by the percentage

you do 150 * 8%

thats also 150 * 0.08

150 * 0.08 is 12

so you pay $12 in tax

Bret paid $12 as sales tax.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. In a fraction say (x/y), [y] is called denominator.

We have Bret buys a dining table that costs $150 before tax. The sales tax is 8%.

Assume that he paid $[x] as sales tax. Then, we can write -

[x] = 8% of 150

[x] = (8/100) x 150

[x] = 12

Therefore, Bret paid $12 as sales tax.

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The chances of picking two of the same candy without looking in the basket and without replacing the candy is approximately 0.132.

To calculate the probability, we need to consider the number of each candy type in the basket. There are 5 KitKats, 6 Reese's, and 10 Almond Joys, making a total of 21 candies. Without replacement means that once a candy is chosen, it is not put back into the basket.

Let's break down the probability calculation. We have three scenarios where we can pick two of the same candy: picking two KitKats, picking two Reese's, or picking two Almond Joys.

The probability of picking two KitKats can be calculated as (5/21) * (4/20) = 1/21.

Similarly, the probability of picking two Reese's is (6/21) * (5/20) = 1/14.

Lastly, the probability of picking two Almond Joys is (10/21) * (9/20) = 3/14.

To find the overall probability, we sum up the probabilities of the three scenarios: 1/21 + 1/14 + 3/14 = 11/84 ≈ 0.131.

Rounding to the nearest thousandths, the probability is approximately 0.132.

Therefore, the chances of picking two of the same candy without looking in the basket and without replacing the candy is approximately 0.132 or 13.2%.

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

Answer:

Hope it helps!~ (Sorry if you get it wrong or I got it wrong-)

Step-by-step explanation:

the state of being oriented. an introduction, as to guide one in adjusting to new surroundings, employment, activity, or the like: New employees receive two days of orientation. Psychology, Psychiatry. the ability to locate oneself in one's environment with reference to time, place, and people. This or ,

the determination of the relative position of something or someone (especially oneself).

"the child's surroundings provide clues to help in orientation"

the relative physical position or direction of something.

plural noun: orientations

"two complex shapes, presented in different orientations"

This-

~The Confuzzeled homan

There are 439 integers between 1 and 1000 that are divisible by at least one of 5, 6, or 7.

To solve this problem, we need to use the principle of inclusion-exclusion. We first find the number of integers divisible by 5, 6, or 7 individually, and then subtract the number of integers divisible by the pairwise combinations of these numbers, and finally add back the number of integers divisible by all three of them.

The number of integers divisible by 5 between 1 and 1000 is 200 (5, 10, 15, ..., 995, 1000). The number of integers divisible by 6 between 1 and 1000 is 166 (6, 12, 18, ..., 996). The number of integers divisible by 7 between 1 and 1000 is 143 (7, 14, 21, ..., 994).

To find the number of integers divisible by the pairwise combinations, we need to find the least common multiple (LCM) of each pair. The LCM of 5 and 6 is 30, and there are 33 integers between 1 and 1000 that are divisible by 30. The LCM of 5 and 7 is 35, and there are 28 integers between 1 and 1000 that are divisible by 35. The LCM of 6 and 7 is 42, and there are 23 integers between 1 and 1000 that are divisible by 42.

To find the number of integers divisible by all three, we need to find the LCM of 5, 6, and 7, which is 210. There are 14 integers between 1 and 1000 that are divisible by 210.

Using the principle of inclusion-exclusion, the total number of integers between 1 and 1000 that are divisible by at least one of 5, 6, or 7 is:

200 + 166 + 143 - 33 - 28 - 23 + 14 = 439

Therefore, there are 439 integers between 1 and 1000 that are divisible by at least one of 5, 6, or 7.

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Cyber safety is the use of information and communication technologies in a responsible and safe manner. It involves protecting information and keeping it secure, but it also entails handling information responsibly, showing consideration for others online, and following proper internet etiquette.

The Essential Eight are a collection of eight mitigation techniques: application control, application patching, configuring Microsoft Office macro settings, user application hardening, limiting administrative rights, operating system patching, multi-factor authentication, and regular backups.

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The correlation coefficient indicative of the weakest linear relationship is option (c) -0.05. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

Correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative linear relationship, 1 indicating a perfect positive linear relationship, and 0 indicating no linear relationship. Therefore, a correlation coefficient closer to 0 indicates a weaker linear relationship. Among the given options, the correlation coefficient of -0.05 is the closest to 0, indicating the weakest linear relationship.

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Answer:

-21 ÷ b = 3, b =        b=-7

3c + 1 = 10, c =        c=1/7

Hope this helps!

Answer:

Audrey paid $5.88

Step-by-step explanation:

$4.59+$1.79=$6.38. That is her total order.

The coupon gives her 50 cents off, so $6.38-$0.50=$5.88

Audrey paid $5.88.

Answer:

answer $5.88 dollars hope this helps. :D

The constant of proportionality between x and y in the given graph above is :  1/5.

The constant of proportionality of a proportional relationship between two variables, x and y, can be defined as the ratio of y to x, which is expressed as, k = y/x, where x and y are the coordinates of one point one the line that represents the proportional relationship.

According to the coordinates of a point on the graph, (5, 1), we need to find the constant of proportionality, k:

Constant of proportionality (k) = y/x = 1/5

Constant of proportionality (k) = 1/5

Therefore, the constant of proportionality that represents the proportional relationship between the variables, x and y, could be 1/5.

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Answer:

Josh has played 12 MORE matches then her. Not 12 TIMES as many matches. The correct answer would be he haas played 12 more matches then her or 3 times as many matches as her.

Step-by-step explanation:

Answer:

E: b/3+3

Step by step:

3 C= b

C + 3 = b/3 + 3                     (Adding 3 to both sides)

Answer: E: b/3 + 3

Hope this helps

Answer:

The answer is 5.29 or the longer answer is 5.29150262

the system of equations that represents the situation is:

x + y = 50

2x + 5y = 145

A system of equations is a set of one or more equations that are to be solved simultaneously. The equations in a system share common variables, and the solution to the system is the set of values for those variables that make all the equations in the system true at the same time.

Let x be the number of multiple-choice questions, and y be the number of short answer questions.

The total number of questions is given as 50, so we can write the first equation as:

x + y = 50 ------------(1)

The total score of the exam is given as 145 points, so we can write the second equation as:

2x + 5y = 145 ------------(2)

Therefore, the system of equations that represents the situation is:

x + y = 50

2x + 5y = 145

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The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio

The relationship that is normally expressed as the quotient of one quantity divided by another is called a ratio. A ratio is a comparison of two numbers or measurements, and it can be written in different ways.

For example, if we have two quantities A and B, the ratio of A to B can be written as

A/B

A:B

"A is to B"

The ratio of A to B tells us how many times A is contained within B, or how many units of A we would need to have to match the amount of B.

Ratios are useful in many fields, such as finance, engineering, and science, where they are used to compare and analyze different quantities and their relationships.

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Answer:

B

Step-by-step explanation:

you're gonna have to use the rules of trigonometry.

so you have all the angles(the other angle on the top is 45 degrees as well) and one of the sides.

let's use the far left angle, 45 degrees, as our main angle. we know the adjacent side, 7√2 / 2, but we want to find the hypotenuse and the opposite side. we can actually find the opposite side very easily. you see, in a right triangle, where the non-right angles are both the same degree, you will know that the sides adjacent to the right angle are equal. so, we can cross our options of A, C, and D off. we know now that the answer is B.

Answer:

Step-by-step explanation:

Since the sides of the rectangle are the same length and perimeter is the measure of all lengths, then you’ll do 3+3+2+2, which is 10 (I think lol).

Answer:

B- The sales price = the original price - 25% of the originial price

Step-by-step explanation:

Answer:

8 wristbands

Step-by-step explanation:

Let us assume that both of the company were ordered to deliver w wristbands.

The amount of money charged by company 1 who sells at $2 and offers free shipping is given as:

2w

The amount of money charged by company 2 who sells at $1.25 and $6 for shipping per order given as:

1.25w + 6

If both companies charge the same amount, hence:

2w = 1.25w + 6

2w - 1.25w = 6

0.75w = 6

w = 6/0.75

w = 8

The two companies charge the same amount for 8 wristbands

The fact that voting might not be compulsory will make the voter ranks the candidate as their proximity, and the median voter wins the vote

The fact that resources are needed to finance reelection campaigns will make the probability of the median voter be in danger

According to median voter model theorem, at-least there must be two candidates

Being that we have two candidates for elected office, let's see how the following may affect the conclusions of the median voter model:

Part a

Voting might not be compulsory:

Here, voter ranks the candidates as per as their proximity, and the median voter will win the vote.

Part b

Resources are needed to finance re-election campaign :

When resources are needed to finance reelection campaign, none can cast their votes and it will distort this strategy. So the probability of median voter is in danger.

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Answer:

50%

hope this answer helps you!

Answer:

C: 5 3/8

Step-by-step explanation:

The length of each straw half is 5.375

A= 6.25

B = 5.65

C = 5.375

D = 5.125

Answer:

3 gallons a minute

Step-by-step explanation:

when you begin filling the tub it only needs 15 additional gallons until it's full

if it takes 5 minutes then the rate at which the tub if filling is 3 gallons per minute

The standard equation for the given situation of the bathtub is w = 5t + 12.

The standard equation to model this linear situation:

w = 5t + 12

where:

w is the number of gallons of water in the bathtub after t minutes

5 is the rate at which the bathtub is being filled (in gallons per minute)

12 is the initial number of gallons of water in the bathtub

To come up with this equation, we know that the bathtub holds 32 gallons of water and initially contains 12 gallons of water. We also know that after 5 minutes, the bathtub is full. This means that in 5 minutes, 32 - 12 = 20 gallons of water were added to the bathtub. Since the bathtub is being filled at a constant rate, we can assume that this rate of 20 gallons per 5 minutes is also the rate at which the bathtub is being filled at any other time.

We can now plug these values into the standard equation for linear relationships:

w = rt + b

where:

w is the dependent variable (the number of gallons of water in the bathtub)

r is the slope of the line (the rate at which the bathtub is being filled)

b is the y-intercept (the initial number of gallons of water in the bathtub)

In this case, we have:

w = 20t + 12

This equation models the linear relationship between the number of gallons of water in the bathtub and the number of minutes it has been filling.

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Correct Question:

A bathtub that holds 32 gallons of water contains 12 gallons of water. You begin filling it, and after 5 minutes the tub is filled. Write a standard equation.

a. The strategy profile (U, L) is a Nash equilibrium when x is greater than or equal to 0 and z is less than or equal to 0.

b. The strategy profile (D, R) is a Nash equilibrium when x is less than or equal to 0 and y is greater than or equal to 0.

c. The strategy profile (D, L) is a Nash equilibrium when x is less than or equal to 0 and y is less than or equal to 0.

To determine the Nash equilibria for the given strategies, we need to consider each player's best response to the strategies chosen by the other players.

a. For the strategy profile (U, L) to be a Nash equilibrium, player 1 (P1) should have no incentive to deviate from playing U, and player 2 should have no incentive to deviate from playing L. In this case, if P1 plays U, their payoff is x, and regardless of the value of y, P2's payoff is always x. Thus, P1 has no incentive to deviate as long as x is greater than or equal to 0. Additionally, P2's best response to U is to play L, earning a payoff of z. Therefore, for (U, L) to be a Nash equilibrium, z should be less than or equal to 0.

b. For the strategy profile (D, R) to be a Nash equilibrium, P1 should have no incentive to deviate from playing D, and P2 should have no incentive to deviate from playing R. When P1 plays D, their payoff is 2, and P2's payoff is y. P1 has no incentive to deviate as long as x is less than or equal to 0. P2's best response to D is to play R, earning a payoff of 0. Therefore, for (D, R) to be a Nash equilibrium, y should be greater than or equal to 0.

c. For the strategy profile (D, L) to be a Nash equilibrium, P1 should have no incentive to deviate from playing D, and P2 should have no incentive to deviate from playing L. P1's payoff when playing D is 2, and P2's payoff is y. P1 has no incentive to deviate as long as x is less than or equal to 0. P2's best response to D is to play L, earning a payoff of y. Thus, for (D, L) to be a Nash equilibrium, both x and y should be less than or equal to 0.

In summary, (U, L) is a Nash equilibrium when x is greater than or equal to 0 and z is less than or equal to 0. (D, R) is a Nash equilibrium when x is less than or equal to 0 and y is greater than or equal to 0. (D, L) is a Nash equilibrium when x and y are both less than or equal to 0.

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Answer:

h

Step-by-step explanation:

So there are 200 different ways a doctor can prescribe the asthma drug to a patient, taking into account the various options for form, manufacturer, and strength.

This illustrates the importance of carefully considering all the available options and selecting the most appropriate prescription for each patient's unique needs.The number of different ways a doctor can prescribe the asthma drug to a patient depends on the number of options available for each of the three factors: form, manufacturer, and strength.

For each of the three factors, there are 10 different options. Therefore, the total number of different ways the doctor can prescribe the drug is the product of the number of options for each factor:

10 options for form x 10 options for manufacturer x 2 options for strength (regular or extra) = 200 total options.

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Precalculus is an example here, since x=−2 is a vertical type line, there is no  y-intercept as well as the slope is undefined.

The slope is undefined and all of the factors on the road have an x-coordinate of that (a few number). For example, if x = -2, then all factors alongside this line can have an x-coordinate of -2, making it a vertical line. y=−2 is a flat line crossing the factor at (0,−2) consequently the gradient is 0 and the the y intercept is -2.

A terrible slope approach that variables are negatively related; that is, whilst x increases, y decreases, and whilst x decreases, y increases. Graphically, a terrible slope approach that as the road on the road graph movements from left to right, the road falls. The x-coordinate -2 is represented throughout. This is NOT a function.

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