A train travels at a constant speed of 75 mi/h. The function f(x) = 75x gives the distance that the train travels in x hours. Graph this function and give its domain and range.

The angle measure of angle 5 is m∠5 = 130 degrees.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Given information:

The two lines m and n are parallel lines.

And line l intersects lines m and n.

m∠1 = 50.

angle 1 and angle 3 are opposite angles.

Therefore, m∠1 = m∠3.

Angle 3 and angle 5 represent a pair of supplementary angles.

So,

m∠3 + m∠5 = 180

m∠5 = 180 -50

m∠3 = 130.

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The complete question:

If m∠1 = 50, then m∠5 = ?

The image is given below.

Answer:

160

Step-by-step explanation:

100 + 4 (15)

100 + 60

160

Answer : The mean, median, and mode of the household pet data is, 1.4, 1 and 0 respectively.

Step-by-step explanation :

Mean : It is determine by adding all the numbers then divided by how many numbers there are.

[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]

Median : It is the middle term that is sorted by the list of numbers. It is determine by placing the numbers in increasing order.

For odd observations the formula will be: [tex]\frac{n+1}{2}[/tex]

For even observations:

First find the value at position [tex]\frac{n}{2}[/tex]

Second find the value at position [tex]\frac{n+1}{2}[/tex]

Then find that average of two values to get the median.

Mode : It is defined as the value that appears most in a set of data.

As we are given that the set of data:

1, 1, 0, 4, 1, 0, 1, 2, 3, 5, 2, 0, 2, 0, 3, 1, 2, 0, 0, 1, 0, 4, 0, 0, 3, 1, 0, 0, 2, 1, 0, 0, 4, 0, 1, 3, 5, 0, 2, 1

First we have to placing the numbers in increasing order.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5

Now we have to determine the mean.

[tex]Mean=\frac{\text{Sum of outcomes}}{\text{Number of outcomes}}[/tex]

Sum of outcomes = 1+1+0+4+1+0+1+2+3+5+2+0+2+0+3+1+2+0+0+1+0+4+0+0+3+1+0+0+2+1+0+0+4+0+1+3+5+0+2+1 = 56

[tex]Mean=\frac{56}{40}=1.4[/tex]

The mean of the household pet data is, 1.4

Now we have to determine the median.

For even data:

[tex]\frac{n}{2}[/tex] and [tex]\frac{n+1}{2}[/tex]

Here, n = 40

[tex]\frac{40}{2}[/tex] and [tex]\frac{40+1}{2}[/tex]

20 and 20.5

The number of pets at 20th position and 21th position is, 1 and 1 respectively.

Then we have to take an average of two values.

[tex]\frac{1+1}{2}=1[/tex]

The median of the household pet data is, 1

Now we have to determine the mode.

In the given set of data, 0 appears 15 times, 1 appears 10 times, 2 appears 6 times, 3 appears 4 times, 4 appears 3 times and 4 appears 2 times.

The value that appears most in a set of data is, 0

The mode of the household pet data is, 0

12 on the x axis you stay on the x axis, because you dont have a Y intercept. Then draw a vertical line from the point

The graph of a function is the representation in the Cartesian plane of an algebraic expression.

Let us consider the equation y=12x.

x              0        1        2        3

y=12x       0       12      24       36

Now plot the values of (x,y) on the graph.

y=12 x has slope 12 and it does not have y intercept.

So 12 on the x axis you stay on the x axis, because you dont have a Y intercept. Then draw a vertical line from the point

Hence the graph is given in the attachment.

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The standard form of fourteen thousand and two hundred eight thousandths is 1.4208 x 10⁴.

Standard form refers to any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten. 1.23 108; If you look closely, 1.23 is a decimal number between 1.0 and 10.0, so the standard form of 123,000,000 is 1.23 108.

Given that the number is fourteen thousand and two hundred eight thousandths.

The standard form of the number will be written as,

14208 = 1.4208 x 10⁴

The standard form is 1.4208 x 10⁴.

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The probability that a card randomly drawn from a well-shuffled 52-card deck is not a spade or a king is approximately 0.846 or 44 out of 52.

In a well-shuffled deck of 52 cards, there are four spades and four kings. Therefore, there are 4 + 4 = 8 cards that could be a spade or a king. The probability that a randomly chosen card is a spade or king can be calculated as the number of favorable outcomes divided by the total number of outcomes. So, the probability is 8/52 or approximately 0.154.

However, the question asks for the probability that the card is not a spade or king. To find this, we calculate 1 minus the probability of drawing a spade or king. Therefore, the probability that a card randomly drawn from a well shuffle deck is not a spade or a king is 1 - 0.154 = 0.846 or 44/52.

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Answer:

35 smaller trucks.

Step-by-step explanation:

Given:

i) The larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload.

ii)  To unload a freight train 21 larger trucks are needed .

Total load of the freight train = 21 times 2.5 tons

= 21  × 2.5

= 52.5 tons

To find the number of small trucks needed, we need to divide 52.5 by 1.5

= 52.5 ÷ 1.5

= 35 small trucks needed.

So, to unload the freight, we need 35 smaller trucks.

Answer:

Part A: Marguerite rented a truck at $125 for 2 days. If she rents the same truck for 5 days, she has to pay a total rent of $275.

Write an equation in the standard form to represent the total rent (y) that Marguerite has to pay for renting the truck for x days. (4 points)

Part B: Write the equation obtained in Part A using function notation. (2 points)

Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

(10 points)

Step-by-step explanation:

-64 Celsius  =

-64 * 9/5 + 32 = minus 83.2 degrees Fahrenheit

Clouds form when temperatures drop below -64°C.

To convert temperatures from Fahrenheit to Celsius, subtract 32, multiply by 5, and divide by 9. -64°C is equal to -83.2°F, the temperature at which certain clouds form.

To convert from Fahrenheit to Celsius:

For this specific question:

Minus 64°C is equal to -83.2°F.

Clouds form when temperatures drop below -64°C.

It's a basic multiplication problem. Simply multiply the number of candles Jane has (7), by 5, which equals 35. So, Aisha has 35 candles.

The problem presented is a multiplication problem. We're told that Aisha has 5 times more tealight candles than Jane.

by calculating how many candles does Aisha have,

To find out how many candles Aisha has, we can multiply the number of candles Jane has (which is 7) by 5. So, the calculation will be as follows: 7 (candles) * 5 = 35 candles. by using basic multiplication i.e. 7*5 = 35.

Therefore, Aisha has 35 candles.

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Answer:

6units

Step-by-step explanation:

Using the Pythagorean Theorem for the given right triangle, we calculated that the worker would need a ladder of at least 25 feet in length to reach the window.

The problem described can be solved by using the Pythagorean Theorem, which is appropriate for any right triangle. In the given problem, we have a right triangle - one side is the distance from the fence to where the ladder touches the building (12ft + 1ft + 9ft = 22ft), the other side is the height of the window from the ground (15ft), and the hypotenuse is the length of the ladder we need to find.

According to the Pythagorean theorem: [tex]A^2 + B^2 = C^2[/tex]. If we plug in our values, it would look like [tex]15^2 + 22^2 = C^2[/tex]. After carrying out the operations, we find that C^2 = 625.

To find the length of the ladder (C), we take the square root of 625, which is 25ft. So, the worker needs a ladder that is at least 25 feet long.

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Solving the system of linear equations provided, we find that the cost of a can of orange is £0.85 and a chocolate bar costs £0.45. Therefore, three cans of orange and four chocolate bars would cost £4.35.

The student's question involves solving a system of linear equations to find the individual prices of a can of orange and a chocolate bar. Once the individual prices are determined, the student wants to know the total cost of three cans of orange and four chocolate bars. Here's a step-by-step approach to solve this problem:

Let the price of a can of orange be 'O' and the price of a chocolate bar be 'C'.

The first equation from the given information would be O + C = £1.30.

The second equation would be 2O + C = £2.15.

Subtract the first equation from the second to find the price of an additional can of orange, which gives us O = £0.85.

Substitute the value of O in the first equation to find C, which yields C = £0.45.

Now, calculate the cost of three cans of orange and four chocolate bars: 3O + 4C = 3(£0.85) + 4(£0.45) = £2.55 + £1.80 = £4.35.

So, three cans of orange and four chocolate bars would cost £4.35 together.

Answer:

The value of (F-G)(6) is -1.

Step-by-step explanation:

The given functions are defined as

[tex]F = \{(0, 1), (2, 4), (4, 6), (6, 8)\}[/tex]

[tex]G = \{(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)\}[/tex]

We need to find the value of (F-G)(6).

Using subtraction of two function property, we get

[tex](F-G)(6)=F(6)-G(6)[/tex]           .... (1)

From the given functions it is cleared that the value of function F is 8 at x=6 and the value of function G is 9 at x=6. It means

[tex]F(6)=8[/tex]

[tex]G(6)=9[/tex]

Substitute F(6)=8 and G(6)=9 in equation (1).

[tex](F-G)(6)=8-9[/tex]

[tex](F-G)(6)=-1[/tex]

Therefore the value of (F-G)(6) is -1.