Togo flew his ultralight plane to a landing field 30 miles away. With the wind, the flight took 3/5 hours. Returning against the wind, the flight took 5/6 hours. Find the rate of the plane in still air and the rate of the wind.



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Answer:

A

Step-by-step explanation:

You are dividing not multiplying

Let X = Individual ticket and y = couples tickets.

Set up two equations:

X + Y = 47 tickets sold

1X + 8y = $200

Rewrite the first equation as X = 47-y

Replace x in the second equation and solve:

1(47-y) = 8y = 200

Simplify:

47 - y + 8y = 200

Combine like terms:

47 +7y = 200

Subtract 47 from both sides:

7y = 153

Divide both sides by 7:

y = 153 / 7

y = 21.857

Because Y does not equal a whole number, the extra dollar does belong in the box.

Final answer:

Given the ticket prices and attendance, total sales amount to $71. The extra dollar found doesn't fit this, so it shouldn't be in the box.

Explanation:

To determine if the dollar Nola found belongs in the box, let's analyze the ticket sales. With individual tickets priced at $1 and couples tickets at $8 for two, we can calculate the total number of tickets sold. If there were 47 students in attendance, and assuming each couple bought the couples' ticket deal, the number of individual tickets sold would be (47 - number of couples) * 2 + number of couples.

Since each couple buys two tickets, the number of couples is 47 / 2 = 23.5, which means there were 23 couples and 1 individual. So, the total number of tickets sold is (47 - 23) * 2 + 23 = 71. Thus, the revenue from ticket sales should be $71.

If the cash box contains $200 and ticket sales total $71, then the extra dollar Nola found does not belong in the box. It's possible someone overpaid for a ticket or dropped a dollar accidentally, but it shouldn't be included in the revenue from ticket sales. Therefore, Nola should keep the dollar aside, perhaps to return it to its rightful owner.

Answer:

The first option:

Prove that the area of the two small squares combined is equal to the area of the larger square

Step-by-step explanation:

The Pythagorean Theorem in an equation would be:

a² + b² = c²

Where:

c = hypotenuse (longest side of the triangle)

a and b = two other legs of the triangle

The theorem states that the sum of the squares of the shorter sides is equal to the square of the longest side in a right triangle or a triangle that has a right angle (90°)

Let's say that we have a right triangle with the lengths of 3cm , 4cm, and 5cm.

(3cm)² + (4cm)² = (5cm)²

9cm² + 16cm² = 25cm²

25cm² = 25cm²

Look at the attached image to see what happens when we draw the squares of each leg.

Deb can use 6.5 ounces of cheese per loaf of bread. The calculation is made by dividing the total amount of cheese by the number of loaves.

Deb has 26 ounces of shredded cheese and she is making 4 small loaves of garlic cheese bread. To equally distribute the cheese across each loaf, we perform division.

We divide the total amount of cheese by the number of loaves: Thus, 26 ounces divided by 4 loaves equals 6.5 ounces of cheese per loaf.

The reasoning here is simple: we are equally distributing the cheese across each loaf, so we divide the total amount by the number of loaves. This ensures each loaf gets the same amount of cheese.

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Answer:

[tex] \frac{3x}{2y + 3} + \frac{ {x}^{2} + 3x}{4xy - 3 - 2y+6x} [/tex]

combine like terms afterwards .. for the polynomial

Answer:

7 weeks

Step-by-step explanation:

500-200=300. 300 divided by 40 is 7.5 so 7 weeks

Answer:

(4y +8 )÷6 -12

Variable = y

Sum = 4y +8

Quotient = 6

coefficient =4

Answer:

y - 2 = 3(x - 5)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 3 and (a, b) = (5, 2), thus

y - 2 = 3(x - 5) ← equation of line

Answer:

y - 2 = 3(x - 5)

Step-by-step explanation:

Start with the general point-slope equation:

y - k = m(x - h)

Now substitute 2 for k, 5 for h and 3 for m:

y - 2 = 3(x - 5)

Answer: Percy, None, 288

Step-by-step explanation:

Divide to find the rate.

Divide 33/2= about 16. 43/3= about 14.

Percy is faster.

Second problem: 50/12=4

120/30=4

No one, they grade the same amount.

Third:

72/2= 36 per hour

36x8= 288

Answer:

Step-by-step explanation:

  Inch   =   Cm

        1   =   2.54

       15   =   ?

We have to find out the question mark. So to do this we have to find out how we got from 1 to 15. We did this by multiplying by 15.

Inch   =   Cm

        1   =   2.54

×15

       15   =   ?

So we must do the same on the other side.

         1   =   2.54

×15                 ×15

       15   =   ?

2.54×15=38.1

   1   =   2.54

×15                 ×15

       15   =   38.1

The answer is therefore 38.1cm

Hope this helped!

Answer:

The town received approximately 44.29 inches of rain during a 31−day month.

Step-by-step explanation:

Given;

The amount of rain for two weeks = 20 inches.

For finding amount of rain for 31 days, we use the unitary method.

∵ Amount of rain for 14 days = [tex]20\ inches[/tex]

∴ Amount of rain for 1 day = [tex]\frac{20\ inches}{14}[/tex]

∴ Amount of rain for 31 day = [tex]\frac{20\ inches}{14}\times31=\frac{620}{14}\ in=44.285\approx 44.29\ in[/tex]

Hence the amount of rain the town received is 44.29 inches approximately.

Answer:

-1

Step-by-step explanation:

if x = 0...

2(0) + 8(0) - 1 =

0 + 0 - 1 =

0 - 1 =

-1

Plant B produced 8000 panels.

Let's denote the number of panels produced by Plant B as B .

The total number of defective panels from Plant A is [tex]\( 0.05 \times 16000 = 800 \)[/tex] , and the total number of defective panels from Plant B is [tex]\( 0.02 \times B \)[/tex].

The total number of panels from both plants is 16000 + B .

The overall percentage of defective panels is given as 4%, so:

[tex]\[ \frac{800 + 0.02 \times B}{16000 + B} = 0.04 \][/tex]

Now, let's solve for  B :

[tex]\[800 + 0.02 \times B = 0.04 \times (16000 + B) \][/tex]

[tex]\[ 800 + 0.02 \times B = 640 + 0.04 \times B \][/tex]

Subtracting [tex]\( 0.02 \times B \)[/tex] from both sides:

[tex]\[ 800 = 640 + 0.02 \times B \][/tex]

Subtracting 640 from both sides:

[tex]\[ 160 = 0.02 \times B \][/tex]

Now, divide by 0.02 to find B :

[tex]\[ B = \frac{160}{0.02} \][/tex]

B = 8000

So, Plant B produced 8000 panels.

The number of panels produced by Plant B is 8,000.

The number of panels produced by Plant A  = 16,000

The number of defective panels from A = 5%

Now, 5% of 16,000 =

So, out of  16,000 panels produced by pant A , 800 are defective. .. (1)

Let us assume number of panels produced by Plant B  = m

The number of defective panels from B = 2%

Now, 2% of m

So, out of total m panels produced by pant B , 0.02 m are defective. .. (2)

Now, total panels produced over all = Panels by A  + Panels by B

= 16,000 + m

The percentage of defective panels over all = 4%

Now, 4% of (16,000 + m)

Also, the total number of defective panels = Defective from A  + Defective from B

⇒(0.04)(16,000 + m)  =  800 +   0.02 m   from (1) and (2)

0.02 m = 160

⇒ m = 160 /0.02 = 8,000

or, m = 8,000

Hence, Number of panels produced by Plant B is 8,000.

A statement that best describes how to translate the graph y = Ixl to obtain the graph of y = |x - 1| - 1 is: C. 1 unit right and 1 unit down.

In Mathematics, the vertex form of the equation for an absolute value function can be modeled by the following:

y = a|x - h| + k.

Where:

By critically observing the equation of the transformed absolute value function, we can logically deduce that the parent absolute value function y = |x| was horizontally shifted to the right by 1 unit and then vertically shifted 1 unit down as follows;

y = a|x - h| + k.

y = |x - 1| - 1

Complete Question:

Which of the following describes how to translate the graph y = Ixl to obtain the graph of y = |x - 1| - 1?

1 unit left and 1 unit down

1 unit left and 1 unit up

1 unit right and 1 unit down

1 unit right and 1 unit up

Answer:

x-intercept: (9,0)

y-intercept: (0,7)

Step-by-step explanation:

x-intercept: when y = 0

7x + 9(0) = 63

7x = 63

x = 9

y-intercept: when x = 0

7(0) + 9y = 63

y = 7

Answer:

x-intercept : (9,0)

y-intercept : (0,7)

Step-by-step explanation: To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Hope this helps you out! ☺

Answer:

1/4

Step-by-step explanation:

You go up 2 and right 8, which translates to 2/8.

Simplify that to 1/4

Answer:

0

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-7)/(8-0)

m=0/8=0

Answer:

0

Step-by-step explanation:

Step-by-step explanation:

it can be expressed in the form of p/q where p and q are co primes,

the basic definition of rational number

Answer:

it can be expressed as a fraction

Step-by-step explanation:

Answer:

x=-27

Step-by-step explanation:

x/-9=3

x=3*-9=-27

The correct answer is option 4: [tex](8.\frac{1}{4}).\frac{3}{5}[/tex]

Step-by-step explanation:

Given expression is:

[tex]8.(\frac{1}{4}.\frac{3}{5})[/tex]

The associative property states that for any three terms that are being multiplied, different order of multiplication (i.e. which two terms are multiplied first) will give the same answer.

Let a,b and c be the three terms

then

[tex]a.(b.c) = (a.b).c[/tex]

So applying the associative property on given expression

[tex]8.(\frac{1}{4}.\frac{3}{5}) = (8.\frac{1}{4}).\frac{3}{5}[/tex]

Hence,

The correct answer is option 4: [tex](8.\frac{1}{4}).\frac{3}{5}[/tex]

Keywords: Associative property, Properties

Learn more about associative property at:

#learnwithBrainly

Answer:

I would estimate 61.3

Step-by-step explanation:

I don't think I answered right but I tried

Answer: 24

Step-by-step explanation:

2-(8-5x6) = 24

Answer:

If by bi-weekly you mean once every two weeks, then the friend who is payed bi-weekly has a higher annual salary. The same for if he is payed twice a week.

Step-by-step explanation:

1458 x 24 = 34992

1346 x 26 =34996

Answer:

B. x < 5

Step-by-step explanation:

Lets go first with 3x – 8 < 23  then with - 4x + 26 > 6 and after that we put them together. (I will use the < > signs but as I see on the pictures these include the =, being less and greater OR equal).

3x – 8 < 23

Lets sum 8 in both sides:

3x < 23 +8

3x < 31

Now, divide both sides by 3:

3x/3 < 31/3

x < 31/3

Here we found one condition. Lets go with the other inequality for the other condition:

- 4x + 26 > 6

Lest sum 4x in both sides to get a potive x:

- 4x + 26 + 4x > 6 +4x

26 > 6 +4x

Now subtract 6 in both sides

26 - 6 > 6 +4x - 6

20 > 4x

Finally, divide both sides by 4:

20/4 > x or 5 > x (simplifying we get the second)

So, our second condition says that x must be less than 5.

So, putting both conditions together:

x < 5

x < 31/3 = 10.33

So, if x must be less than 5 and less than 10.33, is the same that saying that x mus be less than 5. We con obviate the condition that x must be less than 10.33 as it is included in the other. So our answer is:

x < 5

It is the option B in the image (remember I didnt use the less or equal sign because you didn't included it in the statement).

Answer:

20

Step-by-step explanation:

I assume you mean discriminant.

For a quadratic y = ax² + bx + c, the discriminant is b² − 4ac.

Here, a = -4, b = 2, and c = 1.  So the discriminant is:

(2)² − 4(-4)(1) = 20

Answer: 20 ÷ 2.5 = 8

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4 divided by 0.5 equals 8.

Answer:

Step-by-step explanation:

5/10 and 1/2 are both equivalent ratios resulting in half of themselves you can multiply these by any numbers but they will stay as half ratios such as 1:2 x 6 it would be 6:12 divide it by 6 and you have a half

Equivalent ratios have a multiplicative relationship, where multiplying both terms of a ratio by the same number results in another equivalent ratio. For example, multiplying the ratio 1:2 by 2 gives the equivalent ratio 2:4, showing that the ratios are proportional to each other.

Understanding Equivalent Ratios through Multiplication

We can explore the concept of equivalent ratios by looking at their multiplicative relationship. For instance, let's consider the ratios 1:2 and 2:4. These two ratios are equivalent because if we multiply both terms of the first ratio by 2, we get the second ratio. Mathematically, this can be expressed as 1x2/2x2 = 2/4, which is the same as the second ratio. Hence, the multiplication of both the numerator and the denominator of the first ratio by the same number (in this case, 2) maintains the ratio's equivalence to the second ratio.

This concept is crucial when dealing with proportions, unit rates, and unit scales. For example, if a map uses a unit scale of 1 inch = 100 feet, doubling the distance on the map to 2 inches would also double the actual distance to 200 feet, showing a direct multiplicative relationship between the two equivalent ratios.

Understanding how to use multiplication to find equivalent ratios is fundamental in solving problems that involve scaling, such as converting units or working with maps and models.

Answer:

0.75

Step-by-step explanation:

P(A | B) = P(A and B) / P(B)

P(vanilla | sundae) = P(vanilla and sundae) / P(sundae)

P(vanilla | sundae) = 0.15 / 0.2

P(vanilla | sundae) = 0.75

the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75

Given :

P(vanilla) =0.3,  P(sundae)=0.2,  P(vanilla and sundae) =0.15

we need to find the probability that a customer ordered vanilla ice cream given they ordered a sundae.

[tex]P(vanilla | sundae)=\frac{P(vanilla \; and \; sundae)}{P(sundae)}[/tex]

Substitute the values  and find the probability

[tex]P(vanilla | sundae)=\frac{ 0.15}{0.2}=0.75[/tex]

[tex]P(vanilla | sundae)=0.75[/tex]

the probability that a customer ordered vanilla ice cream given they ordered a sundae is 0.75

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Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points (-10, 5) and (5, 5).

Substitute:

[tex]m=\dfrac{5-5}{5-(-10)}=\dfrac{0}{15}=0[/tex]

The slope is equal 0. Therefore given line is a horizontal line.