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Maru [420]
1 year ago
7

The 40th term of the number sequence is 119. (b) Work out the 41st term of the number sequence.

Mathematics
1 answer:
dolphi86 [110]1 year ago
7 0
100000fjwjsnfbc kdjdbf
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Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right
stich3 [128]

Answer:

The value of y is 6\sqrt{3} units ⇒ 2nd answer

Step-by-step explanation:

In the attached figure

∵ ∠MTN is a right angle

∵ TU is the altitude of the triangle

- There are some rules in this triangle let us revise them

  • (NT)² = NU . NM
  • (MT)² = MU . MN
  • (TU)² = MU . NU
  • TM . TN = TU . MN

∵ NU = 9 units

∵ UM = 3 units

∵ MN = UM + NU

∴ MN = 3 + 9 = 12 units

- By using the 1st rule above

∴ (NT)² = 9 × 12

∴ (NT)² = 108

- Take a square root to both sides

∴ NT = \sqrt{108}

- Simplify the root

∴ NT = 6\sqrt{3} units

∵ NT is y

∴ y = 6\sqrt{3} units

The value of y is 6\sqrt{3} units

8 0
2 years ago
Read 2 more answers
A catering company charges $300 plus $40 per guest for a wedding. Sarah and Eric do not want to spend more than $5,000 on cateri
Fynjy0 [20]
Your answer would be either c or d
8 0
2 years ago
Read 2 more answers
A remote control car races straight down the street at 26 miles per hour. Two
Pachacha [2.7K]

Answer:

It will take 4 hours for the second car to catch up with the first car.

Step-by-step explanation:

The first step to solving this problem is determining the difference in speed between the first and second car - you can see that the second car (at 52mph) is twice as fast as the first (26mph) therefore it will take half the time to cover the same distance.

As Car 1 has a 2 hour head start, it will be 52 miles ahead after 2 hours.

In the next 2 hours, Car 1 will travel 52 miles - so 104 in total after 4 hours, and car 2 will travel 104 miles, meaning that it will have caught up after 4 hours.

A)

To calculate distance per minute, divide the miles per hour by 60 (as there's 60 minutes in an hour), so:

Car 1 = 26/60 = 0.43 miles per minute

Car 2 = 52/60 = 0.867 miles per minute

To check your calculation, Car 2 should be exactly twice as far

B) The street, as far as we know, is at least 104 miles

C) See calculation at the top - the first car is 52miles from the start line when the second car starts

D) 2 cars are competing in this race

8 0
2 years ago
The following data show the midterm and final exam scores in an English writing class. Student 1 2 3 4 5 6 7 8 9 10 11 12 Midter
tester [92]

Answer:

The co variance of the midterm and final exam scores is 58.76.

Step-by-step explanation:

The formula to compute the sample co variance is:

Cov(x,y)=\frac{\sum(X-Mean\ of\ X)(Y-Mean\ of\ Y)}{n-1}

The values are computed in the table below.

Compute the co variance as follows:

Cov(x,y)=\frac{\sum(X-Mean\ of\ X)(Y-Mean\ of\ Y)}{n-1}\\=\frac{646.33}{12-1}\\ =58.76

Thus, the co variance of the midterm and final exam scores is 58.76.

7 0
1 year ago
You are given a rectangular sheet of cardboard that measures 11 in. by 8.5 in. (see the diagram below). A small square of the sa
GaryK [48]

Answer:

Terrence's

Step-by-step explanation:

The length of the square that will be cut out is the height of the box.

1. a

Anya's method: 8.5 -1.5 =7, 11- 1.5 =9.5, the height is 1.5, so the volume is height x length x width which is 1.5 x 9.5 x 7 =99.75 squared inches.

Terrence's method: 8.5-3 = 5.5, 11-3 = 8. Vol= 5.5 x 8 x 3 =132 squared inches. 99.75 < 132 squared inches, Terrence's idea would create larger volume.

1. b

The box's size depends on the length/width/height of the cardboard being cut, which is why different measurements / cutting methods for the same size cardboard can result in different box sizes.

2. The square would be cut from all four corners, therefore the sum of the 2 squares on the cardboard cannot exceed the short side of the cardboard. The shorter side of the cardboard is 8.5 inches, divided by 2 = 4.25 inches, hence the squares cannot  be larger than 4.25 inches. Keep in mind that if you cut exactly 4.25 inches you will have a strip of 2.5 inches width that cannot be turned into a box.

If you want to cut 5 inches squares out, depending on how you draw it, it would either overlap or go outside of the paper because 5+5 is ten, surely on the 11 inches side that would still be perfectly fine but for the 8.5 inches side, there isn't any room for the 10 inches.

7 0
2 years ago
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