MATHEMATICS MIDDLE SCHOOL

Three people are kayaking. They all started at the same point and rowed in the same direction for 20 minutes. Laura rowed 7/8 mile
Daniel rowed 1/2 mile
Annabelle rowed 1/4 mile
Part A:
Did Laura row a distance greater than, less than, or equal to the combined distance of Daniel and Annabelle?

Answers

Answer 1
Answer:

Answer:

Greater than

Step-by-step explanation:

In order to compare the distances rowed, we need to come up with a common denominator. Our least common denominator is 8 because 2 and 4 are both divisors of 8.

Laura rowed 7/8 mile

Daniel rowed 4/8 mile ((1)/(2)* 4)

Annabelle rowed 2/8 mile ((1)/(4)*2)

Daniel and Annabelle rowed a combined 6/8 mile ((4)/(8) +(2)/(8)). 7/8 is greater than 6/8. Laura rowed a distance greater than the combined distance of Daniel and Annabelle.

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Answers

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Mrs Larnell is making a snack packs for a a class picnic. She puts 1/4 pound of apples,1/8 pound of nut mix, and 1/16 pound of chocolate in each of the students packs. There are 24 students in the class.What is the total weight of the snack packs? Is there more than one way to solve this problem?

Answers

Answer=10 1/2 pounds

One pack has 1/4+1/8+1/16 pounds of snacks....

Lets starts off giving our fractions of 1/4, 1/8 and 1/16 a common denominator of 16.

1/4=4/16
1/8=2/16
1/16=1/16

So...

x=4/16+2/16+1/16
x=7/16

So... One pack has 7/16lbs of snacks in it

Multiply 7/16lbs by the total number of students(24)..

7/16*24=10 1/2 pounds
________________________________________________________
another way of solving this problem could be...

1/4*24=6
1/8*24=3
1/16*24=1.5

6+3+1.5=10.5 pounds

A cylinder has an 18-inch diameter and is 15 inches tall. It is filled to the top with water. A 6-inch-diameter ball is placed within the cylinder, and then the cylinder is filled with water. How much water is in the cylinder? Give your answer in terms of pi.1,162pi in^3
1,179pi in^3
1,215pi in^3
1,251pi in^3

Answers

Answer: B.1,179π in3

Step-by-step explanation: Took the test

This week there are 144 members at the meeting, which is 90% of the total group​. What is the total number of green team members?

Answers

Answer:

The total number of Green team members is 160.

Step-by-step explanation:

Given 90% of the total members present at the meeting which is 144.

Let the total number of members be x.

90\%\ of x=144\n(90*\ x)/(100)=144\n9x=1440\nx=(1440)/(9)=160

Hence we can say that, The total number of Green team members is 160.

Answer:

160

Step-by-step explanation:

Circle X is shown. Line segment X Y is a radius. Line segment Y Z is a tangent that intersects the circle at point Y. A line is drawn from point Z to point X and goes through a point on the circle. The length of the line segment from point X to the point on the circle is 8, and the length of the line segment from the point on the circle to point Z is 9.What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

14 units
15 units
16 units
17 units

Answers

By applying Pythagorean' theorem, the length of ZY to be tangent to circle X is equal to: B. 15 units.

How to determine the length of ZY?

Since line ZY is tangent at point Y and the radius of a circle is always perpendicular to tangents, we can deduce the following points:

  • Line segment XY is perpendicular line segment ZY.
  • Triangle XYZ is a right-angled triangle.

Thus, the length of XZ is given by:

XZ = 8 + 9

XZ = 17 units.

Next, we would apply Pythagorean' theorem to find the required length of ZY:

XZ² = ZY² + XX²

17² = ZY² + 8²

ZY² = 289 - 64

ZY = √225

ZY = 15 units.

Read more on Pythagorean theorem here: brainly.com/question/23200848

#SPJ9

Answer:

i believe it is 15

Step-by-step explanation:

Circle X is shown. Line segment X Y is a radius. Line segment Y Z is a tangent that intersects the circle at point Y. A line is drawn from point Z to point X and goes through a point on the circle. The length of the line segment from point X to the point on the circle is 8, and the length of the line segment from the point on the circle to point Z is 9.

What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

14 units

15 units    should be 15 units

16 units      NOT

17 units

A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?

Answers

Answer:

  • 120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

  • x: number of pens
  • y: number of pencils

2. Cost

  • each pen costs $1, then x pens costs: x
  • each pencil costs $0.5, then y pencil costs: 0.5y

  • Then, the total cost is: x + 0.5y

  • The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

  • x + 0.5(80 + x) = 220

ii) Solve

  • x + 40 + 0.5x = 220
  • 1.5x = 180
  • x = 180/1.5
  • x = 120 pens

iii) Substitute x = 120 into the equation (2)

  • y = 80 + 120
  • y = 200 pencils

Solution: 120 pens and 200 pencils ← answer
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