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1 year ago

Hadley paddled a canoe 2/3 mile in 1/4 hour. How fast did Hadley paddle in miles per hour ?

Mathematics

1 answer:

Vitek1552 [10]1 year ago

5 0

Answer:2 2/3 miles per hour

Step-by-step explanation:to get one mile you multiply 1/4 by 4 and to keep 1/4 and 2/3 proportional you also have to multiply 2/3 by 4

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What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
${i}^{2}$

The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
${i}^{2} = - 1$
to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0 + 1 + 2 + 3 + 4}$

This implies that,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{10}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( {{i}^{2}} )^{5}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( - 1 )^{5} = - 1$

8 0

2 years ago

Read 2 more answers

Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 9 toothpicks for th

Sergeeva-Olga [200]

Number of toothpicks required per student = At least 9

Total number of students = 30

Number of toothpicks required for the entire class = At least 9 × 30 = At least 270

Number of toothpicks in the bag in the class storage room = 50

Additional number of toothpicks required to be bought to make sure there are enough toothpicks = 270 - 50 = 220

Hence, she needs to buy 220 toothpicks.

4 0

2 years ago

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A cylinder shaped dispenser holds 5,652 cubic centimeters of liquid soap and is now full. The radius of the dispenser is 7.5 cen

attashe74 [19]

We know that

[volume of cylinder]=pi*r²*h------------> h=[volume of cylinder]/(pi*r²)
Volume=5652 cm³
r=7.5 cm
so
h=[5652]/(3.14*7.5²)-----------> h=32 cm

the height of the soap in the full dispenser is 32 cm

the height when 4,239 cubic centimeters of soap remains in the dispenser is
h=[4239]/(3.14*7.5²)-----------> h=24 cm

hence

the difference is 32-24--------> 8 cm

the answer is
8 cm

3 0

2 years ago

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1. which angle is congruent to Angle 1?

Inessa [10]

Part 1) which angle is congruent to Angle 1?

we know that

When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called corresponding angles

m∠5=m∠1 ----------> by corresponding angles postulate

therefore

the answer Part 1) is

Angle $5$

Part 2) Which can be used to directly prove that Angle 1 =~ Angle 8?

we know that

Alternate exterior angles are defined as two exterior angles on opposite sides of a transversal which lie on different parallel lines.

in this problem

m∠1=m∠8 -------> by alternate exterior angles theorem

therefore

the answer part 2) is the option

Alternate Exterior Angles Theorem

Part 3) If m Angle 5 = 42 degrees, what is m Angle 4?

we know that

Alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal

m∠4=m∠5 --------> by alternate interior angles theorem

m∠4= $42\ degrees$

therefore

the answer Part 3) is

$42\ degrees$

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2 years ago

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Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $600 item is $42, what is the s

Dafna11 [192]

Answer: $65.10

Step-by-step work:

1.Set the ratio
$\frac{600}{42} = \frac{930}{x}$
2.Cross-multiply
$600x = 930(42)$
$600x = 39060$
3.Divide to single out x
$600x \div 600 = 39060 \div 600$
$x = 65.10$

4 0

2 years ago