answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Inessa05 [86]
2 years ago
8

Jeanie completed a 27 mile duathlon (a race that is a combination of running and biking) in exactly 2 hours. she ran an average

speed of 8.5 miles per hour and biked an average speed of 16 miles per hour. for how long did jeanie bike during the race?
Mathematics
1 answer:
-Dominant- [34]2 years ago
8 0
<span>Let x = the miles Jeanie ran y = the miles Jeanie biked T = 2 hours total time for the duathlon v1 = 8.5 mph Jeanie's running speed and v2 = 16 mph Jeanie's biking speed But T = Jean's time she ran t1 + time she biked t2 I. e t1 + t2 = 2 So we have average speed v2 when she biked = distance (y) / time (t2) Distance y = v2 * t2 = 16 * t2 and distance when she ran x = 8.5 * t1 Since she covered 27 miles while running and biking we have x + y = 27 8.5t1 + 16t2 =27 ------(1) t1 + t2 = 2 --------------(2) The simultaneous equation gives us t1 = 2/3 and t2 which is time she biked = 4/3 So 4/3 = 1 1/3. Which is 1 hour 20 minutes</span>
You might be interested in
Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably in- finite, exh
mrs_skeptik [129]

Answer:

a) the negative integers set A is countably infinite.

   one-to-one correspondence with the set of positive integers:

   f: Z+ → A, f(n) = -n

b) the even integers set A is countably infinite.

   one-to-one correspondence with the set of positive integers:

   f: Z+ → A, f(n) = 2n

c) the integers less than 100 set A is countably infinite.

   one-to-one correspondence with the set of positive integers:

   f: Z+ → A, f(n) = 100 - n

d) the real numbers between 0 and 12 set A is uncountable.

e) the positive integers less than 1,000,000,000 set A is finite.

f) the integers that are multiples of 7 set A is countably infinite.

   one-to-one correspondence with the set of positive integers:

   f: Z+ → A, f(n) = 7n

Step-by-step explanation:

A set is finite when its elements can be listed and this list has an end.  

A set is countably infinite when you can exhibit a one-to-one correspondence between the set of positive integers and that set.

A set is uncountable when it is not finite or countably infinite.

8 0
1 year ago
Helena needs 3.5 cups of flour per loaf of bread and 2.5 cups of flour per batch of muffins. She also needs 0.75 cup of sugar pe
Arlecino [84]
From the given data, we can generate two equations with two unknowns. 

We let x = number of loaves of bread
            y = number of batches of muffins

For the equation of the flour requirement:
17 = 3.5x + 2.5y

<span>For the equation of the sugar requirement:
</span>4.5 = 0.75x + 0.75y

We evaluate the solutions by manipulating one of the equations into terms of the other. We use the first equation.We write x in terms of y.

x = (4.5/0.75) - y

Substitute the third equation to the second equation.

17 = (3.5((4.5/0.75)-y)) + 2.5y

Evaluating y and x, we have,

y = 4 and x = 2

Thus, from the amounts she has in hand, she can make 4 loaves of bread and 2 batches of muffins.
4 0
1 year ago
Read 2 more answers
Hailey paid \$13$13dollar sign, 13 for 1\dfrac3{7} \text{ kg}1 7 3 ​ kg1, start fraction, 3, divided by, 7, end fraction, start
LenKa [72]

Answer:

The cost of per kilogram of salami is = $9.1

Step-by-step explanation:

Given:

Hailey paid $13 for 1\frac{3}{7} kg of sliced salami.

To find cost per kilogram of salami.

Solution:

We will apply unitary method to find per kilogram cost of salami.

If 1\frac{3}{7} kg of salami costs = $13

Then 1 kg of salami will cost in dollars will be = 13\div 1\frac{3}{7}

In order to divide by mixed numbers, we will convert mixed numbers to fractions.

⇒ 13\div \frac{(7\times1)+3}{7}

⇒ 13\div \frac{10}{7}

In order to divide by fractions we will take reciprocal of divisor and then multiply.

⇒ 13\times \frac{7}{10}

⇒ \frac{13\times7}{10}

⇒ \frac{91}{10}

⇒ 9.1

Thus, cost of per kilogram of salami is = $9.1

3 0
2 years ago
Read 2 more answers
What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2
Margaret [11]

<u>Answer-</u>

\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}

<u>Solution-</u>

Given expression is (x+2)^4

Applying Binomial Theorem

\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i

Here,

a = x, b = 2 and n = 4

So,

\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i

Expanding the summation

=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4

=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4

=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16

=x^4+8x^3+24x^2+32x+16

4 0
2 years ago
Read 2 more answers
Given: m∠AEB = 45° ∠AEC is a right angle. Prove: bisects ∠AEC. Proof: We are given that m∠AEB = 45° and ∠AEC is a right angle. T
NNADVOKAT [17]

Answer:

The proof is explained below.

Step-by-step explanation:

Given ∠AEB=45° and also ∠AEC is right angle i.e ∠AEC=90°

we have to prove that EB is the angle bisector.

In the right angled triangle AEC,

∠AEC=90° and also ∠AEB=45°

∵ ∠AEB+∠BEC=∠AEC

⇒ 45° + ∠BEC = 90°

By subtraction property of equality

∠BEC = 45°

Hence,  ∠AEB = ∠BEC = 45°

The angle ∠AEB equally divides by the line segment EB therefore, the line segment EB is the angle bisector of angle ∠AEB.

7 0
1 year ago
Read 2 more answers
Other questions:
  • If the federal reserve decreases the reserve rate from 2.5% to 1.25% how does this affect the amount of money that would result
    13·1 answer
  • A $1,000 face value bond is currently quoted at 100.8. the bond pays semiannual payments of $22.50 each and matures in six years
    15·1 answer
  • A basketball team plays 3 games in a holiday tournament. According to the tree diagram, how many outcomes are possible?
    5·2 answers
  • A wall in Maria’s bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°
    5·2 answers
  • (4 tens 3 ones) x 10
    8·1 answer
  • must a function that is decreasing over a given interval always be negative over that same interval explain
    15·2 answers
  • Della bought a tree seedling that was 2 1/4 feet tall. During the first year, it grew 1 1/6 Feet. After two years, it was 5 feet
    10·1 answer
  • Consider the three functions: f(x) = Three-halves(4)x g(x) = Three-halves(4)–x h(x) = –Three-halves(4)x Which statements are tru
    10·2 answers
  • Triangle A B C is reflected across line m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated
    5·1 answer
  • Which graph shows the solution set of the compound inequality 1.5 x minus 1 greater-than 6.5 or 7 x + 3 less-than negative 25?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!