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2 years ago

P and q are two numbers such that p > q

Mathematics

2 answers:

raketka [301]2 years ago

5 0

Answer:

3:2

Step-by-step explanation:

p-15: q-15

2:1

Using cross products

p-15 = 2(q-15)

p -15 =2q -30

Add 30 to each side

p +15 = 2q

p =2q - 15

30+p: q+30

5 :4

Using cross products

4(30+p) = 5(30+q)

120+4p = 150+5q

Subtract 120 from each side

4p = 30 +5q

Substitute the first equation in

4(2q -15) = 30 +5q

8q -60 = 30 +5q

Subtract 5q

3q -60 = 30

3q = 90

q = 30

Find p

p =2q - 15

p = 2*30 -15

p = 60-15

p = 45

ratio of p:q

45:30

Divide by 15

45/15 : 30/15

3:2

Ugo [173]2 years ago

5 0

Answer:

Step-by-step explanation:

p - 15 : q - 15 = 2 : 1

We know that when we use ratios, we're using fractions, so when we cross multiply:

1(p - 15) = 2(q - 15)

p - 15 = 2q - 30

p + 15 = 2q

p = 2q - 15 ....(1)

30 + p : q + 30 = 5 : 4

We know that when we use ratios, we're using fractions, so when we cross multiply:

4(30 + p) = 5(30 + q)

120 + 4p = 150 + 5q

4p = 30 + 5q .....(2)

Substituting (1) in (2), we get:

= 4(2q - 15) = 30 + 5q

= 8q - 60 = 30 + 5q

3q - 60 = 30

3q = 90

= 30

Putting q = 30 in (1), we get:

p = 2 * 30 - 15

= 60 - 15

= 45

But we need to find the ratio of p : q (which is p/q)

So, 45 : 30

= 3 : 2

Hope this helps!

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Ben and Josh went to the roof of their 40-foot tall high school to throw their math books offthe edge.The initial velocity of Be

Taya2010 [7]

Answer

Josh's textbook reached the ground first

Josh's textbook reached the ground first by a difference of $t=0.6482$

Step-by-step explanation:

Before we proceed let us re write correctly the height equation which in correct form reads:

$h(t)=-16t^2 +v_{o}t+s$ Eqn(1).

Where:

$h(t)$ : is the height range as a function of time

$v_{o}$ : is the initial velocity

$s$ : is the initial heightin feet and is given as 40 feet, thus Eqn(1). becomes:

$h(t)=-16t^2 + v_{o}t + 40$ Eqn(2).

Now let us use the given information and set up our equations for Ben and Josh.

Ben:

We know that $v_{o}=60ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+60t+40$ Eqn.(3)

Josh:

We know that $v_{o}=48ft/s$

Thus Eqn. (2) becomes:

$h(t)=-16t^2+48t+40$ Eqn. (4).

Now since we want to find whose textbook reaches the ground first and by how many seconds we need to solve each equation (i.e. Eqns. (3) and (4)) at $h(t)=0$ . Now since both are quadratic equations we will solve one showing the full method which can be repeated for the other one.

Thus we have for Ben, Eqn. (3) gives:

$h(t)=0-16t^2+60t+40=0$

Using the quadratic expression to find the roots of the quadratic we have:

$t_{1,2}=\frac{-b+/-\sqrt{b^2-4ac} }{2a} \\t_{1,2}=\frac{-60+/-\sqrt{60^2-4(-16)(40)} }{2(-16)} \\t_{1,2}=\frac{-60+/-\sqrt{6160} }{-32} \\t_{1,2}=\frac{15+/-\sqrt{385} }{8}\\\\t_{1}=4.3276 sec\\t_{2}=-0.5776 sec$

Since time can only be positive we reject the $t_{2}$ solution and we keep that Ben's book took $t=4.3276$ seconds to reach the ground.

Similarly solving for Josh we obtain

$t_{1}=3.6794sec\\t_{2}=-0.6794sec$

Thus again we reject the negative and keep the positive solution, so Josh's book took $t=3.6794$ seconds to reach the ground.

Then we can find the difference between Ben and Josh times as

$t_{Ben}-t_{Josh}= 4.3276 - 3.6794 = 0.6482$

So to answer the original question:

Whose textbook reaches the ground first and by how many seconds?

Josh's textbook reached the ground first
Josh's textbook reached the ground first by a difference of $t=0.6482$

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2 years ago

Which of the following best describes the graph below?

Sonja [21]

Answer: Option A

Step-by-step explanation:

A function is one to one if every element in the range (y) has only one value in the domain (x) associated to it, while a function is many to one if some values in the range (y) have more than one element in the domain (x) associated.

In this function, we can see that the function is almost linear and always increases and it is easy to see that each value of y has only one value of x associated (because the line will always increase) the correct option is A.

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2 years ago

If the area of a park is exactly halfway between 2.4 and 2.5 acres, what is the area of the park

Ierofanga [76]

Answer:

2.45

Explanation:

Halfway of 2.4 and 2.5 is 2.45 because .05 is the halfway mark based on the place value.

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2 years ago

Suppose the weights of fish caught from pier 1 and pier 2 are normally distributed with equal population standard deviations. Th

madreJ [45]

Answer:

H₀: μ₁ = μ₂ vs, Hₐ: μ₁ > μ₂.

Step-by-step explanation:

A two-sample z-test can be performed to determine whether the claim made by the owner of pier 1 is correct or not.

It is provided that the weights of fish caught from pier 1 and pier 2 are normally distributed with equal population standard deviations.

The hypothesis to test whether the average weights of the fish in pier 1 is more than pier 2 is as follows:

H₀: The weights of fish in pier 1 is same as the weights of fish in pier 2, i.e. μ₁ = μ₂.

Hₐ: The weights of fish in pier 1 is greater than the weights of fish in pier 2, i.e. μ₁ > μ₂.

The significance level of the test is:

α = 0.05.

The test is defined as:

$z=\frac{(\bar x_{1}-\bar x_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}$

The decision rule for the test is:

If the p-value of the test is less than the significance level of 0.05 then the null hypothesis will be rejected and vice-versa.

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2 years ago

Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.

alexdok [17]

Answer:

The first digit of a two digit number can be any of digits 1 - 9. It cannot be 0 though. Therefore there are 9 possible digits for the first place.

There are 5 possible digits for the second position. The two digit number has to be odd and therefore the final digit must be 1,3,5,7 or 9

Therefore for each and every one of the nine first digits there are 5 digits that the second can be.

Therefore ANSWER = 9 * 5 = 45 possible permutations.

2. The largest two digit number = 99

Subtract 57 and you get 42

ANSWER = 42

The forty two numbers are 58 ,59, 60, 61......98, 99

7 0

2 years ago

Read 2 more answers