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3 years ago

12

A sum of money is shared in the ratio of 2: 5 between Mark and Peter, respectively. If Mark got $200, how much money did Peter r

eceive?

1 answer:

34kurt3 years ago

8 0

Answer:

Step-by-step explanation:

Set this up as a proportion of M:P

$\frac{M}{P}:\frac{2}{5}=\frac{200}{x}$ and cross multiply to solve for x:

2x = 1000 so

x = 500. Peter got $500

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Man Street Florist charges

Digiron [165]

Answer:

2 dozens, $41

Step-by-step explanation:

Given data

Man Street Florist charges

$18 for a dozen roses and a

$5 delivery fee

let the number of dozens be x

and the total charge for x dozens be y

hence

y= 18x+5--------------1

Blooms and Bouquets

charges $20 for a

dozen roses and a $1

delivery fee.

let the number of dozens be x

and the total charge for x dozens be y

hence

y= 20x+1 -------------2

Equate 1 and 2 we have

18x+5=20x+1

20x-18x= 5-1

2x= 4

x= 4/2

x= 2

Hence the number of dozens is 2

the cost is (put x= 2 in eqn 1 or 2)

y= 20(2)+1

y= 40+1

y= $41

6 0

3 years ago

If y=(x^2-4)^5(3x+4)^4

alexira [117]

Answer:

$y'=2(3x+4)^3(x^2-4)^4(21x^2+20x-24)$

Step-by-step explanation:

$y=(x^2-4)^5(3x+4)^4$

$y'=[\frac{d}{dx}(x^2-4)^5](3x+4)^4+(x^2-4)^5[\frac{d}{dx}(3x+4)^4]$

$y'=10x(x^2-4)^4(3x+4)^4+(x^2-4)^5(12(3x+4)^3)$

$y'=10x(x^2-4)^4(3x+4)^4+12(x^2-4)^5(3x+4)^3$

$y'=2(3x+4)^3(x^2-4)^4(21x^2+20x-24)$

5 0

2 years ago

Please Help. I really don’t get this concept, if you could explain it in detail it would be very appreciated

Dafna11 [192]

<h3>Answer: 24/25</h3>

=================================================

Explanation:

Sine is given to be negative, and so is tangent. This only happens in quadrant Q4

Recall that y = sin(theta), so if sin(theta) < 0, then we're below the x axis.

If tan(theta) < 0, then this means cos(theta) > 0

So we have y < 0 and x > 0 which places the angle somewhere in Q4.

--------------------------

Draw a right triangle as shown below in the attached image. We have AC = 25 and BC = 7. Use the pythagorean theorem to find that AB = 24

So this is what your steps may look like

a^2+b^2 = c^2

7^2+b^2 = 25^2

b^2+49 = 625

b^2 = 625-49

b^2 = 576

b = sqrt(576)

b = 24

So because AB = 24, we know that the cosine of the angle is adjacent/hypotenuse = 24/25

---------------------------

As an alternative, you could use the trig identity

sin^2(x) + cos^2(x) = 1

and plug in the given value of sine to solve for cosine. The cosine value result will be positive since we're in Q4.

So,

sin^2(x) + cos^2(x) = 1

(-7/25)^2 + cos^2(x) = 1

(49/625) + cos^2(x) = 1

cos^2(x) = 1 - (49/625)

cos^2(x) = (625/625) - (49/625)

cos^2(x) = (625-49)/625

cos^2(x) = 576/625

cos(x) = sqrt(576/625)

cos(x) = sqrt(576)/sqrt(625)

cos(x) = 24/25

This is effectively a rephrasing of the previous section since the pythagorean trig identity is more or less the pythagorean theorem (just in a trig form)

6 0

4 years ago

Scrat [10]

I think D is the correct answer

4 0

3 years ago

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

oksian1 [2.3K]

Answer:

0.36 = 36% probability that the land has oil and the test predicts it

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

45% chance that the land has oil.

This means that $P(A) = 0.45$

He buys a kit that claims to have an 80% accuracy rate of indicating oil in the soil.

This means that $P(B|A) = 0.8$

What is the probability that the land has oil and the test predicts it?

This is $P(A \cap B)$ . So

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B \cap A) = P(B|A)*P(A) = 0.8*0.45 = 0.36$

0.36 = 36% probability that the land has oil and the test predicts it

5 0

3 years ago