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3 years ago

You and two friends pay $40 for tickets. The cost was divided three ways in the ratio 1 : 3 : 6. How much did each person pay

Mathematics

1 answer:

Harman [31]3 years ago

7 0

Answer:

first person payed$4, second person payed$12 and the third person payed $24

Step-by-step explanation:

find the sum of the ratio

find

1 divided by the total ratio time $40 to get first person

follow in that order to get the amount each person payed.

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Segment AB is congruent to segment AB.

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Step-by-step explanation:

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3 years ago

Use the discriminant to determine what type of roots the equations will have, and categorize the equations according to their ro

topjm [15]

Step-by-step explanation:

The discriminant of the quadratic equation $ax^2+bx+c=0$ :

$\Delta=b^2-4ac$

If Δ < 0, then the equation has two complex roots $x=\dfrac{-b\pm\sqrt\Delta}{2a}$

If Δ = 0, then the equation has one repeated root $x=\dfrac{-b}{2a}[/tex If Δ > 0, then the equation has two discint roots [tex]x=\dfrac{-b\pm\sqrt\Delta}{2a}$

$1.\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\Delta=(-4)^2-4(1)(2)=16-8=8>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=2\sqrt2\\\\x=\dfrac{-(-4)\pm2\sqrt2}{2(1)}=\dfrac{4\pm2\sqrt2}{2}=2\pm\sqrt2\\\\==============================\\\\2.\ 5x^2-2x+3=0\\\\a=5,\ b=-2,\ c=3\\\\\Delta=(-2)^2-4(5)(3)=4-60=-56$

$3.\ 2x^2+x-6=0\\\\a=2,\ b=1,\ c=-6\\\\\Delta=1^2-4(2)(-6)=1+48=49>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt{49}=7\\\\x=\dfrac{-1\pm7}{(2)(2)}\\\\x_1=\dfrac{-8}{4}=-2,\ x_2=\dfrac{6}{4}=\dfrac{3}{2}\\\\==============================\\\\4.\ 13x^2-4=0\qquad\text{add 4 to both sides}\\\\13x^2=4\qquad\text{divide both sides by 13}\\\\x^2=\dfrac{4}{13}\to x=\pm\sqrt{\dfrac{4}{13}},\ \bold{two\ distinct\ roots}\\\\==============================$

$5.\ x^2-6x+16=0\\\\a=1,\ b=-6,\ c=16\\\\\Delta=(-6)^2-4(1)(16)=36-64=-28$

$7.\ 4x^2+11=0\qquad\text{subtract 11 from both sides}\\\\4x^2=-11\qquad\text{divide both sides by 4}\\\\x^2=-\dfrac{11}{4}\to x=\pm\sqrt{-\dfrac{11}{4}}\\\\x=\pm\dfrac{\sqrt{11}}{2}\ i,\ \bold{two\ complex\ roots}$

6 0

3 years ago

Read 2 more answers

According to the National Association of Colleges and Employers, the average starting salary for new college graduates in health

katen-ka-za [31]

Answer:

a) The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.

b) The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.

c) The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.

d) A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.

Step-by-step explanation:

a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000?

For college graduates in business, the salary distributes normally with mean salary of $53,901 and standard deviation of $15,000.

To calculate the probability of earning at least $65,000, we can calculate the z-value:

$z=\frac{x-\mu}{\sigma} =\frac{65000-53901}{15000} =0.74$

The probability is then

$P(X>65,000)=P(z>0.74)=0.22965$

The probability that a new college graduate in business will earn a starting salary of at least $65,000 is P=0.22965 or 23%.

b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000?

For college graduates in health sciences, the salary distributes normally with mean salary of $51,541 and standard deviation of $11,000.

To calculate the probability of earning at least $65,000, we can calculate the z-value:

$z=\frac{x-\mu}{\sigma} =\frac{65000-51541}{11000} =1.22$

The probability is then

$P(X>65,000)=P(z>1.22)=0.11123$

The probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 is P=0.11123 or 11%.

c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000?

To calculate the probability of earning less than $40,000, we can calculate the z-value:

$z=\frac{x-\mu}{\sigma} =\frac{40000-51541}{11000} =-1.05$

The probability is then

$P(X$

The probability that a new college graduate in health sciences will earn a starting salary of less than $40,000 is P=0.14686 or 15%.

d. How much would a new college graduate in business have to earn in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences?

The z-value for the 1% higher salaries (P>0.99) is z=2.3265.

The cut-off salary for this z-value can be calculated as:

$X=\mu+z*\sigma=51,541+2.3265*11,000=51,541+25,592=77,133$

A new college graduate in business have to earn at least $77,133 in order to have a starting salary higher than 99% of all starting salaries of new college graduates in the health sciences.

8 0

3 years ago

Four polynomials are shown below:

nikklg [1K]

Both B and D are 3rd degree, but only D is a 3rd degree binomial because it has only 2 terms. The answer is D.

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3 years ago

Assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. If 144 people a

Vanyuwa [196]

Answer:

The probability is 0.9938

Step-by-step explanation:

In this question, we are asked to calculate the probability that the mean blood pressure readings of a group of people is less than a certain reading.

To calculate this, we use the z score.

Mathematically;

z = (mean - value)/(standard deviation/√N)

From the question, we can identify that the mean is 125, the value is 123 , the standard deviation is 9.6 and N ( total population is 144)

Let’s plug these values;

z = (125-123)/(9.6/√144) = 2.5

Now we proceed to calculate the probability with a s score less than 2.5 using statistical tables

P(z<2.5) = 0.9938

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3 years ago