Find the measure of z. A. 80° B. 83 ° C. 70 ° D. 87 °

Select all the statements that are true for the following systems of equations

Aleks [24]

Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

System A

2x - 3y = 4 .....equation 1

4x - y = 18 .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8 ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

$y = \frac {10}{5}$

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

$x = \frac {10}{2}$

x = 5

Solutions (x, y) = (5, 2)

System B

3x - 4y = 5 ..... equation 1

y = 5x + 3 ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

$x = \frac {-17}{17}$

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

Solutions (x, y) = (-1, -2)

System C

2x - 3y = 4 ..... equation 1

12x - 3y = 54 ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

$x = \frac {50}{10}$

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

$y = \frac {6}{3}$

y = 2

Solutions (x, y) = (5, 2)

5 0

3 years ago

Suppose that IQ scores have a bell-shaped distribution with a mean of 105 and a standard deviation of 15. Using the empirical ru

Romashka [77]

Answer:

Answer to Suppose that IQ scores have a bell-shaped distribution with a mean of ... Question: Suppose That IQ Scores Have A Bell-shaped Distribution With A Mean Of 105 And A Standard Deviation Of 15. ... Please Do Not Round Your Answer. ... Using the empirical rule, what percentage of IQ scores are greater than 120?Step-by-step explanation:

8 0

3 years ago

The percent decrease in the price of bottled water

Rzqust [24]

20% discount I’m pretty sure

5 0

4 years ago

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op

Mashcka [7]

Answer:

a) P(X<50)=0.9827

b) P(X>47)=0.4321

c) P(-1.5<z<1.5)=0.8664

Step-by-step explanation:

We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.

a) This means we have to calculate P(x<50).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{50-46.7}{1.75}=\dfrac{3.7}{1.75}=2.114\\\\\\P(X$

b) We have to calculatee P(x>47).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{47-46.7}{1.75}=\dfrac{0.3}{1.75}=0.171\\\\\\P(X>47)=P(z>0.171)=0.4321$

c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5

$z=\dfrac{(\mu+1.5\sigma)-\mu}{\sigma}=\dfrac{1.5\sigma}{\sigma}=1.5$

So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):

$P(-1.5$

3 0

3 years ago

Can someone help me with this

Alexxandr [17]

Answer:

B

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2l + 2w ( l is the length and w the width ) , then

P = 2(3 $\sqrt{15}$ ) + 2( $\sqrt{15}$ ) ← distribute both parenthesis )

= 6 $\sqrt{15}$ + 2 $\sqrt{15}$

= 8 $\sqrt{15}$

5 0

2 years ago