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3 years ago

Pick the points that make the systems of equations true.

Mathematics

1 answer:

nata0808 [166]3 years ago

3 0

First, to the author of this piece of instruction. A system of equations would give multiple curves which intersect, as depicted here by a pair of crossing lines. But presumably here the solution space is intended to be the green area. That makes this a system of inequalities, not of equations. Fix it please, you're confusing the children.

We check each point to see if it's in the green space.

a) (2,2) CHECK

b) (0,4) nope

c) (6,1) CHECK

d) (1,6) nope

e) (-2,8) nope

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Sara goes to a furniture store to buy a dining set, end tables, and a loveseat. She sees a lamp for $40 and an end table for $62

BaLLatris [955]

Answer:

$1191.60

Step-by-step explanation:

<u>Option 1:</u>

Leather Loveseat

1200 plus 2% extra charge and NO TAX

What is 2% of 1200??

0.02 * 1200 = 24

So total price = 1200 + 24 = $1224

<u>Option 2:</u>

Lush Blue Loveseat and Lamp

Lush Blue loveseat is 980 + 17% tax, that would be worth 980 + (0.17)(980) = $1146.6

and

lamp is worth 40 with 12.5% tax, that would be worth 40 + (0.125)(40) = $45

Total cost = 1146.6 + 45 = $1191.6

2nd option is cheaper, so that would cost $1191.60

3 0

3 years ago

What is the measurement of x in the equation. 8x+5x+2x-11+6=180

34kurt

Answer:

x = 37/3 = 12.333

Step-by-step explanation:

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

15x - 185 = 5 • (3x - 37)

Equation at the end of step 1 :

Step 2 :

Equations which are never true :

2.1 Solve : 5 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

2.2 Solve : 3x-37 = 0

Add 37 to both sides of the equation :

3x = 37

Divide both sides of the equation by 3:

x = 37/3 = 12.333

4 0

3 years ago

Alyssa fed her dog 2/3 cup of dog food in the morning and another 5/8 cup in the evening. How much did her dog eat over the cour

kotegsom [21]

1 7/24 is the correct answer I will show you how to get it if needed.

8 0

3 years ago

Read 2 more answers

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

3 years ago

Assume that X is normally distributed with a mean of 20 and a standard deviation of 2. Determine the following. (a) P(X 24) (b)

Tems11 [23]

Answer:

a) P( X < 24 ) = 0.9772

b) P ( X > 18 ) =0.8413

c) P ( 14 < X < 26) = 0.9973

d) P ( 14 < X < 26) = 0.9973

e) P ( 16 < X < 20) = 0.4772

f) P ( 20 < X < 26) = 0.4987

Step-by-step explanation:

Given:

- Mean of the distribution u = 20

- standard deviation sigma = 2

Find:

a. P ( X < 24 )

b. P ( X > 18 )

c. P ( 18 < X < 22 )

d. P ( 14 < X < 26 )

e. P ( 16 < X < 20 )

f. P ( 20 < X < 26 )

Solution:

- We will declare a random variable X that follows a normal distribution

X ~ N ( 20 , 2 )

- After defining our variable X follows a normal distribution. We can compute the probabilities as follows:

a) P ( X < 24 ) ?

- Compute the Z-score value as follows:

Z = (24 - 20) / 2 = 2

- Now use the Z-score tables and look for z = 2:

P( X < 24 ) = P ( Z < 2) = 0.9772

b) P ( X > 18 ) ?