Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2 y > –2

Answers

Answer 1

Answer:

False

Step-by-step explanation:

4x + y < 2

y > –2

Substitute the point into the inequalities and see if they are true

4(4) + 2 < 2

16+2 < 2

18 <2  False

2 > –2  True

Since one is false the point is not a solution


Related Questions

The birth rate of a population is b(t) = 2000e0.023t people per year and the death rate is d(t)= 1410e0.017t people per year, find the area between these curves for 0 ≤ t ≤ 10. (Round your answer to the nearest integer.) people

Answers

Answer: 7118

Step-by-step explanation:

Given

Birth rate is [tex]b(t)=2000e^{0.023t}[/tex]

Death rate is [tex]d(t)=1410e^{0.017t}[/tex]

Area between them is given by

[tex]\Rightarrow A=\int _0^{10}2000e^{0.023t}-1410e^{0.017t}dt\\\Rightarrow A=\int _0^{10}2000e^{0.023t}dt-\int _0^{10}1410e^{0.017t}dt\\\Rightarrow A=22486.95652 -15368.99999\\\Rightarrow A=7117.95652[/tex]

Thus, the area between the curves is [tex]7117.95652\approx 7118[/tex]

In a recent health survey, 333 adult respondents reported a history of diabetes out of 3573 respondents. What is the critical value for a 90% confidence interval of the proportion of respondents who reported a history of diabetes

Answers

Answer:

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

The critical value for the 90% confidence interval is [tex]Z_c = 1.645[/tex].

A. Two numbers are in the ratio 5:7. When 3 is added to each number, the new ratio becomes 3 : 4. Find the numbers. ​

Answers

Answer:

answer is 3 and ratio of two different numbers

convert decimal into fraction 17.38​

Answers

Answer:

869/50

Step-by-step explanation:

17.38

= 1738/100

= 869/50

A new restaurant sells cheeseburgers for 6$, french fries for 3$, and salads for 8$ On opening night, the restaurant sold items and made 1070$. They sold 4 times as many fries as salads. How many cheeseburgers were sold?

Answers

Answer:

25 cheeseburger

Step-by-step explanation:

I checked and get that 4 times fries as many as salad means that fries = 4 times Salad.

Brainliest please~

25 cheeseburgers were sold.

What is algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

Let cheeseburger be x

Price of x = 6

Let French Fries be y

Price of y = 3

Let salads be z

Price of z=8

x+ y+ z =220

6x + 3y + 8z = 1070

4 y = z     4 times as many as

= 4 times  - Fries is more than Salad

Substitute 3 in 1

x + 4 z + z =220

x+5z =220

Substitute 3 in 2

6x + 12z +8z = 1070

6x + 20z = 1070

3x + 10z - 535

From 4: x=220-5z

Substitute into 3 (220-5z) +10z = 535

660 - 15z+10z=535

- 5z = - 125

z = 25

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a study of patients who were overweight found that 53% also had elevated blood pressure. if a patient is randomly selected find the probability that he has elevated blood pressure

Answers

Answer:

53%

Step-by-step explanation:

says it in the question lol

A person can see the top of a building at an angle of 65°. The person is standing 50 ft away from
the building and has an eye level of 5 ft. How tall is the building to the nearest tenth of a foot?
O 107.2 ft
O 112.2 ft
O 50.3 ft
O 26.1 ft

Answers

9514 1404 393

Answer:

  (b)  112.2 ft

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

For the given geometry, this becomes ...

  tan(65°) = (height above eye level)/(50 ft)

Then we have ...

  (height above eye level) = (50 ft)tan(65°) = 107.2 ft

Adding the height of eye level will give us the height of the building.

  building height = (eye level height) + (height above eye level)

  building height = (5 ft) + (107.2 ft)

  building height = 112.2 ft

Suppose we roll a pair of fair dice, let A=the numbers I rolled add up to exactly 8, and let B=the numbers I rolled multiply to an even number. Find P(Ac and Bc).

Answers

Answer:

P(Ac and Bc) = 7/36 = 0.1944 = 19.44%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

For the pair of dice:

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

So 36 total outcomes.

Find P(Ac and Bc).

Complement of A(The result of the sum is different of 8) and complement of B(multiply to odd number). So the desired events are:

(1,1), (1,3), (1,5)

(3,1), (3,3)

(5,1), (5,5)

7 desired outcomes. So

P(Ac and Bc) = 7/36 = 0.1944 = 19.44%

Help with question number one please

Answers

Answer:

165 hits

Step-by-step explanation:

27.5% of 600 is 600 x 27.5 / 100 = 165

Can someone please do these three and number them? -Numbers: 10,11,12-

Answers

Answer:

10. Option: c11. Option: a12. Option: a

what value of n make an equation??

Answers

Answer:

[tex]\frac{4}{27}[/tex]

Step-by-step explanation:

simplify the terms on both sides;

12*18*n=32

n*216=32

n=32/216

simplified --> 4/27

you can check by plugging it back into the equation;

12*n*3*6=4*8

12*(4/27)*3*6=32

216*(4/27)=32

32=32

Match each equation with its number of unique solutions.
y = 3x2-6x+3
y = -x2 - 4x + 7
y = -2x2+9x-11
Two Real Solutions
One Real Solution
One Complex Solution
Two Complex Solutionse de

Answers

Answer:

y = 3x^2-6x+3    one real solution  

y = -x^2 - 4x + 7     two real solution

y = -2x^2+9x-11       two complex solutions

Step-by-step explanation:

b^2-4ac = 0   1 repeated real solution

b^2-4ac > 0   2 distinct real solutions

b^2-4ac < 0   2 complex solutions

The quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

The given quadratic functions are y = 3x²-6x+3, y = -x² - 4x + 7 and y = -2x²+9x-11.

What is the discriminant of a quadratic equation?

The discriminant of a quadratic equation ax² + bx + c = 0 is in terms of its coefficients a, b, and c. i.e., Δ OR D = b² − 4ac.

Now, with the function y = 3x²-6x+3, we get

b² − 4ac=(-6)²-4×3×3=36-36=0

Since b=0 it has two real solutions.

Now, with the function y = -x² - 4x + 7, we get

b² − 4ac= (-4)²-4×(-1)×7=16+28=44

Since b>0 it has one real solutions.

Now, with the function y = -2x²+9x-11, we get

b² − 4ac= (9)²-4×(-2)×(-11)=81-88=-7

Since b<0 it has one complex solution.

Therefore, the quadratic functions have the following solutions:

y = 3x²-6x+3 has two real solutions.

y = -x² - 4x + 7 has one real solution.

y = -2x²+9x-11 has one complex solution.

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evaluate 2x-y when x=5 and when y=12

Answers

Answer:

-2

Step-by-step explanation:

GIVEN :-

x = 5 and y = 12

TO FIND :-

2x - y

SOLUTION :-

placing the values of x and y

(2 × 5) - 12

10 - 12

-2

Answer:

- 2

Step-by-step explanation:

2x - y
2(5) - (12)
10 - 12
- 2

Simplify 12w + 2 (w + 3)

Answers

Answer:

= 14w + 6

Step-by-step explanation:

= 12w + 2w + 6

Add similar elements: 12w + 2w = 14w

= 14w + 6

I need help with this ​

Answers

Answer:

C

The lines will intersect once because this systems has one solution

Step-by-step explanation:

Start by putting everything into slope intercept form (AKA y=mx+b

2x-4y=3

2x-3=4y

y= .5x-.75

And the other one

7y-5x=8

-5x-8= -7y

y=(5x+8)/7

Because their slopes are different there's an intersection

Because their y intercepts are different there's only 1 solution

Andreas drew the model below to represent the equation What is the missing value in Andreas’s equation?
on 20 + 10 = blank x (4 + 2)

Answers

Answer:

20 + 10 = blank × (4 + 2)

30 = blank × 6

blank = 30 ÷ 6 = 5

help with plz thank you

Answers

Your answer is in the attachment..

Hope the answer helps you..

.

.

Select it as the BRAINLIEST..

Answer:

38. skipping by 3s

14, 17, 20, 23, 26, 29, 32, 35, 38

The length of a rectangle is 7cm less than 3 times it's width. It's area is 20 square cm. Find the dimensions of the rectangle

Answers

Answer:

4 cm by 5 cm (4 x 5)

Step-by-step explanation:

The area of a rectangle with length [tex]l[/tex] and width [tex]w[/tex] is given by [tex]A=lw[/tex]. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as [tex]3w-7[/tex]. Therefore, substitute [tex]l=3w-7[/tex] into [tex]A=lw[/tex]:

[tex]A=lw,\\20=(3w-7)w[/tex]

Distribute:

[tex]20=3w^2-7w[/tex]

Subtract 20 from both sides:

[tex]3w^2-7w-20=0[/tex]

Factor:

[tex](w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-\frac{5}{3}}\end{cases}[/tex]

Since [tex]w=-\frac{5}{3}[/tex] is extraneous (our dimensions cannot be negative), our answer is [tex]w=4[/tex]. Thus, the length must be [tex]20=4l, l=\frac{20}{4}=\boxed{5}[/tex] and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).

A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.75 days with an approximately normal distribution.
(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.
(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.

Answers

The probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. 0.03310

The probability that their hospital stay is greater than 6 days, rounded to five decimal places. 0.96610

We are given the following information in the question:

Mean, =7.37 days

Standard Deviation, σ =  0.75 days

We are given that the distribution of hospital stays is a bell-shaped distribution that is a normal distribution.

What is the formula for z score?

[tex]z_{score}=\frac{x-\mu }{\sigma}[/tex]

a) P( hospital stay is from 5 to 6 days)

[tex]P(5\leq x\leq 6)=P(\frac{5-7.37}{0.75} \leq z\frac{6-7.37}{0.37})\\=P(-3.16\leq z\leq -1.827)\\=0.034-0.001\\=0.0310\\=3.10%[/tex]

[tex]P(5\leq x\leq 6)=3.31%[/tex]

b) P(hospital stay is greater than 6 days)

P(x > 6)

Calculation of the value from the standard regular z table, we have,

[tex]P(x > 6)=P(z\leq -1.827)[/tex]

[tex]P(x > 6)=1-0.0339\\=0.0399\\=0.96610\\=96.61%[/tex]

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Halp me please. This questions is killing me. I need the answer. Solve $3a + 4b = a - 8b + 24$ for $a$ in terms of $b$.

Answers

Answer:

a=12-6b

Step-by-step explanation:

move b and a to their respective sides, getting a = -6b+12

tada :)

As per linear equation, the value of 'a' in terms of 'b' will be

a = 12 - 6b.

What is a linear equation?

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, (3a + 4b) = (a - 8b + 24)

⇒ 3a - a = - 8b + 24 - 4b

⇒ 2a = - 12b + 24

⇒ a = (- 12b + 24)/2

⇒ a = - 6b + 12

⇒ a = 12 - 6b

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$32,520 divided by 30 people

Answers

Answer: $1,084 per person

Step-by-step explanation:

divide 32520 by 30

[tex]8-x/(x-3)(x-4)[/tex]

Answers

8-/x(x-4)/x-3
That should be it if you can’t understand it the whole equation after the eight is a fraction


please help asap! i rlly need help on this
A. y=x+7
B. y= x-7
C. y=-5x+2
D. y=5x+2

Answers

Answer:
A. y=x+7

Explanation:
All of the answers are in y-intercept form (y=mx+b where m is the slope and b is the y-intercept), so the two points are used to solve for slope and y-intercept. Immediately, (0,7) gives the y-intercept because this point intercepts the y-axis at 7. Slope is found by dividing the rise over run between the two points. The points rise in y from 2 to 7 for a total of 5 units and the points run from -5 to 0 for a total of 5 units. Rise divided by run would be 5/5, simplified to a slope of 1. From this, slope=m=1 and y-intercept=b=7. Plugging these values into y=mx+b, the final answer is y=x+7.

4, 1 and 0, -4 on a graph

Answers

Answer:

Hope this will help.

What’s the answer to the question down below

Answers

Any linear equation can be written as

y = mx+b

where m is the slope and b is the y intercept

m = 1/2 in this case. It represents the idea that the snow fell at a rate of 1/2 inch per hour. In other words, the snow level went up 1/2 an inch each time an hour passed by.

b = 8 is the y intercept. It's the starting amount of snow. We start off with 8 inches of snow already.

The info "snow fell for 9 hours" doesn't appear to be relevant here.

Select all the correct answers.
Charles is reading about computers. He learns that a computer processor can perform one command in approximately 0.000000016
nanoseconds. What is this number expressed in scientific notation?
s
1.6E-8
1.6 x 10-7
1.6 x 10-8
1.6E-7
1.6 x 108
1.6E8
1.6 x 107
1.6E7
Next
Reset
82°F

Answers

9514 1404 393

Answer:

1.6×10^-81.6E-8

Step-by-step explanation:

The place value of a digit to the right of the decimal point is 10 to the negative power of the digit count. The 1st digit right of the decimal point has a place value of 10^-1.

Here, the most significant digit of 0.000000016 is in the 8th place to the right of the decimal point, so its place value is 10^-8.

  0.000000016 = 1.6×10^-8

Another way to write the same number is 1.6E-8. (The "E" is a stand-in for ×10^.)

_____

Your (graphing or scientific) calculator or a spreadsheet can display this in scientific notation for you.

__

That many nanoseconds, as this problem states, would be 1.6×10^-17 seconds. "Nano" is an SI prefix meaning 10^-9.

There are two independent file servers in a web site. Either file server works with a probability of 0.6. And this web site is up if either file server is working. The probability that the web site is up is _____.

Answers

Answer:

The probability that the web site is up is 0.84 = 84%.

Step-by-step explanation:

For each web server, there are only two possible outcomes. Either it is working, or it is not. The probability of a web server being working is independent of any other web server, which meas that the binomial probability distribution is used 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.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

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

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Either file server works with a probability of 0.6.

This means that [tex]p = 0.6[/tex]

Two servers.

This means that [tex]n = 2[/tex]

The probability that the web site is up is

At least one server working, which is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.6)^{0}.(0.4)^{2} = 0.16[/tex]

Then

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.16 = 0.84[/tex]

The probability that the web site is up is 0.84 = 84%.

The following box-and-whisker plots represent the fuel economy rates (combined city and highway) for the entire fleet
of two major car manufacturers.
Car Manufacturer B
Car Manufacturer A
+
5
0
10
40
45
50
15 20 25 30 35
Combined Fule Economy (in miles per gallon)
g
Which of the following statements is not true?
Car Manufacturer A's fleet has a larger range of fuel economy rates than Car Manufacturer B's fleet
The range of the middle half of the rates for both manufacturers is about the same
The median fuel economy rate of Car Manufacturer A is about 7 miles per gallon higher than the median fuel economy rate of Car
Manufacturer B
One of the vehicles in Car Manufacturer B's fleet has the lowest fuel economy rate of either manufacturer

Answers

Answer: Either C or D (explanation below)

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

Explanation:

Let's go through the answer choices to see which are true or which are false. The goal is to find which is false.

A) True. Notice the entire boxplot for fleet A is wider with its whiskers spanning out further compared to fleet B. Therefore, the range for set A is larger than the range of set B.B) True. This is an estimation and it appears the two boxes are the same width, so both seem to have the same IQR. Unfortunately, without the actual values of Q1 and Q3, it's impossible to confirm this 100%. C) False. The middle line in the box plot is the visual marker of the median. We see that the median of set A is less than the median of set B. So we found the answer and we could stop here. D) False. The min of car B's fleet is either at 15 or a little bit above it. Meanwhile, car A's minimum is well below 15 mpg. So saying that car B has the lowest fuel economy, for any car picked, compared to car A's fleet is incorrect.

Unfortunately, we found C and D to be false. So it's not clear if there's a typo or if your teacher meant to say something else.

Find the measure of each angle: Complementary angles with measures (5x) degrees and (4x-18) degrees.

Answers

Answer:

60 and 40

Step-by-step explanation:

As they are complementary, their sum will be 90. 5x+4x-18=90, 9x=108, x=12

Assume that thermometer readings are normally distributed with a mean of 0 degrees C and a standard deviation of 1.00 degrees C. A thermometer is randomly selected and tested. For the case below, draw a sketch, and find the probability of the reading. (The given values are in celsius degrees)
Between -1.42 and 1.61
The probability of getting a reading between -1.42 degrees C and 1.61 degreesC is_______ ( round to four decimal places as needed)

Answers

Answer:

The probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.

Step-by-step explanation:

We are given that

[tex]Mean,\mu=0[/tex] degree C

Standard deviation, [tex]\sigma=1[/tex] degree C

We have to find the probability of the reading between -1.42 and 1.61.

[tex]P(-1.42<x<1.61)=P(\frac{-1.42-0}{1}<\frac{x-\mu}{\sigma}<\frac{1.61-0}{1})[/tex]

[tex]P(-1.42<x<1.61)=P(-1.42<Z<1.61)[/tex]

[tex]P(-1.42<x<1.61)=P(Z<1.61)-P(Z<-1.42)[/tex]

Using the formula

[tex]P(a<z<b)=P(z<b)-P(z<a)[/tex]

[tex]P(-1.42<x<1.61)=0.94630-0.07780[/tex]

[tex]P(-1.42<x<1.61)=0.8685[/tex]

Hence, the probability of getting a reading between -1.42 degree C and 1.61 degree C is 0.8685.

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