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

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:

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).

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%

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%.

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]

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

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.

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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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

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.

[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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Answer:

869/50

Step-by-step explanation:

17.38

= 1738/100

= 869/50

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

Answer:

20 + 10 = blank × (4 + 2)

30 = blank × 6

blank = 30 ÷ 6 = 5

Answer:

Hope this will help.

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].

Answer:

answer is 3 and ratio of two different numbers

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

Answer:

53%

Step-by-step explanation:

says it in the question lol

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

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.

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.

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.

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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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.

Answer: $1,084 per person

Step-by-step explanation:

divide 32520 by 30

Answer:

9514 1404 393

Answer:

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.

Answer:

165 hits

Step-by-step explanation:

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

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.

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.

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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Answer:

= 14w + 6

Step-by-step explanation:

= 12w + 2w + 6

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

= 14w + 6