Given that events A and B are independent with P(A) = 0.4 and P(B) = 0.25,
determine the value of P(A and B), rounding to the nearest thousandth, if
necessary

i hop ....

i hope

ihope

solution

Answer:

[tex]y = 7x - 175[/tex]

Step-by-step explanation:

Given

Initial temperature= 25ºC

Rise = 1ºC

Rate  = 7 joules

Required

Determine the equation of the system

Let the final temperature be represented with x and the heat required be represented with y

This question will be solved using the following heat formula

[tex]Heat\ Required = Rate * Change\ in\ Temperature[/tex]

[tex]Heat\ Required = Rate * (Final\ Temperature - Initial\ Temperature)[/tex]

Substitute y for Heat Required; 7 for Rate; x for Final Temperature and 25 for Initial Temperature

[tex]y = 7(x - 25)[/tex]

Open the bracket

[tex]y = 7x - 7 * 25[/tex]

[tex]y = 7x - 175[/tex]

Hence, the equation of the system is

[tex]y = 7x - 175[/tex]

Answer: A

Step-by-step explanation:

For this problem, we would distribute the outer exponent to each exponent inside. Once we distribute, we multiply the exponents together.

[tex]2^\frac{12}{5} *9^\frac{4}{5}[/tex]

Answer:

When we have exponents (being multiplied) in a parenthesis which also has an exponent, the exponent of the parenthesis gets multiplied by each one of the others. We have to distribute the outer exponent to each exponent inside, like:

[tex](a^n*b^m)^p = a^{n*p}*b^{m*p}[/tex]

If there are numbers but no exponents (inside), it also happens the same, but as the exponent of the parenthesis gets multiplied by 1, we can just put the exponent, like:

[tex](a*b)^p=a^p+b^p[/tex]

So, in our case we have what we have explained: two numbers, one of them with an exponent and the other without it in a parenthesis which also has an exponent, so we multiply that exponent by the ones of the numbers inside the parenthesis.

[tex](2^3*9)^\frac{4}{5}[/tex] = [tex]2^{3*\frac{4}{5}}*9^\frac{4}{5}[/tex] = [tex]2^\frac{12}{5}*9^\frac{4}{5}[/tex]

So the answer is [tex]2^\frac{12}{5}*9^\frac{4}{5}[/tex]

Answer:

24 square cm

Step-by-step explanation:

[tex]area \: of \: \triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 12 \times 4 \\ = 6 \times 4 \\ = 24 \: {cm}^{2} \\ [/tex]

Answer:

x≤ -3/8

Step-by-step explanation:

[tex]4x\le \:-\frac{2}{5}\left(6x+6\right)\\[/tex]

Expand ;

[tex]\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}[/tex]

[tex]4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x[/tex]

Simplify

[tex]\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}[/tex]

Answer:

B. [tex]5*\frac{1}{7}[/tex]

Step-by-step explanation:

5÷7 is also [tex]\frac{5}{7}[/tex]--that divided sign is what the fractional bar represents in a fraction.

now multiply [tex]5*\frac{1}{7}=\frac{5}{1}*\frac{1}{7}=\frac{5*1}{1*7}=\frac{5}{7}[/tex]

both are the same result, so your answer is Choice B.

Answer:

The confidence interval = ($47.41, $53.39)

Step-by-step explanation:

Confidence Interval formula

= Mean ± z × Standard deviation/√n

Mean = $50.40

Standard deviation = $12.30

z score for a 95% confidence interval = 1.96

n = 65

Confidence Interval = $50.40 ± 1.96 × $12.30/√65

= $50.40 ± 2.9902293815

Confidence Interval =

$50.40 - 2.9902293815 =

47.409770618

≈$47.41

$50.40 + 2.9902293815 = 53.390229381

≈$53.39

Therefore, the confidence interval = ($47.41, $53.39)

Answer:

864

Step-by-step explanation:

let's take side of the cube as C. then volume of the cube will be C^3. we know that C^3 is 1728 inches. so C = 12. total surface area of a cube is 6*C*^2. so that is equal to 6×12×12 = 864

Answer:

D) $18,000

Step-by-step explanation:

A company has found that its expenditure rate per day (in hundreds of dollars) on a certain type of job is given by

E'(x) = 10x + 11,

where x is the number of days since the start of the job.

Find the expenditure if the job takes 5 days.

Step 1

We Integrate

E(x) =∫E'(x) dx

=∫[10(x) + 11] in hundreds of dollars

(5x² + 11x + c) in hundreds of dollars

Step 2

(5x² + 11x + c) in hundreds of dollars

x is the number of days since the start of the job.

x = 5

5x² + 11x

[5(5)² + 11(5)] in hundred of dollars

= [5 × 25 + 55] in hundreds of dollars

=[ 125 + 55] in hundreds of dollars

=[180] in hundreds of dollars

Hence the expenditure is 180 in hundreds of dollars

This means, 180 × $100

= $18000

Therefore, the expenditure costs $18,000

Answer:

The critical region is t ≥ t(0.025, 7) = 2.365

Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.

Step-by-step explanation:

We set up our hypotheses as

H0: β= 0   the two variable X and Y are not related

Ha: β  ≠ 0. the two variables X and Y are related.

The significance level is set at α =0.05

The test statistic if, H0 is true, is  t= b/s_b

Where   Sb =S_yx/√(∑(X-X`)^2 )

Syx = √((∑(Y-Y`)^2 )/(n-2))

In the given question we have the estimated regression line as y= 0.449x - 30.27

X Y X2         Y2      XY

72 3 5184 9    216

85 7 7225 49    595

91 10 8281 100      910

90 10 8100 100      900

88 8 7744 64       704

98 15 9604 225      1470

75 4 5625 16       300

100 15 10000 225       1500

80 5 6400 25        400        

∑779 77 68163 813 6995

Now finding the variances

∑(Y-Y`)^2  = ∑〖Y^2- a〗 ∑Y- b∑XY

                      = 813 – (- 30.27)77 - 0.449(6995)

                       = 813+2330.79 – 3140.755

                       = 3.035

∑(X-X`)^2 =  ∑X^2  – (∑〖X)〗^2 /n

                   = 68163 – (779)2/9

                    = 736.22

Syx = √((∑(Y-Y`)^2 )/(n-2))  = √(3.035/7) = 0.65846 and

Sb =S_yx/√(∑(X-X`)^2 ) = (0.65846  )/27.13337 = 0.024267

t= b/s_b  = 0.449/ 0.024267 = 18.50249

The critical region is t ≥ t(0.025, 7) = 2.365

Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.

Answer:

The answer to this question can be defined as follows:

The Lower sum ="0.659"

The Upper sum ="0.859"

Step-by-step explanation:

In the given equation there is some mistype error, so the correct equation and its solution can be defined as follows:

Equation:

[tex]y= \sqrt{1-x^2}[/tex]

calculating the Δx:

[tex]=\frac{(1 - 0)}{5}\\\\=\frac{1}{5}[/tex]

calculating the Upper sum value:

[tex]=\bigtriangleup x \times (f(0) + f(\frac{1}{5}) + f(\frac{2}{5}) + f(\frac{3}{5}) + f(\frac{4}{5})) \\\\= \frac{1}{5} \times (1 + \sqrt{(\frac{24}{25})} + \sqrt{\frac{21}{25}} + \frac{4}{5} + \frac{3}{5})\\\\= 0.859[/tex]

calculating the Lower sum value:

Answer:

The upper sum value is 0.8592

The lower sum value is 0.6592.

Step-by-step explanation:

Given information:

The equation [tex]y=\sqrt{1-x^2}[/tex]

And [tex]n=5[/tex]

now, first find derivative of the above equation:

As, [tex]\Delta x=(1/5)\\\Delta x=0.2[/tex]

Now calculate the upper sum value as :

[tex]U=0.2[\sqrt{1-0}+\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}]+ \sqrt{1-0.8^2}\\U=0.2\times 4.296\\U=0.8592\\[/tex]

Hence, the upper sum value is 0.8592

Now ,calculate the lower sum value as:

[tex]L=0.2[\sqrt{1-0.2^2}+\sqrt{1-0.4^2}+\sqrt{1-0.6^2}+\sqrt{1-0.8^2}+\sqrt{1-1^2}]\\L= 0.2\times 3.296\\L=0.6592\\[/tex]

Hence, the lower sum value is 0.6592.

For more information visit:

https://brainly.com/question/22983262

Answer:

The square root of 4 is 2(not irrational)

The square root of 100 is 10(not irrational

Step-by-step explanation:

Step-by-step explanation:

5x+3x=12+4

8x=16

x=16÷8

x=2

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{5x - 4 = - 3x + 12}[/tex]

Move 3x to left hand side and change it's sign

⇒[tex] \sf{5x + 3x - 4 = 12}[/tex]

Move 4 to right hand side and change it's sign

⇒[tex] \sf{5x + 3x = 12 + 4}[/tex]

Collect like terms

⇒[tex] \sf{8x = 12 + 4}[/tex]

Add the numbers

⇒[tex] \sf{8x = 16}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8x}{8} = \frac{16}{8} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

-7 is the lowest number, since it is a negative. The absolute value of -2, or |-2|, is 2 making it the second lowest. 3 comes next. The absolute value of 4.5 is 4.5, being the greatest number.

Answer:

-7, |-2|, 3, |4.5|

Step-by-step explanation:

First, let's find -2 and |4.5| .

Absolute value of a number is its distance from 0. Remember, absolute value is always zero or positive.

Now, let's use a number line to order the numbers. Numbers to the left are less than numbers to the right.

The values in order from least to greatest is as follows: -7, |-2|, 3, |4.5|.

a.   Since a line doesn't have endpoint, it doesn't matter which

two points we use to name a line so we could call this line DC.

b.   A ray is a figure that starts at and endpoint and continues

forever in one single direction. So a ray here would be ray AB.

c.   Opposite rays are two rays that share a common endpoint,

have no other points of intersection, and all points are collinear.

So ray EC and ray ED would be opposite rays.

A) Line names are made using two letters, since line CD passes through E, line CD could be renamed CE

B) a Ray has one end point and goes in one direction. If A is the endpoint, the line goes through point B

The Ray would be AB with an arrow pointing to the right above the letters.

C) Opposite rays create a straight line and have the same point.

Ray ED is opposite EC

Answer:

Total cost of x students tuition = $2,800x

Step-by-step explanation:

Total cost of x students tuition

= Amount of tuition × number of students

Amount of tuition= $2,800

Number of students = x

Total cost of x students tuition

= Amount of tuition × number of students

= $2,800 * x

= $2,800x

Total cost of x students tuition = $2,800x

For example, if there are 2 students in total

Total cost of x students tuition = $2,800x

When x= 2

= $2,800 × 2

= $5,600

Total Cost of students paying tuition of $2,800 each is $5,600

Answer:

50 seconds

Step-by-step explanation:

2 boxes in 5 seconds

20÷2=10

10×5=50

50 seconds = 20 pizza boxes

Answer:

50

Step-by-step explanation:

2=5secs

20=?

to make 20 from 2 you do =2×10

so,

5×10=50seconds is the time he would take to assemble 20pizza boxes

Some integers are irrational is false

Answer:

A.) Some integers are irrational

Step-by-step explanation:

Integers are natural numbers, their opposites, and zero. (-2,-1,0,1,2)

Natural numbers, whole numbers, and integers are all rational numbers.

Irrational numbers cannot be written as quotients of integers, and they have decimal representations that do not repeat or terminate ([tex]\sqrt{2},\pi[/tex]).

The other statements are true

Answer:

yes it think

Step-by-step explanation:

You are correct. A statistical question is one where you apply things like random sampling and averages to answer questions such as choice B. With that many people, there's variability in the height so there isn't one set height. So instead we have an average height.

The other questions are simple straightforward answers that don't require statistics. There isn't any variability in the dataset for these types of questions.

Answer:

(If they were talking about 3,335, then) 100 times greater

(If they were talking about 3,335 then) 10 times greater

Step-by-step explanation:

When you visualize it, ignore the other numbers and think of only the threes.

Count how many spaces/places they are from each other, and that's how many 0s you should put after a 1 as your answer.

Same as decimal moving and multiplying by 10's.

Answer:

Infrared light

Step-by-step explanation:

Infrared cameras capture heat signals from living or warm objects. Body heat is given off as infrared energy; our natural eyes can't see it.

Answer:

Infra-red Light

Step-by-step explanation:

Answer:

5x - 2 = 8

5x = 8 + 2

5x = 10

x = 10/5

x = 2

Answer:

65x and 32 that your answer

65x and 32 is your answer to the question.

Answer:

E.

Step-by-step explanation:

6^2=x^2+3^2

X^2=36-9

X=

[tex] \sqrt{27} [/tex]

a.

   x   -  the length of the shorter piece

b.

   twice as large means:

   2x  -  the length of the loger piece  

   so:

      x + 2x  - the sum of length of pieces {total of rope}

the equation:   x + 2x = 36

c.

  x + 2x = 36

     3x = 36

    ÷3     ÷3

     x = 12 ft

2x = 2×12 = 24 ft

The length of the shorter piece is 12 ft

The length of the loger piece is 24 ft

Answer:

Profit from selling n cakes = $6.75n - $86

Profit from selling 25 cakes = $82.75

Step-by-step explanation:

You are selling cakes at a bake sale for $6.75 each.

You spend $86 to buy ingredients and supplies.

Profit from selling n cakes is;

Profit = Selling price - cost price

Profit = $6.75n - $86

Profit for selling 25 cakes is;

Profit = $6.75(25) - $86 = $82.75

Answer:

B.) translation and rotation

Step-by-step explanation:

Answer:

B

Step-by-step explanation: