Rafael writes an expression to represent “a number, n, decreased by thirty-one.” Then he evaluates that expression if n = 29. Which statements are true about the expression and its evaluation? Check all that apply.
The correct expression is 31 minus n.
This is a subtraction expression.
This is an addition expression.
To evaluate, substitute 29 for the variable in the expression.
To evaluate, substitute 31 for the variable in the equation.
To evaluate the expression, add 31 to 29.
The correct expression is n minus 31.
To evaluate the expression, subtract 31 from 29.


Please hurry I need this answer ASAP

Answer:

1/2

Step-by-step explanation:

First create like dominators

2/3 -1/6  = 4/6 - 1/6

simplify using subtraction

4/6 - 1/6 = 3/6

Simplify the answer

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

2/3 - 1/6

Subtract the two fractions:

2/3 - 1/6 = 1/2

The answer we get is:

1/2

Divide the numerator by the denominator for the decimal form:

1 ÷ 2 = 0.5

0.5 is our decimal form.

1/2 and 0.5 are our answers.

Hope you learned from this answer!

Answer:

(a) 0.6579

(b) 0.2961

(c) 0.3108

(d) 240

Step-by-step explanation:

The random variable X can be defined as the number of particles in a suspension.

The concentration of particles in a suspension is 50 per ml.

Then in 5 mL volume of the suspension the number of particles will be,

5 × 50 = 250.

The random variable X thus follows a Poisson distribution with parameter, λ = 250.

The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.  

The mean of the approximated distribution of X is:

μ = λ  = 250

The standard deviation of the approximated distribution of X is:

σ = √λ  = √250 = 15.8114

Thus, [tex]X\sim N(250, 250)[/tex]

(a)

Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:

[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]

                             [tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]

Thus, the value of P (235 < X < 265) = 0.6579.

(b)

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]

                             [tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]

Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].

(c)

A 10 mL sample is withdrawn.

Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:

[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]

                             [tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]

Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].

(d)

Let the sample size be n.

[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]

                             [tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]

The value of z for this probability is,

z = 1.96

Compute the value of n as follows:

[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]

Thus, the sample selected must be of size 240.

Answer:

true

Step-by-step explanation:

it equals to

x1= -1

and

x2= 1

Answer:

Step-by-step explanation:

y=x²-1 is not a function for every value of y , x has more than one value

ex: if x=-1 , y=(-1)²-1 then y=0

if x=1 then y=0

Answer:

The first order.

Step-by-step explanation:

What do these symbols mean?

The funny shaped line is a square root, meaning what times itself (so for example, 3 x 3) gets that number. So the square root of 9=3.

The small 2 in the top right of the big numbers means square. The opposite. This means multiply that big number by itself twice. If the small number was say, 7, you would multiply the big number by itself 7 times. A common mistake is propel multiply the big number by the small number. The square used in these is 2 to the power of 3, the small number. This means you do 2x2x2, as the small 3 determines how many time you multiply the big number, 2. The result of 2x2x2=8.

The fraction is 11/9. The 9 means how many parts are in a whole number. The 11 means how many of those parts you actually have. Like a pizza-if you had a pizza (the whole) split into 7 parts, 7 would be your bottom number (as the 9 is here). If you are 4 parts and were left with 3 parts, 3 would be your top number (as the 11 is here). Seeing as 11 is bigger than 9, you have to imagine 2 pizzas. Each is split into 9, and you have 11 parts altogether. Thsi is 1 whole pizza and 2 extra parts, making the fraction 1 and 2/9. This is jaut another way to write 11/9 but I find it easier to look at.

The answer?

So. We have established that 11/9 = 1 & 2/9

And that 2 cubed (with the small 3 on it) = 8.

Amd the square roots of 5, 11 and 20 are approximately (Not exactly, but close enough) the following:

5. 2.2

11. 3.3

20. 4.4

So this leaves us a bunch of numbers to put in order from smallest to largest. This is fairly easy. It's not the second one. 8>3.3. It's not the third one. 8>2.2. It's not the fourth one. 1 & 2/9 may be smaller than 8, but 2.2 isn't. So this leaves the first order.

*Note that the symbol > means greater than or bigger than. So 8>2 means 8,is bigger than 2.

Answer:

-5

Step-by-step explanation:

[tex] \frac{3 - 8}{3 - 2} [/tex]

[tex] \frac{ - 5}{1} [/tex]

[tex] - 5[/tex]

Answer:

C

Step-by-step explanation:

We want to write the equation of a line that is parallel to:

[tex]y=\frac{3}{5}x+8[/tex]

And also passes through (-10, 4).

Remember that parallel lines have the same slope.

The slope of our old line is 3/5.

Therefore, the slope of our new line is also 3/5.

We know that it passes through (-10, 4). So, we can use the point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is a point.

So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:

[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]

Simplify:

[tex]y-(4)=\frac{3}{5}(x+10)[/tex]

Distribute on the right:

[tex]y-4=\frac{3}{5}x+6[/tex]

Add 4 to both sides:

[tex]y=\frac{3}{5}x+10[/tex]

So, our answer is C.

And we're done!

Step-by-step explanation:

Hey there!

The equation of a st.line passing through point (-10,4) is ;

(y-y1)= m1(x-x1) [one point formula]

Put all values.

(y - 4) = m1( x + 10)..........(i)

Another equation is; y = 3/5 + 8.............(ii)

From equation (ii)

Slope (m2) = 3/5 [ By comparing equation with y = mx+c].

As per the condition of parallel lines,

Slope of equation (i) = slope of equation (ii)

(i.e m1 = m2 )

Therefore, the value of m1 is 3/5.

Putting value of slope in equation (i).

[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]

[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]

[tex](y - 4) = \frac{3}{5} x + 6[/tex]

[tex]y = \frac{3}{5} x + 10[/tex]

Therefore the required equation is y = 3/5x + 10.

Hope it helps...

Answer:

$37.8125

Step-by-step explanation:

$2.75 x 12.5 = 34.375

34.375 x 10% = 3.4375

$34.375 + 3.4375 = 37.8125

Answer:

He would need to work 8 weeks for 2300, 16 for 6400, and 22 for 8800

Step-by-step explanation:

You have to divide 3,200 by 400 since thats how much he makes in a week

that gives you 8

and you do the same for the rest

equation:

money wanted/400=weeks

Answer:)

he work for 8 weeks to earn 3,200

he needs to work 8 more weeks to earn 6,400

he needs to work 14 more weeks to earn 8,800

Step-by-step explanation:

Answer:

IM BACK!!!!

The answer is *DRUMROLLLLLLLL* B

jk

its 1 lol

Step-by-step explanation:

Plug in -8 to x and you end up multiplying -8 by 1/2 which is pretty simple but the Muhammad ibn Musa al-Khwarizmi guy invented Algebra, Gottfried Wilhelm Leibniz invented functions, and Brahmagupta of India invented addition, so thanks to them, you can solve this question. -8 times 1/2 is -4 and -4 plus 5 equals 1.

Hope this helps

Answer:

Explained below.

Step-by-step explanation:

A Binomial experiment has the following properties:

If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.

The number of employees selected is, n = 20.

Every employees response is independent of the others.

Each employees response is either: Yes or No.

The probability of an employee responding as "yes" is, p = 0.31.

Thus, the experiment being performed is a binomial experiment.

So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.

But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.

Answer:

18

Step-by-step explanation:

count

The number of students measured in this sample is 18.

The number of students measured is the number of heights that were acquired for the sample.

Looking at the question, the number of heights acquired were 18 which means that there were 18 students.

Knowing the number of students is important as it can help you calculate things such as mean:

Mean = Sum of heights / Number of students

= (75 + 72 + 72 + 73 + 74 + 65 + 69 + 74 + 70 + 70 + 71 + 75 + 71 + 75 + 69 + 75 + 78 + 70) / 18

= 72.11

In conclusion, the number of students measured is 18.

Find out more at https://brainly.com/question/20855935.

Answer:

[tex]\frac{3}{7}[/tex]

Step-by-step explanation:

20% male and 30% female. 20% + 30%= 50% It is asking us what members participating was female. *50% out of 100%

> [tex]\frac{30}{70}[/tex] reduce or divide by 10 we get our fraction and answer, [tex]\frac{3}{7}[/tex].

Answer:

X=21 and Y=121

Step-by-step explanation:

With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.

To solve this problem algebraically we want to add (3x-4)  and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like [tex]3x+6x-5-4=180[/tex]. We then want to add like terms which will leave us with [tex]9x-9=180[/tex]. Now we want to get 9x by itself by adding 9 on each side which leaves us with [tex]9x=189[/tex]. To isolate x we need to divide on each side by 9 which finally leaves us with [tex]x=21[/tex]

Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: [tex]y=6x-5[/tex] and with the value of x found we can plug in the value to get [tex]y=6(21)-5[/tex] which simplifies to [tex]y=126-5[/tex] then to [tex]y=121[/tex].

Answer:

Total area = 141,

the trapezoid = 117, the triangle=24

Answer:

whats rhe question my g

Answer:

2

Step-by-step explanation:

If 1 = 1.5

2 = 3

That is the answer

Answer: 3 cups will make 4.5 cups of cooked rice.

Step-by-step explanation: 3 * 1.5

Answer:

a. 80 students

b. 92 students

Step-by-step explanation:

Represent arts students with A and Dance students with D.

So, we have,

n(A) = 35

n(D) = 57

Required

Determine n(A or D)

Solving (a):

Here, we have:

n(A and D) = 12

n(A or D) is calculated as thus:

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 12

n(A or D) = 80

b. From the given details

n(A and D) = 0 because both students are not mixed up as in (a) above

Using the same formula as (a).

n(A or D) = n(A) + n(D) - n(A and D)

n(A or D) = 35 + 57 - 0

n(A or D) = 92

Answer:

[tex]\sqrt{34}[/tex] or 5.83095

Step-by-step explanation:

Use the distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }[/tex]

Make sure to round the answer appropriately if not asked for in square root form!!

Answer:

I think it's C

Step-by-step explanation:

I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'

Answer: 50

Step-by-step explanation: All you need to do is subtract $100 from $150, and you'll get 50 as your answer. Hope this helps!

Answer:

1 13/ 24

Step-by-step explanation:

2-1=1

5/8 - 1/12=26/48 =13/24

Answer:

x = 9

Step-by-step explanation:

6x + 7 = -x + 70

~Subtract 7 to both sides

6x = -x + 63

~Add x to both sides

7x = 63

~Divide 7 to both sides

x = 9

Best of Luck!

Answer:

x=1

Step-by-step explanation:

i believe its asking at which point is the output the same and when x=1 they both output 3

Answer:

the function would look like: f(x)=(x³+3)-1

the graph would literally look like the cubic parent graph, just shifted 3 left and 1 down

Answer:

C:      7(x+2)-3x = 2/3(6x+3)

Step-by-step explanation:

Graphing both lines shows that they are parallel to each other.

Answer:

There ya go love

Step-by-step explanation:

Answer:

Step-by-step explanation:

You know that all of the angles of a triangle have to add to equal 180°.

Therefore, (3x)+(2x+20)+(4x-20)= 180°

If you combine like terms you get:

9x=180°

Divide both sides by 9 to get:

X=20