a winery has a vat with two pipes leading to it. the inlet pipe can fill the vat in 6 hours, while the outlet pipe can empty it in 10 hours. how long will it take to fill the vat if both pipes are left open? (in hours)

Answer:

[tex]c < 4[/tex]

Step-by-step explanation:

Move the constant to the right-hand side and change its signs:

[tex]c < 16 - 12[/tex]

Subtract the numbers:

[tex]c < 16 - 12 = c < 4[/tex]

Answer:

Yea you are right.

Step-by-step explanation:

Answer:

[tex]{ \bf{(a).}} \\ { \tt{ {n}^{th} = a + (n - 1)d }} \\ { \tt{ {n}^{th} = 6 + (n - 1) \times - 4 }} \\ {n}^{th} = 10 - 4n \\ \\ { \bf{(b).}} \\ { \tt{ {n}^{th} = - 8 + (n- 1) \times - 7 }} \\ { \tt{ {n}^{th} = -1 - 7n}}[/tex]

Answer:

Step-by-step explanation:

Answer:

a) The mean is of [tex]\mu = 0.16[/tex]

b) The standard deviation is of [tex]s = 0.008[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Question a:

Exactly 16% of all applications were from minority members

This means [tex]p = 0.16[/tex], and thus, the mean is of [tex]\mu = p = 0.16[/tex]

b. Find the standard deviation of p.

2100 open positions, thus [tex]n = 2100[/tex].

[tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

[tex]s = \sqrt{\frac{0.16*0.84}{2100}}[/tex]

[tex]s = 0.008[/tex]

The standard deviation is of [tex]s = 0.008[/tex]

Answer:

1.45 h

Step-by-step explanation:

common factor of 8 and 14 is 2.

every 2km dele takes 15 minutes.

we know this because 15 minutes is 1/4 of an hour and 2km is 1/4 of 8km

14km/2km = 7

7*15 minutes = 1.45 hours

Answer:

1.75 hours/ 1hr 45 min

Step-by-step explanation:

1hr = 8 Km

?? = 14 Km

= (14km × 1hr)/ ( 8km)

= 1.75hours

= 1hr 45min

Answer:

m = -2

Step-by-step explanation:

[tex]\frac{m}{m+4} + \frac{4}{4-m} = \frac{m^2}{m^2-16}\\\\\frac{m}{m+4} + \frac{4}{-(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex]                      [tex][ \ ( 4 - m) = - (m -4) \ ][/tex]

[tex]\frac{m}{m+4} + \frac{-4}{(m-4)} = \frac{m^2}{m^2-16}\\\\[/tex]                        [tex][ \ \frac{a}{-b} = \frac{-a}{b}\ ][/tex]

[tex]\frac{m}{m+4} - \frac{4}{m-4} = \frac{m^2}{m^2-16}\\\\[/tex]                         [tex][ \ \frac{x}{y} + \frac{-a}{b} = \frac{x}{y} - \frac{a}{b} \ ][/tex]

[tex]\frac{m(m-4)-4(m+4)}{(m-4)(m+4)} = \frac{m^2}{m^2-16}\\\\\frac{m^2 -4m -4m-16}{(m^2-16)} = \frac{m^2}{m^2-16}\\\\[/tex]                     [tex][ \ T aking \ LCM \ and \ simplifying\ ][/tex]

[tex]m^2 - 8m -16 = m^2[/tex]                           [tex][ \ \frac{a}{b} = \frac{c}{b} => a = c \ ][/tex]

[tex]m^2 - m^2 - 8m - 16 = 0\\\\0 -8m = 16\\\\-8m = 16 \\\\m = \frac{16}{-8} = -2[/tex]

9514 1404 393

Answer:

  21.5 cm

Step-by-step explanation:

Consider rectangle PQRS. Its area is ...

  A = LW

  90 cm² = PQ×QR = PQ×(20 cm)

  (90 cm²)/(20 cm) = PQ = 4.5 cm . . . . . . BC has this value, too

__

Consider the perimeter of ABCD. It is given by ...

  P = 2(L +W)

  52 cm = 2(AB +BC) . . . . substitute known value for P

  26 cm = AB +4.5 cm . . . . use known value for BC, divide by 2

  21.5 cm = AB

Answer:

x=-16

Step-by-step explanation:

x/4-3=-7

x/4=-4

x=-16

Answer:

787.50

Step-by-step explanation:

interest=3500*7.5*3/100

interest=35*7.5*3

interest=787.50

Answer:

324 yds ^2

Step-by-step explanation:

If length=l and width=w, you could write an equation to find the length and width. Then use that to find the area. L=4w. There are two of each side in the rectangle. 4w+4w+w+w=10w. 10w=90. w=9. 4w=36. L=36. 36*9=324yds^2

Answer:

36cm^2

Step-by-step explanation:

total area: 6x(4+3)=42

total area excluding the space: 42-(2x3)=36

Answer:

36 cm squared

Step-by-step explanation:

To solve this problem, I first construct a line. (shown in yellow in the first photo)

I then find the area of the top rectangle. (6 cm * 4 cm = 24 cm squared.)

Next, I find the area of the lower rectangle. But...to do that I have to find the length of the line that I constructed. To do this, I do  6cm-2cm=4cm.

Then I can find the area of the lower rectangle. (4cm*3cm=12cm squared.)

add up the area of both of the rectangles and.........12+24=36 cm squared

Answer:

add a picture so i can see .

Step-by-step explanation:

Answer:

b is the answer am not sure you know

Answer:

a) 3/10

b)3/10

Step-by-step explanation:

let the sample of people be 10

so,

a) total outcome=10

favourable outcome=3

P(seeing a UFO)= 3/10

b) total outcome=10

favourable outcome=2 or 3

P(seeing a UFO)= 2/10+3/10-(2/10

5/10-2/10

=3/10

Step-by-step explanation:

everything can be found in the picture

9514 1404 393

Answer:

  x^3 -x^2 -17x +12

Step-by-step explanation:

Use the distributive property and collect terms.

   (x +4)(x^2 -5x +3) = x(x^2 -5x +3) +4(x^2 -5x +3)

  = x^3 -5x^2 +3x +4x^2 -20x +12

  = x^3 -x^2 -17x +12

Answer:

The x-intercept is the value of the variable x when the value of the function is equal to zero

so

In the table we have

(-1, 0)(−1,0) is a x-intercept, because

For x=-1x=−1 the value of the function is equal to zero

(-6, 0)(−6,0) is a x-intercept, because

For x=-6x=−6 the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

(-1, 0)(−1,0)

(-6, 0)(−6,0)

Answer:

t=2 plz mark me as brainliest

Step-by-step explanation:

Answer: (X-12)(x+4)

The middle number is -8 and the last number is -48.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -8

Multiply together to get -48

Can you think of the two numbers?

Try 4 and -12:

4+-12 = -8

4*-12 = -48

Fill in the blanks in

(x+_)(x+_)

with 4 and -12 to get...

(x+4)(x-12)

Answer:

(x+4)(x−12)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { (x - 12)(x + 4 )}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] {x}^{2} - 8x - 48[/tex]

[tex] = {x}^{2} + 4x - 12x - 48[/tex]

Taking [tex]x[/tex] as common from first two terms and [tex]12[/tex] from last two terms, we have

[tex] = x \: (x + 4) - 12 \: (x + 4)[/tex]

Taking the factor [tex](x+4)[/tex] as common,

[tex] = (x - 12)(x + 4)[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

Y is -1.

Step-by-step explanation:

If you substitute the values, you find that that's the correct answer.

Answer:

theres the graph

Step-by-step explanation:

Answer:

[tex]\sigma = 12.5[/tex] ---- sample standard deviation

[tex]\sigma^2 = 157.2[/tex] ---- sample variance

Step-by-step explanation:

Solving (a): The sample variance

First, we calculate the midpoint of each class (this is the average of the limits)

So, we have:

[tex]x_1 = \frac{56 + 64}{2} = 60[/tex]

[tex]x_2 = \frac{65 + 73}{2} = 69[/tex]

And so on

So, the table becomes:

[tex]\begin{array}{cc}{x} & {f} & {60} & {11} & {69} & {15} & {78} & {14} & {87} & {4} & {96} & 11 \ \end{array}[/tex]

Calculate the mean

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{60*11+69*15+78*14+87*4+96*11}{11+15+14+4+11}[/tex]

[tex]\bar x = \frac{4191}{55}[/tex]

[tex]\bar x = 76.2[/tex]

The variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]\sigma^2 = \frac{(60 - 76.2)^2*11+(69 - 76.2)^2*15+(78 - 76.2)^2 *14+(87 - 76.2)^2*4+(96 - 76.2)^2*11}{11+15+14+4+11-1}[/tex]

[tex]\sigma^2 = \frac{8488.8}{54}[/tex]

[tex]\sigma^2 = 157.2[/tex]

The sample standard deviation is:

[tex]\sigma = \sqrt{\sigma^2[/tex]

[tex]\sigma = \sqrt{157.2[/tex]

[tex]\sigma = 12.5[/tex]

Solving (b): The sample variance

In (a), we calculate the sample variance to be:

[tex]\sigma^2 = 157.2[/tex]

Answer:

0.1111

Step-by-step explanation:

From the given information;

Number of staffs in the actuary = 80

Out of the 80, 10 are students.

i.e.

P(student actuary) = 10/80 = 0.125

number of weeks in a year = 52

off time per year = 10/52 = 0.1923

P(at work || student actuary) = (50 -10/52)

= 42/52

= 0.8077

P(non student actuary) = (80 -10)/80

= 70 / 80

= 0.875

For a non-student, they are only eligible to 4 weeks off in a year

i.e.

P(at work | non student) = (52-4)/52

= 48/52

= 0.9231

∴

P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)

P(at work) =  (0.125 × 0.8077) + ( 0.875 × 0.9231)

P(at work) = 0.1009625 + 0.8077125

P(at work) = 0.90868

Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)

P(he is a student) = (0.125 × 0.8077) ÷ 0.90868

P(he is a student) = 0.1009625 ÷ 0.90868

P(he is a student) = 0.1111

Answer:

d. The purpose of this research is to study how childhood experiences are related to risk of depression.

Step-by-step explanation:

This answer satisfies the requirements of the question as it uses mild language that will not scare off respondents while also maintaining transparency and truthfulness. This can be seen in wordings such as;

a. Childhood experiences: Instead of explicitly using the term child-hood abuse which can scare off respondents, this phrase uses a milder form of the word that is also not dishonest in itself.

b. Risk of depression: Instead of using heavy terms such as "severe depression," or shady terms like "bad expreciences," the phrase, "risk of depression," helps the subjects to honestly identify what the question is about in a mild way.

Answer:

See below.

Step-by-step explanation:

Problem 2.

Left figure: 2 sides and included angle: SAS

Middle figure: 2 angles and included side: ASA

Right figure: 3 sides: SSS

Problem 3.

CPCTC = corresponding parts of congruent triangles are congruent

Answer:

64 cm^3

Step-by-step explanation:

answer for question no 5

length , breadth and height of the cube are always equal .So

here length = 4 cm

volume of a cube = l^3

=4^3

=64 m^2

Answer:

$0.34/pound

Step-by-step explanation:

1 ton = 2000 pounds

3 tons = 6000 pounds

-------------------------

2040/6000 = $0.34/pound