Lengths of pregnancies​ (in humans) have a mean of 267.6 days and a standard deviation of 15.4 days. A woman tracked her pregnancy and found it to be 309 days. Find the z score for 309 days. Is such a length​ unusual?

Hey there! I'm happy to help!

Let's set this up a system of equations where x represents the number of 10 dollar bills and y represents the number of 20 dollar bills.

10x+20y=440

x=y+2

We see that x has a value of y+2, so we can replace the x in the first equation with y+2 so we can solve for y.

10(y+2)+20y=440

We use distributive property to undo the parentheses.

10y+20+20y=440

We combine like terms.

30y+20=440

We subtract 20 from both sides.

30y=420

y=14

Since there are 2 more $10 bills, there would be 16 of those.

Therefore, there are 16 $10 bills and 14 $20 bills.

Have a wonderful day! :D

Answer:

.15* house price = 28,500

house price = 28,500 / .15

house price =  190,000

Step-by-step explanation:

Answer: 190,000

Step-by-step explanation:

the equation looks like this - .15x=28,500. then you divide both sides by .15 and get x=190,000

the answer is 36.36 but the closest to it is 37

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The tank for a car holds 17 gallons. The gasoline gauge shows the tank is 3/4 full. How much gas is still in the tank?

Give your answer as a whole number or as a mixed fraction reduced to lowest terms.

Answer:

[tex]Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]

Step-by-step explanation:

The tank for a car holds 17 gallons.

The gasoline gauge of the car shows that the tank is 3/4 full.

We are asked to find the remaining gasoline in the tank.

[tex]Gas \: \:left = \frac{3}{4} \times 17 \\\\Gas \: \:left = \frac{51}{4} \\\\Gas \: \:left = 12 \frac{3}{4} \: \:gallons \\\\[/tex]

Therefore, the remaining gas in the tank is [tex]12\frac{3}{4}[/tex] gallons.

Alternatively:

[tex]1 - \frac{3}{4} = \frac{1}{4}[/tex]

Amount of gasoline consumed = [tex]\frac{1}{4} \times 17 = \frac{17}{4}[/tex]

Amount of gasoline left = total - consumed

Amount of gasoline left = [tex]17 - \frac{17}{4} = 12\frac{3}{4} \:\: gallons[/tex]

Answer:

The proportion of these light bulbs that will last less than the advertised time is 18.94% or 0.1894

Step-by-step explanation:

The first thing to do here is to calculate the z-score

Mathematically;

z-score = (x - mean)/SD

= (1500-1550)/57 = -50/57 = -0.88

So the proportion we will need to find is;

P( z < -0.88)

We shall use the standard score table for this and our answer from the table is 0.1894 which is same as 18.94%

Answer:

21.7

Step-by-step explanation:

When anything is 5 or above in a decimal place you round up to the next number for example

2.35 this would round up to be 2.4

21.65

Place value of 1 = ones place

Face value of 1 = 1

Note : The face value of a number will not change at all

Hope it helps you..If it's wrong plz say and I'll try to recorrect it :)

Step-by-step explanation:

It is given that,

Total length of a board is 65 inches

It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.

Let x is the length of other piece and y is the length of first piece such that,

y = 2x-7 ....(1)

Also,

x+y = 65 .....(2)

Put the value of y from equation (1) to equation (2) such that,

x+2x-7 = 65

3x=65+7

3x=72

x = 24 inches

Put the value of x in equation (1)

y = 2(24)-7

y = 41 inches

So, the length of first piece is 41 inches while the length of other piece is 24 inches.

Answer:

first is 18

second is 36

third is -10

fourth is -10

Answer: 4

Step-by-step explanation:

Because %s can be expressed as fractions over 100, because 90 is 70% of x, 70% is 70% of 100.  Thus, 90/x = 70/100.

Hope it helps <3

Answer:

4

Step-by-step explanation:

90 is 70% of x.

90 = 70% × x

90 = 70/100x

Divide both sides by x.

90/x = 70/100

Answer: 45.5

Step-by-step explanation:

Im in 6th grade and all you had to do was add 18.3 and 27.2 and you’ll get 45.5

Answer:

The garbage dump is 58.3 miles west of the hotel, and the hotel is 57.1 miles west of the hardware store. The hardware store is 44.8 miles west of the library. The hardware store is 57.9 miles north of the office supply store, and the office supply store is 55.5 miles north of the science lab.

Step-by-step explanation:

You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.

Answer:  x = ¹/₂ ± √⁸¹

                     ------------

                            2

Step-by-step explanation:

First write out the equation

x² - x - 20

Now we now write the equation by equating to 0

x² - x - 20 = 0

We now move 20 to the other side of the equation. So

x² - x    =  20,

We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes

x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²

x² - ( ¹/₂ )²       = 20 + ¹/₄

( x - ¹/₂ )²       = 20  + ¹/₄, we now resolve the right hand side expression into fraction

( x - ¹/₂ )²          =  ⁸¹/₄ when the LCM is made 4

Taking the square root of both side to remove the square,we now have

x - ¹/₂               =  √⁸¹/₄

x - ¹/₂               =     √⁸¹/₂

Therefore,

                    x = ¹/₂ ± √⁸¹

                          -----------

                               2

Answer:

Step-by-step explanation:

7/5 + 3/4 x 2/5 - 3/2

 7/5 + 3/10 - 3/2

    17/10 - 3/2

         1/5

Step-by-step explanation:

Here, the given polynomial are,

=7/5+3/4×2/5-3/2

multiplying 3/4 and 2/5

= 7/5+6/20-3/2

taking LCM and adding them.

=(7×4+6×1-3×10)/20

by simplifying it we get, the answer is 1/5.

Hope it helps..

Answer:

Quantity (lbs) of type 1 candy  x = 8

Quantity (lbs) of type 2 candy  y = 17,5

Step-by-step explanation:

Let´s call  "x" quantity (in pounds) of candy type 1 in the mixture, and "y" quantity (in pounds ) of candy type 2, then according to the problem statement.

x  +  y  =  25,5

2,20*x  +  7,30*y = 5,70 * 25,5   ⇒  2,20*x  +  7,30*y = 145,35

Then we have a two equation system

x  +  y  =  25,5                                   ⇒   y = 25,5 - x

2,20*x  +  7,30*y = 145,35               ⇒ 2,20*x + 7,30* (25,5 - x ) = 145,35

2,20*x + 186,15 - 7,30*x = 145,35

5,1*x  = 40,8

x = 40,8/5,1

x = 8 lbs

And   y  =  25,5 - 8

y = 17,5 lbs

Answer:

[0, infinity)

Step-by-step explanation:

clarence, I believe you meant y = |3x + 1|.  The absolute value of 3x + 1 is never less than 0, so the range of the given function (above) is [0, infinity).

Answer:

Total Area = [tex]104+16\,\sqrt{13}[/tex]

Step-by-step explanation:

If T.A. stands for Total Area, then we need to add the area of two equal right angle triangles of base 6' and height 4', which give : 2 * (6' * 4'/2) = 24 square feet. tothe area of three rectangles (the lateral faces of this triangular base prism):

[tex](8')*(4')+(8')*(6')+(8')*(\sqrt{6^2+4^2})= 32+48+8\,\sqrt{52} =80+8\,*\,2\,\sqrt{13}=80+16\,\sqrt{13}[/tex]

Therefore the total area of the prism is:

[tex]24+80+16\,\sqrt{13} =104+16\,\sqrt{13}[/tex]

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   8      9     10     11     12     13     14  (number of hours spent)

                dot plot

Answer:

(A) Draw a number line from 8 to 14. Show the frequency of each number. Title the dot plot.

Step-by-step explanation:

so amnt of money is x

x - 5 is Mark's remaining amnt

x - 20 is Susan's remaining amount

x - 5 = 2( x - 20) as he has twice the amnt of Susan

x - 5 = 2x - 40

40 - 5 = 2x - x

35 = x

the original amnt is $35

Answer:

i believe it's 4.5

Step-by-step explanation:

Answer:

14 in. hope this helps!!:)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given:      CS ≅ HR

           ∠CHS ≅ ∠HCR

           ∠CSH ≅ ∠HRC

Prove: CR ≅ HS

ΔCHS ≅ ΔHCR (Angle-Angle-Side, AAS, congruence property)

ΔICR ≅ ΔIHS (congruence property)

IS ≅ IR (similarity property)

CS ≅ HR (given)

Thus,

IC = IS + SC (addition property)

IH = IR + RH (addition property)

IC ≅ IH

Then,

CR ≅ HS (similarity property of triangles SCH and RHC)

Answer

Step-by-step explanation:

Answer:

See the argument below

Step-by-step explanation:

I will give the argument in symbolic form, using rules of inference.

First, let's conclude c.

(1)⇒a  by simplification of conjunction

a⇒¬(¬a) by double negation

¬(¬a)∧(2)⇒¬(¬c) by Modus tollens

¬(¬c)⇒c by double negation

Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.

An alternative approach to De Morgan's law is the following:

By contradiction proof, assume h is true.

h⇒d∨h by addition

(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.  

Answer:

45 min

Step-by-step explanation:

Here,

the we take the work as W and Alan's speed as A and Zack's speed as Z.

A = 2Z

W = 30 ( A+Z)

if the time for Alan to done cleaning alone is t then t = W ÷ A

t = ( 30 (A+(A÷2)))÷ A

t = 45 min

I am done .

Answer:

[tex]\boxed{135\°,315\°}[/tex]

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.

[tex]\theta = 135+180n[/tex]

[tex]n[/tex] is any integer value.

The value of [tex]n[/tex] cannot exceed 1 or be less than 0, because the value of [tex]\theta[/tex] must be between 0 and 360 degrees.

[tex]\theta = 135+180(0)[/tex]

[tex]\theta = 135[/tex]

[tex]\theta = 135+180(1)[/tex]

[tex]\theta = 315[/tex]

Answer:

C

Step-by-step explanation:

It is the graph of f(x) translated 3 units down. Think about in numerical terms,

if      y = 5     y-1  = 5- 1 = 4, so that's what is happening with all numbers on the y axis. You have y = f(x) and you do y-3 = f(x)-3, so, all "y" points are translated 3 units down

Answer:

$4800.25

Step-by-step explanation:

$42603 is a yearly salary.

There are 12 months in 1 year.

Monthly salary:

$42603/12 = $3550.25

Monthly travelling allowance: $1250

Total amount earned in 1 month:

$3550.25 + $1250 = $4800.25

If it has a single zero that means it has to be just touching the x-axis with its tip.

We know that if it has only one zero, the discriminant equals 0.

So,

[tex]D=b^2-4ac=0\implies (-k)^2-4(1)(9)=0[/tex]

Solving for k,

[tex]k=\pm\sqrt{36}=\boxed{\pm{6}}[/tex].

Hope this helps.

Step-by-step explanation:

x² + 11x + 121/4 = 125/4

x² + 11x + 121/4 - 125/4 = 0

x² + 11x - 1 = 0

after that apply quadratic formula

x = ( -b + or - √b² - 4ac ) ÷ 2a

x = (-11 + or - √11² - 4×1×-1 ) ÷ 2×1

+ = 0.090169....

- = -11.090168.....

x = 0.090 or x = -11.09

Answer: B) 22

Step-by-step explanation:

y coordinate of line = 3

y coordinate of point = -19

On a number line, distance between 3 & -19 = 22

Answer:

52 minutes

Step-by-step explanation:

This should be a proportional statement, because if each individual person painted there own wall it should still take 52 minutes.

Answer:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: [tex]\rho =0[/tex]

Alternative hypothesis: [tex]\rho \neq 0[/tex]

The statistic to check the hypothesis is given by:

[tex]t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}[/tex]

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

[tex] t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}[/tex]

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always