6x - y = 5
3x + y = 4

Answer:

a) [tex] p = 0.5[/tex]

b) [tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

c) [tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

Step-by-step explanation:

Part a

For this case we don't have any prior info given so then the probability assumed for this case is:

[tex] p = 0.5[/tex]

Part b

For this case the proportion of success is given by:

[tex] \hat p= \frac{X}{n}= \frac{154}{329}= 0.468[/tex]

Part c

The confidence interval for the true proportion would be given by this formula

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For the 90% confidence interval the value of and , and the critical value would be given by:

[tex]z_{\alpha/2}=1.64[/tex]

The confidence interval is given by:

[tex]0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423[/tex]

[tex]0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513[/tex]

And the 90% confidence interval for the true proportion is given by (0.527;0.593).

Answer:

113.1

Step-by-step explanation:

d= 2r

r = 6

area = [tex]\pi r^{2}[/tex] = 36 x [tex]\pi[/tex] = 113.09

Answer:

Step-by-step explanation:

The population average number of raisins per box is 30.

The type of statistical analysis to be run here is the inferential statistical analysis and its assumptions include normality, linearity and equality of variance.

Null hypothesis: Average number of raisins per box is 30: u = 30

Alternative hypothesis: Average number of raisins per box is not 30: u ≠ 30

To perform a two tailed single sample test, we have

z statistic = (the sample mean - hypothesized mean) / (SD/√n)

sample mean = 28.05, SD = 3.87 hypothesized mean = 30 n = 36

Thus, we have 28.05 - 30 / (3.87/√36)

= -1.95 / (3.87/6)

= -1.95 / 0.645

= -3.023

we say this is a left tailed test and use the negative z table

where -3.02 = 0.0013

To determine whether the average number of raisins per box differs from the expected 30.

Using p < 0.05, since the observed value 0.0013 is less than 0.05, we conclude the the average number of raisins per box differs from the expected 30.

Answer:

Step-by-step explanation:

Let S and L represent the numbers of short- and long-sleeved shirts ordered.

The expected earnings were ...

  5S +10L = 1750

The number sold was ...

  (1/3)S + (1/2)L = 100

We can multiply the first equation by 1/5 and the second equation by 6 to put the equations into standard form:

Subtracting the second equation from twice the first gives ...

  2(S +2L) -(2S +3L) = 2(350) -(600)

  L = 100 . . . . . . simplify

  2S +3(100) = 600

  S = 150

150 short-sleeved and 100 long-sleeved shirts were ordered.

Answer:

b

Step-by-step explanation:

i did it on edge

Answer:

rawl- 8 years old

mile- 24 years old

jerry- years old

Step-by-step explanation:

Answer:

cube game

Step-by-step explanation:

one of them wins every time

A number cube is rolled. Player 1 gets a point for any number that is 3 or higher, and player 2 gets a point for any number less than 3

If a number cube is rolled and Player 1 gets a point for any number that is 3 or higher and Player 2 gets a point for any number less than 3 it wouldn't be fair to Player 2 because Player 1 has a higher chance of getting points because he/she has more opportunities.

I hope this is correct

Answer:

b

Step-by-step explanation:

Answer:

3.375 bags of soil are needed for Paj to fill the flower pot

Step-by-step explanation:

This question can be solved using a rule of three.

One bag contains 2 + (2/3) = (8/3) cubic inches of soil. How many bags are needed to fill 9 cubic inches of soil?

1 bag - (8/3) cubic inches

x bags - 9 cubic inches

[tex]\frac{8x}{3} = 9[/tex]

[tex]8x = 27[/tex]

[tex]x = \frac{27}{8}[/tex]

[tex]x = 3.375[/tex]

3.375 bags of soil are needed for Paj to fill the flower pot

Paj needs 3.375 bags of soil to fill the bag.

Each bag contains 2²/₃ inch³ of soil and they need to fill up a 9 inch³ pot of soil.

First convert the mixed fraction to an improper one:

2²/₃ = 8/3

The number of bags needed is:

= Volume of pot / Quantity of soil in each bag

= 9 ÷ 8/3

= 9 x 3/8

= 3.375 bags of soil

Paj therefore needs 3.375 bags of soil to fill the pot

Find out more at https://brainly.com/question/17205287.

Answer:

t=411

Step-by-step explanation:

t+55=466

466-55

Subtract the numbers

t=411

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

27 cubic meters

Step-by-step explanation:

The surface area of this cube is 54 square meters.

Given a cube of side length s,

Therefore:

[tex]6s^2=54\\s^2=54/6\\s^2=9\\s=\sqrt{9}\\ s=3$ meters[/tex]

Volume of a Cube of side length s [tex]=s^3[/tex]

Volume of the cube [tex]=3^3[/tex]

=27 cubic meters

The volume of the cube is 27 cubic meters.

Answer:

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution 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.

10% of his customers buy a magazine

This means that [tex]P = 0.1[/tex]

What is the probability that exactly 5 out of the first 13 customers buy a magazine?

This is P(X = 5) when n = 13. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055[/tex]

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Answer:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Step-by-step explanation:

Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:

[tex]X \sim Binom(n=13, p=0.1)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

We want to find this probability:

[tex] P(X=5)[/tex]

And using the probability mass function we got:

[tex] P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554[/tex]

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Step-by-step explanation:

Answer:

g=56

Step-by-step explanation:

In similar shapes, corresponding sides are always in the same ratio.

For example,

if the sides in triangle 1 were a and b, and triangle 2 had side lengths c and d, c and a had the same ratios, and b and d had the same ratios

and triangle 1 was similar to triangle 2, the ratio between the sides of the triangles would be

a/c, which is also equal to b/d

What that means is that in this situation, 8/5=g/35.

8/5=g/35

Cross multiply.

(8)*(35)=g*(5)

280=5g

g=56

Answer:

2 nickels

6 quarters

Step-by-step explanation:

Let quarters be 3x and nickels be $x

if Mark had 3 times as many quarters as nickels, and if he had $1.60 in all, than

( 0.25)3x + 0.05x=1.6

0.75x+ 0.05x=1.6

0.8x=1.6

x=1.6/0.8

x=2 nickels

and 3 (2)=6 quarters

Answer:

There are 4 quarters and 12 nickels.

Step-by-step explanation:

A quarter is equal to $0.25.

A nickel is equal to $0.05.

Let the number of nickels be y.

Let the number of quarters be x.

Mark had 3 times as many quarters as nickels. This means that:

y = 3x

3x represents the number of nickels.

We are told that he had $1.60 in all. This means that:

0.25x + 0.05y = 1.60

=> 0.25x + 0.05 * 3x = 1.60

0.25x + 0.15x = 1.60

0.40x = 1.60

=> x = 1.6 / 0.4 = 4

Therefore:

y = 3 * 4 = 12

There are 4 quarters and 12 nickels.

Answer:

Step-by-step explanation:

Answer:

40 miles

Step-by-step explanation:

In the attached diagram, Point A is the starting point and C is the end point. We want to determine the distance from A to C.

The path driven forms a right triangle in which AC is the hypotenuse.

We therefore use the Pythagorean Theorem to solve for the AC.

Pythagorean Theorem: [tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

[tex]|AC|^2=32^2+24^2\\|AC|^2=1600\\|AC|=\sqrt{1600}\\ |AC|=40$ miles[/tex]

The  straight  line distance from the starting point is 40 miles.

Answer:

None of the inequalities are correct if p = 3.4

Step-by-step explanation:

Mathematical inequality is an order relation proposition existing between two algebraic expressions connected through the signs: unequal than ≠, greater than>, less than <, less than or equal to ≤, as well as greater than or equal to ≥, resulting in both expressions of different values. That is, an inequality is a relationship that exists between two quantities or expressions and, which indicates that they have different values.

To check an inequality, you must replace the inequality variable with the value of the solution.  In this case, being p=3.4, you must do it with each of the inequalities, as shown below:

A. 3p<10.2 ⇒ 3*3.4<10.2 ⇒ 10.2 <10.2  

This inequality is not true, because 10.2 is not less than 10.2, but they are equal.

B. 13.6<3.9p ⇒ 13.6<3.9*3.4 ⇒ 13.6<13.26  

This inequality is not true, because 13.6 is greater than 13.26 and not less as the inequality shows.

C. 5p>17.1 ⇒ 5*3.4 >17.1 ⇒ 17 > 17.1  

This inequality is not true, because 17 is less than 17.1 and not greater as the inequality shows.

D. 8.5> 2.5p ⇒ 8.5 >2.5*3.4 ⇒ 8.5 > 8.5

This inequality is not true, because 8.5 is not less than 8.5. These values ​​are the same.

None of the inequalities are correct if p = 3.4

The correct answer is C. By substituting the greatest number in each set for p, you can quickly tell which sets make the inequality false.

Answer:

Step-by-step explanation:

Given that :

sample mean = 4.001 inches

sample standard deviation = 0.002 inch

a.

[tex]C_{pk} = min [\dfrac{(USL- \bar X)}{(3*std \ dev)} \ ; \ \dfrac{ (\bar X- LSL)}{(3*std \ dev)}][/tex]

specification = [tex]4 \pm 0.003[/tex]

Upper specification limit USL = 4 + 0.003  = 4.003

Lower specification limit LSL =  4 - 0.003 = 3.997

[tex]\dfrac{ (\bar X- LSL)}{(3*std \ dev)} = \dfrac{ (4.001-3.997)}{(3*0.002)}[/tex]  [tex]= 0.667[/tex]

[tex]\dfrac{(USL- \bar X)}{(3*std \ dev)} =\dfrac{(4.003-4.001)}{(3*0.002)}[/tex][tex]= 0.333[/tex]

Thus ;

[tex]C_{pk} =[/tex][tex]min (0.333 , 0.667)[/tex]  = 0.333

[tex]C_{pk}[/tex]  is a measure of closeness to one's target and the consistency around the average performance.

b) No, C - spec should not use this machine to produce this part because [tex]C_{pk}[/tex] <  1.33 which typical means that the part is not fully capable of hitting the target specification on a consistent basis .

Answer:

5 hours

Step-by-step explanation:

Here we can create an equation to solve for the number of hours (x) this man can skate for.

Since he has to pay a $9 flat fee, that will be a constant value or our y-intercept in this case.

Our equation will be y = 2x + 9

Since we know his budget is $19, we can set our equation equal to 19, or replace y in this case.

So now we have 19 = 2x +9

Now we need to subtract 9 from both sides to get 10 = 2x

Then we need to divide both sides by 2 to get 5 = x

So this man can skate for 5 hours considering his budget

By the chain rule,

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}[/tex]

We have

[tex]w=7ye^x-\ln z\implies\begin{cases}\dfrac{\partial w}{\partial x}=7ye^x\\\\\dfrac{\partial w}{\partial y}=7e^x\\\\\dfrac{\partial w}{\partial z}=-\dfrac1z\end{cases}[/tex]

and

[tex]\begin{cases}x=\ln(t^2+1)\\y=\tan^{-1}t\\z=e^t\end{cases}\implies\begin{cases}\dfrac{\mathrm dx}{\mathrm dt}=\dfrac{2t}{t^2+1}\\\\\dfrac{\mathrm dy}{\mathrm dt}=\dfrac1{t^2+1}\\\\\dfrac{\mathrm dz}{\mathrm dt}=e^t\end{cases}[/tex]

Putting everything together, we get

[tex]\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{14ye^xt}{t^2+1}+\dfrac{7e^x}{t^2+1}-\dfrac{e^t}z[/tex]

[tex]x=\ln(t^2+1)[/tex], so [tex]e^x=e^{\ln(t^2+1)}=t^2+1[/tex], and [tex]z=e^t[/tex], so [tex]\frac{e^t}z=1[/tex].

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14yt+7-1[/tex]

[tex]\dfrac{\mathrm dw}{\mathrm dt}=14t\tan^{-1}t+6[/tex]

Then when [tex]t=1[/tex], the derivative has a value of [tex]\frac{7\pi}2+6[/tex].

Answer:

(1) 23.55mm³

(2) 340.17in³

Step-by-step explanation:

Volume of a cone is: [tex]V=\frac{1}{3} \pi r^2h[/tex]

'r' - radius

'h' - height

The height of Cone 1 is 10 mm. The Diameter of Cone 1 is 3mm.

Radius is half the Diameter.

[tex]3/2=1.5[/tex]

The radius is 1.5 mm.

[tex]\text {Using 3.14 as pi: }\\V=(1/3)3.14*1.5^2*10\\V=(1/3)3.14*2.25*10\\V=(1/3)70.65\\\boxed{V=23.55}[/tex]

The volume of Cone 1 should be about 23.55mm³.

The height of Cone 2 is 13 in. The Radius of Cone 2 is 5 in.

Using 3.14 as pi:

[tex]V=(1/3)3.14*5^2*13\\V=(1/3)3.14*25*13\\V=(1/3)1020.5\\\boxed {V=340.166666667}[/tex]

340.166666667 ≈ 340.17

The volume of Cone 2 should be about 340.17in³.

Answer:

John have to pay back $23,327.50 at the end of two years

Step-by-step explanation:

Simple Interest (I) = (PRT) ÷ 100

where P = Principal, R = Rate, T= Time

I = ($150500 × 7.75 × 2) ÷ 100

I = ($2332750) ÷ 100

I = $23,327.50

Answer:

A

Step-by-step explanation:

The form for a parabola with vertex form is y=(x-h)^2+k, where h is the x coordinate and k is the y. Therefore, since the x coordinate of the graph is -2, the answer is A. Hope this helps!

Answer:

its A

hop this helps

If the final weight is halved then the mass of the object will be 500,550 grams

1 kg of an object = 1000 grams

If an object weighs a quarter of a kilogram, then

New weight = 1/4(1000) = 250 grams

If  I add one-half of a kilogram to the object, then the new weight will be 750grams

If the final weight is halved then the mass of the object will be 500,550 grams

Learn more on measurement here: https://brainly.com/question/13893070

Answer:

7

Step-by-step explanation:

Answer:

the answer is 7

Step-by-step explanation:

Answer:

erm

Step-by-step explanation:

25

Answer:

9: 89°

Step-by-step explanation:

Inside of a triangle is 180, so 180-39-52=89

I'm sorry I can't answer 10 for you

Answer:

D). The American writer and philosopher, Henry David Thoreau comments that by simplifying one's life, "the laws of the universe will appear less complex."

E). The adrenaline produced in our body during a confrontation leads to two possible responses by the person run away to safety, or stand one's ground and fight.

Explanation:

Punctuation marks are elucidated as the signs and symbols that function to enhance the readability of the sentences and indicate the grammatical construction of the readers. It assists them in understanding the meaning of the sentence more clearly and comprehensively.

In the given sentences, the last two sentence are incorrectly punctuated as they both wrongly employ comma(,) in it. Option D inappropriately punctuates comma(,) in the complex sentence while the last option falsely puts comma before conjunction 'or.' Thus, options D and E are the correct answers.

Answer:

children attended= 114

adults attended= 57

students attended= 82

Step-by-step explanation:

children attended= c

adults attended=  a

students attended=  s

c+s+a = 253

5c + 7s + 12a = 1828

c=2a

2a + s + a =253

5*2a + 7s + 12a = 1828

3a + s = 253

22a + 7s = 1828

s = 253 - 3a

22a + 7(253 - 3a) = 1828

22a - 21a + 7*253 = 1828

a = 1828 - 7*253

a = 57

s = 253 - 3a = 253 - 3*57 = 82

s = 82

c=2a=2*57= 114

c=114