An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Suppose a sample of 1519 new car buyers is drawn. Of those sampled, 425 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Answer:

a) Standard error of the mean = 1.433 mm

b) 99% confidence interval = (12.6, 22.2)

c) The precision of the estimate = 4 816

d) The assumptions that are necessary for the validity of the conidence interval constructed include

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.

- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.

Step-by-step explanation:

a) Standard error of the mean is given as

σₓ = (σ/√n)

σ = Sample standard deviation = 4.3 mm

n = sample size = 9

σₓ = (4.3/√9) = 1.433 mm

b) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 17.4 mm

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 9 - 1 = 8.

Significance level for 99% confidence interval

(100% - 99%)/2 = 0.5% = 0.005

t (0.005, 8) = 3.36 (from the t-tables)

Standard error of the mean = 1.433 mm

99% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 17.4 ± (3.36 × 1.433)

CI = 17.4 ± 4.816

99% CI = (12.584, 22.216)

One crate orė

99% Confidence interval = (12.584, 22.216)

c) The precision of the estimate is gven as the length of the, margin of error of the confidence interval. The precision of the estimate = 4.816

d) They include

- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another.

- The sample must be a normal distribution sample or approximate a normal distribution and the best way to establish this is when the population distribution where the sample was extracted from is normal or approximately normal.

Hope this Helps!!!

Answer:

r = -10*cos(t)

Step-by-step explanation:

To write the rectangular equation in polar form we need to replace x and y by:

[tex]x=r*cos(t)\\y=r*sin(t)[/tex]

Replacing on the original equation, we get:

[tex](x+5)^2+y^2=25\\x^2+10x+25+y^2=25\\(r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25[/tex]

Using the identity [tex]sin^2(t)+cos^2(t)=1[/tex] and solving for r, we get that the polar form of the equation is:

[tex](r*cos(t))^2+10*(r*cos(t))+25+(r*sin(t))^2=25\\r^2cos^2(t)+10rcos(t)+r^2sin^2(t)=0\\r^2cos^2(t)+r^2sin^2(t)=-10rcos(t)\\r^2(cos^2(t)+sin^2(t))=-10rcos(t)\\r^2=-10rcos(t)\\\\r=-10cos(t)[/tex]

Answer:

The price per ounce should have been 1.25 per ounce

Step-by-step explanation:

The price per ounce should have been 1.25 per ounce

-google

(found it online)

XD - don't delete/report!

Answer:

1.25

Step-by-step explanation:

Answer:

The mass of half a liter of water is 500g, that is, 0.5kg.

Step-by-step explanation:

Density is mass divided by the volume, that is:

[tex]d = \frac{m}{v}[/tex]

Here, we have to be careful. Since the density is in grams per cm³, m has to be in grams and v in cm³.

We have that:

[tex]d = 1[/tex]

What is the mass of half a liter of water?

One liter is 1000 cm³.

So half a liter is 1000/2 = 500 cm³, which means that [tex]v = 500[/tex]

Then

[tex]d = \frac{m}{v}[/tex]

[tex]1 = \frac{m}{500}[/tex]

[tex]m = 500[/tex]

The mass of half a liter of water is 500g, that is, 0.5kg.

Answer:

0.9099

Step-by-step explanation:

1) =

=

200

800

= .25

2) Identify = . = .23

3) Find the z-value.

=

−

(1−)

=

.25−.23

.23(1−.23)

800

= 1.34

4) The probability is 0.9099.

Answer:1260

Step-by-step explanation:

Kissing has 7 letters, and there are 2 paris of the same letter.

[tex]\frac{7!}{2!2!}[/tex] = [tex]\frac{7*6*5*4*3*2*1}{4}[/tex]= 1260

Answer:

i. Only X and Y kill the bird = 2/5

ii. Only two of them kill the bird= 0.11

iii. Only Z kill the bird= 5/6

iv. Only one of them kill the bird= 1/3

v. None of them kill the bird= 0

vi. All of them kill the bird​= 1

Step-by-step explanation:

Probability of x= 3/5

Probability of y = 2/3

Probability of z = 5/6

i. Only X and Y kill the bird

= 3/5 * 2/3

= 2/5

ii. Only two of them kill the bird

=Either x and y or x and z or y and z

= 2/5 or 1/2 or 5/9

= 0.111

iii. Only Z kill the bird

= 5/6

iv. Only one of them kill the bird

= 3/5 or 2/3 or 5/6

= 1/3

v. None of them kill the bird

0

vi. All of them kill the bird​

1

Answer:

D. SSS theorem

Step-by-step explanation:

The triangles have similarity by 3 sides:

So the answer is SSS

Step-by-step explanation:

[tex]( {n}^{3} )^{2} = {n}^{6} = n \times n \times n \times n \times n \times n [/tex]

Answer:

n x n x n x n x n x n

Step-by-step explanation:

(n^3)^2 = n^6 = n x n x n x n x n x n

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]  

And rounded up we have that n=1076

Step-by-step explanation:

Information given

[tex]ME= 0.025[/tex] represent the desired margin of error

Solution

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by  and . And the critical value would be given by:

[tex]t_{\alpha/2}=-1.64, t_{1-\alpha/2}=1.64[/tex]

The margin of error for the proportion interval is given by this formula:  

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

We can assume that the best estimate for the true proportion is [tex]\hat p=0.5[/tex]. And on this case we have that [tex]ME =\pm 0.025[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex]   (b)  

And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.025}{1.64})^2}=1075.84[/tex]  

And rounded up we have that n=1076

Answer:

See attached

Step-by-step explanation:

Given the numbers 1,2,3,4 and 5

Let O be the event that the number is Odd

Let E be the event that the number is Prime

Then the intersection of Odd and Prime Numbers: [tex]O \cap P =\{3,5\}[/tex]

Since 4 is neither odd nor prime, we place it outside of the two circles.

See the attached diagram for the required Venn diagram.

Answer:

B, C and D

Step-by-step explanation:

Given:

Statement: "Every integer has an additive inverse"

To find: statement that is equivalent to the given statement

Solution:

For any integer x, if [tex]x+y=0[/tex] then y is the additive inverse of x.

Here, 0 is the additive identity.

Statements ''All integers have additive inverses '', '' If x is an integer, then x has an additive inverse'' and  ''Given an integer x, there exists a y such that y is the additive inverse of x'' are equivalent to the given statement "Every integer has an additive inverse".

Answer:

  False

Step-by-step explanation:

Dilation changes the side lengths, but not the angles. The given statement is FALSE.

Answer:

49π m² or 153.94 m²

Step-by-step explanation:

Area of a circle: A = πr²

We are given r as 7, so simply plug it in

A = π(7)^2

A = 49π m²

Answer:

C. 2.75P

Step-by-step explanation:

The original value was P.

It increased by 275%. That means it increased by 275% of P.

275% of P = 2.75P

The increase in value is 2.75P.

Now we add the increase to the original value of P to find today's value.

2.75P + P = 3.75P

Answer: C. 2.75P

Answer:

4 : 3

Step-by-step explanation:

16 : 12 can be simplified by 4 to get 4 : 3

Answer:

[tex]4:3[/tex]

Step-by-step explanation:

[tex]16 : 12[/tex]

The common highest factor of the ratio is 4.

Simplify the ratio.

[tex]16 \div 4:12 \div 4[/tex]

[tex]4:3[/tex]

Answer: £36

Step-by-step explanation:

4 Euros = £3

48 Euros (4x12) = £36 (3x12)

Answer:

£ 36.00

Step-by-step explanation:

£ 3 = € 4

Divide both sides by 4.

£ 3/4 = € 1

1 euro is 3/4 pound.

48 × 3/4 = 36

£ 36 = € 48

48 pounds is 36 euros.

Answer:

He has  2,772 ways

Step-by-step explanation:

Hello,

the teacher has to choose 6 students and there are 11 students in total.

When he chooses the first student he has 11 choices

if he has to choose 1 students he has 11 ways to do it

then for the second one he has 11-1=10 choices

if he has to choose 2 students he has (11*10)/2 ways to do it (we do not count the duplicate - for instance if he chooses Steve and then Nils or Nils and then Steve this is only one group (Steve, Nils) we do not care of the order)

Then for the third student he has 10-1=9 choices

if he has to choose 3 students he has (11*10*9)/(2*3) ways to do it (we do not take into account the order of ppl in the group)

and so on and so forth

...

if he has to choose 6 students he has (11*10*9*8*7*6)/(2*3*4*5)

so he has  2,772 ways

Answer:

C. 462 is correct. I did the test.

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

A).  9.9^2 is close to 10^2 = 100

Round 1.79 to 1.8

So an estimate is 1.8 * 100

= 180.

B).  √97.5 / 1.96

( I am assuming that the square root is of 97.5 only).

is approximately equal to √100 / 2

= 10/2

= 5.

Answer:

They aren't wrong. The program is.

Step-by-step explanation:

The numbers you entered are the answers that matches the correct answers. It is a program error.

Answer:

65

Step-by-step explanation:

We know that,

The Sum of all angles of the triangle is 180°.

As given in the question,

Triangle PQR is similar to Triangle WXY

Therefore ,

Let the third angle be 'x'.

35° + 80° + x = 180°

115 + x = 180°

x = 180° - 115°

x = 65°.

Hence, 65° is the appropriate answer to the question.

I hope my answer helped!!

Answer:

D. d = [tex]\sqrt{58}[/tex]

Step-by-step explanation:

Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2} }[/tex]

The two points are (6, -2) and (3, -9)

Plug the values into the formula:

d = [tex]\sqrt{(3 - 6)^{2}+ (-9 + 2)^{2} }[/tex]

Simplify

d = [tex]\sqrt{(-3)^{2}+ (-7)^{2} }[/tex]

d = [tex]\sqrt{9+ 49 }[/tex]

d = [tex]\sqrt{58}[/tex]

I hope this helps :))

90% of 18% = .9*.18 = 0.162 = 16.2%

So 18 - 16.2 = 1.8 = 18% of them labeled as not defective  

are actually defective.

Please mark me brainliest!

Answer:

1.8%

Step-by-step explanation:

90% × 18% = 16.2%

18% - 16.2% = 1.8%

1.8% is the probability of an incorrect conclusion.

Complete question:

A police car is located 50 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 130 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road.

Answer:

The red car is traveling along the road at 80.356 ft/s

Step-by-step explanation:

Given

Police car is 50 feet side off the road

Red car is 130 feet up the road

Distance between them is decreasing at the rate of 75 feet per sec

Let x be how far the police is off the road.

Let y be how far the red car is up the road.  

Let h be the distance between the police and the red car.

This forms a right triangle so we can use the Pythagorean theorem, to solve for h

h² = x² + y²

h² = 50² + 130²

h² = 19400

h = √19400

h = 139.284 ft

Again;

Let dx/dt be how fast the police is traveling toward the road.

Let dy/dt  be how fast the red car is traveling along the road.

Let dh/dt be how fast the distance between the police and the car is decreasing.

Recall that, h² = x² + y² (now differentiate with respect to time, t)

2h(dh/dt) = 2x(dx/dt) + 2y(dy/dt)

divide through by 2

h(dh/dt) = x(dx/dt) + y(dy/dt)

since the police car is not, dx/dt = 0

and dy/dt is the how fast is the red car actually traveling along the road

139.284(75) = 50(0) + 130(dy/dt)

10446.3 = 0 + 130(dy/dt)

dy/dt = 10446.3 / 130

dy/dt = 80.356 ft/s

Therefore, the red car is traveling along the road at 80.356 ft/s

Answer:

Volume: 1080

Surface area: 654

Step-by-step explanation:

Part A:

How to solve surface Area: 2×(9×15 + 9×8 + 15×8)

How to solve volume: 9x15x8

Part B:

Surface Area

Part C:

Volume

Hope this helps

Answer:

-56/9

Step-by-step explanation:

By Vieta's formulas,

$r + s = -\frac{4}{3}$ and $rs = \frac{12}{3} = 4.$ Squaring the equation $r + s = -\frac{4}{3},$ we get

$r^2 + 2rs + s^2 = \frac{16}{9}.$ Therefore,

$r^2 + s^2 = \frac{16}{9} - 2rs = \frac{16}{9} - 2 \cdot 4 = -\frac{56}{9}}$

Answer:5. 291503

Step-by-step explanation:

√28

2√7

5. 291503

Answer:

after 7 seconds the driver applied the brakes to stop the car.

Step-by-step explanation:

Given:

The position of the car s(t)=[tex]42t-3t^2[/tex]

∴Speed of the car =[tex]\frac{ds}{dt}=\frac{d(42t-3t^2)}{dt}=42-6t[/tex]

When car stopped the speed of car=0

[tex]\Rightarrow42-6t=0\\\Rightarrow6t=42\\\Rightarrow\ t=7[/tex]

Therefore, after 7 seconds the driver applied the brakes to stop the car.

Answer:

B

Step-by-step explanation