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mrs_skeptik [129]
3 years ago
5

A sample of 40 people owned an average of 1.35 hats. It is known from a previous study that the population standard deviation of

hat ownership is 0.63 hats. Construct a 95% confidence interval.
Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

(1,155, 1.545).

Step-by-step explanation:

From Normal distribution tables the z score for 95% CI  = 1.96.

Confidence Interval

= 1.35 +/- 1.96 * 0.63/√40

=  1.35 +/- 0.195

=  (1,155, 1.545).

You might be interested in
I need help asap please!!!!
Brut [27]
So, the easiest thing to do here is to add up the numbers of each option to find the number most similar to the solution of (-4/5)(3/5)(-6/7)(5/6) which is approximately equal to 0.34.
The product of expression A is -0.25
The product of expression B is 0.50
The product of expression C is 3
The product of expression D is -0.05625

So, first of all, we can rule out choices A and D because they are both negative, whereas 0.34 is not. Now, we just have B and C, and clearly, B is much closer to 0.34 than C is, so B is the correct answer. I hope this helps! :)
3 0
3 years ago
the radious of each wheel of a car is 16 inches at how many revolutions per minute should a spin balancer be set to balance the
Alex Ar [27]

Answer:

revolutions per minute for 16 inches is 946 / minute

revolutions per minute for 14 inches is 1081 / minute

Step-by-step explanation:

Given data

radius = 16 inch

speed = 90 mph  = 90/60 = 1.5 miles/minute = 1.5 × 5280 feet /12 inches = 95040 inches /minute

radius 2 = 14 inches

to find out

revolutions per minute

solution

first we calculate the circumference of the wheel i.e. 2×\pi×radius

circumference = 2×\pi×16

circumference = 32\pi

we know that revolution is speed / circumference

revolution = 95040/32\pi

revolution = 945.38 / minute

we have given radius 14 inches than revolution will be i.e.

revolution = speed / circumference

circumference = 2×\pi×14

circumference = 28\pi

revolution =  95040/ 28\pi

revolution = 1080.43 / minute

7 0
2 years ago
Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola
mote1985 [20]

ANSWER

This is an ellipse. The equation is:

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

(a+b)^2=a^2+2ab+b^2

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

16x^2-32x=16(x^2-2x)

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

(x-1)^2=x^2-2x+1

To maintain the equation, we have to subtract 1,

16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

16(x-1)^2-16+9y^2+72y+16=0

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

9y^2+72y=9(y^2+8y)

Following the same reasoning as before, we have that the perfect binomial squared is,

(y+4)^2=y^2+8y+16

Remember to subtract the independent term to maintain the equation,

9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

16(x-1)^2-16+9(y+4)^2-144+16=0

Add like terms,

\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}

Add 144 to both sides,

\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}

As we can see, this is the equation of an ellipse. Its standard form is,

\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\  \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1

Note that we can simplify a and b,

\frac{12}{4}=3\text{ and }\frac{12}{3}=4

Hence, the equation of the ellipse is,

\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1

3 0
1 year ago
Write the equation that modeled the sequence 63,-21,7,-7/3,7/9
Ilya [14]

Answer:

an = 63(-1/3)^(n-1)

Step-by-step explanation:

This is a geometric sequence with first term 63 and common ratio -1/3.

The equation for the nth term  is

an = 63(-1/3)^(n-1).

6 0
3 years ago
Im having trouble figuring out what this question means |7| + -4=?
OverLord2011 [107]

Answer:

3

Step-by-step explanation:

It means absolute value 7 plus -4

This means that if it were a -7, it would become positive because it is under absolute value bars...since it is positive nothing changes

7-4= 3

7 0
2 years ago
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