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2 years ago

ONE EIGHTH OF TONYS BOOKS ARE MYSTERY BOOKS. HE HAS 3 BOOKS. HOW MANY BOOKS DOES TONY HAVE IN ALL

Mathematics

1 answer:

LekaFEV [45]2 years ago

6 0

Answer: If he has 3 mystery books, and those are 1/8 of his whole collection, he has 24 books.

Step-by-step explanation:

3 = 1/8 × x

multiply both sides by the reciprocal of 1/8 which is 8/1 ("flipped fraction")

8 × 3 = 8/1(1/8) x When you multiply a fraction by its reciprocal, it produces 1, so it "cancels" in the multiplication

24 = x 

This may seem complicated, but understanding the process will help you solve more complicated questions like this in the future, I hope.

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For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to les

kaheart [24]

Answer:

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error for this case is given by:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And replacing we got:

$ME = 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.0259$

And replacing into the confidence interval formula we got:

$0.52 - 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.4941$

$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

Step-by-step explanation:

Data given and notation

n=1000 represent the random sample taken

$\hat p=0.52$ estimated proportion of of U.S. employers were likely to require higher employee contributions for health care coverage

$\alpha=0.05$ represent the significance level (no given, but is assumed)

Solution to the problem

The confidence interval would be given by this formula

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

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

The margin of error for this case is given by:

$ME= z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

And replacing we got:

$ME = 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.0259$

And replacing into the confidence interval formula we got:

$0.52 - 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.4941$

$0.52 + 1.64*\sqrt{\frac{0.52(1-0.52)}{1000}}=0.5459$

And the 95% confidence interval would be given (0.4941;0.5459).

5 0

3 years ago

What is the equation of this graphed line?

barxatty [35]

Answer:

$y=-\frac{1}{3}x-5$

Step-by-step explanation:

Given:

The two points on the line are:

$(x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)$

Now, for a line with two points on it, the slope of the line is given as:

$m=\frac{y_2-y_1}{x_2-x_1}$

For the points $(x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7)$ , slope is:

$m=\frac{-7-(-3)}{6-(-6)}\\m=\frac{-7+3}{6+6}\\m=\frac{-4}{12}=-\frac{1}{3}$

Now, for a line with slope 'm' and a point $(x_1,y_1)$ on it is given as:

$y-y_1=m(x-x_1)$

Plug in all the values and determine the equation of the line. This gives,

$y-(-3)=-\frac{1}{3}(x-(-6))\\\\y+3=-\frac{1}{3}(x+6)\\\\y+3=-\frac{1}{3}x-\frac{1}{3}\times 6\\\\y+3=-\frac{1}{3}x-2\\\\y=-\frac{1}{3}x-2-3\\\\y=-\frac{1}{3}x-5$

Therefore, the equation of the line is:

$y=-\frac{1}{3}x-5$

4 0

3 years ago

Solve for x: |3x + 12| = 18

Alla [95]

Answer:

X = 2 or X = -10

Step-by-step explanation:

We know either3x+12=18or3x+12=−18

3x+12=18(Possibility 1)

3x+12−12=18−12(Subtract 12 from both sides)

3x=6

(Divide both sides by 3)

x=2

3x+12=−18(Possibility 2)

3x+12−12=−18−12(Subtract 12 from both sides)

3x=−30

−30

(Divide both sides by 3)

x=−10

Answer:

x=2 or x=−10

4 0

3 years ago

If each cube has a side measure of 12 inch, what is the volume of the rectangular prism?

barxatty [35]

Answer:

nii pata didi plz dil dedo

5 0

3 years ago

Read 2 more answers

38. What is the surface area of a conical grain storage tank that has a height of 62 meters and a diameter of 24 meters? Round t

svetoff [14.1K]

1. The surface area of a cone S is S= $\pi r^{2}+ \pi rl$ , where r is the radius of the base and l is the slant height.

2. The slant height l is found as follows:

$l^{2}= OC^{2}+ OB^{2}$
$l^{2}= 12^{2}+ 62^{2}=144+3844=3988$

$l= \sqrt{3988}=63.15$

3.

$A=\pi r^{2}+ \pi rl=3.14(12)^{2}+3.14*12*63.15
$
$= 452.16+2379.492 =2831.652 ( m^{2} )$

$= 452.16+2379.492 =2831.652 ( m^{2} )$

4. The answer is C

8 0

3 years ago

Read 2 more answers