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saw5 [17]
3 years ago
7

Jalen gets 3 paid vacation days for every 60 days he works. Select all of the expressions that represent the number of vacation

days gets per x days worked. (A) x/20 (B) 3/60x (C) x/3 (D) 0.05x (E) 20x
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
7 0

Answer:

A and D

Step-by-step explanation:

In this question, we are asked to select the expressions that represent the number of vacation days per x days worked.

Now, to do this, what we simply first do is to get the number of days to takes to get one paid vacation. In the question , we are made to know that he gets 3 days paid vacation for 60 days of work. The number of days to get a single paid vacation would thus be 60/3 = 20 days. This means she gets one paid vacation in 20 days.

Now, we are told after working for x days, how many paid days vacation does she get. To know this, what we do is to first know the number of 20 days in x days. That would simply be x/20. This is the number of vacation days she gets in x days.

now, we check if there are similar options to this.

D is also correct. This is because x/20 is same as 0.005x

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A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ=0.0
oksian1 [2.3K]
<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

\overline{x}\pm z^* SE                   (1)

, where \overline{x} = sample mean

z* = critical value.

SE = standard error

and SE=\dfrac{\sigma}{\sqrt{n}} , \sigma = population standard deviation.

n= sample size.

As per given , we have

\overline{x}=74.021

\sigma=0.001

n= 15

It is known that ring diameter is normally distributed.

SE=\dfrac{0.001}{\sqrt{15}}=0.000258198889747\approx0.000258199

By z-table ,

The critical value for 95% confidence  = z*= 1.96

A 99% two-sided confidence interval on the true mean piston diameter :

74.021\pm (2.576) (0.000258199)     (using (1))

74.021\pm 0.000665120624

74.021\pm 0.000665120624\\\\=(74.021- 0.000665120624,\ 74.021+ 0.000665120624)\\\\=(74.0203348794,\ 74.0216651206)\approx(74.020,\ 74.022)  [Rounded to three decimal places]

∴  A 99% two-sided confidence interval on the true mean piston diameter  = (74.020, 74.022)

By z-table ,

The critical value for 95% confidence  = z*= 1.96

A 95% lower confidence bound on the true mean piston diameter:

74.021- (1.96) (0.000258199)    (using (1))

74.021- 0.00050607004=74.02049393\approx74.020 [Rounded to three decimal places]

∴  A 95% lower confidence bound on the true mean piston diameter= 74.020

7 0
3 years ago
Is x+y+1=0 a tangent of both y^2=4x and x^2=4y parabolas?
Lubov Fominskaja [6]

Answer:

  yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

__

For the first parabola, the point of intersection is ...

  y^2 = 4(-y-1)

  y^2 +4y +4 = 0

  (y+2)^2 = 0

  y = -2 . . . . . . . . one solution only

  x = -(-2)-1 = 1

The point of intersection is (1, -2).

__

For the second parabola, the equation is the same, but with x and y interchanged:

  x^2 = 4(-x-1)

  (x +2)^2 = 0

  x = -2, y = 1 . . . . . one point of intersection only

___

If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

_____

Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

7 0
3 years ago
What is 3X^2 × 2X^3​
irinina [24]

Answer:

Step-by-step explanation:

3x^2 * 2x^3= 6x^5

Multiply the 3 and 2 to get 6. Add the exponents.

6 0
3 years ago
A diving board is 12.4 feet above the ground. The bottom of the pool is 16.9 feet below the ground. Write and solve an equation
sergey [27]

Answer:

29.3 feet

Step-by-step explanation:

Okay I don't know the equation to put it in, but all you need to do is add the two values together.

12.4 + 16.9 = 29.3 feet

4 0
3 years ago
Read 2 more answers
Estimate the sum to the nearest whole number <br><br> 29.1 +78.9 + 41.5
lesya692 [45]

I rounded each number to the nearest whole number and added those.

29 + 79 + 42 = 150

If you add the original numbers you would get 149.5, which rounds to 150.

6 0
3 years ago
Read 2 more answers
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