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mash [69]
3 years ago
10

How many three-digit positive integers

class="latex-formula"> satisfy 3874x+481\equiv 1205 \pmod{23}
Mathematics
1 answer:
Anastaziya [24]3 years ago
3 0

Answer:

  40

Step-by-step explanation:

Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.

As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.

_____

The equation reduces, mod 23, to ...

  10x = 11

Its solutions are x = 23n +8.

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7 0
3 years ago
Pediatricians work an average of 48 h per week. The standard deviation is 12 hours. What percentage of pediatricians work more t
cricket20 [7]

Answer: 2.28 %

Step-by-step explanation:

Given : Mean : \mu=\ 48

Standard deviation :\sigma= 12

The formula to calculate the z-score :-

z=\dfrac{x-\mu}{\sigma}

For x = 72

z=\dfrac{72-48}{12}=2

The p-value = P(2

1-0.9772498=0.0227502\approx0.0228

In percent, 0.0228\times100=2.28\%

Hence, the  percentage of pediatricians work more than 72 h per​ week = 2.28 %

4 0
3 years ago
In 3x−7≤ -2 what is the largest integer value of x in the solution
PtichkaEL [24]

Answer:

X is less than or equal to 1.66666666667

Step-by-step explanation:

3x-7(less than or equal to)-2

-7+7= 0

-2+7=5

3x divided by 3 cancles out

5 divided by 3 = 1.66666666667

x is less than or equal to 1.66666666667

8 0
2 years ago
What is the domain of the linear function<br> graphed below?
Tems11 [23]

Answer:

C

Step-by-step explanation:

6 0
2 years ago
You want to wrap a gift shaped like the regular triangular prism shown. How many
kotegsom [21]

Answer:

697.6 \ in^2

Step-by-step explanation:

-Given the dimensions of the box is 8.7 in, 14 in and 10 in.

Let length=14 in, width=10 in and height =8.7 in

#The surface area of a rectangular prism is calculated as:

Surface \ Area=2(wl+hl+hw)\\\\l=length, w=width, h=height\\\\\therefore Surface \ Area=2(14\times 10+10\times 8.7+14\times 8.7)\\\\=697.6 \ in^2

Hence, the wrapping paper needed has an area of 697.6 \ in^2

8 0
3 years ago
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