Two questions please help

Adam currently runs about 40 miles per week, and he wants to increase his weekly mileage by 30%. How many miles will Adam run pe

BigorU [14]

Answer:

52 miles/week (12 more miles per week)

Step-by-step explanation:

In order to know the miles per week with this increasement, we'll use the rule of 3, assuming that 40 miles is the 100% innitially so:

If:

40 miles --------->100%

X miles ----------> 30%

Solving for X we have the following:

X = 30 * 40 / 100 = 12 miles

So, if Adam wants to increase his weekly mileage by 30%, he needs to run 12 more miles, and that makes a total of 52 miles/week

6 0

3 years ago

The table represents the function f(x). If g(x) = -(x + 1)^2 - 10, which statement is true?

miskamm [114]

Answer:

Answer C is correct.

Step-by-step explanation:

f(x) clearly has a maximum: y = +10 at x = 0.

Analyzing g(x) = -(x + 1)^2 - 10, we see that the vertex is at (-1, -10), and that the graph opens down. Thus, -10 is the maximum value; it occurs at x = -1.

Answer A is false. Both functions have max values.

Answer B is false. One max is y = 10 and the other is y = -10.

Answer C is correct. The max value of f(x), which is 10, is greater than the max value of g(x), which is -10.

Answer D is false. See Answer B, above.

5 0

3 years ago

A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day of sharpness. If any dull blade

Alex73 [517]

Answer:

Part a

The probability that assembly is replaced the first day is 0.7069.

Part b

The probability that assembly is replaced no replaced until the third day of evaluation is 0.0607.

Part c

The probability that the assembly is not replaced until the third day of evaluation is 0.2811.

Step-by-step explanation:

Hypergeometric Distribution: A random variable x that represents number of success of the n trails without replacement and M represents number of success of the N trails without replacement is termed as the hypergeometric distribution. Moreover, it consists of fixed number of trails and also the two possible outcomes for each trail.

It occurs when there is finite population and samples are taken without replacement.

The probability distribution of the hyper geometric is,

$P(x,N,n,M)=\frac{(\limits^M_x)(\imits^{N-M}_{n-x})}{(\limits^N_n)}$

Here x is the success in the sample of n trails, N represents the total population, n represents the random sample from the total population and M represents the success in the population.

Probability that at least one of the trail is succeed is,

$P(x\geq1)=1-P(x$

(a)

Compute the probability that the assembly is replaced the first day.

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly N = 48.

Number of blades selected at random from the assembly n= 5

Number of blades in an assembly dull is M = 10.

The probability mass function is,

$P(X=x)=\frac{[\limits^M_x][\limits^{N-M}_{n-x}]}{[\limits^N_n]};x=0,1,2,...,n\\\\=\frac{[\limits^{10}_x][\limits^{48-10}_{5-x}]}{[\limits^{48}_5]}$

The probability that assembly is replaced the first day means the probability that at least one blade is dull is,

$P(x\geq 1)=1- P(x$

(b)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly N = 48

Number of blades selected at random from the assembly N = 5

Number of blades in an assembly dull is M = 10

From the information,

The probability that assembly is replaced (P) is 0.7069.

The probability that assembly is not replaced is (Q) is,

$q=1-p\\= 1-0.7069= 0.2931$

The geometric probability mass function is,

$P(X = x)= q^{x-1} p; x =1,2,....=(0.2931)^{x-1}(0.7069)$

The probability that assembly is replaced no replaced until the third day of evaluation is,

$P(X = 3)=(0.2931)^{3-1}(0.7069)\\=(0.2931)^2(0.7069)= 0.0607$

(c)

From the given information,

Let x be number of blades dull in the assembly are replaced.

Total number of blades in the assembly N = 48

Number of blades selected at random from the assembly n = 5

Suppose that on the first day of the evaluation two of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M = 2.

$P(x=0)=\frac{(\limits^2_0)(\limits^{48-2}_{5-0})}{\limits^{48}_5}\\\\=\frac{(\limits^{46}_5)}{(\limits^{48}_5)}\\\\= 0.8005$

Suppose that on the second day of the evaluation six of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M = 6.

$P(x=0)=\frac{(\limits^6_0)(\limits^{48-6}_{5-0})}{(\limits^{48}_5)}\\\\=\frac{(\limits^{42}_5}{(\limits^{48}_5)}\\\\= 0.4968$

Suppose that on the third day of the evaluation ten of the blades are dull then the probability that the assembly is not replaced is,

Here, number of blades in an assembly dull is M

= 10.

$P(x\geq 1)=1- P(x$

The probability that the assembly is not replaced until the third day of evaluation is,

P(The assembly is not replaced until the third day)=P(The assembly is not replaced first day) x P(The assembly is not replaced second day) x P(The assembly is replaced third day)

=(0.8005)(0.4968)(0.7069)= 0.2811

5 0

4 years ago

Please help .

Iteru [2.4K]

702 can not be written as the product of 2 prime numbers, because if you divide 702 by 2 then you get 351 and that is not a prime number. Therefore 702 is a prime number.

8 0

3 years ago

5) Plot these coordinates and determine the resulting figure. (0, 2) (4, 6) (10, 12) (18, 20) A) circle B) curve C) line D) para

Delicious77 [7]

Answer:

Resulting figure after plotting the given coordinates (0, 2) (4, 6) (10, 12) (18, 20) is a LINE.

Step-by-step explanation:

Please find the attached document for figure plotted.

3 0

3 years ago