Y= 3x-1
2x+6=y substitution method

As the problem states, the variable has a normal distribution, and thus, concepts of this distribution are used to solve this question.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In a health club, research shows that on average, patrons spend an average of 46.2 minutes  on the treadmill, with a standard deviation of 4.8 minutes.

This means that [tex]\mu = 46.2, \sigma = 4.8[/tex]

Find the probability that randomly selected individual would spent  between 30 and 40 minutes on the treadmill.

This is the p-value of Z when X = 40 subtracted by the p-value of Z when X = 30.

X = 40

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40 - 46.2}{4.8}[/tex]

[tex]Z = -1.29[/tex]

[tex]Z = -1.29[/tex] has a p-value of 0.0985

X = 30

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 46.2}{4.8}[/tex]

[tex]Z = -3.38[/tex]

[tex]Z = -3.38[/tex] has a p-value of 0.0004.

0.0985 - 0.0004 = 0.0981

Thus, 0.0981 = 9.81% probability that randomly selected individual would spent  between 30 and 40 minutes on the treadmill.

For another example of the normal distribution, you can check https://brainly.com/question/15181104.

In functions; transformations are used to move lines, points, curves or shapes across the graph (i.e. up, down, right or left). After the transformation of [tex]f(x) = \log\ x[/tex], the resulting function is [tex]g(x) = 2\log\ (-x + 4) - 6[/tex]

Given that:

[tex]f(x) = \log\ x[/tex]

When translated 4 units left, the rule of translation is:

[tex](x,y) \to (x + 4,y)[/tex]

So, we have:

[tex]f'(x) = \log\ (x + 4)[/tex]

When translated 3 units down, the rule of translation is:

[tex](x,y) \to (x,y-3)[/tex]

So, we have:

[tex]f"(x) = \log\ (x + 4) - 3[/tex]

When reflected about the y-axis, the rule of reflection is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]f'"(x) = \log\ (-x + 4) - 3\\[/tex]

Lastly, when it is vertically stretched by 2; the rule is:

[tex](x,y) \to (x,2y)[/tex]

So, we have:

[tex]g(x) = 2[\log\ (-x + 4) - 3][/tex]

Open bracket

[tex]g(x) = 2\log\ (-x + 4) - 6[/tex]

See attachment for the graph of function f(x) and the new function g(x)

Read more about function transformations at:

https://brainly.com/question/24369847

[tex]\text{(H, A and S), (Y, D and T) and (H, D and S)}[/tex]

it is helpful to you

Answer:

Step-by-step explanation:

1500(1.055)^7= 2182.02

Step-by-step explanation:

x=29

y=20

that's the answer

[tex]\\ \sf\longmapsto \dfrac{AK}{DK}=\dfrac{CK}{BK}[/tex]

[tex]\\ \sf\longmapsto \dfrac{14}{12}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto \dfrac{7}{6}=\dfrac{4x+1}{3x+3}[/tex]

[tex]\\ \sf\longmapsto 7(3x+3)=6(4x+1)[/tex]

[tex]\\ \sf\longmapsto 21x+21=24x+6[/tex]

[tex]\\ \sf\longmapsto 24x-21x=21-6[/tex]

[tex]\\ \sf\longmapsto 3x=15[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{15}{3}[/tex]

[tex]\\ \sf\longmapsto x=5[/tex]

Answer:

6.89

Step-by-step explanation:

Well, the number is smaller than 7 so it's 6 or less.

It's 7 when rounded up so it's got to be 6.__

The digit after 6 has to be even and has to be larger than 5 so it's either 6 or 8

The hundredths place digit is the greatest 1-digit odd number which is 9.

6.69 or 6.89 but since none of the digits can be repeated, it's 6.89

Answer:

555

Step-by-step explanation:

hope it may be help you

Step-by-step explanation:

. The mean is less than the median.

The statement that is most likely correct for the negatively skewed data distribution given is: B. The mean is less than the median.

A negatively skewed data distribution has the tail to the left of the number line, and therefore its median is usually greater than its mean.

Negative skewed: Mean < Median < Mode

No skewed: Mean = Median = Mode

Positive skewed: Mean > Median > Mode

The dot plot shows a data distribution that is negatively skewed. Therefore, the statement that is most likely to be true is: B. The mean is less than the median.

Learn more about a negatively skewed data distribution on:

brainly.com/question/20378699

#SPJ2

Step-by-step explanation:

e = 2.7182818 so you can just plug that in to your calculator and solve like normal

Answer:

Supplementary

Step-by-step explanation:

When two positive angles form a linear pair, meaning a straight line, they are supplementary.

Answer:

224π in^2

Step-by-step explanation:

Just plug in the values,

Surface area=2πr(h+r) [Factoring]

r=7in

h=9in

2πr(h+r)=2π*7(9+7)=14π(16)=224π in^2

Answer:

answer 6

Step-by-step explanation:

It has been a long time that i have done that!

[tex]\int\limits^3_2 {\int\limits^2_0 {(4-y^2)} \, dy} \, dx \\\\\\=\int\limits^3_0 {(4-y^2)} \, dy*(2-0)\\\\=2*[4y-\dfrac{y^3}{3} ]^3_0\\\\=2*(12-9)\\\\=6\\[/tex]

Answer:

-3

the blue dot on the no line represent -3

Answer:

The shape could be divided into a rectangle and a trapezoid.

b= 9-(5+2)

b= 2

Area= [tex](3.5\times 9)+1/2(b_1+b_2)h[/tex]

[tex]= [31.5+1/2(9+2)(2)] \:units^{2}[/tex]

[tex]=42.5\ units^{2}[/tex]

OAmalOHopeO

Answer:

4:7

Step-by-step explanation:

18+24=total number of fish=42

silver fish amount= 24

therefore, ratio is 24:42=12:21=4:7

Answer:

h.

[tex] \frac{9 {x}^{10}(y. {x}^{3}) {}^{2} }{y.x(3 {x}^{3}) {}^{3} } \\ \\ = \frac{9 {x}^{10}(y {}^{2} )( {x}^{6} ) }{3y. {x}^{10} } \\ \\ = \frac{ {3}^{2} {x}^{16} {y}^{2} }{3y {x}^{10} } \\ \\ = 3y {x}^{6} [/tex]

j.

[tex] \frac{(3x. {y}^{7} ) {}^{2}. {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{3 {x}^{2} . {y}^{14} . {x}^{5} }{3 {x}^{7} {y}^{4} } \\ \\ = \frac{ {3x}^{7} {y}^{14} }{3 {x}^{7} {y}^{4} } \\ \\ = {y}^{10} [/tex]

Funke has #18.65 LEFT, which was obtained by Subtracting her initial amount from amount spent.

SPENDING:

Total amount = #40

fish fillet = 99k /dozen

vegetable = 3 at #1.25 each

oranges = 27 at 7k each

meat = 4.6kg at #3.20 per kg

To obtain the amount Funke has left, we subtract the total amount of items she purchased from the total amount she has :

Total cost of :

Fish fillet, 1kg = 99K = #0.99

Vegetable, 3kg = 3 * 1.25 = #3.75

Oranges, 27 = 27 * 7 = #1.89

Meat, 4.6 = 4.6 * 3.20 = #14.72

TOTAL AMOUNT SPENT = (0.99 + 3.75 + 1.89 + 14.72) = #21.35

AMOUNT SHE HAS LEFT :

(INITIAL AMOUNT - TOTAL AMOUNT SPENT)

= #40 - #21.35

= #18. 65

Therefore, the amount Funke has left after making the above purchases is #18.65

Learn more about subtraction word problem :

https://brainly.com/question/16479511

Answer: CHoose

option c

1436 ml

= 1.436 l

( divide by 1000)

Answer:

1,436L ,......................

Answer:

Combined cost C(x) = cx + 4c/(x+1)

minimum C(x) ==> C '(x) = 0

==> c - 4c/(x+1)2 = 0

==> 4c/(x+1)2 = c

==> (x+1)2 = 4

==> x +1 = 2

==> x = 1 mile

Hence she should live 1 mile from work to minimise comined costs.

Step-by-step explanation:

252 different samples can be taken.

-------------------------

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

-------------------------

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

-------------------------

In this question, samples of 5 from a set of 10, so:

[tex]C_{10,5} = \frac{10!}{5!5!} = 252[/tex]

252 different samples can be taken.

A similar question is given at https://brainly.com/question/24278448

Answer:

3m=300cm.

15cubi(m)=15,000liter

Step-by-step explanation:

[1m=100cm]

[1cubic(m)=1000liters]

Answer:

x = 66.74715005725

Step-by-step explanation:

First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725

Answer:

6/9 and 10/15

Step-by-step explanation:

they're both 2/3

Answer:

answer is A

Step-by-step explanation:

option A is the answer

Answer:

4

Step-by-step explanation:

BC²=AC × DC

or, 8²=16×DC

or, DC = 64/16

or, DC = 4

Answer:

9076 cm²

Hope my answer helped you