Which product is the better deal
A. Washing Powder
B. Super Clean
(easy)

Answer:

20 days

Step-by-step explanation:

Answer:

[tex](f\ o\ g)(x) = 3x[/tex]

[tex]-\infty < x < \infty[/tex]

Step-by-step explanation:

Given

[tex]f(x) = ln(x^2)[/tex]

[tex]g(x)=\sqrt{e^{3x}}[/tex]

Solving (a): (f o g)(x)

This is calculated as:

[tex](f\ o\ g)(x) = f(g(x))[/tex]

We have:

[tex]f(x) = ln(x^2)[/tex]

[tex]f(g(x)) = \ln((g(x))^2)[/tex]

Substitute: [tex]g(x)=\sqrt{e^{3x}}[/tex]

[tex]f(g(x)) = \ln(\sqrt{e^{3x}})^2[/tex]

Evaluate the square

[tex]f(g(x)) = \ln(e^{3x})[/tex]

Using laws of natural logarithm:

[tex]\ln(e^{ax}) = ax[/tex]

So:

[tex]f(g(x)) = \ln(e^{3x})[/tex]

[tex]f(g(x)) = 3x[/tex]

Hence:

[tex](f\ o\ g)(x) = 3x[/tex]

Solving (b): The domain

We have:

[tex]f(g(x)) = 3x[/tex]

The above function has does not have any undefined points and domain constraints.

Hence, the domain is: [tex]-\infty < x < \infty[/tex]

Answer:

[tex]2\frac{3}{4}[/tex]

Step-by-step explanation:

Let's bring them to the same denominator: 4

[tex]2\frac{1}{4} = 2 + \frac{1}{4} = \frac{2\cdot 4}{4} + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\\~\\5 = \frac{5\cdot 4}{4} = \frac{20}{4}\\~\\5 - 2\frac{1}{4} = \frac{20}{4} - \frac{9}{4} = \frac{11}{4} = \frac{8}{4} + \frac{3}{4} = \frac{2\cdot 4}{4} + \frac{3}{4} = 2 + \frac{3}{4} = 2\frac{3}{4}[/tex]

Answer:

y = 5/4x - 6

Step-by-step explanation:

First, put 4x + 5y= -45​ in y = mx + b form

4x + 5y= -45​

5y = -4x - 45

y = -4/5x - 9

So, the slope is -4/5. Perpendicular lines have a opposite reciprocal slope, so the line's slope will be 5/4

To find the equation of the perpendicular line, plug in the slope and given point into y = mx + b, and solve for b

y = mx + b

-11 = 5/4(-4) + b

-11 = -5 + b

-6 = b

Plug in b and the slope into y = mx + b

y = 5/4x - 6

So, the equation is y = 5/4x - 6

Translation will reduce x coordinate by 2:  (0,4), (5,6) and (3,2)

Rotation 90 CCW will change (x,y) to (-y,x):  (-4,0),(-6,5),(-2,3)

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that [tex]\mu = 36, \sigma = 5.5[/tex]

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that [tex]n = 9[/tex]. So

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333[/tex]

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{38 - 36}{1.8333}[/tex]

[tex]Z = 1.09[/tex]

[tex]Z = 1.09[/tex] has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

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

[tex]Z = \frac{34.5 - 36}{1.8333}[/tex]

[tex]Z = -0.82[/tex]

[tex]Z = -0.82[/tex] has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

Answer:

Option A

Step-by-step explanation:

The complete question is

The pentagon ABCDE is graphed on a coordinate plane with vertices A(0, 0), B(3, 5), C(3, 8), D(8, 5), and E(8, 0). What is the pentagon's perimeter?

Solution -

We will find the length of all the sides of pentagon and then add them  

Length of AB = Sqrt ((3-0)^2+(5-0)^2) = Square root of 9+25 = 5.83

Length of BC = Sqrt ((3-3)^2+(8-5)^2) = Square root of 9 = 3

Length of CD = Sqrt ((8-3)^2+(5-8)^2) = Square root of 5^2+-3^2

= 5.83

Length of DE = Sqrt ((8-8)^2+(0-5)^2) = Square root of 25 = 5

Length of EA = Sqrt ((8-0)^2+(0-0)^2) = Square root of 64= 8

Perimeter=8+5+5.83+5.83+3= 27.66 units  =27.66 units

Option A

Answer:

40 sq. units

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

25-18 = 7 w

45-36=9 l

They don't match up ^

Subtract 6 from the total then divide by 2.

34-6 = 28

28/2 = 14

The length of the other two sides are 14 cm each

Answer:

$3806

Step-by-step explanation:

  230.0

    56.0

+   19.50

  305.50

305.5x12=3666

35x4=140

3666+140=3806

Answer:

2 x − y = 11

Step-by-step explanation:

Step-by-step explanation:

hope this help and pls rate to make me recommended for answering many mathematics questions! have a great day

Answer:

a) 1/2

b)2.5

c)17.5

Step-by-step explanation:

The question gives you two points on the line. From this, you can calculate the slope. Since slope is m=[tex]y_2-y_1/x_2-x_1[/tex], the work for question a is as follows:

m= 5.5-3/6-1

m=1/2 or 0.5

Now, you can use the information given to calculate the y-intercept. Use any of the two points to fill in x and y, and use the slope you just calculated to fill in for m. Fill in the equation and use algebra to isolate the variable and solve for b.

y=mx+b

3=0.5(1)+b

3-0.5=b+0.5-0.5

2.5=b

Finally, plug in all the numbers to find the answer for question c.

y=0.5x+2.5

y=0.5(30)+2.5

y=17.5

Answer:

-p - 30

Step-by-step explanation:

Hope this helps

Answer:

-p-30

Step-by-step explanation:

4p-5(p+6) Distribute -4 to p and 6

4p-5p-30 simplify by adding the p variables

-p-30

Answer:

20.97?

Step-by-step explanation:

Use the Sine rule!

Answer:

12 because imagine 40 / 3  ok?   now what makes 160 40 x 4    so you do that for the button 4 x 3 please put heart

Answer:

4 hours

Step-by-step explanation:

Part of the pool filled by first pipe in an hour = 1/6

Part of the pool filled by second pipe in an hour = 1/12

Part of the pool filled by first pipe and second pipe in an hour = 1/6 +1/12

             [tex]=\frac{1*2}{6*2}+\frac{1}{12}\\= \frac{2}{12}+\frac{1}{12}\\\\=\frac{3}{12}\\\\=\frac{1}{4}[/tex]

Time taken by both the pipes to fill the pool = 4 hours

Answer:

...

Step-by-step explanation:

the vertex is (-1 , 0)

false

true

the domain is R (all real numbers) ( -♾, +♾ )

the range is negative infinity -♾

Answer:

If you mean what is the square root of 36, then the answer is 6.

6 × 6 = 36.

Remeber sqaure root means what two numbers multplied together equal another number. It is irrational when the number doesn't repeat or terminate.

Hope this helps!!

Answer:

so how many large and small posters were there before they order 12 times the amount.

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

You order them but in this case they are already ordered and the middle number is 81 so that is the median(also knows as the middle).

hope this helps,have a great day!!

~Pinky~

Answer:

The median is 81.

Step-by-step explanation:

You can find the median in the middle if it all of them add up to odd.(like your’s say 70, 77, 80,... so that You will count them all. In total you have seven numbers and it’s odd).

if it is an even numbers, you mulitply the middle two numbers and divide them by two. That is the median for even numbers.

Answer:

$80

Step-by-step explanation:

Answer:

4 = function

5 = function

6 = not a function

Step-by-step explanation:

The first two pass the vertical line test

while the last ne doesn't

Answer:

Step-by-step explanation:

I have no clue I just need 5 pionts

Answer:

Step-by-step explanation:

7 red roses

4 white roses

the answer would be 4 to 7, 4/7, and 4:7

I hope this helps!

Answer:

Step-by-step explanation:

X-intercepts are: (-10,-5,0,5,10)

Y-intercepts are: (-32,-24,-16,-8,0)

Answer:

68% rode the bus; 32% walked home

Step-by-step explanation:

Answer:

[tex] {a}^{3} - {b}^{3} [/tex]

[tex] = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]

Hence, simplified.