What is 7 x 10^22 in its expanded form?

What is 1/5 × -3/2 +4/5 × -2/7 × -1/6 × -2/7

velikii [3]

Answer:

$\frac{-457}{1470}$

Step-by-step explanation:

$\frac{1}{5} \times \frac{-3}{2} + \frac{4}{5} \times \frac{-2}{7} \times \frac{-1}{6} \times \frac{-2}{7}$

$(\frac{1}{5} \times \frac{-3}{2}) + (\frac{4}{5} \times \frac{-2}{7} \times \frac{-1}{6} \times \frac{-2}{7})$

$\frac{-3}{10} +\frac{-16}{1470}$

$=\frac{-457}{1470}$

4 0

3 years ago

Read 2 more answers

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

8 0

3 years ago

Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equati

Scrat [10]

The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x f(x)

-2 -46

-1 -22

0 -10

1 -4

2 -1

We have to choose which statement describes better about function

Let us assume $f(x)=ab^x+c$

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

$f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}$

$f'(x) > 0$

So we can say that f(x) is an increasing function.

$g(x) = - 18 (\frac{1}{3} )^ x + 2$

$g^ \prime (x) = - 18 (\frac{1}{3} )^ x ln(1/3)$

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and x∈g(x) $g'(x) > f'(x)$

So, g increases at a faster average rate

Thus, Both functions are increasing, but function g increases at a faster average rate.

Learn more about increasing functions here: brainly.com/question/12940982

#SPJ10

7 0

1 year ago

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owne

MrRissso [65]

The age of the van owned = 12 years

The age of the truck owned = 29 years

Step-by-step explanation:

Here, the given question is INCOMPLETE.

Laura takes very good care of her vehicles. She owns a blue van and a red truck. Although she bought them both new, she has owned the truck for 17 years longer than she has owned the van. If the sum of the ages of the vehicles is 41 years, how old is the van and how old is the truck?

Let us assume the number of years Laura has owned the van = S years

So, according to the question:

The number of years she has owned truck = S + 17 years

Now, Sum of the age of ( Truck + Van) = 41 years

⇒ (S + 17 years) + (S years) = 41 years

or, 2 S + 17 = 41

or, 2 S = 4 1 -1 7 = 24

or, S = 24/2 = 12 years

or, S = 12 years

Hence the age of the van owned = 12 years

The age of the truck owned = S + 17 = 12 + 17 = 29 years

6 0

3 years ago

A navigator plots the course a plane is currently traveling. The plane is 300 miles from its destination. If it continues on its

inna [77]

We have to use the rule of cosx° to solve this problem. Attached is a diagram of the navigator's course for the plane. It is similar to the shape of a triangle. We know the plane is 300 miles from its destination, so that will be one of the sides. On the current course, it is 325 miles from its destination, so that will be another one of the sides. The last side is 125 because that is the distance between the destination and the anticipated arrival. Cosx° is what we are looking for.

To find how many degrees off course the plane is, we must use the rules of Cosx°, which is shown in the attached image.

The plane is approximately 23° off course.

3 0

3 years ago