estimate 328 divided by 11=?

We know that a geometric sequence is given by:

where r is the common ratio of the sequence.

For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:

Therefore the sequence is given by:

Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:

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0. primo

1. secondo

2. terzo

• good

• better

• the best

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ok

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we have that

The area of the composite figure is equal to the area of a rectangle plus the area of a right triangle

so

step 1

Find out the area of the rectangle

A=L*W

A=8*5

A=40 cm2

step 2

Find out the area of the right triangle

A=(1/2)(b)(h)

where

b=8-(2+1)=8-3=5 cm

h=5 cm

A=(1/2)(5)(5)

A=12.5 cm2

therefore

the total area is

A=40+12.5=52.5 cm2

By algebra properties, the sum of four mixed numbers is equal to the mixed number [tex]8\,\frac{37}{40}[/tex].

In this problem we find a sum of four mixed numbers. The simplification process consists in transforming each mixed number into a fraction and apply algebra properties. Then,

[tex]9 \,\frac{1}{2}[/tex] = 9 + 1 / 2 = 18 / 2 + 1 / 2 = 19 / 2

[tex]3\,\frac {7}{8}[/tex] = 3 + 7 / 8 = 24 / 8 + 7 / 8 = 31 / 8

[tex]4\,\frac{4}{5}[/tex] = 4 + 4 / 5 = 20 / 5 + 4 / 5 = 24 / 5

[tex]1 \,\frac{1}{2}[/tex] = 1 + 1 / 2 = 2 / 2 + 1 / 2 = 3 / 2

(19 / 2 - 31 / 8) + (24 / 5 - 3 / 2)

(76 / 8 - 31 / 8) + (48 / 10 - 15 / 10)

45 / 8 + 33 / 10

450 / 80 + 264 / 80

714 / 80

357 / 40

320 / 40 + 37 / 40

8 + 37 / 40

[tex]8\,\frac{37}{40}[/tex]

The sum of mixed numbers is equal to [tex]8\,\frac{37}{40}[/tex].

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We have the following:

The formula for compound interest is as follows

A is amount (current balance 400), P is the principal ( deposit initially), r is the rate (0.07) and is the time ( 7 years)

replacing:

Which means that the initial deposit was $ 249.09

Answer: y=80+2x

Step-by-step explanation:

In y=mx+b format the answer is y=80+2x

A: height is increasing from 0-2 interval.

B: Height remains the same on 2-4

C: 4-6 the height is decreasing the fastest, because the slope is the steepest on that interval.

D: Baloon would be on the ground at 16 seconds, and will not fall down further. that is the way it is in real-world (constraint).

ANSWER

854x

EXPLANATION

We have that:

850x + 40(x)

First, expand the bracket:

850x + 40x

Because the two terms are of the same kind (terms of x) we can add them up:

850x + 4x = 854x

That is the answer.

we have that

The trapezoidal approximation is equal to

where

a=0

b=10

f(a)=f(0)=0.05

f(b)=f(10)=0.043

substitute given values

therefore

Answer:

2. 13/3

Step-by-step explanation:

x will be equal to 13/3.

Given,

5^(2x - 1) = 5^(5x - 14)

We can see that base is the same for both the exponents on each side of the equation.

Now, on using the Logarithm on both sides with base 5, we can see that the base on both sides of the equation cancels out with the log (base 5) function.

And new equation becomes:

(2x - 1) = (5x - 14)

This derives us to another conclusion that if the base of an exponent is equal then,

the powers must be equal too.

(2x - 1) = (5x - 14)

=> 5x - 2x = -1 + 14

=> 3x = 13

which gives us,

=> x = 13/3.

Therefore x = 13/3.

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The statements in (A), (B), (E) are correct and satisfy the conditions in question.

What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. Because b is not equal to 0, the ratio establishes the link between two quantities such as a:b.

Given, for every 7 kids, pizzas needed = 3 --(iii)
Therefore, for every 1 kid, pizza needed = (3/7)
Thus, for every x kids, pizza needed = (3/7)x
Again, ratio of pizzas to kids is = 3:7 --(i)
Also, the ratio of kids to pizza is = 7:3 --(ii)
From (A), using (ii), the statement in (A) is correct.
From (B), using (ii), the statement in (B) is correct.
From (C), using (i), the statement in (C) is incorrect.
From (D), using (i), the statement in (D) is incorrect.
From (E), using (iii), the statement in (E) is correct.
Thus, the statements in (A), (B), (E) are correct and satisfy the conditions in question.

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Answer: 10.6299

Step-by-step explanation:

There are 0.3937 inches in a cm., So, the length of the tooth in inches is [tex]27(0.3937)=10.6299 \text{ in }[/tex]

Okay, here we have this:

Considering the provided table, we are going to find the corresponding linear equation, so we obtain the following:

To do this we will start using the information in the slope formula, then we have:

m=(y2-y1)/(x2-x1)

m=(190-(-30))/(19-9)

m=220/10

m=22

Now, let's find the y-intercept (b) using the point (9, -30):

y=mx+b

-30=(22)9+b

-30=198+b

b=-30-198

b=-228

Finally we obtain that the linear equation is y=22x-228

Answer:

Step-by-step explanation:

These are the two methods to finding the equation of a line when given a point and the slope: Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. Use the m given in the problem, and the b that was just solved for, to create the equation y = mx + b.

Let x be the number of peanut bags Jeff sells. Since he earns $1.75 per bag the total amount he earns for selling x bags is:

Now, to this we have to add the $12 he gets paid, then the total amount he earns is:

To find out how many bags he has to sell to earn $52 we equate the expression above with the amount and solve for x:

therefore he has to sell 24 bags to earn $54.

The radius is given 3.5 ft and height is given 14 ft.

To find the surface area of cylinder,

Use the formula.

Substitute the values.

The volume of cylinder is determined as

Substitute the values

The surface area of cylinder is 384.65 sq.ft.

The volume of cylinder is 538.51 cubic feet.

Given:

Two ships left a port at the same time.

One travelled due north at an average speed of 25.5 km/h

And the other ship was due east at average speeds of 20.8 km/h

We will find their distance apart using the Pythagorean theorem.

The distance = Speed * Time

Let the time = t

So, the distance of the first ship = 25.5t

And the distance of the second ship = 20.8t

So, the distance between the ships (d) will be as follows:

So, the answer will be:

The distance in terms of time = 32.907t

We will find the distance when t = hours

So, distance = 164.54 km

The variable of interest is

X: sodium consumption of an American male.

a) This variable is known to be normally distributed and has a mean value of μ=9.6grams with a standard deviation of δ=0.8gr

Any normal distribution has a mean = μ and the variance is δ², symbolically:

X~N(μ ,δ²)

For this distribution, we have established that the mean is μ=9.6grams and the variance is the square of the standard deviation so that: δ² =(0.8gr)²=0.64gr²

Then the distribution for this variable can be symbolized as:

X~N(9.6,0.64)

b. You have to find the probability that one American man chosen at random consumes between 9.7 and 10.6gr of sodium per day, symbolically:

The probabilities under the normal distribution are accumulated probabilities. To determine the probability inside this interval you have to subtract the accumulated probability until X≤9.7 from the probability accumulated probability until X≤10.6:

Now to determine these probabilities, we have to work under the standard normal distribution. This distribution is derived from the normal distribution. If you consider a random variable X with normal distribution, mean μ and variance δ², and you calculate the difference between the variable and ist means and divide the result by the standard deviation, the variable Z =(X-μ)/δ ~N(0;1) is determined.

The standard normal distribution is tabulated. Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.

So to calculate each of the asked probabilities, you have to first, "transform" the value of the variable to a value of the standard normal distribution Z, then you use the standard normal tables to reach the corresponding probability.

So we have to find the probability between the Z-values 1.25 and 0.125

Using the table of the standard normal tables, or Z-tables, you can determine the accumulated probabilities:

And calculate their difference as follows:

The probability that an American man selected at random consumes between 10.6 and 9.7 grams of sodium per day is 0.344

c. You have to determine the two sodium intake values ​​between which the middle 10% of American men fall. If "a" and "b" represent the values we have to determine, between them you will find 10% of the distribution. The fact that is the middle 10% indicates that the distance between both values to the center of the distribution is equal, so 10% of the distribution will be between both values and the rest 90% will be equally distributed in two tails "outside" the interval [a;b]

Under the standard normal distribution, the probability accumulated until the first value "a" is 0.45, so that:

And the accumulated probability until "b" is 0.45+0.10=0.55, symbolically:

The next step is to determine the values under the standard normal distribution that accumulate 0.45 and 0.55 of probability. You have to use the Z-tables to determine both values:

The value that accumulates 0.45 of probability is Z=-0.126

To translate this value to its corresponding value of the variable of interest you have to use the standard normal formula:

You have to write this expression for X

Replace the expression with a=-0.126, μ=9.6gr, and δ=0.8gr

The value of Z that accumulates 0.55 of probability is 0.126, as before, you have to translate this Z-value into a value of the variable of interest, to do so you have to use the formula of the standard normal distribution and "reverse" the standardization to reach the corresponding value of x:

Replace the expression with b=0.126, μ=9.6gr, and δ=0.8gr and calculate the value of X:

The values of sodium intake between which the middle 10% of American men fall are 9.5 and 9.7gr.

Hello! Let's solve this exercise:

We have some ways to show it, look:

So, as it can be written as a fraction, is a rational number.

the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:

We are given the following expression

Recall the associative property of multiplication

The associative property of multiplication says that when you multiply numbers, you can group the numbers in any order and still you will get the same result.

So, if we apply this property to the given expression then it becomes

Therefore, the following expression is equivalent to the given expression.

Answer:

Step-by-step explanation:

Answer:

A. 6

Step-by-step explanation:

Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²

Where: hypotenus = 10, opposite = x, adjacent = 8

So:

[tex] {10}^{2} = {x}^{2} + {8}^{2} [/tex]

Solving for x

[tex]100 = {x}^{2} + 64[/tex]

Collect like terms to make x the subject of formula

[tex]100 - 64 = {x}^{2} →36 = {x}^{2} [/tex]

[tex]36 = {x}^{2} ⟹ {x}^{2} = 36[/tex]

square root both sides of the equation to find the value of x

[tex] \sqrt{ {x}^{2} } = \sqrt{36} →x = 6[/tex]

Therefore: Option A is correct

Given:

The quadratic model of the ball is given as:

Required:

Find the time when it takes to hit the ground.

Explanation:

When the ball hits the ground then h(t)=0.

Solve the quadratic equation by using the middle term splitting method.

Since time can not be negative.

So t = 7 sec

Final Answer:

The ball will take 7 sec to hits the ground.

Given:

There is a figure given in the question as below

Required:

If

than find the value of angle B

Explanation:

Value of arcADB is

Now to find the angle B

Final answer:

a

⇒It is way more appropriate if I use the product rule. That states that:

⇒f(x)g(x)=f'(x)g(x)+f(x)g'(x)

[tex]t^{4} In(8cos(t))\\=4t^{3}In(8cos(t))+t^{4} \frac{1}{8cos(t)} *(0cos(t)+8*(-sin(t))*1)\\=4t^{3}In(8cos(t))+\frac{t^{4}-8sin(t)}{8cos(t)}[/tex]

Note:

Given F(x)=In(x)

⇒[tex]F'(x)=\frac{1}{x}[/tex]

Goodluck

Answer:

t^3 (4 ln(cos8t) - t tant)

Step-by-step explanation:

Using the Product Rule:

dy/dt = t^4 * d(ln(8cost) / dt + ln(8cost) * d(t^4)/dt

         = t^4 * 1/ (8cost) * (-8sint) + 4t^3 ln(8cost)

         = -8t^4 sint / 8 cost + 4t^3 ln(8cost)    

         = -t^4 tan t + 4t^3 ln(8cost)  

          = t^3 (4 ln(cos8t) - t tant)

the slope will be 5/3 because:

ANSWER

y = -3x

EXPLANATION

We have to determine the slope-intercept form of the equation of the line.

The slope-intercept form of a linear equation is given as:

y = mx + c

where m = slope

c = y intercept

First, we have to find the slope:

where (x1, y1) and (x2, y2) are two points the line passes through.

Therefore:

Now, we have to use the point-slope method to find the equation:

y - y1 = m(x - x1)

=> y - (-3) = -3(x - 1)

y + 3 = -3x + 3

y = -3x + 3 - 3

y = -3x

That is the slope intercept form of the equation.