8. Anna withdrew $50 from her checking account. She spent $28 on a pair of shoes. What fraction of her money does Anna have left?

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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⇒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 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.

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]

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.

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 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.

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.

Answer:

Step-by-step explanation:

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.

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.

The approach is to find the area of the individual sides and add all up

Besides the base, we can identify about 6 rectangles.

area of a rectangle, A = base x height

To change decimal or fraction to percent multiply them by 100

Example: 1/4 x 100% = 25%, 0.2 x 100% = 20%

Let us check the answer of the 3 students

Maggie wrote 75% = 3/5

Since

Then 3/5 = 60%, not 75%

Maggie is wrong

Bieber wrote 0.05 = 50%

Let us check

0.05 x 100% = 5%, not 50%

Bieber is wrong

Yung wrote 3/8 = 0.375

Let us check

Since 0.375 x 100% = 37.5%

Yung is right

The answer is Lee Yung only

The answer is D

we have the equation

y=-4

This is a horizontal line (parallel to the x-axis) that passes through the point (0,-4)

see the graph below to better understand the problem

Answer

Option C is correct.

v = (20, 36)

Explanation

If the initial and terminal points of a vector are given, the vector itself is obtained, per coordinate, by doing a terminal point coordinate minus initial point coordinate.

u = [(5 - 15), (4 - 22)]

u = (-10, -18)

Then, we are told that vector v points in the opposite direction as that of vector u and its magnitude is twice that of vector u too.

In mathematical terms,

v = -2u

v = -2 (-10, -18)

v = (20, 36)

Hope this Helps!!!

Answer:

Slope = 4

Step-by-step explanation:

The slope of a line can be calculated using the following formula:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

From the question can put the points as:

(2, -5) as (x1, y1)

and

(4, 3) as (x2, y2)

Therefore, we can put in the values into the formula to solve for the slope.

[tex] \frac{3 - ( - 5)}{4 - 2} \\ = \frac{3 + 5}{2} \\ = \frac{8}{2} \\ = 4[/tex]

Given the following functions;

f(x) = x^2 + 2

g(x) = 3x - 2

(g+h)(x) = g(x)+h(x)

(g+h) = x^2 + 2 + 3x - 2

(g+h) = x^2+3x + 2-2

(g+h) = x^2 + 3x

To get (g+h) (-3), we will subtitute x = -3 into the resulting function as shown;

(g+h) (-3) = (-3)^2+3(-3)

(g+h) (-3) = 9 - 9

(g+h) (-3) = 0

Hence the value of the expression (g+h) (-3) is 0

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

y=mx+b

replacing y=4, m=2, x=3 in the equation:

4=2(3)+b

then

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.

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

Explanation

To find the percentage of the tip we will use the formula below.

Answer: 13%

The angle measures

m WXZ = 180 - 90 - 24

mWXZ = 66°

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).

The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

For example, a/b, where a will be the numerator and b will be the denominator.

As per the given,

Pat's normal pulse rate is 80 beats per minute.

So, 80 beats → 1 minute

Multiply both sides by 3/4

80 × 3/4 beats  → 1 × 3/4  minute

(3/4) minute → 60 beats.

Hence "The number of times that pat pulse rate maintains the given ratio in 3/4 of a minute is 60 times".

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We know that

• Each protective coat is 2/27 inches thick.

• We need to fill 2/3 inches of this protective coat.

To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression

We solve for x

the slope will be 5/3 because:

test

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0. primo

1. secondo

2. terzo

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• the best

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pl

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