Solve for x:

e^(3x )+ e^x - 6 = 0

Right now I'm having trouble with the step u = e^x, u^3 + u - 6 = 0. Help!

[tex]\large\boxed{Formula: A= P(1+ \frac{R}{100}{)}^{T}}[/tex]

Let's substitute according to the formula.

[tex]A= 50000(1+ \frac{10}{100}{)}^{5}[/tex]

A= $80525.5

Now, we can find the interest paid

[tex]\large\boxed{I= A-P}[/tex]

We'll have to deduct the total amount from the principal amount.

Let's substitute according to the formula.

[tex]I= 80525.5-50000[/tex]

I= $30525.5

Hence, the total amount paid after 5 years is $80525.5 and $30525.5 was paid as interest.

Answer:

$290.55

Step-by-step explanation:

We can use a ratio to solve

33 hours            39 hours

---------------- = -------------

245.85              x dollars

Using cross products

33 * x = 39* 245.85

33x=9588.15

Divide each side by 33

33x/33 = 9588.15-33

x =290.55

Answer:

8 > u > 6

Step-by-step explanation:

We have to solve this inequality as 2 separate inequalities.

==============================================================

Inequality 1 :

⇒ 10 > 5u/4

⇒ 5u < 10 × 4

⇒ 5u < 40

⇒ u < 8 [Box 1]

============================================================

Inequality 2 :

⇒ 5u/4 > 15/2

⇒ 5u/2 > 15

⇒ u/2 > 3

⇒ u > 3 × 2

⇒ u > 6 [Box 2]

============================================================

Solution :

⇒ 8 > u > 6

Answer:

  143

Step-by-step explanation:

The interval of interest extends from the mean score (71) to 2 standard deviations above the mean (71+2(6) = 83). The area under the normal distribution curve in this interval can be found using a suitable table, probability app, spreadsheet, or web site. It can also be found using the "empirical rule", which tells you that the 95% of the area is within 2 standard deviations of the mean.

__

Since the curve is symmetrical, and we're only interested in the area above the mean, the empirical rule tells us that 95%/2 = 47.5% of the sample will be in the range of interest.

  0.475 × 300 = 142.5 ≈ 143

143 students will have a score between 71 and 83.

__

The attachment shows a calculator output for the same calculation. You will notice it is slightly different from the "empirical rule," which is only an approximation. Either way, we find 143 students have scores in the range.

Answer:

[tex]\dfrac{2x+4}{x(x+2)(x-4)} \equiv \dfrac{1}{2(x-4)}-\dfrac{1}{2x}[/tex]

Step-by-step explanation:

Write out the expression as an identity:

[tex]\begin{aligned}\dfrac{2x+4}{x(x+2)(x-4)} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+2)}+\dfrac{C}{(x-4)}\\\\\implies \dfrac{x(2x+4)(x+2)(x-4)}{x(x+2)(x-4)} & \equiv \dfrac{Ax(x+2)(x-4)}{x}+\dfrac{Bx(x+2)(x-4)}{(x+2)}+\dfrac{Cx(x+2)(x-4)}{(x-4)}\\\\\implies 2x+4 & \equiv A(x+2)(x+4)+ Bx(x-4)+Cx(x+2)\end{aligned}[/tex]

Calculate the values of A, B and C using substitution:

[tex]\begin{aligned}2x+4 & = A(x+2)(x-4)+Bx(x-4)+Cx(x+2)\\\\x=4 \implies 12 & = A(0)+B(0)+C(24)\implies C=\dfrac{1}{2}\\\\x=-2 \implies 0 & = A(0)+B(12)+C(0) \implies B=0\\\\ x=0 \implies 4 & = A(-8)+B(0)+C(0) \implies A=-\dfrac{1}{2}\end{aligned}[/tex]

Replace A, B and C in the original identity:

[tex]\begin{aligned}\dfrac{2x+4}{x(x+2)(x-4)} & \equiv \dfrac{A}{x}+ \dfrac{B}{(x+2)}+\dfrac{C}{(x-4)}\\\\& \equiv -\dfrac{1}{2x}+\dfrac{1}{2(x-4)}\\\\\implies \dfrac{2x+4}{x(x+2)(x-4)}& \equiv \dfrac{1}{2(x-4)}-\dfrac{1}{2x}\end{aligned}[/tex]

The shape of the barrier is a circle with a diameter of 5 feet. The correct option is the last option - A circle with a diameter of 5 feet

From the question, we are to determine the statement that describes the shape of the barrier

From the given information,

The barrier is 2.5 feet from the tomato plant in every direction.

This can be likened to a circle that has a radius of 2.5 feet.

Recall: Radius of a circle is the distance from the center of the circle to any point on it's circumference

If radius of a circle is 2.5 feet, the diameter will be 2 × 2.5 feet = 5 feet

Hence, the shape of the barrier is a circle with a diameter of 5 feet. The correct option is the last option-  A circle with a diameter of 5 feet

Here is the complete question:

Serena constructed a wire barrier to protect her tomato plant from squirrels. The barrier is 2.5 feet from the tomato plant in every direction. Which statement describes the shape of the barrier?

A circle with a radius of 5 feet

A square with diagonals 5 feet long

A square with sides 5 feet long

A circle with a diameter of 5 feet

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Answer:

The answer is 1/2

Answer:

1/2

Step-by-step explanation:

[tex]\frac{1}{12}+\frac{5}{12} = \frac{6}{12}\\ \\ \frac{6}{12} = \frac{1}{2}[/tex]They are both equivalent fractions. If you divide the numerator and denominator both by 6, you get 1/2.

19 players x 87kg = 1653 total kg

1653 kg + 102kg = 1755 kg

1755kg / 20 players = 87.75kg mean mass

Answer: 87.75 kg

The function f(x) is a logarithmic function with a horizontal asymptote of y=1. The range of the function is all real numbers greater than 1, and it is decreasing on its domain of x>0. The end behavior on the LEFT side is as x approaches zero, y approaches infinity, and the end behavior on the RIGHT side is as x approaches infinity, y approaches 1.

The answer to the all parts given below.

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function.

For 5 cuts number of pieces will be 11 pieces.

General formula:

Tn= 2n+1

For 153 rope pieces number of rope cutting

2n+1=153

2n= 152

n= 76

For 11 cuttings rope pieces will be

2(11)+1

= 23

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Looking at the problem statement, this question states for us to determine the range of the function that is provided in a graph is.  Let us first determine what range is.

Now moving back to our problem, we can see that we have a vertex at (2, -5) and that the lowest y-values is at y = -5.  Therefore the y-values would be anything greater than or equal to -5 and less than infinity because the lines go forever up in the positive-y-direction.

Therefore, the option that would best match the description that we provided would be option B, -5 ≤ y < ∞.

Answer:

17

Step-by-step explanation:

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

[tex]10, 12, 14, 16, 18, 20, 22, 24[/tex]

Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 16 and 18. The median is the average of these numbers. We have

[tex]{\frac{ 16 + 18 }{2}}[/tex]

Therefore, the median is

[tex]17[/tex]

Ty's brother will get 3/4th part of the pizza.

The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing.

Here, Total number of Pizza = 1

         Number of parts required = 4

Now, each member will get the part of pizza = 1/4

Total number of brothers = 3

Ty's brother will get pizza = 3 X 1/4

                                           = 3/4

Thus, Ty's brother will get 3/4th part of the pizza.

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Answer:

3/4

Step-by-step explanation:

because there are 4 people so ty get 1/4 and his brothers get the rest.

Answer:

You have walked 7.0 steps

Step-by-step explanation:

You just add 4 steps by 3 steps, so 4+3=7

Answer:

radius = √35 mm or 5.916 mm

Explanation:

Here:

Solve for radius:

[tex]\rightarrow \sf \pi r^2 = 110[/tex]

[tex]\rightarrow \sf \dfrac{22}{7} r^2 = 110[/tex]

[tex]\rightarrow \sf r^2 = \dfrac{110(7)}{22} =35[/tex]

[tex]\rightarrow \sf r = \sqrt{35}[/tex]

Let's see

( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than’

Finding the solution for the inequality is as follows:-

y ≤  x² +x-4 by putting x and y equal to 0.

0 ≤ 0 + 0 -4

0 ≤ - 4

This is incorrect so (0,0) can not be the solution for this inequality.

y < x²+2x+1.

0 < 0 + 0 + 1

0 < 1

This inequality is showing the solution for (0,0)

Therefore ( 0,0 ) is not the solution of the first inequality y≤x² +x-4 but ( 0,0) is the solution for the second inequality y <x²+2x+1.

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Answer:

Point D

Step-by-step explanation:

[tex] \huge \qquad \sf Answer[/tex]

How to locate a point on a graph (x - y plane) :

The x - coordinate of a point on the graph shows its distance from y - axis and sign refers to its direction that is +ve sign means right side of y - axis and -ve sign means left side of y - axis.

We have been given its x - coordinate as 9, so the required point should be At a distance of 9 units from y - axis and in right side of y - axis.

And similarly, y - coordinate shows distance of point from x - axis, +ve for upward direction and -ve for downward direction.

and we have given the y - coordinate as 0, ao its distance from x - axis is 0. that means the point lies of x - axis.

And by Observing the points clearly we can figure out that the required point is D. that satisfy the condition.

Answer:

About 12 blue m&m’s

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

I think Mrs. Nygaard would need 2 hours to work over the weekend to finish grading the projects .

The equation of this sinusoidal function is either

f(x) = a sin(bx) + c

or

f(x) = a cos(bx) + c

Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.

If the period is π/2, then

2π/b = π/2   ⇒   b = 4

If the maximum value is 10 and the minimum value is -4, then

-4 ≤ a sin(4x) + c ≤ 10

-4 - c ≤ a sin(4x) ≤ 10 - c

-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a

Recall that sin(x) is bounded between -1 and 1. So we must have

-(4 + c)/a = -1   ⇒   a = c + 4

(10 - c)/a = 1   ⇒   a = -c + 10

Combining these equations and eliminating either variable gives

a + a = (c + 4) + (-c + 10)   ⇒   2a = 14   ⇒   a = 7

a - a = (c + 4) - (-c + 10)   ⇒   0 = 2c - 6   ⇒   c = 3

Finally, we have either

f(x) = a sin(bx) + c   ⇒   f(0) = c = 3

or

f(x) = a cos(bx) + c   ⇒   f(0) = a + c = 3

but the cosine case is impossible since a = 7.  

So, the given function has equation

f(x) = 7 sin(4x) + 3

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to simplify the expression 2(7x+3)+9x.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So, let's compute...

\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\\///\\\////\\\///\\\///\\\///\\\///\\\///\\\//\\//\\\/

After performing multiplication we obtain

[tex]\star~\mathrm{14x+6+9x}[/tex]

Now add 9x:

[tex]\star~\mathrm{23x+6}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

B. 0.08

Step-by-step explanation:

In order to solve this problem, we must account for all possibilities. The sum of all posssiblities must sum up to 1.

1 - High Attendance/No Rain

0.9*0.8 = 0.72

2- High Attendance/ Rain

0.4*0.2 = 0.08

3 - Low Attendance/No Rain

0.1*0.8 = 0.08

4 - High Attendance/No Rain

0.6*0.2 = 0.12

Now we answer the question of rain and high attendance.

0.08/1 = 0.08

The value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a probability distribution shown in the picture.

To find the probability P(X<3) = area up to 3

From the probability distribution:

P(X<3) = (1/2)×3×(0.20)

P(X<3) = 1.5×0.20

P(X<3) = 0.3

Thus, the value of probability P(X<3) is 0.3 after calculating the area up to 3 option second is correct.

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Answer:

£280

Step-by-step explanation:

238/0.85

Answer:

3

Step-by-step explanation:

A function cannot have two y values for any value of x

answer three has two y values for x =1

Answer: 67

Step-by-step explanation:

∛125 = 5

62 + 5 = 67

By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).

In this question we must apply a rigid transformation on a point to find its image, rigid transformations are transformations applied on geometric loci such that Euclidean distances are observed in every point of the loci. A rotation about the origin is a kind of rigid transformation and is defined by the following expression:

(x', y') = (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

Please notice that positive values of θ represents a counterclockwise rotation. If we know that (x, y) = (7, 8) and θ = 90°, then the resulting point is:

(x', y') = (7 · cos 90° - 8 · sin 90°,  7 · sin 90° + 8 · cos 90°)

(x', y') = (-8, 7)

By applying the equation for the rotation around the origin we conclude that the image of the point (7, 8) after rotating 90° counterclockwise is (-8, 7).

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