Solve each exponential equation. round your answer to two decimal places.
4a. 4²x +3=1

4b. ex-1 -5 = 5

Answer:

$230

Step-by-step explanation:

Hes paid 200 for his wages but if he works overtime by 12 hours he gets half of the 5 dollars he earns per hour which is 2.5 which then is 2.5 times 12 which is then 30 plus the 200 he earned for the 40 hours.

Answer:

areas of AXYZ=10 square units1

Answer:

10 units squared

Step-by-step explanation:

Area of a triangle = 1/2 × base × height

Use the distance between two points formula to find the measure of the height and base of ΔXYZ.

Distance between two points

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}\)

Height of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

\(\begin{aligned}\implies \sf height & =\sqrt{(4-2)^2+(5-1)^2}\\& = \sqrt{2^2+4^2}\\& = \sqrt{20}\end{aligned}\)

Base of Triangle

Define the points:

Substitute the points into the distance formula to find the height of the triangle:

\(\begin{aligned}\implies \sf base & =\sqrt{(4-0)^2+(0-2)^2}\\& = \sqrt{4^2+(-2)^2}\\& = \sqrt{20}\end{aligned}\)

Area of Triangle

\(\begin{aligned}\implies \sf Area & = \dfrac{1}{2} \times \sf base \times height\\& = \dfrac{1}{2}\sqrt{20}\sqrt{20}\\& = \dfrac{1}{2}(20)\\& = 10 \sf \:\:units^2 \end{aligned}\)

Answer:

-3

Step-by-step explanation:

-7x=-2x+15

collect like terms

-7x+2x=15

-5x=15

divide both sides by -5

x=15/-5

x=-3

The answer is that The critical point (0, 0) is asymptotically stable (C) and is a proper node (C).

To find the linearization of the given system, we need to calculate the Jacobian matrix and evaluate it at the critical point (0, 0). The given system is:

x' = -6x - y - x^2
y' = 16x - 6y - 2xy^3

The Jacobian matrix J(x, y) is:

J(x, y) = | -6 - 1 - 2x, -1          |
         | 16 - 6y^2 - 2x, -6 - 6x^2 |

Evaluating J(x, y) at the critical point (0, 0):

J(0, 0) = | -6, -1 |
         | 16, -6 |

Now we need to find the eigenvalues of this matrix to determine the stability of the critical point (0, 0). The eigenvalues of J(0, 0) are λ1 = -2 and λ2 = -10. Both eigenvalues are real and negative.

The critical point (0, 0) is asymptotically stable (C) and is a proper node (C).

Now, to find the solution to the linearization with initial conditions x(0) = -0.3 and y(0) = 1, we need to solve the linearized system:

x' = -6x - y
y' = 16x - 6y

Since the initial conditions are x(0) = -0.3 and y(0) = 1, we can't provide a closed-form solution without more information. However, the linearized system can be solved numerically or analytically using various methods such as matrix exponentials or numerical integration.

Your answer:
The critical point (0, 0) is asymptotically stable (C) and is a proper node (C).

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The finite subgroups of C*, the group of non-zero complex numbers under multiplication, are isomorphic to either the cyclic groups of order n or the dihedral groups of order 2n, where n is a positive integer.

A finite subgroup of C* is a group H consisting of finitely many complex numbers such that H is closed under multiplication, contains the identity element 1, and each element of H has an inverse in H. Since C* is an abelian group, any finite subgroup of C* is also abelian. By the fundamental theorem of finite abelian groups, any finite abelian group can be expressed as a direct sum of cyclic groups of prime power order.

Since the elements of C* can be written in polar form as z = re^(iθ), where r is the magnitude of z and θ is the argument of z, any finite subgroup of C* can be expressed as a collection of complex numbers of the form e^(2πki/n), where k and n are positive integers. It follows that any finite subgroup of C* is isomorphic to either the cyclic group of order n or the dihedral group of order 2n, where n is a positive integer. The cyclic group of order n consists of the n-th roots of unity, while the dihedral group of order 2n consists of the 2n-th roots of unity together with reflections.

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Answer:

Linear model

Step-by-step explanation:

A linear model models a real-life situation y = mx + b (m will be the constant rate of change and b is the initial or starting value)

A linear function that mimics a real-world scenario is known as a linear model.

A continuous response variable is described by a linear model as a function of one or more predictor variables. They can assist you in analyzing experimental, monetary, and biological data or in understanding and predicting the behavior of complex systems. A statistical technique used to build a linear model is called linear regression.

It is called a linear model because the formula indicates a link between the left and right sides that is established by "linear" or "constant" parameters for each term, which are then solved for to reduce the overall divergence of the data from the model.

By using a linear combination of predictor variables, linear models can be used to describe a response variable.

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Answer:

A) (3, 6)

B) (2, 3)

C) (4, 2)

D) (6, 0)

Answer:

\(117.8cm ^{2} \)

Step-by-step explanation:

\(a = {r}^{2} \theta \: \div 2 \\ = 100 \times 135 \div 2 \\ = 117.8 \: {cm}^{2} \)

Answer:

27,36,45

Step-by-step explanation:

Pythagorean theorem

\(a^{2} +b^{2} =c^{2}\)

\(6^{2}+ 9^{2}\\ =117\\\neq 12^{2}\)

\(7^{2}+ 10^{2}\\ =149\\\neq 12^{2}\)

\(16^{2}+ 18^{2}\\ =580\\\neq 25^{2}\)

\(27^{2}+ 36^{2}\\ =2025\\= 45^{2}\)

16504 divided by 55 equals

300+ 4/55.

First we know about -

Divisor: The number by which the dividend is divided.

Quotient: The result of division.

Remainder: The amount that is left over after division.

Rules for the Division -

1. Take the first digits of the dividend, the same number of digits that the divisor has. If the number taken from the dividend is smaller than the divisor, you need to take the next digit of the dividend.

2. Divide the first number of the dividend (or the two first numbers if the previous step took another digit) by the first digit of the divisor. Write the result of this division in the space of the quotient.

3. Multiply the digit of the quotient by the divisor, write the result beneath the dividend and subtract it. If you cannot, because the dividend is smaller, you will have to choose a smaller number in the quotient until it can subtract.

4. After subtraction, drop the next digit of the dividend and repeat from step 2 until there are no more remaining numbers in the dividend.

        0 0 3 0 0

5 5 ) 1 6 5 0 4

 − 0        

   1 6      

 −   0      

   1 6 5    

 − 1 6 5    

       0 0  

     −   0  

         0 4

       −   0

           4

16504 divided by 55 equals

300 with a remainder of 4

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The angle measures are A, B, C, D are 35, 55,55,55.

According to the statement

we have given that the bridge is perpendicular to the two towers. a. Angle A is 35 degrees.

And we have to find that the measure of angles B, C, and D.

So, For this purpose, we know that the

Angle A is 35 degrees and hint given is that the all angles in a triangle add to 180 degrees.

So,

A + B + X = 180

we know that A = 35 and X = 90 and

35 + B + 90 = 180

B = 180 - 90 - 35

B = 55

And

Now we find that the another angle Y.

So,

A + B + Y = 180

35 + 55 + Y = 180

Y = 90

Then

In order to calculate C, you have to make an assumption that was not given in the problem. The assumption is that triangles ABX and YCZ are mirror images of each other.

Then,

B = C = 55

And

and also since they are similar triangles,

D = C = 55.

So, The angle measures are A, B, C, D are 35, 55,55,55.

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Answer:

y = 2x - 48

Step-by-step explanation:

2x represents $2 profit for each hot dog

It costs the owner $48 for the supplies, so it's 2x - 48

y = 2x - 48 equation represents the profit earned by the x hot dog sold.

" A linear equation is an algebraic expression in which highest power of the given variable is equals to one."

According to the question,

x represents the number of hot dogs sold

y represents the total profit earned

Cost required for supply = $48

Profit on each hot dog sold = $2

As per the condition given we have

Required linear equation

y = 2x - 48

Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.

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Answer:

  (-5/3, -4/3)

Step-by-step explanation:

  3 < 6c +13 < 5 . . . . given

  -10 < 6c < -8 . . . . . subtract 13

  -10/6 < c < -8/6 . . . divide by 6

We can express the interval using reduced fractions as ...

  (-5/3, -4/3)

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Step-by-step explanation:

can u rephrase please thank u

The number of different ways you can arrange the fruit baskets when using all of the fruit is 30240.

There must be at least 5 but no more than 10 of each type of fruit in each basket.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Now, \(10P_5 = \frac{10!}{(10-5)!}\)

= (10 × 9 × 8 × 7 × 6 × 5!)/5!

= 10 × 9 × 8 × 7 × 6

= 30240

Therefore, the number of different ways you can arrange the fruit baskets when using all of the fruit is 30240.

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The expected amount of time that the 5:30 appointment spends at the barber shop is,  E[W] = 45 + 45/e.

Given that, the barber has scheduled two appointments, one at

5 pm and the other at 5:30 pm.

Since the amount of time that appointments last are independent exponential random variables with mean 45 minutes.

Let W be the time the 2nd person has to wait in chamber Let X be the time the barber takes checking 1st person X-exp(45)

The distribution is,

W= X-45            if X >45

otherwise.

Expected time 2nd person spends in barber chamber

= E (W)+45

[ 45 is the mean time barber takes checking 2nd person]

\(E(W) = \int\limits^{\infinity }_0 {WP(X=45+W)} \, dw\\ \\\\=\int {W.1/45e^{\frac{-45+w}{45} } \, dw\\\\\)

\(=e^{-1} \int\frac{W}{45} e^{\frac{-w}{45} } dw\\=\frac{45}{e}\)

The expected amount of time that the 5:30 appointment spends at the barber's office is,

\(E[W]=45+\frac{45}{e}\).

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The number of items that will maximize the profit is 2000. Thus, the correct answer is option c.

To calculate the maximum profit that can be earned we have to differentiate the equation and find the value of x

dP/dx = 1/dx (-3x² + 12x + 75)

= -6x + 12

Calculating dP/dx = 0

0 = -6x + 12

6x = 12

x = 2

Next, we calculate the next differential of the equation:

It comes out to be -6

Since it is smaller than zero, the value of x calculated is the maxima.

The maxima = 2

Thus, the item that will maximize the profit comes out to be 2000 as x is the number of items made in thousand.

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For a standard normal distribution, given p(z < c) = 0.624, we need to the balance  value of c.

This means that we need to find the z-value that has an area of 0.624 to the left of it in a standard normal distribution.To find this value, we can use a standard normal table or a calculator with a standard normal distribution function.Using a standard normal table:We look up the area of 0.624 in the body of the table and find the z-value in the margins. The closest area we can find is 0.6239, which corresponds to a z-value of 0.31.

Therefore, c = 0.31.Using a calculator:We can use the inverse normal function of the calculator to find the z-value that corresponds to an area of 0.624 to the left of it. The function is denoted as invNorm(area to the left, mean, standard deviation). For a standard normal distribution, the mean is 0 and the standard deviation is 1. Therefore, we have:invNorm(0.624, 0, 1) = 0.31Therefore, c = 0.31.

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Answer:

B. 11 4 (11 with the exponent of 4) because 11 was multiplied 4 times.

Step-by-step explanation:

Answer:

The answer Is 35.

Step-by-step explanation:

Answer:

35!

Step-by-step explanation:

Answer:

a=100

b=1

Step-by-step explanation:

18a+65b=1865

23a+7b=2314

We need to make one of the variables equal to the other

So...

The LCM for 65 and 7 is 455

So multiply 7 with 18a+65b=1865

and Multiply 65 with 23a+7b=2314

7 times 18a+65b=1865 is 126a+455b=13055

65 times 23a+7b=2314 is 1495a+455b=150410

So Subtract 126a+455b=13055 and 1495a+455b=150410

So 1369a=137355

Divide:

Which is about 100 (The actual value is 100.3323594)

Thus a=100

Substitute:

b=1

Hope this helps!

(The answer is rounded)

Answer:

8

Step-by-step explanation:

AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.

P = 3 + 3 + 2 = 8.

Answer:

its A or C

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

30-26.39=3.61

3.61 divided by 0.19 = 19

hope this helps :)

Step-by-step explanation:

y = ax^n + bx^(n-1) ... + z

(0, 1) tells us that the constant term z = 1.

because x = 0 eliminates all other terms. and as the sum is 1, that means z = 1.

for the other pairs I strongly suspect

(-1, 3) : 2×(-1)² + 1 = 2×1 + 1 = 3

(-2, 9) : 2×(-2)² + 1 = 2×4 + 1 = 9

so, the fitting equation is

y = 2x² + 1