Select the function that has a well-defined inverse. Explain
a. : → (x) = x + 4
b. : → (x) = 2x − 5
c. : → + (x) = |x|
d. : → (x) = ⌈x/2⌉

Answer: Domain (3, infinity); Asymptote x = 3

Step-by-step explanation:

log(x) domain is (0, infinity), but in this function the (x - 3) shifts the graph 3 to the right

The asymptote is 3 because log(3-3) = log(0) which does not exist (and any number that is negative inside log too) the function can't reach 3 which makes it the asymptote

Answer:

A:   -1 + 2 log4^x

C: log4 (1/4) + log4 x^2

Step-by-step explanation:

Apply logarithm properties:

log4 (1/4x^2)  =  log4 (1/4) + log4 x^2

Evaluate: log4 (1/4)

log4 (1/4) = -1

Substitute the value back:

-1 + lg4 x^2

Apply logarithm properties:

-1 + 2 log4 ^x

Draw a conclusion:

The expressions equivalent to: log4 (1/4x^2) are:

Answer Choices: A, and C

A= -1 + 2 log4^x

C=  log4 (1/4) + log4 x^2

Hope this helps!

Answer:

f(x)+41 f(-10)=7

Step-by-step explanation:

Answer:

x^2

Step-by-step explanation:

Any even number raised to two is even.

Eg: 4^2 = 16

12^2 = 144

Etc...

And

Any odd number raised to two is odd.

Eg: 5^2 = 25

13^2 = 169

Etc...

And also x^2 is greater than 2x & x+3 & x+2

The measures of the unknown angles are

x = 46

and

y = 88

From the question, we are to determine the measures of the unknown angles in the triangle.

From the diagram, we can observe that the triangle is an isosceles triangle as the legs of the triangle are congruent to each other.

Since the triangle is an isosceles triangle, the base angles of the triangle must be equal

The base angles are 46° and x°

Thus,

x = 46

Also,

We can write that

y° + 46° + x° = 180° (Sum of angles in a triangle)

y° + 46° + 46° = 180°

y° + 92° = 180°

y° = 180° - 92°

y° = 88°

Thus,

y = 88

Hence, x = 46 and y = 88

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Lifesaver:

∠A = ∠C

⇒ AB = BC (Equal angles have equal sides opposite to them)

⇒ 5x+6 = 3x+14

⇒ 5x-3x = 14-6

⇒ 2x = 8

⇒ x= 4

Answer:

Step-by-step explanation: then let's be kinda quaint in the matter. And assume your understanding of word integration in a 5-Manifold?

Answer: Hey! Answer would be 4 Weeks

Step-by-step explanation:

28(days) divided by 7(1week)= 4

The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

It is (40 - x)36 + (92 - 40)48 = C

Answer:

(40 - x)36 + (92 - 40) * 48 = C

I think this is what the answer is. Tell me if I'm wrong please.

Answer:

\(u^{2n+1}\)

Step-by-step explanation:

Assuming you mean \(u^nu^{n+1}\), then \(u^nu^{n+1}=u^{n+n+1}=u^{2n+1}\).

Answer:

\(\Longrightarrow: \boxed{\sf{u^2^n+1}}\)

Step-by-step explanation:

This equation can be solved simply by multiplying by the variable to isolate them on one side.

\(\Longrightarrow: \sf{u^n*u^n+1}\)

\(\sf{u^n*u^n=u^2}\\\\\\\sf{= (u^2)^n}\)

Solve.

\(\sf{\left(u^2\right)^n=u^{2n}=\boxed{\sf{u^{2n}+1}}\)

Therefore, the final answer is \(\boxed{\sf{u^{2n}+1}}\).

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

100 square inches

Step-by-step explanation:

20*4=100

a) The size of each payment = $8718.4

b) The the total amount paid for the purchase = $204620.8

c) The total interest paid over the life of the loan = $104620.8

In this question we have been given that a man buys a house for $175,000. He makes a $75,000 down payment and amortizes the rest of the debt with semiannual payment sover the next 10 years. The interest rate on the debt is 12%, compounded semiannually.

We need to find the size of each payment, the total amount paid for the purchase and the total interest paid over the life of the loan.

From given data we get 175,000 - 75,000 = $100,000 amount to finance.

We know that the formula for semiannual payment of a loan,

C = PV/[1 - (1 + r)^-t / r]

Here, PV = $100,000

t = 20 (10 years times 2 payment per year)

r = 0.06 (12% annual. so, we divide by 2 to get semiannual)

So, C = 100,000/[1 - (1 + 0.06)^-20 / 0.06]

C =  100,000/[0.6882 / 0.06]

C = 100,000/11.47

C = $8718.4

The total interest paid will be the cuota times the time of the loan:

Total interest paid:

8718.4 x 12 = 104620.8

And the total amount paid over the life of the loan = 104620.8 + 100,000

                                                                                    = $204620.8

The interest will be the difference between the total amount paid and the principal of the loan

Therefore, Interest paid = $8718.4

total payment   = $204620.8

principal = $100,000

Interest expense = $104620.8

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The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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Answer:Yes

Step-by-step explanation: 10/5 is 2

Answer:

,

Step-b,y-step explanation:

The slope of the line passes through the points (-5,6) and (-3,2) is 2.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

Given that the line that passes through the points (-5,6) and (-3,2).

The slope of the line is calculated by the formula,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 6 - 2) / ( -3 + 5)

Slope = 4 / 2

Slope = 2

Therefore, the slope of the line passes through the points (-5,6) and (-3,2) is 2.

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In linear equation, The number of suitcases are 503.

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                   Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Equation

y = 1.98x + 7.97

Where,

x = Number of passengers

y = Number of suitcases

Finding the number of suitcases:

y = 1.98x + 7.97

y = 1.98(250) + 7.97

y = 495 + 7.97

y = 502.97 ≈ 503

Hence,

The number of suitcases are 503.

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The 95% confidence interval for the slope will be B. (-0.308,-0.019).

The confidence interval based on the information and diagram will be:

= -0.1636 + 2.228 × 0.06488

= 0.019

Also, -0.1636 - 2.228 × 0.06488

= -0.308

In conclusion, the correct option is (-0.308,-0.019).

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solution of the linear equation is x = (2a - 16)/ 3 and y = - (a+16)/ 9

An algebraic expression that shows a relationship between two variables   that have only first order term. One of the main criteria for linear equation is that we get a straight line when plot this equation in a coordinate system.

.

we are given, two linear equations x - a -3y = 0

and a - 2x -3y - 16 =0

from the first equation, x = a + 3y

we put the value of x in the second equation, a - 2(a +3y) - 3y -16= 0

                                                                     a - 2a - 6y - 3y -16 = 0

                                                          - a - 9y -16 =0

                                                   - (a + 16) = 9y

                                              y = - (a+16) / 9

now we put the value of y in the equation, x = a + 3y

                                    get, x = a+ 3 [ - (a+16)] / 9

                                      x = a + [ - (a+16)] / 3

                                          x = (3a - a -16) / 3

                              x = (2a - 16)/ 3

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Mr. Brown picks out the time that appears the most to find the mode.

He arranges the times in increasing order and picks the middle value to find the median.

The times in seconds for the 100-meter dash are as follows: 12.5, 12.4, 12.4, 12.3, 12.6, and 12.4.

The mode is the value or values that appear most frequently in a dataset.

In this case, the time that appears the most is 12.4, which occurs three times.

Therefore, the mode is 12.4.

The median is the middle value in a dataset when arranged in increasing or decreasing order.

When we arrange the times in increasing order, we have: 12.3, 12.4, 12.4, 12.4, 12.5, 12.6.

The middle value is 12.4, so the median is 12.4.

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Answer:

33.5 units²

Step-by-step explanation:

We can see this figure as 2 shapes: a square and a triangle. The square measures 4 x 4, and it's area is 16. That leaves the triangle, which has half the area of a quadrilateral that measures 5 x 7. The area of the quadrilateral is 35, and the triangle has an area of 17.5, which is half of that. Adding them together, we get 33.5.

Answer:

33.5 unit²

it's a mixture of triangle and square.

draw a imaginary straight line across the figure from that line which has length of 3 units and now you can see the triangle and the square. Use the formula to find area of triangle and area of square and the sum of their area will be the area of this whole figure i.e 35.5 unit²

Answer:

Ok Ill help you :)

Step-by-step explanation:

a)  -125

b)  +27

c)  -9

d)  +9/8

I hope this helps!!! ❤️

Answer:

a1=3, a2=6, a3=12, a4=24, a5=48

Step-by-step explanation:

a7=a*r^6=192

a10=a*r^9=1536, r^3=8, r=2 and a=3

a1=3, a2=6, a3=12, a4=24, a5=48

The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, two equations can you use to find the adult and child admission fees for a puppet show

Let a represent the fee for adults

Let c represent the fee for children.

On day 1 number of adults = 45

So, fees of 45 adults = 45a

On day 1 number of children= 30

So, fees of 30 children = 30c

Total collection on day 1 = 315

Therefore, equation is 45a + 30c = 315

On day 2 number of adults = 50

So, fees of 50 adults = 50a

On day 2 number of children = 40

So, fees of 40 children = 40c

Total collection on day 2 = 370

So, equation = 50a + 40c = 370

Hence, The two equations can you use to find the adult and child admission fees for a puppet show are 45a + 30c = 315 and 50a + 40c = 370

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Answer:

please give the complete question..

Step-by-step explanation:

please give the complete question..

Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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