Identify the domain of a radical function with an odd index.

Answer:

Option B.

Step-by-step explanation:

Option A.

f(x) = [tex](0.5)^{x}[/tex]

Derivative of the given function,

f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]

      = [tex](0.5)^x[\text{ln}(0.5)][/tex]

      = [tex]-(0.693)(0.5)^{x}[/tex]

Since derivative of the function is negative, the given function is decreasing.

Option B. f(x) = [tex]5^x[/tex]

f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]

      = [tex](5)^x[\text{ln}(5)][/tex]

      = [tex]1.609(5)^x[/tex]

Since derivative is positive, given function is increasing.

Option C. f(x) = [tex](\frac{1}{5})^x[/tex]

f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]

      = [tex]\frac{d}{dx}(5)^{(-x)}[/tex]

      = [tex]-5^{-x}.\text{ln}(5)[/tex]

Since derivative is negative, given function is decreasing.

Option D. f(x) = [tex](\frac{1}{15})^x[/tex]

                f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]

                       = [tex]-2.708(15)^{-x}[/tex]

Since derivative is negative, given function is decreasing.

Option (B) is the answer.

Answer: The x-intercept is  4  and the y-intercept is 2.

Step-by-step explanation:

The x is intercept is when y is 0 and the y intercept is when x is 0.So using this information you can put in 0 for x and another 0 for y and solve for the x and y intercepts.

7(0) + 14y = 28

0    + 14y = 28

   14y = 28

  y =  2

7x + 14(0) = 28

7x + 0 = 28

  7x = 28

x =  4

The [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].

Given:

The equation is:

[tex]7x+14y=28[/tex]

To find:

The [tex]x[/tex]-intercept and [tex]y[/tex]-intercept of the given equation.

Explanation:

We have,

[tex]7x+14y=28[/tex]          ...(i)

Substitute [tex]x=0[/tex] in (i) to find the [tex]y[/tex]-intercept.

[tex]7(0)+14y=28[/tex]

[tex]14y=28[/tex]

[tex]\dfrac{14y}{14}=\dfrac{28}{14}[/tex]

[tex]y=2[/tex]

Substitute [tex]y=0[/tex] in (i) to find the [tex]x[/tex]-intercept.

[tex]7x+14(0)=28[/tex]

[tex]7x=28[/tex]

[tex]\dfrac{7x}{7}=\dfrac{28}{7}[/tex]

[tex]x=4[/tex]

Therefore, the [tex]x[/tex]-intercept of the given equation is [tex]4[/tex] and the [tex]y[/tex]-intercept is [tex]2[/tex].

Learn more:

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Work Shown:

v - w = ( v ) - ( w )

v - w = ( -3i ) - ( 2-4i)

v - w = ( 0-3i ) - ( 2-4i)

v - w = 0-3i   -2+4i

v - w = (0-2) + (-3i+4i)

v - w = -2 + i

Answer:

idk what you mean

Step-by-step explanation:

idk

Answer:

see below

Step-by-step explanation:

3 red sections, 2blue sections, and 1 purple section = 6 sections

P( red) = red/total = 3/6 =1/2

P( blue) = blue/total = 2/6 =1/3

P( purple) = purple/total = 1/6

Answer:

This is the answer

Step-by-step explanation:

Answer:

El resto es 9.

Step-by-step explanation:

En una división el cociente es el resultado que se obtiene, el divisor es el número por el que se divide otro número, el dividendo es el número que va a dividirse entre otro y el resto es lo que queda cuando un número no puede dividirse exactamente entre otro. De acuerdo a esto, la división planteada se encuentra en la imagen adjunta donde al resolverla se encuentra que el número que queda es 9 y este es el resto.

Answer:

  1.4

Step-by-step explanation:

The average rate of change is the "rise" divided by the "run".

  rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)

  rise/run = 7/5 = 1.4

The average rate of change on the interval [-1. 4] is 1.4.

We will see that the average rate of change in the given interval is 1.4

For a given function f(x), the average rate of change on an interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this case the interval is [-1, 4], using the graph we can see that:

f(-1) = -7

f(4) = 0

replacing that in the formula we get:

[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]

If you want to learn more about rates of change, you can read:

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Answer:

  $2756 million

Step-by-step explanation:

  2.756×10⁹ = 2756×10⁶

Sales in 2014 were $2756 million.

_____

Comment on the question

In the US, a billion is 1000 million. In some other parts of the world, a billion is a million million. This sort of question can be ambiguous.

Answer:

A.

Step-by-step explanation:

Volume of cone = 1/3πr²h

= (1/3)(3.14)(1.5)²(5)

= (1/3)(3.14)(2.25)(5)

= (1/3)(35.3)

= 11.78

≈ 11.8 cubic inches

Answer:

Please see steps below

Step-by-step explanation:

Notice the following:

(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure)  [tex]\angle 1 \,=\,\angle 5[/tex]

(b) Angles 6 and 3 are also alternate angles  between parallel lines, so they must be congruent (equal measure)  [tex]\angle 3 \,=\,\angle 6[/tex]

Therefore, instead of expressing the addition:

[tex]\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6[/tex]

we can write:

[tex]\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3[/tex]

which in fact clearly add to [tex]180^o[/tex]

Answer:

24

Step-by-step explanation:

Formula

The area of a Trapezoid is given as

A = (b1 + b2)*h/2

Givens

b1 = 8

b2 = 4

h = 4

Solution

Area = (8 + 4)*4/2

Area = 12*4/2

Area = 24

Answer:

50π cm²

Step-by-step explanation:

In this case we have that the area of the boomerang has been the area of the largest semicircle minus the area of the smaller semicircles.

We know that the radius is half the diameter:

r = d / 2 = 20/2

r = 10

Now we have to:

Alargest = π · r²

Alargest = π · (10 cm) ²

Alargest = 100π cm²

Asmaller = π · r²

Asmaller = π · (5 cm) ²

Asmaller = 25π cm²

Finally, the boomerang area has been:

Aboomerang = 100π cm² - 2 · (25π cm²)

Aboomerang = 50π cm²

Answer:

x+(x+2) = 156

Step-by-step explanation:

Let x = 1st odd integer

x+2 = next odd integer

x+(x+2) = 156

2x+2 =156

Subtract 2

2x= 154

Divide by 2

x = 77

x+2 = 79

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12​-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 ​feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the​ wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

Answer:

1.2 km

Step-by-step explanation:

The first thing that we should go over is the formula for the area of a trapezoid.

Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]

From this image, we have the following information

[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]

Now, we can plug this information into our formula and then solve for h.

[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]

Another method that can be employed is to use the pythagorean theorem.

A trapezoid can be be broken into a rectangle and two triangles.

If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.

As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.

[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]

Answer:

h=1.2 km

Step-by-step explanation:

This is the formula of a Trapezium

A=[tex]\frac{h(a+b)}{2}[/tex]

[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]

Answer:

-9

Step-by-step explanation:

5x+8-3x = -10

Combine like terms

2x+8 = -10

Subtract 8 to both sides

2x = -18

Divide both sides by 2

x = -9

Answer:

-9

Step-by-step explanation:

5x + 8 - 3x = -10

Combine like terms

2x + 8 = -10

Subtract 8 to both sides

2x = -18

Divide both sides by 2

x = -9

Answer:

1/3 left

Step-by-step explanation:

The total sandwich is 1 or in fraction form 6/6

He ate 2/6

6/6 -2/6 = 4/6

Then he ate 2/6 more

4/6 -2/6 = 2/6

He has 2/6 left

Simplifying

2/6 =1/3

Answer:

D

Step-by-step explanation:

If <CAD=35, <KNL=55 because the remaining angle is 90 since it's a right angle. Therefore <KNM=110 because 55+55=110

Answer:

Step-by-step explanation:

6.81 - 6.79 - 6.69 - 6.59 - 6.65 - 6.60 - 6.74 - 6.70 - 6.76

6.84 - 6.81 - 6.71 - 6.66 - 6.76 - 6.76 - 6.77 - 6.72 - 6.68

7.71 - 6.79 - 6.72 - 6.72 - 6.72 - 6.79 - 6.83

[tex]\bar x =6.77[/tex]

S.D = 0.21

[tex]I=6.77\pmt\times\frac{s}{\sqrt{n} }[/tex]

df = 24

α = 0.05

t = 2.064

[tex]I=6.77\pm2.064\times\frac{0.21}{\sqrt{25} } \\\\=6.77\pm0.087\\\\=[6.683,6.857][/tex]

b)

[tex]\sqrt{\frac{(1-n)s^2}{X^2_{\alpha /2} } < \mu <\sqrt{\frac{(1-n)s^2}{X^2_{1-\alpha/2} } }[/tex]

[tex]\sqrt{\frac{24 \times 0.21^2}{39.364} } < \mu <\sqrt{\frac{24 \times 0.21^2}{12.401} } \\\\=0.1640<\mu<0.2921[/tex]

Tell me if it is right

Answer:

213, 123

Step-by-step explanation:

Answer:

The substance's half-life is 6.4 days

Step-by-step explanation:

Recall that the half life of a substance is given by the time it takes for the substance to reduce to half of its initial amount. So in this case, where they give you the constant k (0.1088) in the exponential form:

[tex]N=N_0\,e^{-k\,*\,t}[/tex]

we can replace k by its value, and solve for the time "t" needed for the initial amount [tex]N_0[/tex] to reduce to half of its value ([tex]N_0/2[/tex]). Since the unknown resides in the exponent, to solve the equation we need to apply the natural logarithm:

[tex]N=N_0\,e^{-k\,*\,t}\\\frac{N_0}{2} =N_0\,e^{-0.1088\,*\,t}\\\frac{N_0}{2\,*N_0} =e^{-0.1088\,*\,t}\\\frac{1}{2} =e^{-0.1088\,*\,t}\\ln(\frac{1}{2} )=-0.1088\,t\\t=\frac{ln(\frac{1}{2} )}{-0.1088} \\t=6.37\,\,days[/tex]

which rounded to the nearest tenth is: 6.4 days

Answer:

6.4

Step-by-step explanation:

I did it on the same site and got it correct

Answer:

The answer is 2.5 hours

Step-by-step explanation:

Answer:

The answer is 295 square yards.

Step-by-step explanation:

[48(72-12)-15^2] divide by 9

3456-576-225 divide by 9

Subtract 3456 by 576

2880-255

2655 divide by 9

=295 square yards.

Hope this helped!

The answer is 295 square yards.

To find the area of square , take the square of side.

Given expression is [48(72-12)-15^2] divide by 9 .

Let the unknown area is x.

x = {48 * 60 - 15^2 } divide by 9

x = 2880 - 225 divide by 9

x = 2655 divide by 9

x =295 square yards.

Hence, The answer is 295 square yards.

To learn more about the area of square;

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#SPJ2

Answer:

D: 13

I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.

Answer:

P = 62.5 %

Step-by-step explanation:

Of means multiply and is means equals

P * 48  = 30

Divide each side by 48

P = 30/48

P = .625

Change to percent form

P = 62.5 %

Answer:

62.5%

Step-by-step explanation:

30 is 62.5% of 48 since:

30÷48=0.625

0.625×100=62.5%

Answer:

Between 0.01 and 0.20

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 500, p = 0.05[/tex]

So

[tex]\mu = E(X) = np = 500*0.05 = 25[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{500*0.05*0.95} = 4.8734/tex]

Find the probability of winning at least 30 times.

Using continuity correction, this is [tex]P(X \geq 30 - 0.5) = P(X \geq 29.5)[/tex]. So this is 1 subtracted by the pvalue of Z when X = 29.5. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{29.5 - 25}{4.8734}[/tex]

[tex]Z = 0.92[/tex]

[tex]Z = 0.92[/tex] has a pvalue of 0.8212

1 - 0.8212 = 0.1788

So the correct option is:

Between 0.01 and 0.20

Answer:

102, 10, and, 3b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let X denote the life span of a car battery and it follows and exponential distribution with average of 6 years.

Thus , the parameter of the exponential distribution is calculated as,

μ = 6

[tex]\frac{1}{\lambda} =6[/tex]

[tex]\lambda = \frac{1}{6}[/tex]

a) The required probability is

[tex]P(X>4)=1-P(X\leq 4)\\\\=1-F(4)\\\\1-(1-e^{- \lambda x})\\\\=e^{-\frac{4}{6}[/tex]

= 0.513

Hence, the probability that a randomly selected car battery will last more than four years is 0.513

b) The variance of the battery span is calculated as

[tex]\sigma ^2=\frac{1}{(\frac{1}{\lambda})^2 }\\\\\sigma ^2=\frac{1}{(\frac{1}{6})^2 } \\\\=6^2=36[/tex]

The 95% percentile [tex]x_{a=0.05}[/tex] (α = 5%) of the battery span is calculated

[tex]x_{0.05}=-\frac{log(\alpha) }{\lambda} \\\\=-\frac{log(0.05)}{1/6} \\\\=-6log(0.05)\\\\=17.97 \ years[/tex]

c)  

Let [tex]X_r[/tex] denote the remaining life time of a car battery

i)the probability the battery will last an additional five years is calculated below

[tex]P(X_r>5)=e^{-5\lambda}\\\\=e^{-\frac{5}{6} }\\\\=0.4346[/tex]

ii) The average time that the battery is expected to last is calculated

[tex]E(X_r)=\frac{1}{\lambda} \\\\=6[/tex]

Answer:

Step-by-step explanation:

A graphing calculator shows there is one solution to ...

  [tex]\log_7{(3x^2+x)}-\log_7{(x)}=2[/tex]

However, the usual solution method would be to combine the logarithms and take the antilog to get ...

  [tex]\log_7{\left(\dfrac{3x^3+x}{x}\right)}=2\\\\\log_7{(3x^2 +1)}=2\\\\3x^2+1=7^2\\\\x^2=\dfrac{49-1}{3}=16\\\\x=\pm 4\qquad\text{take the square root}[/tex]

This gives two solutions. the "solution" x = -4 is extraneous, as it doesn't work in the original equation. "x" must be positive in the log expressions.

Answer:

x = - 4

Step-by-step explanation:

Got it right :)

Answer:

13

Step-by-step explanation:

I think