Write ln 2x + 2x ln x -ln 3y as a single logarithm.

Answer:

[tex]\text{The coordinates of point is }P(a,b)=(\frac{80}{7}, \frac{17}{7})[/tex]

Step-by-step explanation:

[tex]\text{Given the coordinates of point that is }\frac{1}{6}\text{ of the way from a(14, -1), b(-4, 23)}[/tex]

[tex]\text{If a point }P(a, b)\text{ divides the line joining two points }(x_1,y_1)\text{ and }(x_2, y_2)\\ \text{ in the ratio m:n internally, then the coordinates of point P are given by}[/tex]

[tex]P(a,b)=(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n})[/tex]

The two points given are a(14, -1), b(-4, 23) and ratio m:n=1:6

[tex]P(a,b)=(\frac{1(-4)+6(14)}{1+6}, \frac{1(23)+6(-1)}{1+6})[/tex]

[tex]P(a,b)=(\frac{80}{7}, \frac{17}{7})[/tex]

(2l+2w) is that right

In order to make 20 slices of toast, given the constants provided, it would take approximately 175 seconds total. This is calculated based on the established rate of 4 slices of toast per 35 seconds.

The subject of this question is mathematics, specifically focusing on patterns and ratios. Given that it takes 35 seconds to make 4 slices of toast, we can establish a consistent rate of toast production. Because the toaster can toast 4 slices at a time, every 35 seconds, 4 more slices are ready. If we want to make 20 slices of toast, we can calculate this as follows: 20 slices ÷ 4 slices per 35 seconds = 5 times. Therefore, 5 times multiplied by the 35 seconds it takes to toast a set of 4 slices gives us 175 seconds. So, to toast 20 slices, it would take approximately 175 seconds.

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To make 20 slices of toast, it will take 210 seconds.

To find out how long it will take to make 20 slices of toast, we can determine the time required to make 1 slice of toast and then multiply it by 20.

From the given information, we can create a pattern to determine the time required:

We can observe that doubling the number of slices doubles the time required. Therefore, 20 slices will take twice the time required for 10 slices, which is 105 seconds. So, it will take 210 seconds to make 20 slices of toast.

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Answer:

should be A. Two-Solutions

Answer:log(x-3)

Step-by-step explanation:

log(A)-log(B) is log(A/B) then this would be log[(x^2-9)/(x+3)]

x^2-9 is (x-3)(x+3) then the answer is log(x-3)

One fifth is five people. Twenty five minus five is twenty. So twenty people did not preorder.

Answer:

a.12.0 lb; b.0.34 g; c.120 kg

Step-by-step explanation:

To measure weight using the English system of measurements, we use ounces, pounds, tons, etc.

To measure weight using the metric system, we use grams, milligrams, kilograms, etc.

This means that pounds, grams and kilograms are all acceptable representations of weights.

Kilonewtons (kN) measure force, not weight.

Meters and centimeters (m and cm) measure length, not weight.

Answer:

a.12.0 lb

d.1600 N

Step-by-step explanation:

THe weight of objects is the force with which each object is attracted by the gravitational force where they are located, for example on earth gravitational force is equal to 9.81 m/[tex]s^{2}[/tex], so an object that is 1 kg of mass, would have a weight of 9.81 Newtons, pounds are also a measure of force.

Answer:

A.-7

Step-by-step explanation:

f(x)=-3x+8,

f(5) means let x=5

f(5) = -3(5) +8

f(5) = -15+8

f(5) = -7

Answer:THE ANSWER IS

300% PLEASE BRAINEST ME!

Answer:

The answer is D hope this helps

Step-by-step explanation:

Answer:

The number of vertices in the polyhedron is [tex]9[/tex]  

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

so

[tex]V - E + F = 2[/tex]

In this problem we have

[tex]F=9, E=8+8=16[/tex]

substitute and solve for V

[tex]V - 16 +9 = 2[/tex]

[tex]V = 2+7=9[/tex]  

Answer: 188/45 or 4 8/45.

Step-by-step explanation:

1. Change the mixed numbers to improper fractions.

10 1/9 = 91/9

5 14/15 = 89/15

2. Now, we must find a common denominator by finding the LCM (Least Common Multiple). In this case, it would be 90. 9 x 10 = 90 and 15 x 6 = 90. The numerators must equal the denominators, so we would multiply 91 by 10 and 89 by 6.

Our new fractions are 910/90 and 534/90.

3. Subtract the fractions. 910/90 - 534/90 = 376/90.

4. Simplify. 376 and 90 are both divisible by 2, so our answer will be 188/45 or 4 8/45.

Answer:

a) [tex]N_0=250\; k=0.15 [/tex]

b) 334,858 bacteria

c) 4.67 hours

d) 2 hours

Step-by-step explanation:

a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.

Another way to see that is the following:

Initial number of bacteria is N(0), which implies [tex]t=0[/tex]. And [tex]N(0)=N_0[/tex]. The process is:

[tex]N(t)=250 e^{0.15t}\\N(0)=250 e^{0.15(0)}\\ N_0=250e^{0}\\N_0=250\cdot1\\ N_0=250[/tex]

b) After 2 days means [tex]t=48[/tex]. So, we just replace and operate:

[tex]N(t)=250 e^{0.15t}\\N(48)=250 e^{0.15(48)}\\ N(48)=250e^{7.2}\\N(48)=334,858\;\text{bacteria}[/tex]

c) [tex]N(t_1)=4000; \;t_1=?[/tex]

[tex]N(t)=250 e^{0.15t}\\4000=250 e^{0.15t_1}\\ \dfrac{4000}{250}= e^{0.15t_1}\\16= e^{0.15t_1}\\ \ln{16}= \ln{e^{0.15t_1}} \\  \ln{16}=0.15t_1 \\ \dfrac{\ln{16}}{0.15}=t_1=4.67\approx 5\;h [/tex]

d) [tex]t_2=?\; (N_0→3N_0 \Longrightarrow 250 → 3\cdot250 =750)[/tex]

[tex]N(t)=250 e^{0.15t}\\ 750=250 e^{0.15t_2} \\ \ln{3} =\ln{e^{0.15t_2}}\\ t_2=\dfrac{\ln{3}}{0.15} = 2.99 \approx 3\;h [/tex]

Answer:

12% of men are left-handed.

Answer:

3975

Step-by-step explanation:

fog functions are basically f(g(o)).

So for this problem, it would be f(g(-7)).

Plug in -7 to the g(x) equation first, and you should get -63.

Then plug -63 into the f(x) equation, and you should finish with 3975.

Answer:

B

Step-by-step explanation:

The easiest way to do this is to look at the -1 first. That shifts the small horizontal graph downwards. So that little line is below the x axis as answer B would show you.

The next thing to notice is that the graph is at +6 which is what you might expect because the x carries a minus with it. B and C both do that. I'm not sure what D does but I think it is on the left side of the y axis and that makes it wrong. A also looks like it is on the left side of the y axis and it is not correct either.

The difference between B and C has to be that 2 in front of the cubic. I think the vertical part of the cubic in B is closer to a vertical line through 6. If that is the case B is the answer.

Graph

Red: y = (-x + 6)^3

Blue: y = 2*(-x + 6)      Notice that this is closer to a vertical line at x = 6. That's the function of the 2

Green: y = 2*(x +6)^3 - 1 Notice it is shifted down.

The radius of convergence of [tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex] is 1, and the interval notation is (5,7)

The series is given as:

[tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex]

The ratio test of a series states that:

[tex]L = \lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex]

By applying the ratio test considering that the series converges, we have:

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4(n+1)+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Open the bracket

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+4+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Evaluate the sum

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]

Express as product

[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]

Expand the exponents

[tex]\lim_{n \to \infty} | \frac{(-1)^{n} \times (-1)^1 (x-6)^{n} \times (x-6)}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]

Cancel out the common factors

[tex]\lim_{n \to \infty} | \frac{(-1)(x-6)(4n+1)}{4n+5} |[/tex]

Factor out (-1)(x - 6)

[tex]|x-6|\lim_{n \to \infty} | \frac{(4n+1)}{4n+5} |[/tex]

Assume the limit to infinity is 1, the equation becomes

[tex]|x- 6| < 1[/tex] --- condition for convergence series

Split

[tex]-1 < x - 6 < 1[/tex]

Add 6 to both sides

[tex]5 < x < 7[/tex]

Rewrite as interval notation

(5,7)

Hence, the radius of convergence is 1, and the interval notation is (5,7)

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The radius of convergence, R, of the given series is 1. The interval of convergence, I, is [7,5). These are found using the Ratio Test to determine where the series converges, and then checking behavior at the endpoints.

To find the radius and interval of convergence of a series, we typically use the Ratio Test, where we consider the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term. If this limit L is less than 1, the series converges absolutely; if it is greater than 1, the series diverges; if it equals 1, the test is inconclusive.

From the given series ∞ (−1)n (x − 6)n (4n + 1)/n, let a(n) be the nth term, so a(n+1) = (−1)^(n+1) (x − 6)^(n+1) (4*(n +1) + 1)/(n+1). Thus, we find |a(n+1)/a(n)| = |(x-6) * (4n+1) / (4n+5)|. In the limit as n approaches infinity, this becomes |x-6|. The series converges where this is less than 1, hence the radius of convergence, R, is 1.

For the interval of convergence, I, we need to check the points x = 7 and x = 5 (the endpoints of the interval centered at 6 with radius 1). Substituting these into the original series, we can use the Alternating Series Test and find the series converges for x = 7 and diverges for x = 5. Hence, the interval of convergence is I = [7,5).

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Correct option is A. The term 'kinds' likely refers to informal groupings of organisms and may align with 'species' or higher taxonomic orders. Organisms are classified into a hierarchical system, where species represent closely related organisms capable of interbreeding, but higher levels like genus and family involve organisms that share broader similarities.

The question pertains to the concept of biological classification and how created "kinds" are understood within that framework. The term "kinds" is not particularly scientific and may refer to informal groupings of organisms. However, it could be inferred that the student is asking about how closely these "kinds" align with scientifically recognized categories such as species or higher taxonomic orders (like genus, family, order, etc.).

According to the Linnaean system introduced by Carl Linnaeus, organisms are classified in a hierarchical structure based on shared physical characteristics. This system organizes living organisms into a hierarchy of taxa, with species being the most specific level and kingdoms being the most general. Species are groups of organisms that are very similar and capable of interbreeding, while higher taxonomic levels, such as genus and family, group together organisms that share fewer, but still significant, similarities.

The concept of a species can be complex, as there can be significant variation within what we consider a single species, making the categorization sometimes controversial and subject to scientific debate. Moreover, as our understanding of evolution and phylogeny has advanced, the classification system has evolved to reflect these new insights, leading to changes in how organisms are grouped.

Tommy has 3 and 1/3 jars but 3 of them are full .

Okay so 5*2/3 =10/3 which is 3 1/3

Answer:

A second degree trinomial or a quadratic expression.

Step-by-step explanation:

The expression;

3x^2 -6x +10 , is a Quadratic expression or a second degree trinomial.

A Trinomial is a three term polynomial like the one above; that is,

3x^2 -6x +10.

A second degree trinomial  or polynomial is an expression of the form.

ax2 + bx + c , where a ≠ 0.

15 Answer:  S₁ = 1       S₂ = 4        S₃ = 13        S₄ = 40       Sum = NO            

Step-by-step explanation:

1 + 3 + 9 + 27 + ...    [tex]\implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}[/tex]

16 Answer:      [tex]\bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}[/tex]        

Step-by-step explanation:

[tex]\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}[/tex]

[tex]\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}[/tex]

Answer:

= 22x - 9

Step-by-step explanation:

To find the perimeter of a triangle, we add the three sides

P=(8x-2) + (5x-4) + (9x-3)

Combine like terms

P = 8x+5x+9x + (-2-4-3)

  = 22x - 9

Answer:

22x - 9

Step-by-step explanation:

Its easy.

Answer:

The perimeter would also be multiplied by 2.

Step-by-step explanation:

The perimeter would also be multiplied by 2. Suppose the sides of a triangle are 5, 10 and 13. The perimeter would be the sum of the side lengths or 5 + 10 + 13 = 28 ft.

Multiply each side length so 5*2 = 10, 10*2 = 20 and 13*2 = 26. Find the perimeter by finding their sum, 10 + 20 + 26 = 56.

Divide the new perimeter by the old perimeter to find a scale factor.

56/28 = 2.

The new perimeter is exactly 2 times bigger since 2*28 = 56.

Answer:

C. 20

Step-by-step explanation:

The given limit is

[tex]\lim_{x \to 2} (3x^3 +x^2-8)[/tex]

This a limit of a polynomial function.

We plug in the limit directly to obtain;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(2)^3+(2)^2-8[/tex]

We simplify to get;

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=3(8)+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=24+4-8[/tex]

[tex]\lim_{x \to 2} (3x^3 +x^2-8)=20[/tex]

The correct choice is C

the answer is x=(1/28)y^2

The equation of the parabola with focus at (7, 0) and directrix at x = -7 is x = (1/28)y².

The general equation of a horizontally opening parabola, using the distance between the vertex and the focus or directrix as the value of 'p'.

To find the equation of a parabola with a focus at (7, 0) and a directrix at x = -7, we first note that the vertex of the parabola is midway between the focus and the directrix. This puts the vertex at the origin (0, 0), and the parabola opens to the right since the focus is to the right of the vertex.

The general form of the equation for a parabola that opens horizontally (left or right) is

[tex](y - k)^2 = 4p(x - h)[/tex], where (h, k) is the vertex and p is the distance from the vertex to the focus.

If the parabola opens to the right (as in this case), the equation will be

[tex](y - 0)^2 = 4*(7)(x - 0)[/tex]

y² = 28x.

However, to match the format of the original options given to the student, we divide every term by 28, leading to the equation x = (1/28)y², which is the correct parabolic equation for the given focus and directrix.

Answer:

150 miles

Step-by-step explanation:

Find the unit rate (MPH) by dividing miles travlled by hours.

    300/6 = 50 MPH

    250/5 = 50 MPH

Multiply the hours on day 3 (3) by 50 MPH

    3*50 = 150 miles

Answer:

150 miles

Step-by-step explanation:

The relationship between speed, time and distance is such that the product of speed and time is distance.

Given that they drove the same speed throughout the trip

Speed on day one given that distance covered is 300 miles in 6 hours,

Speed = 300 miles/ 6 hours

= 50 miles per hour

Speed on day two given that distance covered is 250 miles in 5 hours

= 250 miles/ 5 hours

= 50 miles per hour

If on the third day, the speed is maintained and they drove for 3 hours,

Distance covered = 50 miles per hour × 3 hours = 150 miles

Answer:

Step-by-step explanation:

Well 7 is the only number that can be divided by itself and 1

Answer:

Hello!

Great question.

The correct answer would be "Prime Number."

Step-by-step explanation:

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number.

Answer:

x ≈ 5 years

Step-by-step explanation:

Given amount = A = 500 mg

Decay rate = r = 10% per year

Remaining amount = L = 295.25 mg

The formula to calculate remaining amount after x years decay =

L = A((100-r)/100)^x

By putting values in this formula, we get

295.25 = 500 ((100-10)/10)^x

295.25 = 500 (0.90)^x    

295.25/500 = 0.90^x

0.5905 = 0.90^x

0.90^x =0.5905

taking log on both sides

ln(0.90^x) =ln(0.5905)

x*ln(0.90) =ln(0.5905)  using property of log

x = ln(0.5905)/ln(0.90)

x = 4.9984

x ≈ 5 years

Answer:

j:19 days

s:23 days

23-19=4

4 days

Step-by-step explanation:

Answer:

B.   y = e^(-2/x).

Step-by-step explanation:

dy/dx = 2y / x^2

Separate the variables:

x^2 dy = 2y dx

1/2 * dy/y =  dx/x^2

1/2  ln y = = -1/x  + C

ln y = -2/x +  C

y = Ae^(-2/x)  is the general solution ( where A is a constant).

Plug in the given conditions:

e = A e^(-2/-2)

e = A * e

A = 1

So the specific solution is y = e^(-2/x).

Final answer:

The separable differential equation [tex]dy/dx = 2y/x^2[/tex] can be solved by separating variables, integrating both sides, and then applying the given initial condition y(-2) = e to find the specific solution, which is [tex]y = e^{-2/x},[/tex] corresponding to answer option B.

Explanation:

To solve the given separable differential equation [tex]dy/dx = 2y/x^2[/tex], we first separate the variables:

[tex]\( \frac{dy}{y} = \frac{2}{x^2}dx \)[/tex]

Next, we integrate both sides:

[tex]\( \int \frac{1}{y}dy = \int 2x^{-2}dx \)[/tex]

Which gives:

[tex]ln|y| = -2/x + C[/tex]

Now, we apply the initial condition y(-2) = e to find C:

ln(e) = [tex]-2/(-2) + C \Rightarrow 1 = 1 + C \Rightarrow C = 0[/tex]

Thus, the specific solution is:

[tex]y = e^{-2/x}[/tex]

So, the correct answer is option B, y equals e raised to the negative 2 over x power.

Answer:

True

Step-by-step explanation:

We have the serie:

[tex]\frac{1}{25}+ \frac{1}{36} + \frac{1}{49}+...[/tex]

To test whether the series converges or diverges first we must find the rule of the series

Note that:

[tex]5^2 = 25\\\\6^2 = 36\\\\7^2 = 49[/tex]

Then we can write the series as:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+...[/tex]

Then:

[tex]\frac{1}{5^2}+ \frac{1}{6^2} + \frac{1}{7^2}+... = \sum_{n=5}^{\infty}\frac{1}{n^2}\\\\\sum_{n=5}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+4)^2}[/tex]

The series that have the form:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]

are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].

In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges