Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings?

Answer:

2(w+3)

Step-by-step explanation:

2(w+3) or 2w+6

Answer:

f(x) = 3ex - e

Step-by-step explanation:

In this equation we have basically the times e by 3x and -1

so first let's do e times 3x

here...

e X 3x = 3ex

so let's rewrite the equation

3ex - 1

now we times e by 1. (Note - Negative sign stays)

3ex - 1e

we don't have to write 1e cause 1e = e, they are the same.

Therefore the answer is 3ex - 1e

Following are the calculation of inverse:

Given:  

[tex]\to f(x)=e^{3x-1}[/tex]

To find:

inverse function=?

Solution:

A function g is the inverse of function F if for [tex]y=f(x), x=g(y)[/tex]

[tex]\to y=e^{3x-1}[/tex]

Replacing the value of x with y  

[tex]\to x=e^{3y-1}[/tex]

Solve for [tex]y, x=e^{3y-1}[/tex]

Therefore, the answer is [tex]\frac{\log(x)+1}{3}[/tex].

Learn more about the inverse function:

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Answer:

C) 2

Step-by-step explanation:

From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.

Answer:

Step-by-step explanation:

x+y = 67

2x-y = 38

Add the equations together

3x = 108

x = 36

y = 67-x = 31

Answer:

-33

Step-by-step explanation:

-p/3-8=3

or,(-p-24)/3=3

or,(-p-24)=9

or,-p=33

Therefore, p=-33

Answer:

95%

Step-by-step explanation:

Mean , xbar = 64.3; standard deviation, s= 2.4

Using the empirical formula where ;

68% of the distribution is within 1 standard deviation from the mean ;

95% of the distribution is within 2 standard deviation from the mean

percent of heights that lie between 59.5 inches and 69.1 inches.

Number of standard deviations from the mean /

Z = (x - μ) / σ

(x - μ) / σ < Z < (x - μ) / σ

(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4

-2 < Z < 2

Thia is within 2 standard deviations of the means :

2 standard deviation form the mean = 95% according to the empirical rule.

Answer:

The measure of ∠1 and ∠2 is 105° and 75° respectively

Step-by-step explanation:

In the given figure, line a is parallel to line b.

We need to find the measure of angles 1 and 2.

∠2 = 75° (because they form corresponding angles)

We know that, interior angles add up to 180. So,

∠1 +75 = 180

∠1 = 180-75

∠1 = 105°

So, the measure of ∠1 and ∠2 is 105° and 75° respectively.

Let

We know

[tex]\boxed{\sf Area =Length\times Width}[/tex]

[tex]\\ \sf\longmapsto x(8x-38)=4050[/tex]

[tex]\\ \sf\longmapsto 8x^2-38x=4050[/tex]

[tex]\\ \sf\longmapsto 8x^2-38x-4050=0[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{81}{4}\:or\:x=25[/tex]

[tex]\\ \sf\longmapsto Length=8x-38=8(25)-38=200-38=162m[/tex]

Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a

2x^2 - 3x = 12

2x^2 - 3x - 12 = 0

a = 2

b = -3

c = -12

(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)

3 +/- sqrt( 9 + 96 ) / 4

3 +/- sqrt(105) / 4

Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]

Hope this helps!

9514 1404 393

Answer:

  (a) The blue line ... solution ... (-6, -2)..

Step-by-step explanation:

The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.

The blue line represents the equation 2x -3y = -6.

The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.

everything seems to be correctly filled.

if you wanted confidence by confirmation: here, take some

It is an exponentially decaying function.

An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.

Exponential functions are of two types one is exponentially growing function and exponentially decaying function.

when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.

In the given question f(x) = 8e⁻ˣ

when, x = 0 f(x) = 8

f(x) = 8e⁻ˣ

f(0) = 8e⁰

f(0) = 8

Learn more about Exponential functions here :

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Answer:

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

4+z/y = 36/18

Step-by-step explanation:

a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:

16/4 = 18/y

Note that the arrangement depends on which of the triangles sides cones first.

Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.

b) Same rule in (a) applies to the sum as well. Hence;

4+z/y = 16+20/18

4+z/y = 36/18

Answer: multiply 631.6 by 0.8​ = 505.28

Answer:

Step-by-step explanation:

No that is true. I can't make anything more out of it.

log₉(x - 7) + log₉(x - 7) = 1

2 log₉(x - 7) = 1

log₉(x - 7) = 1/2

Take the base-9 antilogarithm of both sides; in other words, make both sides powers of 9:

[tex]9^{\log_9(x-7)} = 9^{1/2}[/tex]

[tex]9^{1/2}[/tex] can also be written as √9 = 3, and [tex]b^{\log_b(a)}=a[/tex], so the equation reduces to

x - 7 = 3

Solve for x :

x = 10

First simplify the expression into polynomial form,

[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]

[tex]x^4+8x^3-10x^2-104x+105=297[/tex]

[tex]x^4+8x^3-10x^2-104x-192=0[/tex]

Now factor into,

[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]

Which means the solutions are,

[tex]x-4=0\implies\boxed{x_1=4}[/tex]

[tex]x+8=0\implies\boxed{x_2=-8}[/tex]

and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],

[tex]x^2+4x+6=0[/tex]

[tex]x^2+4x+4=-2[/tex]

[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]

Hope this helps :)

Answer:

x=4

Step-by-step explanation:

(4-1)(4-3)(4+5)(4+7)=297

Answer:

(-∞,∞) is the domain.

2 is the range

Step-by-step explanation:

A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.

So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.

Answer:

a.

[tex] \frac{36}{40} [/tex]

Answer:

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Answer:

x=4

Step-by-step explanation:

2x-2+x+2x-2+x=3+7+3+7

6x-4=20

6x=24

x=4

Answer:

5180.56 Dollars...........

Answer:

The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.

The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.

Given:

Probability of student smoke,

P = 27.7%

  = 0.277

Number of students (n) = 632

[tex]q = 1-p[/tex]

  [tex]=1-0.277[/tex]

  [tex]=0.723[/tex]

(i)

Here,

Number of students (n) = 60

then,

⇒ [tex]n_P=60\times 0.277[/tex]

         [tex]=16.62[/tex]

⇒ [tex]n_q=60\times 0.723[/tex]

        [tex]=43.38[/tex]

We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.

Now,

[tex]\mu = n_P= 16.62[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

  [tex]= \sqrt{60\times 0.277\times 0.723}[/tex]

  [tex]=3.9664[/tex]

Now,

⇒ [tex]P(X<19) = P(X<18.5)[/tex]

                      [tex]=P(Z_{18.5})[/tex]

The Z-score is:

= [tex]\frac{18.5-16.62}{3.4664}[/tex]

= [tex]0.5423[/tex]

hence,

The probability will be:

⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]

or,

⇒ [tex]P(Z<19) = 0.7062[/tex]

(ii)

Here,

Number of students (n) = 75

[tex]\mu = n_P = 75\times 0.277[/tex]

            [tex]=20.775[/tex]

[tex]\sigma = \sqrt{n_{Pq}}[/tex]

   [tex]=\sqrt{75\times 0.277\times 0.723}[/tex]

   [tex]=3.8756[/tex]

Now,

⇒ [tex]P(X>17) = P(X> 17.5)[/tex]

                      [tex]=1-P(X \leq 17.5)[/tex]

                      [tex]=1-P(Z_{17.5})[/tex]

The Z-score is:

= [tex]\frac{17.5-20.775}{3.8756}[/tex]

= [tex]-0.9740[/tex]

then, [tex]P(Z_{17.5}) = 0.165[/tex]

hence,

The probability will be:

⇒ [tex]P(X>17) = 1-0.165[/tex]

                      [tex]=0.835[/tex]    

Learn more about Probability here:

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Answer:

By finding LCM of 9 and 12 the answer is 36

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

Both are true.

Step-by-step explanation:

Answer:

It will be 31.4 cm rounded off for circumference

It will be 78.53 cm2 rounded off for area

Step-by-step explanation:

Diameter = 10 cm

Radius = 10/2 cm = 5 cm

Circumference = 2×pi×radius

= 2pi×5

= 31.4 cm

Area = pi × r square

= 25 pi

= 78.53cm2