Clarissa has a budget of $1,200 a month to spend for rent and food. She has already spent $928 this month. Which inequality represents the amount she can still spend this month and remain within her budget?

If

f(x) = x⁶ (x - 8)⁷ / (x² + 2)²

then taking the logarithm of both sides lets us expand the right side as

ln(f(x)) = ln(x⁶ (x - 8)⁷ / (x² + 2)²)

ln(f(x)) = ln(x⁶) + ln((x - 8)⁷) - ln((x² + 2)²)

using the property ln(ab) = ln(a) + ln(b).

We can also use the property ln(aⁿ) = n ln(a), so that

ln(f(x)) = 6 ln(x) + 7 ln(x - 8) - 2 ln(x² + 2)

Then differentiating both sides using the chain rule gives

f'(x)/f(x) = 6 x'/x + 7 (x - 8)'/(x - 8) - 2 (x² + 2)'/(x² + 2)

f'(x)/f(x) = 6 (1)/x + 7 (1)/(x - 8) - 2 (2x)/(x² + 2)

f'(x)/f(x) = 6/x + 7/(x - 8) - 4x/(x² + 2)

Solve for f'(x) :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) f(x)

and replace f(x) with the given function :

f'(x) = (6/x + 7/(x - 8) - 4x/(x² + 2)) • x⁶ (x - 8)⁷ / (x² + 2)²

We can expand the product :

f'(x) = 6 x⁵ (x - 8)⁷ / (x² + 2)²+ 7x⁶ (x - 8)⁶ / (x² + 2)² - 4x⁷ (x - 8)⁷ / (x² + 2)³

then simplify by factoring :

f'(x) = x⁵ (x - 8)⁶/(x² + 2)³  • (6 (x - 8) (x² + 2) + 7x (x² + 2) - 4x² (x - 8))

Simplify the rest :

f'(x) = x⁵ (x - 8)⁶ (9x³ - 16x² + 26x - 96)/(x² + 2)³

Answer:

O It is less than 5.

Step-by-Step

OK so, first u check if it has a negative. It does, so its at the left of 0. SO you know its less than.

A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744

The formula for calculating the confidence interval is expressed as;

[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]

Substitute the given parameters into the formula to have:

[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]

Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744

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Answer:

[tex] \frac{1}{14} [/tex]

Step-by-step explanation:

7 x (7+7)=7

7x [(14)]=7

x=

[tex] x = \frac{1}{14} [/tex]

Answer:

Hello again! Fellow Connexus user? Because I just had this on my Honors Algebra 1 test today. Anyways the answer is: A. x + y = 126 and 2.25x + 1.50y = 225.75; 49 Hot Dogs and 77 Sodas.

Step By Step Explanation:

To verify just use the substitution method to solve the equations x+y=126 and 2.25x + 1.50y = 225.75 then you'll get your x (Number of Hotdogs) and y (Number of Sodas)

Hope this helps!

The required equations are use to solve this problem;

[tex]x + y =126[/tex]

[tex]2.25x + 1.50y = 223.75[/tex]

There are x = 49 hot dogs, and y = 77 sodas were sold.

Given that,

Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

You sold a total of 126 hot dogs and sodas combined.

We have to determine,

What equations did you use to solve this.

And How many hot dogs were sold and how many sodas were sold.

According to the question,

Let, The x represent the number of hot dogs,

And y represent the number of sodas.

Then,

You sold a total of 126 hot dogs and sodas combined.

Number of sell hot dogs + number of sell sodas = Total of hot dogs and sodas combined.

[tex]x + y =126[/tex]

And Each hot dog costs $2.25 and each soda costs $1.50.

At the end of the night, you made a total of $225.75.

Then,

Cost of each hot dogs + cost of each soda = total earning end of the night

[tex]2.25x + 1.50y = 223.75[/tex]

On solving both the equation,

[tex]x + y = 126\\\\x = 126-y[/tex]

Substitute the value of x in the equation 2,

[tex]=2.25(126-y) + 1.50y = 225.75\\\\= 283.5 -2.25y + 1.50y = 225.75\\\\= - 0.75 y = 225.75 - 283.5\\\\= - 0.75y = -57.75\\\\= y = \dfrac{-57.75}{-0.75}\\\\= y = 77[/tex]

Then,

Substitute the value of y in the equation 1,

[tex]x + y = 126\\\\x + 77 = 126\\\\x = 126-77\\\\x = 49[/tex]

Hence, There are x = 49 hot dogs, and y = 77 sodas were sold.

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Answer:

a = b = 1 , c = - 8

Step-by-step explanation:

ax² + bx + c = y

( - 5 )² a - 5b + c = 12

c = - 8

3² a + 3b + c = 4

25a - 5b - 8 = 12 ⇔ 25a - 5b = 20 ⇔ 5a - b = 4 ........ (1)

9a + 3b - 8 = 4 ⇔ 9a + 3b = 12 ⇔ 3a + b = 4 .......... (2)

(1) + (2)

8a = 8 ; a = 1

b = 1

y = x² + x - 8

Answer:

just make something that is eqivalant to 4= or 14=

Step-by-step explanation:

Answer:

4/5 = 8/10

Step-by-step explanation:

x/5 = 8/10

x = 8/10 × 5

x = 4

Answer: The graph for x cubed has a steep incline levels for a little before another steep incline

explanation: Since choice B is the only one that looks like this the answer is B

The total cost of the trip Lisa wants to take over the weekend is $500.

Given the following data:

To determine the total cost of the trip Lisa wants to take over the weekend:

Since the percentage of the money in Lisa's savings account is equal to forty percent (40%) of what is required for the total cost of the trip. Thus, we would multiply the total cost of her trip by 40% and equate it to $200.

Total cost of her trip:

[tex]\frac{40}{100} \times T = 200\\\\0.4T=200\\\\T=\frac{200}{0.4}[/tex]

Total cost, T = $500.

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Answer:

75%

Step-by-step explanation:

100/64*48=75%

Answer:

Last on is the answer!! (The relation is a function, and the range is (-2,-1, 1, 3, 4). Hope this helps:)

Answer:

A3

Step-by-step explanatio

Answer:

mean = 4.5

SD = 1.2

Z value = (3-4.5)/1.2 = - 1.25

Percentage based on z value = 1 - pnorm(1.25) =  0.1056498 = 10.56498%

The response times under 3 minutes is 10.56%

'Normal distribution is a continuous probability distribution wherein values lie in a symmetrical fashion mostly situated around the mean.'

According to the given problem,

mean = 4.5

SD = 1.2

Z value = [tex]\frac{3 - 4.5}{1.2}[/tex] = - 1.25

Percentage based on z value = 1 - pnorm(1.25)

                                                 =  0.1056498

                                                 = 10.56498%

Hence, we can conclude that the response time of fire station under 3 minutes is 10.56%.

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Answer:

x = 4.5

x = 4.1

Step-by-step explanation:

Answer:

maybe it's 12 but i don't know...

The y-intercept of [tex]2y = 3x - 4[/tex] and the y-intercept of [tex]4x - 2y=4[/tex] are equal

The equations are given as:

[tex]2y = 3x - 4[/tex]

[tex]4x - 2y=4[/tex]

Make y the subject in both equations

First equation

[tex]2y = 3x - 4[/tex]

[tex]y = \frac 32x - 2[/tex]

Second equation

[tex]4x - 2y=4[/tex]

[tex]y = 2x - 2[/tex]

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where b represents the y-intercept

So: By comparison,

[tex]b_1 = 2[/tex] --- the y-intercept of the first equation

[tex]b_2 = 2[/tex] --- the y-intercept of the second equation

2 = 2.

Hence, the y-intercept of [tex]2y = 3x - 4[/tex] and the y-intercept of [tex]4x - 2y=4[/tex] are equal

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Answer:

1870

Step-by-step explanation:

Answer : 1,870

Step - by - step explanation :

When there is multiple math signs in a problem you use PEMDAS . . .

Parentheses, Exponents, Multiplication and Division ( from the left side to right ), Addition and Subtraction ( from the left side to right )

212 + 115 x 6 + 968 --> 212 + 690 + 968

212 + 690 + 968 --> 902 + 968

902 + 968 --> 1,870

Answer:

18 + s = 33 (drag to 15)

27 = 9 × s (drag to 3)

40 - s = 23 (drag to 17)

5 × s = 35 (drag to 7)

18/s = 3 (drag to 6)

m/5 = 10 (drag to 50)

m + 14 = 18 - m (drag to 2)

m + m + 12 = 22 (drag to 5)

n + 7 = 18 (drag to 11)

n-9 = 22 (drag to 31)

Answer:

coin B

Better Date 2000 American Silver Eagle 1 Troy Oz .999 Fine Silver BU Unc

Coin C

1923 United Kingdom Great Britain GEORGE V Silver Florin 2 Shillings Coin i63027

you can get those coins from ebay

Answer:

1/15

Step-by-step explanation:

2/3 x 1/10 = 2/30 or 1/15

Answer:

1/15

Step-by-step explanation:

[tex]5^x = 3^{2x-1}\\\\\implies \ln(5^x) = \ln\left(3^{2x-1}\right)\\\\\implies x \ln 5 = (2x-1) \ln 3\\\\\implies x \ln 5 = 2x \ln 3 - \ln 3\\\\\implies 2x \ln 3 - x \ln 5 = \ln 3\\\\\implies x(2 \ln3 - \ln 5) = \ln 3\\\\\implies x =\dfrac{\ln 3}{2 \ln 3 - \ln 5} = 1.87[/tex]

The solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

To solve the equation 5ˣ = 3²ˣ⁻¹ using logarithms, we'll take the logarithm of both sides to bring down the exponent. Since the bases are different (5 and 3), we can use either the natural logarithm (ln) or the common logarithm (log base 10). Let's use the natural logarithm (ln):

Take the natural logarithm (ln) of both sides:

ln(5^x) = ln(3²ˣ⁻¹)

Apply the logarithm rule: ln(a^b) = b * ln(a):

x * ln(5) = (2x - 1) * ln(3)

Expand the equation:

x * ln(5) = 2x * ln(3) - ln(3)

Move the terms with "x" to one side of the equation:

x * ln(5) - 2x * ln(3) = -ln(3)

Factor out "x" from the left side:

x * (ln(5) - 2 * ln(3)) = -ln(3)

Solve for "x":

x = -ln(3) / (ln(5) - 2 * ln(3))

Now, we can calculate the value of "x" using a calculator:

ln(3) ≈ 1.099

ln(5) ≈ 1.609

x ≈ -1.099 / (1.609 - 2 * 1.099) ≈ -1.099 / (1.609 - 2.198) ≈ -1.099 / (-0.589) ≈ 1.864

Therefore, the solution to the equation is x ≈ 1.864 (correct to 3 significant figures).

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Answer:

1/24

Step-by-step explanation:

multiply 1/9 and 3/8. The product of the two factors is 3/ 72. Seeing the two factors on the other hand, we can cancel out 3. Hence the final answer to this problem in lowest terms becomes 1/24.

Step-by-step explanation:

1) plot a point at (0,-5)

2) count 3 units up and 5 units to the right, plot the new point

3) connect the points with a straight line

Answer: 6 possibilities.

Carol, Beryl, and Darryl

Carol, Darryl, and Beryl

Darryl, Carol, and Beryl

Darryl, Beryl, and Carol

Beryl, Darryl, and Carol

Beryl, Carol, and Darryl

Hope this helps :)

Answer:

-19

Step-by-step explanation:

-20 + 55 + 10 + -15 = 30

30 - 11 = 19

-19

Answer:

if it's only translated left 3, then it should be A (-5, -1) B (-1, -1) and C (-1, 2)

Answer:

Step-by-step explanation:

You already have the slope. It is + 1 as in y = (+1)x when you have been given

y = x + b

That means all you need do is subtract to find out what  b is

y =   x + b

x = 5

y = 11

Difference is 11 - 5 = 6

Try it a couple more times.

x = 10

y = 16

y = x + b

16 = 10 + b        Subtract 10

16 - 10 = b

b = 6 just as it did before.

y = x + b

x = 20

y = 26

26 = 20 + b      Subtract 20

26-20 = b

b = 6

So ? = 6

Find the sum of 12.351 and 0.5362

12.351 + 0.5362 = 12.8872