Ellis is going on a tour that costs $65 while on vacation. He was told to bring $118 to pay for the cost of the tour and dinner. Which of the following inequalities represents the money Ellis can spend on dinner?

A. $118 + d < $65
B. $118 + d > $65
C. $65 + d > $118
D. $65 + d < $118

Answer:

2 good scoops

Step-by-step explanation:

I got you I think

Answer:

[tex]f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

Step-by-step explanation:

Given function:

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

Replace f(x) with y:

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

Take natural logs of both sides:

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

Apply the Power Log Law   [tex]\ln x^n=n\ln x[/tex] :

[tex]\implies \ln y = (3x-1)\ln e[/tex]

As [tex]\ln e=1[/tex] then:

[tex]\implies \ln y = 3x-1[/tex]

Rearrange to make x the subject:

[tex]\implies 3x=\ln y +1[/tex]

[tex]\implies x=\dfrac{1}{3}(\ln y +1)[/tex]

Swap x for [tex]f^{-1}(x)[/tex]  and y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{3}(\ln x +1)[/tex]

A second-degree polynomial takes the form

[tex]f(x) = ax^2 + bx + c[/tex]

for some constants a, b, and c. Such a function is continuous and differentiable everywhere in its domain.

Differentiating f(x) with respect to x gives

[tex]\dfrac{df}{dx} = 2ax + b[/tex]

We're told that

• f(x) is increasing on [0, 8]

• f(x) is decreasing on ]-10, 0]

and since df/dx is continuous, this tells us that df/dx = 0 when x = 0. It follows that b = 0, and we can write

[tex]f(x) = ax^2 + c[/tex]

We're also given that the curve passes through the point (-8, 4), which gives rise to the constraint

[tex]f(-8) = 64a - 8b + c = 4 \implies 64a + c = 4[/tex]

Since f(x) is decreasing on ]-10, 0], we have df/dx < 0 when x = -8, so

[tex]2ax+b < 0 \implies -16a < 0 \implies a > 0[/tex]

This means f(x) is minimized when x = 0, with min{f(x)} = c, so the co-domain of f(x) is the set {f(x) ∈ ℝ : f(x) ≥ c}.

Without another condition, that's all we can say about the co-domain. There are infinitely many choices for the constants a and c that satisfy the given conditions. For example,

a = 1, c = -60   ⇒   f(x) = x² - 60   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -60}

a = 2, c = -124   ⇒   f(x) = 2x² - 124   ⇒   f(-8) = 4

⇒   co-domain = {f(x) ∈ ℝ : f(x) ≥ -124}

etc.

The interval which the function is negative is (-∞, -6)

The equation of the function is given as:

[tex]g(x) = \sqrt[3]{x + 6}[/tex]

When the function is negative.

It means that g(x) is less than 0

i.e. g(x) < 0

So, we have:

[tex]\sqrt[3]{x + 6} < 0[/tex]

Take the cube of both sides

x + 6 < 0

Subtract 6 from both sides

x < -6

The above represents a value from negative infinity to -6

i.e.  (-∞, -6)

Hence, the interval which the function is negative is (-∞, -6)

Read more about functions at:

https://brainly.com/question/10197594

#SPJ1

Answer:

3/4 cups

Step-by-step explanation:

3 1/2 divided by 2

Answer:

8x

Step-by-step explanation:

(3x+1)+(3x-1), the 1's cross out, so it is 3x+3x=6x. 6x+2x=8x.

Answer:

8x

Step-by-step explanation:

got it right!!!

I think it's 12 because here it comes out

The new sample size based on the information will be B-M, B-C, B-R, 8.

Sample size is the number of participants or observations that are included in a study. This is usually represented by n.

When the boys and girls are to be chosen, the new sample size based on the information will be B-M, B-C, B-R, 8.

Learn more about samples on:

https://brainly.com/question/17831271

#SPJ1

Answer:

Step-by-step explanation:

B-M, B-C, B-R, 8.

The area of the figure is 51.4 unit²

Figure ABCDEF is shown. A is located at 5, negative 8. B is located at 11, negative 8. C is located at 11, 0. D is located at 6

See attachment for the figure

The figure can be divided into the following shapes:

The area of the trapezoid is:

Area = 0.5 * (Sum of opposite sides) * height

So, we have:

Trapezoid 1 = 0.5 * (8 + 5) * 5 = 32.5

Trapezoid 2 = 0.5 * (5 + 4.8) * 2 = 9.8

The area of the triangle is:

Area = 0.5 * Base * Height

This gives

Triangle = 0.5 * 4.8 * 4 = 9.6

Add the individual areas

Area = 32 + 9.8 + 9.6

Evaluate the sum

Area = 51.4

Hence, the area of the figure is 51.4 unit²

Read more about areas at:

https://brainly.com/question/24487155

#SPJ1

The value of y based on the values given ib the equilateral triangle will be 4.

From the information given, MN is one of the sides of the equilateral triangle. Therefore, side MR will be:

= 1/2 × 8 = 4

In the above, it should be noted that MR was calculated since it's half of the value of MN which is 8.

Here, value of y based on the values given ib the equilateral triangle will be 4.

Learn more about triangles on:

https://brainly.com/question/17335144

#SPJ1

Answer:

Step-by-step explanation:

4

Hi Student!

This question is fairly simple because it gives us an equation and they also give us a value for the variable that is within the equation and they tell us evaluate the expression.  So let's plug in the values and solve.

Plug in the values

Factor out the exponent

Combine

Therefore, the final answer that we would get when substituting m with 9 in the given equation is that we get 86.

Answer: None

Step-by-step explanation:

There is only one pair of angles and one pair of sides, which is not sufficient to prove triangle congruence.

AnswEr :

Let's assume , three Consecutive integers be x , ( x +1 ) & ( x+2 ) , such that , x < ( x +1 ) < ( x +2 ) .

⠀⠀⠀⠀⠀⠀[tex]\underline {\boldsymbol{\star\: According \: to \: the \: Given \: Question \::}}\\[/tex]

⠀⠀⠀⠀⠀— The product of three consecutive integers is 30 times the smallest of the three integers.

[tex] \sf \dashrightarrow \:30\: \bigg\{ \: Smallest_{(\:integer\:)}\:\bigg\}\:\:=\: \:\bigg\{ \: I^{st} \:Integer\:\bigg\}\: \:\bigg\{\: II^{nd}\:Integer\:\bigg\}\: \:\bigg\{ \: III^{rd} \:Integer\:\bigg\}\:\:\: \\\\\sf \dashrightarrow \:30\: \bigg\{ \:x\:\bigg\}\:\:=\: \:\bigg\{ \: x\:\bigg\}\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:\bigg\{ \: x + 1\:\bigg\}\: \:\bigg\{ \: x +2 \:\bigg\}\:\:\: \\\\ \sf \dashrightarrow \:30\: \:\:=\: \:x^2 + 3x + 2 \:\:\: \\\\ \sf \dashrightarrow \:x^2 + 3x - 28 \:= \:0\: \\\\ \sf \dashrightarrow \:\:\bigg\{ \: x - 2 \:\bigg\}\:\:\bigg\{ \: x + 7 \:\bigg\}\: \:= \:0\: \\\\ \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:-7\: \&\:2\:}}}}}\:\bigstar \: \\\\\\[/tex]

Therefore ,

When , x = 2 ,

When , x = –7 ,

Answer:

Hi,

Step-by-step explanation:

If the "is" means is equal to

Let's say a-1, a, a+1 the 3 consecutive integers.

[tex](a-1)*a*(a+1)=30*(a-1)\\\\(a-1)*(a*(a+1)-30)=0\\\\(a-1)(a^2+a-30)=0\\\\(a-1)(a^2+6a-5a-30)=0\\\\(a-1)(a(a+6)-5(a+6))=0\\\\(a-1)(a+6)(a-5)=0\\\\a=1\ or\ a=-6\ or\ a=5\\[/tex]

[tex]\begin{array}{|c|c|c|c|c|}a&a-1&a+1&Prod&30*(a-1)\\---&----&----&----&--------\\1&0&2&0&30*0=0\\5&4&6&120&4*30=120\\-6&-7&-5&-210&30*(-6)=-180\end{array}\\[/tex]

The two sets are : (0,1,2) and (4,5,6).

Answer:

8

Step-by-step explanation:

(a) The precision of this measurement is 17.64 mm ± 0.01 mm.

(b) he uncertainty of the measurement is 0.057%.

(c) The tolerance of the measurement is 0.02 mm.

(d) The acceptable diameter in the format, nominal value uncertainty is 17.64 mm ± 0.057%.

A micrometer screw gauge is used in the measurement of a wire. The measuring accuracy of a micrometer screw gauge is 0.01 mm.

The precision of the measurement is 17.64 ± 0.01 mm.

The uncertainty of the measurement is calculated as follows;

uncertainty = (error/actual measurement) x 100%

uncertainty =  (0.01/17.64) x 100% = 0.057%

Tolerance = maximum measurement - minimum measurement

                 = (17.64 + 0.01)mm - (17.64 - 0.01)mm

                 = 0.02 mm

0.057% of 17.64 mm = 0.01 mm

Range of uncertainty = (17.64 mm - 0.01 mm) to (17,64 mm + 0.01 mm)

                                    = 17.63 mm to 17.65 mm

Acceptable diameter format, = 17.64 mm ± 0.057%

Learn more about uncertainty here: https://brainly.com/question/14756645

#SPJ1

The value of x for each radical equation is 243 , 125,8,256 respectively.

The correct question is attached as an image with the answer.

When in an equation the variable is under a radical it is called a Radical Equation.

It is given in the question that

which radical matches to the solution

[tex]\rm \sqrt[5]{x^4} = 81 \\\\\sqrt[3]{x^4} = 625\\\\\sqrt[3]{x^5} = 32\\\\ \sqrt[4]{x^3}=64[/tex]

[tex]\rm x^4 = 81^5\\x = 243[/tex]

[tex]\rm x^4 = 625^3\\x = 125\\[/tex]

[tex]x^5 = 32^3\\x = 8\\[/tex]

[tex]\rm x ^3 = 64^4\\x = 256[/tex]

Therefore for each radical the value of x is determined.

To know more about Radical Equation

https://brainly.com/question/8606917

#SPJ1

Step-by-step explanation:

an open (empty) point means the point itself is not included.

a closed (filled) point means the point itself is included.

the x values going from -3 (not included) to -1 (included) means

-3 < x <= -1

so, the second answer is correct.

Answer:

Width = 2

Length = 5

Step-by-step explanation:

let A be the area of the rectangle

   L be the length of the rectangle

   w be the width of the rectangle

Formula: ‘area of a rectangle’

A = L × w

…………………………………………………

A = L × w

⇔ 10 = (w + 3) × w

⇔ 10 = w² + 3w

⇔ w² + 3w - 10 = 0  

Solving the quadratic equation w² + 3w - 10 =  0 :

Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49

then √Δ = 7

[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]

  [tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]

-5 is not valid ,because w represents the width

which must be a positive number

Then  w = 2

Conclusion:

Width = 2

Length = 2 + 3 = 5

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

Answer:

360 degrees

..............

Answer:

9: 50

10: 90

11: 60

12: 25 and 115

13: 130 and 40

Thats all i can do, im sorry but i hope this helps ^^

Answer:

4,186.67 in³

Step-by-step explanation:

V = (4/3)πr³

V = (4/3)(3.14)(10 in)³

V = (4/3)(3.14)(1,000 in³)

V = 4,186.666667 in³

Answer:

24%

Step-by-step explanation:

there are 50 numbers total

number of 4's: 7
number of 7's: 5

it's asking for the odds of a 4 or a 7 meaning that they're fine with either one. that means you can ADD the number of them up!

7 + 5 = 12

to get the odds, we need to divide!

convert that into a percent!

24%

let me know if you're still confused :))

Answer:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

For the given function h(x), we have:

a) at x = -2 and x = 2.

b) y = 0 and y = 3.

First, we want to get the values of x at which we have maximums. To do that, we need to see the value in the horizontal axis at where we have maximums.

By looking at the horizontal axis, we can see that the maximums are at:

x = -2 and at x = 2.

Now we want to get the maximum values, to do that, we need to look at the values in the vertical axis.

If you want to learn more about maximums:

https://brainly.com/question/1938915

#SPJ1

Answer:

Yes

Step-by-step explanation:

The sum must be greater than 8 it can't be 7 anyway. Sums can be 9, 10 or 12. P = (4+3+1)/36 = 3/36

105600

Significant figures are used in scientific fields to show precision.

Multiplication

When rounding to significant figures you need to first do the operation shown. So, before we round we need to multiply 573.06 * 184.25.

This is an important step whenever you are rounding to significant figures. If you preround, you will be left with the wrong answer.

Significant Figures

Now that we have the answer before rounding, we need to know how to determine significant figures. If there is a decimal point present, then start counting significant figures at the first non-zero digit from the left.

For example:

If the decimal point is not present, then start counting significant figures from the first non-zero digit from the right.

For example:

Rounding

Finally, we can round our answer. Firstly, there are more than 4 digits before the decimal point. This means that our rounded answer will not have a decimal point, so when counting sig figs we will start from the right. Remember, even when rounding, a number should always have the same number of digits before the decimal point, even if they are not all significant.

Since we are rounding to 4 sig figs, we need to look at the 5th digit from the left, which is 8. This means we will round up.

So, write the first 4 digits of the number, but round the last one up. Then, write the remaining digits before the decimal point as 0.

Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected number of trials until q successes is:

[tex]E_s(X) = \frac{q}{p}[/tex]

In this problem, the parameters are given as follows:

q = 50, p = 0.32.

Hence:

[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]

More can be learned about the binomial distribution at https://brainly.com/question/24863377

#SPJ1

The 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

MOE is an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

MOE = z x s/√n

Where ,

Z = the z-score at the confidence interval

s =  the standard deviation

n = the number of samples.

We have p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence

0.075 = 1.282 x √0.50(1- 0.50)/ n

After solving,

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if a MOE of at most 0.075 with 80% confidence.

Learn more about the Margin of error here:

brainly.com/question/13990500

#SPJ1