The bill at a restaurant came to $136.40.The customer decided to leave a 15% tip.What was the total bill including tip.

Answer:

d = 6

Step-by-step explanation:

3d + 9 = 27

Subtract 9 from each side

3d + 9-9 = 27-9

3d = 18

Divide each side by 3

3d/3 = 18/3

d = 6

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{d = 6}}}}}\)

Step-by-step explanation:

\( \sf{3d + 9 = 27}\)

Move 9 to right hand side and change its sign

\( \dashrightarrow{ \sf{3d = 27 - 9}}\)

Subtract 9 from 27

\( \dashrightarrow{ \sf{3d = 18}}\)

Divide both sides by 3

\( \dashrightarrow{ \sf{ \frac{3d}{3} = \frac{18}{3}}} \)

Calculate

\( \dashrightarrow{ \sf{d = 6}}\)

Hope I helped!

Best regards! :D

Parallel lines have equal slope so

Lets check

Now

Lines are parallel

Answer:

The two lines are parallel

Step-by-step explanation:

If two lines are parallel, they have the same slope.

If two lines are perpendicular, the slopes will be negative reciprocals (the product of the slopes will be -1).

Given slopes:

\(\sf m_1=\dfrac{3}{4}\)

\(\sf m_2=\dfrac{12}{16}\)

Reduce m₂ to its simplest form by dividing the numerator and denominator by the largest common factor:

\(\sf m_2=\dfrac{12 \div 4}{16\div 4}=\dfrac{3}{4}\)

Therefore,

\(\sf as \quad \dfrac{3}{4}=\dfrac{3}{4} \implies m_1=m_2 \quad\)

As the given slopes are the same, the two lines are parallel.

In the word problem, if mike has 10 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 30 cents more, he has 2 quarters.

A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation.  Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:

x + y = 10

The amount of the total coins would be 0.1x + 0.25y.

If the dimes were quarters and quarters were dimes, he would have 30 cents more than the amount he has now.

Hence,

0.25x + 0.10y = 0.1x + 0.25y + 0.9

Solving,

0.25x – 0.1x = 0.25y – 0.1y +0.9

0.15x = 0.15y + 0.9

As x + y = 10, x = 10 – y

Substituting,

0.15 (10 – y) = 0.15y + 0.9

1.5 - 0.15 y = 0.15y + 0.9

0.15y + 0.15y = 1.5 – 0.9

0.3y = 0.6

y = 0.6/0.3 = 2

Hence, the number of quarters are 2

Learn more about of Word problem here

https://brainly.com/question/29350889

#SPJ4

Torsion refers to the twisting of a structural member due to the application of torque. Pure torsion occurs when a structural member is subjected to torsional loading only. It is analyzed using assumptions such as linear elasticity, circular cross-sections, and small deformations. The torsion equation relates the applied torque, the polar moment of inertia, and the twist angle of the member. However, this formula has limitations in cases of non-circular cross-sections, material non-linearity, and large deformations.

Torsion is the deformation that occurs in a structural member when torque is applied, causing it to twist. In pure torsion, the member experiences torsional loading without any other external forces or moments acting on it. This idealized scenario allows for simplified analysis and calculations. The assumptions made in pure torsion analysis include linear elasticity, which assumes the material behaves elastically, circular cross-sections, which simplifies the geometry, and small deformations, where the twist angle remains small enough for linear relationships to hold.

To analyze pure torsion, engineers use the torsion equation, also known as the Saint-Venant's torsion equation. This equation relates the applied torque (T), the polar moment of inertia (J), and the twist angle (θ) of the member. The torsion equation is given as T = G * J * (dθ/dr), where G is the shear modulus of elasticity, J is the polar moment of inertia of the cross-section, and (dθ/dr) represents the rate of twist along the length of the member.

However, the torsion equation has its limitations. It assumes circular cross-sections, which may not accurately represent the geometry of some structural members. Non-circular cross-sections require more complex calculations using numerical methods or specialized formulas. Additionally, the torsion equation assumes linear elasticity, disregarding material non-linearity, such as plastic deformation. It also assumes small deformations, neglecting cases where the twist angle becomes significant, requiring the consideration of non-linear relationships. Therefore, in practical applications involving non-circular cross-sections, material non-linearity, or large deformations, more advanced analysis techniques and formulas must be employed.

To learn more about torsion click here: brainly.com/question/30612977

#SPJ11

Answer:

72 squared meters

Step-by-step explanation:

triangle area= 1/2 bh

16 x 9 = 144

144 x 1/2 = 72

Hope this helps

Answer:

A = 72m



The sides we would need to multiply are:
9m x 16m

The formula for finding the area of a triangle is:
L x W X 1/2


9m x 16m =

9m x 10m = 90
9m x 6m = 54


90m + 54m = 144m

144m / 2 = ?m

? = 72m

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

100ft I'm not completely sure but

Step-by-step explanaon                                                                                                                    5x5=25 2x2=4 25x4=100    

The actual number of deer in the forest is the total number of deer in the forest and it is 150 deers

The warden captures and tags 60 deer in a forest.

A month later he captures 100 deer and find out 10 of them are already tagged.

This means he had already captured those other deer initially.

Therefore, the second month he actually captured 90 deers.

The actual number of deer in the forest is 90 + 60 = 150 deers

learn more on algebra here: https://brainly.com/question/27482803

#SPJ1

Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.

In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.

To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.

Labor cost per hour = $109 ÷ 8 = $13 per hour

Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).

Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour

Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.

Labor cost per part = $13 ÷ 2.125 = $6.12 per part

Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.

Learn more about labour content

https://brainly.com/question/14701647

#SPJ11

Answer:

the last one

Step-by-step explanation:

Answer: The answer is the last graph.

Step-by-step explanation:

The first graph's difference is not a constant ratio.

The 2nd is multipled first by -5, then 5. Therefore wrong.

The third's difference is changing: (4,8,16...._) It would have to be always 4 if it was a linear.

The last one has the same increase every time.

SOLUTION

Liquids have to be poured into a container that is caliberated with measurements before it's volume can be measured because a liquid does not have a definite shape, it only takes the shape of the container which it is placed. So if the volume of the cotainer is known, that becomes the volume of the liquid.

Hence the answer is

Liquids do not have a definite shape, option 3

To solve the given logarithmic equations, I'll work on each one separately.

log₂(x²+6) = log₋₂(8x-9):

Since the bases of the logarithms are different, we need to use the logarithmic identity that states:

logₐ(b) = log(c, b)/log(c, a),

where a, b, and c are positive numbers and a ≠ 1. Applying this identity to our equation, we have:

log₂(x²+6) = log(8x-9)/log(-2, 8)

Now, we can equate the expressions inside the logarithms:

x² + 6 = (8x - 9) / log(-2, 8)

Please note that log(-2, 8) does not exist since the logarithm of a negative number is undefined. Therefore, this equation has no solution.

log(2x) - log(x+1) = log₃6:

We can simplify the equation using logarithmic properties:

log(2x/(x+1)) = log₃6

Now, we can eliminate the logarithms by equating the expressions inside:

2x/(x+1) = 6

To solve for x, we can cross-multiply and solve the resulting equation:

2x = 6(x + 1) 2x = 6x + 6 6x - 2x = 6 4x = 6 x = 6/4 x = 3/2

So, the solution to the equation is x = 3/2.

log₂x + log₂(x-1) = 1:

Using the logarithmic property logₐ(b) + logₐ(c) = logₐ(b * c), we can rewrite the equation:

log₂(x(x-1)) = 1

Simplifying further:

x(x-1) = 2¹

x² - x - 2 = 0

Factoring the quadratic equation:

(x - 2)(x + 1) = 0

Setting each factor to zero and solving for x:

x - 2 = 0 --> x = 2

x + 1 = 0 --> x = -1

However, we must discard the solution x = -1 because logarithms are only defined for positive values. Thus, the only valid solution is x = 2.

Learn more about equation here : brainly.com/question/29657983
#SPJ11

The inference is that the proportion of 2, 3, or 4 letters are very high compared to the popular science.

It should be noted that an inference simply means the conclusion that can be deduced based on the information or data given.

Here, the inference is that the proportion of 2, 3, or 4 letters used by Shakespeare are very high compared to the popular science.

Learn more about inference on:

brainly.com/question/25280941

#SPJ4

Answer:

The answer is 2200cm to the 3rd power

Step-by-step explanation:

Answer:

y = 10

Step-by-step explanation:

\(\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y\)

3

6+9+18

=

2

12+y

3

33

=

2

12+y

11=

2

12+y

22=12+y

10=y

answer: 10=y

(a) The probability of finding oil is 0.85

(b) The firm interpret the soil test as the probability of finding oil has decreased since the prior probabilities.

c) The revised probabilities is 100%.

A oil company has purchased an option on land in Alaska.

To determine the likelihood of finding oil, the company conducted preliminary geologic studies to assign prior probabilities of finding high-quality oil (0.65), medium-quality oil (0.20), or no oil (0.15). Therefore, the probability of finding oil is 0.65 + 0.20 = 0.85.

After 200 feet of drilling on the first well, a soil test was taken to determine the likelihood of finding high-quality oil (0.20), medium-quality oil (0.80), or no oil (0.20).

The results of this test should be interpreted as follows: the probability of finding oil has decreased since the prior probabilities.

Therefore, the revised probabilities are 0.20 + 0.80 = 1.00. This means that the oil company has a 100% probability of finding either high-quality or medium-quality oil.

To know more about probability here.

https://brainly.com/question/11234923

#SPJ4

Answer:

X ≥ 3

Step-by-step explanation:

First you simplify, as if the ≤ is an = (just don't multiply with a negative number)

27 = 7X + 6

27 - 6 = 7X

21 = 7X

3 = X

Then you put the ≤ back in

3 ≤ X

and put the X up front. The ≤ then swaps into a ≥

Finally, you can do a test with X = 2 (should be false) and X=4 (should be true), to check wether you made any mistakes.

Answer:

x = 31

Step-by-step explanation:

2^x > 4^ 15

Rewrite 4 as 2^2

2^x > 2^2^ 15

We know a^b^c = a^(b*c)

2^x > 2^ (2*15)

2^x > 2^30

Since the bases are the same, the exponents must follow the inequality

x> 30

Answer:

what is the figure my guy

Step-by-step explanation: blah blah blah math blah blah blah

Answer:

Step-by-step explanation:

i think you should use the graph it will help you to get your answer and see what’s the slope

Answer:  

1/9 chance that you will select a green block

Step-by-step explanation:

5+3+1=9 only one green block out of the nine

For the given fraction x^2-8x+16/x^2-16 if x≠4 and x≠-4 the simplified fraction is (x-4)/(x+4).

Simplified fraction refers to the fractions in their lowest form which has been reduced and simplified. The numerator and denominator in the fraction are reduced in simplified fraction to the extent that the only common factor between them is 1.

In order to simplify the fraction (x^2-8x+16)/(x^2-16), first, we must factor the numerator and denominator of the fraction:

Numerator: x^2-8x+16 = (x-4)(x-4) = (x-4)^2

Denominator: x^2-16 = (x-4)(x+4)

So the fraction becomes:

(x-4)^2/(x-4)(x+4)

Next, we can simplify the fraction by canceling out the (x-4) term in the numerator and denominator:

(x-4)/(x+4)

Therefore, the simplified fraction is (x-4)/(x+4) if x≠4 and x≠-4.

Learn more about Simplified fraction:

https://brainly.com/question/15178106

#SPJ11

Answer:

5/6 x 48 = 5 x 8=40

Step-by-step explanation:

Pls mark as brainliest

Answer:

40

Step-by-step explanation:

\( \frac{5}{6} \times 48 \\ \frac{5 \times 48}{6} \\ \frac{240}{6} = 40\)

The positive integer representing possible values for third side length of the triangle as per given measure of two side length are 45.

Two side length of a triangle be 'x' and 'y'

Side length 'x' = 23

Side length 'y' = 53

Third side length be 'n'

Using triangle inequality we have ,

x + y > n

⇒ 23 + 53 > n

⇒ 76 > n ___(1)

And x + n > y

⇒ 23 + n > 53

⇒ n > 53 - 23

⇒ n > 30 ___(2)

We know 'n' is a positive integer .

30 < n < 76

All the positive integer between 30 and 76 are possible values for 'n'.

Possible values are : 75 - 30 = 45

Therefore, there are 45 possible values for the third side of a triangle.

Learn more about triangle here

brainly.com/question/2773823

#SPJ4

The inequality for the given information is:

x+5y≤25.

The graph for the inequality x+5y≤25 is attached below:

One of the basic ideas of social justice theories is the existence of unequal status, rights, and opportunities1. In public conversation, it might be confusing because various people often interpret it differently. There are some frequent variants, though. In mathematics, an unjust comparison between two numbers or other mathematical expressions is referred to as an inequality. Different types of inequality are indicated by a variety of notations, including:

A less than sign, such as a, denotes that an is greater than b.

Given,

$25 has to spend on in-app purchases for a game.

The cost of extra lives is $1

The cost of bags of gold is $5

The inequality for the given information is:

x+5y≤25.

The graph for the inequality x+5y≤25 is attached below:

To know more about inequality, visit:

https://brainly.com/question/28823603

#SPJ1

By calculating we can say that the series ∑(n=1 to infinity) sin^2(n)/(4n^2+3) converges.

To determine whether the series ∑(n=1 to infinity) sin^2(n)/(4n^2+3) converges or diverges, we can use the Comparison Test or the Limit Comparison Test.

Using the Comparison Test, we note that 0 ≤ sin^2(n) ≤ 1 for all n, and therefore:

0 ≤ sin^2(n)/(4n^2+3) ≤ 1/(4n^2)

Since the series ∑(n=1 to infinity) 1/(4n^2) converges (as a p-series with p=2), we can conclude that ∑(n=1 to infinity) sin^2(n)/(4n^2+3) converges by the Comparison Test.

Alternatively, we can use the Limit Comparison Test by finding a comparable series that is easier to determine convergence. Let's consider the series ∑(n=1 to infinity) 1/(n^2), which converges. Then, using the fact that sin^2(n) ≤ 1 for all n, we have:

0 ≤ sin^2(n)/(4n^2+3) ≤ 1/(4n^2)

Taking the limit as n approaches infinity of the ratio of the terms of the two series, we get:

lim(n→∞) (sin^2(n)/(4n^2+3))/(1/(n^2)) = lim(n→∞) (n^2sin^2(n))/(4n^2+3)

Since sin^2(n) is bounded between 0 and 1, we can see that the limit is 0. Therefore, by the Limit Comparison Test, we can conclude that ∑(n=1 to infinity) sin^2(n)/(4n^2+3) also converges.

To learn more about series click on,

https://brainly.com/question/28144066

#SPJ4

Answer:

the first table

Step-by-step explanation:

Answer:

\(x=65\)

Step-by-step explanation:

In this case, we can determine the two given angles are vertical angles using the diagram. This means that they are congruent, or equal.

We can use this information to set up an equation:

\(145=2x+15\)

Subtract 15 from both sides:

\(130=2x\)

Divide both sides by 2

\(x=65\)

we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To compute n, we can use the formula:
n = ((zα/2)^2 * 2p*(1-p*)) / (ε^2)
Where zα/2 is the z-score associated with a confidence level of 1-α, p* is the probability of success for a binomial distribution, and ε is the margin of error.
Since we are given that the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 is at least 0.80, we can set α = 0.20 to find the corresponding z-score of 1.28.
Using p* = 1/2 as an upper bound for both P1 and P2, we can calculate the margin of error as:
ε = zα/2 * sqrt((p*(1-p*)) / n)
Plugging in the values, we get:
0.05 = 1.28 * sqrt((0.25) / n)
Solving for n, we get:
n = 501.76
Therefore, we would need a sample size of at least 502 for the approximate probability of the random interval (Y1/n - Y2/n) ‡ 0.05 covering pi - p2 to be at least 0.80.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ11

The power series representation for the function f(x) = x sin(4x) can be found as follows:

Firstly, we can find the power series representation of sin(4x) using the formula for the sine function:$

$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}x^{2n+1}$$

Substitute 4x for x to obtain:$$\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}(4x)^{2n+1}

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+1}$$

Multiplying this power series by x gives:

$$x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function

f(x) = x sin(4x) is:$$f(x)

= x\sin 4x

= \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Therefore, the power series representation for the function f(x) = x sin(4x) is:$$f(x) = x\sin 4x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!}4^{2n+1}x^{2n+2}$$

Learn more about power series here:

brainly.com/question/29896893

#SPJ11