which point best approximates the square root of 3?

Answer:

Step-by-step explanation:

First, set up a proportional fraction.

[tex]\frac{5 sec}{30 gallons}[/tex] = [tex]\frac{x sec}{1gallon}[/tex]

Cross multiply

5 * 1 = 5

30 * x = 30x

So,

30x = 5

Divide 5 by 30

x = 5 / 30

x = 1 / 6 or 0.17

Do the same thing to find for 17 gallons.

30x = 85

x = 85 / 30

x = 17 / 6 or 2.8

Answer:

Step-by-step explanation:

Instead of x put (t - 3) in the equation of the function f(x) = 4x² - 8x + 4:

f(t - 3) = 4(t - 3)² - 8(t - 3) + 4

use (a - b)² = a² - 2ab + b² and the distributive property a(b + c) = ab + ac

f(t - 3) = 4(t² - (2)(t)(3) + 3²) + (-8)(t) + (-8)(-3) + 4

f(t - 3) = 4(t² - 6t + 9) - 8t + 24 + 4

f(t - 3) = (4)(t²) + (4)(-6t) + (4)(9) - 8t + 28

f(t - 3) = 4t² - 24t + 36 - 8t + 28

f(t - 3) = 4t² + (-24t - 8t) + (36 + 28)

f(t - 3) = 4t² - 32t + 64

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies V=\cfrac{\pi (9)^2(13)}{3} \\\\\\ V=351\pi \implies V\approx 1102.70[/tex]

Answer:

z = 19

Step-by-step explanation:

Given

2(4z - 9 - 7) = 166 - 46 ← simplify both sides

2(4z - 16) = 120 ← distribute parenthesis on left side

8z - 32 = 120 ( add 32 to both sides )

8z = 152 ( divide both sides by 8 )

z = 19

Answer:

z = 19.

Step-by-step explanation:

2(4z − 9 − 7) = 166 − 46

 2(4z − 9 − 7) = 120

Divide both sides by 2:

4z − 9 − 7 = 60

4z = 76

z = 19.

Answer:0.16091954023

Step-by-step explanation:

Answer: Based on the calculator it’s...

0.16091954023

Step-by-step explanation:

Answer:

The trip lasted for a total of 8 hours.

Step-by-step explanation:

Distance planned = S = 640 miles

Constant speed = V

Thus the time to be taken would be = T = V/S

We have an equation 640 = VT ----- eq (a)

Time For First Quarter = T/4

speed = V

Distance = 640/4 = 160

After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.

So, the remaining distance = 640 - 160 = 480 miles.

Speed = V + 20 mph

Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours

We have an equation for remaining distance s = vt

=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)

using eq (a), we have V = 640/T. Putting it in eq (b), we have:

[tex]480 = (\frac{640}{T} + 20)(3\frac{T}{4} - 1.2)\\480 = 480 - \frac{768}{T}  + 15T - 24\\=> 15T - \frac{768}{T} -24 = 0\\=> 15T^{2} - 24T - 768 = 0\\[/tex]

Solving the equation, we get T = 8 or T = -32/5(which is not possible.

So, the right answer is T = 8 hours

Final answer:

To calculate the number of complete revolutions a bicycle wheel makes after traveling 440 meters, we find the wheel's circumference using its diameter and then divide the travel distance by the circumference. With a diameter of 0.7 meters and using 22/7 as an approximation for π, the wheel's circumference is 2.2 meters. The wheel makes 200 complete revolutions to cover 440 meters.

Explanation:

Finding the Number of Complete Revolutions

To find the number of complete revolutions made by a bicycle wheel when the bicycle travels a certain distance, we firstly need to calculate the circumference of the wheel. The circumference 'C' of a circle can be found using the formula C = πd, where π (Pi) is a constant (approximately 22/7 or 3.14) and 'd' is the diameter of the circle. In this case, we are given that the diameter of the bicycle wheel is 0.7 meters.

Using the approximation for π of 22/7 and the given diameter, the circumference is: C = π × d = (22/7) × 0.7 meters = 2.2 meters.

To find the number of complete revolutions 'N', we divide the total distance the bicycle travels by the circumference of the wheel: N = total distance / circumference = 440 meters / 2.2 meters. So, the number of complete revolutions the wheel makes is 200.

Answer:

x = ±11

Step-by-step explanation:

x^2 = 121

Take the square root of each side

sqrt(x^2) = sqrt(121)

x = ±11

Answer:

Population size:10

Mean (μ): 16

Mean Absolute Deviation (MAD): 7.2

Step-by-step explanation:

Mean absolute deviation (MAD) Mean absolute deviation (MAD) of a data set is the average distance between each data value and the mean. ... Mean absolute deviation helps us get a sense of how "spread out" the values in a data set are.

Credit cards offer more flexibility compared to other payment methods.

The correct answer is

A: more flexibility.

A: more flexibility - Credit cards provide users with the flexibility to make purchases without needing to have the full amount of money upfront. Instead, they can borrow funds up to a certain limit, known as the credit limit, and repay them later, often with interest. This flexibility allows cardholders to manage their cash flow more effectively and make purchases even when they may not have sufficient funds available in their bank account.

B: purchases are automatically deducted - This feature describes a debit card rather than a credit card. With a debit card, purchases are automatically deducted from the linked bank account at the time of the transaction, meaning that the cardholder needs to have sufficient funds available in their account to cover the purchase.

C: requires a linked bank account - While credit cards may require applicants to have a bank account for verification purposes, they do not necessarily need to be linked to a specific bank account for transactions to be processed. Credit cards operate on a revolving line of credit extended by the issuer, allowing cardholders to borrow money up to a certain limit regardless of their bank account balances.

D: similar to cash - Credit cards are not similar to cash. Unlike cash, which involves immediate payment and does not incur any interest charges, credit cards allow users to defer payment for purchases and may accrue interest if the balance is not paid in full by the due date. Additionally, credit cards offer various benefits such as rewards, cashback, and purchase protection, which are not typically associated with cash transactions.

Therefore the correct option is A: more flexibility

Complete question

Which of the following is a feature of a credit card?

A: more flexibility

B: purchases are automatically deducted

C: requires a linked bank account

D: similar to cash

Answer:

24

Step-by-step explanation:

⇒The question is on probability, to be specific its about counting principal

⇒You need to understand the counting rule where we multiply events together to get the total number of outcomes .

⇒In general  if we have an event t and another event s the total outcome for the events is given by t×s

⇒In this question  you multiply the number of ways we can make the different sandwiches

Given

meat=3 choices

cheese=2 choices

bread=4 choices

Outcomes= 3×2×4=24

The  total number of sandwiches that can be made = 24

There are 24 different sandwiches that can be made with 3 choices of meat, 2 choices of cheese, and 4 choices of bread.

The subject of this question is related to combinatorics, a topic in mathematics. The question asks, 'How many different sandwiches with one meat, one cheese, and one type of bread can be made if there are 3 choices of meat, 2 choices of cheese, and 4 choices of bread?'.

To find the answer, you would use the fundamental principle of counting which states that if there are n ways to do one thing and m ways to do another thing, then there are n * m total ways to perform both actions. In this case, we multiply the number of options together:

Hence, the total number of different sandwiches that can be made is given by 3 (choices of meat) * 2 (choices of cheese) * 4 (choices of bread), which equals 24 different sandwiches.

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Identities have INFINITE solutions.

Hope I could help! :)

Answer:

Infinite solution

Step-by-step explanation:

We are given an equation is identity

We have to find that how many solutions equation have

Identity equation:Identity equation is that true equation in which no matter what value is substitute for variable .It is always true statement.

Suppose that we have an identity equation

[tex]x=x[/tex]

[tex]x-x=0[/tex]

[tex]0=0[/tex]

If this type of condition is obtained then we have infinite solutions.

So, if an equation is identity then the equation have infinite solutions.

Answer: 1.8

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

(67 degrees - 58 degrees) / 5 minutes

1.8 degrees per minute

the correct answer is OB. 7.

Answer:

1.A. X6Y5

Step-by-step explanation:

#2 I have no clue on that one.

So sorry but I simply forgot to answer your questions.

The answer to question 1 is A.

The answer to question 2 is D.

All you must do to find out how much is with held from his paycheck is

solve this

x amount of dollars

÷                                     = 4.63%

$895

To solve, multiply $895 by 0.0463 (the equivalent of 4.63%)

You get:  $41 . 43

That is how much is withheld from Wes' check

The amount of tax withheld from his paychecks is $41.43

Percentage is defined as a given part or amount in every hundred

Income tax rate given in the question = 4.63%

Weekly income given in the question = $895

Tax deducted = (4.63 / 100) * 895 = $41.43

Hence, $41.43 will be deducted from his paychecks every week.

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Answer:

£270

Step-by-step explanation:

Works 7.5 hours per shift and there are 5 shifts in a week, hence

hours worked per week = 7.5 × 5 = 37.5

Pay per hour = £7.20, thus

Earnings for a week = 37.5 × 7.20 = £270

119 square inches long

Answer:

119

Step-by-step explanation:

(✿◠‿◠)

Answer:

I would say 50%

Step-by-step explanation:

The answer is 50%. Hope that helps!

The answer would be 0.6 if you divide 21/35.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To simplify divide the numerator/denominator by the highest common factor of 21 and 35, that is 7

[tex]\frac{21}{35}[/tex] = [tex]\frac{3}{5}[/tex] ← in simplest form

4+96=100 when you follow PEMDAS

Answer:

c) 100

Step-by-step explanation:

We want to evaluate

[tex]4\times1+6\times 16+0[/tex]

We use the order of operations, PEDMAS to solve this problem.

The first step here is to multiply to get:

[tex]4+96+0[/tex]

We now add to obtain:

[tex]100[/tex]

The correct answer is C) 100

Answer:

The inequality x3 − 14x2 + 48x − 1,680 ≤ 0 can be used to find pool’s length.

⇒The water level in the pool cannot exceed 14 feet.

Step-by-step explanation:

The question is on inequalities

Given;

Length= x ft

depth= x-6  ft

Width= x-8 ft

volume ≤ 1680 ft³

Forming the inequality to find length x of the pool

Volume= base area × depth

base area × depth ≤ volume

x(x-8) × (x-6) = 1680

(x²-8x )(x-6) = 1680

x(x²-8x) -6 (x²-8x)=1680

x³-8x²-6x²+48x=1680

x³-14x²+48x=1680

x³-14x²+48x-1680 ≤ 0

⇒The water level in the pool cannot exceed 14 feet...why?

taking the value of x at maximum to be 17 according to the graph, then maximum depth will be;

d=x-6 = 17-6=11 ft

⇒11 ft is less than 14ft

"Something" is a variable. A variable is a number that we do not know. The variable will be x.

5,652 is the total; the total is 12 plus x.

5652 = 12 + x

Subtract 12 from each side

5652 - 12 = 12 + x - 12

5640 = x

change it around

x = 5640.

5640 is your answer

Answer:

B

Step-by-step explanation:

The expression can be written as

[tex]\sqrt{-20}[/tex]

The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression

[tex]2i\sqrt{5}[/tex]

Answer:

Correct option is:

B

Step-by-step explanation:

We have to find a expression which is similar to:

[tex]\sqrt{-20}[/tex]

Now we start solving

[tex]\sqrt{-20}[/tex] could also be written as:

[tex]\sqrt{-2\times 2\times 5}[/tex]

When we take - sign out of the square root it becomes i

i.e. [tex]\sqrt{-1}=i[/tex]

And there are two 2's inside the square root when we take square root it becomes 2

Hence, [tex]\sqrt{-20}=2i\sqrt{5}[/tex]

Hence, Correct option is:

B

[tex]\bf \cfrac{\textit{Alex's cars}}{\textit{Jim's cars}}=\cfrac{8}{3}\qquad \qquad \cfrac{\stackrel{\textit{40 more than \underline{j}}}{j+40}}{j}=\cfrac{8}{3}\implies 3j+120=8j \\\\\\ 120=5j\implies \cfrac{120}{5}=j\implies 24=j \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Jim}}{j = 24}\qquad \qquad \stackrel{\textit{Alex}}{24+40\implies 64}\qquad \qquad \stackrel{\textit{altogether}}{24+64\implies 88}[/tex]

The total number of cars that Alex and Jim have altogether is 84 cars.

A ratio is a quantitative relationship between two different numbers that express the number of times in which a number is divisible within the other number. Sometimes ratios can be expressed in fraction form.

From the given information:

Then, we can express them in fraction form as:

[tex]\mathbf{\dfrac{8}{3} = \dfrac{x +40}{x}}[/tex]

8x = 3(x +40)

8x = 3x + 120

8x = 3x = 120

5x = 120

x = 120/5

x = 24

Jim = x = 24 cars

Alex = x + 40 = 24 + 40 = 64 cars.

The total number of cars they have altogether is 24+64 = 84 cars.

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Distribute sum groups

a(2a^2 - 5a - 2) - 2(2a^2 - 5a - 2)

Expand

2a^3 - 5a^2 - 2a - (4a^2 - 10a - 4)

Simplify brackets

2a^3 - 5a^2 - 2a - 4a^2 + 10a + 4

Collect like terms

2a^3 + (-5a^2 - 4a^2) + (- 2a + 10a) + 4

Simplify

= 2a^3 - 9a^2 + 8a + 4

Final answer:

To convert the decimal 0.612 to a fraction, express it as 612/1000 and then divide both the numerator and the denominator by their greatest common divisor, which is 4, to get the simplified fraction 153/250.

Explanation:

To rewrite 0.612 as a simplified fraction, one can first recognize that it's equivalent to 612/1000. After realizing that, we can simplify the fraction by finding the greatest common divisor (GCD) of both the numerator and the denominator. In this case, the GCD of 612 and 1000 is 4. Hence, we can divide both numerator and denominator by 4 to simplify the fraction.

Dividing both 612 and 1000 by 4, we obtain 153/250. So, 0.612 as a simplified fraction is 153/250.

Answer:

Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Step-by-step explanation:

It is given that you deal three cards from a regular deck which contains 52 cards.

We are to find the probability of getting all three Jack cards.

We know that there are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

3 chances of jacks out of 52 cards

Answer:   $65 dollars to johnson plumbing

Step-by-step explanation:

she would owe johnson plumbing 40 for the check plus the returned check fee of 25

$40 + $25 = $65 to johnson plumbing

plus whatever her bank charged ( i did not see that amount listed)

Final answer:

Sarah Saver must have enough money to cover the original $40 check, the $25 fee from Johnson Plumbing, and any additional bank charges. The expression representing the total amount needed is $40 + $25 + B, where B represents the bank's charges.

Explanation:

The student is asking about the total amount Sarah Saver must have to balance her debts after writing a $40 check that was returned with additional charges and a $25 fee for the returned check from the company. To find the total amount Sarah owes, you need to sum the amount of the check and the additional fees charged by her bank and Johnson Plumbing.

Add the original check amount: $40.

Add the fee charged by Johnson Plumbing for the returned check: $25.

Add any additional charges by her bank (the question doesn't specify an amount, so let's denote this amount as B).

The total amount Sarah needs to settle her debts will be $40 + $25 + B.

Therefore, without knowing the specific bank charges, we cannot provide a numerical answer, but the expression $40 + $25 + B represents the total amount Sarah needs to cover her debts, with B being the additional bank charges.