Before your trip to the mountains your gas tank was 7/9 full. When you returned home, the gas gauge registered 1/3 of a tank. If your gas tank holds 18 gallons did you use to drive to the mountains and then back home?

Answer:

Step-by-step explanation:

$15,000×0.08 = $1,200 interest for 360 days

$1,200 × 30/360 = $100 interest

Answer:

∠ B = 85°

Step-by-step explanation:

the inscribed angle B is half the measure of its intercepted arc AC , then

∠ B = \(\frac{1}{2}\) × 170° = 85°

11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

After answering the presented question, standard deviation t Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.

Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):

t = t(0.05, 8) = 1.860

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound = X - \((t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94\)

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The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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Answer:

45g + 60h

Step-by-step explanation:

Multiply 5 times everything in the parentheses

5(9g+12h) =

45g + 60h

Answer:

The width of the poster will be 17 inches

Step-by-step explanation:

The area = 204  square inches

Note:

- both length and width are whole numbers

- The width of the poster is greater than 11 inches

- The width is a prime

The prime numbers greater than 11 are

13, 17, 19, 23, 29, ...,

all these numbers divide 204 with a remainder except for 17

Therefore, the width will be 17 inches, and the length will be 12

since 17 divides 204 into 12 places

Answer:

Area- (4x+3)(3x-1)

Area- (12x^2 + 9x-4x-3)

Area- (12x^2 +5x-3)

Area- 12x^2 + 5x - 3

Let  me know if this helps!

The statement that are consistent with the guidelines for hitching trailers are:

A. Trailers must be connected to the tow vehicle before loading.

D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.

Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.

Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.

Therefore the correct option is A and D.

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Answer:

50(64+36)

Step-by-step explanation:

Answer:

50x8=  400x4=1,600

Step-by-step explanation:

In the metric system, centimeters per minute (cpm) represents speed or velocity. It counts the centimeters that are covered in a minute.

65 mi/hr to 174346 centimeters per minute.

$1 mi/h = 2682.2346355307 cm/ min.

65 × 2682.2346355307 cm/min = 174345.2513095 Centimeters Per Minute.

Always check the results; rounding errors may occur.

The base unit of [speed] (meters per second), 1 Miles Per Hour (mi/h) exists equivalent to

0.44704 meters-per-second,

while 1 Centimeters Per Minute (cm/min) = 0.000166667 meters-per-second.

65 Miles Per Hour to common speed units

65 mi/ h = 65 miles per hour (mi/h)

65 mi/h = 1.0833333333333 miles per minute (mi/m)

65 mi/h = 174346 centimeters per minute

Therefore, the correct answer is 174346 centimeters per minute.

The base unit for speed is meters per second (Non-SI Unit)

[Miles Per Hour] symbol/abbreviation: (mi/h)

[Centimeters Per Minute] symbol/abbreviation: (cm/min)

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There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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The amount $600 would be after 3 years at 8% interest compounded continuously is $755.83

Compound interest are amount of money added on amiunt invested.

Given the following parameters

P = $600
r = 8% = 0.08
t = 3 years

Using the compound interest formula

A(t) = Ao(1+r)^t
A(t) = 600(1.08)^3
A(3) = $755.83

Hence the $600 would amount to after 3 years at 8% interest compounded continuously is $755.83

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Answer: Probably A

Step-by-step explanation: You need to use a ruler for this, because without one its impossible to get it exact

Using the ruler though, you'd measure each side of the wall and either use a ratio of 0.5in:4ft or multiply every 0.5in by 4ft.

Answer:

n = 12

I hope this helps!

Answer: 4/6 = 2/32/3 = 2/3

Step-by-step explanation: hope this help

The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10

The third option is correct.

High price value: 115 shares * $105.19 per share = $12,084.85

Low price value: 115 shares * $103.25 per share = $11,858.75

High price value: 30 shares * $145.18 per share = $4,355.40

Low price value: 30 shares * $143.28 per share = $4,298.40

The overall value at high price:

$12,084.85 + $4,355.40

= $16,440.25

The overall value at low price:

$11,858.75 + $4,298.40

= $16,157.15

In conclusion, the difference in overall gain or loss:

$16,440.25 - $16,157.15 = $280.10

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Quantity of water with Henri = 16 litres

Quantify of water he will need for one cup of coffee = 200 ml

Number of cups of coffee he can make with a full cup of water :-

\( = 16 \: litres \: = 16000 \: ml\)

\( = \frac{16000}{200} \)

\( = 80 \: cups \: of \: coffee\)

So , Henri can make 80 cups of coffee with one full bottle of water .

Quantity of water needed to make 80 cups of coffee = 16,000 ml

Quantity of water needed to make one cup of coffee :-

\( = \frac{16000}{80} \)

\( = 200 \: ml\)

So , 200 ml of water is needed to make one cup coffee .

Quantity of water he needs to make 250 cups of coffee :-

\( = 200 \times 250\)

\( = 50000 \: ml\)

So , Henri needs 50,000 ml of water to make 250 cups of coffee .

Number of water containers he will use :-

\( = \frac{50000}{16000} \)

\( = 3.125 \\ = 3 \: water \: containers\)

So , Henri will use 3 full water containers to make 250 cups of coffee .

Money charged per one coffee = 8 cents

Money charged for 250 coffees :-

\( = 250 \times 8\)

\( = 2000 \: cents\)

So , Henri will make 2000 cents if he sells 250 cups of coffee .

Therefore , Henri will use 3 full containers of water to make 250 cups of coffee and he he will make 2000 cents by selling 250 cups of coffee .

(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.

Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.

Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.

(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).

Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.

(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.

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Answer: 0.9577

Step-by-step explanation:

Formula for margin of error (E):

\(E= z^*\sqrt{\dfrac{p(1-p)}{n}}\) , where p = sample proportion, n =sample space, z* critical z-value.

Given: n= 200

\(p=\dfrac{147}{200}\)

Critical value for 97% confidence level = 2.17

Margin of error (E) = \(2.17\sqrt{\dfrac{147}{200}(1-\dfrac{147}{200})}\)

\(=2.17\sqrt{\dfrac{147}{200}(\dfrac{53}{200})}\\\\=2.17\times \sqrt{0.194775}\\\\=2.17\times0.441333207452\approx0.9577\)

Hence, the margin of error for a 97% confidence interval = 0.9577

Answer:

The answer is A

Step-by-step explanation:

Answer:

y=5

solution,

X=2

now,

\( \\ 5x - y = 5 \\ or \: 5 \times x - y = 5 \\ or \: 5 \times 2 - y = 5 \\ or \: 10 - y = 5 \\ or \: - y = 5 - 10 \\or \: - y = - 5 \\ y = 5\)

hope this helps..

Good luck on your assignment..

Answer:

cannot understand the language man

but please follow

The volume of the tank is 410.

What is volume?

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Here, we have

Given: V(t) = 65t+280....(1)

The volume in the tank after two hours of the pumps running.

We have to find the volume of the tank.

t = 2

we put the value of t in equation(1) and we get

V(t) = 65(2) + 280

V(t) = 130 + 280

V(t) = 410

Hence, the volume of the tank is 410.

Question:   A water tank is being filled by pumps at a constant rate. The volume of water in the tank V, in gallons, is given by the equation: V(t) = 65t+280, where r is the time, in minutes, the pump has been on:(c)What is the volume in the tank after two hours of the pumps running?

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