Raul’s car averages 17.3 miles per gallon of gasoline. How many miles can Raul drive if he fills his tank with 10.5 gallons of gasoline

The resistance of the third bulb can be found by subtracting 3 ohms from the resistance of the other two bulbs.

Let's assume the resistances of the two bulbs with equal resistances are represented by R, and the resistance of the third bulb is R - 3. According to the formula for the total resistance in a parallel circuit, which is 1 / (1/R₁ + 1/R₂ + 1/R₃), we can substitute the given values.

For the parallel circuit with three bulbs and a total resistance of 1.5 ohms, the equation becomes 1 / (1/R + 1/R + 1/(R - 3)). Simplifying this equation further, we can combine the denominators and solve for the common denominator:

1 / (2/R + 1/(R - 3)) = 1.5.

To eliminate the fraction, we can multiply both sides of the equation by the common denominator (2(R - 3)). This gives us:

1 * (2(R - 3)) = 1.5 * (2/R + 1/(R - 3)).

Simplifying the equation, we get:

2(R - 3) = 3(2/R + 1/(R - 3)).

Expanding and rearranging the terms, we have:

2R - 6 = 6/R + 3/(R - 3).

To solve this equation for R, we can multiply both sides by R(R - 3) to eliminate the denominators:

2R(R - 3) - 6R(R - 3) = 6(R - 3) + 3R.

Simplifying further, we obtain:

\(2R^2 - 6R - 6R^2\) + 18R = 6R - 18 + 3R.

Combining like terms, we get:

\(-4R^2\) + 9R + 18 = 0.

Using the quadratic formula, we can solve for R:

R =\((-b ± √(b^2 - 4ac)) / (2a).\)

Substituting the values into the quadratic formula, we have:

R = \((-9 ± √(9^2 - 4(-4)(18))) / (2(-4))\).

After solving this equation, we find two possible values for R, representing the equal resistances of the two bulbs. Finally, the resistance of the third bulb can be calculated by subtracting 3 ohms from the value of R obtained.

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Answer:

$6.80

Step-by-step explanation:

1.79 x 3.8 = 6.802

So $6.80

Answer:

18

Step-by-step explanation:

x + x + 7 = 43

2x + 7 = 43

     -7     -7

2x = 36

x = 18

Answer:

x = 2

Step-by-step explanation:

Since the central angles are congruent, and all radii are congruent, the triangles are congruent. By CPCTC x = 2.

nope. bc...

0 ≠ 72 + 9.

yw!

Answer:

no.

Step-by-step explanation:

y (0) = 8(9) + 9

0 = 72 + 9

0 = 81

0 does not equal 81

Answer:

325 x 7.00 = 2275.

2495 - 2275 = 220.

The random sample of \(24\) students has a mean of \(1.9149\), and the data suggests that the mean is \(20^{0}\).

x = (xi) / n is the general solution for computing the sample mean. Thus, xi refers to all X sample values, xi represents the sampling distribution, and n is the total number of specimen terms inside the data collection.

The statistic known as the sampling distribution is created by arithmetically averaging the values of the variables in a group. The sample mean is an estimate of the anticipated value if the sample is taken from probabilistic with a common expected value.

(a) Sample mean \(= (17 + 21 + 20 + 19 + 23 + 22 + 20 + 20 + 18 + 21 + 19 + 24 + 22 + 20 + 19 + 20 + 19 + 20 + 21 + 22 + 23 + 21 + 18 + 22)/24 = 20.5\)Sample standard deviation \(= 1.9149\)

Next, we can use a t-distribution with \(23\) degrees of freedom

Confidence interval \(= (20.5 - 0.8277, 20.5 + 0.8277) = (19.6723, 21.3277)\)

b) The assumption required in order to generalize the estimate to the population of students at this university is that the \(24\) students in the study formed a random sample of students at this university.

(c) There is not enough evidence to suggest that the mean wrist extension for people using the new mouse design is greater than \(20^{0}\).

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The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

A. February 26th

B. $3,500 - Balance ≈ $6,697.26

C. $2,500 - Balance ≈ $4,263.46

D. $4,284.81

Step-by-step explanation:

a) What is the due date of the loan?

The loan term is given as 317 days, and the loan starts on April 15th. To find the due date, we will add 317 days to April 15th.

April 15th + 317 days = April 15th + (365 days - 48 days) = April 15th + 1 year - 48 days

Subtracting 48 days from April 15th, we get:

Due date = February 26th (of the following year)

b) Calculate the interest due on October 12th and the balance of the loan after the October 12th payment.

First, we need to calculate the number of days between April 15th and October 12th:

April (15 days) + May (31 days) + June (30 days) + July (31 days) + August (31 days) + September (30 days) + October (12 days) = 180 days

Now, we will calculate the interest for 180 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $10,000 × 0.04 × (180 / 365)

Interest ≈ $197.26

Peter will make a payment of $3,500 on October 12th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $10,000 + $197.26 - $3,500

Balance ≈ $6,697.26

c) Calculate the interest due on January 11th and the balance of the loan after the January 11th payment.

First, we need to calculate the number of days between October 12th and January 11th:

October (19 days) + November (30 days) + December (31 days) + January (11 days) = 91 days

Now, we will calculate the interest for 91 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $6,697.26 × 0.04 × (91 / 365)

Interest ≈ $66.20

Peter will make a payment of $2,500 on January 11th. So, we need to find the balance of the loan after this payment:

Balance = Principal + Interest - Payment

Balance = $6,697.26 + $66.20 - $2,500

Balance ≈ $4,263.46

d) Calculate the final payment (interest + principal) Peter must pay on the due date.

First, we need to calculate the number of days between January 11th and February 26th:

January (20 days) + February (26 days) = 46 days

Now, we will calculate the interest for 46 days:

Interest = Principal × Interest Rate × (Days Passed / 365)

Interest = $4,263.46 × 0.04 × (46 / 365)

Interest ≈ $21.35

Finally, we will calculate the final payment Peter must pay on the due date:

Final payment = Principal + Interest

Final payment = $4,263.46 + $21.35

Final payment ≈ $4,284.81

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

k = -3

Step-by-step explanation:

In this question, you would have to work backward. You know that the whole polynomial is 2x^2 - x + k and a factor of it is (x + 1). That will lead to you getting (2x + ?). It takes a little bit of guessing and checking to get the ? value, but in the end, you should find it. and figure out the other factor is (2x - 3). Multiplying (x + 1) and (2x - 3), you should get that the equation is 2x^2 - x - 3, so the value of k is -3.

Answer:

To determine the length of the other side of the triangle, we must use Pythagora's theorem.

a^2 = b^2 + c^2

( where a = |EG| )

=> a^2 = 5,8^2 + 4,9^2 = 33,64 + 24,01 = 57,65

<=> a = the square root of 57,65 = 7,6

To determine what angle G is, we must use the tangens of angle G;

tanG = |EF|/|FG|

=> tanG = 5,8/4,9 = 1,2

therefor angle G = 49°48'28"

because the sum of the angles of a triangle equals 180;

180°-90°-49°48'28"6= 40°11'31"4 = angle E

Answer:

I think this is right for the 2nd problem

Step-by-step explanation:

a1=7+(3)(1)

Step 1: Simplify both sides of the equation.

a1=7+(3)(1)

a=7+3

a=(7+3)(Combine Like Terms)

a=10

a=10

Answer:

a=10

Given:

a.) He has 12 1/2 cups of milk.

b.) The chef has 3 1/2 more cups of broth than milk.

Step 1: Since it is said that the chef has 3 1/2 more cups of broth than milk, and he has 12 1/2 cups of milk, we will be adding 3 1/2 and 12 1/2 to get the actual number of cups of broth.

We get,

In adding mixed numbers, we add separately the whole numbers and fractions and add them together later on.

Therefore, the chef has 16 cups of broth.

Step 2: Let's now determine the remaining cups of broth after using 14 1/2 cups to make soup. We will be subtracting the current 16 cups of broth by 14 1/2 cups for the soup.

We get,

Let's first convert them into similar fractions before subtracting.

Let's now proceed in subtracting them,

Therefore, the chef will have a remaining 1 1/2 cups of broths after using 14 1/2 cups for the soup.

The radius and height of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area are approximately 2.89 cm and 13.15 cm, respectively. These dimensions are closer to the dimensions of a real soda can compared to the dimensions obtained in part (a).

a. To minimize the surface area of a cylindrical soda can, we need to find the values of radius and height that minimize the surface area equation.

Let's denote the radius of the can as r and the height as h. The volume of the can is given as 354 cm^3, so we have:

πr^2h = 354

Solving for h, we get:

h = 354 / (π\(r^2\))

The surface area of the can can be calculated as follows:

A = 2πr^2 + 2πrh

Substituting the expression for h in terms of r, we get:

A = 2πr^2 + 2πr(354 / πr^2)

Simplifying:

A = 2πr^2 + 708 / r

To minimize the surface area, we need to find the value of r that makes the derivative of A with respect to r equal to zero:

dA/dr = 4πr - 708 / r^2

Setting dA/dr = 0, we get:

4πr = 708 / r^2

Multiplying both sides by r^2, we get:

4πr^3 = 708

Solving for r, we get:

r = (708 / 4π)^(1/3) ≈ 3.64 cm

Substituting this value of r back into the expression for h, we get:

h = 354 / (π(3.64)^2) ≈ 9.29 cm

Therefore, the radius and height of the cylindrical soda can with minimum surface area and volume of 354 cm^3 are approximately 3.64 cm and 9.29 cm, respectively.

b. Real soda cans do not seem to have an optimal design because their dimensions are not the same as the ones obtained in part (a). The radius of a real soda can is 3.1 cm and the height is 12.0 cm. However, real soda cans have a double thickness in their top and bottom surfaces, which means that their dimensions are not directly comparable to the dimensions of the cylindrical can we calculated in part (a).

To find the dimensions of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area, we can use the same approach as in part (a), but with the appropriate modification to the surface area equation:

A = 4πr^2 + 708 / r

Setting dA/dr = 0, we get:

8πr^3 = 708

Solving for r, we get:

r = (708 / 8π)^(1/3) ≈ 2.89 cm

Substituting this value of r back into the expression for h, we get:

h = 354 / (π(2.89)^2) ≈ 13.15 cm

Therefore, the radius and height of a real soda can with a double thickness in the top and bottom surfaces that minimize its surface area are approximately 2.89 cm and 13.15 cm, respectively. These dimensions are closer to the dimensions of a real soda can compared to the dimensions obtained in part (a).

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Answer:

105cm^2

Step-by-step explanation:

5 times 6 = 30

30 div 2 = 15

6 times 15 = 90

90 + 15 = 105

The true population mean is (222.52, 227.48) with a 95% confidence interval.

The critical factor for a 90% confidence interval for the true population mean is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

⇒ P(-1.96< (x-μ)/(s/√n) < 1.96) = 0.95

⇒ P(-1.96×(s/√n) < (x-μ) < 1.96×(s/√n)) = 0.95

⇒ P(x - 1.96×(s/√n) < μ < x + 1.96×(s/√n)) = 0.95

95% confidence interval for

⇒ μ = (x - 1.96×(s/√n) , x + 1.96×(s/√n))

Here, x = 225, s  = 8.5, and n = 45

⇒ μ = (225- 1.96×(10.81/√13) , 225+ 1.96×(10.81/√13))

⇒ μ = (222.52, 227.48)

Hence, the true population mean is (222.52, 227.48) with a 95% confidence interval.

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The question seems to be incomplete the correct question would be

Calculate the 95% confidence interval for the true population mean based on a sample with x=225, s=8.5, and n=45.

Answer:

148cm^2

Step-by-step explanation:

The formula for surface area of a rectangular prism is 2(hl)+2(hw)+2(wl).

we just plug in the values.

2(6 x 5) + 2(6 x 4) + 2(4 x 5)

= 2(30) + 2(24) + 2(20) then simplify

= 60 + 48 + 40

= 148

The mean absolute deviation of the given scores of Robin as shown in the diagram atatched is: 5.2.

The mean absolute deviation of a data set is determined by finding the average of the distance of each data point from the mean of the data set.

Given that the distance from the mean are: 8, 1, 5, 0, 12,

Mean absolute deviation = (8 + 1 + 5 + 0 + 12)/5

Mean absolute deviation = 26/5

Mean absolute deviation = 5.2.

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Answer: The slope is infinite

Step-by-step explanation:

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.

Answer:

Sin A = 4/5

Step-by-step explanation:

sin theta = opposite / hypotenuse

sin A = 40/50

Sin A = 4/5

Answer:

0.8

Step-by-step explanation:

SinA = opposite/hypotenuse

= CB/CA

= 40/50

= 4/5

= 0.8

Answer:1

Step-by-step explanation:

Answer:

its -5,

x=-5

Don't listen to the other guy who said "1"

Step-by-step explanation:

Answer:

\(10^5\)

Step-by-step explanation:

Exponents are basically just saying how many times the number is multiplied by itself.

In the expression \(10\cdot10\cdot10\cdot10\cdot10\), we can see that 10 is being multiplied by itself 5 times.

So the exponent becomes 5, and the base is 10.

\(10^5\).

Hope this helped!

\(10^{5}\)

Step-by-step explanation:

God bless

10 to the power of 5

Answer: D. 3x +28 > 52

Step-by-step explanation:

Based on the information given, the inequality that Maria can use to find how many more bracelets she needs to sell to make more money than she spent on supplies will be calculated thus:

With the question above, the total sales must be greater than the amount spent on supplies. Let the number of bracelets that needs to be sold be represented by x.

Therefore, (3 × x) + 28 > 52

= 3x + 28 > 52.

We can calculate further

3x > 52 - 28

3x > 24

x > 24/3

x > 8

Therefore, 9 or more bracelets needs to be sold since x is greater than 8.

Therefore, the correct option is D 3x +28 > 52

Answer:

D. 3x + 28 > 52

Step-by-step explanation:

Ben's family can start their tour of Chicago and still make it to dinner is 3:50 PM.

What are basic arithmetic operations?

Basic arithmetic operations are the fundamental mathematical operations used in mathematics and everyday life. The four basic arithmetic operations are addition, subtraction, multiplication, and division. These operations are used to perform calculations on numbers and solve mathematical problems.

If Ben's family has dinner reservations at 5:20 P.M., then they need to finish their tour and arrive at the restaurant before that time.

The total time they will spend sightseeing is:

1 hour and 20 minutes at the Willis Tower + 3 hours at Navy Pier + 1 hour and 30 minutes shopping = 6 hours and 50 minutes

To make it to dinner on time, they need to finish their tour 1 hour and 30 minutes before their reservation time to allow for travel and unexpected delays.

Therefore, the latest time Ben's family can start their tour of Chicago is:

5:20 PM (dinner reservation time) - 1 hour and 30 minutes = 3:50 PM

If they start their tour by 3:50 PM, they will have 6 hours and 50 minutes to complete their sightseeing and shopping, and still make it to their dinner reservations on time.

Hence, Ben's family can start their tour of Chicago and still make it to dinner is 3:50 PM.

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Answer:

The trucker was cited for speeding because his speed was above that of the speed limit of the toll road by 14.5mph

Step-by-step explanation:

Step 1

We calculate the speed of the trucker

Speed = Distance(miles)/Time(hours)

Distance = 159 miles

Time = 2 hours

Speed = 159 miles/2 hours

Speed = 79.5 miles per hour = 79.5 mph

From the question, we are told that: that toll road has a speed limit of 65mph

Step 2

We calculate the difference

= 79.5 mph - 65 mph

= 14.5 mph

Hence, the trucker was cited for speeding because his speed was above that of the speed limit of the toll road by 14.5mph

Answer:

turn pls

Step-by-step explanation:

The length and width of the rectangular field is 316 ft and 133 ft respectively.

An algebraic equation is a mathematical statement that equalises two expressions. A variable, coefficients, and constants are common components of an algebraic equation. Also look into Algebraic Expressions. Equality is represented by equations or the equal sign.

It is balanced because both sides are equal in value. To avoid making an error that throws the equation out of balance, ensure that any change on one side is reciprocated on the other.

Given,

perimeter of rectangular field = 898 ft

let width be 'x'

then,

length = x+183

The perimeter of a rectangle is,

\(P = 2(length + width)\\\\898 = 2( ( x + 183 ) + x )\\\\898 = 2(2x+183)\\\\898 = 4x + 366\\\\4x = 898 - 366\\\\4x = 532\\\\x=\frac{532}{4}\\\\x=133\)

Thus, the width is 133 ft and length is (133+183)=316 ft.

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Your question is incomplete, here is the complete question.

A certain field is a rectangle with a perimeter of 898 ft. The length is 183 ft more then the width. Find the width and length of the rectangular field?