a certain european automobile has a gas mileage of 19 km/l. what is the gas mileeage in miles per gallon

The equivalent expression of this 19 - 6(-k + 4) will be 6k + 5.

Given that:

Expression, 19 - 6(-k + 4)

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less complicated.

Simplify the expression, then we have

⇒ 19 - 6(-k + 4)

⇒ 19 + 6k - 24

⇒ 6k - 5

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

Answer:  Yes, the car is breaking the speed limit

Work Shown:

22 min = 22/60 = 0.36667 of an hour approximately

distance = rate*time

rate = distance/time

rate = (19 mi)/( 0.36667 hr)

rate = 51.818 mph approximately

The car is slightly over the 50 mph speed limit.

Answer:

270.4 miles

Step-by-step explanation:

First we will convert the 40 liter gas tank into gallons.

There are about 0.26 gallons in 1 liter, so we can find how many gallons are in 40 liters by solving \(40 * 0.26\), which equals to \(10.4\) gallons.
We can now find how far we can travel on a full tank.

\(\mbox{26 miles per gallon } * \mbox{10.4 gallons} = \mbox{270.4 miles}\)

This means we can travel 270.4 miles on a full tank.

That is the answer

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Answer:

1 . is a function

2. is not a function

If a trapezoid has an area of 100 square units, the scale factor that would be required to dilate the trapezoid to have each area is:

sqrt(A / 100)

To find the scale factor required to dilate a shape, you need to determine what ratio of the new area to the original area you want to achieve.

Let's call the scale factor "k". If the original area of the trapezoid is 100 square units, and the new area is "A", the relationship between the two areas can be expressed as:

So to find the scale factor required to achieve a specific new area, you can solve for k by dividing the new area by 100 and taking the square root:

Note that: This equation assumes that the dilation is proportional, meaning that all dimensions of the trapezoid are scaled by the same factor.

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The given equation is equivalent to the system

\(\begin{cases}y = 17x-8\\y = 3x+16\end{cases}\)

The linear equations have different slopes (m = 17 and m = 3), so that means the two lines intersect at exactly one location. This one intersection point means there is exactly one solution to the system.

That means there is exactly one solution to the equation 17x-8 = 3x+16

----------------

That solution is....

17x-8 = 3x+16

17x-3x = 16+8

14x = 24

x = 24/14

x = 12/7

A possible vertex of the quadratic function is (4, 0). The vertex form of the quadratic function can be written as y = a(x - h)^2 + k, where (h, k) represents the vertex. In this case, h = 4 and k = 0.

The zeros of a quadratic function represent the x-values where the function intersects or crosses the x-axis. Since the given zeros are (0, 0) and (8, 0), we can infer that the quadratic function intersects the x-axis at these points.

To find a possible vertex of the function, we can take the average of the x-values of the zeros. In this case, the x-values of the zeros are 0 and 8, so the average is (0 + 8) / 2 = 4.

Now, to find the y-value of the vertex, we can substitute the x-value (4) into one of the zeros. Let's use (0, 0):

0 = a(0 - 4)(0 - 8)

0 = -32a

Solving for 'a', we find that a = 0.

So, a possible vertex of the quadratic function is (4, 0), meaning the function is symmetric and opens upwards.

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Answer:

15

Step-by-step explanation:

Percentages represent a proportion of a number. This means that a percentage represents part of a whole.

In this question, Captain Perguin ate 10% of 150 crackers. There are 2 ways to solve this problem explained below.

Multiplication

One way to find a percentage is through multiplication.

Shortcut

Multiplication is not the only way to find the answer. This question is special because it asks for 10%. Instead of multiplication, you could simply move the decimal point of the original number 1 digit to the left. This means that 10% of 150 must be 15. Remember this trick does not work for percentages other than 10%.

Yes the triangle with dimension 3 cm , 4cm , 5 cm is  a right angled triangle.

Given,

Dimensions : 3 cm , 4cm , 5 cm .

Here,

In any right angled triangle the Pythogoras theorem holds trure .

Pythogoras theorem ,

P² + B² = H²

P = perpendicular

B = base

H = hypotenuse .

So,

In triangle ,

3cm , 4cm , 5cm

Apply pythogoras theorem .

Let ,

P =3cm

B = 4cm

H = 5cm

3² + 4² = 5²

25 = 25 .

Thus the triangle is right angled triangle .

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the total amount will be $10000, for present value of $1,490.30

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

if the required return is 8 percent.

the present value of $1,490.30

The total year will be 10.

So the amount after 10 years will be:

Then Present value

$1490.30 x 6.71008140

10,000.03 = $10000

Hence, the total amount will be $10000.

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Answer:

y=3/4x-2

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

given f(x) = 2(3x - 5) and f(x) = 74 , then equating gives

2(3x - 5) = 74 ( divide both sides by 2 )

3x - 5 = 37 ( add 5 to both sides )

3x = 42 ( divide both sides by 3 )

x = 14

Answer:

I think it is 0.12P because 16-4 is 12 so yeah. that is what I think

Answer:

5.6 - (-8.6)

Step-by-step explanation:

Answer:

a) r = 2

b)
GP a₆ = 384

AP a₆ = 32

Step-by-step explanation:

First term a₁ = 12 for both progressions

r = common ratio, d = common difference

nth term of geometric progression = a₁ x rⁿ⁻¹
nth term of arithmetic progression = a₁ + (n - 1)d

Second term of GP = Fourth term of AP

=> 12r¹ = 12 + 3d

==> 12r = 12+ 3d  (1)

Third term of GP = 10th term of AP

=> 12r² = 12 + 9d (2)

3 x (1) => 3(12r = 12 + 3d) => 36r  = 36 +  9d (3)

(2) - (3) gives12r² -36r = 12 - 36
12r² - 36r = 12 + 9d - (36 + 9d)

12r² -36r = -24

12r² -36r + 24 = 0

Dividing by 12 gives
r² - 3r + 2= 0

We can factor r² - 3r + 2 as (r - 1)(r-2)

r² - 3r + 2= 0
=>  (r - 1)(r-2) = 0

=> r = 1 or r = 2

r cannot be 1 since all terms of the GP will be equal with a common ratio of 1

Therefore r = 2  (Part a)

Using equation (1) we get:
12r = 12+ 3d
12 x 2 = 12 + 3d

24 = 12 + 3d

3d = 24 - 12 = 12

d = 12/3 = 4

So the common ratio, r,  is 2. Common difference d = 4

6th term of GP =12 x r⁵ =  12 x 2⁵ = 12 x 32 = 384

6th term of Ap = 12 + 5d = 12 + 5(4) = 12 + 20 = 32

(a) This grammar generates strings of the form "012n" where n is a non-negative integer. The production rule S -> "0" S allows for the recursive generation of any number of "0" characters followed by "12".

(b) This grammar generates strings of the form "0n12n" where n is a non-negative integer. The production rule S -> "0" S "1" allows for the recursive generation of any number of "0" characters followed by the same number of "1" characters.

(c) This grammar generates strings of the form "0n1m0n" where m and n are non-negative integers. The production rules allow for the recursive generation of any number of "0" characters followed by any number of "1" characters, with a block of "0" characters in between.

What is a set?

In mathematics, a set is a well-defined collection of distinct objects, considered as an entity on its own. The objects within a set are called its elements or members. Sets are fundamental objects in set theory, which is a branch of mathematical logic and a foundation for many areas of mathematics.

a) Phrase-structure grammar for {012n | n ≥ 0}:

Start symbol: S

Production rules:

S -> "0" S | ε

This grammar generates strings of the form "012n" where n is a non-negative integer. The production rule S -> "0" S allows for the recursive generation of any number of "0" characters followed by "12".

Example derivations:

S -> "0" S -> "0" "0" S -> "0" "0" "0" S -> "0" "0" "0" ε = "000"

S -> "0" S -> "0" "0" S -> "0" "0" "0" S -> "0" "0" "0" "0" S -> "0" "0" "0" "0" "12" = "00012"

S -> "0" S -> "0" "0" S -> "0" "0" "0" S -> "0" "0" "0" "0" S -> "0" "0" "0" "0" "12" S -> "0" "0" "0" "0" "12" "12" = "0001212"

b) Phrase-structure grammar for {0n12n | n ≥ 0}:

Start symbol: S

Production rules:

S -> "0" S "1" | ε

This grammar generates strings of the form "0n12n" where n is a non-negative integer. The production rule S -> "0" S "1" allows for the recursive generation of any number of "0" characters followed by the same number of "1" characters.

Example derivations:

S -> "0" S "1" -> "0" ε "1" = "01"

S -> "0" S "1" -> "0" "0" S "1" "1" -> "0" "0" ε "1" "1" = "0011"

S -> "0" S "1" -> "0" "0" S "1" "1" -> "0" "0" "0" S "1" "1" "1" -> "0" "0" "0" ε "1" "1" "1" = "000111"

c) Phrase-structure grammar for {0n1m0n | m ≥ 0 and n ≥ 0}:

Start symbol: S

Production rules:

S -> "0" S "1" | T

T -> ε | "0" T "0"

This grammar generates strings of the form "0n1m0n" where m and n are non-negative integers. The production rules allow for the recursive generation of any number of "0" characters followed by any number of "1" characters, with a block of "0" characters in between.

Example derivations:

S -> "0" S "1" -> "0" "0" S "1" "1" -> "0" "0" ε "1" "1" = "0011"

S -> "0" S "1" -> "0" "0" S "1" "1" -> "0" "0" "0" S "1" "1" "1" -> "0" "0" "0" ε "1" "1" "1" = "000111"

S -> "0" S "1" -> "0" T "1" -> "0" "0" T "0" "1" -> "0" "0" ε "0" "1" = "00001"

S -> "0" S "1" -> "0" "0" S "1" "1" -> "0" "0" "0" S "1" "1" "1" -> "0" "0" "0" T "1" "1" "1" -> "0" "0" "0" "0" T "0" "1" "1" "1" -> "0" "0" "0" "0" ε "0" "1" "1" "1" = "0000111"

Therefore, this grammar allows for the generation of strings with any number of "0" characters, followed by any number of "1" characters, with a block of "0" characters in between. The T non-terminal is introduced to handle the generation of the block of "0" characters, allowing for any number of repetitions.

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Answer:

Let the distance from the base of the statue to the ship be d, then

tan 18 = 250/d

d = 250 / tan 18 = 769.4

The distance from the base of the statue to the ship to the nearest foot is 769 feet.

Step-by-step explanation:

The range of the p-value for the statistical test to check whether the training program can reduce the mean finish time of the 40-yard dash is (0.025, 0.05). This means that the p-value falls between 0.025 and 0.05, indicating moderate evidence against the null hypothesis.

To determine the range of the p-value, we need to conduct a statistical test. The null hypothesis is that the training program does not reduce the mean finish time of the 40-yard dash. The alternative hypothesis is that the training program does reduce the mean finish time.

We can perform a t-test for the mean difference in the before-training and after-training times. Given that the sample mean of the differences is 0.079 min and the sample standard deviation is 0.255 min, we can calculate the t-statistic using the formula t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean (which is 0 in this case), s is the sample standard deviation, and n is the sample size.

Using the given values, we find that the t-statistic is approximately 1.556.

Next, we can compare the t-statistic to the critical value from the t-distribution for a given significance level (α). Since the problem does not specify the significance level, we will assume α = 0.05.

By looking up the critical value in the t-distribution table with 23 degrees of freedom and α = 0.05, we find that the critical value is approximately 2.069.

Comparing the t-statistic (1.556) to the critical value (2.069), we see that it falls within the range (0.025, 0.05). This means that the p-value, which is the probability of observing a t-statistic as extreme as or more extreme than the observed value, falls between 0.025 and 0.05. Thus, there is moderate evidence against the null hypothesis, suggesting that the training program may reduce the mean finish time of the 40-yard dash.


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The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Answer

-11.76 dollars

Step-by-step explanation

First, we need to calculate the probability of winning, that is, the probability of drawing three black cards in succession without replacement.

In the beginning, there are a total of 52 cards, and 26 of them are black, then the probability that the first card drawn is black is:

After drawing 1 black card, there are a total of 51 cards, and 25 of them are black, then the probability that the second card drawn is black is:

After drawing 2 black cards, there are a total of 50 cards, and 24 of them are black, then the probability that the third card drawn is black is:

Therefore, the probability of winning, that is, the three cards are black is calculated as follows:

The probability of losing is the complement of the probability of winning, that is,

Finally, the expected value is calculated as follows:

Answer:

2 GB per month

Step-by-step explanation:

mean = (0.9+1.85+3.82+2.19+1.24)/5

mean = 2

Answer:

50 square inches

Step-by-step explanation:

The pan radius is 4", and so the approximate area of the pan bottom is

A = pi(4 ")^2, or 16 pi, or 50 square inches.

The value of h in the intersected secants is 10 degrees.

If two secants intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

In other words, the theorem of intersecting secant states that the angle made by two secants intersecting outside a circle is half the difference between the intercepted arc measures.

Therefore,

50 = 1 / 2 (110 - h)

50 = 55 - 0.5h

50 - 55 = -0.5h

-5 = -0.5h

divide both sides by -0.5

h = - 5 / -0.5

h = 10

Therefore,

h = 10 degrees

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We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

File < Options < (A) Formulas < Automatic

We should choose Formulas as X in the given series of clicks to calculate formulas automatically.

Therefore, File < Options < (A) Formulas < Automatic

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The complete question is given below:

What would you choose as X in the given series of clicks to calculate formulas automatically: File < Options < X < Automatic?

a. Formulas

b. Language

c. Proofing

d. Advanced

The constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

A variable in mathematics is a sign that denotes a value that may vary, as opposed to a constant, which is a set number that never changes. Variables are used to represent unknown or changing quantities, such as time (t) or the distance (d) travelled by an item, whereas constants are used to represent fixed numerical values, such as pi or the speed of light (c). In contrast to variables, which are often represented by lowercase letters, constants are typically represented by capital letters. In mathematical equations and formulae, the distinction between constants and variables establishes which values are fixed and which values are subject to change.

The slope of line is given as:

m = (change in y) / (change in x)

Substitute the values from the table:

m = (135 - 150) / (9 - 10) = -15/-1 = 15

For the equation to be of the form y = mx we have:

y = mx + b

150 = 15(10) + b

b = 0

Substituting the values the equation is:

y = 15x

Hence, the constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

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The accumulated amount 54675 (\(2.7^{t}\\\)) in dollars of an account with an initial deposit of $7,500 and earns 3. 4% compound interest semi-annually.

A compound interest is calculated by the formula,

\(A = P [ 1 + ( r/n )]^{nt}\)

where, A is the accumulated amount at the end of the period ,

P is the initial amount of deposit,

r is the rate of interest earned on the initial deposit in the period

t is the time periods elapsed

and n is the number of times interest is applied per time period

Here the account has an initial deposit , P = $7500 and earns 3.4% rate of interest, say r, compounded semi- annually, that is n= 2 ( as rate of interest is applied twice a year or twice per time period) in time period, say t.

Therefore by the formula of compound interest we get,

Accumulated amount, A = \(7500[ 1 + 3.4/2]^{2t}\)

⇒ A = \(7500[ 1 + 1.7]^{2t}\) in dollars

⇒ A = \(7500(2.7)^{2t}\) in dollars

⇒ A = 7500 (2.7)² (\(2.7^{t}\) ) in dollars

⇒ A = 54675 (\(2.7^{t}\\\)) in dollars

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Answer:

The answer is 1 1/2 = 3/2 1 = 2/2 LCD=2

Answer:

66,5 sm

Step-by-step explanation:

The sides of a triangle: 2x+7x+3x=114

12x=114

x=9,5

2×9,5=19,

7×9,5=66,5

3×9,5=28,5

Answer: 66,5