Wyatt drove 468 miles on 14. 4 gallons of gas. How far can Wyatt drive on a full tank of gas, which is 16. 8 gallons?

Answer:

4+x=-3+2x

4+3=2x-x

7=x

9x=9*7

=63

Step-by-step explanation:

Answer:

\(4 + x = - 3 + 2x \\ x - 2x = - 3 - 4 \\ - x = - 7 \\ x = 7 \\ therefore = \\ 9x = 9 \times 7 \\ 9x = 63 \\ i \: hope \: this \: was \: helpful \)

Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

37 is at the 50th percentile in the given set of values.

To find the percentile of 37 in the given set of values, we need to count the number of values in the set that are less than or equal to 37, and then divide by the total number of values in the set.

The given set has 16 values, and there are 8 values that are less than or equal to 37.

So, the percentile of 37 is:

Percentile = (number of values below score / total number of values) × 100

Percentile = (8 / 16) × 100

Percentile = 50

Therefore, 37 is at the 50th percentile in the given set of values.

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Answer:

312

Step-by-step explanation:

Assuming that the car is not moving, the force the car exerts against the driveway is equal in magnitude and opposite in direction to the force of gravity acting on the car. We can break down the force of gravity into two components: one perpendicular to the driveway and one parallel to the driveway.

The component of gravity perpendicular to the driveway is equal to the weight of the car times the cosine of the angle of inclination:

F_perp = mgcos(4°)

where m is the mass of the car, g is the acceleration due to gravity, and F_perp is the perpendicular component of the force of gravity.

The component of gravity parallel to the driveway is equal to the weight of the car times the sine of the angle of inclination:

F_parallel = mgsin(4°)

where F_parallel is the parallel component of the force of gravity.

Since the car is not moving, the force the car exerts against the driveway is equal in magnitude to the force required to keep the car from rolling down the driveway:

F_exerted = 480 lb

Thus, we have the equation:

F_exerted = F_parallel

Substituting the expressions for F_parallel and F_perp, we get:

mgsin(4°) = 480 lb

Solving for the mass of the car, we get:

m = 480 lb / (g*sin(4°))

Substituting the mass of the car into the expression for the perpendicular component of the force of gravity, we get:

F_perp = mgcos(4°) = (480 lb / (gsin(4°))) * gcos(4°)

Simplifying, we get:

F_perp = 480 lb / tan(4°)

Thus, the force the car exerts against the driveway is:

F_exerted = F_parallel = 480 lb

And the force of gravity perpendicular to the driveway is:

F_perp = 480 lb / tan(4°) ≈ 6,837 lb

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Answer:

x=20

Step-by-step explanation:

How I did it was I divided 3/12 to get .25 and 5 divided by .25 is 20. So x is equal to 20.

The inverse Laplace transform of A(s + K) + B/7 using the shifting property is A(e^(-Kt) + δ(t)) + B/7.The Laplace transform is a mathematical tool used to analyze and solve linear differential equations.

The shifting property is a fundamental property of the Laplace transform that allows us to simplify calculations by shifting the function in the time domain.

In this case, we have the function A(s + K) + B/7, where A, B, and K are constants. To find the inverse Laplace transform using the shifting property, we need to split the function into two terms: A(s) + B/7 and AK.

The inverse Laplace transform of A(s) + B/7 is A(e^(-Kt)) + B/7, which can be obtained by applying the shifting property. This term represents the effect of A(s) + B/7 on the time domain.

The inverse Laplace transform of AK is simply AK multiplied by the Dirac delta function, δ(t). The Dirac delta function represents an impulse or a sudden change at t = 0.

By combining the two terms, we get the inverse Laplace transform of A(s + K) + B/7 as A(e^(-Kt) + δ(t)) + B/7. This expression represents the function in the time domain, which can be useful for further analysis or calculations.

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To solve this problem, we can use the central limit theorem and the standard error of the mean formula.

The population mean of the truck weights is 15.8 tons and the population standard deviation is 4.2 tons. The sample size is 49.

The standard error of the mean (SE) is calculated by dividing the population standard deviation by the square root of the sample size:

SE = σ / √n

where σ is the population standard deviation and n is the sample size.

In this case, the standard error of the mean is:

SE = 4.2 / √49 = 4.2 / 7 = 0.6 tons

To find the probability that the sample mean is 14.3 tons or less, we need to calculate the z-score corresponding to this value and then find the area under the standard normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

z = (14.3 - 15.8) / 0.6 = -2.5 / 0.6 = -4.1667

Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -4.1667. The probability is approximately 0.0000062, which is very close to option (a) 0.0062.

Therefore, the correct answer is (a) 0.0062.

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Answer:

Step-by-step explanation:

700.5

The first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

For given question,

We have been given a sequence \(a_n=\frac{n^2-9}{n^3+3}\)

We need to find the first five terms, a1, a2, a3, a4, a5, of the sequence.

For n = 1,

\(a_1=\frac{1^2-9}{1^3+3} \\\\a_1=\frac{-8}{4} \\\\a_1=-2\)

For n = 2,

\(a_2=\frac{2^2-9}{2^3+3}\\\\ a_2=\frac{-5}{11}\)

For n = 3,

\(a_3=\frac{3^2-9}{3^3+3} \\\\a_3=\frac{0}{30}\\\\ a_3=0\)

For n = 4,

\(a_4=\frac{4^2-9}{4^3+3} \\\\a_4=\frac{7}{67}\)

For n = 5,

\(a_5=\frac{5^2-9}{5^3+3} \\\\a_5=\frac{16}{128}\\\\ a_5=\frac{1}{8}\)

Given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

Therefore, the first five terms of the given sequence are:

a1 = -2

a2 = -5/11

a3 = 0

a4 = 7/67

a5 = 1/8

Also, given sequence should converge to a limit of 0, since the denominator is growing faster than the numerator.

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Answer:

Step-by-step explanation:

We are expected to solve for the amount off the reader after 40% discount and  $25 refund(rebate)

Now given that the book is $150

40% of 150

=(40/100)*150

=0.4*150

=$60

The total amount off includes the markdown and rebate.

the total amount is

60+25=$85

The 11 people that were going to Canada with Harriet Tubman put an ashcake and salt herring in an old bandanna to keep themselves from getting hungry during their long journey.

The ash cake was made of cornmeal and water, which was cooked over an open fire. It was one of the cheapest and most convenient foods for the slaves to carry during their journey.

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The percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.The number of cookies in a shipment of bags is normally distributed, with a mean of 64 and a standard deviation of 4.

What percentage of bags of cookies will contain between 64 and 68 cookies

When X is normally distributed with mean µ and standard deviation σ, the z-score formula can be used to find the probability that X is between two values.

Z = (X - µ) / σ

First, we convert both 64 and 68 to z-scores:

Z for 64 cookies = (64 - 64) / 4 = 0Z for 68 cookies = (68 - 64) / 4 = 1

Next, we find the probability that X is between these two z-scores using a standard normal distribution table or calculator:

Prob (0 < Z < 1) = 0.3413 - 0.5(0) - 0.159

= 0.1823

So, the percentage of bags of cookies that will contain between 64 and 68 cookies is approximately 18.23%.

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The value of m + p is related to the function f(x) and the values of x and m.

Given the function f(x) = -3(x - m)^2 + p and the point T(2, 5) on the parabola, let's find m + p when f(x) = -3(x - m)^2 + p.

Step 1: Substitute the coordinates of the point T(2, 5) into the function.

5 = -3(2 - m)^2 + p

Step 2: Expand and simplify the equation.

5 = -3(4 - 4m + m^2) + p
5 = -12 + 12m - 3m^2 + p

Step 3: Rearrange the equation to solve for m and p.

3m^2 - 12m + p = 7

Now, we have one equation with two unknowns, which cannot be solved for specific values of m and p. However, the question asks for m + p, which we can express in terms of the given function f(x).

The question asks to find m + p when f(x) = -3(x - m)^2 + p. Since we cannot find specific values for m and p, we can instead write an equation relating f(x), m, and p:

m + p = f(x) + 3(x - m)^2

This equation shows how m + p is related to the function f(x) and the values of x and m.

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Answer:

B

Step-by-step explanation:

Volume = Volume of cylinder + Volume of semi sphere

= pi*r^2*h+(2/3)*pi*r^3

=pi*(4*12+16/3)=pi*53.3

The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.

We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.

(a) Using the standard normal distribution, we can standardize X as follows:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.

Substituting the values, we get:

z = (74 - 69.0) / 2.8 = 1.75

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:

P(Z ≤ 1.75) ≈ 0.9599

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

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(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."

Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.

The angle in degrees separates these lines or planes.

So, we know that:

The side opposite to the largest angle is also the largest side of the triangle and vica-versa.

Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.

Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

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Correct question:

Which angle in AXYZ has the largest measure?

A. ∠X

B. ∠Y

C. ​∠Z

D. Cannot be determined

Answer:

The correct answer is 10n ≥ 470.

Step-by-step explanation:

Since, the school club wants to collect at least 500 canned goods, then we know that they don't want to collect any less: they must collet 500 or more canned goods.

They already collected 30 canned goods, therefore we can subtract this quantity from out goal.

500 - 30 = 470

Since there are 10 club members, the number of members multiplied by "n" the minimum amount of canned goods that they can collect, will equal the total amount of canned goods that they need.

Hope this helps! :D

The number of vowels is:

The total number of tiles is:

Therefore, the total number of letters not vowels is given by:

Hence, the probability of picking a letter that is not a vowel:

Therefore the required probability is 4/5

The required value of AD is 35 units in the given figure.

Geometry is the description of figures in a space with a specific number of dimensions and types. Plane geometry is the most prevalent sort of geometry (dealing with objects like the point, lines, circles, triangles, and polygons),

As per the given figure, we can write be as:

(GH + EK)/2 = FJ

(8x - 7 + 10x - 1)/2 = 7x +2

18x - 8 = 2(7x +2)

18x - 8 = 14x + 4

Rearrange the likewise terms and solve for x:

4x = 12

x = 3

GH = 8(3) - 7 = 17

EK = 10(3) - 1 = 29

FJ = 7(3) + 2 = 23

Now, (FJ + AD)/2 = EK

Substitute the known values and solve for AD:

⇒ (23 + AD)/2 = 29

⇒ 23 + AD = 58

⇒ AD = 35 units

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer:

$20

Step-by-step explanation:

trust me

Answer:

I believe $20 since 25% is 1/4 of 100% so 80/4 is 20 sorry if im wrong <3

75 cm

......................

Answer:

P = 16w - 4

Step-by-step explanation:

P = (5w-2 + 3w)2

P = (8w-2)2

P = 16w - 4

Using percentage we can calculate that the team is expected to lose 4 matches.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.

By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.

Given in percentages the team will win 65% , team will draw =15%

Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %

Now calculating the total number of matches the team will lose :

20% of 20 matches = 4 matches

Hence the team is expected to lose 4 matches out of 20.

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Answer:

3,900,000,000

Step-by-step explanation:

The current global population is 7,800,000,000.

Half of this is 3,900,000,000.