A seventh grade class and 7 adults go on a field trip. Two-thirds of the people ride on a bus.
Everyone else rides in vans. If 54 people ride on the bus, how many seventh graders go on the
field trip?

Jane should land 1.5 mi down the shoreline and walk the remaining 4.5 mi to the village to minimize her travel time.

Let x = distance travelled along the shore over water.

Then, 6 − x = distance travelled along the shore over land.

Let T = the total time taken to reach the destination.

T = distance/velocity = √(4 + x²)/3 + (6-x)/5 on [0, 6].

Note that T must be non negative and that x = 6 means the destination

is reached solely by rowing and without the benefit of faster land

travel. In actual fact, T is valid over [0, ∞) but [0, 6] is reasonable here.

T' = x/3√(4 + x²) - 1/5 = 5x - 3√(4 + x²) = 0

⇒5x = 3√(4 + x²)

⇒25x² = 9(4 + x²)

⇒16x² = 36

⇒x = ±6/4 = ±1.5

The negative x value is discarded since it does not belong to [0,6].

T(0) = 28/15 = 1.8667

T(1.5) = 1.733

T(6) = 2.1082

Therefore, Jane should land 1.5 mi down the shoreline and walk the

remaining 4.5 mi to the village to minimize her travel time.

Her minimum travel time will be T(1.5) = 1.733 hrs. or 1hr 44 min.

--The given question is incomplete, the correct question is

"Jane is 2 mi, offshore in a boat and wishes to reach a coastal village 6 mi, down a straight shoreline from the point nearest the boat. She can row at 3mph and can walk at 5 mph. Where should she land her boat to reach the village in the least amount of time?"--

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Answer:1000000

Step-by-step explanation:

On solving the provided question, we can say that by the help of unitary method total 28 + 40 = $ 68

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

One package of chicken costs  = $7

steaks cost  = $4 per pound.

cost of 4 chicken = 4 * 7 = $28

cost of 10 steaks = 4*10 = $40

total 28 + 40 = $ 68

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The measure of angle is, 62°.

The sum of two or more angle is 90 degree then the angle is called the complementary angle.

We have to given that;

⇒ Supplement of an angle is 6 more than 4 times of its complement.

Now,

Let measure of an angle = x

So, By given condition, we can formulate;

The supplement of an angle = 180 - x

And, The complement an angle = 90 - x

Hence, We get;

⇒ (180 - x) = 6 + 4 (90 - x)

Solve for x as;

⇒ 180 - x = 6 + 360 - 4x

⇒ 4x - x = 366 - 180

⇒ 3x = 186

⇒ x = 62°

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There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

(p-value of 1 - (0.05/2)).

Hence the decision rule is given as follows:

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is of:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]

z = 1.24.

|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

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The phrase b2 - 4ac is referred to as the discriminant for the quadratic equation ax2 + bx + c = 0.

The phrase b2 - 4ac is known as the discriminant for the quadratic equation ax2 + bx + c = 0. How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0.

D=b2 - 4ac, discriminatory

The constant term c.

In mathematics, a discriminant is a parameter of an object or system that is calculated to help with its classification or solution. For the cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc 4b3 4a3c 27c2, while the discriminant for the quadratic equation ax2 + bx + c = 0 is b2 4ac.

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The builder needs building sand weighing 6.3 * 10⁶ g and contains 9 * 10¹⁰ grains

An equation is used to show the relationship between numbers and variables.

A brick layer needs 6300 kg of building sand

The conversion from kg to g is:

1 kg = 1000 g

a) 6300 kg in grams is:

6300 kg = 6300 kg * 1000 g per 1 kg = 6,300,000 g = 6.3 * 10⁶ g

b) 1 grain = 7 * 10⁻⁵ g

6.3 * 10⁶ g = 6.3 * 10⁶ g * 1 grain / (7 * 10⁻⁵ g) = 9 * 10¹⁰ grain

The builder needs 6.3 * 10⁶ g of building sand

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The remaining miles are 660 miles.

This month, Diaz drives 28 miles each day using the car allotted to him by his company.

But the company allows him to drive up to 1500 miles each month by his car.

To calculate the remaining miles that Diaz has not traveled this month, we have to use the formula m = 1500 - 28d, where d is the number of days in that particular month.

A month general consists of 30 days.

So, this month Diaz has traveled 28×30 miles = 840 miles ( using multiplication)

Therefore, the remaining miles(m) that Diaz has not traveled this month comes to 1500 - 840 = 660 miles.

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The complete question is:

Diaz has a company car that allows him to drive up to 1,500 miles each month. He averages 28 miles each day. The remaining miles for this month can be calculated using the formula m = 1500 - 28d where m is the remaining miles and d is the number of days driven this month. What are the remaining miles?

No, 10, 12, and 15 are not the lengths of the sides of a right triangle.

A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).

The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.

In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:

10^2 + 12^2 = 15^2

100 + 144 = 225

244 ≠ 225

Therefore, 10, 12, and 15 are not the side lengths of a right triangle.

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Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

Step-by-step explanation:

there are a few things from school everybody has to burn into their brains for life. one of them : Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the triangle side opposite of the 90° angle), a and b are the triangle legs.

now, it depends on what you teacher agreed with you regarding naming the sides of such a triangle.

sometimes "base" is the Hypotenuse (baseline), sometimes it is one of the legs, and then the height is the second leg (as the legs are standing at a 90° or right angle at each other).

we have to assume the second one, as for the first one we have not enough information to solve the question (because with just a given Hypotenuse and the height to the Hypotenuse we can draw infinitely many different triangles with different perimeters).

so, we have

Hypotenuse² = 24² + 7² = 576 + 49 = 625

Hypotenuse = sqrt(625) = 25 m

the perimeter of the triangle is then

25 + 24 + 7 = 56 m

The given expression , 4x2 – 3xy is having two terms which are 4x2 and –3xy.

The term 4x2 is a product of 4 and x, whereas the other  term (–3xy) is a product of (–3), x and y.

When we will join these two terms using the addition operation we will get the result as  4x2 – 3xy .

The given equation is an example of an algebraic expression and they are made up of combination of constants and variables. They are joined to each other by various operations such as addition , multiplication , division and subtraction.

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The closest number to the circumference of the circle is 157 feet.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.

Given:

Kate bought a circular swimming pool with a diameter of 50 feet.

We have to find the closest number to the circumference of the circle.

Since,

Circumference = 2πr

where r is the radius of circle.

Here diameter of circle = 50 feet.

⇒ Radius of circle = 25 feet.

⇒ Circumference = 2*π*25 = 157.08

Hence, the closest number to the circumference of the circle is

157 feet.

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A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

In a right triangle, the hypotenuse is the longest side, the "opposite" side is the one that faces a particular angle, and the "adjacent" side is the one that faces that angle.

Step 1: Simplify both sides of the equation.

[tex]$$4 g-6=8$$\\Step 2: Add 6 to both sides.$$\begin{aligned}& 4 g-6+6=8+6 \\& 4 g=14\end{aligned}$\\$Step 3: Divide both sides by 4 .$$\begin{aligned}& \frac{4 g}{4}=\frac{14}{4} \\& g=\frac{7}{2}\end{aligned}$$[/tex]

[tex]$g=3 \frac{1}{2}$[/tex]

Therefore, the correct answer is option a)[tex]$g=\frac{7}{2}$[/tex].

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The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

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Therefore , the solution of the given question of triangle  comes out to be the only true option is A.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. One of the first geometric shapes to be examined was them. They are especially crucial because any polygon, regardless of its number of sides (four, five, six, or n), may be divided into a triangle.

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Relief refers to the highest and lowest point elevation in an area.

Relief

Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.

elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.

geology

Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.

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Answer: Relief

Step-by-step explanation:

Relief refers to the highest and lowest point elevation in an area.

Slope is the measure of steepness

Topography refers to the arrangement of the land in an area

Elevation on the other hand is the distance above sea level

Answer:

Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)

Step-by-step explanation:

Let's reorganize the given expression:

(1/3x+2x−5/3x)−(−1/3x+5)

1/3x+2x−5/3x + 1/3x-5       [Expand the parentheses]

2/3x+2x−5/3x -5       [Combine like terms]

-3/3x+2x -5

-x + 2x - 5

x - 5                       One of the equivalent expressions

The option 4x-5-3x also reduces to x - 5

The ordered pairs are a linear equation if the graph plotted is the straight line.

A linear equation can be represented by a graph in the Cartesian coordinate system as a straight line. If the equation is in the form of "y = mx + b" where m and b are constants, it is a linear equation. The ordered pairs of a linear equation will always satisfy this equation, and when plotted on a graph, will fall on a straight line. To check if a set of ordered pairs is a linear equation, you can plot them on a graph and see if they form a straight line or can substitute the x- and y-values of the ordered pairs into the equation "y = mx + b" and see if they make the equation true.

So, if the graph plotted is the straight line, then the ordered pairs are of a linear equation.

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Answer: In this exercise we have to calculate the values ​​of the people who voted to expand the parking lot, so we have to:

Yes: parents will be 150 and not parents 40

No; parents will be 40 and not parents 30

As it is about sets, we have to use the data that were:

   total: 250 adults

   180 of whom were parents a park should be expanded.

   40 of the adults who were not parents thought the park should be expanded.

then calculate that:

Step-by-step explanation:

The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

The two-way table shown in the table is attached below.

What is two way table?

Two-way table is a way of representing of data to better understand it.

Given information-

The total number of adults took the survey is 250.

Total number of parents took the survey is 180.

150 of the adults with children and 40 of those without thought the park should be expanded.

Suppose the number of adults who are not the parents and took the survey is .

As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,

Suppose the parents who does not thing that the park should be expanded is .

There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,

Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.

Hence the two way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

the two way

YES                    NO

                          30  

                          30

(parents 150

not parents_40

The number of hours that Julius can spend online this week is 1 1/3 hours.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Julius is allowed to surf the internet for only 3 hours a week. He has already been online for 1 2/3 hours this week.

This will be Illustrated as x.

x + 1 2/3 ≤ 3.

x ≤ 3 - 1 2/3

x ≤ 1 1/3.

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Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

Answer:

6

Step-by-step explanation:

x² + 8² = 10²

x² + 64 = 100

x² = 36

x = 6

The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.

A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.

To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.

To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:

log_2(8) = 4

This is a logarithmic equation, as the form of the equation matches log_b(x) = y.

If the equation is b^x = 16, then plug in x = 4. The calculation would then be:

2^4 = 16

This is an exponential equation, as the form of the equation matches b^x = y.

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The relationship between the input  and output  is that the perimeter of a square is always equal to four times the length of one of its sides.

The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S

1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.

2.Yes, the function can be represented with an equation. The equation would be:

Perimeter = 4 × Side Length.

Side Length (input) 1  2  3  4  5

Perimeter (output)  4 8 12 16 20

This equation states that the perimeter of a square is equal to four times the length of one of its sides.

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Answer:

Function Domain and Range

g(x)=\sqrt{x} -5

what is the range and domain

To find the range of g(x), we can substitute a few values of x into the expression for g(x) to see what the output is. For example, when x = 0, g(x) = sqrt(0) - 5 = 0 - 5 = -5. When x = 1, g(x) = sqrt(1) - 5 = 1 - 5 = -4. When x = 2, g(x) = sqrt(2) - 5 = 1.4142 - 5 = -3.5858.

As we can see, the output of g(x) is always a negative number for any value of x in the domain. Therefore, the range of g(x) is the set of all negative real numbers, or (-infinity, 0).

So, the domain of g(x) is all real numbers x such that x >= 0, and the range of g(x) is all negative real numbers (-infinity, 0).

Answer:

4.42857142857

Rounded:

4.4

The sample space for the experiment, S= {Q, R, S, T}.

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Given:

From the Spinner we can see four portions as

Q(Orange)

R(Green)

S(Blue)

T(Purple)

So, if the spinner spined then it will point Q, R, S or T which is the Sample space for the Spinner.

Hence, the Sample space is {Q, R, S, T}.

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Answer: B: S = {Q, R, S, T}

Step-by-step explanation:

This is the only answer listed with the letters on the spinner.